prokon user manual

PROKON User's Guide

(Win 32 Version)

March 2010

Information in this document is subject to change without notice. Companies, names and data

used in examples are fictitious.

This document may be reproduced for the sole purpose of reference by PROKON users. No part of this document may be reproduced or transmitted in any form or by any means,

electronic or mechanical, for any other reason without the express written permission of

Prokon Software Consultants

Copyright © 1988-2010 Prokon Software Consultants (Pty) Ltd. All rights reserved

PROKON is the registered trademark of Prokon Software Consultants (Pty) Ltd

Microsoft, Dos and Windows are registered trademarks of Microsoft Corporation.

Adobe Acrobat Reader is a registered trademark of Adobe System Incorporated.

Introduction i

Introduction

This is a guide to using the 32-bit Windows version of the PROKON suite of structural

analysis and design programs. It is designed to help you be more productive by explaining

ways of integrating everyday structural analysis, design and detailing tasks.

In this manual, the basic procedures of installing and using PROKON are explained.

Components of the suite not covered in this manual include the PROKON Drawing and

Detailing System, Padds, and the geotechnical analysis modules. These are explained

separately in the following manuals:

Padds User's Guide and Command Reference: Information on using the PROKON

Drawing and Detailing System.

Geotechnical Analysis and Design: Background on using the geotechnical analysis

modules are given on the online help, available on the Help menu of each module.

All analysis and design modules also have complete context-sensitive help to introduce you to

the use of the system. The on-line help information is updated on a regular basis and may

occasionally contain information not included in the manual.

This manual is also available in electronic form on the PROKON Structural Analysis and

Design installation CD-Rom. The complete text can be viewed and printed for the purpose of

reference by PROKON users a PDF viewer such as Adobe Acrobat Reader.

Note: A copy of this manual is available PDF format on the PROKON installation CD-Rom.

Introduction ii

Using this manual

The manual should introduce you to both the basic and more advanced features of the

PROKON suite of programs. The various procedures relating to installing and using the suite

are discussed in sequence to gradually lead you to productive use of the system:

Chapter 1 - Installing PROKON: This chapter deals with installing and activating the

software for use. The procedures for stand-alone and network installation are explained

in detail.

Chapter 2 - The PROKON basics: Essential reading for all new users and for users

upgrading to the 32-bit Windows version. Subjects covered include using Calcpad, setting

preferences and customising projects.

Chapter 3 - Structural analysis: Detailed discussion of the frame, beam and finite element

analysis modules.

Chapter 4 - Steel member design: Explains how you can design a variety of steel members

using elastic or plastic methods. The post-processing of frame analysis results is discussed

in detail.

Chapter 5 - Steel connection design: Design and generation of drawings of typical steel

connections.

Chapter 6 - Concrete design: Detailed explanation of the design and detailing of

reinforcement for typical concrete members.

Chapter 7 - Timber design: Detailed discussion of the design of timber members.

Chapter 8 - General analysis tools: Overview of using the general analysis utilities.

Chapter 9 – Masonry section and Masonry wall design

Introduction iii

Getting help

An important part of the service provided to PROKON users, is technical support. If you are a

registered user, you can obtain free program updates and support information from the World

Wide Web or your nearest branch of PROKON Software Consultants.

Who qualifies for support?

You automatically qualify for free software maintenance and support in the following cases:

If you are renting programs on an annual basis.

If you purchased your software less than a year ago.

If you have entered a maintenance agreement with respect to your purchased programs.

Internet support

Access answers to frequently asked questions, news on new developments, revision

information and programs updates on-line:

PROKON Home Page: Visit www.prokon.com for news on the latest developments.

PROKON Support Web: Browse www.prokon.com/support for solutions to problems and

to obtain program updates and the latest versions of the help files and manuals.

Direct support

If you experience difficulties resolving your problems using PROKON, you may contact

Prokon Software Consultants directly for assistance:

South Africa United Kingdom Canada

Telephone

Facsimile

E-mail

+27-12-346-2231

+27-12- 346-3331

[email protected]

+44-20- 8780-5454

+44-20- 8788-8363

[email protected]

+1-8888-PROKON

+1-866-323-7393

[email protected]

Postal address P O Box 17295

Groenkloof

0027

South Africa

75 Lower Richmond Rd

Putney

London SW15 1ET

United Kingdom

PO Box 91693

West Vancouver, BC

V7V 3P3

Canada

Quick Reference iv

Quick Reference

Use the thumbnails alongside for quick access to the chapters in this manual.

Quick Reference v

Chapter 1: Installing PROKON

Chapter 2: The PROKON Basics

Chapter 3: Structural Analysis

Chapter 4: Steel Member Design

Chapter 5: Steel Connection Design

Chapter 6: Concrete design

Chapter 7: Timber Design

Chapter 8: General Applications

Chapter 9 : Masonry Design

Quick Reference vi

Installing PROKON 1-1

Chapter

1 Installing PROKON

This explains the procedures for installing and activating PROKON. step-by-step to help new

and experienced users alike avoid pitfalls.

Installing PROKON 1-2

Quick Reference

System Requirements 1-3

Program Installation 1-5

Updating PROKON 1-17


System Requirements

The minimum system requirements and recommended specification to run the 32-bit Windows

version of PROKON are:

Required Recommended

PC with 1RAM PC with dual CPU cores, 4GB RAM or more

1,024 x 768 SVGA display. Nvidia Quaddro FX or quivalent

graphics adaptor that supports OpenGL support.

CD-Rom drive or access to one over a

network

Any version of Windows XP, Windows

Vista, or Windows 7 (32-bit or 64-bit). Windows 7(32-bit or 64-bit).

Internet connection required for activation

The suite often needs to save temporary information on your hard disk. For this purpose, the

Windows temporary folder, e.g. ' C:\Users\YourName\AppData\Local\Temp', is used. When

analysing large structures, a significant amount of disk space may be required.


Program Installation

You can install PROKON on a stand-alone computer, or on a network for access by multiple

computers on your network. Setting up your system PROKON consists of the following steps:

1. Install PROKON on your computer or on your network.

2. Activate PROKON.

3. Set up the design codes and section and material databases. This is explained in Chapter 2.

PROKON uses a sophisticated licensing scheme that allows a lot of flexibility in your choices:

The software is modular: No need to pay for features you don't use; order only the

modules you need.

Short-term license available: In addition to the conventional way of purchasing software,

you can rent PROKON modules on an annual basis. You may have a special project, for

example, that requires certain design modules that you would not normally use.

Network use: PROKON software can be installed on stand-alone computers or on a

network server. When installing on a network server, multiple workstation computers can

access the software (the number of concurrent users is limited to the number of

workstations including in the license). No special network license is required to use

PROKON software on a network.

License portability: You can deactivate and activate your programs (storing your license

on the PROKON license server) at any time. Moving your license between computers at

the office (and even your home computer) is simple.

Note: When not activated, e.g. directly after the initial installation, the PROKON suite will

function in 'demo mode' – a special mode with reduced functionality meant for evaluation

purposes.


PROKON installation tree

Before installing PROKON, please take a moment to study the folder tree that will be created

during installation. The main components are:

The main suite folder: This is the folder enclosing all

program folders and is always called 'Prokon'. You can

locate this folder on the root of your hard drive, i.e.

'C:\Prokon', or elsewhere, e.g. 'C:\Program

Files\Prokon'.

The main program folder: The 'bin' folder that

contains all the executable programs and other files that make up the system. The folder has a child folder

'Updates' that is used for storage by the PROKON Live

Update utility.

The default data folder: This is the folder used for

data storage. Directly after installation, the working

folder is set to '\Prokon\Data\Demo'. When you start to

use the suite, you will be creating new working folders

where input and output data will be stored. Working

folders can be created anywhere on your computer or

on your network.

The license folder: When you activate PROKON, the 'Prolock' folder is created and your license key stored in it. Please do not remove this folder without first deactivating your

programs; doing so will destroy your license.

User folders: Each user's preferences, e.g. favourite design codes and on-screen layout of

each program, are automatically stored in a dedicated folder.

Note: When installing PROKON on a network, you need to adjust some folder permissions

to enable network users to access PROKON. See page 1-12 for more information.


PROKON licence structure

Below are some key concepts regarding your PROKON license:

License key: A special file that contain your license information. Your license key is

supplied either on your CD-Rom or made available via electronic download.

Expiry date: Annual rental license have a fixed expiry date 12 months after order.

Purchased licences allow perpetual use of the programs, but software maintenance

(program updates and technical support) expires after 12 months. Both annual rental and

software maintenance of purchased programs can be renewed.

Sets: The modules that you order is grouped in a set. Your license can include up to two

sets. Here is an example: You have a group of engineers that specialise in steel design, and another group that specialises in concrete design. Both groups use the Frame Analysis

module to calculate forces in building frames. Your PROKON license can be configured

with two sets. Set 1(Steel) will contain the Frame Analysis module and some steel member

and connection design modules. Set 2 (Concrete) will also contain the Frame Analysis

module and some concrete design modules. The two sets form part of the same license

key, and can be activated and used separately. When combining two sets in the same

license key, a substantial discount is applicable to modules that are included in both sets.

Workstations: A workstation is one set of programs that is accessible on a standalone

computer or network. Each set of modules in your license key has a number of

workstations assigned to it. The number of workstations determine the number of times the

set of programs can be used simultaneous. Simultaneous use can either be standalone computers that have been activated individually, or users accessing PROKON on a

network at the same time. Expanding on the example above, imagine that Set 1 (Steel) has

three workstations and Set 2 (Concrete) two. The license key therefore allows five users to

access PROKON at the same time: three using the steel design modules, and two using the

concrete design modules. All five users will be able to access Frame Analysis that is

included in both sets.

Activation: You have to activate your programs in order to access their full capacity.

When you activate your programs, you can choose the number of workstations for Set 1

and Set 2 to activate. The number of available (for activation) workstations is decremented

accordingly. In the above example, Set 1 can be activated on three standalone computers,

or on a network for simultaneous use by three engineers.

Deactivation: You can deactivate an active set of programs at any time. The number of

available workstations is incremented accordingly.

Note: The PROKON license server (an internet service) keeps track of the number of

workstations that have been activated and the number of workstations available for

activation. An internet connection is required to activate or deactivate your programs.


Installing on a standalone computer

You can install PROKON on a stand-alone computer or on a network for sharing between

multiple users. This section describes the installation procedure for a standalone computer.

Note: Your PROKON license proper functioning is sensitive to your computer's date and

time. To guarantee error-free operation, ensure that the date and time is correct.

Installing the program files to your hard disk.

Depending on your system settings the PROKON Setup application will auto-run automatically when you insert the PROKON CD-Rom. If it does not, explore the CD-Rom contents and

launch Setup.exe manually.

Note: If the Setup program appears to freeze while copy program files, it may be because of

your anti-virus software scanning the program files. For a faster installation, we recommend

you temporarily disable your anti-virus software.

Follow the prompts to copy the program files to your computer:

Read and accept the license agreement before you can continuing with the installation.

Enter an installation folder.

By default, PROKON is

installed in the 'C:\Prokon'

folder. Optionally click

Change to choose a

installation folder. If you

browse to 'C:\Program Files',

for example, the suite will be

installed in 'C:\Program Files\Prokon'.

Choose whether you want to

set up program shortcuts for

the current logged in user

(you) only, or for all users that

uses the computer..

Allow the Setup program to complete the installation


Activating the programs

The above installation procedure copies all necessary program files to your computer. To

access the full capability of your licensed modules, you need to activate them. If you do not

activate your software, all modules will function in 'demo mode' – a special mode with reduced

functionality meant for evaluation purposes.

To activate your PROKON software:

Run PROKON.

On the Tools menu, choose Activate Programs, and then choose one of the displayed

activation methods:

Direct Internet activation: This is the preferred

method, and instructs your PROKON software to

communicate directly with the PROKON license

server for instantaneous activation. In some situations,

e.g. restrictive corporate firewalls, the direct

communication may not work and you have to use to

one of the other methods below.

Browser: This method uses your web browser to

exchange a Report Code and Return Code with the

PROKON license server.

E-mail: This method is similar to the browser method, except that it uses your email

client, e.g. Microsoft Outlook, to exchange a Report Code and Return Code. Even

though the PROKON license server responds to activation emails, possible delays in

email communication and spam filters make this method less desirable.

Phoning Prokon: If all else fails, use this option to call a Prokon branch for

activation assistance.

Enter the number of workstations to activate in Set 1 and Set 2. For a standalone

installation, you would typically not enter '1' workstation for Set 1 and/or Set 2.


Click Ok to process the activation:

If using the Direct Internet activation method, the result will be displayed within a

few seconds.

If using the Browser activation method, your web browser will display a page with a

Return Code that you should enter.

If you using the E-mail activation method, open your email client and send the activation request message. The PROKON license server will reply automatic reply to

your message with a Return Code that you should enter.

When using the option to Phone Prokon, a Report Code will be displayed. Contact

your local Prokon branch and request a matching Return Code.

Note: For the Direct Internet activation method to work, your firewall should allow

communication on TCP port 80 (HTTP) as well as 20 and 21 (FTP).

Deactivating an active workstation

Deactivation is a procedure similar to activation described on the previous page:

Run PROKON Structural Analysis and Design.

On the Tools menu, choose Deactivate Programs, and then choose one of the

deactivation methods. As with activation, the Direct Internet deactivation method is the

preferred method for a instantaneous result.

If using one of the indirect methods, submit the Report Code to the Prokon license server

(via your web browser, e-mail, or phoning Prokon). This step is essential to ensure that

your deactivation workstation(s) is correctly credited back to your license key on the

Prokon license server.

After deactivation, PROKON will operate in 'demo mode' – a special mode with reduced

functionality meant for evaluation purposes.

Note: Deactivating does not delete any files. Instead, all program and data files are left in position to enable you to later activate the workstation again. To completely remove

PROKON from a PC, you must uninstall the software 1-15


Activating a deactivated workstation

To reactivate a deactivated workstation, simply follow the activation procedure described on

page 1-9.

Installation, activation and deactivation suggestions

Here are a few suggestions to consider for simplifying your license management:

Use the Direct Internet method for activating and deactivating whenever possible. This

allows for direct communication with the PROKON license server and instantaneous

results. Note that firewall restrictions on your company network may prevent this method

from working.

You can install PROKON on any number of standalone computers. However, activation of

the programs will be limited to the number of available workstations. You can any time

deactivate an active workstation (storing it the PROKON license server) and then activate

your programs on another computer.

If you find that you have to deactivate and activate PROKON very often, consider installing your PROKON a USB memory stick (instead of a hard drive on your computer),

and moving the memory stick from between computers.

If you have about five or more engineers using PROKON on a regular basis, consider a

network installation instead of separate installations on standalone computers. Doing so

can save you money (more optimal use of fewer licensed workstations) and will make

upgrading PROKON more convenient (only one instance requires updating).


Installing on a network

PROKON can be installed on a network for simultaneous use by more than one person. The

number of simultaneous users will be limited to the number of workstations ordered, e.g. if

Set 1 has three workstations, then a maximum of three engineers can use that set at a time.

The network installation procedure has three steps:

1. Copying the program files to the server.

2. Activating the programs for simultaneous use.

3. Configure folder permissions for network access

4. Configuring each workstation that will use PROKON.

You do not need a dedicated file server to be able to install PROKON on your network. Any PC on the network, even an ordinary PC connected to a peer-to-peer network, can be identified

as the 'server' for the purpose of sharing PROKON on your network.

Note: To install PROKON on a server version of Windows, you may need to be seated at

the server (or accessing its desktop remotely) and logged in as an administrator.

Copying the program files to the server

The procedure for installing the program files to the server is the same as described from

page 1-8 for installing on a standalone computer. The only difference is that the target folder

should be located on the server, i.e. a shared drive or folder on the network. (If seated at the

server when performing the installation, this will off course be a local folder.)

Activating the programs for simultaneous use over the network

The procedure to activate the network instance of PROKON is the same as described on

page 1-9 for a standalone computer. There is one difference though, and that is that you would likely want to activate not only one, but all the available workstations on the server.

Once activated on the server, PROKON is ready for use from multiple PCs on the network. No

further steps are required to make the license activation network-aware.

Note: When not activated, e.g. directly after the initial installation, the PROKON will operate

in 'demo mode' – a special mode with reduced functionality meant for evaluation purposes.


Configure folder permissions

To allow network users to access PROKON on the server, you need to adjust some folder

preferences. All installed folders may have read-only access except for the following folders

that require full control:

The 'User' folder and sub-folders where each user's preferences are saved.

The 'Prolock' folder contains the PROKON installation status and keeps a log of users

accessing the system.

The 'Data' folder is the default location for saving program input and output data. You will

likely have a different project storage location set up elsewhere on your network. To

change the default storage location, set the Working Folder. See Chapter 2 for more information.

Refer to page 1-6 for more detail regarding the PROKON folder tree.

Configuring the network workstations to use PROKON

After successfully installing and activating PROKON on your server, configuring the individual workstations is a simple case of creating a shortcut on each station.

To create a shortcut on a workstation:

Seated at the workstation, use

Windows Explorer to browse to the

PROKON prorgam folder on the

network, e.g. \\server\prokon\bin

Locate the file, 'Prokon32.exe' within

the main program folder.

Right-click the file, select Sent To in

the context menu to appears, and then

choose Desktop (create shortcut)

Optionally rename the shortcut from

'Prokon32.exe' to 'Prokon Structural

Analysis'.

Note: For a network installation it is not necessary to install the PROKON CD on each

individual workstation.

Deactivating your network installation

The procedure to deactivate is identical that that for a standalone installation described on page

1-10.


Switching between Set 1 and Set 2

If your license key contains workstations on both Set 1 and Set 2, then you can switch between

them while using PROKON (assuming both sets have been activated on the computer or on the

network).

In the example used before, your license

key may contain some steel design

modules in Set 1 (Steel) and some

concrete design modules in Set 2

(Concrete). To switch between the two

sets, run PROKON, open the Settings menu, and select Username. You can then

edit your username and select the set of

programs you want to use.

You set selection will remain active until

your change it againMore detail regarding

the setting of a user name are in given in

Chapter 2.


Uninstalling PROKON

To remove PROKON from a PC or network, follow the steps below:

Deactivate your PROKON license as described on page 1-10. Failure to deactivate your

license before uninstalling PROKON may result in your license being destroyed.

Seated at the PC where PROKON is installed (or at the server in the case of a network

installation), open the Windows Control Pane.

Choose Uninstall or Change a Program (Add/Remove Programs in some versions of

Windows).

Select PROKON from the list and follow the steps to uninstall.

As a safeguard, PROKON data is not erased during the uninstall procedure. If you wish to remove PROKON data as well, then manually delete the PROKON installation tree – see page

1-6 for more information.

Note: Before uninstalling , please deactivate the software first as discussed on page 1-10.


Precautionary measures to protect your license

The activation status of your PROKON programs may be damaged in some instances. The

following situations require the programs to be deactivated first and activated again afterwards:

Moving the programs to another folder on a local or network drive. You are free to move

or copy data folders though.

Converting the hard disk file structure, e.g. from to FAT32 to NTFS.

Upgrading of hardware, e.g. replacement of the hard disk.

Note: Disk defragmenting utilities can be used safely with PROKON.

To deactivate the PROKON suite, follow the procedures described on page 1-10.

The importance of dates and times

The date are recorded as part of the suite's copy protection system. To prevent unnecessary

errors, it is important that all relevant computers should have the correct date and time.


Updating PROKON

The PROKON development team is continuously working at improving the software. Changes

in design codes, support for additional design codes, new program features and occasional bug

fixes make for regular program updates.

Upgrade Eligibility

You are eligible for free program updates in the following cases:

If you have an annual rental agreement.

If you have a maintenance agreement for your purchased PROKON software.

If you do not have a maintenance agreement but have purchased or upgraded your PROKON software less than 12 months ago.

Upgrading your Programs

You can use either of the following methods to update your PROKON programs:

PROKON Live Update: An automated utility that downloads the latest versions of your

programs and installs them for you. This is the preferred method if you are already using

the current major version of PROKON.

PROKON Service Pack: A package that contains all program modules for manual

installation. This is the preferred method when upgrading from one major version of

PROKON to another, i.e. from an older version to the current version.

Tip: For up-to-date version information and update instructions, please refer to the following web page: www.prokon.com/updates.


Using PROKON Live Update

The Live Update utility allows to you easily update all your PROKON modules to the latest

versions. To use Live Update:

Close all running PROKON programs except Calcpad. Launch Live Update from the

Tools menu in Calcpad. Alternatively, launch it from the PROKON group on the

Windows Start Menu.

Live Update will automatically connect with the PROKON update server to retrieve the

latest version information. After a few moments, it will show which modules have updates

available.

Download and install the updates. Depending on your internet connection speed and anti-virus scanning, the process should complete in a few minutes.

Note: Firewall restrictions on your network can prevent Live Update from communicating

with the PROKON server. Please refer to the following web page for alternative update

options: www.prokon.com/updates.

The PROKON Basics 2-1

Chapter

2 The PROKON Basics

The basic principles of using PROKON are discussed in this chapter. Starting with the issues

you need to address when using the program for the first time, e.g. setting up a working folder,

the text progresses to everyday tasks like running analysis and design modules. The chapter

ends with explaining advanced procedures like creating an equation library and customising the

page layout for your projects.

The PROKON Basics 2-2

Quick Reference

Using PROKON for the First Time 2-3

Using the Analysis and Design Modules 2-11

Using the Table Editor 2-15

Using the PROKON Calculator 2-23

Working with Pictures 2-25

Adding Text and Graphics 2-31

Working with Equations 2-37

Customising the Page Layout 2-47

Configuring the Section Database 2-53

Configuring the Material Database 2-57


Using PROKON for the

First Time

Depending on the shortcut options chosen during the installation procedure, you will be able to

run PROKON by double-clicking the shortcut on the Desktop or selecting it from the Start

Menu.


Configuring PROKON

On launching PROKON, the main program, called Calcpad, is displayed. From here, you are

able to launch the individual analysis and design modules. Calcpad is also the application that

you will use to collect analysis and design results and save them in project files.

Some aspects are best attended to immediately when using PROKON for the first time:

Creating a user folder.

Setting the preferred design codes, design parameters and units of measurement.

Setting up a working folder.

Selecting a wallpaper.

Customising your project's appearance.

Note: When running PROKON for the very first time, the default design codes and units of

measurement are automatically set to match your current Windows Regional Settings. To

check or change your settings, open Control Panel and double-click Regional Settings.

Once you start using the PROKON analysis and design modules, you will want to progress to working with project files:

Entering a header for a project.

Working with more than one project at a time.

File management.

Setting your user name

The PROKON suite can be made to adapt to your style of working by automatically saving

your preferences in a user folder. Information recorded include:

Preferences: Design codes, units of measurement and custom sections.

Display properties: Size and position of each module on the screen.

To select your user folder or create a new one, open the Settings menu and choose User. The

user folder resides under the main PROKON program folder. If you use the system on a

network, you will be able to select your user folder regardless of which workstation on the

network you use.


If you are using multiple sets on a network

Your license key may include two sets of programs. You may, for example, have set 1

configured with mainly steel design modules and set 2 with mainly concrete design modules. If

configured this way, different users can use the respective sets simultaneously.

The set selected is saved as part of the

user preferences. In other words, using

the example of separate steel design and concrete design sets, a steel

designer needs to select the steel

design set only the first time he uses

PROKON. The next time he uses the

system, he will automatically be

presented with the steel design set.

More details regarding the activating license keys and individual sets are in given in Chapter 2.

Selecting your preferences

During program installation, the default design

codes and units of measurement are automatically

set according to your PC's regional settings, i.e. the

information recorded in the Regional settings

function of the Windows Control Panel.

To change your preferred design code and

parameters, use the General preferences command on the Settings menu.

The design modules use the selected preferences to

determine the default values for design codes and

relevant design parameters. You can however

temporarily override these setting using the Design

code, Units or Preferences command on a design

module's File menu.

If a particular preference is not available in module,

e.g. the preferred design code is not supported, the

module will automatically make a next-best

selection.


Setting up a working folder

By default, all input and

output data is saved in the

working folder. The first

time you use PROKON, the

working folder will be set to

'. . .\Prokon\Data\Demo'.

Once you get accustomed to

using the suite, it is

recommended that you create

a new working folder for each project you are working

on. Working folders can be

created in any convenient

location, be it on you own

hard disk or on the network.

To create a new working

folder or select another

existing folder, open the

Settings menu and choose

Working Folder. When

naming a new working folder, you should use a valid

Windows folder name:

A folder name may contain up to 255 characters, including spaces.

A folder name may not contain any of the following characters: \ / : * ? " < > |.

Selecting a wallpaper

To personalise your PROKON workstation, you may want to display a wallpaper in Calcpad.

To load a wallpaper, open the Settings menu and choose Wallpaper. The following limitations

apply to wallpapers:

Supported graphics formats include: Windows Bitmap (.bmp), Icon (.ico), Metafile (.wmf)

and Enhanced Metafile (.emf).

The wallpaper image is scaled to fit the Calcpad working area. Therefore, not all images

will necessarily look well.


Working with project files

Apart from acting as a launch platform for the analysis and design modules, you can use

Calcpad to group analysis results and design calculations and then save all the information in a

project file.

You can use project files to keep a complete record of all your analysis and design calculations:

In an analysis or design module, the input data and results are typically collected on the

module's Calcsheets page from where you send it to Calcpad. For an explanation of the

procedure, refer to page 2-13.

Results obtained from the various analysis and design modules are then saved together in a

project file.

You can then use Calcpad to supplement the results from the analysis and design modules

with additional design notes and pictures. Refer to page 2-31 for more detail.

Links are retained with each individual analysis via data file objects. These objects are

visible in the right-hand margin as yellow folders. Double-clicking a data file object recalls

the original input data in the relevant analysis or design module.

To perform calculations not covered in the scope of the design modules, you can use

equations – a feature built into Calcpad. The use of the Equation Editor is explained on

page 2-37.

Entering a header for a project

The information at the top each page should be completed to reflect the designers name, the

date etc. To edit the header information:

Select the Header

command from the

Edit menu or double-

click the header in Calcpad.

Type the information

for each field.

To insert the current

date, click Insert date.

If you use similar headers for your different projects, you can save retyping information by

saving the header information. Click Save as default to save the information and Load default

to retrieve it.


Click OK to apply the new header to the active project. The new header will apply to the

current and following pages. This allows you, for example, to use different people's names in

the Designed by field if more than one person is working on the same project file.

The composition of the header can be changed to suit your own needs by customising the page

template. For more details, refer to the customisation procedures explained from page 2-47.

Working with more than one project at a time

You can open more than one project in Calcpad at a time. The current selected project is

referred to as the active project. All results sent to Calcpad from the analysis and design

modules are placed in the active project.

To select an open project and make it the active project, click its tab with the mouse.

File management

Use the File menu commands to open and save project files in the working folder or any other

location on your own computer or on a network drive that you have write access to:

To create a new project file, select New Project.

To open an existing project file, use the Open Project command.

Use Save Project to save the active project.

To save a new, unnamed project file, use Save Project as.

To close the active projects or all open projects, use Close Project or Close All.

To open a recently used project file, click the file name at the bottom of the File menu.

PROKON Project files as saved with the extension '.PPF' for easy recognition.

To open a project file on your hard disk or network

1. On the File menu, click Open Project.

2. In the Look in box, click the drive and folder that contains the document.

3. In the folder list, double-click folders until you locate the folder that contains the

document you want.

By default, the file list is filtered to show only project files created by Calcpad. You can

change this by selecting All files in the Files of type box, e.g. when wanting to open a text

file. You can also type a filter File name box; for example, type 'p*.*' to find all files

starting with the letter p.

4. To change the appearance of the file list, click List or Details. With Details selected, you

can click a column heading to sort the data files by name, size, date or type.


5. Double-click the document you want to open.

Saving a new, unnamed project file

1. On the File menu, click Save Project.

2. To save the project in a different folder, click a different drive in the Save Project in box,

or double-click a different folder in the folder list.

3. To save the document in a new folder, click Create New Folder.

4. In the File name box, type a name for the document. You can use long, descriptive file names if you want. The program will automatically add an appropriate file extension.

5. Click Save.

Customising your project's appearance

Once you get accustomed to using PROKON, it is recommended that you use the procedures explained from page 2-47 to load another page template or create your own template.


Using the Analysis and Design

Modules

To run a PROKON analysis or design module, click its icon on the shortcut bar or select it

from the Program menu. If a particular module's shortcut icon or menu item is dimmed, it

means that the module is not included in your workstation.

A number of discontinued modules, notably Plastic Frame Analysis and Design and Finite

Element Slab Design are available on the Program menu only.


Using the analysis and design modules

The analysis and design modules follow a similar pattern. By familiarising yourself with a few

concepts, you should find using the PROKON suite relatively simple and intuitive.

Setting the preferred design codes

Use the General preferences command on the Settings menu to select the design codes and

parameters to use. More detail of the procedure is given on page 2-5.

Similar layout

All modules present you with a number of tabbed pages or menus:

The File menu: Standard Windows commands are provided for opening and saving data

files. The commands are similar to those described on page 2-8.

The Input page: All input

data is entered on this page.

In the case of some of the

larger analysis modules, e.g.

the frame analysis modules,

this page will itself contain a

number of tabbed input pages. Some modules also

allow specialised input

trough a separate Settings

page or button.

The Analysis or Design

page: Selecting this page

typically starts the analysis

and displays the results.

The Calcsheets page: Analysis and design results can be accumulated in a single

calcsheet. You can choose between printing or sending the information to Calcpad.

The Drawings or Bending Schedules page: Most design modules are capable of

generating a detailed drawing or bending schedule of the designed element. Drawings and bending schedules can be edited and printed using Padds.

The Help menu: Access is provided to on-line Help topics and built-in Examples.

To display a particular page or menu, click it with the mouse. Alternatively use F11 and F12 to

move forward and back between the pages.


Data input

Except when using Padds for graphical input, e.g. for frames, all data is entered in tables. Data

is normally evaluated immediately as entered. If invalid input is detected, a list of errors is

normally displayed.

Entered data is typically shown in Pictures that interact with the Table Editor to automatically update with every entry in the tables. Pictures can be zoomed and panned for more detail.

Some pictures have visible zoom buttons, others not. However, all pictures can be zoomed by

right-clicking it and using the pop-up menu. Pictures can also be saved as drawings.

The use of the Table Editor is explained in detail on page 2-15 and the manipulation of

Pictures on page 2-25.

Sending analysis results to Calcpad

After a successful analysis or design, you can group the results in a calcsheet. You can then

choose to print or send the information to Calcpad. To send results to Calcpad:

Access the relevant module's Calcsheets page.

Use the Settings function to select the components to include in the calcsheet. You can

optionally select the Data File to have the input data saved as part of the Calcpad project.

Note: In the case of some of the larger modules, e.g. the frame analysis modules, you need to first view the results and select individual components to be included in the calcsheet.

Click Send to Calcpad to append the results to the active project in Calcpad.

Saving input

You can use the File menu of a module to

save and open input data files. However, if

you enable the Data File option before

sending a calcsheet to Calcpad, you can

later recall the input data by double-clicking

the relevant object in Calcpad. A data file

embedded in Calcpad is saved as part of a

project and does not need to be saved in the relevant module as well.

If you do save a data file in an analysis or

design module, the file name extension will

automatically be set to the program number

for easy recognition, e.g. '.A03' for Frame

Analysis.


Using the online help

You can access context-sensitive help by pressing F1. Alternatively use the Help menu to

display an overview of the program.

It is easier to update electronic information than printed manuals. Therefore, you may

occasionally find that the on-line help is more up to date that the manual.

Updated help files are published regularly on the PROKON Website. Additional information

not given in either the manual or Help, e.g. answers to frequently asked questions and details

of program revisions, is also available on the PROKON Support Web. Refer to the

introduction of this manual to read more about support service included with your purchase of

PROKON software.


Using the Table Editor

You can edit text in tables using the standard Windows functions, i.e. as employed by most

spreadsheet applications such as Microsoft Office Excel. The standard Windows functions are

supplemented with a number of special functions that speed up table editing.


Moving around and editing text

You can move around in tables and edit cells in very much the same way as you do in your

favourite spreadsheet program.

Moving the cursor in a table

Use the arrow keys to move between cells. Press Enter to jump to the left-most cell in the

next row. Pressing Tab moves one cell to the right and Shift+Tab one cell to the left. If you

press Tab at the end of a row, the cursor will jump to the left-most cell in the next row.

Home jumps to the first cell in the row and End to the last. PgUp and PgDn moves one screen

up or down. To jump to the top left or bottom right corner of the table, press Ctrl+Home or

Ctrl+End.

Tip: Click a cell with the mouse to quickly move the cursor to that cell.

Entering and editing text

To enter text into a cell, position the cursor on the cell and start typing. Press Enter or one of

the arrow keys to accept the new text and move to a next cell. Depending on the key pressed,

the cursor will move to a specific cell:

Pressing Enter accepts the entry and moves the cursor to the left-most cell in the next row.

If you press the right, up or down arrow key, the cursor will move one cell right, up

or down.

If you wish to move one cell to the left, use Shift+Tab.

Note: Some cells have special drop-down lists for selecting values. Depending on the specific application, you may be able to select common values from the list or optionally

type values.

While entering or editing text, you can move left and right using the left and right arrow keys.

To jump to the left-most or right-most positions, press Home or End. To move one word to the

left or right, use Ctrl with the left and right arrows.

To edit text in a cell, move the cursor to the cell and press F2 or double-click it. If you want to

replace the text in the cell rather than change it, simply retype the text without first pressing F2.


Deleting text

Press Del or Backspace to clear the current cell's contents. While entering or editing text in a

cell, Del and Backspace will delete one character to the right or left respectively.

Inserting lines

Press Enter to move to the first cell on the next line. To insert a blank line at the cursor,

press Ctrl+I.

Finding and replacing text

You can search for and replace text in a

table by pressing Ctrl+F. This feature can

be especially handy when working with

large tables, e.g. when entering nodes for a frame analysis.

To repeat the last search without first

opening the dialog box, press F3.


Working with blocks

You can copy, move or delete cells using the block commands. These actions typically require

two steps:

Marking a cell or block of cells – you can choose between using the normal Windows

methods of selecting cells or the extended PROKON functions.

Using a block command to manipulate the block.

Marking blocks

When marking blocks, you can choose between using the standard Windows functions and the

extended PROKON block functions – the behaviour of the resulting blocks are different.

Using the standard Windows functions

To select a cell or block of cells using standard Windows commands, use any of the following

procedures:

Click and drag the mouse to select a rectangular block of cells.

Position the cursor on one of the corner cells. Press and hold Shift and then use the arrow

keys to move to the opposite corner.

Note: When marking a block this way, moving the cursor will undo the selection.

Marking persistent blocks

The extended functions allow you to mark persistent blocks, i.e. blocks that remain selected even if you move the cursor. Persistent blocks are marked as follows:

To select one or more rows, move the cursor to the first row and press Ctrl+L. Then move

to the last row and press Ctrl+L again.

To select one or more columns, move the cursor to the first column and press Ctrl+K and

then move to the last column and press Ctrl+K again.

To mark a rectangular block of cells, position the cursor on the top left cell and then press

Ctrl+B. To end the selection, move to the bottom right cell and press Ctrl+E.

Note: A persistent selection will remain active until unmarked with Ctrl+U. While the cells are selected, you are free to move the cursor without the block being de-selected.


Copying, moving or deleting cells

A selected cell or group of cells can be copied, moved or deleted using the standard Windows

functions or the extended PROKON block functions.

Using the Windows clipboard functions

You can use the normal Windows clipboard Cut, Copy and Paste functions:

To copy a cell or block to the clipboard, press Ctrl+C. Alternatively right-click it and

choose Copy.

To cut a block, i.e. remove it from the table and copy it to the clipboard, press Ctrl+X.

Alternatively right-click it and choose Cut.

To paste the clipboard contents into the table at the cursor position, press Ctrl+V. alternatively right-click and choose Paste. If you are pasting a block of cells, the current

cursor position will be taken as the top left corner of the block.

Examples:

To copy cells in the table, first select the cell or block of cells and Copy the information to

the clipboard. Then position the cursor to the new position and Paste the text.

To move one or more selected cells, Cut them to the clipboard and Paste them at the new

position.

To delete one or more selected cells, select and Cut them. Alternatively press Del to delete

the selected cells.

Copying, moving and deleting cells using persistent blocks

You can use the extended functions to mark persistent blocks and then copy and move text without using the Windows clipboard.

To copy one or more cells, first mark a persistent block, move to the new position and

then press Ctrl+V.

To move a persistent block, use Ctrl+M.

To delete a persistent block selection, use Ctrl+D.


Advantages of using persistent blocks

The normal block selection functionality offered by Windows allows you to quickly mark an

area with the mouse or keyboard. However, the selection is cancelled as soon as you move the

cursor. In contrast, persistent blocks offer the following advantages:

You are allowed to move the cursor while defining the selection, without cancelling the

selection. You could, for example, move up or down in the table without undoing the

selection.

You do not need to first Copy or Cut information to the Windows clipboard - while a

persistent block is selected, you can Paste or Move it directly.

You can quickly mark persistent blocks using the keyboard.

Copying text from another program

You may sometimes find it easier to generate tables of values using another application, e.g.

your favourite spreadsheet program. Relevant information can then be copied to a PROKON

table (or from PROKON to the other program) using the Windows clipboard:

Select relevant text and Copy it to the clipboard.

Press Alt-Tab to swap to the destination program or click it on the Windows Task Bar.

Position the cursor and Paste the information from the clipboard.


Summary of commands

Moving around:

Arrows : Move one cell up, down, left or right.

Enter : Jump to the first cell in the next row.

Tab : Move one cell right.

Shift+Tab : Move one cell left.

Home : Jump to the first cell of the current row.

End : Jump to the last cell of the current row.

Ctrl+Home : Jump to the top left corner of the table.

Ctrl+End : Jump to the bottom left corner of the table.

Del : Delete the cell at the cursor.

Ctrl+Y : Delete the line at the cursor (irrespective of any block selected).

Backspace : Delete the cell at the cursor and open it for editing.

Ctrl+I : Insert a blank line.

Ctrl+F : Find or replace text

Editing cells:

F2 : Edit the cell at the cursor.

Left/right : Move the cursor inside the text.

Ctrl+left/right : Move the cursor left or right one word.

Up/down : Accept the changed text and moves to the adjacent cell.

Enter : Accept the changed text and jumps to the first cell in the next row.

Del : Delete the character to the right.

Backspace : Delete the character to the left.

Marking persistent blocks:

Ctrl+A : Select all cells.

Ctrl+B : Mark the top left corner of a rectangular block.

Ctrl+E : Mark the bottom right corner of a rectangular block.

Ctrl+K : Mark the first or last column of a block.


Ctrl+L : Mark the first or last line of a block.

Ctrl+U : Unmark the current block.

Clipboard commands

Ctrl+C : Copy the block to the clipboard.

Ctrl+X : Cut the block to the clipboard.

Ctrl+V : Paste the clipboard to the cursor position.

Persistent block commands

Ctrl+V : Copy the persistent block to the cursor position

Ctrl+M : Move the persistent block to the cursor position.

Ctrl+D : Delete the block.


Using the PROKON Calculator

Use the PROKON calculator for basic calculations. You can copy a result to the Windows

clipboard and then paste it into Calcpad or an input table of a design module.


Using the Calculator

Use the PROKON calculator for basic calculations. You can copy a result to the Windows

clipboard and then paste it into Calcpad or an input table of a design module.

During installation, the calculator can be configured to automatically load when Windows

starts. If so, the calculator will be visible in the Windows system tray that is typically located

in the bottom right corner of the screen, i.e. next to the clock.

Clicking its icon or pressing Ctrl+1 can display the calculator. To

close the calculator, click Exit or press Esc. On closing, the

calculator will return to its idle status in the system tray.

To close the calculator and remove it from memory, right-click its icon and choose Close.

Doing calculations

Operation is similar to a conventional hand-held calculator:

Enter an equation using the normal mathematical operators.

To enter a mathematical function, click the relevant button or write out the function.

Simplify complex equations by enclosing portions in brackets.

Press Enter to display the result.

To remove the displayed equation and continue working with the result, press Clear left.

Sending calculation results to other programs

The result of a calculation can be copied to the Windows clipboard for reuse in another

program:

Click Copy or press Alt-C to copy the result to the clipboard and close the calculator.

In the relevant application, e.g. Calcpad or an input table of a design module, use the

Paste command or press Ctrl+V to paste the value.

Tip: When using a Dos module, press Ctrl+Z to display a calculator. Use F10 to send the result back to the module's input table.


Working with Pictures

The analysis and design modules often have pictures linked to the input tables to make data

entry interactive and more intuitive. Pictures are also often used to present analysis results.


Zooming and panning pictures

You can 'zoom in' to get a close-up view of a picture. Some pictures have Zoom buttons for

this purpose. If a picture does not have such buttons, you can still zoom it by right-clicking the

picture and choosing a command from the pup-up menu.

The following zoom commands are normally available for all pictures:

Window: Indicate a rectangular area to zoom into.

All: Display the whole picture, based on the size defined internally for the

background.

Last: Revert to the last zoom setting.

Extents: Display the whole picture, based on the drawn entities.

In: Zoom in by 50%.

Out: Zoom out by 50%.

Pan: Drag the project in any direction to view an adjoining portion.

Print: Send the picture to the printer.

Saving pictures

In addition to the Zoom button commands, the right-click pop-up menu also allows you to

save the picture in the following file formats:

PAD: Fully editable Padds drawing.

PIC: Prokon picture file.

EMF: Enhanced Windows metafile, readable by many graphics and

presentation packages.

DXF: 2D or 3D DXF drawings for use in other CAD systems.

In some modules, e.g. the frame analysis modules, a special button may is available

for adding a picture to the Calcsheets.


Working with 3D pictures

Because of their nature, some analysis and design modules need to display

3D pictures. The commands available for 3D pictures are:


All: Display the visible portion of structure from the current view point.


Extents: Display the complete structure, moving forward or back if necessary.

In: Zoom in by 50%.


Pan: Drag the project in any direction to view an adjoining portion. You can

also click and drag the picture using the middle mouse button.

Print: Print the current view of the structure.

Viewpoint: Display the View Point Control dialog box for defining the view

point and other view characteristics.

View plane: Display the View Plane Control dialog box for defining a view

plane.

Rotate left: Rotate the structure to the left about the Y-axis. The rotation angle

is defined in the View Point Control dialog box.

Rotate right: Rotate the structure to the right about the Y-axis.

Rotate up: Rotate the structure backward.

Rotate down: Rotate the structure forward.

Orbit: Rotate the image freely about the centre of the model. Alternatively, hold

the Shift key, and rotate the image with the picture using the middle mouse

button.

Detailed settings

Some modules allow detailed configuration of pictures. In the frame analysis

modules, for example, you can access the Graphics Options to enable or disable

display of node numbers, global axes etc. Pictures can also be rendered in 3D or

shown as simple line diagrams.


View point control

Use the view Point Control Dialog function to define the viewpoint and other view properties:

View point: Imagine viewing the structure

through a camera lens. The view point is then

defined as the position of the camera. Enter the

view point coordinates or use the Walk function

to move the camera by the distance defined as

the Step size.

View direction: The direction in which the

camera is aimed. The default position is the centre of the structure. Enter the view direction

or use the Turn function to rotate the camera

through the angle defined as the Turn angle.

View angle: The lens angle. A larger angle will

show more of the structure in a close-up

situation.

Projection: Choose between using an orthogonal or perspective projection. The latter gives

a more realistic view of the structure. However, you may get a distorted picture when

using a large view angle in a close-up situation.

Elevations: For a quick view from the top or one of the sides, choose a positive or negative

X, Y or Z-elevation.

Perpendicular on view-plane: If a view plane is set, you can move the view point to be

perpendicular to it.

Default: Moves the view point to a position that looks down at the centre of the model

with a view direction of equal amount along the positive X, Y and Z-axes (i.e. dX, dY and

dZ all equal to -1.00) and zooms to the model extents.

Tip: The default view angle of 50° works well with perspective projections of structures. If

you cannot see the complete structure, the view point is probably to near to the structure.

Reset the View Point using the Default button or use the Zoom extents function to move back far enough to view the complete structure.

The View Point Control dialog box can be left open while you work in the program. You can

also use the zoom and pan functions while the dialog box is open.


View plane control

When viewing a complicated 3D structure, you may often find it difficult to identify points in

the structure. Use the View Plane Control function to define only certain planes to be viewed.

View planes can be defined in three ways:

Nodes: Enter or use the mouse to indicate

three nodes that describe a plane. The plane

does not need to vertical or horizontal.

Axis: Define a view plane perpendicular to

the X, Y, or Z-axis. Enter the position along

the indicated axis.

Coordinates: Enter three 3D coordinates to

describe a plane.

Enter a view plane thickness

to define how much of the

structure should be visible.

Click Clear to restore the

settings to displaying the whole

structure. Click Apply to make

the entered view plane take

effect. Click Close to close the dialog box

The View Plane Control dialog

box can be left open while you

work in the program. You can

also use the zoom and pan

functions and the View Point

Control while the dialog box is

open.

Tip: If your PC's screen resolution permits, you may move the View Point Control and View Plane Control dialog boxes to one side so as not to clutter the display of the

underlying program.


Saving and recalling views

You can use viewpoints and view planes to display

the whole structure or portions of it in convenient

ways, e.g. a plan view of a floor of a multi-storey

building. You can save each combination of view

point and view plane as a view for later re-use.

Some pictures display the name of the current

view and allow you to select another saved view by

clicking the view name.


Adding Text and Graphics

The analysis output generated by the various analysis and design modules will provide

normally sufficient detail of your designs. However, you may want to enhance your project

files by adding additional design notes, pictures and even additional calculations.

The procedure to write and edit text and to insert and manipulate pictures in Calcpad is

described in the following text. Equation writing is explained from page 2-37.


Writing and editing text

You can use Calcpad as a simple word processor to write and edit text. You may possibly find

that you can use the exact same or similar editing and formatting commands as in your

favourite word processor.

Typing text

Type text as you would in any other word processor or text editor.

Typing over existing text

Press the Ins key to toggle between overtype and insert modes. In overtype mode, you will

replace existing text as you type, one character at a time.

Replacing selected text

Select the text to be replaced and start typing to replace it.

Inserting symbols or special characters

You can insert Greek symbols and other special characters using the Symbol command on the

Insert menu. You can also insert a character or symbol by typing the character code on the numeric keypad, e.g. 'Alt-225' inserts the ß character.

Insert the date and time in a project

You can insert the current date or time in a project using the Date command on the Insert

menu.

Insert a text file

To insert a complete text file, use the Text File command on the Insert menu. To insert only a

portion of a text file instead:

1. Open the text file using the Open Project command on the File menu. Change the Files of

type field to 'All files' and select the file.

2. Select and copy the relevant text using the procedures described on page 2-35.

Deleting text

Use Del and Backspace to delete a character to the left or right. To delete words or paragraphs,

select the text and press Del.


Changing the appearance of text

To change the appearance of text, e.g. underline text or numbers:

1. Select the text you want to change.

2. On the formatting toolbar, select a font or click a style or point size.

The change will be applied to the selected text only or, if you did not select any text, to new

text from the cursor position and further.

You can also use the keyboard shortcuts Ctrl+B, Ctrl+I and Ctrl+U to make text bold, italic

or underlined.

When changing font style of text with mixed style, the style will toggle between normal,

formatted and mixed, e.g. all normal, all bold and mixed normal and bold.

Check spelling

Click the Check Spelling button in the toolbar to check the spelling of text in the document.

The built-in dictionary includes terminology commonly used in structural engineering.

Note: Prior to version 2.5, the spell checker required Microsoft Office to be installed. This is no longer the case in the current version.

Moving around in a project

You can scroll through a project by using the mouse or shortcut keys.

To scroll through a project by using the mouse:

Scroll up one line: Click the up arrow on the scroll bar.

Scroll down one line: Click the down arrow on the scroll bar.

Scroll up one screen: Click above the scroll box.

Scroll down one screen: Click below the scroll box.

Scroll left: Click the left arrow on the horizontal scroll bar (if displayed).

Scroll right: Click the right arrow on the horizontal scroll bar (if displayed).


After scrolling, click where you want to start typing. To move the cursor using the keyboard:

Move up or down one line: Press the Up or Down arrow.

Move up or down one screen: Press PgUp or PgDn.

Move left or right one word: Press Ctrl+Left or Ctrl+Right.

To jump to the beginning or end of the current line: Press Home or End.

To jump to the first or last lines in the project: Press Ctrl+Home or Ctrl+End.

To move to the reference column on the far right: Press Ctrl+Tab.Using graphics in your

project

Graphics can be used to supplement text and serve to enhance your projects. Inserted graphics

can be moved, copied and resized.

Inserting a graphic

Use the commands on the Insert menu to insert graphics:

To insert a Windows Bitmap or Metafile: Click Picture and select the file.

To insert a Padds drawing: Click Drawing and select the file.

Moving and resizing graphics

To move a graphic:

1. Select the graphic by

clicking it.

2. Drag it to the new position.

To resize a graphic:

1. Select the graphic.

2. Drag the graphic's edge to

change its horizontal or

vertical size.

3. Drag one of the graphic's corners to proportionally

change its horizontal or

vertical size.


Moving and copying text and graphics

You can move or copy text and graphics within a project, between projects, or between

Calcpad and another program.

Selecting text and graphics to move or copy

You can select text and graphics by using the mouse or shortcut keys. To select text and

graphics using the mouse:

To select any amount of text, drag over the text.

To select a graphic, click it.

To select a whole word, double-click the word.

Using the keyboard, select text by holding down Shift and pressing the same key that moves

the cursor. To extend a selection:

One character to the left or right: Shift+Left or Right arrow.

To the beginning or end of a word: Ctrl+Shift+Left or Right arrow.

To the beginning or end of a line: Shift+Home or End.

One line up or down: Shift+Up or Down arrow.

One screen up or down: Shift+PgUp or PgDn.

To the beginning or end of the project: Ctrl+Shift+Home or End.

To select all the words in a line: Ctrl+L.

To select the entire project: Ctrl+A.

Moving or copying text and graphics

To move or copy text and graphics:

1. Select the text or graphics you want to move or copy.

2. To move the selection, click Cut or press Ctrl+X.

3. To copy the selection, click Copy or enter Ctrl+V.

4. If you want to move or copy the text or graphics to another document, switch to it.

5. Click where you want your text or graphics to appear.

6. Click Paste or press Ctrl+V.


Zooming a text and graphics

You can 'zoom in' to get a close-up view of a project or 'zoom out' to see more of the page at a

reduced size. Use the Zoom buttons or right-click the project for a pop-up menu with zoom

commands:


Margin: Display the whole page width between the left and right margins.

Page: Display the whole page.


In: Zoom in by 50%.


Pan: Drag the project in any direction to view an adjoining portion.

Page up: Scroll one page up. Same as pressing PgUp.

Page down: Scroll one page down. Same as pressing PgDn.


Working with Equations

You can use the Equation Editor to create your own equations in Calcpad. The Equation

Editor is also used to edit existing equations or save equation objects for re-use in future,

e.g. create a library of equations


Inserting and editing equations

To open the Equation Editor for inserting or editing an existing equation:

To insert a new equation: Choose Equation from the Insert menu.

To edit an existing equation: Select and right-click the equation. Then choose Edit from

the pop-up menu.

To create or edit an equation, work through the different pages to create an equation object:

Equations: Use one or more lines to enter equations. When creating a new equation, this

page is displayed first.

Variables: Assign a value to each variable used on the Equations page. When editing an

exiting equation, this page is displayed by default.

Settings: Choose how the equations should be displayed and optionally attach a picture.

Note: When sending a series of equations to Calcpad, the equations are grouped together as

a unit, called an equation object.


Entering equations

Enter one or more lines of equations on the Equations page. Equations are written in 'normal

English' and then automatically displayed in the correct mathematical format.

Writing equations

A few simple rules apply when writing equations:

Like when using a simple calculator, use 'normal English' to write an equation – the

equation is automatically formatted for you. For example, if you want to enter the equation

y = a · x2 + b · x + c, enter 'y=ax^2+bx+c'.

The mathematical operators that can be used include +, –, /, and ^.

Use parenthesis to simplify an equation, e.g. for dc

ba

enter 'y=(a+b)/(c+d)'.Use

multiple lines for a sequence of equations. Variable values are inherited by equations that

follow. Refer to page 2-44 for more detail on using a series of equations.


Defining variables

A variable can be a single letter or several letters and/or numbers, e.g. a, a2 and ab. The

program intelligently takes care of formatting variables with sub-scripting and italic characters.

The following simple rules apply:

Enter numbers using normal or scientific notation. Example, '0.002' and '2E-3' has the

same meaning.

When entering a variable, the second and following characters are used as sub-scripts, e.g.

enter 'abc' to get abc.

Variables are case sensitive, e.g. 'a' and 'A' are seen as two different variables.

A variable cannot start with a number. Using '1' and 'a' separately yields a valid number

and variable respectively, but entering '1a' is not allowed.

Using Greek symbols

Greek symbols are treated exactly like normal letters. To create a Greek symbol, enter a hash

before the equivalent Roman letter, e.g. enter '#S' and '#s' to get Σ and σ respectively.

The following rules apply:

Greek symbols are case sensitive, e.g. Σ and σ are seen as two different variables.

You may mix Greek symbols with normal characters.

Note: The Greek symbols Π and π are reserved and cannot be used as variable. Their values

are fixed at 3.141593 etc. You may however use the symbol e as a normal variable.

Entering normal text

Normal text entries, e.g. headings and comments, are distinguished from equations by

enclosing or preceding them in double quotes, e.g. "Comments" or "Comments without a trailing quote.


Using mathematical functions

You can use the built-in mathematical functions as necessary, e.g. 'sqrt(...)' to determine the square root of an expression. Built-in functions include:

Trigonometry

Normal functions

Arc functions

sin, cos, tan

asin, acos, atan

Logarithmic functions

ln, log

Other functions

Square root

Absolute value

sqrt

abs

Additional functions can be derived using the standard mathematical operators and functions.

A few simple examples include:

Instead of using the built-in square root function, you may determine the square root and

other roots as follows: cba can be entered as 'a=sqrt(b+c)' or

'a=(b+c)^(1/2)’

If a = log(b), then b = 10a, which is entered as 'b=10^a'.

Trigonometric functions are inter-dependent, e.g.

tan

1cot . To enter the equation

a = cot(θ), type 'a=1/tan(#h)' or 'a=(tan(#h))^(-1)'.


Assigning values to variables

Assign values to variables on the Variables page. A list of all variables used on the Equations

page is displayed:

Assigned variables: Variables that are not calculated but require values to be assigned to

them are listed first.

Calculated variables: Variables denoting equation results are listed last. The values for

these items are typically shown as 'EqX:Y', where X is the relevant row number in the

table on the Equations page and Y is the equation result.

To explain the symbols, an image can be displayed alongside the list of variables. Refer to

page 2-42 for more information on using images with equations.


Equation settings

The Settings page is used to configure the display properties of an equation object:

Title: You can enter a title for an equation object. When inserting the equation in Calcpad,

the title can optionally be displayed above it.

Image: An image can be loaded and optionally displayed when inserting the equation in

Calcpad. The image is also displayed on the Variables page.

Numeric format: You can choose to display equation results in decimal, scientific or

engineering format.

Font: Select a font, style and height to use for the equation.


Advanced techniques

Once you have mastered the basic functions of the Equation Editor, you may want to proceed

to creating more sophisticated equation objects.

Using units of measurement

You may enhance your equations by adding units of measurement. Units are designated by

enclosing them in curly brackets.

The following rules apply:

The unit should be written in curly brackets immediately after the variable.

You may use a mathematical operator to create derivatives of units, e.g. use 'm^2' for m2.

You may use either Metric or Imperial units.

Examples:

To determine the circumference of a circle in feet, you may enter 'Circ{ft}=#p*r{ft}'. The result in Calcpad will be:

To calculate the area of a circle in square meter, you may enter 'A{m^2}=#p*r{m}^2'. The result will be:

r = 2.5m

=A p r2. = 19.635 m2

Note: The program does not evaluate the consistancy of units within equations.

Using a series of equations

When entering multiple lines of equations, all assigned and calculated values of variables are

carried over to equations down the list – a characteristic referred to as inheritance. This allows

you to break complex equations into smaller pieces, making them a lot easier to write and

verify. It also allows you to use multiple inter-dependent equations in a complex calculation.


Conditional branching

You can use the inheritance characteristic of equations to your further advantage. By

combining inheritance with conditional branching, you can create equation objects that can

intelligently adjust for different values of the variables.

To create a conditional branch:

Define the condition using the 'if' statement, e.g. 'if a>b' will do something only if a is greater than b. For comparison, you may use the operators <, >, =, >= and <=.

In the lines following the 'if' statement, enter one or more equations to be evaluated if the

condition is met. Use the 'end' or 'else' statement to terminate such a series of equations and continue with the normal flow.

If a condition is not met, an alternative series of equations can be entered after an 'else'

statement. Terminate the series of equations with an 'end'.

In the following example, taken from the Help menu of the Equation Editor, the area of reinforcement in a rectangular beam is calculated using the formulae in BS 8110 - 1997:

#bb=(100-%RD)/100

if %RD<10 then (first conditional branch)

K'=0.156

else (if condition is not met)

K'=0.402*(#bb-0.4) - 0.18*(#bb-0.4)^2

end (end of first branch)

K=M{kNm}*1e6/(b{mm}*d{mm}^2*fcu{MPa})

if K<=K' then (second conditional branch)

"Compression reinforcement not required because K<=K'"

z=d*(0.5+sqrt(0.25-K/0.9))

x=(d-z)/0.45

As{mm^2}=M*1e6/(0.95*fy{MPa}*z)

else (if condition is not met)

"Compression reinforcement required because K>K'"

z=d*(0.5+sqrt(0.25-K'/0.9))

x=(d-z)/0.45

A's{mm^2}=(K-K')*fcu*b*d^2/(0.95*fy*(d-d'{mm})

As{mm^2}=(K'*fcu*b*d^2)/(0.95*fy*z) + A's (end of second branch)

In the example, the first conditional branch causes K' to determined differently for different

values of the percentage of redistribution, %RD. Further, by comparing the values of K and K',

additional compression reinforcement is calculated when necessary.


Creating an equation library

You can use the File menu commands to save and recall all

useful equations.

The advantages of saving equation objects in a library will

become obvious once you have created a number of intelligent

equation objects comprising multiple equations and conditional

branching.

You are free to save your equations in any folder on your PC or

on the network. Using a dedicated and well-structured

folder is recommended to ensure easy access to a large library

of equations.

Use the Open command on the File menu to retrieve an equation object from disk. When

working with an existing equation, the Variables page is displayed automatically, i.e. the

program assumes that you want to reuse the equations with new values.

The usability of an equation library can be greatly enhanced by using titles and pictures with

equations, even if you do plan on displaying them when inserting equations in Calcpad.

Equation objects with descriptive titles and explanatory pictures are easier to use, especially in

a multi-user environment. Refer to page 2-42 for information on equation titles and pictures.


Customising the Page Layout

By default, projects are displayed on a framed page with the PROKON logo. The top portion of

the page, called the header, also includes a number of pre-defined fields like 'Designed by',

'Date' etc. The page layout and header items are collectively referred to as a template.


Selecting another template or creating a new template

You can select one of the other pre-defined templates or create your own using the Page Setup

command on the File menu:

To select a template, click Select template.

To modify an existing template or create a new one, click Edit template.

Click OK to close the Page Setup dialog box.

The following templates are available when you run PROKON for the first time:

Default: The default template with frame and PROKON logo. For a start, you may want to

replace the PROKON logo and contact details with your own.

Frame: No-frills template with a frame only. This template offers a larger workspace.

Nothing: A blank template, in case you prefer printing on blank sheets.


Creating your own template

A template is defined using a simple scripting language that has been derived from the Padds

macro language. In essence, the script is a series of two-letter commands similar to the

keyboard shortcuts used in Padds. Several new commands have been introduced to for special

effects like setting margins.

To create a new template, it may be easiest to modify an existing template:

1. Click Edit template to open the template script in the Text Editor.

2. Use the Save As command on the File menu to save the template with a new name.

3. Edit the script as necessary.

4. Choose Save on the File menu to save the script.

5. To preview your new template, press Alt-Tab to swap back to the Page Setup dialog box or select it from the task bar.

6. Click Select template and open the new template.

7. To make further modifications, swap back to the Text Editor.

Repeat steps 3 to 7 until you are satisfied with the new template.

8. Finally close the Text Editor and the Page Setup dialog box to return to Calcpad.

Script commands

A number of script commands are available to draw lnes, write text and define special items.

All commands use parameters, i.e. values, to define certain entities. Parameters are separated

with spaces or commas.

The template script commands can be categorised as follows:

Global page layout:

XO Xleft and YO Ybot : Define the origin, or reference point, from where all entities are

measured, e.g. 'XO 5' and 'YO 7.5' . The position of the origin is measured from the bottom left corner of the page. In fact, if you do not enter an origin the bottom left corner

of the page will be used. You may repeatedly redefine the origin – the last definition is

used for subsequent lines in the script.

MA Mleft,Mbot,Mright,Mtop : Set the left, bottom, right and top margins in millimetres, e.g.

'MA 15,15,285,195'. The margins define the workspace in Calcpad and the values are

measured from the origin rather than the edges of the page. The margin command does not

draw any lines.


RT colpos : Right column tab stop, measured in millimetres from the origin, e.g.

'RT 170'. The design modules use the right column for code references and other comments.

Graphics:

BM Xleft,Ybot,Xright,Ytop,filename : Insert a Bitmap image and stretch it between the

coordinates Xleft,Ybot and Xright,Ytop , e.g. 'BM 5,261,34.6.5,2779.5,LOGO.BMP'. The Bitmap is assumed to reside in the same folder as the template file. For the best printing

results, the bitmap should be sized so that it can be placed at true size, e.g. an image of 700

pixels wide by 300 pixels high, placed 29.6mm wide by 12.7mm high should print well at

600 dpi.

Line drawing:

LT thickness: Set the line thickness in millimetres, e.g. 'LT 0.25'.

LL X1,Y1,X2,Y2: Draw a line from the coordinate X1,Y1 to X2,Y2, e.g. 'LL 5,10,5,110' to draw a vertical line 100mm long.

Text:

TF font,style: Set the font and style, e.g.'TF Times New Roman, Normal'

TS size: Set the text height in points, e.g. 'TS 11'.

TT Xleft,Ybot,text: Write text at the coordinate Xleft,Ybot , e.g. 'TT 5,10,Project No'.

Header items:

HI Xleft,Ybot,Xright,Ytop,description: Insert a header item in the rectangle defined by the

coordinates Xleft,Ybot and Xright,Ytop, e.g. 'HI 150,270,Designed by'. In Calcpad, the header item is later referenced by its description. See page 2-7 for details on entering

header information.

Other:

Comments can be written after two slashes, e.g. '//comment'.


Example

Below is an abstract from the Default template script:

XO 15 // X Origin

YO 15 // Y Origin

BM 1,260, 41,267 PROKON.BMP // Load Bitmap x1,y1,x2,y2

LT 0.3 // Line Thickness mm

LL 0, 0,186, 0 // Line x1,y1,x2,y2

LL 0,248,186,248

LL 0,268,186,268

LL 0, 0, 0,268

. . .

. . .

. . .

LL 166, 0,166,248

TF Arial Italic // Text Font

TS 8 // Text Size Points

TT 156.5,267.8, Sheet // Text x,y,text

TT 42.5,267.8, Job Number

TT 42.5,262.8, Job Title

TT 42.5,257.8, Client

TT 42.5,252.8, Calcs by

TT 90.5,252.8, Checked by

TT 138.5,252.8, Date

TT 3,259 , Software Consultants Pty Ltd

TT 3,255.5, Internet: http://www.prokon.com

TT 3,252 , E-Mail : [email protected]

MA 1, 1, 185, 247 // Margins left, b, r, t

RT 166.5 // Right column tab stop

TS 10 // Text Size Points

HI 165.0,267.2, First Sheet No // Header Item

HI 60.0,267.2, Job Number // x,y,Description

HI 55.0,262.2, Job Title

HI 55.0,257.2, Client

HI 55.0,252.2, Calcs by

HI 106.0,252.2, Checked by

HI 150.0,252.2, Date


Configuring the Section

Database

The Section Database utility is a base component for all steel member and connection design

modules. The module contains section databases for several countries, comprising standard

steel profiles and common concrete and timber profiles. You can expand the database to

include custom sections.

Use the Section database command on the Tools menu to edit the database or select another

country database.


Using the section database

The section database is accessible from all the steel member and connection design modules.

Before using any of these modules, you may wish to first configure the database to your

requirements.

Selecting a database

Depending on the Windows Regional Settings, PROKON will automatically select an

appropriate section database when you run it for the first time. You can load another country's

database as follows:

On the Country menu, choose the country of your choice.

On the File menu, choose Safe as Default to save the selected database as the default

database for all PROKON modules, Sectable.dat

Creating a database for another country

If a section database is not available for your country, you can build your own database. Use

the Edit Countries command on the Country meno for this purpose. The currently loaded

database will be used as the starting point for the new country database. A good starting point

will therefore be to load a similar database (e.g. the UK or USA databases that are used in

many parts of the world) and then making adjustments. The procedure to add new sections is explained below.

Adding new sections to the database

You can edit any of the sections in the database and add your own. You are free to add other

welded and other non-standard sections.

If a section' shape conforms to the basic definition of one of the standard shapes, you can add it

as a standard section. Non-standard shapes can be added to the 'custom profiles' group.

Adding a standard section

To add a new I-section, for example, press I to access the current list of I-sections. Enter the

section dimensions and then press F2 to have the section properties calculated and added to the

database.

Typical examples include:

I-shaped plate girders can be added with the other standard I-sections.

Older steel structures built with imperial sections can be checked after first adding the

relevant sections to the database.


A haunch in a portal can be conservatively modelled as an I-section with an increased

depth.

Tip: The normal text editing commands apply when entering sections. Refer to Chapter 2 for detail on copying, deleting and inserting lines.

Adding a custom (non-standard) section

Sections with non-standard shapes should be entered as 'custom profiles'. These properties can

be calculated manually or using Prosec. When using Prosec to calculate the section properties,

not only the section properties but also the section shape is saved in the database. Such sections

can be used in Frame Analysis, for example, with full 3D rendering.

To calculate a section's properties with Prosec:

In the Custom Profiles table, double-click in the Designation column. Enter a section

designation. Prosec will then open automatically.

Enter the section shape and calculated the bending and torsional properties.

Optionally save your input, and then exit Prosec.


On returning to the Section Database, the section properties and shape will be inserted

into the database.

Instructions for using Prosec is given in Chapter 8.

Tip: Some modules, e.g. Steel Member Design for Combined Stress, support certain section types only. Therefore, it may in some cases be better to simplify a non-standard

section and then add it as a standard shape. That way, the simplified version of the section

will be available to the relevant design modules.


Configuring the Material

Database

Use the Material database command on the Tools menu to edit the database. The material

database is a base component for the analysis and design modules. The default database

contains lists properties for common grades of steel, concrete, timber and aluminium available

in various countries in the world. The database also includes stress-strain curves for use in non-

linear analyses in Frame Analysis. You can add new materials to the database using the

Material Database utility that is accessible on the tools menu in Calcpad.


Using the Material database

Selecting a country database

The system-wide material database is saved in a file called defaults.mtl in the \Prokon\User

folder. You can open a country database, edit it, or create your own material database:

Opening a country database: Use the open command on the file menu to select a list of

country databases to.

Saving a database. Use the save command on the file menu to store any changes you have

made.

Setting a database as system default: Open the database (if it is not open already), and use

the save as command on the file menu to save it as defaults.mtl.

Adding materials

You can edit existing grades of materials or add new grades as needed. Material grades are

categorised as steel, concrete and aluminium. For other material types, use the other group.

Terminology

The meaning of the symbols used is as follows:

Grade: Name of the material grade, e.g. 350W. The grade will be visible in the Frame

Analysis module when you select from the available items in the material database.

E: Modulus of elasticity (kN/m2 or psi)

Poisson's ratio: Transverse strain ratio

Density: Unit weight (kN/m3 or lb/in3)

Expansion coefficient: Thermal expansion coefficient (strain per °C )

fy: Steel and aluminium yield stress (kN/m2 or psi)

fu: Steel and aluminium ultimate stress (kN/m2 or psi)

fcu: Concrete cube strength

f'c: Concrete cylinder strength

Stress-strain designation: Select a stress-strain curve if you wish to model non-linear

material behaviour in Frame Analysis.

Yield criterion: Select a yield criterion if you wish to model non-linear material behaviour in Frame Analysis. The Von Mises yield criterion is suitable for materials that exhibit

similar behaviour under compression and tension, e.g. steel, and the Drucker-Prager


criterion is suitable for materials with pressure dependent behaviour, e.g. concrete and soil

that has negligible tensile resistance.

c: Cohesion (kN/m2 or psi). Optionally enter this value if using the Drucker-Prager yield

criterion, e.g. when modelling soil.

φ: Angle of internal friction (°). Optionally enter this value if using the Drucker-Prager

yield criterion, e.g. when modelling soil.

Note: By default, all materials in the database have no stress-strain curves or yield criteria

assigned to them. The reason for this is that non-linear analyses (in Frame Analysis) are

usually performed to evaluate geometric non-linearity (i.e. where deflection are large

enough to have an effect on the analysis). To include non-linear (inelastic) material

behaviour, you must associate an appropriate stress-strain curve and yield criterion to each

material concerned.


Stress-Strain curves

When performing a non-linear analysis using the Frame Analysis module, you can model non-

linear material behaviour.

Adding a new curve

To add a new curve, enter its designation and press add new curve. Proceed to enter the curve

parameters:

Stress-strain parameters: The values for the modulus of elasticity and strain limits for

positive (compression) and negative (tension) strain are used for the Von Mises and

Drucker-Prager yield criteria.

Stress-strain curve coordinates: Enter two or more pairs of strain and stress value that

define the stress-strain curve.


Predefined curves

The database includes a number of stress-strain curves:

Parabolic stress-strain relationship for concrete (based on the design curve in

BS 8110 - 1997) with a small amount of strain hardening up to the maximum allowable

compression strain. For tension, cracking is modelled using a linear stress-strain relationship up to a maximum stress of 1.0 MPa.

Non-linear stress-strain relationship based on test results for duplex stainless steel 1.4462.

Linear elasto-plastic behaviour for and structural steel. The plastic zone includes a small

amount of strain hardening to allow a nominal stress increase after reaching the yield

point.

Elasto-plastic behaviour for reinforcing steel and prestressing tendons.

Yield criteria

The yield criterion supplements the stress-strain curve in defining a material's behaviour:

The Von Mises yield criterion is suitable for ductile materials with similar compressive

and tensile properties, e.g. steel. If presented in three-dimensional space of principal

stresses, it would be a circular cylinder of infinite length with its axis inclined at equal

angles to the three principal stresses.

The Drucker-Packer yield criterion is suitable for materials that do not exhibit the same

behaviour in tension and compression, e.g. concrete and soil. Its three-dimensional presentation would be a cone. The Drucker-Prager yield surface is a "smooth version" of

the Mohr-Coulomb yield surface, and therefore it is often expressed in terms of the

cohesion, c, and the angle of internal friction, φ, that are used to describe the Mohr-

Coulomb yield surface.

Structural Analysis using PROKON 3-1

Chapter

3 Structural Analysis

The structural analysis collection includes frame analysis and also some specialised finite

element and beam analysis modules.


Quick Reference


Frame Analysis 3-5

Plane Stress/Strain Analysis 3-85

Single Span Beam Analysis 3-97

Beam on Elastic Support Analysis 3-105


Structural Analysis using

PROKON

The accent of the analysis modules falls on user friendliness, speed and efficiency. The frame

analysis module is ideally suited for the analysis of small to medium sized structures, not to say

that the analyses of large structures are not possible. Frame has a comprehensive array of static

and dynamic analysis modes.

Extensive use is made of interactive graphic representations during both the input and output

phases. The input modules incorporate error checking to help eliminate input errors as they

occur.

Frame analysis

Frame can take account of own weight, temperature changes, prescribed displacements and

elastic supports. Loads are entered as load cases and grouped in load combinations at ultimate

and serviceability limit states.

The following static analysis modes are available:

Linear analysis: Normal elastic frame analysis.

Second order analysis: Models sway behaviour by incorporating P-delta effects. The solution is obtained by iterative analysis, thereby allowing for options like tension

elements.

Non – linear analysis. This takes the second order analysis a bit further. The load is

applied in steps and the deflected structure at the end of each step is used to apply the next

step. Material non – linearity is not yet supported.

Buckling analysis: For calculating safety factors for structural instability due to buckling.

Dynamic analysis modes available include:

Modal analysis: Calculation of a frame’s natural modes of vibration.

Harmonic analysis: For determining a frame’s response to harmonic loading.

Earthquake analysis: Quasi-dynamic analysis of a frame subjected to ground

acceleration.


Finite element analysis

Frame allows you to use finite shell elements and solid elements alongside normal beam

elements. The shell elements enables you to model the combination of plate bending and

membrane action in 3D. To model plate bending in concrete slabs, you may prefer using the

Finite Element Slab Design – see Chapter 6 for details.

You can also use the Plane Stress/Strain Analysis module to perform a finite element analysis

of any general plane geometry subjected to plane stress or strain. The module features an

automated element grid generation facility to help speed up the input and analysis processes.

Beam analysis

Modules are available for the analysis of simple beams and beams on elastic supports.

Post-processing of analysis results

Linear and second-order analysis output can be post-processed by the steel member design modules, Strut and Com, to evaluate and optimise section profiles. The Space Frame Analysis

module can also design finite shell elements as reinforced concrete members.

Frame Analysis 3-5

Frame Analysis

Frame can be used for the analysis of the following types of structures by selecting a domain

on the ‘General’ input page:

Plane Frames: Analysis of a frames in a vertical (X-Y) plane.

Grillages: Analysis of a structure in a horizontal (X-Z) plane.

Space Frames: Analysis of three-dimensional structures made up of beam and/or shell

elements and design of concrete shells.

Space Trusses: Analysis of three-dimensional trusses where only axial forces are

considered.

Frame analysis results can be post-processed using some of the steel and steel design modules.

Frame Analysis 3-6

Theory and application

The following text explains the sign conventions used and gives a brief background of the

analysis techniques.

Sign conventions

Frame input and output uses a mixture of global axis and local axes values.

Global axes

The global axis system is nearly

exclusively used when entering frame

geometry and loading. Global axes are

also used in the analysis output for

deflections and reactions.

The global axes are defined as follows:

For the sake of this definition, the

X-axis is chosen to the right.

The Y-axis always points vertically

upward.

Using a right-hand rule, the Z-axis

points out of the screen.

Note: Unlike some other 3D programs that put the Z-axis vertical, Frame take the Y-axis as

being vertical.

Beam element local axes

Local axes are used in the output for element forces. You can also apply loads in the direction of

a beam element's local y-axis.

Frame Analysis 3-7

The local axes for beam elements are defined as follows:

The local z-axis and axial force is chosen in the direction from the smaller node number to

the larger node number.

The y-axis is taken in a vertical plane perpendicular to the z-axis. The y and z-axes thus

describe a vertical plane with the y-axis pointing vertically or diagonally upward.

The x-axis is taken perpendicular to the y and z-axes, using a left-hand rule.

One special case exists: In the case of a vertical member, the z-axis is taken parallel to the

global Y-axis. A unique definition of the y-axis is obtained by taking it parallel to the

global X-axis.

Shell element local axes

For shell elements, the local axes are defined as follows:

The local x and y-axes are chosen in the

plane of the shell in such a way that the

x-axis is horizontal and the y-axis lies

perpendicular to and upward from the

x-axis.

Using a right-hand rule the z-axis is taken

perpendicular to the shell element to point diagonally upward.

Two special cases exist:

Horizontal elements: The local x is

chosen parallel to the global X-axis

and the y-axis parallel to the negative

Z-axis. The z-axis is then taken parallel

to the Y-axis.

Vertical elements: The y-axis is taken vertically upward, i.e. parallel to the global

Y-axis. The x-axis is taken horizontal in the plane of the shell and z-axis is taken

horizontal perpendicular to the shell. The z-axis points towards you if the shell's nodes

are defined in an anti-clockwise direction and away if defined clockwise.

To simplify the analysis output, the orientation of the local shell axes can sometimes be

manipulated by slight rotation of the shell elements. In the case of horizontal slab, for example,

the local x and y-axes (and stresses) are taken parallel to the global X and Z-axes. In the case of a circular slab, radial and concentric stresses may often be more desirable. By generating the

shell elements at a slight slope towards the centre, they will not be considered as horizontal

anymore. As a result, local y-axes will point (upward) towards the centre and the x-axes taken

Frame Analysis 3-8

perpendicular to that, i.e. radial and concentric respectively. The small inclination will

normally have no significant effect on the analysis.

Note: Rotating elements (for the sake of manipulating the local axes) can induce additional support conditions in some cases. Such manipulation should thus be performed with

great care.

Beam element forcesThe sign

conventions are as follows:

The axial force, Pz, is taken in the

z-direction.

The shear forces, Vx and Vy, are

given in the x and y-directions respectively.

Torsional moment, T, is taken about

the z-axis using a right-hand rule.

The moments, Mxx and Myy, are

about the x and y-axes respectively.

Note: In this manual, the global and local axes are written in uppercase and lowercase respectively.

Shell element stresses

Shell element stresses are given using the local axes:

Bending stresses: The entities Mx and My are moment per unit width about the local x and

y-axes. Mxy represents a torsional moment in the local x-y plane. The principal bending moments per unit width are represented as Mmax and Mmin.

Plane stresses: The stresses in the plane of a shell, Sx and Sy, are given in the directions of

the local x- and y-axes. Sxy represents the shear stress in the plane of the element. Values

are also given for the principal plane stresses, Smax and Smin.

Note: To assist you in evaluating shell element stresses, stress contour diagrams show

orientation lines at the centre of each shell element. An orientation line indicates the

direction (not axis) of bending or plane stress. In a concrete shell, the orientation line would

indicate the direction of reinforcement resisting the particular stress.

Frame Analysis 3-9

Shell reinforcement axes

Reinforcement is calculated in the user-defined x' and y'-directions. Refer to page 3-61 for

detail.

Solid element stresses

Shell element stresses are given using the global axes:

Direct stresses, Sx , Sy and Sz, are given in the directions of the global X-, Y- and Z-axes. Sxy

represents the shear stress in the XY-plane of the element. Sxz represents the shear stress in the XZ-plane of the element. Syz represents the shear stress in the YZ-plane of the element. Values

are also given for the principal plane stresses, S1, S2, and S3. Von Mises stresses are also

calculated.

Units of measurement

The following units of measurement are supported:

Units Metric Imperial

Distance mm, m ft, inch

Force N, kN lb, kip

Use the Convert Units button on the Settings page to change the units for the current analysis:

Convert Units: Changes the units and converts all numeric data from the old to the new

units of measurement.

Analysis modes

The following types of analysis are possible:

Linear analysis: Basic linear elastic analysis. A linear analysis is normally sufficient for

the static analysis of a frame or truss with negligible sway.

Second order analysis: Choose this mode to include p-delta effects in the analysis. This

option is recommended for structures where sway may have a marked effect on the member forces, e.g. portal frames. The second order analysis is an iterative procedure. The

total strain energy of the frame is calculated after each iteration. The analysis is deemed to

have converged once the total strain energy of two sequential iterations differs by less than

the specified tolerance. If convergence was not possible, e.g. structural instability due to

buckling of critical members, a message to that effect will be displayed.

Non Linear analysis: Choose this mode where non-linear effects and large deflections

may be expected or where second order analysis might not provide sufficient accuracy.

Frame Analysis 3-10

Loading is applied in a series of steps and an iterative analysis is carried out at each step so

that the forces in the deflected structure at that point balance with the applied loading.

Modal analysis: For calculating the natural modes of vibration. The modal analysis is an

iterative procedure during which several sets of trial vectors are selected and evaluated.

The process takes relatively long to complete and it is therefore recommended that the

structure size be limited to a few hundred nodes. You can specify the number of mode

shapes to be calculated and other dynamic analysis parameters.

Harmonic analysis: Choose harmonic analysis to determine the response of the frame to

harmonic loading. Load amplitudes are entered exactly like static nodal and element loads.

You can enter a load frequency and phase angle for each harmonic load case. The first step

of a harmonic analysis is the calculation of the frame's natural modes of vibration.

Therefore, if preceded by a modal analysis, the results of that analysis are re-used and only

the harmonic response calculated. The harmonic response is taken as the sum of the square

(SSRS) of the maximum modal responses, a method that is considered fundamentally

sound when modal frequencies are well separated. When frequencies of major contributing

modes are very close together, the SSRS method can give poor results.

Earthquake analysis: Use this option to calculate the response of the frame to the

specified a seismic acceleration parameters. Nodal and element loads entered are treated as static loads. The analysis procedure starts by calculating the frame's natural modes of

vibration. Therefore, if preceded by a modal analysis, the results of the modal analysis are

re-used and only the seismic response calculated.

Buckling analysis: Use this option to determine the buckling load factors and mode shapes

for each load case or combination. Being the critical case, the first buckling mode shape is

normally the only one of interest.

Finite element shells

Frame allows you to use finite shell elements alongside normal beam elements. For this

purpose the program uses four-node quadrilateral and three-node triangular isoparametric shell

elements with plate bending and membrane behaviour.

Element formulation

The bending formulation of the quadrilateral shell element was derived from the Discrete

Kirchoff-Midlin Quadrilateral. The membrane behaviour of the element was improved by

introducing the drilling degree of freedom using an interpolation technique by Alman. The

result is a shell finite element that shows good plate and membrane performance characteristics.

Accuracy of triangular elements

Both the quadrilateral and triangular elements yield accurate stiffness modelling. However,

stress recovery from the triangular elements is not as accurate as is the case for quadrilateral

Frame Analysis 3-11

elements. This means that deflections calculated using triangular elements are generally quite

accurate, but moments may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stresses

are calculated at the Gaussian integration points and subsequently extrapolated bi-linearly to

the corner point and centre point of each element. Taking the average of all contributing stress

components smooths stresses at common nodes.

Element layout

Consider a typical continuous flat concrete slab supported on columns or walls. To ensure

accurate modelling of curvature, a minimum of about four elements should be used between

bending moment inflection points. This translates to a minimum of about eight elements per

span in both directions.

Using more elements per span often does not yield a significant improvement in analysis

accuracy. In addition, the particular finite element formulation yields its most accurate results

when the element thickness does not greatly exceed its plan dimensions.

For a typical concrete slab with a thickness of about one-tenth or one-fifteenth of the span

length, a reasonable rule of thumb is to make the plan dimensions of the shell elements no

smaller than the thickness of the slab. In other words, use a maximum of about ten to fifteen elements per span.

Finite element solids

Frame also provides 8-noded hexahedral and 4-noded tetrahedral solid finite elements. The

elements have 3 rotational degrees of freedom per node and are generally more accurate than more commonly used solid elements that do not have rotational degrees of freedom.

Accuracy of tetrahedral elements

Both the hexahedral and tetrahedral elements yield accurate stiffness modelling. However,

stress recovery from the tetrahedral elements is not as accurate as is the case for hexahedral

elements. This means that deflections calculated using tetrahedral elements are generally quite

accurate, but stresses may be less accurate.

Stress smoothing


are calculated at the Gaussian integration points and subsequently extrapolated to the corner

nodes of each element. Taking the average of all contributing stress components smooths

stresses at common nodes.

Frame Analysis 3-12

Element layout

To ensure accurate modelling of curvature, a minimum of about four elements should be used

between bending moment inflection points. This translates to a minimum of about eight

elements per span direction in a continuous slab.

Concrete design

Frame can perform reinforced concrete design for shell elements. The Wood and Armer

equations are used to transform the bending and torsional stresses to effective bending

moments in the user-defined x' and y'-directions.

To allow for the effect of in-plane forces, bending moments Mx, My and Mxy are increased to

include the effects of these forces. The moments are increased by conservatively taking the in-

plane forces to act with a lever arm of a quarter of the section depth. The Wood and Armer equations are then evaluated in same manner as described above.

Codes of practice

The following concrete design codes are supported:

ACI 318 - 1995.

BS 8110 - 1997.

CSA A23.3 - 1993.

Eurocode 2 - 1992.

SABS 0100 - 1992.

Steel member design

Frame analysis results can be opened in the steel member design modules for design. The

available options are:

Steel Member Design for Axial Stress, Strut: Can design steel trusses.

Steel Member Design for Combined Stress, Com: Can design beam members.

Frame Analysis 3-13

Settings

Settings are done on the Settings page:

Analysis type

Linear analysis: Normal linear elastic frame analysis. A linear analysis is normally

sufficient for the static analysis of a frame or truss with negligible sway. The linear

analysis procedure is performed faster than any other type of analysis. If you need to

perform a second order, buckling or dynamic analysis, it will be wise to first verify the

basic integrity of the frame input by performing a linear analysis.

Second order analysis: Models sway behaviour by incorporating P-delta effects. The

solution is obtained by iterative analysis, thereby allowing for options like tension

elements.

Frame Analysis 3-14

Non-linear analysis: This analysis is used when large deflections or non-linear behaviour

are expected. Only geometric non-linearity is supported a this stage. Material non-linearity

will be added in the near future. The solution is obtained by a stepped iterative analysis.

Loads are added in steps. The analysis is iterated to convergence for each step so that the

reactions and forces are in balance with the applied loads after each step. The deflected

structure at the end of each step is then used to apply the next load step and the process is

repeated until the total load has been applied.

Modal analysis: Calculation of a frame’s natural modes of vibration. The process takes

relatively long to complete and it therefore recommended that the structure size be limited

to a few hundred nodes. You can specify the number of mode shapes to be calculated and

other dynamic analysis parameters.

Harmonic analysis: For determining a frame’s response to harmonic loading.

Earthquake analysis: Quasi-dynamic analysis of a frame subjected to ground

acceleration.

Buckling analysis: For calculating safety factors for structural instability due to buckling.

You can specify the number of mode shapes to be calculated.

Analysis parameters

Depending on the selected analysis type, you may need to specify additional analysis parameters:

Concrete design parameters: Concrete and reinforcement properties. Details are given

on page 3-61.

Second order and buckling parameters: Required analysis tolerance and number of

buckling mode shapes. Refer to page 3-62 for detail.

Dynamic parameters: Values influencing modal, seismic and harmonic analysis. A

detailed discussion is given on page 3-64.

Non linear parameters: Values influencing the non-linear analysis. A detailed discussion

is given on page 3-64.

Own weight

The own weight of the frame can be calculated using the entered cross-sectional areas and member lengths. If you specify a load case, the own weight is calculated and added to the other

loads of that case.

The following are points of importance:

By default, the own weight of the frame is set to not be included in the analysis. Be sure to

select the appropriate load case for own weight or, alternatively, to include the frame's

own weight in the values of the loads entered.

Frame Analysis 3-15

The list of load cases from which you can select is based on the load cases defined on the

Nodal loads, Beam loads, and Shell loads input pages. You may thus prefer to specify the

own weight load case only after completing all other input for the frame. However, you

can also enter the own weight load case at the start of the frame input process in which

case you may ignore the warning message (that the load case does not exist).

Tip: If you wish to use own weight in its own separate load case, you can do so by defining an empty load case. You can enter a zero load at any node number, for example, and then

select that load case as the one to use for own weight.

The own weight or beam elements are modelled as uniformly distributed loads along the

lengths of the beams. In the case of a vertical beam element, own weight is modelled as two

equal point loads at the ends of the beam, yielding a constant axial force equal to half the own weight. In the case of shell elements, own weight is modelled as point loads at the corner

nodes. In the case of solids, the weight is added as point loads at the nodes.

Graphics Options

Click on the graphics options button to have the graphics options dialog displayed.

Select whether you want

items like node numbers

and supports to be

displayed.

Choose whether you want

all beam elements or only a

certain type to be displayed.

Display the structure with full 3D rendering, e.g. to

verify section orientations.

3D rendering is

automatically suppressed

when viewing output.

Choose quick or detailed

rendering. Quick rendering

is faster than the detailed

method, but you may find that some surfaces are drawn incorrectly.

All surfaces are drawn as polygons. You can choose to make the surfaces transparent or have

them filled and outlined.

Tip: The Graphics options and 3D rendering function can also be accessed using the buttons

next to the displayed picture.

Frame Analysis 3-16

Views: You can save the current

viewpoint and view plane. The

current view's name is displayed on

the picture. To re-use a saved view,

click the view name on the picture to

drop down a list of saved views.

The functions described above can also be used when viewing output. Contour

diagrams, for example, are drawn as

polygons. You can therefore use the

Graphics options setting for polygons to

change their appearance. Views defined

during input are also available when

viewing output and vice versa.

Frame Analysis 3-17

Input

Work through the relevant Input pages to enter the frame geometry and loading:

General input: Select the domain (Plane frame, grillage etc.) The input wizards can also

be selected here. More about these wizards later.

Nodes input: Frame coordinates.

Beams input: Join nodes with beam elements.

Beam sections input: Enter properties or read sections from the database.

Shells input: Define shell elements.

Solids input: Define 4- or 8- noded solid elements

Spring elements input: For special effects, optionally enter spring elements.

Supports input: External supports.

Nodal loads input: Point loads and moments.

Beam element loads input: Uniform distributed, triangular, trapezium and point loads on

beams.

Shell loads input: Apply uniform distributed loads to shells.

Load combinations input: Group dead, live and wind loads in load combinations.

Alternative methods of generating frame analysis input are discussed on page 3-58.

Viewing the structure

You may want to enlarge portions of the picture of the structure or rotate it on the screen.

Several zoom and rotate functions, all of which are described in detail in Chapter 2, are

available to help you using pictures of the structure:

Use the Zoom buttons to zoom into a part of the structure or view it from another angle.

Use the View Point Control to set a new viewpoint or camera position.

Use the View Planes Control to view a slice of the structure.

Frame Analysis 3-18

General input

Wizards

The wizards are suitable for the

rapid generation of complete

input files for some typical structures. Because the resulting

input data is presented in the

normal way on the input pages,

you are free to edit and append

to the data as necessary.

Input generated this way can

optionally be appended to

existing data – you can therefore

repeatedly use the wizards to

generate complicated structures.

Note: The frame analysis modules are not limited to modelling only those frames generated

by the wizards. Any general two or three-dimensional frame can be collectively built up.

The wizards merely serve to simplify input of typical frames.

Adding input data to the Calcsheets

You can append the input tables (as they appear on the screen) to the Calcsheets by clicking

the Add input tables to Calcsheets button.

You can add a picture from any input pages to the Calcsheets by clicking the Add to

Calcsheets button next to the picture in question.

Title

Enter a descriptive name for the frame. It should not be confused with the file name you use

when you save the input data.

Frame Analysis 3-19

Nodes input

Use as many lines as necessary to enter the nodes defining the frame. A unique number must

be assigned to each node. The node number is entered in the No column, followed by the X, Y

and Z-coordinates in the X, Y and Z columns. If you leave X, Y or Z blank, a value of zero is

used.

You are allowed to skip node numbers to simplify the definition of the frame. You may also

leave blank lines in the input to improve readability. If a node number is defined more than

once, the last definition will be used.

Note: Most of the examples given in this section show 3D co-ordinates as would be applicable if the domain is set to Space Frame or Space Truss. If the domain is set to

Plane Frame or Grillage use the X-Y and X-Z planes respectively.

Frame Analysis 3-20

Error checking

The program checks for nodes lying at the same position. If a potential error is detected, an

Error list button will appear.

Generating additional nodes

When defining a node, you can have additional nodes generated at regular intervals. Example:

The Y-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate

(0.805,0,14.614).

The No of is set to '2', meaning that two additional nodes must be generated.

Setting Increment to '7' means that the node numbers are incremented by seven.

Therefore, node 4 is copied to node 11 and node 11 is copied to node 18.

The values in the X-inc, Y-inc and Z-inc columns set the distance between copied nodes.

The coordinates 4 to 18 are horizontally spaced at 1.140 m and 0.472 m along the X and negative Z-axis respectively. The coordinates of the additional nodes are thus

(1.945,0,14.142) and (3.085,0,13.670).

An alternative method to generate equally spaced nodes is to use the Inc to End option. This

method allows you to define two nodes and then generate a number of nodes in-between:

Use the same procedure as above to define the first node's coordinates.

Set the values of X-inc, Y-inc and Z-inc to the total coordinate difference to the last node

and enable the Inc to End option. The last node's coordinates are then first calculated and

the specified number of intermediate nodes then generated.

Second order generation

Once you have defined one or more nodes in the table, you can copy that relevant line’s nodes

by entering a '–' character in the No column of the next line. Then enter the number of

additional sets of nodes to be generated in the No of column and the coordinate increments in

the X-inc, Y-inc and Z-inc columns.

Frame Analysis 3-21

Second order generation example:

The following nodes are generated:

No X Y Z

15 0.00 5.12 0.00

16 2.00 5.12 0.10

17 4.00 5.12 0.20

18 0.00 5.62 1.00

19 2.00 5.62 1.10

20 4.00 5.62 1.20

Block generation

A group of nodes can be repeated by entering a 'B' in the No column followed by the first and

last table line numbers in which the nodes were defined. Separate the line numbers with a '–'.

Block generation example:

The nodes defined in lines 11 to 26 are copied twice. Node numbers are incremented by thirty for

each copy. The X, Y and Z-coordinate increments are 10 m, zero and zero respectively.

To copy one line only, simply omit the end line number, e.g. 'B10' to copy line 10 only.

Tip: The current line number is displayed in the status bar at the bottom left of the program's window.

The block generation function may be used recursively. That means that the lines specified may themselves contain further block generation statements.

Moving nodes

To move a group of nodes to a new location without generating any new nodes, use the block

generation function and set No-of to '1' and Inc to '0'.

Arc generation

A group of nodes can be repeated on an arc by entering an 'A' in the No column, followed by

the start and end line numbers. Enter the centre of the arc in the X, Y and Z columns and use

the X-inc, Y-inc or Z-inc column to specify the angle increment about the X, Y or Z-axis

respectively. If the program domain is set to Plane Frame or Grillage, the angle increment

should be entered in the last column. Rotation will be about the Z and Y-axis respectively.

Frame Analysis 3-22

Example:

All nodes defined in lines 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10,0,1.5). The node

number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle

between the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise using

a right-hand rule.

To copy one line only, simply omit the end line numbers, e.g. 'A12' to copy line 12 only.

Note: The arc generation function may be used recursively.

Rotating nodes

To rotate a group of existing nodes without generating any new nodes, use the arc generation

function and set the No-of to '1' and Increment to '0'.

Deleting nodes

Nodes can be deleted by entering 'Delete' in the Inc to end column. This can be especially

handy if you have generated a large group of nodes and then need to remove some of them

again.

Example:

Nodes 15 and the additional nodes 18 and 21 are deleted.

Graphical input

The following graphical input functions are available on the left hand side of the screen. The

toolbar containing the graphics options buttons can also be dragged and docked on any side of

the picture.

To delete nodes click the ‘Delete

nodes’ button and then select the nodes to be deleted on the screen

using the mouse. Click ‘Done’ when

finished. Clicking ‘Undo’ will undo

the deletions in reverse order.

To block delete nodes click the

‘Block delete nodes’ button. Select a

Frame Analysis 3-23

rectangle on the screen with the mouse. All nodes inside the rectangle will be deleted. Press

‘Done’ when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one.

Pressing ‘Undo All’ will undo all deletions done with this function.

Click the ‘Explode nodes’ button to

explode the node input. This results in

the list of nodes being written, each

on a separate line without block & arc generations etc. Once done, it cannot

be reversed.

Click the ‘Join loos structure segments’ button

to have all duplicate nodes (having the same

co-ordinates) that are not connected by spring

elements, deleted. This will ensure that loose

pieces of the structure become connected. The

function is not reversible.

Click on ‘Delete loose nodes’ to have all

nodes not connected to elements deleted.

The program will ignore loose nodes in the

analysis, but the input is neater and easier

to interpret if unwanted nodes are

removed. The function is not reversible.

Deleted nodes can however be undeleted if

the bottom of the input table is edited and

the nodes entered as ‘deleted’ are removed.

Beam elements input

A beam or frame element is defined by entering the node numbers at each end, separated with a

'–'. For example, '3–9' is the element linking nodes 3 and 9. The elements themselves are not

numbered.

A series if elements can be input in a string, e.g. '2-6-10-14-18-22-24'. If the node number increment of a series is constant, you can replace intermediate nodes with two '–' characters. In

the string above, nodes 2 to 22 have a constant increment of four. Therefore, the string can be

rewritten as '2-6- - 22-24'. The node increment of four is derived from '2-6'.

Frame Analysis 3-24

An element definition must include a section number entered in the Section Name column.

The section name is used to identify the relevant section. The actual section properties for each

section number defined on the Beam Sections input page.

Section orientation in a 3D analysis

In 3D analysis, the local y-z plane of an

element is taken as vertical by default. The

principle can be illustrated by considering an

I-section in its normal orientation. For this

case, the web will always be considered to be

in a vertical plane.

If the element is aligned vertically, i.e. a

column, the web will be in a vertical plane

anyway. For this special case, the local y-axis

is aligned with the global X-axis, i.e. the web

is taken in the global X-Y plane.

Frame Analysis 3-25

An element can be rotated about its axis by entering a beta angle. The beta angle is measured

about the z-axis, taking the default orientation as 0°. Instead of entering a beta angle, you may

also enter a reference node – the beta angle is then taken in the plane described by the element's

nodes and the reference point. To use a reference point, first define a node with the relevant

coordinate and then enter 'N' followed by the node number in the Beta column

Tip: Enable full 3D rendering in the Graphics options to view the true beam orientation.

Section orientation in a 2D analysis

In the case of a 2D analysis, the local y-z plane of an element is taken in the global X-Y plane.

The principle can be illustrated by considering an I-section in its normal orientation. For this

case, the web will always be considered to be in a vertical plane.


A section can be rotated through ninety degrees by selecting the alternative orientation when

reading it from the section database.

Note: In a space truss analysis the section orientation is of no importance. The analysis results are influenced by the section area and not by it's second moment of inertia.

End fixity

The fixity at each end of an element, i.e. continuous or pinned, must also be defined in the

Fixity columns. Pins are modelled on the element itself and not on the node. External pinned

supports should be defined on the supports input table. External supports are described in the

next section.

The following types of end fixities can be specified:

Fixed: Specify 'F' to provide full rotational continuity. If you leave the field blank, 'F' is

assumed.

Pinned: Use 'P' to for no rotational restraint, i.e. a ball-joint.

Torsional fixity: Use 'T' to provide restraint for rotation about the element axis only. This

option is only available in the Grillage domain and the Space Frame domain.

Entered fixities are applied at an element's lower node number (designated as the 'left' end) and

higher node number (the 'right' end). The order of the node numbers entered in the first column

of the table has no bearing on the application of the fixity codes.

To define a pin only at the two remote ends of a group of elements, enable the Group fix

option by entering a 'Y'. In this case, the normal convention of smaller and larger node

numbers does not apply. Instead, pins are put at the remote ends in the same order that the nodes have been entered.

Frame Analysis 3-26

Example:

The group of elements from node 42 to 24 is continuous except for the pins used at nodes

42 and 24.

Note: Do not use an internal pin on an element to model an external support that allows free

rotation. Rather allow the beam to be fixed to the node and define a simple support on the

Support input page.

If the Group fix is left blank or 'N' is entered, the normal individual element fixity mode is

assumed.

Tip: Element fixity can be displayed graphically on the screen. For this, edit the Graphics

options to disable the Elements Continuous option.

When using pins, especially in the Space Frame domain, you should take care to ensure

overall stability of the frame. Consider two elements on a straight line with pins at all three

relevant nodes, for example. The centre node will be unrestrained for rotation about the

element axis, resulting in instability during the analysis.

Note: When performing a second order analysis, you can use tension elements to model

bracing, for example. For this, special settings need be made on the Beam Sections input

page. Refer to page 3-31 for detail.

Tapered beams

A beam can be made to taper between by entering two or three section names, separated with

commas:

Use two sections, e.g. 'Rafter,Haunch' or '1,2', to make the program vary the section

properties linearly along the length of the beam element. The first and second sections are

taken at the lower and higher node numbers respectively.

For a more accurate non-linear variation, enter three section names, e.g.

'Rafter,Middle,Haunch'. The first, second and third sections are taken at the at the lower

node number, the centre of the element and at higher node number respectively.

The procedure the enter haunches is described on page 3-31.

Frame Analysis 3-27

Rigid links

You can use rigid links to rigidly offset sub-structures, e.g. slabs with downstand beams. To

define a rigid link, enter 'R' in the Section Name column.

Rigid links are modelled as very stiff beams. The stiffness of a rigid link is determined by

multiplying the maximum area and bending stiffness of the other beams with a factor, typically

one thousand. The rigid multiplication factors can be adjusted using the Advanced option on

the Beam sections input page. Refer to page 3-32 for detail.

Rigid link example:

Rigid links are defined between nodes 12 and 24, 14 and 26 and 16 and 26.

Generating additional elements

You can generate additional elements with the same section and fixity code values using the

No of extra and Node No Inc columns. Example:

The elements between nodes 251 and 266 are copied ten times with the node numbers

decrementing by five with each copy.

Block generation

A group of elements can be repeated by entering a 'B' in the No column. Then enter the first

and last table line numbers in which the elements were defined, separated with a '–'.


All elements defined in lines 11 to 26 will be copied twice with a node number increment of

thirty. The copied elements will use the same section number and fixity codes as the original

elements.



Frame Analysis 3-28

The block generation function may be used recursively. The group of lines referenced may thus

contain block generation statements.

Tip: When entering a complicated structure it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert

additional nodes at a later stage without upsetting block and arc generations.

Deleting elements

Beam elements can be deleted by entering a special section name 'Delete'. This can be

especially handy if you have generated a large group of elements at regular increments and

need to remove some of them again.

Example:

Elements 25-27-29 and 35-37-39 are deleted.

Note: The display of selected beam element groups can be activated or suppressed by

editing the Graphics options.

Error checking

The program checks for duplicate elements and elements with zero length. It also checks that a

section number is assigned to each element. If an error is detected, an Error list button will be

displayed.

Graphical input



the picture.

To add beams click the ‘Add beams’ button. Enter the section name, ß angle

and fixities for the beams. By clicking

two successive nodes, a beam will be

inserted between them. If ‘follow on’ is

checked, the last node of the previous

beam is taken as the first node of the

next beam. If ‘Link end nodes only’ is

checked, only one beam is placed

between the last two nodes entered. If

not, all nodes between the last two nodes

are also added into the beam string. The

Frame Analysis 3-29

nodes must lie within a certain tolerance from the straight line between the end nodes to be

included. This tolerance can be entered in the Tolerance (%) field. If e.g. 1% is entered, any

node closer than 1% of the distance between the end nodes from the line joining them is

included. Pressing ‘Undo’ will delete the beams in reverse order, in which they were entered,

one by one.

To delete beams click the ‘Delete

beams’ button and then select the beams to be deleted on the screen using

the mouse. Click ‘Done’ when finished.

Clicking ‘Undo’ will undo the deletions

in reverse order.

To block delete beams click the ‘Block

delete beam elements’ button. Select a

rectangle on the screen with the mouse. All

beams inside the rectangle will be deleted.

Press ‘Done’ when finished. Pressing

‘Undo’ will undo the deletions in reverse

order one by one beam. Pressing ‘Undo All’ will undo all deletions done with this function.

Click the ‘Change beam properties’

button to change beam properties. Enter

the desired properties for the beam(s) on

the dialog. One can also use the ‘Get

properties’ button to do this. Click the

button and then click on a beam. The

beam’s properties will then be

transferred to the dialog. Clicking on

beams will now change their properties

to those specified on the dialog. The

‘Undo’ button will undo the changes in

reverse order.

Click the ‘Explode beams’ button to

explode the beam input. This results in the

list of beams being written, each on a

separate line without block generations etc.

Once done, it cannot be reversed.

On the beams input page one can also delete nodes and groups of nodes in the same way as on

the nodes input page. Refer to page 3-22 for details

Frame Analysis 3-30

Beam sections input

Section properties should be assigned to all section names used on the Beam elements input

page. The following properties are required for all sections:

Cross sectional area, A.

Second moment of area about the local x-axis, Ix (not required for Space Truss analysis).

Second moment of area about the local y-axis, Iy (Space Frame domain only).

Torsional moment of inertia, J (Grillage and Space Frame domain only).

Each section should also have an associated material selected. If no section or material

properties are entered, the values applicable to the previous line in the table are used.

Frame Analysis 3-31

Reading sections from the database

Use the Section database function to display and select sections from database. You can add

your own sections, e.g. plate girders, to the database using the procedures described in

Chapter 2.

Entering haunches

Haunches are entered by appending the haunch depth to the section designation. To add a

haunch of 180 mm to a '305x102x66' BS taper flange I-section, enter '305x102x66 (0.280h)'. The overall depth is then taken to be 305 mm + 280 mm = 585 mm.

Tip: You can verify your definition of haunches by enabling 3D rendering. For more detail,

refer to page 3-17.

Tension members

When performing a second order analysis, you can designate members to have tension stiffness

only, e.g. slender bracing members. To make a member be ignored during the analysis when it

would act in compression:

1. Enter the member's section properties in the usual manner.

2. Edit the value for the cross sectional area and change its sign to negative.

Note: The program uses the absolute value of the cross sectional area. The negative sign

entered merely enables the tension-only behaviour for beams of the given section group.

Own weight

If a material's definition includes a density value, the own weight of a member is calculated

automatically and added to the load case specified on the Settings page.

Selecting materials

Each section should have an associated

material.

To add one or more materials to a frame

analysis data file, click Materials. Open

the relevant material type screen and

select the materials that are required for the current frame input.

After adding the selected materials to

the input, you can select them by

clicking the Material column to drop

down a list.

Frame Analysis 3-32

Adding materials to the global database

The procedure to permanently add more materials to the database is described in Chapter 2.

Advanced section options

Clicking the Advanced button allows

you to configure the behaviour of rigid

links. A rigid link is modelled as a very stiff beam of which the area, second

moment of inertia and modulus of

elasticity are taken as the maximum

corresponding properties all other

beams multiplied with the specified

factors.

Refer to page 3-26 for detail on

defining rigid links.

Graphical input



the picture.

Click the ‘Change beam properties’

button to change beam properties. Enter

the desired properties for the beam(s) on

the dialog. One can also use the ‘Get

properties’ button to do this. Click the

button and then click on a beam. The

beam’s properties will then be

transferred to the dialog. Clicking on

beams will now change their properties to those specified on the dialog. The

‘Undo’ button will undo the changes in

reverse order.

Frame Analysis 3-33

Shell elements input

You can use finite shell elements alongside beam elements, except in the Space truss domain.

Shell elements can be optionally designed as reinforced concrete members.

Elements are defined by referring to corner nodes, four in the case of quadrilaterals and three

for triangles. You should enter the node numbers in sequence around the perimeter, either clockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define a

triangular element.

Note: Quadrilateral elements generally yield more accurate analysis results than triangular

elements. Refer to page 3-10 for more detail.

An element definition must include a thickness and material type. Refer to page 3-31 for more

detail on using materials.

Frame Analysis 3-34

Own weight



Tip: When entering a complicated slab, it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert

additional elements at a later stage without upsetting block and arc generations.

Error checking

The program checks for duplicate elements and nodes not connected to elements. It also checks

that a group number is assigned to each element. If an error is detected, an Error list button

will be displayed.


You can generate additional elements with the same group number using the Number of Extra

and Node no Inc columns.

Block generation

You can use the block generation to copy shells you defined earlier in the table. A group of

shells can be repeated by entering a 'B' in the Node 1 column followed by the first and last

table line numbers in which the nodes were defined. Separate the line numbers with a '–'.

To copy a single line only, simply omit the end line number, e.g. 'B11' to copy line 11 only.

Tip: The current line number is displayed in the status bar at the bottom left of the

program's window.



Deleting elements

Shell elements can be deleted by entering 'Delete' in the Material column. This can be useful if

you have generated a large group of elements and need to remove some of them again.

Example:

The element 15-16-26-25 and the generated element 18-19-29-28 are deleted.

Frame Analysis 3-35

Graphical input



the picture.

To add shells click the ‘Add

shell elements’ button. Enter the

material, thickness and shell type (triangular or quadrilateral).

The easiest way to enter shells is

to define a plane in which they

lie. Click 3 nodes to indicate the

plane. The three node numbers

can also be typed directly into

the dialog. Also enter the

thickness of the plane. Only the

nodes lying in the plane and half

of the thickness on either side

are now displayed. If one now moves the mouse across the

picture, possible shells are

shown in purple. Click the

mouse to have each shell entered

into the input table. If you do not want to use a plane in this way, click ‘Don’t use plane’.

Pressing ‘Undo’ will delete the shells in the reverse order in which they were entered, one by

one.

To delete shells click the ‘Delete

shells’ button and then select the

shells to be deleted on the screen

using the mouse. Click ‘Done’

when finished. Clicking ‘Undo’ will undo the deletions in reverse

order.

To block delete shells click the ‘Block

delete shell elements’ button. Select a

rectangle on the screen with the

mouse. All shells inside the rectangle

will be deleted. Press ‘Done’ when

finished. Pressing ‘Undo’ will undo the deletions in reverse order one by one. Pressing ‘Undo

All’ will undo all deletions done with this function.

Frame Analysis 3-36

Click the ‘Change shell

element properties’ button to

change shell properties. Enter

the desired properties for the

shell(s) on the dialog. One

can also use the ‘Get

properties’ button to do this. Click the button and then

click on a shell. The shell’s

properties will then be transferred to the dialog. Clicking on shells will now change their

properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse

order.

Click the ‘Explode shells’ button to

explode the shell input. This results

in the list of shells being written,

each on a separate line without block

generations etc. Once done, it cannot

be reversed.

On the shells input page one can also delete nodes and groups of nodes in the same way as on


Solid elements input

You can use solid elements alongside beam and shell elements, if the domain is set as Space

frame.

Elements are defined by referring to corner nodes, eight in the case of hexahedrons and four for

tetrahedrons. You should enter the node numbers in sequence around the perimeter, either

clockwise or anti-clockwise, in the Node 1 to Node 8 columns. First define the back face

going either clockwise or anti-clockwise in the node 1 to node 4 columns. Next define the

front face starting with node 5 above the node defined as node 1 and moving around in the

same direction as nodes 1 to 4. For tetrahedrons the four nodes can be entered in any order in

columns 1 to 4.

Note: Hexahedral elements generally yield very accurate analysis results. The tetrahedrons

should only be used as filler elements where it is not possible to use hexahedrons.

Frame Analysis 3-37

An element definition must include a material type. Refer to page 3-31 for more detail on

using materials.

Own weight



Tip: When entering a complicated model, it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert


Error checking



will be displayed.

Frame Analysis 3-38


You can generate additional elements with the same group number using the Number of Extra

and Node no Inc columns.

Block generation

You can use the block generation to copy shells you defined earlier in the table. A group of

solids can be repeated by entering a 'B' in the Node 1 column followed by the first and last

table line numbers in which the nodes were defined. Separate the line numbers with a '–'.

To copy a single line only, simply omit the end line number, e.g. 'B11' to copy line 11 only.


program's window.

The block generation function may be used recursively. The group of lines referenced may thus contain block generation statements.

Deleting elements

Solid elements can be deleted by entering 'Delete' in the Material column. This can be useful if


Example:

The element 201-202-152-151-226-227-177-176 and the generated element 251-252-201-201-

276-277-227-226 are deleted.

Frame Analysis 3-39

Graphical input



the picture.

To add solids click the ‘Add

solids elements’ button. Enter the

material and solid type (tetrahedral, wedges or

hexahedra). At the time of

writing only hexahedra were

available for this function. The

easiest way to enter solids is to

define a plane in which they lie.

Click the ‘set up plane’ button to

do this. Click three nodes to

indicate the plane. The three

node numbers can also be typed

directly into the dialog. Also enter the thickness of the plane.

Only the nodes lying in the plane

and half of the thickness on

either side are now displayed. If

one now moves the mouse across

the picture, possible solids are shown in purple. Click the mouse to have each solid entered into

the input table. If you do not want to use a plane in this way anymore, click ‘Clear Plane’.

Pressing ‘Undo’ will delete the solids in the reverse order in which they were entered, one by

one.

To delete solids click the ‘Delete

solid elements’ button and then select

the solids to be deleted on the screen using the mouse. Click ‘Done’ when



To block delete solids click the

‘Block delete solid elements’

button. Select a rectangle on the

screen with the mouse. All solids

inside the rectangle will be deleted.

Press ‘Done’ when finished.

Pressing ‘Undo’ will undo the deletions in reverse order one by one. Pressing ‘Undo All’ will

undo all deletions done with this function.

Frame Analysis 3-40

Click the ‘Change solid element properties’ button to change solid element properties. Enter

the desired material for the

solid(s) on the dialog. One can

also use the ‘Get properties’

button to do this. Click the button

and then click on a solid. The

solid’s material property will then be transferred to the dialog.

Clicking on solids will now change their material to that specified on the dialog. The ‘Undo’

button will undo the changes in reverse order.

Click the ‘Explode solids’

button to explode the solids

input. This results in the list of

solids being written, each on a

separate line without block

generations etc. Once done, it

cannot be reversed.

On the solids input page one can also delete nodes and groups of nodes in the same way as on


Spring elements input

You can use spring elements to provide elastic links between sub-structures, e.g. to model elastomeric bearings between a slab and supporting walls. In theory, two nodes connected with

a spring element should have the same coordinates. The program will warn if this is not the

case and still allow you to continue.

Enter linear spring constants in the Kx, Ky and Kz columns and rotational spring constants in

the Rx, Ry and Rz columns.

The orientation of a spring element is defined by entering a bearing between any two nodes

that do not necessarily need to be connected to the same or other spring elements as well. The

directions of the axes are defined as followed:

A spring element's x-axis is taken in the direction of the orientating nodes.

The y-axis defined in the same way as for a normal beam element, i.e. perpendicular to

spring element in a vertical plane.

The z-axis is taken perpendicular to the x and y-axes using aright-hand rule.

Spring element example:

Frame Analysis 3-41

Spring elements are defined between nodes 16 and 116, 17 and 117 up to 19 and 119. The

spring elements are aligned parallel to the imaginary line joining nodes 3 and 4.

Tip: Spring elements can also be made "rigid" to force two nodes to have the same translation and/or rotation. In the above example, a very large value for Kx would

cause nodes 16 and 116 to have identical displacements in the direction described by

nodes 3 and 4.

Graphical input



the picture.

To add springs click the ‘Add spring elements’ button. Enter the spring

stiffnesses and orientation nodes on

the dialog.. Now click the mouse on

nodes to have springs entered into

the input table. Pressing ‘Undo’ will

delete the springs in the reverse

order in which they were entered,

one by one.

To delete springs click the ‘Delete

spring elements’ button and then

select the springs to be deleted on the

screen using the mouse. Click ‘Done’

when finished. Clicking ‘Undo’ will

undo the deletions in reverse order.

To block delete springs click the

‘Block delete spring elements’ button. Select a rectangle on the

screen with the mouse. All springs

inside the rectangle will be deleted.

Frame Analysis 3-42

Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse

order, one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Click the ‘Change spring element

properties’ button to change

spring element properties. Enter

the desired spring stiffnesses and

orientation on the dialog. One can also use the ‘Get properties’

button to do this. Click the button

and then click on a spring. The

spring’s properties will then be

transferred to the dialog. Clicking

on springs will now change their

properties to those specified on

the dialog. The ‘Undo’ button will

undo the changes in reverse order.

Click the ‘Explode springs’

button to explode the spring


springs being written, each on

a separate line without block


cannot be reversed.

On the springs input page one can also delete nodes and groups of nodes in the same way as on


Supports input

Frames require external supports to ensure global stability. Supports can be entered to prevent

any of the six degrees of freedom at a node, i.e. translation in the X Y and Z-directions and

rotation about the X, Y and Z-axes. You can also define elastic supports, e.g. an elastic soil support, and prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a

combination of the letters 'X', 'Y' and 'Z' can be entered to indicate the direction of fixity. Use

capitals and lowercase to define restraint of translation and rotation respectively, e.g. 'XYZy'

means fixed against movement in the X, Y and Z-direction and rotation about the Y-axis.

Frame Analysis 3-43

Note: The use of lowercase for rotational restraints should not be confused with the convention of using lowercase for local element axes.

Tip: To enter a simple support with no moment restraint, one would typically enter a 'XYZ'

or 'Y'. Avoid using a pin on an element to model an external hinge.

If you want to repeat the supports defined on the previous line of the table, you need only enter

the node number, i.e. you may leave the Fixity column blank. If the XYZxyz column is left

blank, the supports applicable to the previous line will be used automatically.

Prescribed displacements and elastic supports

Use the X, Y, Z, Rx, Ry and Rz columns to enter prescribed displacements and rotations in

the direction of and about the X, Y and Z-axes. Being a global support condition, the effect of

the prescribed displacement is not considered to be a separate load case. Instead, the effect

Frame Analysis 3-44

of prescribed displacements is added once only to the analysis results of each load case and

load combination.

Elastic supports, or springs, are defined by entering spring constants in the X, Y, Z, x, y and z

columns. The spring constant is defined as the force or moment that will cause a unit displace-

ment or rotation in the relevant direction. Enter an 'S' in the P/S column to indicate that an

entered value is a spring constant rather than a prescribed displacement. If you leave the P/S

column blank, the entered values are taken as prescribed displacements.

Gap supports

Gap support are supports that work in one direction only and allow free movement in the

opposite direction, e.g. allow uplift. The sign of the gap support corresponds to the global axis

direction, e.g. a [+] input in the Y-direction provides support in the positive Y-direction

(upward reaction) and none in the negative Y-directions (i.e. uplift is allowed).

Note: The display of supports can be activated or suppressed by editing the Graphics

options.

Error Checking

The program does a basic check on the structural stability of the frame. If a potential error is

detected, an Error list button will appear.

Note: You cannot define an elastic support and a prescribed displacement at the same node

because it will be a contradiction of principles.

Generating additional supports

Additional supports and prescribed displacements can be generated using the Number of extra

and Node number inc columns. The procedure is similar to that described on page 3-20 for

generating additional nodes.

Graphical input



the picture.

Frame Analysis 3-45

To add supports click the ‘Add

supports’ button. Enter the fixities,

prescribed displacements, spring

constants and fixity type on the

dialog. Now click the mouse on

nodes to have supports entered into

the input table. Pressing ‘Undo’ will delete the supports in the reverse

order in which they were entered,

one by one.

To delete supports click the ‘Delete supports’ button and then select the

supports to be deleted on the screen

using the mouse. Click ‘Done’ when



To block delete supports click the

‘Block delete supports’ button.

Select a rectangle on the screen

with the mouse. All supports inside

the rectangle will be deleted. Press

the ‘Done’ button when finished.

Pressing ‘Undo’ will undo the deletions in reverse order, one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Frame Analysis 3-46

Click the ‘Change support

properties’ button to change

support properties. Enter the

desired support fixities, type,

prescribed displacements and

spring constants on the dialog.

One can also use the ‘Get properties’ button to do this.

Click the button and then click

on a support. The support’s

properties will then be

transferred to the dialog.

Clicking on supports will now

change their properties to

those specified on the dialog.

The ‘Undo’ button will undo

the changes in reverse order.

Click the ‘Explode supports’ button

to explode the support input. This

results in the list of supports being

written, each on a separate line

without block generations etc. Once

done, it cannot be reversed.

On the supports input page one can also delete nodes and groups of nodes in the same way as

on the nodes input page. Refer to page 3-22 for details

Nodal loads input

Loads on beam elements are categorised as nodal loads, i.e. loads at node points, and element

loads, i.e. loads between nodes. Uniform distributed loads can be applied to shell elements.

All loads are organised in load cases, e.g. 'DL' for own weight, 'ADL' for additional dead loads,

'LL' for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads.

To define a load case, type a descriptive name for each load case in the Load Case column.

Use up to six characters to describe each load case. If the load case name is not entered, the

load case applicable to the previous line in the table is used.

Frame Analysis 3-47

The load case at the cursor position is displayed graphically. Press Enter or Display to update

the picture.

A nodal load can, as its name implies, only be applied at a node. If a point load is required on

an element, use the Beam loads input table instead.

Sign conventions

Nodal loads are applied parallel to the global axes – an explanation of the sign conventions are

given on page 3-6.

Tip: For a typical steel or timber frame or roof truss, it may be easiest to define a node at

each purlin position. Roof loads transferred via the purlins can then be entered as

nodal loads.

Error checking

The program checks that specified nodes have indeed been defined in the Nodes input table. If

an error is detected, an Error list button will appear.

Frame Analysis 3-48

Generating additional nodal loads

Additional nodal loads can be generated using the Number of extra and Node number inc

columns respectively.

Block generation of nodal loads

You can use the block function to copy blocks of nodal loads. The procedure is similar to that

for generating additional nodes – see page 3-21 for more detail.

Graphical input



the picture.

To add nodal loads click the ‘Add nodal loads’ button.

Enter the forces, moments and the load case on the

dialog. Now click the mouse on nodes to have nodal

loads entered into the input table. Pressing ‘Undo’ will

delete the nodal loads in the reverse order in which

they were entered, one by one.

Frame Analysis 3-49

To block add nodal loads click the ‘Block add nodal

loads’ button. Enter the forces, moments and the load

case on the dialog. Select a rectangle on the screen

with the mouse. All nodes inside the rectangle will

have a nodal load added. Pressing ‘Undo’ will delete

the nodal loads in the reverse order in which they were

entered, one by one.

To delete nodal loads click the ‘Delete nodal

loads’ button and then select the nodal loads to be

deleted on the screen using the mouse. The load

case for which loads are to be deleted should also

be entered on the dialog. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions

in reverse order.

To block delete nodal loads click the ‘Block

delete nodal loads’ button. Select a rectangle on

the screen with the mouse. All nodal loads inside

the rectangle will be deleted. Press the ‘Done’

button when finished. Pressing ‘Undo’ will undo

the deletions in reverse order, one by one.

Click the ‘Explode nodal loads’

button to explode the nodal loads input. This results in the list of

nodal loads being written, each on



cannot be reversed.

Frame Analysis 3-50

Beam element loads input

Distributed loads and point loads on beam elements are all referred to as element loads. The

Nodal loads input page provides the easiest way of applying point loads and moments at

nodes.

Use up to six characters to enter a descriptive name for each load case in the Load Case

column. Then enter the element string of nodes in the Beam element definition column.

Entering the beam element definition follows the same convention used as for the Elements

input table – see page 3-23 for detail.

Sign conventions

Depending on the selected load direction, beam loads are applied parallel to the global axes or

parallel to the local y-axis – the definitions of the global and local axes are given on page 3-6

and 3-6 respectively.

Frame Analysis 3-51

The load direction is entered in the Direction column. Enter a global direction 'X', 'Y' or 'Z'.

Element loads are applied to the relevant projected length of the elements. Therefore, if a 'Y'

load is entered for a vertical element, for example, the resulting load will therefore be zero.

You can also load a beam element parallel to its local y-axis by setting the load direction

to 'L' – refer to page 3-6 for an explanation of the local axis convention used.

Types of beam loads

The following loads can be entered:

A point load's magnitude is entered in the P column and its position from the smaller node

number in the a column.

For a distributed load, entered in the load intensity at the smaller and larger node numbers

in the W-begin and W-end columns respectively. If the load is constant over the length of

the element, W-end may be left blank.

To define a temperature load, enter the temperature difference in the dT column. A

temperature change is used with the temperature expansion coefficient of the relevant

material used.

Note: Positive vertical loads act upward and negative loads act downward.

Error checking

The program checks that element definitions match previously defined elements. If an error is


Generating additional element loads

The No of extra and Node number Inc columns can also be used to generate additional

element loads.

Block generation of beam loads

You can use the block function to copy blocks of beam loads. The procedure is similar to that

used to generating additional beam elements – see page 3-27 for detail.

Graphical input



the picture.

To add beam loads click the ‘Add beam loads’

button. Enter the loads, direction and

temperature change on the dialog. The load

case also needs to be entered. Now click the

Frame Analysis 3-52

mouse on beams to have beam loads entered into the input table. Pressing ‘Undo’ will delete

the beam loads in the reverse order in which they were entered, one by one.

To block add beam loads click the ‘Block add

beam loads’ button. Enter the loads, direction

and temperature change on the dialog. The

load case also needs to be entered. Select a

rectangle on the screen with the mouse. All beams inside the rectangle will have a beam

load added. Pressing ‘Undo’ will delete the

beam loads in the reverse order in which they

were entered, one by one.

To delete beam loads click the ‘Delete

beam loads’ button and then select the

beam loads to be deleted on the screen using the mouse. The load case for

which loads are to be deleted should

also be entered on the dialog. Click

‘Done’ when finished. Clicking

‘Undo’ will undo the deletions in

reverse order.

To block delete beam loads click the

‘Block delete beam loads’ button.

Select a rectangle on the screen with

the mouse. All beam loads inside the

rectangle will be deleted. Press the

‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in

reverse order, one by one.

Click the ‘Explode beam loads’

button to explode the beam loads


beam loads being written, each on



cannot be reversed.

Frame Analysis 3-53

Shell loads

Distributed loads can be applied on shell elements. Enter a load case description in the Load

case column followed by the relevant element numbers in the Shell numbers column. The

program automatically assigns numbers to all shell elements in the sequence they are defined

on the Shells input page.

A series of elements can be entered by separating the first and last element numbers by a '–'

character, e.g. '1–6' to define elements 1 up to 6.

Tip: If the shell element numbers are not visible in the picture, edit the graphics options to

enable detailed rendering and disable the full 3D view. Refer to page 3-17 for detail on

changing the graphics options.

Sign conventions

Shell loads are applied parallel to the element's local z-axes – an explanation of the local axes

of shell elements are given on page 3-6.

Types of shell loads

The following shell loads can be entered:

For a distributed load, entered in the load intensity in the UDL column.

To define a temperature load, enter the temperature difference in the dT column. A

temperature change is used with the temperature expansion coefficient of the relevant

material used.


Frame Analysis 3-54

Error checking

The program checks that the entered element numbers are valid. If an error is detected, an



The No of extra and Node number Inc columns can also be used to generate additional shell

loads.

Block generation of shell loads


used to generating additional shell elements – see page 3-34 for detail.

Frame Analysis 3-55

Graphical input



the picture.

To add shell loads click the ‘Add shell loads’ button. Enter the UDL, direction and

temperature change on the dialog. The load

case also needs to be entered. Now click the

mouse on shells to have shell loads entered

into the input table. Pressing ‘Undo’ will

delete the shell loads in the reverse order in

which they were entered, one by one.

To block add shell loads click the ‘Block add

shell loads’ button. Enter the UDL, direction

and temperature change on the dialog. The

load case also needs to be entered. Select a

rectangle on the screen with the mouse. All

shells inside the rectangle will have a shell

load added. Pressing ‘Undo’ will delete the

shell loads in the reverse order in which they

were entered, one by one.

To delete shell loads click the ‘Delete shell loads’ button and then select the shell loads to

be deleted on the screen using the mouse. The

load case for which loads are to be deleted

should also be entered on the dialog. Click

‘Done’ when finished. Clicking ‘Undo’ will

undo the deletions in reverse order.

Frame Analysis 3-56

To block delete shell loads click the ‘Block

delete shell loads’ button. Select a rectangle on

the screen with the mouse. All shell loads inside

the rectangle will be deleted. Press the ‘Done’ button when finished. Pressing ‘Undo’ will

undo the deletions in reverse order, one by one.

Click the ‘Explode shell loads’

button to explode the shell loads


shell loads being written, each on



cannot be reversed.

Frame Analysis 3-57

Load combinations input

You can model practical scenarios by grouping load cases together in load combinations. Enter

the load combination name in the Load comb column; followed by the load case name and

relevant load factors.

If the Load comb column is left blank, the load combination is taken to be the same as for the previous line of the table. The load cases to consider in a load combination are entered one per

line in the Load case column. Enter the relevant ultimate and serviceability limit state load

factors in the ULS factor and SLS factor columns.

Tip: You may leave one or more blank lines between load combination definitions to

improve readability.

The ultimate and serviceability limit states are used as follows:

Deflections are calculated using the entered SLS loads. A set of reactions is also calculated

at SLS for the purposes of evaluating support stability and bearing pressures.

Frame Analysis 3-58

Element forces and a second set of reactions are determined using the entered ULS forces.

Tip: If you plan to use a working stress method to design the frame members, e.g. steel

design according to SABS 0162 - 1984, you may use the same load factors at ULS and SLS.

Error checking

The program only checks that valid load cases are specified. It has no knowledge of the design

code that will be used in the member design and therefore does not check the validity of the

entered load factors.

Alternative frame input methods

Alternative means of frame input are available:

Input Wizards: Modules are available for the rapid generation of input for typical frame

structures.

External Graphical input: Structures can be drawn in Padds or another CAD system and

converted to frame analysis input.

Input Wizards

A number of typical frames can be input by entering a number of parameters. The Input

Wizards do most of the data input. See page 3-18 for more detail on the Input wizards.

Note: The frame analysis modules are not limited to modelling only those frames generated by the input wizards modules. Instead, the input wizards merely serve to simplify input of

some typical frames.

External Graphical input

In some situations, it may be easier to define a frame's geometry graphically. With Padds you

can draw a frame and then generate a frame analysis input file.

Using Padds for frame input

To use Padds to define a frame's geometry:

1. Use Padds to draw the frame. Alternatively, import a drawing from another CAD system.

2. The frame should be drawn to scale using millimetres as unit. Identify different beam

sections by using different pen numbers.

3. Use the Generate input command on the Macro to display the drawing conversion

options. Choose the target frame analysis module and press OK to start the conversion

procedure.

Frame Analysis 3-59

The file is saved in the working folder as a last file, e.g. 'Lastsf.a03' for Frame

Analysis.

4. Close Padds.

Tip: To see a graphical input example, open '..\prokon\data\demo\inputgen.pad' in Padds.

Importing drawings

You can also use your favourite CAD system to save a frame's geometry in a 2D or 3D

Dxf/Dwg format drawing and then use the Import -> Dxf/Dwg files command on the File

menu to convert it to frame input.

The same basic rules apply as given above:

The drawing should be to scale.

You should use millimetre units.

Different pen numbers should be used for different beam sections.

Frame Analysis 3-60

When importing 3D .Dxf & .Dwg drawings, you can optionally interchange the Z- and Y-axes.

This option is given to correctly import a drawing where the Z-axis is taken as vertical, into

Frame Analysis where the Y-axis is vertical.

Typical problems experienced include the following:

Polylines may not be recognised correctly. Break or explode polylines into single lines

before saving the .Dxf file.

Blocks may not import correctly and may need to be broken or exploded into individual entities.

Using AutoCAD, lines colours set 'by layer' translates to the default pen number. Rather

set colours using pen numbers to ensure correct section numbering.

If you experience problems importing a DXF file saved using a brand new version of your

CAD system, it may help saving the file as an older DXF file version, e.g. version 12.

CIMsteel

The Space Frame Analysis module can import complete frame models, including geometrical

and loading data, defined in the CIMsteel (Computer Integrated Manufacturing for

Constructional Steelwork) integration standard. Modelling packages that can create CIMsteel

files include Intergraph Frameworks and Microstation Structural Triforma. Note that at the

time of writing this feature had not been fully developed.

Frame Analysis 3-61

Settings

The Settings page allows you to set the parameters relevant to the analysis method.

Analysis type

Select the type of analysis to be performed. Refer to page 3-13 for a description of the various

analysis modes.

Concrete design parameters input

It is generally impractical to design reinforcement to resist torsional moments in slabs.

Reinforcement is usually fixed in two directions approximately, but not necessarily,

perpendicular to each other. This justifies the use of transformed moments to calculate

reinforcement.

Frame uses the Wood and Armer theory to convert calculated bending and torsional moments

to transformed bending moments. More detail is given on page 3-12. Please note that these

parameters only apply to shell elements and not to beams or solids.

The required concrete design parameters are:

Enter the concrete and reinforcement material characteristics, fcu and fy.

Frame Analysis 3-62

Define the orientation for the 'main' and 'secondary' reinforcement, i.e. the x' and y'-axis.

Looking from the top, the x'-axis is measured anti-clockwise from the local x-axis to the

reinforcement x'-axis. The y'-axis is in turn measured anti-clockwise from the local x'-axis.

The direction of the local x-axis of a shell element is explained on page 3-6.

Define the reinforcement levels in the slab by entering the concrete cover values for the

top and bottom reinforcement in both directions.

Optionally incorporate membrane behaviour by including the effect of in-plane stresses.

Reinforcement contours can be displayed on the Reinforcement tab under the View Output

age. Values are calculated for reinforcement at the top and bottom of shell elements. In this

context, top and bottom are defined as follows:

The top of a shell element is taken on the side towards which its local z-axis points.

For a non-vertical element, the top side is the visible side when looking down on the

element.

For a vertical element, the top side is the visible side if the nodes (as entered on the Shell

elements input page) defining the element are orientated anti-clockwise.

Second order parameters input

If you want to perform a second order analysis of the frame, you need to set the relevant

analysis parameters:

Second order analysis tolerance: The second

order analysis is an iterative procedure. The

analysis is deemed to have converged once the total strain energies of two sequential iterations

differ by less than the specified tolerance

Buckling parameters input

When performing a buckling analysis:

Number of buckling mode shapes: Set the

number of buckling mode shapes to be

calculated when determining the load factor

for buckling for each load case or

combination. The first mode shape is often

critical since it represents the most likely buckling failure mechanism. For practical

reasons, only the first mode shape would normally be of interest. However, the accuracy of

the analysis improves with the number of mode shapes analysed. It is therefore suggested

that you allow at least four mode shapes to be calculated. The program supports a

Frame Analysis 3-63

maximum number of forty mode shapes. Note that internally the program actually

calculates quite a few more mode shapes than specified to improve the accuracy of the

output for the modes that are specified. Because of this, the model should not contain too

few nodes. If no convergence is obtained, split the members into smaller portions by

adding extra nodes.

Non-linear analysis parameters input

Number of load steps:

Each load case is applied to the structure in a

number of steps. The accuracy increases with

the number of steps entered. Ten steps should

be adequate for most problems.

One must be aware that for each step, the

structure is completely analysed a number of

times for each load case to obtain convergence

for that step. The analysis time can therefore become very long if a high number of steps are

specified on a large structure with many load cases. It is suggested that one use say 3-5 steps

initially, to ensure that the solution progresses properly, before increasing the number of steps

for a final analysis.

Frame Analysis 3-64

Dynamic analysis parameters input

Edit the dynamic analysis parameters if you will be performing a modal, harmonic or

earthquake analysis. Some parameters should be entered in all cases while others are specific

to harmonic or earthquake analysis. The graphic below shows all the possible input fields,

although some of them might not be visible, depending on the type of dynamic analysis

selected.

Number of mode shapes

Enter the number of natural modes of vibration to be calculated. You can use the following

guidelines when deciding on the number of mode shapes to be calculated:

The number of mode shapes should preferably not exceed the number of degrees of

freedom in the structure divided by twelve.

In a harmonic analysis, use enough mode shapes so that the highest natural frequency is at

least 50% higher than the applied loading frequency.

For an earthquake analysis, the first three or four mode shapes are normally sufficient to

obtain the probable maximum combined effects.

Frame Analysis 3-65

Do not use too few nodes. If convergence is not obtained when calculating the natural

frequencies, add more nodes and split the elements. See also the first point above.

Add axial force effects to stiffness

Compression forces in a frame's members reduce the effective stiffness of the frame. The

frequencies of vibration are therefore reduced with corresponding changes in the mode shapes.

If the option is enabled, the effect of axial force is incorporated as follows:

A static analysis is first performed with the mass of the structure, i.e. own weight and the Y-components of the specified load cases, being the only load case.

The resulting axial forces are then incorporated when calculating the modified geometric

stiffness matrix of the structure. The geometric stiffness matrix is subsequently used to

modify the global stiffness matrix to account for the axial force effects.

Include torsional modelling

This applies to beam elements. If included, the torsional modes of the beams will also be

included.

Include load cases as mass

A frame's frequencies of vibration and mode shapes depend on its inertia or mass distribution

in relation to its stiffness distribution. Any loads on the structure will therefore influence the

natural frequencies and therefore its response to dynamic loadings. The user must select the loads to be included as mass in the right hand side list. Only the Y-components (vertical) of the

loads are added as mass.

The program uses the following components for compiling the mass matrix:

The own weight of the frame, calculated using the density values entered in the Section

properties input table.

The loads cases entered by the user.

Note: In a harmonic or seismic analysis, all dead and live load that move with the structure

during its dynamic response will influence the dynamic response of the structure. Such loads should be considered as masses for the purpose of determining the mode shapes.

Own weight and distributed vertical loads are added using the consistent mass matrix

formulation. Point loads are added as lumped masses at the relevant nodes.

Note: In a seismic analysis all loads not selected as masses will be excluded from the analysis.

Frame Analysis 3-66

Average damping ratio

The dynamic response of a frame will include some viscous effects. The average damping ratio

depends on the type and condition of the structure. Typical values, taken from TMH7 - Part 2,

are tabled below:

Stress level Type and condition of structure Damping

ratio

Welded steel. Prestressed concrete, well reinforced concrete (slight cracking)

2%

Working stress no more than about

half of yield stress

Reinforced concrete with considerable cracking

3% to 5%

Bolted and riveted steel 5% to 7%

Welded steel, prestressed concrete under

full pre-stress (slight cracking) 5%

Working stress near yield point

Prestressed concrete in cracked state 7%

Reinforced concrete 7% to 10%

Bolted and/or riveted steel 10% to 15%

Frame Analysis 3-67

Design ground acceleration (seismic analysis only)

For an earthquake analysis, specify the maximum ground accelerations. TMH7 - Part 2 gives

the following typical values according to a modified Mercalli classification:

Modified Mercalli

intensity at epicentre

Design ground

acceleration

ii – iii 0.003 g

iv – v 0.01 g

Vi 0.03 g

vii – viii 0.1 g

Ix 0.3 g

x – xi 1.0 g

Note: Refer to local seismic data for relevant acceleration data.

TMH 7 - Part 2, when considering the influence of seismic disturbances, gives the following

guidelines:

Symmetrical structures: The influence of seismic disturbances should be considered along

both principal axes of symmetry.

Non-symmetrical structures: It would normally be sufficient to consider the seismic effects

along any two arbitrarily chosen orthogonal axes.

For structures, symmetrical and non-symmetrical, the seismic effects along two orthogonal

axes may normally be considered independently of each other.

Design load factor (seismic analysis only)

Seismic action is normally not considered in combination with other secondary loads. For this

reason, the following approach is used:

The vertical components of selected load cases are included as masses when determining

the mode shapes. Refer to page 3-65 for detail.

All other effects of all load cases and combinations are ignored.

The dynamic response of the structure to the applied ground accelerations is amplified with the specified design load factor.

Frame Analysis 3-68

The design load factor for forces and moments should be chosen in accordance with the

relevant loading code. At ultimate limit state, an average factor between 1.3 and 1.5 is

normally applied.

Spectrum reduction factor for vertical direction (seismic analysis only)

The relevant resonance frequencies of a structure in the vertical direction are generally quite

different from those in the horizontal direction. If it is deemed necessary to consider the effects

of vertical seismic motions, the average vertical design spectrum can often be reduced.

For typical bridge structures, TMH7 - Part 2 allows the average vertical design spectrum to be

taken as two-thirds the average horizontal seismic response spectrum.

Ductility (seismic analysis only)

The ductility of a structure is a function of the type and arrangement of the elements resisting

lateral forces. A unity value corresponds to perfect elastic behaviour and a value greater than

unity elastic-plastic behaviour.

Typical ductility values, taken from TMH7 - Part 2, are given below.

Type or arrangement of resisting elements Structural

ductility factor

Un-braced structural steel structures with elements adequately designed to resist the total lateral forces in

bending

4

Structures with braced flexural vertical members of structural steel

Slender reinforced columns carrying superstructure of braced structural steel, reinforced concrete or prestressed

concrete designed to resist the total lateral force

3

Vertical elements of shear wall proportions with superstructure in monolithic reinforced or prestressed

concrete designed to resist the total lateral force

2

If you enter a value greater than one, the elastic response spectrum will be adjusted to obtain an

appropriate inelastic response spectrum. The program allows you to adjust the design response

spectrum as required.

Frame Analysis 3-69

Foundation soil type (seismic analysis only)

Additional factors not covered above can be accounted for by adjusting this load factor.

TMH7 - Part2, for example, gives an additional factor relating to the type of founding material.

Description of founding material Foundation

factor f

Rock, dense and very dense coarse-grained soils, very stiff and hard fine-grained soils

Compact coarse-grained soils, and firm and stiff fine-grained soils from 0 to 15 m deep

1.0

Compact coarse-grained soils, firm and stiff fine grained soils with a depth greater than 15 m

Very loose and loose coarse-grained soils and very soft and soft fine-grained soils from 0 to 15 m deep

1.2

Very loose and loose coarse-grained soils and very soft

and soft fine-grained soils with depths greater than 15 m 1.5

Acceleration response spectrum (seismic analysis only)

Acceleration response spectra are empirically derived definitions for typical responses of

structures to a range of ground accelerations. Choose an applicable response spectrum:

SABS 0160 - 1989.

TMH7 - Part2.

UBC 1194.

Alternatively, define a custom response spectrum by entering the ground acceleration for

damping ratios of 0.5%, 3%, 5% and 10% for nine different periods. Any period values can be

entered, including those for the acceleration/velocity and velocity/displacement bound regions dividing points.

If the ductility value greater than unity is specified, the elastic response spectrum is adjusted to

obtain an inelastic response spectrum. The elastic spectrum, for any given damping ratio, is

modified along the displacement bound region by multiplying it with a factor 1/. Along the

acceleration bound region the elastic spectrum is multiplied by a factor 1/(2)½..

Frame Analysis 3-70

Analysis

To analyse your model, open the analysis page and press start analysis. You can abort an

analysis in progress by pressing abort analysis, or clear the last analysis results by pressing

reset. Once the analysis has completed, you can view the results by opening the view output

page.

Analysis options

You can set the following options prior to analysis:

Load combinations only: Select this option to analyse only load combinations. If you do

not select this option, the individual load cases will also be analysed. Having the results

available for load cases will help you verify the accuracy of you analysis or understand the

behaviour of your model under those load cases, but it can slow down the analysis process

in some cases, e.g. non-linear analysis of large models.

Store output with input: With this option selected, the analysis results are saved with

your Frame Analysis input file. If you open the input file again at a later date, your analysis results will be available immediately, allowing you to continue without needed to

run the analysis again. This feature is particularly useful when dealing with complex cases

that require a long analysis time.

Output file: If you choose to not store your output with your input, the program will store

your analysis results in a separate text file. You can enter the name for the output file;

historically Frame Analysis used the output file SF.OUT.

Save before analysing: If enabled, this option will automatically save your input file

before commencing the analysis. If something would go wrong during the analysis, you

will not lose your work.

Frame Analysis 3-71

The analysis progress is displayed to help you judge the time remaining to complete the

analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load

combination or, in the case of modal or buckling analysis, the first mode shape.

Error checking during analysis

During the input phase, the frame geometry and loading data is checked for errors. Not all

reported errors are necessarily serious. To define duplicate elements between two nodes, for

example, could be an accidental error on your side. However, the program can deal with a

situation like this and will allow the analysis procedure to continue.

Other input errors could be serious enough to prevent an analysis from being completed

successfully. Nodes with no elements, for example, have no restraints and will cause numeric

instability during the analysis.

The first step of any analysis is the final verification of the input data. In the case of critical

errors still present, a warning message will be displayed. If you then choose to not proceed

with the analysis, you will be taken to the input table with the error. However, choosing to

proceed and ignore the warning will have an unpredictable result.

Frame Analysis 3-72

Fixing errors that occurred during the analysis

Even if all input data seems valid, numeric errors may still occur during an analysis. For

example, if you entered incorrect section properties, such as a very small E-value, the mistake

may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness

matrix or extremely large deflections. The same applies to the stability of the frame. Although the frame may appear stable, some combinations of internal hinges may result in some nodes

being unstable.

If an error was detected during the analysis, a warning will be displayed. The cause of the error

should become clear when studying the output file:

The text at the end of the output file normally gives the reason for the error.

If the output file seems complete, the problem will require more careful attention. Scan all

output tables for excessively large or small values.

Second order and buckling analysis problems

The following points should be kept in mind when trouble-shooting a second order analysis:

During a second-order analysis, an element is removed from the frame as soon as its axial

force exceeds its Euler buckling load. If one or more elements have been removed from the frame in this way, structural stability cannot necessarily be guaranteed any more. The

removal of a single element may cause a chain reaction of elements failing. If the

remaining members do not constitute a stable structure, the structure will fail. All member

forces in the output file will then be shown as ''.

A second order analysis fails in instability can be verified using a buckling analysis. You

can examine the buckling mode shapes to easily locate problem areas in the structure that

may require stiffening.

Slender non-structural elements often buckle before major structural members, distorting

analysis results. Such elements should preferably be excluded from the model.

If the linear and second order analysis results show negligible differences, the structure is

likely not sensitive to p-delta effects for the given loading. This is often true for truss-type

frames.

Tip: Perform a buckling analysis to get an indication of the general stability of the frame under the entered loads. A frame with a buckling load factor less than unity normally

experiences the same local or global stability problems during a second order analysis.

Verifying analysis accuracy and integrity

Your analysis output will only be as good as your input. Even if the program does not display

an error or warning message, you should verify the accuracy of the analysis. Always use your

engineering judgement to do a few basic checks on your analysis:

Frame Analysis 3-73

View the deflection diagrams for each load case and satisfy yourself that their shapes and

magnitudes seem realistic. In the case of a dynamic analysis, check the shapes and

frequencies of the primary modes of vibration.

View the output file and compare the calculated total own weight with your estimates.

Inspect the equilibrium check to verify that each load case's applied loads and reactions

matches your hand calculations. If the program warns about an equilibrium problem, there may be a stability problem in your model. In such cases, consider performing a buckling or

non-linear analysis to identify problem points in your model, e.g. members buckling in

compressions.

If the results of second order or non-linear analysis do not differ much from the results of a

linear analysis, the structure is likely not sensitive to p-delta effects or large deflections for

the given loading. This is typically true for truss-type frames and floor systems (grillages).

Accuracy of a shell finite element analysis

The mesh stress error indicator output gives an indication of the accuracy of a shell finite

element analysis. The program calculates the maximum estimated error by taking the

difference in the smoothed and raw stresses anywhere in the model. The program displays the

error level across the model as contours, with the 100% level indicating the maximum

estimated error level. If the estimated maximum error is 20%, for example, then the 50% contour would suggest an estimated error of 10% (the smoothed stresses differs by 10% from

the raw stresses) at the point considered.

Large estimated errors often spell problems, but do not necessarily mean that the stress values

all across a model are inaccurate or wrong. It does, however, helps you identify zones where

refinement of the finite element mesh may improve the analysis accuracy. Keep the following

factors in mind:

Error distribution: Peaks in estimated errors only in certain parts of the model suggests that

the basic mesh layout is sound. Refinement of the mesh may be needed in the zones where

the estimated errors are large.

Error location: Small stress differences in critical portions of the model may be significant.

Likewise, if you are interested in the stresses in a certain part of the model, large stress difference in remote portions may have not significant effect in the part considered.

Stress smoothing: By smoothing stress, you can improve accuracy in some cases (by

balancing out errors). However, you should not use stress smoothing to try hide real

problems in your model.

In most cases you can be improved the accuracy of the analysis by optimising the finite

element mesh, e.g. using smaller elements is zones of stress concentration. When making this

decision, you should consider both the local and global characteristics of your model.

Frame Analysis 3-74

Design Links

Once the analysis is complete, Frame can link up with other Prokon modules for further post-

processing and design. This is done on the ‘Design links’ tab:

Selecting a design link

The following links are available:

Steel connections: Select this option on the left hand side of the screen. Now click on any

node in the structure. A dialog with possible connections will appear as shown above. The

program will look at the types of members meeting at the node. These members must be

steel members selected from the Prokon database. There should also be at least two

members meeting at the node. If for example, there are no hollow sections at the node, the

‘Hollow section connection’ option will remain greyed. For the ‘Apex connection’ the

members must be I- or H-sections. Check the type of connection that you want. Sometimes

there is more than one possible connection of the chosen type at the node. The desired

connection can be chosen from the drop-down(s) to the right of the connection type

Frame Analysis 3-75

chosen. Pressing ‘OK’ will convert the output data and transfer it to the relevant

connection design module.

Concrete columns: Select ‘rectangular’ or ‘circular’ column on the left hand side of the

screen. Now select a member on the screen with the mouse. The data will be transferred

from Frame and the relevant column design module will be opened.

Concrete base: Select ‘Concrete base’ on the left hand side of the screen. Now select a support node on the screen with the mouse. The data will be transferred from Frame and

the base design module will be opened. Note that only support nodes can be selected.

Member design modules: Separate buttons are provided to call up ‘Member design for

axial stress’, ‘Member design for combined stress’ and ‘Timber member design’. Each of

these modules will open with the current structure and output, ready for further processing.

Important note regarding load combinations: If the analysis was a linear analysis, the

load combinations are broken up using the load factors entered in Frame. In the case of a

second-order analysis, the results of a combination are not necessarily equal to the sum of

the load cases times their load factors, due to the secondary effects taken into account. The

program will calculate appropriate load factors, which will be similar to the ones entered,

but adjusted so that the sum of load case forces times load factors gives the final forces

calculated by Frame.

Frame Analysis 3-76

Viewing output

The analysis results can be viewed graphically or in tabular format. Output data, including

graphics and tabled values, can be selectively appended to the Calcsheets using the Add to

Calcsheets function on each output page.

Viewing output graphics

Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of

any load case:

Deflections: Deflections are generally small in relation to dimensions of the structure. To

improve the visibility of the deflection diagram, you can enter a screen magnification

factor. You can optionally display the deflected shape without the original geometry.

Mode shapes: In the case of a dynamic or buckling analysis, you can display the mode

shapes one-by-one. Use the Animate function to bring a mode shape to life. If you tick the

‘record animation’ box, the animation is stored as an animated .gif file as shown below.

Frame Analysis 3-77

Note: Mode shapes should not be confused with deflections. Mode shapes represent the natural dynamic characteristics of a structure. Values are normalised with the maximum

"displacement" given as one thousand.

Reactions: The reactions forces and moments at all supported nodes are displayed. The

arrowheads points in the direction of each reaction.

Beam element forces:

Axial forces: The force is shown as expanded red and blue lines. Compression forces are shown in red and tension forces in blue. The distance of a line from the element

centre line is in proportion to the size of the axial force.

Moments: Bending moments about the local x and y-axes. A plot factor can also be

entered to enlarge or reduce the bending moment diagram on the frame.

Shear: Shear force diagrams are drawn for the local y and x-directions. A beam

element's shear force diagram is constructed by viewing it with its local z-axis

pointing to the right. Since the direction of the z-axis depends on the node numbers,

irregular numbering of nodes can result in apparent irregular signs used in the shear

Frame Analysis 3-78

force diagrams. Refer to page 3-7 for detail on the sign conventions used for beam

element forces.

Torsion: The torsional moment about the z-axis, i.e. element axis.

Beam element force envelopes:

Envelopes: Enter a series of elements

and select the

load case and

combinations

to include in

the envelopes.

Envelopes are

drawn using

the values as

tabulated

from the output file. Positive moments, for example, are drawn below the line and

negative above. Because members of different orientations can be included in the same envelope, no simple distinction is made between tension and compression faces

of members.

Frame Analysis 3-79

In-plane stresses in shells:

Stresses in x, y and xy directions: Display contours of the membrane stresses in the

local x and y-directions and the shear stresses. Refer to page 3-6 for detail on the local

axis convention for shell elements.

Maximum and minimum stresses: These correspond to the largest tensile and

compression stresses respectively. Positive values indicate compression and negative

values tension.

Von Mises stresses: The Von Mises stresses give a graphical indication of a yield

criterion, i.e. a general indication of the combined effect of all stresses. The

Von Mises stresses takes into account in-plane stresses as well as bending stresses and

is presented for both the top and bottom faces of the shell elements..

Frame Analysis 3-80

Bending moments and shear forces in shells:

The x, y and xy bending moments: The bending moments about the local x and y-

axes and the torsional moment. The direction (not axis) of bending is shown as a small

line on each shell element.

Maximum and minimum bending moments: The principal bending moments.

The x, y and maximum shear forces: The shear forces are in local x and y-axes.

The maximum shear stress is also given and is obtained by dividing the maximum

shear force by the thickness of the element.

Frame Analysis 3-81

Reinforcement in shells:

Contours of the required reinforcement in the top and bottom faces in the x' and y'-

directions are given. The corresponding ‘Wood & Armer’ moments from which the

reinforcement was calculated is also given. The reinforcement direction is shown as a

small line on each shell. Refer to page 3-61 for the definition of the reinforcement

directions.

Tip: If the lines indicating the direction of bending or of the reinforcement is not clearly visible, enable detailed rendering under the graphics options. Refer to page 3-17 for

instructions.

Tip: Shell element stress contours are drawn on the deflected shape of the structure. Careful

choice of the deflection magnification factor can enhance contour diagrams.

Frame Analysis 3-82

Stresses in solids:

The stresses presented are the direct stresses in the X, Y and Z directions, the shear stresses in the XY, XZ and YZ planes, the 3 principal stresses 1,2 and 3 as well as the maximum shear

stress and the von Mises stress. For solids all the stresses are plotted in the global co-ordinates.

Frame Analysis 3-83

Viewing output tables

Open the Output file page for a tabular display of the frame analysis output file. You can filter

the information sent to the calcsheets by enabling or disabling the relevant sections.

The Find heading function allows you to quickly locate any main section of the output file.

If you right click on the output, various editing functions are available. For example, you can

search for any string by pressing Ctrl and F.

Frame Analysis 3-84

Calcsheets

Frame analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To

include a particular component of the output in the calcsheets, view the relevant output

information and then click Add to Calcsheets.

Recalling a data file

The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall

the frame by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the frame analysis

module as well.


Plane Stress/Strain Analysis

The Plane Stress/Strain Analysis module can be used to perform a finite element analysis of a

membrane of any general geometry subjected to plane stress or strain. An automated element

grid generation facility helps speeding up the input and analysis processes.



The following text gives an overview of the finite element analysis theory and its application.

Scope

The program analyses membrane structures of any general shape, including openings. The

cases of plane stress and plane strain are both supported. Element grids are automatically

generated with a customisable grid size.

Plane strain and plane stress

The conditions of plane stress and plane strain are two similar two-dimensional states of

stress and are subsequently often confused. However, their definitions set them apart as two

very distinct conditions.

When forces are applied to a thin two-dimensional plate in its own plane, the state of stress and

deformation in the plate is called plane stress. A typical example would be a shear wall that,

due to it being a thin plate, will experience mainly in-plane stresses. No restraint is provided

for out-of-plane deformation.

On the other hand, a prismatic solid subjected to a constant loading normal to its axis can be

analysed as an infinite length of two-dimensional slices of unit thickness experiencing plane

strain. A dam wall, for example, would typically be subjected to hydrostatic and soil pressures

normal to its surface. A slice is taken from the wall will be restrained from deforming out-of-plane.

Finite element modelling

The program uses eight-noded quadrilateral and six-noded triangular isoparametric finite elements formulated for plane stress and plane strain.

A mesh of isoparametric quadrilateral or triangular is automatically generated and optimised

during analysis. You can specify the grid spacing in the X and Y-directions as part of the

analysis parameters. A finer grid will often improve accuracy. However, the time taken to

perform an analysis is a function of the number of finite elements – the finer the grid, the

longer the analysis time.


Sign conventions

When entering coordinates and forces, the following sign convention is used:

Positive Y-coordinates and vertical forces are taken upward, i.e. parallel to the Y-axis.

Positive X-coordinates and horizontal forces are taken to the right, i.e. parallel to the

X-axis.

In the analysis results, deflections are measured along the Y-axis. A positive deflection

therefore denotes an upward movement.


Input

Use the four input tables, i.e. Nodes, Supports, Material properties and Loads, to define the

structure's geometry and loading.

Nodes input

A structure is defined by entering one or more shapes. A shape may comprise straight lines and

arcs. When more than one shape is entered, the shapes will accumulate and form one structure.

Often, a complicated section is easier defined using more than one shape.

Note: Shapes must be entered in an anti-clockwise order.

An explanation of the node input table is given below:

The Mat. No. column is used for categorise the data that follows in the next columns:

1 to 9 : The start of a new polygon with the specified material property. An absolute

reference coordinate must be entered in the X and Y columns. If you leave X or

Y blank, a value of zero is used.

0 : Start of an opening. An absolute reference coordinate must be entered in the X

and Y columns.

R : If you enter an 'R' or leave the Mat. No. column blank, a line is drawn using

relative coordinates, i.e. measured from the previous coordinate.

A : Enter an 'A' in the Mat. No. column blank to make the coordinate absolute.

The X and Y columns are used for entering coordinates:

X : Absolute or relative X coordinate. Values are taken positive to the right and

negative to the left.

Y : Absolute or relative Y coordinate. Values are taken positive upward and

negative downward.

Use the Bulge column to define an arc of a specified radius. Consider an imaginary line

joining the previous coordinate and the coordinate entered in the X and Y columns. A

bulge greater than zero then defines an arc to the right of the line. Similarly, a negative

bulge draws an arc to the left of the line. If no bulge is specified, a zero value is used, i.e. a

straight line.

You do need to close the polygon defining a shape – the starting coordinate is automatically

used as the ending coordinate. If two polygons intersect, the geometry of the last polygon takes preference and the previous polygon is clipped. A hole in a structure can, for example, be

entered on top of previously entered shapes.


Nodes are automatically numbered as they are input. You can later use the node numbers to

position supports and loads.

Supports input

You can define point supports, distributed support and prescribed displacements anywhere

along the edges of the structure. Supports are entered as follows:

Nodes : Enter a single node number for a point support or a range of nodes for a

distributed support, e.g. '2' for node 2 only and '2-5' for the zone described by

the straight line joining nodes 2 and 5.

XY support : Enter 'X' and/or 'Y' for horizontal and/or vertical support.

Displ. : Specify the value of any horizontal or vertical prescribed displacement in the

relevant column (m).

Note: Point supports invariably result in localised stress concentrations, with the effect

increasing for smaller element grids. It is therefore recommended to avoid point supports and rather distribute each support over as large a width as possible.


Material properties

The following material properties must be input for every material property code used in the

Code column of the Nodes input table:

t : Thickness (m).

E : Modulus of elasticity (kN/m3). If left blank, the value for the preceding material type is used. Typical values are tabled below.

Poisson : Poisson ratio. If left blank, the value for entered in the previous row is used.

Typical values are tabled below.

Dens : Density on (kN/m3). Typical values are tabled below.

Material E modulus

(kPa)

Poison's

ratio

Density

(kN/m3)

Masonry 10E6 0.20 20 - 25

Concrete (normal strength)

25E6 to 35E6 0.20 ± 24

Aluminium ± 70E6 0.16 ± 27

Structural steel ± 205E6 0.30 ± 78

Loads input

Point loads and distributed loads can be defined anywhere along the edges of the structure. Use

as many lines as necessary to define the loads.

Loads are entered as follows:

Nodes : Enter a single node number for a point load or a range of nodes for a

distributed load, e.g. '2' for node 2 only and '2-5' for the zone described by the

straight line joining nodes 2 and 5.

X : The load direction can be either 'X' or 'Y' for horizontal or vertical respectively.

Wleft : Distributed load intensity at the smaller node number (kN/m).

Wright : Distributed load intensity at the larger node number (kN/m).


a : Distance from first node to beginning of distributed load (m). A value of zero

is used if field is left blank.

b : Length in m, of distributed load. The load is taken up to the ending node if this

field is left blank.

Note: Positive forces are taken to work upward and to the right.


Analysis

On completing the input, go to

the Analyse page to analyse the

structure. Following a successful

analysis, use the View page the

display the analysis results.

The following text describes the

analysis options that are

available and gives information

on finding and fixing analysis problems.

Analysis options

During the analysis, the program generates a rectangular grid of nodes in which rectangular

and, where necessary, triangular finite elements are placed. The grid spacing can be set

independently in the horizontal and vertical directions.

Choose Settings to set the grid spacing and other analysis options:

Finite element size: Horizontal and vertical grid spacings (m).

Type of analysis: Enter 'E' for plane stress or 'A' for plane strain.

Angle increment: The program models arcs as straight

lines at the specified angle increment. Although a

smaller angle would yield a smoother modelling of an arc, the resulting increase in modes will mean that more

elements will be used. Generally, an angle increment

between 5° and 15° would yield good results.


Analysis results

The analysis results can be viewed and printed in tabular or graphical format:

Elastic deflections.

Maximum principal stresses, i.e. the largest tensile stresses. Positive values indicate

tension and negative values

compression.

Minimum principal stresses,

i.e. the largest possible

compression stresses.

Negative values indicate compression.

The Von Mises yield

condition if often used to

determine whether a

material is behaving

elastically under combined

stress. According to the

Von Mises theory, the total

elastic energy comprises

volumetric changes and

shearing distortions. By

considering only the shearing distortion at yield

in simple tension in relation

to that under combined

stress, the yield criterion can

be established. The

Von Mises theory assumes a

ductile isotropic material.

Principal stress vectors, with

compression stresses in red

and tension stresses in blue.

You can also inspect the results in tabular format by

displaying the output file,

named PS.OUT



Some common problems during plane stress and plain strain analyses are:

If the program is unable to analyse the structure, there may be errors in the input. A

common mistake is the definition of shapes in a clockwise direction – the program expects

anti-clockwise input.

Stress concentrations will be present at positions of point loads and point supports. Such

concentrations are further exaggerated when using finer element grids. In practice, loads

and supports rarely act at points, but rather on small areas. It is likewise recommended to

spread all point loads and supports over small lengths.


Calcsheets

The finite element analysis output can be grouped on a calcsheet for printing or sending to

Calcpad. Various settings can be made with regards to the inclusion of design results and

pictures.

Tip: You can embed the Data File in the calcsheet for easy recalling from Calcpad.


If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall

its design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the analysis module as

well.


Single Span Beam Analysis

The Single Span Beam Analysis module can be used to quickly analyse a beam. The beam

can be a single span beam or a single span taken from a continuous beam with the appropriate

end conditions. The analysis results of steels beams can be post-processed with the steel

member design module for combined stress, Com.


Sign conventions

When entering forces and moments, the following sign convention is used:

Positive vertical forces act downward, i.e. parallel to the negative Y-axis.

Positive moments work anti-clockwise.

In the analysis results, the following applies:

Deflections are measured along the Y-axis. A

positive deflection indicates uplift and negative

deflection a downward movement.

Shear forces are measured along the Y-axis. A positive shear force at the left edge of the beam,

for example, represents an upward vertical

reaction.

Moments are drawn on the tension face of the

beam.


Input

The beam definition has two main input components:

Geometry and material properties.

Loads.

Beam input

The following values must be entered:

Length : The overall length of the beam (m).

M Left : The applied moment at the left-hand end (kNm). If you leave the field blank, a

zero moment is used, e.g. the beam is simply supported. You can also fix an

end by entering an 'F' or make it a free cantilever end with a 'C'.

M Right : The applied moment at the right-hand end (kNm).


I : The second moment of inertia of beam (m4).

E : Young's modulus of the beam (kPa). A value of 205x106 kPa, i.e. steel, is used

if this field is left blank. Typical values are:

Material E modulus (kPa)

Timber 5E6 to 15E6

Concrete

(normal strength) 25E6 to 35E6

Aluminium ± 70E6

Structural steel ± 205E6

Section input

The moment of inertia of a standard steel section can be selected from the section database.

You can also define your own sections or remove sections from the database.

Own weight

On selecting a steel section form the database, the own weight is automatically entered as a

uniform distributed load.

Loads input

Use as many lines as needed to enter any general loading on the beam in the Loads input table:

W Left : Distributed load intensity (kN/m) applied at the left-hand starting position of

the load. If you do not enter a value, the program will use a value of zero.

W Right : Distributed load intensity (kN/m) applied on the right-hand ending position of

the load. If you leave this field blank, the value is made equal to Wleft, i.e. a

uniformly distributed load is assumed.

P : Point load (kN).

M : Moment (kNm).


a : The start position of the distributed load, position of the point load or position

of the moment (m). The distance is measured from the left-hand edge of the

beam. If you leave this field blank, a value of zero is used, i.e. the load is taken

to start at the left-hand edge of the beam.

b : The end extent of the distributed load, measured from the start position of the

load (m). Leave this field blank if you want the load to extend up to the right-

hand edge of the beam.

Note: Positive forces and moments are taken to work downward and taken anti-clockwise

respectively.


Analysis

Press Analyse to display the analysis results:

Elastic short-term deflections.

Bending moment diagram.

Shear force diagram.


Calcsheet

The beam analysis results can be grouped on a calcsheet for printing or sending to Calcpad.

Various settings can be made with regards to the inclusion of design results and pictures.




the beam analysis by double-clicking the relevant object in Calcpad. A data file embedded in

Calcpad is saved as part of a project and therefore does not need to be saved in the beam

analysis module as well.


Beam on Elastic Support

Analysis

The Beam on Elastic Support Analysis module can be used to quickly analyse a beam or slab

on an elastic foundation. The beam cross-section may vary along its length and the elastic

foundation can include gaps and rigid supports.



The following text gives a background into the analysis technique used.

Sign conventions and units of measurement

When entering forces and moments, the following sign convention is used:

Positive vertical forces act downward, i.e. parallel to the negative Y-axis.

Positive moments work anti-clockwise.

In the analysis results, the following applies:

Deflections are measured along the Y-axis. A positive deflection indicates uplift and

negative deflection a downward movement.

Bearing pressure is also measured along the Y-axis. A positive bearing pressure denotes an

upward reaction.

Shear forces are measured along the Y-axis. A positive shear force at the left edge of the

beam, for example, represents an upward vertical reaction.

Moments are drawn on the tension face of the beam.

Analysis procedure

The program performs a linear analysis in which the beam is modelled as a two-dimensional

frame on a series of least fifty closely spaced springs. Rigid supports are put at the specified positions and gaps in the elastic support where the supporting width is set to zero. Nodes are

taken at close intervals along the length of the beam. A node is also introduced at every support

and load position.

If negative soil pressures are not allowed, i.e. uplift is allowed, springs with negative reactions

are removed and the analysis repeated. Likewise, previously removed springs are restored if

downward deflections are calculated at the points concerned. The analysis procedure is

repeated until the iteration converges to a stable solution.

A beam is considered unstable, i.e. to overturn under the applied load, if the analysis yields less

than two springs with compressive forces.


Input

The beam definition has several input components:


Supports input

Loads.

Beam input

The beam is defined as one or more segments, each with its own properties. The following

values must be entered:

Lsec : The length of a beam segment with a specified stiffness and support width (m).

You may enter more than one segment to define a beam varying section or an

elastic medium of varying stiffness. Each additional beam segment entered is

added to the right-hand side of beam.

Isec : The stiffness of the beam segment, express as the second moment of inertia of

the relevant cross section (m). The value of Young's modulus, applicable to the whole beam, is entered under the analysis settings.

Bsec : The support width of the beam segment (m). This beam width is multiplied by

the foundation modulus of the soil, Km, to obtain the support stiffness per unit

length of the beam. Enter a zero value for no foundation stiffness, i.e. a gap in

the elastic medium.

Supports input

Use the Support input columns to enter rigid supports in the elastic medium:

Position : A rigid support position, measured from the left-hand side (m).

Support : You can set the support type to vertical and/or rotational:

Support Description

Y Vertical support, e.g. a solid rock intrusion in the elastic medium

R Rotational support, e.g. a rigid column above built into the beam

YR Vertical and rotational support, e.g. a rigid pile below that is built into the beam.


Loads input

Use as many lines as needed to enter any general loading on the beam in the Loads input table:

W Left : Distributed load intensity (kN/m) applied at the left-hand starting position of


W Right : Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a



M : Moment (kNm).





b : The end position of the distributed load, measured from the start position of the

load (m). Leave this field blank if you want the load to extend up to the right-

hand edge of the beam.

Note: Positive forces and moments are taken to work downward and taken anti-clockwise

respectively.

Analysis settings

Press Settings to edit the material constants and other parameters to be used in the analysis:

E modulus: Young's modulus for the beam (kPa). Values for typical building materials are

tabled below:

Material E modulus (kPa)

Timber 5E6 to 15E6

Concrete (normal strength)

25E6 to 35E6

Aluminium ± 70E6

Structural steel ± 205E6


K modulus: Foundation modulus or modulus of subgrade reaction (kN/m3). Typical

empirical values derived suggested by Bowles are given below:

Soil type K modulus (kN/m3)

Loose sand

Medium dense sand

Dense sand

Clayey medium dense sand

Silty medium dense sand

Clayey soil:

qa 200 kPa

200 kPa qa 800 kPa

qa > 800 kPa

4 800 to 16 000

9 600 to 80 000

64 000 to 128 000

32 000 to 80 000

24 000 to 48 000

12 000 to 24 000

24 000 to 48 000

> 48 000

The foundation modulus, K, is a conceptual relationship between the soil pressure and

deflection of the beam. Because the beam stiffness is usually ten or more times as great as

the soil stiffness as defined by K, the bending moments in the beam and calculated soil

pressures are normally not very sensitive to the value used for K. Recognizing this,

Bowles suggests that the value of K can be approximated from the serviceability limit state

bearing capacity, qa, as being 40 × qa (kN/m3) or 12 × qa (k/ft3).

Allow negative pressure: Enter 'Y' to enable full

adhesion between beam and elastic medium. Enter

'N' to allow uplift, i.e. zero adhesion between beam and elastic medium.

Note: The foundation modulus, Km, is multiplied with the support width to obtain the support stiffness per unit length of the beam. Enter a zero value for no foundation stiffness,

i.e. a gap in the elastic medium.

'Foundation Analysis and Design, Fifth Edition', by Joseph E. Bowles, published by McGraw Hill


Example

The sketch shows an 800 mm wide by 300 mm deep beam is modelled on an elastic

foundation:

The first fourteen meters of its length is supported on very stiff clay. The foundation

modulus is set to 40 000 kN/m3.

The beam crosses a rock intrusion ten meters from the left that provides vertical support.

The beam then spans four meters over a ditch, i.e. no support. This is modelled by entering

a zero section width.

On the other side support is provided on a strip of hard clay, two meter wide. The hard

clay is modelled by increasing the support width to 1.2 m. The resulting effective foundation modulus is then given by 1.2/0.8 x 40 000 = 60 000 kN/m3.

The beam is loaded with a long trapezoidal distributed load, twelve meters long, a point

load and a moment at its right-hand end.


Analysis

Press Analyse to display the analysis results:

Bearing pressure.

Bending moment.

Shear force diagram.


Calcsheet

The beam analysis results can be grouped on a calcsheet for printing or sending to Calcpad.





the beam analysis by double-clicking the relevant object in Calcpad. A data file embedded in

Calcpad is saved as part of a project and therefore does not need to be saved in the beam

analysis module as well.

Steel Member Design

4-1

Chapter

4 Steel Member Design

The steel member design modules can be used for elastic and plastic design of structural steel

members. Several modules act as post-processors for the frame analysis modules, facilitating

integrated frame analysis and design.

Steel Member Design 4-2

Quick Reference

Steel Member Design using PROKON 4-3

Steel Member Design for Axial or Combined Stress 4-5

Plastic Frame Design 4-33

Crane Gantry Girder Design 4-65

Plate Girder Design 4-77


Steel Member Design using

PROKON

A variety of steel member design modules are included in the PROKON suite. These are

considered useful tools when designing members using either elastic or plastic methods.

Elastic member design

When designing struts and ties, you can post-process frame analysis results using the member

design module for axial stress, Strut. Similarly, the member design module for combined

stress, Combine, can be used to design members subjected to both axial force and moment, or

beam-columns.

Plastic frame design

The Plastic Frame Design module can be used to design steel frames using plastic design

methods. The same module can also optimise sections for better economy.

Note: This module is no longer developed or supported, and was removed from the program

toolbar in PROKON version 2.4. However, for the sake of users that purchased this module

in the past, it is still access via the Program menu. To evaluate non-linear behaviour of

frames, the recommended procedure is to use the Frame Analysis module and perform a

non-linear analysis.

Girder design

Specialised modules are available for designing crane gantry girders and plate girders.


Steel Member Design for

Axial or Combined Stress

The steel member design modules are suitable for the following design tasks:

Use Strut for checking and optimising steel members subjected to axial stress only,

e.g. truss members.

Combine is used for checking and optimising steel members subjected to a combination of

axial and uniaxial or biaxial bending stresses, e.g. beams and columns in frames.

The steel member design modules primarily act as post-processors for the frame analysis

modules. Both modules also have an interactive mode for the quick design or checking of

individual members without needing to perform a frame analysis.



A brief background is given below regarding the application of the design codes.

Design scope

The steel member design modules can design hot-rolled sections subjected to axial stress or a

combination of axial and bending stresses.

Strut can be used to design any hot-rolled section for axial stress. Because the design

procedure is relatively simple, design results are presented in tabular format. This feature

makes the program especially useful when designing of a large number of struts and ties.

Combine can design hot-rolled double symmetric sections and channels subjected to axial

and bending stress. Non-symmetric sections like angles are not supported. More design

checks need to be performed for each member requiring more detailed output.

Strut and Combine use a similar design approach. Although there may seem to be a degree of

overlapping in their design features, the two modules rather complement each other with

specialised individual design functions. You will typically use them to design the different components of the same structure, e.g. design a roof truss in Strut and its supporting columns

in Combine.

Note: Support for cold-formed sections is not provided. However, hot-rolled hollow circular

and rectangular sections may be designed with the programs if such sections are deemed to

have relatively thick walls with a resulting low risk of local buckling.

Tapered sections

The current versions of Strut nor Combine cannot design tapered sections, e.g. haunches in

portal frames. When evaluating members with varying sections, the section type at the first

node is used over the whole length of the member.

Design codes

The program designs axially loaded steel members according to the following design codes:

AISC - 1989 ASD (Strut only).

AISC - 1993 LRFD.

AS4100 - 1998.

BS 5950 - 1990.

BS 5950 - 2000.

CAN/CSA-S16.1-94.


CSA S16-01 - 2001.

Eurocode 3 - 1992 (Strut only).

GBJ 17-88 (Strut only).

IS:800-1984 (Strut only).

IS:800-2007 (Combine only).

SABS 0162 - 1984 (allowable stress design).

SABS 0162 - 1993 (limit state design).

SABS 0162-2 - 1993 (Combine only).

SANS 10162 - 2005


The steel design modules support the following units of

measurement:

Metric.

Imperial (Strut only).

The preferred unit of measurement can be selected using the Units

command on the File menu.

Symbols

Where possible, the same symbols are used as in the design codes:

Ane/Ag : Effective area factor with which the gross sectional area must be multiplied to

obtain the effective sectional area, reduced for fasteners holes. The factor

applies to elements subjected to tensile axial stress only.

Ke : Factor with which the member length is multiplied to obtain the effective

length for lateral torsional buckling (Combine only).

Kv : Factor with which the member length is multiplied to obtain the effective

length for buckling about the v-v (weakest) axis of the member (Strut only).

Kx : Factor with which the member length is multiplied to obtain the effective

length for buckling about the x-x axis of the member.


Ky : Factor with which the member length must be multiplied to obtain the effective

length for buckling about the local y-y axis of the member.

AISC:

F : Applied axial force (kN or kip).

Fy : Specified minimum yield strength of steel (MPa or ksi).

Fu : Specified minimum tensile strength of steel (MPa or ksi).

L/r : Slenderness ratio.

Pu : Ultimate axial stress (MPa or ksi).

Pn : Allowable axial stress based on the slenderness ratio (MPa or ksi).

Sc : Actual axial stress in member (MPa or ksi).

BS 5950:



M : Applied moment (kNm or kipft).

Ma : Maximum buckling moment in presence of axial load (kNm or kipft).

Mb : Lateral torsional buckling resistance moment (kNm or kipft).

Mc : Moment resistance in the absence of axial force (kNm or kipft).

m : Equivalent uniform moment factor.

n : Slenderness correction factor.

Pc : Allowable axial stress based on the slenderness ratio (MPa or ksi).

Py : Design strength of steel (MPa or ksi).


Z : Elastic modulus (mm³ or in³).

CSA S16.1:

Ce : Euler buckling strength (kN or kip).

Cr : Factored compression resistance (kN or kip).

Cu : Ultimate compression force (kN or kip).


Fu : Ultimate strength of steel (MPa or ksi).

Fy : Design yield strength of steel (MPa or ksi).


Mcr : Elastic buckling moment (kNm or kipft).

Mr : Factored moment resistance (kNm or kipft).

Mu : Ultimate bending moment (kNm or kipft).

Tr : Factored tensile resistance (kN or kip).

Tu : Ultimate tensile force (kN or kip).

U1 : Capacity factor to account for moment gradient and second-order effects.

Zpl : Plastic modulus (mm³ or in³).

1 : Equivalent uniform bending moment factor.

2 : Moment gradient factor giving increased moment resistance of laterally

unsupported members.

Eurocode 3 - 1992 (Strut only):


fy : Design yield strength of steel (MPa or ksi).

L/i : Slenderness ratio.



SABS 0162 - 1984:

f 'cr : 0.6 times the Euler buckling stress (MPa or ksi).





Pmc : Allowable compressive bending stress (MPa or ksi).

Pmt : Allowable tensile bending stress (MPa or ksi).


St : Average axial tensile stress (MPa or ksi).

Smc : Maximum compressive bending stress (MPa or ksi).

Smt : Maximum tensile bending stress (MPa or ksi).

: Coefficient allowing for varying bending moment.


SABS 0162 - 1993 and SANS 10162:

Ce : Euler buckling strength (kN or kip).

Cr : Factored compression resistance (kN or kip).

Cu : Ultimate compression force (kN or kip).


fu : Ultimate strength of steel (MPa or ksi).


Mcr : Elastic buckling moment (kNm or kipft).

Mr : Factored moment resistance (kNm or kipft).

Mu : Ultimate bending moment (kNm or kipft).

Tr : Factored tensile resistance (kN or kip).

Tu : Ultimate tensile force (kN or kip).


Zpl : Plastic modulus (mm³ or in³).


2 : Moment gradient factor giving increased moment resistance of laterally unsupported members.


Sign conventions

Member design is done in the local element axes. Bending about the x-x axis generally

corresponds to strong axis bending and bending about the y-y axis to weak axis bending. For

non-symmetric sections like angles, the x-x and y-y axes are horizontal and vertical with the

v-v axis representing the weakest axis.

Tip: The exact orientation of the v-v axis of a mono-symmetric section can be determined

using the Section Properties Calculation module, Prosec.

Axial force and moment

The local axes system and force directions are defined as follows:

Axial force: The local z-axis and axial force is

chosen in the direction from the smaller node

number to the larger node number. A positive axial

force indicates compression and a negative force

tension.

Bending: Moments about the x and y-axes represent bending about the section's strong and weak axes

respectively. Positive moments are taken

anticlockwise in all diagrams.

P-delta effects

Design codes generally allow stability effects to be taken into account in buckling checks by

reducing design capacities or amplifying design moments or axial forces. Trusses are normally

not sensitive to sway. However, in any structure, if you judge P-delta effects to be an important

part of the analysis, you should perform a second order frame analysis.

Second order analyses

The desirability of a second order analysis is echoed in the various design codes:

AISC LRFD: Section C1 states that an analysis of second order effects is required for

frames. This is done by second order elastic analysis or first order analysis with

amplification factors B1 and B2.

BS 5950: Accounts for stability effects by amplification of design moments by suggesting

a 'more exact approach' in clause 4.8.3.3.2.

CSA S16.1: Desirability is expressed in clause 8.6.1.

Eurocode 3: See clause 5.2.1.2.


SABS 0162 - 1984: Encourages second order analysis of frames with sway by limiting the

coefficient for variable bending moment, , to no less than 0.85 in the absence of second order analysis.

SABS 0162 - 1993 and SANS 10162: Same as CSA S16.1.

The programs do not make automatic adjustments to take account of stability effects. If

deemed necessary, you should conduct a second order analysis using the Plane Frame

Analysis or Space Frame Analysis modules.

When post-processing a second order frame analysis, Combine also performs a second order analysis for each member. This generally results in more economic design of sections.

Design parameters

Different design parameters can be set for each group of elements designed:

Effective area factor

When an element is subjected to a tensile axial force, allowance should be made for the reduction

in sectional area due to fastener holes.

The various design codes follow similar approaches for calculating the effective area factor, for

example:

AISC LRFD: Guidance is given in section B3.

BS 5950: See clauses 3.3 and 3.4.

CSA S16.1: When calculating the allowable tensile force, allowance is made for reduction

of the effective net area for shear lag (clause 12.3). The effective area is thus effectively a

function of the yield strength and ultimate strength of the steel (clause 13.2).

Eurocode 3: See clause 5.4.2.2.

SABS 0162 - 1984: See clauses 5.3 and 9.2.

SABS 0162 - 1993 and SANS 10162: The same clauses apply as for CSA S16.1 - M89.

Effective length factors for struts and ties

The effective length factors depend on the degree of restraint to be expected at each end of

compression members. Examples of guidelines are given in the codes:

AISC: See section E1.

BS 5950: Refer to clause 4.7.2 and Appendix D.

CSA S16.1: See clause 9.3 and Annex C.

Eurocode 3: See clause 5.8.2.


SABS 0162 - 1984: See clause 8.2.1 and Appendix E.

SABS 0162 - 1993 and SANS 10162: The same clauses apply as for CSA S16.1.

Considering a plane truss, the effective length Lx relates to in-plane buckling. For struts where

rotational fixity is provided by the connection, e.g. two or more fasteners or a welded connection,

a value between 0.70 and 0.85 is usually appropriate. Where rotation at the joints are possible,

e.g. single bolted connection, a value of 1.0 would normally be applicable.

The effective length Ly relates to buckling out of the vertical plane. This phenomenon can often

govern the design of the top and bottom chords of a truss that can buckle in a snakelike 'S'

pattern, giving an effective length equal to unrestrained length. Lateral restraints are normally

provided to reduce this effective length. For example, with braced purlins connected to the top

flange of the truss, the effective length could be taken equal to the purlin spacing.

The effective length Lv relates to buckling about the v-v axis, i.e. the weakest axis, and requires

special attention. Because movement about the v-v axis requires movement about both the x-x

and y-y axes, Lv is usually set equal to the least of Lx and Ly.

Effective length factors for beam-columns

The codes give similar guidelines, for example:

AISC: See section E1.

BS 5950: Refer to clause 4.3.5 guidance on factors to use for members in bending. Refer to clause 4.7.2 and Appendix D for members in compression.

CSA S16.1: Refer to clauses 9.1 to 9.4 and Annexes B and C.

Eurocode 3: See clause 5.8.2.

SABS 0162 - 1984: See clause 7.2.2 for flexural members. Refer to clause 8.2.1 and

Appendix E for compression members.

SABS 0162 - 1993 and SANS 10162: Same as for CSA S16.1.

Note: CSA S16.1, SABS 0162 and SANS 10162 clause 9.3.2 allows the effective length factor for compression members to be reduced to 1.0 if a second-order frame analysis has

been performed. A second order analysis will therefore normally yield a more economic

design.

Consider a typical portal frame subjected to dead and live load. The effective length Lx relates

to buckling in the plane of the portal, i.e. about the strong axis of each member. The length Ly

relates to out-of plane buckling, i.e. weak axis buckling. This value is typically set equal to the

distance between restraining purlins and sheeting rails.


The effective length Le relates to lateral torsional buckling of a member’s compression flange

about its weak axis. The length depends on the distance between restraints of the compression

flange. For rafters with purlins restraining the top flange, Le can therefore be set equal to Ly in

zones of sagging moment. However, if the rafter is relatively deep and no special precautions

are taken, the purlins could possibly have no effective restraint on the bottom flange. Therefore, where the bottom flange is in compression, i.e. zones of hogging moment, longer

effective lengths for lateral torsional buckling will apply.

Note: The current versions of Strut and Combine cannot design tapered sections. The use

of haunches in the sketch is merely for the sake of explaining the effective lengths. See

page 4-6 for more detail.

Slenderness limits

The different codes specify similar slenderness ratios for members in compression, typically 200.

For tension members, a maximum slenderness ratio of 300 is generally used. When launching

Strut or Combine, the slenderness limits given by the selected design code will be used by

default.

You are free to alter the maximum slenderness ratio for each individual load case or combination

if required. For example, in the case where uplift due to wind is dominant, the maximum

slenderness ratio may possibly be increased, e.g. SABS 0162 - 1984 clause 8.4 and

BS 5950 -1990 clause 4.7.3.2 allows a slenderness ratio of 250.


Member design techniques

The programs have two basic modes of operation:

Read and post-process the frame analysis results.

Alternatively, you can do an independent interactive design of one or more members.

Uses and limitations of the member design modules

Strut considers only axial forces during the design – any prevailing bending moments are

ignored. This means that you should use the program for the design of trusses and truss-type

sub-structures of frames only, i.e. where members experience predominantly axial forces.

Use Combine when working with members that have significant bending moments. This

program can however not design non-symmetrical sections like angles. Such members are typically used for constructing trusses or bracing frames and often have negligible bending

moments, making Strut the appropriate design tool.

Reading and post-processing frame analysis results

Given the nature of the different frame analysis modules, selective compatibility exists between the various frame analysis and the steel member design modules:

Strut designs members for axial stress only and can therefore read the results of Plane

Frame Analysis, Space Frame Analysis and Space Truss Analysis. The Grillage

Analysis and Single Span Beam Analysis modules are used to analyse beams and are

therefore excluded.

Combine designs members for combined axial and bending stress can therefore read the

results of Plane Frame Analysis, Grillage Analysis, Space Frame Analysis and Single

Span Beam Analysis. The Space Truss Analysis is used to analyse trusses with axial

forces only and is therefore supported by Strut instead.

Design steps

Working through the input and design pages, the frame design procedure can be broken up into the following steps:

The Input page: Defining design tasks by choosing a design approach, selecting members

to be designed, setting the design parameters and selecting load cases and slenderness

limits. The concept of tasks is described in detail on page 4-17.

The Members page (Combine only): Define internal nodes and enter effective lengths.

Refer to page 4-27 for detail.

The Design page (Combine only): Evaluating the design results. See page 4-29 for detail.

The Calcsheet page: Accumulate design results. See page 4-31 for detail.


Re-analysis of the frame

Having evaluated the various member sizes, you may find it necessary to return to the original

frame analysis and make some changes to section sizes. Before exiting the member design

module, first save the task list using the Save command on the File menu. After re-analysing

the frame, you can return to the member design module and recall the task list to have the

modified structure re-checked without delay.

Note: For a task list to be re-used with a modified frame, a reasonable degree of compatibility is required. Tasks that reference specific laterally supported nodes, for

example, will require modification if relevant node numbers have changed.

Interactive design of members

As an alternative to the above procedure, individual members can be designed without needing

to perform a frame analysis. To enable the interactive design mode:

In Strut, select the Interactive page.

In Combine, select 'Interactive input of data' on the Input page.

Design steps

Working through the input and design pages, the interactive design procedure can be broken up

into the following steps:

The Interactive page (Strut) or Input page (Combine): Choose a design approach, set the

design parameters and enter the element loads. In Strut, results are displayed interactively

on the same page. Refer to page 4-23 for a detailed explanation.

The Design page (Combine): Evaluate the design results. More detail is given on

page 4-29.

The Calcsheet page: Accumulate design results to print or send to Calcpad. See page 4-31

for detail.


Tasks input

On entering Strut or Combine, it defaults to reading the last compatible frame analysis for

post-processing. You can then choose to:

Read and post-process the frame analysis results: Define one or more design tasks by

grouping members with relevant design parameters.

Interactive design: Ignore the frame analysis and interactively input and design members.

The pages that follow describe the use of the programs for reading and post-processing frame

analysis results. Information regarding interactive design is given on page 4-23.

Choosing the data input and design mode

In Combine, the appearance of the Input page determined by your selection of the mode of

operation:

If you choose to read and post-process the results of the frame analysis modules, you will

use the Input page to define design tasks.

However, if you opt for interactive design of members, the Input page displays a table for entering member geometry and loading.

The appearance and behaviour of Strut is slightly different:

The Input page is used to manage design tasks for post-processing frame analysis output.

The Interactive page is used for entering data pertaining to interactive design of members.

Reading frame analysis output files

You can select another frame output file or view the current file:

Read data from: Use this option to load the output of a different frame module than the

one displayed. Click the box and select the relevant file from the list or enter a file name.

View output: To display the current frame analysis output file.

Defining design tasks

Central to the process of post-processing frame analysis results, are design tasks. By grouping

selective members with their relevant design parameters into one or more design tasks, you

should find it easy to manage the vast amount of frame analysis data generated for larger

frames.


The design of a frame should be simplified by breaking it into one or more manageable tasks.

Each task then defines a group of members to be designed together with the relevant design

parameters to be used.

Once you have defined one or more design tasks, the Calcsheet page (Strut) or Design page

(Combine) is enabled – viewing that page automatically performs all design tasks.

After having carefully defined a number of tasks, you can save the task list to disk for later

re-use. This means that you can return to the relevant frame analysis module, make some changes to the structure, re-analyse it and then repeat the previous design tasks by simply

reloading the task list.

Defining tasks

To define design tasks, you have to select or enter the following information:

1. Select a design approach.

2. If you choose to select the lightest section, then also choose a profile to use.

3. Select the members to be designed.

4. Enter the design parameters.

5. Select the load cases to be considered.

To save a task, enter a Task title and click Add task. Once added to the task list, a task will be

automatically performed when you go to the Calcsheet page. Define as many tasks as necessary to design the frame in the required detail.


Modifying design tasks

To modify an exiting task:

1. Click Task title to display a list of defined tasks.

2. Select the task you want to modify.

3. Make the necessary changes to the selected members, design parameters etc.

4. Click Update task to save the changes.

Deleting tasks

To remove a task from the list, first select the task and then click Delete task. To save the

complete task list to disk, use the Save commands on the File menu.

Note: In Combine, saving the task list with File | Save also saves the intermediate nodes and effective lengths entered in the Members page.


Selecting a design code

The current selected design code is displayed in the status bar. To

select a different design code, use the Code of Practice command on

the File menu or click the design code on the status bar.

Choosing a design approach

Depending on what you would like to achieve, e.g. preliminary sizing

or final design checks, you can choose between the following design

approaches:

Select lightest sections: Elements are optimised for economy

using mass as the criterion. Specify the type of section to be

used, e.g. equal leg angles, using Profile (F5). If you are unsure

about the section sizes to use or want to do some preliminary

sizing, this is the probably best approach to follow.

Evaluate current sections: The sections specified in the original frame analysis are checked. This approach is best suited

for final design checks.

Note: The section type selected under Profile (F5) is used when the design approach is set

to 'Select lightest section'. However, the selected section type has no bearing on the design

when the approach is set to 'Evaluate current sections'.

Selecting members for design in Strut

Use the Element groups (F6) function to select one or more element groups from the list or by

clicking members in the picture. Lateral supports are assumed at all nodes. If certain nodes are

not laterally supported, you can indicate them as follows:

Use the Laterally unsupported (F7) function to indicate those nodes that are supported –

all other nodes are then assumed to by unsupported. The program uses the shortest path

between the specified nodes to identify the relevant elements. Leave a blank line to end a

series of supported nodes or use the New group function to start a new series of laterally

supported nodes. You can manually enter node numbers or click them on the picture.


The following apply to the calculation of effective lengths when you indicate laterally

unsupported members:

Ly is based on the cumulative length between the specified supported nodes.

Lx and Lv remain a function of the individual element lengths between adjacent nodes.

Tip: To keep the design of a large truss manageable, consider using more tasks and specifying fewer nodes at a time.

Selecting members for design in Combine


clicking members in the picture. A lateral supports is assumed at each node. If certain internal

nodes are not laterally supported, you can indicate them on the Members page. For more detail,

refer to page 4-27.

Setting the design parameters

Use the Design parameters (F8) function to enter appropriate design parameters and material

properties. You can select a different set of design parameters with each task.

Note: In Combine, effective length factors are entered on the Members page. Refer to page

4-28 for details on entering effective lengths in Combine.

Selecting load cases and limiting slenderness ratios

When loading the last frame analysis results, the program automatically displays a list of all

load cases and combinations that can be designed and also the default slenderness limits for

struts and ties.

In the Maximum L/r ratios (F9) table, you can exclude any load case or combination from the

current design task by clicking its right-most column. A cross next to a load case means that

the particular load case will be included.

Tip: In the frame analysis modules you can also select to analyse load combinations only. The analysis output will then be more compact due to the omission of individual load case

results.

You are free to modify the slenderness limit for each individual load case or combination as

required. In the case where uplift due to wind is dominant, for example, you may be able to set

a higher slenderness limit. The code requirements regarding slenderness limits are discussed on

page 4-14.


Controlling design output

The amount of information that will be added to the

Calcsheet page can be controlled using the Settings

function on the Input page:

In Strut, you can select whether all members should be added to the Calcsheet or only a

number of most critical members.

In Combine, you can choose between showing

detailed calculation with or without diagrams or

a summary of results.


Interactive input

The interactive design mode offers an alternative method of designing members. Instead of

performing a frame analysis and then and post-processing the results, you can enter member

length and forces and design them interactively.

To enable the interactive design mode:

In Strut, select the Interactive page.

In Combine, select 'Interactive input of data' on the Input page.

The pages that follow describe the use of the programs for interactive member design. The

procedure to reading and post-processing frame analysis results is explained on page 4-15


The current selected design code is displayed in the status bar. To

select a different design code, use the Code of Practice command on

the File menu or click the design code on the status bar.


Depending on what you would like to achieve, e.g. preliminary sizing

or final design checks, you can choose between the following design

approaches:

Select lightest sections: Using mass as the criterion, the most

economical section size will be determined for each member.

The type of section that will be selected will be as specified

above. Specify the type of section to be used, e.g. equal leg

angles, using Profile (F5). This approach is very useful for if

one is unsure about the section sizes to use or if one wants to do

some preliminary sizing.

Evaluate current sections: This approach allows you to specify a section size for each

member. Use the Profile (F5) function to select a section.


In Combine, use the Effective lengths (F6) function to enter effective length factors. Use

Design parameters (F8) to enter appropriate design parameters. All members designed in a

particular interactive session use the same set of design parameters.


Specifying slenderness limits

Use the Maximum L/r ratios (F9) function to enter appropriate maximum allowable

slenderness ratios for compression and tension.

Entering member lengths and forces in Strut

Use as many lines as necessary to enter member lengths and axial forces:

L: Length of the member (m or ft).

F: Axial force (compression positive) (kN or kip).

Designation: Profile or section chosen using Profile (F5). With 'select lightest section' enabled, you only need to choose the type of profile. With 'Evaluating current section'

selected, you should select a section for evaluation.

Note: All entered forces and moments are ULS design values. For allowable stress design with SABS 0162 - 1984, you should enter working loads.


Entering member lengths and forces in Combine

One or more lines of information can be entered for each member. The program automatically

accumulates multiple lines of loads for the same member. The following input data is required:

Name: A descriptive name for each member.

L: Length of the member (m or ft).

F: Axial force with compression being positive (kN or kip).

X/Y: Axis of bending relating to the values that follow next. Use as many lines as

necessary to define the loading on the member about the x-x and y-y axes.

M1: Moment applied at the left end (anti-clockwise positive) about the X or Y axis (kNm

or kipft).

M2: Moment at the right end (anti-clockwise positive) (kNm or kipft).

W1: Distributed load at the left end. The load works over the whole length of the member

load and varies linearly between the left and right ends (downward positive) (kN/m or

kip/ft).


W2: Value of distributed load on right side (kN/m or kip/ft).

P: Point load applied on the member (downward positive) (kN or kip).

A: Position of the point load, measured from the left end (m or ft).

Note: All entered forces and moments are ULS design values. For allowable stress design with SABS 0162 - 1984, you should enter working loads.

The profile of the members to evaluate is chosen using the Profile (F5) function. On opening

the Design page, the lightest section will be chosen for each member. Lighter or heavier

sections of the same profile can then be browsed as required.

Viewing design results

Similar design criteria are applied in Strut and Combine. The presentation of the design

results are however done quite differently. Refer to page 4-29 for detail.


Beam-column member definition

In Combine, internal nodes and effective lengths are defined on the Members page. The data

entered on the Members page is applicable to all design tasks defined on the Input page. To

use different effective lengths for different design tasks lateral support group tasks with

identical effective lengths and save them in separate files.

Defining internal nodes

An internal node is defined as a node in-between the end nodes of a member. When you add

internal nodes, the program joins relevant members to allow for easy input of effective lengths

Adding an internal node

You can add internal as follows:

Enter internal node numbers in the table or click them with the mouse.

Use the Auto Select function to let the program detect all internal nodes.

Removing an internal node

You can remove an internal node by deleting it form the list or by clicking it again in the picture.

Consolidation of members

With the addition of each internal node, the relevant node is 'removed' by joining the two

adjacent members into a single member. The table of members is continuously updated to

show the new member layout.

The program uses the following guidelines to decide which members to join at an internal

node:

For the automatic selection of internal nodes, adjoining members must have the same

section.

Only members with an included angle greater than 100° (where 180° corresponds to a

perfectly straight member) are joined.

Where members of different sections intersect, the larger section defines the main member

that should be joined.

Where two or more members intersect, the internal node is taken to belong to one of the

intersecting members only. The chosen member will be the straightest member or, if the

same, the first in the table of members.


Entering effective lengths

Enter effective length factors as follows:

Apply the same value of Kx, Ky or Ke to all members by clicking the Kx, Ky en Ke

buttons in the table heading.

Enter the effective length factors for individual elements.

Note: The list of internal nodes and effective length factors are automatically saved when

you save the task list. See page 4-17 for detail.

Tip: You can quickly find a member in the

table by pressing Ctrl+F. Enter the member

name by referring to one or both of its end

node numbers.


Design results

In Strut the design results are shown on the Calcsheet page. In Combine, select the Design page

to perform all design tasks and display the design results. All specified load cases and

combinations are considered for each member designed. Unless a very large number of elements

and load cases are involved, the design procedure will normally be completed almost

instantaneously.

By default, the results for the design task active on the Input page are displayed. The results of

any other design task can be displayed by selecting the task from the list (see description below).

If an interactive member design was performed, the displayed results will be for the interactive

design task instead.

The design criteria

The following criteria are used in the design:

The interaction formulae given by the relevant design code are used to evaluate the effect

of axial stress or combined effect of axial stress and bending stress. In calculating the allowable stresses, the program takes account of the member slenderness and effective

tension area.

The slenderness ratio checked against the specified maximum allowable slenderness ratio

for compression and tension.

Note: Strut designs members for axial stress only and ignores any bending stresses.

Viewing design results in Strut

The design results are given in tabular format with 'OK' and 'FAIL' remarks to indicate success or

failure. The mass of each group of elements is summarised below the relevant table. The results of each new design are appended to the bottom of the existing output.

Viewing results in Combine

The complete interaction formulae are displayed for the critical load case of the first member of

the first design task. Individual calculations have 'OK' and 'FAIL' remarks to indicate success or failure.

To view the results of another task, member, section or load case:

Use the Up and Down buttons to move up or down the list of available options. Tasks and

load cases are listed in the order of definition. Sections are ordered by mass. Alternatively

click the item, i.e. sections, and use the Up and Down arrow keys.

Alternatively click the relevant input box and select an item from the list that drops down.


Click the Detailed Equations button to view step-by-step design calculations for the current

member.

Adding results to the Calcsheet page

In Strut, the design results are automatically displayed on the Calcsheet page.

In Combine, the following options are available when adding design results to the Calcsheet

page:

Member to Calcsheet: Add the current displayed member only.

Task to Calcsheet: Add the design results of all members in the current task, including

those members not currently displayed.

All tasks to Calcsheet: Add all members of all tasks.

Note: The level of detail of the information added to the Calcsheet can be set using the Settings function on the Input page. Refer to page 4-22 for detail.


Calcsheet

The design results of all tasks are grouped on the Calcsheet page for sending to Calcpad or

immediate printing.

Use the Output settings function on the Calcsheets page and Settings function on the Input

page for the following:

Embed the Data File in the calcsheet for easy recalling from Calcpad.

Clear the Calcsheet page.



the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the member design

module as well.


Plastic Frame Design

The Plastic Frame Design module can perform a linear elasto-plastic analysis of any general

two-dimensional framed structure. The program can be used in the following plastic design

modes:

The plastic collapse mechanism and load factors can be determined for a series of load

combinations.

The frame’s plastic behaviour can be optimised to achieve more economical sections.

Elastic design of a steel frames can be done using the Plane frame Analysis or Space Frame

Analysis modules in conjunction with the steel member design modules axial and combined stress, Strut and Combine. See Chapter 4 for detail.

Note: This module is no longer developed or supported, and was removed from the program

toolbar in PROKON version 2.4. However, for the sake of users that purchased this module

in the past, it is still access via the Program menu. To evaluate non-linear behaviour of

frames, the recommended procedure is to use the Frame Analysis module and perform a

non-linear analysis. See Chapter 3 for more information.





Design scope

The use of plastic design methods is normally limited to the design of continuous beams and

single storey frames with rigid joints, e.g. portal frames. It may also be acceptable to use plastic

methods for designing some braced multi-storey planar frames.

Determining plastic mechanisms

The program performs an elasto-plastic analysis of plane frames. A rational analysis approach

is followed to obtain a true collapse mechanism for each load case or combination:

1. A linear elastic analysis is performed to determine the position of the first plastic hinge.

2. The bending moment at that position is then limited to the relevant plastic moment while

the position of the next hinge is calculated.

3. The procedure is repeated to obtain more plastic hinges.

4. If the formation of further plastic hinges results in the bending moment at one of the

existing hinges to decrease, that hinge is removed and elastic behaviour re-instated at that

position.

5. The procedure is repeated until a collapse mechanism forms.

Analysis modes

Depending on the analysis module used, the following types of analysis can be performed:

Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically

performed markedly faster than a plastic analysis. It therefore is recommended that you

verify the basic integrity of the frame input by performing a linear analysis prior to

attempting a plastic analysis.

Plastic analysis: Choose between evaluating the adequacy of the frame as entered or

optimising the section sizes. When optimising, the program will search for a more

economic configuration of sections. The plastic modulus, Zpl, is used as the criterion for

section economy.

Two design modes are available during plastic analysis:

No optimisation: Evaluate the frame with sections as entered and calculate the adequacy

against collapse for each load combination.


Optimise sections: Optimise the frame's plastic behaviour by determining more

economical sections.

Design codes

The program uses general plastic theory. Working within their scope, the program can be

considered to support the all the limit state design codes supported by Strut and Combine. See

page 4-6 for a list of design codes.

Note: SABS 0162 - 1984 use an allowable stress design method for elastic design. For plastic design, however, it adopts an ultimate limit state design method.

Sign conventions

Frame input and output uses a mixture of global axis and local axes values.

Global axes

The global axis system is nearly

exclusively used when entering frame

geometry and loading. Global axes are

also used in the analysis output for

deflections and reactions.


The X-axis is chosen to the right.

The Y-axis points vertically upward. A positive vertical load thus works

up and a negative load down.

Using a right-hand rule, the Z-axis

points out of the screen.

Local axes

Local axes are used in the output for element forces. You can also apply loads in the direction of

a beam element's local y-axis. The local axis system is defined as follows for beam elements:

The local z-axis and axial force is chosen in the direction from the smaller node number to

the larger node number.


The x-axis is taken parallel to the global Z-axis, i.e. pointing towards you. A rotation about

the x-axis is thus always anti-clockwise.

The y-axis is taken perpendicular to the x and z-axes, using a right-hand rule.

Beam element forces

The element forces are given in the local

element axis system. The following conventions apply to beam elements:

The axial force, Pz, is taken in the

z-direction.

The shear force, Vy, is taken in the

y-direction.

The moment, Mxx, is taken about the

x-axis, i.e. anti-clockwise.

Note: In this manual the global and local axes are written in uppercase and lowercase respectively.




Distance mm, m ft, inch

Force N, kN lb, kip

Use the Units commands on the Options menu to change the units for the current analysis:

Set Units: Changes the units of measurement without altering the input data.

Convert Units: Changes the units and converts all numeric data from the old to the new

units of measurement.


Input

Work through the relevant Input pages to enter the frame geometry and loading:

General input: Select the analysis type and special analysis parameters.

Nodes input: Frame coordinates.

Beams input: Join nodes with beam elements.

Beam sections input: Enter properties or read sections from the database.

Spring elements input: For special effects, optionally enter spring elements.


Nodal loads input: Point loads and moments.

Beam element loads input: Uniform distributed, triangular and trapezium loads on beams.

Load combinations input: Group dead, live and wind loads in load combinations.

Alternative methods of generating frame analysis input are discussed on page Error!

Bookmark not defined..

Viewing the frame


Several functions, all of which are described in detail in Chapter 2, are available to help you

using pictures of the frame:


Use the View Point Control to set a new view point or camera position.

The Options menu makes the following additional functions available:

Graphics:

Select whether you want items like node numbers and supports to be displayed.

Choose whether you want all beam elements or only a certain type to be displayed.


Display the structure with full 3D

rendering, e.g. to verify section

orientations. 3D rendering is

automatically suppressed when

viewing output.

Choose quick or detailed rendering. Quick rendering is

faster than the detailed method,

but you may find that some

surfaces are drawn incorrectly.

All surfaces are drawn as

polygons. You can choose to make the

surfaces transparent or have them filled

and outlined.

Tip: The Graphics options and 3D rendering

function can also be accessed using the buttons

next to the displayed picture.

Views: You can save the current view point and view plane. The current view's name is

displayed on the picture. To re-use a saved

view, click the view name on the picture to

drop down a list of saved views.

The functions described

above can also be used

when viewing output.

Contour diagrams, for

example, are drawn as

polygons. You can

therefore use the Graphics

options setting for

polygons to change their

appearance. Views defined

during input are also

available when viewing

output and vice versa.


Saving and printing pictures

Any picture can be saved or printed using the relevant buttons next the picture. Pictures on the

Input and Output pages can also be added to the Calcsheets.

Tip: You can zoom into a picture and print, save or add the picture to the Calcsheets.

General input

The General input page handles several important analysis parameters.

Analysis type

Choose between performing a simple linear elastic analysis or a plastic analysis. Refer to page 4-34 for an explanation of the analysis modes.

Plastic design parameters

You need to set the following analysis parameters when performing a plastic analysis:

Plastic analysis tolerance: The plastic analysis is an iterative procedure. The analysis is

deemed to have converged once the total strain energies of two sequential iterations differ

by less than the specified tolerance.

Maximum number of iterations: The analysis procedure calculates as many hinges as

necessary to form a plastic mechanism. You can terminate the analysis at an earlier stage.

A complex analysis that takes a very long time to converge can also be forced terminate

earlier. To force the analysis to end before the formation of the final collapse mechanism,

you can limit the maximum number of iterations to be performed.

Own weight

The own weight of the frame can be calculated using the entered cross-sectional areas and

member lengths. If you specify a load case, the own weight is calculated and added to the other

loads of that case.


By default the own weight of the frame is set to not be included in the analysis. Be sure to




Nodal loads and Beam loads input pages. You may thus prefer to specify the own weight

load case only after completing all other input for the frame. However, you can also enter


the own weight load case at the start of the frame input process in which case you may

ignore the warning message (that the load case does not exist).



Parametrics

The parametric plastic frame

input modules are suitable for the


input files for some typical

structures. Because the resulting input data is presented in the

normal way on the input pages,

you are free to edit and append to

the data as necessary.




repeatedly use the parametric

input modules to generate

complicated structures.

Note: Plasdes is not limited to analysing only those frames generated by the parametric modules. The program can treat any general two-dimensional frame. The parametric

modules merely serve to simplify input of typical frames.






Title

A descriptive name for the frame. It should not be confused with the file name you use when

you save the input data.


Nodes input

Use as many lines as necessary to enter the nodes defining the frame. A unique number must

be assigned to each node. The node number is entered in the No column, followed by the X and

Y-coordinates in the X and Y columns. If you leave X or Y blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the frame. You may also



Error checking

The program checks for nodes lying at the same coordinate. If a potential error is detected, an





The Y-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate

(0.805,0).

The No of is set to '2', meaning that two additional nodes are generated.



The values in the X-inc and Y-inc columns set the distance between copied nodes. The

coordinates 4 to 18 are horizontally spaced at 1.140 m to the right at 0.472 m downward,

i.e. along the X and negative Y-axis respectively. The coordinates of the additional nodes

are thus (1.945,-0.472) and (3.085,-0.944).




Set the values of X-inc, Y-inc and Z-inc to the total coordinate difference to the last node

and enable the Inc to End option. The last node's coordinates are then first calculated and

the specified number of intermediate nodes then generated.


Once you have defined one or more nodes in the table, you can copy that relevant line’s nodes

by entering a '–' character in the No column of the next line. Then enter the number of


the X-inc and Y-inc columns.




No X Y

15 0.00 5.12

16 2.00 5.12

17 4.00 5.12

20 0.00 5.62

21 2.00 5.62

22 4.00 5.62

Block generation


last table line numbers in which the nodes were defined. Separate the line numbers with a '–'.


The nodes defined in lines 11 to 26 are copied twice. Node numbers are incremented by thirty for

each copy. The X and Y-coordinate increments are 10 m and zero respectively.



program's window.

The block generation function may be used recursively. That means that the lines specified

may themselves contain further block generation statements.

Moving nodes

To move a group of nodes to a new location without generating any new nodes, use the block

generation function and set No-of to '1' and Inc to '0'.

Arc generation


the start and end line numbers. Enter the centre of the arc in the X and Y columns and use the

X-inc column to specify the angle increment about the Z-axis.

Example:

All nodes defined in lines 5 to 9 of the table will be repeated eleven times on an imaginary

horizontal arc. The centre point of the arc is located at the coordinate (10.0,1.5). The node



between the generated groups of nodes is 30 degrees about the Z-axis, i.e. anti-clockwise on

the screen using a right-hand rule.

To copy one line only, simply omit the end line numbers, e.g. 'A12' to copy line 12 only.


Rotating nodes



Mirror

Nodes of a plane frame or grillage can be mirrored horizontally or vertically by entering an 'M'

in the No column, followed by the start and end line numbers.

Mirror example:

All nodes defined in lines 5 to 9 are mirrored about a vertical (horizontal for a grillage) line

through X=10 m. Node numbers are incremented with 5. By specifying a Y or Z-value instead

of an X-value, nodes can be mirrored about a horizontal line passing through the specified Y or

Z-value.

Deleting nodes

Nodes can be deleted by entering 'Delete' in the Inc to end column. This can be especially

handy if you have generated a large group of nodes and then need to remove some of them

again.

Example:



Beam elements input

A beam or frame element is defined by entering the node numbers at each end, separated

with a '–'. For example, '3–9' is the element linking nodes 3 and 9. The elements themselves are

not numbered.

A series if elements can be input in a string, e.g. '2-6-10-14-18-22-24'. If the node number

increment of a series is constant, you can replace intermediate nodes with two '–' characters. In

the string above, nodes 2 to 22 has a constant increment of four. Therefore, the string can be

rewritten as '2-6- - 22-24'. The node increment of four is derived from '2-6'.

An element definition must include a section number entered in the Section Name column.

The section name is used to identify the relevant section. The actual section properties for each

section number defined on the Beam Sections input page.


Section orientation

The local y-z plane of an element is taken

in the global X-Y plane. The principle

can be illustrated by considering an I-

section in its normal orientation. For this

case, the web will always be considered

to be in a vertical plane.

A section can be rotated through ninety

degrees by selecting the alternative

orientation when reading it from the

section database.


End fixity

The fixity at each end of an element, i.e. continuous or pinned, must also be defined in the

Fixity columns. Pins are modelled on the element itself and not on the node. External pinned

supports should be defined on the Supports input table. External supports are described in the

next section.

The following types of end fixities can be specified:

Fixed: Specify 'F' to provide full rotational continuity. If you leave the field blank, 'F' is

assumed.

Pinned: Use 'P' to for no rotational restraint, i.e. a pin.

Note: To retain compatibility with the Dos version, you may also use '0' or'1' instead of 'F'

and 'P' respectively.

Entered fixities are applied at an element's lower node number (designated as the 'left' end) and

higher node number (the 'right' end). The order of the node numbers entered in the first column

of the table has no bearing on the application of the fixity codes.

To define a pin only at the two remote ends of a group of elements, enable the Group fix

option by entering a 'Y'. In this case the normal convention of smaller and larger node numbers

does not apply. Instead, pins are put at the remote ends in the same order that the nodes have

been entered.


Example:

The group of elements from node 42 to 24 is continuous except for the pins used at nodes

42 and 24.

If the Group fix is left blank or 'N' is entered, the normal individual element fixity mode is

assumed.

Tip: Element fixity can be displayed graphically on the screen. For this, edit the Graphics

options to disable the Elements Continuous option.

When using pins, you should take care to ensure overall stability of the frame. Consider two

elements on a straight line with pins at all three relevant nodes, for example. The centre node

will be unrestrained for rotation about the element axis, resulting in instability during

the analysis.

Note: Do not use an internal pin on an element to model an external support that allows free

rotation. Rather allow the beam to be fixed to the node and define a simple support on the Support input page.

Tapered beams

The current version of Plasdes does not support tapered sections.

Rigid links

You can use rigid links to rigidly fix sub-structures to each other. To define a rigid link, enter

'R' in the Section Name column.

Rigid links are modelled as very stiff beams. The stiffness of a rigid link is determined by

multiplying the maximum stiffnesses of the other beams with a factor, typically one thousand.

Rigid link example:

Rigid links are defined between nodes 12 and 24, 14 and 26 and 16 and 26.




No of extra and Node No Inc columns. Example:

The elements between nodes 251 and 266 are copied ten times with the node numbers

decrementing by five with each copy.

Block generation


and last table line numbers in which the elements were defined, separated with a '–'.


All elements defined in lines 11 to 26 will be copied twice with a node number increment of

thirty. The copied elements will use the same section number and fixity codes as the original

elements.





Tip: When entering a complicated structure it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert

additional nodes at a later stage without upsetting block and arc generations.

Deleting beams

Beam elements can be deleted by entering a special section name 'Delete'. This can be

especially handy if you have generated a large group of elements at regular increments and

need to remove some of them again.


Example:

Elements 25-27-29 and 35-37-39 are deleted.

Note: The display of selected beam element groups can be activated or suppressed by

editing the Graphic options.

Error checking

The program checks for duplicate elements and elements with zero length. It also checks that a

section number is assigned to each element. If an error is detected, an Error list button will be

displayed.

Beam sections input

Section properties should be assigned to all section names used on the Beam elements input

page. The following properties are required for all sections:

Cross sectional area, A.

Second moment of area about the local x-axis, Ixx.

Plastic modulus about the local x-axis, Zxx.

Each section should also have an associated material selected. If no section or material

properties are entered, the values applicable to the previous line in the table are used.

Reading sections from the database

Use the Section database function to display and select sections from database. You can add

your own sections, e.g. plate girders, to the database using the procedures described in

Chapter 2.

Entering haunches

Haunched sections are entered by appending the haunch depth to the section designation. To

add a haunch of 280 mm to a '305x102x66' BS taper flange I-section, enter '305x102x66

(0.280h)'. The overall depth is then taken to be 305 mm + 280 mm = 585 mm.

Tip: You can verify your definition of haunches by enabling 3D rendering. Refer to page

for 4-15 more detail.


Note: Although haunched sections can be entered, Plasdes does not support analysis of members with tapered sections. A tapered haunch in a typical portal frame, for example,

should be modelled by entering one or more members that approximate the stiffness of the

actual haunch.

Own weight


automatically and added to the load case specified on the General input page.


Selecting materials

Each section should have an associated material. To add one or more materials to a frame

analysis data file, click Materials. Open the relevant material type screen and select the

materials that are required for the current frame input.

After adding the selected materials to the input, you can select them by clicking the Material

column to drop down a list.



Spring elements input

You can use spring elements to provide elastic links between sub-structures. In theory, two

nodes connected with a spring element should have the same coordinates. The program will warn if this is not the case and still allow you to continue.

Note: By default the Spring elements input page is not visible. This behaviour can be

changed using the Advanced command on the Options menu.

Enter linear spring constants in the Kx, Ky and Kz columns and rotational spring constants in the Rx, Ry and Rz columns.

The orientation of a spring element is defined by entering a bearing between any two nodes

that do not necessarily need to be connected to the same or other spring elements as well. The

directions of the axes are defined as followed:

A spring element's x-axis is taken in the direction of the orientating nodes.

The y-axis defined in the same way as for a normal beam element, i.e. perpendicular to

spring element in a vertical plane.

The z-axis is taken perpendicular to the x and y-axes using aright-hand rule.

Spring element example:

Spring elements are defined between nodes 16 and 116, 17 and 117 up to 19 and 119. The

spring elements are aligned parallel to the imaginary line joining nodes 3 and 4.


Tip: Spring elements can also be made "rigid" so as to force two nodes to have the same translation and/or rotation. In the above example, a very large value for Kx would

cause nodes 16 and 116 to have identical displacements in the direction described by

nodes 3 and 4.

Supports input

Frames require external supports to ensure global stability. Supports can be entered to prevent

any of the three degrees of freedom at a node, i.e. translation in the X and Y-directions and

rotation about the Z-axes. You can also define elastic supports, e.g. an elastic soil support, and

prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a

combination of the letters 'X', 'Y' and 'z' can be entered to indicate the direction of fixity. Use

capitals and lowercase to define restraint of translation and rotation respectively, e.g. 'XYz'

means fixed against movement in the X and Y-direction and rotation about the Z-axis.



Tip: To enter a simple support with no moment restraint, you should enter 'XY' or 'Y'.

If you want to repeat the supports defined on the previous line of the table, you need only enter

the node number, i.e. you may leave the Fixity column blank. If the XYZxyz column is left

blank, the supports applicable to the previous line will be used automatically.

Prescribed displacements and elastic supports

Use the X, Y and Rz columns to enter prescribed displacements and rotations in the direction of the X or Y-axis or about the Z-axis. Being a global support condition, the effect of the

prescribed displacement is not considered to be a separate load case. Instead, the effect of

prescribed displacements is added once only to the analysis results of each load case and load

combination.

Elastic supports, or springs, are defined by entering spring constants in the X, Y and z columns.

The spring constant is defined as the force or moment that will cause a unit displacement or

rotation in the relevant direction. Enter an 'S' in the P/S column to indicate that an entered

value is a spring constant rather than a prescribed displacement. If you leave the P/S column

blank, the entered values are taken as prescribed displacements.

Note: The display of supports can be activated or suppressed by editing the Graphic

options.

Error Checking

The program does a basic check on the structural stability of the frame. If a potential error is


Note: You cannot define an elastic support and a prescribed displacement at the same node because it will be a contradiction of principles.






Nodal loads input

Loads on beam elements are categorised as nodal loads, i.e. loads at node points, and element

loads, i.e. loads between nodes. Uniform distributed loads can be applied to shell elements.


'LL' for live load, etc. Load cases apply equally to the various load input screens, meaning that

you can build up a load case using different types of loads.



load case applicable to the previous line in the table is used.

The load case at the cursor position is displayed graphically. Press Enter or Display to update

the picture.

A nodal load can, as its name implies, only be applied at a node. If a point load is required on

an element, use the Beam loads input table instead.

Sign conventions


Nodal loads are applied parallel to the global axes – an explanation of the sign conventions are

given on page 4-35.

Tip: For a typical steel frame or roof truss, it may be easiest to define a node at each purlin position. Roof loads transferred via the purlins can then be entered as nodal loads.

Error checking



Generating additional nodal loads

Additional nodal loads can be generated using the Number of extra and Node number inc

columns respectively.

Block generation of nodal loads

You can use the block function to copy blocks of nodal loads. The procedure is similar to that

for generating additional nodes – see page 4-43 for more detail.

Beam element loads input

Distributed loads and point loads on beam elements are all referred to as element loads. The

Nodal loads input page provides the easiest way of applying point loads and moments at

nodes.

Use up to six characters to enter a descriptive name for each load case in the Load Case

column. Then enter the element string of nodes in the Beam element definition column. Entering the beam element definition follows the same convention used as for the Elements

input table – see page 4-23 for detail.

Sign conventions

Depending on the selected load direction, beam loads are applied parallel to the global axes or

parallel to the local y-axis – the definitions of the global and local axes are given on page 4-35

and 4-35 respectively.

The load direction is entered in the Direction column. Enter a global direction 'X' or 'Y'.

Element loads are applied to the relevant projected length of the elements. Therefore, if a 'Y'

load is entered for a vertical element, for example, the resulting load will therefore be zero.



For a distributed load, entered in the load intensity at the smaller and larger node numbers in

the W-begin and W-end columns respectively. If the load is constant over the length of the

element, W-end may be left blank.

Error checking

The program checks that element definitions match previously defined elements. If an error is



The No of extra and Node number Inc columns can also be used to generate additional

element loads.

Block generation of beam loads


used to generating additional beam elements – see page 4-48 for detail.




the load combination name in the Load comb column, followed by the load case name and

relevant load factors. Use up to six characters for a descriptive load combination name.

If the Load comb column is left blank, the load combination is taken to be the same as for the previous line of the table. The load cases to consider in a load combination are entered one per

line in the Load case column. Enter the relevant ultimate and serviceability limit state load

factors in the ULS factor and SLS factor columns.



The ultimate and serviceability limit states are used as follows:

Deflections are calculated using the entered SLS loads. A set of reactions is also calculated

at SLS for the purposes of evaluating support stability and bearing pressures.

A second set of reactions and all element forces are determined using the entered ULS

forces.


Note: Unlike elastic design, which is done using an allowable stress design technique, plastic design to SABS 0162 - 1984 is done at ultimate limit state. Refer to clause 12.2 and

Table 30 for guidance on load factors to be used.

Error checking


code that will be used in the member design and therefore does not check the validity of the entered load factors.


Analysis

On completing the frame input, you should set the analysis options before commencing the

actual analysis.

Analysis options

Use the General input page to select the analysis mode:

Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically

performed markedly faster than a plastic analysis. It therefore is recommended that you

verify the basic integrity of the frame input by performing a linear analysis prior to

attempting a plastic analysis.

Plastic analysis: Choose between evaluating the adequacy of the frame as entered or

optimising the section sizes. When optimising, the program will search for a more

economic configuration of sections. The plastic modulus, Zpl, is used as the criterion for

section economy.

Note: The results of an optimising plastic analysis should not be regarded as a final solution. You should return to the input data and enter the suggested or other preferred sections and

then re-analyse the frame as a final check.

On the Analysis page, select the following:

Output file: Enter an output file name or accept the

default file name, e.g.

'Pasdes.out'.

Analyse load combinations

only: Enable this option if

the results of only the load

combinations are required.

Generally one would require

results for the load

combinations only. How-

ever, you may have a special

need to view the results of specific load cases as well.

Disable this option to

include the results for the

individual load cases as well.


Analysing the structure

To analyse the structure, open the Analysis page and press Start Analysis. The analysis

progress of displayed to help you judge the time remaining to complete the analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load

combination.


During the input phase, the frame geometry and loading data is checked for errors. Not all


example, could be an accidental error on your side. However, the program is quite capable of

dealing with a situation like this and will therefore allow the analysis procedure to continue.


successfully. Nodes with no elements, for example, have no restraints and will cause numeric

instability during the analysis.



with the analysis, you will be taken to the input table with the error. However, choosing to proceed and ignore the warning, will have an unpredictable result.



example, if you entered incorrect section properties, such as a very small E-value, the mistake may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness

matrix or extremely large deflections. The same applies to the stability of the frame. Although

the frame may appear stable, some combinations of internal hinges may result in some nodes

being unstable.







Viewing output





Diagram can be displayed for the following:

Deflections: Deflections are generally small in relation to dimensions of the structure,

especially in the case of linear analyses. To improve the visibility of the deflection

diagram, you can enter a screen magnification factor. You can optionally display the

deflected shape without the original geometry.

Beam element forces:

Axial forces: The force is

shown as expanded red and

blue lines. Compression forces are shown in red and

tension forces in blue. The

distance of a line from the

element centre line is in

proportion to the size of the

axial force.

Moments: Bending

moments about the local x

and y-axes. A plot factor

can also be entered to

enlarge or reduce the bending moment diagram

on the frame.

Shear: Shear force

diagrams are drawn for the

local y and x-directions. A

beam element's shear force

diagram is constructed by

viewing it with its local z-

axis pointing to the right.

Since the direction of the z-

axis depends on the node numbers, irregular

numbering of nodes can


result in apparent inconsistent signs used in the shear force diagrams. For detail on the

sign conventions used for beam element forces, refer to page 4-36.

Envelopes: Enter a series of elements and select the load case and combinations to

include in the envelopes. Envelopes are drawn using the values as tabulated from the

output file. Positive moments, for example, are drawn below the line and negative

above. Because members of different orientations can be included in the same

envelope, no simple distinction is made between tension and compression faces of members.

Tip: When working with complicated frames, you may prefer adding one or more zoomed

pictures to the Calcsheets instead of a single cluttered picture. To do this, simply into a

picture and then use the Add to Calcsheets function.


Open the Output file page for a tabular display of the frame analysis output file. You can filter

the information appended to the Calcsheets by enabling or disabling the relevant sections.

The Find output function allows you to quickly locate any section of the output file.


Calcsheets

Frame analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To





the frame by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the frame analysis

module as well.


Crane Gantry Girder Design

The Crane Gantry Girder Design module can be used to design and optimise multi-span

crane gantry girders with one or two cranes. Girders may be continuous or simply supported.

The program supports multiple combinations of main beams and capping beams, including

standard I-sections, plate girders and box girders.



A brief summary is given below regarding the design theory and design codes.

Design scope

Crane gantry girders are generally constructed from rolled I-beams or welded plate girder, and

channel capping beams are often used to stiffen top flanges. The program checks and optimises

crane gantry girders made of rolled or welded I-sections or box sections with or without

capping beams. One or two simultaneous cranes can be specified.

The design procedure for crane gantry girders is similar to that used for statically loaded

girders. The various loading codes recognise the varying degree of duty of different types of

crane and give parameters for horizontal transverse effects. In the case of heavier duty cranes,

especially, certain aspects of the design and construction may additional special consideration.

Design codes

The program designs plate girders according to the following design codes:

AISC - 1999 LRFD.

BS 5950 - 1990.

BS 5950 - 2000.

CAN/CSA S16.1-94.

CSA S16-01 - 2001.

IS:800 - 2007.



Symbols

Where possible, the same symbols are used as in the design codes. A list is given below.

A : Cross-sectional area (mm2).

b : Width of capping beam top flange (mm).

bbot : Width of main beam bottom flange (mm).

btop : Width of main beam top flange (mm).

Cw : Warping torsional constant (mm4).


h : Height of section (mm).

Ixx : Second moment of area about major axis (mm4).

Iyt : Second moment of area top flange only (mm4).

Iyy : Second moment of area about minor axis (mm4).

J : St. Venant's torsional constant (mm4).

r1 : Radius between flange and web (mm).

r2 : Outside radius at end of taper flange in (mm).

ry : Radius of gyration about minor axis (mm).

tf bot : Main beam bottom flange thickness (mm).

tf top : Main beam top flange thickness (mm).

tw : Web thickness (mm).

Zpl : Plastic section modulus about major axis (mm3).

Zpt : Top flange plastic modulus about minor axis (mm3).

Zyt : Top flange section modulus about minor axis (mm3).

ß : Angle between web and inside taper flange surface (°).

Stresses, forces and related entities

BS 5950:

F : Applied axial load (kN).

M : Applied moment (kNm).

Ma : Maximum buckling moment in presence of axial load (kNm).

Mb : Lateral torsional buckling resistance moment (kNm).

Mc : Moment resistance in absence of axial load (kNm).



Pc : Compression resistance (kN).

py : Design strength of steel (MPa).

CSA S16.1:

Cr : Factored compression resistance (kN).

Cu : Ultimate compression force (kN).


fy : Yield strength (MPa).

Mr : Factored moment resistance (kNm).

Mu : Ultimate bending moment (kNm).

U1 : Capacity factor to account for moment gradient and second-order effects. The

value depends on the bending moment diagram and the member stability.

Vr : Factored shear resistance (kN).

Vu : Ultimate shear force moment (kN).

ω1 : Equivalent uniform bending moment factor.

ω2 : Moment gradient factor for laterally unsupported members.

SABS 0162 - 1984:

f'cr : 0.6 times the Euler buckling stress (MPa).


Pc : Allowable axial compressive stress (MPa).

Pco : Maximum allowable axial compressive stress (MPa).

Pmc : Allowable compressive bending stress (MPa).

Pmco : Maximum allowable compressive bending stress (MPa).

σc : Average axial compressive stress (MPa).

σmc : Maximum compressive bending stress (MPa)

ω : Coefficient allowing for varying bending moment.

SABS 0162 - 1993:









ω1 : Equivalent uniform bending moment factor.

ω2 : Moment gradient factor for laterally unsupported members.


Design parameters

Various design parameters need to be set when designing a crane gantry girder:

Effective lengths

The codes give guidelines for determining effective length factors for flexural members:

BS 5950: Refer to clause 4.3.5 guidance on factors to use for members in bending. Refer

to clause 4.7.2 and Appendix D for members in compression.

CSA S16.1: Refer to clauses 9.1 to 9.4 and Annexes B and C.



SABS 0162 - 1993: Same as for CSA S16.1.


Input

Design input comprises five categories:

General parameters: Design parameters including general characteristics of the girder, load

factors, support conditions.

Main beam sections: Dimensions and material properties of main beams sections.

Capping beam sections: Dimensions and material properties of optional capping beams.

Spans: Section composition and lengths along the length of the girder.

Crane data: Capacity, weight and dimensions of each crane.

General parameters

Various design parameters, some of which depend on the code used, should be entered.

General design parameters

Spans can be made continuous or simply supported. If this entry is left blank, full

continuity at supports is assumed.

Modulus of elasticity. The entered value is used for all main beam and capping beam

sections.

The rail height is used as eccentricity when applying horizontal crane loads.

The effective length factor for a typical span relates to effective length for lateral torsional

buckling. This will depend on the degree of fixity at the supports and the de-stabilizing

effect of applied loads.

During the analysis each crane is moved step-wise across the beam to determine the force

and deflection envelopes. A larger step can be used for an initial analysis and a smaller

step for the final design. A smaller step size will yield a more accurate analysis and

smoother output diagrams but will result in a longer analysis time.

ULS load factors:

Dead load factor: Factor by which the dead load, i.e. the self-weight of the girder,

bridge and crab, is to be multiplied to obtain the ultimate limit state design load.

Live load factor: Factor by which the live loads are to be multiplied

Combined live load factor: Factor by which both the horizontal and vertical live loads

must be multiplied if they are considered as acting together. This factor is usually

smaller than the normal live load factor.

When designing a girder for two cranes, enter the minimum spacing between the cranes.


You can choose to make either end of the girder pinned (simply supported), fixed (built-in)

or free (cantilevered).

Dynamic load factors and deflection limits

By default, the tabled values are set to those given by the selected design code:

Vertical: Amplification factor for vertical loading per wheel, including the effect of

impact.

Horizontal surge: Factor for transverse force due to acceleration and braking of the crab.

The program assumes that surge forces are transmitted via the wheel flanges. The full

effects of such forces are applied perpendicular to the crane track.

Misalignment: For the effects of misalignment of the bridge's wheels or the crane tracks.

The misalignment forces are applied as two equal opposing forces.

Skewing: Allows for skewing of the bridge. Skewing forces are applied as two equal

opposing forces.

L/D vertical: Vertical deflection limit, given as a ration of the span length.

L/D horizontal: Horizontal deflection limit.

Note: The program does not include the effects of horizontal force due to acceleration, braking or force exerted on end stops.

Design options

Two design approaches are available:

You can choose to evaluate the capacity of entered beam sections to carry the specified

loads.

The main beams and capping beam sections can be optimised to obtain the lightest sections capable of resisting the design loads.

Main beam sections

Enter the properties for all the main beam sections that will be used in the analysis. You can

read the properties of any standard I, H, square or rectangular hollow section from the database.

Plate girder and box girder sections can also be used as main beams. The properties for these

should be entered manually. Only fields relevant to the type of section need be completed:

The designation column is optional and is used to describe a section.

For square and rectangular hollow sections only h, b-top and tf-top are required.


The value for r2 and ß applies to sections with tapered flanges only.

Each main beam section must be given a unique number for easy reference when defining

the girder.

Capping beams section data

Main beam sections may optionally have channels or flat plates as capping beams. Enter each

section that will be used during the analysis. Standard channels can be read from the database

and flat plates can be defined by entering values for h and b.

Each capping beam section must be given a unique number for easy reference when defining

the girder. Main and capping beam sections are numbered independently. The various sections

are combined when defining the girder geometry.

Spans

The data for a typical span comprises a span number, span length, main beam section number

and, if required, capping beam section number.

Information required for each span:


Length : The length of a segment (m). Segment lengths are added to get the total length

of the girder.

Section M : Main beam section number.

Section C : Capping beam section number. Leave blank if no capping beam is used.

Any combination of previously defined main and capping beams may be used. However, you

should take care that the capping beam will correctly fit over the main beam.

Crane data

Enter the loading and dimensional data for the cranes. In the case of a single crane analysis,

simply leave the information for the second crane blank.

Capacity : The rated lifting capacity of crane (T, i.e. 10 kN units).

Class : The crane class designates it’s type of use:

Class Type of use

1 Light duty and hand operated cranes

2 Medium duty cranes

3 Heavy duty cranes

4 Extra heavy duty cranes

Weight bridge : Weight of the bridge assembly (kN).

Weight crab : Weight of the crab assembly (kN). The crab is defined as the portion that

can move across the bridge.

Tip: If the exact value of the crab weight is not known, a value of 15% of the capacity of the crane will usually be a reasonable estimate.

Wheel spacing : Spacing between the bridge wheel assemblies (m).

Wheel load : For web buckling and crippling checks, the maximum load that any single

wheel will exert on the girder is required. This value should be obtained

from the manufacturer's technical data.


Viewing analysis output

The analysis output is displayed

graphically. To view the detailed

design calculation, select the

Calcsheets page.

You can view the following

results and use the mouse to read

values from the diagrams:

The vertical and horizontal

deflected shape of the crane gantry girder.

Ultimate limit state bending

moment diagrams about the

X-X (horizontal) and Y-Y

(vertical) axes. Bending

moment diagrams are drawn

on the tension face of the

girder.

Vertical and horizontal

shear force diagrams.

To append a deflection, moment or shear force diagram to design

results on the Calcsheets page,

first display the diagram and

then click Add to Calcsheets.


Calcsheet

The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad.

The design calculations include the following:

Section properties for each combination of main beam and capping beam sections used.

Web buckling and crippling checks for each section.

Design checks for each span, including checks for the critical section and overall member

strength.

The design output shows the complete interaction formulae, with the zero values for axial

force. If required, the output equations can be edited to include bending about the minor axis.

To edit an equation, select it in the calcsheet, right-click it and choose Edit.


You can later recall the design by double-clicking the Data File object in Calcpad. Because a

data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you

normally will not need to explicitly save your plate girder input using the Save command on

the File menu as well.


Plate Girder Design

The Plate Girder Design module can be used to design I-shaped welded plate girders. The

program checks the behaviour of girders under specified loading and gives guidance regarding

bearing and intermediate stiffeners.



A brief background is given below regarding the application of the theory and principles given

by the design codes.

Design scope

Welded plate girders can often be effectively and economically used as flexural sections. Modern

mechanised manufacturing and automated welding techniques have simplified the production of

plate girders greatly, boosting their popularity.

The program is capable is designing I-shaped sections with identical or different top and

bottom flanges. You can also make the section properties vary along the length of the girder to

model a tapered element.

Tapered sections

CSA S16.1 - M89 and SABS 0162 - 1993 do not cover the design of tapered sections. You can

however choose to use the approach given by BS 5950 - 1990 to design tapered elements.

Bi-axial bending moment

Plate girders are normally used to resist high bending moments and/or vertical shear forces.

The program correspondingly assumes that these effects would govern the design and does not

explicitly perform the checks for bi-axial bending moment.

The design output shows the complete interaction formulae, with the zero values for bending

moments about the minor axis. If required, the output formulae can be manually adjusted to

include bending about the minor axis.

Buckling under axial compression

The program assumes that the effect of axial compression is small and therefore uses the full

moment capacity for bending about the major axis. No capacity reduction is made on account

of buckling about the major axis.

Design codes

The program designs plate girders according to the following design codes:

AISC - 1999 LRFD.

BS 5950 - 1990.

BS 5950 - 2000.

CAN/CSA S16.1-94.

CSA S16-01 - 2001.




Symbols

Where possible, the same symbols are used as in the design codes. A list is given below.


A : Cross-sectional area (mm2).

Bbot : Width of bottom flange (mm).

Btop : Width of top flange (mm).

Cw : Warping torsional constant (mm4).

fyf : Yield strength of flange (MPa).

fyw : Yield strength of web (MPa).

h : Total height of section (mm).

Ix : Second moment of area about major axis (mm4).

Iy : Second moment of area about minor axis (mm4).

J : St. Venant torsional constant (mm4).

ry : Radius of gyration about minor axis (mm).

Tb : Bottom flange thickness (mm).

Tt : Top flange thickness (mm).

Tw : Web thickness (mm).

Zcx : Compression flange section modulus about major axis (mm3).

Ztx : Tension flange section modulus about major axis (mm3).

Zplx : Plastic section modulus about major axis (mm3).

Zply : Plastic section modulus about minor axis (mm3).

Zy : Section modulus of entire section about minor axis (mm3).


BS 5950:

Ag : Gross sectional area (mm2).

F : Applied axial load (kN).


M : Applied moment (kNm).

Ma : Maximum buckling moment in presence of axial load (kNm).

Mb : Lateral torsional buckling resistance moment (kNm).

Mc : Moment resistance in absence of axial load (kNm).



Pc : Compression resistance (kN).

py : Design strength of steel (MPa).

CSA S16.1.:











SABS 0162 - 1984:

f'cr : 0.6 times the Euler buckling stress (MPa).

Pc : Allowable axial compressive stress (MPa).

Pco : Maximum allowable axial compressive stress (MPa).

Pmc : Allowable compressive bending stress (MPa).

Pmco : Maximum allowable compressive bending stress (MPa).

c : Average axial compressive stress (MPa).

mc : Maximum compressive bending stress (MPa)

: Coefficient allowing for varying bending moment.


SABS 0162 - 1993:











Design parameters

Various design parameters need to be set when designing a plate girder:

Effective lengths

The effective length of a member depends on the degree of restraint to be expected at each end

of the member. The program assumes that the effect of axial compression is relatively small

and hence uses the full bending capacity for bending about the major axis.

However, the program allows you to specify positions of restraints for lateral torsional

buckling of the compression flange. You can apply a different effective length factor to each

unsupported length, e.g. different factors for a cantilever end and internal continuous lengths.

Guidelines given in the codes include:

BS 5950 - 1990: Refer to clause 4.3.5 guidance on factors to use for members in bending.

Refer to clause 4.7.2 and Appendix D for members in compression.

CSA S16.1 - M89: Refer to clauses 9.1 to 9.4 and Annexes B and C.



SABS 0162 - 1993: Same as for CSA S16.1 - M89.


Bending moment factors

A flexural member's lateral torsional behaviour is influenced by the shape of its bending

moment diagram. This phenomenon is acknowledged by the design codes through their

introduction of special design factors:

BS 5950-1990: The equivalent uniform moment and slenderness correction factors, m and

n, may not be less than 0.43 and 0.65 respectively.

CSA S16.1 - M89: The equivalent uniform bending moment, 1, may not be less than 0.4

and the moment gradient factor, 2, may not be higher than 2.5.

SABS 0162-1984: The values of the coefficient for varying bending moment, , may not

be less than 0.4. For members subjected to sway, should not be taken less than 0.85.

SABS 0162 - 1993: Same as for CSA S16.1 - M89.

The program automatically calculates the above factors and restrict their values to the

minimum and maximum values specified.


Input

Design input comprises five categories:

General: Design parameters, supports and axial load.

Sections: Dimensions and material properties of section webs and flanges.

Spans: Section variations and lengths along the length of the girder.

Loads: Ultimate loads.

Lateral supports: Compression flange supports.

General parameters

Various design parameters, some of which depend on the code used, should be entered:

The shape of a flexural member's bending moment diagram influences its lateral torsional

stability. The design codes use different design factors to accommodate this phenomenon.

See page 4-82 for more details.

The entered support width is used to calculate local buckling and crushing of the girder's web at every support.

Specify whether the program should calculate and add the girder's own weight in the

analysis.

You can choose to make either end of the girder pinned (simply supported), fixed (built-in)

or free (cantilevered).

Enter an axial force, with a positive force denoting compression (kN or kip).

Note: Although the program allows you to enter an axial force, it does not check for

buckling under axial load. The effect of axial compression is assumed to be so small as not to cause a reduction in the moment capacity for bending about the major axis.

Sections

You can define a variety if I-section by entering the dimensions for the web and top and

bottom flanges. If different grades of steel are used for the flanges and web, you should enter

the appropriate yield strengths for each. Each section should be given a unique number for easy

reference when defining the girder.


Spans

The plate girder is entered as one more continuous

segments. Up to twenty segments may be defined by

entering the following values in the Section Lengths

input table:

Length: The length of a segment (m or ft).

Segment lengths are added to the right hand side

of the girder.

Section Left/Right: Section numbers to be used

at left and right ends of a segment. You can define a tapered section by specifying different

section numbers for the left and right ends.

Note: CSA S16.1 - M89 and SABS 0162 - 1993 do not cover the design of tapered sections.

When designing such elements, the program gives the option to use the weakest portion of such elements or to design of them using the approach given by BS 5950 - 1990.

Loads

Applied loads may comprise distributed loads, point loads and moments. Positive forces and

moments are taken to work downward and anti-clockwise respectively:

Wleft : Distributed load intensity (kN/m or kip/ft) applied at the left-hand starting

position of the load. If you do not enter a value, the program will use a value of

zero.

Wright : Distributed load intensity (kN/m or kip/ft) applied on the right-hand ending

position of the load. If you leave this field blank, the value is made equal to

Wleft, i.e. a uniformly distributed load is assumed.

P : Point load (kN or kip).

M : Moment (kNm or kipft).


of the moment (m or ft). The distance is measured from the left-hand edge of

the girder. If you leave this field blank, a value of zero is used, i.e. the load is

taken to start at the left-hand edge of the beam.


load (m or ft). Leave this field blank if you want the load to extend up to the

right-hand edge of the girder.


Note: Applied forces are taken to be design loads at ultimate limit state. For allowable stress design according to SABS 0162 - 1984, you should enter working loads.

Lateral supports

Specify the positions of lateral support by entering the unsupported lengths. A unique effective

length factor can also be entered for each length. Refer to page 4-69 for more details.

Note: The program always draws the specified lateral supports on the top flange. During the

analysis, however, these positions are taken to define lateral supports of the compression

flange, whether it is the top or bottom flange that is actually in compression.


Viewing analysis output

The analysis output can be viewed graphically. To view the detailed design calculation, select

the Calcsheets page.

You can view the following results and use the mouse to read values from the diagrams:

The deflected shape of the

plate girder.

Ultimate limit state bending

moment diagram. The

bending moment diagram is

drawn on the tension face of the girder.

Ultimate limit state shear

force diagrams.

Bending stresses at ultimate

limit state. The critical

stresses is shown in red.

The shear stresses at

ultimate limit state together

with the shear capacity for

various web stiffener

spacings. The actual stresses are shown in red and the

shear capacities in blue.


Calcsheet

The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad.

The calcsheets include a Data File for easy recalling of the analysis from Calcpad.

The design output shows the complete interaction formulae, with the zero values for bending

moments about the minor axis. If required, the output equations can be edited to include

bending about the minor axis. To edit an equation, select it in the calcsheet, right-click it and

choose Edit.


You can later recall the design by double-clicking the Data File object in Calcpad. Because a

data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you

normally will not need to explicitly save your plate girder input using the Save command on the File menu as well.

Steel Connection Design 5-1

Chapter

5 Steel Connection Design

The steel connection design modules can be used for design of common welded and bolted

steel connection.

Steel Connection Design 5-2

Quick Reference

Steel Connection Design using PROKON 5-3

Base Plate Design 5-5

Moment Connection Design 5-15

Hollow Section Connection Design 5-25

Shear Connection Design 5-33

Simple Connection Design 5-45


Steel Connection Design using

PROKON

The PROKON suite includes several design modules for typical steel connections.

Shear connections

Bolt groups and weld groups can be designed for eccentric in-plane shear.

Moment connections

The following types of moment transmitting connections can be designed:

Stiffened and unstiffened column base plates.

Bolted and welded beam-column connections with or without haunches.

Bolted or welded apex connections with or without haunches.

Axial force connections

Welded hollow section connections can be designed for typical trusses, included triangulated

space trusses.

Simple connections

Simple beam to column connections that do not transmit moments:

Web angle cleat connections.

Flexible end plate connections.

Fin plate connections.


Base Plate Design

The Base Plate Design module designs column base plates subjected to axial force and

bi-axial moment. Both stiffened or unstiffened base plates can be designed. Base plates can

bear on concrete or grout or can be supported on studs. Detailed drawings can be generated for

editing and printing using the PROKON Drawing and Detailing System, Padds.



A brief discussion of the application of the theory is given below.

Design scope and assumptions

The program can analyse column base plates that carry axial force and bi-axial moment. The

following assumptions are made:

The effective applied column force and moment is applied to the base plate as a point load

in the flanges and a uniform distributed load in the webs of the approximated section.

The application of the axial force as uniform distributed load in the webs serves as a

mechanism to model the stiffening effect of the webs on the base plate.

The case of bi-axial bending is simplified by transforming the moments to an effective

design moment about one axis. Given the interaction between the base plate and the

concrete bearing surface, the clauses of the concrete design codes for bi-axially bent

concrete columns are deemed reasonable for this purpose.

The base plate is analysed as a beam on an elastic support. The resulting concrete bearing stresses or stud forces are applied to the base plate during its analysis.

Unstiffened base plates are analysed using elastic theory. A rectangular perimeter that

encloses the column cross-section is considered and the bending stress in the base plate

evaluated on each of its four sides. The required base plate thickness is calculated by

limiting the bending stress on each of the lines that extend from edge to edge and passing

over a side of the rectangle.

Stiffened base plates are analysed using yield line theory. Since this is an upper bound

method, allowable stresses are reduced by 20%.

The interaction between the base plate and supporting concrete or grout layer is taken in

accordance with the relevant code. When using BS 5950 - 1990, for example, the parabolic

stress-strain relationship given in BS 8110 - 1997 is used. Similarly, the parabolic relationship given by SABS 0100 - 1992 is used when designing the base plate using

SABS 0162 - 1993 and CSA A23.3 – M89 for CSA S16.1 - 1989. In the case of allowable

stress design to SAB 0162 - 1984, a linear stress-strain relationship is assumed.


Design codes

The program designs axially loaded steel members according to the following design codes:

BS 5950 - 1990.



Symbols



a1 : Distance from the left edge of the base plate to the centre line of the

bolts (mm).

a2 : Distance from the right edge of the base plate to the centre line of the

bolts (mm).

a3 : Distance from the bottom edge of base plate, as shown on the screen, to the

centre line of the bolts (mm).

a4 : Distance from the top edge of base plate, as shown on the screen, to the centre

line of the bolts (mm)

bg : Bolt grade, e.g. 4.8.

B : Width of the column flange (mm).

D : Overall depth of the column (mm).

fcu : Cube strength of bedding concrete or grout (MPa).

L : Length of the base plate (mm).

L1 : Distance from the left edge of the base plate to the column flange (mm).

Studs : Enter 'Y' if the bolts are used as studs, i.e. the base plate transmits all tension

and compressions forces to the bolts. Enter 'N' to transmit compression forces

to the bedding concrete or grout.

W : Width of the base plate (mm).

W1 : Distance from the top edge of the base plate, as shown on the screen, to the

corner of the column flange (mm).


C : Design compression force in the connection (kN).


T : Design tensile force in the connection (kN).

BS 5950-1990:

Pu : Ultimate design axial force in the column (kN). A positive value is taken as a

downward force and negative value as an uplift force.

Mux : Ultimate design column moment applied about the X-axis (kNm).

Mux : Ultimate design column moment applied about the Y-axis (kNm).

Ys : Yield strength of steel (MPa).

Us : Ultimate strength of weld (MPa).

SABS 0162 - 1984:

P : Working design axial force in the column (kN). A positive value is taken as a


Mx : Working design column moment about the X-axis (kNm).

My : Working design column moment about the Y-axis (kNm).

fy : Yield strength of steel (MPa).

fw : Strength of weld (MPa).

CSA S16.1 - M89 and SABS 0162 - 1993:

Pu : Ultimate design axial force in the column (kN). A positive value is taken as a


Mux : Ultimate design column moment applied about the X-axis (kNm).

Mux : Ultimate design column moment applied about the Y-axis (kNm).

fy : Yield strength of steel (MPa).

fuw : Ultimate strength of weld (MPa).


Input

Define the beam and column connection geometry by entering the relevant information in the

input table.

Column dimensions

To read a column section from the section database, select the section type and choose a

profile. For non-standard sections such as plate girders, you can enter the relevant dimensions.

Tip: To move the column to the centre of the base plate, use the Centralise Column

function.

Forces acting on the connection

Enter the forces transmitted from the column to the base plate using the sign conventions given

in the list of symbols. The entered forces are multiplied by the entered load factors to obtain

the design forces.


Special configurations

You can model some special configurations:

The bolts can be moved inside the column flanges by sufficiently increasing the values of

a1 and a2.

Use a negative column load to model an uplift force.

The input table allows you to change the bolts to studs, i.e. transfer the column loads in the

bolts rather than support the plate on the bedding concrete.


Design

The base plate connection is designed twice, with and without plate stiffeners.

Calculation of design forces acting on the connection

The entered column moments are converted to an effective moment about one axis. The

moment and axial force is then applied to the base plate via the column flanges. For a design

moment about the X-axis, a point load is applied at each of the two column flanges. If the

design moment works about the Y-axis, a trapezium-shaped distributed force is applied over

the width of the flanges.

Analysis of the base plate

In the case of the base plate bearing on concrete or grout, the plate is analysed as a beam on

elastic foundation. The resulting bearing stresses are then used to calculate the moment in the

base plate and the base plate thickness. This approach is slightly conservative due to stiffening effect of the column web being neglected.


The unstiffened base plate thickness is calculated using normal elastic theory. For a stiffened

base plate, however, the required plate thickness is determined using yield line theory. If

tensile forces are dominant, the number of bolts used also influences the plate thickness.

Analysis of the bolts

In the case of the base plate bearing on the concrete or grout, the bolts are designed to resist

tensile forces only. For the case where the bolts are used as studs, the bolts are designed to

resist the full compressions and tension forces. It is then assumed that there is no bearing stress

on the concrete or grout.


Calcsheets

The base plate connection design output can be grouped on a calcsheet for printing or sending

to Calcpad. Various settings can be made with regards to the inclusion of design results and

pictures.



If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it

by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved

as part of a project and therefore does not need to be saved in the connection design module as

well.


Drawing

Detailed drawings can be generated for designed connections. Drawings can be edited and

printed using Padds.

Generating a drawing

Based on your initial input and the design results, initial values are chosen for the dimensions.

Change the values to suite your special requirements.

Required information:

Drawing file name: Name of

the Padds drawing file.

Drawing scale to use.

Connection properties:

Plate thickness.

Stiffener size.

Weld sizes.

Bolt and hole sizes and

quantities.

Press Generate to create a

Padds drawing with the entered

settings.


Moment Connection Design

The moment connection design modules are suitable for the design of the following

connections:

Beam-column connection, BeamCol: Beam connected to the flange of a column.

Apex connection, Apex: Symmetrical beam apex with end plates.

The connections incorporate beams and columns made of I and H-sections.



The following text gives a brief background of the application of the design codes.

Design scope

The moment connection design modules can analyse connections that transmit shear, moment

and axial force. Only forces in the plane of the connection are considered, i.e. vertical shear,

axial compression or tension and in-plane moment. The connections may be bolted or welded.

The following assumptions are made:

The centre lines of the connecting beams or beam and column are in the same plane.

All bolt holes are normal clearance holes.

Bolts have threads in their shear plane.

Connections are deep enough for each section’s flanges to resist the prevailing

compressive and tensile forces.

Compressive forces in the flanges and stiffeners are transmitted through the welds and not through bearing.

The following additional assumptions apply to BeamCol:

Any axial force in the column is ignored.

Longitudinal and transverse welds in the web plates are full size butt welds.

Codes of practice

The following codes are supported:

AISC - 1993 LRFD.

BS5950 - 1990.

BS5950 - 2000.

CAN/CSA S16.1-94.

Eurocode 3 - 1992.

IS:800 - 2007.

SABS0162 - 1984 (allowable stress design).

SABS0162 - 1993.

SANS 10162 - 2005.



Both Metric and Imperial units of measurement are supported.

Sign conventions

Design loads are the forces transmitted by the right-hand side beam onto the connection:

A positive axial force is taken as a compression force.

A positive moment corresponds to a tensile force in the top flange of the beam.

Downward shear is taken as positive.

Tip: Positive loads on the connection correspond to the directions of forces in a typical single bay portal frame subjected to dead and live load.

List of symbols

Where possible the same symbols are used as in the design codes. The meanings of the

symbols are clear from their use in the design output.

Analysis of bolted moments connections

When moments are transferred by bolted connections the bolts are loaded in tension (and

shear). The programs allow you to use an elastic or plastic method of analysis for determining

the bolt forces:

With an elastic analysis, the bolt furthest from the compression flange will have the largest

tensile force. Forces load will reduce linearly in bolts closer to the compression flange.

In the case of a plastic analysis, all the bolts have the same force.

Prying action

In moment connection, prying action can be prevalent. The prying forces and method of failure

depend on the layout of the design, the thickness of the plate or flange in question and the

strength of the bolts.

A yield line analysis method is used to calculate three resistance values for each relevant

portion of the connection:

Plate yielding at the web and the bolts.

Plate yielding at the web and bolt failure.

Bolt failure only.

The smallest of the three resistance values is taken to be the ultimate resistance.


Input

The moment connection design modules use a similar procedure for data entry:

Members: Set the connection type and properties of the beams or beam and column.

Setting: Select the connection type and main design parameters.

Loads: Enter the loads applied to the connection.

Members

Define the type of connection and the design parameters:

Define the connection type by selecting an end plate configuration, e.g. no end plate, end

plate flush at the top and bottom of the beam or extending at the tope and/or bottom.

Beam and column designations.

Inclination of the beam.

Haunch depth and length. If either value is zero, no haunch is used.

Settings

Use Settings to set the bolt, weld and member material properties:

Select between elastic and plastic

analysis of bolts in tension. The

analysis mode determines the distribution of the bolt forces. See

page 5-17 for detail.

Enter a bolt type, grade and

diameter. For high strength

friction grip bolts, additional

information needs to be supplied

with regards to the analysis

method.

Enter the strength properties of the

beam, column and connection

members.

Specify the weld strength.

Note: If you need to modify the available bolt grades or bolt sizes, edit the General

Preferences from the Settings menu in Calcpad.


Loads

Enter any number of load cases. For each load case:

Use a maximum of six characters to enter a descriptive load case name or load case

number, e.g. 'Dead', 'DL + LL' or '1'.

Specify the axial force, shear force and moment that the right-hand side beam exerts on the connection.

The SLS factor is divided into the entered ULS loads to obtain service loads.

Note: All entered loads should be ULS loads. The corresponding SLS loads are obtained by

dividing the entered ULS loads by the SLS factor. The SLS factor should thus be set equal

to the relevant ULS load factor divided by the SLS load factor.


Design

The design table lists all variable dimensions and parameters of the connection. A value for

any property in the table can be calculated using the Optimise function. You can also

selectively fix values for any individual properties to suite your preferences:

Select values for all properties that should have specific values. To obtain a specific bolt

layout, for example, enter preferred values for the bolt offsets.

Set the values of all other properties to "Optimise".

Click Optimise to calculate values for the latter.

Tip: For a table summarising the design results, go to the Calcsheet page.


After optimisation, you should evaluate each of the values calculated by the program. You are

then free to refine the results by selectively entering more appropriate values. After adjusting

some values, you may wish to optimise some of the other values again.

Note: Several valid design solutions are possible for any particular connection. The optimised results calculated by the programs should be regarded as one such solution.


Calcsheet

Open the Calcsheet page to view the detailed design calculation. The information on the can

be printed or sending to Calcpad. Various settings can be made to include input data, tabular

design summaries and the complete design calculations.



The Data File can be included when sending a calcsheet to Calcpad. You can later recall the

data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the connection design

module as well.


Drawing

Detailed drawings can be generated for designed connections. Drawings can be edited and

printed using Padds.

Printing or saving a drawing

A drawing is displayed using the dimensions of the final design. To save or print the drawing

to disk, use the buttons next to picture. Drawings can be saved a variety of formats, including

Padds and DXF formats.


Hollow Section Connection

Design

The Hollow Section Connection Design module does a complete design of welded structural

hollow section connections. The connecting members may transmit axial force and can be

circular, square or rectangular hollow sections. I-sections and H-sections can also be used for

the main chord.



The program designs structural hollow section connections that transmit axial forces. Various

connection layouts can be designed. These include K, T, N, X, and Y joints and combinations

thereof.

Design codes

The program designs according to recommendations given in Annex K of Eurocode 3 - 1992.

Symbols

Where possible, the same symbols and sign conventions are used as in the design codes:

Section dimensions

bi : Width of a section (mm or inches).

hi : Height of a section (mm or inches).

hw : Web height of an I-section or H-section (mm or inches).

i : Section number. The main chord is identified by i = 0 and the left, right and

centre chords by i = 1 to 3 respectively.

ro : Radius between the web and flange of an I-section or H-section (mm or

inches).

ti : Thickness of a section, i.e. wall thickness of a hollow section or flange

thickness of an I-section or H-section (mm or inches).

tw : Web thickness of an I-section or H-section (mm or inches).

Joint geometry

g : The clear gap between bracing as measured member on the chord surface (mm

or inches). A negative value denotes an overlap.

Symmetry : Enter 'Y' to make an X-joint symmetric, i.e. mirrored about the main chord. If

you enter 'N', bracing members continue along their axes to the other side of

the main chord.

X-joint : Enter 'Y' to put bracing elements on both sides of the main chord, i.e. an X-

joint. This option can only be used in combination with K, N and T joints

where a circular hollow section is used as the main chord. Enter 'N' for bracing

members on one side of the main chord only.


: Out-of-plane separation angle between two sets of bracing members (°). The angle must lie between 60° and 90°. This option is useful when modelling

joints in triangulated trusses. If this option is used, all setting relating to

X-joints are ignored. Leave this field blank if you do not want to use this

option. The option can only be enabled when a circular hollow section is used

as main chord.

1 : Angle between the main chord and the left bracing member (°). The angle must be between 30° and 90°.

2 : Angle between the main chord and the right bracing member (°). The angle must be between 30° and 90°.

3 : Angle between the main chord and the centre bracing member (°). The angle

must be between 30° and 150°. The angle must also by greater than 1 and

smaller than (180° - 3).

Forces and stresses

Es : Modules of elasticity of steel (GPa or Mpsi).

fy : Yield strength of main chord or bracing members (MPa or ksi).

N0 : Ultimate axial force in the main chord (kN or kip). A positive value denotes a

compression force.

N1 : Ultimate axial force in the left bracing member (kN or kip). A positive value

denotes a compression force.

N2 : Ultimate axial force in the right bracing member (kN or kip). A positive value

denotes a compression force.

N3 : Ultimate axial force in the centre bracing member (kN or kip). A positive value

denotes a tensile force.


Both Metric and Imperial units of measurement are supported. When changing from one

system of units to another, the program automatically converts all input data.


Input

The definition of the connection requires you to enter geometrical and loading data.

Chord and bracing sections

Click Section Database to read a chord or bracing section from the section database. The main

chord can be an I-section, H-section or a circular, square or rectangular hollow section. You

can use circular, square or rectangular hollow sections as bracing members.

The following general guidelines apply when defining bracing members:

You should define at least one bracing member.

A single bracing member should be entered as either the left or right bracing member.

The centre bracing member can be defined only after defining both the left and right

bracing members.

X-joints can be defined only if the main chord is a circular hollow section.

X-joints can be made symmetric by enabling the relevant option in the table.

A separation angle for a 3D joint can only be used if the main chord is a circular hollow

section.

Tip: Use the 3D rendering option to view and rotate the connection in 3D.


Forces acting on the connection

Enter the forces in each member using the sign conventions displayed in the picture. With the

exception of the right bracing member, positive forces work in compression towards the centre

of the connection.


Design

The design checks are performed as prescribed in the code, including the following:

Geometrical evaluation of the connection to ensure compliance with the design codes.

Checking the main chord for plastification.

Checking punching shear of the main chord.

Design of welds.


Calcsheet

The connection design output is given on a calcsheet. You can choose to print the information

immediately or rather send it to Calcpad.

Tip: The Data File embedded in the calcsheet can be used for easy recalling of the design from Calcpad.


The Data File is automatically included when sending a calcsheet to Calcpad. You can later

recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in

Calcpad is saved as part of a project and therefore does not need to be saved in the connection

design module as well.


Shear Connection Design

The shear connection design modules are suitable for the design of the following connections:

Bolt Group Design, Boltgr: Eccentrically loaded bolt groups.

Weld Group Design, Weldgr: Eccentrically loaded weld groups.



When a bolt group or weld group is loaded in its plane and the load does not work through the

centroid of the group, additional shear forces are caused in the bolts or welds. The shear

connection design modules calculate the maximum resistance of bolt and weld groups.

The modules also determine the smallest bolt or weld size that can be used to resist an in-plane

force with arbitrary orientation. In the case of bolt groups, both the cases of single and double

shear can be considered.

The groups are analysed using either linear or non-linear strength relationships.

Design codes

The programs support the following design codes:

AISC - 1999 LRFD.

BS 5950 - 1990.

BS 5950 - 2000.

CAN/CSA S16.1 - 94.

Eurocode 3 - 1992.

IS:800 - 2007.


SABS 0162 - 1993.

Symbols


Bolt group geometry

d : Bolt Size.

a1 : Horizontal bolt spacing

a2 : Vertical bolt spacing

nr : Number of rows of bolts in the group.

nc : Number of columns.


Material properties

fu : Ultimate strength of steel or weld.

fy : Yield strength of steel.

Applied loads

F : Force.

x : Force horizontal eccentricity

y : Force vertical eccentricity

: Force angle


Both Metric and Imperial units of measurement are supported. In addition, you can also choose

between units within the selected system, e.g. between mm and cm.

Analysis principles

The program designs bolt groups and fillet weld groups subjected to eccentric shear using

either linear or non-linear strength relationships.

Linear analysis

Eccentrically loaded fastener groups are usually analysed by considering the group areas as an elastic cross-section subjected to direct shear and torsion. Assuming elastic behaviour, the

group's centre of rotation is taken as the group's centroid. The deformation of each fastener is

then assumed proportional to its distance from the assumed centre of rotation.

The elastic method has been popular because of its simplicity and has been found conservative.

Salmon and Johnson1 quotes the ratio between actual strength and service loads to be in the

range of 2.5 to 3.0.

Non-linear analysis

The non-linear method, also called plastic analysis or instantaneous centre of rotation method,

assumes that the eccentric load causes a rotation as well as a translation effect on the fastener

group. The translation and rotation is reduced to a pure rotation about a point defined as the

instantaneous centre of rotation.

1 C. G. Salmon and J. E. Johnson, "Steel Structures, Design and Behaviour", Third Edition

(1990), Harper Collins Publishers.


Similar to the linear method, the deformation of each fastener is taken proportional to its

distance from the instantaneous centre of rotation. The load in each fastener is however

determined using the non-linear strength expression proposed by Fisher2 and used by

Crawford and Kulak3:

55.0101 eRR ulti

The relationship assumes a bearing-type connection and ignores slip. The coefficients 10 and

0.55 were experimentally determined. For the given experimental setup, the maximum

deformation, , at failure was about 0.34 inches (8.6 mm).

Salmon and Johnson1 conclude that the plastic analysis method is the most rational approach

to obtain the strength of eccentric shear connections.

Application of the non-linear strength relationship

For the purpose of its application

in the connection design

modules, the strength relationship

has been normalised and

rewritten:

55.04.31018.1 eRnorm

The capacity of a fastener group

is governed by the yield of the

fastener furthest from the

instantaneous centre of rotation.

Taking the deformation at that

point as unity, the normalised

deformations for the other

fasteners are determined using linear variance. The force of each

fastener is calculated using the

strength relationship.

2 J. W. Fisher, "Behaviour of Fasteners and Plates with Holes", Journal of the Structural

Division, ASCE, 91, STD6 (December 1965). 3 S. F. Crawford and G. L. Kulak, "Eccentrically Loaded Bolted Connections", Journal of the

Structural Division, ASCE, 97, ST3 (March 1971).


Non-linear analysis of weld groups

Although the load-deformations characteristics of fillet welds depend on the direction of

loading, current design codes generally use a lower bound approach based on the longitudinal

strength, irrespective the actual loading direction. An expression developed by Lesik and

Kennedy4 can be used to determine the ultimate strength of fillet welds loaded in any

direction.

Assuming that the resistance for compression and tension-induced shear is the same, the resistance of a weld element for the calculated angle of loading is given by:

0.1sin5.05.1 uRR

where

Ru = Ultimate strength of a fillet weld loaded with longitudinal shear

R = Resistance of a fillet weld when the loading angle equals .

The relationship was determined empirically and implies the resistance in a weld element will

vary between 1.0Ru for longitudinal shear and 1.5Ru for transverse shear.

Application of non-linear method

The program divides the weld group into a discrete number of finite weld elements. When

performing a non-linear analysis, the instantaneous centre of rotation is determined through

iteration. The following criteria are used:

The Lesik and Kenedy equation is used to determine the resistance of each weld element

for the relevant load direction.

The deformation in an element is taken to vary linearly with the distance from the

instantaneous centre of rotation. At ultimate limit state, the element furthest from the

centre of rotation is assumed to experience the maximum deformation.

The ultimate resistance of each element for longitudinal shear is determined using the

non-linear strength relationship explained above.

4 D. F. Lesik and D. J. L. Kennedy, "Ultimate Strength of Eccentrically Loaded Fillet Welded

Connections", Structural Engineering Report 159, Department of Civil Engineering, University

of Alberta


Input

The definition of bolt groups and weld groups follow the same basic pattern. However, the

geometry of weld groups is entered using a slightly more complex method of polygon

definition.

Defining bolt groups

A bolt group analysis requires the following input:

Analysis method.

Number of shear planes, i.e. single or double shear.

Number of rows and columns of bolts.

Horizontal and vertical spacing of the bolts.

Applied force, its orientation and offsets.

Defining weld groups

A weld group definition has the following components:

Analysis method.

Material strengths.

In-plane force, angle and offsets.

Weld geometry.

The weld group input table

A weld group's geometry is defined by entering one or more shapes in the input table. A shape

may comprise straight lines and arcs or may be a circle. When more than one shape is entered,

the shapes will accumulate and form one weld group.

To be able to enter a weld, you should understand the use of the input table:

The Code column is used for categorise the data that follows in the next columns:

'+' : The start of a new weld. An absolute reference coordinate must be entered in

the X/Radius and Y/Angle columns.

Blank : Indicates a line drawn with relative coordinates.

'L' : Indicates a line drawn using polar coordinates.


'A' : An arc that continues from the last line or arc. The arc radius and angle are

entered in the X/Radius and Y/Angle columns respectively. The angle is

measured anti-clockwise from the previous line or arc end point.

'B' : Sets the bearing, or starting angle, for the next entity, likely an arc.

'C' : A circle with the radius entered in the X/Radius column.

Note: If the Code column is left blank, relative coordinates are used.

The X/Radius and Y/Angle columns are used for entering coordinates, radii and angles:

X : Absolute or relative X-coordinate. Values are taken positive to the right and


Radius : Radius of a circle or an arc.

Y : Absolute or relative Y coordinate. Values are taken positive upward and

negative downward.

Angle : Angle that an arc is extending through.

Note: If the X/Radius or Y/Angle column is left blank, a zero value is used.


Weld group definition

The definition of each portion of a weld group has three basic components:

A reference coordinate which gives the starting point of a weld or the centre of a circle. In

the Code column, enter a '+' to indicate the start of a new weld.

One or more entries defining the weld's coordinates of lines and arcs or a circle’s radius.:

Enter the absolute values of the reference coordinate in the X/Radius and Y/Angle

columns.

If the Code column is left blank, the coordinate is taken relative from the last point

entered.

Set the Code to '+' if you want to enter an absolute coordinate.

The coordinate values are entered in the X/Radius and Y/Angle columns. A negative

X or Y coordinate must be preceded by a minus sign. The plus sign before a positive

X or Y coordinate is optional.

A circular arc is defined by setting the Code to 'A' and entering the radius in the

X/Radius column. The arc is then taken to extend from the end point of the last line

or arc, starting at the angle that the previous line or arc ended and extending through

the angle specified in the Y/Angle column. To set the bearing, or starting angle, of an arc use a 'B' in the Code column followed by the angle in the Y/Angle column.

Define a circle by setting the centre point using the Code '+' described above. On the

next line enter the Code to 'C' and the radius in the X/Radius column.

The weld size.

Weld generation

Click the 'standard' shapes for

quick generation of welds.

Enter the required dimensions

and orientation angle. Press

Add to input to append the

shape to the bottom of the

table. The default values of X, Y and ß are set to the ending

values of the last weld

segment.


Design

Shear distribution in bolt groups and weld groups are calculated in similar ways:

Calculation of design shear forces in bolt groups

A simple procedure is followed during linear analysis:

The applied force causes an equal force in each of the bolts parallel to the force.

The rotational shear force in each bolt is taken proportional to the distance to the centroid.

Non-linear analysis requires an iterative procedure:

An arbitrary rotational centre is chosen.

The strain of each bolt is proportional to its distance from the centre.

The force on each bolt is calculated assuming the non-linear strength model explained

form page 5-35.


Equilibrium of external and internal forces is considered and the rotational centre adjusted.

This procedure is repeated until convergence is achieved.

Calculation of design shear stresses in weld groups

Assuming linear variation, rotational shear stresses in a weld group is calculated as follows:

The centroid of the weld group is calculated.

The rotational shear force in each segment of a weld is taken proportional to its distance

from the centroid.

Non-linear analysis requires an iterative procedure:

An arbitrary rotational centre is chosen.

The strain in each segment of the weld is taken proportional to its distance from the centre of rotation.

The force on each segment is calculated assuming the non-linear strength relationship

explained from page 5-35.

External and internal forces are compared and the centre of rotation adjusted to improve

equilibrium.

This procedure is repeated until convergence is achieved.


Calcsheet

The connection design output can be grouped on a calcsheet for printing or sending to

Calcpad. Various settings can be made to include input data, tabular design summaries etc.





Calcpad is saved as part of a project and therefore does not need to be saved in the connection

design module as well.


Simple Connection Design

The simple connection design modules are suitable for the design of the following connections:

Double Angle Cleat Connection Design, Cleat: Web cleat connections.

End Plate Connection Design, Endplate: Flexible end plate connections.

Fin Plate Connection Design, Finplate: Fin plate connections.



The following text gives a brief background of the application of the design codes.

Design scope

The simple connection design modules can analyse connections that transmit end shear and

axial force only. A designed connection has negligible resistance to rotation and is thus

incapable of transmitting significant moments at ultimate limit state.

The following assumptions are made:

The centre lines of the beam and column are in the same plane.

The connection transmits end shear only.

Bolts have normal clearance holes.

All bolts have threads in their shear planes.

Codes of practice


AISC - 1993 LRFD.

BS5950 - 1990.

BS5950 - 2000.

CAN/CSA S16.1 - 94.

Eurocode 3 - 1992.

IS:800 - 2007.

SABS0162 - 1984 (allowable stress design).

SABS0162 - 1993 (limit state design).




Sign conventions

All applied shear forces are entered as loads in the beam’s local axes:

A positive axial force is taken as a compression force.

A downward shear force is taken as positive.

List of symbols

Where possible the same symbols are used as in the design codes. The meaning of the symbols

should be clear from their use in the design output.

Analysis of bolts in shear

Bolt groups in shear can be analysed using a linear or non-linear strength relationship. Refer to

page 5-35 for a detailed explanation of the analysis methods.


Input

The simple connection design modules use a similar procedure for data entry:

Settings: Select the connection type and main design parameters.

Members: Specify the properties for the beam and column.

Connection: Define the layout of the fasteners.

Loads: Enter the loads applied to the connection.

Members

Define the connection orientation and profile to use for each member:

Select a connection type by clicking the Member orientation buttons.

The column and the beam can be set to I or H-sections.

The definition of the connecting member depends on the type of connection:

Double angle cleat connection: Select an angle section and enter the cleat length.

Fin plate and end plate connections: Enter a plate height, width and thickness.

Define the relative element positions by entering the spacing between the column and

beam and the vertical position of the cleat or connecting plate.

Tip: Click the Auto size and Auto spacing buttons for quick input of workable dimensions.

Design parameters

Select the connection shear

analysis method and define the

fastener and member material

properties:

Select between linear and

non-linear analysis of bolts

in shear. For a detailed

explanation of the analysis

methods, refer to page 5-35.

Enter a bolt type, grade and

diameter. For high strength

friction grip bolts, additio-

nal information needs to be


supplied with regards to the analysis method.

Enter the strength properties of the beam, column and connection members.

Connections

The layout of the bolts on the

connecting member is defined

by entering their number and

spacing.

In the case of angle cleats, the

connections to the beam and

column are defined indepen-dently.

Tip: Click the Auto size and

Auto spacing buttons to

quickly input a workable bolt

layout.

View connection

To verify that you have defined

the connection geometry as you intended, you can view it from

several angles:

Dimensioned elevations are

an easy way to check bolt

spacings and the spacing

between the members.

Use the 3D view to verify

the overall layout and check

that bolts are far enough

from webs and flanges. You

can rotate a 3D view and use the View point and

View plane controls as

described in Chapter 2.


Loads

Enter any number of load cases. For each load case:

Use a maximum of six

characters to enter a

descriptive load case name

or load case number, e.g.

'Dead', 'DL + LL' or '1'.

Specify the end shear forces

by entering the axial force

and shear force in the beam.

When designing high

strength friction grip bolts at

serviceability limit state,

also enter the relevant

service loads.


Calcsheet

Open the Calcsheet page to design the connection. The design output is grouped on a calcsheet

for printing or sending to Calcpad. Various settings can be made to include input data, tabular

design summaries and the complete design calculations.

To view the individual bolt forces, open the Bolt forces page.



The Data File can be included when sending a calcsheet to Calcpad. You can later recall the

data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad

is saved as part of a project and therefore does not need to be saved in the connection design

module as well.

Concrete Design 6-1

Chapter

6 Concrete Design

The concrete design modules can be used for the design of reinforced and pre-stressed concrete

beams and slabs, columns, column bases and retaining walls.

Concrete Design 6-2

Quick Reference

Concrete Design using PROKON 6-3

Continuous Beam and Slab Design 6-5

Pre-stressed Beam and Slab Design 6-41

Finite Element Slab Analysis 6-97

Rectangular Slab Panel Design 6-125

Column Design 6-137

Retaining Wall Design 6-155

Column Base Design 6-171

Section Design for Crack width 6-185

Concrete Section Design 6-193

Punching Shear Design 6-201


Concrete Design using

PROKON

Several concrete design modules are included in the PROKON suite. These are useful tools for

the design and detailing typical reinforced and pre-stressed concrete members.

Beam and slab design

The Continuous Beam and Slab Design and Pre-stressed Beam and Slab Design modules

are used to design and detail reinforced and pre-stressed beams and slabs. Simplified design of

flat slab panels is available through the Rectangular Slab Panel Design module. In contrast,

the Finite Element Slab Design module is better suited for the design of slabs with more

complicated geometries. Punching shear in flat reinforced concrete slabs can be checked with

the Punching Shear Design module.

Column design

Rectangular Column Design and Circular Column Design offer rapid design and detailing

of simple short and slender columns. Columns with complicated shapes can be designed using

the General Column Design module.

Substructure design

Use the Column Base Design and Retaining Wall design to design and detail typical bases

and soil retaining walls.

Section design

Two modules, Concrete Section Design and Section Design for Crack width, are available

for the quick design of sections for strength and crack width requirements.


Continuous Beam and

Slab Design

The Continuous Beam and Slab Design module is used to design and detail reinforced

concrete beams and slabs as encountered in typical building projects. The design incorporates

automated pattern loading and moment redistribution.

Complete bending schedules can be generated for editing and printing using Padds.



The following text gives an overview of the theory and application of the design codes.

Design scope

The program designs and details continuous concrete beams and slabs. You can design

structures ranging from simply supported single span to twenty-span continuous beams and

slabs. Cross-sections can include a mixture rectangular, I, T and L-sections. Spans can have

constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. At

ultimate limit state, moments and shears are redistributed to a specified percentage.

Reinforcement can be generated for various types of beams and slabs, edited and saved as

Padds compatible bending schedules.

Design codes


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.

Reinforcement bending schedules are generated in accordance to the guidelines given by the

following publications:

General principles: BS 4466, BS 8666 and SANS 282.

Guidelines for detailing: 'Standard Method of Detailing Structural Concrete' published by the British Institute of Structural Engineers.


Sub-frame analysis

A two-dimensional frame model is constructed from the input data. Section properties are

based on the gross un-cracked concrete sections. Columns can optionally be specified below

and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.

Pattern loading

At ultimate limit state, the dead and live loads are multiplied by the specified ULS load

factors (see page 6-14). Unity load factors are used at serviceability limit state. The following

load cases are considered (the sketch uses the load factors applicable to BS8110):

All spans are loaded with

the maximum design load.

Odd numbered spans (spans

1, 3, 5, etc.) are loaded with the minimum design dead

load and even numbered

spans (spans 2, 4, etc.) with

the maximum design

ultimate load (dead plus

live load).

Even numbered spans are

loaded with the minimum

design dead load and odd

numbered spans loaded

with the maximum design ultimate load.

Note: The case where any two adjacent spans are loaded with maximum load and all other

spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, is not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

SABS 0100 - 1992 suggests a constant ULS dead load factor of 1.2 for all pattern load

cases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for

calculating the minimum ultimate dead load. The program uses the more approach given

by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and

the maximum load factor specified for maximum dead load.


The South African loading code, SANS 10162, prescribes an additional load case of

1.5×DL. This load case is not considered during the analysis – if required, you should

adjustment the applied loads manually. In cases where the dead load is large in comparison

with the live load, e.g. lightly loaded roof slabs, this load case can be incorporated by

increasing the entered dead load or increasing the ULS dead load factor. This adjustment

applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using

an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.

Moment redistribution

Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is

set to 'optimised', the design moments are further minimised by redistributing span moments

upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern

loading and then

redistributed using the

procedures explained in the

following text.

Downwards redistribution

The downward distribution

method aims to reduce the

hogging moments at the

columns without increasing

the sagging moments at

midspan. The redistribution of moments and shear forces

procedure is performed as

follows:

1. The maximum hogging

moment at each column

or internal support is

adjusted downward by

the specified maximum

percentage.

2. The corresponding span

moments are adjusted


downward to maintain static equilibrium. The downward adjustment of hogging moments

above is limited to prevent any increase in the maximum span moments of end spans.

3. The shear forces for the same load cases are adjusted to maintain static equilibrium.

Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward

distribution of the span moments. The envelopes for the three pattern load cases are

redistributed as follows:

1. The maximum hogging moment at each internal support is adjusted downward by the

specified percentage. This adjustment affects the moment diagram for the load case where

the maximum design load is applied to all spans.

2. The relevant span moments are adjusted accordingly to maintain static equilibrium.

3. The minimum hogging moment at each internal support is subsequently adjusted upward

to as close as possible to the reduced maximum support moment, whilst remaining in the

permissible redistribution range. A second load case is thus affected for each span.

4. The relevant span moments are adjusted in line with this redistribution of the column

moments to maintain static equilibrium.

5. For each span, the moment diagram for the remaining third load case is adjusted to as near

as possible to the span moments obtained in the previous step. The adjustment is made in such a way that it remains within the permissible redistribution range.

6. Finally, the shear force envelope is adjusted to maintain static equilibrium.

7. The following general principles are applied when redistributing moments:

8. Equilibrium is maintained between internal and external forces for all relevant

combinations of design ultimate load.

9. The neutral axis depth is checked at all cross sections where moments are redistributed. If,

for the specified percentage of moment redistribution, the neutral axis depth is greater than

the limiting value of (ßb0.4)d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

10. The amount of moment redistribution is limited to the specified percentage. The maximum

amount of redistribution allowed by the codes is 30%.

Note: The exact amount of moment redistribution specified is always applied, irrespective of the degree of ductility of the relevant sections. Where necessary, ductility is improved by

limiting the neutral axis depth. This is achieved by adding additional compression

reinforcement.


Deflection calculation

Both short-term and long-term deflections are calculated. No moment redistribution is done at

serviceability limit state.

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-

cracked concrete sections are used.

Long-term deflections

Long-term deflections are determined by first calculating the cracked transformed sections:

1. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

2. The cracked transformed sections are then calculated at 250 mm intervals along the length

of the beam. The results of these calculations are tabled in the Crack files on the View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the

amount of reinforcement required at ULS. However, once reinforcement is generated for

beams, the actual entered reinforcement is used instead. You can thus control deflections by

manipulating reinforcement quantities.

Next, the long-term deflection components are calculated by numerically integrating the

curvature diagrams:

1. Shrinkage deflection is calculated by applying the specified shrinkage strain.

Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in

the beam.

2. The creep deflection is calculated by applying the total dead load and the permanent

portion of the live load on the beam. The modulus of elasticity of the concrete is reduced

in accordance with the relevant design code.

3. The instantaneous deflection is calculated by applying the transient portion of the live load

on the transformed crack section.

4. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together

with cracked transformed sections, which implies plastic behaviour. Although this

procedure is performed in accordance with the design codes, the use of elastic moments

together with cracked sections in the same calculation is a contradiction of principles. As a

result of this, long-term deflection diagrams may show slight slope discontinuities at

supports, especially in cases of severe cracking.


Calculation of flexural reinforcement

The normal code formulae apply when calculating flexural reinforcement for rectangular

sections and for flanged sections where the neutral axis falls inside the flange.

If the neutral axis falls outside the flange, the section is designed by considering it as two

sub-sections. The first sub-section consists of the flange without the central web part of the section and the remaining central portion defines the second sub-section. The reinforcement

calculation is then performed as follows:

1. Considering the total section, the moment required to put the flange portion in

compression can be calculated using the normal code formulae. This moment is then

applied to the flange sub-section and the required reinforcement calculated using the

effective depth of the total section.

2. The same moment is then subtracted from the total applied moment. The resulting moment

is then applied to the central sub-section and the reinforcement calculated.

3. The tension reinforcement for the actual section is then taken as the sum of the calculated

reinforcement for the two sub-sections. If compression reinforcement is required for the

central sub-section, it is used as the required compression reinforcement for the actual section.

Design and detailing of flat slabs

When entering the input data for a flat slab, you should use its whole width, i.e. the transverse

column spacing (half the spacing to the left plus half the spacing to the right). The program will then calculate bending moments and shear forces for the whole panel width.

When generating reinforcement, however, the program considers the column and middle strips

separately. The program does the column and middle strip subdivision as suggested by the

design codes. The procedure is taken a step further by narrowing the column strip and

widening the middle strip to achieve a simpler reinforcement layout – a procedure allowed by

the codes.

Initial column and middle strip subdivision

The flat slab panel is divided into a column strip and middle strip of equal widths and then

adjusted to simplify reinforcement detailing:

1. The width of the column strip is initially taken as half the panel width. The total design

moment is then distributed between the column and middle strips as follows:

Moment position Column strip Middle strip

Moment over columns 75% 25%

Moments at midspan 55% 45%


2. Reinforcement is calculated for each of the column and middle strips.

Adjusted column and middle strip subdivision

The design codes require that two-thirds of the column strip reinforcement be concentrated in

its middle half. The codes also state that a column strip may not be taken wider than half the

panel width, thereby implying that it would be acceptable to make the column strip narrower

than the half the panel width.

To simplify the reinforcement layout and still comply with the code provisions, the program narrows the column strip and widens the middle strip. The widening of the middle strip is done

as follows:

1. The middle strip is widened by fifty percent from half the panel width to three-quarters of

the panel width.

2. The reinforcement in the middle

strip is accordingly increased by

fifty percent. Reinforcement

added to the middle strip is taken

from the column strip.

The column strip is subsequently

narrowed as follows:

1. The column strip is narrowed to

a quarter of the panel width.

2. As explained above, rein-

forcement is taken from the

column strip and put into the

widened middle strip.

3. The remaining reinforcement is

checked and additional rein-

forcement added where

necessary. This is done to ensure

that the amount of reinforcement

resisting hogging moment is greater than or equal to two-

thirds of the reinforcement

required for the original column

strip.


Designing the slab for shear

The program considers the column strip like a normal beam when doing shear calculations. A

possible approach to the shear design of the slab is:

Consider the column strip like a beam and provide stirrups equal to or exceeding the

calculated required shear steel.

In addition to the above, perform a punching shear check at all columns.

Implications of modifying the column and middle strips

In applying the above modifications, the moment capacity is not reduced. The generated

reinforcement will be equal to, or slightly greater, than the amount that would be calculated

using the normal middle and column strip layout.

The above technique gives simplified reinforcement details:

A narrower column strip is obtained with a uniform transverse distribution of main bars

and a narrow zone of shear links.

Detailing of the adjoining middle strips is also simplified by the usage of uniform

reinforcement distributions.

The design procedures for flat slabs and coffer slabs are described in more detail on page 6-38.


Input

The beam/slab definition has several input components:

Parameters: Material properties, load factors and general design parameters.

Sections: Enter cross-sectional dimensions.

Spans: Define spans and span segments.

Supports: Define columns, simple supports and cantilevers.

Loads: Enter dead and live loads.

Parameters input

Enter the following design parameters:

fcu : Characteristic strength of concrete (MPa).

fy : Characteristic strength of main reinforcement (MPa).

fyv : Characteristic strength of shear reinforcement (MPa).

Redistr : Percentage of moment redistribution to be applied.

Method : Method of moment redistribution, i.e. downward or optimised. For more

information, refer to page 6-8.

Cover top : Distance from the top surface of the concrete to the centre of the top steel.

Cover bottom: Distance from the soffit to the centre of the bottom steel.

DL factor : Maximum ULS dead load factor.

LL factor : Maximum ULS live load factor.

Note: The ULS dead and live load factors are used to calculate the ULS design loads. The

ULS dead and live loads are then automatically patterned during analysis. Refer to page 6-7 for more information.

Density : Concrete density used for calculation of own weight. If the density filed is left

blank, the self-weight of the beam/slab should be included in the entered dead

loads.

LL perm : Portion of live load to be considered as permanent when calculating the creep

components of the long-term deflection.

: The thirty-year creep factor used for calculating the final concrete creep strain.

cs : Thirty-year drying shrinkage of plain concrete.


The graphs displayed on-screen give typical values for the creep factor and drying shrinkage

strain. In both graphs, the effective section thickness is defined for uniform sections as twice

the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion

in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made,

stresses and relative humidity may vary considerably during the lifetime of the structure and

appropriate judgements should be made.

Sections input

You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a

basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their

webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be move horizontally to obtain eccentric sections, for example L-sections. Whole sections can

also be moved up or down to obtain vertical eccentricity.


Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a straight line. Vertical and horizontal offsets of sections are use used for presentation and

detailing purposes only and has no effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are

displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

Sec no : The section number is used on the Spans input page to identify specific

sections.

Bw : Width of the web (mm).

D : Overall section depth, including any flanges (mm).

Bf-top : Width of optional top flange (mm).

Hf-top : Depth of optional top flange (mm).

Bf-bot : Width of optional bottom flange (mm).

Hf-bot : Depth of optional bottom flange (mm).


Y-offset : Vertical offset the section (mm). If zero or left blank, the top surface is aligned

with the datum line. A positive value means the section is moved up.

Web offset : Horizontal offset of the web portion (mm). If zero or left blank, the web is

taken symmetrical about the beam/slab centre line. A positive value means the

web is moved to the right.

Flange offset : Horizontal offset of both the top and bottom flanges (mm). If zero or left blank,

the flanges are taken symmetrical about the beam/slab centre line. A positive value means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to

enter a thin web with a wide top flange. You can also enter wide web (actual top flange)

with a thin bottom flange (actual web). The shear steel design procedure works with the

entered web area, i.e. Bw × D, as the effective shear area. Although the two methods produce

similar pictures, their shear modelling is vastly different.

Spans input

Sections specified on the Sections input page are used here with segment lengths to define spans of constant or varying sections.


Spans are defined by specifying one or more span segments, each with a unique set of section

properties. The following data should be input for each span:

Span no : Span number between 1 and 20. If left blank, the span number as was

applicable to the previous row is used, i.e. another segment for the current

span.

Section length : Length of span or span segment (m).

Sec No Left : Section number to use at the left end of the span segment.

Sec No Right : Section number to use at the right end of the span segment. If left blank, the

section number at the left end is used, i.e. a prismatic section is assumed. If

the entered section number differs from the one at the left end, the section

dimensions are varied linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are

interpreted literally. If a rectangular section should taper to an L-section, for example, the

flange will taper from zero thickness at the rectangular section to the actual thickness at the

L-section. If the flange thickness should remain constant, a dummy flange should be defined for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than

the web and its depth made equal to the desired flange depth.

Supports input

You can specify simple supports, columns below and above, fixed ends and cantilever ends. To

allow a complete sub-frame analysis, columns can be specified below and above the beam/slab.

If no column data is entered, simple supports are assumed.

The following input is required:

Sup no : Support number, between 1 to 2'. Support 1 is the left-most support.

C,F : The left-most and right-most supports can be freed, i.e. cantilevered, or made

fixed by entering 'C' or 'F' respectively. By fixing a support, full rotational

fixity is assumed, e.g. the beam/slab frames into a very stiff shaft or column.

D : Depth/diameter of a rectangular/circular column (mm). The depth is measured in the span direction of the beam/slab.

B : Width of the column (mm). If zero or left blank, a circular column is assumed.

H : Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple

supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank.

In the analysis, the support will still be considered as a normal simple support. However,

when generating reinforcement bars, the program will extend the bars a distance equal to

half the support depth past the support centre line.


Code : A column can be pinned at its remote end by specifying 'P'. If you enter 'F' or

leave this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.

Loads input

Dead and live loads are entered separately. The entered loads are automatically patterned

during analysis. For more detail on the pattern loading technique, refer to page 6-7.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines

as necessary to define each load case. Defined loads as follows:

Case D,L : Enter 'D' or 'L' for dead load or live load respectively. If left blank, the previous

load type is assumed. Use as many lines as necessary to define a load case.

Span : Span number on which the load is applied. If left blank, the previous span

number is assumed, i.e. a continuation of the load on the current span.


Wleft : Distributed load intensity (kN/m) applied at the left-hand starting position of


Wright : Distributed load intensity (kN/m) applied on the right-hand ending position of

the load. If you leave this field blank, the value is made equal to Wleft, i.e. a



M : Moment (kNm).






load (m). Leave this field blank if you want the load to extend up to the

right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation. For more detail, refer to the explanation of the Parameters input on page 6-14.


Note: If you enter a concrete density on the Parameters input page, the own weight of the beam/slab is automatically calculated and included with the dead load.

Wind load input

If the beam or slab forms part of a frame subjected to sway due to wind loading, you can enter

the bending moments caused by the wind loads. The program does not calculate the wind

forces; you need to perform a frame analysis to determine them.

Wind loads are combined with dead and live loads with the load factors indicated on the

screen.


Design

The analysis is performed automatically when you access the Design pages.

Analysis procedure

Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections are calculated by analysing the beam/slab under pattern loading using the

gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected

to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm

intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections

are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-10 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-7.

The resultant bending moment and shear force envelopes are then redistributed. Finally, the

required reinforcement is calculated.

Detailed design calculations

You can view the detailed design calculations at any

position along the length of the beam by displaying the

Steel output page, and then clicking on the Detailed

Calculations button.



The Input pages incorporate extensive error checking. However, serious errors sometime still

slip through and cause problems during the analysis. Common input errors include:

Using incorrect units of measurement. For example, span lengths should be entered in

metre and not millimetre.

Entering too large reinforcement cover values on the Parameters input screen, gives

incorrect reinforcement. Cover values should not be wrongly set to a value larger than half

the overall section depth.

Not entering section numbers when defining spans on the Spans input screens causes

numeric instability. Consequently, the program uses zero section properties.

Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful

examination of the analysis output. View the long-term deflection diagrams and determine

which component has the greatest effect:

The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom

reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the

middle of spans generally induces negative shrinkage deflection, i.e. uplift.

Large creep deflections (long-term deflection under permanent load) are often caused by

excessive cracking, especially over the supports. Compare the span to depth ratios with the

recommended values in the relevant design code.

Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection component.

To verify the extent of cracking along the length of the beam/slab, you can study the contents

of the Crack file. Check the cracked status and stiffness of the relevant sections. The extent of

cracking along the length of the beam/slab is usually a good indication of its serviceability.







any load case.

Deflections

The elastic deflection envelope

represents the deflections due to

SLS pattern loading.

The long-term deflection diagram represents the behaviour of the

beam/slab under full SLS

loading, taking into account the

effects of shrinkage and creep:

The green line represents the

total long-term deflection.

The shrinkage deflection is

shown in red.

The creep deflection (long-term

deflection due to permanent loads)

is given by the distance between the red and blue lines.

The distance between the blue and

green lines represents instantaneous

deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-term deflection values are based on the reinforcement required at ultimate limit state. Once

reinforcement has been generated for a beam, the long-term deflections will be based on the

actual reinforcement instead.


Moments and shear forces

The bending moment and shear

force diagrams show the

envelopes due to ULS pattern

loading.

Steel diagrams

Bending and shear reinforcement

envelopes are given for ULS

pattern loading. The bending

reinforcement diagram sows required top steel above the zero

line and bottom steel below.


Open the Output file page for a tabular display of the beam/slab design results. Results include

moments and reinforcement, shear forces and reinforcement, column reactions and moments

and deflections.

The Crack file gives details of the cracked status, effective stiffness and concrete stresses in the beam/slab at regular intervals. You should find the information useful when trying to

identify zones of excessive cracking.


Reinforcing

Reinforcement can be generated for the most types of continuous beam and slabs using the

automatic bar generation feature. Reinforcement is generated in accordance to the entered

detailing parameters after which you can edit the bars to suit your requirements.

To create a bending schedule, use each detailing function in turn:

Detailing parameters: Select the detailing mode, enter you preferences and generate the

reinforcement.

Main reinforcement: Review the main bars and adjust as necessary.

Stirrups: Enter one or more stirrup configurations.

Shear reinforcement: Distribute stirrups over the length of the beam.

Sections: Specify positions where of cross-sections details should be generated.

Bending schedule: Create the Padds file.

Detailing parameters

The detailing parameters set the rules to be used by the program when generating

reinforcement:

Beam/slab type: Different detailing rules apply to different types of beams and slabs:

Type Description Main reinforcement Shear reinforcement

1 Normal beam Nominal reinforcement as for beams

Beam shear reinforcement

2 One way spanning

flat slab

Nominal reinforcement

as for slabs.

No shear

reinforcement.

3 Column strip portion of flat slab

on columns

Main reinforcement in

accordance with

moment distribution

between column and

middle strips. Nominal

reinforcement as for slabs.

No shear

reinforcement.

Separate punching

shear checks should

be performed. 4 Middle strip

portion of flat slab

on columns

5 Rib Nominal reinforcement as for slabs.

Shear reinforcement as for beams.


Maximum bar length: Absolute maximum main bar length to be used, e.g. 13 m.

Minimum diameter for top bars, bottom bars and stirrups: The minimum bar diameter to

be used in each if the indicated positions.

Maximum diameter for top bars, bottom bars and stirrups: The maximum main bar

diameter to be used in each if the indicated positions.

Tip: To force the program to use a specific bar diameter, you can enter the same value for both the minimum and maximum diameters.

Note: The default bar types used for main bars and stirrups, e.g. mild steel or high tensile, are determined by the yield strength values entered on the Parameters input page – refer to

page 6-14 for detail. High tensile steel markings, e.g. 'T' or 'Y', will be used for specified

values of fy and fyv exceeding 350MPa.

Stirrup shape code: Preferred shape code to use for stirrups. Valid shape codes include:

BS 4466 and BS 8666: 55, 61, 77, 78 and 79.


SANS 282: 55, 60, 72, 73 and 74.

First bar mark - top: The mark of the first bar in the top of the beam/slab. Any

alphanumerical string of up to five characters may be specified. The rightmost numerical

or alpha portion of the bar mark is incremented for subsequent bars. Examples of valid

marks include:

'001' will increment to 002, 003 etc.

'A' will increments to B, C, etc.

'B002' will increment to B003, B004 etc.

First bar mark - middle: The mark of the first bar in the middle of the beam/slab. If you

do not enter a mark, the bar marks continue from those used for the top reinforcement.

Middle bars are generated for all beams with effective depth of 650 mm or greater.

First bar mark - bottom: The mark of the first bar in the bottom the beam/slab. If you

leave this field blank, the bar marks will continue from those used for the top or middle

reinforcement.

Cover to stirrups: Concrete cover to use at the top, bottom and sides of all stirrups.

Minimum stirrup percentage: Nominal shear reinforcement is calculated according to

the code provisions for beams and slabs. In some cases, it may be acceptable to provide less than the nominal amount stirrups, e.g. for fixing top bars in a flat slab. The minimum

amount of stirrups to be generated can be entered as a percentage of the nominal shear

reinforcement.

Note: For beams and ribs, the minimum stirrup percentage should not be taken less than

100% of nominal shear reinforcement.

Loose method of detailing: The envisaged construction technique can be taken into

account when detailing reinforcement:

With the 'loose method' of detailing, also referred to as the 'splice-bar method', span

reinforcement and link hangers are stopped short about 100 mm inside each column

face. This is done at all internal columns were congestion of column and beam

reinforcement is likely to occur. The span bars and stirrups are often made into a cage,

lifted and lowered between supports. For continuity, separate splice bars are provided

through the vertical bars of each internal column to extend a lap length plus 100 mm

into each span. Top bars will extend over supports for the required distance and

lapped with nominal top bars or link hangers. Allowance is made for a lap length of

40· and a 100 mm tolerance for the bottom splice bars that are acting in compression.

Alternatively, where accessibility during construction allows, the 'normal' method of

detailing usually yields a more economical reinforcement layout. This method allows bottom bars to be lapped at support centre lines. Top bars will extend over supports


for the required distance and lapped with link hangers. Where more practical, top bars

over adjacent supports may be joined. Adjacent spans are sometimes detailed together.

Note: The 'normal' method of detail may give rise to congested reinforcement layouts at beam-column junctions, especially on the bottom beam/slab layer. Reinforcement layout

details at such points should be checked.

Generating reinforcement

Use the Generate reinforcing to have the program generate bars according the detailing

parameters.

Note: The aim of the automatic reinforcement generation function is to achieve a reasonable optimised reinforcement layout for any typical beam or slab layout. More complicated

layouts will likely require editing of the generated reinforcement as described in the text that

follows. Very complicated layouts may require more detailed editing using Padds.

Editing reinforcement

You can modify the generated reinforcement to suite your requirements by editing the

information on the Main reinforcing, Stirrups, Shear reinforcing and Sections pages.

Main reinforcing

The main reinforcement bars are defined as follows:

Bars: The quantity, type and diameter of the bar, example '2T20' or '2Y16'. The bar

defined at the cursor position is highlighted in the elevation.

Mark: An alphanumerical string of up to five characters in length, example 'A', '01' or 'A001'.

Shape code: Standard bar shape code. Valid shape codes for main bars include 20, 32, 33,

34, 35, 36, 37, 38, 39 and 51.

Span: The beam/slab span number.

Offset: Distance from the left end of the span to the start point of the bar (m). A negative

value makes the bar start to the left of the beginning of the span, i.e. in the previous span.

Length: Length of the bar as seen in elevation (m).

Hook: If a bar has a hook or bend, enter 'L' or 'R' to it on the left or right side. If this field

is left blank, an 'L' is assumed.

Layer: Position the bar in the top, middle or bottom layer. Use the letters 'T', 'M' or 'B'

with an optional number, e.g. 'T' or 'T1' and 'T2'.


The bending reinforcement diagram is shown on the lower half of the screen. The diagrams for

required (blue) and entered (red) reinforcement are superimposed for easy comparison. Bond

stress development is taken into consideration in the diagram for entered reinforcement.

Stirrups

Define stirrup layouts as follows:

Stirrup number: Enter a stirrup configuration number. Configuration numbers are used

on the Shear reinforcing input page (see page 6-32) to reference specific configuration. If

left blank, the number applicable to the previous row is assumed, i.e. an extended definition of the current configuration.

Section number: Concrete cross section number as defined on the Sections input page

(see page 6-33). If left blank, the number applicable to previous row in the table is used.

Bars: Type and diameter of bar, example 'R10'.


Note: Mild steel bars are normally used for shear reinforcement. However, in zones where much shear reinforcement is required, you may prefer using high yield stirrups. You can do

this by entering 'T' or 'Y' bars instead of 'R' bars. In such a case, the yield strength ratio of

the main and shear reinforcement, i.e. fy/fYV as entered, will be used to transpose the entered

stirrup areas to equivalent mild steel areas.

Mark: Any alphanumerical string of up to five characters in length, e.g. 'SA1', '01' or

'S001'.

Shape code: Standard double-leg bar shape code. The following shape codes can be used:

BS 4466 and B S8886: 55, 61, 77, 78 and 74.

SANS 282: 55, 60, 72, 73 and 74.

Bars are automatically sized to fit the section web. The first stirrup entered is put against the

web sides. Subsequent stirrups are positioned in such a way that vertical legs are spaced

equally.

Tip: Open stirrups, e.g. shape code 55, can be closed by entering a shape code 35.


Shear reinforcing

Stirrup layouts defined on the Stirrups input page (see page 6-30) are distributed over the

length of the beam/slab:

Stirrup number: The stirrup configuration number to distribute.

Spacing: Link spacing (mm).

Span: The beam/slab span number.

Offset: Distance from the left of the span to the start point of the distribution zone (m). A

negative value makes the zone start to the left of the beginning of the span, i.e. in the

previous span.

Length: Length of the stirrup distribution zone (m).

The diagrams for required and entered shear reinforcement are superimposed. The required

steel diagram takes into account shear enhancements at the supports.


It may sometimes be acceptable to enter less shear steel than the calculated amount of nominal

sheer steel, e.g. when the stirrups are only used as hangers to aid the fixing main steel in slabs.

This option can be set as default on the Detailing parameters input screen – see page 6-26

for detail.

Sections

Cross-sections can be generated anywhere along the length of the beam/slab to show the main

and shear steel layout:

Label: The cross-section designation, e.g. 'A'.

Span no: The beam/slab span number.

Offset: The position of the section, given as a distance from the left end of the span (m).

Sections are displayed on the screen and can be used to check the validity of steel entered at the

different positions. Stirrup layouts defined on the Stirrups input (see page 6-30) rely on

appropriate section positions specified. All specified sections will be included in the final

bending schedule.


3D View

View a 3D rendering of the beam with longitudinal and shear reinforcement to help you spot

layout conflicts and gaps.

Bending schedule

The Bending schedule input page is used generate a complete Padds compatible bending

schedule. The parameters allow flexibility in the bending schedule creation, e.g. you can have

the details of a beam/slab on a single bending schedule or split it onto more than one schedule

to improve clarity. Each bending schedule can then be given a unique name and the associated

spans entered.

The following information should be entered:

File name: The name of the Padds drawing and bending schedule file

First span: For clarity, a beam/slab with many spans can be scheduled put on more than one bending schedule. Enter the first span number to be included in the bending schedule.

Last span: Enter the last span number to be included in the bending schedule.


Grid lines: Optionally display grid lines and numbers appear on the bending schedule

drawing.

Columns: Optionally display column faces on the bending schedule drawing.

First grid: The name or number of the first grid. Use one or two letters and/or numbers.

Number up or down: Specify whether grids must be numbered in ascending or

descending order, i.e. 'A', 'B' and 'C' or 'C', 'B' and 'A'

Drawing size: Select A4 or A5 drawing size. If A4 is selected, the drawing is scaled to fit

on a full page and the accompanying schedule on a separate page. The A5 selection will

scale the drawing to fit on the same page with the schedule. Typically, a maximum of

three to four spans can be shown with enough clarity in A5 format and four to six spans in

A4 format.

Note: When combining a drawing and schedule on the same page, the number of schedule

lines is limited to a maximum of twenty-four in Padds. Using more lines will result in the

drawing and schedule being printed on separate pages.

Use the Generate schedule function to create and display the Padds bending schedule.

Editing and printing of bending schedules

Detailed editing and printing of bending schedules are done with Padds. For this, following the

steps below:

Exit the program and launch Padds.

Choose Open on the File menu and double-click the relevant file name. The file will be

opened and displayed in two cascaded widows. The active windows will contain the

drawing of the beam and the second window the bar schedule.

Make any necessary changes to the drawing, e.g. editing or adding bars and adding

construction notes.

Click on any visible part of the window containing the cutting list to bring it to the front.

Enter the following information at the relevant positions:

Member description: Use as many lines of the member column to enter a member

description, e.g. '450x300 BEAM'.

General schedule information: Press PgDn to move to the bottom of the bending

schedule page and enter the detailers name, reference drawing number etc.

Bending schedule title: Enter the project name and bending schedule title in the centre

block at the bottom of the bending schedule.


Bending schedule number: The schedule number in the bottom right corner defaults to

the file name, e.g. 'BEAM.PAD'. The schedule number can be edited as required to

suite your company's schedule numbering system, e.g. 'P12346-BS001'.

Note: The bottom left block is reserved for your company logo and should be set up as described in the Padds User's Guide.

Finally, combine the beam drawing and schedule onto one or more pages using the Title Block

and Print button on the bending schedule window.


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad.

Various settings are available to include input and design diagram and tabular result.





is saved as part of a project and therefore does not need to be saved in the design module

as well.


Appendix: Suggested design procedures for slabs

Some suggestions are made below with regards the design and detailing of solid slabs and

coffer slabs.

Suggested design procedure for solid slabs

The suggestions are explained by way of an example. A flat slab with a regular rectangular

column layout of 6.0 m by 5.5 m is considered.

Typical strip over a row of internal columns (Strip A)

The strip is modelled as a 6000 mm wide panel, i.e. 3000 mm either side of the columns. The

program calculates moments and shear forces for the whole panel width. It then details a

column strip, 1500 mm wide, and middle strip, 4500 mm wide. For an explanation of the

division into column and middle strips, see page 6-11.

External strip (Strip B)

The external strip, strip B, is defined as the portion over the external columns that extending

halfway to the first row of internal columns. Strip C is the first internal strip and it extends to midspan on both sides.

Consider the end panel,

i.e. the portion between

edge columns and the

first row of internal

columns or, in other

word, strip B together

with half of strip C. The

portion over the internal

columns (portion of strip

C) will tend to attract more moment than the

portion over the external

columns (strip B). Using

a rule of thumb, a

reasonable moment distri-

bution ratio would be

about 62.5% to 37.5%.

The external strip (strip

B) can thus be

conservatively modelled


as a panel with width equal to half the transverse column spacing, i.e. 3000 mm, carrying the

full load for that area. The program will analyse the strip and the generate reinforcement for a

column strip, 750 mm wide, and a middle strip, 2250 mm wide.

First internal strip (Strip C)

The first internal strip can subsequently be modelled using the same width as a typical internal

panel, i.e. 6000 mm. Because of the moment distribution explained above, the loading is

increased to 50% + 62.5% = 112.5% of the typical panel loading. The small overlap in loading between the edge and first internal panels should take care of any adverse effects due to pattern

loading.

Note: If the own weight is modelled using a density, you should account for the increased

loading by either increase the density value by 12.5% or increasing the applied dead load.

The program will analyse the panel and generate a column strip, 1500 mm wide, and a middle

strip 4500 mm wide.

Reinforcement layout

Careful combination of the column and middle strips generated above, should yield a

reasonably economical reinforcement layout:

For typical internal strips (strip A), use the generated column strip (CA) and middle

strip (MA).

For the column strip over the external row of columns, use no less than the column strip

reinforcement (CB) generated for the external strip (strip B).

For the column strip over the first row of internal columns, use no less than the column

strip reinforcement (CC) generated for the first internal strip (strip C).

The first middle strip from the edge (MC/MB) can be conservatively taken as the worst of middle strip generated for the first internal strip (MC) and twice that generated for the

external strip (MB).

Suggested design procedure for coffer slabs

Coffer slabs can normally be designed and detailed using the design procedure for solid slabs.

The procedure suggested for solid slabs should be also a reasonable design approach for coffer

slabs if the following conditions are met:

The solid bands should be as wide or slightly wider than the generated column

strips, i.e. L/4 or wider.

Assuming that the concrete compression zone of each coffer rib falls in the coffer flange,

the slab can be modelled as a solid slab.


Setting the density to zero and appropriately increasing the applied dead load can model

the own weight of the slab.

The linear shear requirements should be verified for the column strips, i.e. solid bands.

The areas around columns slab should also be checked for punching shear.

The coffer webs should be checked for linear shear and compression reinforcement.

Note: You should validate the design procedure by checking that, in zones of sagging moment, the concrete compression zones of coffer ribs fall within the coffer flanges. Zones

of hogging moment should be located inside solid bands.


Pre-stressed Beam and

Slab Design

Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design and

detail most types of continuous pre-stressed beam and slab systems encountered in typical

building projects. The design incorporates automated pattern loading and moment

redistribution.

Both unbounded systems, e.g. flat slabs, and bonded systems, e.g. bridge decks, can be

designed. Estimates for quantities are calculated and tendon profile schedules can be generated

for use with Padds.




Design scope

The program designs and details continuous pre-stressed concrete beams and slabs. You can

design structures ranging from simply supported single span to twenty-span continuous beams

or slabs.

Cross-sections can include a mixture rectangular, I, T and L-sections. More complex sections,

e.g. box bridge decks, can be modelled with the aid of the section properties calculation

module, Prosec. Spans can have constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. You

can also enter individual load cases and group them in load combinations. At ultimate limit

state, moments and shears are redistributed to a specified percentage.

Pre-stressed tendons can be generated to balance a specified percentage of dead load.

Conventional reinforcement can be added to help control cracking, deflection and increase the ULS capacity.

Tendon profiles can be scheduled and saved as Padds compatible drawings.

Design codes


ACI 318 - 1999.

ACI 318 - 2005.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

SABS 0100 - 2000.

Reinforcement bending schedules are generated in accordance to the guidelines given by the

following publications:

Report No 2 of the Joint Structural Division of SAICE and ISA (JSD), 'Design of Pre-

stressed Concrete Flat Slabs'.

Technical Report 25 of the Concrete Society, published in 1984.

Attached torsional members are treated in accordance with ACI 318 - 1989.


Sub-frame analysis

A two-dimensional frame model is constructed from the input data. Section properties are

based on the gross un-cracked concrete sections. Columns can optionally be specified below

and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.

Column stiffness

BS 8110 and SABS 0100 - 2000 assume that columns are rigidly fixed to slabs over the whole

width of the panel. If the ultimate negative moment at an outer column exceeds the moment of

resistance in the adjacent slab width, the moment in the column should be reduced and the

sagging moment in the outer span should be increased to maintain equilibrium.

In ACI 318 - 1989, on the other hand, allowance is made for the reduction of column stiffness

due to torsion. Report 2 of the JSD adapts a similar column stiffness reduction approach. The

program incorporates this approach by allowing you to optionally enable attached torsional

members.

Note: When the approach to include the attached torsional members is followed, column

heads will also be taken into account in the column stiffness.

Pattern loading

At ultimate limit state, the dead and live loads are multiplied by the specified ULS load factors (see page 6-70). Unity load factors are used at serviceability limit state. The following

load cases are considered (the sketch uses the load factors applicable to BS8110):

All spans are loaded with the

maximum design load.

Odd numbered spans (spans

1, 3, 5, etc.) are loaded with

the minimum design dead

load and even numbered

spans (spans 2, 4, etc.) with

the maximum design ultimate

load (dead plus live load).

Even numbered spans are

loaded with the minimum

design dead load and odd

numbered spans loaded with

the maximum design ultimate

load.


Note: The case where any two adjacent spans are loaded with maximum load and all other

spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 2000, is

not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

SABS 0100 suggests a constant ULS dead load factor of 1.2 for all pattern load cases. In

contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for

calculating the minimum ultimate dead load. The program uses the more approach given

by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and

the maximum load factor specified for maximum dead load.

The South African loading code, SANS 10162, prescribes an additional load case of

1.5×DL. This load case is not considered during the analysis – if required, you should

adjust the applied loads manually. In cases where the dead load is large in comparison

with the live load, e.g. lightly loaded roof slabs, increasing the entered dead load or

increasing the ULS dead load factor can incorporate this load case. This adjustment

applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except

where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.

Moment redistribution

Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is

set to 'optimised', the design moments are further minimised by redistributing span moments

upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern loading and then redistributed using the procedures explained in the following text.

Code requirements

The JSD Report 2 recommends that the maximum moment redistribution should not

exceed 20%.

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns

without increasing the sagging moments at midspan. The redistribution of moments and shear

forces procedure is performed as follows:


4. The maximum hogging moment at each column or internal support is adjusted downward

by the specified maximum percentage.

5. The corresponding span moments are adjusted downward to maintain static equilibrium.

The downward adjustment of hogging moments above is limited to prevent any increase in

the maximum span moments of end spans.

6. The shear forces for the same load cases are adjusted to maintain static equilibrium.

Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward

distribution of the span moments. The envelopes for the three pattern load cases are

redistributed as follows:

11. The maximum hogging

moment at each internal

support is adjusted

downward by the

specified percentage.

This adjustment affects

the moment diagram for

the load case where the maximum design load is

applied to all spans.

12. The relevant span

moments are adjusted

accordingly to maintain

static equilibrium.

13. The minimum hogging

moment at each internal

support is subsequently

adjusted upward to as

close as possible to the

reduced maximum support moment, whilst

remaining in the

permissible

redistribution range. A

second load case is thus

affected for each span.

14. The relevant span

moments are adjusted in

line with this redis-

tribution of the column


moments to maintain static equilibrium.

15. For each span, the moment diagram for the remaining third load case is adjusted to as near

as possible to the span moments obtained in the previous step. The adjustment is made in

such a way that it remains within the permissible redistribution range.

16. Finally, the shear force envelope is adjusted to maintain static equilibrium.

17. The following general principles are applied when redistributing moments:

18. Equilibrium is maintained between internal and external forces for all relevant combinations of design ultimate load.

19. The neutral axis depth is checked at all cross sections where moments are redistributed. If,

for the specified percentage of moment redistribution, the neutral axis depth is greater than

the limiting value of (ßb0.4)d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

20. The amount of moment redistribution is limited to the specified percentage. The maximum

amount of redistribution allowed by the codes is 30%.

Note: As would be the case in typical pre-stressed sections, the program assumes that all

sections have adequate ductility to allow moment redistribution. The actual ductility of sections is not verified.

Tendon generation procedures

Captain is capable of generating tendons for typical beam and slabs. The procedure aims to

balance a specified percentage of the dead load in the span.

For purposes of the generation, all the dead loads on the span, including self weight, UDL's,

partial UDL's, trapezoidal and point loads, are summed and divided by the span length to

obtain an equivalent UDL for the span.

Parabolic or harped tendons are then selected to balance the required percentage of this

equivalent dead load. In the case of harped tendons, the tendons are chosen to provide two

upward point loads per span that balance the selected percentage of the sum of all the dead load

components.

Note: The program uses load balancing only for the purpose of generating tendons.

Since long-term losses are not known beforehand, a 15% loss of pre-stress is assumed. Further,

the generation procedure that tendons are stressed to 70% of their ultimate tensile

strength (UTS).

The details of the tendon generation procedure are explained in the following text.


Parabolic tendons in cantilever spans

Consider a typical cantilever span with a tendon

following a parabolic profile. The profile is chosen

with a zero eccentricity at the cantilever end. At

the internal support the tendon is taken as high as

possible.

The program chooses the following values:

The left offset, L, is chosen as zero.

The right offset, R, is chosen equal to the span length divided by twenty, with a minimum

of 250 mm.

The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the

right end) is chosen on the neutral axis.

The tendon position over the internal support is taken as high as possible. The value of b3

(b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed

tendon diameter.

The tendon force, T, required to produce the balanced load Wbal is given by

))((2

)(15.1

13

2

RLengthbb

LengthRLengthWT bal

req

and the number of tendons required by

tendon

reqtendons

UTS

TN

7.0

Parabolic tendons in internal spans and end spans

For a typical internal span, a parabolic tendon

profile is chosen to give maximum eccentricities

over supports and at midspan.

The same also applies to an end span, except that

the tendon as moved to the neutral axis at the

anchor.

The program chooses the following default values:

The left and right offsets, L and R, are chosen by the program to be equal to the span

length divided by twenty, with a minimum of 250 mm.


Over the supports, the tendons are taken as high as possible. The values of b1 and b2 are

made equal to the top cover plus half the sheathed tendon diameter. At the end of the

beam/slab, i.e. at an anchor, the tendons are taken on the neutral axes.

At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as

being equal to the bottom cover plus half the sheathed tendon diameter.

The drape of the tendon is then calculated as

Length

RLLengthbbbdrape

22/31

The tendon force required to produce the balanced load Wbal is then given by

drape

LengthRLLengthWT bal

req

8

)(15.1 2


tendon

reqtendons

UTS

TN

7.0

Harped tendons in cantilever spans

For a cantilever span with a harped tendon profile,

the profile is taken as a straight line from the

neutral axis at the cantilever end to the highest

position over the internal support.

In the calculations, the minimum radius Rmin

specified is used in determining the final slopes of

the tendons. The program chooses the following values:

The left offset, L, is chosen as zero.

The right offset, R, is set equal to the span length.

The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the

right end) is chosen on the neutral axis.

The tendon position over the internal support is taken as high as possible. The value of b3

(b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed

tendon diameter.


The position of the start of the radius of the internal support, xw, is calculated as

)(2 13min2 bbRLengthLengthxw

Further, the corresponding vertical offset for the start of the radius, yw, is given by

min

2

2R

xy w

w

and the slope of the tendon as

w

w

xLength

ybb 13arctan


sin

15.1 balreq

WT


tendon

reqtendons

UTS

TN

7.0

Harped tendons in end spans

For an external span, a harped tendon profile is

chosen to give maximum eccentricities over the

internal support and at midspan. The eccentricity

at the end support is chosen to be zero to eliminate

moments.

The following values are chosen:

The left and right offsets, L and R, are set to span length divided by four.

The eccentricity at the end of the beam/slab end is taken as zero, i.e. b1 (b3 for a right end

span) is chosen on the neutral axis.

The eccentricities at both ends are taken as high as possible. The value of b3 (b1 for a right end span) is thus taken as the top cover plus half the sheathed tendon diameter.


being equal to the bottom cover plus half the sheathed tendon diameter.



)(244

23min

2

bbRLengthLength

xw

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2R

xy w

w


w

balreq

xLength

d

Length

d

WT

3

16

3

16

15.1

21

where

3

)(2 211

bbd

3

)(2 232

bybd w

The number of tendons required is then given by

tendon

reqtendons

UTS

TN

7.0

Harped tendons in internal span

Maximum eccentricities are chosen over the

supports and at midspan for an internal span with a harped tendon profile.

The following values are chosen:

The left and right offsets, L and R, are set to

span length divided by four.

The eccentricities at both ends are taken as high as possible. The values of b1 and b3 are

thus taken as the top cover plus half the sheathed tendon diameter.


being equal to the bottom cover plus the half the sheathed tendon diameter.



)(244

23min

2

bbRLengthLength

xw

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2R

xy w

w


w

balreq

xLength

dd

WT

3

1616

15.1

22

where

3

)(2 211

bybd w

3

)(2 232

bybd w

The number of tendons required is then given by

tendon

reqtendons

UTS

TN

7.0

Pre-stress losses

In the following text, an explanation as given for the various components of pre-stress losses:

Friction losses.

Wedge-set.

Long-term losses.

Friction losses in parabolic tendons

Friction losses are calculated for each span in turn. The calculation is started at the active end

of each tendon. The effective tendon force is calculated at the end of the span taking into

account the friction losses. This force is then carried over to the start of the next span for the

process to be repeated.


The following is applicable to parabolic tendon profiles, including those cases where L and R

are zero:

LengthLengthRan

LaRLengthm

)(

)2(

1

2

where

12 aaadif

These values are used to determine the position of the lowest point on the parabola, X, and are

derived from the basic parabolic equations describing the tendon profiles. The position of the

lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difa

px

2

where

namp dif 2

If x 0, then the vertical position of the left inflection point, c1, is given by

X

Lac 1

1 else c1 is zero.

If L X then the vertical position of the right inflection point, cs, is given by

XLength

Rac

2

2 else c2 is zero.

The following can then be calculated:

2

321

22

22112

11

)(16

8

3

2

)()(

8

3

Length

ddd

cd

cacad

cd


The effective pre-stressing force at the end of the span, Pe, can now be calculated:

Lengthkoe ePP )(

where

Po = Applied tendon force

= Friction coefficient of the tendon against the sheath

= Cumulative angle of curvature over length

k = Friction coefficient for unintentional variation form specified profile ('wobble' in

sheath)

Friction losses in harped tendons

The following is applicable to harped tendon

profiles, including those cases where L and R are

zero:

RLLengthl 2

The position of the end of the left minimum radius, xwL, is given by

1min2 2 aRLLxwL for 1min

2 2 aRL

0wLx otherwise.

Corresponding to this

min

2

2R

xy wL

wL

Similarly, the position of the start of the right minimum radius, xwR, is given by

2min3 2 aRRRxwR for 2min

2 2 aRR

0wRx in all other cases.

Corresponding to this

min

2

2R

xy wR

wR


The slopes of the three sections of tendon are now known. The change in slope at each kink is then determined. At the first kink, friction losses occur over a length xwL and at the second

kink over a length of 2 xwL. At the Last kink, friction losses occur over a length xwR and at the

third kink over a length of 2 xwR.

Starting from the one side the force at the end of each kink is calculated as:

fricLk

beginend ePP)(

where

Lfric = Portion over which the losses occur.

Wedge-set

As soon as the stressing jacks are

released, a phenomenon known as

'wedge-set' or 'wedge pull-in' occurs.

In typical building slabs, the tendons

normally pull in by about 5mm to

10 mm before the tendons grip onto

the wedges in the anchor head. The

influence on the tendon force is

significant.

Because of frictional losses, the effect of wedge-set is to reduce the effective pre-stress over a

limited length of tendon only. This length, labelled lw, is calculated by considering the average

force loss over the entire length of the tendon:

lengthtendonTotal

PPm

endbegin

The length effected by wedge-set is then given by

m

EAdl

spswsw

where

Aps = Area of tendons

Es = Modulus of elasticity of tendons

ds = Wedge-set


The force loss over the length affected by the wedge-set can then be calculated:

w

pssws

losswsl

AEdP

The tendon force profile can then be adjusted by reducing the tendon force at the live anchor by 2Plossws and taking the negative pre-stress loss gradient up to the position of wedge-set

influence, lw.

Long-term tosses

The average steel strain in all the tendons is given by

pss

endpanbeginspanst

AE

PsP

2

)(

This summation is carried out over all spans for all tendons.

The creep strain is estimated as

cc

avg

creepEA

P

where

Pavg = Average pre-stressing force

Ac = Concrete area

Ec = Concrete modulus of elasticity

= Creep factor

The percentage total losses can be calculated as

pss

creepshrinkage

AErelaxationLoss

)(100%%

where

shrinkage = Shrinkage strain

creep = Strain due to creep


Load balancing

Captain uses a load balancing approach when generating tendons. The average tendon force,

Pav, is calculated for each span and each tendon. Pav is used to calculate the equivalent load

from the central portion of the tendon. The tendon force values at the beginning and end of

each span are used to calculate the equivalent loads for the reversed parabolic portions of

parabolic tendons and for the point loads from harped tendons at supports.

Equivalent load for parabolic tendons

Consider a typical span with parabolic tendons.

The procedure described next for calculating the

equivalent loads is applicable to cantilever and end

spans as well.

The following values are used to determine the

position of the lowest point on the parabola and

are derived from the basic parabolic equations

describing the tendon profiles.

LengthLengthRan

LaRLengthm

)(

)2(

1

3

where

13 aafadi

These values are used to determine the position of the lowest point on the parabola, X, and are

derived from the basic parabolic equations describing the tendon profiles. The position of the lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difa

pX

2

where

namp dif 2

If x ≠ 0 then vertical position of left inflection point, c1, is given by

X

Lac 1

1 else c1 is zero.


If L ≠ X then the vertical position of right inflection point, cs, is given by

XLength

Rac

3

2 else c2 is zero.

If L > 0, the equivalent load starting at the left support is given by

21

2

L

PW

begin

If L = 0 then W1 = 0.

The central portion of the equivalent tendon load is calculated by using a length lcalc. The

distance lcalc is measured from the lowest point of the parabola to the nearest inflection point.

If the left inflection point is nearest to the lowest point, then

LXlcalc

and the equivalent load in the centre portion

211

2

)(

calc

av

l

caPW

Else, if the right inflection point is nearest to the lowest point, then

RXLengthlcalc

and the equivalent load in the centre portion

223

2

)(

calc

av

l

caPW

If R > 0, the equivalent load ending at the right support is given by

23

2

R

PW end

If R = 0 then W3 = 0.

If the value of X is equal to zero, it implies that the tendon is horizontal at the beginning or end

of the span. If the value of L or R is equal to zero, it means that there is no reverse portion of

the parabola. In such a case a point load is calculated which acts downwards at the support.


If L is zero, the slope of the tendon is calculated as

X

a12arctan

The downward point load is then given by

sinPP begint

Similarly, if R is zero, the slope of the tendon is calculated as

X

a32arctan

The downward point load is then given by

sinendt PP

If a tendon is stopped off away from the neutral axis, a point moment is generated in the slab.

The magnitude of this moment is given by:

tendontendont ePM

where

etendon = Tendon eccentricity measured from the section neutral axis.

Equivalent load for harped tendons

Consider a typical span with harped tendons. The

procedure described next for calculating the

equivalent loads is applicable to both cantilever and end spans.

The four point loads caused by the typical harped

tendon are labelled P1 to P4. The central portion of

the tendon is assumed to be horizontal, causing no

vertical components of force.

The sloped ends with offset lengths L and R cause upward or downward point loads where they

change direction at the support or at the offset points to the horizontal portion. In practice, the

change in direction of the tendon occurs over a short distance dictated by the allowable

minimum radius of the tendon. For calculation purposes the vertical components are calculated

as point loads at the theoretical intersection points of the straight portions.


The tendon forces used in the calculation are Pbegin end Pend, which are the tendon forces at the

beginning and end of each span. For calculating the values of P2 and P3, the tendon force is

interpolated linearly between the end values.

The equivalent loads are given by

223

34

43

12

221

11

)(1

)(1

Rb

bPP

LengthP

RPPPP

LengthP

LPPPP

Lb

bPP

end

end

endbegin

begin

endbegin

begin

Calculation of concrete stresses

Tensile stresses calculated on un-cracked sections do not always correlate well with cracking.

For this reason, Report 2 of the JSD does attach great value to concrete stresses as a serviceability limit state. However, tensile stresses are a good indicator of where cracking may

be a problem and could therefore be useful during preliminary design. The stress checks will

be useful if you have been using the Report 25 provisions in the past.

Stress envelopes are calculated for the following two cases:

At transfer of tendon forces: Only initial dead loads are considered at transfer. Additional

dead loads are only considered later at SLS. On the Loads input screen, a dead load is

considered as an initial dead load except if the letter 'A' is entered before or after the load

value. In that case, the load is taken as an additional dead load to be considered at SLS

only and will not be considered at transfer.

At SLS: The full SLS loads, i.e. initial dead load, additional dead load and live load, are

applied and long-term losses in tendon forces are included.

Note: Tensile concrete stresses are not considered when generating tendon profiles. The pre-

stressing is considered as an external load with a load balancing effect. Typical bridge

design code checks for class 1, 2 and 3 structures should be done in an iterative way by

manually checking the stress diagrams.


Reports 2 and 25 gives the following allowable concrete stresses for flat slab construction:

Loading

Condition

Permissible

Compression

Permissible Tension

Bonded Un-bonded

Transfer

Sagging 0.33fci 0.45fci 0.15fci

Hogging 0.24fci 0.45fci 0

Serviceability limit state

Sagging 0.33fcu 0.45fcu 0.15fcu

Hogging 0.24fcu 0.45fcu 0

The allowable stresses tabled above apply to post-tensioned flat slab design. Different values

may apply to the design of other types of members. Refer to the relevant design code for

allowable stresses for class 1, 2 and 3 pre-tensioned and post-tensioned members.


Deflection calculation

Both short-term and long-term deflections are calculated. No moment redistribution is done at


Code guidelines

Deflection can generally be controlled in the preliminary design by limiting span to depth

ratios. Report 2 of the JSD gives the following guidelines for flat slabs where at least half of

the dead plus live load is balanced by pre-stress:

Type of Slab Loading

Intensity

Maximum span

to depth ratio

Flat Slabs

Light 40 to 48

Normal 34 to 42

Heavy 28 to 36

Waffle Slabs Heavy 28 to 32

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-

cracked concrete sections are used.


Long-term deflections are determined by first calculating the cracked transformed sections:

3. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

4. The cracked transformed sections are then calculated at 250 mm intervals along the length

of the beam. The results of these calculations are tabled in the Crack files on the

View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the

amount of reinforcement required at ULS. However, once reinforcement is generated for

beams, the actual entered reinforcement is used instead. You can thus control deflections by manipulating reinforcement quantities.


Next, the long-term deflection components are calculated by numerically integrating the

curvature diagrams:

5. Shrinkage deflection is calculated by applying the specified shrinkage strain.

Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in

the beam.

6. The creep deflection is calculated by applying the total dead load and the permanent

portion of the live load on the beam. The modulus of elasticity of the concrete is reduced in accordance with the relevant design code.

7. The instantaneous deflection is calculated by applying the transient portion of the live load

on the transformed crack section.

8. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together

with cracked transformed sections, which implies plastic behaviour. Although this

procedure is performed in accordance with the design codes, the use of elastic moments

together with cracked sections in the same calculation is a contradiction of principles. As a result of this, long-term deflection diagrams may show slight slope discontinuities at

supports, especially in cases of severe cracking.

Crack width calculation

In the calculation of crack widths, the program takes into account all bonded tendons and also

any additional reinforcement that has been entered. The effect of the axial compressive

concrete stress due to pre-stressing is also taken into account. Un-bonded tendons are ignored.

The crack spacing is calculated on the assumption that all unstressed bars and bonded tendons

are spaced equally across the widest portion of the section. In flat slab design, it is common

practice to have tendons banded in one direction. In such cases, tensile concrete stresses will

tend to be concentrated at the position of the tendons. Therefore, the assumption that all

unstressed bars and bonded tendons are spaced equally across the section, will likely yield

conservative crack width values.

Calculation of additional flexural reinforcement

The required reinforcement is based on supplying reinforcement for the tensile force in the

concrete at a stress of 0.58fy. This is the method employed by the British Concrete Society

Technical Report 25, published in 1984.

Note: Because the additional reinforcement is calculated using stress considerations, the

suggested values are normally conservative. In the final analysis, you should check that the

beam/slab has adequate strength at ultimate limit state.


Calculation of ULS capacity

Ultimate limit state calculations are performed for the following:

Bending moment.

Linear shear.

Punching shear.

Moment capacity

The moment capacity is calculated using general flexural theory. The tendon strain at ultimate

limit state is given by

papepb

where

pe = Strain due to tendon pre-stress after losses

pa = Additional strain due to applied loading

The strain due to pre-stress is determined from the stress-strain curve. If the pre-stress is within

the elastic limit, the strain is given by

s

pe

peE

f

The additional strain, pa, is determined by considering the change in concrete strain at the level of the tendon. The concrete strain distribution resulting from the effective pre-stress force

is shown as a dashed line in the figure.


Thus, for bonded tendons, the additional tendon strain is given by

uepa

where

ce

E

prestressConcrete at the level of the tendons

For un-bonded tendons

uepa

In general, one can say

uepa 21

where

1 and 2 = Bond coefficients

The program uses the following typical bond coefficients values:

Tendon bond

coefficients

Pre-tensioned and bonded

post-tensioned tendons

Un-bonded post-

tensioned tendons

1 1.0 0.5

2 1.0 0.1

It now follows that

cuepax

xd

21

and

cuape

papepb

x

xd

21

This can be rewritten as

cpepbcu

cu

d

x

12

2


From equilibrium it follows that

bxfkAf cupspb 1

Therefore

cpepbcu

cu

ps

cupb

A

bdfkf

12

21

The values of fpb and pb are solved by iteration using the stress-strain curve to subsequently yield the neutral axis depth, x.

The ultimate moment of resistance is then calculated as

)( 2xkdAfM pspbu

The calculated ULS capacity envelopes for bending moment and shear force incorporate all

tendons and additional reinforcement entered. Strain is calculated on the assumption that plane

sections remain plane and concrete and steel stresses are then calculated correspondingly.

Note: The secondary moments, or a portion thereof, caused by pre-stressing may optionally be included in the ULS calculations. Refer to page 6-70 for information on specifying the

percentage of secondary moment to be included in the analysis.

Linear shear

The linear shear checks performed by the program are done according to the provisions of

codes using the procedure described below.

An analysis is done on the sub-frame with only the equivalent tendon loads applied. The

minimum fibre stress as a result of the tendon forces is then calculated as

Z

M

A

Pf

concrete

tendonspt

The section modulus, Z, is taken at the top for negative bending and at the bottom for positive

bending.

The cracking moment is then calculated as

Z

f.M

pt

o

80

The section is considered as cracked in areas where the ultimate moment exceeds the cracking

moment.


In areas that are un-cracked, the shear capacity is calculated as

tcptwco ff.fhb. V 806702

where

ft = Concrete tensile strength

= cuf.240

fcp = Average concrete compressive pre-stress

= concrete

tendons

A

Pfor rectangular sections

= I

zP

A

P ftendons

concrete

tendons for flanged sections

zf = Distance from the neutral axis to the junction of the flange and the web of the

section which falls inside the compression zone

In areas that are cracked, the shear capacity s given by

M

VMdb)v

f

f.- ( V o

wcpu

pe

cr 5501

where

tendon

tendons

pu

pe

UTS

P

f

f

tendonsofNo

The value of vc is calculated by taking into account the total area of pre-stressing tendons and

unstressed steel.

In areas that are cracked, the shear capacity Vcap is the minimum of Vco and Vcr calculated

above.

The shear forces are reduced by the vertical components of the tendon forces if this was

specified. Where the shear force V is less than 0.5 × the shear capacity Vcap, no shear

reinforcement is required. Shear reinforcement must be supplied in zones where

(Vcap + 0.4bwd) V 0.5Vcap:

f.

b.

S

A

yv

w

v

sv

870

40


If V > Vcap + 0.4bwd then

tyv

cap

v

sv

df.

V - V

S

A

870

where

dt = Depth to the bottom reinforcement or tendons about which the stirrups are taken.

Linear shear is normally not a problem in flat slabs, but comes into play if ribbed slabs and

beams are analysed. For flat slabs, punching shear is normally the main shear design criterion.

Evaluation of punching shear

The first item to be determined is the enhanced shear. Columns have to be considered as either

internal, edge or corner columns. For purposes of calculations done by the program, the

following is assumed:

If no edges are closer than 5d from

the column centre, the column is

considered to be an internal column.

If one edge is closer than 5d from

the column centre, the column is

considered to be an edge column.

If two edges are closer than 5d from

the column centre, the column is taken as a corner column.

The enhanced shear force, Veff, for an

internal column is then calculated as the

largest of

1 1 05

1 1 05

1 15

txeff

b

ty

eff

b

eff

MV V( . )

Vy

MV V( . )

Vx

V . V


where

Mty = Moments transferred between slab and column in the X direction, i.e. about the

Y-Y axis

Mtx = Moments transferred between slab and column in the Y direction

xb = Projected width of the critical perimeter in the X directions

yb = The projected width of the critical perimeter in the Y direction

Note: The factor 1.05 is derived from 1.5M as given by the codes, with a 30% reduction allowed if the equivalent frame method with pattern loading has been used in calculating the

moments.

For an edge column, the enhanced shear force is the largest of

V. V

)Vx

M.. V( V

eff

eff

251

051251

If the edge lies parallel with the X-axis, then M = Mty and x = yb. Similarly M = Mtx and x = xb

for the edge parallel to the Y-axis.

For a corner column, the enhanced shear force is given by

V. Veff 251

The effective shear force is then adjusted by the vertical components of the tendon forces as

specified. The shear capacity is subsequently checked for each perimeter and reinforcement

calculated.

The shear capacity on a specific perimeter is given by

duvV critccap

where

ucrit = Critical perimeter

d = Effective slab depth

The value of vc is calculated for both the x and y-directions and the average of the two values

used. If Veff exceeds Vcap, shear reinforcement is calculated as

yv

crit

yv

critceff

svf

du

f

duvVA

87.0

4.0

87.0

The shear reinforcement represents vertical links to be placed in slabs deeper than 200 mm.


Circular columns

Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992,

the use of circular perimeters seems a more rational approach to evaluating punching shear for

circular columns. The program recognises this and uses the following design approach for

checking punching by circular columns:

As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx

and vcy. Put differently, one could consider an imaginary square shear perimeter when determining vc.

The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter

circular perimeter (compared to a rectangular perimeter) yields a lower (conservative)

shear force capacity.


Input

The beam/slab definition has several input components:

Parameters: Material properties, load factors and general design parameters.

Tendon data: Tendon properties and profile generation options.

Sections: Enter rectangular, I, T and L-sections.

User-defined sections: Complex section geometries.

Spans: Define spans and span segments.

Supports: Define columns, simple supports and cantilevers.

Column heads: Square and tapered drop panels.

Loads: Uniform distributed loads, point loads and moments.

Load combinations: User-defined combination of load cases.

Parameters input

The following general parameters are required for analysis and design:

fcu: Characteristic 28day strength of concrete (MPa).

fy: Characteristic strength of additional un-tensioned reinforcement (MPa).

fyv: Characteristic strength of shear reinforcement (MPa).

fci: Characteristic strength of concrete at transfer of pre-stress (MPa).

Ec: Concrete modulus of elasticity (kPa).

Est: Modulus of elasticity of unstressed steel (kPa).

Density: Concrete density used for calculation of own weight.

Note: Own weight is automatically added to the dead load with the 'auto load combination' mode selected and to the first load case with the 'user load combination' mode selected –

refer to page 6-82 for more detail on the load combination modes.

Top cover: Concrete cover to top of tendon sheaths (mm).

Bottom cover: Concrete cover to bottom of tendon sheaths (mm).

Reduce moments to column face: If selected, this option will take the moments at the

column faces as the design moments rather than the moments at support centres.


Reduce shear by tendon force component: Select this option to include the effect of

tendons in punching shear checks.

SLS DL factor: Serviceability limit state dead load factor used for calculation of

deflection, stresses and crack widths.

SLS LL factor: Serviceability limit state live factor.

ULS DL factor: Ultimate limit state dead load factor used for calculation of moments, shear and reactions.

ULS LL factor: Ultimate limit state live load factor.

Note: In the automatic load combination mode, the ULS load factors are used with the

patterned dead and live loads. The load factors are ignored when using the user load

combination mode. Refer to page 6-82 for more detail on specifying your own load

combinations. The procedure of automated pattern loading is explained on page 6-43.

Redistribution: Percentage of moment redistribution to be applied. Redistribution should

be limited 10% in structures over four storeys high where the frame provides lateral

stability.

Optimised/downward: Method of moment redistribution.


Secondary moment: Moments resulting from reactions to the pre-stress in statically

indeterminate beams. Some design methods, e.g. the method given in Report 25, ignore

secondary moments. Report 2 of the JSD recommend the tendons be considered as

external forces with a load-balancing effect and hence secondary moments are to be taken

into account.

Live load permanent: Percentage of live load to consider as permanent when calculating long-term deflections.

Attached torsional members: This option enables the reduction in column stiffnesses as

allowed for by ACI 318 - 1989. To prevent overestimation of column moments, it is

recommended that this option should be enabled. For more detail on the sub-frame

analysis technique used by the program, refer to page 6-43.

Edge beam: This option only applies if attached torsional members are used and allows

for the case where the columns are framing into the slab on one side only.

: The thirty-year creep factor used for calculating the final concrete creep strain.

cs: Thirty-year drying shrinkage of plain concrete.

The graphs displayed on-screen give typical values for the creep factor and drying shrinkage

strain. In both graphs, the effective section thickness is defined for uniform sections as twice

the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion

in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made,

stresses and relative humidity may vary considerably during the lifetime of the structure and

appropriate judgements should be made.

Tendon data input

Characteristics can be entered for up to three types of tendons or cables:

Bonded: Classify tendons as bonded (grouted after stressed) or un-bonded.

Ultimate strength: Ultimate tensile strength (UTS) of one tendon or cable (kN).

Maximum stress: Maximum tensile stress as a percentage of the UTS.

Outside diameter of sheath: The diameter of a tendon or cable, including sheath or duct (mm). The program measures concrete cover to the outside diameter.

Tendon area: The cross sectional area of the tendon or cable itself (mm2).

k: Friction coefficient due to unintentional variation from the specified profile ('wobble' in

the sheath). Both BS 8110 and SABS 0100 - 1992 recommend a value of not less than

33E-4 in general. Where wobbling is limited, e.g. rigid ducts with close supports, a


reduced value of 17E-4 may be used. For greased tendons in plastic sheaths, a value

of 25E-4 may be taken. However, for greased tendons, both FIP and Report 2 of the JSD

recommend a value of 10E-4.

μ: Friction coefficient due to curvature of the tendon. BS 8110 - 1997 and SABS 0100 -

1992 recommend values ranging from 0.55 to 0.05, depending on the condition of the

strand and the duct. For greased tendons, FIP and Report 2 of the JSD recommend values

of 0.05 and 0.06 respectively.

Wedge pull-in: Movement of the tendon will occur when the pre-stressing force is

transferred from the tensioning equipment to the anchorage, causing a loss in pre-stress.

The magnitude of the draw-in depends on the type of tendons used and the tensioning

equipment. Values of 4 to 8 mm are common for flat slab construction.

Tendon / Cable relaxation: Percentage long-term loss of force due to cable steel

relaxation.

Es: Modulus of elasticity of tendon (kPa). This value is typically set to 195E6 kPa.

Minimum radius: The minimum radius to use for harped tendons at change of slope (m).

This value is ignored when using parabolic tendons.


Sections input

You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a

basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their

webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be

move horizontally to obtain eccentric sections, for example L-sections. Whole sections can

also be moved up or down to obtain vertical eccentricity.

Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a

straight line. Vertical offsets of sections are used when calculation of tendon eccentricities and has no other effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are

displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

Sec no: The section number is used on the Spans input page to identify specific sections

(see page 6-77).

Bw: Width of the web (mm).


D: Overall section depth, including any flanges (mm).

Bf-top: Width of optional top flange (mm).

Hf-top: Depth of optional top flange (mm).

Bf-bot: Width of optional bottom flange (mm).

Hf-bot: Depth of optional bottom flange (mm).

Y-offset: Vertical offset the section (mm). If zero or left blank, the top surface is aligned with the datum line. A positive value means the section is moved up.

Web offset: Horizontal offset of the web portion (mm). If zero or left blank, the web is

taken symmetrical about the beam/slab centre line. A positive value means the web is

moved to the right.

Flange offset: Horizontal offset of both the top and bottom flanges (mm). If zero or left

blank, the flanges are taken symmetrical about the beam/slab centre line. A positive value

means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to enter a thin web with a wide top flange. You can also enter wide web (actual top flange)

with a thin bottom flange (actual web). The linear shear steel design procedure works with

the entered web area, i.e. Bw × D, as the effective shear area. Although the two methods

produce similar pictures, their linear shear modelling is vastly different.


User-defined sections input

Complicated sections can be

defined with the aid of the

section properties calculation

module, Prosec.

If Prosec is included in your set

of programs, it can be used for

entering sections as follows:

Enter the section dimensions

in millimetres.

Save the input data to a file,

e.g. 'Deck.G01'.

Calculate the bending sect-

ion properties.

Section properties calculated by Prosec are subsequently used to derive an equivalent

I-section. It is important that the area and inertia values of the effective I-section tie up. The

program limits the non-dimensional parameter I/(Ad2) to the range 0.02 to 0.225.

The properties of the user-defined sections are:

Sec no: Number of the section to be referenced when you enter spans on the Spans

input page (see page 6-77).

Designation: Prosec file name. If the cursor is on a defined section when you press the Prosec button, the relevant section will automatically be loaded and displayed in Prosec.

Area: Gross sectional area as calculated by Prosec (mm2).

Shear Area: Enter the area likely to transmit the vertical shear (mm2). Use your own

judgement on what portions of the section are suitable for transmitting shear.

Ix: Second moment of inertia about the X-axis calculated by Prosec (mm4)

Neut Axis: Position of the neutral axis as measured from the bottom of the section (mm).

Y-plas: Plastic neutral axis position. (mm).

Y-top: Offset of top surface from the datum line (mm). This value will initially be set to

zero but can be adjusted to move the section up (positive) or down.

Y-bottom: Offset of bottom surface from the datum line (mm). The section depth is given by Y-top minus Y-bottom.


Note: The derived equivalent I-section is not unique – more than one solution is possible. The derived section merely serves the purpose of simplifying the section for use by the

program. If a particular equivalent section does not seem like a realistic approximation of

the original section, you should consider entering the section as a normal I-section on the

preceding input page, using more appropriate section dimensions.

Spans input

Sections specified on the Sections input and User sections input pages are used here with

segment lengths to define spans of constant or varying sections.

Spans are defined by specifying one or more span segments, each with a unique set of section properties. The following data should be input for each span:

Span no: Span number between 1 and 20. If left blank, the span number as was applicable

to the previous row is used, i.e. another segment for the current span.

Section length: Length of span or span segment (m).

Sec No Left: Section number to use at the left end of the span segment.


Sec No Right: Section number to use at the right end of the span segment. If left blank,

the section number at the left end is used, i.e. a prismatic section is assumed. If the entered

section number differs from the one at the left end, the section dimensions are varied

linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are

interpreted literally. If a rectangular section should taper to an L-section, for example, the

flange will taper from zero thickness at the rectangular section to the actual thickness at the

L-section. If the flange thickness should remain constant, a dummy flange should be defined

for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than

the web and its depth made equal to the desired flange depth.

Supports input

You can specify simple supports, columns below and above, fixed ends and cantilever ends. To

allow a complete sub-frame analysis, columns can be specified below and above the beam/slab.

If no column data is entered, simple supports are assumed.

The following input is required:

Sup no: Support number, between 1 to 2'. Support 1 is the left-most support.


C,F: The left-most and right-most supports can be freed, i.e. cantilevered, or made fixed

by entering 'C' or 'F' respectively. By fixing a support, full rotational fixity is assumed, e.g.

the beam/slab frames into a very stiff shaft or column.

D: Depth/diameter of a rectangular/circular column (mm). The depth is measured in the

span direction of the beam/slab.

B: Width of the column (mm). If zero or left blank, a circular column is assumed.

H: Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple

supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank.

In the analysis, the support will be considered as a normal simple support. However, when

generating reinforcement bars, the program will extend the bars a distance equal to half the

support depth past the support centre line.

Code: A column can be pinned at its remote end by specifying 'P'. If you enter 'F' or leave

this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.


Column heads input

The punching shear capacity of a flat slab can be enhanced by defining column heads or drop

panels. If the ACI approach of column stiffness reduction is used, the stiffness of column heads

is also included in the sub-frame analysis.

The following data can be entered at each column head:

S/T: Specify a square or tapered column head. If left blank, a tapered head is used.

Diameter/Depth: The depth (in span direction) or diameter, in the case of circular column

heads (mm).

Width: The width of a rectangular column head (mm). Leave this field blank if the

column head is circular.

Height: The height of the column head (mm).

Note: The program will not check the validity of a column head in relation to column. It is

possible, for example, to define an unpractical circular column head for a rectangular

column.


Loads input

Dead and live loads are entered separately. The entered loads are automatically patterned

during analysis. For more detail on the pattern loading technique, refer to page 6-43.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines

as necessary to define each load case. Defined loads as follows:

Case D,L: Enter 'D' or 'L' for dead load or live load respectively. If left blank, the previous

load type is assumed. Use as many lines as necessary to define a load case.

Span: Span number on which the load is applied. If left blank, the previous span number

is assumed, i.e. a continuation of the load on the current span.

Wleft: Distributed load intensity (kN/m) applied at the left-hand starting position of the

load. If you do not enter a value, the program will use a value of zero.

Wright: Distributed load intensity (kN/m) applied on the right-hand ending position of the

load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly

distributed load is assumed.

P: Point load (kN).

M: Moment (kNm).


a: The start position of the distributed load, position of the point load or position of the

moment (m). The distance is measured from the left-hand edge of the beam. If you leave

this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of

the beam.

b: The end position of the distributed load, measured from the start position of the

load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation.

For more detail, refer to the explanation of the Parameters input on page 6-70.

Note: If you enter a concrete density on the Parameters input page, the own weight of the

beam/slab is automatically calculated and included with the dead load.


Load cases can be optionally be combined into load combinations.


Two loading modes are available:

'Automatic load combinations' allows for automatic pattern loading of dead and live loads,

e.g. as for typical building slabs.

'User load combinations' allows for combinations of the entered load cases, e.g. as for

bridge decks.

Note: No load combinations need be entered if the automatic load combination mode is selected.

As many lines as necessary may be used to input combinations of the various load cases:

Load Combination: Name of the load combination. If this field is left blank, the load

combination is taken to be the same as for the previous row in the table.

Load Case: Number or name of the load case.

ULS Factor: Load factor with which the load case should be multiplied for the ultimate

limit state.

SLS Factor: Load factor with which the load case should be multiplied for the



Tendon Profiles

You can let the program generate tendon profiles or you can enter profiles as required. The

program is capable of generating reasonable tendon profiles for typical beams and slabs that

you can adjust and change to obtain the required result.

Generated tendons can have parabolic or harped profiles. The program attempts to generate

tendons to balance the specified percentage of dead load. Profiles generated will not be perfect

for all cases and may require some manual adjustment.

Tendon profiles are displayed one set at a time, where a set is defined as one or more tendons

with the same profile and force distribution. The following parameters define the profile for

each span:

L: Left offset of tendon inflection point (parabolic) or slope change (harped) from left end of span (m).

R: Right offset of tendon inflection point or slope change from right end of span (m).

b1: Distance from top surface to tendon centre line at left end of the span (mm).


b2: Distance from bottom surface at midspan to tendon centre line (mm).

b3: Distance from top surface to tendon centre line at right end of the span (mm).

Tip: The values of L and R are normally taken is the greater of span divided by and 250mm for parabolic cables and span divided by four for harped cables.

The following properties cab be set for each group of tendons:

Number of tendons: Number of tendons in the set.

Tendon property no: Tendon property number 1, 2, or 3 as defined in the original input.

Life end position: Position of live end from left hand side of entire beam or slab.

Dead end position: Position of dead end from left hand side of entire beam or slab.

Parabolic / Harped: Parabolic or harped tendons.

The plotted tendon force diagrams represent the total force of all tendons:

The initial tendon forces are shown in blue and include losses due to friction, wedge slip

and elastic shortening of the concrete.

The final tendon forces are shown in red and include the long-term effects, tendon

relaxation, shrinkage and creep of the concrete.

The equivalent balancing loads are also displayed. The balancing loads are shown as

percentage of the equivalent dead load. The latter is defined as the total dead load for each

span, including own weight and any applied dead load, divided by span length.

Tip: Even if you want to specify your own tendon profile, it is nearly always easier to allow the program to generate the tendon profiles and then edit them, delete some or add more

tendon groups.


Reinforcement

Additional bending reinforcement and punching shear reinforcement can be designed

interactively.

Additional bending reinforcement

Diagrams are displayed for additional reinforcement required (blue lines) and reinforcement

entered (red lines). Anchorage and bond lengths are taken into account.

The required additional unstressed reinforcement is calculated in accordance with the Concrete

Society Technical Reports 17 (paragraph 3.3 and 4.3) and 25 (paragraph 4.11):

A minimum of 0.15% unstressed reinforcement is taken over columns over a width equal

to the column width plus four times the slab width.

Where tensile stress prevails over supports, reinforcement is supplied to resist

tensile force.

At midspan and where the tensile concrete stress exceeds 0.15fcu, a working stress of

0.58fy is used in the reinforcement.


Tip: The method used to calculate reinforcement aims to limit tensile concrete stress by adding sufficient reinforcement and tends to be conservative. Less reinforcement can

normally be used, say three quarters of the peak values. In the final analysis you should

check that the various requirements for crack width, ULS capacity and nominal

reinforcement are met.

Reinforcement bars are entered as follows:

Span: Span number

T/B: Reinforcement at Top or Bottom

Bar: Specify the steel as individual bars, e.g. 3T16, 2Y20 or 4R16, or groups of bars, e.g.

Y25@300. One can also combine bars, e.g. 2T16 + T10@250.

L/R: If a hook or bend is required on the left end of the bar, enter an 'H' or 'B' in the L

column. For a hook or bend on the right end of the bar, use the R column.

X: Position of left end of the bar measured from the left end of the span (m).

Length: Length of the bar (m).

Punching shear reinforcing

The data required for punching shear design is categorised as follows:

Geometrical input.

Forces and parameters required calculating the effective shear force Veff.

Tendons and additional reinforcement to consider when calculating the allowable shear

stress, vc.

The following parameters are required to define the column and slab geometry:

A: Column dimension in longitudinal direction (mm). If a column below was originally

input, its D value will be used as default.

B: Column dimension in transverse direction (mm). If a column below was originally

input, its B value will be used as default.

C: Column head dimension in longitudinal direction (mm). Leave this field blank if there

is no column head.

D: Column head dimension in the transverse direction (mm). Leave this field blank if there

is no column head.

Deffx: Effective depth for reinforcement orientated in the X-direction (mm).

Deffyx: Effective depth for reinforcement orientated in the Y-direction (mm).


X: Longitudinal distance from the support centre to the edge of the slab (mm).

Y: Transverse distance from the support centre to the edge of the slab (mm).

Corner: Enter 'Y' for an outside corner or 'N' for an inside corner.

For the calculation of the effective shear force Veff, the program detects internal, edge and

corner columns as follows:

Internal column: Both edges further than 5deff from the column centre.

Edge column: One edge closer than 5deff from the column centre.

Corner column: Two edges closer than 5deff from the column centre.

Information required calculating the effective shear force Veff:

Vt: Total Shear force transferred from slab to column.

Mtx: Moment transferred between slab and column in X-direction.

Mty: Moment transferred between slab and column in Y-direction.

Note: Irrespective of the selected loading combination mode, the program will assume that

pattern loading would have been applied. The program therefore automatically reduces the entered values for Mtx and Mty by 30%. Refer to BS 8110 - 1997 clauses 3.7.6.2 and 3.7.6.3

and SABS 0100 - 1992 clauses 4.6.2.2 and 4.6.2.3 for detail.

UDL: Uniform ultimate load in the region of the column (kN/m). The shear force is

reduced by the portion of load within each perimeter considered.

Pcx: The pre-stressing force in the longitudinal direction deemed to have a shear relieving

effect (kN). The value will default to the total pre-stressing force of all tendons. This may

be accurate for banded tendons. However, for tendons spaced further apart, only those

passing through the shear perimeters should be considered. The vertical component of the entered total pre-stressing force is deducted from the effective shear force.

Pcy: The pre-stressing force in the transverse direction deemed to have a shear relieving

effect (kN). This value must be entered manually.

Slope-X: Average slope of tendons in X-direction crossing the punching shear perimeters.

The slope is used to calculate the vertical component of the pre-stress relieving the

effective shear force. The program will base the initial value on the generated tendon

profiles.

Slope-Y: Average slope of tendons in Y-direction crossing the punching shear perimeters.

The value must be entered manually.

Note: Although the program performs a uni-directional analysis for bending moment, deflections, etc, bi-directional effects are included in the punching shear design procedure.


Tip: For orthogonally stressed slabs, it is recommended that you design one direction, e.g.

the banded direction, and record the relevant punching shear values. On analysing the other

direction, you can enter these parameters for the Y-direction entered for complete

bi-directional punching shear checks.

The shear capacity is based on the following parameters:

Type: The number of the tendon types entered on the Parameters input page – refer to

page 6-70 for detail. The specified type's properties are used to calculate the pre-stressed

reinforcement passing through each perimeter.

N cables: Number of cables passing longitudinally through each perimeter (average per

side) in the X (longitudinal) and Y-directions (transverse). The area of the pre-stressed

cables is then incorporated in the calculation of the shear resistance Vc.

Note: When calculating the shear resistance Vc, both bonded and un-bonded tendons are considered.


Ast: Amount of conventional

reinforcement passing longitudinally

through each shear perimeter in the X and

Y-directions. The reinforcement values

Asx and Asy represent the minimum

amount of main reinforcement crossing

each perimeter in the X and Y-directions.

For a perimeter edge on both side if the

column, e.g. y1 in the sketch, you should

use the minimum of the amount of reinforcement crossing the left edge and

the amount crossing the right edge. For a

perimeter edge on one side only, e.g. y2 in

the sketch, use the amount of

reinforcement crossing that single edge.

Note: The amount of conventional reinforcement can be taken as the average (minimum for unsymmetrical reinforcement) amount passing through the perimeter on the left and the

right (as seen on the screen) of the column. For an edge or corner column, the amount

should be taken equal to the amount passing through the perimeter on the span side.


Design

The analysis is performed automatically when you access the View output pages.

Analysis procedure

Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections, concrete stresses and cracking are calculated by analysing the beam/slab

under pattern loading using the gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected

to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm

intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections

are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-61 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-43.

The resultant bending moment and shear force envelopes are then redistributed. Finally, the

required reinforcement is calculated.


The Input pages incorporate extensive error checking. However, serious errors sometime still

slip through and cause problems during the analysis. Common input errors include:

Entering too large reinforcement cover values on the Parameters input screen, gives incorrect reinforcement. Cover values should not be wrongly set to a value larger than half

the overall section depth.

Not entering section numbers when defining spans on the Spans input screens causes

numeric instability. Consequently, the program uses zero section properties.


Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful

examination of the analysis output. View the long-term deflection diagrams and determine

which component has the greatest effect:

The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom

reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the

middle of spans generally induces negative shrinkage deflection, i.e. uplift.

Large creep deflections (long-term deflection under permanent load) are often caused by

excessive cracking, especially over the supports. Compare the span to depth ratios with the

recommended values in the relevant design code.

Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection

component.






any load case.

Deflections

The elastic deflection envelope

represents the deflections due to

SLS pattern loading. The long-term deflection diagram

represents the behaviour of the

beam/slab under full SLS

loading, taking into account the

effects of shrinkage and creep:

The green line represents the

total long-term deflection.

The shrinkage deflection is

shown in red.


The creep deflection (long-term

deflection due to permanent loads) is

given by the distance between the red

and blue lines.

The distance between the blue and

green lines represents instantaneous deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-

term deflection values are based on the reinforcement required at ultimate limit state. Once

reinforcement has been generated for a beam, the long-term deflections will be based on the actual reinforcement instead.

Moments and shear forces

The bending moment and shear

force diagrams show the

envelopes due to ULS pattern

loading. The capacities are

calculated from the entered

tendons and conventional rein-forcement. Capacities are shown

in blue and actual moments and

shear forces in red.


Concrete stress

Serviceability limit state stress envelopes are displayed for the following cases:

At transfer of tendon forces:

Only initial dead loads and

no additional dead loads are

considered.

At SLS: The full SLS loads are applied and long-term

losses in tendon forces

included.

The actual stress envelopes are

shown in red and the allowable

stresses in blue. Guidelines for

allowable concrete stresses are

given on page 6-59.

Crack widths

In the calculation of crack widths, the program takes into

account all bonded tendons and

also any additional

reinforcement that has been

entered. The crack spacing is

calculated on the assumption

that all the bars and bonded

tendons are spaced equally

across the widest portion of the

section.

Un-bonded tendons are ignored when calculating crack widths.

If too few bars or bonded

tendons are present, rotations in

the sections will be high and

unrealistic values of deflection

will result. The program will

give a warning when this occurs.


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad.

Various settings are available to include input and design diagram and tabular result.





is saved as part of a project and therefore does not need to be saved in the design module

as well.


Profile Scheduling

Designed tendons can be

scheduled as Padds compatible

drawings. Profile properties are

taken from the Tendon profiles

input page. Enter Padds file name

special notes that should appear

on the schedules and then click

Generate schedules.

The resulting schedule can be opened in Padds for further

editing and printing.

Tendon detailing in Padds

Apart from other reinforcement detailing commands, Padds cab also draw tendons in plan.


Finite Element Slab Analysis

Fesd (Finite Element Slab Design) can perform linear elastic plate bending analyses of

two-dimensional concrete slab structures. Reinforcement can be calculated from moments

transformed using the Wood and Armer equations.

To design concrete membranes, use the Space Frame Analysis module instead.

Note: This module is no longer developed or supported, and was removed from the program toolbar in PROKON version 2.4. However, for the sake of users that purchased this module

in the past, it is still access via the Program menu. To analyse and design flat slabs, the

recommended procedure is to use shell finite elements in the Frame Analysis module. See

Chapter 3 for more information.





Sign conventions

Slab input is done using the global axes. The analysis output is given in a mixture of global

axis and local axes values.

Global axes

The global axis system is nearly exclusively used when entering slab geometry and loading.

Global axes are also used in the analysis output for deflections and reactions.


For the sake of this definition, the

X-axis is chosen to the right.

The Y-axis always points vertically

upward.

Using a right-hand rule, the Z-axis points out of the screen.

Note: Unlike some other 3D programs that put the Z-axis vertical, this program takes the

Y-axis vertical.

Local axes

Local axes are used in the output for

bending stresses:

The local x-axis is chosen parallel to

the global X-axis.

The y-axis is taken parallel to the

negative Z-axis.

The z-axis is then taken vertical parallel

to the Y-axis.


Shell element stresses

Shell element stresses are given using the local axes:

Bending stresses: The entities Mx and My are moment per unit width about the local x and

y-axes.

Mxy represents a torsional moment in the local x-y plane.

The principal bending moments per unit width are represented as Mmax and Mmin.

Note: To assist you in evaluating shell element stresses, stress contour diagrams show

orientation lines at the centre of each shell element. An orientation line indicates the

direction the direction (not axis) of bending or plane stress. In a concrete shell, the

orientation line would indicate the direction of reinforcement resisting the particular stress.

Wood and Armer moments and shell reinforcement axes

Reinforcement is calculated in the user-defined x' and y'-directions. Unlike the shell bending

stresses that are taken about the x and y-axes, the Wood and Armer moments are given in the x'

and y'-directions. Refer to page 6-118 for detail.




Distance mm,m ft, inch

Force N, kN lb, kip

Finite element analysis

Fesd uses four-node quadrilateral and three-node triangular isoparametric shell elements with

plate bending behaviour. The bending formulation of the quadrilateral shell element was

derived from the Discrete Kirchoff-Midlin Quadrilateral.

Accuracy of triangular elements

Both the quadrilateral and triangular elements yield accurate stiffness modelling. However,

stress recovery from the triangular elements is not as accurate as is the case for quadrilateral

elements. This means that deflections calculated using triangular elements are generally quite

accurate, but moments may be less accurate.


Stress smoothing


are calculated at the Gaussian integration points and subsequently extrapolated bi-linearly to

the corner point and centre point of each element. Stresses at common nodes are smoothed by

taking the average of all contributing stress components.

Element layout

Consider a typical continuous flat concrete slab supported on columns or walls. To ensure accurate modelling of curvature, a minimum of about four elements should be used between

bending moment inflection points. This translates to a minimum of about eight elements per

span in both directions.

Using more elements per span often does not yield a significant improvement in analysis

accuracy. In addition, the particular finite element formulation yields its most accurate results

when the element thickness does not greatly exceed its plan dimensions.

For a typical concrete slab with a thickness of about one-tenth or one-fifteenth of the span

length, a reasonable rule of thumb is to make the plan dimensions of the shell elements no

smaller than the thickness of the slab. In other words, use a maximum of about ten to fifteen

elements per span.

Concrete design

Fesd can perform reinforced concrete design for shell elements. The Wood and Armer

equations are used to transform the bending and torsional stresses to effective bending

moments in the user-defined x' and y'-directions.

Note: The Space Frame Analysis modules can design shells for in-plane stresses as well. Refer to Chapter 3 for detail.


Codes of practice

The following concrete design codes are supported:

ACI 318 - 1999.

ACI 318 - 2005.

AS 3600 - 2001.

BS 8110 - 1985..

BS 8110 - 1997.

CP65 - 1999.

CSA A23.3 - 1994.

Eurocode 2 - 1992.

HK Oncrete - 2004.

IS: 456 - 2000.

SANS 0100 - 2000.


Input

Work through the relevant Input pages to enter the slab geometry and loading:

General input: Enter special design parameters.

Nodes input: Slab coordinates.

Shell elements input: Define shell elements.


Point loads input: Point loads and moments.

Shell loads input: Apply uniform distributed loads to shells.

Load combinations input: Group dead and live loads in load combinations.

Alternative methods of generating slab analysis input are discussed on page 6-117.

Viewing the structure during input


Several functions, all of which are described in detail in Chapter 2, are available to help you using pictures of the structure:


Use the View Point Control to set a new viewpoint or camera position.

Use the View Planes Control to view a slice through the slab.

The Options menu makes the following additional functions available:

Graphics:

Select whether you want items

like node numbers and supports to

be displayed.

Display the structure with full 3D

rendering, e.g. to verify the thickness of slab sections.

Choose quick or detailed

rendering. Quick rendering is

faster than the detailed method,

but you may find that some

surfaces are drawn incorrectly.


All surfaces are drawn as polygons. You can choose to make the surfaces transparent

or have them filled and outlined.

Contour values, like those on the reinforcement contour diagrams, can optionally be

shown.

Tip: The Graphics options and 3D rendering function can also be accessed using the buttons next to the displayed picture.

Views: You can save the current viewpoint and graphic display options. The current

view's name is displayed on the picture. To re-use a saved view, click the view name

on the picture to drop down a list of saved views. A detailed explanation is given

in Chapter 2.

The functions described above can also be used when viewing output. Contour diagrams, for example, are drawn as polygons. You can therefore use the Graphics options setting for

polygons to change their appearance. Views defined during input are also available when

viewing output and vice versa.

General input

The General input page handles several important analysis parameters.

Concrete design parameters

Specify the concrete and reinforcement material properties, concrete cover to reinforcement

and orientate the reinforcement axes. Refer to page 6-118 for more detail.

Envelope of load cases

Fesd calculates a set of results, including reinforcement values, for each load case or

combination analysed. To enable you to easily identify the worst-case scenario, you can

specify an envelope of load cases for which the minimum and maximum values are extracted.

The envelope can comprise load cases and/or load combinations. Results for the envelope is

presented and can be accessed as if a separate load case.

Wizards

The wizards are suitable for the


input files for some typical slabs.




repeatedly use the wizards to

generate complicated structures.


Note: The program is not limited to modelling only those slabs generated by the parametric modules. Any general two-dimensional slab can be treated. The parametric modules merely

serve to simplify input of typical slabs.

Own weight

The own weight of the frame can be calculated using the entered cross-sectional areas and

member lengths. If you specify a load case, the own weight is calculated and added to the other loads of that case.


By default, the own weight of the frame is set to not be included in the analysis. Be sure to




Point loads and Shell loads input pages. You may thus prefer to specify the own weight

load case only after completing all other input for the frame. However, you can also enter

the own weight load case at the start of the frame input process in which case you may

ignore the warning message (that the load case does not exist).








Title

Enter a descriptive name for the frame. It should not be confused with the file name you use

when you save the input data.


Nodes input

Use as many lines as necessary to enter the nodes defining the slab. A unique number must be

assigned to each node. The node number is entered in the No column, followed by the X and

Z-coordinates in the X and Z columns. If you leave X or Z blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the slab. You may also




Error checking

The program checks for nodes lying at the same coordinate. If a potential error is detected, an




The X-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate

(0,14.614).

The No of is set to '2', meaning that two additional nodes must be generated.



The values in the X-inc and Z-inc columns set the distance between copied nodes. The

coordinates 4 to 18 are spaced at 1.140 m and 0.472 m along the X and negative Z-axis

respectively. The coordinates of the additional nodes are thus (1.140,14.142) and (2.280,13.670).




Set the values of X-inc and Z-inc to the total co-ordinate difference to the last node and

enable the Inc to End option. The last node's coordinates are then first calculated and the

specified number of intermediate nodes then generated.


Once you have defined one or more nodes in the table, you can copy that relevant row’s nodes

by entering a '–' character in the No column of the next row. Then enter the number of


the X-inc and Z-inc columns.




No X Z

15 0.00 5.12

16 2.00 5.22

17 4.00 5.32

18 0.50 6.12

19 2.50 6.22

20 4.50 6.32

Block generation


last table row numbers in which the nodes were defined. Separate the row numbers with a '–'.


The nodes defined in rows 11 to 26 are copied twice. Node numbers are incremented by thirty for

each copy. The X and Z-coordinate increments are 10 m and zero respectively.

To copy one row only, simply omit the end row number, e.g. 'B10' to copy row 10 only.

The block generation function may be used recursively. That means that the rows specified

may themselves contain further block generation statements.

Tip: To move a group of nodes to a new location without generating any new nodes, set the

No-of to '1' and Inc to '0'.

Arc generation


the start and end row numbers. Enter the centre of the arc in the X and Z columns and use the X-inc column to specify the angle increment.

Example:


All nodes defined in rows 5 to 9 of the table will be repeated eleven times on an imaginary

horizontal arc. The centre point of the arc is located at the coordinate (10,1.5). The node


between the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise using

a right-hand rule.

To copy one row only, simply omit the end row numbers, e.g. 'A5' to copy row 5 only.


Rotating nodes



Deleting nodes

Nodes can be deleted by entering a special X-coordinate of '1E-9' or by entering 'Delete' in the

Inc to end column. This can be especially handy if you have generated a large group of nodes

and then need to remove some of them again.

Example:


Rigid links input

Point loads and supports invariably result in stress concentrations. In the case of slabs

supported on columns, it may be reasonable to ignore stress concentrations within the column

areas and rather work with the stress values at the column faces. An alternative approach could be to smooth the stresses that prevail with the close surrounds of each of the columns, e.g.

within a perimeter at a distance equal to the depth of the slab away from the column face.

Another more rational approach to modelling a slab at column supports is to introduce rigid

links. This approach entails stopping shell elements at the column face and then linking the

perimeter with the supported node at the position of the column centre. The high bending

stiffness of the rigid links gives a reasonable approximation of the increased stiffness of the

slab inside the perimeter of the column. The approach has the advantage of ridding the analysis

of high shell bending stress peaks at the points of support.


Shell elements input

Elements are defined by referring to corner nodes, four in the case of quadrilaterals and three

for triangles. You should enter the node numbers in sequence around the perimeter, either

clockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define a

triangular element.

Note: Quadrilateral elements generally yield more accurate analysis results than triangular elements. Refer to page 6-99 for more detail.


Selecting materials

Each slab element should have an associated

material.

To add one or more

materials to a slab analysis

data file, click Materials.

Open the relevant material

type screen and select the

materials that are required

for the current slab input.

After adding the selected

materials to the input, you

can select them by clicking the Material column to

drop down a list.




Error checking



will be displayed.



No of extra and Node No Inc columns.

Example:

The element enclosed by nodes 15, 16, 26 and 25 are copied ten times with a node number

increment of three, i.e elements (18,19,29,28), (21,22,32,310 etc.

Block generation


and last table row numbers in which the elements were defined, separated with a '–'.


All elements defined in rows 5 to 7 will be copied ten times with a node number increment of

twelve. The copied elements will use the same thickness and material properties as the original elements.

To copy one row only, simply omit the end row number, e.g. 'B5' to copy row 5 only.



Tip: When entering a complicated slab it may help to leave a few blank lines between

groups of elements. Not only will it improve readability, but it will also allow you to insert



Deleting elements

Shell elements can be deleted by entering 'Delete' in the Material column. This can be useful if


Example:

Elements 15-16-26-25 and 18-19-29-28 are deleted.

Supports input

Slabs require external supports to ensure global stability. Supports can be entered at nodes to

prevent any of the three degrees of freedom associated with plate bending, i.e. translation in the

Y-direction and rotation about the X and Z-axes. You can also define elastic supports and

prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a combination of the letters 'Y', 'x' and 'z' can be entered to indicate the direction of fixity. Use


capitals and lowercase to define restraint of translation and rotation respectively, e.g. 'Yxz'

means fixed against movement in the Y-direction and rotation about the X and Z-axes.


Tip: To enter a simple support with no moment restraint, one would typically enter a 'Y'.

If you want to repeat the supports defined on the previous row of the table, you need only enter

the node number, i.e. you may leave the Fixity column blank. If the Yxz column is left blank,

the supports applicable to the previous row will be used automatically.

Skew supports

The rotational supports 'x' and 'z' can be made skew by entering a value in the Angle column.

This feature may be useful when modelling slabs with rotational support perpendicular to skew edges.

Prescribed displacements

Use the X, x, and z columns to enter prescribed displacements and rotations. Being a global

support condition, the effect of the prescribed displacement is added once only to the analysis

results of each load case and load combination. Optionally enter a 'P' in the P/S column to

designate the values as prescribed displacements.

Elastic supports

Elastic supports, or springs, are defined by entering spring constants in the X, x, and z

columns. The spring constant is defined as the force or moment that will cause a unit displace-

ment or rotation in the relevant direction. Enter an 'S' in the P/S column to indicate that an

entered value is a spring constant rather than a prescribed displacement. If you leave the P/S

column blank, the entered values are taken as prescribed displacements.

Tip: The effect of a column above or below the slab can be modelled by entering their

bending stiffnesses as rotational spring supports about the x and z-axes. From simple elastic

theory, the rotational stiffness of a column that is fixed at the remote end is given as 4EI/L.

The stiffness of a column that is simply supported at the remote end is equal to 3EI/L.

Error Checking

The program does a basic check on the structural stability of the slab. If a potential error is


Note: You cannot define an elastic support and a prescribed displacement at the same node

because it will be a contradiction of principles.






Note: The display of supports can be enabled by editing the Display Options.

Point loads input

Loads on shell elements are categorised as point loads, i.e. concentrated loads at specific

coordinate, and element loads, i.e. uniform distributed loads.


'LL' for live load, etc. Load cases apply equally to the various load input screens, meaning that

you can build up a load case using different types of loads.



load case applicable to the previous row in the table is used.


Enter the coordinates and load values in the appropriate columns, using the global axis sign

conventions given on page 6-98. The load case at the cursor position is displayed graphically.

Press Enter or Display to update the picture.

Error checking



Generating additional point loads

Additional point loads can be generated using the Number of extra and X-increment and

Z-increment columns.

Shell loads

Distributed loads can be applied on shell elements. Enter a load case description in the Load

case column followed by the relevant element numbers in the Shell numbers column. The

program automatically assigns numbers to all shell elements in the sequence they are defined

on the Shells input page.


A series of elements can be entered by separating the first and last element numbers by a '–'

character, e.g. '1–6' to define elements 1 up to 6.Enter the distributed load intensity in the UDL

column.


Error checking

The program checks that the entered element numbers are valid. If an error is detected, an



The No of extra and Shell number Inc columns can also be used to generate additional shell

loads. The procedures are similar to that used to generating additional shell elements – see

page 6-111 for detail.



the load combination number in the Load Combination column; followed by the load case

name and relevant load factors.

If the Load Combination column is left blank, the load combination is taken to be the same as

for the previous row of the table. The load cases to consider in a load combination are entered

one per row in the Load case column. Enter the relevant ultimate and serviceability limit state

load factors in the ULS factor and SLS factor columns.



The ultimate and serviceability

limit states are used as follows:

Deflections are calculated

using the entered SLS loads.

A set of reactions is also

calculated at SLS for the

purpose of evaluating

stability and bearing

pressures.

A second set of reactions and all element forces are

determined using the

entered ULS forces.


Error checking


code that will be used in the member design and therefore does not check the validity of the

entered load factors.

Alternative slab input methods

Alternative means of slab input are available:

Parametric input: Modules are available for the rapid generation of input for typical slab

structures.

Graphical input: Structures can be drawn in Padds or another CAD system and converted

to slab analysis input.

Wizards

A number of typical frames can be input by entering a number of parameters. The Wizards do

most of the data input. See page 6-103 for detail on the wizards.

Graphical input

In some situations, it may be easier to define a slab's geometry graphically. With Padds you

can draw a slab and then generate a slab analysis input file.

Using Padds for slab input

To use Padds to define a slab's geometry:

1. Use Padds to draw the slab. Alternatively, import a DXF drawing from another CAD

system.

2. The slab should be drawn to scale using millimetres as unit.

3. The element grid is drawn using lines.

Tip: You may sometimes find it quicker to hatch an area with a line pattern and then

vectorise the hatch to turn it into normal lines.

4. Use the Generate input command on the Macro to display the drawing conversion

options. Choose the Fesd and press OK to start the conversion procedure.

5. Close Padds.

Tip: To see a graphical input example, open '\prokon\data\demo\inputgen.pad' in Padds.


Analysis parameters input

The General input page allows you to set the parameters relevant to the analysis.

Concrete design parameters input

It is generally impractical to design reinforcement to resist torsional moments in slabs.

Reinforcement is usually fixed in two directions approximately, but not necessarily,

perpendicular to each other. This justifies the use of transformed moments to calculate

reinforcement.

Fesd uses the Wood and Armer theory; to convert calculated bending and torsional moments

to transformed bending moments. More detail is given on page 6-100.

The required concrete design parameters are:

Enter the concrete and reinforcement material characteristics, fcu and fy.

Define the orientation for

the 'main' and 'secondary'

reinforcement, i.e. the x' and y'-axis. Looking from

the top, the x'-axis is

measured anti-clockwise

from the local x-axis to the

reinforcement x'-axis. The

y'-axis is in turn measured

anti-clockwise from the x'-

axis.

Define the reinforcement

levels in the slab by

entering the concrete cover values for the top and

bottom reinforcement in

both directions.

Reinforcement contours can be displayed on the Bending stresses output page.


Analysis

On completing the slab input, you should set the analysis options before commencing the

actual analysis.

Analysis options

Analysis options available on the General input page include:

Concrete design: If the model includes finite shell elements, you can optionally design the

shells as reinforced concrete members.

Add own weight: Select a load case to which the self-weight of the beam and shell

members should be added.

On the Analysis page, select the following:

Output file: Enter an output file name or accept the default file name, e.g. 'Fesd.out'.

Analyse load combinations only: Enable this option if the results of only the load

combinations are required. Generally, one would require results for the load combinations only. However, you may have a special need to view the results of specific load cases as

well. Disable this option to include the results for the individual load cases as well.

Analysing the slab

To analyse the slab, open the Analysis page and press Start

Analysis. The analysis progress

of displayed to help you judge

the time remaining to complete

the analysis.

After a successful analysis, the

deflected shape is displayed for

the first load case or load

combination or, in the case of

modal or buckling analysis, the

first mode shape.



During the input phase, the slab geometry and loading data is checked for errors. Not all


example, could be an accidental error on your side. However, the program can deal with a

situation like this and will allow the analysis procedure to continue.


successfully. Nodes with no elements, for example, have no restraints and will cause numeric instability during the analysis.



with the analysis, you will be taken to the input table with the error. However, choosing to

proceed and ignore the warning will have an unpredictable result.



example, if you entered incorrect section properties, such as a very small E-value, the mistake

may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness

matrix or extremely large deflections. The same applies to the stability of the slab.







Viewing output

The analysis results can be viewed graphically or in tabular format.


Diagram can be displayed for the following:

Deflections: Deflections are

generally small in relation to

dimensions of the structure.

To improve the visibility of

the elastic deflection

diagram, you can enter a

screen magnification factor.

Bending stresses in shells:

The x, y and xy

bending stresses: The bending stresses about

the local x and y-axes

and the torsional

stresses. The direction

(not axis) of bending is

shown as a small line on each shell element.

Maximum and minimum bending stresses: The principal bending stresses.

Reinforcement and Wood and Armer moments: Contours of the effective bending

moments and corresponding required reinforcement at the top and bottom in the x' and

y'-directions. The reinforcement direction is shown as a small line on each shell. Refer

to page 6-99 for an explanation of the use of the Wood and Armer equations and to page 6-118 for the definition of the reinforcement directions.

Note: Shell bending stresses are taken about the x and y-axes. In contrast, the Wood and

Armer bending moments are given in the x' and y'-directions.



Open the Output file page for a tabular display of the slab analysis output file. You can filter

the information sent to the calcsheets by enabling or disabling the relevant sections.

You can also quickly locate a section of the output file using the Find output function.


Calcsheets

Slab analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To





the slab by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is

saved as part of a project and therefore does not need to be saved in the slab analysis module as well.


Rectangular Slab Panel Design

The Rectangular Slab Panel Design module designs rectangular flat slab panels with a variety

of edge supports. The program should best be used for designing slabs with approximately

rectangular panel layouts. You can use the Space Frame Analysis or Finite Element Slab

Design module to analyse slabs with irregular panel layouts and openings.




Design scope

The program designs rectangular reinforced concrete flat slab panels. Design loads include

own weight, distributed and concentrated dead and live loads. Slab edges can be made free,

simply supported or continuous.

Bending moment is transformed to include torsional moment using the Wood and Armer

equations. Reinforcement is calculated using the normal code formulae.

Irrespective the selected design codes, long-term deflections are estimated in accordance with

clause 9.5.2.3 of ACI318 - 1992

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.




List of symbols

The design code symbols are used as far as possible:

Slab geometry

dx : Effective depth for reinforcement in the longer span direction, i.e. parallel to

the X-axis (mm or in).

dy : Effective depth for reinforcement in the shorter span direction, i.e. parallel to

the Y-axis (mm or in).

h : Overall slab depth (mm or in).

Lshort : Length of the short side of the slab, taken parallel to the Y-axis (m or ft).

Llong : Longer side length of the slab, taken parallel to the X-axis (m or ft).

Material properties

fcu : Concrete cube strength (MPa or psi).

fy : Reinforcement yield strength (MPa or psi).

ε : Time factor for long-term deflection

: Poisson's ratio, typically equal to 0.2.

: Unit weight of concrete (kN/m³ or lb/ft³)

Applied loads

WADL : Additional distributed dead load (kN/m² or kip/ft²).

WLL : Additional distributed dead load (kN/m² or kip/ft²).).

PDL : Additional dead point load (kN or kip).

PLL : Additional live point load (kN or kip).

Design output

Abotx : Bottom steel parallel to the X-axis (mm²/m or in²/ft).

Atopx : Top steel parallel to the X-axis (mm²/m or in²/ft).

Aboty : Bottom steel parallel to the Y-axis (mm²/m or in²/ft).

Atopy : Top steel parallel to the Y-axis (mm²/m or in²/ft).


Analysis of the slab

The program calculates bending stresses and elastic deflection by means of a finite element

analysis. Thirty-six plate elements are placed on a 6 x 6 grid. The program uses eight-noded

isoparametric finite elements that are well suited for thin plate analysis.

The analysis procedure employs a 2 x 2 Gaussian integration technique to calculate the element stiffness matrix. The stresses are calculated at the Gaussian integration points and

subsequently extrapolated to the eight nodes and centre point of each element. The stresses at

common nodes are smoothed by taking the average of all contributing stress components.


The program estimates long-term deflections by adjusting the stiffness of the slab based on the

level of cracking. The use of a time factor ε for estimating creep behaviour, is based on the

approach by ACI 318 – 1999 clause 9.5.2.3.

Typical values for ε are:

Duration of load Time factor ε

5 years or more 2.0

12 months 1.4

6 months 1.2

3 months 1.0

Instantaneous 0.0

Note: The calculated long-term deflections are not exact and should be considered a reasonable estimate only.

Reinforcement calculation

The finite element analysis yields values for bending stresses about the X and Y-axes and

torsional stresses. Due to the practical difficulties involved in reinforcing a slab to resist

torsion, the Wood and Armer equations are used to transform the bending and torsional

stresses to effective bending moments in the X and Y-directions.


Correlation with the design code values

The moments and reinforcement calculated by the program are generally lower than the values

given by the design codes. The discrepancy can be ascribed to the differences in the analysis

techniques used. In particular, the code values include allowances for pattern loading and

moment redistribution.

Considering continuous slabs, negative moments will generally correlate well while positive

span moments would be about ten to fifteen percent too low.

Note: In cases where pattern loading is important, e.g. continuous slabs, it is suggested that the calculated bottom reinforcement be increased by about fifteen percent.


Input

Use the single input table to define the slab and its loading.

Geometry and loads input

The following general points should be noted:

If the aspect ratio of the slab exceeds 3:1, it may be more appropriate to design it as

spanning in one direction only.

Long-term deflections are calculated if you specify a time factor, ε, larger than one.

Own weight is modelled by entering a value for the unit weight. The own weight is

automatically added to each load case entered.

For the ultimate limit state calculations, the own weight, additional dead load and dead

point loads are multiplied by the entered dead load factors. All live loads are similarly

multiplied by the live load factor.


To create load combinations, simply repeat the relevant loads in the table. Copying lines in

the table is easily accomplished using the table editor commands.

Tip: You can use the mouse to click on the slab picture and stretch its dimensions.

Supports input

The corners of the slab are supported vertically at all times. The edges can be supported using

the following codes:

Displacement: To support an edge in the vertical direction, i.e. simply supported. A typical

example would be a slab simply supported on a masonry wall that provides no rotational

support.

Rotation: To restrain rotation about an axis parallel to the slab edge, i.e. continuous. This

could be a reasonable model for a slab panel supported on columns if it is continuous with

one or more adjacent panels.

Displacement and rotation: The support conditions can be used together to support an edge

vertically and prevent rotation, e.g. a continuous slab resting on a wall.

Note: Edges that are made continuous are given zero rotation during the analysis. This could be a reasonable assumption provided that the adjacent panel has a similar flexural stiffness.

Where adjacent spans differ significantly in terms of span length and thickness, spans

should be modelled individually with continuous supports. Differences in the negative

moments on the continuous edges should then be redistributed manually according to the

relative stiffness of each panel.


Design

Due to the simple finite element arrangement used, the analysis procedure will complete

almost instantaneously. You can view the design results graphically:

Moments: Transformed

moment diagrams, using

the Wood and Armer

equations, for the top and

bottom in the X and

Y-directions are shown.

Values are given per unit width. The transformed

moments in the top and

bottom fibres represent the

moments to be resisted by

the calculated

reinforcement.

Deflections: Short-term

elastic deflections, based

on the un-cracked gross

concrete section are

shown. To view an estimate of the long term

effects like shrinkage and

creep, enable the show

long term deflections option.

Reinforcement: Required

reinforcement for the top

and bottom in the X and

Y-directions is shown. The

calculated reinforcement is

based on the transformed

moments and therefore includes the effects of

torsion.


Calcsheets

The slab panel design output can be grouped on a calcsheet for printing or sending to Calcpad.






is saved as part of a project and therefore does not need to be saved in the column design

module as well.


Detailing

Reinforcement bending schedules can be generated for designed slab panels. Bending

schedules can be edited and printed using Padds.

Generating a bending schedule

Based on your initial input and the design results, initial values are chosen for the

reinforcement. Change the values to suit your detailing requirements.


Schedule file name: Name of the Padds drawing and schedule file.

Detailing parameters:

First bar mark: Mark to

use for the main bar.

You may use any

alphanumeric string of

up to five characters, e.g. 'A', '01' or 'A01'.

The mark is incre-

mented automatically

for subsequent bars.

Concrete cover to

reinforcement

Reinforcement bond

length.

Drawing scale: The

drawing paper is sized

to fit the complete detail.

Reinforcement for top and bottom layers in each of the X and Y-directions.

Press Generate to create a Padds bending schedule with the entered settings. To discard all

changes you have made and revert to the default values for the designed column, press Reset.

Note: To detail slabs of more complex shape, use Padds.



Detailed editing and printing of bending schedules are done with Padds. For this, follow the

steps below:

In Padds, choose Open on the File menu and double-click the relevant file name. The file

will be opened and displayed in two cascaded widows. The active windows will contain

the drawing of the slab panel and the other window the bar schedule.


construction notes.



Member description: Use as many lines of the Member column to enter a description,

e.g. 'SLAB PANEL E'.






the file name, e.g. 'SLABE.PAD'. The schedule number can be edited as required to

suit your numbering system, e.g. 'P123456-BS405'.




Column Design 6-137

Column Design

The concrete column design modules are suitable for the design of the following column types:

Rectangular Column Design, RecCol: Solid rectangular columns of which the larger

column dimension does not exceed four times the smaller dimension.

Circular Column Design, CirCol: Solid circular columns where the simplified design

approach applicable to rectangular columns may be applied.

General Column Design, GenCol: Columns of any general shape and columns with

openings.

All column design modules can design reinforced concrete columns subjected to bi-axial bending. Bending schedules can be generated for editing and printing using the PROKON

Drawing and Detailing System, Padds.

Column Design 6-138



Design scope

The column design modules design reinforced concrete columns subjected to axial force and

bi-axial bending moment.

The following conditions apply to the design of rectangular and circular columns:

The design codes give simplified procedures for designing columns of which the ratio of

the larger to the smaller dimension does not exceed 1:4.

The procedure used for the design of rectangular columns is applied to the design of

circular columns.

The reinforcement layout is assumed to be symmetrical.

Reinforcement bending schedules can be generated for designed columns. Schedules can be

opened in Padds for further editing and printing.

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.



Column Design 6-139

List of symbols


Rectangular column geometry

b : Width of cross section, perpendicular to h (mm or in). This smaller column

dimension is taken parallel the X-axis.

d'x : Distance from the column face to the centre of the reinforcement resisting

moments about the X-axis (mm or in).

d'y : Distance from the column face to the centre of the reinforcement resisting

moments about the Y-axis (mm or in).

h : Depth of the cross section (mm or in). This larger column dimension is taken

parallel the Y-axis.

Circular column geometry

d' : Distance from the column face to the centre of the reinforcement (mm or in).

Ø : Diameter of column (mm or in).

Effective lengths

ßx : Effective length factor for bending about the X-axis

ßy : Effective length factor for bending about the Y-axis

Material properties



Es : Modulus of elasticity of reinforcement (GPa or ksi).

Applied loads

Mx top : Moment about the X-axis applied at the top end of the column (kNm or kipft).

If left blank, a value of zero is used. A positive moment is taken anti-

clockwise.

Mx bot : Moment about the X-axis applied at the bottom (kNm or kipft).

My top : Moment about the Y-axis applied at the top (kNm or kipft). A positive moment

is taken anti-clockwise.

My bot : Moment about the Y-axis applied at the bottom (kNm or kipft).

Column Design 6-140

P : Axial force in the column (kN of kip). A positive value denotes a downward

compression force and a negative value an uplift force.

Design output

Ac : Gross concrete area (mm² or in²).

Ascx : Area of vertical reinforcement to resist the effective design moment about

the X-axis (mm² or in²).

Ascy : Area of vertical reinforcement to resist the effective design moment about the Y-axis (mm² or in²).

b' : Effective depth to reinforcement in shorter direction of rectangular

column (mm or in).

h' : Effective depth to reinforcement in longer direction of rectangular

column (mm or in).

Lex : Effective length for bending about the X-axis (m or ft).

Ley : Effective length for bending about the X-axis (m or ft).

Madd : Additional moment about the design axis of a circular column (kNm or kipft).

Madd x : Additional slenderness moment about the X-axis due to the column deflection

(kNm or kipft).

Madd y : Additional moment about the Y-axis (kNm or kipft).

Mmin x : Minimum design moment for bending about the X-axis (kNm or kipft).

Mmin y : Minimum design moment about the Y-axis (kNm or kipft).

Mx : Design moment about the X-axis for rectangular column (kNm or kipft).

My : Design moment about the X-axis for rectangular column (kNm or kipft).

M' : Design moment (kNm or kipft).

M'x : Effective uniaxial design moment about the X-axis for rectangular

column (kNm or kipft).

M'y : Effective uniaxial design moment about the Y-axis for rectangular

column (kNm or kipft).

Column Design 6-141

Code requirements

The supported design codes have similar clauses with respect to bracing and end fixity

conditions.

Braced and un-braced columns

A column is braced in a particular plane if lateral stability to the structure as a whole is

provided in that plane. A column should otherwise be considered as un-braced.

Global lateral stability is normally provided by means of shear walls or other bracing systems.

Such bracing systems should be sufficiently stiff to attract and transmit horizontal loads acting

on the structure to the foundations.

RecCol and Circol allow you to set independent bracing conditions for bending about the X

and Y-axis of rectangular columns.

Effective length of columns

The effective length or height of a column depends on its end conditions, i.e. the degree of

fixity at each end. Four end condition categories are defined in the design codes:

End condition 1: The end of the column is connected monolithically to beams or slabs that

are deeper than the column dimension in the relevant plane.

End condition 2: The end of the column is connected monolithically to beams or slabs

which are shallower than the overall column dimension in the relevant plane.

End condition 3: The end of the column is connected to members that provide some

nominal restraint. In the context of this program, this condition is regarded as pinned.

End condition 4: The end of the column has no lateral or rotational restraint, i.e. a free end

of a cantilever column. In the context of this program, this condition is regarded as free.

The various codes generally suggest effective length factor, ß, in line with the following:

End condition

at the top

End condition

at the bottom

ß (Effective

length factor)

Column in braced frame (ß 1.0)

Fixed Fixed

Pinned

0.75 to 0.85

0.90 to 0.95

Pinned Fixed

Pinned

0.90 to 0.95

1.00

Column Design 6-142

End condition

at the top

End condition

at the bottom

ß (Effective

length factor)

Column in unbraced frame (ß > 1.0)

Fixed Fixed

Pinned

1.2 to 1.5

1.6 to 1.8

Pinned Fixed

Pinned

1.6 to 1.8

N.A.

Free Fixed 2.2

Note: The column design modules automatically calculate the effective length factors in relation to the specified end conditions. You may however manually adjust the effective

length factors if necessary.

Short and slender columns

A column is considered to be short if the effects of its lateral deflection can be ignored.

Slenderness in a given plane is expressed as the ratio between the effective length and the column dimension in that plane. The slenderness limits for short and slender columns set by

some of the supported codes of practice are:

Slenderness limit BS 8110 - 1997 SABS 0100 – 1992

Short Braced

h

lex and b

ley < 15 h

lex and b

ley < 2

1

M

M717

Column Unbraced

h

lex and b

ley < 10 h

lex and b

ley < 10

Maximum All lo 60b Lo 60b and b

4

h

Slenderness Cantilevers b60

h

b100lo

2

lo 25b and b 4

h

Note: In the above expressions for maximum slenderness, h and b are taken as the larger

and smaller column dimensions respectively.

Column Design 6-143

Input

The column definition has several input components:


Bracing conditions and fixity at the column ends.

Load cases.

Geometry input

The RecCol and CirCol modules have been simplified for the design of rectangular and

circular columns. Entering a column's geometry input in either of these modules is therefore

straightforward.

Tip: You can use the mouse to click on the column pictures and stretch certain dimensions,

e.g. the column length.

Column Design 6-144

General column geometry input

GenCol is used to design columns of any general shape and hence has a reasonably intricate

input procedure. A column section is entered as one or more shapes or polygons:


+ : The start of a new polygon. An absolute reference coordinate must be entered

in the X/Radius and Y/Angle columns. If you leave either blank, a value of

zero is used.

– : Start of an opening. An absolute reference coordinate must be entered in the

X/Radius and Y/Angle columns.

R : If you enter an 'R' or leave the Code column blank, a line is drawn using

relative coordinates, i.e. measured from the previous coordinate.

L : Enter an 'L' in the Code column blank to make the following coordinate

absolute.

A : To enter an arc that continues from the last line or arc. The arc radius and angle

are entered in the X/Radius and Y/Angle columns respectively. The angle is

measured clockwise from the previous line or arc end point.

Column Design 6-145

C : A circle with the radius entered in the X/Radius column.

B : A reinforcement bar with its diameter entered in the X/Radius column.

Note: Bar positions and diameters do not need to be entered when using RecCol and CirCol.

The X/Radius/Bar dia and Y/Angle columns are used for entering coordinates:

X : Absolute or relative X coordinate (mm or in). Values are taken positive to the

right and negative to the left.

Y : Absolute or relative Y coordinate (mm or in). Values are taken positive upward

and negative downward.

You do need to close the polygon – the starting coordinate is automatically used as the ending

coordinate. If two polygons intersect, the geometry of the last polygon takes preference and the previous polygon is clipped. A hole in a structure can, for example, be entered on top of

previously entered shapes.

Tip: You can leave blank lines between polygons/bars to improve readability.

If convenient, e.g. to simplify loading input, the column can be rotated by entering an angle.

Material properties input

The following material property values are required:

Concrete cube strength, fcu (MPa or psi).

Reinforcement yield strength, fy (MPa or psi).

GenCol also requires a value for the modulus of elasticity of the reinforcement, Es (GPa or ksi).

Specifying bracing and fixity conditions

Define the bracing and fixity conditions by making the appropriate selections. For an explanation of the terms used, refer to page 6-141. The effective length factors are

automatically adjusted in relation to the specified bracing and end fixity conditions. If

necessary, you may manually edit the effective length factors.

Note: RecCol allows the bracing and end fixities to be set independently for bending about

the X and Y-axis.

Column Design 6-146

Loads input

More than one ultimate load case can be entered:

Enter a case number and description for each load case.

Axial load (kN or kip). A positive value denotes a compression force. The program does

not automatically include the self-weight of the column. The self-weight should be

calculated and manually included in the applied loads.

Moment values (kNm or kipft). Use the same sign for the top and bottom moments about

an axis to define double-curvature about that axis.

Note: All entered loads should be factored ultimate loads.

You can use as many lines as necessary to define a load case – all values applicable to a

specific load case are added together.

Column Design 6-147

Design

The column design modules follow different design approaches:

RecCol and CirCol calculate the required reinforcement for the column.

GenCol evaluates the column for the entered reinforcement or calculates a single bar

diameter to be used at each defined bar position.

Irrespective the approach followed, additional moments are calculated for slender columns and

automatically added to the applied moments. The design moment is taken to be equal to or

larger than the minimum moment set by the code.

Rectangular column design

The design procedure given in the codes is applied. The column is evaluated at the top, middle

and bottom and the critical section identified as the section requiring the greatest amount of

reinforcement.

The design procedure can be summarised as follows:

Column design charts are constructed for bending about the X and Y-axis.

If the column is slender, additional slenderness moments are calculated as required about a

single or both axes.

For slender columns, the applied moments and additional moments are summed for each

axis.

In the case of bi-axial

bending, the moments are

converted to an effective

design moment about a

single design axis.

The reinforcement required

to resist the design moment is read from the applicable

column design chart.

Using the same procedure, a

design moment is derived

about the axis perpendicular

to the design axis.

Reinforcement resisting the

secondary design moment is

read from the relevant chart.

Column Design 6-148

Circular column design

The same simplified design

procedure as for rectangular

columns is used. The major and

minor column dimensions, h and b, are both set equal to the

column diameter.

The column is evaluated at the

top, middle and bottom and the

critical section identified as the

section requiring the greatest

amount of reinforcement.

Note: The design procedure for bi-axially bent slender columns tend to be conservative due

to he codes' allowance for additional moment about both the X and Y axes.

General column design

GenCol designs columns that do not necessarily fall inside the scope of the code requirements.

The program therefore reverts to basic principles, e.g. strain compatibility and equilibrium, to

analyse columns. This is achieved using an automated finite difference analysis.

The following calculations are followed:

The section properties are

calculated and the column

slenderness evaluated.

For a slender column, the

additional slenderness

moment is calculated and

applied about the weak axis,

i.e. axis of lowest second

moment of inertia. The

output gives the X and

Y-axis components.

The design moment and axis

are determined by taking the

Column Design 6-149

vector sum of the applied and additional moments.

An iterative solution is obtained using strain compatibility and equilibrium as criteria. The

simplified rectangular stress block given by the codes is used.

Note: Given the differences in the design procedures described above, GenCol will not yield identical results to RecCol and Circular Column Design modules when designing

simple rectangular or circular columns.

Column Design 6-150

Design charts

The column design charts can be displayed for the specified column geometry and material

properties:

Rectangular columns: Separate charts are given for bending about the X and Y-axis for

various percentages of reinforcement.

Circular columns: Due to axial symmetry, a single design chart is shown.

General columns: Separate charts are given for bending about the X and Y-axis.

Displaying design charts about other axes

You can use Gencol to define a column and then rotate it about any angle. Design charts can then be displayed for the resultant horizontal and vertical axes.

Column Design 6-151

Calcsheets

The column design output can be grouped on a calcsheet for printing or sending to Calcpad.

The different column design modules allow various settings, including design charts, tabular

design summaries and detailed design calculations.





is saved as part of a project and therefore does not need to be saved in the column design

module as well.

Column Design 6-152

Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedules

can be edited and printed using Padds.





Schedule file name: Name

of the Padds drawing and

schedule file.

Main bars (high yield steel

is assumed):

Rectangular columns:

Bar diameter for the corner bars and the

number and diameter of

the intermediate bars in

the horizontal and

vertical faces of a

rectangular column, as

displayed on the screen.

Circular columns: The

diameter and number of

main bars. It is

generally assumed good practice to use at least

six bars.

General columns: Main

bar diameters are

defined in the initial

input. The shape code

can be selected for each

individual bar.

Lap length factor for

main bars.

Column Design 6-153

Note: To ensure that the amount of reinforcement supplied is not less than the amount required, the relevant values are shown in a table.

Level at the bottom of the column (m or ft).

Level at the top of the column or, in the case of starter bars, at the top of the

base (m or ft).

Links:

Rectangular columns: Enter a link diameter and spacing, e.g. 'R10@200, and choose a

link layouts. Link type '2' should only be used with square columns.

Circular columns: Enter a link diameter and spacing and choose between using

circular or spiral links.

General columns: Select a shape code and follow the prompts to indicate the link

coordinates. Available shape codes include '35' (normally used for holding

intermediate bars in position), '60' or '61' (used to enclose four bars by a rectangular

link) and '86' or '87' (spiral bar for use with circular columns).

Link type: Choose one of the displayed link layouts.

Concrete cover on links (mm or in).

Detailing style to use:

First bar mark: Mark to use for the first main bar. You may use any alphanumeric

string of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incremented

automatically for subsequent bars.

Select a size for the sketch: If A4 is selected, the drawing is scaled to fit on a full page

and the accompanying schedule on a separate page. The A5 selection will scale the

drawing to fit on the same page with the schedule.

The following additional settings should be made:

Column continuous: Enable this option to make the column bars continuous and have it

detailed with a splice at the top. If this option is disabled the column is detailed with bends

at the top to anchor it in a beam or slab.

Starter bars only: If enabled, starter bars are generated instead of complete column bars.

Double links at kinks: If enabled, a set of double links is provided at the position of the

main bar kinks. Circular columns are detailed with straight bars, removing the need for

this option.


changes you have made and revert to the default values for the designed column, press Reset.

Column Design 6-154



steps below:



the drawing of the column and the other window the bar schedule.


construction notes.



Member description: Use as many lines of the Member column to enter a member

description, e.g. 'COLUMN TYPE 5'.






the file name, e.g. 'COLUMN5.PAD'. The schedule number can be edited as required

to suit your numbering system, e.g. 'P123456-BS201'.


Finally, combine the column drawing and schedule onto one or more pages using the Title

Block and Print command on the bending schedule window.


Retaining Wall Design

The Retaining Wall Design module is used to analyse retaining walls for normal soil and

surcharge loads or seismic load conditions. Various types of walls can be considered, including

cantilever, simply supported and propped cantilever walls.

Padds compatible bending schedules can also be generated for designed walls.



The following text gives an overview of the application of retaining wall analysis theory. For

more detailed information, reference should be made to specialist literature.

Design scope

The program can design most conventional retaining walls, including cantilever, simply

supported and propped cantilever walls. Both static and seismic load conditions are supported.

Analyses are performed using either the Coulomb or the Rankine theory.

Walls can be made to slope forward or backwards and the wall thickness can vary with height.

Toes may optionally be included. Line loads, point loads and distributed loads can be placed on

the backfill. A water table can be defined behind the wall. If required, the soil pressure

coefficients can be adjusted manually.

Padds compatible bending schedules can be generated for designed walls.

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.


List of symbols

Where possible, the same symbols are used as in the design codes.

Wall geometry

At : Wall thickness at the top (m).

Ab : Wall thickness at the bottom (m).

B : Horizontal base dimension in front of the wall (m).

C : Depth of the base (m).

D : Horizontal base dimension at back of the wall (m).

F : Depth of the shear key (m).

H1 : Total wall height (m).

H2 : Height of soil in front of the wall (m).

H3 : Height from top of wall to soil level at back of wall (m).

Hr : Height of the support point from the top of the wall for a simply supported or

propped cantilevered wall (m).

Hw : Height of water table, measured from the top of wall (m).

x : Inclination of the wall (m).

xf : Position of the shear key, measured from the front of the base (m).

xL : Position of the line load, measured from the front edge of the wall (m).

xP : Position of the point load, measured from the front edge of the wall (m).

ß : Angle of soil behind wall (°).

Material properties

fcu : Concrete cube compressive strength (MPa).

fy : Reinforcement yield strength (MPa).

: Angle of friction between wall and soil (°). Must be zero if Rankine theory is specified.

: Angle of internal friction (°).

: Poisson’s ration for the soil. The plane strain value should be used rather than the triaxial value – see geometry and loads input.


Applied loads

kh : Horizontal acceleration for seismic analysis (g).

kv : Vertical acceleration for seismic analysis (g).

L : Line load on or behind the wall (kN/m).

Lh : Horizontal line load at top of wall (kN/m).

P : Point load on or behind the wall (kN).

W : Uniform distributed load behind the wall (kN/m2).

Design parameters

DLfact : Ultimate limit state dead load factor.

LLfact : Ultimate limit state live load factor.

Pmax : Design bearing pressure at serviceability limit state (kPa)

SFOvt : Allowable safety factor for overturning at serviceability limit state.

SFSlip : Allowable safety factor for slip at serviceability limit state.

Design output

As1 : Flexural reinforcement in the wall (mm2).

As2 : Flexural reinforcement in the back part of the base (mm2).

As3 : Flexural reinforcement in the front part of the base (mm2).

Ac1 : Compression reinforcement in the wall (mm2).

Ac2 : Compression reinforcement in the back part of the base (mm2).

Ac3 : Compression reinforcement in the front part of the base (mm2).

Ds : Density of soil (kN/m3).

K : Active pressure coefficient, including seismic effects.

Ka : Active pressure coefficient.

Kp : Passive pressure coefficient.

Kps : Passive pressure coefficient including seismic effects.

M1 : Maximum ultimate moment in the wall (kNm).

M2 : Maximum ultimate moment in back part of the base (kNm).

M3 : Maximum ultimate moment in front part of the base (kNm).

Pfac : Pressure factor used for Terzaghi-Peck pressure distribution diagram.


V : Shear force in wall at base-wall junction (kN).

v : Shear stress in wall at base-wall junction (MPa).

vc : Allowable shear stress in wall at base-wall junction (MPa).

: Friction coefficient between base and soil.

General assumptions

The following assumptions are applicable to the analysis:

A unit width of the wall is considered.

Predominantly active soil pressures are assumed to act on the right-hand side of the wall

Predominantly passive pressures are present on the left-hand side of the wall.

Soil pressure, soil weight and wall self-weight are taken as dead loads.

Applied distributed loads, line loads and point loads are considered to be live loads.

If a water table is specified behind the wall, a linear pressure distribution is used along its

depth. The pressure applied on the bottom of the base is varied linearly from maximum at

the back, to zero at the front.

Point loads are distributed along the depth of the soil. In contrast, line loads are taken

constant in the transverse direction of the wall.

Application of Coulomb and Rankine theories

The program can analyse retaining walls using either the Coulomb wedge theory or the

Rankine theory.

Note: This manual does not attempt to explain the applicable theories in detail, but merely

highlights some aspects of their application. For more detail, reference should be made to

specialist literature.

Friction between the wall and soil

The higher the value of the angle of friction between the wall and soil, , the greater the degree of rotation of the system is implied. If the Coulomb theory is used, the friction angle should

preferable be set equal to the internal angle of friction, . This will yield pressures that

correlate better with the Rankine theory, than would be the case if is set equal to zero.

Active pressure on the shear key

Depending on its position, the shear key (if any) may be subjected to active pressure. The

program allows for active pressure to be included or excluded from the analysis.


Saturated and submerged soil

To keep input as simple as possible, the program does no provide an option to enter values for

specific gravity, void ratio, moisture content and degree of saturation. However, reasonable

modelling of saturated soil and submerged conditions is still possible:

If no water table is present, soil should be taken as a value that includes moisture content that can reasonably expected.

If a water table is present, the portion of the soil above the water table will likely have a

degree of saturation close to unity. Using the wet density rather than the dry density should yield reasonable results.

Point loads and line loads

Point loads and line loads behind the wall are incorporated using the Boussinesq theory. The

theory can be found in ‘Foundation Analysis and Design’ by Joseph E Bowles, chapter 11-13,

published by McGraw – Hill. It is recommended that the plane strain be used instead of the

tri-axial . Values of plain strain versus tri-axial can be found in the table below.

Tri-axial 0.30 0.33 0.35 0.40 0.45 0.50 0.60

Plane strain 0.42 0.50 0.54 0.67 0.82 1.00 1.50

Seismic analysis

The program uses the Okabe-Monobe equations, based on the Coulomb wedge theory, to

calculate revised active and passive pressure coefficients. The seismic portion of the active

pressure is assumed to act at 60% of the soil height behind the wall, effectively increasing the

lever arm of the soil pressure.

The densities of the materials are also adjusted by multiplying with (1-kv). An upward

acceleration therefore effectively decreases the stabilising effect of the wall and soil weight.

Live loads can be optionally included in a seismic analysis. If included, live loads are applied

with the same pressure coefficients as for dead loads.

Modelling of soil pressure behind rigid walls

The program suggests values for the active and passive pressure coefficients, Ka and Kp. These

values generally yield reasonable results for cantilever walls. However, simply supported and

propped cantilever walls tend to be very rigid. This means that the actual active soil pressures

could potentially rise well above the level normally assumed. The program therefore allows

uniform pressure distribution to be specified, i.e. Factive = Pfac Hwall soil Ka. Typical values


for the uniform pressure coefficient, Pfact, was determined by Terzaghi and Peck*. An average

value of 0.65 should yield reasonable results in most cases.

Seepage modelling

When a water table is modelled, seepage can optionally be allowed below the wall. If seepage

is allowed, hydrostatic pressure is modelled as follows:

The pressure behind the wall is taken as zero on the level of the water table and then

linearly increased with depth.

At the front of the wall, the pressure is taken as zero at ground level and linearly varied

with depth.

The hydrostatic pressure below the base is varied linearly between the values calculated behind and in front of the wall. If seepage is not allowed, the hydrostatic pressure in front

of the wall or below the base is taken as zero.

* Soil Mechanics in Engineering Practice, Third Edition, by Karl

Terszaghi, Ralph B. Peck and Gholamreza Mesri, published by Wiley-Interscience


Input

Use the input tables to enter the wall geometry, loading and general design parameters.


When entering the dimensions and loads working on the wall, you should keep the following

in mind:

Leave the value for F blank if a shear key is not required.

The value for Hr is only required for simply supported and propped cantilever walls.

Leave the Hw field blank if you do not want to define a water table. If you wish to design a

liquid retaining wall, you may set the water table above the soil level.

All applied loads work downward. Point loads are distributed at 45° through the depth of

the soil. Line loads are applied uniformly along the width of the wall.


Disable the option to allow seepage below the base if applicable, e.g. for liquid retaining

walls.

Allow active pressure to be applied to the back of the shear key (if any) if applicable, e.g.

if it is positioned towards the back of the base with compacted backfill.

Note: For suggestions on modelling saturated soil and submerged conditions, refer to page 6-159.

Enabling seismic analysis

When enabling Seismic analysis, you should also enter the following analysis parameters:

Enter the equivalent seismic accelerations in the horizontal and vertical directions.

Optionally include live loads in the analysis.

Soils pressure coefficients

The program will calculate the soil pressure coefficients by default. To use your own

coefficients, select User defined design values:

Active and passive

pressure coefficients,

Ka and Kp.

Soil friction constant

below the base, .

For simply supported

and propped cantilever walls, you

can choose between

triangular or uniform

pressure

distributions. In the

case of rigid walls, a

uniform pressure

coefficient can also

be entered. See page

6-160 for more

detail.


Selecting a wall type

Choose one of the following wall types:

Cantilever: The base is fixed against rotation with the wall cantilevering from it.

Simply supported: The base has no fixity, i.e. free to rotate. The wall is supported

horizontally at the bottom and at the level defined by Hr.

Propped cantilever: Fixed at the bottom and simply supported at the level defined by Hr.

Selecting an analysis theory

Choose between the Column and Rankine analysis theories. The Rankine theory cannot be

used if the slope of the backfill is less than zero. Due to this and other limitations of the

Rankine theory, use of the Coulomb wedge theory is often preferred.


Design

You can design the entered wall configuration or use the optimisation functions to obtain a

more economic design.

Analysing the entered wall configuration

The analysis includes several ultimate and serviceability limit state checks.

Calculating the ultimate design loads

Loads due to soil pressure and all weights, including concrete and soil, are multiplied by the

dead load factor. Applied loads are considered to be live loads and are therefore multiplied

with the live load factor.

Additional checks for propped cantilever walls

In the case of a propped cantilever wall, the program checks whether fixity can be obtained at

the base. Fixity is attained by balancing loads such as own weight and soil weight plus the

pressure distribution under the base against the fixity moment. If the fixity moment attainable

is less than one and a half times the theoretical fixed moment, the fixity moment is reduced and the bending moment diagram and soil pressures adjusted accordingly.

Checking stability

Stability against overturning of

the wall is checked by assuming

rotation about the lower front

corner of the base. If a shear key

is used and it is located within

one quarter of base width from

the front, the program also

checks for rotation about the

bottom of the shear key.

Design results

The design output gives the

following values at ultimate limit

state:

Bending moment diagrams (kNm).

Required reinforcement in the base and wall (mm2).

Maximum shear stress in the wall, v, and concrete shear capacity, vc (MPa).


Note: The wall design does not include any axial effects due to friction or applied loads.

Results for serviceability limit state checks include:

Safety factor for overturning.

Safety factor for slip.

Bearing pressure diagram below the base.

Optimising the wall dimensions

Optimise the wall using the following functions:

Select B: Optimise the horizontal base dimension in front of the wall. The smallest value

of B is calculated to not exceed the allowable bearing pressure and safety factor for

overturning. A warning message is displayed if an appropriate value could not be

calculated.


Select D: Optimise the horizontal base dimension behind wall. The smallest value of D is

calculated to satisfy the requirements set for the allowable bearing pressure and safety

factor for overturning.

Select F: The value of F is optimised using the safety factor for slip as only criterion.

Note: None of the optimisation functions considers all design criteria. It is therefore possible that after optimising the value of B, for example, the safety factor for slip is

exceeded. You may thus need to alternate optimisation functions to arrive at a workable

solution.


Calcsheets

The retaining wall design output can be grouped on a calcsheet for printing or sending to


pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall


is saved as part of a project and therefore does not need to be saved in the wall design module

as well.


Detailing

Reinforcement bending schedules can be generated for designed retaining wall. Bending

schedules can be edited and printed using Padds.







schedule file.

Wall and base reinforcement:

Reinforcement is

generated at various

positions in the wall and base using the

calculated ultimate

bending moments.

Change the diameters

and spacing as required.

Bond stress: Allowable

stress for evaluating bar anchorage of the wall starter bars. If 90° bends proof

insufficient, the program automatically uses full 180° hooks. Bar spacing is also

reduced to lower bond stress.


First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incremented


Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page




changes you have made and revert to the default values for the designed retaining wall, press

Reset. Also press Reset if you have changed the reinforcement bond stress and want to

recalculate the reinforcement.




steps below:


will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the retaining wall and the other window the bar schedule.


construction notes.




e.g. 'WALL TYPE C'.






the file name, e.g. 'WALLC'. The schedule number can be edited as required to suit

your numbering system, e.g. 'P123456-BS303'.

Note: The bottom left block is reserved for your company logo and should be set up as

described in the Padds User's Guide.




Column Base Design

The Column Base Design module is used to design and optimise rectangular column bases.

Padds compatible bending schedules can be generated for designed bases.




Design scope

The program designs rectangular concrete column bases subjected to vertical force and bi-axial

bending moment. The program designs the base at ultimate limit state for bending moment and

shear.

The program also verifies the stability requirements for overturning and bearing pressure.

Stability checks can be performed at ultimate limit state or using the working force method.

Refer to page 6-176 for details.

Reinforcement bending schedules can be generated for designed bases. Schedules can be

opened in Padds, for further editing and printing.

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.




List of symbols

The design code symbols are used as far as possible.

Geometry:

A, B : Horizontal and vertical base dimensions as shown on the screen (m or ft).

C, D : Horizontal and vertical column dimensions as shown on the screen (m or ft).

E, F : Horizontal and vertical column eccentricity as shown on the screen (m or ft).

X : Stub column height (m or ft).

X : Base thickness (m or ft).

Z : Soil cover on base (m or ft).

Rebar depth : Concrete cover plus half of the reinforcement diameter (mm or in).

Materials:

Density : Concrete and soil densities (kN/m³ or lb/ft³).

Friction angle : Internal friction angle for calculating passive soil stress.

Friction constant : Coefficient for calculating horizontal friction between the base and soil.

fci : Concrete cylinder strength of base and column (MPa or psi).

fcu : Concrete cube strength of base and column (MPa or psi).


Safety factors:

SFover : Safety factor for overturning.

SFslip : Safety factor for slip.

Loads:

Hx, Hy : Horizontal forces in X and Y direction (kN or kip).

LFovt : Load factor to use for evaluating overturning stability.

LFuls : Load factor for ultimate limit state calculations.

Mx, My : Moment in X and Y direction (kNm or kipft).

P : Vertical load (kN or kip).


Sign conventions

The X and Y-axes lie in the horizontal plane. Using a

right-hand rule, the Z-axis points vertically upward.

The sign conventions applicable to forces and

moments are as follows:

The vertical force, P, works downward.

The horizontal forces Hx and Hy are applied

parallel to the X and Y-axes.

The moments Mx and My are applied in the X

and Y-directions, i.e. about the positive Y and negative X-axes respectively

Post-processing frame analysis results

Forces are usually obtained using the reaction values calculated by frame analysis. When

extracting frame analysis output, the differences in the sign conventions and axis systems used

should be kept in mind:

Frame Analysis Mode

Applied load in Column Base Design module

P Hx Hy Mx My

Frame analysis reaction value to use

Plane Frame Analysis Ry – Rx None M None

Grillage Analysis Ry None None Mz Mx

Space Frame Analysis Ry – Rx Rz Mz Mx


Input

The column base definition has several input components:


Load cases and stability criteria.

Geometry input

Enter the base and column dimensions, omitting the values for the either column if only one

column is used. A column is positioned at the centre of the base unless non-zero values are

entered for E and/or F.

Tip: You can use the mouse to click on the base pictures and stretch certain dimensions, e.g. the base thickness and column sizes.


Material properties input

You are required to enter the properties of the concrete and soil fill and also specify the

concrete cover to the reinforcement.

Setting the stability criteria

Relevant limits should be entered for checking overturning, slip and bearing pressure at

serviceability and ultimate limit state.

Modern design codes tend to consider stability checks like overturning at ultimate limit state.

Depending on your own preference, you can use the program to check stability at ultimate limit

state or using the older method of working loads (permissible working stress):

Checking overturning at ultimate limit state

The ratio of the cumulative effects of factored destabilising loads to the effect of the factored

stabilising forces should not exceed unity. In this ratio, all forces are multiplied by the

appropriate ULS factors that exceed unity and only the self-weight components of stabilising

forces by the minimum ULS load factor that does not exceed unity.

When using this approach in the program, you will likely want to set the load factors for

overturning for all stabilising components of self-weight to the minimum prescribed ULS dead

load factor, typically between 0.9 and 1.0. For all other loads, a ULS load factor of between 1.2

and 1.6 (depending on the relevant code) will be appropriate.

Checking overturning using working loads

The older method requires the ratio of the cumulative effects of destabilising loads to

stabilising loads to be greater than an appropriate safety factor, typically 1/0.7 or 1.5.

When using this approach, you should enter unity values for all load factors for overturning

and specify relevant safety factors for overturning.

Checking slip at ultimate limit state

The program uses the entered load factors for ultimate limit state, LFuls, to evaluate slip. The

safety factor for slip should thus normally be set to unity.

Loads input

Enter one or more load cases. The following should be kept in mind:

All loads are applied at the centre of the columns. A column is positioned at the centre of the base unless values for E and/or F are entered.


For the case of a concrete column extending to the slab above, no stub column should be

entered, i.e. the value for X should be left blank.

For a steel base plate bearing directly on the base, enter the plate dimensions for the

column dimensions, C and D, and use zero for the stub column height, X.

Seen in elevation, the horizontal forces Hx and Hy are applied at the top of the stub

column.

All loads are entered un-

factored. The ultimate

design loads are obtained by

multiplying the entered

forces by the specified

load factor.

A positive value of P

denotes a downward force.

Use a negative value for

uplift.

Moments are applied in the

X and Y directions, rather than about the X and

Y-axes.

For detail on the sign conventions used for loads, refer to page 6-174.

Load factors

Each load has two load factors:

LFovt: Load factor to use for overturning stability check.

LFULS: Load factor to use for calculating bending moment, shear and reinforcement at

ultimate limit state analysis.

Own weight of the base is considered as a separate load case. Load factors for own weight is

entered in the geometry input table.

Note: Although overturning is also considered an ultimate limit state, the ULS abbreviation is used to designate the strength ultimate limit state.

For more detail on calculating the safety factor for overturning at ultimate limit state, refer to

page 6-178.


Design

A column base is designed for compliance with ultimate limit state and serviceability limit

state conditions:

The required reinforcement to resist ultimate moments is calculated.

Linear and punching shear checks are performed.

The stability of the base is evaluated at both ultimate and serviceability limit state.

Stability checks

Stability values for overturning, slip and bearing pressure are calculated at both ultimate limit

state and serviceability limit state. The following general principles apply:

Overturning: When considering overturning at ultimate limit state, the applied loads are

multiplied by the entered load factors for overturning to calculate the ratio of destabilising

to stabilising effects. At serviceability limit state calculations are performed using the

entered un-factored working loads.

Slip: At ultimate limit state, all forces are multiplied by their ULS load factors. The safety

factor for slip is calculated by dividing the resisting passive soil pressure and friction by

the horizontal forces causing slip. The same calculation is performed at serviceability limit

state using un-factored forces.

Bearing pressure: Entered loads are multiplied by their respective ULS load factors before

calculating the bearing pressure. The un-factored loads are used at serviceability limit

state.

Note: With careful manipulation of the load factors for overturning, you can manipulate the program to evaluate overturning stability at ultimate limit state or using the working loads

method. Refer to page 6-176 for more information.

Reinforcement calculation

The loads are multiplied by the specified load factor to obtain the ultimate design loads. The

design forces, including the base self weight and weight of the soil cover, are used to calculate

the ultimate bearing pressure below the base. The program calculates the bending moments in

the base and uses the normal code formulae to obtain the required reinforcement. Nominal

reinforcement is also calculated where applicable.


Shear checks

The required reinforcement for bending is used to calculate the shear resistance, vc, in the X

and Y-directions. For punching shear, the value is based on the average required reinforcement

in the two directions.

Linear shear

When considering

linear shear, lines are considered at a

distance equal to the

base depth in front of

each face of the

column. The

contribution of the

soil pressure block

outside the lines is

then used to calculate

the shear stress.

Punching shear

For punching shear, shear perimeters are considered at one and a half time the base thickness

from the column faces.

Various combinations as for internal, edge and corner columns are considered.

Design results

Results of stability checks:

Bearing pressure beneath the base. The 3D pressure diagram is shown in elevation.

Safety factor for overturning.

Safety factor for slip.

Note: Stability checks are performed at ultimate limit state (modern limit state approach)

and serviceability limit state (older working load approach). Depending of your way of

working and the design code used, you may prefer to use only one or both sets of results.

Results of strength checks at ultimate Limit State:

Design moments in the X and Y-directions in the bottom and top of the base (kNm or

kipft).

The corresponding required reinforcement (mm² or in²)


Linear and punching shear stresses and allowable shear stresses (MPa or psi).

Optimising base dimensions

The base dimensions can be optimised using the following functions:

Optimise A, B and Y: Calculate the optimum values for all the base dimensions. The

optimisation procedures take into account the specified material costs.

Select B: Calculate the optimum value for the base dimension in the Y-direction. All other

dimensions are left unchanged.

Select A: Calculate the optimum value for the base dimension in the X-direction. All other dimensions are left unchanged.

Note: When optimising the base dimensions A and B, the base thickness is kept constant

and no shear checks are performed. Where necessary, the base thickness should be adjusted

manually.


Calcsheets

The column base design output can be grouped on a calcsheet for printing or sending to


pictures.





is saved as part of a project and therefore does not need to be saved in the design module as

well.


Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedules

can be edited and printed using Padds.







schedule file.

Main reinforcement:

Change the displayed

bottom and top steel in

the X and Y-directions as necessary.

Top steel will only be

given for bases thicker

than 600 mm, or where

tension reinforcement is

required.

Column reinforcement:

At each column portion used, specify whether a normal column, stub column or no

column should be detailed.

Main bars: Diameter of column corner bars.

Middle bars: The number and diameter of intermediate bars in the horizontal and vertical column faces, as displayed on the screen.

Lap length factor: Splice length to allow for column starter bars.

Links: Diameter, dimensions and number of stirrups to hold column starter bars in

position.


First bar mark: Mark to use for the first main bar. You may use any alphanumeric

string of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incremented



Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page



Choose a configuration of bar shape codes to use for the bottom and, where

applicable, the top reinforcement.

Press Generate to create a Padds bending schedule with the entered settings. To discard all changes you have made and revert to the default values for the designed column, press Reset.



steps below:



the drawing of the column base and the other window the bar schedule.


construction notes.




e.g. 'BASE 6'.






the file name, e.g. 'BASE6.PAD'. The schedule number can be edited as required to

suit your numbering system, e.g. 'P123456-BS206'.

Note: The bottom left block is reserved for your company logo and should be set up as

described in the Padds User's Guide.




Section Design for Crack width

The Section Design for Crack width can be used to design reinforced concrete sections to

meet specific crack requirements. Both beam and slab sections can be designed for the

combined effects of axial tension, bending moment and temperature.



The following text gives an overview of the application of the theory.

Design scope

The program can determine reinforcement layouts to contain cracks. Both rectangular beam

and slab sections can be designed to resist the effects of axial tension, bending moment and

temperature and the combination thereof. Temperature effects are also included to evaluate

early cracking and long-term thermal cracking.

Shrinkage

Concrete shrinkage due to hydration is accounted for by a combination of the thermal

expansion coefficient and the restraint factor. The design method employed by the codes is

ideally suited for non-temperate regions like Europe.

Reinforcement type

Concrete cracking has traditionally been correlated with the prevailing tensile steel stress.

Eurocode 2 - 1984 also takes account of the type of reinforcement, i.e. bond between concrete and reinforcement.

Codes of practice

Design calculations are done according to BS 8007 - 1987 and Eurocode 2 - 1992.



List of symbols


Section dimensions

bt : Width of the section (mm or in).

h : Overall height of the section (mm or in).

he : Effective surface zone depth (mm or in).

Material properties



fy : Main reinforcement yield strength (MPa or psi).

Applied loads

R : Restraint factor.

T1 : Hydration temperature difference (°C).

T2 : Seasonal temperature variation (°C).

: Thermal expansion coefficient of concrete (m/m per °C or in/in per °C).

TSLS : The tensile force on the full section at serviceability limit state (kN or kip).

TULS : The tensile force on the full section at ultimate limit state. (kN or kip).

MSLS : Serviceability limit state moment (kNm or kipft).

MULS : Ultimate limit state moment (kNm or kipft).

Ro critical : The minimum percentage of reinforcement to be supplied.

Design output

Ast : Area of suggested reinforcement layout. (mm² or in²).

fst : Tensile stress in reinforcement (MPa or psi).

Mu : Ultimate moment capacity of section (kNm or kipft).

TU : Ultimate tensile capacity of surface zone (kN or kip).


Input

The section geometry and loading is entered using the single input table. The following points

require special attention.

The program evaluates an effective surface zone where crack control would be effective,

rather than the complete section. The surface zone is normally entered as half the section

depth but not more than 250 mm.

Because only a surface zone is considered, only half of the entered tensile forces

(applicable to the overall section) is used.

Reinforcement is calculated for the surface zone. The same reinforcement should be

supplied in full in both faces of the section.

Eurocode 2 requires additional information regarding the type of reinforcement bond

applicable i.e. high-bond or plain bars.

Select Beam mode if you wish cracking to be evaluated at the section corners as well.

Tip: It is recommended that wide sections be designed using Slab mode.


The hydration temperature, T1, is defined as the difference between the environmental

temperature and the peak temperature due to hydration. The value is used to evaluate early

thermal cracking. Typical values, taken from Table A.2 of the code, are given below.

OPC content (kg/m3)

Section 325 350 400 325 350 400

Thickness (mm) Steel formwork 18 mm plywood formwork

300 11* 13* 15* 23 25 31

500 20 22 27 32 35 43

700 28 32 39 38 42 49

1000 38 42 49 42 47 56

* Generally a minimum value of 20°C should be used.

The seasonal temperature variation, T2, is used to calculate long term thermal cracking:

If movement joints are provided as per Table 5.1 of the code, the seasonal variation

can normally be set equal to zero when considering early cracking only.

The seasonal temperature variation should always be considered for long-term thermal

cracking in combination with the applied moments and tensile forces.

Section OPC content (kg/m3)

Thickness (mm) 325 350 400

300 15 17 21

500 25 28 34

The restraint factor describes the amount of restraint in the system. The factor varies

between 0.0 to 0.5. For more detail, refer to Figure A3 of the code.

Tip: A higher restraint factor generally gives rise to more severe cracking. Therefore, when in doubt, use a restraint factor of 0.5.

Enter a value for Ro critical, i.e. the minimum percentage of reinforcement to be supplied.

The value applies to the gross concrete section of the surface zone. The program gives a

default value of 100 · fct / fy, where fct is the three-day tensile strength of the immature

concrete. For more detail, refer to paragraph A.2 of the code.


Design

The following checks are considered for each load case at serviceability limit state:

The combined effect of bending moment, tensile force and the seasonal temperature

variation, i.e. MSLS + TSLS + T2.

Early thermal movement, T1 only.

Early thermal movement and seasonal variation combined, i.e. T1 + T2.

The section is also evaluated at ultimate limit state by considering the combined effect of

bending moment and tensile force, i.e. MULS + TULS.

Up to four sets of bars are calculated for slab sections. Each set has a different diameter and

spacing to comply with the crack width requirements. A fifth column is provided where you

could enter a bar configuration of choice.

For beams, up to four sets of bars are calculated. Each set of bars consists of a number of bars

of not more than two different diameters. The bar diameters are chosen to not differ by more

than one size.


Calcsheets

The crack width design output can be grouped on a calcsheet for printing or sending to


pictures.





as part of a project and therefore does not need to be saved in the design module as well.


Concrete Section Design

The Concrete Section Design module is a simple utility for designing concrete sections for

combined bending, shear and torsion. Rectangular and T-sections are accommodated.



The following text gives an overview of the application of the theory.

Design scope

The program performs reinforced concrete design of rectangular and T-sections to resist

bending moment, shear and torsion.

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.

List of symbols


Section dimensions

B : Width of the web (mm).

Bf : Width of the flange (mm).

Dct, Dcb : Distance from the top or bottom face to the centre of the steel (mm).

H : Overall height of the section (mm).

Hf : Depth of the flange (mm).


Material properties

fcu : Concrete cube strength (MPa).

fy : Main reinforcement yield strength (MPa).

fy : Shear reinforcement yield strength (MPa).

Design output

As : Bottom steel required for bending (mm2).

A's : Top steel required for bending (mm2).

Anom : Nominal flexural reinforcement (mm2).

Asv : Required shear reinforcement (mm2/mm).

Asvn : Nominal shear reinforcement (mm2/mm).

Mu : Ultimate moment capacity for bottom reinforcement only (kNm).

v : Shear stress (MPa)

vc : Allowable shear stress (MPa).

vt : Torsional shear stress (MPa).

Calculation of flexural reinforcement

The normal code formulae apply when calculating flexural reinforcement for rectangular

sections and for flanged sections where the neutral axis falls inside the flange. If the neutral

axis falls outside the flange, the section is designed as two separate sub-sections:

The first sub-section consists of the flange without the central web part of the section and

the remaining central portion defines the second sub-section.

By considering the total section, the moment required to put the flange portion in

compression can be calculated using the normal code formulae. This moment is then applied to the flange sub-section and the required reinforcement calculated using the

effective depth of the total section.

The same moment is then subtracted from the total applied moment, the resulting moment

applied to the central sub-section and the reinforcement calculated.

The tension reinforcement for the actual section is then taken as the sum of the calculated

reinforcement for the two sub-sections. If compression reinforcement is required for the central

sub-section, it is used as the required compression reinforcement for the entire section.


Calculation of shear reinforcement

The program assumes that shear is resisted by the web portion of the section only. Shear

stress, v, is therefore calculated using the web area and checked to not exceed the ultimate

allowable shear stress given in the code. The shear capacity, vc, is calculated using the required

bending reinforcement, As, and the shear reinforcement calculated using the normal code formulae.

Calculation of torsion reinforcement

Depending on the option chosen, torsion can be resisted by the section as a whole or by the

web portion only. For flanged beams, the torsion is calculated separately for the flange and web along the guidelines given in the code. The torsional shear stresses are checked so as not

to exceed the ultimate allowable shear stress. Reinforcement requirements are also evaluated

separately for the flange and web using the normal code formulae.


Input

The section geometry and ultimate loading are entered using the single input table. The

following should be kept in mind:

If the values for Bf and Hf are left blank, a rectangular section is assumed.

A positive moment is assumed to cause compression in the top flange.

The program puts the flange at the top. To model the case where the flange is at the bottom

or where the flange is in tension, enter a rectangular section without a flange. The effects

of bending and shear will still be evaluated correctly. In the absence of a flange, the

torsion checks will however be conservative.

Tip: You can use the mouse to click on the picture and stretch certain section dimensions,

e.g. flange width or overall depth.


Design

Press Analyse to design the section for the entered moment, shear and torsion. The following

results are given:

The moment capacity of the section using tensile reinforcement only. The tabled flexural

reinforcement values are the required values at the top (compression) and bottom (tension)

and the nominal reinforcement.

Shear stress in the web and the shear capacity of the section together with the required and

nominal shear reinforcement.

For torsion in the web and flanges, values are tabled for the torsional shear stress and

required shear and longitudinal reinforcement.

Some reinforcement configurations are also suggested:

Number and diameters of

reinforcement bars to resist

bending only.

Links to resist shear only in

the web.

Links to resist torsion only

in the web and flange.

Longitudinal reinforcement

bars to resist combined

bending and torsion in the web. The bottom and top bar

configurations are chosen to

exceed the required flexural

reinforcement at that

position plus half the total

longitudinal torsional reinforcement.

Note: The suggested reinforcement configurations are given as guidelines only. You can use

the tabled values for required reinforcement to determine rebar layouts more suitable to your requirements.


Calcsheets

The section design output can be grouped on a calcsheet for printing or sending to Calcpad.






as part of a project and therefore does not need to be saved in the design module as well.


Detailed calculations

The detailed calculations page displays the complete step-by-step calculations for the section.


Punching Shear Design

The Punching Shear Design module designs flat slabs for punching shear at edge, corner or

internal columns. Only reinforced concrete slabs are designed – to design pre-stressed concrete

slabs for punching shear, use the Pre-stressed Beam/Slab Design module, Captain, instead.




Design scope

The program designs reinforced concrete flat slabs for punching shear at edge, corner and

internal columns.

Codes of practice


ACI 318 - 1999.

ACI 318 - 2005.

AS3600 - 2001.

BS 8110 - 1985.

BS 8110 - 1997.

CP65 - 1999.

Eurocode 2 - 1992.

Eurocode 2 - 2004.

HK Concrete - 2004.

IS:456 - 2000.

SABS 0100 - 2000.



List of symbols


Slab geometry

A : Horizontal column dimension, as shown on the screen, or diameter of circular column (mm or in).

B : Vertical column dimension, as shown on the screen (mm or in).


Deff : Average effective depth of the slab (mm or in).

X : Horizontal distance from the column centre to the slab edge (mm or in).

Y : Vertical distance from the column centre to the slab edge (mm or in).

Material properties

fcu : Concrete cube compressive strength (MPa of psi).

fy : Yield strength of flexural reinforcement (MPa or psi)

fyv : Yield strength of shear reinforcement (MPa or psi).

Slab reinforcement

Asx1-4 : Average area of main steel parallel to the X-axis crossing each of the four

perimeters (mm² or in²). The first perimeter denotes the innermost perimeter.

Asy1-4 : Average area of main steel parallel to the Y-axis crossing each of the four

perimeters (mm² or in²).

Design output

Asv : The total area of stirrups to be provided within 1.5Deff inside a perimeter (mm²

or in²).

Ucrit : Length of critical perimeter (mm or in).

vc : Allowable punching shear stress (MPa or kip).

Vc : Shear force capacity at a stress of vc (MPa of psi).

Veff : The effective shear force as a function of Vt, Mtx and Mty (kN or kip).

Applied loads

Mtx : Ultimate bending moment about the X-axis (kNm or kipft).

Mty : Ultimate bending moment about the Y-axis (kNm or kipft).

Vt : Ultimate vertical load on column (kN or kip).

Effective shear force

The effective shear force, Veff, is calculated using the code formulae. The following minimum

values are assumed:

Internal columns: 1.15Vt.

Edge columns: 1.25Vt, irrespective of the direction the column is bent.

Corner columns: 1.25Vt.


Edge, corner and internal columns

The following rules are used to determine whether a column should be considered an internal,

edge or corner column:

If one edge is closer than five times the effective slab depth, i.e. 5 · Deff, from the column

centre, the column is considered to be an edge column.

If two edges are closer than five times the effective slab depth from the column centre, the

column is taken to be a corner column.

If all edges are further than five times the effective slab depth from the column centre, the

column is analysed as an internal column.

Reduction of design moments

The program assumes that the design forces are obtained from an equivalent frame analysis

that incorporates pattern loading. As allowed for by the codes, the values of the ultimate

moments, Mtx and Mty, are subsequently reduced by 30% prior to calculating the effective

shear force, Veff.

Shear capacity

The program calculates the shear capacity in the X and Y-directions, vcx and vcy, based on the

main reinforcement in those directions and the average effective depth. The design shear

capacity, vcx, is then taken as the average of the values in the X and Y-direction.

Circular columns

Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992,

the use of circular perimeters seems a more rational approach to evaluating punching shear for

circular columns. The program recognises this and uses the following design approach for

checking punching by circular columns:

As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx

and vcy. Put differently, one could consider an imaginary square shear perimeter when

determining vc.

The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter circular perimeter (compared to a rectangular perimeter) yields a lower (conservative)

shear force capacity.


Input

The slab geometry and loading is entered using the single input table. The following

parameters may require special attention:

The reinforcement values Asx and Asy

represent the minimum amount of main

reinforcement crossing each perimeter in

the X and Y-directions. For a perimeter

edge on both side if the column, e.g. y1 in

the sketch, you should use the minimum

of the amount of reinforcement crossing the left edge and the amount crossing the

right edge. For a perimeter edge on one

side only, e.g. y2 in the sketch, use the

amount of reinforcement crossing that

single edge.

By careful choice of the values for X and

Y, you can force a column to be

considered as an edge, corner of internal

column. See page 6-204 for detail.

The program assumes pattern loading and

subsequently reduces Mtx and Mty by 30%.

Note: If the ultimate moments, Mtx and Mty, do not incorporate pattern loading, their values

should be increased by 30% to ensure a correct analysis.


Design

The design procedure includes the following steps:

The effective shear force, Veff, is calculated. See page 6-203 for an explanation of the

assumptions that apply.

The program chooses four shear perimeters. The first perimeter is taken a distance

1.5 · Deff away from the column face. Subsequent perimeters are spaced at 0.75 · Deff. The

perimeters are chosen to be as short as possible, extending to the slab edge when

necessary.

For each perimeter, the allowable stress, vc, is taken as the weighted average of the values

calculated for the X and Y-directions, using the flexural reinforcement ratio for the

respective directions. Refer to page 6-204 for more detail.

The required shear reinforcement for each perimeter is then calculated using the normal

code formulae. The calculated reinforcement should be supplied within a distance

1.5 · Deff inside the relevant perimeter.


Calcsheets

The slab design output can be grouped on a calcsheet for printing or sending to Calcpad.






is saved as part of a project and therefore does not need to be saved in the design module as

well.


Detailed calculations

The detailed calculations page displays the complete step-by-step calculations for the section.

Timber Design 7-1

Chapter

7 Timber Design

The timber design module can be used to design timber members in frames and trusses.

Timber Design 7-2

Quick Reference

Timber Design using PROKON 7-3

Timber Member Design 7-5


Timber Design using PROKON

The PROKON suite includes a module that is suitable for design of timber members in frames

and trusses. A suite of timber connection design modules is planned.


Timber Member Design

The timber member design module, Timsec, is used to check and optimise timber members

subjected to a combination of axial and biaxial bending stresses, e.g. beams, frames and

trusses.

The program primarily acts as a post-processor for the frame analysis modules. It also has an

interactive mode for the quick design or checking of individual members without needing to

perform a frame analysis.



A brief background is given below regarding the application of the design codes.

Design scope

The timber member design module can design timber and glued laminated timber load bearing

members. Timsec currently has the following limitations:

Only rectangular sections bent about their major or minor axes can be designed.

Design of tapered and haunched sections is not supported.

Design codes

The program designs timber members according to the following allowable stress design

codes:

BS 5268 - 1991.

SABS 0163 - 2001.


Timsec supports Metric units of measurement only.

Symbols


Dimensions

B : Section breadth (mm).

D : Section depth (mm).


Leff : Effective length (m).

Design parameters

Ke : Factor with which the member length is multiplied to obtain the effective

length for lateral torsional buckling. Refer to page 7-8 for detail.

Kx : Factor with which the member length is multiplied to obtain the effective length for buckling about the x-x axis of the member. Refer to page 7-9 for

more detail.


Ky : Factor with which the member length must be multiplied to obtain the effective

length for buckling about the local y-y axis of the member.

Modification factors

k1 to k5 : Stress modification factors for SAB 1063 - 1989.

K1 to K14 : Stress and dimensional modification factors for BS 5268. Refer to page 7-11 for detail.

Stresses

fb : Allowable bending stress (MPa).

fc : Allowable compression stress (MPa).

ft : Allowable tension stress (MPa).

sb : Actual bending stress (MPa)

sc : Actual compression stress (MPa)

st : Actual tension stress (MPa)

Sign conventions

Member design is done in the local element axes. Bending about the x-x axis corresponds to

strong axis bending and bending about the y-y axis to weak axis bending.

Axial force and moment

The local axes system and force directions are defined as follows:

Axial force: The local z-axis and axial force is

chosen in the direction from the smaller node number to the larger node number. A positive

axial force indicates compression and a

negative force tension.

Bending: Moments about the x and y-axes

represent bending about the section's strong

and weak axes respectively. Positive moments

are taken anticlockwise in all diagrams.


P-delta effects

Trusses are normally not sensitive to sway. However, in any structure, if you judge P-delta

effects to be an important part of the analysis, you should perform a second order frame

analysis.

Design parameters

Different design parameters can be set for each group of elements designed:

Effective length factors beams

The lateral torsional stability of a beam depends on the degree of restraint to be expected at

each end of the beam and of the compression edge along the length of the beam.

The codes treat lateral buckling by limiting section dimensions and specifying effective length

factor, Ke:

BS 5268: To ensure there is no risk of lateral buckling of beams, limiting depth to breadth

rations are given in clause 14.8, Table 19.

Degree of lateral support Maximum

D:B ratio

No lateral support 2

Ends held in position 3

Ends held in position and members held in line at centres not more than 30 times the breadth of the member, e.g. by purlins

or tie rods

4

Ends held in position and compression edge held in line, e.g. direct connection of sheathing, deck or joists

5

Ends held in position and compression edge held in line, e.g. direct connection of sheathing, deck or joists, together with

adequate bridging or blocking spaced at intervals not

exceeding 6 times the depth

6

Ends held in position and both edges held firmly in line 7


SABS 0163: Lateral stability of beams is treated in clause 6.2.3.2. The laterally

unsupported should be multiplied with the effective length factor given in Table 11:

Type of beam span Position of applied load Effective length

factor, Ke

Single span beam

Concentrated at centre 1.61

Uniformly distributed 1.92

Equal end moments 1.84

Cantilever beam

Concentrated at unsupported end 1.69

Uniformly distributed 1.06

The effective length factor may conservatively be taken as 1.92 for all situations.

Effective length factors for struts and ties

The effective length factors depend on the degree of restraint to be expected at each end of

compression members. Guidelines are given in the codes:

BS 5268: Refer to clause 15.3, Table 21.

SABS 0163: Compression members are discussed in clause 6.4.3, Table 12


Effective length factors of compression members are summarised below:

End condition Effective

length factor

Fully restrained at both ends in position and direction 0.7

Restrained at both ends in position and one end in

direction

0.85

Restrained at both ends in position only 1.0

Restrained at one end and in position and direction

and at the other end in direction only

1.5

Restrained at one end in position and direction and free at the other end

2.0

Considering a typical plane timber truss, the effective length Lx relates to in-plane buckling. For

struts where rotational fixity is provided by the connection, e.g. two or more fasteners, a value

between 0.70 and 0.85 is usually appropriate. Where rotation at the joints are possible, e.g. single

bolted connection, a value of 1.0 would normally be applicable.

For a typical plane truss, the effective length Ly relates to buckling out of the vertical plane.

This phenomenon can often govern the design of the top and bottom chords of a truss that can

buckle in a snakelike 'S' pattern, giving an effective length equal to unrestrained length. Lateral

restraints are normally provided to reduce this effective length. For example, with braced purlins connected to the top chord of the truss, the effective length could be taken equal to the

purlin spacing.

The effective length Le relates to lateral torsional buckling of a member about its weak axis.

The length depends on the spacing and type of restraint of the member's compression edge.

Using an effective length factor Ke of 1.92 would be conservative for all cases.


Stress modification factors

The codes list several stress and other modification factors, not all of which are applicable to

Timsec. Some factors are not covered by scope of the program and other are supported

indirectly only by modification of other factors or design parameters.

BS 5268 – 1991:

K1 : Modification factor by which the geometrical properties of timber in the dry condition should be multiplied to obtain values for the wet exposure condition.

If applicable, you should manually adjust section sizes for the wet exposure

condition.

K2 : Modification factor to be applied to dry stresses and moduli (Tables 9 through

13 and 15 of the code) to obtain values for the wet exposure condition. The

same K2 factor is applicable to bending and tension while a different factor is

applicable to compression.

K3 : Modification factor for duration of loading. Values from Table 17 of the code

are summarised below:

Duration of load K3

Long term, e.g. dead and permanent

imposed loads

1.00

Medium term, e.g. snow and temporary imposed loads

1.25

Short term, e.g. temporary imposed loads 1.50

Very short term, e.g. wind loads 1.75

Note: Since load duration factor may differ for different loads on the structure, you should

divide the relevant loads with this factor at the analysis stage.

K4 : Modification factor for bearing stress. Not applicable.

K5 : Shear strength factor to allow for notches. Not applicable.

K6 : Form factor for solid non-rectangular sections. Not applicable.


K7 : Multiplication factor for grade bending stresses for members graded to

BS 4978, BS 5756 or "NGLA and NGRDL Joist and Plank rules". Likewise

grade tension stresses can be multiplied with K14. The factors K7 and K14 are

depended on the section dimensions and are automatically calculated during

the design process if required.

K8 : Factor for load sharing by members connected in parallel. All grade stresses

are multiplied by this factor.

Tip: You may use the factor for load sharing to include any other modification factors

that are not applicable to standard timber sections, e.g. factors applicable to glued

laminated timber.

K9 : Load sharing factor for calculating deflections. Not applicable.

K10, K11 : Size factor for modification of grade compression stresses and moduli of

elasticity for members graded in accordance with North American NLGA and

NGRDL rules. If applicable, the K10 and K11 modification factors can be

included by adjusting the grade stresses.

K12 : Factor for allowable compression stress due to slenderness. This factor is

automatically calculated during the design process.

K13 : Modification factor for the effective length of spaced columns. Instead of using

this factor, you should adjust the effective length factors Kx, Ky and Ke if

required.

K14 : See K7.

SABS 0163:

k1 : Load duration factor. Since load duration factor may differ for different loads

on the structure, you should divide the relevant loads with the Cr factor at the

analysis stage. Load division coefficients are given in Table 9 of the code and

summarised below:

Duration of load Cf

Longer than three months, e.g. dead and permanent imposed loads

1.0

Medium term (one day to three months), e.g. snow and temporary imposed loads

0.8

Short term (less than one day), e.g. wind

loads and infrequently imposed loads

0.66


k2 : Factor for load sharing by members connected in parallel. All grade stresses

are multiplied by this factor.

Tip: You may use the factor for load sharing to include any other modification factors

that are not applicable to standard timber sections, e.g. factors applicable to glued

laminated timber.

k3 : Stress modification factor for the type of structure. The value may be taken as

1.10 where the consequences of failure are small. For other structures a value

of unity should be used.

k4 : Modification factor for quality of fabrication. If the fabricated member

complies with an SABS specification, the value may be taken as 1.05.

k5 : Stress modification factor for moisture content. If the moisture content in a

compression member may occasionally exceed 20%, use a value of 0.75.

Slenderness limits

BS 5269 (clause 15.4) and SABS 0163 (clause 6.4.4) specify similar slenderness ratios for

members in compression. The slenderness limit for compression is taken as 180 in most cases. For tension members, a maximum slenderness ratio of 250, as specified by BS 5268, is

generally used.

When launching Timsec, the slenderness limits given by the selected design code will be used by

default. You are free to alter the maximum slenderness ratio for each individual load case or

combination if required. For example, in the case where a member is carrying self-weight and

wind load only, the codes allow the maximum slenderness ratio for compression members to be

increased to 250.


Member design techniques

The programs have two basic modes of operation:

Read and post-process the frame analysis results.

Alternatively, you can do an independent interactive design of one or more members.

The following text gives details of the design techniques and also explains how the database of

timber grades and sections sizes can be customised.

Limitations of the timber member design module

Timsec can be used to design timber members subjected to any combination of axial force,

uni-axial and biaxial bending moment. The program cannot design non-rectangular sections or

members of varying section.

Reading and post-processing frame analysis results

Working through the input and design pages, the frame design procedure can be broken up into

the following steps:

The Input page: Defining design tasks by choosing a design approach, selecting members

to be designed, setting the design parameters and selecting load cases and slenderness

limits. The concept of tasks is described in detail on page 7-18.

The Members page: Define internal nodes and enter effective lengths. Refer to page 7-24 for detail.

The Design page: Evaluating the design results. See page 7-26 for detail.

The Calcsheet page: Accumulate design results. See page 7-28 for detail.

Re-analysis of the frame

Having evaluated the various member sizes, you may find it necessary to return to the original

frame analysis and make some changes to section sizes. Before exiting the member design

module, first save the task list using the Save command on the File menu. After re-analysing

the frame, you can return to the member design module and recall the task list to have the

modified structure re-checked without delay.

Note: For a task list to be re-used with a modified frame, a reasonable degree of compatibility is required. Tasks that reference specific laterally supported nodes, for

example, will require modification if relevant node numbers have changed.


Interactive design of members

As an alternative to the above procedure, individual members can be designed without needing

to perform a frame analysis. To enable the interactive design mode, select 'Interactive input of

data' on the Input page.

Design steps

Working through the input and design pages, the interactive design procedure can be broken up

into the following steps:

The Input page: Choose a design approach, set the design parameters and enter the

element loads.

The Design page: Evaluate the design results. More detail is given on page 7-26.

The Calcsheet page: Accumulate design results to print or send to Calcpad. See page 7-28

or detail.

Modifying timber grades and sections

Depending on the selected design codes, the program uses the relevant timber grades and nominal rough-sawn dimensions, i.e. as typically available in the United Kingdom or South

Africa. You can customise the default grades and sections to include grades and sections

readily available in your country.


To add, delete or modify grade properties or section sizes:

Use the Edit Timber Grades (F5) function on the Input page to display the database of

grades and sections. Refer to page 7-15 for details.

Edit the properties on the Timber Grades page as required. Note that each grade requires

a size number.

On the Section Sizes page, enter available section dimensions for each size number used on the Timber Grades page.

Press OK to permanently save your changes.

Use Save as Default and Load Defaults to record your preferred grades and sections

independent from the selected design code.


Tasks input

On entering Timsec, it defaults to reading the last compatible frame analysis for post-processing.

You can then choose to:

Read and post-process the frame analysis results: Define one or more design tasks by

grouping members with relevant design parameters.

Interactive design: Ignore the frame analysis and interactively input and design members.

The text that follows describe the use of the programs for reading and post-processing frame

analysis results. Information regarding interactive design is given on page 7-21.

Choosing the data input and design mode

The appearance of the Input page determined by your selection of the mode of operation:

If you choose to read and post-process the results of the frame analysis modules, you will

use the Input page to define design tasks.


However, if you opt for interactive design of members, the Input page displays a table for

entering member geometry and loading.

Reading frame analysis output files

You can select another frame output file or view the current file:

Read data from: Use this option to load the output of a different frame module than the

one displayed. Click the box and select the relevant file from the list or enter a file name.

View output: To display the current frame analysis output file.

Defining design tasks

Central to the process of post-processing frame analysis results, are design tasks. By grouping

selective members with their relevant design parameters into one or more design tasks, you

should find it easy to manage the vast amount of frame analysis data generated for larger

frames.

The design of a frame should be simplified by breaking it into one or more manageable tasks.

Each task then defines a group of members to be designed together with the relevant design parameters to be used, e.g. timber grade, section sizes and load cases considered.

Once you have defined one or more design tasks, the Design page is enabled – viewing that

page automatically performs all design tasks.

After having carefully defined a number of tasks, you can save the task list to disk for later

re-use. This means that you can return to the relevant frame analysis module, make some

changes to the structure, re-analyse it and then repeat the previous design tasks by simply

reloading the task list.

Defining tasks

To define design tasks, you have to select or enter the following information:

1. Select the timber grade to use

2. Select the members to be designed.

3. Enter the design parameters and select the section dimensions to use.

4. Select the load cases to be considered and enter the maximum slenderness ratios.

To save a task, enter a Task title and click Add task. Once added to the task list, a task will be

automatically performed when you go to the Calcsheet page. Define as many tasks as

necessary to design the frame in the required detail.


Modifying design tasks

To modify an exiting task:

1. Click Task title to display a list of defined tasks.

2. Select the task you want to modify.

3. Make the necessary changes to the selected members, design parameters etc.

4. Click Update task to save the changes.

Deleting tasks

To remove a task from the list, first select the task and then click Delete task. To save the

complete task list to disk, use the Save commands on the File menu.

Note: Saving the task list with File | Save also saves the intermediate nodes and effective

lengths entered in the Members page.


The current selected design code is displayed in the status bar. To select a different design

code, use the Code of Practice command on the File menu or click the design code on the

status bar.


Depending on what you would like to achieve, e.g. preliminary sizing or final design checks, you

can choose between the following design approaches:

Select lightest sections: Elements can be optimised for economy using mass as the criterion. You can optimise the section breadth and height separately or simultaneously by

setting the respective values to 'Auto'.

Evaluate specific sections: To check specific section sizes, select the required sized for

breadth and depth.

Selecting the timber grade

Select the required timber grade from the list. To modify the grade properties, add a new grade or

delete existing grades, use Edit Timber Grades (F5). Refer to page 7-15 for details.

Selecting members for design


clicking members in the picture. A lateral supports is assumed at each node. If certain internal


nodes are not laterally supported, you can indicate them on the Members page. Refer to page 7-

24 for detail.

Note: To modify the available section sizes for the selected timber grade, click Edit Timber

Grades (F5). Refer to page 7-15 for details.


Use the Design parameters (F8) function to enter appropriate design parameters and material

properties. You can select a different set of design parameters with each task.

Refer to page 7-7 for a discussion of the K-factors for modifying stress and other parameters.

Note: Effective length factors are entered on the Members page.

Selecting load cases and limiting slenderness ratios

When loading the last frame analysis results, the program automatically displays a list of all

load cases and combinations that can be designed and also the default slenderness limits for struts and ties. In the Maximum L/r ratios (F9) table, you can exclude any load case or

combination from the design by clicking its right-most column.

Tip: In the frame analysis modules you can also select to analyse load combinations only.

The analysis output will then be more compact due to the omission of individual load case

results.

You are free to modify the slenderness limit for each individual load case or combination as

required. In the case where uplift due to wind is dominant, for example, you may be able to set

a higher slenderness limit. Refer to page 7-11 for more detail.

Controlling design output

The amount of information that will be added to the

Calcsheet page can be controlled using the Settings

function on the Input page. You can choose

between showing detailed calculation with or

without diagrams or a tabular summary of results.

The option to add the Timsec Data File to the output

on the Calcsheet page, allows you to later recall the

design tasks by double-clicking the data file object

in Calcpad.


Interactive input

The interactive design mode offers an alternative method of designing members. Instead of

performing a frame analysis and then and post-processing the results, you can enter member

length and forces and design them interactively.

To enable the interactive design mode, select 'Interactive input of data' on the Input page.

The pages that follow describe the use of the programs for interactive member design. The

procedure to reading and post-processing frame analysis results is explained on page 7-14.


The current selected design code is displayed in the status bar. To select a different design code, use the Code of Practice command on the File menu or click the design code on the

status bar.


Depending on what you would like to achieve, e.g. preliminary sizing or final design checks, you

can choose between the following design approaches:

Select lightest sections: Elements can be optimised for economy using mass as the

criterion. You can optimise the section breadth and height separately or simultaneously by

setting the respective values to 'Auto'.


Evaluate specific sections: To check specific section sizes, select the required sized for

breadth and depth.


Use the Effective lengths (F6) function to enter effective length factors. Use Design

parameters (F8) to enter appropriate design parameters. All members designed in a particular

interactive session use the same set of design parameters.

Refer to page 7-6 for a discussion of the K-factors for modifying stress and other parameters.

Effective length factors

Specify the effective length factors to be used for bending about the major and minor axes and

for lateral torsional buckling. For more detail on the code requirements regarding effective

length factors, refer to page 7-8.

Specifying slenderness limits

Use the Maximum L/r ratios (F9) function to enter appropriate maximum allowable

slenderness ratios for compression and tension.

Entering member lengths and forces

One or more lines of information can be entered for each member. The program automatically

accumulates multiple lines of loads for the same member. The following input data is required:

Name: A descriptive name for each member.

L: Length of the member (m).

F: Axial force with compression being positive (kN).

X/Y: Axis of bending relating to the values that follow next. Use as many lines as necessary to define the loading on the member about the x-x and y-y axes.

M1: Moment applied at the left end (anti-clockwise positive) about the X or Y-axis (kNm).

M2: Moment at the right end (anti-clockwise positive) (kNm).

W1: Distributed load at the left end. The load works over the whole length of the member

load and varies linearly between the left and right ends (downward positive) (kN/m).

W2: Value of distributed load on right side (kN/m).

P: Point load applied on the member (downward positive) (kN).

A: Position of the point load, measured from the left end (m).


Note: For allowable stress design with BS 5268 or SABS 0163, you should enter working loads.

The profile of the members to evaluate is chosen using the Profile (F5) function. On opening

the Design page, the lightest section will be chosen for each member. Lighter or heavier

sections of the same profile can then be browsed as required.

Viewing design results

The design results are presented on the Design page. Refer to page 7-26 for detail.


Member definition

Internal nodes and effective lengths are defined on the Members page. The data entered on the

Members page are applicable to all design tasks defined on the Input page.

Defining internal nodes

An internal node is defined as a node in-between the end nodes of a member. When you add

internal nodes, the program joins relevant members to allow for easy input of effective lengths

Adding an internal node

You can add internal as follows:

Enter internal node numbers in the table or click them with the mouse.

Use the Auto Select function to let the program detect all internal nodes.


Removing an internal node

You can remove an internal node by deleting it form the list or by clicking it again in the

picture.

Consolidation of members

With the addition of each internal node, the relevant node is 'removed' by joining the two

adjacent members into a single member. The table of members is continuously updated to

show the new member layout.

The program uses the following guidelines to when joining members at an internal node:

For the automatic selection of internal nodes, adjoining members must have the same

section.

Only members with an included angle greater than 100° (where 180° corresponds to a

perfectly straight member) are joined.

Where members of different sections intersect, the larger section defines the main member

that should be joined.

Where two or more members intersect, the internal node is taken to belong to one of the

intersecting members only. The chosen member will be the straightest member or, if the

same, the first in the table of members.

Entering effective lengths

Enter effective length factors as follows:

Apply the same value of Kx, Ky or Ke to all members by clicking the Kx, Ky and Ke

buttons in the table heading.

Enter the effective length factors for individual elements.

Note: The list of internal nodes and effective length factors are automatically saved when

you save the task list. See page 7-18 for detail.

Tip: You can quickly find a member in the table by pressing Ctrl+F. Enter the member name by referring to one or both of its end node numbers.


Design results

Select the Design page to perform all design tasks and display the design results. All specified

load cases and combinations are considered for each member designed. Unless a very large

number of elements and load cases are involved, the design procedure will normally be

completed almost instantaneously.

By default, the results for the design task active on the Input page are displayed. The results of

any other design task can be displayed by selecting the task from the list (see description below).

If an interactive member design was performed, the displayed results will be for the interactive

design task instead.

The design criteria

The following criteria are used in the design:

The interaction formulae given by the relevant design code are used to evaluate the

combined effect of axial stress and bending stress. In calculating the allowable stresses, the

program takes account of the member slenderness.


The slenderness ratio checked against the specified maximum allowable slenderness ratio

for compression and tension.

Viewing results

The complete interaction formulae are displayed for the critical load case of the first member of

the first design task. Individual calculations have 'OK' and 'FAIL' remarks to indicate success or

failure.

To view the results of another task, member, section or load case:

Use the Up and Down buttons to move up or down the list of available options. Tasks and

load cases are listed in the order of definition. Sections are ordered by mass. Alternatively

click the item, i.e. sections, and use the Up and Down arrow keys.

Alternatively click the relevant input box and select an item from the list that drops down.

Adding results to the Calcsheet page

The following options are available when adding design results to the Calcsheet page:

Member to Calcsheet: Add the current displayed member only. This option is not available when the design results are set to include only a tabular summary.

Task to Calcsheet: Add the design results of all members in the current task, including

those members not currently displayed.

All tasks to Calcsheet: Add all members of all tasks. This option is not available in the

interactive design mode because only a single design task, i.e. the interactive design task,

is involved.

Note: The level of detail of the information added to the Calcsheet can be set using the

Settings function on the Input page. Refer to page 7-20 for detail.


Calcsheet

The design results of all tasks are grouped on the Calcsheet page for sending to Calcpad or

immediate printing.

Use the Output settings function on the Calcsheet page and Settings function on the Input

page for the following:

Embed the Data File in the calcsheet for easy recalling from Calcpad.

Clear the Calcsheet page.


If you enable the Data File option (Settings function on the Input page) before sending a

calcsheet to Calcpad, you can later recall the design tasks by double-clicking the relevant

object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore

does not need to be saved in the member design module as well.

General Applications 8-1

Chapter

8 General Applications

The general analysis modules can be used to calculate section properties, wind pressures on

buildings and evaluate drainage systems of building roofs.


Quick Reference

General PROKON Analysis Tools 8-3

Section Properties Calculation 8-5

Wind Pressure Analysis 8-19

Gutter and Down pipe Design 8-27


General PROKON

Analysis Tools

The PROKON suite includes a number of simple analysis tools to simplify everyday

calculations. These include:

Section Properties Calculation: For the calculation of bending and torsional properties of

any generalised section.

Wind Pressure Analysis: For determining the free stream velocity pressure on a building.

Gutter Design: Use this module to design a drainage system for a roof by sizing a gutter,

outlet and down pipe.


Section Properties Calculation

You can use the Section Properties Calculation module, Prosec, to calculate the bending,

shear and torsional properties of any arbitrary section. The section can be solid or have one ore

more openings. A section is assumed to be made of one material; for a composite section, you

have to enter equivalent sizes based on modular ratios.



An overview is given below regarding the theories used to calculate section properties.

Scope

Prosec can be used to calculate the properties of any arbitrary section. The section can be solid

or have openings. For bending property calculation, the program uses a simple technique of

division into smaller trapezoidal sub-sections, and adding up the properties of all the sub-

sections. The program uses the Prandtl membrane analogy to determine the shear and torsional

section properties, including the shear centre, St. Venant torsional constant and torsional

warping constant.

Sign convention

A simple Cartesian sign convention applies:

X-coordinates are taken positive to the right and negative to the left.

Y-coordinates are taken positive upward and negative downward.

Angles are measured clockwise.


All input and output values are used without a unit of measurement. Whether you define a

section using sizes for millimetres, metres, inches or feet, the output will effectively be given

in the same unit of measurement.

You can optionally specify a unit of measurement using the Analysis Settings option on the

Input page, and that unit will then be used in the output.

List of symbols

Below is a list of symbols used for the bending and torsional section properties:

Bending properties

A : Area of the cross section.

Ixx, Iyy : Second moment of inertia about X and Y-axis.

Ixy : Deviation moment of inertia.

Iuu, Ivv : Second moment of inertia about major axis and minor axis.

Ir : Polar moment of inertia


Ang : Anti-clockwise angle from the X-axis to the U-axis.

Zxx : Elastic section modulus in relation to the top or bottom edge.

Zyy : Elastic section modulus in relation to the left or right edge.

Zuu : Minimum section modulus in relation to the U-axis.

Zvv : Minimum section modulus in relation to the V-axis.

Zplx, Zply : Plastic modulus about X and Y-axis.

Xc : Horizontal centroid position measured from the leftmost extremity of the section.

Yc : Vertical centroid position measured from the bottom most extremity of the

section.

rx, ry : Radius of gyration about the X or Y-axis.

ru, rv : Radius of gyration about the U or V-axis.

Xpl : Horizontal distance from leftmost extremity to centre of mass.

Ypl : Horizontal distance from topmost extremity to centre of mass.

Perim : Outside perimeter

V : Void ratio = 1 - A / (width × depth)

Г : Section efficiency factor = Ixx / (A × yt × yb)

Torsional properties

: Shear stress.

Ashear : Effective shear area in X or Y direction

X : Horizontal position of shear centre from the leftmost extremity of the section.

Y : Vertical position of shear centre from the bottom of the section.

J : St. Venant torsional constant.

Shear centre : X and Y coordinates of shear centre, xo and y

ßx : Mono-symmetry constant ßx = 1/Ixx∫(x2y + y3)dA - 2yo

Zt : Torsional modules.

Cw : Warping torsional constant.


Input

To define a section, enter one or more shapes (polygons) that define its outline and any

openings.

Entering a section


'+' : The start of a new polygon or circle. An absolute reference coordinate must be

entered in the X/Radius and Y/Angle columns.

'–' : Start of an opening. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

'R' : Indicates a line drawn with relative coordinates.

'L' : Indicates a line drawn with absolute coordinates.

'A' : An arc that continues from the last line or arc. The arc radius and angle are

entered in the X/Radius and Y/Angle columns respectively. The angle is

measured clockwise from the previous line or arc end point.

'C' : A circle with the radius entered in the X/Radius column.

'B' : Bulge altitude to apply to the previous line, changing it to an arc segment.

Enter the bulge altitude in X/Radius column. A positive bulge value

corresponds to an upward bulge for a line drawn from left to right.

Tip: If the Code column is left blank, relative coordinates are used.

The X/Radius and Y/Angle columns are used for entering coordinates, radii and angles:

X : Absolute or relative X-coordinate. Values are taken positive to the right and


Radius : Radius of a circle or an arc.

Y : Absolute or relative Y-coordinate. Values are taken positive upward and negative downward.

Angle : Angle that an arc is extending through.

Note: If the X/Radius or Y/Angle column is left blank, a zero value is used.


Anatomy of a section

A section comprises one or more shapes that define its outline and any openings. Any shape is

a polygon, and has two basic components:

A reference coordinate, which gives the starting point of a polygon or the centre of a

circle.

One or more entries defining the polygon’s coordinates of lines and arcs or a circle’s

radius.

After entering each coordinate, the image of the polygon updated.

Note: The starting point of a polygon is also used as the ending point and the polygon is closed automatically. It is therefore not necessary to re-enter the starting coordinate to close

a polygon.

Entering the reference coordinate

Every polygon has a start point and every circle has a centre point. These points are called

reference points and are entered as absolute coordinates:

In the Code column, enter either a '+' or '–' to indicate the start of a new shape. Entering a '+' means that the shape will be added to the section. Likewise, a '–' means that the shape

will be subtracted, e.g. an opening.

Enter the absolute values of the reference coordinate in the X/Radius and Y/Angle

columns.

Entering the polygon coordinates

Given a reference coordinate, two or more additional coordinates are required to define the

shape of a polygon. In the case of a circle, only a reference coordinate and radius is required.

A coordinate may be entered using absolute or relative values:

If the Code column is left blank, the coordinate is taken relative from the last point

entered.

Set the Code to 'L' if you want to enter an absolute coordinate.

The coordinate values are entered in the X/Radius and Y/Angle columns. A negative X or

Y-coordinate must be preceded by a minus sign. The plus sign before a positive X or Y-

coordinate is optional.

A circular arc is defined by setting the Code to 'A' and entering the radius in the X/Radius

column. The arc is then taken to extend from the end point of the last line or arc, starting at

the angle that the previous line or arc ended and extending through the angle specified in

the Y/Angle column.


Define a circle by setting the Code to 'C' and entering the coordinate for the centre point.

On the next line, enter the radius in the X/Radius column.

To define a bulge between two points, enter a line segment and then apply the bulge in the

next input line. Enter 'B' in the Code column and the bulge altitude in the X/Radius

column. The bulge altitude is defined as the from the centre point of the line segment, and

perpendicular to it to the circular arc. A positive bulge value corresponds to a clockwise rotation from the start to end point of the line segment.

Rotating a section

To rotate an entered section by a set angle, click on Settings.

Note: The torsional properties can only be calculated for a single contiguous section. You

may use several shapes to define an outline and one or more openings for the section, but

the section must be contiguous if you require torsional analysis results.


Procedures for entering shapes

Step-by-step procedures for entering typical section Codes are given below:

Entering a polygon comprising straight lines

A polygon is defined by entering a start point followed by a few lines of additional coordinates.

The polygon can be defined using relative or absolute coordinates or both.

Using relative coordinates:

Define the start position of the polygon by setting the Code to '+' and entering the absolute

coordinate in the X/Radius and Y/Angle columns.

Next, leaving the Code column blank, enter the consecutive corner points of the polygon

in the X/Radius and Y/Angle columns. By leaving the Code column blank, the entered coordinates are set to relative coordinates.

Using absolute coordinates:



For each following coordinate, enter an L in the Code column and enter the absolute

coordinate values in the X/Radius and Y/Angle columns.

Entering a polygon comprising lines and arcs

A polygon with one or more arcs is defined in a similar way as a normal polygon:



Define straight lines by entering the consecutive corner points using relative or absolute coordinates.

For an arc, set the Code to A and enter its radius and angle in the X/Radius and Y/Angle

columns. The arc will be taken to extend from the previous line/arc through the specified

angle. A positive angle is taken as a clockwise rotation and a negative angle as an anti-

clockwise rotation.

Tip: If an arc is to start at a certain angle, simply precede it with a short line at that angle.

Entering a circle

A circle is defined by entering the centre point followed by its radius in the next line:


Define the centre point of the circle by setting the Code to '+' and entering the absolute X

and Y-coordinates. If you leave either of the coordinates blank, a value of zero is used.

On the next line, set the Code to C and enter the radius of the circle in the X/Radius

column.

Note: A circle should be considered as a complete shape. If a circle has to be incorporated in another shape, a polygon with arcs should be used.

Entering an opening

An opening is defined exactly like any other shape, with the exception that it is entered as a

negative shape:

Define the start position of the polygon by setting the Code to '–' and entering the absolute


Define lines, arcs or a circle by entering the relevant points as described in the examples

above.

Examples

A number of examples are available on the Help menu to illustrate the input functions:

Simple square rectangular section

T-section that shows the use of relative X and Y-coordinates.

Circular tube that illustrates the use of circles and entering an opening.

Bridge deck with two openings.

Rail section that uses several circular arcs.

Section Input using CAD

You can convert CAD drawings to Prosec sections using Padds. For complex sections, this is

often the preferred way of creating input for Prosec:

Import a DWG or DXGF drawing into Padds, or draw the section in Padds.

On the Macro menu, use the Generate Input file to create input for Prosec. Follow the

prompts to select the lines and arcs that form the section outline, and select any openings.


Analysis

To calculate the bending section properties, or shear and torsional section properties, display

the Properties or Shear and torsion page respectively.

To calculate the bending properties, or shear and torsional section properties, click the Bending Properties or Torsion Properties buttons respectively.

Analysis settings

Click Settings to adjust the analysis settings applicable to the bending and torsional analyses:

Rotation angle: Enter an angle

if you wish to calculate the

bending properties for a rotated

section.

Poisson ratio: The ratio

influences the torsional shear

stress distributions in a section. It therefore also has an effect on

the position of the shear centre

and warping torsion constant.

Material Poisson Ratio

Aluminium 0.16

Concrete 0.20

Steel 0.30

Number of equations: For determination of the torsional section properties, the finite difference mesh is sized to yield approximately the specified number of equations. More

equations will take longer to solve, but may yield better accuracy, especially when

analysing thin-walled sections.

Units: Entering the units of measurement is optional – the calculated section properties are

always given in the same units as the input. However, when you do enter the units of

measurement, relevant units will be displayed in the output. This may be useful to interpret

the order of unit of a specific section property, e.g. mm3 versus mm4.


Calculating bending section properties

The bending section properties are calculated using a simple method of division into sub-

sections:

Circles and arcs are first converted to polygons with approximately the same shapes. The

program uses lines at 30° angle increments for this purpose.

The section is then sub-divided into a series of trapeziums and the properties are calculated

for each trapezium.

The global section properties are finally calculated through summation of the values

obtained for each trapezium.


Calculating torsional section properties

For calculating the shear and torsional section properties, the program uses a finite difference

analysis method:

The analysis routine uses Prandtl membrane analogy for determining the Y and X-shear

stresses and J, the St. Venant torsional constant.

The shear stress distributions in the Y and X-directions are determined for a unit load

applied in the Y-direction. The shear centre is then calculated by considering the moment

of shear stresses about the centre of mass.

The torsional constant, J, is taken as twice the volume below the membrane. The

maximum slope of the membrane then gives the torsional modulus. The maximum

torsional shear stress is obtained by dividing the torsional moment with the torsional

modulus Zt.

Warping torsion is evaluated by using the relationship between shear and axial

deformation from classical elastic theory. The shear deformation is obtained from the pure

torsion analysis. The warping constant, Cw, is then determined from the longitudinal

displacements.


Note: The number of equations has an effect on the accuracy of the torsional analysis. More equations typically yield better results, especially for thin-walled sections, but take longer to

solve. To set the number of equations, adjust the Analysis Settings.

Calculating shear area

Strain energy density for shear stress1:

22

10 xy

GU (1)

Internal strain energy:

dAUUi .0 (2)

External work2 :

s

e

GA

VU

2

2

(3)

From 1 and 2:

dAG

U xyi .2

12

(4)

From 3 and 4:

dAAs

xy.

1

1 Stresses In Plates and Shells, by Ansel Ugural, published by McGraw-Hill 2 Theory of Elasticity, by Stephen P. Timoshenko and J.N. Goodier, published by

McGraw-Hill


Calcsheet

The section property calculations can be grouped on a calcsheet for printing or sending to


pictures.




it by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved

as part of a project and therefore does not need to be saved in the analysis module as well.


Wind Pressure Analysis

Wind Pressure Analysis calculates free stream velocity pressures, wind loads on various

building geometries, and frictional effects on cladding materials.


Theory and Application

A brief summary is given below with respect to the supported design codes and symbols used.

Scope

The program calculates the free stream velocity pressure applicable to a building structure, and

then considers the internal and external pressure coefficients for the given building geometry to

calculate the design wind loads on the walls and roof.

Design codes

The following codes of practice are supported:

CP3 - 1972.

SABS 0160 - 1989.


The program support metric and imperial units of measurement.

List of symbols

The code symbols are used as far as possible:

k : Pressure coefficient that depends on altitude.

Cpe : External pressure coefficient

Cp, : Internal pressure coefficient

Qz : Free stream velocity pressure (kPa).

V : Regional wind speed (m/s).

vz : Characteristic wind speed at a height z (m/s)


Input

Define the building and wind loading condition to be analysed:

Environmental and general geometric parameters.

Building geometry.

Wall permeability.

Environmental parameters

Enter the following parameters to define the environment:

Mean return period: A return period to indicate the importance of the structure.

Return Period Description

100 High risk buildings, e.g. hospitals and

communication centres

25 Low risk structures, e.g. farm outbuildings

5 Temporary structures

50 Most other structures

Terrain category: An indication of the likely exposure of the structure to wind loading. A

higher value denotes increased shielding and lower wind pressures.

Terrain

Category

Description

1 Open terrain

2 Outskirts of towns

3 Built-up and residential areas

4 City centres

Regional wind speed: The design wind speed for a fifty-year return period for the location

of the building (m/s or ft/s). Refer to the relevant design code for regional values.


Class of structure: The class of structure quantifies the importance of the analysis:

Class Description

A Structural component

B Structure as a whole

C For checking structural stability

Altitude: Height above sea level (m or ft).

Roof cladding type: A description of the surface profile of the material used to clad the

building, affecting friction. Choices include ribs, corrugations, and smooth.

Building geometry

Enter the following parameters to define the building geometry:

Type of roof: Double-pitched or mono-pitched roof.

Plan dimensions: Building length and width (m or ft).

Wall dimensions: Eaves and apex heights (m or ft).

Wind direction to consider for analysis: 0°, 90° or 180°.

Wall permeability

Define the wall permeability (for calculation of internal pressure coefficient Cpi) by selecting

the option that best describes the permeability of the wall. Alternatively enter a custom Cpi

value.


Wind Profile

Display the free stream wind profile for the building location.


Wind Pressures

Display the calculated wind pressures on the walls and roof of the building.


Calcsheet

The Calcsheets page assembles the analysis results for printing and sending to Calcpad. Use

the Options button to select the information to be displayed.




Calcpad is saved as part of a project and therefore does not need to be saved in the Wind

Pressure Analysis module as well.


Gutter and Down pipe Design

The Gutter Design module analyses gutters and down pipes to drain roof of building

structures for specified rain intensities and durations.



Below is a brief summary of the application scope and symbols used.

Scope

The program can evaluate roof drainage systems subjected to intense short duration rains. It

takes into account the shape of the gutter, the outlet into which the gutter discharges and the

pipe-work that conveys the flow to below.

Note: Gutters and down pipes may normally be omitted for roofs with area of 6 m2 or less

and no other area drains onto it (clause NC.5).

Design code

The program is based on the requirements of BS 12056-3 - 2000.


The program supports both Metric and Imperial units of measurement.

List of symbols

The code symbols are used as far as possible:

B : Width of the gutter at its top (mm or in).

Br : Width of roof from gutter to ridge (m or ft).

Bs : Width of the gutter at its base (mm or in).

H : Overall gutter depth (mm or in).

Hr : Height of roof from gutter to ridge (m or ft).

Lr : Length of roof to be drained at the position of the gutter (m or ft).

Tx1 : Horizontal offset the start of the ridge of the roof (m or ft). Leave blank or

enter zero for a rectangular roof area.

TLr : Length of the roof at the ridge (m or ft). Enter the same value as for Lr for a

rectangular roof area.

x1 : Position of the start of the gutter along the length of the roof (m or ft).

x2 : Position of the gutter end (m or ft).

yd : Sloped depth of a trapezium-shaped gutter (mm or in).


Input

Define the drainage system and storm to be drained:

Storm characteristics

Gutter geometry

Outlet and down pipe definition.

Storm characteristics

Enter the following parameters to define the storm:

Return period (years): This parameter is used as a measure of the security of an

acceptable degree of damage. A return period of between five and fifty years is normally

used for typical situations. For higher risk scenarios, a value of one and a half times the

expected life of the building and higher should be used. Refer to the code for detail.

Two minute M5 rainfall (mm): This quantity is defined as the expected rainfall in a two

minute period during a one in five year storm. Press 2 Minute M5 Rainfall Constants to display regional data for the United Kingdom and South Africa. Refer to the code or other

relevant hydrological data for regions not listed.

Design duration (1 to 10 minutes): The M5 rainfall is adjusted for the actual duration in

accordance with Table NB.1 of the code.


Gutter geometry

You can define rectangular and

trapezium-shaped gutters:

Width at the top of the gutter, B.

Gutter base width, Bs. Set the

value equal to the top width for a

rectangular gutter.

Overall gutter depth, H.

Sloped depth, yd of a trapezium

shaped gutter, enter the depth in which the gutter slopes outward

from the base. Leave this input

blank or zero for a rectangular

gutter.

Roof layout

Define the roof layout by entering the

roof and downpipe dimensions.

Roof dimensions

The roof being drained can have a rectangular or trapezoidal layout:

Width of roof from gutter to ridge, Br.

Length of roof to be drained at the position of the gutter, Lr.

Horizontal offset the start of the ridge of the roof. Leave blank or enter zero for a

rectangular roof area, Tx1.

Length of the roof at the ridge. Enter the same value as for Lr for a rectangular roof

area, TLr

Height of roof from gutter to ridge, Hr.

Gutter and wind characteristics

Position of the start of the gutter along the length of the roof, x1. Leave blank or enter zero

if the gutter extends for the whole length of the roof.

Position of the gutter end, x2. Enter the same value as for Lr if the gutter extends for the

whole length of the roof.


The wind characteristics determine whether there will be increased water flow compared

to the case where rain is falling vertically:

Driven: The rain is driven unto the roof (at an angle of 26°) resulting in increased

water flow due to rain on sloping roofs. This is accounted for in the analysis by

increasing the impermeable area of the roof (Table 3 of the code).

Perpendicular: The impermeable area of the roof is calculated using Tr, the distance from the gutter to the ridge measured along the slope of the roof.

None: Rain is falling vertically, and the impermeable roof areas is calculated using the

horizontal distance from the gutter to the ridge, Br.

Downpipes

Define one or more downpipes using the following parameters:

Position of the downpipe from, measured from the edge of the roof (m or ft).

The type of outlet influences the flow collected from the gutter (code clause 5.4). The

following types of outlets can be specified:


Type 1: Outlet with sharp corners.

Type 2: Outlet with rounded corners.

Type 3: Outlet with tapered edges not exceeding 45° with the vertical.

Breadth to width ratio: Use a unity value for square and circular down pipes.

Width: The larger dimension of the down pipe. Use the diameter in the case of a circular

down pipe.

Rectangular: Indicate if the downpipe is rectangular or circular.

Drop box: Indicate if the downpipe has a box receiver or sump increases the drainage

capacity before overtopping.

Additional inflow

If draining one or more other roofs into this gutter, enter the location (measured from the

start of the roof) (m or ft) and the equivalent drainage areas (m2 or ft2) for each.


Design

The Design page gives a graphic summary of the drainage catchments and gutter draining.


Calcsheets

The Calcsheets page displays the design calculations. The program evaluates the following

three components of the drainage system:

The gutter that collects the flow from the roof.

The outlet into which the flow from the gutter discharges.

The pipe-work that conveys the flow from the outlet to a lower drainage system.


The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in

Calcpad is saved as part of a project and therefore does not need to be saved in the Gutter

Design module as well.

Masonry Design 9-1

Chapter

9 Masonry Design

The masonry design section contains modules for the analysis of reinforced masonry beams

subjected to pure bending and unreinforced masonry walls subjected to axial compression and

out of plane bending about two axes.

Masonry Design 9-2

Quick Reference

Masonry Design using PROKON 9-3

Masonry Section Design 9-5

Masonry Wall Design 9-15


Masonry Design using

PROKON

The masonry section design module, MasSec, is mainly used for the design

of members such as lintels and masonry that span large openings in walls.

MasWall, on the other hand is ideally suited for the design of wall panels and

bearing walls.

Code of practice support is currently limited to SABS 0164-1992.

Characteristic compression strengths for masonry units are calculated based

on unit geometry, nominal strengths and tables in the abovementioned code

of practice.

All the masonry modules provide a detailed Calcsheet on design

methodology and results, i.e. a complete record of the design is generated automatically.


Masonry Section Design

The masonry section design module, MasSec, determines the resistance of a

reinforced masonry section loaded in pure bending.

The module is standalone, i.e. it does not post process results from any of the

analysis modules.



A brief background is given below regarding the application of the design

codes.

Design scope

The masonry section design module verifies the resistance of a reinforced

masonry beam at a critical section. It is assumed that the loads imposed on

the beam causes uniaxial bending and a shear force only.

The following limitations apply:

No direct support for composite action, e.g. masonry beam and

prestressed a lintel.

No support for doubly reinforced sections.

Design codes

The program designs masonry sections according to the following codes of

practice:

SABS 0164 - 1992.


MasSec supports both Metric and Imperial units.

Symbols

Where possible, the same symbols are used as in the codes of practice:

Dimensions

b : Section breadth (mm).

d : Effective depth, i.e. distance from the compression face to the

tension steel centroid (mm).

z : Moment lever arm (mm).


Design results

Mr : Moment resistance (kNm).

Mu : Applied ULS moment (kNm).

Vr : Shear resistance (kN).

Vu : Applied ULS shear (kN).

a : Shear span (m), or unit correction factor (unitless).

Design parameters

As : Tension steel area (mm²).

mm : Partial material safety factor for the masonry unit.

ms : Partial material safety factor for the reinforcement.

Lmax1,2 : Limiting lengths due to stability considerations (m).

Stresses

fy : Ultimate tensile strength of the tension steel (Mpa).

fyy : Ultimate tensile strength of the shear steel (Mpa).

fnom : Nominal compression strength of the masonry unit (MPa).

fk : Characteristic compression strength of the masonry unit

(MPa), i.e. the strength of the unit in a beam or wall,

dependence on unit aspect ratio removed.

fv : Shear stress due to Vu (MPa).

fv’ : Adjusted shear stress (MPa), modified based on the shear

span.

fbr : Bond resistance (MPa).

fbu : ULS bond stress due to Vu (MPa).

Design parameters

Tension steel area

As MasSec only verifies the resistance of a section, the diameter and number

of bars are required parameters during the input stage.


Physically, the tension reinforcement is usually either conventional bars, as

used for concrete, or hard drawn wires. The conventional bars are used with

special concrete block masonry units which have voids specifically intended

for reinforcement. These voids are then filled with concrete after steel

placement to form a solid, reinforced unit.

Wires are placed in bedding joints, and as such, are suitable for use with

standard format brickwork.

Partial material safety factors

The safety factors for masonry units have a fairly wide range, due to the wide

range of materials and the measure of control during manufacturing and

construction. See the applicable code of practice for details.

Stresses

Manufacturers usually quote a nominal compression strength for the masonry

units that they provide. This nominal strength is derived from a simple

crushing test.

Due to the variability in masonry unit dimensions, this nominal strength

cannot be used as the actual crushing strength of the unit. Values from

crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter.

This can be by testing a small, standard, wall panel to failure and using

equations provided in the applicable code of practice to determine

characteristic compression strength for the unit.

Alternatively, most codes of practice also provide tables of characteristic

strengths versus aspect ratio and nominal strengths.

In MasSec, any one of the two approaches can be used.


Input

Design input comprises two steps:

General: Parameters concerning materials and masonry unit.

Geometry and loads: Parameters concerning the beam and loading.

General input

The masonry unit to be used in the beam is completely defined by the first

table on this page. The three available unit types and associated input

parameters are tabulated below:

Solid unit Width, Length, Height, Joint size

Hollow unit Width, Length, Height, Joint size

Shell thickness*, % solid material

Hollow grouted unit Width, Length, Height, Joint size


*This parameter is only used for the graphical output.


Percentage solid material refers to the area perpendicular to the loading in the

crushing test, usually this would be width x length. The percentage solid

material would then be (total area – void area) as a percentage of the total

area.

Masonry unit sizes are based on the modular concept, i.e. any dimension of

the unit added to a joint thickness of 10mm yields a multiple of 100.

The table below indicates the recommended nominal unit dimensions applicable to South Africa.

Burnt clay

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

Calcium silicate

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 100 x 190 mm

Concrete

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

The second table on this page contains the parameters pertaining to material

strengths and reinforcement position. If the masonry units have been tested to failure as specified by the applicable code then fk can be entered directly in

this table. If only nominal strengths are available, enter the nominal strength

and MasSec will calculate fk.


The table below lists the available nominal strengths available in

South Africa:

Burnt clay

3.5 MPa

7 MPa

10.5 MPa

14 MPa

17 MPa

Calcium silicate

7 MPa

14 MPa

21 MPa

35 MPa

Concrete

3.5 MPa

7 MPa

10.5 MPa

14 MPa

21 MPa

Steel strength, positioning and type, as well as mortar class must be chosen in

this table as well.


The first table on this page defines the type and geometry of the masonry

beam.

The following beam types are supported:

Single leaf - Single leaf of masonry

Collar jointed - Double leaf of masonry, where the small void between

the two leaves of masonry is filled with mortar or concrete

Grouted cavity - Double leaf of masonry, where the larger void between the two leaves is filled with concrete with strength of at least fk.


The dimensions of the beam section, the clear span and the type of support

are also chosen on this table.

The second table provides parameters for the steel as well as a load distance parameter and a bearing length. The load distance is the distance of the

critical section from the left hand support – the resulting shear enhancement

is allowed in certain cases. The last table requires the input of ULS loads on

the critical section.


Design

The design page provides a tabular and diagrammatic summary of the design.

Two cases of bending failure are presented on the diagram and the minimum

chosen as the section strength in bending:

1) Compression failure – Over-reinforced beam, masonry ruptures in

compression before the steel yields.

2) Tension failure – Under-reinforced beam, steel yields before the masonry

ruptures in compression.

Other design checks are tabulated with action effect (loading) versus the

resistance effect (strength). Steel required and provided is tabulated in the left

bottom corner of the tab.


Calcsheets

The Calcsheet provides a fully annotated design document which can be

printed or sent to the CalcPad for permanent storage.

Display settings for the Calcsheet are controlled by the output settings button,

on the left bottom corner of the page.

Note: The Calcsheet is not saved with the rest of the input when the file is saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet

output, send it to the CalcPad where it can be edited and saved.


Masonry Wall Design

The masonry wall design module, MasWall, determines the resistance of an

unreinforced masonry wall axially loaded in its plane or loaded out of plane.

The module is standalone, i.e. it does not post process results from any of the

analysis modules.



A brief background is given below regarding the application of the design

codes.

Design scope

The masonry wall design module verifies the resistance of an unreinforced

masonry wall, subjected to one of the following loads:

In plane axial loading (Bearing walls)

Out of plane loading, causing biaxial plate bending (Wall panels)

The following limitations apply:

Currently no support for combined loading, i.e. bending and

compression.

No support for reinforced walls.

Design codes

The program designs unreinforced masonry walls according to the following

codes of practice:

SABS 0164 - 1992.


MasSec supports both Metric and Imperial units.

Symbols

Where possible, the same symbols are used as in the codes of practice:

Dimensions

t : Wall thickness (mm).

h : Wall height (mm)

ex : Calculated or actual eccentricity (mm).

Design results


Mr : Moment resistance (kNm).

Mcr : Cracked moment resistance (kNm).

Mu : Applied ULS moment (kNm).

Cr : Axial resistance (kN/m).

Cu : Applied ULS axial force (kN/m).

qlat : Lateral pressure resistance, assuming a three pin arch

collapse mechanism. (kN/m²)

Design parameters

mm : Partial material safety factor for the masonry unit.

R : Slenderness ratio

Z : Section modulus (mm³)

ea : Additional eccentricity due to slenderness (mm).

et : Total eccentricity (mm).

em : Design eccentricity (mm), maximum of et and ex.

: Capacity reduction factor

teff : Effective wall thickness (mm)

heff : Effective wall thickness (mm)

Stresses

fnom : Nominal compression strength of the masonry unit (MPa).

fk : Characteristic compression strength of the masonry unit

(MPa), i.e. the strength of the unit in a beam or wall, dependence on unit aspect ratio removed.

fkx perp : Flexural tensile strength perpendicular to the bedding joints

(MPa).

fkx par : Flexural tensile strength parallel to the bedding joints (MPa).


Design parameters

Eccentricities

Actual load eccentricity is assumed to vary from ex at the top of the wall to

zero at the bottom, subject to additional eccentricity due to slenderness

effects.

Partial material safety factors

The safety factors for masonry units have a fairly wide range, due to the wide

range of materials and the measure of control during manufacturing and

construction. See the applicable code of practice for details.

Stresses

Manufacturers usually quote a nominal compression strength for the masonry

units that they provide. This nominal strength is derived from a simple

crushing test.

Due to the variability in masonry unit dimensions, this nominal strength

cannot be used as the actual crushing strength of the unit. Values from

crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter.

This can be by testing a small, standard, wall panel to failure and using

equations provided in the applicable code of practice to determine

characteristic compression strength for the unit.

Alternatively, most codes of practice also provide tables of characteristic

strengths versus aspect ratio and nominal strengths.

In MasWall, any one of the two approaches can be used. Similarly flexural

tensile resistances parallel and perpendicular to the bed joints can be

specified or left to MasWall for calculation.


Input

Design input is divided into two steps:

General: Parameters concerning materials and masonry unit, as well as

wall design type.

Wall geometry: Parameters concerning the wall type and dimensions.

General input

The masonry unit to be used in the beam is completely defined by the first

table on this page. The three available unit types and associated input

parameters are tabulated below.

Solid unit Width, Length, Height, Joint size

Hollow unit Width, Length, Height, Joint size


Hollow grouted unit Width, Length, Height, Joint size


*This parameter is only used for the graphical output.


Percentage solid material refers to the area perpendicular to the loading in the

crushing test, usually this would be width x length. The percentage solid

material would then be (total area – void area) as a percentage of the total

area.

Masonry unit sizes are based on the modular concept, i.e. any dimension of

the unit added to a joint thickness of 10mm yields a multiple of 100.

The table below indicates the recommended nominal unit dimensions applicable to South Africa.

Burnt clay

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

Calcium silicate

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 100 x 190 mm

Concrete

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

The second table on this page contains the parameters pertaining to material

strengths. If the masonry units have been tested to failure as specified by the applicable code then fk can be entered directly in this table. If only nominal

strengths are available, enter the nominal strength and MasWall will

calculate fk.


The table below lists the available nominal strengths available in

South Africa.

Burnt clay

3.5 MPa

7 MPa

10.5 MPa

14 MPa

17 MPa

Calcium silicate

7 MPa

14 MPa

21 MPa

35 MPa

Concrete

3.5 MPa

7 MPa

10.5 MPa

14 MPa

21 MPa

Similarly values for flexural tensile resistances should be available in the

applicable code of practice.

The design type should be chosen on this page:

Vertical loads – axially loaded bearing walls

Lateral loads on panels – design for biaxial plate bending

The layout of subsequent pages in the input process will vary according to the design type chosen.

Wall geometry input – Vertical loads

The table on this tab defines the type, geometry and stiffeners (if any) of the

masonry wall.

The following wall types are supported:


Collar jointed - Double leaf of masonry, where the small void between

the two leaves of masonry is filled with mortar or concrete


Cavity - Double leaf of masonry, with a void between the two leaves.

Wall height, length and cavity size (if required) can be entered on this page.

Possible values for the horizontal restraint are: (Refer to SABS 0164 for

details)

Simple – No rotational fixity at the top of the wall.

Enhanced – Partial rotational fixity at the top of the wall.

Similar rotational fixities can be specified for the vertical edge(s) of the wall.

MasWall also supports vertical stiffeners between the wall edges. These

stiffeners can be either piers (small columns) or intersecting walls. Once

vertical stiffeners have been selected, they need to be dimensioned as well.


Wall geometry input – Lateral loads on panels

The table on this page defines the type, geometry and edge restraint of the

masonry wall panel.

The following wall types are supported:


Collar jointed - Double leaf of masonry, where the small void

between the two leaves of masonry is filled with mortar or concrete

Cavity - Double leaf of masonry, with a void between the two

leaves.

Wall height, length and cavity size (if required) can be entered on this page.

Edge restraints can be specified for each edge individually as free, simple or

fixed.

Loads input – Vertical loading

For this loading type, axial forces and eccentricity with respect to the wall

centreline can be entered on this page. Multiple load cases are supported.

Note that all loads should be ULS loads.


Loads input – Lateral loads on panels

For this loading type, moments parallel and perpendicular to the bedding

joints can be entered directly. A dead load pressure on the level of moment

parallel to the bedding joints is required to calculate the cracked moment

resistance.

Alternatively the moment calculator button can be

used to calculate moments based on a lateral

pressure.

This calculation makes use of the moment tables in

the code of practice which are in turn derived from

yield line equations.


Design

This page provides a tabular and diagrammatic summary of the design. The

two resistance moments are shown on the diagram.

Other design checks are tabulated with action effect (loading) versus the

resistance effect (strength).


Calcsheets

The Calcsheet provides a fully annotated design document which can be

printed or sent to the CalcPad for permanent storage.

Display settings for the Calcsheet are controlled by the output settings button,

on the left bottom corner of the page.

Note: The Calcsheet is not saved with the rest of the input when the file is

saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet

output, send it to the CalcPad where it can be edited and saved.

prokon user manual

Documents

prokon structural analysis

prokon drawing

prokon basics

prokon users guide

prokon suite of programs

prokon installation

rights reserved prokon

design modules