rcb manual

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Analysis & Design of Reinforced ConcreteBuildings for Earthquake and Wind Forces


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COPYRIGHT

The computer program EngSolutions RCB and all associated documentation are proprietaryand copyrighted products. Worldwide rights of ownership rest with EngSolutions, Inc.Unlicensed use of the program or reproduction of the documentation in any form, without prior

written authorization from EngSolutions, Inc., is explicitly prohibited.

Further information and copies of this documentation may be obtained from:

EngSolutions, Inc.At: Dr. Ricardo E. Barbosa

8170 SW 29th CtFt. Lauderdale FL 33328

Tel: (954) 370-6603

Fax: (954) 370-0150www.EngSolutionsRCB.comEmail: [email protected]

EngSolutions, Inc., 2000-2009 Ricardo E. Barbosa, Ph.D.1992-2000
http://www.engsolutionsrcb.com/mailto:[email protected]:[email protected]://www.engsolutionsrcb.com/


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Table of Contents

Chapter 1 Introduction 1

EngSolutions RCB .................................................................... 1Technical Overview ......................................................... 2Organization of Manual .......................................................... 3Program Versions ........................................................... 3Technical Support....................................................................... 4

Chapter 2 Installation 5

System Requirements ..................................................... 5Software Installation ............................................................ 6Software Initialization .......................................................... 6Protection Key .................................................................... 7Network License .................................................................... 8

Chapter 3 EngSolut ions RCB Interface 11

Running the Program ............................................................. 11EngSolutions RCB Main Window .............................................. 12Commands ................................................................................. 15

Activating Commands ............................................................ 15Types of Commands .................................................................. 15User Interaction ............................................................... 16Element Selection .............................................................. 16Property Window .......................................................... 16Context Menu ............................................................................. 17Rotating the Structure ............................................................. 17Exiting EngSolutions RCB ...................................................... 17What to do Next ..................................................................... 17


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Chapter 4 EngSolut ions RCB Concepts 19

The Structure .............................................................................. 19The Geometry.... 20The Elements . 22

Support Conditions ... 26Loads .................................................................................. 30Self Weight ................................................................................. 32Vertical Floor Loads ........................................................... 32Wind Forces ....................................................................... 33Equivalent Static Earthquake Forces ................................. 33Response Spectra .............................................................. 36Dynamic Time-History Analysis .... 37Load Combinations ......................................................... 39

Analysis ..................................................................................... 40Modes / Frequency Analysis ........................ 40Gravity and Lateral Load Analysis .......................................... 41Linear Analysis 42P-Delta Analysis .................................................................. 42Gravity Load Analysis ................................................................ 43Incremental Analysis . 43Seismic Analysis 45Time History Analysis ... 45Stiffness of Elements 47

Analysis Results ......................................................... 47Design of Reinforced Concrete Elements ................................. 55Design of Beams ....................................................................... 55Column Design .................................................................. 56Shear Wall Design ...................................................................... 58Design of Foundation Beams .. 61Design of Footings . 61Design Results ................................................................ 61

Design of Structural Steel Elements ... 63Printing ................................................................................ 65

Chapter 5 EngSolut ions RCB Training Session 67

The Structure .............................................................................. 67Creating the Structure ............................................................ 68

Assigning Supports ............................................................... 86Applying Loads Manually ...................................................... 87Generating Self Weight of Elements ............................................ 89Generating Floor Loads ................................................. 89Modes and Frequency Analysis ....... 90

Displaying Mode Shapes 91Generating Earthquake Forces . 92

Analyzing the Structure .. 95Displaying Analysis Results .. 96Checking Story Drift Ratios 99Defining Load Combinations . 101Designing of Structural Elements .... 104Displaying Design Results . 109Seismic Shear Resisted by Shear Walls . 111Design Check for Dual System . 113


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Cost of the Structure .. 114Modifying the Model .. 116

Chapter 6 Reference 117

Earthquake Records ............................................................ 117Differences in Use with RCBE ................................................. 118RCBE v5.2 Structures ...................................................... 119Rotating the Structure ................... 119Wall Element Output ..................................................... 121Load Scale .................................................. 125Estimate of Building Materials ..................................................... 126

References 127

Appendix A EngSolut ions RCB Appl ications 129

Covert Ocean Park Tower 1 & 2 Punta Pacifica, Panama, Rep. of Panama,Structural Engineer Gonzalo Sosa from Grupo G.S., S.A., Panama.


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Chapter 1

Introduction

EngSolutions RCB

EngSolutions RCB is a structural engineering program for tridimensional analysis anddesign of reinforced concrete buildings. EngSolutions RCBconsists of several modulesintegrated into an exceptionally easy to use software package. Through its graphicalinterface it is possible to easily create, analyze and design complex building structures

for earthquake and wind forces, according to different building codes.

Creation of the structure, assignment of element properties, definition of supports andapplication of loads, are all performed interactively. Hence, there is no need for an inputfile. All operations including analysis and design are carried out within the programsgraphical interface.

Generation of loads is fully automated releasing the engineer from lengthy manualcalculations. Vertical floor loads can be automatically converted to span loads onadjoining beams and walls. Wind forces and earthquake forces can be generatedautomatically according to different international building codes.

Once a building structure is created, it remains interactively displayed and all programcommands remain available. The engineer can make changes at any time on thestructure, such as change coordinates, add or remove elements, add or remove stories,modify element properties, change support conditions, change loading, etc., and see theinfluence of these changes on the analysis and design results. All these steps areaccomplished with just a few mouse clicks.

The program allows modeling the incremental construction of tall buildings, checkinglateral story drifts, computing redundancy factors, and designing structural elementsaccording to various seismic codes. It is possible to run simultaneously multipleinstances of the program, which makes it easier to compare different structural solutions.


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Technical Overview

EngSolutions RCB is a mature and stable software system that has a proven trackrecord of improving the profitability of engineering firms and enhancing the efficiency of

regulatory building agencies. The main technical features of EngSolutions RCBare thefollowing:

Native Windows 32 bit application that operates under Windows Vista\XP/2000/NT.

No limit on number of nodes, elements or equations.

Interactive procedure to create building models through typical floor framing plans.

Automatic generation of seismic forces, static equivalent, spectral, and time-history,according to numerous international building codes, including: USA IBC-2003, ASCE7-2005, UBC-97, UBC-94, ASCE7-93/95, NERPH-97, NERPH-85, Mexico RCDF-2004, GUAD-97, CFE-93, Panama REP-04, REP-93, Colombia NSR-98 andCCCSR-84, Venezuela COVENIN-82, Peru E030-2000, Ecuador CEC-01 and CEC-93, Chile NCH433.Of93, Dominican Republic DNRS/SEOPC-80, Costa Rica CSCR-

86. Complete library of earthquake records.

Automatic generation of wind forces, according to various international codes,including: USA ASCE7-95, ASCE 7- 88, UBC- 94, Mexico RCDF-87, CFE-93,DominicanRepublic DNRS/SEOPC-80.

Accurate modeling of torsion effects: The engineer may specify different designeccentricities based on inherent and accidental eccentricities, and may choose fromdifferent methods of modal combination available, including SAV, SRSS, CQC, 1/2SAV+SRSS, and 0.25 SAV + 0.75 SRSS.

Automatic distribution of floor loads to span loads on adjoining beams and walls.Various floor systems can be considered, including one-way and two-way slabsystemsas well as one-wayand two-way joist systems.

Automated incremental analysis to model the construction sequence of high-risebuildings. Instead of applying gravity loads in a single step, the analysis can modelthe sequential addition of floors to the structure.

Graphical display of lateral inter-story drifts that allows immediate check forcompliance with building codes.

New finite element formulations for accurate modeling of buildings with shear walls.

Automated design of shear-walls, which includes dimensioning of boundary zones forspecial (ductile) seismic design.

Boundary zones for shear walls can be design either according to the stress designmethod of the ACI-318-99 or to the strain method of UBC-97 and ACI-318-05.

Automatic detailing of steel reinforcement for beams.

Automatic generation of design load combinations according to different international

building codes. Buildings can be modeled as supported on theoretical dimensionless nodal supports

or on rigid footings, including spread footings for columns, continuous footings forwalls, combined footings and mats.

Automatic re-sizing of footings according to specified allowable soil pressure.

Design of spread and continuous footings.

Specification of member end-releases.

Automatic generation of load combinations: according to several international codes.


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Structural elements can be separated into elements that are part of the lateral forceresisting system only, elements that are part of the gravity load resisting system andelements are part of both structural systems.

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Technical Support

Technical support is available to registered users only, therefore be sure to complete andreturn the registration card. Registered users are eligible for the following supportservices at no extra charge.

Fax support. If you need assistance beyond what the EngSolutions RCBmanual canprovide, you may fax messages at (954) 370-0150. Please include the followinginformation:

Your name, company name, fax & phone numbers and Email address. EngSolutions RCBversion number and License number. Your hardware and operating system configuration. A concise description of the problem. Selected information and/or printouts documenting the problem.

Email support. You may also send Email messages to [email protected]. Pleaseinclude the same information requested above.

Telephone support. To help us provide a more efficient support service, we request thatyou send first a fax/Email message with the information requested above, before you call.Telephone support is used to discuss and solve cases already described in written form.Please contact us at (954) 370-6603.

EngSolutions RCBtechnical support program is subject to change without notice.

If you would like to share ideas with the creators of EngSolutions RCB, make commentsabout the software, or suggest improvements, please use any of the technical supportoptions described above. Occasionally, we are unable to implement some requests foradditions to the software as fast as we would like, and sometimes we cannot implementat all some of the suggested modifications, however, we do study and consider all the

suggestions that we-receive.
mailto:[email protected]:[email protected]


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Chapter 2

Installation

This chapter deals with the installation of EngSolutions RCB on computers withWindows Vista/XP/2000. The complete EngSolutions RCBpackage includes a CD anda software protection key.

System Requirements

To run EngSolutions RCB you must have certain hardware and software installed inyour computer. The system requirements include:

Personal computer with a Pentium processor.

At least 518 MB of RAM.

A color monitor with a minimum resolution 1024 x 768.

A hard drive with at least 300 MB of free hard disk space.

Operating system Windows Vista/XP/2000.

Software Installation

To run EngSolutions RCB you need to install the software and then to initialize it. Toinstall EngSolutions RCBfollow the steps below:

1. If you are upgrading from a previous version of EngSolutions RCBuninstall such aversion by opening the Control Panel, from the Windows Startbutton, and clicking the

Add/Remove Programsicon. This command activates the EngSolutions RCBuninstallprogram. The uninstall program does not remove any folder; therefore, structure filespreviously saved remain untouched.


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Next, delete manually the folder Bitmaps, located on the folder where the previousversion of EngSolutions RCBwas installed.

Users of RCBE(our program predecessor to EngSolutions RCB) do not need touninstall such a program, as EngSolutions RCBand RCBEare completely independentprograms.

2. Insert theEngSolutions RCBCD in the CD drive.3. Use Windows explorer to locate and activate the SetUp.exe program. Alternatively, you

may activate the Windows RUN command and type the command line: D:\SETUP(assuming the CD drive is D)

4. Follow the screen instructions.

In the first window of the installation program (Welcome to the EngSolutionsRCB installation program) clickon the OK button to continue. In the secondwindow, where the installation folder is selected, clickon the installation buttonnot in the exit button (Exit Setup). The installation button is the one locatedunder the message: Begin the installation procedure by clicking the buttonbelow.

If your operating system is Windows Vista, do not install the program in thedefault folder (C:\Program Files\) but create a different folder such as C:\RCB\

If during the installation process a window pops up, warning that a more recentversion of a given file is already present in your system, answer affirmatively tothe question whether you want to keep the existing file. (A file being copied isolder than the file currently in your system. It is recommended that you keepyour existing file. Do you want to keep this file?Yes.)

Note:

Software Initialization

Once the installation process is finished, initialize the program by running the initializationprogram from the Windows Start button (Start > Programs > Initialize EngSolutionsRCB).

The initialization program performs various tasks. First it displays the license agreement.Then, it asks user information (company name, user name, country). Next, the programinstalls the device driver for the protection key, which is required to run EngSolutionsRCB. Finally, the program creates a shortcut in the Windows desktop, for an easieraccess to EngSolutions RCB.

Protection Key

After the program has been initialized, connect the software protection key to yourcomputer. Without the key EngSolutions RCBwill not run. The key is transparent to theoperation of your computer and connected peripherals. The only software that detects itspresence is EngSolutions RCB. There are two types of protection keys available: (a)HASP USB keys which are connected to a USB port and (b) HASP parallel port keyswhich are connected to a parallel printer port. If your protection key is a HASP parallelport key and you have a printer connected to the parallel printer of your computer,


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disconnect the printer, connect the key to the parallel port, and then connect the printer tothe protection key.

Network License

In the case of network licenses, a single protection key (HASP4 Net) is provided which isconnected to one of the computers in the network. This HASP4 Net key is pre-programmed to allow a determined number of stations to run EngSolutions RCBat thesame time. The computer to which the HASP4 Net key is connected does not have to bethe network file server but any computer on the network, providing the HASP LicenseManager is installed on the same machine.

The HASP License Manager is included in the EngSolutions RCBdistribution CD. It isthe application that communicates EngSolutions RCBand the protection Key (HASP4Net key), functioning as a link between the two. When EngSolutions RCBis activatedfrom a network station, it accesses the HASP License Manager and request permissionto run. The HASP License Manager then checks that the correct protection key isconnected and access the HASP4 Net key to verify that EngSolutions RCBis licensed

to run and that the number of stations allowed to run EngSolutions RCBat the sametime has not been exceeded.

The following steps are necessary to run EngSolutions RCBin a network environment:

The following steps are necessary to run EngSolutions RCBin a network environment:

Install and initialize EngSolutions RCBin each computer in the network wherethe program is going to be run, as indicated above.

Connect the HASP4 Net key to a computer in the network. Install and start the HASP License Manager on the same computer the

HASAP4Net key is connected to.

If necessary, customize the HASP License Manager and EngSolutions RCB toadapt them to your network environment.

The HASP License Manager is available for the following environments: WindowsNT/2000/XP/Vista, and Novell 3.12 and higher.

HASP License Manager for Windows

The HASP License Manager is available as an executable for Windows NT/2000/XP andas a service for Windows NT/2000/XP/Vista. Both types of HASP License Managers canbe installed with the setup file lmsetup.exein the folder HASP4Net\Servers\Win32 in theEngSolutions RCBdistribution CD.

The HASP License Manager for Windows can communicate via TCP/IP, IPX andNetBIOS. The protocols can be loaded and unloaded using the HASP License Managergraphical user interface or command-line switches.

Installing HASP License Manager on a Windows NT/2000/XP/Vista Station


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The HASP License Manager for Windows NT/2000/XP/Vista is nhsrvice.exe. Install it byrunning the setup file lmsetup.exe from the EngSolutions RCB distribution CD andfollowing the instructions of the installation wizard. As installation type, select Service.The setup file lmsetup.exe is located in the folder HASP4Net\Servers\Win32.

It is recommended that you install the HASP License Manager as an NT service, so there

is no need to log in to the station to provide the functionality.

If the HASP4 Net key is going to be connected to a Windows station in whichEngSolutions RCB is not going to be used (and was not installed), beforeinstalling the HASP License Manager it is necessary to install the HASP devicedriver. To install the HASP device driver copy the file Hinstall.exe (from theHASP4Net folder in the EngSolutions RCBdistribution CD). Then typehinstall ifrom the command line.

Nota:

Activat ing and Deactivat ing HASP License Manager

To activate the HASP License Manager start it from the Start menu or the WindowsExplorer. The HASP License Manager application is always active when any protocol isloaded and a HASP4 Net key is connected. To deactivate it, select Exit from the mainmenu. If the HASP License Manager is installed as a Windows NT service, you cannotexit using this menu option. Instead, use the standard Windows Service Administration inthe Control Panel.

Operating The HASP License Manager

For information on how to operate the HASP License Manager including loading protocols,removing protocols, viewing the log for specific protocols, refer to NetLicenses.docin theHASP4Net folder in the EngSolutions distribution CD.

HASP License Manager for Novell File Server

The HASP License Manager for Novell Netware file servers is haspserv.nlm. It cancommunicate via IPX.

Loading HASP License Manager

To load the HASP License Manager:

Connect the HASP key to a Novell server. Copy haspserv.nlmfrom the EngSolutions CD to the system directory of the

file server. Load the HASP License Manager by entering:

Load haspser v

The HASP License Manager screen appears showing operation details.

To load the HASP License Manager automatically, add the line loadhaspservto the autoexec.ncffile in the systemdirectory.Nota:

Removing HASP License Manager


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To remove the HASP License Manager enter unl oad haspser v.

Customizing the HASP License Manager

When installing and operating the HASP License Manager you may want to adapt it to the

network environment. You can use one of the following methods:

Operate the HASP License Manager with switches. Use the configuration file nhsrv.ini. A copy of nhsrv.ini is included in the

HASP4Net\Servers folder in the EngSolutions RCB distribution CD.

For information on customizing the HASP License Manager refer to NetLicenses.docinthe HASP4Net folder in the EngSolutions distribution CD.

Configuring EngSolutions RCB to the Network

EngSolutions RCBcan be configured to your network environment with a configuration

file. If EngSolutions RCB finds the configuration file, it reads the file and uses theinformation. If not, default values are used. In the configuration file you can fine-tune howEngSolutions RCB searches for the HASP License Manager. The configuration file isnethasp.ini. A copy of nethasp.ini is included in the HASP4Net\Servers folder in theEngSolutions RCB distribution CD. For information on how to configure EngSolutions RCBrefer to NetLicenses.doc in the HASP4Net folder in the EngSolutions RCBdistributionCD.


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Chapter 3

EngSolutions RCB Interface

This chapter describes the main elements of the EngSolutions RCBgraphical interfaceand explains how the engineer interacts with them.

Runing the Program

To run EngSolutions RCBdouble-click the shortcut to the program.

After a few seconds, a splash window is shown, displaying copyright information, licensenumber, and name of the engineer. The starting window, shown in Figure 3.1, follows thesplash window. In this later window, the engineer chooses between creating a newstructural model and opening a previously saved model.

Figure 3.1EngSolutions RCBs starting window


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EngSolutions RCB Main Window

The main window of EngSolutions RCB is shown in Figure 3.2. In this window, differentviews of the model can be shown, along with different diagrams displaying analysis anddesign results.

Figure 3.2Main Window of EngSolutions RCB

The main window of program EngSolutions RCBinclude the following elements:


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1. Title Bar(at the top) includes buttons to minimize, maximize and exit EngSolutionsRCB.

Figure 3.3 Menu Bar

2. Menu Bar(under title bar) provides access to menus and submenus to activateEngSolutions RCBcommands.

3. Toolbarsincludes the most frequently used commands.

Standard ToolbarLocated by default to the left under the menu bar.

View ToolbarLocated by default to the left of the standard toolbar.

Element ToolbarLocated by default vertically on the left border of the mainwindow.

Figure 3.4Toolbars

4. Main View Windowdisplays the structural model along with analysis and designresults. Also in this area occasionally dialog windows and message windows areshown.

5. Status Bar presents messages along with pertinent information about the model.

6. Active Command WindowThis window is shown when an interactive command isactivated. It shows subcommands available and options for multiple selection of


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structural elements. By default, this window is shown in the right top corner of themain window. A typical active command window is shown in Figure 3.5.

Figure 3.5Active command window

7. Property Windowis a table containing properties of the selected element. The firstline of this window shows the name of the selected element and is followed by a two-column table with the name and de value of each property. This window is shownsimultaneously and below the Active command window.

Figure 3.6Property window

8. Selected element w indow presents a solid 3D view of the selected elementdisplaying its local axes. This window is displayed simultaneously and below theProperty window.


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Figure 3.7Selected element window

9. Rotation windowshows a reference system to rotate the model.

Figure 3.8Rotation window

Commands

EngSolutions RCBis a procedure-oriented program. At any stage, only one commandor procedure can be active. Some examples of EngSolutions RCBcommands that at agiven instant may be active are:

Create a new model , Save current model , Edit properties of columns , Run

a static analysis , compute natural frequencies and modes of vibration , etc.

Activating CommandsA command is activated when the engineer selects it with the mouse in either a menu inthe menu bar or in a toolbar. The name of the active command is shown in the Activecommandwindow.

Types of Commands

There are three types of commands in EngSolutions RCB, which require differentdegrees of user interaction. These are action commands, automated commands andinteractive commands.

Action commandsrequire little or no user interaction. These commands are executedas soon as the user activates them. Some of these commands may require the user to


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input additional information such as a file name o some parameter values. When thecommand is completed it is deactivated and the program remains idle waiting for the userto activate a new command. Examples of this type of command are: Save current

structure , run analysis , etc.

Automated commands lead the engineer through a series of generation steps. Thereare usually available Next >>and Cancelbuttons to go from one step to the following orto abort the command. At each step the program requires the input of pertinentparameters. The command is deactivated when it is completed or cancelled by the user.Examples of this type of command are the commands for generating new structures,automatic generation of wind loads, automatic generation of earthquake loads, etc.

Interactive commandsare executed numerous times and remain active until the userdeactivates them or activates a new command. Examples of this type of command are:

Edition of columns , beams , walls , definition of supports , manual

application of loads , display of analysis results, etc. To execute these commands, theengineer interacts with the model selecting nodes or structural elements. Interactiontakes place in the Main view window.

User Interaction

Element SelectionTo select a member the user places the mouse cursor near the member and thenpresses and holds-down the left mouse button. The selected member is highlighted anddisplayed in the Selected element window. The command is executed when the mousebutton is released. If the cursor is moved away from the selected member, the member isdeselected and no command is executed upon mouse button release. A similarprocedure is used to select nodes.

To select a wall panel or a floor panel the user places the mouse cursor at about thecenter of the panel and then presses the left mouse button. The same holding-down-the-mouse-button applies to panels.

By default nodes and structural elements are selected individually. The Selection optionswindowincludes options that allow selection of multiple elements. For example, optionssuch as Beams upor Beams down, allow selecting in a single step, the beam pointed-atand all the beams above or below it.

Property WindowAll elements have default properties that can be viewed by activating Edition commandsand selecting elements. Properties are shown in the Property window . These propertiescan be edited entering new values for each property, pressing ENTER after each entry.

The edited properties are assigned to the selected elements by clicking the Assign button in the property window.

Context MenuA pop-up menu with display commands can be displayed in the Main working area usingthe right mouse button. This menu can be displayed only if there is a structure. Themenu contains commands for zooming, moving selecting parts of the structure, andseveral display options.


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Rotating the Structure

In EngSolutions RCB structures can be viewed from any angle in a tridimensionalspace. To change the view angle the user interacts with the device-reference system inthe Rotation Window. Refer to Rotating the Structurein Chapter 6 for an explanation onhow to view the building structure from different angles.

Exiting EngSolutions RCB

To exit EngSolutions RCB click the exit button in the main window or activate theExitcommand in theFile menu

What to do Next

The EngSolutions RCB software package is so intuitive and easy to use, that many

engineers have started using it productively in complex designs, before reading anydocumentation. As you learn to use EngSolutions RCB, its intuitive design will stand outmore and more indeed, you will be able to anticipate how features of EngSolutionsRCBwill work without having used them. This quality is what makes EngSolutions RCBattractive to so many structural engineers around the world. However, to understand thecapabilities, assumptions and limitations of the program,it is highly recommended thatthe next chapter, EngSolutions RCB Concepts, be read before using the software.

For a more through introduction to EngSolutions RCB it is recommended to followChapter 5, preferably at the computer, to understand the fundamentals of using theanalysis and design interface.


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Chapter 4

EngSolutions RCB Concepts

The Structure

In EngSolutions RCB, the structure of a building is idealized as an assemblage ofcolumn, beam, brace and wall elements, interconnected by horizontal floor diaphragmslabs, rigid in their own plane. The basic building geometry is defined with reference to asimple tridimensional grid system, formed by intersecting floor planes and vertical columnaxes. Column axes are defined through an architectural grid of either longitudinal andtransverse axes, in the case of rectangularbuildings, or radial and circumferential axes,in the case of cylindrical buildings. The program includes wizards that allow creatingcomplex building models with minimum data entry.

To generate the structure, the engineer enters story heights and spacing betweenframes. Based on this information the program presents a floor-framing plan that theengineer modifies interactively moving column axes, adding or removing slab panels,shear walls, columns and beams. This typical floor plan can be used to generate variousstories of the model. It is possible to define various typical floor-framing plans. The easein creating the model is the main reason why EngSolutions RCB has resulted soattractive to so many structural engineers around the world.

It is possible to specify either rigid or deformable supports, elastic beams on elastic

foundations or rigid footings on elastic foundations, which allows analyzing buildingsfounded on compressible soils. Rigid supports include the usual fixed, hinge, roller, andspecial supports for which the engineer specifies the degrees of freedom to be restricted.Deformable supports are defined as multiaxial springs. Deformable supports can also beused to model the lateral ground support on basement walls. For footings and beams onelastic foundations the program accepts different values of the subgrade reactionmodulus for gravity load analyses and for lateral load analyses.


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Once a building structure is created, the engineer may modify it, adding and removingelements, and changing the coordinates of the reference grid system of floors planes andcolumn axes. The final building may be unsymmetrical and arbitrarily irregular in plan.Torsional behavior of the floors and interstory compatibility of the floors are properlymodeled. The solution satisfies complete tridimensional force equilibrium anddisplacement compatibility at the nodes.

Modeling of partial diaphragms, such as mezzanines and openings is possible. It ispossible also to model cases with multiple diaphragms at each level, allowing to analyzebuildings consisting of several towers, rising from a common base structure at the lowerlevels.

The Geometry

The geometry of building models in EngSolutions RCB is based on a grid systemdefined by an architectural grid system of axes, which define the plan view of the model,and floor levels, which define the elevation of the model. This tridimensional grid is used

to define the location of all structural elements.

Figure 4.1Plan created from a rectangular architectural grid. Floor level 2

Most building models can be created from a rectangular grid system of longitudinal andtransversal axes. First, an orthogonal grid system is created, by specifying separation

between axes. Then the coordinates of the axis intersections are edited to accommodatethe real geometry of the building. The command for editing axis intersections can be

activated in the Elements Toolbarand in the Elements menu .

EngSolutions RCB allows moving axes intersections arbitrarily as long as axesoriginally parallel do not intersect. That is, longitudinal axes (alphabetical axes in Figure4.1) cannot intersect each other, neither transversal axes (numerical axes in Figure 4.1)can intersect each other


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Figure 4.2 (a)Floor level 6

The coordinates of nodes can be varied from floor to floor, allowing the creation ofcomplex tridimensional building systems with a limited number of axes, as shown inFigure 4.2. The command to edit nodal coordinates can be activated in the Elements

toolbarand in the Elements menu .

Figure 4.2 (b) 3D view (Faro del Saber Library, Structural Engineer A. Muns, PuertoRico)


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Before modeling the structure of a building, it is recommended to plan the model andidealize the structure minimizing the number of axes along each direction. It is preferableto have a model with a reduced number of architectural axes in a zigzag fashion thandefining the model using an orthogonal grid consisting of a large number of axes. Theedition and processing of the model as well as its visualization and interpretation ofresults is easier in models with a reduced number of axes, and when beams and shear

walls are aligned along axes. Appendix A includes several actual models of realstructures designed with EngSolutions RCB.

The Elements

Members

Columns, beams and braces are modeled as either prismatic elements or variablesection elements, which may be subjected to axial and shear forces and torsion andbending moments. Shear and bending can act in any two perpendicular planes. Momentreleases can be assigned near the ends of members. The effects of the finite dimensionsof the beams and columns on the stiffness of the structure are automatically included inthe analysis.

In EngSolutions RCBthe engineer may specify which frames or structural elements arepart of the lateral force resisting system. Any element may be part of the lateral forceresisting system only, part of the gravity load resisting system only, or part of bothstructural systems.

Members are added and edited with the commands: columns , beams and braces

, located in the Elements toolbarand in the Elements menu.

(a) (b)

Figure 4.3(a) Column Property Window (b) Table of column sections

When any of the above commands is activated and an element is selected, the programshows the elements Property window. Figure 4.3 (a) shows column properties. Theseinclude the structural system to which the element belongs (Gravity, Lateral, Gravity andLateral), the name of the section, name of the material, the angle defining the elementplan orientation, alignment of the member along each direction, type of conection at eachend (rigid or pinned), reinforcement cover to centroid of steel (for reinforced concrete


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columns) and in the case of structural steel members, spacing between intermediatesupports (-1 if there are no intermediate supports, 0 for continuous support).

When a new building model is created, by default all column elements are assigned asection named Column1, which have some particular cross section properties. If thename of the section in the Property Window is clicked, a window is displayed showing the

table of column sections. This table, shown in Figure 4.3 b, includes a list of availablecolumn sections and the properties of the selected section. The cross section propertiescan be edited in this window. Furthermore, in this window, it is also possible to add newsections (Add), remove existing sections (Remove), import sections from existing filessuch as the AISC database (which is included in the EngSolutions RCB softwarepackage) or tables saved from previous projects (Import), and to save tables of sections(Save). Any change made to the properties of a particular section applies to all elementsthat have assigned such section.

Similarly, the default material for all elements is Rconcrete1.If the name of the material inthe Property window is clicked, a window is displayed showing the table of materials, asshown in Figure 4.7 b. This table includes a list of available materials, and the propertiesof the selected material. These properties include modulus of elasticity (E), shearmodulus (G), unit weight, compressive strength of concrete (fc), yield strength oflongitudinal reinforcement (fy), yield strength of stirrups (fys), etc. In this window, it ispossible to edit these properties, to add new materials (Add) such as reinforced concreteof a different quality or structural steel, to remove existing materials (Remove), to importmaterials previously saved (Import), and to save materials (Save) to be used in futureprojects. Any change made to the properties of a particular material apply to all elementswhich have been assigned such material

Figure 4.4Local axes and orientation of columns Plan view

By default all column elements are created centered with respect to the nodes. That is,the centroid of a column coincides with the intersection between architectural axes. Inthe case of facades, it is possible to shift columns, fixing the distance between column

faces and the node, using the alignment properties D2 and D3. In a Plan Viewof themodel, the program draws column sections with their actual orientation, location anddimensions. Therefore, there is no ambiguity regarding the orientation and/or orientationof columns

Properties of beam and brace elements are similar to those of column elements. Bydefault all beam elements are assigned a section named Beam1. If the name of thesection is clicked at, in the Property window, a new window is displayed showing thetable of beam sections. In this table, it is possible to edit the properties of sections, to addnew sections, to import sections from the AISC library, etc.

2

b

h3

2

= 90o = 0

bGlobal Axes

Z Y

X

h3


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The alignment property D3 of beam elements, shown in Figure 4.5, represents thedistance between the top face of the beam and the centroid of the slab. Thus, in the caseof a typical two-way slab with beams, the D3 property for all beams would be one half thethickness of the slab. In the case of spandrel beams, it is possible to locate vertically thelocation of each beam element using the D3 property.

Figure 4.5Local axes and D3 alignment property of beam elements

When any property is changed in the Property window such as the section, the material,alignment, etc., it is necessary to click theAssign button in that window to apply suchchange.

Shear walls

In EngSolutions RCBwalls can be modeled using three types of finite elements. Shellelements, membrane elements, and plate elements. Membrane elements are elementsthat only resist in-plane forces (i.e. they only have in-plane stiffness). Plate elements areelements that only resist out-of-plane forces (i.e. they only have out-of-plane stiffness).Shell elements are elements that resist both in-plane and out-of-plane forces. By default,shear walls in EngSolutions RCBare modeled as shell elements.

Both shell elements and membrane elements include in-plane rotational stiffness(drilling-degrees of freedom). Therefore, any beam or column connected in the wall planewill have complete moment continuity, without any additional artificial elements such asrigid beams.

Connecting individual panels makes easy to model general three-dimensional wallconfigurations, such as C-shaped core elevator walls, curved shear walls, discontinuousshear walls and shear walls with arbitrarily located openings. Various elements can beused to model a planar or three-dimensional wall. These modeling options along with thepossibility to specify the structural system property allows an accurate modeling ofbuildings with shear walls, with the possibility of differentiating between structural walls

and nonbearing walls.

Walls are added and edited with the command Wallsis located in the Elements toolbar

and in theElements menu, . Shear walls are always added manually, preferably in aplan viewor in an elevation view, selecting two extreme nodes. The properties of eachpanel are: Structural system (Gravity, Lateral, Gravity & lateral), type of finite element(Shell, Membrane, Plate), name of material and element thickness. The wall lengthBandwall height H, are computed based on the coordinates of the nodes defining the element.


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Figure 4.6EngSolutions RCB model of a bearing wall system (Project El Faro Fajardo, StructuralEngineer A. Muns, Puerto Rico)

The finite element used to model shear walls is a quadrilateral hybrid element developedfor National Aeronautics and Space Administration, NASA (M. Aminpour, NASAContractor Report 4282, Direct Formulation of a 4-Node Hybrid Shell Element With

Rotational Degrees of Freedom, 1990).

(a) (b)

Figure 4.7(a) Wall Property Window (b) Table of materials


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Slabs

Floors are in general idealized as rigid horizontal diaphragms. However, to distributeautomatically floor loads to span loads on adjacent beams and walls, the engineer mayassign load propertiesto individual slab elements.

The default slab properties are selected by the engineer. When a new structural model is

created, the engineer selects the predominant floor system. The program considers thefollowing floor systems: one-way joist slabs, one-way slabs, two-way joist slabs, two-wayslabs and one-way deck on secondary beams. Next, the engineer enters the propertiesof the predominant floor system, including slab thickness, geometry and spacingbetween joists (for joist systems), reinforcement direction, unit weight, superimposeddead load (partitions, equipment, etc.) and live load per unit area. With this data theprogram creates slab type Slab1, which is assigned to all existing floor panels. Once themodel is created, the engineer may define other slab types and assign them to individualpanels. Slabs are edited with the command Slabslocated in the Elements Toolbarand in

the Element menu . This command is also used to edit the slab geometry defining slabregions and slab holes.

Support ConditionsNodal supports

The structure can be modeled as supported on theoretical nodal supports or on footings.Nodal supports can be rigid or deformable. Rigid supports include fixed supports, hinges,rollers, and special supports, for which the engineer specifies for each degree of freedomwhether it is free or fixed. Deformable supports consist of elastic springs. In this case,the engineer specifies the spring constant for each degree of freedom, which can insteadbe fixed or free (0: free, -1: fixed, >0: spring constant). Figure 4.8 shows Supportproperty windows for a rigid hinge support and for a deformable support.

Nodal supports are added and edited with the command Supports located in the

Elements toolbar and in the Elements menu . Selection options in the Activecommand windowinclude the option: All ground nodes, which allow defining in a singlestep all the supports at the base of the model.

(a) (b)

Figure 4.8 Nodal support properties: (a) rigid support (b) deformable support


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Footings

In the early stages of building design it is preferably to model the structure as supportedon theoretical nodal supports. Once the final section of elements have been defined, it ispossible to include the footings considering their actual size.

The program considers three types of footings. Spread footingsfor columns, continuousfootingsfor walls and matsfor combinations of columns and walls. Footings are idealizedas rigid elements that can be fixed, pinned, or supported on vertical springs distributed onthe area of the footing, representing the foundation soil. Footings are added and editedwith the command Footingsin the Element toolbarand the Elements menu .

A spread footing is created by selecting with the mouse the corresponding column. Theengineer must input the footing dimensions (B, L) and to indicate the relative position ofthe column within the footing. By default footings are concentric. At this stage of addingfootings, the program does not check if the dimensions are appropriate. A spread footingis associated to a single column. Even if the user inputs large footing dimensions suchthat the program graphically shows several columns within the footing, in themathematical model only the selected column is actually supported. The other columnswithin the footing are not supported. With the automatic resizing commands, which areavailable after analyzing the model, the program can compute the footing dimensions Band L so that the allowable soil pressure is not exceeded.

A continuous footing is created by selecting the corresponding wall. The user must inputthe footing width B. The program computes the length of the footing as equal to thelength of the wall. A continuous footing is associated to a single wall. The automaticresizing commands computes the required footing width such that he allowable soilpressure is not exceeded.

Figure 4.9(a) Properties of spread footings (b) Table of foundation soil properties

Combined footings and mat footings are created by drawing the footing contour. Allelements (columns and walls) within are supported on the footing. Automatic resizing ofmat footings shrinks or expands the footing geometry (keeping the original shape) suchthat the allowable soil pressure is not exceeded.

Foundation Soil Properties


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Foundation soil properties can be different for each footing. The properties the programrequires are the allowable pressure, Pa, the increase in allowable pressure forcombinations that include wind and earthquake, dPa(33% in most building codes) andthe modulus of subgrade reaction. The user may input two values of the modulus ofsubgrade reaction. A subgrade reaction modulus for gravity load analysis, Kg, and asubgrade reaction modulus for lateral load analysis, Ks.

For gravity load analysis, which is a permanent load condition, the subgrade reactionmodulus Kg, can be estimated as the ratio between the allowable pressure and theexpected long-term settlement under the footing. For earthquake and wind load analysis,which are rapid and transient loads under which the foundation soil has no time toconsolidate, the soil stiffness is greater and the modulus of subgrade reaction Ks, can beestimated as the ratio between the allowable pressure and the expected short-termsettlement.

For pile caps an equivalent admissible pressure can be input, computed as theadmissible load per pile divided by the square of the center-to-center spacing betweenpiles. Similarly, an equivalent modulus of subgrade reaction can be computed as the ratiobetween the equivalent allowable pressure and the settlement of the pile group.

Footing Support ConditionsFootings may be considered fixed or may be allowed to rotate and/or undergo a verticaldisplacement. If footings are modeled as fixed elements, the subgrade reaction modulusis not used in the analysis; hence any arbitrary values can be input. If verticaldisplacements (settlements) are permitted, the program computes a vertical springconstant based on the subgrade reaction modulus and the footing area. If rotations arepermitted, the program computes the rotational stiffness of the footing based on thesubgrade reaction modulus and the moments of inertia of the footing.

The analysis of building systems allowing rotation of footings is more realistic thananalysis based on the usual assumption of fixed supports, particularly in combinedframe-wall systems. In these systems, with the usual fixed support assumption, theanalysis results show that the walls resist most of the lateral forces. In reality, just a small

rotation at the wall footings is enough to produce a significant redistribution of lateralforces with columns resisting part of the loads initially resisted by walls. If these columnsare not designed for these larger lateral loads, these overstressed elements may be endup suffering significant damage under lateral loading.

The analysis of building systems allowing rotation of footings though more realistic hasthe disadvantage that produces larger computed story drifts and greater computed steelratios. Considering that most building codes allow to model the building as completelyfixed at its base and that the story drift limitations were established for that usual fixedbase assumption, it turns out disadvantageous to use a model permitting footingrotations, as it leads to a more costly structural solution. For this reason, the programallows to model footings (spread, continuous and mats) as fixed.

It should be kept in mind that if footings are modeled as fixed, it is not possible to modeleither tie beams or strap beams. If these elements are to be modeled as part of thestructure, to obtain their real design it is necessary to allow rotation of the connectedfootings. When designing, eccentric footings, with strap beams, it is necessary to allowrotation of at least the eccentric footings.

Foundation Beam Elements

The foundation beam element is an element that resists flexure and shear, and issupported continually and elastically on subjacent soil. The element is based on a


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Winkler model implemented as a displacement based finite element. The element can beused for analysis and design of cellular and two-way slab-and-beam mat foundations,analysis and design of combined footings, and for static and dynamic soil-structureinteraction studies.

Foundation beams are added and edited with the command F-Beams located in the

Elements Toolbar and the Elements menu. In addition to the structural properties ofconventional beam elements (including section and material), the foundation beamelement has to additional properties. Soil type and tributary width B. Each soil type has inturn various properties buit from those only the subgrade reaction modulus is used in theanalysis of foundation beams. The product of subgrade reaction modulus and tributarywidth represents the stiffness of the foundation soil, as a continuous spring uniformlydistributed under the foundation beam element. Consistent with the Winkler model, thesoil reaction at any point is equal to the product of such stiffness and the transversaldisplacement (settlement) of the element. The inertia of the structural element is definedby the section properties and is independent of the tributary width.

Figure 4.10Models of beam on elastic foundation. (a) Using multiple beam elements (30

elements) and springs in auxiliary nodes (b) using 3 foundation beam elements.

The program allows considering two different values of the modulus of subgradereaction. A value Kg, which represents the long-term soil stiffness or stiffness underpermanent loading, and a value Ks, which represents the short-term soil stiffness orstiffness for transitory loads. The Kgvalue is used in the gravity load analysis and the Ksvalue is used in the lateral load analysis.

The soils engineer based on his evaluation of settlements can estimate values of thesugrade reaction moduli Kg and Ks. The Kg value represents the ratio between thecontact pressure of a continuous footing of width B, and its long-term settlement. The Ksvalue represents the ratio between the contact pressure of a continuous footing of width

B, and its immediate settlement. The Ks value can also be estimated from K1 valuescorresponding a a rapid plate load test (B= 1ft) either measured or estimated frompublished typical values for different foundation soils, corrected to the actual footing widthB.

Although it is possible to model foundation beams using conventional beam elements,segmenting them by introducing numerous auxiliary nodes, and adding elastic springs atthose nodes, as shown in Figure 4.10 (a), applying this procedure to complete models ofmat foundations, or in interaction-studies to models that include the superstructure,would result in unnecessarily complex models. The main advantage of using the


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foundation beam element is that it is not necessary to introduce auxiliary nodes to modelthe soil reaction. The element formulation considers the presence of a continuous elasticsupport under the element.

Figure 4.11Model to study soil-structure interaction using foundation beams.

The foundation beam element may be used in models of individual beams or in completemodels of one-way or two-way cellular mats foundations. Cellular mats are those inwhich the stiffer elements are beams or joists and the slab is made up of a grillage ofthese elements in contact with foundation soil, working under flexure and shear, having athin slab at the plane in contact with the subsoil.

The element can also be used in soil-structure interaction studies in which both thesuperstructure and the complete slab are modeled. Alternatively a simpler idealized slabmay be modeled in this kind of studies, assigning to each beam element equivalenttributary widths and equivalent sections.

Loads

Loads in EngSolutions RCBare grouped into load cases. Load cases are independentloadings for which the structure is analyzed internally, such as dead load (DL), live load(LL), snow load (SL), wind load (WL), earthquake load (EQ), etc. There can be up to 12independent load cases. Load cases should not be confused with load combinations,which are defined later.


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Loads for any load case can be applied manually to the nodes, members and walls,through graphical mouse interaction. Nodal loads are composed of concentrated forcesand moments. Member loads include concentrated loads and moments, and trapezoidaldistributed loads. Wall loads include concentrated and distributed loads at the top andsides of the wall. Loads and moments can be applied at any location along the memberor wall, and can be referred either to the local axes of the element (1,2,3), or to the global

coordinate system of the structure (x,y,z).

Figure 4.11Property window with member load data.

The commands to apply loads manually are located in the Load menu. When any ofthose commands is activated, the program presents a property window where the

engineer enters the load data. The load assignment is carried out by selecting with themouse the elements to be loaded. Figure 4.11 shows an example of member load data.

Figure 4.12Command for automatic generation of loads.

EngSolutions RCBcan also generate automatically the loads of complete load cases,representing significant savings in tedious manual calculations. Figure 4.5 shows the


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automatic loading submenu. The load cases that can be generated automatically are: selfweight (D0), vertical floor loads (DL, LL1, LL2), wind loads (WLx, WLy), and earthquakeloads (EQx, EQy), which can be static equivalent, spectral, o may correspond to a timehistory analysis.

Self weight

The self-weight of elements can be generated automatically with the command SelfWeight. The program uses the cross sectional area of each element defined in theSections tableand the unit weight defined in the Materials table. Weight of beams andbraces is applied as a uniformly distributed load along the length of the member. Theweight of columns is applied as a concentrated load in the upper node of the element.The weight of walls is represented as a uniformly distributed load at the top of theelement. Self-weight loads are grouped in a load case named Self Weight, D0.

Vertical Floor Loads

Vertical floor panel loads can be automatically converted to span loads on adjoiningbeams and walls using the properties assigned to slabs: Thickness, reinforcement

direction, superimposed dead load and live load.

Figure 4.13. Distribution of floor loads to beams and walls (Sky Loft Tower, StructuralEngineer J. Robert & Associates, Puerto Rico)

The program reports the total floor dead load (self weight of the slab plus superimposeddead load) (DL) and live load (LL ) for each floor and the total for the whole building, anddisplays for each beam and wall the corresponding tributary slab load, as shown in


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Figure 4.13. This way, the engineer can visualize how the floor loads are beingdistributed in her model.

Wind Forces

Wind forces can be generated according to various building codes, including American

codes: ASCE 7-95, ASCE 7-88, UBC-94; Mexican codes: RCDF-87, CFE-93 andDominican code: DNRS/SEOPC. EngSolutions RCB load generator guides the userthroughout the generation process. First, the program asks for wind load parameterssuch as basic wind speed, importance factor, exposure category, topographic factor andwall pressure coefficients. Then the program classifies the structure, according to itsresponse to wind loading, as either rigid or flexible, and computes the gust effects factor,using the rational analysis of the selected code. The velocity pressure at each floor levelis reported. The program automatically identifies exterior nodes, determines nodaltributary areas, and computes wind forces on the roof and windward, leeward, and sidewalls. Load cases for two orthogonal directions (x & y) are generated in a single step.

The program reports total wind forces at each floor level as well as all the values neededfor the overturning and sliding check. (i.e. total base wind shear, overturning momentsdue to lateral forces and to roof uplift forces, total building weight and stabilizing gravitymoment). The program generates two wind load cases: WXand WY

Equivalent Static Earthquake Loads

Static equivalent earthquake loads can be generated automatically according tonumerous international building codes, including, American codes: IBC-2003, UBC-97,

ASCE 7-05, ASCE 7-95; Mexican codes: RCDF-04, RCDF-93, CFE-93, GUAD-97;Colombian codes: NSR-98 (includding seismic microzoning of Bogota, Armenia andMedellin) and CCCSR-84; Venezuela COVENIN-82, Peru E030 2003, Ecuador CEC-01,Chile NCh433-93, Panama REP-2004 and REP-94, Costa Rica CSCR-86 andDominican Republic DNRS/SEOPC-80. New building codes are continually added toEngSolutions RCB.

The load generation process is guided by the program. The engineer selects a buildingcode from a list of available codes, enters the number of basements, and then inputsseismic parameters. Seismic parameters include parameters such as effective peakacceleration (or seismic zone factor, or spectral response accelerations), importancefactor, site profile coefficient, response modification factor (ductility factor). Theappropriate parameters with the proper terminology for the selected building code arerequested by the program. Figure 4.14 shows this stage of the generation for IBC-2003.

Next, the program computes and reports the seismic base shear. The engineer maychange the value of the computed base shear. The engineer may also specify anaccidental eccentricity and a definition of the design eccentricity, in terms of both theactual static (inherent) eccentricity (es, distance from center of mass to center of rigidity),and the accidental eccentricity (). The program proposes the definition, appropriate for

the selected code, however, the user makes the final selection. In most building codesthe design eccentricity is simply: = es.

Next, the program reports for each story the center of mass, center of rigidity, static(inherent) eccentricity, accidental eccentricity, and design eccentricity. Then the programcomputes inertial forces shifting the center of mass according to the accidentaleccentricities. Then, the program reports seismic forces for each story for two orthogonaldirections (x & y). Then, the program produces a report with the results of the seismicforces.


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Figure 4.14Seismic parameters for generating seismic forces according to IBC-2003

Next, the program reports for each story the center of mass, center of rigidity, static

(inherent) eccentricity, accidental eccentricity, and design eccentricity. Then the programcomputes inertial forces shifting the center of mass according to the accidentaleccentricities. Then, the program reports seismic forces for each story for two orthogonaldirections (x & y). Then, the program produces a report with the results of the seismicforces.

It is noticed that the nodal forces applied by the program are simply inertial forcesproportional to nodal masses and do not represent the seismic response of the structure.These forces are not proportional to the stiffness of elements and do not show thedistribution of shear forces in the structure, The way these seismic inertial forces are


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resisted by the different structural elements is determined in the analysis, based on thestiffness characteristics of the different elements conforming the lateral load resistingsystem and their connection with the floor diaphragms.

Figure 4.15Report with summary of seismic forces

Accidental TorsionNota:

Starting with version 6.1, in the automatic generation of seismic forces only twoload cases are generated: EQUAKE X (EQX) and EQUAKE Y (EQY). In previousversions, two load cases were generated for each direction according to the twopossible signs of accidental torsion, for a total of 4 load cases: (EQX1, EQX2 yEQY1, EQY2.)

Starting with version 6.1, each one of the load cases generated represents anenvelope for the two definitions of accidental torsion. For each load case (forinstance EQX) the program generates a set of seismic forces without accidentaltorsion and computes two sets of accidental torsion. During the analysis, thestructure is subjected first to the set of seismic forces with no accidental torsion.In this analysis, the program computes nodal displacements, story drifts alongeach column and wall boundary, and internal forces in all structural elements(moments, shears, axial loads, wall stresses, etc.). Next, the program applies thefirst set of accidental torsion. In those locations (or elements) where the result of


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displacement, drift or internal force increase, such result is updated. On thecontrary, on those locations where the displacement, drift or internal forcedecreases, the result is not modified. Then, the program applies the second setof accidental torsion and updates the results according to the same criterion, toobtain this way an envelope of seismic results.

Response Spectra

EngSolutions RCB can also perform response spectra analysis according to variousinternational building codes. Figure 4.16 shows the seismic building codes implementedin the program. The analysis can be performed in a single step for two orthogonaldirections or for a specified attack angle. Before doing the seismic analysis however, theengineer must perform a dynamic analysis, using the EngSolutions RCB analysiscommands that will be discussed in a later section, to compute the tridimensional modesof vibration, natural frequencies, modal participation factors, and percentages ofparticipating mass.

The load generation process is guided by the program. The engineer selects a buildingcode and enters the number of basements. In computing the approximate empiricalperiod of vibration Ta, based on the building height, the program considers only thosestories above ground. That is, the program assumes that during earthquake loading,buried stories move along with the surrounding soil. Next, the program asks the engineerto input the seismic parameters corresponding to the selected building code. Theprogram computes the spectral acceleration for each mode, according to the selectedcode. The engineer can edit the values of spectral acceleration, which allows consideringany other design response spectra, such as that corresponding to a specific earthquakerecord.

Various methods of modal combination are available in EngSolutions RCB, includingsummation of absolute values (SAV), square roof of summation of squares (SRSS),complete quadratic combination (CQC), and a combination of the first two:(SAV+SRSS) and 0.25(SAV)+0.75(SRSS).

Next, The program computes the base shear for each mode and the combined baseshear. The program also evaluates the equivalent static base shear, that the selectedcodes requires as a minimum design base shear. This minimum static shear is usuallycomputed based on an empirical fundamental period defined by the code. The programsuggests a design base shear, based on the combined value and the minimum staticshear. The engineer may change the proposed value. If the design base shear isdifferent from the combined base shear, the program automatically scales the combinedshears for all story levels.

A set of inertial forces is obtained by combining the modal nodal forces, scaling them toobtain the appropriate floor shear. The treatment of accidental torsion is the same as thatin the equivalent static analysis, specifying a design eccentricity and shifting the center of

mass, a set of static forces is computed which is later combined with the spectralanalysis results to obtain an envelope of analysis results.

Once again is noticed that the set of combined nodal forces that the program presentsare just inertial forces rather than the seismic response, which is later determined duringthe analysis stage.


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Figure 4.16Building codes for seismic spectral and time history analyses.

Dynamic Time-History Analysis

The dynamic time history analysis is guided by the program and consists of varioussteps. First, the engineer selects the building code that will gobern the analysis, form thelist shown in Figure 4.16. Next she enters the damping ratio (defaultis 5% for all modes)and enters the corresponding seismic parameters. The program computes the spectralaccelerations according to the code, and determines the static base shear.

Next the engineer selects the earthquake records to be applied to the model. Theprogram includes an extensive database of earthquake records. In a later section it isshwon how to add new accelergrams to this database.

Figure 4.16 shows the window in which earthquake records are selected and scaled. Foreach record, the engineer must input first the acceleration scaling factor, then, add it tothe list of selected records by clicking theAdd button. The engineer can add up to 5different records. By default, only the horizontal component with maximum peakacceleration is considered. However, the engineer can include the two horizontalcomponents and the vertical component, marking the corresponding checkmark in thiswindow. When the vertical component is included, it is necessary to include computationof vertical mode shapes during the modes-frequency analysis. By default the verticalmodes are inhibited in the modes-frequency analysis.


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After selecting the earthquake records, the program presents a table comparing theresponse spectra of the selected records and the code-specified design responsespectrum, and applies the scaling required by the selected code. Next, the programreports the dynamic base shears for the scaled selected records and the static baseshear, and performs again any scaling required by the selected code.

The procedure to comply with accidental torsion requirements is the same used in theequivalent static force and spectral procedures. Accidental torsion is applied staticallyshifting the center of mass.

Figure 4.17Selection and scaling of earthquake records

In this stage of seismic force generation all the information required to perform theanalysis is assembled. However, the actual dynamic analysis is conducted when theengineer activates the Run analysiscommand in theAnalysismenu. At this later stage,the program applies, at the base of the structure, each one of the selected earthquakerecords along each direction (X y Y), obtaining the response of the structure at every timeinstant and saving the maximum values of drifts, displacements and internal forces ineach one of the resisting elements.


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Load Combinations

Load combinations are the loading conditions for which the building is designed. Loadcombinations are assembled as combinations of the load cases. An example of a loadcombination is: 1.4DL + 1.7LL, where DL is the dead load and LL is the live load. InEngSolutions RCBthere can be up to 150 load combinations.

To generate load combinations the engineer selects in the menu shown in Figure 4.18,the building code according to which the load combinations are to be generated. Theprogram generates all the combinations considering all sign combinations (sense) forseismic and wind forces.

Figure 4.18Command for automatic generation of load combinations

The engineer may specify to consider bidirectional effects in earthquake loading (e.g.100% of earthquake in one direction acting simultaneously with 30% in the otherdirection), to generate the load combinations accordingly. Depending on the buildingcode used to generate seismic forces the program determines whether seismic forcesare strength level or service level loads, to select the appropriate seismic loadcoefficients. The engineer may alter this determination.

When seismic forces have been design according to ASCE 7-05, IBC-2003, or UBC-97,the program includes in the load combinations the redundancy factors, which aredetermined during the analysis. For these codes, the program also considers through

load combinations the effects of the vertical component of the ground motion, creatingadditional combinations increasing and decreasing factors for gravity loads.

The generated load combinations are displayed in a table, as shown in Figure 4.19. Inthis table the engineer may edit load coefficients for any combination, add manually newcombinations by entering individual load case coefficients, and may remove anycombination specified by the selected code.

Load combinations can only be generated after load cases have been created.


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Figure 4.19Table of load combinations

Analysis

EngSolutions RCBperforms two types of analysis. Modes/frequency analysis in whichthe program determines the free vibration characteristics of the structure, and loadanalysis in which the program determines the response of the structure, in terms ofdisplacements and internal forces, to each one of the load cases.

The engineer may base both types of analyses on cracked sections by specifying inertiamodification factors, torsion-constant modification factors, and area modification factorsfor beams, columns and braces. For walls, the user may specify independentmodification factors for in-planeand out-of-planeflexural and shear stiffness.

Modes/Frequency Analysis

EngSolutions RCBprovides the solution for the free vibration response of the building interms of its three-dimensional mode shapes and natural frequencies. Mode shapes,frequencies and modal participation factors are obtained using the Lanczos method withselective orthogonalization described by Golub et al, 1985, which is an improved versionof the subspace iteration method used in most commercial software. For large buildings,the program improves computational speed using the iterative procedure for largesparced matrices described by Underwood, 1975.


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The implementation of the Lanczos procedure is general allowing analyses of complexbuildings. The building may be unsymmetrical and arbitrarily irregular in plan. Torsionalbehavior of the floors and interstory compatibility of the floors are properly modeled.Instead of the usual 3 degree-of-freedom-per-floor-level simplified analysis,EngSolutions RCBconsiders the full stiffness matrix of the structure, allowing modelingpartial diaphragms, such as mezzanines and openings, as well as cases with multiple

independent diaphragms at each level, allowing to analyze buildings consisting of severaltowers, rising from a common base structure at the lower levels.

The mass matrix is created automatically, based on the gravity loads acting on thestructure. The program asks for the coefficients of each load case to be used in theevaluation of the lumped mass matrix. The load combination for the mass matrix couldbe for instance: M = (1.0 DL + 0.25 LL)/g.

The program asks the engineer for the number of modes to be computed and performsthe analysis. Obviously, the modes/frequency analysis can only be conducted aftergravity loads have been created.

The dynamic analysis can be linear (first order) or P-Delta (second order) allowing toconsider the effects of initial stresses on the natural frequencies and modes of vibrationof the structural model.

It is pointed out that approximated methods for computing periods, such as the Rayleight-Ritz procedure, presented in most building codes (T = 2 ((wi i) / (g fi i))

1/2), would

produce accurate results only in the case of regular buildings of simple geometryconsisting of a single diaphragm per floor level.

On the other hand, approximated fundamental periods evaluated with empiricalequations such as Ta = 0.1Nand Ta = Ct(hn)

3/4, which are based on field measurementson real buildings (mostly during the San Fernando Earthquake), will typically predictshorter periods as these real buildings, with their partitions, stairs, facades, and othernon-structural elements, are stiffer than the naked structural model analyzed.

It is a good practice (not a requirement) to do the modes/frequency analysis before thegeneration of wind loads. The natural frequency is needed to classify the main wind forceresisting system, in terms of its response to wind loading, and to evaluate the gust effectsfactor of flexible buildings. If it is not available, it is estimated based on the overallfeatures of the building, using the approximated equations of the selected code.

It is also advisable (not a requirement) to do the modes/frequency analysis before thegeneration of seismic loads, even if the design is based on static equivalent seismicloads. The fundamental period of the structure is needed to compute the base shearforce. Furthermore, the fundamental mode shapes in each direction, which contain all theinformation of stiffness and mass distribution in the building, allow an accurate evaluationof the center of rigidity of the structure.

Gravity and Lateral Load Analysis

EngSolutions RCBperforms a tridimensional finite element analysis to determine nodaldisplacements, story drifts, internal forces and moments on members, and internalstresses on walls, for each load case that has been defined. Prior to the actual analysis,the program determines the rigid length at the end of each member, based on theelement sections and a specified rigid zone factor, to consider the finite dimensions ofelements. Next, the program computes buckling loads for columns. Then, the programinitiates the actual solution procedure. Figure 4.20 shows the different analysis options.


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Linear Analysis

The linear analysis is a first order elastic analysis in which the equilibrium equations areformulated in the original undeformed configuration. The program assembles thestiffness matrix of the whole structure adding the contribution of individual elements.Then the program triangularizes the stiffness matriz using the Gauss eliminationprocedure. Then, the program computes by backsubstitution nodal displacements and

determines internal forces and stresses on the elements.

Figure 4.20Analysis Options

P-Delta Analysis

The P-Delta analysis is a second order elastic analysis in which the equilibrium equationsare formulated in the deformed configuration. It is considered that as the structureundergoes deformation, it carries the applied loads with it. The changes in position ofapplied forces are cumulative in nature and cause additional second-order forces,moments and displacements, which are not included in the first-order analysis. Theanalysis is carried out in exact form, incorporating directly in the stiffness matrix of eachelement a geometric component. This way, secondary effects are represented exactly inall aspects of the structural analysis without any additional computational effort oriterative approximations, such as those required in the Direct Method used in somecommercial programs.

When the P-Delta analysis option is selected, the program requests the engineer to inputthe gravity load combination to perform the P-Delta analysis. This combination

represents the permanent gravity load, or better yet, the gravity load acting when theearthquake loading occurs. The default gravity load combination is: 1.0DL+ 0.25 LL. Thisis the vertical load that is going to be carried by the structure laterally when it deformsunder lateral loading. The change in position of this gravity load is what will cause theadditional second-order forces, moments and displacements.

The P-Delta analysis involves two analyses. First, the program performs a preliminarylinear elastic analysis and determines the solution (displacements and internal forces forall elements). From this preliminary analysis the program determines the internal


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forces/stresses in each element, corresponding to the above gravity load combination.Next, the program performs the actual P-Delta analysis. In this stage, when assemblingthe stiffness matrix for each element, instead of using the conventional stiffness matrixfor stress-free elements, the program assembles the nonlinear stiffness matrix forelements carrying the stresses corresponding to the gravity load combination. Theadditional terms in this stiffness matrix resulting from the existing stresses correspond to

the so-called geometric matrix. Triangularizing the assembled stiffness matrix, usingGauss elimination, and backsubstituting the load vectors for each case, the programcomputes nodal displacements, and determines internal forces and stresses on theelements.

Gravity Load Analysis

The program performs the gravity load analysis and the lateral load analysis separately.In the gravity load analysis only those elements that are part of the gravity load resistingsystem are considered to contribute stiffness, and the program solves for vertical loadcases including self weight of elements (D0), floor dead loads (DL), live loads (LL), andsnow loads (SL).

Incremental Analysis

Building design is usually based on the analysis of an idealized structure, whosegeometry corresponds to the final configuration of the building. Dead loads are applied tothis idealized structure in a single step. In the real structure, on the other hand, thegeometry changes continually during construction, and loading is incremental as newfloors are added. In cases of tall buildings (more than 15 stories), this basic differencebetween the real structure and the system analyzed can result in important errors due tothe fact that the final state of stresses and deformations depends on the construction andload history, even if the material behaves elastically.

The application of vertical loads to the whole structure in a single step may result inunrealistic moment diagrams on the upper beams and columns, due to excessive axialdeformations of the interior columns. The difference between the axial deformation of

interior and exterior columns, which in the analysis accumulates from one floor to thenext, is not real. Each floor is built as a horizontal surface. Any difference in axialdeformation that may exist between the columns directly under a particular floor isdeleted when the concrete of that floor is placed.

Not only the displacement pattern in a given level, obtained from a conventional analysis,is wrong, but also, for any particular column, the variation of vertical displacementsthroughout the height of the building is completely different from the real one. In theconventional analysis the vertical deformation increases with the height, reaching amaximum at the top roof. In reality, floors are built at project elevations and thedisplacements at the roof are minimal. The column displacement at the top level isproduced only the weight of the floor slab, rather than the accumulated from lower floors.

The errors in displacements that occur in conventional analyses have naturally an effecton the internal forces and moments, calculated from those deflections. Figure 6.10shows the moment diagrams and the variation with height of the negative moments in thefloor beams, from (a) a conventional analysis and (b) an incremental analysis. While inthe incremental analysis the negative moments in the floor beams tend to be constantwith height, in the conventional analysis, the negative moments at the central column-support decrease with height, due to excessive axial deformations of the central column,while at the end supports the negative moment increase.


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Figure 4.21 Displacements, (a) conventional analysis, applying dead load in a single

step, (b) incremental analysis, modeling the construction process

The differences in the distribution of internal forces and moments that exist between thestructure loaded in a single step and that build incrementally, are clearly reflected in thedesign of elements, specially in that of beams and columns of the upper levels. Theconventional analysis, underestimates the negative reinforcement of beams at the interiorsupports and overestimates it at the ends. With regard to the exterior columns of theupper levels, the conventional analysis leads to steel ratios greater than actuallyrequired, due to the excessive moments that are obtained for these low-axial-loadelements.

Figure 4.22Moment diagrams (a) conventional analysis (b) incremental analysisThe incremental analysis method implemented in EngSolutions RCB, takes into accountthe story-by-story construction process, eliminating the limitations present in theconventional linear analysis, used in most structural analysis programs. The method isdescribed in detail in Barbosa (1994).


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The incremental construction analysis, implemented in EngSolutions RCB, consistssubstantially of a series of stages, each one corresponding to the addition of a new floor(or some new floors). In each stage, columns, girders and walls of new floors are addedto the structure (i.e. to the finite element mesh representing the structure). The updatedstructure is subjected only to the dead load associated to the new elements. Thedisplacements and internal forces and moments, obtained in each stage, are added to

the previous values. The process is automated to perform all the incremental analysis ina single run. Obviously, the live load and lateral load analyses are performed on the finalconfiguration, in single step.

In the automated incremental analysis, the engineer specifies how many floors are to beadded in each stage of the analysis. The user controlled incremental analysis is moregeneral as it can consider any arbitrary construction sequence. The engineer assigns toeach element in the model (beams, columns, braces, walls, slabs, supports, footing

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