concrete design using prokon

Concrete Design 6-1

Chapter

6Concrete Design

The concrete design modules can be used for the design of reinforced and prestressed concretebeams and slabs, columns, column bases and retaining walls.

Concrete Design6-2

Quick Reference

Concrete Design using PROKON 6-3

Continuous Beam and Slab Design 6-5

Prestressed Beam and Slab Design 6-7

Finite Element Slab Analysis 6-9

Rectangular Slab Panel Design 6-35

Column Design 6-45

Retaining Wall Design 6-63

Column Base Design 6-77

Section Design for Crackwidth 6-91

Concrete Section Design 6-99

Punching Shear Design 6-107

Concrete Design using PROKON 6-3

Concrete Design usingPROKON

A variety of concrete design modules are included in the PROKON suite. These are usefultools for the design and detailing typical reinforced and prestressed concrete members.

Beam and slab design

The Continuous Beam and Slab Design and Prestressed Beam and Slab Design modulesare used to design and detail reinforced and prestressed beams and slabs. Simplified design offlat 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 morecomplicated geometries. Punching shear in flat reinforced concrete slabs can be checked withthe Punching Shear Design module.

Column design

Rectangular Column Design and Circular Column Design offer rapid design and detailingof simple short and slender columns. Columns with complicated shapes can be designed usingthe General Column Design module.

Substructure design

Use the Column Base Design and Retaining Wall design to design and detail typical basesand soil retaining walls.

Section design

Two modules, Concrete Section Design and Section Design for Crackwidth, are availablefor the quick design of sections for strength and crackwidth requirements.

Concrete Design using PROKON6-4

Continuous Beam and Slab Design 6-5

Continuous Beam andSlab Design

The Continuous Beam and Slab Design program is a powerful, yet easy-to-use, tool in thehands of the designer and detailer of reinforced concrete beams and slabs. The program can beused to design and detail most types of continuous beam and slab systems encountered intypical building projects. The analysis includes automated pattern loading and momentredistribution. Complete bending schedules can be generated for editing and printingusing Padds.

For more information on using this module, consult the Dos Version User's Guide.

Continuous Beam and Slab Design6-6

Prestressed Beam and Slab Design 6-7

Prestressed Beam and SlabDesign

Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design anddetail most types of continuous prestressed beam and slab systems encountered in typicalbuilding projects. Complicated cross sections are supported through an interface with thesection properties calculation module, Prosec. This, together with the facility of defining loadcases and combinations, makes the program suitable for bridge deck design as well.

Both unbonded systems, e.g. flat slabs, and bonded systems, e.g. bridge decks, can bedesigned. Estimates for quantities are calculated and tendon profile schedules can be generatedfor use with Padds.

For more information on using this module, consult the Dos Version User's Guide.

Prestressed Beam and Slab Design6-8


Finite Element Slab Analysis

Fesd (Finite Element Slab Design) can perform linear elastic plate bending analyses oftwo-dimensional concrete slab structures. Reinforcement can be calculated from momentstransformed using the Wood and Armer equations.

To design concrete membranes, use the Space Frame Analysis module instead.

Finite Element Slab Analysis6-10

Theory and application

The following text explains the sign conventions used and gives a brief background of theanalysis techniques.

Sign conventions

Slab input is done using the global axes. The analysis output is given in a mixture of globalaxis 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.

The global axes are defined as follows:

• The X-axis is chosen to the right.

• The Y-axis points vertically upward. A positive vertical load thus works up and a negativeload down.

• 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, PROKON takes theY-axis vertical.

Local axes

Local axes are used in the output for bendingstresses:

• The local x is chosen parallel to the globalX-axis.

• The y-axis is taken parallel to the negativeZ-axis.

• The z-axis is then taken vertical parallel tothe 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 andy-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 showorientation lines at the centre of each shell element. An orientation line indicates thedirection the direction (not axis) of bending or plane stress. In a concrete shell, theorientation 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 z'-directions. Unlike the shell bendingstresses that are taken about the x and y-axes, the Wood and Armer moments are given in the x'and z'-directions. Refer to page 6-29 for detail.

Units of measurement

The following units of measurement are supported:

Units Metric Imperial

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 withplate bending behaviour. The bending formulation of the quadrilateral shell element wasderived 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 as accurate as is the case for quadrilateralelements. This means that deflections calculated using triangular elements are generally quiteaccurate, but moments may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stressesare calculated at the Gaussian integration points and subsequently extrapolated bi-linearly tothe corner point and centre point of each element. Stresses at common nodes are smoothed bytaking the average of all contributing stress components.

Element layout


Consider a typical continuous flat concrete slab supported on columns or walls. To ensureaccurate modelling of curvature, a minimum of about four elements should be used betweenbending moment inflection points. This translates to a minimum of about eight elements perspan in both directions.

Using more elements per span often does not yield a significant improvement in analysisaccuracy. Also, the particular finite element formulation yields its most accurate results whenthe 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 spanlength, a reasonable rule of thumb is to make the plan dimensions of the shell elements nosmaller than the thickness of the slab. In other words, use a maximum of about ten to fifteenelements per span.

Concrete design

Fesd can perform reinforced concrete design for shell elements. The Wood and Armerequations are used to transform the bending and torsional stresses to effective bendingmoments in the user-defined x' and z'-directions. To allow for the design of membranes, theequations have been suitably adjusted to incorporate axial stresses.

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.


Input

Work through the relevant Input pages to enter the slab geometry and loading:

• Nodes input: Slab coordinates.

• Shell elements input: Define shell elements.

• Supports input: External supports.

• 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 6-27.

Viewing the structure during input

You may want to enlarge portions of the picture of the structure or rotate it on the screen.Several functions, all of which are described in detail in Chapter 2, are available to help youusing 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 view point 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 itemslike node numbers and supports tobe displayed.

• Display the structure with full 3Drendering, e.g. to verify thethickness of slab sections.

• Choose quick or detailedrendering. Quick rendering isfaster than the detailed method,but you may find that somesurfaces are drawn incorrectly.

• All surfaces are drawn as polygons. You can choose to make the surfaces transparentor have them filled and outlined.


Tip: The Graphics options and 3D rendering function can also be accessed using the buttonsnext to the displayed picture.

• Views: You can save the current view point and view plane. The current view's name isdisplayed on the picture. To re-use a saved view, click the view name on the picture todrop down a list of saved views.

The functions described above can also be used when viewing output. Contour diagrams, forexample, are drawn as polygons. You can therefore use the Graphics options setting forpolygons to change their appearance. Views defined during input are also available whenviewing output and vice versa.

Nodes input

Use as many lines as necessary to enter the nodes defining the slab. A unique number must beassigned to each node. The node number is entered in the No column, followed by the X andZ-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 alsoleave blank lines in the input to improve readability. If a node number is defined more thanonce, the last definition will be used.


Error checking

The program checks for nodes lying at the same coordinate. If a potential error is detected, anError list button will appear.

Generating additional nodes

When defining a node, you can have additional nodes generated at regular intervals. Example:

• 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.

• 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 and Z-inc columns set the distance between copied nodes. Thecoordinates 4 to 18 are spaced at 1.140 m and 0.472 m along the X and negative Z-axisrespectively. The coordinates of the additional nodes are thus (1.140,14.142) and(2.280,13.670).

An alternative method to generate equally spaced nodes is to use the Inc to End option. Thismethod 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 and Z-inc to the total coordinate difference to the last node andenable the Inc to End option. The last node's coordinates are then first calculated and thespecified 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 row’s nodesby entering a '–' character in the No column of the next row. Then enter the number ofadditional sets of nodes to be generated in the No of column and the coordinate increments inthe X-inc and Z-inc columns.


Second order generation example:

The following nodes are generated:

No X Z15 0.00 5.1216 2.00 5.2217 4.00 5.3218 0.50 6.1219 2.50 6.2220 4.50 6.32

Block generation

A group of nodes can be repeated by entering a 'B' in the No column followed by the first andlast table row numbers in which the nodes were defined. Separate the row numbers with a '–'.

Block generation example:

The nodes defined in rows 11 to 26 are copied twice. Node numbers are incremented by thirty foreach 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 specifiedmay themselves contain further block generation statements.

Tip: To move a group of nodes to a new location without generating any new nodes, set theNo-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 bythe start and end row numbers. Enter the centre of the arc in the X and Z columns and use theX-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 imaginaryhorizontal arc. The centre point of the arc is located at the coordinate (10,1.5). The nodenumber increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation anglebetween the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise usinga right-hand rule.

To copy one row only, simply omit the end row numbers, e.g. 'A5' to copy row 5 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 generationfunction and set the No-of to '1' and Increment to '0'.

Deleting nodes

Nodes can be deleted by entering a special X-coordinate of '1E-9' or by entering 'Delete' in theInc to end column. This can be especially handy if you have generated a large group of nodesand then need to remove some of them again.

Example:

Nodes 15 and the additional nodes 18 and 21 are deleted.

Rigid links input

Point loads and supports invariably result in stress concentrations. In the case of slabssupported on columns, it may be reasonable to ignore stress concentrations within the columnareas and rather work with the stress values at the column faces. An alternative approach couldbe 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 rigidlinks. This approach entails stopping shell elements at the column face and then linking theperimeter with the supported node at the position of the column centre. The high bendingstiffness of the rigid links gives a reasonable approximation of the increased stiffness of theslab inside the perimeter of the column. The approach has the advantage of ridding the analysisof 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 threefor triangles. You should enter the node numbers in sequence around the perimeter, eitherclockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define atriangular element.

Note: Quadrilateral elements generally yield more accurate analysis results than triangularelements. Refer to page 6-11 for more detail.


Selecting materials

Each slab element shouldhave an associatedmaterial.

To add one or morematerials to a slab analysisdata file, click Materials.Open the relevant materialtype screen and select thematerials that are requiredfor the current slab input.

After adding the selectedmaterials to the input, youcan select them by clickingthe Material column todrop down a list.


Adding materials to the global database

If you want to use a material that is not yet included in the database, you should first add it tothe database:

1. Use Alt-Tab to swap to Calcpad or select it from the Windows Task Bar.

2. Select the Materials Database command on the Tools menu.

3. Open the appropriate materials type page and enter the properties for the new material:

• Material: A descriptivename for the new material.

• E: Young's modulus.

• Poisson's ration, ν.

• Density: This value isoptional. If defined, the ownweight of the material canbe calculated.

• Thermal expansion coeffi-cient, α (not used by Fesd).

4. To permanently add the new material to the database, open the File menu, choose Saveand Exit.

The use of the Materials database module is described in more detail Chapter 7.

Own weight

If a material's definition includes a density value, the own weight of a member is calculatedautomatically and added to the load case specified on the General input page.

Tip: When entering a complicated slab, it may help to leave a few blank lines betweengroups of elements. Not only will it improve readability, but it will also allow you to insertadditional 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 checksthat a group number is assigned to each element. If an error is detected, an Error list buttonwill be displayed.

Generating additional elements

You can generate additional elements with the same section and fixety code values using theNo 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 numberincrement of three, i.e elements (18,19,29,28), (21,22,32,310 etc.

Block generation

A group of elements can be repeated by entering a 'B' in the No column. Then enter the firstand last table row numbers in which the elements were defined, separated with a '–'.

Block generation example:

All elements defined in rows 5 to 7 will be copied ten times with a node number increment oftwelve. The copied elements will use the same thickness and material properties as the originalelements.

To copy one row only, simply omit the end row number, e.g. 'B5' to copy row 5 only.

The block generation function may be used recursively. The group of lines referenced may thuscontain block generation statements.

Tip: When entering a complicated slab it may help to leave a few blank lines betweengroups of elements. Not only will it improve readability, but it will also allow you to insertadditional elements at a later stage without upsetting block and arc generations.

Deleting elements

Shell elements can be deleted by entering 'Delete' in the Material column. This can be useful ifyou have generated a large group of elements and need to remove some of them again.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 toprevent any of the three degrees of freedom associated with plate bending, i.e. translation in theY-direction and rotation about the X and Z-axes. You can also define elastic supports andprescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column acombination of the letters 'Y', 'x' and 'z' can be entered to indicate the direction of fixety. Usecapitals 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.

Note: The use of lowercase for rotational restraints should not be confused with theconvention of using lowercase for local element 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 enterthe node number, i.e. you may leave the Fixety 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 skewedges.

Prescribed displacements

Use the X, x, and z columns to enter prescribed displacements and rotations. Being a globalsupport condition, the effect of the prescribed displacement is added once only to the analysisresults of each load case and load combination. Optionally enter a 'P' in the P/S column todesignate the values as prescribed displacements.

Elastic supports

Elastic supports, or springs, are defined by entering spring constants in the X, x, and zcolumns. 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 anentered value is a spring constant rather than a prescribed displacement. If you leave the P/Scolumn blank, the entered values are taken as prescribed displacements.

Tip: The effect of a columns above or below the slab can be modelled by entering theirbending stiffnesses as rotational spring supports about the x and z-axes. From simple elastictheory, 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 isdetected, an Error list button will appear.

Note: You cannot define an elastic support and a prescribed displacement at the same nodebecause it will be a contradiction of principles.

Generating additional supports

Additional supports and prescribed displacements can be generated using the Number of extraand Node number inc columns. The procedure is similar to that described on page 6-15 forgenerating additional nodes.

Note: The display of supports can be activated or suppressed by editing the DisplayOptions.


Point loads input

Loads on shell elements are categorised as point loads, i.e. concentrated loads at specificcoordinate, and element loads, i.e. uniform distributed loads.

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 thatyou 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, theload 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 signconventions given on page 6-10. The load case at the cursor position is displayed graphically.Press Enter or Display to update the picture.

Error checking

The program checks that specified nodes have indeed been defined in the Nodes input table. Ifan error is detected, an Error list button will appear.


Generating additional nodal loads

Additional nodal loads can be generated using the Number of extra and X-increment andZ-increment columns.

Shell loads

Distributed loads can be applied on shell elements. Enter a load case description in the Loadcase column followed by the relevant element numbers in the Shell numbers column. Theprogram automatically assigns numbers to all shell elements in the sequence they are definedon 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 UDLcolumn.

Note: Positive vertical loads act upward and negative loads act downward.


Error checking

The program checks that the entered element numbers are valid. If an error is detected, anError list button will appear.

Generating additional element loads

The No of extra and Node number Inc columns can also be used to generate additional shellloads. The procedures are similar to that used to generating additional shell elements – seepage 6-20 for detail.

Load combinations input

You can model practical scenarios by grouping load cases together in load combinations. Enterthe load combination number in the Load Comb column, followed by the load case name andrelevant load factors.

If the Load Comb column is left blank, the load combination is taken to be the same as for theprevious row of the table. The load cases to consider in a load combination are entered one perrow in the Load case column. Enter the relevant ultimate and serviceability limit state loadfactors in the ULS factor and SLS factor columns.

Tip: You may leave one or more blank lines between load combination definitions toimprove readability.

The ultimate and serviceabilitylimit states are used as follows:

• Deflections are calculatedusing the entered SLS loads.A set of reactions is alsocalculated at SLS for thepurpose of evaluating sta-bility and bearing pressures.

• A second set of reactionsand all element forces aredetermined using theentered ULS forces.

Error checking

The program only checks thatvalid load cases are specified. It has no knowledge of the design code that will be used in themember 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 slabstructures.

• Graphical input: Structures can be drawn in Padds or another CAD system and convertedto slab analysis input.

Parametric input

From the General input page,you can access severalparametric slab input modules.These are suitable for the rapidgeneration of complete inputfiles for some typical slabs.

Input generated this way canoptionally be appended toexisting data – you can thereforerepeatedly use the parametricinput modules to generatecomplicated structures.

Graphical input

In some situations it may be easier to define a slab's geometry graphically. With Padds you candraw 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 CADsystem.

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 are with a line pattern and thenvectorise the hatch to turn it into normal lines.


4. Use the Generate input command on the Macro to display the drawing conversionoptions. Choose the Fesd and press OK to start the conversion procedure.

The resultant Fesd input file will be compatible with both the Dos and Windows versionsof the slab analysis modules. The file is saved in the working folder as a last file, e.g.'Lastfesd.a01'.

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 calculatereinforcement.

Fesd uses the Wood and Armer theory, to convert calculated bending and torsional momentsto transformed bending moments. More detail is given on page 6-12.

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 z'-axis.The x'-axis is defined by entering the angle formed with the local x-axis. The z'-axis is inturn measured from the x'-axis.

• Define the reinforcement levels in the slab by entering the concrete cover values for thetop 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 theactual 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 theshells as reinforced concrete members.

• Add own weight: Select a load case to which the self-weight of the beam and shellmembers 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 loadcombinations are required. Generally one would require results for the load combinationsonly. However, you may have a special need to view the results of specific load cases aswell. Disable this option to include the results for the individual load cases as well.

Analysing the slab

To analyse the slab, open theAnalysis page and press StartAnalysis. The analysis progressof displayed to help you judgethe time remaining to completethe analysis.

After a successful analysis, thedeflected shape is displayed forthe first load case or loadcombination or, in the case ofmodal or buckling analysis, thefirst mode shape.


Error checking during analysis

During the input phase, the slab geometry and loading data is checked for errors. Not allreported errors are necessarily serious. To define duplicate elements between two nodes, forexample, could be an accidental error on your side. However, the program is quite capable ofdealing with a situation like this and will therefore allow the analysis procedure to continue.

Other input errors could be serious enough to prevent an analysis from being completedsuccessfully. Nodes with no elements, for example, have no restraints and will cause numericinstability during the analysis.

The first step of any analysis is the final verification of the input data. In the case of criticalerrors still present, a warning message will be displayed. If you then choose to not proceedwith the analysis, you will be taken to the input table with the error. However, choosing toproceed and ignore the warning, will have an unpredictable result.

Fixing errors that occurred during the analysis

Even if all input data seems valid, numeric errors may still occur during an analysis. Forexample, if you entered incorrect section properties, such as a very small E-value, the mistakemay go by unnoticed. However, the analysis will then yield an invalid value in the stiffnessmatrix or extremely large deflections. The same applies to the stability of the slab.

If an error was detected during the analysis, a warning will be displayed. The cause of the errorshould 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 alloutput tables for excessively large or small values.


Viewing output

The analysis results can be viewed graphically or in tabular format.

Viewing output graphics

Diagram can be displayed for the following:

• Deflections: Deflections aregenerally small in relation todimensions of the structure.To improve the visibility ofthe deflection diagram, youcan enter a screen magni-fication factor.

• Bending stresses in shells:

• The x, y and xybending stresses: Thebending stresses aboutthe local x and y-axesand the torsionalstresses. The direction(not axis) of bending isshown 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 bendingmoments and corresponding required reinforcement at the top and bottom in the x' andz'-directions. The reinforcement direction is shown as a small line on each shell. Referto page 6-11 for an explanation of the use of the Wood and Armer equations and topage 6-29 for the definition of the reinforcement directions.

Note: Shell bending stresses are taken about the x and y-axes. In contrast, the Wood andArmer bending moments are given in the x' and z'-directions.


Viewing output tables

Open the Output file page for atabular display of the slabanalysis output file. You canfilter the information sent to thecalcsheets by enabling ordisabling the relevant sections.

You can also quickly locate asection of the output file usingthe Find output function.


Calcsheets

Slab analysis output can be grouped on a calcsheet for printing or sending to Calcpad. Toinclude a particular component of the output in the calcsheets, view the relevant outputinformation 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 recallthe slab by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad issaved as part of a project and therefore does not need to be saved in the slab analysis module aswell.


Rectangular Slab Panel Design

The Rectangular Slab Panel Design module designs rectangular flat slab panels with a varietyof edge supports. The program should best be used for designing slabs with approximatelyrectangular panel layouts. You can use the Space Frame Analysis or Finite Element SlabDesign module to analyse slabs with irregular panel layouts and openings.

Rectangular Slab Panel Design6-36


The following text gives an overview of the theory and application of the design codes.

Design scope

The program designs rectangular reinforced concrete flat slab panels. Design loads includeown 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 Armerequations. Reinforcement is calculated using the normal code formulae.

Codes of practice

The following codes are supported:

• ACI 318-95.

• BS 8110 - 1997.

• CSA A23.3-93.

• Eurocode 2.

• SABS 0100 - 1992.


Both Metric and Imperial units of measurement are supported.

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 tothe X-axis (mm or in).

dy : Effective depth for reinforcement in the shorter span direction, i.e. parallel tothe 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).

ν : Poisson's ratio, typically equal to 0.2.

γ : 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 elementanalysis. Thirty-six plate elements are placed on a 6 x 6 grid. The program uses eight-nodedisoparametric finite elements that are well suited for thin plate analysis.

The analysis procedure employs a 2 x 2 Gaussian integration technique to calculate theelement stiffness matrix. The stresses are calculated at the Gaussian integration points andsubsequently extrapolated to the eight nodes and centre point of each element. The stresses atcommon nodes are smoothed by taking the average of all contributing stress components.

Reinforcement calculation

The finite element analysis yields values for bending stresses about the X and Y-axes andtorsional stresses. Due to the practical difficulties involved in reinforcing a slab to resisttorsion, the Wood and Armer equations are used to transform the bending and torsionalstresses 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 valuesgiven by the design codes. The discrepancy can be ascribed to the differences in the analysistechniques used. In particular, the code values include allowances for pattern loading andmoment redistribution.

Considering continuous slabs, negative moments will generally correlate well while positivespan 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 thatthe 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, the accuracy of the finite element analysis maybe impaired.

Tip: A slab with an aspect ratio larger than 3:1 can normally be designed as spanning in onedirection only.

• Own weight is modelled by entering a value for the unit weight. The own weight is addedto each load case entered.

• For the ultimate limit state calculations, the own weight, additional dead load and deadpoint loads are multiplied by the entered dead load factors. All live loads are similarlymultiplied by the live load factor.


•

• To create load combinations, simply repeat the relevant loads in the table. Copying lines inthe 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 usingthe following codes:

• Displacement: To support an edge in the vertical direction, i.e. simply supported. A typicalexample would be a slab simply supported on a masonry wall that provides no rotationalsupport.

• Rotation: To restrain rotation about an axis parallel to the slab edge, i.e. continuous. Thiscould be a reasonable model for a slab panel supported on columns if it is continuous withone or more adjacent panels.

• Displacement and rotation: The support conditions can be used together to support an edgevertically 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 couldbe 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, spansshould be modelled individually with continuous supports. Differences in the negativemoments on the continuous edges should then be redistributed manually according to therelative stiffness of each panel.


Design

Due to the simple finite element arrangement used, the analysis procedure will completealmost instantaneously. You can view the design results graphically:

• Moments: Transformedmoment diagrams, using theWood and Armerequations, for the top andbottom in the X andY-directions are shown.Values are given per unitwidth. The transformedmoments in the top andbottom fibres represent themoments to be resisted bythe calculatedreinforcement.

• Deflections: Short-termelastic deflections, based onthe uncracked grossconcrete section are shown.The deflections do notinclude long-term effectslike shrinkage and creep.

• Reinforcement: Requiredreinforcement for the topand bottom in the X andY-directions is shown. Thecalculated reinforcement isbased on the transformedmoments and thereforeincludes the effects oftorsion.


Calcsheets

The slab panel 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.

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 recallthe design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the column designmodule as well.


Detailing

Reinforcement bending schedules can be generated for designed slab panels. Bendingschedules 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 thereinforcement. Change the values to suit your detailing requirements.

Required information:

• Schedule file name: Name of the Padds drawing and schedule file.

• Detailing parameters:

• First bar mark: Mark touse for the main bar.You may use anyalphanumeric string ofup to five characters,e.g. 'A', '01' or 'A01'.The mark is incre-mented automaticallyfor subsequent bars.

• Concrete cover toreinforcement

• Reinforcement bondlength.

• Drawing scale: Thedrawing paper is sizedto 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 allchanges 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.


Editing and printing of bending schedules

Detailed editing and printing of bending schedules are done with Padds. For this, follow thesteps below:

• In Padds, choose Open on the File menu and double-click the relevant file name. The filewill be opened and displayed in two cascaded widows. The active windows will containthe drawing of the slab panel and the other window the bar schedule.

• Make any necessarychanges to the drawing, e.g.editing or adding bars andadding construction notes.

• Click on any visible part ofthe window containing thecutting list to bring it to thefront. Enter the followinginformation at the relevantpositions:

• Member description: Use asmany lines of the Membercolumn to enter adescription, e.g. 'SLABPANEL E'.

• General schedule information: Press PgDn to move to the bottom of the bending schedulepage and enter the detailers name, reference drawing number etc.

• Bending schedule title: Enter the project name and bending schedule title in the centreblock at the bottom of the bending schedule.

• Bending schedule number: The schedule number in the bottom right corner defaults to thefile name, e.g. 'SLABE.PAD'. The schedule number can be edited as required to suit yournumbering system, e.g. 'P123456-BS405'.

Note: The bottom left block is reserved for your company logo and should be set up asdescribed in the Padds User's Guide.

Finally, combine the column drawing and schedule onto one or more A4 pages using theMake BS Print Files command on the File menu. Use Alt-P to print the schedule immediatelyor Alt-F to save it as a print file for later batch printing.

Column Design 6-45

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 largercolumn dimension does not exceed four times the smaller dimension.

• Circular Column Design, CirCol: Solid circular columns where the simplified designapproach applicable to rectangular columns may be applied.

• General Column Design, GenCol: Columns of any general shape and columns withopenings.

All column design modules can design reinforced concrete columns subjected to bi-axialbending. Bending schedules can be generated for editing and printing using the PROKONDrawing and Detailing System, Padds.

Column Design6-46



Design scope

The column design modules design reinforced concrete columns subjected to axial force andbi-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 ofthe larger to the smaller dimension does not exceed 1:4.

• The same procedure 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 beopened in Padds for further editing and printing.

Codes of practice


• ACI 318 - 1993.

• BS 8110 - 1987.

• BS 8110 - 1997.

• CSA-A23.3 - 1994.

• Eurocode 2 -1992.

• SABS 0100 - 1992.



List of symbols


Rectangular column geometry

b : Width of cross section, perpendicular to h (mm or in). This smaller columndimension is taken parallel the X-axis.

Column Design 6-47

d'x : Distance from the column face to the centre of the reinforcement resistingmoments about the X-axis (mm or in).

d'y : Distance from the column face to the centre of the reinforcement resistingmoments about the Y-axis (mm or in).

h : Depth of the cross section (mm or in). This larger column dimension is takenparallel 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 momentis taken anti-clockwise.

My bot : Moment about the Y-axis applied at the bottom (kNm or kipft).

P : Axial force in the column (kN of kip). A positive value denotes a downwardcompression 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 aboutthe X-axis (mm² or in²).

Column Design6-48

Ascy : Area of vertical reinforcement to resist the effective design moment about theY-axis (mm² or in²).

b' : Effective depth to reinforcement in shorter direction of rectangularcolumn (mm or in).

h' : Effective depth to reinforcement in longer direction of rectangularcolumn (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 rectangularcolumn (kNm or kipft).

M'y : Effective uniaxial design moment about the Y-axis for rectangularcolumn (kNm or kipft).

Code requirements

The supported design codes have similar clauses with respect to bracing and end fixetyconditions.

Braced and unbraced columns

A column is braced in a particular plane if lateral stability to the structure as a whole isprovided in that plane. A column should otherwise be considered as unbraced.

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 actingon the structure to the foundations.

RecCol and Circol allow you to set independent bracing conditions for bending about the Xand Y-axis of rectangular columns.

Column Design 6-49

Effective length of columns

The effective length or height of a column depends on its end conditions, i.e. the degree offixety 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 thatare deeper than the column dimension in the relevant plane.

• End condition 2: The end of the column is connected monolithically to beams or slabswhich 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 somenominal 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 endof a cantilever column. In the context of this program, this condition is regarded as free.

The codes suggest the follow values for the effective length factor, ß:

End conditionat the top

End conditionat the bottom

ß (Effectivelength factor)

Column in braced frame (ß ≤ 1.0)

FixedFixed

Pinned

0.75 to 0.85

0.90 to 0.95

PinnedFixed

Pinned

0.90 to 0.95

1.00

Column in unbraced frame (ß > 1.0)

FixedFixed

Pinned

1.2 to 1.5

1.6 to 1.8

PinnedFixed

Pinned

1.6 to 1.8

N.A.

Free Fixed 2.2

Note: The column design modules automatically calculate the effective length factors inrelation to the specified end conditions. You may however manually adjust the effectivelength factors if necessary.

Column Design6-50

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 to thecolumn dimension in that plane. The slenderness limits for short and slender columns set bysome of the supported codes of practice are:

Slenderness limit BS 8110 - 1997 SABS 0100 - 1992

ShortBraced

h

lex and b

ley < 15h

lex and b

ley < 2

1

M

M717 −

ColumnUnbraced

h

lex and b

ley < 10h

lex and b

ley < 10

MaximumAll lo ≤ 60b Lo ≤ 60b and b ≥

4

h

SlendernessCantilevers b60

hb100

lo2

≤≤ lo ≤ 25b and b ≥ 4

h

Note: In the above expressions for maximum slenderness, h and b are taken as the largerand smaller column dimensions respectively.

Column Design 6-51

Input

The column definition has several input components:

• Geometry and material properties.

• Bracing conditions and fixety at the column ends.

• Load cases.

Geometry input

The RecCol and CirCol modules have been simplified for the design of rectangular andcircular columns. Entering a column's geometry input in either of these modules is thereforestraightforward.

Tip: You can use the mouse to click on the column pictures and stretch certain dimensions,e.g. the column length.

Column Design6-52

General column geometry input

GenCol is used to design columns of any general shape and hence has a reasonably intricateinput procedure. A column section is entered as one or more shapes or polygons:

• The Code column is used for categorise the data that follows in the next columns:

+ : The start of a new polygon. An absolute reference coordinate must be enteredin the X/Radius and Y/Angle columns. If you leave either blank, a value ofzero is used.

– : Start of an opening. An absolute reference coordinate must be entered in theX/Radius and Y/Angle columns.

R : If you enter an 'R' or leave the Code column blank, a line is drawn usingrelative coordinates, i.e. measured from the previous coordinate.

L : Enter an 'L' in the Code column blank to make the following coordinateabsolute.

A : To enter an arc that continues from the last line or arc. The arc radius and angleare entered in the X/Radius and Y/Angle columns respectively. The angle ismeasured clockwise from the previous line or arc end point.

Column Design 6-53

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 andCirCol.

• 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 theright and negative to the left.

Y : Absolute or relative Y coordinate (mm or in). Values are taken positive upwardand negative downward.

You do need to close the polygon – the starting coordinate is automatically used as the endingcoordinate. If two polygons intersect, the geometry of the last polygon takes preference and theprevious polygon is clipped. A hole in a structure can, for example, be entered on top ofpreviously 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 fixety conditions

Define the bracing and fixety conditions by making the appropriate selections. For anexplanation of the terms used, refer to page 6-48. The effective length factors are automaticallyadjusted in relation to the specified bracing and end fixety conditions. If necessary, you maymanually edit the effective length factors.

Note: RecCol allows the bracing and end fixeties to be set independently for bending aboutthe X and Y-axis.

Column Design6-54

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 doesnot automatically include the self-weight of the column. The self-weight should becalculated and manually included in the applied loads.

• Moment values (kNm or kipft). Use the same sign for the top and bottom moments aboutan 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 aspecific load case are added together.

Column Design 6-55

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 bardiameter to be used at each defined bar position.

Irrespective the approach followed, additional moments are calculated for slender columns andautomatically added to the applied moments. The design moment is taken to be equal to orlarger 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, middleand bottom and the critical section identified as the section requiring the greatest amount ofreinforcement.

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 asingle or both axes.

• For slender columns, the applied moments and additional moments are summed for eachaxis.

• In the case of bi-axialbending, the moments areconverted to an effectivedesign moment about asingle design axis.

• The reinforcement requiredto resist the design momentis read from the applicablecolumn design chart.

• Using the same procedure, adesign moment is derivedabout the axis perpendicularto the design axis.Reinforcement resisting thesecondary design moment isread from the relevant chart.

Column Design6-56

Circular column design

The same simplified designprocedure as for rectangularcolumns is used. The major andminor column dimensions, h andb, are both set equal to thecolumn diameter.

Note: The design procedure forbi-axially bent slender columnstend to be conservative due tohe codes' allowance foradditional moment about boththe X and Y axes.

The column is evaluated at thetop, middle and bottom and the critical section identified as the section requiring the greatestamount of reinforcement.

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, toanalyse columns. This is achieved using an automated finite difference analysis.

The following calculations are followed:

• The section properties arecalculated and the columnslenderness evaluated.

• For a slender column, theadditional slendernessmoment is calculated andapplied about the weak axis,i.e. axis of lowest secondmoment of inertia. Theoutput gives the X andY-axis components.

• The design moment and axisare determined by taking thevector sum of the appliedand additional moments.

Column Design 6-57

• An iterative solution is obtained using strain compatibility and equilibrium as criteria. Thesimplified rectangular stress block given by the codes is used.

Note: Given the differences in the design procedures described above, GenCol will notyield identical results to RecCol and Circular Column Design modules when designingsimple rectangular or circular columns.

Column Design6-58

Design charts

The column design charts can be displayed for the specified column geometry and materialproperties:

• Rectangular columns: Separate charts are given for bending about the X and Y-axis forvarious 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 canthen be displayed for the resultant horizontal and vertical axes.

Column Design 6-59

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, tabulardesign summaries and detailed design calculations.



If you enable the Data File option before sending a calcsheet to Calcpad, you can later recallthe design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the column designmodule as well.

Column Design6-60

Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedulescan be edited and printed using Padds.




• Schedule file name: Nameof the Padds drawing andschedule file.

• Main bars (high yield steelis assumed):

• Rectangular columns:Bar diameter for thecorner bars and thenumber and diameter ofthe intermediate bars inthe horizontal andvertical faces of arectangular column, asdisplayed on the screen.

• Circular columns: Thediameter and number ofmain bars. It isgenerally assumed goodpractice to use at leastsix bars.

• General columns: Mainbar diameters aredefined in the initialinput. The shape codecan be selected for eachindividual bar.

• Lap length factor formain bars.

Column Design 6-61

Note: To ensure that the amount of reinforcement supplied is not less than the amountrequired, 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 thebase (m or ft).

• Links:

• Rectangular columns: Enter a link diameter and spacing, e.g. 'R10@200, and choose alink layouts. Link type '2' should only be used with square columns.

• Circular columns: Enter a link diameter and spacing and choose between usingcircular or spiral links.

• General columns: Select a shape code and follow the prompts to indicate the linkcoordinates. Available shape codes include '35' (normally used for holdingintermediate bars in position), '60' or '61' (used to enclose four bars by a rectangularlink) 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 alphanumericstring of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incrementedautomatically for subsequent bars.

• Select a size for the sketch: If A4 is selected, the drawing is scaled to fit on a full pageand the accompanying schedule on a separate page. The A5 selection will scale thedrawing 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 itdetailed with a splice at the top. If this option is disabled the column is detailed with bendsat 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 themain bar kinks. Circular columns are detailed with straight bars, removing the need forthis option.


Column Design6-62



• In Padds, choose Open on the File menu and double-click the relevant file name. The filewill be opened and displayed in two cascaded widows. The active windows will containthe drawing of the column and the other window the bar schedule.



• Member description:Use as many lines ofthe Member column toenter a memberdescription, e.g.'COLUMN TYPE 5'.

• General schedule information: Press PgDn to move to the bottom of the bendingschedule page and enter the detailers name, reference drawing number etc.


• Bending schedule number: The schedule number in the bottom right corner defaults tothe file name, e.g. 'COLUMN5.PAD'. The schedule number can be edited as requiredto suit your numbering system, e.g. 'P123456-BS201'.




Retaining Wall Design

The Retaining Wall Design module is used to analyse retaining walls for normal soil andsurcharge loads or seismic load conditions. Various types of walls can be considered, includingcantilever, simply supported and propped cantilever walls.

Padds compatible bending schedules can also be generated for designed walls.

Retaining Wall Design6-64


The following text gives an overview of the application of retaining wall analysis theory. Formore detailed information, reference should be made to specialist literature.

Design scope

The program can design most conventional retaining walls, including cantilever, simplysupported 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 onthe backfill. A water table can be defined behind the wall. If required, the soil pressurecoefficients can be adjusted manually.

Padds compatible bending schedules can be generated for designed walls.

Codes of practice


• BS 8110 - 1997.

• SABS 0100 - 1992.

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 orpropped 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).

δ : Angle of friction between wall and soil (°). Must be zero if Rankine theory isspecified.

φ : Angle of internal friction (°).

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).

µ : 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 itsdepth. The pressure applied on the bottom of the base is varied linearly from maximum atthe back, to zero at the front.

• Point loads are distributed along the depth of the soil. In contrast, line loads are takenconstant 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 theRankine theory.

Note: This manual does not attempt to explain the applicable theories in detail, but merelyhighlights some aspects of their application. For more detail, reference should be made tospecialist literature.

Friction between the wall and soil

The higher the value of the angle of friction between the wall and soil, δ, the greater the degreeof rotation of the system is implied. If the Coulomb theory is used, the friction angle shouldpreferable be set equal to the internal angle of friction, φ. This will yield pressures thatcorrelate better with the Rankine theory, than would be the case if δ is set equal to zero.

Saturated and submerged soil

To keep input as simple as possible, the program does no provide an option to enter values forspecific gravity, void ratio, moisture content and degree of saturation. However, reasonablemodelling of saturated soil and submerged conditions is still possible:

• If no water table is present, ρsoil should be taken as a value that includes a moisture contentthat can reasonably expected.

• If a water table is present, the portion of the soil above the water table will likely have adegree of saturation close to unity. Using the wet density rather than the dry density shouldyield reasonable results.

Point loads and line loads

Point loads and line loads behind the wall are incorporated using the Coulomb and Rebhann*

theories. Even if Rankine theory is used for the analysis, the effects of these loads are stillcalculated using Coulomb theory with the value of δ set equal to that of φ.

* 'Foundation Engineering Handbook', published by Van Nostrand Reinhold of New York


Seismic analysis

The program uses the Okabe-Monobe equations, based on the Coulomb wedge theory, tocalculate revised active and passive pressure coefficients. The seismic portion of the activepressure is assumed to act at 60% of the soil height behind the wall, effectively increasing thelever arm of the soil pressure.

The densities of the materials are also adjusted by multiplying with (1-kv). An upwardacceleration therefore effectively decreases the stabilising effect of the wall and soil weight.

Modelling of soil pressure behind rigid walls

The program suggests values for the active and passive pressure coefficients, Ka and Kp. Thesevalues generally yield reasonable results for cantilever walls. However, simply supported andpropped cantilever walls tend to be very rigid. This means that the actual active soil pressurescould potentially rise well above the level normally assumed. The program therefore allowsuniform pressure distribution to be specified, i.e. Factive = Pfac ⋅ Hwall ⋅ γsoil ⋅ Ka. Typical valuesfor the uniform pressure coefficient, Pfact, was determined by Terzaghi and Peck. An averagevalue 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 seepageis allowed, hydrostatic pressure is modelled as follows:

• The pressure behind the wall is taken as zero on the level of the water table and thenlinearly increased with depth.

• At the front of the wall, the pressure is taken as zero at ground level and linearly variedwith depth.

• The hydrostatic pressure below the base is varied linearly between the values calculatedbehind and in front of the wall.

If seepage is not allowed, the hydrostatic pressure in front of the wall or below the base istaken as zero.


Input

Use the input tables to enter the wall geometry, loading and general design parameters.

Geometry and loads input

When entering the dimensions and loads working on the wall, you should keep the followingin 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 aliquid 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 ofthe soil. Line loads are applied uniformly along the width of the wall.

Note: For suggestions on modelling saturated soil and submerged conditions, refer topage 6-67.


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 owncoefficients, select User defined design values:

• Active and passive pressurecoefficients, Ka and Kp.

• Soil friction constant belowthe base, µ.

• For simply supported andpropped cantilever walls,you can choose betweentriangular or uniformpressure distributions. In thecase of rigid walls, auniform pressure coefficientcan also be entered. Seepage 6-68 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 fixety, i.e. free to rotate. The wall is supportedhorizontally 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 beused if the slope of the backfill is less than zero. Due to this and other limitations of theRankine 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 amore 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 thedead load factor. Applied loads are considered to be live loads and are therefore multipliedwith the live load factor.

Additional checks for propped cantilever walls

In the case of a propped cantilever wall, the program checks whether fixety can be obtained atthe base. Fixety is attained by balancing loads such as own weight and soil weight plus thepressure distribution under the base against the fixety moment. If the fixety moment attainableis less than one and a half times the theoretical fixed moment, the fixety moment is reducedand 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 frontcorner of the base. If a shear key is used and it is located within one quarter of base width fromthe 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 valueof B is calculated to not exceed the allowable bearing pressure and safety factor foroverturning. A warning message is displayed if an appropriate value could not becalculated.

• Select D: Optimise the horizontal base dimension behind wall. The smallest value of D iscalculated to satisfy the requirements set for the allowable bearing pressure and safetyfactor 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 thereforepossible that after optimising the value of B, for example, the safety factor for slip isexceeded. You may thus need to alternate optimisation functions to arrive at a workablesolution.


Calcsheets

The retaining wall design output can be grouped on a calcsheet for printing or sending toCalcpad. Various settings can be made with regards to the inclusion of design results andpictures.


Recalling a data fileIf you enable the Data File option before sending a calcsheet to Calcpad, you can later recallthe design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the wall design moduleas well.


Detailing

Reinforcement bending schedules can be generated for designed retaining wall. Bendingschedules can be edited and printed using Padds.





• Wall and base reinforcement:

• Reinforcement isgenerated at variouspositions in the wall andbase using thecalculated ultimatebending moments.Change the diametersand spacings asrequired.

• Bond stress: Allowable stress for evaluating bar anchorage of the wall starter bars. If90° bends proof insufficient, the program automatically uses full 180° hooks. Barspacing is also reduced to lower bond stress.




Press Generate to create a Padds bending schedule with the entered settings. To discard allchanges you have made and revert to the default values for the designed retaining wall, pressReset. Also press Reset if you have changed the reinforcement bond stress and want torecalculate the reinforcement.




• In Padds, choose Open on the File menu and double-click the relevant file name. The filewill be opened and displayed in two cascaded widows. The active windows will containthe drawing of the retaining wall and the other window the bar schedule.



• Member description: Use asmany lines of the Membercolumn to enter adescription, e.g. 'WALLTYPE C'.

• General schedule information: Press PgDn to move to the bottom of the bending schedulepage and enter the detailers name, reference drawing number etc.


• Bending schedule number: The schedule number in the bottom right corner defaults to thefile name, e.g. 'WALLC'. The schedule number can be edited as required to suit yournumbering system, e.g. 'P123456-BS303'.




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.

Column Base Design6-78



Design scope

The program designs rectangular concrete column bases subjected to vertical force and bi-axialbending moment. The program designs the base at ultimate limit state for bending moment andshear.

The program also verifies the stability requirements for overturning and bearing pressure.Overturning can be evaluated at ultimate limit state or using the older working force method.Refer to page 6-82 for details.

Reinforcement bending schedules can be generated for designed bases. Schedules can beopened in Padds, for further editing and printing.

Codes of practice


• ACI 318 - 1993.

• BS 8110 - 1987.

• BS 8110 - 1997.

• CSA-A23.3 - 1994.

• Eurocode 2 -1992.

• SABS 0100 - 1992.



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 aright-hand rule, the Z-axis points vertically upward.

The sign conventions applicable to forces andmoments are as follows:

• The vertical force, P, works downward.

• The horizontal forces Hx and Hy are appliedparallel to the X and Y-axes.

• The moments Mx and My are applied in the Xand Y-directions, i.e. about the negative Y andX-axes respectively

Post-processing frame analysis results

Forces are usually obtained using the reaction values calculated by frame analysis. Whenextracting frame analysis output, the differences in the sign conventions and axis systems usedshould be kept in mind:

Applied load in Column Base Design module

P Hx Hy Mx MyFrame Analysis Module

Frame analysis reaction value to use

Plane Frame Analysis Ry – Rx None Mz None

Grillage Analysis Ry None None Mz Mx

Space Frame Analysis Ry – Rx Rz Mz Mx

Space Truss Analysis Ry – Rx Rz None None


Input

The column base definition has several input components:

• Geometry and material properties.

• Load cases and stability criteria.

Geometry input

Enter the base and column dimensions, omitting the values for the either column if only onecolumn is used. A column is positioned at the centre of the base unless non-zero values areentered 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 theconcrete cover to the reinforcement.

Setting the stability criteria

Relevant limits should be entered for checking overturning, slip and bearing pressure atserviceability 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 limitstate 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 factoredstabilising forces should not exceed unity. In this ratio, all forces are multiplied by theappropriate ULS factors that exceed unity and only the self-weight components of stabilisingforces 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 foroverturning for all stabilising components of self-weight to the minimum prescribed ULS deadload factor, typically between 0.9 and 1.0. For all other loads, a ULS load factor of between 1.2and 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 tostabilising 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 overturningand 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. Thesafety factor for slip can 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 ofthe base unless values for E and/or F are entered.

• Seen in elevation, the horizontal forces Hx and Hy are applied at the top of the stubcolumn.

• All loads are entered asworking loads. The ultimatedesign loads are obtained bymultiplying the enteredforces by the specified loadfactor.

• A minimum and maximumload factor should bespecified for each load tocalculate the worstoverturning and slip cases.

• A positive value of Pdenotes a downward force.Use a negative value foruplift.

• Moments are applied in the X and Y directions, rather than about the X and Y-axes.

• For the case of a concrete column extending to the slab above, no stub column should beentered, 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 thecolumn dimensions, C and D, and use zero for the stub column height, X.

For detail on the sign conventions used for loads, refer to page 6-14.


Design

A column base is designed for compliance with ultimate limit state and serviceability limitstate 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 limitstate and serviceability limit state. The following general principles apply:

• Overturning: When considering overturning at ultimate limit state, the applied loads aremultiplied by the entered load factors for overturning to calculate the ratio of destabilisingto stabilising effects. At serviceability limit state calculations are performed using theentered unfactored working loads.

• Slip: At ultimate limit state, all forces are multiplied by their ULS load factors. The safetyfactor for slip is calculated by dividing the resisting passive soil pressure and friction bythe horizontal forces causing slip. The same calculation is performed at serviceability limitstate using unfactored forces.

• Bearing pressure: Entered loads are multiplied by their respective ULS load factors beforecalculating the bearing pressure. The unfactored loads are used at serviceability limit state.

Note: With careful manipulation of the load factors for overturning, you can manipulate theprogram to evaluate overturning stability at ultimate limit state or using the working loadsmethod. Refer to page 6-82 for more information.

Reinforcement calculation

The loads are multiplied by the specified load factor to obtain the ultimate design loads. Thedesign forces, including the base self weight and weight of the soil cover, are used to calculatethe ultimate bearing pressure below the base. The program calculates the bending moments inthe base and uses the normal code formulae to obtain the required reinforcement. Nominalreinforcement is also calculated where applicable.

Shear checks

The required reinforcement for bending is used to calculate the shear resistance, vc, in the Xand Y-directions. For punching shear, the value is based on the average required reinforcementin the two directions.


Linear shear

When consideringlinear shear, lines areconsidered at adistance equal to thebase depth in front ofeach face of thecolumn. Thecontribution of thesoil pressure blockoutside the lines isthen used to calculatethe shear stress.

Punching shear

For punching shear, shear perimeters are considered at one and a half time the base thicknessfrom 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 ofworking 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 orkipft).

• 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. Theoptimisation procedures take into account the specified material costs.

• Select B: Calculate the optimum value for the base dimension in the Y-direction. All otherdimensions are left unchanged.

• Select A: Calculate the optimum value for the base dimension in the X-direction. All otherdimensions are left unchanged.

Note: When optimising the base dimensions A and B, the base thickness is kept constantand no shear checks are performed. Where necessary, the base thickness should be adjustedmanually.


Calcsheets

The column base design output can be grouped on a calcsheet for printing or sending toCalcpad. Various settings can be made with regards to the inclusion of design results andpictures.



If you enable the Data File option before sending a calcsheet to Calcpad, you can later recallthe design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the design module aswell.


Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedulescan be edited and printed using Padds.





• Main reinforcement:

• Change the displayedbottom and top steel inthe X and Y-directionsas necessary.

• Top steel will only begiven for bases thickerthan 600 mm, or wheretension reinforcement isrequired.

• Column reinforcement:

• At each column portion used, specify whether a normal column, stub column or nocolumn should be detailed.

• Main bars: Diameter of column corner bars.

• Middle bars: The number and diameter of intermediate bars in the horizontal andvertical 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 inposition.





• Choose a configuration of bar shape codes to use for the bottom and, whereapplicable, the bottom reinforcement.




• In Padds, choose Open on the File menu and double-click the relevant file name. The filewill be opened and displayed in two cascaded widows. The active windows will containthe drawing of the column base and the other window the bar schedule.



• Member description:Use as many lines ofthe Member column toenter a description, e.g.'BASE 6'.

• General schedule information: Press PgDn to move to the bottom of the bendingschedule page and enter the detailers name, reference drawing number etc.


• Bending schedule number: The schedule number in the bottom right corner defaults tothe file name, e.g. 'BASE6.PAD'. The schedule number can be edited as required tosuit your numbering system, e.g. 'P123456-BS206'.


Section Design for Crackwidth

The Section Design for Crackwidth can be used to design reinforced concrete sections tomeet specific crack requirements. Both beam and slab sections can be designed for thecombined effects of axial tension, bending moment and temperature.

Section Design for Crackwidth6-92


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 beamand slab sections can be designed to resist the effects of axial tension, bending moment andtemperature and the combination thereof. Temperature effects are also included to evaluateearly cracking and long-term thermal cracking.

Codes of practice

Design calculations are done according to BS 8007 - 1987 and Eurocode 2 - 1984.



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).

α : 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 pointsrequire 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 sectiondepth 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 besupplied in full in both faces of the section.

• Eurocode 2 requires additional information regarding the type of reinforcement bondapplicable i.e. high-bond or plain bars.

• Select Beam mode if 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 environmentaltemperature and the peak temperature due to hydration. The value is used to evaluate earlythermal 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 variationcan normally be set equal to zero when considering early cracking only.

• The seasonal temperature variation should always be considered for long-term thermalcracking 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 variesbetween 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, whenin 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 adefault value of 100 · fct / fy, where fct is the three-day tensile strength of the immatureconcrete. 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 temperaturevariation, 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 ofbending 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 andspacing to comply with the crack width requirements. A fifth column is provided where youcould 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 barsof not more than two different diameters. The bar diameters are chosen to not differ by morethan one size.


Calcsheets

The crackwidth design output can be grouped on a calcsheet for printing or sending toCalcpad. Various settings can be made with regards to the inclusion of design results andpictures.



If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall itby double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is savedas 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 forcombined bending, shear and torsion. Rectangular and T-sections are accommodated.

Concrete Section Design6-100


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 resistbending moment, shear and torsion.

Codes of practice


• ACI 318-95.

• BS 8110 - 1997.

• CSA A23.3-93.

• Eurocode 2.

• SABS 0100 - 1992.

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 rectangularsections and for flanged sections where the neutral axis falls inside the flange. If the neutralaxis 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 andthe remaining central portion defines the second sub-section.

• By considering the total section, the moment required to put the flange portion incompression can be calculated using the normal code formulae. This moment is thenapplied to the flange sub-section and the required reinforcement calculated using theeffective depth of the total section.

• The same moment is then subtracted from the total applied moment, the resulting momentapplied to the central sub-section and the reinforcement calculated.

The tension reinforcement for the actual section is then taken as the sum of the calculatedreinforcement for the two sub-sections. If compression reinforcement is required for the centralsub-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. Shearstress, v, is therefore calculated using the web area and checked to not exceed the ultimateallowable shear stress given in the code. The shear capacity, vc, is calculated using the requiredbending reinforcement, As, and the shear reinforcement calculated using the normal codeformulae.


Calculation of torsion reinforcement

Depending on the option chosen, torsion can be resisted by the section as a whole or by theweb portion only. For flanged beams, the torsion is calculated separately for the flange andweb along the guidelines given in the code. The torsional shear stresses are checked so as notto exceed the ultimate allowable shear stress. Reinforcement requirements are also evaluatedseparately for the flange and web using the normal code formulae.


Input

The section geometry and ultimate loading are entered using the single input table. Thefollowing 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 bottomor where the flange is in tension, enter a rectangular section without a flange. The effectsof bending and shear will still be evaluated correctly. In the absence of a flange, thetorsion 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 followingresults are given:

• The moment capacity of the section using tensile reinforcement only.

• Required, nominal and suggested flexural reinforcement at the bottom and top.

• Shear stress in the web and the shear capacity of the section if no links are used.

• The required, nominal and suggested shear steel.

• Torsional shear stress in the flange and web.

• The required and suggestedtorsional shear links in theflange and web. The torsionreinforcement should besupplied in addition to thereinforcement calculated forshear.

• Required and suggestedadditional longitudinal tor-sion reinforcement in theflange and web. Thelongitudinal torsion rein-forcement should besupplied in addition to therequired flexural rein-forcement.


Calcsheets

The section 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 itby double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is savedas part of a project and therefore does not need to be saved in the design module as well.


Punching Shear Design

The Punching Shear Design module designs flat slabs for punching shear at edge, corner orinternal columns. Only reinforced concrete slabs are designed – to design prestressed concreteslabs for punching shear, use the Prestressed Beam/Slab Design module, Captain, instead.

Punching Shear Design6-108



Design scope

The program designs reinforced concrete flat slabs for punching shear at edge, corner andinternal columns.

Codes of practice


• ACI 318-95.

• BS 8110 - 1997.

• CSA A23.3-93

• Eurocode 2.

• SABS 0100 - 1992.



List of symbols


Slab geometry

A : Horizontal column dimension, as shown on the screen, or diameter of circularcolumn (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, as shown on the screen, from the column centre to the slabedge (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 fourperimeters (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 fourperimeters (mm² or in²).

Design output

Asv : The total area of stirrups to be provided within 1.5Deff inside a perimeter (mm²or 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 minimumvalues 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 columncentre, 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, thecolumn is taken to be a corner column.

• If all edges are further than five times the effective slab depth from the column centre, thecolumn is analysed as an internal column.

Circular columns

Concentric circular rather than square shear perimeters are used for circular columns.

Reduction of design moments

The program assumes that the design forces are obtained from an equivalent frame analysisthat incorporates pattern loading. As allowed for by the codes, the values of the ultimatemoments, Mtx and Mty, are subsequently reduced by 30% prior to calculating the effective shearforce, Veff.


Input

The slab geometry and loading is entered using the single input table. The followingparameters may require special attention:

• The reinforcement values Asx and Asy to be entered for each perimeter, represent theaverage amount for each direction. For an internal column, for example, Asx represents theaverage of the reinforcement quantities crossing the left and right sides of the perimeter.

• By careful choice of the values for X and Y, you can force a column to be considered as anedge, corner of internal column. See page 6-109 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 valuesshould 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 6-109 for an explanation of theassumptions that apply.

• The program chooses four shear perimeters. The first perimeter is taken a distance1.5 · Deff away from the column face. Subsequent perimeters are spaced at 0.75 · Deff. Theperimeters are chosen to be as short as possible, extending to the slab edge whennecessary.

• For each perimeter, the allowable stress, vc, is taken as the weighted average of the valuescalculated for the X and Y-directions, using the flexural reinforcement ratio for therespective directions.

• The required shear reinforcement for each perimeter is then calculated using the normalcode 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.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 recallthe design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the design module aswell.

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