concrete design prokon

Concrete Design 6-1

Chapter

Concrete Design

The concrete design modules can be used for the design of reinforced and pre-stressed concrete beams and slabs, columns, column bases and retaining walls.

Concrete Design 6-2

Quick Reference

Concrete Design using PROKON 6-3 Continuous Beam and Slab Design 6-5 Pre-stressed Beam and Slab Design 6-9 Finite Element Slab Analysis 6-9 Rectangular Slab Panel Design 6-9 Column Design 6-9 Retaining Wall Design 6-9 Column Base Design 6-9 Section Design for Crack width 6-9 Concrete Section Design 6-9 Punching Shear Design 6-9

Concrete Design using PROKON 6-3

Concrete Design using PROKON

Several concrete design modules are included in the PROKON suite. These are useful tools for the design and detailing typical reinforced and pre-stressed concrete members.

Beam and slab design The Continuous Beam and Slab Design and Pre-stressed Beam and Slab Design modules are used to design and detail reinforced and pre-stressed beams and slabs. Simplified design of flat slab panels is available through the Rectangular Slab Panel Design module. In contrast, the Finite Element Slab Design module is better suited for the design of slabs with more complicated geometries. Punching shear in flat reinforced concrete slabs can be checked with the Punching Shear Design module.

Column design Rectangular Column Design and Circular Column Design offer rapid design and detailing of simple short and slender columns. Columns with complicated shapes can be designed using the General Column Design module.

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

Section design Two modules, Concrete Section Design and Section Design for Crack width, are available for the quick design of sections for strength and crack width requirements.

Concrete Design using PROKON 6-4

Continuous Beam and Slab Design 6-5

Continuous Beam and Slab Design

The Continuous Beam and Slab Design module is used to design and detail reinforced concrete beams and slabs as encountered in typical building projects. The design incorporates automated pattern loading and moment redistribution.

Complete bending schedules can be generated for editing and printing using Padds.


Theory and application

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

Design scope The program designs and details continuous concrete beams and slabs. You can design structures ranging from simply supported single span to twenty-span continuous beams and slabs. Cross-sections can include a mixture rectangular, I, T and L-sections. Spans can have constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. At ultimate limit state, moments and shears are redistributed to a specified percentage.

Reinforcement can be generated for various types of beams and slabs, edited and saved as Padds compatible bending schedules.

Design codes The following codes are supported:

• BS 8110 - 1985.

• BS 8110 - 1997.

• SABS 0100 - 1992.

Reinforcement bending schedules are generated in accordance to the guidelines given by the following publications:

• General principles: BS 4466 and SABS 082.

• Guidelines for detailing: ’Standard Method of Detailing Structural Concrete’ published by the British Institute of Structural Engineers.

Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties are based on the gross un-cracked concrete sections. Columns can optionally be specified below and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.


Pattern loading At ultimate limit state, the dead and live loads are multiplied by the specified ULS load factors (see page 6-9). Unity load factors are used at serviceability limit state. The following load cases are considered (the sketch uses the load factors applicable to BS8110):

• All spans are loaded with the maximum design load.

• Equal spans are loaded with the maximum design ultimate load and unequal spans with the minimum design dead load.

• Unequal spans are loaded with the maximum design load and equal spans loaded with the minimum design dead load.Note: The case

where any two adjacent spans are loaded with maximum load

and all other spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, is not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

• SABS 0100 - 1992 suggests a constant ULS dead load factor of 1.2 for all pattern load cases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for calculating the minimum ultimate dead load. The program uses the more approach given by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and the maximum load factor specified for maximum dead load.

• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of 1.5×DL. This load case is not considered during the analysis – if required, you should adjustment the applied loads manually. In cases where the dead load is large in comparison with the live load, e.g. lightly loaded roof slabs, this load case can be incorporated by increasing the entered dead load or increasing the ULS dead load factor. This adjustment applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.


Moment redistribution Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is set to ’optimised’, the design moments are further minimised by redistributing span moments upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern loading and then redistributed using the procedures explained in the following text.

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns without increasing the sagging moments at midspan. The redistribution of moments and shear forces procedure is performed as follows:

1. The maximum hogging moment at each column or internal support is adjusted downward by the specified maximum percentage.

2. The corresponding span moments are adjusted downward to maintain static equilibrium. The downward adjustment of hogging moments above is limited to prevent any increase in the maximum span moments of end spans.

3. The shear forces for the same load cases are adjusted to maintain static equilibrium.


Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward distribution of the span moments. The envelopes for the three pattern load cases are redistributed as follows:

1. The maximum hogging moment at each internal support is adjusted downward by the specified percentage. This adjustment affects the moment diagram for the load case where the maximum design load is applied to all spans.

2. The relevant span moments are adjusted accordingly to maintain static equilibrium.

3. The minimum hogging moment at each internal support is subsequently adjusted upward to as close as possible to the reduced maximum support moment, whilst remaining in the permissible redistribution range. A second load case is thus affected for each span.

4. The relevant span moments are adjusted in line with this redistribution of the column moments to maintain static equilibrium.

5. For each span, the moment diagram for the remaining third load case is adjusted to as near as possible to the span moments obtained in the previous step. The adjustment is made in such a way that it remains within the permissible redistribution range.

6. Finally, the shear force envelope is adjusted to maintain static equilibrium.

7. The following general principles are applied when redistributing moments:

8. Equilibrium is maintained between internal and external forces for all relevant combinations of design ultimate load.

9. The neutral axis depth is checked at all cross sections where moments are redistributed. If, for the specified percentage of moment redistribution, the neutral axis depth is greater than the limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

10. The amount of moment redistribution is limited to the specified percentage. The maximum amount of redistribution allowed by the codes is 30%.

Note: The exact amount of moment redistribution specified is always applied, irrespective of the degree of ductility of the relevant sections. Where necessary, ductility is improved by limiting the neutral axis depth. This is achieved by adding additional compression reinforcement.


Deflection calculation Both short-term and long-term deflections are calculated. No moment redistribution is done at serviceability limit state.

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-cracked concrete sections are used.

Long-term deflections

Long-term deflections are determined by first calculating the cracked transformed sections:

1. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

2. The cracked transformed sections are then calculated at 250 mm intervals along the length of the beam. The results of these calculations are tabled in the Crack files on the View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the amount of reinforcement required at ULS. However, once reinforcement is generated for beams, the actual entered reinforcement is used instead. You can thus control deflections by manipulating reinforcement quantities.

Next, the long-term deflection components are calculated by numerically integrating the curvature diagrams:

1. Shrinkage deflection is calculated by applying the specified shrinkage strain. Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in the beam.

2. The creep deflection is calculated by applying the total dead load and the permanent portion of the live load on the beam. The modulus of elasticity of the concrete is reduced in accordance with the relevant design code.

3. The instantaneous deflection is calculated by applying the transient portion of the live load on the transformed crack section.

4. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together with cracked transformed sections, which implies plastic behaviour. Although this procedure is performed in accordance with the design codes, the use of elastic moments together with cracked sections in the same calculation is a contradiction of principles. As a result of this, long-term deflection diagrams may show slight slope discontinuities at supports, especially in cases of severe cracking.


Calculation of flexural reinforcement The normal code formulae apply when calculating flexural reinforcement for rectangular sections and for flanged sections where the neutral axis falls inside the flange.

If the neutral axis falls outside the flange, the section is designed by considering it as two sub-sections. The first sub-section consists of the flange without the central web part of the section and the remaining central portion defines the second sub-section. The reinforcement calculation is then performed as follows:

1. Considering the total section, the moment required to put the flange portion in compression can be calculated using the normal code formulae. This moment is then applied to the flange sub-section and the required reinforcement calculated using the effective depth of the total section.

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

3. The tension reinforcement for the actual section is then taken as the sum of the calculated reinforcement for the two sub-sections. If compression reinforcement is required for the central sub-section, it is used as the required compression reinforcement for the actual section.

Design and detailing of flat slabs When entering the input data for a flat slab, you should use its whole width, i.e. the transverse column spacing (half the spacing to the left plus half the spacing to the right). The program will then calculate bending moments and shear forces for the whole panel width.

When generating reinforcement, however, the program considers the column and middle strips separately. The program does the column and middle strip subdivision as suggested by the design codes. The procedure is taken a step further by narrowing the column strip and widening the middle strip to achieve a simpler reinforcement layout – a procedure allowed by the codes.

Initial column and middle strip subdivision

The flat slab panel is divided into a column strip and middle strip of equal widths and then adjusted to simplify reinforcement detailing:

1. The width of the column strip is initially taken as half the panel width. The total design moment is then distributed between the column and middle strips as follows:

Moment position Column strip Middle strip

Moment over columns 75% 25%

Moments at midspan 55% 45%


2. Reinforcement is calculated for each of the column and middle strips.

Adjusted column and middle strip subdivision

The design codes require that two-thirds of the column strip reinforcement be concentrated in its middle half. The codes also state that a column strip may not be taken wider than half the panel width, thereby implying that it would be acceptable to make the column strip narrower than the half the panel width.

To simplify the reinforcement layout and still comply with the code provisions, the program narrows the column strip and widens the middle strip. The widening of the middle strip is done as follows:

1. The middle strip is widened by fifty percent from half the panel width to three-quarters of the panel width.

2. The reinforcement in the middle strip is accordingly increased by fifty percent. Reinforcement added to the middle strip is taken from the column strip.

The column strip is subsequently narrowed as follows:

1. The column strip is narrowed to a quarter of the panel width.

2. As explained above, rein-forcement is taken from the column strip and put into the widened middle strip.

3. The remaining reinforcement is checked and additional rein-forcement added where necessary. This is done to ensure that the amount of reinforcement resisting hogging moment is greater than or equal to two-thirds of the reinforcement required for the original column strip.


Designing the slab for shear

The program considers the column strip like a normal beam when doing shear calculations. A possible approach to the shear design of the slab is:

• Consider the column strip like a beam and provide stirrups equal to or exceeding the calculated required shear steel.

• In addition to the above, perform a punching shear check at all columns.

Implications of modifying the column and middle strips

In applying the above modifications, the moment capacity is not reduced. The generated reinforcement will be equal to, or slightly greater, than the amount that would be calculated using the normal middle and column strip layout.

The above technique gives simplified reinforcement details:

• A narrower column strip is obtained with a uniform transverse distribution of main bars and a narrow zone of shear links.

• Detailing of the adjoining middle strips is also simplified by the usage of uniform reinforcement distributions.

The design procedures for flat slabs and coffer slabs are described in more detail on page 6-9.


Input

The beam/slab definition has several input components:

• Parameters: Material properties, load factors and general design parameters.

• Sections: Enter cross-sectional dimensions.

• Spans: Define spans and span segments.

• Supports: Define columns, simple supports and cantilevers.

• Loads: Enter dead and live loads.

Parameters input Enter the following design parameters:

fcu : Characteristic strength of concrete (MPa).

fy : Characteristic strength of main reinforcement (MPa).

fyv : Characteristic strength of shear reinforcement (MPa).

Redistr : Percentage of moment redistribution to be applied.

Method : Method of moment redistribution, i.e. downward or optimised. Refer to page 6-8 for detail.

Cover top : Distance from the top surface of the concrete to the centre of the top steel.

Cover bottom: Distance from the soffit to the centre of the bottom steel.

DL factor : Maximum ULS dead load factor.

LL factor : Maximum ULS live load factor.

Note: The ULS dead and live load factors are used to calculate the ULS design loads. The ULS dead and live loads are then automatically patterned during analysis. Refer to page 6-7 for more information.

Density : Concrete density used for calculation of own weight. If the density filed is left blank, the self-weight of the beam/slab should be included in the entered dead loads.

LL perm : Portion of live load to be considered as permanent when calculating the creep components of the long-term deflection.

φ : The thirty-year creep factor used for calculating the final concrete creep strain.

εcs : Thirty-year drying shrinkage of plain concrete.


The graphs displayed on-screen give typical values for the creep factor and drying shrinkage strain. In both graphs, the effective section thickness is defined for uniform sections as twice the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made, stresses and relative humidity may vary considerably during the lifetime of the structure and appropriate judgements should be made.

Sections input You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be move horizontally to obtain eccentric sections, for example L-sections. Whole sections can also be moved up or down to obtain vertical eccentricity.


Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a straight line. Vertical and horizontal offsets of sections are use used for presentation and detailing purposes only and has no effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

Sec no : The section number is used on the Spans input page to identify specific sections.

Bw : Width of the web (mm).

D : Overall section depth, including any flanges (mm).

Bf-top : Width of optional top flange (mm).

Hf-top : Depth of optional top flange (mm).

Bf-bot : Width of optional bottom flange (mm).

Hf-bot : Depth of optional bottom flange (mm).


Y-offset : Vertical offset the section (mm). If zero or left blank, the top surface is aligned with the datum line. A positive value means the section is moved up.

Web offset : Horizontal offset of the web portion (mm). If zero or left blank, the web is taken symmetrical about the beam/slab centre line. A positive value means the web is moved to the right.

Flange offset : Horizontal offset of both the top and bottom flanges (mm). If zero or left blank, the flanges are taken symmetrical about the beam/slab centre line. A positive value means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to enter a thin web with a wide top flange. You can also enter wide web (actual top flange) with a thin bottom flange (actual web). The shear steel design procedure works with the entered web area, i.e. Bw × D, as the effective shear area. Although the two methods produce similar pictures, their shear modelling is vastly different.

Spans input Sections specified on the Sections input page are used here with segment lengths to define spans of constant or varying sections.


Spans are defined by specifying one or more span segments, each with a unique set of section properties. The following data should be input for each span:

Span no : Span number between 1 and 20. If left blank, the span number as was applicable to the previous row is used, i.e. another segment for the current span.

Section length : Length of span or span segment (m).

Sec No Left : Section number to use at the left end of the span segment.

Sec No Right : Section number to use at the right end of the span segment. If left blank, the section number at the left end is used, i.e. a prismatic section is assumed. If the entered section number differs from the one at the left end, the section dimensions are varied linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are interpreted literally. If a rectangular section should taper to an L-section, for example, the flange will taper from zero thickness at the rectangular section to the actual thickness at the L-section. If the flange thickness should remain constant, a dummy flange should be defined for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than the web and its depth made equal to the desired flange depth.

Supports input You can specify simple supports, columns below and above, fixed ends and cantilever ends. To allow a complete sub-frame analysis, columns can be specified below and above the beam/slab. If no column data is entered, simple supports are assumed.

The following input is required:

Sup no : Support number, between 1 to 2’. Support 1 is the left-most support.

C,F : The left-most and right-most supports can be freed, i.e. cantilevered, or made fixed by entering ’C’ or ’F’ respectively. By fixing a support, full rotational fixity is assumed, e.g. the beam/slab frames into a very stiff shaft or column.

D : Depth/diameter of a rectangular/circular column (mm). The depth is measured in the span direction of the beam/slab.

B : Width of the column (mm). If zero or left blank, a circular column is assumed.

H : Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank. In the analysis, the support will still be considered as a normal simple support. However, when generating reinforcement bars, the program will extend the bars a distance equal to half the support depth past the support centre line.


Code : A column can be pinned at its remote end by specifying ’P’. If you enter ’F’ or leave this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.

Loads input Dead and live loads are entered separately. The entered loads are automatically patterned during analysis. For more detail on the pattern loading technique, refer to page 6-7.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines as necessary to define each load case. Defined loads as follows:

Case D,L : Enter ’D’ or ’L’ for dead load or live load respectively. If left blank, the previous load type is assumed. Use as many lines as necessary to define a load case.

Span : Span number on which the load is applied. If left blank, the previous span number is assumed, i.e. a continuation of the load on the current span.

Wleft : Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.


Wright : Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.

P : Point load (kN).

M : Moment (kNm).

a : The start position of the distributed load, position of the point load or position of the moment (m). The distance is measured from the left-hand edge of the beam. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam.

b : The end position of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation. For more detail, refer to the explanation of the Parameters input on page 6-9.

Note: If you enter a concrete density on the Parameters input page, the own weight of the beam/slab is automatically calculated and included with the dead load.


Design

The analysis is performed automatically when you access the Design pages.

Analysis procedure Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections are calculated by analysing the beam/slab under pattern loading using the gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-9 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-7. The resultant bending moment and shear force envelopes are then redistributed. Finally, the required reinforcement is calculated.

Fixing errors that occurred during the analysis The Input pages incorporate extensive error checking. However, serious errors sometime still slip through and cause problems during the analysis. Common input errors include:

• Using incorrect units of measurement. For example, span lengths should be entered in metre and not millimetre.

• Entering too large reinforcement cover values on the Parameters input screen, gives incorrect reinforcement. Cover values should not be wrongly set to a value larger than half the overall section depth.

• Not entering section numbers when defining spans on the Spans input screens causes numeric instability. Consequently, the program uses zero section properties.


Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful examination of the analysis output. View the long-term deflection diagrams and determine which component has the greatest effect:

• The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the middle of spans generally induces negative shrinkage deflection, i.e. uplift.

• Large creep deflections (long-term deflection under permanent load) are often caused by excessive cracking, especially over the supports. Compare the span to depth ratios with the recommended values in the relevant design code.

• Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection component.

To verify the extent of cracking along the length of the beam/slab, you can study the contents of the Crack file. Check the cracked status and stiffness of the relevant sections. The extent of cracking along the length of the beam/slab is usually a good indication of its serviceability.


Viewing output graphics The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of any load case.

Deflections

The elastic deflection envelope represents the deflections due to SLS pattern loading.

The long-term deflection diagram represents the behaviour of the beam/slab under full SLS loading, taking into account the effects of shrinkage and creep:

• The green line represents the total long-term deflection.

• The shrinkage deflection is shown in red.

• The creep deflection (long-term deflection due to permanent loads) is given by the distance between the red and blue lines.

• The distance between the blue and green lines represents instantaneous deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-term deflection values are based on the reinforcement required at ultimate limit state. Once reinforcement has been generated for a beam, the long-term deflections will be based on the actual reinforcement instead.


Moments and shear forces

The bending moment and shear force diagrams show the envelopes due to ULS pattern loading.

Steel diagrams

Bending and shear reinforcement envelopes are given for ULS pattern loading. The bending reinforcement diagram sows required top steel above the zero line and bottom steel below.

Viewing output tables Open the Output file page for a tabular display of the beam/slab design results. Results include moments and reinforcement, shear forces and reinforcement, column reactions and moments and deflections.

The Crack file gives details of the cracked status, effective stiffness and concrete stresses in the beam/slab at regular intervals. You should find the information useful when trying to identify zones of excessive cracking.


Reinforcing

Reinforcement can be generated for the most types of continuous beam and slabs using the automatic bar generation feature. Reinforcement is generated in accordance to the entered detailing parameters after which you can edit the bars to suit your requirements.

To create a bending schedule, use each detailing function in turn:

• Detailing parameters: Select the detailing mode, enter you preferences and generate the reinforcement.

• Main reinforcement: Review the main bars and adjust as necessary.

• Stirrups: Enter one or more stirrup configurations.

• Shear reinforcement: Distribute stirrups over the length of the beam.

• Sections: Specify positions where of cross-sections details should be generated.

• Bending schedule: Create the Padds file.

Detailing parameters The detailing parameters set the rules to be used by the program when generating reinforcement:

• Beam/slab type: Different detailing rules apply to different types of beams and slabs:

Type Description Main reinforcement Shear reinforcement

1 Normal beam Nominal reinforcement as for beams

Beam shear reinforcement

2 One way spanning flat slab

Nominal reinforcement as for slabs.

No shear reinforcement.

3 Column strip portion of flat slab on columns

4 Middle strip portion of flat slab on columns

Main reinforcement in accordance with moment distribution between column and middle strips. Nominal reinforcement as for slabs.

No shear reinforcement. Separate punching shear checks should be performed.

5 Rib Nominal reinforcement as for slabs.

Shear reinforcement as for beams.


• Maximum bar length: Absolute maximum main bar length to be used, e.g. 13 m.

• Minimum diameter for top bars, bottom bars and stirrups: The minimum bar diameter to be used in each if the indicated positions.

• Maximum diameter for top bars, bottom bars and stirrups: The maximum main bar diameter to be used in each if the indicated positions.

Tip: To force the program to use a specific bar diameter, you can enter the same value for both the minimum and maximum diameters.

Note: The default bar types used for main bars and stirrups, e.g. mild steel or high tensile, are determined by the yield strength values entered on the Parameters input page – refer to page 6-9 for detail. High tensile steel markings, e.g. 'T' or 'Y', will be used for specified values of fy and fyv exceeding 350MPa.

• Stirrup shape code: Preferred shape code to use for stirrups. Valid shape codes include:

• BS 4466: 55, 61, 77, 78 and 79.

• SABS 082: 55, 60, 72, 73 and 74.


• First bar mark - top: The mark of the first bar in the top of the beam/slab. Any alphanumerical string of up to five characters may be specified. The rightmost numerical or alpha portion of the bar mark is incremented for subsequent bars. Examples of valid marks include:

• ’001’ will increment to 002, 003 etc.

• ’A’ will increments to B, C, etc.

• ’B002’ will increment to B003, B004 etc.

• First bar mark - middle: The mark of the first bar in the middle of the beam/slab. If you do not enter a mark, the bar marks continue from those used for the top reinforcement. Middle bars are generated for all beams with effective depth of 650 mm or greater.

• First bar mark - bottom: The mark of the first bar in the bottom the beam/slab. If you leave this field blank, the bar marks will continue from those used for the top or middle reinforcement.

• Cover to stirrups: Concrete cover to use at the top, bottom and sides of all stirrups.

• Minimum stirrup percentage: Nominal shear reinforcement is calculated according to the code provisions for beams and slabs. In some cases, it may be acceptable to provide less than the nominal amount stirrups, e.g. for fixing top bars in a flat slab. The minimum amount of stirrups to be generated can be entered as a percentage of the nominal shear reinforcement.

Note: For beams and ribs, the minimum stirrup percentage should not be taken less than 100% of nominal shear reinforcement.

• Loose method of detailing: The envisaged construction technique can be taken into account when detailing reinforcement:

• With the ’loose method’ of detailing, also referred to as the ’splice-bar method’, span reinforcement and link hangers are stopped short about 100 mm inside each column face. This is done at all internal columns were congestion of column and beam reinforcement is likely to occur. The span bars and stirrups are often made into a cage, lifted and lowered between supports. For continuity, separate splice bars are provided through the vertical bars of each internal column to extend a lap length plus 100 mm into each span. Top bars will extend over supports for the required distance and lapped with nominal top bars or link hangers. Allowance is made for a lap length of 40·φ and a 100 mm tolerance for the bottom splice bars that are acting in compression.

• Alternatively, where accessibility during construction allows, the 'normal' method of detailing usually yields a more economical reinforcement layout. This method allows bottom bars to be lapped at support centre lines. Top bars will extend over supports for the required distance and lapped with link hangers. Where more practical, top bars over adjacent supports may be joined. Adjacent spans are sometimes detailed together.


Note: The ’normal’ method of detail may give rise to congested reinforcement layouts at beam-column junctions, especially on the bottom beam/slab layer. Reinforcement layout details at such points should be checked.

Generating reinforcement

Use the Generate reinforcing to have the program generate bars according the detailing parameters.

Note: The aim of the automatic reinforcement generation function is to achieve a reasonable optimised reinforcement layout for any typical beam or slab layout. More complicated layouts will likely require editing of the generated reinforcement as described in the text that follows. Very complicated layouts may require more detailed editing using Padds.

Editing reinforcement

You can modify the generated reinforcement to suite your requirements by editing the information on the Main reinforcing, Stirrups, Shear reinforcing and Sections pages.

Main reinforcing The main reinforcement bars are defined as follows:

• Bars: The quantity, type and diameter of the bar, example ’2T20’ or ’2Y16’. The bar defined at the cursor position is highlighted in the elevation.

• Mark: An alphanumerical string of up to five characters in length, example ’A’, ’01’ or ’A001’.

• Shape code: Standard bar shape code. Valid shape codes for main bars include 20, 32, 33, 34, 35, 36, 37, 38, 39 and 51.

• Span: The beam/slab span number.

• Offset: Distance from the left end of the span to the start point of the bar (m). A negative value makes the bar start to the left of the beginning of the span, i.e. in the previous span.

• Length: Length of the bar as seen in elevation (m).

• Hook: If a bar has a hook or bend, enter ’L’ or ’R’ to it on the left or right side. If this field is left blank, an ’L’ is assumed.

• Layer: Position the bar in the top, middle or bottom layer. Use the letters ’T’, ’M’ or ’B’ with an optional number, e.g. ’T’ or ’T1’ and ’T2’.


The bending reinforcement diagram is shown on the lower half of the screen. The diagrams for required (red) and entered (blue) reinforcement are superimposed for easy comparison. Bond stress development is taken into consideration in the diagram for entered reinforcement.

Stirrups Define stirrup layouts as follows:

• Stirrup number: Enter a stirrup configuration number. Configuration numbers are used on the Shear reinforcing input page (see page 6-9) to reference specific configuration. If left blank, the number applicable to the previous row is assumed, i.e. an extended definition of the current configuration.

• Section number: Concrete cross section number as defined on the Sections input page (see page 6-9). If left blank, the number applicable to previous row in the table is used.

• Bars: Type and diameter of bar, example ’R10’.


Note: Mild steel bars are normally used for shear reinforcement. However, in zones where much shear reinforcement is required, you may prefer using high yield stirrups. You can do this by entering ’T’ or ’Y’ bars instead of ’R’ bars. In such a case, the yield strength ratio of the main and shear reinforcement, i.e. fy/fYV as entered, will be used to transpose the entered stirrup areas to equivalent mild steel areas.

• Mark: Any alphanumerical string of up to five characters in length, e.g. ’SA1’, ’01’ or ’S001’.

• Shape code: Standard double-leg bar shape code. The following shape codes can be used:

• BS4466: 55, 61, 77, 78 and 74.

• SABS082: 55, 60, 72, 73 and 74.

Bars are automatically sized to fit the section web. The first stirrup entered is put against the web sides. Subsequent stirrups are positioned in such a way that vertical legs are spaced equally.

Tip: Open stirrups, e.g. shape code 55, can be closed by entering a shape code 35.


Shear reinforcing Stirrup layouts defined on the Stirrups input page (see page 6-9) are distributed over the length of the beam/slab:

• Stirrup number: The stirrup configuration number to distribute.

• Spacing: Link spacing (mm).

• Span: The beam/slab span number.

• Offset: Distance from the left of the span to the start point of the distribution zone (m). A negative value makes the zone start to the left of the beginning of the span, i.e. in the previous span.

• Length: Length of the stirrup distribution zone (m).

The diagrams for required and entered shear reinforcement are superimposed. The required steel diagram takes into account shear enhancements at the supports.

It may sometimes be acceptable to enter less shear steel than the calculated amount of nominal sheer steel, e.g. when the stirrups are only used as hangers to aid the fixing main steel in slabs.


This option can be set as default on the Detailing parameters input screen – see page 6-9 for detail.

Sections Cross-sections can be generated anywhere along the length of the beam/slab to show the main and shear steel layout:

• Label: The cross-section designation, e.g. 'A'.

• Span no: The beam/slab span number.

• Offset: The position of the section, given as a distance from the left end of the span (m).

Sections are displayed on the screen and can be used to check the validity of steel entered at the different positions. Stirrup layouts defined on the Stirrups input (see page 6-9) rely on appropriate section positions specified. All specified sections will be included in the final bending schedule.


Bending schedule The Bending schedule input page is used generate a complete Padds compatible bending schedule. The parameters allow flexibility in the bending schedule creation, e.g. you can have the details of a beam/slab on a single bending schedule or split it onto more than one schedule to improve clarity. Each bending schedule can then be given a unique name and the associated spans entered.

The following information should be entered:

• File name: The name of the Padds drawing and bending schedule file

• First span: For clarity, a beam/slab with many spans can be scheduled put on more than one bending schedule. Enter the first span number to be included in the bending schedule.

• Last span: Enter the last span number to be included in the bending schedule.

• Grid lines: Optionally display grid lines and numbers appear on the bending schedule drawing.

• Columns: Optionally display column faces on the bending schedule drawing.

• First grid: The name or number of the first grid. Use one or two letters and/or numbers.

• Number up or down: Specify whether grids must be numbered in ascending or descending order, i.e. ’A’, ’B’ and ’C’ or ’C’, ’B’ and ’A’

• Drawing size: Select A4 or A5 drawing size. If A4 is selected, the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule. Typically, a maximum of three to four spans can be shown with enough clarity in A5 format and four to six spans in A4 format.

Note: When combining a drawing and schedule on the same page, the number of schedule lines is limited to a maximum of twenty-four in Padds. Using more lines will result in the drawing and schedule being printed on separate pages.

Use the Generate schedule function to create and display the Padds bending schedule.

Editing and printing of bending schedules

Detailed editing and printing of bending schedules are done with Padds. For this, following the steps below:

• Exit the program and launch Padds.

• Choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the beam and the second window the bar schedule.


• Make any necessary changes to the drawing, e.g. editing or adding bars and adding construction notes.

• Click on any visible part of the window containing the cutting list to bring it to the front. Enter the following information at the relevant positions:

• Member description: Use as many lines of the member column to enter a member description, e.g. ’450x300 BEAM’.

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

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

• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’BEAM.PAD’. The schedule number can be edited as required to suite your company’s schedule numbering system, e.g. ’P12346-BS001’.

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

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


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings are available to include input and design diagram and tabular result.

Tip: You can embed the Data File in the calcsheet for easy recalling from Calcpad.

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


Appendix: Suggested design procedures for slabs

Some suggestions are made below with regards the design and detailing of solid slabs and coffer slabs.

Suggested design procedure for solid slabs The suggestions are explained by way of an example. A flat slab with a regular rectangular column layout of 6.0 m by 5.5 m is considered.

Typical strip over a row of internal columns (Strip A)

The strip is modelled as a 6000 mm wide panel, i.e. 3000 mm either side of the columns. The program calculates moments and shear forces for the whole panel width. It then details a column strip, 1500 mm wide, and middle strip, 4500 mm wide. For an explanation of the division into column and middle strips, see page 6-9.

External strip (Strip B)

The external strip, strip B, is defined as the portion over the external columns that extending halfway to the first row of internal columns. Strip C is the first internal strip and it extends to midspan on both sides.

Consider the end panel, i.e. the portion between edge columns and the first row of internal columns or, in other word, strip B together with half of strip C. The portion over the internal columns (portion of strip C) will tend to attract more moment than the portion over the external columns (strip B). Using a rule of thumb, a reasonable moment distri-bution ratio would be about 62.5% to 37.5%.

The external strip (strip B) can thus be conservatively modelled


as a panel with width equal to half the transverse column spacing, i.e. 3000 mm, carrying the full load for that area. The program will analyse the strip and the generate reinforcement for a column strip, 750 mm wide, and a middle strip, 2250 mm wide.

First internal strip (Strip C)

The first internal strip can subsequently be modelled using the same width as a typical internal panel, i.e. 6000 mm. Because of the moment distribution explained above, the loading is increased to 50% + 62.5% = 112.5% of the typical panel loading. The small overlap in loading between the edge and first internal panels should take care of any adverse effects due to pattern loading.

Note: If the own weight is modelled using a density, you should account for the increased loading by either increase the density value by 12.5% or increasing the applied dead load.

The program will analyse the panel and generate a column strip, 1500 mm wide, and a middle strip 4500 mm wide.

Reinforcement layout

Careful combination of the column and middle strips generated above, should yield a reasonably economical reinforcement layout:

• For typical internal strips (strip A), use the generated column strip (CA) and middle strip (MA).

• For the column strip over the external row of columns, use no less than the column strip reinforcement (CB) generated for the external strip (strip B).

• For the column strip over the first row of internal columns, use no less than the column strip reinforcement (CC) generated for the first internal strip (strip C).

• The first middle strip from the edge (MC/MB) can be conservatively taken as the worst of middle strip generated for the first internal strip (MC) and twice that generated for the external strip (MB).

Suggested design procedure for coffer slabs Coffer slabs can normally be designed and detailed using the design procedure for solid slabs. The procedure suggested for solid slabs should be also a reasonable design approach for coffer slabs if the following conditions are met:

• The solid bands should be as wide or slightly wider than the generated column strips, i.e. L/4 or wider.

• Assuming that the concrete compression zone of each coffer rib falls in the coffer flange, the slab can be modelled as a solid slab.


• Setting the density to zero and appropriately increasing the applied dead load can model the own weight of the slab.

• The linear shear requirements should be verified for the column strips, i.e. solid bands. The areas around columns slab should also be checked for punching shear.

• The coffer webs should be checked for linear shear and compression reinforcement.

Note: You should validate the design procedure by checking that, in zones of sagging moment, the concrete compression zones of coffer ribs fall within the coffer flanges. Zones of hogging moment should be located inside solid bands.

Pre-stressed Beam and Slab Design 6-39

Pre-stressed Beam and Slab Design

Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design and detail most types of continuous pre-stressed beam and slab systems encountered in typical building projects. The design incorporates automated pattern loading and moment redistribution.

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




Design scope The program designs and details continuous pre-stressed concrete beams and slabs. You can design structures ranging from simply supported single span to twenty-span continuous beams or slabs.

Cross-sections can include a mixture rectangular, I, T and L-sections. More complex sections, e.g. box bridge decks, can be modelled with the aid of the section properties calculation module, Prosec. Spans can have constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. You can also enter individual load cases and group them in load combinations. At ultimate limit state, moments and shears are redistributed to a specified percentage.

Pre-stressed tendons can be generated to balance a specified percentage of dead load. Conventional reinforcement can be added to help control cracking, deflection and increase the ULS capacity.

Tendon profiles can be scheduled and saved as Padds compatible drawings.

Design codes The following codes are supported:

• BS 8110 - 1985.

• BS 8110 - 1997.

• SABS 0100 - 1992.

Reinforcement bending schedules are generated in accordance to the guidelines given by the following publications:

• Report No 2 of the Joint Structural Division of SAICE and ISA (JSD), ’Design of Pre-stressed Concrete Flat Slabs’.

• Technical Report 25 of the Concrete Society, published in 1984.

• Attached torsional members are treated in accordance with ACI 318 - 1989.


Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties are based on the gross un-cracked concrete sections. Columns can optionally be specified below and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.

Column stiffness

BS 8110 and SABS 0100 - 1992 assume that columns are rigidly fixed to slabs over the whole width of the panel. If the ultimate negative moment at an outer column exceeds the moment of resistance in the adjacent slab width, the moment in the column should be reduced and the sagging moment in the outer span should be increased to maintain equilibrium.

In ACI 318 - 1989, on the other hand, allowance is made for the reduction of column stiffness due to torsion. Report 2 of the JSD adapts a similar column stiffness reduction approach. The program incorporates this approach by allowing you to optionally enable attached torsional members.

Note: When the approach to include the attached torsional members is followed, column heads will also be taken into account in the column stiffness.

Pattern loading At ultimate limit state, the dead and live loads are multiplied by the specified ULS load factors (see page 6-9). Unity load factors are used at serviceability limit state. The following load cases are considered (the sketch uses the load factors applicable to BS8110):

• All spans are loaded with the maximum design load.

• Equal spans are loaded with the maximum design ultimate load and unequal spans with the minimum design dead load.

• Unequal spans are loaded with the maximum design load and equal spans loaded with the minimum design dead load.


Note: The case where any two adjacent spans are loaded with maximum load and all other spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, is not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

• SABS 0100 - 1992 suggests a constant ULS dead load factor of 1.2 for all pattern load cases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for calculating the minimum ultimate dead load. The program uses the more approach given by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and the maximum load factor specified for maximum dead load.

• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of 1.5×DL. This load case is not considered during the analysis – if required, you should adjust the applied loads manually. In cases where the dead load is large in comparison with the live load, e.g. lightly loaded roof slabs, increasing the entered dead load or increasing the ULS dead load factor can incorporate this load case. This adjustment applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.

Moment redistribution Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is set to 'optimised', the design moments are further minimised by redistributing span moments upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern loading and then redistributed using the procedures explained in the following text.

Code requirements

The JSD Report 2 recommends that the maximum moment redistribution should not exceed 20%.

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns without increasing the sagging moments at midspan. The redistribution of moments and shear forces procedure is performed as follows:

4. The maximum hogging moment at each column or internal support is adjusted downward by the specified maximum percentage.


5. The corresponding span moments are adjusted downward to maintain static equilibrium. The downward adjustment of hogging moments above is limited to prevent any increase in the maximum span moments of end spans.

6. The shear forces for the same load cases are adjusted to maintain static equilibrium.

Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward distribution of the span moments. The envelopes for the three pattern load cases are redistributed as follows:

11. The maximum hogging moment at each internal support is adjusted downward by the specified percentage. This adjustment affects the moment diagram for the load case where the maximum design load is applied to all spans.

12. The relevant span moments are adjusted accordingly to maintain static equilibrium.

13. The minimum hogging moment at each internal support is subsequently adjusted upward to as close as possible to the reduced maximum support moment, whilst remaining in the permissible redistribution range. A second load case is thus affected for each span.

14. The relevant span moments are adjusted in line with this redis-tribution of the column moments to maintain static equilibrium.


15. For each span, the moment diagram for the remaining third load case is adjusted to as near as possible to the span moments obtained in the previous step. The adjustment is made in such a way that it remains within the permissible redistribution range.

16. Finally, the shear force envelope is adjusted to maintain static equilibrium.

17. The following general principles are applied when redistributing moments:

18. Equilibrium is maintained between internal and external forces for all relevant combinations of design ultimate load.

19. The neutral axis depth is checked at all cross sections where moments are redistributed. If, for the specified percentage of moment redistribution, the neutral axis depth is greater than the limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

20. The amount of moment redistribution is limited to the specified percentage. The maximum amount of redistribution allowed by the codes is 30%.

Note: As would be the case in typical pre-stressed sections, the program assumes that all sections have adequate ductility to allow moment redistribution. The actual ductility of sections is not verified.

Tendon generation procedures Captain is capable of generating tendons for typical beam and slabs. The procedure aims to balance a specified percentage of the dead load in the span.

For purposes of the generation, all the dead loads on the span, including self weight, UDL's, partial UDL's, trapezoidal and point loads, are summed and divided by the span length to obtain an equivalent UDL for the span.

Parabolic or harped tendons are then selected to balance the required percentage of this equivalent dead load. In the case of harped tendons, the tendons are chosen to provide two upward point loads per span that balance the selected percentage of the sum of all the dead load components.

Note: The program uses load balancing only for the purpose of generating tendons.

Since long-term losses are not known beforehand, a 15% loss of pre-stress is assumed. Further, the generation procedure that tendons are stressed to 70% of their ultimate tensile strength (UTS).

The details of the tendon generation procedure are explained in the following text.


Parabolic tendons in cantilever spans

Consider a typical cantilever span with a tendon following a parabolic profile. The profile is chosen with a zero eccentricity at the cantilever end. At the internal support the tendon is taken as high as possible.

The program chooses the following values:

• The left offset, L, is chosen as zero.

• The right offset, R, is chosen equal to the span length divided by twenty, with a minimum of 250 mm.

• The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the right end) is chosen on the neutral axis.

• The tendon position over the internal support is taken as high as possible. The value of b3 (b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed tendon diameter.

The tendon force, T, required to produce the balanced load Wbal is given by

))((2)(15.1

13

2

RLengthbbLengthRLengthW

T balreq −−

−=

and the number of tendons required by

tendon

reqtendons UTS

TN

7.0=

Parabolic tendons in internal spans and end spans

For a typical internal span, a parabolic tendon profile is chosen to give maximum eccentricities over supports and at midspan.

The same also applies to an end span, except that the tendon as moved to the neutral axis at the anchor.

The program chooses the following default values:

• The left and right offsets, L and R, are chosen by the program to be equal to the span length divided by twenty, with a minimum of 250 mm.


• Over the supports, the tendons are taken as high as possible. The values of b1 and b2 are made equal to the top cover plus half the sheathed tendon diameter. At the end of the beam/slab, i.e. at an anchor, the tendons are taken on the neutral axes.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus half the sheathed tendon diameter.

The drape of the tendon is then calculated as

( )( )( )Length

RLLengthbbbdrape

−−−+= 22/31

The tendon force required to produce the balanced load Wbal is then given by

drapeLengthRLLengthW

T balreq ×

−−=

8)(15.1 2


tendon

reqtendons UTS

TN

7.0=

Harped tendons in cantilever spans

For a cantilever span with a harped tendon profile, the profile is taken as a straight line from the neutral axis at the cantilever end to the highest position over the internal support.

In the calculations, the minimum radius Rmin specified is used in determining the final slopes of the tendons. The program chooses the following values:

• The left offset, L, is chosen as zero.

• The right offset, R, is set equal to the span length.

• The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the right end) is chosen on the neutral axis.

• The tendon position over the internal support is taken as high as possible. The value of b3 (b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed tendon diameter.


The position of the start of the radius of the internal support, xw, is calculated as

)(2 13min2 bbRLengthLengthxw −−−=

Further, the corresponding vertical offset for the start of the radius, yw, is given by

min

2

2Rx

y ww =

and the slope of the tendon as

−−−

=Θw

w

xLengthybb 13arctan


Θ=

sin15.1 bal

reqW

T


tendon

reqtendons UTS

TN

7.0=

Harped tendons in end spans

For an external span, a harped tendon profile is chosen to give maximum eccentricities over the internal support and at midspan. The eccentricity at the end support is chosen to be zero to eliminate moments.

The following values are chosen:

• The left and right offsets, L and R, are set to span length divided by four.

• The eccentricity at the end of the beam/slab end is taken as zero, i.e. b1 (b3 for a right end span) is chosen on the neutral axis.

• The eccentricities at both ends are taken as high as possible. The value of b3 (b1 for a right end span) is thus taken as the top cover plus half the sheathed tendon diameter.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus half the sheathed tendon diameter.



)(244 23min

2

bbRLengthLength

xw −−

−=

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2Rx

y ww =


( )w

balreq

xLengthd

Lengthd

WT

−⋅+

⋅

=

316

316

15.1

21

where

3)(2 21

1bb

d−

=

3)(2 23

2byb

d w −−=

The number of tendons required is then given by

tendon

reqtendons UTS

TN

7.0=

Harped tendons in internal span

Maximum eccentricities are chosen over the supports and at midspan for an internal span with a harped tendon profile.

The following values are chosen:

• The left and right offsets, L and R, are set to span length divided by four.

• The eccentricities at both ends are taken as high as possible. The values of b1 and b3 are thus taken as the top cover plus half the sheathed tendon diameter.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus the half the sheathed tendon diameter.



)(244 23min

2

bbRLengthLength

xw −−

−=

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2Rx

y ww =


( )( )

−⋅

+=

w

balreq

xLengthdd

WT

31616

15.1

22

where

3)(2 21

1byb

d w −−=

3)(2 23

2byb

d w −−=

The number of tendons required is then given by

tendon

reqtendons UTS

TN

7.0=

Pre-stress losses In the following text, an explanation as given for the various components of pre-stress losses:

• Friction losses.

• Wedge-set.

• Long-term losses.

Friction losses in parabolic tendons

Friction losses are calculated for each span in turn. The calculation is started at the active end of each tendon. The effective tendon force is calculated at the end of the span taking into account the friction losses. This force is then carried over to the start of the next span for the process to be repeated.


The following is applicable to parabolic tendon profiles, including those cases where L and R are zero:

LengthLengthRan

LaRLengthm

)(

)2(

1

2

−=−−=

where

12 aaadif −=

These values are used to determine the position of the lowest point on the parabola, X, and are derived from the basic parabolic equations describing the tendon profiles. The position of the lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difap

x2

=

where

namp dif−= 2

If x ≠ 0, then the vertical position of the left inflection point, c1, is given by

XLa

c 11 = else c1 is zero.

If L ≠ X then the vertical position of the right inflection point, cs, is given by

XLengthRa

c−

= 22 else c2 is zero.

The following can then be calculated:

2321

22

22112

11

)(168

32

)()(8

3

Length

ddd

cd

cacad

cd

++=

=

−+−=

=

α


The effective pre-stressing force at the end of the span, Pe, can now be calculated:

Lengthkoe ePP )( += µα

where

Po = Applied tendon force

µ = Friction coefficient of the tendon against the sheath

α = Cumulative angle of curvature over length

k = Friction coefficient for unintentional variation form specified profile (’wobble’ in sheath)

Friction losses in harped tendons

The following is applicable to harped tendon profiles, including those cases where L and R are zero:

RLLengthl −−=2

The position of the end of the left minimum radius, xwL, is given by

1min2 2 aRLLxwL −−= for 1min

2 2 aRL >

0=wLx otherwise.

Corresponding to this

min

2

2Rx

y wLwL =

Similarly, the position of the start of the right minimum radius, xwR, is given by

2min3 2 aRRRxwR −−= for 2min

2 2 aRR >

0=wRx in all other cases.

Corresponding to this

min

2

2Rx

y wRwR =


The slopes of the three sections of tendon are now known. The change in slope α at each kink is then determined. At the first kink, friction losses occur over a length xwL and at the second kink over a length of 2 xwL. At the Last kink, friction losses occur over a length xwR and at the third kink over a length of 2 xwR.

Starting from the one side the force at the end of each kink is calculated as:

fricLkbeginend ePP )( += µα

where

Lfric = Portion over which the losses occur.

Wedge-set

As soon as the stressing jacks are released, a phenomenon known as ’wedge-set’ or ’wedge pull-in’ occurs.

In typical building slabs, the tendons normally pull in by about 5mm to 10 mm before the tendons grip onto the wedges in the anchor head. The influence on the tendon force is significant.

Because of frictional losses, the effect of wedge-set is to reduce the effective pre-stress over a limited length of tendon only. This length, labelled lw, is calculated by considering the average force loss over the entire length of the tendon:

lengthtendonTotal

PPm endbegin −

=

The length effected by wedge-set is then given by

m

EAdl spswsw =

where

Aps = Area of tendons

Es = Modulus of elasticity of tendons

ds = Wedge-set


The force loss over the length affected by the wedge-set can then be calculated:

w

psswslossws l

AEdP =

The tendon force profile can then be adjusted by reducing the tendon force at the live anchor by 2Plossws and taking the negative pre-stress loss gradient up to the position of wedge-set influence, lw.

Long-term tosses

The average steel strain in all the tendons is given by

pss

endpanbeginspanst AE

PsP

Σ+Σ

=2

)(ε

This summation is carried out over all spans for all tendons.

The creep strain is estimated as

φεcc

avgcreep EA

P=

where

Pavg = Average pre-stressing force

Ac = Concrete area

Ec = Concrete modulus of elasticity

φ = Creep factor

The percentage total losses can be calculated as

pss

creepshrinkage

AErelaxationLoss

Σ+

+=)(100

%%εε

where

εshrinkage = Shrinkage strain

εcreep = Strain due to creep


Load balancing Captain uses a load balancing approach when generating tendons. The average tendon force, Pav, is calculated for each span and each tendon. Pav is used to calculate the equivalent load from the central portion of the tendon. The tendon force values at the beginning and end of each span are used to calculate the equivalent loads for the reversed parabolic portions of parabolic tendons and for the point loads from harped tendons at supports.

Equivalent load for parabolic tendons

Consider a typical span with parabolic tendons. The procedure described next for calculating the equivalent loads is applicable to cantilever and end spans as well.

The following values are used to determine the position of the lowest point on the parabola and are derived from the basic parabolic equations describing the tendon profiles.

LengthLengthRan

LaRLengthm

)(

)2(

1

3

−=−−=

where

13 aafadi −=

These values are used to determine the position of the lowest point on the parabola, X, and are derived from the basic parabolic equations describing the tendon profiles. The position of the lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difap

X2

=

where

namp dif−= 2

If x ��WKHQ�YHUWLFDO�SRVLWLRQ�RI�OHIW�LQIOHFWLRQ�SRLQW��c1, is given by

XLa

c 11 = else c1 is zero.


If L ��X then the vertical position of right inflection point, cs, is given by

XLengthRa

c−

= 32 else c2 is zero.

If L > 0, the equivalent load starting at the left support is given by

21

2

L

PW begin=

If L = 0 then W1 = 0.

The central portion of the equivalent tendon load is calculated by using a length lcalc. The distance lcalc is measured from the lowest point of the parabola to the nearest inflection point.

If the left inflection point is nearest to the lowest point, then

LXlcalc −=

and the equivalent load in the centre portion

211

2)(

calc

av

l

caPW

−=

Else, if the right inflection point is nearest to the lowest point, then

RXLengthlcalc −−=

and the equivalent load in the centre portion

223

2)(

calc

av

l

caPW

−=

If R > 0, the equivalent load ending at the right support is given by

232

R

PW end=

If R = 0 then W3 = 0.

If the value of X is equal to zero, it implies that the tendon is horizontal at the beginning or end of the span. If the value of L or R is equal to zero, it means that there is no reverse portion of the parabola. In such a case a point load is calculated which acts downwards at the support.


If L is zero, the slope of the tendon is calculated as

=Θ

Xa12

arctan

The downward point load is then given by

Θ= sinPP begint

Similarly, if R is zero, the slope of the tendon is calculated as

=Θ

Xa32

arctan

The downward point load is then given by

Θ= sinendt PP

If a tendon is stopped off away from the neutral axis, a point moment is generated in the slab. The magnitude of this moment is given by:

tendontendont ePM ⋅=

where

etendon = Tendon eccentricity measured from the section neutral axis.

Equivalent load for harped tendons

Consider a typical span with harped tendons. The procedure described next for calculating the equivalent loads is applicable to both cantilever and end spans.

The four point loads caused by the typical harped tendon are labelled P1 to P4. The central portion of the tendon is assumed to be horizontal, causing no vertical components of force.

The sloped ends with offset lengths L and R cause upward or downward point loads where they change direction at the support or at the offset points to the horizontal portion. In practice, the change in direction of the tendon occurs over a short distance dictated by the allowable minimum radius of the tendon. For calculation purposes the vertical components are calculated as point loads at the theoretical intersection points of the straight portions.


The tendon forces used in the calculation are Pbegin end Pend, which are the tendon forces at the beginning and end of each span. For calculating the values of P2 and P3, the tendon force is interpolated linearly between the end values.

The equivalent loads are given by

223

34

43

12

221

11

)(1

)(1

Rb

bPP

LengthP

RPPPP

LengthP

LPPPP

Lb

bPP

end

end

endbegin

begin

endbegin

begin

+=

−+=

−+=

+=

Calculation of concrete stresses Tensile stresses calculated on un-cracked sections do not always correlate well with cracking. For this reason, Report 2 of the JSD does attach great value to concrete stresses as a serviceability limit state. However, tensile stresses are a good indicator of where cracking may be a problem and could therefore be useful during preliminary design. The stress checks will be useful if you have been using the Report 25 provisions in the past.

Stress envelopes are calculated for the following two cases:

• At transfer of tendon forces: Only initial dead loads are considered at transfer. Additional dead loads are only considered later at SLS. On the Loads input screen, a dead load is considered as an initial dead load except if the letter ’A’ is entered before or after the load value. In that case, the load is taken as an additional dead load to be considered at SLS only and will not be considered at transfer.

• At SLS: The full SLS loads, i.e. initial dead load, additional dead load and live load, are applied and long-term losses in tendon forces are included.

Note: Tensile concrete stresses are not considered when generating tendon profiles. The pre-stressing is considered as an external load with a load balancing effect. Typical bridge design code checks for class 1, 2 and 3 structures should be done in an iterative way by manually checking the stress diagrams.


Reports 2 and 25 gives the following allowable concrete stresses for flat slab construction:

Permissible Tension Loading

Condition Permissible

Compression Bonded Un-bonded

Transfer

Sagging 0.33fci 0.45√fci 0.15√fci

Hogging 0.24fci 0.45√fci 0

Serviceability limit state

Sagging 0.33fcu 0.45√fcu 0.15√fcu

Hogging 0.24fcu 0.45√fcu 0

The allowable stresses tabled above apply to post-tensioned flat slab design. Different values may apply to the design of other types of members. Refer to the relevant design code for allowable stresses for class 1, 2 and 3 pre-tensioned and post-tensioned members.


Deflection calculation Both short-term and long-term deflections are calculated. No moment redistribution is done at serviceability limit state.

Code guidelines

Deflection can generally be controlled in the preliminary design by limiting span to depth ratios. Report 2 of the JSD gives the following guidelines for flat slabs where at least half of the dead plus live load is balanced by pre-stress:

Type of Slab Loading Intensity

Maximum span to depth ratio

Light 40 to 48

Normal 34 to 42 Flat Slabs

Heavy 28 to 36

Waffle Slabs Heavy 28 to 32

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-cracked concrete sections are used.

Long-term deflections

Long-term deflections are determined by first calculating the cracked transformed sections:

3. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

4. The cracked transformed sections are then calculated at 250 mm intervals along the length of the beam. The results of these calculations are tabled in the Crack files on the View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the amount of reinforcement required at ULS. However, once reinforcement is generated for beams, the actual entered reinforcement is used instead. You can thus control deflections by manipulating reinforcement quantities.


Next, the long-term deflection components are calculated by numerically integrating the curvature diagrams:

5. Shrinkage deflection is calculated by applying the specified shrinkage strain. Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in the beam.

6. The creep deflection is calculated by applying the total dead load and the permanent portion of the live load on the beam. The modulus of elasticity of the concrete is reduced in accordance with the relevant design code.

7. The instantaneous deflection is calculated by applying the transient portion of the live load on the transformed crack section.

8. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together with cracked transformed sections, which implies plastic behaviour. Although this procedure is performed in accordance with the design codes, the use of elastic moments together with cracked sections in the same calculation is a contradiction of principles. As a result of this, long-term deflection diagrams may show slight slope discontinuities at supports, especially in cases of severe cracking.

Crack width calculation In the calculation of crack widths, the program takes into account all bonded tendons and also any additional reinforcement that has been entered. The effect of the axial compressive concrete stress due to pre-stressing is also taken into account. Un-bonded tendons are ignored.

The crack spacing is calculated on the assumption that all unstressed bars and bonded tendons are spaced equally across the widest portion of the section. In flat slab design, it is common practice to have tendons banded in one direction. In such cases, tensile concrete stresses will tend to be concentrated at the position of the tendons. Therefore, the assumption that all unstressed bars and bonded tendons are spaced equally across the section, will likely yield conservative crack width values.

Calculation of additional flexural reinforcement The required reinforcement is based on supplying reinforcement for the tensile force in the concrete at a stress of 0.58fy. This is the method employed by the British Concrete Society Technical Report 25, published in 1984.

Note: Because the additional reinforcement is calculated using stress considerations, the suggested values are normally conservative. In the final analysis, you should check that the beam/slab has adequate strength at ultimate limit state.


Calculation of ULS capacity Ultimate limit state calculations are performed for the following:

• Bending moment.

• Linear shear.

• Punching shear.

Moment capacity

The moment capacity is calculated using general flexural theory. The tendon strain at ultimate limit state is given by

papepb εεε +=

where

εpe = Strain due to tendon pre-stress after losses

εpa = Additional strain due to applied loading

The strain due to pre-stress is determined from the stress-strain curve. If the pre-stress is within the elastic limit, the strain is given by

s

pepe E

f=ε

The additional strain, εpa, is determined by considering the change in concrete strain at the level of the tendon. The concrete strain distribution resulting from the effective pre-stress force is shown as a dashed line in the figure.


Thus, for bonded tendons, the additional tendon strain is given by

uepa εεε +=

where

ce E

prestressConcrete=ε at the level of the tendons

For un-bonded tendons

uepa εεε +<

In general, one can say

uepa εβεβε 21 +=

where

β1 and β2 = Bond coefficients

The program uses the following typical bond coefficients values:

Tendon bond coefficients

Pre-tensioned and bonded post-tensioned tendons

Un-bonded post-tensioned tendons

β1 1.0 0.5

β2 1.0 0.1

It now follows that

cuepa xxd εβεβε −+= 21

and

cuape

papepb

xxd εβεβε

εεε−++=

+=

21

This can be rewritten as

cpepbcu

cu

dx

εβεεεβεβ

12

2

−−+=


From equilibrium it follows that

bxfkAf cupspb 1=

Therefore

cpepbcu

cu

ps

cupb A

bdfkf

εβεεεβεβ

12

21

−−+⋅=

The values of fpb and εpb are solved by iteration using the stress-strain curve to subsequently yield the neutral axis depth, x.

The ultimate moment of resistance is then calculated as

)( 2xkdAfM pspbu −=

The calculated ULS capacity envelopes for bending moment and shear force incorporate all tendons and additional reinforcement entered. Strain is calculated on the assumption that plane sections remain plane and concrete and steel stresses are then calculated correspondingly.

Note: The secondary moments, or a portion thereof, caused by pre-stressing may optionally be included in the ULS calculations. Refer to page 6-9 for information on specifying the percentage of secondary moment to be included in the analysis.

Linear shear

The linear shear checks performed by the program are done according to the provisions of codes using the procedure described below.

An analysis is done on the sub-frame with only the equivalent tendon loads applied. The minimum fibre stress as a result of the tendon forces is then calculated as

ZM

AP

fconcrete

tendonspt +=

The section modulus, Z, is taken at the top for negative bending and at the bottom for positive bending.

The cracking moment is then calculated as

Z

f.M pt

o

80=

The section is considered as cracked in areas where the ultimate moment exceeds the cracking moment.


In areas that are un-cracked, the shear capacity is calculated as

tcptwco ff.fhb. V 80670 2 +=

where

ft = Concrete tensile strength

= cuf.240

fcp = Average concrete compressive pre-stress

= concrete

tendons

AP

for rectangular sections

= I

zP

AP ftendons

concrete

tendons + for flanged sections

zf = Distance from the neutral axis to the junction of the flange and the web of the section which falls inside the compression zone

In areas that are cracked, the shear capacity s given by

MVM

db)vf

f.- ( V o

wcpu

pecr += 5501

where

tendon

tendons

pu

pe

UTSP

f

f

×=

tendonsofNo

The value of vc is calculated by taking into account the total area of pre-stressing tendons and unstressed steel.

In areas that are cracked, the shear capacity Vcap is the minimum of Vco and Vcr calculated above.

The shear forces are reduced by the vertical components of the tendon forces if this was specified. Where the shear force V is less than 0.5 × the shear capacity Vcap, no shear reinforcement is required. Shear reinforcement must be supplied in zones where (Vcap + 0.4bwd) ≥ V ≥ 0.5Vcap:

f.

b.

SA

yv

w

v

sv

87040=


If V > Vcap + 0.4bwd then

tyv

cap

v

sv

df.

V - V

SA

870=

where

dt = Depth to the bottom reinforcement or tendons about which the stirrups are taken.

Linear shear is normally not a problem in flat slabs, but comes into play if ribbed slabs and beams are analysed. For flat slabs, punching shear is normally the main shear design criterion.

Evaluation of punching shear The first item to be determined is the enhanced shear. Columns have to be considered as either internal, edge or corner columns. For purposes of calculations done by the program, the following is assumed:

• If no edges are closer than 5d from the column centre, the column is considered to be an internal column.

• If one edge is closer than 5d from the column centre, the column is considered to be an edge column.

• If two edges are closer than 5d from the column centre, the column is taken as a corner column.

The enhanced shear force, Veff, for an internal column is then calculated as the largest of

V. V

)Vx

M. V( V

)VyM

. V( V

eff

b

yeff

b

xeff

151

0511

0511

=

+=

+=


where

Mx = Moments transferred between slab and column in the X direction, i.e. about the Y-Y axis

My = Moments transferred between slab and column in the Y direction

xb = Projected width of the critical perimeter in the X directions

yb = The projected width of the critical perimeter in the Y direction

Note: The factor 1.05 is derived from 1.5M as given by the codes, with a 30% reduction allowed if the equivalent frame method with pattern loading has been used in calculating the moments.

For an edge column, the enhanced shear force is the largest of

V. V

)VxM

.. V( V

eff

eff

251

051251

=

+=

If the edge lies parallel with the X-axis, then M = Mx and x = yb. Similarly M = My and x = xb for the edge parallel to the Y-axis.

For a corner column, the enhanced shear force is given by

V. Veff 251=

The effective shear force is then adjusted by the vertical components of the tendon forces as specified. The shear capacity is subsequently checked for each perimeter and reinforcement calculated.

The shear capacity on a specific perimeter is given by

duvV critccap =

where

ucrit = Critical perimeter

d = Effective slab depth

The value of vc is calculated for both the x and y-directions and the average of the two values used. If Veff exceeds Vcap, shear reinforcement is calculated as

yv

crit

yv

critceffsv f

duf

duvVA

87.04.0

87.0≥

−=Σ

The shear reinforcement represents vertical links to be placed in slabs deeper than 200 mm.


Circular columns

Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992, the use of circular perimeters seems a more rational approach to evaluating punching shear for circular columns. The program recognises this and uses the following design approach for checking punching by circular columns:

• As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx and vcy. Put differently, one could consider an imaginary square shear perimeter when determining vc.

• The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter circular perimeter (compared to a rectangular perimeter) yields a lower (conservative) shear force capacity.


Input

The beam/slab definition has several input components:

• Parameters: Material properties, load factors and general design parameters.

• Tendon data: Tendon properties and profile generation options.

• Sections: Enter rectangular, I, T and L-sections.

• User-defined sections: Complex section geometries.

• Spans: Define spans and span segments.

• Supports: Define columns, simple supports and cantilevers.

• Column heads: Square and tapered drop panels.

• Loads: Uniform distributed loads, point loads and moments.

• Load combinations: User-defined combination of load cases.

Parameters input The following general parameters are required for analysis and design:

• fcu: Characteristic 28day strength of concrete (MPa).

• fy: Characteristic strength of additional un-tensioned reinforcement (MPa).

• fyv: Characteristic strength of shear reinforcement (MPa).

• fci: Characteristic strength of concrete at transfer of pre-stress (MPa).

• Ec: Concrete modulus of elasticity (kPa).

• Est: Modulus of elasticity of unstressed steel (kPa).

• Density: Concrete density used for calculation of own weight.

Note: Own weight is automatically added to the dead load with the ’auto load combination’ mode selected and to the first load case with the ’user load combination’ mode selected – refer to page 6-9 for more detail on the load combination modes.

• Top cover: Concrete cover to top of tendon sheaths (mm).

• Bottom cover: Concrete cover to bottom of tendon sheaths (mm).

• Reduce moments to column face: If selected, this option will take the moments at the column faces as the design moments rather than the moments at support centres.


• Reduce shear by tendon force component: Select this option to include the effect of tendons in punching shear checks.

• SLS DL factor: Serviceability limit state dead load factor used for calculation of deflection, stresses and crack widths.

• SLS LL factor: Serviceability limit state live factor.

• ULS DL factor: Ultimate limit state dead load factor used for calculation of moments, shear and reactions.

• ULS LL factor: Ultimate limit state live load factor.

Note: In the automatic load combination mode, the ULS load factors are used with the patterned dead and live loads. The load factors are ignored when using the user load combination mode. Refer to page 6-9 for more detail on specifying your own load combinations. The procedure of automated pattern loading is explained on page 6-9.

• Redistribution: Percentage of moment redistribution to be applied. Redistribution should be limited 10% in structures over four storeys high where the frame provides lateral stability.

• Optimised/downward: Method of moment redistribution.


• Secondary moment: Moments resulting from reactions to the pre-stress in statically indeterminate beams. Some design methods, e.g. the method given in Report 25, ignore secondary moments. Report 2 of the JSD recommend the tendons be considered as external forces with a load-balancing effect and hence secondary moments are to be taken into account.

• Live load permanent: Percentage of live load to consider as permanent when calculating long-term deflections.

• Attached torsional members: This option enables the reduction in column stiffnesses as allowed for by ACI 318 - 1989. To prevent overestimation of column moments, it is recommended that this option should be enabled. For more detail on the sub-frame analysis technique used by the program, refer to page 6-9.

• Edge beam: This option only applies if attached torsional members are used and allows for the case where the columns are framing into the slab on one side only.

• I: The thirty-year creep factor used for calculating the final concrete creep strain.

• Hcs: Thirty-year drying shrinkage of plain concrete.

The graphs displayed on-screen give typical values for the creep factor and drying shrinkage strain. In both graphs, the effective section thickness is defined for uniform sections as twice the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made, stresses and relative humidity may vary considerably during the lifetime of the structure and appropriate judgements should be made.

Tendon data input Characteristics can be entered for up to three types of tendons or cables:

• Bonded: Classify tendons as bonded (grouted after stressed) or un-bonded.

• Ultimate strength: Ultimate tensile strength (UTS) of one tendon or cable (kN).

• Maximum stress: Maximum tensile stress as a percentage of the UTS.

• Outside diameter of sheath: The diameter of a tendon or cable, including sheath or duct (mm). The program measures concrete cover to the outside diameter.

• Tendon area: The cross sectional area of the tendon or cable itself (mm2).

• k: Friction coefficient due to unintentional variation from the specified profile (’wobble’ in the sheath). Both BS 8110 and SABS 0100 - 1992 recommend a value of not less than 33E-4 in general. Where wobbling is limited, e.g. rigid ducts with close supports, a


reduced value of 17E-4 may be used. For greased tendons in plastic sheaths, a value of 25E-4 may be taken. However, for greased tendons, both FIP and Report 2 of the JSD recommend a value of 10E-4.

• � Friction coefficient due to curvature of the tendon. BS 8110 - 1997 and SABS 0100 - 1992 recommend values ranging from 0.55 to 0.05, depending on the condition of the strand and the duct. For greased tendons, FIP and Report 2 of the JSD recommend values of 0.05 and 0.06 respectively.

• Wedge pull-in: Movement of the tendon will occur when the pre-stressing force is transferred from the tensioning equipment to the anchorage, causing a loss in pre-stress. The magnitude of the draw-in depends on the type of tendons used and the tensioning equipment. Values of 4 to 8 mm are common for flat slab construction.

• Tendon / Cable relaxation: Percentage long-term loss of force due to cable steel relaxation.

• Es: Modulus of elasticity of tendon (kPa). This value is typically set to 195E6 kPa.

• Minimum radius: The minimum radius to use for harped tendons at change of slope (m). This value is ignored when using parabolic tendons.


Sections input You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be move horizontally to obtain eccentric sections, for example L-sections. Whole sections can also be moved up or down to obtain vertical eccentricity.

Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a straight line. Vertical offsets of sections are used when calculation of tendon eccentricities and has no other effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

• Sec no: The section number is used on the Spans input page to identify specific sections (see page 6-9).

• Bw: Width of the web (mm).


• D: Overall section depth, including any flanges (mm).

• Bf-top: Width of optional top flange (mm).

• Hf-top: Depth of optional top flange (mm).

• Bf-bot: Width of optional bottom flange (mm).

• Hf-bot: Depth of optional bottom flange (mm).

• Y-offset: Vertical offset the section (mm). If zero or left blank, the top surface is aligned with the datum line. A positive value means the section is moved up.

• Web offset: Horizontal offset of the web portion (mm). If zero or left blank, the web is taken symmetrical about the beam/slab centre line. A positive value means the web is moved to the right.

• Flange offset: Horizontal offset of both the top and bottom flanges (mm). If zero or left blank, the flanges are taken symmetrical about the beam/slab centre line. A positive value means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to enter a thin web with a wide top flange. You can also enter wide web (actual top flange) with a thin bottom flange (actual web). The linear shear steel design procedure works with the entered web area, i.e. Bw × D, as the effective shear area. Although the two methods produce similar pictures, their linear shear modelling is vastly different.


User-defined sections input Complicated sections can be defined with the aid of the section properties calculation module, Prosec.

If Prosec is included in your set of programs, it can be used for entering sections as follows:

• Enter the section dimensions in millimetres.

• Save the input data to a file, e.g. ’Deck.G01’.

• Calculate the bending sect-ion properties.

Section properties calculated by Prosec are subsequently used to derive an equivalent I-section. It is important that the area and inertia values of the effective I-section tie up. The program limits the non-dimensional parameter I/(Ad2) to the range 0.02 to 0.225.

The properties of the user-defined sections are:

• Sec no: Number of the section to be referenced when you enter spans on the Spans input page (see page 6-9).

• Designation: Prosec file name. If the cursor is on a defined section when you press the Prosec button, the relevant section will automatically be loaded and displayed in Prosec.

• Area: Gross sectional area as calculated by Prosec (mm2).

• Shear Area: Enter the area likely to transmit the vertical shear (mm2). Use your own judgement on what portions of the section are suitable for transmitting shear.

• Ix: Second moment of inertia about the X-axis calculated by Prosec (mm4)

• Neut Axis: Position of the neutral axis as measured from the bottom of the section (mm).

• Y-plas: Plastic neutral axis position. (mm).

• Y-top: Offset of top surface from the datum line (mm). This value will initially be set to zero but can be adjusted to move the section up (positive) or down.

• Y-bottom: Offset of bottom surface from the datum line (mm). The section depth is given by Y-top minus Y-bottom.


Note: The derived equivalent I-section is not unique – more than one solution is possible. The derived section merely serves the purpose of simplifying the section for use by the program. If a particular equivalent section does not seem like a realistic approximation of the original section, you should consider entering the section as a normal I-section on the preceding input page, using more appropriate section dimensions.

Spans input Sections specified on the Sections input and User sections input pages are used here with segment lengths to define spans of constant or varying sections.

Spans are defined by specifying one or more span segments, each with a unique set of section properties. The following data should be input for each span:

• Span no: Span number between 1 and 20. If left blank, the span number as was applicable to the previous row is used, i.e. another segment for the current span.

• Section length: Length of span or span segment (m).

• Sec No Left: Section number to use at the left end of the span segment.


• Sec No Right: Section number to use at the right end of the span segment. If left blank, the section number at the left end is used, i.e. a prismatic section is assumed. If the entered section number differs from the one at the left end, the section dimensions are varied linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are interpreted literally. If a rectangular section should taper to an L-section, for example, the flange will taper from zero thickness at the rectangular section to the actual thickness at the L-section. If the flange thickness should remain constant, a dummy flange should be defined for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than the web and its depth made equal to the desired flange depth.

Supports input You can specify simple supports, columns below and above, fixed ends and cantilever ends. To allow a complete sub-frame analysis, columns can be specified below and above the beam/slab. If no column data is entered, simple supports are assumed.

The following input is required:

• Sup no: Support number, between 1 to 2’. Support 1 is the left-most support.


• C,F: The left-most and right-most supports can be freed, i.e. cantilevered, or made fixed by entering ’C’ or ’F’ respectively. By fixing a support, full rotational fixity is assumed, e.g. the beam/slab frames into a very stiff shaft or column.

• D: Depth/diameter of a rectangular/circular column (mm). The depth is measured in the span direction of the beam/slab.

• B: Width of the column (mm). If zero or left blank, a circular column is assumed.

• H: Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank. In the analysis, the support will be considered as a normal simple support. However, when generating reinforcement bars, the program will extend the bars a distance equal to half the support depth past the support centre line.

• Code: A column can be pinned at its remote end by specifying ’P’. If you enter ’F’ or leave this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.


Column heads input The punching shear capacity of a flat slab can be enhanced by defining column heads or drop panels. If the ACI approach of column stiffness reduction is used, the stiffness of column heads is also included in the sub-frame analysis.

The following data can be entered at each column head:

• S/T: Specify a square or tapered column head. If left blank, a tapered head is used.

• Diameter/Depth: The depth (in span direction) or diameter, in the case of circular column heads (mm).

• Width: The width of a rectangular column head (mm). Leave this field blank if the column head is circular.

• Height: The height of the column head (mm).

Note: The program will not check the validity of a column head in relation to column. It is possible, for example, to define an unpractical circular column head for a rectangular column.


Loads input Dead and live loads are entered separately. The entered loads are automatically patterned during analysis. For more detail on the pattern loading technique, refer to page 6-9.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines as necessary to define each load case. Defined loads as follows:

• Case D,L: Enter ’D’ or ’L’ for dead load or live load respectively. If left blank, the previous load type is assumed. Use as many lines as necessary to define a load case.

• Span: Span number on which the load is applied. If left blank, the previous span number is assumed, i.e. a continuation of the load on the current span.

• Wleft: Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.

• Wright: Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.

• P: Point load (kN).

• M: Moment (kNm).


• a: The start position of the distributed load, position of the point load or position of the moment (m). The distance is measured from the left-hand edge of the beam. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam.

• b: The end position of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation. For more detail, refer to the explanation of the Parameters input on page 6-9.

Note: If you enter a concrete density on the Parameters input page, the own weight of the beam/slab is automatically calculated and included with the dead load.

Load combinations input Load cases can be optionally be combined into load combinations.


Two loading modes are available:

• ’Automatic load combinations’ allows for automatic pattern loading of dead and live loads, e.g. as for typical building slabs.

• ’User load combinations’ allows for combinations of the entered load cases, e.g. as for bridge decks.

Note: No load combinations need be entered if the automatic load combination mode is selected.

As many lines as necessary may be used to input combinations of the various load cases:

• Load Combination: Name of the load combination. If this field is left blank, the load combination is taken to be the same as for the previous row in the table.

• Load Case: Number or name of the load case.

• ULS Factor: Load factor with which the load case should be multiplied for the ultimate limit state.

• SLS Factor: Load factor with which the load case should be multiplied for the serviceability limit state.


Tendon Profiles

You can let the program generate tendon profiles or you can enter profiles as required. The program is capable of generating reasonable tendon profiles for typical beams and slabs that you can adjust and change to obtain the required result.

Generated tendons can have parabolic or harped profiles. The program attempts to generate tendons to balance the specified percentage of dead load. Profiles generated will not be perfect for all cases and may require some manual adjustment.

Tendon profiles are displayed one set at a time, where a set is defined as one or more tendons with the same profile and force distribution. The following parameters define the profile for each span:

• L: Left offset of tendon inflection point (parabolic) or slope change (harped) from left end of span (m).

• R: Right offset of tendon inflection point or slope change from right end of span (m).

• b1: Distance from top surface to tendon centre line at left end of the span (mm).

• b2: Distance from bottom surface at midspan to tendon centre line (mm).


• b3: Distance from top surface to tendon centre line at right end of the span (mm).

Tip: The values of L and R are normally taken is the greater of span divided by and 250mm for parabolic cables and span divided by four for harped cables.

The following properties cab be set for each group of tendons:

• Number of tendons: Number of tendons in the set.

• Tendon property no: Tendon property number 1, 2, or 3 as defined in the original input.

• Life end position: Position of live end from left hand side of entire beam or slab.

• Dead end position: Position of dead end from left hand side of entire beam or slab.

• Parabolic / Harped: Parabolic or harped tendons.

The plotted tendon force diagrams represent the total force of all tendons:

• The initial tendon forces are shown in blue and include losses due to friction, wedge slip and elastic shortening of the concrete.

• The final tendon forces are shown in red and include the long-term effects, tendon relaxation, shrinkage and creep of the concrete.

The equivalent balancing loads are also displayed. The balancing loads are shown as percentage of the equivalent dead load. The latter is defined as the total dead load for each span, including own weight and any applied dead load, divided by span length.

Tip: Even if you want to specify your own tendon profile, it is nearly always easier to allow the program to generate the tendon profiles and then edit them, delete some or add more tendon groups.


Reinforcement

Additional bending reinforcement and punching shear reinforcement can be designed interactively.

Additional bending reinforcement Diagrams are displayed for additional reinforcement required (blue lines) and reinforcement entered (red lines). Anchorage and bond lengths are taken into account.

The required additional unstressed reinforcement is calculated in accordance with the Concrete Society Technical Reports 17 (paragraph 3.3 and 4.3) and 25 (paragraph 4.11):

• A minimum of 0.15% unstressed reinforcement is taken over columns over a width equal to the column width plus four times the slab width.

• Where tensile stress prevails over supports, reinforcement is supplied to resist tensile force.

• At midspan and where the tensile concrete stress exceeds 0.15fcu, a working stress of 0.58fy is used in the reinforcement.


Tip: The method used to calculate reinforcement aims to limit tensile concrete stress by adding sufficient reinforcement and tends to be conservative. Less reinforcement can normally be used, say three quarters of the peak values. In the final analysis you should check that the various requirements for crack width, ULS capacity and nominal reinforcement are met.

Reinforcement bars are entered as follows:

• Span: Span number

• T/B: Reinforcement at Top or Bottom

• Bar: Specify the steel as individual bars, e.g. 3T16, 2Y20 or 4R16, or groups of bars, e.g. Y25@300. One can also combine bars, e.g. 2T16 + T10@250.

• L/R: If a hook or bend is required on the left end of the bar, enter an ’H’ or ’B’ in the L column. For a hook or bend on the right end of the bar, use the R column.

• X: Position of left end of the bar measured from the left end of the span (m).

• Length: Length of the bar (m).

Punching shear reinforcing The data required for punching shear design is categorised as follows:

• Geometrical input.

• Forces and parameters required calculating the effective shear force Veff.

• Tendons and additional reinforcement to consider when calculating the allowable shear stress, vc.

The following parameters are required to define the column and slab geometry:

• A: Column dimension in longitudinal direction (mm). If a column below was originally input, its D value will be used as default.

• B: Column dimension in transverse direction (mm). If a column below was originally input, its B value will be used as default.

• C: Column head dimension in longitudinal direction (mm). Leave this field blank if there is no column head.

• D: Column head dimension in the transverse direction (mm). Leave this field blank if there is no column head.

• Deffx: Effective depth for reinforcement orientated in the X-direction (mm).

• Deffyx: Effective depth for reinforcement orientated in the Y-direction (mm).


• X: Longitudinal distance from the support centre to the edge of the slab (mm).

• Y: Transverse distance from the support centre to the edge of the slab (mm).

• Corner: Enter ’Y’ for an outside corner or ’N’ for an inside corner.

For the calculation of the effective shear force Veff, the program detects internal, edge and corner columns as follows:

• Internal column: Both edges further than 5deff from the column centre.

• Edge column: One edge closer than 5deff from the column centre.

• Corner column: Two edges closer than 5deff from the column centre.

Information required calculating the effective shear force Veff:

• Vt: Total Shear force transferred from slab to column.

• Mtx: Moment transferred between slab and column in X-direction.

• Mty: Moment transferred between slab and column in Y-direction.

Note: Irrespective of the selected loading combination mode, the program will assume that pattern loading would have been applied. The program therefore automatically reduces the entered values for Mtx and Mty by 30%. Refer to BS 8110 - 1997 clauses 3.7.6.2 and 3.7.6.3 and SABS 0100 - 1992 clauses 4.6.2.2 and 4.6.2.3 for detail.

• UDL: Uniform ultimate load in the region of the column (kN/m). The shear force is reduced by the portion of load within each perimeter considered.

• Pcx: The pre-stressing force in the longitudinal direction deemed to have a shear relieving effect (kN). The value will default to the total pre-stressing force of all tendons. This may be accurate for banded tendons. However, for tendons spaced further apart, only those passing through the shear perimeters should be considered. The vertical component of the entered total pre-stressing force is deducted from the effective shear force.

• Pcy: The pre-stressing force in the transverse direction deemed to have a shear relieving effect (kN). This value must be entered manually.

• Slope-X: Average slope of tendons in X-direction crossing the punching shear perimeters. The slope is used to calculate the vertical component of the pre-stress relieving the effective shear force. The program will base the initial value on the generated tendon profiles.

• Slope-Y: Average slope of tendons in Y-direction crossing the punching shear perimeters. The value must be entered manually.

Note: Although the program performs a uni-directional analysis for bending moment, deflections, etc, bi-directional effects are included in the punching shear design procedure.


Tip: For orthogonally stressed slabs, it is recommended that you design one direction, e.g. the banded direction, and record the relevant punching shear values. On analysing the other direction, you can enter these parameters for the Y-direction entered for complete bi-directional punching shear checks.

The shear capacity is based on the following parameters:

• Type: The number of the tendon types entered on the Parameters input page – refer to page 6-9 for detail. The specified type's properties are used to calculate the pre-stressed reinforcement passing through each perimeter.

• N cables: Number of cables passing longitudinally through each perimeter (average per side) in the X (longitudinal) and Y-directions (transverse). The area of the pre-stressed cables is then incorporated in the calculation of the shear resistance Vc.

Note: When calculating the shear resistance Vc, both bonded and un-bonded tendons are considered.


• Ast: Amount of conventional reinforcement passing longitudinally through each shear perimeter in the X and Y-directions. The reinforcement values Asx and Asy represent the minimum amount of main reinforcement crossing each perimeter in the X and Y-directions. For a perimeter edge on both side if the column, e.g. y1 in the sketch, you should use the minimum of the amount of reinforcement crossing the left edge and the amount crossing the right edge. For a perimeter edge on one side only, e.g. y2 in the sketch, use the amount of reinforcement crossing that single edge.

Note: The amount of conventional reinforcement can be taken as the average (minimum for unsymmetrical reinforcement) amount passing through the perimeter on the left and the right (as seen on the screen) of the column. For an edge or corner column, the amount should be taken equal to the amount passing through the perimeter on the span side.


Design

The analysis is performed automatically when you access the View output pages.

Analysis procedure Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections, concrete stresses and cracking are calculated by analysing the beam/slab under pattern loading using the gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-9 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-9. The resultant bending moment and shear force envelopes are then redistributed. Finally, the required reinforcement is calculated.

Fixing errors that occurred during the analysis The Input pages incorporate extensive error checking. However, serious errors sometime still slip through and cause problems during the analysis. Common input errors include:

• Entering too large reinforcement cover values on the Parameters input screen, gives incorrect reinforcement. Cover values should not be wrongly set to a value larger than half the overall section depth.

• Not entering section numbers when defining spans on the Spans input screens causes numeric instability. Consequently, the program uses zero section properties.


Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful examination of the analysis output. View the long-term deflection diagrams and determine which component has the greatest effect:

• The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the middle of spans generally induces negative shrinkage deflection, i.e. uplift.

• Large creep deflections (long-term deflection under permanent load) are often caused by excessive cracking, especially over the supports. Compare the span to depth ratios with the recommended values in the relevant design code.

• Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection component.

Viewing output graphics The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of any load case.

Deflections

The elastic deflection envelope represents the deflections due to SLS pattern loading. The long-term deflection diagram represents the behaviour of the beam/slab under full SLS loading, taking into account the effects of shrinkage and creep:

• The green line represents the total long-term deflection.

• The shrinkage deflection is shown in red.


• The creep deflection (long-term deflection due to permanent loads) is given by the distance between the red and blue lines.

• The distance between the blue and green lines represents instantaneous deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-term deflection values are based on the reinforcement required at ultimate limit state. Once reinforcement has been generated for a beam, the long-term deflections will be based on the actual reinforcement instead.


Moments and shear forces

The bending moment and shear force diagrams show the envelopes due to ULS pattern loading. The capacities are calculated from the entered tendons and conventional rein-forcement. Capacities are shown in blue and actual moments and shear forces in red.

Concrete stress

Serviceability limit state stress envelopes are displayed for the following cases:

• At transfer of tendon forces: Only initial dead loads and no additional dead loads are considered.

• At SLS: The full SLS loads are applied and long-term losses in tendon forces included.

The actual stress envelopes are shown in red and the allowable stresses in blue. Guidelines for allowable concrete stresses are given on page 6-9.


Crack widths

In the calculation of crack widths, the program takes into account all bonded tendons and also any additional reinforcement that has been entered. The crack spacing is calculated on the assumption that all the bars and bonded tendons are spaced equally across the widest portion of the section.

Un-bonded tendons are ignored when calculating crack widths. If too few bars or bonded tendons are present, rotations in the sections will be high and unrealistic values of deflection will result. The program will give a warning when this occurs.


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings are available to include input and design diagram and tabular result.




Profile Scheduling

Designed tendons can be scheduled as Padds compatible drawings. Profile properties are taken from the Tendon profiles input page. Enter Padds file name special notes that should appear on the schedules and then click Generate schedules.

The resulting schedule can be opened in Padds for further editing and printing.

Tendon detailing in Padds

Apart from other reinforcement detailing commands, Padds cab also draw tendons in plan.

Finite Element Slab Analysis 6-97

Finite Element Slab Analysis

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

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



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

Sign conventions Slab input is done using the global axes. The analysis output is given in a mixture of global axis and local axes values.

Global axes

The global axis system is nearly exclusively used when entering slab geometry and loading. Global axes are also used in the analysis output for deflections and reactions.

The global axes are defined as follows:

• For the sake of this definition, the X-axis is chosen to the right.

• The Y-axis always points vertically upward.

• Using a right-hand rule, the Z-axis points out of the screen.

Note: Unlike some other 3D programs that put the Z-axis vertical, this program takes the Y-axis vertical.

Local axes

Local axes are used in the output for bending stresses:

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

• The y-axis is taken parallel to the negative Z-axis.

• The z-axis is then taken vertical parallel to the Y-axis.

Shell element stresses

Shell element stresses are given using the local axes:


• Bending stresses: The entities Mx and My are moment per unit width about the local x and y-axes.

• Mxy represents a torsional moment in the local x-y plane.

• The principal bending moments per unit width are represented as Mmax and Mmin.

Note: To assist you in evaluating shell element stresses, stress contour diagrams show orientation lines at the centre of each shell element. An orientation line indicates the direction the direction (not axis) of bending or plane stress. In a concrete shell, the orientation line would indicate the direction of reinforcement resisting the particular stress.

Wood and Armer moments and shell reinforcement axes

Reinforcement is calculated in the user-defined x’ and y’-directions. Unlike the shell bending stresses that are taken about the x and y-axes, the Wood and Armer moments are given in the x’ and y’-directions. Refer to page 6-9 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 with plate bending behaviour. The bending formulation of the quadrilateral shell element was derived from the Discrete Kirchoff-Midlin Quadrilateral.

Accuracy of triangular elements

Both the quadrilateral and triangular elements yield accurate stiffness modelling. However, stress recovery from the triangular elements is not as accurate as is the case for quadrilateral elements. This means that deflections calculated using triangular elements are generally quite accurate, but moments may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stresses are calculated at the Gaussian integration points and subsequently extrapolated bi-linearly to


the corner point and centre point of each element. Stresses at common nodes are smoothed by taking the average of all contributing stress components.

Element layout

Consider a typical continuous flat concrete slab supported on columns or walls. To ensure accurate modelling of curvature, a minimum of about four elements should be used between bending moment inflection points. This translates to a minimum of about eight elements per span in both directions.

Using more elements per span often does not yield a significant improvement in analysis accuracy. In addition, the particular finite element formulation yields its most accurate results when the element thickness does not greatly exceed its plan dimensions.

For a typical concrete slab with a thickness of about one-tenth or one-fifteenth of the span length, a reasonable rule of thumb is to make the plan dimensions of the shell elements no smaller than the thickness of the slab. In other words, use a maximum of about ten to fifteen elements per span.

Concrete design Fesd can perform reinforced concrete design for shell elements. The Wood and Armer equations are used to transform the bending and torsional stresses to effective bending moments in the user-defined x’ and y’-directions.

Note: The Space Frame Analysis modules can design shells for in-plane stresses as well. Refer to Chapter 3 for detail.

Codes of practice

The following concrete design codes are supported:

• ACI 318 - 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:

• General input: Enter special design parameters.

• 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 6-9.

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 you using pictures of the structure:

• Use the Zoom buttons to zoom into a part of the structure or view it from another angle.

• Use the View Point Control to set a new viewpoint or camera position.

• Use the View Planes Control to view a slice through the slab.

The Options menu makes the following additional functions available:

• Graphics:

• Select whether you want items like node numbers and supports to be displayed.

• Display the structure with full 3D rendering, e.g. to verify the thickness of slab sections.

• Choose quick or detailed rendering. Quick rendering is faster than the detailed method, but you may find that some surfaces are drawn incorrectly.


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

• Contour values, like those on the reinforcement contour diagrams, can optionally be shown.

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

• Views: You can save the current viewpoint and graphic display options. The current view’s name is displayed on the picture. To re-use a saved view, click the view name on the picture to drop down a list of saved views. A detailed explanation is given in Chapter 2.

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

General input The General input page handles several important analysis parameters.

Concrete design parameters

Specify the concrete and reinforcement material properties, concrete cover to reinforcement and orientate the reinforcement axes. Refer to page 6-9 for more detail.

Envelope of load cases

Fesd calculates a set of results, including reinforcement values, for each load case or combination analysed. To enable you to easily identify the worst-case scenario, you can specify an envelope of load cases for which the minimum and maximum values are extracted.

The envelope can comprise load cases and/or load combinations. Results for the envelope is presented and can be accessed as if a separate load case.

Wizards

The wizards are suitable for the rapid generation of complete input files for some typical slabs.

Input generated this way can optionally be appended to existing data – you can therefore repeatedly use the wizards to generate complicated structures.


Note: The program is not limited to modelling only those slabs generated by the parametric modules. Any general two-dimensional slab can be treated. The parametric modules merely serve to simplify input of typical slabs.

Own weight

The own weight of the frame can be calculated using the entered cross-sectional areas and member lengths. If you specify a load case, the own weight is calculated and added to the other loads of that case.

The following are points of importance:

• By default, the own weight of the frame is set to not be included in the analysis. Be sure to select the appropriate load case for own weight or, alternatively, to include the frame’s own weight in the values of the loads entered.

• The list of load cases from which you can select is based on the load cases defined on the Point loads and Shell loads input pages. You may thus prefer to specify the own weight load case only after completing all other input for the frame. However, you can also enter the own weight load case at the start of the frame input process in which case you may ignore the warning message (that the load case does not exist).

Tip: If you wish to use own weight in its own separate load case, you can do so by defining an empty load case. You can enter a zero load at any node number, for example, and then select that load case as the one to use for own weight.

Adding input data to the Calcsheets

You can append the input tables (as they appear on the screen) to the Calcsheets by clicking the Add input tables to Calcsheets button.

You can add a picture from any input pages to the Calcsheets by clicking the Add to Calcsheets button next to the picture in question.

Title

Enter a descriptive name for the frame. It should not be confused with the file name you use when you save the input data.


Nodes input Use as many lines as necessary to enter the nodes defining the slab. A unique number must be assigned to each node. The node number is entered in the No column, followed by the X and Z-coordinates in the X and Z columns. If you leave X or Z blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the slab. You may also leave blank lines in the input to improve readability. If a node number is defined more than once, the last definition will be used.


Error checking

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

Generating additional nodes

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

• The 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. The coordinates 4 to 18 are spaced at 1.140 m and 0.472 m along the X and negative Z-axis respectively. The coordinates of the additional nodes are thus (1.140,14.142) and (2.280,13.670).

An alternative method to generate equally spaced nodes is to use the Inc to End option. This method allows you to define two nodes and then generate a number of nodes in-between:

• Use the same procedure as above to define the first node’s coordinates.

• Set the values of X-inc and Z-inc to the total co-ordinate difference to the last node and enable the Inc to End option. The last node’s coordinates are then first calculated and the specified number of intermediate nodes then generated.

Second order generation

Once you have defined one or more nodes in the table, you can copy that relevant row’s nodes by entering a '–' character in the No column of the next row. Then enter the number of additional sets of nodes to be generated in the No of column and the coordinate increments in the X-inc and Z-inc columns.


Second order generation example:

The following nodes are generated:

No X Z 15 0.00 5.12 16 2.00 5.22 17 4.00 5.32 18 0.50 6.12 19 2.50 6.22 20 4.50 6.32

Block generation

A group of nodes can be repeated by entering a ’B’ in the No column followed by the first and last 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 for each copy. The X and Z-coordinate increments are 10 m and zero respectively.

To copy one row only, simply omit the end row number, e.g. 'B10' to copy row 10 only.

The block generation function may be used recursively. That means that the rows specified may themselves contain further block generation statements.

Tip: To move a group of nodes to a new location without generating any new nodes, set the No-of to '1' and Inc to '0'.

Arc generation

A group of nodes can be repeated on an arc by entering an 'A' in the No column, followed by the start and end row numbers. Enter the centre of the arc in the X and Z columns and use the X-inc column to specify the angle increment.

Example:


All nodes defined in rows 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10,1.5). The node number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle between the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise using a right-hand rule.

To copy one 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 generation function 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 the Inc to end column. This can be especially handy if you have generated a large group of nodes and then need to remove some of them again.

Example:

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

Rigid links input Point loads and supports invariably result in stress concentrations. In the case of slabs supported on columns, it may be reasonable to ignore stress concentrations within the column areas and rather work with the stress values at the column faces. An alternative approach could be to smooth the stresses that prevail with the close surrounds of each of the columns, e.g. within a perimeter at a distance equal to the depth of the slab away from the column face.

Another more rational approach to modelling a slab at column supports is to introduce rigid links. This approach entails stopping shell elements at the column face and then linking the perimeter with the supported node at the position of the column centre. The high bending stiffness of the rigid links gives a reasonable approximation of the increased stiffness of the slab inside the perimeter of the column. The approach has the advantage of ridding the analysis of high shell bending stress peaks at the points of support.


Shell elements input Elements are defined by referring to corner nodes, four in the case of quadrilaterals and three for triangles. You should enter the node numbers in sequence around the perimeter, either clockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define a triangular element.

Note: Quadrilateral elements generally yield more accurate analysis results than triangular elements. Refer to page 6-9 for more detail.


Selecting materials

Each slab element should have an associated material.

To add one or more materials to a slab analysis data file, click Materials. Open the relevant material type screen and select the materials that are required for the current slab input.

After adding the selected materials to the input, you can select them by clicking the Material column to drop down a list.


Adding materials to the global database

The procedure to permanently add more materials to the database is described in Chapter 2.

Error checking

The program checks for duplicate elements and nodes not connected to elements. It also checks that a group number is assigned to each element. If an error is detected, an Error list button will be displayed.

Generating additional elements

You can generate additional elements with the same section and fixity code values using the No of extra and Node No Inc columns.

Example:

The element enclosed by nodes 15, 16, 26 and 25 are copied ten times with a node number increment of three, i.e elements (18,19,29,28), (21,22,32,310 etc.

Block generation

A group of elements can be repeated by entering a ’B’ in the No column. Then enter the first and 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 of twelve. The copied elements will use the same thickness and material properties as the original elements.

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

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

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


Deleting elements

Shell elements can be deleted by entering ’Delete’ in the Material column. This can be useful if you have generated a large group of elements and need to remove some of them again. Example:

Elements 15-16-26-25 and 18-19-29-28 are deleted.

Supports input Slabs require external supports to ensure global stability. Supports can be entered at nodes to prevent any of the three degrees of freedom associated with plate bending, i.e. translation in the Y-direction and rotation about the X and Z-axes. You can also define elastic supports and prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a combination of the letters ’Y’, ’x’ and ’z’ can be entered to indicate the direction of fixity. Use capitals and lowercase to define restraint of translation and rotation respectively, e.g. ’Yxz’ means fixed against movement in the Y-direction and rotation about the X and Z-axes.


Note: The use of lowercase for rotational restraints should not be confused with the convention of using lowercase for local element axes.

Tip: To enter a simple support with no moment restraint, one would typically enter a ’Y’.

If you want to repeat the supports defined on the previous row of the table, you need only enter the node number, i.e. you may leave the Fixity column blank. If the Yxz column is left blank, the supports applicable to the previous row will be used automatically.

Skew supports

The rotational supports ’x’ and ’z’ can be made skew by entering a value in the Angle column. This feature may be useful when modelling slabs with rotational support perpendicular to skew edges.

Prescribed displacements

Use the X, x, and z columns to enter prescribed displacements and rotations. Being a global support condition, the effect of the prescribed displacement is added once only to the analysis results of each load case and load combination. Optionally enter a ’P’ in the P/S column to designate the values as prescribed displacements.

Elastic supports

Elastic supports, or springs, are defined by entering spring constants in the X, x, and z columns. The spring constant is defined as the force or moment that will cause a unit displace-ment or rotation in the relevant direction. Enter an ’S’ in the P/S column to indicate that an entered value is a spring constant rather than a prescribed displacement. If you leave the P/S column blank, the entered values are taken as prescribed displacements.

Tip: The effect of a column above or below the slab can be modelled by entering their bending stiffnesses as rotational spring supports about the x and z-axes. From simple elastic theory, the rotational stiffness of a column that is fixed at the remote end is given as 4EI/L. The stiffness of a column that is simply supported at the remote end is equal to 3EI/L.

Error Checking

The program does a basic check on the structural stability of the slab. If a potential error is detected, an Error list button will appear.

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


Generating additional supports

Additional supports and prescribed displacements can be generated using the Number of extra and Node number inc columns. The procedure is similar to that described on page 6-9 for generating additional nodes.

Note: The display of supports can be enabled by editing the Display Options.

Point loads input Loads on shell elements are categorised as point loads, i.e. concentrated loads at specific coordinate, and element loads, i.e. uniform distributed loads.

All loads are organised in load cases, e.g. ’DL’ for own weight, ’ADL’ for additional dead loads, ’LL’ for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads.

To define a load case, type a descriptive name for each load case in the Load Case column. Use up to six characters to describe each load case. If the load case name is not entered, the load case applicable to the previous row in the table is used.


Enter the coordinates and load values in the appropriate columns, using the global axis sign conventions given on page 6-9. 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. If an error is detected, an Error list button will appear.

Generating additional point loads

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

Shell loads Distributed loads can be applied on shell elements. Enter a load case description in the Load case column followed by the relevant element numbers in the Shell numbers column. The program automatically assigns numbers to all shell elements in the sequence they are defined on the Shells input page.


A series of elements can be entered by separating the first and last element numbers by a ’–' character, e.g. '1–6' to define elements 1 up to 6.Enter the distributed load intensity in the UDL column.

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, an Error list button will appear.

Generating additional element loads

The No of extra and Shell number Inc columns can also be used to generate additional shell loads. The procedures are similar to that used to generating additional shell elements – see page 6-9 for detail.

Load combinations input You can model practical scenarios by grouping load cases together in load combinations. Enter the load combination number in the Load Combination column; followed by the load case name and relevant load factors.

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

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

The ultimate and serviceability limit states are used as follows:

• Deflections are calculated using the entered SLS loads. A set of reactions is also calculated at SLS for the purpose of evaluating stability and bearing pressures.

• A second set of reactions and all element forces are determined using the entered ULS forces.


Error checking

The program only checks that valid load cases are specified. It has no knowledge of the design code that will be used in the member design and therefore does not check the validity of the entered load factors.

Alternative slab input methods Alternative means of slab input are available:

• Parametric input: Modules are available for the rapid generation of input for typical slab structures.

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

Wizards A number of typical frames can be input by entering a number of parameters. The Wizards do most of the data input. See page 6-103 for detail on the wizards.

Graphical input In some situations, it may be easier to define a slab’s geometry graphically. With Padds you can draw a slab and then generate a slab analysis input file.

Using Padds for slab input

To use Padds to define a slab’s geometry:

1. Use Padds to draw the slab. Alternatively, import a DXF drawing from another CAD system.

2. The slab should be drawn to scale using millimetres as unit.

3. The element grid is drawn using lines.

Tip: You may sometimes find it quicker to hatch an area with a line pattern and then vectorise the hatch to turn it into normal lines.

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

The resultant Fesd input file will be compatible with both the Dos and Windows versions of 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 calculate reinforcement.

Fesd uses the Wood and Armer theory; to convert calculated bending and torsional moments to transformed bending moments. More detail is given on page 6-9.

The required concrete design parameters are:

• Enter the concrete and reinforcement material characteristics, fcu and fy.

• Define the orientation for the ’main’ and ’secondary’ reinforcement, i.e. the x’ and y’-axis. Looking from the top, the x’-axis is measured anti-clockwise from the local x-axis to the reinforcement x’-axis. The y’-axis is in turn measured anti-clockwise from the x’-axis.

• Define the reinforcement levels in the slab by entering the concrete cover values for the top and bottom reinforcement in both directions.

Reinforcement contours can be displayed on the Bending stresses output page.


Analysis

On completing the slab input, you should set the analysis options before commencing the actual analysis.

Analysis options

Analysis options available on the General input page include:

• Concrete design: If the model includes finite shell elements, you can optionally design the shells as reinforced concrete members.

• Add own weight: Select a load case to which the self-weight of the beam and shell members should be added.

On the Analysis page, select the following:

• Output file: Enter an output file name or accept the default file name, e.g. ’Fesd.out’.

• Analyse load combinations only: Enable this option if the results of only the load combinations are required. Generally, one would require results for the load combinations only. However, you may have a special need to view the results of specific load cases as well. Disable this option to include the results for the individual load cases as well.

Analysing the slab To analyse the slab, open the Analysis page and press Start Analysis. The analysis progress of displayed to help you judge the time remaining to complete the analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load combination or, in the case of modal or buckling analysis, the first mode shape.


Error checking during analysis

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

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

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

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

If an error was detected during the analysis, a warning will be displayed. The cause of the error should become clear when studying the output file:

• The text at the end of the output file normally gives the reason for the error.

• If the output file seems complete, the problem will require more careful attention. Scan all output tables for excessively large or small values.


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 are generally small in relation to dimensions of the structure. To improve the visibility of the elastic deflection diagram, you can enter a screen magnification factor.

• Bending stresses in shells:

• The x, y and xy bending stresses: The bending stresses about the local x and y-axes and the torsional stresses. The direction (not axis) of bending is shown as a small line on each shell element.

• Maximum and minimum bending stresses: The principal bending stresses.

• Reinforcement and Wood and Armer moments: Contours of the effective bending moments and corresponding required reinforcement at the top and bottom in the x’ and y’-directions. The reinforcement direction is shown as a small line on each shell. Refer to page 6-9 for an explanation of the use of the Wood and Armer equations and to page 6-9 for the definition of the reinforcement directions.

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


Viewing output tables Open the Output file page for a tabular display of the slab analysis output file. You can filter the information sent to the calcsheets by enabling or disabling the relevant sections.

You can also quickly locate a section of the output file using the Find output function.


Calcsheets

Slab analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To include a particular component of the output in the calcsheets, view the relevant output information and then click Add to Calcsheets.

Recalling a data file The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall the slab by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the slab analysis module as well.

Rectangular Slab Panel Design 6-124

Rectangular Slab Panel Design

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




Design scope The program designs rectangular reinforced concrete flat slab panels. Design loads include own weight, distributed and concentrated dead and live loads. Slab edges can be made free, simply supported or continuous.

Bending moment is transformed to include torsional moment using the Wood and Armer equations. Reinforcement is calculated using the normal code formulae.

Irrespective the selected design codes, long-term deflections are estimated in accordance with clause 9.5.2.3 of ACI318 - 1992

Codes of practice The following codes are supported:

• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.

Units of measurement 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 to the X-axis (mm or in).

dy : Effective depth for reinforcement in the shorter span direction, i.e. parallel to the Y-axis (mm or in).

h : Overall slab depth (mm or in).


Lshort : Length of the short side of the slab, taken parallel to the Y-axis (m or ft).

Llong : Longer side length of the slab, taken parallel to the X-axis (m or ft).

Material properties

fcu : Concrete cube strength (MPa or psi).

fy : Reinforcement yield strength (MPa or psi).

: Time factor for long-term deflection

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 element analysis. Thirty-six plate elements are placed on a 6 x 6 grid. The program uses eight-noded isoparametric finite elements that are well suited for thin plate analysis.

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


Long-term deflections The program estimates long-term deflections by adjusting the stiffness of the slab based on the leveO� RI� FUDFNLQJ��7KH�XVH�RI�D� WLPH� IDFWRU� � IRU�HVWLPDWLQJ�FUHHS�EHKDYLRXU�� LV�EDVHG�RQ� WKH�approach by ACI 318 – 1992 clause 9.5.2.3.

7\SLFDO�YDOXHV�IRU� �DUH�

Duration of load 7LPH�IDFWRU�

5 years or more 2.0

12 months 1.4

6 months 1.2

3 months 1.0

Instantaneous 0.0

Note: The calculated long-term deflections are not exact and should be considered a reasonable estimate only.

Reinforcement calculation The finite element analysis yields values for bending stresses about the X and Y-axes and torsional stresses. Due to the practical difficulties involved in reinforcing a slab to resist torsion, the Wood and Armer equations are used to transform the bending and torsional stresses to effective bending moments in the X and Y-directions.

Correlation with the design code values The moments and reinforcement calculated by the program are generally lower than the values given by the design codes. The discrepancy can be ascribed to the differences in the analysis techniques used. In particular, the code values include allowances for pattern loading and moment redistribution.

Considering continuous slabs, negative moments will generally correlate well while positive span moments would be about ten to fifteen percent too low.

Note: In cases where pattern loading is important, e.g. continuous slabs, it is suggested that the calculated bottom reinforcement be increased by about fifteen percent.


Input

Use the single input table to define the slab and its loading.

Geometry and loads input The following general points should be noted:

• If the aspect ratio of the slab exceeds 3:1, it may be more appropriate to design it as spanning in one direction only.

• Long-term deflections are calculated if you specify a time factor, ��ODUJHU�WKDQ�RQH�

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

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


• To create load combinations, simply repeat the relevant loads in the table. Copying lines in the table is easily accomplished using the table editor commands.

Tip: You can use the mouse to click on the slab picture and stretch its dimensions.

Supports input The corners of the slab are supported vertically at all times. The edges can be supported using the following codes:

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

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

• Displacement and rotation: The support conditions can be used together to support an edge vertically and prevent rotation, e.g. a continuous slab resting on a wall.

Note: Edges that are made continuous are given zero rotation during the analysis. This could be a reasonable assumption provided that the adjacent panel has a similar flexural stiffness. Where adjacent spans differ significantly in terms of span length and thickness, spans should be modelled individually with continuous supports. Differences in the negative moments on the continuous edges should then be redistributed manually according to the relative stiffness of each panel.


Design

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

• Moments: Transformed moment diagrams, using the Wood and Armer equations, for the top and bottom in the X and Y-directions are shown. Values are given per unit width. The transformed moments in the top and bottom fibres represent the moments to be resisted by the calculated reinforcement.

• Deflections: Short-term elastic deflections, based on the un-cracked gross concrete section are shown. The deflections do not include long-term effects like shrinkage and creep.

• Reinforcement: Required reinforcement for the top and bottom in the X and Y-directions is shown. The calculated reinforcement is based on the transformed moments and therefore includes the effects of torsion.


Calcsheets

The slab panel design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


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


Detailing

Reinforcement bending schedules can be generated for designed slab panels. Bending schedules can be edited and printed using Padds.

Generating a bending schedule Based on your initial input and the design results, initial values are chosen for the reinforcement. Change the values to suit your detailing requirements.

Required information:

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

• Detailing parameters:

• First bar mark: Mark to use for the main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incre-mented automatically for subsequent bars.

• Concrete cover to reinforcement

• Reinforcement bond length.

• Drawing scale: The drawing paper is sized to fit the complete detail.

• Reinforcement for top and bottom layers in each of the X and Y-directions.

Press Generate to create a Padds bending schedule with the entered settings. To discard all changes you have made and revert to the default values for the designed column, press Reset.

Note: To detail slabs of more complex shape, use Padds.


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

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



• Member description: Use as many lines of the Member column to enter a description, e.g. ’SLAB PANEL E’.



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


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

Column Design 6-134

Column Design

The concrete column design modules are suitable for the design of the following column types:

• Rectangular Column Design, RecCol: Solid rectangular columns of which the larger column dimension does not exceed four times the smaller dimension.

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

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

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

Column Design 6-135



Design scope The column design modules design reinforced concrete columns subjected to axial force and bi-axial bending moment.

The following conditions apply to the design of rectangular and circular columns:

• The design codes give simplified procedures for designing columns of which the ratio of the larger to the smaller dimension does not exceed 1:4.

• The procedure used for the design of rectangular columns is applied to the design of circular columns.

• The reinforcement layout is assumed to be symmetrical.

Reinforcement bending schedules can be generated for designed columns. Schedules can be opened in Padds for further editing and printing.


• ACI 318 - 1993.

• BS 8110 - 1987.

• BS 8110 - 1997.

• CSA-A23.3 - 1994.

• Eurocode 2 -1992.

• SABS 0100 - 1992.



Column Design 6-136

Rectangular column geometry

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

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

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

h : Depth of the cross section (mm or in). This larger column dimension is taken parallel the Y-axis.

Circular column geometry

d’ : Distance from the column face to the centre of the reinforcement (mm or in).

Ø : Diameter of column (mm or in).

Effective lengths

ßx : Effective length factor for bending about the X-axis

ßy : Effective length factor for bending about the Y-axis

Material properties



Es : Modulus of elasticity of reinforcement (GPa or ksi).

Applied loads

Mx top : Moment about the X-axis applied at the top end of the column (kNm or kipft). If left blank, a value of zero is used. A positive moment is taken anti-clockwise.

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

My top : Moment about the Y-axis applied at the top (kNm or kipft). A positive moment is taken anti-clockwise.

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

P : Axial force in the column (kN of kip). A positive value denotes a downward compression force and a negative value an uplift force.

Design output

Ac : Gross concrete area (mm² or in²).

Column Design 6-137

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

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

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

h' : Effective depth to reinforcement in longer direction of rectangular column (mm or in).

Lex : Effective length for bending about the X-axis (m or ft).

Ley : Effective length for bending about the X-axis (m or ft).

Madd : Additional moment about the design axis of a circular column (kNm or kipft).

Madd x : Additional slenderness moment about the X-axis due to the column deflection (kNm or kipft).

Madd y : Additional moment about the Y-axis (kNm or kipft).

Mmin x : Minimum design moment for bending about the X-axis (kNm or kipft).

Mmin y : Minimum design moment about the Y-axis (kNm or kipft).

Mx : Design moment about the X-axis for rectangular column (kNm or kipft).

My : Design moment about the X-axis for rectangular column (kNm or kipft).

M' : Design moment (kNm or kipft).

M'x : Effective uniaxial design moment about the X-axis for rectangular column (kNm or kipft).

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

Code requirements The supported design codes have similar clauses with respect to bracing and end fixity conditions.

Braced and un-braced columns

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

Global lateral stability is normally provided by means of shear walls or other bracing systems. Such bracing systems should be sufficiently stiff to attract and transmit horizontal loads acting on the structure to the foundations.

Column Design 6-138

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

Effective length of columns

The effective length or height of a column depends on its end conditions, i.e. the degree of fixity at each end. Four end condition categories are defined in the design codes:

• End condition 1: The end of the column is connected monolithically to beams or slabs that are deeper than the column dimension in the relevant plane.

• End condition 2: The end of the column is connected monolithically to beams or slabs which are shallower than the overall column dimension in the relevant plane.

• End condition 3: The end of the column is connected to members that provide some nominal restraint. In the context of this program, this condition is regarded as pinned.

• End condition 4: The end of the column has no lateral or rotational restraint, i.e. a free end of a cantilever column. In the context of this program, this condition is regarded as free.

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

End condition at the top

End condition at the bottom

ß (Effective length factor)

Column in braced frame (ß ≤ 1.0)

Fixed Fixed

Pinned

0.75 to 0.85

0.90 to 0.95

Pinned Fixed

Pinned

0.90 to 0.95

1.00

Column in unbraced frame (ß > 1.0)

Fixed Fixed

Pinned

1.2 to 1.5

1.6 to 1.8

Pinned Fixed

Pinned

1.6 to 1.8

N.A.

Free Fixed 2.2

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

Column Design 6-139

Short and slender columns

A column is considered to be short if the effects of its lateral deflection can be ignored.

Slenderness in a given plane is expressed as the ratio between the effective length and the column dimension in that plane. The slenderness limits for short and slender columns set by some of the supported codes of practice are:

Slenderness limit BS 8110 - 1997 SABS 0100 – 1992

Short Braced

hlex and

b

ley < 15 h

lex and b

ley < 2

1

MM

717 −

Column Unbraced

hlex and

b

ley < 10 h

lex and b

ley < 10

Maximum All lo ≤ 60b Lo ≤ 60b and b ≥ 4h

Slenderness Cantilevers b60

hb100

lo2

≤≤ lo ≤ 25b and b ≥ 4h

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

Column Design 6-140

Input

The column definition has several input components:

• Geometry and material properties.

• Bracing conditions and fixity at the column ends.

• Load cases.

Geometry input The RecCol and CirCol modules have been simplified for the design of rectangular and circular columns. Entering a column’s geometry input in either of these modules is therefore straightforward.

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

Column Design 6-141

General column geometry input

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

• The 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 entered in the X/Radius and Y/Angle columns. If you leave either blank, a value of zero is used.

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

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

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

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

Column Design 6-142

C : A circle with the radius entered in the X/Radius column.

B : A reinforcement bar with its diameter entered in the X/Radius column.

Note: Bar positions and diameters do not need to be entered when using RecCol and CirCol.

• The X/Radius/Bar dia and Y/Angle columns are used for entering coordinates:

X : Absolute or relative X coordinate (mm or in). Values are taken positive to the right and negative to the left.

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

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

Tip: You can leave blank lines between polygons/bars to improve readability.

If convenient, e.g. to simplify loading input, the column can be rotated by entering an angle.

Material properties input The following material property values are required:

• Concrete cube strength, fcu (MPa or psi).

• Reinforcement yield strength, fy (MPa or psi).

• GenCol also requires a value for the modulus of elasticity of the reinforcement, Es (GPa or ksi).

Specifying bracing and fixity conditions Define the bracing and fixity conditions by making the appropriate selections. For an explanation of the terms used, refer to page 6-9. The effective length factors are automatically adjusted in relation to the specified bracing and end fixity conditions. If necessary, you may manually edit the effective length factors.

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

Column Design 6-143

Loads input More than one ultimate load case can be entered:

• Enter a case number and description for each load case.

• Axial load (kN or kip). A positive value denotes a compression force. The program does not automatically include the self-weight of the column. The self-weight should be calculated and manually included in the applied loads.

• Moment values (kNm or kipft). Use the same sign for the top and bottom moments about an axis to define double-curvature about that axis.

Note: All entered loads should be factored ultimate loads.

You can use as many lines as necessary to define a load case – all values applicable to a specific load case are added together.

Column Design 6-144

Design

The column design modules follow different design approaches:

• RecCol and CirCol calculate the required reinforcement for the column.

• GenCol evaluates the column for the entered reinforcement or calculates a single bar diameter to be used at each defined bar position.

Irrespective the approach followed, additional moments are calculated for slender columns and automatically added to the applied moments. The design moment is taken to be equal to or larger than the minimum moment set by the code.

Rectangular column design The design procedure given in the codes is applied. The column is evaluated at the top, middle and bottom and the critical section identified as the section requiring the greatest amount of reinforcement.

The design procedure can be summarised as follows:

• Column design charts are constructed for bending about the X and Y-axis.

• If the column is slender, additional slenderness moments are calculated as required about a single or both axes.

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

• In the case of bi-axial bending, the moments are converted to an effective design moment about a single design axis.

• The reinforcement required to resist the design moment is read from the applicable column design chart.

• Using the same procedure, a design moment is derived about the axis perpendicular to the design axis. Reinforcement resisting the secondary design moment is read from the relevant chart.

Column Design 6-145

Circular column design The same simplified design procedure as for rectangular columns is used. The major and minor column dimensions, h and b, are both set equal to the column diameter.

The column is evaluated at the top, middle and bottom and the critical section identified as the section requiring the greatest amount of reinforcement.

Note: The design procedure for bi-axially bent slender columns tend to be conservative due to he codes’ allowance for additional moment about both the X and Y axes.

General column design GenCol designs columns that do not necessarily fall inside the scope of the code requirements. The program therefore reverts to basic principles, e.g. strain compatibility and equilibrium, to analyse columns. This is achieved using an automated finite difference analysis.

The following calculations are followed:

• The section properties are calculated and the column slenderness evaluated.

• For a slender column, the additional slenderness moment is calculated and applied about the weak axis, i.e. axis of lowest second moment of inertia. The output gives the X and Y-axis components.

• The design moment and axis are determined by taking the

Column Design 6-146

vector sum of the applied and additional moments.

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

Note: Given the differences in the design procedures described above, GenCol will not yield identical results to RecCol and Circular Column Design modules when designing simple rectangular or circular columns.

Column Design 6-147

Design charts

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

• Rectangular columns: Separate charts are given for bending about the X and Y-axis for various percentages of reinforcement.

• Circular columns: Due to axial symmetry, a single design chart is shown.

• General columns: Separate charts are given for bending about the X and Y-axis.

Displaying design charts about other axes You can use Gencol to define a column and then rotate it about any angle. Design charts can then be displayed for the resultant horizontal and vertical axes.

Column Design 6-148

Calcsheets

The column design output can be grouped on a calcsheet for printing or sending to Calcpad. The different column design modules allow various settings, including design charts, tabular design summaries and detailed design calculations.


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

Column Design 6-149

Detailing

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




• Main bars (high yield steel is assumed):

• Rectangular columns: Bar diameter for the corner bars and the number and diameter of the intermediate bars in the horizontal and vertical faces of a rectangular column, as displayed on the screen.

• Circular columns: The diameter and number of main bars. It is generally assumed good practice to use at least six bars.

• General columns: Main bar diameters are defined in the initial input. The shape code can be selected for each individual bar.

• Lap length factor for main bars.

Column Design 6-150

Note: To ensure that the amount of reinforcement supplied is not less than the amount required, the relevant values are shown in a table.

• Level at the bottom of the column (m or ft).

• Level at the top of the column or, in the case of starter bars, at the top of the base (m or ft).

• Links:

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

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

• General columns: Select a shape code and follow the prompts to indicate the link coordinates. Available shape codes include ’35’ (normally used for holding intermediate bars in position), ’60’ or ’61’ (used to enclose four bars by a rectangular link) and ’86’ or ’87’ (spiral bar for use with circular columns).

• Link type: Choose one of the displayed link layouts.

• Concrete cover on links (mm or in).

• Detailing style to use:

• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incremented automatically for subsequent bars.

• Select a size for the sketch: If A4 is selected, the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

The following additional settings should be made:

• Column continuous: Enable this option to make the column bars continuous and have it detailed with a splice at the top. If this option is disabled the column is detailed with bends at the top to anchor it in a beam or slab.

• Starter bars only: If enabled, starter bars are generated instead of complete column bars.

• Double links at kinks: If enabled, a set of double links is provided at the position of the main bar kinks. Circular columns are detailed with straight bars, removing the need for this option.


Column Design 6-151


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



• Member description: Use as many lines of the Member column to enter a member description, e.g. ’COLUMN TYPE 5’.



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



Retaining Wall Design 6-152

Retaining Wall Design

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

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



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

Design scope The program can design most conventional retaining walls, including cantilever, simply supported and propped cantilever walls. Both static and seismic load conditions are supported. Analyses are performed using either the Coulomb or the Rankine theory.

Walls can be made to slope forward or backwards and the wall thickness can vary with height. Toes may optionally be included. Line loads, point loads and distributed loads can be placed on the backfill. A water table can be defined behind the wall. If required, the soil pressure coefficients can be adjusted manually.

Padds compatible bending schedules can be generated for designed walls.


• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• 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 or propped cantilevered wall (m).

Hw : Height of water table, measured from the top of wall (m).

x : Inclination of the wall (m).

xf : Position of the shear key, measured from the front of the base (m).

xL : Position of the line load, measured from the front edge of the wall (m).

xP : Position of the point load, measured from the front edge of the wall (m).

ß : Angle of soil behind wall (°).

Material properties

fcu : Concrete cube compressive strength (MPa).

fy : Reinforcement yield strength (MPa).

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

φ : Angle of internal friction (°).

ν : Poisson’s ration for the soil. The plane strain value should be used rather than the triaxial value – see geometry and loads input.

Applied loads

kh : Horizontal acceleration for seismic analysis (g).

kv : Vertical acceleration for seismic analysis (g).

L : Line load on or behind the wall (kN/m).

Lh : Horizontal line load at top of wall (kN/m).

P : Point load on or behind the wall (kN).

W : Uniform distributed load behind the wall (kN/m2).

Design parameters

DLfact : Ultimate limit state dead load factor.

LLfact : Ultimate limit state live load factor.


Pmax : Design bearing pressure at serviceability limit state (kPa)

SFOvt : Allowable safety factor for overturning at serviceability limit state.

SFSlip : Allowable safety factor for slip at serviceability limit state.

Design output

As1 : Flexural reinforcement in the wall (mm2).

As2 : Flexural reinforcement in the back part of the base (mm2).

As3 : Flexural reinforcement in the front part of the base (mm2).

Ac1 : Compression reinforcement in the wall (mm2).

Ac2 : Compression reinforcement in the back part of the base (mm2).

Ac3 : Compression reinforcement in the front part of the base (mm2).

Ds : Density of soil (kN/m3).

K : Active pressure coefficient, including seismic effects.

Ka : Active pressure coefficient.

Kp : Passive pressure coefficient.

Kps : Passive pressure coefficient including seismic effects.

M1 : Maximum ultimate moment in the wall (kNm).

M2 : Maximum ultimate moment in back part of the base (kNm).

M3 : Maximum ultimate moment in front part of the base (kNm).

Pfac : Pressure factor used for Terzaghi-Peck pressure distribution diagram.

V : Shear force in wall at base-wall junction (kN).

v : Shear stress in wall at base-wall junction (MPa).

vc : Allowable shear stress in wall at base-wall junction (MPa).

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 its depth. The pressure applied on the bottom of the base is varied linearly from maximum at the back, to zero at the front.

• Point loads are distributed along the depth of the soil. In contrast, line loads are taken constant in the transverse direction of the wall.

Application of Coulomb and Rankine theories The program can analyse retaining walls using either the Coulomb wedge theory or the Rankine theory.

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

Friction between the wall and soil

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

Active pressure on the shear key

Depending on its position, the shear key (if any) may be subjected to active pressure. The program allows for active pressure to be included or excluded from the analysis.

Saturated and submerged soil

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

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

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

Point loads and line loads

Point loads and line loads behind the wall are incorporated using the Boussinesq theory. The


theory can be found in ‘Foundation Analysis and Design’ by Joseph E Bowles, chapter 11-13, published by McGraw – Hill. It is recommended that the plane strain ν be used instead of the tri-axial ν. Values of plain strain ν versus tri-axial ν can be found in the table below.

Tri-axial ν 0.30 0.33 0.35 0.40 0.45 0.50 0.60

Plane strain ν 0.42 0.50 0.54 0.67 0.82 1.00 1.50

Seismic analysis

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

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

Live loads can be optionally included in a seismic analysis. If included, live loads are applied with the same pressure coefficients as for dead loads.

Modelling of soil pressure behind rigid walls The program suggests values for the active and passive pressure coefficients, Ka and Kp. These values generally yield reasonable results for cantilever walls. However, simply supported and propped cantilever walls tend to be very rigid. This means that the actual active soil pressures could potentially rise well above the level normally assumed. The program therefore allows uniform pressure distribution to be specified, i.e. Factive = Pfac ⋅ Hwall ⋅ γsoil ⋅ Ka. Typical values for the uniform pressure coefficient, Pfact, was determined by Terzaghi and Peck. An average value of 0.65 should yield reasonable results in most cases.

Seepage modelling When a water table is modelled, seepage can optionally be allowed below the wall. If seepage is allowed, hydrostatic pressure is modelled as follows:

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

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

• The hydrostatic pressure below the base is varied linearly between the values calculated behind and in front of the wall. If seepage is not allowed, the hydrostatic pressure in front of the wall or below the base is taken as zero.


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 following in mind:

• Leave the value for F blank if a shear key is not required.

• The value for Hr is only required for simply supported and propped cantilever walls.

• Leave the Hw field blank if you do not want to define a water table. If you wish to design a liquid retaining wall, you may set the water table above the soil level.

• All applied loads work downward. Point loads are distributed at 45° through the depth of the soil. Line loads are applied uniformly along the width of the wall.


• Disable the option to allow seepage below the base if applicable, e.g. for liquid retaining walls.

• Allow active pressure to be applied to the back of the shear key (if any) if applicable, e.g. if it is positioned towards the back of the base with compacted backfill.

Note: For suggestions on modelling saturated soil and submerged conditions, refer to page 6-9.

Enabling seismic analysis When enabling Seismic analysis, you should also enter the following analysis parameters:

• Enter the equivalent seismic accelerations in the horizontal and vertical directions.

• Optionally include live loads in the analysis.

Soils pressure coefficients The program will calculate the soil pressure coefficients by default. To use your own coefficients, select User defined design values:

• Active and passive pressure coefficients, Ka and Kp.

• Soil friction constant below the base, µ.

• For simply supported and propped cantilever walls, you can choose between triangular or uniform pressure distributions. In the case of rigid walls, a uniform pressure coefficient can also be entered. See page 6-9 for more detail.


Selecting a wall type Choose one of the following wall types:

• Cantilever: The base is fixed against rotation with the wall cantilevering from it.

• Simply supported: The base has no fixity, i.e. free to rotate. The wall is supported horizontally at the bottom and at the level defined by Hr.

• Propped cantilever: Fixed at the bottom and simply supported at the level defined by Hr.

Selecting an analysis theory Choose between the Column and Rankine analysis theories. The Rankine theory cannot be used if the slope of the backfill is less than zero. Due to this and other limitations of the Rankine theory, use of the Coulomb wedge theory is often preferred.


Design

You can design the entered wall configuration or use the optimisation functions to obtain a more economic design.

Analysing the entered wall configuration The analysis includes several ultimate and serviceability limit state checks.

Calculating the ultimate design loads

Loads due to soil pressure and all weights, including concrete and soil, are multiplied by the dead load factor. Applied loads are considered to be live loads and are therefore multiplied with the live load factor.

Additional checks for propped cantilever walls

In the case of a propped cantilever wall, the program checks whether fixity can be obtained at the base. Fixity is attained by balancing loads such as own weight and soil weight plus the pressure distribution under the base against the fixity moment. If the fixity moment attainable is less than one and a half times the theoretical fixed moment, the fixity moment is reduced and the bending moment diagram and soil pressures adjusted accordingly.

Checking stability

Stability against overturning of the wall is checked by assuming rotation about the lower front corner of the base. If a shear key is used and it is located within one quarter of base width from the front, the program also checks for rotation about the bottom of the shear key.

Design results

The design output gives the following values at ultimate limit state:

• Bending moment diagrams (kNm).

• Required reinforcement in the base and wall (mm2).

• Maximum shear stress in the wall, v, and concrete shear capacity, vc (MPa).


Note: The wall design does not include any axial effects due to friction or applied loads.

Results for serviceability limit state checks include:

• Safety factor for overturning.

• Safety factor for slip.

• Bearing pressure diagram below the base.

Optimising the wall dimensions Optimise the wall using the following functions:

• Select B: Optimise the horizontal base dimension in front of the wall. The smallest value of B is calculated to not exceed the allowable bearing pressure and safety factor for overturning. A warning message is displayed if an appropriate value could not be calculated.

• Select D: Optimise the horizontal base dimension behind wall. The smallest value of D is calculated to satisfy the requirements set for the allowable bearing pressure and safety factor for overturning.


• Select F: The value of F is optimised using the safety factor for slip as only criterion.

Note: None of the optimisation functions considers all design criteria. It is therefore possible that after optimising the value of B, for example, the safety factor for slip is exceeded. You may thus need to alternate optimisation functions to arrive at a workable solution.


Calcsheets

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


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


Detailing

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




• Wall and base reinforcement:

• Reinforcement is generated at various positions in the wall and base using the calculated ultimate bending moments. Change the diameters and spacing as required.

• Bond stress: Allowable stress for evaluating bar anchorage of the wall starter bars. If 90° bends proof insufficient, the program automatically uses full 180° hooks. Bar spacing is also reduced to lower bond stress.


• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incremented automatically for subsequent bars.

• Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

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



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



• Member description: Use as many lines of the Member column to enter a description, e.g. ’WALL TYPE C’.



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



Column Base Design 6-168

Column Base Design

The Column Base Design module is used to design and optimise rectangular column bases. Padds compatible bending schedules can be generated for designed bases.




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

The program also verifies the stability requirements for overturning and bearing pressure. Stability checks can be performed at ultimate limit state or using the working force method. Refer to page 6-9 for details.

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


• 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 a right-hand rule, the Z-axis points vertically upward.

The sign conventions applicable to forces and moments are as follows:

• The vertical force, P, works downward.

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

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

Post-processing frame analysis results

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

• Applied load in Column Base Design module

• P • Hx

• Hy

• Mx

• My

• Frame Analysis Mode

• Frame analysis reaction value to use

• Plane Frame Analysis

• Ry

• – Rx

• None • M • N

one

• Grillage Analysis • Ry

• None

• None

• Mz

• Mx

• Space Frame Analysis

• Ry

• – Rx

• Rz

• Mz

• Mx


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 one column is used. A column is positioned at the centre of the base unless non-zero values are entered for E and/or F.

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


Material properties input You are required to enter the properties of the concrete and soil fill and also specify the concrete cover to the reinforcement.

Setting the stability criteria Relevant limits should be entered for checking overturning, slip and bearing pressure at serviceability and ultimate limit state.

Modern design codes tend to consider stability checks like overturning at ultimate limit state. Depending on your own preference, you can use the program to check stability at ultimate limit state or using the older method of working loads (permissible working stress):

Checking overturning at ultimate limit state

The ratio of the cumulative effects of factored destabilising loads to the effect of the factored stabilising forces should not exceed unity. In this ratio, all forces are multiplied by the appropriate ULS factors that exceed unity and only the self-weight components of stabilising forces by the minimum ULS load factor that does not exceed unity.

When using this approach in the program, you will likely want to set the load factors for overturning for all stabilising components of self-weight to the minimum prescribed ULS dead load factor, typically between 0.9 and 1.0. For all other loads, a ULS load factor of between 1.2 and 1.6 (depending on the relevant code) will be appropriate.

Checking overturning using working loads

The older method requires the ratio of the cumulative effects of destabilising loads to stabilising loads to be greater than an appropriate safety factor, typically 1/0.7 or 1.5.

When using this approach, you should enter unity values for all load factors for overturning and specify relevant safety factors for overturning.

Checking slip at ultimate limit state

The program uses the entered load factors for ultimate limit state, LFuls, to evaluate slip. The safety factor for slip should thus normally be set to unity.


Loads input Enter one or more load cases. The following should be kept in mind:

• All loads are applied at the centre of the columns. A column is positioned at the centre of the base unless values for E and/or F are entered.

• For the case of a concrete column extending to the slab above, no stub column should be entered, i.e. the value for X should be left blank.

• For a steel base plate bearing directly on the base, enter the plate dimensions for the column dimensions, C and D, and use zero for the stub column height, X.

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

• All loads are entered un-factored. The ultimate design loads are obtained by multiplying the entered forces by the specified load factor.

• A positive value of P denotes a downward force. Use a negative value for uplift.

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

For detail on the sign conventions used for loads, refer to page 6-9.

Load factors

Each load has two load factors:

• LFovt: Load factor to use for overturning stability check.

• LFULS: Load factor to use for calculating bending moment, shear and reinforcement at ultimate limit state analysis.

Own weight of the base is considered as a separate load case. Load factors for own weight is entered in the geometry input table.


Note: Although overturning is also considered an ultimate limit state, the ULS abbreviation is used to designate the strength ultimate limit state.

For more detail on calculating the safety factor for overturning at ultimate limit state, refer to page 6-9.


Design

A column base is designed for compliance with ultimate limit state and serviceability limit state conditions:

• The required reinforcement to resist ultimate moments is calculated.

• Linear and punching shear checks are performed.

• The stability of the base is evaluated at both ultimate and serviceability limit state.

Stability checks Stability values for overturning, slip and bearing pressure are calculated at both ultimate limit state and serviceability limit state. The following general principles apply:

• Overturning: When considering overturning at ultimate limit state, the applied loads are multiplied by the entered load factors for overturning to calculate the ratio of destabilising to stabilising effects. At serviceability limit state calculations are performed using the entered un-factored working loads.

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

• Bearing pressure: Entered loads are multiplied by their respective ULS load factors before calculating the bearing pressure. The un-factored loads are used at serviceability limit state.

Note: With careful manipulation of the load factors for overturning, you can manipulate the program to evaluate overturning stability at ultimate limit state or using the working loads method. Refer to page 6-9 for more information.

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

Shear checks


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

Linear shear

When considering linear shear, lines are considered at a distance equal to the base depth in front of each face of the column. The contribution of the soil pressure block outside the lines is then used to calculate the shear stress.

Punching shear

For punching shear, shear perimeters are considered at one and a half time the base thickness from the column faces.

Various combinations as for internal, edge and corner columns are considered.

Design results Results of stability checks:

• Bearing pressure beneath the base. The 3D pressure diagram is shown in elevation.

• Safety factor for overturning.

• Safety factor for slip.

Note: Stability checks are performed at ultimate limit state (modern limit state approach) and serviceability limit state (older working load approach). Depending of your way of working and the design code used, you may prefer to use only one or both sets of results.

Results of strength checks at ultimate Limit State:

• Design moments in the X and Y-directions in the bottom and top of the base (kNm or kipft).

• The corresponding required reinforcement (mm² or in²)

• Linear and punching shear stresses and allowable shear stresses (MPa or psi).


Optimising base dimensions The base dimensions can be optimised using the following functions:

• Optimise A, B and Y: Calculate the optimum values for all the base dimensions. The optimisation procedures take into account the specified material costs.

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

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

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


Calcsheets

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




Detailing

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




• Main reinforcement:

• Change the displayed bottom and top steel in the X and Y-directions as necessary.

• Top steel will only be given for bases thicker than 600 mm, or where tension reinforcement is required.

• Column reinforcement:

• At each column portion used, specify whether a normal column, stub column or no column should be detailed.

• Main bars: Diameter of column corner bars.

• Middle bars: The number and diameter of intermediate bars in the horizontal and vertical column faces, as displayed on the screen.

• Lap length factor: Splice length to allow for column starter bars.

• Links: Diameter, dimensions and number of stirrups to hold column starter bars in position.


• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incremented automatically for subsequent bars.


• Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

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



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



• Member description: Use as many lines of the Member column to enter a description, e.g. ’BASE 6’.



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

Section Design for Crack width 6-184

Section Design for Crack width

The Section Design for Crack width can be used to design reinforced concrete sections to meet specific crack requirements. Both beam and slab sections can be designed for the combined effects of axial tension, bending moment and temperature.



The following text gives an overview of the application of the theory.

Design scope The program can determine reinforcement layouts to contain cracks. Both rectangular beam and slab sections can be designed to resist the effects of axial tension, bending moment and temperature and the combination thereof. Temperature effects are also included to evaluate early cracking and long-term thermal cracking.

Shrinkage

Concrete shrinkage due to hydration is accounted for by a combination of the thermal expansion coefficient and the restraint factor. The design method employed by the codes is ideally suited for non-temperate regions like Europe.

Reinforcement type

Concrete cracking has traditionally been correlated with the prevailing tensile steel stress. Eurocode 2 - 1984 also takes account of the type of reinforcement, i.e. bond between concrete and reinforcement.

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



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 points require special attention.

• The program evaluates an effective surface zone where crack control would be effective, rather than the complete section. The surface zone is normally entered as half the section depth but not more than 250 mm.

• Because only a surface zone is considered, only half of the entered tensile forces (applicable to the overall section) is used.

• Reinforcement is calculated for the surface zone. The same reinforcement should be supplied in full in both faces of the section.

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

• Select Beam mode if you wish cracking to be evaluated at the section corners as well.

Tip: It is recommended that wide sections be designed using Slab mode.


• The hydration temperature, T1, is defined as the difference between the environmental temperature and the peak temperature due to hydration. The value is used to evaluate early thermal cracking. Typical values, taken from Table A.2 of the code, are given below.

OPC content (kg/m3) Section 325 350 400 325 350 400

Thickness (mm) Steel formwork 18 mm plywood formwork 300 11* 13* 15* 23 25 31

500 20 22 27 32 35 43

700 28 32 39 38 42 49

1000 38 42 49 42 47 56

* Generally a minimum value of 20°C should be used. • The seasonal temperature variation, T2, is used to calculate long term thermal cracking:

• If movement joints are provided as per Table 5.1 of the code, the seasonal variation can normally be set equal to zero when considering early cracking only.

• The seasonal temperature variation should always be considered for long-term thermal cracking in combination with the applied moments and tensile forces.

Section OPC content (kg/m3) Thickness (mm) 325 350 400

300 15 17 21

500 25 28 34

• The restraint factor describes the amount of restraint in the system. The factor varies between 0.0 to 0.5. For more detail, refer to Figure A3 of the code.

Tip: A higher restraint factor generally gives rise to more severe cracking. Therefore, when in doubt, use a restraint factor of 0.5.

• Enter a value for Ro critical, i.e. the minimum percentage of reinforcement to be supplied. The value applies to the gross concrete section of the surface zone. The program gives a default value of 100 · fct / fy, where fct is the three-day tensile strength of the immature concrete. For more detail, refer to paragraph A.2 of the code.


Design

The following checks are considered for each load case at serviceability limit state:

• The combined effect of bending moment, tensile force and the seasonal temperature variation, i.e. MSLS + TSLS + T2.

• Early thermal movement, T1 only.

• Early thermal movement and seasonal variation combined, i.e. T1 + T2.

• The section is also evaluated at ultimate limit state by considering the combined effect of bending moment and tensile force, i.e. MULS + TULS.

Up to four sets of bars are calculated for slab sections. Each set has a different diameter and spacing to comply with the crack width requirements. A fifth column is provided where you could enter a bar configuration of choice.

For beams, up to four sets of bars are calculated. Each set of bars consists of a number of bars of not more than two different diameters. The bar diameters are chosen to not differ by more than one size.


Calcsheets

The crack width design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


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

Concrete Section Design 6-192

Concrete Section Design

The Concrete Section Design module is a simple utility for designing concrete sections for combined bending, shear and torsion. Rectangular and T-sections are accommodated.



The following text gives an overview of the application of the theory.

Design scope The program performs reinforced concrete design of rectangular and T-sections to resist bending moment, shear and torsion.


• ACI 318 - 1995.

• BS 8110 - 1985.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.


Section dimensions

B : Width of the web (mm).

Bf : Width of the flange (mm).

Dct, Dcb : Distance from the top or bottom face to the centre of the steel (mm).

H : Overall height of the section (mm).

Hf : Depth of the flange (mm).

Material properties

fcu : Concrete cube strength (MPa).

fy : Main reinforcement yield strength (MPa).

fy : Shear reinforcement yield strength (MPa).

Design output


As : Bottom steel required for bending (mm2).

A’s : Top steel required for bending (mm2).

Anom : Nominal flexural reinforcement (mm2).

Asv : Required shear reinforcement (mm2/mm).

Asvn : Nominal shear reinforcement (mm2/mm).

Mu : Ultimate moment capacity for bottom reinforcement only (kNm).

v : Shear stress (MPa)

vc : Allowable shear stress (MPa).

vt : Torsional shear stress (MPa).

Calculation of flexural reinforcement The normal code formulae apply when calculating flexural reinforcement for rectangular sections and for flanged sections where the neutral axis falls inside the flange. If the neutral axis falls outside the flange, the section is designed as two separate sub-sections:

• The first sub-section consists of the flange without the central web part of the section and the remaining central portion defines the second sub-section.

• By considering the total section, the moment required to put the flange portion in compression can be calculated using the normal code formulae. This moment is then applied to the flange sub-section and the required reinforcement calculated using the effective depth of the total section.

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

The tension reinforcement for the actual section is then taken as the sum of the calculated reinforcement for the two sub-sections. If compression reinforcement is required for the central sub-section, it is used as the required compression reinforcement for the entire section.

Calculation of shear reinforcement The program assumes that shear is resisted by the web portion of the section only. Shear stress, v, is therefore calculated using the web area and checked to not exceed the ultimate allowable shear stress given in the code. The shear capacity, vc, is calculated using the required bending reinforcement, As, and the shear reinforcement calculated using the normal code formulae.


Calculation of torsion reinforcement Depending on the option chosen, torsion can be resisted by the section as a whole or by the web portion only. For flanged beams, the torsion is calculated separately for the flange and web along the guidelines given in the code. The torsional shear stresses are checked so as not to exceed the ultimate allowable shear stress. Reinforcement requirements are also evaluated separately for the flange and web using the normal code formulae.


Input

The section geometry and ultimate loading are entered using the single input table. The following should be kept in mind:

• If the values for Bf and Hf are left blank, a rectangular section is assumed.

• A positive moment is assumed to cause compression in the top flange.

• The program puts the flange at the top. To model the case where the flange is at the bottom or where the flange is in tension, enter a rectangular section without a flange. The effects of bending and shear will still be evaluated correctly. In the absence of a flange, the torsion checks will however be conservative.

Tip: You can use the mouse to click on the picture and stretch certain section dimensions, e.g. flange width or overall depth.


Design

Press Analyse to design the section for the entered moment, shear and torsion. The following results are given:

• The moment capacity of the section using tensile reinforcement only. The tabled flexural reinforcement values are the required values at the top (compression) and bottom (tension) and the nominal reinforcement.

• Shear stress in the web and the shear capacity of the section together with the required and nominal shear reinforcement.

• For torsion in the web and flanges, values are tabled for the torsional shear stress and required shear and longitudinal reinforcement.

Some reinforcement configurations are also suggested:

• Number and diameters of reinforcement bars to resist bending only.

• Links to resist shear only in the web.

• Links to resist torsion only in the web and flange.

• Longitudinal reinforcement bars to resist combined bending and torsion in the web. The bottom and top bar configurations are chosen to exceed the required flexural reinforcement at that position plus half the total longitudinal torsional reinforcement.

Note: The suggested reinforcement configurations are given as guidelines only. You can use the tabled values for required reinforcement to determine rebar layouts more suitable to your requirements.


Calcsheets

The section design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


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

Punching Shear Design 6-200

Punching Shear Design

The Punching Shear Design module designs flat slabs for punching shear at edge, corner or internal columns. Only reinforced concrete slabs are designed – to design pre-stressed concrete slabs for punching shear, use the Pre-stressed Beam/Slab Design module, Captain, instead.




Design scope The program designs reinforced concrete flat slabs for punching shear at edge, corner and internal columns.


• ACI 318 - 1995.

• BS 8110 - 1985.

• BS 8110 - 1997.

• CSA A23.3 - 1993


• SABS 0100 - 1992.



Slab geometry

A : Horizontal column dimension, as shown on the screen, or diameter of circular column (mm or in).

B : Vertical column dimension, as shown on the screen (mm or in).

Deff : Average effective depth of the slab (mm or in).

X : Horizontal distance, as shown on the screen, from the column centre to the slab edge (mm or in).

Y : Vertical distance from the column centre to the slab edge (mm or in).


Material properties

fcu : Concrete cube compressive strength (MPa of psi).

fy : Yield strength of flexural reinforcement (MPa or psi)

fyv : Yield strength of shear reinforcement (MPa or psi).

Slab reinforcement

Asx1-4 : Average area of main steel parallel to the X-axis crossing each of the four perimeters (mm² or in²). The first perimeter denotes the innermost perimeter.

Asy1-4 : Average area of main steel parallel to the Y-axis crossing each of the four perimeters (mm² or in²).

Design output

Asv : The total area of stirrups to be provided within 1.5Deff inside a perimeter (mm² or in²).

Ucrit : Length of critical perimeter (mm or in).

vc : Allowable punching shear stress (MPa or kip).

Vc : Shear force capacity at a stress of vc (MPa of psi).

Veff : The effective shear force as a function of Vt, Mtx and Mty (kN or kip).

Applied loads

Mtx : Ultimate bending moment about the X-axis (kNm or kipft).

Mty : Ultimate bending moment about the Y-axis (kNm or kipft).

Vt : Ultimate vertical load on column (kN or kip).

Effective shear force The effective shear force, Veff, is calculated using the code formulae. The following minimum values are assumed:

• Internal columns: 1.15Vt.

• Edge columns: 1.25Vt, irrespective of the direction the column is bent.

• Corner columns: 1.25Vt.


Edge, corner and internal columns The following rules are used to determine whether a column should be considered an internal, edge or corner column:

• If one edge is closer than five times the effective slab depth, i.e. 5 · Deff, from the column centre, the column is considered to be an edge column.

• If two edges are closer than five times the effective slab depth from the column centre, the column is taken to be a corner column.

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

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

Shear capacity The program calculates the shear capacity in the X and Y-directions, vcx and vcy, based on the main reinforcement in those directions and the average effective depth. The design shear capacity, vcx, is then taken as the average of the values in the X and Y-direction.

Circular columns Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992, the use of circular perimeters seems a more rational approach to evaluating punching shear for circular columns. The program recognises this and uses the following design approach for checking punching by circular columns:

• As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx and vcy. Put differently, one could consider an imaginary square shear perimeter when determining vc.

• The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter circular perimeter (compared to a rectangular perimeter) yields a lower (conservative) shear force capacity.


Input

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

• The reinforcement values Asx and Asy represent the minimum amount of main reinforcement crossing each perimeter in the X and Y-directions. For a perimeter edge on both side if the column, e.g. y1 in the sketch, you should use the minimum of the amount of reinforcement crossing the left edge and the amount crossing the right edge. For a perimeter edge on one side only, e.g. y2 in the sketch, use the amount of reinforcement crossing that single edge.

• By careful choice of the values for X and Y, you can force a column to be considered as an edge, corner of internal column. See page 6-9 for detail.

• The program assumes pattern loading and subsequently reduces Mtx and Mty by 30%.

Note: If the ultimate moments, Mtx and Mty, do not incorporate pattern loading, their values should be increased by 30% to ensure a correct analysis.


Design

The design procedure includes the following steps:

• The effective shear force, Veff, is calculated. See page 6-9 for an explanation of the assumptions that apply.

• The program chooses four shear perimeters. The first perimeter is taken a distance 1.5 · Deff away from the column face. Subsequent perimeters are spaced at 0.75 · Deff. The perimeters are chosen to be as short as possible, extending to the slab edge when necessary.

• For each perimeter, the allowable stress, vc, is taken as the weighted average of the values calculated for the X and Y-directions, using the flexural reinforcement ratio for the respective directions. Refer to page 6-9 for more detail.

• The required shear reinforcement for each perimeter is then calculated using the normal code formulae. The calculated reinforcement should be supplied within a distance 1.5 · Deff inside the relevant perimeter.


Calcsheets

The slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.



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