Concrete Design6-1 Chapter Concrete Design The concrete design modules can be used for the design of reinforced and pre-stressed concretebeams and slabs, columns, column bases and retaining walls.Concrete Design6-2 Quick Reference Concrete Design using PROKON6-3Continuous Beam and Slab Design6-5Pre-stressed Beam and Slab Design6-9Finite Element Slab Analysis6-9Rectangular Slab Panel Design6-9Column Design6-9Retaining Wall Design6-9Column Base Design6-9Section Design for Crack width6-9Concrete Section Design6-9Punching Shear Design6-9Concrete Design using PROKON6-3 Concrete Design using PROKON Several concrete design modules are included in thePROKON suite. These are useful tools forthe design and detailing typical reinforced and pre-stressed concrete members.Beam and slab design TheContinuous Beam and Slab Design and Pre-stressed Beam and Slab Design modulesare used to design and detail reinforced and pre-stressed beams and slabs. Simplified design offlat slab panels is available through theRectangular Slab Panel Design module. In contrast,theFinite Element Slab Design module is better suited for the design of slabs with morecomplicated geometries. Punching shear in flat reinforced concrete slabs can be checked withthePunching Shear Design module.Column design Rectangular Column Design and Circular Column Design offer rapid design and detailingof simple short and slender columns. Columns with complicated shapes can be designed usingtheGeneral Column Design module.Substructure design Use theColumn Base Design and Retaining Wall design to design and detail typical basesand soil retaining walls.Section design Two modules,Concrete Section Design and Section Design for Crack width, are availablefor the quick design of sections for strength and crack width requirements.Concrete Design using PROKON6-4 Continuous Beam and Slab Design6-5 Continuous Beam and Slab Design TheContinuous Beam and Slab Design module is used to design and detail reinforcedconcrete beams and slabs as encountered in typical building projects. The design incorporatesautomated pattern loading and moment redistribution.
Complete bending schedules can be generated for editing and printing usingPadds.Continuous Beam and Slab Design6-6 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 designstructures ranging from simply supported single span to twenty-span continuous beams andslabs. Cross-sections can include a mixture rectangular, I, T and L-sections. Spans can haveconstant or tapered sections.
Entered dead and live loads are automatically applied as pattern loads during the analysis. Atultimate 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 asPadds 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 thefollowing publications:
• General principles: BS 4466 and SABS 082.
• Guidelines for detailing: ’Standard Method of Detailing Structural Concrete’ published bythe British Institute of Structural Engineers.Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties arebased on the gross un-cracked concrete sections. Columns can optionally be specified belowand 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.Continuous Beam and Slab Design6-7 Pattern loading At ultimate limit state, the dead and live loads are multiplied by the specified ULS loadfactors (see page 6-9). Unity load factors are used at serviceability limit state. The followingload cases are considered (the sketch uses the load factors applicable to BS8110):
• All spans are loaded withthe maximum design load.• Equal spans are loaded withthemaximumdesignultimate load and unequalspans with the minimumdesign dead load.• Unequal spans are loadedwith the maximum designload and equal spans loadedwith the minimum designdead load.Note: The casewhere any two adjacent spansare loaded with maximum loadand all other spans with minimum load, as was the case with CP 110 - 1972 andSABS 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 loadcases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 forcalculating the minimum ultimate dead load. The program uses the more approach givenby the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load andthe maximum load factor specified for maximum dead load.• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of1.5×DL. This load case is not considered during the analysis – if required, you shouldadjustment the applied loads manually. In cases where the dead load is large in comparisonwith the live load, e.g. lightly loaded roof slabs, this load case can be incorporated byincreasing the entered dead load or increasing the ULS dead load factor. This adjustmentapplies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Usingan increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases exceptwhere 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.Continuous Beam and Slab Design6-8 Moment redistribution Ultimate limit state bending moments are redistributed for each span by adjusting the supportmoments downward with the specified percentage. If the method of moment redistribution isset to ’optimised’, the design moments are further minimised by redistributing span momentsupward 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 theprocedures explained in the following text.Downwards redistribution
The downward distributionmethod aims to reduce thehogging moments at thecolumns without increasingthe sagging moments atmidspan. The redistributionof moments and shear forcesprocedure is performed asfollows:
1. The maximum hoggingmoment at each columnor internal support isadjusted downward bythe specified maximumpercentage.2. The corresponding spanmoments are adjusteddownward to maintainstatic equilibrium. Thedownward adjustmentof hogging momentsabove is limited toprevent any increase inthe maximum spanmoments of end spans.3. The shear forces for thesame load cases areadjusted to maintainstatic equilibrium.Continuous Beam and Slab Design6-9 Optimised redistribution:
The optimised distribution procedure takes the above procedure a step further by upwarddistribution of the span moments. The envelopes for the three pattern load cases areredistributed as follows:
1. The maximum hogging moment at each internal support is adjusted downward by thespecified percentage. This adjustment affects the moment diagram for the load case wherethe 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 upwardto as close as possible to the reduced maximum support moment, whilst remaining in thepermissible 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 columnmoments to maintain static equilibrium.5. For each span, the moment diagram for the remaining third load case is adjusted to as nearas possible to the span moments obtained in the previous step. The adjustment is made insuch 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 relevantcombinations 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 thanthe limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section tosufficiently reduce the neutral axis depth.10. The amount of moment redistribution is limited to the specified percentage. The maximumamount of redistribution allowed by the codes is 30%.Note: The exact amount of moment redistribution specified is always applied, irrespectiveof the degree of ductility of the relevant sections. Where necessary, ductility is improved bylimiting the neutral axis depth. This is achieved by adding additional compressionreinforcement.Continuous Beam and Slab Design6-10 Deflection calculation Both short-term and long-term deflections are calculated. No moment redistribution is done atserviceability 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 lengthof the beam. The results of these calculations are tabled in theCrack files on theView output pages.Note: The calculation of the cracked transformed section properties is initially based on theamount of reinforcement required at ULS. However, once reinforcement is generated forbeams, the actual entered reinforcement is used instead. You can thus control deflections bymanipulating reinforcement quantities.Next, the long-term deflection components are calculated by numerically integrating thecurvature diagrams:
1. Shrinkage deflection is calculated by applying the specified shrinkage strain.Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature inthe beam.2. The creep deflection is calculated by applying the total dead load and the permanentportion of the live load on the beam. The modulus of elasticity of the concrete is reducedin accordance with the relevant design code.3. The instantaneous deflection is calculated by applying the transient portion of the live loadon 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 togetherwith cracked transformed sections, which implies plastic behaviour. Although thisprocedure is performed in accordance with the design codes, the use of elastic momentstogether with cracked sections in the same calculation is a contradiction of principles. As aresult of this, long-term deflection diagrams may show slight slope discontinuities atsupports, especially in cases of severe cracking.Continuous Beam and Slab Design6-11 Calculation of flexural reinforcement The normal code formulae apply when calculating flexural reinforcement for rectangularsections and for flanged sections where the neutral axis falls inside the flange.
If the neutral axis falls outside the flange, the section is designed by considering it as twosub-sections. The first sub-section consists of the flange without the central web part of thesection and the remaining central portion defines the second sub-section. The reinforcementcalculation is then performed as follows:
1. Considering the total section, the moment required to put the flange portion incompression can be calculated using the normal code formulae. This moment is thenapplied to the flange sub-section and the required reinforcement calculated using theeffective depth of the total section.2. The same moment is then subtracted from the total applied moment. The resulting momentis 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 calculatedreinforcement for the two sub-sections. If compression reinforcement is required for thecentral sub-section, it is used as the required compression reinforcement for the actualsection.Design and detailing of flat slabs When entering the input data for a flat slab, you should use its whole width, i.e. the transversecolumn spacing (half the spacing to the left plus half the spacing to the right). The programwill then calculate bending moments and shear forces for the whole panel width.
When generating reinforcement, however, the program considers the column and middle stripsseparately. The program does the column and middle strip subdivision as suggested by thedesign codes. The procedure is taken a step further by narrowing the column strip andwidening the middle strip to achieve a simpler reinforcement layout – a procedure allowed bythe codes.Initial column and middle strip subdivision
The flat slab panel is divided into a column strip and middle strip of equal widths and thenadjusted to simplify reinforcement detailing:
1. The width of the column strip is initially taken as half the panel width. The total designmoment is then distributed between the column and middle strips as follows:Moment positionColumn stripMiddle stripMoment over columns75%25%Moments at midspan55%45%Continuous Beam and Slab Design6-12 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 inits middle half. The codes also state that a column strip may not be taken wider than half thepanel width, thereby implying that it would be acceptable to make the column strip narrowerthan the half the panel width.
To simplify the reinforcement layout and still comply with the code provisions, the programnarrows the column strip and widens the middle strip. The widening of the middle strip is doneas follows:
1. The middle strip is widened by fifty percent from half the panel width to three-quarters ofthe panel width.2. The reinforcement in the middlestrip is accordingly increased byfifty percent. Reinforcementadded to the middle strip is takenfrom the column strip.The column strip is subsequentlynarrowed as follows:
1. The column strip is narrowed toa quarter of the panel width.2. As explained above, rein-forcement is taken from thecolumn strip and put into thewidened middle strip.3. The remaining reinforcement ischecked and additional rein-forcementaddedwherenecessary. This is done to ensurethat the amount of reinforcementresisting hogging moment isgreater than or equal to two-thirds of the reinforcementrequired for the original columnstrip.Continuous Beam and Slab Design6-13 Designing the slab for shear
The program considers the column strip like a normal beam when doing shear calculations. Apossible approach to the shear design of the slab is:
• Consider the column strip like a beam and provide stirrups equal to or exceeding thecalculated 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 generatedreinforcement will be equal to, or slightly greater, than the amount that would be calculatedusing 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 barsand a narrow zone of shear links.• Detailing of the adjoining middle strips is also simplified by the usage of uniformreinforcement distributions.The design procedures for flat slabs and coffer slabs are described in more detail on page 6-9.Continuous Beam and Slab Design6-14 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. TheULS dead and live loads are then automatically patterned during analysis. Refer to page 6-7for more information.Density : Concrete density used for calculation of own weight. If the density filed is leftblank, the self-weight of the beam/slab should be included in the entered deadloads. LL perm : Portion of live load to be considered as permanent when calculating the creepcomponents 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.Continuous Beam and Slab Design6-15 The graphs displayed on-screen give typical values for the creep factor and drying shrinkagestrain. In both graphs, the effective section thickness is defined for uniform sections as twicethe cross-sectional area divided by the exposed perimeter. If drying is prevented by immersionin 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 relativehumidity 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 andappropriate judgements should be made.Sections input You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises abasic 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 theirwebs symmetrically around the vertical beam/slab centre line. The web and/or flanges can bemove horizontally to obtain eccentric sections, for example L-sections. Whole sections canalso be moved up or down to obtain vertical eccentricity.Continuous Beam and Slab Design6-16 Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on astraight line. Vertical and horizontal offsets of sections are use used for presentation anddetailing purposes only and has no effect on the design results.Section definitions are displayed graphically as they are entered. Section cross-sections aredisplayed 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 specificsections.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).Continuous Beam and Slab Design6-17 Y-offset : Vertical offset the section (mm). If zero or left blank, the top surface is alignedwith 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 istaken symmetrical about the beam/slab centre line. A positive value means theweb 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 positivevalue means the flanges are moved to the right.Note: There is more than one way of entering a T-section. The recommended method is toenter 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 theentered web area, i.e. Bw × D, as the effective shear area. Although the two methods producesimilar pictures, their shear modelling is vastly different.Spans input Sections specified on theSections input page are used here with segment lengths to definespans of constant or varying sections.Continuous Beam and Slab Design6-18 Spans are defined by specifying one or more span segments, each with a unique set of sectionproperties. The following data should be input for each span:Span no : Span number between 1 and 20. If left blank, the span number as wasapplicable to the previous row is used, i.e. another segment for the currentspan.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, thesection number at the left end is used, i.e. a prismatic section is assumed. Ifthe entered section number differs from the one at the left end, the sectiondimensions are varied linearly along the length of the segment.Tip: When using varying cross sections on a span segment, the section definitions areinterpreted literally. If a rectangular section should taper to an L-section, for example, theflange will taper from zero thickness at the rectangular section to the actual thickness at theL-section. If the flange thickness should remain constant, a dummy flange should be definedfor the rectangular section. The flange should be defined marginally wider, say 0.1mm, thanthe 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. Toallow 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 madefixed by entering ’C’ or ’F’ respectively. By fixing a support, full rotationalfixity 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 measuredin 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 simplesupports at the ends of the beam/slab. Simply enter a value forD 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 tohalf the support depth past the support centre line.Continuous Beam and Slab Design6-19 Code : A column can be pinned at its remote end by specifying ’P’. If you enter ’F’ orleave 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 patternedduring 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 linesas 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 previousload 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 spannumber 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 ofthe load. If you do not enter a value, the program will use a value of zero.Continuous Beam and Slab Design6-20 Wright : Distributed load intensity (kN/m) applied on the right-hand ending position ofthe load. If you leave this field blank, the value is made equal toWleft, i.e. auniformly 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 positionof the moment (m). The distance is measured from the left-hand edge of thebeam. If you leave this field blank, a value of zero is used, i.e. the load is takento start at the left-hand edge of the beam.b : The end position of the distributed load, measured from the start position of theload (m). Leave this field blank if you want the load to extend up to theright-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 theParameters input on page 6-9.Note: If you enter a concrete density on the Parameters input page, the own weight of thebeam/slab is automatically calculated and included with the dead load.Continuous Beam and Slab Design6-21 Design The analysis is performed automatically when you access theDesign 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 thegross un-cracked sections.
When determining long-term deflections, however, the all spans of the beam/slab are subjectedto the maximum design SLS load. Sections are then evaluated for cracking at 250 mmintervals, assuming the reinforcement required at ultimate limit state. The long-term deflectionsare then calculated by integrating the curvature diagrams.Tip: After having generated reinforcement for a beam, the long-term deflections will berecalculated 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, therequired reinforcement is calculated.Fixing errors that occurred during the analysis TheInput pages incorporate extensive error checking. However, serious errors sometime stillslip through and cause problems during the analysis. Common input errors include:
• Using incorrect units of measurement. For example, span lengths should be entered inmetre and not millimetre.• Entering too large reinforcement cover values on the Parameters input screen, givesincorrect reinforcement. Cover values should not be wrongly set to a value larger than halfthe overall section depth.• Not entering section numbers when defining spans on the Spans input screens causesnumeric instability. Consequently, the program uses zero section properties.Continuous Beam and Slab Design6-22 Long-term deflection problems
The cause of unexpected large long-term deflections can normally be determined by carefulexamination of the analysis output. View the long-term deflection diagrams and determinewhich component has the greatest effect:
• The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottomreinforcement. Adding bottom reinforcement over supports and top reinforcement at in themiddle of spans generally induces negative shrinkage deflection, i.e. uplift.• Large creep deflections (long-term deflection under permanent load) are often caused byexcessive cracking, especially over the supports. Compare the span to depth ratios with therecommended values in the relevant design code.• Reduced stiffness due to cracking also has a direct impact on the instantaneous deflectioncomponent.To verify the extent of cracking along the length of the beam/slab, you can study the contentsof theCrack file. Check the cracked status and stiffness of the relevant sections. The extent ofcracking along the length of the beam/slab is usually a good indication of its serviceability.Continuous Beam and Slab Design6-23 Viewing output graphics The analysis results can be viewed graphically or in tabular format. Output data, includinggraphics and tabled values, can be selectively appended to the Calcsheets using theAdd toCalcsheets function on each output page.
Diagrams can be displayed for deflection, member forces and stress and shell reinforcement ofany load case.Deflections
The elastic deflection enveloperepresents the deflections due toSLS pattern loading.
The long-term deflection diagramrepresents the behaviour of thebeam/slab under full SLSloading, taking into account theeffects of shrinkage and creep:
• The green line represents thetotal long-term deflection.• The shrinkage deflection isshown in red.• The creep deflection (long-termdeflection due to permanent loads)is given by the distance between thered and blue lines.• The distance between the blue andgreen lines represents instantaneousdeflection 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. Oncereinforcement has been generated for a beam, the long-term deflections will be based on theactual reinforcement instead.Continuous Beam and Slab Design6-24 Moments and shear forces
The bending moment and shearforcediagramsshowtheenvelopes due to ULS patternloading.Steel diagrams
Bending and shear reinforcementenvelopes are given for ULSpattern loading. The bendingreinforcement diagram sowsrequired top steel above the zeroline and bottom steel below.Viewing output tables Open theOutput file page for a tabular display of the beam/slab design results. Results includemoments and reinforcement, shear forces and reinforcement, column reactions and momentsand deflections.
TheCrack file gives details of the cracked status, effective stiffness and concrete stresses inthe beam/slab at regular intervals. You should find the information useful when trying toidentify zones of excessive cracking.Continuous Beam and Slab Design6-25 Reinforcing Reinforcement can be generated for the most types of continuous beam and slabs using theautomatic bar generation feature. Reinforcement is generated in accordance to the entereddetailing 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 thereinforcement.• 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 generatingreinforcement:
• Beam/slab type: Different detailing rules apply to different types of beams and slabs:TypeDescriptionMain reinforcementShear reinforcement1Normal beamNominal reinforcementas for beamsBeam shearreinforcement2One way spanningflat slabNominal reinforcementas for slabs.No shearreinforcement.3Column stripportion of flat slabon columns4Middle stripportion of flat slabon columnsMain reinforcement inaccordance withmoment distributionbetween column andmiddle strips. Nominalreinforcement as forslabs.No shearreinforcement.Separate punchingshear checks shouldbe performed.5RibNominal reinforcementas for slabs.Shear reinforcementas for beams.Continuous Beam and Slab Design6-26 • 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 tobe used in each if the indicated positions.• Maximum diameter for top bars, bottom bars and stirrups: The maximum main bardiameter 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 forboth 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 theParameters input page – refer topage 6-9 for detail. High tensile steel markings, e.g. 'T' or 'Y', will be used for specifiedvalues of fy and fyvexceeding 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.Continuous Beam and Slab Design6-27 • First bar mark - top: The mark of the first bar in the top of the beam/slab. Anyalphanumerical string of up to five characters may be specified. The rightmost numericalor alpha portion of the bar mark is incremented for subsequent bars. Examples of validmarks 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 youdo 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 youleave this field blank, the bar marks will continue from those used for the top or middlereinforcement.• 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 tothe code provisions for beams and slabs. In some cases, it may be acceptable to provideless than the nominal amount stirrups, e.g. for fixing top bars in a flat slab. The minimumamount of stirrups to be generated can be entered as a percentage of the nominal shearreinforcement.Note: For beams and ribs, the minimum stirrup percentage should not be taken less than100% of nominal shear reinforcement.• Loose method of detailing: The envisaged construction technique can be taken intoaccount when detailing reinforcement:• With the ’loose method’ of detailing, also referred to as the ’splice-bar method’, spanreinforcement and link hangers are stopped short about 100 mm inside each columnface. This is done at all internal columns were congestion of column and beamreinforcement 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 providedthrough the vertical bars of each internal column to extend a lap length plus 100 mminto each span. Top bars will extend over supports for the required distance and lappedwith nominal top bars or link hangers. Allowance is made for a lap length of 40·φ and a100 mm tolerance for the bottom splice bars that are acting in compression.• Alternatively, where accessibility during construction allows, the 'normal' method ofdetailing usually yields a more economical reinforcement layout. This method allowsbottom bars to be lapped at support centre lines. Top bars will extend over supports forthe required distance and lapped with link hangers. Where more practical, top bars overadjacent supports may be joined. Adjacent spans are sometimes detailed together.Continuous Beam and Slab Design6-28 Note: The ’normal’ method of detail may give rise to congested reinforcement layouts atbeam-column junctions, especially on the bottom beam/slab layer. Reinforcement layoutdetails at such points should be checked.Generating reinforcement
Use the Generate reinforcing to have the program generate bars according the detailingparameters.Note: The aim of the automatic reinforcement generation function is to achieve a reasonableoptimised reinforcement layout for any typical beam or slab layout. More complicatedlayouts will likely require editing of the generated reinforcement as described in the text thatfollows. Very complicated layouts may require more detailed editing usingPadds.Editing reinforcement
You can modify the generated reinforcement to suite your requirements by editing theinformation on theMain 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 bardefined 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 negativevalue 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 fieldis 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’.Continuous Beam and Slab Design6-29 The bending reinforcement diagram is shown on the lower half of the screen. The diagrams forrequired (red) and entered (blue) reinforcement are superimposed for easy comparison. Bondstress 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 usedon theShear reinforcing input page (see page 6-9) to reference specific configuration. Ifleft blank, the number applicable to the previous row is assumed, i.e. an extendeddefinition 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’.Continuous Beam and Slab Design6-30 Note: Mild steel bars are normally used for shear reinforcement. However, in zones wheremuch shear reinforcement is required, you may prefer using high yield stirrups. You can dothis by entering ’T’ or ’Y’ bars instead of ’R’ bars. In such a case, the yield strength ratio ofthe main and shear reinforcement, i.e. fy/fYV as entered, will be used to transpose the enteredstirrup 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 theweb sides. Subsequent stirrups are positioned in such a way that vertical legs are spacedequally.Tip: Open stirrups, e.g. shape code 55, can be closed by entering a shape code 35.Continuous Beam and Slab Design6-31 Shear reinforcing Stirrup layouts defined on theStirrups input page (see page 6-9) are distributed over thelength 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). Anegative value makes the zone start to the left of the beginning of the span, i.e. in theprevious span.• Length: Length of the stirrup distribution zone (m).The diagrams for required and entered shear reinforcement are superimposed. The requiredsteel diagram takes into account shear enhancements at the supports.
It may sometimes be acceptable to enter less shear steel than the calculated amount of nominalsheer steel, e.g. when the stirrups are only used as hangers to aid the fixing main steel in slabs.Continuous Beam and Slab Design6-32 This option can be set as default on theDetailing parameters input screen – see page 6-9for detail.Sections Cross-sections can be generated anywhere along the length of the beam/slab to show the mainand 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 thedifferent positions. Stirrup layouts defined on theStirrups input (see page 6-9) rely onappropriate section positions specified. All specified sections will be included in the finalbending schedule.Continuous Beam and Slab Design6-33 Bending schedule TheBending schedule input page is used generate a complete Padds compatible bendingschedule. The parameters allow flexibility in the bending schedule creation, e.g. you can havethe details of a beam/slab on a single bending schedule or split it onto more than one scheduleto improve clarity. Each bending schedule can then be given a unique name and the associatedspans 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 thanone 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 scheduledrawing.• 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 ordescending 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 fiton a full page and the accompanying schedule on a separate page. The A5 selection willscale the drawing to fit on the same page with the schedule. Typically, a maximum ofthree to four spans can be shown with enough clarity in A5 format and four to six spans inA4 format.Note: When combining a drawing and schedule on the same page, the number of schedulelines is limited to a maximum of twenty-four inPadds. Using more lines will result in thedrawing and schedule being printed on separate pages.Use theGenerate 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 withPadds. For this, following thesteps below:
• Exit the program and launch Padds.
• Choose Open on the File menu and double-click the relevant file name. The file will beopened and displayed in two cascaded widows. The active windows will contain thedrawing of the beam and the second window the bar schedule.Continuous Beam and Slab Design6-34 • Make any necessary changes to the drawing, e.g. editing or adding bars and addingconstruction 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 memberdescription, e.g. ’450x300 BEAM’.• General schedule information: Press PgDn to move to the bottom of the bending schedulepage and enter the detailers name, reference drawing number etc.• Bending schedule title: Enter the project name and bending schedule title in the centreblock at the bottom of the bending schedule.• Bending schedule number: The schedule number in the bottom right corner defaults to thefile name, e.g. ’BEAM.PAD’. The schedule number can be edited as required to suiteyour 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 asdescribed in thePadds User’s Guide.Finally, combine the beamdrawing and schedule onto oneor more A4 pages using theMake BS Print Files commandon theFile menu. Use Alt+P toprint the schedule immediatelyorAlt+F to save it as a print filefor later batch printing.Continuous Beam and Slab Design6-35 Calcsheets The beam/slab design output can be grouped on a calcsheet for printing or sending toCalcpad.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 theData File option before sending a calcsheet to Calcpad, you can later recallthe design by double-clicking the relevant object inCalcpad. A data file embedded in Calcpadis saved as part of a project and therefore does not need to be saved in the design moduleas well.Continuous Beam and Slab Design6-36 Appendix: Suggested design procedures for slabs Some suggestions are made below with regards the design and detailing of solid slabs andcoffer slabs.Suggested design procedure for solid slabs The suggestions are explained by way of an example. A flat slab with a regular rectangularcolumn 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. Theprogram calculates moments and shear forces for the whole panel width. It then details acolumn strip, 1500 mm wide, and middle strip, 4500 mm wide. For an explanation of thedivision 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 extendinghalfway to the first row of internal columns. Strip C is the first internal strip and it extends tomidspan on both sides.
Consider the end panel,i.e. the portion betweenedge columns and thefirst row of internalcolumns or, in otherword, strip B togetherwith half of strip C. Theportion over the internalcolumns (portion of stripC) will tend to attractmore moment than theportion over the externalcolumns (strip B). Usinga rule of thumb, areasonable moment distri-bution ratio would beabout 62.5% to 37.5%.
The external strip (stripB)canthusbeconservatively modelledContinuous Beam and Slab Design6-37 as a panel with width equal to half the transverse column spacing, i.e. 3000 mm, carrying thefull load for that area. The program will analyse the strip and the generate reinforcement for acolumn 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 internalpanel, i.e. 6000 mm. Because of the moment distribution explained above, the loading isincreased to 50% + 62.5% = 112.5% of the typical panel loading. The small overlap in loadingbetween the edge and first internal panels should take care of any adverse effects due to patternloading.Note: If the own weight is modelled using a density, you should account for the increasedloading 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 middlestrip 4500 mm wide.Reinforcement layout
Careful combination of the column and middle strips generated above, should yield areasonably economical reinforcement layout:
• For typical internal strips (strip A), use the generated column strip (CA) and middlestrip (MA).• For the column strip over the external row of columns, use no less than the column stripreinforcement (CB) generated for the external strip (strip B).• For the column strip over the first row of internal columns, use no less than the columnstrip 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 ofmiddle strip generated for the first internal strip (MC) and twice that generated for theexternal 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 cofferslabs if the following conditions are met:
• The solid bands should be as wide or slightly wider than the generated columnstrips, 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.Continuous Beam and Slab Design6-38 • Setting the density to zero and appropriately increasing the applied dead load can modelthe 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 saggingmoment, the concrete compression zones of coffer ribs fall within the coffer flanges. Zonesof hogging moment should be located inside solid bands.Pre-stressed Beam and Slab Design6-39 Pre-stressed Beam and Slab Design Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design anddetail most types of continuous pre-stressed beam and slab systems encountered in typicalbuilding projects. The design incorporates automated pattern loading and momentredistribution.
Both unbounded systems, e.g. flat slabs, and bonded systems, e.g. bridge decks, can bedesigned. Estimates for quantities are calculated and tendon profile schedules can be generatedfor use withPadds.Pre-stressed Beam and Slab Design6-40 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 pre-stressed concrete beams and slabs. You candesign structures ranging from simply supported single span to twenty-span continuous beamsor 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 calculationmodule,Prosec. Spans can have constant or tapered sections.Entered dead and live loads are automatically applied as pattern loads during the analysis. Youcan also enter individual load cases and group them in load combinations. At ultimate limitstate, 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 theULS capacity.
Tendon profiles can be scheduled and saved asPadds 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 thefollowing 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.Pre-stressed Beam and Slab Design6-41 Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties arebased on the gross un-cracked concrete sections. Columns can optionally be specified belowand 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 wholewidth of the panel. If the ultimate negative moment at an outer column exceeds the moment ofresistance in the adjacent slab width, the moment in the column should be reduced and thesagging 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 stiffnessdue to torsion. Report 2 of the JSD adapts a similar column stiffness reduction approach. Theprogram incorporates this approach by allowing you to optionally enable attached torsionalmembers.Note: When the approach to include the attached torsional members is followed, columnheads 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 loadfactors (see page 6-9). Unity load factors are used at serviceability limit state. The followingload cases are considered (the sketch uses the load factors applicable to BS8110):
• All spans are loaded withthe maximum design load.• Equal spans are loaded withthemaximumdesignultimate load and unequalspans with the minimumdesign dead load.• Unequal spans are loadedwith the maximum designload and equal spans loadedwith the minimum designdead load.Pre-stressed Beam and Slab Design6-42 Note: The case where any two adjacent spans are loaded with maximum load and all otherspans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, isnot 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 loadcases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 forcalculating the minimum ultimate dead load. The program uses the more approach givenby the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load andthe maximum load factor specified for maximum dead load.• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of1.5×DL. This load case is not considered during the analysis – if required, you shouldadjust the applied loads manually. In cases where the dead load is large in comparisonwith the live load, e.g. lightly loaded roof slabs, increasing the entered dead load orincreasing the ULS dead load factor can incorporate this load case. This adjustmentapplies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Usingan increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases exceptwhere 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 supportmoments downward with the specified percentage. If the method of moment redistribution isset to 'optimised', the design moments are further minimised by redistributing span momentsupward 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 theprocedures explained in the following text.Code requirements
The JSD Report 2 recommends that the maximum moment redistribution should notexceed 20%.Downwards redistribution
The downward distribution method aims to reduce the hogging moments at the columnswithout increasing the sagging moments at midspan. The redistribution of moments and shearforces procedure is performed as follows:
4. The maximum hogging moment at each column or internal support is adjusted downwardby the specified maximum percentage.Pre-stressed Beam and Slab Design6-43 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 inthe 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 upwarddistribution of the span moments. The envelopes for the three pattern load cases areredistributed as follows:
11. The maximum hoggingmoment at each internalsupport is adjusteddownwardbythespecifiedpercentage.This adjustment affectsthe moment diagram forthe load case where themaximum design load isapplied to all spans.12. Therelevantspanmoments are adjustedaccordingly to maintainstatic equilibrium.13. The minimum hoggingmoment at each internalsupport is subsequentlyadjusted upward to asclose as possible to thereducedmaximumsupport moment, whilstremaininginthepermissibleredistribution range. Asecond load case is thusaffected for each span.14. Therelevantspanmoments are adjusted inline with this redis-tribution of the columnmoments to maintainstatic equilibrium.Pre-stressed Beam and Slab Design6-44 15. For each span, the moment diagram for the remaining third load case is adjusted to as nearas possible to the span moments obtained in the previous step. The adjustment is made insuch 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 relevantcombinations 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 thanthe limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section tosufficiently reduce the neutral axis depth.20. The amount of moment redistribution is limited to the specified percentage. The maximumamount of redistribution allowed by the codes is 30%.Note: As would be the case in typical pre-stressed sections, the program assumes that allsections have adequate ductility to allow moment redistribution. The actual ductility ofsections is not verified.Tendon generation procedures Captain is capable of generating tendons for typical beam and slabs. The procedure aims tobalance 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 toobtain an equivalent UDL for the span.
Parabolic or harped tendons are then selected to balance the required percentage of thisequivalent dead load. In the case of harped tendons, the tendons are chosen to provide twoupward point loads per span that balance the selected percentage of the sum of all the dead loadcomponents.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 tensilestrength (UTS).
The details of the tendon generation procedure are explained in the following text.Pre-stressed Beam and Slab Design6-45 Parabolic tendons in cantilever spans
Consider a typical cantilever span with a tendonfollowing a parabolic profile. The profile is chosenwith a zero eccentricity at the cantilever end. Atthe internal support the tendon is taken as high aspossible.
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 minimumof 250 mm.• The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on theright 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 sheathedtendon diameter.The tendon force, T, required to produce the balanced load Wbal is given by))((2)(15.1132RLengthbbLengthRLengthWTbalreq−−−=and the number of tendons required bytendonreqtendonsUTSTN7.0=Parabolic tendons in internal spans and end spans
For a typical internal span, a parabolic tendonprofile is chosen to give maximum eccentricitiesover supports and at midspan.
The same also applies to an end span, except thatthe tendon as moved to the neutral axis at theanchor.
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 spanlength divided by twenty, with a minimum of 250 mm.Pre-stressed Beam and Slab Design6-46 • Over the supports, the tendons are taken as high as possible. The values of b1 and b2 aremade equal to the top cover plus half the sheathed tendon diameter. At the end of thebeam/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 asbeing equal to the bottom cover plus half the sheathed tendon diameter.The drape of the tendon is then calculated as()()()LengthRLLengthbbbdrape−−−+=22/31The tendon force required to produce the balanced load Wbal is then given bydrapeLengthRLLengthWTbalreq×−−=8)(15.12and the number of tendons required bytendonreqtendonsUTSTN7.0=Harped tendons in cantilever spans
For a cantilever span with a harped tendon profile,the profile is taken as a straight line from theneutral axis at the cantilever end to the highestposition over the internal support.
In the calculations, the minimum radius Rminspecified is used in determining the final slopes ofthe tendons. The program chooses the followingvalues:
• 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 theright 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 sheathedtendon diameter.Pre-stressed Beam and Slab Design6-47 The position of the start of the radius of the internal support, xw, is calculated as)

filetype:pdf
file time: 2004-06-14
file size:3078939
Click Here To Download...