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RC Slab Design master classIan Feltham, ArupLinear elastic material do not reflect the cracked nature of concreteFE analysis gives stresses in equilibrium with applied loadsStructure will have sufficient strength if appropriate reinforcement is provided for FE stressesIf slab loaded by out-of-plane loads, it is unsafe simply to provide reinforcement for Mx and My - twisting moment Mxy must also be consideredFor simple orthogonal arrangements, you can design for Wood-Armer |Mx|+|Mxy| and |My|+|Myx| moments RC Slab undertakes strength design for reinforcement in any direction, not necessarily orthogonalRC Slab will also design for in-plane loads, either in their own, or in combination with out-of-plane loadsEasier to consider in-plane loads firstInterpretation of 2D FE analysis resultspxpxpypypvpvpvpvReinforcing for in-plane forcesfxfyss/tanTo determine fx and fy:Resolve horizontallys/tan.(px+fx) = s.pv fx = pv .tan - pxResolve verticallys.(py+fy) = s/tan.pv fy = pv /tan - pypx, py and pv are applied in-plane stressesfx and fy are stresses taken by reinforcementReinforcing for in-plane forcess/tanpypypxpxpvpvpvpvfxfyfcs/sinTo determine fc:Resolve horizontallys.(px+fx) + s/tan.pv = (s/sin.fc).sin fc = px+fx + pv/tan = pv .tan + pv/tan fc = 2pv/sin2To determine fx and fy:Resolve horizontallys/tan.(px+fx) = s.pv fx = pv .tan - pxResolve verticallys.(py+fy) = s/tan.pv fy = pv /tan - pyfc is the stress in the concretes

px = 5py = 0pv = 5

px = 0py = -5pv = 5

px = 5py = -5pv = 5 (degrees)stress (MPa)

px = 0py = 0pv = 5

fs = fx+ fyReinforcing for in-plane forces - effect of varying Simple approachGeneral approachProvided concrete stress satisfactory

stress in concretestress in reinforcementtensile strength of concreteConsider tensile stresses in concrete between crackstensile strength of concrete will vary along barwhen the tensile stress reaches the local strength, a new crack will formx (compression)y (compression)fckfckfctkfctkcompressive strength of concrete with transverse tensiontensile stress in concreteBi-axial strength of concretestress taken by Y reinforcementstress taken by X reinforcementshear stresscompressive stresscompressive strength of concreteprincipal tensile stressReinforcing for in-plane forces - simple approach using Mohrs circlesNote that the stress taken by both the X and Y reinforcement is equal to the principal tensile strengthapplied stressX (px,pv)Y (py,-pv)stress in concreteYXfcd uncracked fcd cracked stress taken by Y reinforcementstress taken by X reinforcementshear stresscompressive stresscompressive strength of concreteprincipal tensile stressapplied stressX (px,pv)Y (py,-pv)stress in concreteY (pv,-pv)X (pv,pv)Note that the stress taken by the X reinforcement is equal to (pv- px) and that taken by the Y reinforcement is equal to (pv- py)fcd uncracked fcd cracked Reinforcing for in-plane forces - general approach using Mohrs circles

Reinforcing for in-plane forces - general approach formulae7equivalent, but more complex, formulae for skew reinforcementCompression reinforcement in strutscentre line of struthorizontal steelvertical steelcompressive strainshear strain/2Principal tensile strain is approximately 3.6 x design strain of reinforcement

principal compressive strain 0.003520compression steel40strain at 20 to strut 0.0022 strain in vertical steel -0.0022 strain in horizontal steel -0.0022 Although compression reinforcement should be avoided, any provided should be within 15 of centre line of strut to ensure strain compatibilityApplied forces and moments resolved into in-plane forces in sandwich layersLayers are not generally of equal thicknessReinforcement requirements for each layer calculated and apportioned to reinforcement positions (considering in- and out-of-plane strain compatibility)Number and thickness of layers adjusted to determine arrangement that gives best reinforcement arrangementReinforcing for in- and out-of -plane forcesMxMyMxyMxyNxNyVVIntroduction of faster algorithms for pure in-plane and out-of-plane conditions, which should greatly increase speedIntroduction of bands over which reinforcement areas can be averaged

Interaction between GSA and AdSec to estimate deflections in slabsRC Slab future developmentsChart12-3.66025403788.66025403782012.3205080757-3.56627307127.437072219218.87079914811.0033452904-3.47134659276.354263092417.88291649979.8256096851-3.37540151885.388417685917.0130161678.7638192047-3.27836193364.521054388416.24269245487.7994163219-3.18014882873.737387097315.55723826866.9175359259-3.08067982483.025445323514.94476549866.1061251483-2.97986887082.375434267114.39556539635.3553031379-2.8776259191.779261829113.90163591024.6568877481-2.77385657351.230183869513.45632729614.004040443-2.66846170920.722534602513.05407289333.3909963118-2.56133705720.251519207912.69018215072.8128562651-2.4523727525-0.186947472512.3606797752.639320225-2.3414528417-0.596367673312.0621794852.937820515-2.2284547427-0.979761223611.79178403363.2082159664-2.1132486541-1.339745962211.54700538383.4529946162-1.9956969049-1.678602588211.32570050693.6742994931-1.8756532405-1.998327354811.12601940483.8739805952-1.752962034-2.300675180910.94636278514.0536372149-1.6274574158-2.587195157410.78534742684.2146525732-1.498962309-2.859259966310.64177772484.3582222752-1.36728736-3.118090397610.51462224244.4853777576-1.2322297495-3.364775891910.40299435864.5970056414-1.0935718675-3.60029183910.30613629354.6938637065-0.951079834-3.825514217310.22340594874.7765940513-0.8045018441-4.04123203710.15426611894.8457338811-0.6535663109-4.248157963910.09827572524.9017242748-0.4979797785-4.446937425910.05508279564.9449172044-0.3374245693-4.638156449910.02441898084.9755810192-0.171556126-4.82234843110.0060954434.9939045570-51050.177651569-5.17155612610.0060954435.34920769490.3618435501-5.337424569310.02441898085.69926811940.5530625741-5.497979778510.05508279566.05104235270.7518420361-5.653566310910.09827572526.4054083470.958767963-5.804501844110.15426611896.76326980711.1744857827-5.95107983410.22340594877.12556561671.399708161-6.093571867510.30613629357.49328002841.6352241081-6.232229749510.40299435867.86745385761.8819096024-6.3672873610.51462224248.24919696232.1407400337-6.49896230910.64177772488.63970234272.4128048426-6.627457415810.78534742689.04026225842.6993248191-6.75296203410.94636278519.45228685313.0016726452-6.875653240511.12601940489.87732588573.3213974118-6.995696904911.325700506910.31709431663.6602540378-7.113248654111.547005383810.77350269194.0202387764-7.228454742711.791784033611.24869351914.4036323267-7.341452841712.06217948511.74508516844.8130525275-7.452372752512.36067977512.26542528015.2515192079-7.561337057212.690182150712.81285626515.7225346025-7.668461709213.054072893313.39099631186.2301838695-7.773856573513.456327296114.0040404436.7792618291-7.87762591913.901635910214.65688774817.3754342671-7.979868870814.395565396315.35530313798.0254453235-8.080679824814.944765498616.10612514838.7373870973-8.180148828715.557238268616.91753592599.5210543884-8.278361933616.242692454817.799416321910.3884176859-8.375401518817.01301616718.763819204711.3542630924-8.471346592717.882916499719.825609685112.4370722192-8.566273071218.87079914821.003345290413.6602540378-8.66025403782022.3205080757

fxfyfcfs

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Sheet1

fxfyfcfstheta (degrees)stress (MPa)

Sheet2

fxfyfcfs

Sheet3