Stress2DR/C"DeepBeam"DesignIllustrativeExample

InthisexamplewewilldemonstratetheusageofStress2Dsoftwareinadesignofareinforcedconcrete"deepbeam".

Inthisexamplethe"deepbeam",isactuallya"deepcantilever"wall.(seefigureonleft).Thecantileverwallis3.0mlong,5.0mdeep,and0.5thick(estimated).Itcarries15floorsfromabove,whichincludesprecastconcretefacadepanelsandthefloorstructure.Theestimatedload(G+Q)is750kN/m.Thecantileverwallissupportedbyaseriesofcolumns.

Thedesigntaskistoevaluatethestressesinthecantileverwallandtodesignthereinforcement.

ThebuildingislocatedinSydneyCBD,NSWAustralia,justbehindtheTownHall.

Inthefiguresbelowthecantileverwallisshowninalargerscale.

Thisisatypical2Dstressanalysisproblem,suitableforfiniteelementapproach.Inthiscase,"beamanalogy"willnotprovidereliableresults.ThefiniteelementmodelwascreatedusingStress2Dsoftware.Themodelconsistsofseveral2Dpanels,representingthecantilever,andfourcolumns.Thisisaverysimplemodel,andittakes5to10min.todrawitusingStress2Dinteractiveeditor.

Once,themodelispreparedandallmaterialpropertiesareentered,wecanperformthestaticanalysisbytheusingStress2Dsoftware.Thedeflectionresultsareshowninthefigurebelow.

Inthefigurebelowthehorizontalstresses(SigmaX)areshownintwocharacteristicsections.Thecriticalsectionisabovethecolumn,wherethereareatotaltensionforceof1,150kN.Atthecolumn,almost3/4ofthesectionisintension.Wehavetoputasufficientnumberofhorizontalbarstotakethetensionstresses

Thecompressionstressesweremuchsmallerthanthantheconcretestrength,andthereisnoneedforanyadditionalreinforcementtotakethecompressionstresses.

WecanusesteelbarsY16,inthehorizontaldirections.(Astofonebaris201mm^2)

Ifweallowthatthestressinthesteelwillgoupto50%oftheyieldstrengthof400MPa,thenwecancalculatetherequiredareaofreinforcement.

Ast.tot=1,150/200,000=0.00575m2or5,750mm2(requiredareaofsteel)

TotalTensionForce=1,150kN

50%SteelYieldStrength=200,000kPa

Numberofbars=5,750/201=28barsor14barseachsideofthewall

Ifweplace28horizontalY16bars,thentheloadwillgeneratetensionstressinthebarsof200MPa,whichisonly50%oftheyieldstress.Thisisactually,asafetyfactorof2,whichissufficientinthiscase.

Thehorizontalbarswillbeplacedoveralengthof2mfromthetopedge,i.e.Y16@150eachface.

Therestofthestructurewillneedsomenominalhorizontalreinforcement,forinstanceY16@300.

Also,itisagoodideatoputafewextrahorizontalbarsatthetopedge,say5Y24,totaketheconcentrationofthetensionstresses.Theextrabarswillhaveacrosssectionof2,260mm2,whichwillmakeatotalor7,890mm2.Thiswilldropthestressinthesteelto146MPa.Now,thesafetyfactoris400/146=2.7.

Theverticalreinforcementmaybedesignedinthasimilarmanner.

Themaximumshearstressesare2.7MPa,whichissmallerthan10%oftheconcretestrength,andnospecialshearreinforcementisrequired.

Thedeflectionatthetipofthecantileverisabout1mm,whichisconsideredacceptable.(assumingEc=31GPa).

NOTE:INDUCTAEngineeringwasnotinvolvedintheactualdesignoftheabovestructure,noranyofoursoftwarewasusedinthedesign.Wehavechosenthisparticularstructurebecauseofitsspecificgeometry,inordertoillustratethepotentialusageoffiniteelementsoftwareinstructuraldesignof"deepbeams".