8/13/2019 TG_Designing for Effect of Mxy by Wood-Armer Method

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DesigningforEffectofMxybyWoodArmerMethod

1. IntroductionTypically finite element software packages are used in design offices to find out stresses

generated in slabsdue to applied loads. The generated stresses are in equilibriumwith the

applied loads. Compatibility is satisfied at boundaries where kinematic conditions are

prescribedbytheuser.

However the flipsideof thiscomputationalaccuracy is that,generallyany loadexcept in the

mostsimplest

of

cases,

results

in

atwisting

moment

Mxy

along

with

the

two

bending

moments

inorthogonaldirections.Thismoment isgeneratedasaprerequisite tosatisfyequilibrium in

somecasesandcompatibilityinothers.GenerallythismomentMxyisneglectedindesignand

asgeneralconsensusisthatitisnotexpectedtocauseanydrasticerror.Partofthereasonfor

thisis,theMxyfieldgenerallyhasitsmaximumsandminimumsatdifferentlocationsthanthe

fieldsforMxandMyandhencedirectcombinationofthemaximumsalmostneveroccurs.

Even then, for those caseswhen comparable twistingmoments and flexuralmoments are

expected at nearby locations, a framework is desired to analyze in the quickest manner

possible, theeffectof theMxy fieldonnormal flexuraldesign.TheWoodArmerMethodof

combiningMxywithMxandMyprovidesapossibleanswer,subjecttosome limitations.(see

section3)

2.WoodArmerFormulationTheWoodArmerFormulationisbasedontheLowerBoundMethodsofAnalysis.Thelower

boundmethodshaveacommonsetoffundamentalassumptions

Ifadistributionofmomentsforthewholeplatecorrespondingtoanultimateloadisfound

suchthat

Equilibriumconditionsaresatisfiedatallpoints Yieldcriteriondefiningthestrengthoftheplateelementsisnotexceededanywhereintheplate

BoundaryconditionsarecompliedwithTheultimateloadcorrespondingtothisdistributionwouldeitherbelowerthanorequaltothe

actualultimateloadthatcanbecarriedbytheslab.