光波导系统 - 收发器设计

Chapter7TransverseShear17.1ShearinStraightMembers*Abeamsupportsbothshear(V)andmoment(M).*TheshearforceVistheresultoftransverseshearstressdistribution.*Sinceshearmustappearinpairforbalance,thetransverseshearstressandlongitudinalshearstresscoexist.27.2TheShearFormulaCutthebeamatlocationx,andtakeasmallsegmentoflengthdx.NormalstressdistributionNormalstressdistribution3ConsiderareaA(abovey),andwriteequilibriumequation45

-shearstressatpointyofthecrosssectionatxV–internalshearforceatthiscrosssectionI–momentofinertiaofthiscrosssectiont–thicknessaty

SinceV=V(x),Q=Q(y),=(x,y)–functionofxandy.6RectangularCrossSection

7*Onneutralplane(y=0),shearstressismaximum.

*Ontopandbottomsurfaces(y=h/2),shearstressiszero.*Comparisonwiththenormalstress:

=0onneutralplane

=

maxontopandbottom89*Aty=0,bothtransverseshearandlongitudinalshearreachmaximum.*Woodstandslargelongtudinalnormalstress,butsmalllongitudinalshearstress.1011LimitationsontheUseoftheShearFormula*Shearformulaisapplicablefor

b/h<<1.12*Shearformulaisnotapplicableattheflange-webjunction.But,itismostimportanttodetermine

maxaty=0.For

max,thetheoreticalvalueandactualoneareveryclose.13*Shearformulaisnotapplicableforcrosssectionwithirregularboundary.Atboundary,shearmustbetangentialtothesurface.14EXAMPLE7.1

15161718192021EXAMPLE7.3

222324257.3ShearFlowinBuilt-upMembers*Additionalmembersarebuilt-uponabeambyusingfasteners,suchnails,bolts,glue,etc.*Thefastenersmustresistlongitudinalshearforces.26*Shearflowq–shearforceperunitlengthofbeam.27A–crosssectionareaattachedtothebeam

V–internalshearforceatthiscrosssectionI–momentofinertiaofentirecrosssectionabouttheneutralaxis28EXAMPLE