05-2009机制2材料力学试卷a答案

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1、AccordingtoMohr^scircle,wehave2009机制材料力学试卷A一、(20)Thesolid80・mm・diameterbarcarriesatorqueTandatensileforceof125kNacting20mmfromthecenterlineofthebar.FindthelargestsafevalueofTiftheworkingstressesareqw=100MPaandtw=80MPa.承受偏心距为20mm,偏心拉力为125kN,扭矩T的直径为80-mm圆截面杆，

2、其许用正应力为Ow=100MPa,许用剪应力为tw=80MPa求最大扭矩。SolutionMmax=125kNX0.02m=2.5(kN.m)MnrixP32M卄PmdxJI__SA7id'A732x2.5x106(Wjw71)4x125x10‘(N)=；F龙x80’伽加)'7tx802(mm)2=49.7+24.9=74.6(Mpa)Tr16T16xTxlO6(/V.mm)_——=995T§TheunitofTis(kN.m)DrawtheMohr'scircleSettleit,weget

3、7.3+J37.3?+(9.95T)2)<100MPaT=5.07(kN.m)rmax=(737.32+(9.95T)2)

4、iisEst/EWCj=15.Determinetheincreaseintheallowablebendingmomentduetothereinforcement.上下用钢板加I古I的木梁，弹性模量比为Est/Ewd=15,木头许用应力为8MPa,钢板许用应力为120MPa。求加固的木梁比未加固的木梁增加的弯矩。AsaresultofEst/EWC

5、=15,theresultsinthetransformedsectionshowninFig.(b),whichismadeofwood.nAst=15x1

6、20x10=18000(mm2)nb=15x120=1800(mm)Themomentofinertia5r1800x320"I=12(1800—250)x300’12=(4.915-3.488)xl09=1.43xl09(mm4)ThelargestbendingstressMcwdA/X150、(rwd=——=亍<8(MPa)dI1.43X109M<76.3xl0&(N.加加)=76.3伙Nm)stMcstt_Mxl60八、6=n——-=15x<20(MPa)stI1.43x10°M571.5x10°(

7、N.加加)=71.5伙Nm)SowegetM<71.5xl06(N.mm)=7l.5(kN.m)12ThelargestbendingstressIfthereonlyisthewood,themomentofinertia,250x30030.5625x109伽『)Mxl50/q/md、<8(MPa)0.5625X109M<30.0x1()6(Mm)=30.0伙Nm)Soincreaseintheallowablebendingmoment71.5—30.0=41.5伙Nm)三、(20)Thepropped

8、cantileverbeamcarriestwoconcentratedloads,eachofmagnitudeRFindthesupportreactionatAandBo求支座的皮力。pSolutionAccordingtotheslopeanddisplacementformulasforbeams,weknow2Pxg—Px心)+—36EI7PL3Ra&/6EI~'162EI162E/3EIWehave3EI10ra=—pA162Accordingtotheequilibriumequation,w

9、ehaveRa+Rr=02PI—LR+M63A3—PL,162Sowehave心佶，Rb63162卩四、(20)Thebeamshownincrosssectionisfabricatedbyboltingthree80-mmby200-mmwoodplankstogether.Thebeamisloadedsothatthemaximumshearstressinthewoodis1.4Mpa.