材料力學(xué)考研綜合試題

.APlhkBAPlhkB處有一重量為P的物體自B正上方高度h處自由下落，已知：P=10kN，P(P一F)l3/(3EI)=Fl/(EA)hNNhF=P/2ABNABlΔ=Fl/(EA)=0.0354mmlstNlldstF=P/2=42.9kNF=π2EI/l2=78.48kNNddcrw=Fl/(EA)=0.303mmdBNd擊。桿AC長(zhǎng)為l，橫截面面積為A，材料彈性模量為E，彈簧剛度為kN/mm，dmaxCdmaxFFPFBF+F=PABFl/(EA)=F/kABA6=Fl/(EA)=P/(EA/l+k)stAdstst(1)沖擊時(shí)，梁內(nèi)的最大正應(yīng)力。.MaMa9=CCEI2EIPPACBhhbAPCB解：6=Pl3/(48EI)+P/k=0.0345m=Pl/(4W)=24MPada6彈簧受壓力F(靜荷時(shí))k(PF)l3/(48EI)=F/k,F=149N,PF=101Nkkkk=(PF)l/(4W)=9.70MPastbkmKstbkd,byOPxEAPxEaBDaCBD+(MPa)a=0C2GIp7M=Pa(I=2I)，pT=MBAC2st,C3EI2EI3EIGIpPa37Pa3Pa3Pa36EI36EI6EI7.2EI=5Pa3AaBMaBM19.P/2MAl/2CP/2MAl/2CKh)1/2=3.41dst,Cd,C性模量為E，重量為P的重物自梁中點(diǎn)C處正上方高h(yuǎn)處自由落下。試求沖擊0時(shí)的最大動(dòng)應(yīng)力。PChC0BABl/2l/2P(l)2Ml9=22一C2=0C2EIEIM=Pl，M=PlC8A8()3M()3M()2Δ=22一C2=Pl3C3EI2EI192EIK=1+(1+2h0)=1+[1+384EIh/(Pl3)]dΔ0CddWbhPl300(1)若已知重物自由下落時(shí)的動(dòng)荷因數(shù)K=1+(1+2h/Δ)1/2，用此式如何導(dǎo)dst出有初速度v時(shí)的K；0dPAEPBPvhFAEvhFBCDClCD解：K=1+(1+2h/6)1/2=1+{1+2[h+v2/(2g)]/6}1/2d1B0BF=FEDEEEDDEDPlEIFl/(3EI)=Fl3/(3EI)EDED.dAMEB3EI3EI2EI8EId0dE1M=Pl{1+[1+8EI(2gh+v2)/(13Pl3g)]2}max07圖a所示半徑為R，彎曲剛度為EI的等截面薄圓環(huán)在直徑AB兩端作用一DFFABFCARQXCF/2D橫截面剪力為零，靜定基如圖b：?M?M?XCEI0?X，2πCEI0?X，2πCyEI0FCyEI0F8πEIΔΔCy4πEIEIK=2ddABstEI (1)使桿CD中軸力達(dá)臨界力時(shí)的高度h；0 (2)桿CD中軸力達(dá)臨界力時(shí)梁內(nèi)的最大動(dòng)應(yīng)力(()。dmax.PPhACl/2ldDl/2B0解：桿CDhhbPACFBPcr(P一F)l3Flw=編l，N=NCCD48EIEAN若KF=F，則dNcrK=F/F=39.5dcrNd0st0stdstEA0 d,maxd22dNzz定安全因數(shù)n=3，桿CD可視為大柔度桿。試確定許用載荷[M]值。MMeCBlDlABMCFB,FCDEI3EIEIEAzzzlFMFBCBFlEIlEIADFzAcrAcr1cr1cr1cr2cr2cr2cr=M/W=Fl/W=0.719M/W160106maxBFFn幾2EI/(nl2)=82.7kN=0.719M/lcrcrstst許可載荷FFaaaAB12lM=0，F(xiàn)'a+F''2a=F3aAM=0，F(xiàn)'a+F''2a=F3aAcrcrcrF=(F'+2F'')/3=51kNcrcrcr=235MPa，彈性模量E=200GPa，橫截面均為圓形，直徑d=30mm，s1d=36mm。試求結(jié)構(gòu)的極限載荷F。2uFFDC2aGaaE1aABF1BCF2FD2crcrcr2Fa+2Fa=F3ascruF=(F+2F)/3=131kNuscr.1CEE1CEE中性軸(水平方向)的位置，圖中C為形心。圖a為均質(zhì)直梁彈性彎曲；圖bECC且M0(d)(e)dA0來確定，下圖中nn表示AE1nCnnCnnCnnCnnCnEE21abcd(e)受均布載荷(載荷集度q未知)作用。試求當(dāng)梁上最大正應(yīng)力等于[]時(shí)，梁ABqAADBCaaabhmaxD解：當(dāng)梁受到最大沖擊力F作用時(shí)，上梁的最大d撓度為Δ，下梁的最大撓度為ΔΔ，根據(jù)能量守恒dd原理，有1kΔ21k(ΔΔ)2P(hΔ)，其中k3EI2d2ddl3lkΔ2(kΔP)ΔkΔ2Ph0dd2PhΔ.appapappappF-F=kΔ,F=k(Δ-Δ)dddF最大沖擊力F=k(2Δ-Δ)=3EI(2Δ-Δ)ddl3d 11直間距為l/2。若在兩梁的自由端裝配細(xì)長(zhǎng)桿BD，其拉壓剛度為2222BABl2lDlBD受壓力為F，加工過盈量為Δ。變形協(xié)調(diào)條件為N2Fl3N+FlN=Δ3EI2EA11224π2EIF不22ll/3pl/3l/3FR123壓縮量相等Fl編l=編l=-R133EA中段伸長(zhǎng)量編l=cl23.2d=B2d=B解出F=2vpA=2kNR3=一3EI3EIEAE3EI2EI6EI111dΔDddE向支承，折桿各段長(zhǎng)度相等，即l=l=l，未受沖擊前，彈簧為原長(zhǎng)。今有ABBC重量為P的物體以水平速度v沿垂直于ABC平面方向沖擊點(diǎn)B處，試求彈簧所kClvBPlAFPlFlFCPBAdlCBdlCBl俯視圖AAB3EIPlddddyyoAROBAAR9OXv9OXddqqq22q2?Xvq2?XBEI0?X1jM?MBEI0?XB4A(2)4A..Δ2+1)|st3EI3EIGIπd4(3E2G)p突加載荷，動(dòng)荷因數(shù)K=2，故dΔ=2Δ=64Pl3(|4+1)|dstπd4(3EG)ChPXRX9OBAOBAOPP?MΔ=1jM?Δ=1jM?M.Rd9=0，X=PΔ=1jM?M.Rd9Δ=1jM?M.Rd9 (2)PR2hEICstEId0.01894PR3Bx,ddL0.0189PR3」πhhPCRABOACX9.Δ1MMΔ1MM2lF3l)lFF)34(FF)3F3D