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1、1Nanjing University of TechnologyNanjing University of Technology 2 345ablxPABRARBRARBxMMPRlP bARP blAlaPRBlPbxxRMAlbPRQA678 9FPllABCDMO=2FPl 10FPFPllABCDMO=2FPl MA0AClFPMA011FQCMCFPMA0FPllABCDMO=2FPlCAFPlMA0PQ00yCFFF，P00CCAMMMFl，QPCFFPCMF l12FPMA0FPllABCDMO=2FPlMDFQDAFPMA0llMO=2FPlDQP00yDFFF，P020DD
2、AOMMMMFlQPDFF0DM 1314解：由得MB0RqaA54由得MA0RqaB74MRaqaA1254M2MRaqa aqaA322322454qaM Q1RqaA54 Q2RqaqaA4Q3Q4qaRqaB34 BA1 21 233441516Mll Mll 171.5m1.5m1.5m3m2m 得由0BM由得MA0 Q1=+RAP=158=7kN181.5m1.5m1.5m3m2mP=8KNq=12KN/m 192021FPllABMO=2FPl Oyx x1x222FQ(x)M(x)1P00yFQ xF 1P1020M xMMFlxFPllABMO=2FPlOyxCFPMO=2F
3、Pll2l x1CB x1 1P10Q xFxl 1P1PP1P112220M xMFlxF lFlxF xxl=23FQ(x2)M(x2)2P00yFQ xF2P2020MM xFlx FPllABMO=2FPlOyxCFP2l x2B2P12Q xFlxl2P2120M xFlxxl x2 24qBACRRABFFql FRBFRAOyxxFRAFQ(x)M(x)x25xFRAFQ(x)M(x)xOyxllBACqFRBFRA0yF 0M R02AxM xFxqx R0AFqxQ x R02AQ xFqxqlqxxl 2022qxM xqlxxl26RRqlAB2M xqlxqxx()22
4、RARBABlxq()0 xl qxlql22822()0 xlMql2ql2ql28 Q(xRqxqlqxA227RPblRPalAB,AC段：()0 xaM xRxPblxA()()0 xaCB段：()axlM xRlxPallxB()()()()axlRARBPablxxACBQ(xRPblA)Q(xRPalB)Pb l/Pa l/Pab l/M 28ARBR11:(0)()()ABAAMRRLA CxaMQxRLMMxRxxLLMLMaLMbab注意：集中力偶注意：集中力偶MM作用点作用点C C处弯矩的跳跃处弯矩的跳跃ccMMMM )()()()()(:22xLLMxLRxMLMRxQ
5、lxaCBBB29Mmax(x)=Px(L-x)/L dMc dx=0 x=L/2时，时，Mmax=P L/430BCAFN=0Q=10kNM=-10 x kNm (0 x2)FN=-10kNQ=20kNM=-20-20 x kNm (0 x3)10kN 3132dxxFQFQ+dFQMM+d Mq(x)考察考察 dx 微段的受力与平衡微段的受力与平衡OxydxFy=0:MC=0:QFdq xQQdFF0MdMMQdFxdd2xq x0CqxFddQqxM22ddQddFxM33q(x)=0QC0C00有有极小值极小值)(d)(d22xqxxM当0有有极大值极大值Qq0q0q0q0EDxCxx
6、MDCxxQ(xxM221)()d)(d求出求出0)d)(dxQ(xxM35载荷情况剪力图 弯矩图无载荷（q=0）均布载荷（q=c）P mCCPCQ0Q0Q0Q0q0q0q0q036 37FA1kN.m1.5m1.5m1.5mFRAFRF0,0AFMM 38xQ/kNOxM/kN.mO1.11f0.89d d,e 1.665f0b1.3351.11eb0.89,ca0a0.89FA1kN.m2kN1.5m1.5m1.5mFRFBCDEFRAc0.335max1.11kNQmax1.665kN mMmaxMmaxQ 39qBADa4aqaFAyFBy00ABMM，93,44AyByFqaFqa4
7、0qBADa4aqaFAyFByCOxQOxM 9qa/4a7qa/4bdqacqaab,cqa2d Qmax2max948132FqaMqa414m4m4m3mABCDE1P2PmkN10mkN1kN221MqPP解：解：ARBRkNRkNRBA577331kNqRQkNRQACACAA347:段kNPqRFskNPqRFsCDADAC3814:11段424m4m4m3mABCDE1P2PARBR731322020.516kNqRMMACACA202440:抛物线 mkNQB3kNPQB22mqPRxPqxRx)Q(AA50:11令kNmPRMkNmqqxxRMADA16441885.2021max434m4m4m3mABCDE1P2PARBR731322020.51666xkNmMkNmMMMBDBDD63261016:斜直线0:EMBE斜直线44aqQMqPqaaaqa2qaqa22/qa22/qaqaqa一般作剪力图一般作剪力图时，从左往右，时，从左往右，随力的方向走。随力的方向走。45qa3qa2qa22qa22qa22qaq2qaa2aaMqa5qaACBDQ46qa22/qaaMqqa/2qa/2qaqa/2qa/2qa22/qa28/Q
工程力学弯曲强度1剪力图与弯矩图PPT课件
