工程力学弯曲刚度课件.ppt

1、NanjingNanjing University of Technology University of Technology 摇臂钻床的摇摇臂钻床的摇臂或车床的主轴变臂或车床的主轴变形过大，就会影响形过大，就会影响零件的加工精度，零件的加工精度，甚至会出现废品。甚至会出现废品。桥式起重机的横梁变形过大桥式起重机的横梁变形过大,则会使小车行走困则会使小车行走困难，出现爬坡现象。难，出现爬坡现象。但在另外一些情况下，有时却要求构件具有较大但在另外一些情况下，有时却要求构件具有较大的弹性变形，以满足特定的工作需要。的弹性变形，以满足特定的工作需要。例如，车辆上的板例如，车辆上的板弹簧，要求有足够

2、大的弹簧，要求有足够大的变形，以缓解车辆受到变形，以缓解车辆受到的冲击和振动作用。的冲击和振动作用。xyxy()y f x d()dyfxx tanKyy()/123 2zEIM12 3/21(1)yy zMyEIyMEI 或y M 0 xy0y MMMMM 00yxyEIyM l2mx1m()EIyM x 2121mmlm2xm1M 0Mm2m10y()EIyM x()dEIyM xxC()d dEIyM xx xCxD0AByy0,0BByCccccyyx21()02M xq lxxl 212EIwMq lx 316EIwEIq lxC 4124EIwq lxCxD 316EIwEIq l

3、xC 4124EIwq lxCxD00 xw，d00dwxx，=33,624qlqlCD 336qlxlEI 434424qwlxl xlEI336qlxlEI 434424qwlxl xlEI 3max6BqlEI4max8BqlwwEI 1P3044lMxF xx 2PP3444llMxF xFxxl 211P2d30d44wlEIMxF xxx 222PP2d3d444wllEIMxF xFxxlx 12P183CxFEI22P2P242183ClxFxFEI113P181DxCxFEIw223P3P246181DxClxFxFEIw D1D2=02P211287lFCC 22P3781

4、28FxxlEI xlxEIFxw23P128781 222P317824128FlxxxlEI xllxxEIFxw233P128746181 EIlFwB3P25632P7128AF lEI2P5128BF lEIxylqM xqlxqx()222222qlqEIyxx 2346qlqEIyxxC 341224qlqEIyxxCxD000 xyxly时，时，CqlD 3240,xqlxyABqEIlxxl2464233()233(2)24qxylxxlEIqEIlxxl2464233()233(2)24qxylxxlEImax ABqlEI3244max25384lxqlyyEI xqlx

5、yAB A ByaqABCxaaaDEMxqaxxa11110()()112222()2EIyqaxqEIyqaxxayaqABCxaaaDEqaqax1x2Mxqaxqxaaxa22222222()()()121212,xxayyyy时21112qaEIyxC得CCDD1212110,0 xy时得 D10222,0 xay时得 Cqa23116 11EIyqax2222()2qEIyqaxxa3111 116qaEIyxC xD232222()26qaqEIyxxaC34222222()624qaqEIyxxaC xD22111233222223111134322222(113)06 3()

6、1126(11)06 4()44224qaaxxaEIqaxxaaaxaEIqaya xxxaEIqyaxxaa xaxaEI 13max10116AxqaEI 24max22198xaqayyEI 2lAB2l2IIC02lxx()M xP x EIyP x 212PEIyxC 3116PEIyxCx D2lxl()M xP x 2EIyP x 2222PEIyxC 32226PEIyxC xD,0,0 xly时,2CCCClxyy左右左右时232211,23CPlDPl 231153,1616CPlDPl 3231153()61616yPxPl xPlEI0 x 3316APlfEI （）

7、l/2l/2l/2 l/2 l/2 Cf53844qlEIPlEI348mlEI216AqlEI324PlEI216mlEI3BqlEI324PlEI216mlEI3（）（）（）2LwwwwBBcBcLaCABCCfc1EIpafc331EIpac221CABPPaEIPaLafBc32223BPaLEI 21cccfff21ccc 45(2)384CqafEI PaaEI()2162 0Pqa56qPA C B D qA C B D PA C B D PPA C B D 2 A C B D 434(2)(2)14833BqaqaaqafEIEIEI 342(2)82483BDfqaaqafE

8、IEIqABq 2q CBD2 q2q A C B D用叠加法求图示变截面梁用叠加法求图示变截面梁B、C截面的截面的挠度挠度 fB、fC。2 ABC323(2)2(2)BPaPa afEIEI33BBCfaPafEI 3512PaEIBPaEIPa aEI22 22()234PaEI顺时针 332PaEIEIC2EIAB PCEIBPEIP2EIABPP ABC3364BCqaqaEIEI顺时针BqaaEIqaaEI22223216()312qaEI顺时针 445824BCqaqafEIEIaABCBABC kEIa232ABC 41332CqaqafkEI 342(2)243CqaqafaE

9、IEI 41283CCCqafffEIBqa处 反 力=2 ABC 2 ABC 2 ABC414322218112128482,CCBBqlwEIlqlqllwwEIEI EIqlEIqlCC323148161,EIqlwwiCiC42138441EIqliCiC321487 maxff max BBEIlaFB3P B111mmm10111m100.52063101802120643-493dCBA2L2L31430ZWcm432240ZIcm80.4qkg m2max48P Lq LM32(50 10)10(80.4 9.8)10483134.8 10 N mCBA2L2LmaxmaxZM

10、W36134.810Pa14301094.3MPa 140MPaPqCCCfff34548384ZZPLqLEIEI3349898(50 10)105(80.4 9.8)1048(200 10)(32240 10)384(200 10)(32240 10)317.76 10 m17.76mm()1500fL10m20mm500Cf f 3-3=0lMA ABFAyFAxq4-3=1l ABMAFAyFAxFB532FBxBl AMAFAyFAxFBy633MBBl AMAFAyFAxFBxFBy 0Bf 即R lEIqlEIB34380RqlB38ABAB A 0即M lEIqlEIA32403MqlA182ABBAABCDDDABCDff3335633DDR aR aPaEIEIEI即 54DRPBACDABCBBABBCff334833BBR aR aqaEIEIEI即316BRqaABBC2L2L2L2LCRCDClf3()48CCRaPRLEAEI3348CA LRPA LI a