位移法典型方程

4.3位移法(DisplacementMethod)一.单跨超静定梁的形常数与载常数4.3位移法二.位移法基本概念三.位移法基本结构与基本未知量四.位移法典型方程qll/2l/2EI=常数qlqlqlqlqZ1Z2R2R1R1=0R2=0四.位移法典型方程qll/2l/2EI=常数qlqlqlqlqZ1Z2=1R2R1R1=0R2=0Z1=1r12r21r22r111Z2ZqlqlqR1PR2P002222121212121111PPRZrZrRRZrZrR---位移法典型方程rij(i=j)主系数0rij=rji反力互等刚度系数,体系常数RiP荷载系数rij(i=j)副系数qll/2l/2EI=常数qlqlqlqlqZ1Z2=1R2R1R1=0R2=0Z1=1r12r21r22r111Z2ZqlqlqR1PR2P002222121212121111PPRZrZrRRZrZrRi4i3i2M28/2qlMP8/2qlli/6M1li/3iqlZ22927r112/3li2/12lir12li/6211/15lirlir/6122/31qlRPR1P2/qlqlr21li/6r22i4i3lir/621ir722R2P8/2ql8/2ql4/22qlRPiqlZ31233PMZMZMM221118465184139239一.单跨超静定梁的形常数与载常数4.3位移法二.位移法基本概念三.位移法基本结构与基本未知量四.位移法典型方程五.算例例1.作M图ll/2qlllqEI1.5EIEIEI2/5EIqqZ1Z2R2R1R1=0R2=0002222121212121111PPRZrZrRRZrZrR解:ll/2qlllqEI1.5EIEIEI2/5EIqqZ1Z2R2R1Z1=1r11r21li/4li/3M1Z2=1r22r12i3i2i4i3M2qqR1PR2P8/2ql8/2qlMPr1123/16li2/3li2/3lir12li/4R1P8/32ql8/32ql2113/34lirlir/421lir/4124/321qlRPr21li/4r22i3i3i4R2Pir102202PRiqlZ292/932iqlZ584/4521ll/2qlllqEI1.5EIEIEI2/5EIZ1=1r11r21li/4li/3M1Z2=1r22r12i3i2i4i3M2iqlZ292/932iqlZ584/4521PMZMZMM2211qqR1PR2P8/2ql8/2qlMP8/2ql73/18M73/2673/26146/27292/272ql校核平衡条件292/27146/27292/27例2.作M图Z2R2R1=0R2=0002222121212121111PPRZrZrRRZrZrR解:lEIEAPllEIEI2EIR1Z1Pr21r11Z1=1Z2=1r22r12R2PR1PP3i/l12i/l12i/l3i/lM18i4i3iM2MPr112/3li2/3li2/24lir12li/3li/12R1PPr21li/3li/12r22i3i8R2P211/30lirlirr/92112ir1122PRP102PRiPlZ/044.021iPlZ/036.02PMZMZMM22110.24Pl0.13Pl0.39PlM例3.作M图，EI=常数R1=001111PRZr解:ir811PlRP1iPlZ8/1PMZMM11PllllZ1R1PM14iZ1=1r112i3iiMPR1PPPli4r11i3iR1PPlPMpl8/3pl4/pl2/pl8/pl例4.作M图，EI=常数R1=0解:0022221211212111PPRZrZrRZrZrR2=0PlllPllllPPZ2Z1R1=0解:PlllPZ2Z1i22M1r11i2Z1=1r21i2i4M2li/6li/232/2112/2=+R2PPR1PMP0022221211212111PPRZrZrRZrZrR2=0ir)224(11lir/)623(120AM01PRPRP2r22r12li/232/12lili/6AR2PAP222/)2612(lir0AMiPlZ/013.01iPlZ/05.022r12r22Z2=1例5.作M图解:0022221211212111PPRZrZrRZrZr2118/51lir22112/6lirr01PRPRP2222/30lirPlll1EIEIlEIEIEIEIEAPZ2Z1Z1=1M1li4/3li/3li/3M2li/3Z2=1li/3li/6r112/3li2/3li28/3lir212/3li2/3lir222/12li2/3li2/12li2/3liPMPiPlZ207821iPlZ4141722作M图，EI=常数R1=001111PRZr练习1:2/321qlRPiqlZ16/321PMZMM11M14iZ1=1r112i3iii4r11i3i2qlllllqZ1q2ql2/2ql2qlR1Pir811MPR1P2/2qlM16/916/616/1216/32/2ql作M图，EI=常数R1=0练习2:2/1PlRPPlllll/2l/2lP/2P/2P/2Z1=1i2i4ii6M1MP2/PlP/2Z1ir111101111PRZriPlZ22/1PMZMM11作M图R1=001111PRZr练习3:8/31qlRPiqlZ48/31PMZMM111EIlllqEIEI2EIqZ1M16i/lZ1=1q8/2qlMP11r2/12li2/6liPR18/3ql211/18lir1)建立位移法基本体系,列出典型方程EI=常数练习4:lllqlqZ4Z2Z3Z100004444343242141343433323213124243232221211414313212111PPPPRZrZrZrZrRZrZrZrZrRZrZrZrZrRZrZrZrZr2)求出典型方程中系数r14,r32,R4P。2)求出典型方程中系数r14,r32,R4P。qZ4Z2Z3Z13i/lZ4=1r146i/l3i/l6i/lM4R4P=-ql/23ir324i3i6i/lM2Z2=12ir14=-3i/lqR4P12/2qlMPr32=2i