工程力學(xué)教學(xué)一九

4.3位移法(DisplacementMethod)一.單跨超靜定梁的形常數(shù)與載常數(shù)4.3位移法二.位移法基本概念三.位移法基本結(jié)構(gòu)與基本未知量四.位移法典型方程qll/2l/2EI=常數(shù)qllqlqlZ1Z2R2R1R1=0R2=0四.位移法典型方程qll/2l/2EI=常數(shù)qllqlqlZ1Z2=1R2R1R1=0R2=0Z1=1r12r21r22r11qlqlR1PR2P---位移法典型方程rij(i=j)主系數(shù)>0rij=rji反力互等剛度系數(shù),體系常數(shù)RiP荷載系數(shù)rij(i=j)副系數(shù)qll/2l/2EI=常數(shù)qllqlqlZ1Z2=1R2R1R1=0R2=0Z1=1r12r21r22r11qlqlR1PR2PM2MPM1r11r12R1Pr21r22R2P一.單跨超靜定梁的形常數(shù)與載常數(shù)4.3位移法二.位移法基本概念三.位移法基本結(jié)構(gòu)與基本未知量四.位移法典型方程五.算例例1.作M圖ll/2lllEI1.5EIEIEIZ1Z2R2R1R1=0R2=0解:ll/2lllEI1.5EIEIEIZ1Z2R2R1Z1=1r11r21M1Z2=1r22r12M2R1PR2PMPr11r12R1Pr21r22R2Pll/2lllEI1.5EIEIEIZ1=1r11r21M1Z2=1r22r12M2R1PR2PMPM校核平衡條件例2.作M圖Z2R2R1=0R2=0解:lEIPllEIEI2EIR1Z1Pr21r11Z1=1Z2=1r22r12R2PR1PP3i/l12i/l12i/l3i/lM18i4i3iM2MPr11r12R1PPr21r22R2P0.24Pl0.13Pl0.39PlM例3.作M圖，EI=常數(shù)R1=0解:PllllZ1R1PM14iZ1=1r112i3iiMPR1PPPlr11R1PPM例4.作M圖，EI=常數(shù)R1=0解:R2=0PlllPllllPPZ2Z1R1=0解:PlllPZ2Z1M1r11Z1=1r21M211=+R2PPR1PMPR2=0r22r12AR2PAPr12r22Z2=1例5.作M圖解:PlllEIlEIEIEIEIPZ2Z1Z1=1M1M2Z2=1r11r21r22PMP作M圖，EI=常數(shù)R1=0練習(xí)1:M14iZ1=1r112i3iir11llllZ1R1PMPR1PM作M圖，EI=常數(shù)R1=0練習(xí)2:Plllll/2l/2lP/2P/2P/2Z1=1M1MPP/2Z1作M圖R1=0練習(xí)3:lllEIEI2EIZ1M16i/lZ1=1MP1)建立位移法基本體系,列出典型方程EI=常數(shù)練習(xí)4:llllZ4Z2Z3Z12)求出典型方程中系數(shù)r14,r32,R4P。2)御求仰出典腔型方耐程中坐系數(shù)r14,r32,R4P。Z4Z2Z3Z13i/lZ4=1r146i/l3i/l6i/