力矩分配法至诚土木课件

,9-1,力矩分配法的基本概念,9-2,单结点的力矩分配,基本运算,9-3,多结点的力矩分配,渐进运算,9-4,计算结果的校核,2,i,12,4,i,12,i,13,i,13,1,3,i,14,i,12,i,14,i,13,2,1,3,4,M,(1),位移法方程,k,11,图,M,F,1P,代入位移法方程,1,转动刚度,：梁端发生单位转角产生的弯矩。,2,分配系数,：与转动刚度成正比,3,传递系数,：近端发生转角时，远端弯矩与近端弯矩的比值.,9-2,单结点的力矩分配,基本运算,例题,固端弯矩,-M,分配、传递,2,M,/7,4,M,/7,3,M,/7,0,杆端弯矩,2,M,/7,4,M,/7,3,M,/7,0,3/7,4/7,2,M,/7,4,M,/7,3,M,/7,M,图,i,i,M,i,i,A,B,C,B,（a）,加载变形曲线,B,M,BA,M,BC,M,AB,A,B,C,M,F,BA,M,F,BC,=0,M,F,AB,M,B,（b）,约束节点B,A,B,C,M,BA,M,BC,M,AB,（C）,放松节点B,M,F,BA,+M,BA,=M,BA,9-2,单结点的力矩分配,基本运算,例题,3/7,4/7,固端弯矩,-ql,2,/8,分配、传递,2,ql,2,/56,4,ql,2,/56,3,ql,2,/56,0,杆端弯矩,2,ql,2,/56,4,ql,2,/56,-4,ql,2,/56,0,M,图,4,ql,2,/56,4,ql,2,/56,q,i,i,l,l,求固端弯矩；,将会交于结点的固端弯矩之和按分配系数分配给每一个杆端。,各杆按各自的传递系数向远端传递。,将固端弯矩和分配（或传递的弯矩）相加，得杆端最后弯矩。,例题,固端弯矩,-36 36,-18,0.6,0.4,最后M,-39.6 28.8,-,28.8 0,分配、传递,-3.6 ,-7.2,-10.8, 0,12kN/m,2,i,i,16,kN,6,m,3,m,3,m,39.6,M,图,(,kNm,),28.8,例题,固端弯矩,-F,P,l,杆端弯矩,F,P,l/2,F,P,l,-F,P,l,0,分配、传递,F,P,l,/2,F,P,l,0,l,l,2,i,i,F,P,1,0,F,P,l,F,P,l/2,M,图,例题,30kN/m,100kN,4,m,B,A,C,D,i,=2,i,=1.5,i,=2,4,m,3,m,2,m,-2.4,-3.6,-4.8,-3.6,-1.8,60,-48,72,56.4,-4.8,51.6,70.2,B,C,D,A,AB AC AD,0.3,0.4,0.3,4.8,M,图(kNm),2.4,56.4,51.6,70.2,-ql,2,/12,-2ql,2,/60,-7ql,2,/60,ql,2,/12,-4ql,2,/60,-ql,2,/60,ql,2,/60,ql,2,/60 -ql,2,/60 ql,2,/60,例题,l,q,l,B,A,C,i,i,C,A,0.8,0.2,M,图,ql,2,/60,7ql,2,/60,S,ik,=,4,i,ik,S,ik,=Kl,2,S,ik,=,4,i,ik,S,ik,=,4,i,ik,S,ik,=,4,i,ik,练习,i,k,i,k,i,k,i,k,S,ik,=,3,i,ik,S,ik,=,0,K,l,i,k,i,k,i,k,EI,=,A,B,C,D,B,C,A,B,C,D,M,B,M,C,M,F,BC,M,F,CB,（a）,加载变形曲线,（b）,约束节点后的变形曲线,9-3,多结点的力矩分配,渐进运算,A,B,C,D,M,C,=M,C,+M,C,B,C,D,B,-M,B,M,C,M,BC,M,CB,M,AB,（c）,放松节点,B,（c） b+c,的累加曲线,9-3,多结点的力矩分配,渐进运算,A,B,C,D,C,M,B,-M,C,M,BC,M,CB,M,CD,0,（d）,放松节点,C,A,B,C,D,（d）,加载变形曲线,9-3,多结点的力矩分配,渐进运算,A,B,C,D,20kN/m,8,0kN,EI,6m,1.5EI,2EI,3m,3m,6m,固端弯矩,分配系数,0.4,0.6,0.5,0.5,-60,+60,-90,0,36,24,12,18,6,6,3,放松B,放松C,放松B,放松C,放松B,放松C,-0.9,-1.8,0.45,0.45,0.23,-1.2,-0.6,-0.09,-0.05,-0.07,-0.14,0.04,0.03,杆端弯矩,11.35,22.71,-22.71,83.52,-83.52,0,例题,9-3,多结点的力矩分配,渐进运算,杆端弯矩,22.9,0.5 0.3,-100,-200/3,200/3,-100,1/2,1/2,4/7,3/7,1,0,固端弯矩,分配,与,传递,分配系数,50 50, 25 16.7 ,33.3,-3.6 - 3.6, -1.8 -2.7 ,-5.4,7.2 ,14.3 10.7, 5.4,1.3 ,2.6 1.9, 1,-0.7 - 0.6, -0.3 -0.5 ,-1,45.7 54.3 40.3 40.3 100 -100,9-3,多结点的力矩分配,渐进运算,8kN/m,0.75EI,100kNm,10kN,10m,EI,EI,10m,10m,10m,22.9,45.7,54.3,40.3,100,100,9-3,多结点的力矩分配,渐进运算,-100,-100+50,100,16,32,18,杆端弯矩,1/2,1/2,16/25,9/25,固端弯矩,分配,与,传递,分配系数,45.5,54.5,40.2,-40.2,23,21,42,42,1.7,3.3,3.4,-6.7,-13.4,-7.6,0.2,0.3,-1.1,-0.6,-0.5,8kN/m,EI,100kNm,10m,100kNm,A,B,C,D,10m,10m,EI,0.75EI,23,46,54,40,100,100,-125,125,-125,125,-62.5,-62.5,-31.2,-31.2,0.5,0.5,0.5,0.5,15.6,15.6,7.8,7.8,-2,-3.9,-3.9,-2,1,1,0.5,0.5,-0.3,-0.2,杆端,弯矩,-116.7,141.6,-141.6,-66.6,66.6,-33.2,100kN,5m,5m,100kN,EI=,常数,A,B,C,D,5m,5m,分配,与,传递,结点,杆端,分配,系数,固端,弯矩,A,B,C,D,AB,BA,BC,CB,CD,DC,141.6,116.7,66.6,33.2,250,250,M,图,(kNm),5m,5m,100kN,EI=,常数,A,B,C,D,5m,5m,100kN,10m,12.5kN,5m,5m,100kN,EI=,常数,A,B,C,D,5m,5m,100kN,125kNm,ABCD,部分:,弯矩图一样,剪力图一样,轴力图不一样,9-4,计算结果的校核,因为,汇交于同一刚结点的各杆转角都相等,所以,都应满足上式.,消去远端转角,平衡条件:每次分配时,自然满足,变形协调条件:,分配系数 0.6 0.4 0.5 0.5,固端弯矩 90 -250 250 -187.5 112.5,分配,与,传递,96 64 32,-,23.6 -47.3 -47.3 -23.6,14.2 9.4 4.7,-1.2 -2.3 -2.3 -1.2,0.7 0.5 0.3,-0.1 -0.2,杆端弯矩 200.9 -200.9 237.3 -237.3 87.7,i=2 i=1 i=1,80kN,160kN,30kN/m,3m 3m 10m 3m 5m,例题,237.3,87.7,200.9,M,图(kNm),同理,可对C点进行校核,对于B点,