单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,多结点的力矩分配法,* 基本理论为单结点理论,* 反复使用单结点原理,* 渐近收敛,多结点的力矩分配法* 基本理论为单结点理论,1,单结点弯矩分配法,1,、附加刚臂，写固端弯矩、求约束力矩,R,P,2,、计算分配系数,3,、,R,P,反号分配 、传递,4,、统计（合计）、作图,单结点弯矩分配法1、附加刚臂，写固端弯矩、求约束力矩RP2、,2,分配与传递,50,50,固端弯矩,0,0,-45,0,合计,0,50,5,0,2m,4m,60 kN,55 kNm,A,B,C,2m,分配系数与约束力矩,0.5,-100,0.5,50,5,50,50,62.5,分配与传递5050固端弯矩00-450合计050502m4m,3,多结点力矩分配法源出于单结点，使用时保证放松的结点是单结点即可,例题,1,：用力矩分配法计算下列结构。,EI=,常数,2m,2m,2m,2m,4m,2m,8 kN,16 kN,8 kN/m,多结点的力矩分配,多结点力矩分配法源出于单结点，使用时保证放松的结点是单结点即,4,8 kN,16 kN,8 kN/m,16 kNm,解：把悬臂杆等效如下结构,8 kN,16 kN,8 kN/m,16 kNm,R,1P,R,2P,8 kN16 kN8 kN/m16 kNm解：把悬臂杆等效如,5,8 kN,16 kN,8 kN/m,16 kNm,R,1P,R,2P,-R,1P,-R,2P,-R,1P,-R,2P,+,8 kN16 kN8 kN/m16 kNmR1PR2P-R1,6,-R,1P,R,-R,-R,2P,-R,1,R,1,=R,2P,+R,-R,1P,-R1PR-R-R2P-R1R1=R2P+R-R1P,7,-R,1,-R,1,右结点可分配了,R,-R,+,把上述过程写在一起,就是如下的步骤,:,-R1-R1右结点可分配了R-R+把上述过程写在一起,就是如,8,R,2P,右结点约束,反号分配左结点,左结点约束,右结点反号分配,此时该结点平衡了,R,2,此时该结点平衡了,此结点又不平衡了,此结点约束力有变化,R,1,=R+R,2P,-R,1P,-R,1,R,R,1P,R,2P,R2P右结点约束左结点约束此时该结点平衡了R2此时该结点平衡,9,。,如此完成渐近过程,-R,2,右结点加约束,左结点反号分配,此时该结点平衡了,此结点约束力有变化,R,3,。-R2右结点加约束此时该结点平衡了此结点约束力,10,8 kN,16 kN,8 kN/m,16 kNm,分配系数,0.5,0.5,4/7,3/7,固端弯矩,-4,4,-8,8,-8,16,锁,C,，放,B,2,2,1,1,B,C,锁,B,，放,C,-4/7,-3/7,-2/7,0,锁,C,，放,B,1/7,1/7,1/14,1/14,锁,B,，放,C,-4/98,-3/98,0,-41/14,合计,43/7,-43/7,119/14,-119/14,16,多结点的力矩分配,具体演算过程,8 kN16 kN8 kN/m16 kNm分配系数0.50.,11,弯矩图,2.93,6.14,8.5,16,例题,2,8 kN,12 kN/m,8 kN,4m,4m,4m,2m,3m,EI,EI,5EI/8,EI,多结点的力矩分配,-41/14,43/7,-43/7,119/14,-119/14,16,弯矩图 2.93 6.14 8.5 16 例题2 8 kN1,12,解：,8 kN,12 kN/m,16 kNm,分配系数,0.2,0.8,8/11,3/11,固端弯矩,16,16,-16,16,8,16,-17.45,-6.55,-8.73,0,分配、传递,1.75,6.98,-1.75,3.49,分配、传递,分配、传递,-2.54,-0.95,-1.27,0,分配、传递,0.25,1.02,-0.25,0.51,分配、传递,-0.37,-0.14,-0.19,0,分配,0.04,0.15,合计,14,18.04,-18.04,-0.36,0.36,16,4m,EI,4m,EI,5m,5EI/8,不思，故有惑；不求，故无得；不问，故无知,解：8 kN12 kN/m16 kNm 分配系数0.20.8,13,弯矩图,14,18.04,0.36,16,单位：,kNm,例题,3,20 kNm,3 kN/m,2m,4m,4m,4m,EI =,常数,不思，故有惑；不求，故无得；不问，故无知,弯矩图1418.040.3616单位：kNm 例题320 k,14,解：,0.5,0.5,20,4/11,4/11,3/11,-2.67,-2.67,2.67,-10,-10,-5,-5,2.79,2.09,2.79,1.40,1.40,-0.7,-0.7,-0.35,-0.35,0.13,0.09,0.13,-5.35,-10.7,-9.3,-2.43,2.18,0.25,4.13,你能画出弯矩图吗？,解：0.50.5204/114/113/11-2.67-2.,15,弯矩图,5.35,10.7,9.3,2.18,2.43,4.13,0.25,单位：,kNm,不思，故有惑；不求，故无得；不问，故无知,弯矩图5.3510.79.32.182.434.130.25,16,例题,4,7.5m,5m,5m,7.5m,5m,5m,20kN/m,20kN/m,例题47.5m5m5m7.5m5m5m20kN/m20kN/,17,解：取半结构计算。,A,B,C,D,E,F,解：取半结构计算。 ABCDEF,18,41.67,2/7,1/7,4/7,0,1/3,1/3,1/3,41.67,-41.67,0,0,0,0,0,41.67,-41.67,-11.9,-23.8,-,5.95,-11.9,5.95,3.97,3.97,3.97,1.99,1.99,1.99,-,0.57,-,1.14,-,0.28,0.28,-12.47,18.42,-6.23,6.23,-49.98,45.83,-39.6,3.97,1.99,41.672/71/74/701/31/31/341.67-,19,12.47,6.23,18.42,49.98,45.83,39.6,3.98,1.99,12.476.2318.4249.9845.8339.63.,20,例,5,8 kN,16 kN,6 kN/m,R,1,R,2,8 kN,16 kN,6 kN/m,2,2,m,4m,2,2,m,EI=,常数,-R,1,-R,2,+,例58 kN16 kN6 kN/mR1R28 kN16 kN,21,8 kN,16 kN,3 kN/m,分配系数,0.5,0.5,0.8,0.2,固端弯矩,-4,4,-8,8,-16,-8,分配与传递,6.4,1.6,-1.6,3.2,分配与传递,0.4,0.4,0.2,0.2,分配与传递,-0.16,-0.04,0.04,-0.08,分配与传递,0.04,0.04,0.02,合计,3.78,4.44,-4.44,14.44,-14.44,-9.56,8 kN16 kN3 kN/m分配系数0.50.50.80.,22,例,5,用力矩分配法计算下列结构。 杆长都是,L,。,P,P,EI,1,=,EI,EI,EI,A,B,C,D,E,解：,（,1,）力矩分配法是计算无侧移刚架，,但对剪力静定杆也可使用。,因为在,B,结点附加刚臂后：,BC,杆为一端固定，另端可滑动杆，,AB,杆成为,A,端固定铰，另端可滑动杆。,例5用力矩分配法计算下列结构。 杆长都是L。 PPEI1=,23,(2),关于分配系数,P,P,EI,1,=,EI,EI,EI,A,B,C,D,E,B,B,A,C,(2)关于分配系数PPEI1= EIEIEIABCDEBB,24,A,B,支座,B,转动时无弯矩产生,位移图,不思，故有惑；不求，故无得；不问，故无知,A,B,E,C,P,PL,P,AB支座B转动时无弯矩产生位移图不思，故有惑；不求，故无得；,25,1/4,3/4,0,-PL/2,-PL/2,-2PL,-5PL/2,5PL/8,15PL/8,-,5PL/8,-9PL/8,PL/8,15PL/8,-2PL,9PL/8,PL/8,2PL,15PL/8,1/43/40-PL/2-PL/2-2PL-5PL/2 5P,26,例题,6,用力矩分配法计算具有剪力静定杆结构,10kN,10kN,5 kN/m,4m,5m,4m,1m,i =,常数,例题6 用力矩分配法计算具有剪力静定杆结构 10kN10k,27,20,50,50,10,A,B,20,不思，故有惑；不求，故无得；不问，故无知,20505010AB20不思，故有惑；不求，故无得；不问，故,28,-20,-20,-50,-50,10,3/4,1/4,1/5,1/5,3/5,-20,-60,12,-12,36,12,-12,24,8,-8,1.6,-1.6,4.8,1.6,-1.6,1.2,0.4,-0.4,0.08,0.24,0.08,25.2,-25.2,-14.72,51.04,-36.32,-63.53,0,0,0,-20-20-50-50103/41/41/51/53/5-,29,25.2,51.04,63.53,36.32,14.72,25.251.0463.5336.3214.72,30,小结,：,多结点力矩分配时，先附加刚臂求出固端弯矩，然后,放松若干结点，保证每个结点都是单结点，分配，传递后，再锁,紧这些结点，然后放松先前锁紧的结点，进行分配与传递，然后,锁紧，两组结点轮换进行。,例如下图。,1,2,3,4,先放松,1,，,3,结点，锁紧,2,，,4,结点，则,1,，,3,各是单结点分配,然后，锁紧,1,，,3,结点，放松,2,，,4,结点，则,2,，,4,结点也为单结点分配,1,2,3,4,小结：多结点力矩分配时，先附加刚臂求出固端弯矩，然后1234,31,对下列结构，可进行如下的结点分组。,对下列结构，可进行如下的结点分组。,32,练习题,8 kN,3 kN/m,2m,2m,4m,EI,EI,1,2,EI=,常数,2m,2m,2m,2m,2m,30 kN/m,练习题8 kN3 kN/m2m2m4mEIEI12EI=常数,33,8 kN,3 kN/m,2m,2m,4m,EI,EI,答案,分配系数,0.75,0.25,7.5,2.5,固端弯矩,0,6,-16,-8,-2.5,0,0,13.5,-13.5,-10.5,8 kN3 kN/m2m2m4mEIEI答案分配系数0.75,34,结构力学下多结点力矩分配法课件,35,3/11,4/11,4/11,1/3,1/3,1/3,1/4,1/4,1/4,1/4,1/4,1/4,1/4,1/4,15,-10,10,-10,10,-1.36,-1.82,-1.82,-0.91,-0.91,0.23,0.23,0.23,0.23,0.3,0.3,0.3,0.12,0.15,0.12,0.12,0.15,-0.07,-0.07,-0.07,0.07,-0.035,-0.035,13.64,-1.82,-11.82,-0.68,9.4,0.3,-9.7,10.15,0.08,0.12,0.23,0.23,0.12,0.23,0.19,-0.07,-0.07,-0.035,-0.035,3/114/114/111/31/31/31/41/41/,36,13.64,11.82,9.4,9.7,10.15,1.82,0.68,0.3,0.08,0.23,0.12,0.12,0.035,0.07,0.035,0.19,0.23,13.6411.829.49.710.151.820.680,37,作业：,0.3,0.3,0.4,-12,0.32,0.36,0.32,4.5,0.4,0.3,0.3,7.5,-12,12,-7.5,7.5,3.6,3.6,4.8,-2.25,-3,-2.25,2.4,-1.5,5.4,-1.728,-1.944,-1.728,-0.86,-0.86,0.258,0.258,0.344,0.344,0.258,0.258,0.172,0.172,-0.11,-0.11,-0.124,3.86,3.86,-7.72,12.73,-2.06,3.98,-10.67,-1.99,-1.99,作业：0.30.30.4-120.320.360.32 4.,38,3.86,3.86,-7.72,12.73,-2.06,3.98,-10.67,-1.99,-1.99,3.863.86-7.7212.73-2.063.98-10,39,结构力学下多结点力矩分配法课件,40,结构力学下多结点力矩分配法课件,41,谢谢你的阅读,知识就是财富,丰富你的人生,谢谢你的阅读知识就是财富,42,