法律资料6渐近法

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,*,结构力学,Structural mechanics,渐 近 法,successive approximation method,6-1 引言,foreword,渐近法,Chapter 11 successive approximation method,逐次逼近,approach gradually,收敛,convergence,精确解,accurate solution,特点：,characteristic,不组成求解方程,not form equation,生动形象，重复步骤，易于手算,vivid,repeated step,easy to manual calculation,渐近法,Successive,approximation method,力矩分配法,moment distribution method,无剪力分配法,no-shear distribution method,迭代法,iteration method,11-2 力矩分配法的根本原理basic principle of moment distribution method,一、根本概念 basic concept,1、劲度系数(转动刚度)S,:,stiffness coefficient(rotation stiffness),近端转动端仅发生单位转角时，引起的近端杆端弯矩。Bar-end moment of near end when only unit angle of rotation appears in near end(rotating end),A,A,A,i,A,B,i,B,A,i,B,A,2、传递系数C：,carry-over coefficient,当近端有转角时，远端弯距与近端弯距的比值。,the ratio of far-end moment and near-end moment when near end has angle of rotation,A,A,A,i,A,B,i,B,A,i,B,A,远,端,约,束,far-end restriction,S,C,固,定,fix,0.5,铰,支,hinge,0,滑,动,slip,-1,劲度系数S与传递系数C：,stiffness coefficient and carry-out coefficient,3、节点不平衡力矩：,unbalance moment of joint,4、分配系数：,distribution coefficient,5、分配弯矩：,distribution moment,6、传递弯矩：,carry-out moment,(Couple M acted at joint A is distributed to near end of each member by distribution coefficient,and far-end moment is equal to that near-end moment multiplies carry-over coefficient),i,14,节点转动,moment of Z1 angle when joint rotates,角产生的弯矩,Z,1,M,12,m,于是得,(,so),近端弯矩可写为：,near-end moment write as,分配系数,distribution coefficient,分配弯矩,distribution moment,固端弯矩,fix-end moment,F,M,12,将不平衡力矩变号后按劲度系数大小的比例分配给各近端,reverse the unbalance moment and distribute to every near-end by the proportion of stiffness coefficient,1,F,j,M,F,M,M,12,12,+,=,m,F,F,j,M,M,M,12,1,12,12,),(,+,-,=,m,远端弯矩,：,far-end moment,同理,(as same as),：,同理,(as same as)：,distribute every near-end moment to every far-end by the ratio of carry-out coefficient,归纳:,conclusion,fix joint,every bar has fix-end bending moment and,unbalance moment of joint,relax joint,distribute bending moment,carry-out,bending moment,二、计算步骤：,calculation steps,例,(e.g.),计算步骤,结点,B,A,D,杆端,BA,AB,AC,AD,DA,1 求各杆分配系数,/,1/2,1/6,1/3,/,2 求固端弯矩,0,40,0,-75,-25,3 力矩分配与传递,0,35/2,35/6,35/3,-35/3,4 计算最后杆端弯矩,0,57.5,5.8,-63.3,-36.7,结点A不平衡力矩为：,总结：conclusion,应用条件：,application condition,只有角位移的刚架和连续梁,rigid frame and beam,only,with angular displacement,三概念：,three concepts,刚度系数、分配系数、传递系数,stiffness、distribution、carry-out coefficient,符号规定：,sign stipulation,单结点力矩分配法根本原理：,basic principle of moment distribution method,加刚臂去刚臂叠加,add rigid arm remove rigid arm superposition,步骤:,step,1、计算固端弯距，不平衡力矩,calculate fix-end bending moment,unbalance moment,2、计算分配系数、传递系数,calculate distribution coefficient、carry-over coefficient,3、分配传递,distribute and carry,over,4、绘内力图,draw internal force diagram,与位移法一致,identical to displacement method,11-3 力矩分配法计算连续梁和无侧移刚架,calculate beam and rigid frame without sidesway with moment distribution method,一、计算步骤的形象化介绍,visualized introduction of calculation step,锁住结点1、2：,lock joint 1、2,放松结点,1,：,relax joint 1,P,1,2,1,2,1,2,P,P,1,2,1,1,重新锁住1结点，放松2结点：,lock joint 1 again,relax joint 2,然后再依次放松1、2结点，进行第二、三轮计算,。,relax joint 1、2 one by one,calculate by the second、third turn,最后：,finally,P,1,2,1,2,2,二、举例说明example,例1,计算分配系数：,calculate distribution coefficient,0.5,0.5 4/7,3/7,分配和,传递,Distribute and transfer,-80 80,-200 200,30 ,60,60,30,-66 ,-131,-99,17 ,33,33,17,-5 ,-10,-7,2 ,3,2,-31 176,-176 106,-106,先放松结点不平衡力矩的绝对值大的结点加快收敛。,firstly relax the joint whose absolute value of unbalance moment is biggest,.,例2,解：,solve,(3)计算分配系数、传递系数,calculate distribution coefficient、carry-out coefficient,(1)简化,simplify,(2)计算固端弯距,calculate fix-end moment,查表,check list,4分配、传递,distribution、carry-overA-C-A-C-A次序,5绘弯距图draw bending moment picture,例3EI=36000KN.m2,正、负最大弯矩绝对值相等，B、C支座应升降多少？,solve the sedimentation of support B、C,设B、C支座下沉,B,(if the settlement of support B is,B,),18KN/m,A,B,C,D,2/3,1/3,81,-96 -48,-3000,B,0,10+2000,B,5+1000,B,-5-1000,B,令，M,E,=M,B,得,B,=0.019m,例4 作内力图,draw internal picture,1、计算劲度系数：,calculate stiffness coefficient,2、求分配系数：,solve distribution coefficient,结点,(joint),B：,结点,(joint),C：,3、弯矩分配与传递：,moment distribution and carry-over,4、作弯矩图M,draw bending moment picture M,例5:绘弯矩图。,draw bending picture,A,i=2,i=1,i=1,80kn,160kn,30kn/m,B,D,分配系数,固端弯矩,B点一次分、传,C点一次分、传,B点二次分、传,C点二次分、传,B点三次分、传,C点第三次分配,最后弯矩,0.6,0.4,0.5,0.5,+90.0,-250.0,+250.0,-187.5,+112.5,0.0,0.0,+96.0,+64.0,+32.0,-23.7,-47.3,-23.7,-47.3,0.0,+14.2,+9.5,+4.8,-1.2,-2.4,-1.2,-2.4,0.0,+0.7,+0.5,+0.3,-0.2,-0.2,0.0,+200.9,-200.9,+237.4,-237.4,+87.6,3m,3m,10m,3m,5m,A,B,C,D,120,200.9,375,237.4,300,87.6,M图(kn.m),C,本章小结,conclusion,1、力矩分配法,moment distribution method,是以杆件的杆端弯矩为计算对象，采用了“固定放松传递的物理概念，采取逐次逼近的方法，求得杆端弯矩的精确解。,Object to the bar-end bending moment,adopt the physics concept of“fix relaxcarry-over,and the method of gradually approach to solve the accurate solution of bar-end bending moment.,2、明确概念,clear concept,记住：,remember,4、力矩分配法与位移法之关系无结点线位移：the relation between moment distribution method and displacement method(no joint linear di