中农大土木结构力学-力矩分配法.ppt

结构力学,傅向荣,第八章 渐进法,第一讲 基本思想,力矩分配法,力矩分配法是基于位移法的逐步逼近精确解的近似方法。单独使用时只能用于无侧移（线位移）的结构。,力矩分配法,一.基本概念,固定状态:,-不平衡力矩,顺时针为正,固端弯矩-荷载引起的单跨梁两端的杆端弯矩,绕杆端顺时针为正.,放松状态:需借助分配系数,传递系数等概念求解,转动刚度：使AB杆的A端产生单位转动，在A端所需施加的杆端弯矩称为AB杆A端的转动刚度，记作SAB。,A端一般称为近端（本端），B端一般称为远端（它端）。,对等直杆，SAB只与B端的支撑条件有关。,-分配弯矩,-分配系数,一个结点上的各杆端分配系数总和恒等于1。,令,令,-分配弯矩,-分配系数,一个结点上的各杆端分配系数总和恒等于1。,-传递系数,远端固定时:,远端铰支时:,远端定向时:,C=1/2,C=0,C=-1,传递弯矩,与远端支承情况有关,固定状态:,放松状态:,最终杆端弯矩:,M,例1.计算图示梁,作弯矩图,解:,例2.计算图示刚架,作弯矩图,解:,1/2,3/8,1/8,-1/4,1/4,1/8,所的结果是近似解吗?,练习,求不平衡力矩,作图示梁的弯矩图(利用传递系数的概念),40kN.m,20kN.m,练习:作弯矩图,解:,-57.1,固定状态:,二.多结点力矩分配,-28.6,-42.9,-9.2,-12.2,-6.1,3.5,2.6,1.8,.,放松结点2(结点1固定):,放松结点1(结点2固定):,0.571,0.429,0.571,0.429,0,150,-100,100,0,0,-57.1,-42.9,0,-28.6,-12.2,-9.2,0,-6.1,3.5,2.6,0,1.8,-0.8,-1.0,0,140,-140,40.3,-40.3,0,140,40.3,M,作剪力图,求反力,例：试求作图示连续梁的M图。EI等于常数，l1=6 m,l2=5 m，P=1000kN。（只计算二轮）,883,-735,-281,-469,-151,-151,47,29,54,-44,-1922,656,-656,-595,594,1721,-1721,-3279,作业：力矩分配法计算图示连续梁，作弯矩图。,-0.065,0.508,M,0.492,AG,AC,CA,GA,CE,CH,HC,EC,0,-2.083,AK,0,0.781,-1.042,0.398,0.398,0.204,1.302,0.641,0.661,-0.661,0.321,0.321,-0.321,-0.128,-0.128,-0.065,0.065,-0.064,-0.064,-0.064,-0.064,0.064,0.031,0.033,-0.033,0.608,-1.389,0.781,-1.736,0.193,-0.128,0.065,-0.064,无剪力分配法,同力矩分配法一样是基于位移法的逐步逼近精确解的近似方法。单独使用时只能用于一些特殊的有侧移（线位移）的结构。,应用条件：刚架中除两端无相对线位移的杆件外，其余杆件都是剪力静定杆件。,-6.60,-6.60,-22.5,0.0,0.0,MAB,MAD,MBA,MBC,MBE,MCB,-22.5,0.60,0.85,27.65,-0.60,0.15,7.05,-0.15,0.0,0.01,0.14,-0.85,-0.01,单位：,AB,BA,BC,CB,1/3,2/3,M,-20,20,0,0,-75,-50,-25,-25,-45,-30,-25,40,Z1,8-5力矩分配法与位移法的联合应用,基本思路：由位移法处理线位移，由力矩分配法处理转角位移，各尽所长。,AD,AB,BA,BE,BC,CB,CF,0.5,0.5,0.5,0.5,1/3,1/3,1/3,M,-6,-6,-6,DA,EB,FC,M,-6,-6,-6,0,0,0,0,6,3,3,1.5,1.5,1.5,1.5,3,3,3,1,1,1,0.5,0.5,1.5,0.5,-0.5,-0.25,-0.25,-0.25,-0.25,-0.125,-0.125,-0.125,-0.125,-0.125,0.25,0.083,0.083,0.083,-3.25,3.25,2.458,2.458,-4.917,3.25,-3.25,-4.625,-4.625,-5.5,