L截面几何特性.docx

静矩：Sy=1000*40*500+50*360*25=2.045*107Sz=1000*40*20+50*360*220=4.76*106面积：A1=1000*40=4*104A2=50*360=1.8*104A=A1+A2=5.8*104形心：yc= Sz/A=4.76*106/5.8*104=82.07zc= Sy/A=2.045*107/5.8*104=352.59惯性矩：Iy1=Iyc1+a2A1=40*10003/12+(500-352.59)2*4*104=4.203*109Iy2=Iyc2+a2A2=360*503/12+(25-352.59)2*1.8*104=1.935*109Iy=Iy1+Iy2=4.203*109+1.935*109=6.138*109Iz1=Izc1+b2A1=1000*403/12+(20-82.07)2*4*104=1.594*108Iz2=Izc2+b2A2=50*3603/12+(220-82.07)2*1.8*104=5.368*108Iz=Iz1+ Iz2=1.594*108+5.368*108=6.962*108惯性积：I1yz=abA1=（500-352.59）（20-82.07）*4*104=-3.66*108I2yz=abA2=(25-352.59）（220-82.07）*1.8*104=-7.143*108=-8.133 *108 Iyz= I1yz+I2yz=-11.793*108y=ycos+zsinz=-ysin+zcosIy=z2dA=(-ysin+zcos)2dA=IZ*sin2+Iycos2-Iyzsin2Iz=y2dA=(ycos+zsin)2dA= IZ*cos2+Iysin2+Iyzsin2Iyz=yzdA=ycos+zsin(-ysin+zcos)dA= (Iy-Iz)/2*sin2+Iyzcos2令Iyz=0，有(Iy-Iz)/2*sin2+Iyzcos2=0tan2=-2Iyz/（Iy-Iz）=0.433=11.720sin=0.2027cos=0.979sin2=0.398Iy =IZ*sin2+Iycos2-Iyzsin2=6.962*108*（0.2027）2+6.138*109*（0.979）2-（-11.793*108）*0.398=63.81*108mm4Iz= IZ*cos2+Iysin2+Iyzsin2=6.962*108*（0.979）2+6.138*109*（0.2027）2+（-11.793*108）*0.398=4.501*108y=qz24EIYl3=10*0.979*3*3*3/（24*2.55*107*63.81*108*10-12）=6.76872E-05z=qy24EIzl3=10*0.2027*3*3*3/（24*2.55*107*4.501*108*10-12）=1.98681 E-04主轴方向：y=y*cos=(6.76872E-05)* 0.979=6.63E-05z=z* sin=(1.98681 E-04)* 0.2027=4.02727E-05圆截面的惯性矩为Ix= Iy=d464矩形截面为Ix=BH312半圆形截面，形心在y轴上，取高度为y处微面积为dA=2R2-r2dy静矩Sz=2R33形心yc=SzA=4R3圆环形截面Ix= Iy=D4(1-4)64静矩：Sy=1000*200*1100+100*1000*500=2.7*108Sz=0面积：A1=1000*200=2*105A2=100*1000=1*105A=A1+A2=3*105形心：yc= Sz/A=0zc= Sy/A=2.7*108/3*105=900惯性矩：Iy1=Iyc1+a2A1=1000*2003/12+(1100-900)2*2*105=8.66*109Iy2=Iyc2+a2A2=100*10003/12+(500-900)2*1*105=24.33*109Iy=Iy1+Iy2=33*109Iz1=Izc1+b2A1=200*10003/12+0=166.67*108Iz2=Izc2+b2A2=1000*1003/12+0=0.83*108Iz=Iz1+ Iz2=1.675*1010轴对称图形，惯性积为0。Iy=500*503/12+2*50*4503/12+2*2502*50*450= 3.77*109Iz=50*5003/12+2*450*503/12=5.302*108轴对称，惯性积为0截面扭转常数就是抗扭刚度（Tors