如何计算图示截面形心位置?

2025-03-16 01:09:48
推荐回答(2个)
回答1:

形心计算公式可以参考上图中给出的计算方法,

在本题中:

由于图形关于y轴对称,所以不需要考虑形心在x轴上的位置

可将“工字梁”分成三部分

  1. 上部矩形区域(长150,宽20),形心坐标(y=190)

  2. 中部矩形区域(长20,宽160),形心坐标(y=100)

  3. 下部矩形区域(长200,宽20),形心坐标(y=10)

可以计算总图形的形心坐标90

y=(S1*y1+S2*y2+S3*y3)/(S1+S2+S3)=(150*20*190+20*160*100+200*20*10)/(150*20+20*160+200*20)

于是就可以求出结果,这里我不再计算,希望你能自己算一遍。

回答2:

我只能告诉你方法,不可以越俎代庖,代替你完成!
1、这是左右对称的工字形截面,截面形心在Y轴上,所以不用求Xc;
2、此截面可分为上、下翼缘及腹板共三部分,欲求此组合截面的形心,可先分别计算出此三部分的截面积及组合截面的截面积,设为A1、A2、A3及A总;
3、然后分别计算出此三部分截面形心到某水平轴的距离(例如工字型底边),设为Y1、Y2、Y3;
4、最后得到组合截面的形心到工字型底边的距离, 式子 Yc·A总=Y1·A1+Y2·A2+Y3·A3。
所以Yc=(Y1·A1+Y2·A2+Y3·A3)/A总。Yc就是X轴到底边的距离。
解答完毕。请楼主亲自演算三遍,则会记住一生不忘,若遇各种复杂截面,如法炮制就是。

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