圆截面的抗弯截面系数和抗扭截面系数怎么求?谢谢,材料力学的一个基本的推导,谢谢各位。

2025-03-16 05:52:26
推荐回答(5个)
回答1:

抗扭截面系数:Wt=Ip/r(Wt为抗扭截面系数,Ip为横截面的极惯性矩,r为截面半径)

抗弯截面系数:Wz=Iz/y(Wz为抗弯截面系数,Iz为横截面对z轴惯性矩,y为截面离圆心最大值)

在横截面距圆心为ρ处取一微面积dA,该微面积上的内力为τdA,对圆心的力矩为ρ*τdA,在整个横截面积分得横截面上的内力系对圆心之矩,这就是横截面上的扭矩T。T=∫ρ*τdA

又有τp=Gρdφ/dx,将T代入其中的T=Gdφ/dx*∫ρ²dA,令Ip=∫ρ²dA,代入化简得τmax=T*r/Ip

令Wt=Ip/r,即为抗扭截面系数的来由。

对于中性轴为横截面的对称轴,最大拉、压应力相等,都为σ=My/Iz。令Wz=Iz/y即得抗弯截面系数。

扩展资料:

以上公式都为在平面假设的基础上导出的。试验结果表明,只有对等直圆轴,平面假设才成立,所以这些公式只适用于等直圆轴。对于圆截面沿周线缓慢变化的小锥度圆锥周,也可以近似的应用这些公式。

实心轴:Ip=πd⁴/32,Wt=Ip*2/d=πd³/16,Iz=πd⁴/64,Wz=πd³/32

空心轴:α=d/D,Wt=πD⁴(1-α⁴)/32,Wz=πD³(1-α⁴)/32

回答2:

回答3:

回答4:

空心轴:α=d/D,Wt=πD⁴(1-α⁴)/32,Wz=πD³(1-α⁴)/32
公式是否有点小问题

回答5:

元截面的抗弯截面系数和抗扭截面系数怎么求?这道题我姐答不上来。请老师回答。

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