位移图法计算桁架节点位移精度的讨论

Discussion on Computational Accuracy of Truss Joint Displacement by Displacement Graph Method

在桁架的几何变形的基础上,建立了外载荷作用下节点处的静力平衡方程。考虑几何变形协调关系,求出了桁架节点位移的解析解。通过算例,把位移图法计算结果与解析法计算结果进行对比可知:解析法计算结果均大于位移图法计算结果。采用图解法对桁架节点位移进行简化计算时,位移图法计算结果与解析法计算结果的误差有时会超过10%。所以,采用位移图法计算桁架的节点位移时,应根据桁架的受力实际情况对节点位移方向做出合理的判断假设,这样才能控制位移图法的计算精度不超过实际工程所允许的误差5%。

Based on the geometric deformation of truss,the static equilibrium equation at the joints under external load is established,and the analytical solution of the truss joint displacement is obtained by considering the coordination relationship of the geometric deformation.By comparing the calculated results based on the displacement graph method with the ones based on the analytical method,it can be seen that the calculated results based on the analytical method are all larger than the ones based on the displacement graph method.When the calculation process for node displacement is simplified by displacement graph method,the error is sometimes more than 10%.Therefore,when the displacement diagram method is used to calculate the displacement of the truss joint,a reasonable judgment assumption should be made on the displacement direction of the joint according to the actual stress condition of the truss,so that the computational accuracy based on the displacement diagram method will not exceed the 5%allowed error in the actual project.