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Cable theory of computation and analytical form finding algorithm based on mass conservation

DOI：10.7511/jslx20230420001

 作者 单位 E-mail 朱伟华 湖南城市学院 土木工程学院, 益阳 413000长沙理工大学 土木工程学院, 长沙 410001 1542475739@qq.com 颜东煌 长沙理工大学 土木工程学院, 长沙 410001 许红胜 长沙理工大学 土木工程学院, 长沙 410001

旨在解决既有缆索计算理论的基本假定不合理问题,基于质量守恒原则推导了精细化缆索计算理论;根据拉格朗日坐标建立了考虑缆索截面变形后受拉刚度变化的改进弹性悬链线计算理论。研究结果表明,精细化缆索计算理论与改进的分段悬链线计算理论具有等价性;自重下跨度为888 m的缆索找形计算案例中,精细化缆索计算理论与悬链线方程理论的缆力及高程差值分别为61.5 kN和-158.7 mm,与弹性悬链线理论计算差值对应分别为1.9 kN和0.5 mm;受外载下跨度为1038 m缆索找形计算案例中,推导的精细化缆索计算理论与悬链线方程理论缆力差值分别为77.8 kN,与弹性悬链线理论无应力长度计算差值控制为1.0 mm。精细化缆索单元计算理论及缆索找形算法可作为缆索承载结构体系一种完备的精细化计算理论与方法。

In order to solve the problem that the basic assumptions of the existing cable theory of computation are unreasonable, the refined cable theory of computation is derived based on the principle of mass conservation.Based on Lagrangian coordinates,an improved elastic catenary theory of computation considering the change of tensile stiffness after the cable section deformation is established.The results show that the refined cable theory of computation is equivalent to the improved piecewise catenary theory of computation.In the case of form finding of a cable with a span of 888 m under the dead weight,the difference in the cable force and elevation between the refined cable theory and the catenary theory is 61.7 kN and -156.5 mm respectively,and the corresponding difference with the elastic catenary theory is 1.6 kN and -0.2 mm respectively.In the case of form finding of a cable with a span of 1038 meters under external load,the difference in the cable force between the refined cable theory and the catenary theory of equations is 77.8 kN,and the difference in the unstressed length is made to be below 1.0 mm.The refined cable element theory of computation and cable form finding algorithm can be used as a complete refined theory of computation and method for the cable bearing structure system.