考虑弯曲非线性效应的修正悬链线方程及其对悬链线垂弧的影响  

Modified catenary equation considering bending nonlinear effect and its influence on the catenary sag

作　　者：杨新航 肖奉英 肖先志 黄模佳[1] YANG Xinhang;XIAO Fengying;XIAO Xianzhi;HUANG Mojia(School of Infrastructure Engineering,Nanchang University,Nanchang 330000,China)

机构地区：[1]南昌大学工程建设学院,江西南昌330000

出　　处：《南昌大学学报(理科版)》2024年第6期511-520,共10页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11572147)。

摘　　要：现有的悬链线理论通常建立在结构是完全柔性的假设之上,未考虑弯曲效应对悬链线构形的影响。截面的抗弯刚度引起的弯曲效应会对悬链线的构形产生影响,悬链线大斜率引发的非线性效应会影响弯曲效应,进一步影响悬链线的构形。柔性梁的截面结构具备一定的抗弯刚度,柔性梁理论在计算中考虑了弯曲效应对柔性梁构形的影响。目前的研究没有有效地将悬链线理论与柔性梁理论结合起来。通过结合经典的悬链线理论和柔性梁理论,通过深入的理论分析,推导得到了包含弯曲非线性效应的修正后的悬链线方程。研究发现,在结构的长径比相对较小、跨中截面应力较低,以及结构承受较大向下荷载的情况下,弯曲非线性效应产生的影响较大,这种效应会导致结构的垂弧减小。利用有限元仿真软件对多种不同情况下的悬索进行了计算,结果表明,有限元仿真的结果与文中理论推导公式的计算结果基本一致,有效地证明了理论推导公式的可靠性。The existing catenary theory is typically based on the assumption that the structure is completely flexible,without considering the impact of bending effects on the configuration of the catenary.The bending effect caused by the flexural rigidity of the cross-section can affect the configuration of the catenary.The large slope of the catenary induces nonlinear effects that influence the bending effect,further affecting the configuration of the catenary.The cross-sectional structure of flexible beams has a certain flexural rigidity,and the flexible beam theory takes into account the effect of bending on the configuration of flexible beams in calculations.Currently,research has not effectively combined catenary theory with flexible beam theory.This paper combines classic catenary theory with flexible beam theory and through in-depth theoretical analysis,derives a modified catenary equation that includes bending nonlinear effects.The study finds that in cases where the structure has a relatively small length-to-diameter ratio,low mid-span crosssectional stress,and is subjected to significant downward loads,the impact of bending nonlinear effects is significant.This effect leads to a reduction in the sag of the structure.Finite element simulation software was used to calculate various catenaries under different conditions.The results show that the finite element simulation results are consistent with the theoretically derived formula,effectively proving the reliability of the theoretical derivation.

关 键 词：修正悬链线方程 弯曲非线性效应 抗弯刚度 柔性梁 垂弧 

分 类 号：TU351[建筑科学—结构工程]