重刚比对悬索静态位形影响的建模与分析

为探究悬索的自重、刚度及分布荷载对悬索的静态平衡位形的影响,通过悬索状态分类与悬索单元的受力分析与数学模型,引入无量纲参数,分析了悬索在自然态、无荷自重作用状态与有分布荷载作用状态下的基本静态性能。建立了考虑自重和分布荷载同时作用下的悬索静态张力与悬索单位长度重刚比、挠度及支座间距的数学模型。研究表明:当重刚比小到一定程度时(β≤10-2),悬索的静态位形基本重合,此时悬索的刚度对静态位形起主导作用,悬索的静态位形可以看成不可伸长的悬索进行处理;重刚比很大时(β≥10-1),悬索的自重与分布载荷对静态位形起主导作用,悬索自重与分布荷载越大,悬索的中央挠度也越大。重刚比小的悬索在接近原长跨距时,最大张力与水平张力会明显增大,但重刚比大的悬索增加的幅度不明显,说明重刚比大的悬索因为弹性模量小,主要产生了弹性变形,因此不能盲目拉紧悬索。最后利用挂重法对悬索的静态位形参数进行了实验验证,实验结果与理论结果的相对误差均在4.95%以内,说明了模型的可行性并达到了工程应用相对误差不超过5%的精度要求。

Modeling and analysis of the static configuration of cableway suspension by the ratio of cable weight to stiffness

This paper intends to investigate the influence of self-weight, stiffness and distributed load on the static equilibrium configuration of suspension cables.The static suspension configuration of a level-supported cableway was analyzed by classifying cable states and force equilibrium analysis in a mathematical model of a cable element.Using dimensionless parameters, the basic static performance of a suspension cable in various conditions were analyzed including a natural state, unload self-weight state and distributed load state. A mathematical model of the static tension considering the cable unit length weight-to-stiffness ratio, deflection, and bearing spacing under the action of self-weight and cable distributed load was established. The paper found that , for a small ratio to an extent of β≤10-2, the cable static state coincided in general. The cable stiffness played a leading role in the static analysis and the static suspension cable can be treated as an inextensible cable. For a high weight-to-stiffness ratio, the self-weight and distributed load were significant in the static state analysis. In these conditions, it was concluded that the greater the self-weight and the distributed load, the larger the central deflection of suspension cable. When the cable length with a small weight-to-stiffness ratio approached the original span, the maximum tension and the horizontal tension obviously increased. On the other hand, the increase in tension was not obvious for a high weight-to-stiffness ratio.Therefore, it was concluded in this paper that the suspension cable with a high weight-to-stiffness ratio was governed by mainly elastic deformation and yield failure due to its small elastic modulus. Consequently, it was not advisable to blindly tighten a suspension cable in engineering practice. Lastly, the configuration parameters of static suspension cables were verified by experiments to verify the feasibility and accuracy of the model.The relative error between the experimental results and theoretical results were within 4.95% and less than 5% of the engineering application accuracy requirements.