基于挠度理论的三塔四跨悬索桥静力特性分析

为研究三塔四跨悬索桥活载效应下的静力特性,拓展单跨悬索桥挠度理论公式,建立了多塔连跨悬索桥挠度理论非线性微分方程组,引入“代换梁法”求解方程组。基于MATLAB语言平台考虑了集中力引起的主缆水平力增量对影响线的非线性影响,开发出基于挠度理论的多塔连跨悬索桥内力线形的程序。研究结果表明:挠度理论解与有限元法的计算结果具有较好的一致性,位移相对最大偏差为5.3%,弯矩最大相对偏差为13.9%; 加劲梁最大挠度发生在两个主跨跨中处; 挠度理论的位移和弯矩大于有限元的计算结果,依此控制结构设计是较安全的。挠度理论在三塔四跨悬索桥设计中具有足够的适用性,可以应用在多塔连跨悬索桥的初步或者概念设计方面。

Analysis of static characteristic triple-tower-four-span suspension bridge by deflection theory

In order to study the static characteristic of the triple-tower-four-span suspension bridge under a dynamic load, the traditional deflection theory of single span suspension bridge was expanded to the theory of multi-tower-multi-span suspension bridge. Based on the expanded theory, the corresponding nonlinear differential equations were established, and then an equivalent beam method were employed to solve the equations. The static characteristics of the multi-tower-multi-span suspension bridge were analyzed by a program developed using MATLAB for the purpose of calculating the internal force and deflection. The nonlinear effect of the main cable force increment due to the concentrated load was considered when the lines calculation was affected. The calculation results showed good consistency in both bending moment and deflection between the deflection theory and finite element method. The maximum deflection deviation was 5.3% and the maximum bending moment was 13.9%. The maximum girder deflection was located in the middle of the two mid-span. The results of deflection and bending moment calculated by the deflection theory were greater than that of the finite element method, thus, a structure designed according to the deflection theory is considered safer. Calculation results also indicated that the deflection theory has broad application future in the triple-tower-four-span suspension bridge and can also be applied in static analysis of the multi-tower-multi-span suspension bridge, especially in the preliminary or conceptual design stage.