三塔悬索桥中塔适宜刚度数值解析算法

Numerical Analytic Algorithm for Suitable Stiffness of Middle Tower of Three-tower Suspension Bridge

为实现三塔悬索桥在设计阶段中塔适宜刚度的精细化计算,提出一种数值解析算法。基于悬链线理论及索塔变形协调关系建立主缆迭代方程组,基于力学平衡条件建立加劲梁平衡方程组,基于主缆吊点与加劲梁吊点间变形后几何关系建立吊索变形协调方程组,根据吊索力与吊索倾斜角闭合条件为收敛准则,建立联合迭代计算方程组。最后,基于最不利活载作用下中塔索鞍抗滑性及加劲梁挠跨比规范要求分别迭代求解中塔刚度上下限值,并对主跨跨度、矢跨比及恒活载比对于中塔适宜刚度限值的影响进行对比分析。将所提算法与有限元法进行比较分析,结果表明:当主跨垂跨比为1/9时,中塔刚度上限计算值与有限元计算值分别为31.5、29.4 kN·mm^(-1),计算值相对误差为7.1%;中塔刚度下限计算值与有限元计算值分别为6.5、6.7 kN·mm^(-1),计算值相对误差为-3.0%,有限元模型中塔刚度计算限值较所提算法计算值偏保守。中塔适宜刚度上限值随着跨度增加而增加,而下限值随着跨度增加而降低;在合理的相同恒活载比条件下,中塔刚度上限值随着主跨矢跨比减小而增加,下限值变化幅度相对较小;设计阶段应选择适宜的主跨矢跨比并避免不合理的恒活载比值。所提算法可应用于多塔悬索桥索塔适宜刚度精细化计算及悬索桥静力分析计算。

To accurately calculate the appropriate stiffness of the middle tower of a three-tower suspension bridge in the design stage,a numerical analytical algorithm is proposed,and the iterative equations of the main cable are established based on the catenary theory and deformation coordination relationship of the cable and tower.The equilibrium equations of the stiffening girder are established based on the mechanical equilibrium conditions,and the deformation coordination equations of the hanger are established based on the geometric relationship between the suspension points of the main cable and that of the stiffening girder after deformation.Join iterative calculations were established according to the convergence criterion of the closure condition of the hanger force and slant angle.Finally,the upper and lower stiffness values of the middle tower were iteratively calculated based on the cable saddle sliding resistance of the middle tower under the most unfavorable live load and deflection-span ratio of the stiffening girder.The effects of the main span,sag-to-span ratio,and dead-to-live load ratio on the suitable stiffness limit of the middle tower were compared and analyzed.A comparison of the proposed algorithm and FEM shows that when the vertical-span ratio of the main span is 1/9,the calculated upper limit and FEM value of the tower stiffness are 31.5and 29.4kN·mm^(-1),respectively,and the relative error of the calculated value is 7.1%.The calculated lower limit and FEM value are 6.5 and 6.7kN·mm^(-1),respectively,and the relative error of the calculated value is-3.0%.The calculation limit of tower stiffness in the FEM is more conservative than that obtained with the proposed algorithm.For the same constant dead-to-live-load ratio,the upper limit of the stiffness of the middle tower increased with a decrease in the sag-to-live-span ratio,and the range of the change in the lower limit was small.In the design stage,the appropriate sag-to-live-span ratio of the main span should be selected,an unreasonable dead-to-live-load ratio should be avoided,and the algorithm could be applied to the accurate calculation of the suitable stiffness of multi-tower suspension bridges and the static analysis and calculation of suspension bridges.