基于主弦管偏心距最小法的拱轴线优化研究

Study on Optimization of Arch Axis Based on Minimum Eccentricity Method for Main Chord

对于大跨径钢管混凝土拱桥,拱轴线与压力线的偏差会极大影响桥梁的受力状态。为了解决拱轴线优化问题,克服既有拱轴线优化方法存在拱桥主弦管受力不均、无法充分发挥钢管混凝土拱桥受力性能、结构参数利用率低等问题,提出了一种基于主弦管偏心距最小的拱轴线优化方法,充分发挥了每根弦杆的受力性能,结合图乘法与有限元理论,详细推导了该方法的建立与求解步骤。将全拱肋主弦管偏心距作为优化目标,设置全拱肋主弦管偏心距容许值进行迭代计算,通过迭代的方式实现了拱肋主弦管偏心距的优化。为保证线形的美观性与合理性,通过3次样条函数拟合的方式,实现了进一步优化,得到了可用于指导实际施工的拱轴线。在合江长江公路大桥上对该方法进行了验证。结果表明:本方法优化得到的拱轴线能够有效减小主弦管偏心距与弯矩峰值,结构参数利用率更高,相较于合江长江公路大桥初始线形的最大弯矩,优化幅值达到80%;各关键截面弯矩基本控制在100 kN·m以内,相较于抛物线、悬链线优化得到的最优拱轴线形,在内力方面整体最优;采用主拱圈全节点坐标的简便计算方法,可结合任意编程语言,实现模型全桥节点坐标的快速修改,配合优化方法便捷地实现拱轴线的优化。

For long-span CFST arch bridge,the deviation of arch axis and pressure line will influence the stress state of the bridge greatly.In order to solve the issue of arch axis optimization,and overcome the problems(uneven stress on the main chord of arch bridge,unable to give full play to the mechanical performance of CFST arch bridge and low utilization rate of structural parameters,etc)in the existing arch axis optimization method,a method for optimizing arch axis based on minimum eccentricity for main chord is put forward to give full play to the mechanical performance of each chord.Combining with graph multiplication and finite element theory,the establishment and solving steps of the method are derived in detail.Taking the eccentricity of main chord with full arch rib for the optimization object,and setting the allowable value of the eccentricity of main chord with full arch rib for iterative calculation,the optimization of eccentricity of main chord with arch rib is realized with iterative way.In order to ensure the aesthetics and rationality of the line shape,the further optimization is realized by using cubic spline function fitting method,and the arch axis that can be used to guide the actual construction is obtained.The proposed method is verified on Hejiang Yangtze River Highway Bridge.The result shows that(1)The arch axis optimized with this method can effectively reduce the main chord eccentric distance and the peak bending moment,and the structural parameter utilization is higher.Compared with the maximum bending moment of the initial linear shape of Hejiang Yangtze River Bridge,the optimized amplitude of arch axis can reach 80%.(2)The bending moment of each key section is basically controlled within 100 kN·m,the overall internal force is optimal compared with the optimal arch axis linear shapes obtained by using the optimization of parabola and catenary.(3)Adopting the simple calculation method of the full node coordinates on main arch ring,and it can realize the rapid modification of the node coordinates of the whole bridge model combining with any programming language,and realize the optimization of arch axis conveniently with the optimization method.