In-plane nonlinear elastic stability of pin-ended parabolic multi-span continuous arches
In-plane nonlinear elastic stability of pin-ended parabolic multi-span continuous arches
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DOI：
10.1016/j.engstruct.2019.04.013
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发表时间：
2019-07
影响因子：
5.5
通讯作者：
Chang-Fu Hu;Yan Huang
中科院分区：
文献类型：
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作者：
Chang-Fu Hu;Yan Huang
对于单拱的平面内非线性弹性稳定问题，国内外已有很多学者进行了研究，而对于多跨连续拱的平面内非线性弹性稳定问题，尽管其在拱桥工程中得到了广泛的应用，但还没有类似的研究。本文提出了一种分析端铰抛物型多跨连续拱平面内非线性弹性屈曲和后屈曲的解析方法。在所提出的方法中有四个关键部分。首先，基于非圆拱在直角坐标系下的应变表达式和虚功原理，推导了各拱的面内非线性平衡微分方程。其次，基于各拱端变形协调条件，建立了连续拱的非线性平衡方程，得到了三个关键系数。然后根据各拱端的受力平衡条件，推导了拱的失稳要求。最后，屈曲和后屈曲预测的解析解。通过与有限元法计算结果的比较，包括荷载-位移曲线、屈曲行为和屈曲预测，表明该解析解具有较高的精度。理论分析和参数分析结果表明：多跨连续拱对称屈曲和非对称屈曲的变形形态与单跨拱完全不同，无载拱的力学效应是作用于荷载拱的非线性水平弹簧支承，稳定参数比对多跨连续拱的屈曲性能有显著影响。
The in-plane nonlinear elastic stability of single arches has been investigated by many researchers, however, a similar research of multi-span continuous arches is not available even though they are extensively used in arch bridge engineering. This paper proposes an analytical method for the in-plane nonlinear elastic buckling and post-buckling of pin-ended parabolic multi-span continuous arches. There are four key parts in the proposed method. Firstly, the in-plane nonlinear equilibrium differential equations of each arch were derived based on the strain expression in the Cartesian coordinate system of non-circular arches and the virtual work principle. Secondly, the nonlinear equilibrium equation of continuous arches was proposed based on the deformation compatibility condition of each arch end, and three key coefficients were obtained. Thirdly, the buckling requirements were deduced according to the force balance condition in each arch end. Lastly, analytical solutions for buckling and post-buckling predictions were derived. Comparisons with the results of finite element method, including the load-displacement curve, buckling behavior and buckling predictions, demonstrate that the proposed analytical solution is equipped with high accuracy. The results of theoretical and parametric analysis show that the deformation shape of symmetric and asymmetric buckling of multi-span continuous arches is thoroughly different from the single arches, the mechanical effect of the unloaded arches is a nonlinear horizontal spring support acting on the loaded arch, and the stability parameter ratio has a significant influence on the buckling behavior of multi-span continuous arches.