李双蓓, 梁睿, 梅国雄. 考虑弹性压缩的弹性支承抛物线拱内力解析解[J]. 工程力学, 2023, 40(11): 1-10. DOI: 10.6052/j.issn.1000-4750.2022.02.0108
引用本文: 李双蓓, 梁睿, 梅国雄. 考虑弹性压缩的弹性支承抛物线拱内力解析解[J]. 工程力学, 2023, 40(11): 1-10. DOI: 10.6052/j.issn.1000-4750.2022.02.0108
LI Shuang-bei, LIANG Rui, MEI Guo-xiong. ANALYTICAL SOLUTION OF INTERNAL FORCE OF PARABOLIC ARCH WITH ELASTIC SUPPORTS CONSIDERING ELASTIC COMPRESSION[J]. Engineering Mechanics, 2023, 40(11): 1-10. DOI: 10.6052/j.issn.1000-4750.2022.02.0108
Citation: LI Shuang-bei, LIANG Rui, MEI Guo-xiong. ANALYTICAL SOLUTION OF INTERNAL FORCE OF PARABOLIC ARCH WITH ELASTIC SUPPORTS CONSIDERING ELASTIC COMPRESSION[J]. Engineering Mechanics, 2023, 40(11): 1-10. DOI: 10.6052/j.issn.1000-4750.2022.02.0108

考虑弹性压缩的弹性支承抛物线拱内力解析解

ANALYTICAL SOLUTION OF INTERNAL FORCE OF PARABOLIC ARCH WITH ELASTIC SUPPORTS CONSIDERING ELASTIC COMPRESSION

  • 摘要: 为解决非理想边界约束的拱结构内力理论计算问题,将非理想边界约束简化为弹性支承,基于弹性中心法对其力法方程进行简化,考虑弹性压缩的影响,采用精确曲线积分,推导了竖向移动荷载作用下计算弹性支承抛物线拱刚臂长度、常变位、载变位和内力的解析解,研究了弯压刚度比、矢跨比和水平弹性约束对支承处水平推力的影响规律,以及水平弹性约束对拱轴内力分布的影响。研究表明:该文提出的解析解物理概念清晰、正确可靠,可以显式地明确呈现弹性支承相关参数对内力计算的影响过程;不考虑拱肋弹性压缩影响导致的水平推力计算误差随弯压刚度的增大而增大,拱趾支承为刚性约束时误差最大,可以达到27.8%;水平弹性支承对拱轴内力分布和水平推力具有显著的调控作用;水平推力影响系数随矢跨比的增大呈非线性增大,当弯压刚度比为1.93、水平弹性支承柔度系数为0.02时,常见矢跨比对应的水平推力影响系数在0.15左右。

     

    Abstract: In order to solve the theoretical calculation problem of the internal force of arch structures with non-ideal boundary constraints, this paper simplifies the non-ideal boundary constraints as elastic support, and simplifies the force method equation based on the elastic center method. The elastic compression is considered and the precise curve integral method is adopted. The analytical solutions are derived for rigid arm length, constant displacement, load displacement and internal force of parabolic arch with elastic support and under vertical moving load. The influences of flexural compression stiffness ratio, rise span ratio and horizontal elastic restraint on horizontal thrust at the support are studied. The influence of horizontal elastic restraint on internal force distribution of arch axis is also studied. The results show that the analytical expression proposed in this paper has a clear physical concept, is correct and reliable, and can explicitly show the influence process of elastic support parameters on internal force calculation. The calculation error of horizontal thrust increases with the increase of bending and flexural compression stiffness, ignoring the influence of elastic compression of arch rib. The calculation error of horizontal thrust is the largest when the arch toe support is a rigid constraint, which can reach 27.8%. Horizontal elastic support can significantly change the distribution of horizontal thrust and arch axis internal force at the support. The influence coefficient of horizontal thrust increases nonlinearly with the increase of rise span ratio. The influence coefficient of horizontal thrust corresponding to the common rise span ratio is about 0.15 when the flexural stiffness ratio is 1.93 and the flexibility coefficient of horizontal elastic support is 0.02.

     

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