多源荷载作用下合理拱轴的近似解析
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胡常福(1980—),男,副教授,博士,研究方向为拱桥力学。

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U441

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国家自然科学基金项目(51568020)


Approximate Analytical Solution for Rational Arch Axis under Multi-type Loads
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    摘要:

    针对多源荷载下合理拱轴没有通用求解方法的现状,提出该问题的近似解析方法———线型组合法。 该方法通过对多源荷载的分析,将其拆分为若干个单一类型荷载的和,分别求解各单一类型荷载作用下的压力线及水平推力的解析,按照各单一荷载的水平推力对总推力的贡献比例,对各自压力线进行线性组合,即得到多源荷载作用下合理拱轴线的近似解析。 基于数学与力学的基本原理,通过对多源荷载中单一类型荷载数学表达函数三个层次的推演,证明了本文方法。 以若干典型多源荷载作用下合理拱轴线的求解作为算例,从压力线坐标、主拱圈弯矩及水平推力等方面,验证本文方法的通用性与精确性。 算例结果表明,本文方法可以简便的求得多源荷载作用下合理拱轴线的近似解析,具有较好的通用性;本文方法所得到的拱轴线与实际的合理拱轴线误差很小,主拱圈弯矩也较小;本文方法的推力在连续荷载工况下是精确解,当有离散集中力时,推力的微小误差主要来自离散集中力的连续化。

    Abstract:

    The arch axis combination method of approximate analytical solution for rational arch axis under muti- type loads was proposed in this paper as there was no general method solving this problem. Based on the analy- sis of multi-type loads, the multi-type loads were firstly divided into a series of single type loads, and then the analytical solution for rational arch axis and horizontal thrust was deduced in every single type load; according to the contributions to total horizontal thrust, a linear combination of these rational arch axes was the approximate analytical solution for muti-type loads. Based on the basic principles of mathematics and mechanics, the pro- posed method was verified through the deduction of three aspects for single type load mathematical function. By taking several typical deduction work of rational arch axis under muti-type loads as examples, the universality and accuracy of proposed method were tested from the aspects of pressure line coordinates, main arch bending moment and horizontal thrust. The research results show that approximate analytical solution of rational arch axis can be easily deduced by the proposed method, which is of great universality; axis deviation between approxi- mate analytical solution and actually rational arch axis is very small, and the bending moment of main arch ring is close to zero; the horizontal thrust is a precise solution under continuous loads, and the continuous transfor- mation of discrete concentrated force will bring some small errors in horizontal thrust of the proposed method.

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胡常福,廖妙星.多源荷载作用下合理拱轴的近似解析[J].华东交通大学学报,2018,35(2):46-55.

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  • 在线发布日期: 2021-05-25
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