The curve integration along arch axis is a basic problem of analytical solution method in arch structure mechanics, and it has no closed form analytical solution when the arch axis is not an arc. An approximate curve integration method was proposed to solve this problem. It took approximate display arc-length differentiation to replace the complex exact one to obtain the practical closed form analytical solution of arch structure mechanics problem. Based on the proposed method, some practical analytical solutions were deduced, by studying arch structure elastic constant and main arch ring inner force under main arch ring and deck system dead load in a new complex axis arch structure, since it had a lot of complex curve integrations along arch axis in these mechanics problems. Numerical integration solution of elastic constant using exact arc-length differentiation and finite element solution of inner force were taken as exact solutions to verify high precision of the display result of proposed method. The results show that compared with the normal method which takes curve integration simplified to horizontal line integration, the proposed method can get higher precision approximate expression results, and the maximum relative error of all elastic constants is less than 2％;compared with finite element solution, the proposed method have more general approximate expression, and the maximum relative error of all inner force is less than 4％.%拱结构力学问题的解析解大多基于沿拱轴的曲线积分,当拱轴线为非圆弧线时该曲线积分往往没有闭合解析解.针对该问题,提出近似曲线积分方法,将精确弧长微分近似显示表达,用以得到拱结构力学问题的实用解析解.基于本文方法,以包含大量复杂曲线积分的新型拱轴线弹性常数表达式及主拱圈自重、桥面系自重作用时内力表达式为研究对象,推演得到其实用解析解,并以弹性常数精确曲线积分的数值解与内力的有限元解为精确解,验证本文方法的高精确性与实用性.研究结果表明:与常规方法将曲线积分简化为直线积分相比,本文方法能得到更高精度的实用解析解,各弹性常数表达式最大相对误差小于2％;与内力的有限元解相比,本文方法具有更通用的实用表达式,且内力的最大相对误差小于4％.
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