基于近似积分的悬链线拱实用解析解  

Practical analytical solution of catenary arch based on approximate integration method

作　　者：胡常福[1] 陆小雨[2] 甘慧慧[3] 任伟新[4] 

机构地区：[1]华东交通大学土木建筑学院,江西南昌330013 [2]北京交通大学土木建筑学院,北京100044 [3]江西外语外贸职业学院,江西南昌330099 [4]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《中南大学学报（自然科学版）》2015年第3期1058-1065,共8页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(51278163;51468019);江西省科技支撑计划项目(20141BBG70089);中国铁建科技项目(2011)~~

摘　　要：针对悬链线拱各种弹性积分表达式没有解析解的现状,提出一种近似积分方法以求得悬链线拱实用解析解。在两铰拱与无铰拱结构图式下,基于此近似方法,对悬链线拱积分常数实用解析解、主拱圈自重及桥面均布荷载的实用内力解析解进行求解,并以积分常数的数值积分解和内力的有限元解作为精确解,验证本文方法结果的精确性与表达式的实用性。研究结果表明:与数值积分法相比,本文方法的积分常数最大相对误差不超过4%;与有限元法结果相比,本文方法轴力最大相对误差不超过5%,弯矩最大相对误差不超过12%;本文实用解析解表达式简洁,能得到任意拱轴系数下的结果。An approximate integral method was proposed for this problem that no analytical solution exsits in catenary arch elastic integration constant. Based on this method, the practical analytical solution of catenary arch in two hinge arches and hingless arch elastic integration constant, practical analytical solution of inner forces of main arch ring weight and deck system uniformly distributed weight were deduced. By taking numerical integral method results of integration constants and finite element method internal forces results as exact solution, actenary arch practical analytical solution expression of proposed method was verified. The results show that the maximum relative error of elastic integration constant obtained by the proposed method in the paper is less than 4% compared with those obtained by the numerical integration method. Compared with the finite element method, the maximum relative error of axial force results error does not exceed 5%, the maximum relative error of proposed method bending moment results does not exceed 12% of those obtained by the proposed method, and the expression of proposed method is simply enough, which is suitable for any arch axis coefficient condition.

关 键 词：悬链线拱 近似积分法 实用解析解 弹性积分常数 

分 类 号：U441[建筑科学—桥梁与隧道工程]