任意活载形式的简支梁支反力通用算法研究  

Research on Generalized Algorithm to Calculate Support Reaction of Simply-Supported Beam Under Arbitrary Live Loads

作　　者：王雨权 霍学晋[2] 廖立坚 勾红叶[3] WANG Yu-quan;HUO Xue-jin;LIAO Li-jian;GOU Hong-ye(China Railway Design Corporation,Tianjin 300308,China;China Railway Major Bridge Reconnaissance&Design Institute Co.,Ltd.,Wuhan 430056,China;School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]中国铁路设计集团有限公司,天津300308 [2]中铁大桥勘测设计院集团有限公司,湖北武汉430056 [3]西南交通大学土木工程学院,四川成都610031

出　　处：《桥梁建设》2022年第4期53-60,共8页Bridge Construction

基　　金：中国铁路设计集团有限公司科技开发课题(2021A240602)。

摘　　要：为实现不同类型铁路活载下简支梁支反力的快速准确求解,提出了一种利用Heaviside函数推导任意活载作用下简支梁支反力通用完备解的算法。该算法构建了一种可自定义的活载格式以定义任意活载,即将任意活载分解为集中荷载、有限长度均布荷载、无限长度均布荷载三大类荷载;利用弯矩平衡法以及各加载边界条件与Heaviside函数的等价变换关系,推导得到任意活载的支反力通用完备解;将该算法编入设计程序,结合铁路墩台设计控制工况的判据,采用冒泡法可得到控制工况的支反力。以3组不同梁跨组合下的双孔重载控制工况为简支梁支反力算例,计算结果表明:该通用算法与MIDAS Civil软件计算的简支梁支反力误差均在1%以内,计算精度高;ZK活载、ZC活载与UIC活载的比例关系进一步验证了本文提出的支反力通用算法计算结果的正确性。In this paper,an algorithm using Heaviside function to derive the generalized and complete solution of the support reaction of simply-supported beam under arbitrary live loads is proposed,which is able to achieve rapid and accurate solution of support reaction of the simply-supported beam under diverse railway live loads.The algorithm can generate a customizable live load format to define arbitrary live loads,by which arbitrary loads are decomposed into three major types:concentrated loads,finite-length uniform loads,and infinite-length uniform loads,furthermore,the generalized and complete solution of reaction force under arbitrary live loads is derived using moment balance method and taking into account the equivalence transformation relationship between each loading boundary condition and Heaviside function.The algorithm is compiled into a design program,based on which the support reaction under different control loading conditions are determined by bubbling sort in conjunction with the control condition criteria of railway pier and abutment.Three groups of two-span simply-supported beam structures that have different span length combination and are applied with heavy loads are prepared for calculation.The results demonstrate that the errors of support reaction of the simply-supported beam calculated by the presented algorithm and MIDAS Civil are all less than 1%,exhibiting high calculation accuracy.In addition,the proportional relationship between ZK,ZC and UIC live loads verifies the accuracy of the presented generalized algorithm in calculating support reaction.

关 键 词：简支梁 活载 墩台基础 支反力 Heaviside函数 通用算法 

分 类 号：U448.217[建筑科学—桥梁与隧道工程] U441.2[交通运输工程—道路与铁道工程]