均布与集中荷载共同作用下固支梁弯扭屈曲临界弯矩精确解研究  

Study on the Exact Solution for Critical Flexural Torsional Buckling Moments of Fixed Beams Under Combined Action of Uniform Load and Concentrated Load

作　　者：张文福[1,2] 杭昭明 刘迎春[1] 赵文艳[1] 严威 华俊凯 ZHANG Wenfu;HANG Zhaoming;LIU Yingchun;ZHAO Wenyan;YAN Wei;HUA Junkai(College of Civil Engineering and Architecture,Northeast Petroleum University,Daqing 163000,China;College of Civil Engineering,Nanjing Institute of Technology,Nanjing 211167,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215000,China)

机构地区：[1]东北石油大学土木建筑工程学院,大庆163318 [2]南京工程学院建筑工程学院,南京211167 [3]苏州科技大学建筑工程学院,苏州215000

出　　处：《结构工程师》2021年第5期32-40,共9页Structural Engineers

基　　金：国家自然科学基金面上项目(51578120、5217843、51178087)。

摘　　要：目前对复合荷载下钢梁弯扭屈曲的求解多数为采用单一三角函数,其解答是近似解。本文以作者前期关于单一荷载钢梁屈曲荷载精确解的研究为基础,对均布与集中荷载下的单轴对称固支梁弯扭屈曲的临界弯矩进行了理论研究,首先给出本问题一阶近似解析解,进而推得此种情况下钢梁弯扭屈曲临界弯矩的无穷项级数解,并以100项级数为参考,应用MATLAB程序对其收敛性进行研究,最后又建立有限元模型进行了验证。研究表明,对于复合荷载下钢梁弯扭屈曲问题,无穷项级数解具有较高的精度,与FEM的最大误差在5%以内,而由单一三角函数获得的一阶近似解析解与FEM的误差非常大,对本文的双轴和单轴对称截面,其最大误差分别可达22.50%和-27.13%。At present,the solution of the flexural torsional buckling of steel beams under multiple loads is mostly based on a single trigonometric function,and the solution is approximate.Based on the author’s previous research on the exact solution of flexural load of steel beam load,the critical lateral torsional buckling moment of the fixed axisymmetric beam under the uniform and concentrated loads is studied theoretically.At first,the first order approximate analytic solution is given,and then the infinite series solution of critical flexural torsional buckling moment of the steel beam under this condition could be conducted.100 series is taken into reference and MATLAB is applied to prove the convergence of the final solution.Finally,the finite element model is established for verification.The results show that the infinite series solution has a high accuracy for flexural torsional buckling of steel beam under composite load,and the maximum error of FEM is with 5%.While the error of the first order approximate analytic solution obtained by a single trigonometric function is very large.For the biaxial and uniaxial symmetric sections in this paper,the maximum error could reach 22.5%and-27.13%respectively.

关 键 词：弯扭屈曲 临界弯矩 能量法 固支梁 无穷项解 

分 类 号：TU391[建筑科学—结构工程]