摘要
边界约束条件是影响钢梁弯扭屈曲临界弯矩的重要因素之一,但当前复合荷载作用下钢梁临界弯矩的研究仅为平面内、外均简支的情况。本文基于完备的总势能方程,采用Euler微分方程推导了完备的钢构件弯扭屈曲平衡微分方程组,进而简化得到钢梁弯扭屈曲侧移与扭转角独立及耦合时的平衡微分方程。分别采用Galerkin法、Rayleigh-Ritz法求解平衡微分方程(组)、总势能方程,得到了复合荷载作用下钢梁临界弯矩Mcr的计算式、双重求和形式的复合弯矩系数计算式以及单一荷载作用下的Mcr三系数(C1,i、C2,i、C3,i)通式,揭示了单一荷载两两共同作用时相关系数C1,ij的互等性和统一性特征,得到了平面外不同边界约束条件下比值C2,i/C1,i和C3,i/C1,i的关系,对影响Mcr三系数数值的因素进行了分析。研究表明:钢梁临界弯矩Mcr的计算式、复合弯矩系数Cb计算式以及Mcr的三系数通式适用于平面外4种不同边界约束条件的简支钢梁和固支钢梁;三系数形式的临界弯矩Mcr的计算式是基于扭转角试函数的基函数取1项得到的,系数C1,i的精度仅受侧移与扭转角是否耦合的影响,比值C2,i/C1,i和C3,i/C1,i不受侧移与扭转角是否耦合的影响,与采用Galerkin法还是Rayleigh-Ritz法无关。
Boundary conditions are one of the most important factors that affect the critical moment of steel beams failed with flexural-buckling.However,the in-plane boundary condition and the out-of-plane boundary condition of steel beams subjected to combined loads,are only simply supported in the current researches.General equilibrium equations for flexural-torsional buckling of steel members were derived based on the complete total energy equation and Euler differential equation.The uncoupled equilibrium equations and the torsion equilibrium equation of flexural-torsional buckling for steel beams are simplified.The Galerkin method and Rayleigh-Ritz method are employed for deriving the expressions for the critical moment by solving the equilibrium differential equation(or equation set)and the total energy equation,the combined moment coefficient in double summation form and the general expressions for the three coefficients(C1,i,C2,i,C3,i)of Mcr under single load.The reciprocal and unifying characteristics of the interaction coefficient C1,ij for the combination of two single loads,and the relationships between C2,i/C1,i and C3,i/C1,i for different out-of-plane boundary conditions were obtained.The facts that influence the accuracy of the three coefficients of Mcr were analyzed.The results show that the expression of the critical moment Mcr,the combined moment coefficient Cb,and the general expressions for the three coefficients of Mcr are applicable to both simply supported and fixed-ended steel beams with four different types out-of-plane boundary conditions;the formula for the critical bending moment Mcr in the form of the three coefficients is obtained based on one basic function of the torsion displacement.Regardless of whether the Galerkin method or the Rayleigh-Ritz method is used,the accuracy of the C1,i coefficient is affected by whether the lateral displacement and the torsion displacement are coupled,but the ratios C2,i/C1,i and C2,i/C1,i are not affected by the condition.
作者
刘占科
支圆圆
文天星
曹舒
LIU Zhanke;ZHI Yuanyuan;WEN Tianxing;CAO Shu(Key Laboratory of Mechanics on Disaster and Environment in Western China of the Ministry of Education,Lanzhou University,Lanzhou 730000,China;College of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China)
出处
《建筑结构学报》
EI
CAS
CSCD
北大核心
2020年第8期154-164,共11页
Journal of Building Structures
基金
国家自然科学基金项目(51308272)
甘肃省科技计划(18JR3RA287)。
关键词
钢梁
弯扭屈曲
临界弯矩
基准弯矩
临界弯矩三系数通式
复合弯矩系数
steel beam
flexural-torsional buckling
critical moment
benchmark moment
general expressions of three coefficients of critical moment
combined moment coefficient
