考虑分布力偶作用的梁变形和内力的简易计算  

Simple Calculation of Internal Force and Deformation of Beam Considering the Effect of Distributed Couple

作　　者：魏鹏云 李林[1] WEI Pengyun;LI Lin(College of Water Conservancy and Civil Engineering,Tarim University,Alar 843300,Xinjiang,China)

机构地区：[1]塔里木大学水利与建筑工程学院,新疆阿拉尔843300

出　　处：《工程与试验》2024年第3期1-5,30,共6页Engineering and Test

基　　金：农业水利工程省级一流本科专业建设项目(22000030107);校长基金项目(编号:TDZKSS202260)

摘　　要：从梁的挠曲线近似微分方程出发,考虑分布力偶的作用,推导了含有待定系数的挠曲线方程、转角方程、弯矩及剪力方程等,指明了各种外荷载及支座反力对梁挠曲线及转角的贡献,指出了挠曲线方程的最高次数由分布荷载与分布力偶的具体荷载形式对比决定,还给出了将分布力偶作等效处理后的求解思路。计算方法具有程式化和一般化的特点,可通过建立边界条件确定待定系数,进而可同时获得梁的变形、内力及支座反力。本文内容是对材料力学经典内容的拓展,可加深学生对梁变形和内力计算的认识。The equations of deflection curve,slope,moment and shear with undetermined coefficients are derived from the approximate differential equation for the deflection curve of the beam,taking into account the effect of the distributed couple,and the contribution of various loads and support reactions to the deflection curve and slope of the beam is specified.It is pointed out that the maximum number of the equation of the deflection curve is determined by the specific load form comparison between the distributed loads and the distributed couple.The solution idea of equating the distributed force couples is also given.The calculation method in this paper has the characteristics of stylization and generalization and allows the undetermined coefficients to be determined by establishing boundary conditions,thus allowing the deflection,internal forces and support reactions of the beam to be obtained simultaneously.The content of the paper is an extension of the classical content of material mechanics,which can deepen students'understanding of beam deformation and internal force calculation.

关 键 词：分布荷载 分布力偶 挠曲线方程 转角方程 弯矩方程 剪力方程 

分 类 号：O341[理学—固体力学]