三肢剪力墙在水平荷载作用下内力位移解析解法  

Analytical solution for internal force and displacement of three-limb shear wall under horizontal load

作　　者：朱彦鹏[1,2] 严紫豪 杨校辉[1,2] Zhu Yanpeng;Yan Zihao;Yang Xiaohui(School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China;Western Engineering Research Center of Disaster Mitigation in Civil Engineering of the Ministry of Education,Lanzhou University of Technology, Lanzhou 730050, China)

机构地区：[1]兰州理工大学土木工程学院,甘肃兰州730050 [2]兰州理工大学西部土木工程防灾减灾教育部工程研究中心,甘肃兰州730050

出　　处：《土木工程学报》2019年第10期56-66,82,共12页China Civil Engineering Journal

基　　金：教育部长江学者创新团队支持计划(IRT_17R51);甘肃省科技重大专项计划(1302FKDA030)

摘　　要：随着高层结构应用日益广泛,多肢剪力墙及其组合结构成为高层结构中不可或缺的一部分,但是在土木类规范、教材中对于多肢剪力墙内力求解的核心部分:对连梁约束弯矩构成的微分方程组采取叠加分配的计算方法有失偏颇。文章对连梁约束弯矩求解过程中产生的 2 个二阶微分方程组采取转化为 4 个一阶微分方程组,进而求微分方程组系数矩阵的基解矩阵的办法,从而给出多肢剪力墙中三肢剪力墙在 3 种水平荷载作用下内力、位移的解析计算公式。比较两种方法的内力计算结果与 Midas 计算模型内力的差距,发现运用传统方法连梁的内力结果较计算模型和文中计算小 10%左右。该方法避免对连梁刚度以及连梁相对位置和墙肢整体性等一系列参数的讨论,避开分配系数这个概念,改进传统解析方法,为剪力墙与框架组合结构内力、位移解析表达式的推导夯实基础。Multi-limb shear walls and the relevant composite structures are essential components of high-rise structures in modern designs. However, it is inaccurate to demonstrate the core method that calculating the internal force of multi-limb walls in codes, specifications, and textbooks of civil engineering, in which the superposition distribution method is adopted to solve the differential equations for the restrained moment of coupling beams. In this paper, a new method is proposed to solve the inertial forces and displacements of three limb shear walls under three types of horizontal loads, and the analytical equations are given. The method solves the restrained bending moment of coupling beams by transforming the two second-order differential equations into the four first-order differential equations. Then the fundamental solution matrix is obtained for the coefficient matrix of differential equations. By comparing the internal force calculated by these two methods with those from Midas, it is found that the results from the traditional method are 10% less than those from the FE method and the new method. Besides, the new method improves the traditional way by avoiding the concept of distribution factor, the stiffness and the relevant position of coupling beams, and the integrity of the shear wall, etc. The proposed new method can provide reference for the expression of internal forces and displacements in composite structures of shear wall and frame.

关 键 词：连梁 三肢剪力墙 内力 位移 解析解 

分 类 号：TU311.4[建筑科学—结构工程]