正多边形双向受弯薄壁截面塑性极限承载力研究  

Research on plastic ultimate bearing capacity of thin-walled section with regular polygon under biaxial bending

作　　者：李雨城 王伟 孙强 李晓芳 LI Yu-cheng;WANG Wei;SUN Qiang;LI Xiao-fang(School of Urban Construction,Anhui Wenda Information Engineering College,Hefei 231201,China)

机构地区：[1]安徽文达信息工程学院城市建设学院,安徽合肥231201

出　　处：《空间结构》2023年第1期89-95,共7页Spatial Structures

基　　金：安徽高校自然科学研究项目(KJ2020A0805,2022AH052853);安徽高校省级自然科学研究重大项目(KJ2014ZD06);安徽省自然科学基金项目(1408085QE96);安徽省级质量工程项目(2021xjxtd02);安徽文达信息工程学院校级自然科学重点项目(XZR2019B04)。

摘　　要：基于双向受弯构件的截面静力平衡准则,在构件全截面进入塑性屈服状态时,将正多边形薄壁构件截面分解为多个全等狭长矩形,分析每一个分块矩形的应力分布情况.在引入正多边形薄壁构件截面的3个基础参数的基础上推导出相关衍生参数表达式,确定了正多边形薄壁构件截面的基础单元,即推导出分块矩形的塑性极限弯矩计算式.运用坐标变换,从局部到整体,整合了每个边所在矩形对截面总塑性极限弯矩的贡献,推导出任意正多边形双向受弯构件薄壁截面塑性极限弯矩的简化表达式.对所得公式进行数值计算验证,采用数值分析对3个基础参数两两组合,在控制一个变量的基础上分析双因素对截面总体塑性极限弯矩的影响.结果表明:正多边形双向受弯构件截面塑性极限弯矩计算公式与文献提出的程序算法所得计算结果一致,且计算较为简便实用.文中列出了实际工程中常见构件截面的塑性极限弯矩表,可供工程应用参考.Based on the static equilibrium criterion of bi-directional bending member,the section of regular polygon thin-walled member is decomposed into several congruent and narrow rectangles when the whole section of the member enters into the plastic yield state.The stress distribution of each block rectangle is analyzed.Based on the introduction of three basic parameters of thin-walled section of the regular polygon,the related parameter expression is derived,and the basic element of regular polygon thin-walled section is solved,that is,the calculation formula of plastic ultimate moment of block rectangle is derived.By using coordinate transformation,from local to global,the contribution of each side rectangle to the total plastic limit moment of section is integrated,and the simplified expression of plastic ultimate moment for the thinwalled section in the bi-directional bending member of an arbitrary regular polygon is derived.The formula is verified by numerical calculation.The combination of three basic parameters by numerical analysis is adopted,and the double factor is analyzed on the basis of controlling one variable.The results show that the calculation formula for the plastic ultimate moment of the bi-directional bending member in the regular polygon is consistent with the calculation result of the program algorithm proposed in the literature,and the calculation is simple and practical.The table of plastic limit moment for commonly-used sections is provided,which can be adopted as reference for engineering application.

关 键 词：薄壁构件截面 双向受弯 塑性极限弯矩 正多边形 坐标变换 

分 类 号：TU313.3[建筑科学—结构工程]