轴向约束梁柱在火灾引起温度沿截面不均匀分布条件下的大变形分析  

Large Deformation Analysis of Axially Restrained Beam Column under Transversely Non-uniform Temperature Distribution in Localized Fire

作　　者：李国强[1] 王培军[1] 

机构地区：[1]同济大学建筑工程系,上海300092

出　　处：《力学季刊》2007年第2期246-255,共10页Chinese Quarterly of Mechanics

摘　　要：火灾升温引起钢材强度和刚度降低,对温度沿截面分布不均匀的构件还将产生热弯曲,火灾下结构分析同时涉及几何非线性和材料非线性,无法求得解析解,只能通过数值方法求解。本文基于轴线可伸长梁理论,用勒让德多项式作为基函数逼近梁柱轴向和横向变形,根据平衡方程误差平方和最小的条件确定多项式系数的方法,分析了轴向约束钢柱在火灾引起的沿截面线性分布温度场下的受力和变形性能。考虑了温度梯度、轴向约束刚度比、荷载比、构件长度等参数的影响和升温条件下钢材的弹塑性性能的影响,该方法结果与解析结果和有限元分析结果吻合。研究表明,随着荷载比的增大构件的临界温度迅速降低,轴向约束刚度、温度梯度和构件长度仅影响构件的变形,对构件的临界温度影响较小。The strength and stiffness of steel degrade at elevated temperatures in fire. And non-uniformly temperature distribution across the member section will cause thermal bowing. The analysis of structural member in fire involves both geometric nonlinearity and material nonlinearity, So it can only be solved numerically. Based on the extensional beam theory, adopting Legendre polynomial as base function to approximate axial and lateral deformation, and determining the coefficients by mininizing the sum of squares of equilibrium equation＇s residual error, the axial force-temperature relationship of axially restrained steel column with transversely non-uniform temperature distribution was analyzed. Parameters including thermal gradient, axially restrained ratio, load ratio and member length were studied. The outcomes of this method agree well with both the theoretical and finite element analysis results. It indicates that columns with higher load ratio failure at lower temperature. The axially restrained ratio, thermal gradient and column length only affect the column deformation. They have no influence on the column critical temperature.

关 键 词：温度梯度 轴向约束 热弯曲 Levenberg-Marquardt非线性最小二乘法 抗火计算 

分 类 号：TU318.1[建筑科学—结构工程]