弹性地基上非线性混凝土梁的热弯曲分析  

Thermal bending analysis of nonlinear concrete beams on an elastic foundation

作　　者：肖珍 李政 赵恒 孟阳君 XIAO Zhen;LI Zheng;ZHAO Heng;MENG Yangjun(School of Intelligent Building,Changde College,Changde 415008,China;School of Civil Engineering and Architecture,Hunan University of Arts and Science,Changde 415006,China)

机构地区：[1]常德学院智能建筑学院,湖南常德415008 [2]湖南文理学院土木建筑工程学院,湖南常德415006

出　　处：《四川建筑科学研究》2025年第1期64-72,共9页Sichuan Building Science

基　　金：国家自然科学基金青年基金项目(52008164);湖南省自然科学基金资助项目(2021JJ50136)。

摘　　要：利用Timoshenko广义位移梁理论,研究了弹性地基上非线性混凝土梁在线性温度场中的热弯曲问题。根据混凝土梁的几何方程及非线性本构关系,在考虑剪切效应的基础上,推导了线性温度场中弹性地基梁的平衡方程,得到了弹性地基上混凝土梁的热弯曲微分方程。结合弹性地基梁边界条件,推导了弹性地基上简支、简固混凝土梁的挠度曲线方程及转角曲线方程,以及固支混凝土梁的热屈曲特征方程。算例分析表明:线性温度场作用下,弹性地基上混凝土梁内产生了较大的热弯矩和热轴力,其内力随着温度的增加而增大;在相同温度场中,简支混凝土梁的挠度曲线和转角曲线具有一定的对称性,而简固混凝土梁的最大弯曲挠度明显大于简支混凝土梁;剪切变形对弹性地基上混凝土梁热弯曲挠度的影响可以忽略不计。The thermal bending of nonlinear concrete beams on an elastic foundation in linear temperature field was studied by using Timoshenko generalized displacement beam theory.Based on the geometric equation and the nonlinear constitutive relation of the concrete beam,the equilibrium equation of the beam on elastic foundation in linear temperature field was derived,and the thermal bending differential equation of the concrete beam on elastic foundation was obtained.Combined with the boundary conditions of beams on elastic foundation,the deflection curve equation and the angle curve equation of simply-supported concrete beams and propped cantilever concrete beams were derived.And the characteristic equation of thermal buckling of fixed-end concrete beams was obtained.The results show that under the action of linear temperature field,large thermal bending moment and thermal axial force will be generated in the concrete beam on elastic foundation,and it will increase with the increase of temperature.In the same temperature field,the deflection curves and angle curves of the simply-supported concrete beam have certain symmetry,and the maximum bending deflection of the propped cantilever concrete beam is obviously greater than that of the simply-supported concrete beam.The influence of shear deformation on thermal bending deflection of concrete beams on elastic foundation can be neglected.

关 键 词：弹性地基 非线性 混凝土梁 温度场 热弯曲 挠度 转角 

分 类 号：TU470[建筑科学—结构工程]