均布荷载下两端固支深梁的解析解  

An Analytical Solution of a Fixed Deep Beam under a Uniformly Distributed Load

作　　者：梅甫良[1] Mei Fuliang(College of Civil Engineering and Architecture,Jiaxing University,Jiaxing,Zhejiang 314001)

机构地区：[1]嘉兴学院建筑工程学院,浙江嘉兴314001

出　　处：《嘉兴学院学报》2023年第6期25-30,共6页Journal of Jiaxing University

摘　　要：为了降低固支约束简化对应力和位移精度的影响,提出了一种固支边位移简化条件,包括令固支边的纵向位移、横向位移以及纵向位移对横坐标的一阶导数沿高度方向积分后都为零.用半逆解法推导了两端固支深梁在均布荷载下的应力和位移解析式,并讨论了固支边不同位移简化对应力和位移精度的影响.计算结果证明:该固支边位移简化对应力和位移精度的影响较小.To decrease the impact of the simplification of fixed end constraint on the accuracy of stresses and displacements,a newly simplified condition for the fixed end with the integrals of the vertical displacement,the transverse displacement and the first derivative of the vertical displacement with respect to the transverse coordinate along the transverse direction of the fixed end being zero is put forward.The analytical formulations of the stresses and displacements of a fixed deep beam under a uniformly distributed load are deduced by a semi-inverse approach,and the effects of different displacement simplifications of the fixed end on the accuracy of stresses and displacements are discussed.The calculation results prove that our simplified displacement of the fixed end has little influence on the accuracy of stresses and displacements.

关 键 词：深梁 平面应力 应力函数 固支边简化条件 

分 类 号：O347.4[理学—固体力学]