Structural Calculation of Rectangular Plates with Different Support Conditions of Four Edges

被引：0
作者：
Yang C. [1 ]
Xu Q. [2 ]
Ma W. [3 ]
Han X. [1 ]
机构：
[1] School of Civil Engineering, Beijing Jiaotong University, Beijing
[2] Anhui Transport Consulting & Design Research Institute Co.，Ltd., Hefei
[3] Beijing Urban Rail Transit Construction Engineering Co.，Ltd., Beijing
来源：
Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences | 2024年 / 51卷 / 01期
基金：
中国国家自然科学基金;
关键词：
convergence; one-way plate; rectangular thin plate; series solution; structural analysis; support conditions;
D O I：
10.16339/j.cnki.hdxbzkb.2024010
中图分类号：
学科分类号：
摘要：
For a rectangular thin plate with different support conditions of four edges，a double Fourier series with additional terms was taken as the deflection function，and linear algebraic equations for solving the undetermined coefficients were derived. A unified structural calculation formula was obtained for the plate with any combination of simply supported，clamped，and free edges. The non-convergence of a series solution of bending moment at a point where a concentrated load is applied was discussed. In addition，the aspect ratio problem that needs to be achieved when simplifying a two-way plate is also discussed. The results show that the bending moment at the point can be calculated through the finite difference method using the deflection value，where a differential step length of 10 mm was selected. A plate with two opposite edges supported and two other edges free，and a plate with one edge clamped and the other three edges free，can be taken as a one-way plate. A plate with all four edges supported can be treated as a one-way plate with two ends clamped，one end simply supported and the other end clamped，or two ends simply supported if its aspect ratio reaches 2∶1，2.5∶1，or 4.5∶1，respectively. A plate with three edges supported and the last edge free can be seen as a one-way plate with two ends clamped（and one end simply supported and the other end clamped），or two ends simply supported if its aspect ratio gets 1∶1 or 2∶1，separately；this type of plate can also be simplified as a cantilevered one-way plate at an aspect ratio of no less than 6∶1. A plate with two adjacent edges supported and the other two edges free can be taken as a cantilevered one-way plate if its aspect ratio reaches 2∶1 when the two supported edges are all clamped，or if the aspect ratio reaches1.5∶1 when one edge is clamped and an adjacent edge is simply supported. © 2024 Hunan University. All rights reserved.
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页码：101 / 111
页数：10
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