Improvement of the Graphical Method for Plotting the Shear and Moment Diagrams for Members Subjected to Linearly Varying Loads

Q3 Chemical Engineering

International Journal of Applied Mechanics and Engineering Pub Date : 2022-03-01 DOI:10.2478/ijame-2022-0004

M. A. Husain, Abdulkhaliq Salim Ali

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引用次数: 0

Abstract

Abstract This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.

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线性变化荷载作用下构件剪力弯矩图绘制方法的改进

摘要本文提出了一种改进的线性变化荷载(三角形和梯形荷载)下结构构件剪力和弯矩图的图解方法。根据剪切函数的抛物线性质，在荷载线性变化时，根据荷载、剪切和弯矩之间的关系，建立了零剪切点定位的数学方程，并提出了计算抛物线剪切面积的几何方法。本文选取了五个具有线性变化荷载的梁的综合实例来说明所提出的技术的解决步骤。结果表明了该方法的适用性，并与基本图解法相比较，给出了准确的图。结果表明，与基本图解法相比，改进的方法不需要剖分、求解平衡方程和二次公式，总体上更方便、更省时、计算量更少。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Applied Mechanics and Engineering Engineering-Civil and Structural Engineering

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

35 weeks

期刊介绍： INTERNATIONAL JOURNAL OF APPLIED MECHANICS AND ENGINEERING is an archival journal which aims to publish high quality original papers. These should encompass the best fundamental and applied science with an emphasis on their application to the highest engineering practice. The scope includes all aspects of science and engineering which have relevance to: biomechanics, elasticity, plasticity, vibrations, mechanics of structures, mechatronics, plates & shells, magnetohydrodynamics, rheology, thermodynamics, tribology, fluid dynamics.