Title: Variable substitution integral method and its application for solving displacement curves of framed structures

Authors: Yuguo Zheng; Yu Wang; Xiangshou Xiao

Addresses: School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China ' School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China ' School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China

Abstract: Structural displacement curves are very important for framed structures in structural engineering. However, the analytical solutions of the curves cannot be provided by the classical material mechanics method and the conventional structural mechanics one directly. So, a general analytical method, the variable substitution integral method, was proposed mainly based on the unit load method. The basic principle and operation procedure of the method was constructed. Then it was applied to some classical cases in structural analysis. The research results show the correctness and effectiveness of the method, which can figure out displacement curves of kinds of framed structures under various types of internal forces directly and conveniently. It can fully compensate for the shortcomings of the two usual methods. The clear mathematics and mechanics background of the method makes it understood easily. The simplicity and practicality of this method make it be applied in structural engineering extensively in great possibility.

Keywords: structural mechanics; framed structure; displacement calculation; virtual work principle; unit load method; variable substitution integral method.

DOI: 10.1504/IJISE.2021.116236

International Journal of Industrial and Systems Engineering, 2021 Vol.38 No.3, pp.346 - 361

Received: 14 May 2019
Accepted: 29 Aug 2019
Published online: 14 Jul 2021 *

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