Title: Graph theory implementation in plane frame analysis

Authors: Rajkumar V. Raikar; D.S. Revankar; Basavaraj G. Katageri

Addresses: Department of Civil Engineering and Dean R&D, Dr. M.S. Sheshgiri College of Engineering and Technology, KLE Technological University, Belgaum 590 008, Karnataka, India ' Department of Engineering Science and Humanities, Dr. M.S. Sheshgiri College of Engineering and Technology, KLE Technological University, Belgaum 590 008, Karnataka, India ' Dr. M.S. Sheshgiri College of Engineering and Technology, KLE Technological University, Belgaum 590 008, Karnataka, India

Abstract: Graph theory has wide application in solving the network problems in multidisplinary domains. This paper presents the application of graph theory in the analysis of determinate plane frames using flow graph representation. The detailed procedure of analysing the plane frames is presented in the paper. Three different plane frames are analysed using graph theory and the results are compared with static law using method of joints. The member forces determined by graph theory match very well with those computed from equilibrium method of joints. In addition, the comparison results obtained for a particular plane frame with two different spanning trees is also included indicating that any spanning tree can be used to analyse a plane frame. Detailed guidelines for analysing plane are also discussed in the paper.

Keywords: graph theory; cut-set matrix; plane frames; trusses; analysis.

DOI: 10.1504/IJSTRUCTE.2023.134342

International Journal of Structural Engineering, 2023 Vol.13 No.4, pp.426 - 444

Received: 26 Jul 2022
Accepted: 03 Jul 2023

Published online: 18 Oct 2023 *

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