Graph theory implementation in plane frame analysis

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.