Analysis of Statically Determinate Trusses using Exact Method (Joint Resolution Method) and Matrix Stiffness Method

Abstract

Matrix Stiffness Method (MSM) as a tool for static analysis of structures is premised on the principle of Finite Element Method (FEM), which in itself is a numerical/approximate method capable of giving only approximate results. However, Joint Resolution Method (JRM) is one of the most popular classical/exact methods of static analysis capable of giving exact results. This paper presents an analysis of a statically determinate 2-D truss using Exact/Joint Resolution Method (JRM) and Matric Stiffness Method (MSM) to ascertain the validity of the latter against the former. In the JRM, the support reactions and internal member forces were obtained from considerations of the equilibrium conditions of the entire truss and isolated joints respectively. On the other hand, a computer program was written in MATLAB 7.8.0 (R2009a) based on the principles of MSM for ease of computation and increased accuracy to solve for member forces and reactions of the same truss. The element properties were obtained and employed to calculate the element stiffness matrices, these were then assembled into the global stiffness matrix, from which the unknown displacements, member forces and support reactions were calculated. The results obtained from using both JRM and MSM were found to be exactly the same or very close, with percentage errors ranging between 0% and 3%. Hence MSM results as compared to JRM have 97% accuracy and above, and can therefore be relied upon.