A new jacobi-based iterative method for the classical analysis of structures

Abstract

Traditionally, classical methods of structural analysis such as slope-deflection and moment distribution methods (Cross method) are used for primary analysis of structures and also controlling the results of computer programs. The main objective of this paper is to introduce a new method for classical computing and extending it to a matrix formulation. The proposed approach, named the “Slope Distribution Method (SDM)”, is based on a Jacobi iterative procedure, in which without forming the system of linear equations, structural displacement values are obtained. Also, to make the method applicable and to use it in computer softwares, the matrix formulation of the approach is developed, where there is no need for iterative procedures and the nodal rotations are obtained through solving only one matrix equation. The SDM is able to analyze frames with non-vertical columns and those with nodal vertical displacement. Whereas current analysis softwares have some elimination for the analysis of non-prismatic members, the proposed method can be applied to analyze structures with any non-prismatic member. The SDM process is also developed for the analysis of dual lateral load resisting systems (moment resisting frames with other lateral load resisting elements such as bracings and shear walls). The advantages of the method over previous ones and also, its accuracy and reliability are presented through the article.