Algorithm for Calculating Statically Indeterminate Trusses Using the Force Method

Abstract

The study focuses on developing an algorithm for calculating statically indeterminate trusses using the force method. The main challenge in algorithmizing the force method lies in obtaining the solution to the homogeneous equilibrium equations, which is complicated by the ambiguity in selecting the primary system. The idea behind the presented algorithm is based on using the transposed compatibility matrix of the structure as the general solution to the homogeneous equilibrium equations. The governing system of equations eliminates the need to select redundant unknowns, as the column of unknowns is generated automatically. The method for obtaining compatibility equations in statically indeterminate truss cells is presented through a direct examination of changes in the area of truss loops. The compatibility matrix of the system is composed of rows of compatibility equations for independent statically indeterminate truss loops. Compatibility equations for the deformations of triangular and rectangular truss cells are derived, and a method for obtaining compatibility equations for externally statically indeterminate trusses is described. Using the proposed algorithm, the flexibility matrix of a truss with parallel chords is presented. The algorithm removes the ambiguity in selecting the primary system, and the structure of the flexibility matrix is determined by the numbering of the statically indeterminate loops of the system. There is no need to use the equilibrium equations when constructing the flexibility matrix of the structure.

Keywords

• planar truss
• general solution of the equilibrium equations
• strain compatibility equations
• continuity conditions of the area
• forse method algorithm
• flexibility matrix