The Application of Equilibrium Equations Matrix with Stiffness Method for Statically Indeterminate Structural Analysis

Abstract

The stiffness method is one of the classical approaches used for the analyses of statically indeterminate frame structures with inclined members. Most of the text books use global coordinate systems to calculate the resultant and correction forces corresponding to structural sidesway modes. However, member forces in local coordinates are often desired in practical civil and structural engineering designs. Thus, additional computational efforts must be performed in order to transform the forces in global coordinates into the local systems. In our approach, the equilibrium equations at joints and correction forces of sidesway are derived in the local coordinates and expressed in form of matrices. Together with the application of stiffness method, the solution can be readily obtained in the local member forces without extra computational efforts in transforming the global coordinate system. The matrix solving procedure can be achieved using a general spreadsheet software such as Microsoft Excel.