Practical analysis procedures of steel portal frames having different connections rigidities using modified stiffness matrix and end-fixity factor concept

The real behaviour of connections in the steel buildings is often underestimated by designers at the structural analysis and design stages, despite their influences on the structural performance, deflection limits and a possibility of achieving a reduction in the material weights, which can significantly reduce the overall cost and amount of energy embodied. This paper, therefore, described systematic and simplified procedures to conduct a first-order elastic structural analysis of the semi-rigid steel portal frames in order to implement a design optimization using a Generalized Reduced Gradient (GRG) algorithm within Solver Add-in tool in Microsoft Excel. The written program used the robustness and efficiency of the Finite Element (FE) method with the versatility of a spreadsheet format in Excel. To simulate the semi-rigid response of the connections, the mathematical representation through End-Fixity Factor and the Modified Stiffness Matrix were used to incorporate such behaviour into structural analysis packages. To validate the written program, a computer-based analysis was conducted using Prokon® software and comparing analysis results with those obtained from the Excel spreadsheet. It demonstrates that Excel’s results were perfectly accurate. Consequently, the procedure of establishing spreadsheets as a finite element analysis software for a certain form of frames demonstrates its validity.