Effect of Columns Discretization on P-δ Analysis

Abstract

Utilizing recently available high-strength materials and design codes along with the current complex design layouts have led to frequent use of slender compression members where P-δ analysis should be included in the analysis and design. This type of analysis is usually executed using commercial software. Therefore, designers need to be fully aware of the aspects that affect the results of P-δ analysis including the method of analysis used by the program, matrix method or the finite element method, and column discretization ratio. Ideal column mesh size is not covered by software manuals and has been a controversial topic for engineers’ discussion as there is no available guidance for engineers to follow. Improper selection of column mesh size may lead to inaccurate or even misleading analysis results. The interest of this study is to investigate the influence of column discretization on P-δ analysis in order to provide a scientific base for engineers to rely on. The research also diagnoses the difference between software that utilizes matrix method and those that utilizes finite element method when adopted in P-δ analysis of columns. Loading case is also examined in this study as a factor that could affect the ideal mesh size for each method of analysis. Two loading scenarios are investigated; nodal loads and member loads. A Matlab code has been written to show the difference between the two approaches, matrix and finite element methods, when used for a column with nodal forces without the influence of different solving techniques used by software. Two programs are then implemented to study the effect of column discretization on P-δ analysis under different solving approaches and different level of axial loading. STAAD Pro software has been considered as an example on software that adopts matrix method for skeleton structures and that is used in routine design works. On the other hand, Abaqus software is taken as an example for software that completely implements finite element method and is usually used in research field. Results for different case studies indicate that the solving approach, matrix or finite element methods, significantly affect the choice of ideal column discretization ratio. The results also show that columns that are subjected to member forces seem more sensitive to mesh size comparing to the corresponding columns that are subjected to nodal forces.