### Scientific Research and Essays

• Abbreviation: Sci. Res. Essays
• Language: English
• ISSN: 1992-2248
• DOI: 10.5897/SRE
• Start Year: 2006
• Published Articles: 2755

## The geometrical nonlinear analysis of the prismatic plane frames with the stiffness matrice method

##### Rifat Sezer
Department of Civil Engineering, Engineering and Architecture Faculty, Selcuk University 42075, Konya, Turkey.
Email: [email protected]

•  Accepted: 05 October 2010
•  Published: 18 November 2010

Abstract

In this study, the geometrical non-linear analysis of the prismatic plane frames was researched with the stiffness matrice method by using the stability functions. First of all, having assumed the axial forces acting on the members as zero, the system was solved linearly under the initially set external loads, and the member axial forces were determined. The Stability Functions were calculated by using the obtained axial forces and the system was resolved under the same external loads. The operations were repeated for each iteration under the same external loads until the axial forces became constant. At the end of the iteration, the determinant and the eigenvalues of the system stiffness matrice, the system displacements and the axial forces of the members were determined. The external loads were regularly increased at the beginning of each iteration by multiplying them with a load factor of λ, or the operations were continued until the least Eigenvalue became zero. Thus, at this stage, the critical load or buckling load of the system was found.

Key words: The geometrical non-linear analysis, the stiffness matrice method, instability, frames analysis.