Analysis of second order effects: case study

Abstract

This paper presents a nonlinear static analysis of a reinforced concrete plane frame. It has as main objective is to realize a global stability verification of a plane frame, by using geometric stiffness matrix. In order to obtain first and second order combined effects, equilibrium and kinematic relations were studied in the deformed geometric configuration. These results were obtained by using geometric stiffness matrix and multiplying horizontal forces by Gamma-Z coefficient. Both procedures disclosed very similar results in the study, indicating that Gamma-Z can be used to study equilibrium and kinematic relations in deformed geometrical configuration of the structure.

Comparative Study of Non-Linear Simulations of a Reinforced Concrete Slender Column Using Finite Element Method and P-Delta

“…Plumbridge, Matela and Westwater (2003) presented the formulations for linear and nonlinear analysis by FEM and compared the main differences between them. Bueno and Loriggio (2016) point out that the choice of the most appropriate procedure to be used depends on several factors, such as the magnitude of the displacements and rotations in the structure, the level of normal working forces, the sensitivity of the structure to second order effects, among others.…”

Evaluation of the P-Δ (P-Delta) effect in columns and frames using the two-cycle method based on the solution of the beam-column differential equation

“…Then, a fictitious lateral load that would cause the same moment is applied, hence giving a new linear displacement and the process is repeated iteratively until a tolerance is reached. Since this process can be seen as a geometric progression, with ratio given by the relation between the additional moment (P-Δ) and the first order moment (M 1 ), the result of the iterative method is the sum of this progression [10] . Eq.…”