New Bi-modular Material Approach to Buckling Problem of Reinforced Concrete Columns

Ahmad Salah Edeen Nassef,Mohammed A Dahim

doi:10.5539/mer.v6n1p19

Abstract

<p class="1Body">This paper was investigating the buckling problem of reinforced concrete columns considering the reinforced concrete as bi – modular material. Governing differential equations was driven. The relation between the non-dimensional transverse deflection and non-dimensional distance between centroid axis and the neutral axis "eccentricity" was drawn to enable the solution of the governing differential equation. The new approach was verified with different experimental results and different codes of practice.<strong></strong></p>

Highlights

Bi – modular material term was recognized, where some materials have different elastic behavior when they are loaded in tension and compression
W is the transverse deflection of the column
As previously mentioned that bi-modular section is considered from the non-dimensional eccentricity of 1/2, the column of bi-modular material should not be governed by the single differential equation

Summary

Introduction

Bi – modular material term was recognized, where some materials have different elastic behavior when they are loaded in tension and compression. Both fiber reinforced and composite materials have different moduli in tension and compression as displayed in Table (1). Two material models were widely used in dealing with bi-modular material within the engineering research .The first model is the criterion of positive-negative signs in the longitudinal strain proposed (Bert, 1977). A semi-analytical method for the critical buckling loads of variable–cross section slender rods with different moduli was developed based on the variational principle. A numerical model to simulate the nonlinear behavior of slender RC columns considering the long-term deformations of concrete was presented (Kwak & Kim, 2006). A linear elastic – perfectly plastic material behavior of the reinforcement and a parabolic material behavior of the concrete with no tensile strength were assumed, the behavior of columns and beam-columns are analyzed numerically and compared with experimental data

Neutral Axis Position

Eigenvalue Analysis

Solution of Governing Differential Equation

Bi-modular Material Approach For Reinforced Concrete Columns:

Results and Discussion

Conclusion