Effect of Material Nonlinearity on Deflection of Beams and Frames

Abstract

Background/Objectives: To examine the effect of material nonlinearity of mild steel on the total deflection of beams and frames. Method of Analysis: In the linear analysis, value of Young’s modulus is same in all over the analysis, hence the load-deflection plot is also linear, whereas in material nonlinear analysis of structures the elastic modulus is constant upto yield stress and it decreases thereafter. In the present study linear and material nonlinear analysis of beams and frames are carried out using ANSYS mechanical APDL software. The linear deflection of the structures is also computed using a finite element based MATLAB code. Material nonlinearity is incorporated using bilinear stress-strain curves with tangent modulus E/65. E is the elastic modulus of the material. It has been found that the tangent modulus of stress-stress curve of mild steel is more resemble to E/3, so this value is also considered separately for the nonlinear analysis. In this paper cantilever beam with an end load and a two storey building frame with horizontal load is considered with above tangent modulus. The loads are applied incrementally, deflection and stress at each load increment is computed. Findings: In linear analysis the full strength of the material is not utilized and it is assumed that material will fail after reaching the yield stress. In material nonlinear analysis the strain hardening property is considered by taking the tangent modulus after the yield stress. The linear analysis is giving linear variation of deflection and stress with respect to load, but for material nonlinear (bilinear) the deflection and stress will be same as that of linear upto yield point and after that the deflection is found more and stress value found less than that of linear values. Application/Improvements: For the economical usage of materials nonlinear analysis is preferred over the linear analysis, because it is giving the actual behavior of structures and we are utilizing the maximum capacity of the material.