A strain based nonlinear finite element analysis of reinforced concrete beams using secant stiffness approach

Abstract

The aim of the present work is to study the nonlinear failure characteristics with an emphasis on tension stiffening of reinforced concrete (RC) beams subjected to flexure. An analysis of failure of the reinforced concrete beam and the variation of strains and stresses in concrete and adjoining reinforcement in tension is carried out using a FE based numerical model. A strain based nonlinear finite element analysis program [NLFEARCB]® in MATLAB (R2009a) is developed by using 2D plane stress formulation, modified compression field theory, secant stiffness formulation, smeared rotating crack approach and the load deformation behavior is observed. The load deformation response of present numerical model (NLFEARCB) is compared with the numerical model by Wei et al (2006) and also with the RC beam tested by present authors under four point loading in the laboratory and is in well agreement. Tension softening, tension stiffening and crack band width are well captured in the present analysis and are discussed. It is observed that the cracks in reinforced concrete in tension are developed at regular interval and the concrete in between adjacent cracks remains intact and carries some tensile stresses along with the reinforcement.