Non-linear Analysis of Reinforced Concrete Frame Structure using Applied Element Method

Abstract

In the last two decades many structures underwent failure due to extreme loadings such as earthquake, flood, explosion, hurricane and different terrorist attacks. It leads to major damage to the structure such that the partial or complete collapse can eventuate that might cause the great human as well as the economic loss. Therefore, the determination of the deflection capacity and failure mechanism beyond the elastic limit of Reinforced Concrete (RC) structures due to these extreme loadings is very important. RC structures are slender in nature which produces large deformations causing geometric nonlinearity. Nonlinear analysis including both material and geometrical nonlinearity of RC structures is very complex in nature and hence a highly efficient numerical method is required. Applied Element Method (AEM) is a displacement-based method which can track nonlinear behavior of the structure i.e. crack initiation and propagation, element separation, rigid body motion of structural elements and total collapse process with high accuracy. In AEM structure or structural members are discretized with rigid elements connected by springs. Deformation characteristics of the structure are represented by normal and shear springs connected between the faces of rigid elements. The objective of the present study is to perform the nonlinear analysis of the Reinforced Concrete frame structure considering both geometrical and material nonlinearity. This study includes the fundamentals of AEM, development of computer programs & illustrative examples of analysis of RC structures using AEM. Application of AEM for one dimensional analysis is illustrated through the problem of axially loaded column. While for two dimensional analysis, examples of RC beam and RC frame structures are solved using AEM. The analysis results in terms of displacement and stresses are compared by considering the different number of springs and variation in size of an element. Shear force and bending moment calculation for RC cantilever beam is presented in this report and the results obtained using AEM are compared with the results of numerical analysis using Finite Element Method (FEM). This report includes the geometric nonlinear analysis of RC beam and five different RC frame structures using AEM. The combined geometric and material nonlinear analysis of RC frame structure using AEM is also discussed. The objective of the geometrical nonlinear analysis is to predict the deflection magnitude of the RC structure at various loading intervals. The structure is divided into a number of elements connected with springs representing properties of concrete and reinforcement. Parametric study is carried out considering different number of elements, different number of springs and various load increments. The geometric nonlinear analysis results of RC cantilever beam are compared with the analysis results of FEM obtained using the ABAQUS software and analytical solution. The study also includes the combined material and geometrical nonlinear analysis of RC simply supported beam and RC frame in which the analysis results obtained using AEM are compared with the experimental and FEM based results. The static linear analysis results of AEM using 1D element for axially loaded column and 2D element for RC simply supported beam and portal frame are similar to FEM based results. Also the analysis results in terms of stress, shear force and bending moment at desired locations obtained using AEM shows close agreement with FEM based results and theoretical values. The geometric nonlinear analysis results of RC beam shows that, the AEM performs better than FEM and gives close results with analytical results. The combined material and geometric nonlinear analysis of RC frame structures shows that, AEM can be effectively used to predict the failure load, ultimate load and crack locations without performing the actual experiment which will reduce the cost and time of experimental investigation. The study shows that, AEM can be effectively used for the linear and nonlinear analysis of RC structures.