Equivalent Truss Model Of Reinforced Concrete Finite Element Analysis

The FEM is needed to analyze the force and deformation characteristics of the complex continuum such as RC structural members.It is effective and practical in all kinds of structural analysis because of its solid theoretical basis and its reasonable meshing style.Although the traditional FEM is extensively used in the analysis of RC structures,there are still some disadvantages to it.Firstly, complex displacement field functions are to be set to fulfill essential boundary conditions.Secondly, the two-dimensional or three-dimensional constitutive relation of concrete is uncertain according to the past research.Thirdly, the simulation of concrete crack has been a difficult problem for normal FEM ever since.In order to solve these problems,a new type of finite element model called equivalent truss model is proposed.The equivalent truss model composed of six two-force bars is equivalent to a RC micro-body. The equivalent axial stiffness of each bar is calculated according to the displacement and energy equivalent principle.This model has the features of simple structure and definite force transfer mechanisms.Besides the advantages of the traditional FEM,it has its own superior characteristics.First,the element stiffness matrix is integrated directly according to the meshing size and the analysis object without setting displacement field functions.Second,the one-dimensional constitutive relation of concrete applied in the analysis of the equivalent truss model is generally acknowledged. Third, a random crack model that the bars of the equivalent truss model will be subject to tensile failure according to their random material strength is adopted for the simulation of concrete crack.On the basis of previous research works, this paper mainly discusses the following aspects:Firstly, the stiffness of each bar of the equivalent truss model is derived in detail based on the displacement and energy equivalent principle,and the general procedures in actual analysis using this model are briefly described.Secondly, according to the superiority in the process of practical analysis and its own features, the equivalent truss model plane stress program is compiled by means of MATLAB. The feasibility of the model has been proved by examples of a simply supported concrete beam and a concrete cantilever beam through this MATLAB program. Thirdly,given the characteristics of the RC plane equivalent truss model,a reasonable constitutive relation of concrete and steel is determined.Fourthly, in the practical application of the RC plane equivalent truss model,equivalent truss integrated model, equivalent truss separated model and equivalent truss combined model are proposed based on the existing reinforced concrete finite element models.The theoretical foundation and applicable condition of each model is discussed.In order to simulate the behavior of concrete crack,the nonlinear analysis of the equivalent truss model is expounded under the condition of positive or non-positive definite matrix,as the element stiffness matrix is adjusted when the bars of the model are subject to yield or failure point.Lastly, the practical application of equivalent truss model is further stated by nonlinear full-range analysis of a simply supported RC beam and a short-leg shear wall.