Research On The Equivalent Truss Model Of Reinforced Concrete Structure

Reinforced concrete structure is mostly wised used in civil engineering. FEM is generally used to analyze the mechanical behavior of important structures or structures under complicated loads. For traditional finite element, firstly, it is complex to built the displacement field function and often with lager computational calculation; secondly, because the constitutive relation curve of concrete has various forms, different selection of constitutive relation curve leads to great different calculation results; thirdly, there are shortcomings whether using discrete cracking model or using smeared cracking model to simulate crack and crush of concrete. Based on this engineering application background, a new element is proposed in domestic studies. The new element is equivalent truss model.Equivalent truss model is composed of six two-force bars. The form is simple. And it is convenient to analyze. Firstly, this model is equivalent from 4-node rectangular element. The equivalent area of each bar is calculated according to stiffness equivalent principle. Element stiffness matrix is then integrated directly without using of displacement field function. Secondly, composed bars are all under one dimensional stress state, so it is possible to use uniaxial stress-strain relation, avoiding the diversity and complexity of stress-strain relation under multiaxial stress states. Thirdly, a random cracking model is used in equivalent truss model to solve the crack simulating problem.Based on the outcomes of existed researches, this paper makes several supplements: Firstly, this paper derives systematically element stiffness matrixes, strain matrixes and stress matrixes of rectangular equivalent truss model, square equivalent truss model, triangular equivalent truss model and quadrilateral isoparametric. Secondly, equivalent truss model plane stress source program is compiled by using MATLAB. The model has been proved by examples through this MATLAB program. Thirdly, to the existing reinforced concrete finite element models, equivalent truss integrated model, equivalent truss separated model and equivalent truss combined model are proposed and the element stiffness matrixes of them are derived. Finally, the practical application of equivalent truss model is further stated by nonlinear full-range analysis of a reinforced concrete simple-supported beam and a reinforced concrete wall panel with openings. The load-displacement curve is obtained and model calculation value of ultimate strength is compared with code calculation value and test date, meanwhile, the main causes of the error is analyzed.