Numerical Analysis Of Reinforced Concrete Structures Based On Equivalent Truss Model

When the traditional finite element method used for numerical analysis of reinforced concrete structures, it needs to construct shape function, complex material constitutive relations, besides concrete structures usually work with cracks, it also has shortcomings even though discrete or distribution of crack mode is taken to analyze structures, traditional finite element method still has the following problems: computational complexity, time consuming, and difficult to converge. Therefore, domestic and foreign scholars have proposed a simplified numerical model:Equivalent truss model. This model is consisted of a combination of discrete hinge levers, which are made according to certain rules. As two-force member, hinge lever only bear axial force and does not use complex multi-parameter analysis constitutive relation, and it can simulate the crack development process, thereby, the calculation model is simplified.Based on the existing study of equivalent truss model and combined with the traditional finite element analysis of concrete structures, the main research work of this paper is reflected in the following aspects:First of all, this paper refers to the previous proposed equivalent plane truss model, and conducts stiffness equivalent analysis between traditional four-node finite element and equivalent plane truss element model unit on the condition of tension, compression, and shear stress, besides equivalent plane truss model unit sizes and stiffness coefficient values are calculated. Then comparisons of elastic analysis on simple supported beams, columns and shear wall structures are made, it is compared solutions of different divisions between equivalent truss model and mechanical model, also confirmed the rationalities of each rod stiffness value of equivalent plane truss model and given the range of cell divisions.Secondly, according to the characteristics of equivalent plane truss model and the properties of reinforced concrete structure, the paper has selected appropriate material constitutive relations, damage and convergence criteria, solution of nonlinear equations, what is more, displacement-increment method is used to simulated the falling section of load-displacement curves. This paper has offered a computer program that based on MATLAB language, which is used for nonlinear analysis of reinforced concrete structures. Reinforced concrete simply supported beam and pier are made to solve nonlinear problems, their results of load-displacement curve, crack positions and development tends are compared with ANSYS solutions. Theoretical analysis and calculation results show that equivalent truss model simplified analytical model on the conditions of meeting the engineering precision, which are used for the analysis of reinforced concrete structures is feasible.Finally, taking into account that truss model 24 lever cannot be better handle structural rigidity matrix of singular problems caused by lever cracking, this paper proposed 28 bars space truss model. Referring research and analysis ideas of equivalent plane truss model, the paper obtained each sectional area and its applicable conditions by stiffness equivalent of this equivalent space truss model. It gives a more perfect and reasonable rod stiffness expression by calculating a simply supported beam, and improves the correctness and accuracy of the analysis; Then selected a space forced cantilever instance, comparative analysis solutions are made between space truss model unit and material mechanics, as the paper showed that the results fit well, which further confirmed the rationality and feasibility of the equivalent method.