Heoretical Analysis Of Frame-supported Shear Wall Equivalent Truss Model (ETM)

The finite element method is a numeric method which is grown from the continuum mechanics. Its basic theory is dividing a continuous body into finite elements. The FEM is adapt and applied to various complex structures; It is very reliable as based on rigorous theory; and it is highly effective as using computer to calculate. Along with the development of computer hardware and software, the FEM has been become a requisite numerical calculation tool in the engineering field when dealing with complex issues.Based on the displacement equivalent principles and finite element method basic ideology, in the way of truss member, this paper constructs a new element model - equivalent plane truss element to seek a more simple and practical approximate calculation method, having the same level of engineering precision, to solve the two-dimensional complex issues. At the same time, reinforced concrete equivalent truss finite element model is proposed for frame-supported shear wall structure with transition beam under complex stress, which provides a means for engineering analysis.Firstly, theoretical derivation of quadratic equivalent truss model and triangle equivalent truss model is discussed. The prerequisite qualification of equivalent is the equivalent relationship of nodal displacement between quadrilateral micro element and equivalent truss model under the same support. That is equivalent of stiffness. On this account, the element stiffness matrix and equivalent section area of every bar of the equivalent truss element are derived. Secondly, starting from the transfer structure used commonly in practical engineering applications, the transfer member(including transfer deep beam and upper shear wall)is discreted using equivalent truss model in this paper, and numerical simulation is carried out ,then the result is compared with a universal finite element procedure -ansys10.0, to check the feasibility and engineering precision of this program. Finally, equivalent truss model nonlinear finite element analysis is proposed on the following points: Firstly, reinforced concrete plane equivalent truss finite element model: separated model, combined model and integrated model; Secondly, element failure criterion, cracking model and treatment after cracking; Thirdly, material constitutive model of steel and concrete commonly used in reinforced concrete structure, as well as material constitutive model used in this paper.In the model, reinforced concrete structure is dispersed into equivalent truss element and reinforced element is dispersed into one-dimension bar element. The equivalent truss element and bar element have the same nodes through mesh control. Each bar of equivalent truss element is two-force beam, so one dimension stress-strain relationship of concrete is used in elastic-plastic analysis of reinforced concrete structure to simplify the problem and improve efficiency of nonlinear analysis. In the traditional elastic-plastic analysis, it is difficult to judge the section failure or not. In this paper, section failure or not is judged by the fault of equivalent truss bar. Using the method, though the finite element analysis software ANSYS10.0, full-frame-shear wall and double-shear wall with material nonlinear are analyzed, and then the calculated results are compared with the test data. The calculated results agree with the test results very well.