Elastic-plastic analysis of coupled shear walls

ABSTRACT Recently, the coupled wall and/or shear(structural) wall systems are being most frequently used in medium and high-rise buildings in earthquake zones. It is well known that, in the medium and high-rise buildings, shear walls and coupled shear wall systems are needed to provide the necessary stiffness and strenght. In a structural and/or section design analysis of a building, determining the interactions between the frames and shear walls is the main issue. The two types of modelling are used actually for the lateral load analysis of coupled shear wall systems: finite element modelling and the bar frame modelling. The use of bar frame model for analysing the coupled wall system is still one of the practical methods in design. The structural behaviour of coupled shear walls is mostly influenced by the behaviour of their coupling beams; therefore the design of those elements has a great importance. This study consist of mainly two parts; firstly the elastic analysis and secondly the plastic analysis of coupled shear walls are studied. First chapter contains the goal of the work and summaries the similar precedent studies. In chapter two, general assessments of analysis are given related to the shear walls, shear- wall frame and the coupled wall systems which are being largely used in RC building structures. Third chapter contains elastic analysis of coupled shear walls; the parameters of the problem are defined and the necessary explanations dealing with the subject are given. The stiffness of the coupling members, and the geometrical and material parameters that effect to the stiffness directly are defined in linear-elastic space. The adequate number of result which are obtained by finite element analysis in linear-elastic space, are considered as statistical sample data, and then using SPSS package program, an equivalent bar stiffness formula is provided: m\a = neTiûi (1) in which, f,\ 0.0282 s,\ 1.6824 rf =1.9210 b -0.5860 (2) or, by rounding, f/JV,-0VjiY-7V//V0,60 77e =1.9 - - - (3) K*-J İJ U) where rje is a factor and h, b, d, i are the geometrical parameters of the problem. The numerical examples and the comparison made with some available data in literature, as well as with the results produced by finite element analysis, show that the provided formulae which take into account the principal geometrical and mechanical parameters, are quietly satisfactory. IXIn chapter four, concrete and reinforced concrete members are analyzed under the classical plasticity concepts by the ANSYS program working with the NLFEA (Non-Linear Finite Element Analysis) techniques, for producing sample data of statistical assessment. Since it is a quasi-brittle material, the nonlinear behaviour of concrete can be modeled using the concepts of classical plasticity theory provided an adequate yield function. It is essential to choose a suitable yield criterion in order to analyze any member using classical plasticity concepts. In this study, the analytical model of Drucker-Prager yield criterion which is a smooth approximation to the Mohr-Coulomb theory, is used to model the nonlinear behaviour. A smooth approximation to the Mohr-Coulomb surface was expressed by Drucker and Prager in the form (Chen and Han, 1988): f(Il,J2) = aIl+J7^-k = 0 (4) where a and k are positive constants pertaining to the material, a and k related to Mohr- Coulomb constants c (cohesion) and ^ (friction) by, 2sin^ 6ccos0 V3(3-sin^) ' V3(3-sin^) (5) These two parameters which define the strength of the material are used by the ANSYS and LUSAS (in chapter five) programs in the plastic analysis. c=2.80 -3.40 MPa and =25°-35° are suitable values for RC members and c=3.40 MPa and ^ =32° are used in this study. In chapter five, coupled wall systems are analyzed under the classical plasticity concepts by the LUSAS program. Whole numerical results for the plastic analysis and the equivalent rigidity multipliers for tie elements are given. The adequate number of result obtained by finite element analysis in plastic space, are considered as statistical samples, and then using SPSS package program, an equivalent coupling beam stiffness formula is provided by similar way as indicated in the third chapter: T}p =1.507 ^0.0281^1.6896 or, by rounding, >0.03/, > J, \*J v -0.5124 ( - \ -0.345 u (6) c J 77' =1.5 fh^ \<- J 1.70.-0.51 ( " \ -0.35 \Jc J (7) where, acl fc defines the various exciting (loading) levels. Examples made by using the produced formulae are clearly proved that the obtained procedure is accurate enough. Finally, in chapter six, whole obtained results and the suggestions are presented. Keywords: Coupled shear wall, coupling beams, plastic analysis.