Keywords: geometrically nonlinear analysis, buckling load, stiffened coupled shear walls, energy method, continuous medium, stiffening beam.

In most of the tall buildings, a portion of the lateral load is carried by the shear walls. Such shear walls usually have openings for doors or windows. For interactive action of the shear walls existing at the two sides of the openings, the two shear walls are connected by so called "connecting beams" and hence, coupled shear walls are produced. In these walls according to the architectural limits, depths of the connecting beams are restricted. So, in some cases, the necessary stiffness to withstand the lateral load may not be afforded because of the low depth of the connecting beams. In order to increase the capacity of the coupled shear walls, beams with high stiffness will be added to the system at one or several levels and so, stiffened coupled shear walls will be produced. The axial loads due to the weight affects the behavior of the walls because of the excessive height of the walls. The existence of the stiffening beam increases the stiffness and decreases the bending moments in each wall dramatically. Reference [1] deals with the effects of the position and stiffness of the stiffening beam on the behavior of the stiffened coupled shear walls which are placed on rigid and flexible supports. In this reference, it is shown that the position of the stiffening beam has an important effect on the behaviour of the structure. In references [2,3] it is shown that the structure performance improves noticeably due to the presence of the stiffening beam. In reference [4] coupled shear walls have first been divided into two separate shear walls and then the stiffness matrix of the whole system has been developed according to the boundary conditions. Hence, the analysis of the coupled shear walls with constant specifications throughout the height, leads to the solution of a linear differential equation with constant coefficients and critical load results have been presented for a limited range of stiffness parameters for the coupled shear walls. In reference [5] upper bound of critical loads for a wide range of the governing parameters have been computed. In this paper a method has been introduced for the geometrically nonlinear analysis of the stiffened coupled shear walls. A formulation has also been suggested for the determination of the buckling load of the stiffened coupled shear walls under gravity loading. In this method, the discontinuous system of the connecting beams has first been replaced by a shear continuous medium and then the effects of the axial force on the lateral deformations have been taken into consideration. Then, the governing equation for deformation of the stiffened coupled shear walls has been obtained by setting up the equilibrium equations and the moment-curvature relationships for each wall by eliminating the laminar shear from the relationships. In the governing equation, the effects of the axial force and the stiffening beam have been accounted for. The exact solution of the governing equation is very difficult so, the energy method has been adopted. In this method, a shape function compatible with boundary conditions has been chosen and the total potential energy of the system has been calculated and by minimizing this function in terms of the unknown coefficients, the deformation equation of the stiffened coupled shear walls has been obtained. The critical load of the stiffened coupled shear walls has been obtained equating the determinant of the coefficients of the equations to zero. At the end, several numerical examples have been solved using the proposed method. In order to indicate the capability of the proposed method, the results arising from the proposed method have been compared to the results arising from the ANSYS software model. The effects of the stiffness and the position of the stiffening beam on nonlinear behavior and critical gravity load of the stiffened coupled shear walls have also been investigated. The diagrams prepared show that the best position for the stiffening beam is about 2/3 H where the most reduction in the displacement of the top level of the wall and the most gravitational critical load of the wall result.

1

Coull, A. and Bensmil, L., "Stiffened Coupled Shear Walls", Journal of structural Engineering, ASCE, Vol. 117, No. 8, pp. 2205-2223, 1991. doi:10.1061/(ASCE)0733-9445(1991)117:8(2205)

2

Chan, H.C. and Koung, J.S., "Elastic Design charts for Stiffened Coupled Shear Walls", Journal of structural Engineering, ASCE, Vol. 115, No. 2, pp.247-267, 1989. doi:10.1061/(ASCE)0733-9445(1989)115:2(247)

3

Chan, H.C. and Koung, J.S., "Stiffened Coupled Shear Walls", Journal of Engineering mechanics, ASCE, Vol. 115, No. 4, pp. 689-703, 1989. doi:10.1061/(ASCE)0733-9399(1989)115:4(689)

4

Rosman, R., "Stability and Dynamics of shear-wall Frame Structures", Building Science, Vol. 9, pp. 55-63, 1974. doi:10.1016/0007-3628(74)90040-1

5

Grzelak, E., "The Approximate Free Vibration and Stability Analysis of Shear-Flexure Cantilevers", M.Sc Project Report. Dept. of Civ. Engrg., McGill Univ., Montreal.

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