Keywords: static analysis, continuous connection method, non-planar, coupled shear wall, warping deformation, thin-walled beam, Vlasov theory.

Recently, a rapid increase has taken place in the number of tall buildings. In multistory buildings made of reinforced concrete, the lateral loads are often resisted by specially arranged shear walls. Shear wall components may be planar and are usually located at the sides of the building or in the form of a core which houses staircases or elevator shafts. Weakening of shear walls in tall buildings by doors, windows and corridor openings is one of the most frequently encountered problems of structural engineering. When the coupling action between the piers separated by openings becomes important, some of the external moment is resisted by the couple formed by the axial forces in the walls due to the increase in the stiffness of the coupled system by the connecting beams. In planar coupled shear wall analyses, the lateral loads are applied in such a way that the deformation of the shear wall is confined within its own plane. Actually, the deformation of a coupled shear wall subjected to lateral loading is not confined to its plane. Studies considering in-plane, out-of-plane and torsional deformations in the investigation of coupled shear walls are called non-planar coupled shear wall analyses. In non-planar coupled shear walls, both the flexural and torsional behaviours under external loading have to be taken into account in the analysis.

In the present work, the static analysis of non-planar coupled shear walls is carried out which is applicable for non-symmetric structural systems as well as symmetric ones on rigid foundation. The analysis is based on the Continuous Connection Method (CCM), in conjunction with Vlasov's theory of thin-walled beams, following an approach similar to the one used by Tso and Biswas [1]. In the CCM, the connecting beams are assumed to have the same properties and spacing along the entire height of the wall. The discrete system of connecting beams is replaced by continuous laminae of equivalent stiffness [2]. The CCM has been employed in the analysis and the compatibility equation has been written at the mid-points of the connecting beams. For this purpose, the connecting beams have been replaced by an equivalent layered medium. The warping of the cross-sections of the piers due to their twist, as well as their bending, has been considered in obtaining the displacements. Vlasov's thin-walled beam theory has been used for this purpose [3]. Tso and Biswas [1] presented the analysis of a coupled non-planar wall structure based on the CCM and Vlasov's theory. Although Tso and Biswas claimed that their analytical results are verified by their experimental results, it is observed that their governing differential equation, where the rotation is taken as the main unknown, misses some terms. Furthermore, all of the previous authors apply their methods to a single symmetrical coupled shear wall originally used by Tso and Biswas. To be more general, the present paper deals with non-symmetrical structures both in the formulation and in the numerical applications. To consolidate the analysis, the present work has taken the rotation and axial force as the main unknown, each at a time, and the results have been found to coincide. The present formulation is implemented with a Fortran computer program. Using this computer program, both symmetrical and asymmetrical examples have been solved and compared with the solutions found using the SAP2000 [4,5] structural analysis program and a perfect match has been observed.

1

W.K. Tso, J.K. Biswas, "General Analysis of Non-planar Coupled Shear Walls", Journal of Structural Division, ASCE, 100(ST5), 365-380, 1973.

2

R. Rosman, "Approximate Analysis of Shear Walls Subject to Lateral Loads", Journal of the American Concrete Institute, 61(6), 717-732, 1964.

3

V.Z. Vlasov, "Thin-walled Elastic Beam", 1-2, U. S. Department of Commerce, Washington, D.C., USA, 1961.

4

I.A. MacLeod, H.M. Hosny, "Frame Analysis of Shear Wall Cores", Journal of Structural Division, ASCE, 103(10), 2037-2045, 1977.

5

E.L. Wilson, "SAP2000 Integrated Finite Element Analysis and Design of Structures", Computers and Structures, Inc., USA, 1997.

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