Keywords: continuous connection technique, non-planar, pierced shear wall, thin-walled beam, static analysis, Vlasov theory.

In tall buildings, lateral forces, induced by wind and earthquake, are generally resisted by shear walls. A solid shear wall can, easily, be accounted for as a cantilever beam. However, shear walls pierced by doors, windows and corridors are harder to analyze since they are highly indeterminate. As a result of their high resistance to lateral forces, shear walls have become very popular in tall buildings.

In this study, the static analysis of flexibly connected non-planar non-symmetric pierced shear walls is carried out by a simplifying method widely used in the past for the static analysis of similar structures [1]. This method, called the Continuous Connection Technique (CCT), comprises an elegant tool for the predesign computations related to the treatment of high-rise buildings. In this method, the connecting beams are assumed to have the same properties and spacing along the entire height of the wall. The constant of the equivalent elastic rotational springs to model the plastically deformed beam-wall connections is assumed to be determined by suitable experiments and are assumed to have the same value at all connections in the shear wall. Consequently, the discrete system of connecting beams can be assumed to be replaced by continuous laminae of equivalent stiffness capable of transmitting action of the same type as the connecting beams. The properties of the structure are expressed as continuous functions of the longitudinal coordinate by employing the foregoing model.

The present analysis is based on a joint use of the CCT and Vlasov's theory of thin-walled beams, appreciable for non-symmetric structural systems as well as symmetric ones on rigid foundation, following an approach similar to the one used by Tso and Biswas [2]. Employing the CCT, the compatibility equation has been written at the mid-points of the connecting beams. 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 [2] took the rotation as the main unknown and applied their analytical results to a structure which is symmetrically arranged in the horizontal plane. However, in the present study, pierced non-planar nonsymmetrical shear walls with yielded beam-wall connections are analyzed taking rotation and axial force as the main unknown, each at a time, and the results have been found to coincide. To implement the foregoing analysis a computer program has been prepared in the Fortran language. Using this computer program, both symmetrical and asymmetrical examples have been solved by the program prepared in the present study and compared with the solutions found by the SAP2000 [4,5] structural analysis program and a perfect match has been observed. The rotational springs have been simulated in the SAP2000 structural analysis program by extremely small beams having suitable bending stiffness values.

1

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

2

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

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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