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

In multi-storey buildings made of reinforced concrete, lateral loads are often resisted by specially arranged shear walls. Shear wall components may be planar, are usually located at the sides of the building or in the form of a core which houses staircases or elevator shafts. 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. 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. When thin-walled structures are twisted, there is a so-called warping of the cross-section and the Bernoulli-Navier hypothesis is violated.

When the height restrictions prevent connecting beams from fulfilling their tasks of reducing the maximum total shear wall bending moments and the maximum lateral displacements at the top, beams with high moments of inertia, called "stiffening beams", are placed at certain heights to make up for this deficiency. Stiffening of coupled shear walls decreases the lateral displacements, thus, rendering an increase in the height of the building possible. Hence, assigning some stories of the building as storage or service areas and the like and placing high beams on those floors seems to be a logical solution. Such coupled shear walls are called "stiffened coupled shear walls". Such beams can be steel trusses or reinforced concrete beams of very high bending stiffness.

All of the analyses in the literature on stiffened coupled shear walls concern themselves with planar coupled shear walls. No study has been made, to the knowledge of the authors, concerning the static analysis of stiffened non-planar coupled shear walls.

In the present work, the static analysis of non-planar coupled shear walls with any number of stiffening beams, is carried out which is applicable to 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 discrete system of connecting beams is replaced by continuous laminae of equivalent stiffness. The CCM has been employed in the analysis and the compatibility equation has been written at the mid-points of the connecting beams. The axial force in the piers is determined from the differential equation which is obtained by using the compatibility and the equilibrium equations. Then, all relevant quantities of the problem are determined employing their expressions in terms of the axial force. The present formulation is implemented with a Fortran computer program. Using this computer program an asymmetrical example has been solved and compared with the solutions found by the SAP2000 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.

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