Keywords: forced vibration analysis, non-planar, coupled shear wall, stiffening beams, Vlasov's theory, warping deformation, continuous connection method, Newmark method.

In multi-storey buildings made of reinforced concrete, lateral loads are often resisted by shear walls. 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 behaviour under external loading have to be taken into account in the analysis.

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.

In the present research, the general dynamic analysis of a non-planar non-symmetrical coupled shear wall, resting on a rigid foundation, is studied. All of the dynamic 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 dynamic analysis of stiffened non-planar coupled shear walls, so far.

The analysis is based on the continuous connection method (CCM) [1], in conjunction with Vlasov's theory [2] of thin-walled beams, following an approach similar to the one used by Tso and Biswas [3]. In this study, CCM and Vlasov's theory of thin-walled beams are employed to find the stiffness matrix.

The system mass matrix has been found in the form of lumped masses at the heights where the unit forces have been applied. Following the free vibration analysis, uncoupled stiffness, damping and mass matrices have been found employing the mode superposition method. A time-history analysis has been carried out using the Newmark numerical integration method to find the system displacement vector for every time step.

The present formulation is implemented in a Fortran computer program. Using this computer program an asymmetrical example has been solved and compared with the solutions found by the frame method [4] and a perfect match has been observed. This method is an effective method in terms of the simplicity of its data and the extremely short computation time for the predesign of high-rise buildings.

1

E. Emsen, C.D. Turkozer, O. Aksogan, R. Resatoglu, M. Bikce, "Non-Planar Coupled Shear Walls with Stiffening Beams", Scientific Research and Essay, 4(4), 328-345, 2009.

2

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

3

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

4

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

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