Keywords: coupled shear wall, seismic, natural frequency, continuum method.

Coupled shear walls are generally used in multi-storey buildings as they demonstrate good performance under lateral loads (e.g. wind pressure or earthquake inertia forces). Under seismic event, coupled shear walls drastically reduce inter-storey distortion and, consequently damage to non-structural elements, which in many cases represent most of the value of the building [1]. An efficient and economic design of a building depends mostly on the adoption of a minimum design base shear. Therefore, natural vibration analysis plays an important role in the design of structural analysis. To determine this very important property of buildings, present practice of building design heavily relies on various building code provided empirical formulas that depend on the building material.

For a building yet to be designed, the present practice depends on various codes of practice to provide empirical formulae that are not very accurate, which, in turn, lead to very conservative values of base shear, and results in over-designing of the structure [2,3,4]. A simple and accurate method for determination of natural vibration of buildings, at least for preliminary design, is in high demand by structural engineers.

The objective of this paper is to present a simple analytical method to estimate the periods of vibration of coupled shear wall buildings. A governing equation derived using continuum approach is used in the analysis. Power-series method is applied for solving the governing equation using the proper boundary conditions. While solving the equation, it is assumed that the transverse displacement of the coupled shear wall is harmonic in nature. Two numerical examples are performed. Care has been exercised to retain sufficient accuracy in evaluating natural frequencies. Comparisons are also made with results available in the published literature to show the accuracy of the proposed method.

It can be seen from both examples that the results calculated by the proposed method agree very well with the results obtained from the methods by Wallace and Moehle [5] and Wang and Wang [4]. In fact, the accuracy depends on the number of terms included in the equations to solve. The method proposed in this paper can be used as an alternative method to determine the natural frequencies of structures with coupled shear walls with a very high accuracy but with much less effort.

1

D. Capuni, M. Merli and M. Savoia, "Dynamic analysis of coupled shear wall-frame systems", Journal of Sound and Vibration, 192(4), 867-883, 1996. doi:10.1006/jsvi.1996.0222

2

R.K. Goel and A.K. Chopra, "Period formulas for concrete shear wall buildings", Journal of Structural Engineering, 124(4), 426-433, 1998. doi:10.1061/(ASCE)0733-9445(1998)124:4(426)

3

B.S. Smith and E. Crowe, "Estimating period of vibration of tall buildings", Journal of Structural Engineering, 112(5), 1005-1019, 1986. doi:10.1061/(ASCE)0733-9445(1986)112:5(1005)

4

Q. Wang and L.Y. Wang, "Estimating periods of vibrations with coupled shear walls", Journal of Structural Engineering, 131(12), 1931-1935, 2005. doi:10.1061/(ASCE)0733-9445(2005)131:12(1931)

5

J.W. Wallace and J.P. Moehle, "Ductility and detailing requirements of bearing wall buildings", Journal of Structural Engineering, 118(6), 1625-1644, 1992. doi:10.1061/(ASCE)0733-9445(1992)118:6(1625)

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