Keywords: multi-bay coupled shear wall, continuous connection method, pierced shear wall, dynamic analysis, stiffening beam, forced vibration analysis.

Shear walls are frequently pierced by windows, doors and corridors with three or more rows of openings. Koo and Cheung [1] have obtained high percentages of error in the example, which they solved in their static analysis using a number of coordinate functions to express the axial forces in the piers. Elkholy and Robinson [2] presented the static analysis of multi-bay shear walls employing the finite difference method.

Following a host of purely analytical works on the static and dynamic analyses of coupled shear walls, Bikce, Aksogan and Arslan [3] have presented the static analysis of multi-bay coupled shear walls with any number of stiffening beams resting on a rigid or flexible foundation. The present work considers the dynamic analysis of the same problem using the mode superposition technique and the Newmark method along with the continuous connection technique [4].

The special method used in the present study comprises two steps. In the first step, the structure is modelled as a system of lumped masses. The number of lumped masses gives the degree of freedom of the structure and is selected freely by the analyst. To find the stiffness matrix, each lumped mass is loaded with a unit horizontal force at a time and the corresponding horizontal displacement vectors for the whole structure is found. For each loading, the compatibility equation is written for the vertical displacements at the midpoints of the connecting beams in each span using the CCM. To solve the system of second order, linear, coupled differential equations, thus obtained, first, a matrix orthogonalization is applied to uncouple it [5]. Then, this system of equations with diagonal coefficient matrices is solved numerically. After finding the displacements for all unit loading cases, the flexibility matrix for the multi-bay shear wall can be written in a straightforward manner. The inverse of this matrix is the stiffness matrix. Substituting this stiffness matrix and the previously obtained mass matrix in the free vibration equation, the natural frequencies and the corresponding mode vectors are obtained.

The forced vibration analysis of the structure is resolved by uncoupling the system of differential equations obtained, using mode superposition technique, which renders the mass and stiffness matrices diagonal. Abovementioned matrices having been diagonalized, the Newmark method is employed to carry out the time- history analysis.

A computer program has been prepared in the MATHEMATICA computer algebra system, to implement the computations explained in the foregoing paragraphs. This computer program has been first, used, for the dynamic analysis of a multi-bay coupled shear wall example [3], for which the static analysis has been carried out in the literature. The example problem has been solved both by the program prepared in the present study and by the SAP2000 [6] structural analysis program. The results of the two programs have been compared and observed to be consistent with each other.

1

K.K. Koo, Y.K. Cheung, "The Static Analysis of Multi-Bay Coupled Shear Walls", Building and Environment, 19(2), 93-99, 1984. doi:10.1016/0360-1323(84)90034-9

2

N.S. Elkholy, N. Robinson, "Analysis of Multi-Bay Coupled Shear Walls", Building Science, 8, 153-157, 1973. doi:10.1016/0007-3628(73)90033-9

3

M. Bikce, O. Aksogan, H.M. Arslan, "Stiffened Multi-Bay Coupled Shear Walls on Elastic Foundation", Iranian Journal Science and Technology, 28(B1), 2004 [in Press].

4

O. Aksogan, H.M. Arslan, B.S. Choo, "Forced Vibration Analysis of Stiffened Coupled Shear Walls Using Continuous Connection Method", Engineering Structures, 25, 499-506, 2003. doi:10.1016/S0141-0296(02)00192-X

5

L. Meirovitch, "Computational Methods in Structural Dynamics", Sijthoff and Norrdhoff, Netherlands, 1980.

6

E.L. Wilson, "SAP2000 Integrated Finite Element Analysis and Design of Structures", 1-2, Comput & Struct Inc, California, 1997.

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