Keywords: shear wall-frame system, lateral drift control, displacement sensitivity, approximation concept, optimal design, resizing technique.

The control of lateral drifts such as top lateral drift and interstory drift is an important problem not only for the serviceability but also for the safety in the design of tall buildings. Many design software systems now provide design features to satisfy member strength requirements according to design codes. However, very little work has been done to consider the more difficult and dominating problem of satisfying lateral drift (stiffness) criteria for tall building. So far, the general optimal design approaches of tall building subject to lateral drifts usually consider all degrees of freedom of overall structure. But, as such structures generally consist of thousands of members, it is very difficult and complicated to resize members so that the lateral drift constraints are satisfied. So, some structural engineers often perform the control of lateral drifts by a trial and error approach based on their experience and repetitious analysis. Moreover, the compatibility problem of displacement degree of freedom between the frame and shear wall should be solved to perform sensitivity analysis for tall structure considering the interaction between frame and shear wall.

In 1992, Saka presented the optimum design of multi-storey structures with shear walls based on optimality criteria method [1]. But this approach depends upon the behaviour of the structure and does not guarantee the convergence to the optimum value. On the contrary, mathematical programming method has the generality to consider any objective function and constraint and it is not necessary to predict the set of active constraints. However, no single method can solve efficiently all optimization problems and there are no accurate methods for optimizing effectively large structures. The efficient mathematical programming method for practical problems with a large number of variables and constraints is often based on approximation concepts [2].

Therefore, this study presents an effective lateral drift control technique for shear wall-frame buildings subject to lateral drift constraints. To this end, the element stiffness matrices are constituted to solve the compatibility problem of displacement degrees of freedom between the frame and the shear wall. Also, the approximation concept that can effectively solve the large scale problems is introduced. And, the displacement sensitivity depending on the section property relationships is considered in order to reduce the number of design variables and differentiate easily the stiffness matrices. Specifically, the constant-shape assumption which is uniformly varying in size during the optimal process is applied to the frame structure. The thickness or length of the shear wall can be changed depending on user's intent. A twenty-story building with a shear wall-frame system is presented to illustrate the features of the design method.

The analysis results show the rapid and steady convergence through the repetitious processes within a few cycles. Also, the results demonstrate that the proposed design method requires the greater increase of lateral stiffness in lower storey levels so as to control the displacements within the allowed drift limit. This shows that it is most efficient to increase the lateral stiffness of lower storeys of buildings to improve the resistance against lateral drift under lateral loads. Therefore, the proposed design method provides an effective strategy for the practical application of the optimization technique to the design of tall buildings under lateral drifts.

1

M.P. Saka, "Optimum Design of Multistory Structures with Shear Walls", Computers & Structures, Vol.44, No.4, pp.925-936, 1992. doi:10.1016/0045-7949(92)90480-N

2

U. Kirsch, "Reduced Basis Approximations of Structural Displacements for Optimal Design", AIAA Journal, Vol. 29, pp.1751-1758, 1991. doi:10.2514/3.10799

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