Urban Lifestyle is of a rapidly growing nature and the dense commercial and residential neighborhoods are only to get bigger and denser with population numbers keep rising. With that in mind, the need for tall buildings is obvious. One type of lateral load resisting structural system is the damped outrigger (DO) structure. It has been the subject of numerous researches in the field of tall building in the past decade and has been commonly associated with wind loads. Nevertheless, in recent years it has been shown that DO’s exhibit positive behavior in reducing responses of interest under seismic excitations as well. The height of the outrigger has a great effect on the structure’s behavior. Thus, optimization may lead to a large improvement in structural behavior or costs. This is even more pronounced when accounting for the flexibility of the columns.
This paper presents a formal optimization methodology for the seismic design of tall buildings with damped outriggers excited by a stochastic stationary ground motion. The outriggers heights and the dampers' sizes serve as the design variables. The objective is to minimize a cost function related to the dampers while constraining any number of responses of interest to allowable values (e.g. inter-story drifts, absolute accelerations, over-turning moments etc.) subjected to a filtered white noise excitation. Lyapunov’s equation is used to reach the root-mean-square responses. A first-order optimization method is adopted, and the gradients required are derived efficiently using the adjoint analytical method. Constraints are first normalized by their allowable values then manipulated into a single constraint on their maximal value. Locations of the damped outriggers are represented by continuous, differentiable shape functions that are adjusted throughout the optimization process to reach the desired discrete solution. The perimeter column flexibility is expressed as a Maxwell spring model.
Results show that when the perimeter column flexibility is considered, the optimized structure differs than that obtained when assuming stiff columns. The main contribution arises from this work is the simple, robust and efficient tool to for the optimal design. Moreover, the responses of interest, which are to be constrained, are not limited meaning one can account for the floor's accelerations, drifts, displacements, shear, moment and more as a single constraint.
Structural engineers will receive a simple methodology for the optimized design of damped outriggers of new and existing structures. Academics will gain a new approach for discrete optimization.