Optimal placement of steel diagonal braces for upgrading the seismic capacity of existing structures and its comparison with optimal dampers

In this study, the optimal placement of X steel diagonal braces (SDBs) is presented to upgrade the seismic response of a planar building frame. The optimal placement is defined as the optimal size and location of the SDBs in a frame structure. Steady state response of the structure evaluated at the undamped fundamental natural frequency is defined by means of transfer functions that are independent of initial values and the input excitation. The objective functions are chosen as the amplitude of transfer function of the top displacement and the amplitude of transfer function of the base shear force evaluated at the undamped fundamental natural frequency of the structure. In the optimization procedure, the stiffness parameters of the added braces are described as the design variables. Principal optimality criteria are derived using Lagrange Multipliers Procedure. The obtained nonlinear equations are solved with “Steepest Direction Search Algorithm”. Sensitivities of the objective functions are determined analytically. A simplified algorithm for the state of the base shear force as the objective function is also proposed. The response of the structure is examined for both of the objective functions in terms of the transfer function. Seismic rehabilitation with SDBs is compared to the rehabilitation with viscous dampers. Therefore, a total equivalent stiffness parameter is defined so that the transfer function amplitude of the top displacement of building structure with SDB attains the same value with the transfer function amplitude of the top displacement of building structure with optimal dampers based on the top displacement. The time history analysis is performed using El Centro earthquake ground motion records to demonstrate the validity of the proposed design method. The results of the numerical procedure point out that the proposed procedure based on the transfer function of the base shear force and the top displacement can also be beneficial in the rehabilitation of seismic response of the structures.