An optimal design procedure for a simple frame equipped with elastic-deformable dissipative braces

• A design procedure of an elastic frame equipped with dissipative braces is proposed.
• Design parameters are the brace stiffness and the viscous/friction damping.
• The proposed procedure joins an analytical treatment to a numerical validation.
• An analytical treatment provides optimal parameters as function of brace stiffness.
• Numerical analysis is needed to validate and calibrate theoretical optimal values.

In the present work, the authors find a solution to a design optimization problem for a simple linear-elastic one-bay one-story frame equipped with elastic-deformable viscous or friction dissipative braces, i.e. additional elements able to increase both damping and stiffness of the original structural system. Against earthquake induced energy, bracing systems are devoted to reduce damage to the frame structure by limiting inter-story drifts. The main advantage of dissipative braces despite traditional ones is base shear and stress state reduction thanks to supplemental damping. An analytical approach is suggested for determining the theoretical optimal value of the viscous damping or the yielding force parameter, able to minimize the maximum displacements: properly defined design spectra are provided in the first part of the paper. The proposed analytical method is validated by means of numerical analyses carried out on a simple frame subjected to seven spectrum-compatible earthquake records, according to the Italian Code for Constructions. Therefore, an effective design method is delivered: proposed optimal values can be assumed as a starting point of the optimization operative procedure; then, an iterative analysis is needed in seismic perspective in order to determine the effective optimal values of the design parameters for the minimization of the desired response.