Risk-Based Optimization of Bracing Systems for Seismic Retrofitting of RC Buildings

This paper presents a risk-based optimal design procedure for seismic retrofitting of existing RC buildings with dissipative bracing systems. The procedure extended to retrofit interventions an existing method for probabilistic displacement-based design of new RC buildings. Performance objectives for multiple performance levels or limit states were formulated in terms of maximum mean annual frequency of exceedance (MAF) modeled with closed-form equations based on a second-order approximation of the hazard curve. Retrofit design variables included the characteristics of the braces, conceived as a series arrangement of an elastoplastic dissipative device and a steel truss. To make the gradient-based optimization procedure suitable for practical application, the response under seismic loading was obtained by means of response spectrum analyses for multiple hazard levels, which in turn required the use of linear equivalent models to describe the inelastic behavior of both braces and RC members. Specific member-level expressions for secant stiffness and dissipated energy were used for this purpose. A multistory low-code, height-irregular RC frame taken from an existing building was adopted as a case study. Results in terms of brace properties, interstory drift ratio profiles for each hazard level, and MAF of exceedance were shown and discussed. Finally, the procedure was validated computing MAF of exceedance by means of inelastic response-history analyses carried out within a multistripe analysis scheme, with natural ground motion records selected to match hazard-consistent conditional spectra.