Energy-Based Design for the Seismic Improvement of Historic Churches by Nonlinear Modelling

This study investigates the seismic retrofit of historic single-nave churches through the optimization of roof diaphragms designed to enhance energy dissipation. The proposed strategy introduces a deformable box-type diaphragm above the existing roof, composed of timber panels and steel connectors with a cover of steel stripes, where energy dissipation is concentrated in the connections. The retrofit design is guided by the estimation of Equivalent Damping Ratio (EDR) instead of the usually adopted resistance criterion, considering an energy-based approach to improve global seismic performance while preserving architectural integrity. In this way, the retrofitted configuration of the roof can be considered a damper. Three numerical phases are presented to assess the effectiveness of the equivalent damping-based intervention. In the first one, the seismic response of the initial non-retrofitted configuration is implemented using a 3D linear finite element model subjected to a response spectrum. Subsequently, nonlinear equivalent models subjected to spectrum-compatible accelerograms are implemented, simulating the possible retrofitted configurations of the roofs to detect the optimum damping and finding the corresponding roof diaphragm configuration. In the third one, the response of the detected retrofitted configuration is also evaluated by nonlinear 3D model subjected to accelerograms. The three phases with the relative numerical approaches are here applied to a case study, located in a high seismic hazard area. The results demonstrate that the EDR-based methodology can optimize the retrofitted roof diaphragm configuration; the nave transverse response is improved in comparison with that designed with the traditional approach, considering only the over-strength of the interventions. Comparisons about the approaches based on the EDR and the strength criteria are presented in terms of lateral displacements, in-plane shear acting on the roof diaphragm, and in-plane stresses on the façade.