Different methodologies for evaluating the equivalent damping ratio due to cross laminated timber roof structure in seismic restoration of an historical church

The paper shows different methods to evaluate the Equivalent Damping Ratio for historical churchrein forced by cross laminated timber roof structure. The role of roof in the seismic restoration of historical churches, characterized by one nave configuration and masonry walls, is crucial in orderto avoid the out-of-plane rocking mechanisms of the lateral walls and reduce the in-plane shear forces stressing the façade. Wooden based roof structures are preferable for this kind of constructions because they respect the conservation requirements, being compatible to the original materials. Therefore, the roof should be able to dissipate the seismic inertia forces in the nave transversal response, working as a dissipative diaphragm. Some solutions for the roof-diaphragm are here discussed and the relative Equivalent Damping Ratio is evaluated for a case study modelled with finite elements. Equivalent damping ratio is initially estimated by nonlinear static analyses(pushover analyses) based on the Coefficient Method and the Capacity Spectrum Method. Moreover, the equivalent damping ratio is determined also by nonlinear dynamic analyses where the seismic action is represented by seven spectrum-compatible accelero grams. Finally, the equivalent damping ratio values are compared themselves to optimize the wooden based roof structures in terms of strength and stiffness by showing possible configurations for type of wood(hardwood in double planks or industrial technology as Cross Laminated Timber panels) and steel connections.