Most of the procedures proposed in literature for the design of viscous dampers to be inserted in existing buildings are referred to plane structures, or to spatial plan-symmetric structures. The purpose of this study is to extend one of these procedures, which is based on energy criteria and accounts for the nonlinear response of the structure, to 3D plan-asymmetric buildings. In particular the extension regards the determination of the damping ratio as well as the estimation through simplified methods of analysis of the maximum response parameters, as the maximum damper forces and the maximum inter-storey drifts.

The proposed procedure has been verified through a case study characterized by a six storey RC building dimensioned only for gravity loads and rehabilitated with nonlinear fluid-viscous dampers. Both plan-symmetric and plan-asymmetric configurations have been considered for comparisons. The seismic assessment of the considered structures is performed by developing nonlinear models and by applying pushover procedures. The considered rehabilitation strategy is based on the insertion of nonlinear fluid-viscous dampers at each storey and is aimed at reducing the ductility demand to an acceptable level.

Initially the design of the viscous dampers is performed for the two structures considering only the translational components of the first mode. Then for the irregular structure the design is repeated considering both the translational and the rotational components of the first translational modes in the two principal directions. The maximum  response parameters as the maximum damper forces and the inter-storey drifts are calculated considering also the higher modes of vibration. The results of the design performed considering the spatial response are compared with the ones obtained neglecting the plan-asymmetry. The effectiveness of the different design procedures has then been evaluated through comparisons with nonlinear dynamic analyses, carried out considering the nonlinear response of both structural members and viscous dampers and applying a set of spectrum-compatible ground motions.