Seismic performance of frame structures coupled with an external rocking wall

Frame structures can be coupled with external mechanical systems to improve their behaviour under external loads. Some examples of such mechanical systems are oscillating masses working as tuned mass dampers, dynamic mass absorbers, elasto-plastic dampers. Among the others possibilities, a rocking rigid block can be used to improve the seismic behaviour of a frame structure. In this paper a two degree of freedom model is considered representative of a general frame structure. It is coupled with a rocking rigid block through a visco-elastic device, which connects the lower part of the structure with the top of the rocking block. A Lagrangian approach is used to derive the nonlinear equation of motion that are successively solved numerically. A simulation campaign is performed to analyse the seismic behaviour of the coupled system by considering several registered earthquakes. In the analyses, the presence of rocking rigid block is assumed to be beneficial for the system if the coupling of frame structure with rocking rigid block reduces the absolute displacements and/or the inter-storey drifts. An extensive parametric analysis is performed varying the geometric characteristics of the block and the constitutive behaviour of the visco-elastic devices. The results of such analyses are presented through behaviour maps. For each of the parameters varied in the analyses, the corresponding value on the map provides ratio between displacements (or inter-storey drifts) of coupled system and of uncoupled bare frame. Such maps allow an immediate understanding of the effects of the block that has a beneficial effect when the ratio of the displacements is less than unity. Results reveal that in large ranges of the parameters' values the rocking rigid block improves the seismic response of frame structure.