### State of the Art  
The influence of a considerable axial load on the horizontal stiffness of bearings has been investigated in [7; 8; 9; 10; 11] while a nonlinear extension of the two-spring model proposed for the bearings in [12], consisting of one shear spring and one rotational spring, is found in [13] to take into account the variation of the horizontal and vertical stiffnesses with the axial load and the lateral deformation, respectively. The influence of severe displacement on the vertical stiffness of bearings has been investigated in [14], where experimental tests on different types of bearings have been used to validate four models, two empirical, proposed by the same authors, and two physical, presented in [8]. Further effects on the critical load and horizontal stiffness of bearings, from increasing horizontal displacement and axial load, have been studied in [15] where a nonlinear model predicting an unstable postcritical reaction has been developed by including large displacements and rotations in the linear model by [PERSON], originally based on small displacements and rotations. Lately, an analytical model has been also introduced in [16] to describe the coupled horizontal-vertical behaviour of the elastomeric bearings when the vertical stiffness decreases and the vertical deformation increases beyond the point of stability. In this model, geometric effects like axial shortening are distinct from the vertical deformation of the isolator when the relationships between horizontal and vertical deformations are defined by using experimental results corresponding to quasi-static and dynamic loadings. Another important issue concerns the evaluation of the stability limit of the base-isolation system. This problem has been tackled in [17; 18; 19] where the evaluation of the critical load of an elastomeric bearing, the definition of a relationship between the vertical stiffness and the overlapping area of an elastomeric bearing and the validation of this expression have been studied, respectively. The stability limit of the base-isolation system can also be influenced by the end rotation of the bearings which can occur in configurations without bottom girders. To simulate this effect, a model has been introduced in [20] which includes a series of axial springs at the top, mid-height, and bottom of the bearing to vertically reproduce asymmetric bending moment distribution in the bearings. The simplified or refined models, usually adopted to describe the behavior of the elastomeric bearings, work well so long as these devices do not undergo large tensions. These stresses, which often occur in high-rise buildings under severe near-fault EQs, can produce the onset of voids inside the rubber after exceeding the theoretical yielding point, as described in [21; 22; 23] and the buckling of the bearings at a load close to that for buckling in compression, as shown in [24; 25]. Other consequences are the reduction of both tensile stiffness and compressive stiffness in the high damping rubber bearings and the reduction in the damping effect in the lead rubber bearings under tension or low compression, mentioned in [26], which suggest that the energy dissipation target could not be reached in structures base-isolated by these devices. Moreover, the survey of the effects produced by EQs worldwide in Asia (i.e., Chi-Chi, Taiwan 1999) and South America (i.e., Chile, 2010) have shown that the bearings can undergo local tensile stress even when they exhibit a shear and compressive global response [27; 28]. The numerical study [29] into the response of bearings subjected to variable axial loads and the development of tensile stresses has instead allowed researchers to define the range of variation in the stiffness and damping ratio and the local tensile stresses corresponding to notable cyclic shear displacements and variable axial load. Currently, few codes and standards, like the Eurocode 8 [30] and the Chinese seismic design code [31], consider the response in axial tension of the bearings.