## 1 Introduction  
Prestressed concrete segmental bridges built in the 1950s-1970s by cantilevering with medium-large span lengths are now at the end of their nominal service life, even though they are currently in service. Hence, road authorities need to carry out assessments of the static and seismic vulnerabilities of these bridges. The latter needs an estimate of the internal force redistribution allowed by the plastic resources of the structure and a comparison of resistance, deformation capacity, and demand, ruled by the collapse mechanism that is activated. In this context, nonlinear response history analysis (NRHA) is the most trustworthy procedure to find out the strength and ductility demand of bridges due to seismic action. Nevertheless, by carrying out NRHA, large computational efforts are required in either reliable modeling of the bridge and seismic excitation, the execution of the analysis, and results post-processing to get design values of the response quantities needed for the design. Furthermore, the great sensitivity of the response to seismic excitation modeling and the non-linear cyclic behavior of the bridge have deferred the use of NRHA by the designer. Conversely, non-linear static analysis (NSA), often referred to as PushOver Analysis (POA), has become, in the last decades, the most common analysis method for the seismic vulnerability assessment of buildings and, more recently, of bridges. Many studies in the literature, e.g., [1; 2; 3; 4; 5], explored the extension of POA, initially formulated for the evaluation of the nonlinear seismic response of buildings, to the assessment of the seismic vulnerability of bridges. Most of the papers highlighted that the extension is not straightforward since bridge dynamic behavior very often depends on a large number of modes, while POA is particularly efficient when the seismic response is mainly ruled by the fundamental mode of vibration. To solve this weakness, several multimodal procedures derived for the assessment of the nonlinear seismic response of buildings [1; 5] were extended to the assessment of bridge seismic response; in other cases, procedures specifically formulated for bridges [3; 4; 5; 6; 7; 8] have been attempted. Recently, machine learning methods were also used for the seismic risk assessment of bridges [9]. Regarding the assessment of the seismic vulnerability of buildings, Modal Pushover Analysis (MPA), formulated and accurately developed by [PERSON] and [PERSON] [6; 7], is one of the most effective procedures. The method can be seen as a direct extension to the nonlinear behavior of the well-known dynamic modal analysis with response spectrum technique for the elastic system since it is based on the following: pushover analyses performed independently for each relevant mode with invariant load pattern; evaluation for each mode of the target displacement by definition of an equivalent Single Degree Of Freedom (SDOF) system; evaluation of strength and deformation demand according to the corresponding configuration of the structure derived by each pushover analysis; and subsequent superimposition of the displacement response parameters by an appropriate modal combination rule (SRSS or CQC). A more conventional approach for taking into account the effect of higher modes in pushover analysis is to derive load patterns, either fixed [4] or time-variant (adaptive) [5], on the basis of the elastic, initial, or tangent modal response of the structure. Concerning the adaptation of MPA to bridges, [PERSON] et al. [3] highlighted the following items: the modes to be considered should be properly restricted since the number of modes needed to obtain a total modal participant mass ratio of 85% could be very large; for each mode, an appropriate control point should be chosen; in this connection, [PERSON] stressed that the natural choice for the control point is the deck mass center, or the top of the nearest pier, the point of the deck with the maximum displacement, or the center of the seismic forces for the given mode.