## 1 Introduction  
Bridges are often sensitive to higher modes, so the seismic response (e.g., the response of the critical piers) depends on local behavior. Therefore, nonlinear static analysis (NSA) can be considered a valid alternative to nonlinear response history analyses (NRHA), only if the effects of higher modes are considered. Recently, similar to what happened for building structures [1; 2; 3; 4; 5], many scientific works have been oriented to propose innovative NSA procedures for bridges. In 2006, [PERSON] et al. [6] discussed, through the application to a case study of a continuous-deck viaduct, the relevance of higher modes, performing a simplified inelastic seismic analysis and indicated that there are major differences between the structural system and the seismic response of buildings and bridges, particularly when the response of a bridge is analyzed in transverse direction. Therefore, the application of NSA should be specialized for bridges, as confirmed by many papers published on this topic. In 2007 and 2009, [PERSON] et al. [7; 8] discussed the nonlinear analysis of continuous multi-span bridges and conducted a parametric study of 14 continuous-span bridges; they concluded that the accuracy of pushover methods is strongly related to the irregularity of the bridge, and, therefore, further investigation is needed to find a method suitable for irregular bridges. In the same year, [PERSON] [9] applied the modal pushover analysis [10] to a girder bridge with a continuous deck, highlighting that the nonlinear and linear range have a similar trend and therefore the modal pushover could be considered efficient under the following conditions: (a) the deck is elastic, and (b) the bridge is not characterized by relevant irregularities. In 2008-2010, [PERSON] et al. [11; 12] applied, to some case studies of existing bridges (girder bridges with continuous deck), a multimodal pushover procedure generally similar to the MPA proposed by [PERSON] et al. [13; 14; 15], and, in 2012, several interesting studies were collected in the volume edited by the [PERSON] et al. [16]; the volume specifically discusses NSA and its application to case studies of bridges, providing some theoretical background on this topic. Similarly, in existing codes or guidelines, the use of NSA for bridges is not deepened as it is for buildings, and it is generally based on two classic pushover procedures: the capacity spectrum method (CSM) [17] and the inelastic demand spectrum method, also known as the N2 method [18]. In the Eurocode 8, a pushover procedure based on the N2 is proposed to assess the seismic behavior of regular buildings, and only few specifications for bridges are reported in parts one and two. In FEMA 356 [19], ATC 40 [20] and Caltrans [21], adopting the CSM, NSA is proposed, but the contribution of higher modes is not considered, and the procedure for bridges is not detailed (e.g., there is no discussion on the monitoring point selection for bridges). All the cited scientific works propose a nonlinear static procedure for bridges that is validated with a direct comparison with the incremental dynamic analysis (IDA) [22; 23] (currently considered the reference method). Those procedures are proposed to be alternative to IDA; since this latter is pushover-based, it does not require the execution of NRHA, which involves several difficulties in the development of the structural numerical model and requires a high computational cost. The computational effort of NHRA (and therefore of IDA) is extremely relevant if an iterative procedure (e.g., for modeling errors, designing a new structure or retrofitting an existing one) is performed or because the set of ground motions (GMs) commonly selected for the nonlinear dynamic analysis have seven or more time histories.