## 5 Conclusions  
This work has presented a study finalized to develop a pushover-based procedure to perform a comprehensive assessment of the behavior of bridges under near-fault seismic loads. This innovative procedure, named IMPA\(\beta\), is alternative to what is currently considered the most reliable procedure, the incremental dynamic analysis (IDA), and its reliability has been demonstrated through the application to an irregular bridge. This study follows previous experiences of the same authors developing a nonlinear static procedure for buildings and bridges. The primary objective of this paper was to verify the validity of results of the IMPA\(\beta\) (incremental procedure for bridges) subjected to near-fault ground motions. The procedure requires nonlinear static analyses to estimate the seismic demands for bridge structures. In a previous study, IMPA\(\beta\) was developed specifically for bridges and it was tested with far-field events only, proving its effectivity for the same irregular bridge. The procedure, summarized in Figure 19, requires the following main steps:  
1. Definition of the seismic capacity of the bridge performing two different pushover procedures: the modal pushover (MPA) and a pushover with uniform load pattern (UPA);
2. Definition of the seismic demand in terms of response spectrum;
3. Selection of a performance point with both the pushover approaches within a predefined range of intensities (the modal pushover requires to combine results from any pushover performed required (step 2a);
4. Evaluation of the structural response in terms of deck displacement and base shear or in terms of deck displacement (using this parameter as a damage index) and seismic intensity. The deck displacement is described selecting a representative joint (the monitoring point). The influence of different load patterns, including the solution proposed in IMPA\(\beta\), on different seismic demands (deck displacement, capacity curve) was investigated in this paper. The following  
Figure 19: Flowchart of IMPA\(\beta\) procedure for nonlinear static analysis of bridges. conclusions can be drawn from this study that is limited to a single case study and, therefore, will be followed by a more extended validation. The application presented shows that in case of pulse-like near-fault seismic events the use of MPA is equivalent to the use of EMPA (that is a modal pushover performed including the vertical seismic action). According to what was already observed also for far-field events, the response evaluated with MPA, UPA (or even SPA) presents some differences. In particular, considering NF events and comparing pushover and NRHA, the following considerations emerges:  
* MPA overestimates the response at P1 and underestimates the response at P2 and P3 (Figure 5). * UPA underestimates the response at P1 while at P2 and P3, gives results very similar to NRHA. * Performing IMPA\(\beta\), according to the procedure originally defined (enveloping UPA and MPA) the obtained response is very similar to IDA, according to what was already observed considering FF events. Therefore, this new application of the procedure IMPA\(\beta\) shows a satisfactory estimation of the structural response of a bridge under near-field events in terms of deck displacement for intensities up to the achievement of the first collapse (ultimate curvature achieved in a pier plastic hinge). Good results were obtained in terms of definition of the capacity curve both considering the maximum values of the displacement Vs base shear or the monitoring point displacement Vs seismic intensity. Therefore, the proposed procedure, which has been proved accurate for the response to near-fault pulse like seismic events as well, can give a valid contribution in the field of bridge seismic assessment. IMPA\(\beta\) is a valid nonlinear static procedure alternative to nonlinear dynamic-based methods. Conceptualization, A.V.B. ; methodology, A.V.B., C.N., G.F.; Resources, A.V.B, C.N., G.F., D.L. and B.B., software-analysis, A.V.B.