# Investigating the Reliability of Nonlinear Static Procedures
## 6 Conclusions  
This paper investigated the effectiveness of nonlinear static procedures in evaluating the seismic performance of URM buildings through a comprehensive comparison with the outcomes derived from nonlinear dynamic analyses. The latter are assumed as the reference solution and as the target for the validation of the reliability of the static approach. This paper contributes to enriching the work already conducted in the literature validating the use of assessment methods based on nonlinear static analyses for URM buildings, which, despite their widespread use in engineering practice and at the research level, is still limited. Various structural configurations of a URM building inspired by a real structure were analyzed to this aim. This paper primarily focused on the so-called global response of URM buildings, specifically examining the in-plane response of URM walls. Various nonlinear static procedures were examined in this paper, which included both proposals from the literature and recommendations already included in current or updated versions of the European Standards. The sensitivity of the safety outcomes to various alternative options in quantifying the displacement demand (i.e., methods alternatively based on the use of inelastic or overdamped spectra) as well as for the conversion of the original pushover curve into an equivalent bilinear--when requested by the method, as in the N2-oriented ones--was examined. The reliability of the NSPs against the reference solution provided by NLDAs was checked by incorporating the fragility curve concept. The results achieved are very useful in identifying the advantages and disadvantages of the present and next generation of Standards and possibly outlining future developments. Firstly, the results confirm what has already been proven by other literature works [1; 32], i.e., that NSPs based on the use of inelastic spectra, which are the current procedures adopted in the Italian and European codes and of more common use in engineering practice, produce results that are often not conservative in the case of stiff URM structures. Alternative proposals of the N2 method specifically developed in the literature for URM structures led to appreciable improvements, but they are not always sufficient to produce safe outcomes, and, in addition, they require the appropriate calibration of some coefficients (such as [PERSON]'s method, which implies the choice of factors that regulate the dissipation properties of the system). Moreover, approaches based on the use of inelastic spectra strictly require the conversion of the pushover curve into an equivalent bilinear and are strongly sensitive to the consequent definition of the equivalent period of SDOF (T*). Among the three criteria investigated in this paper to address such conversion, the more promising one is the one that assimilates the strength degradation through a reduction in the equivalent stiffness, keeping the maximum base shear strength constant (i.e., [PERSON]'s proposal in [32]). However, relying only on the bilinear conversion rule is not sufficient to establish robust consistency between static and dynamic approaches, as aforementioned. Furthermore, if T* exceeds \(T_{\text{C}}\) (i.e., the corner period of the response spectrum), the demand for inelastic displacement is equivalent to that for elastic displacement; while there is no doubt regarding the validity of the equal displacement rule, a limitation of these methods is the strong influence on the definition of \(T_{\text{C}}\) and its relationship with T*. The only method that results in estimates close to the ones of NLDA is the capacity spectrum method. Even if, in some cases, the results provided by the CSM are too conservative, another strong advantage of such a method is that it is insensitive to the bilinear conversion rule. The CSM method is already explicitly recommended in the Italian Structural Code (NTC2018) as Method b, but it is still very rarely used by engineers in real applications.