Vertical irregularity is one of the major causes of the failure of the structure. Buildings with vertical irregularities are widespread and unavoidable during rapid urbanization in almost all countries. The safety of such buildings is most important against vulnerability in an earthquake. The vulnerability of structures is assessed using the damage indices of fragility curves. These fragility curves were developed using the HAZUS method, which is used to find the probability of structural damage due to various seismic excitations. This fragility curve determines the probability of none, slight, moderate, extensive, and complete damage to the structures. These fragility curves help to identify the vulnerability percentage of vertical irregularities compared to the regular building. Research also reveals that the vulnerability of the irregular building is similar to the vulnerability identified in terms of roof displacement, base shear, and drift ratio using the THA method. This research also helps to determine the possibility of damage being observed for the structures carrying stiffness and mass irregularities. It is found that stiffness irregularity is more vulnerable than mass irregularity. An increment in collapse probability is observed in stiffness and mass irregularity on the ground floor. Considerable slight to moderate damage possibility is observed in mass irregularity models, and collapse possibility is observed high in stiffness irregularity models. Also, it is observed that the SSI affects adversely on the structures.

Engineers are tasked with the challenging task of evaluating the performance and analyzing the risk of systems in the context of performance-based seismic design. All sources of random uncertainty must be taken into account during the design phase in order to complete this assignment. The performance limit states for a structure must be defined using appropriate procedures that take into consideration the system characteristics describing the structure, the soil, and the loads applied to the structural reactions. The main objective of this study is to conduct an in-depth analysis, both linear and non-linear (Pushover), of seismic vulnerability for a reinforced concrete (RC) structure. This aims to probabilistically evaluate the effectiveness of composite materials, particularly those reinforced with glass and carbon fibers, in reducing seismic risk when used to reinforce structural columns. The outcomes of this study will provide valuable insights into the efficacy of FRP reinforcements in enhancing seismic resistance, regardless of the analytical approach adopted (linear or non-linear). They reveal a seismic risk reduction of 48 % for structures equipped with glass fiber-reinforced columns and 67 % for those with carbon fiber-reinforced columns.

This study analyzes the progression, utilization, and inherent challenges of traditional non-linear static procedures (NSPs) such as the capacity spectrum method, the displacement coefficient method, and the N2 method for evaluating seismic performance in structures. These methods, along with advanced versions such as multi-mode, modal, adaptive, and energy-based pushover analysis, help determine seismic demands, enriching our grasp on structural behaviors and guiding design choices. While these methods have improved accuracy by considering major vibration modes, they often fall short in addressing intricate aspects such as bidirectional responses, torsional effects, soil-structure interplay, and variations in displacement coefficients. Nevertheless, NSPs offer a more comprehensive and detailed analysis compared to rapid visual screening methods, providing a deeper understanding of potential vulnerabilities and more accurate predictions of structural performance. Their efficiency and reduced computational demands, compared to the comprehensive nonlinear response history analysis (NLRHA), make NSPs a favored tool for engineers aiming for swift seismic performance checks. Their accuracy and application become crucial when gauging seismic risks and potential damage across multiple structures. This paper underscores the ongoing refinements to these methods, reflecting the sustained attention they receive from both industry professionals and researchers.