27 Journal of Structural Engineering and Geotechnics, 10(2), 27-34, Summer & Autumn 2020 QIAU Structural Drift Corresponding to the Critical Excitations M. H. Soltani a , Seyed Hooman Ghasemi b,* a Department of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran b Department of Civil Engineering, Auburn University, USA Received 07 March 2019, Accepted 19 May 2020 Abstract Although the probability of the occurrence of a critical earthquake is low, the consequences of the critical excitation events are beyond the disaster. Therefore, there is a need to consider the critical excitation analysis for important structures such as power plants, infrastructure, and buildings. Indeed, one of the important criteria in the seismic design of the structures using the critical excitation is to control the maximum structural displacement. However, the required characteristics of the analysis and design of the structures are generally random variables and have many uncertainties. Therefore, the probability-based analysis should be accomplished to determine the most probable structural responses. The main objective of this research is to investigate the reliability level of steel frame buildings subjected to critical excitations. In due course, the wide range of the SDOF structures investigated subjected to real ground motions of the critical excitations. Eventually, the reliability index of structural displacement for extreme events limit state function concerning the critical excitations were computed. Keywords:Reliability Index; Critical Excitation; Random Variables and Uncertainty; Power Spectral Density; Serviceability Displacement. 1. Introduction One of the most fundamental goals of structural engineering design code is to provide specific provisions to preserve a rational safety level for design criteria. However, due to the existing uncertainties in loads and structural resistance properties, the probabilistic-based methods are required to perform. However, several structural design provisions are still based on deterministic considerations. In fact, the probabilistic-based methods ensure that the structure's reliability level using the structural statistical parameters (Nowak and Collins (2013). Due to the random nature of loading, material specifications, and implementation issues, it is necessary to utilize the probabilistic-based analyses. Thus, considering the statistical parameters associated with the distribution of random variables should be determined. Considering uncertainty leads to a new way in structural analysis and design which is called reliability-based analysis. The development of reliability theory in the present age has a history of almost 90 years. In the first period, from 1920 to 1960, the gradual beginning of the theory of structural trust has been begun. Then, Cornell (1967) and Hosofer Lind (1974) provided a reliability index definition. Their suggestion is the first criterion for the size of acceptable safety factors among structural engineers. To solve the problem of the invariance of the shape of the limit state function, Hasofer and Lind (1974) transformed the problem space into a normalized space by normalizing random variables. Subsequently, Rackwitz and Fiessler (1978) conducted a study that led to the development of a gradient-based approach. In this method, which is called the HL-RF method, the problem is implicitly approached with a very good approximation. All of these methods, which require a mathematical form of a limit state function, are known as analytic methods, and this requires the mathematical closed- form of the limit state function. To solve the non- closed-form problem, the Monte Carlo assessment method has been proposed and utilized by many types of research including Nowak and Collins *Corresponding Author: Email Address: szg0046@tigermail.auburn.edu