Most civil structures will be subjected to some form of lateral loading during their lifetime. Loads produced by earthquakes, wind or explosions mainly induce lateral displacements on structures. The effect of gravitational loads acting through the lateral displacement of the structure was called the P-∆ effect. This effect can initiate a pernicious cycle against structural systems because the influence of gravitational loads increases as the lateral displacement increases and, at the same time, the lateral displacement is amplified as a consequence of the gravitational loads acting on them. From this brief description the non-linear nature of the problem is clear. Furthermore, the possible incursion of structures into the realm of inelastic deformation further increases the complexity of this already difficult problem.1.1. Historical PerspectiveFor ​​many years, the P-∆ effect has been a subject of study and concern by structural engineers. In 1934 Ruge [1] carried out what was probably the first examination of the effects of gravity on the response of simple elastic structures. He was able to estimate the change in period and deflection of a vertical cantilever beam supporting a weight. In 1968, Jennings and Husid [2], also working with single degree of freedom (SDOF) systems, were the first to report on the effects of gravity on the inelastic structural response. They conclude that gravity increases the amount of plastic drift significantly compared to that found when gravity is neglected, leading in many cases to system collapse. They also determined the critical value of the post-yield slope of the backbone force-strain curve of the SDOF system above which collapse will not occur. Response studies… half of the sheet… stability coefficient ( θ), does not accurately represent inelastic P-∆ effects [9]. Increasing evidence shows that the use of elastic stiffness in determining the theoretical P-∆ response of highly inelastic systems is not conservative [9]. Several researchers [6, 10, 11, 12] believe that the stability coefficient calculated based on the initial elastic stiffness has the purpose of verifying the static stability of only elastic or slightly inelastic structures. Any θ-based procedure would not be able to capture the inelastic response because the actual post-yield stiffness is underestimated [10]. For the usual case of designing structures that are expected to respond beyond their elastic limit, Bernal [11] and Adam et al. [10]suggested the use of two stability coefficients: an initial or elastic stability coefficient (θe ) and an inelastic stability coefficient (θi ).