Monte Carlo simulation is a useful method for reliability analysis. But in Monte Carlo, a large number of simulations are required to assess small failure probabilities. Many methods, such as Importance sampling, have been proposed to reduce the computational time. In this paper, a new importance sampling Monte Carlo method is proposed that reduces the numbers of calculation of the limit state function. On the other hand, the proposed algorithm does not need the knowledge about the position of the design point or the shape of the limit state function. The key-idea of the proposed algorithm is that the mean of sampling density function is changed throughout the simulation. In fact, in random point generating process each point with lower absolute value of limit state function and nearer distance from space center is considered the mean of the sampling density function. Based on this, the centralization of the sampling will be on the important area.

In previous studies, reinforced concrete (RC) frame–shear wall structures subjected to partial wall removals have been investigated using the nonlinear dynamic alternate path method (APM). However, in the case of an arrested collapse, the APM is not able to obtain the residual capacity. Moreover, less attention has been paid to resisting mechanisms of partially damaged shear walls due to extreme loading on different stories. In the present study a perimeter dual system from a prototype RC frame–shear wall building is investigated using pushdown analysis. The structure is modeled based on a reliable framework established by validating modeling approaches. Load redistribution mechanisms of partially damaged shear walls are indicated and the collapse resistance is quantitatively evaluated following wall (column) removals from different stories. Based on the results, shear walls show considerably high resistance to progressive collapse, which can be implemented in collapse-resistant design. Detailed descriptions of modeling approaches and validations in this study provide guidelines for simulation of different RC structural elements under large deformations.