The damages caused to buildings in recent earthquakes show that seismic evaluation is vital and necessary in order to predict the possibility of building damage. Iran is considered a seismically dangerous region due to its location on numerous faults. Many of the multi-story buildings constructed in these areas are reinforced concrete buildings, which are more likely to fail if they have torsional irregularities. In this article, the risk assessment in reinforced concrete buildings with torsional irregularity is discussed using fragility curves. Fragility curves express the probability of structural failure based on a function of an earthquake intensity criterion such as maximum ground acceleration, acceleration response spectrum in the fundamental period of the structure under a 5% damping ratio, or other intensity criteria. To investigate the effect of torsion, reinforced concrete buildings with intermediate moment frame, with variable heights (3, 6 and 9 floors) and for different torsions (5%, 10%, and 20% due to the difference between the center of mass and the center of stiffness) in three dimensions are modeled using SAP2000 version 19 software. Buildings are designed based on equivalent static analysis and incremental dynamic analysis according to ASCE 41-13, and capacity curves are extracted as the output of incremental dynamic analysis. Using the results of the analysis and with the help of statistical analysis, fragility curves have been drawn, which are used to describe the probability of exceedance a certain level of failure. Almost all the failure levels used in previous studies are based on hypothetical values ​​of the failure criterion. It is very difficult to determine these limit values ​​of the failure criterion analytically. These values ​​are obtained based on the results of experience, engineering judgment, and past earthquake experiences. In this study, fragility curves for four levels of failure, including low, moderate, high, and complete failure, are generated based on FEMA 433: Using HAZUS-MH for Risk Assessment (2004), which correspond to maximum relative displacement ratios of 0.5%, 0.9%, 3.2%, and 6%, respectively. For validation, the standard ICONS model was used, which is a 4-story, 3-span structure and was built in full scale by Carvalho et al. in 1999. The results obtained from the ICONS model and the modeling in SAP2000 software showed that there is a good correlation between the real structure data and the simulated model. Therefore, the suitability of the modeling method and its results were confirmed.
The results showed that with the increase of torsion in reinforced concrete buildings, in all failure limit states, the probability of exceeding each limit state increases, so that for buildings with 3, 6 and 9 floors, 5% torsion causes an increase in the probability of exceeding all limit states between 6% and 11% with 20% torsion, this value reaches 17-30%. Also, with the increase in the number of floors (increase in height) in all buildings, the probability of exceeding all failure limit states increases. The cause of this phenomenon in reinforced concrete buildings with a lateral bearing system of the moment frame can be considered to be the activation of the effects of higher modes with the increase in height. In 3- and 6-story buildings, considering the acceleration design (0.3g), the probability of exceeding the limit state of complete failure is less than 10%, which shows good performance of these buildings. In the 9-story building, this value is slightly higher; however, the probability of exceeding for the regular building is still less than 20%. The worst case is a building with a torsion of 20%, which gives a probability of exceeding by approximately 33%, and is still acceptable considering that the structure has not been designed for torsion