Today, the applied of analytical methods to determine the vulnerability and to decide on the applied of different design methods has been noticed by researchers and fragility curves is a appropriate method for determining the probability of increasing the amount of damage from the specified value at different levels of injury.The production of failure curves requires the determination of the damage index as a criterion for evaluating the performance of the structures. In research, Park Ang damage index has been applied for its desirable performance. The aim of this research is to prove the claims of modern design methods to enable the design basing on control the seismic damage and the optimal performance of these methods in comparison with force based design (FBD) approach. This study carry out the possibility of damage to RC frames designed with direct displacement based design (DDBD) and FBD approach. For this purpose, RC flexural frames of 5 and 11 floors are designed with DDBD and FBD approach. Then, their likelihood of failure is compared with the applied of the analysis of additive time history in five failure modes.For the purpose of producing failure curves, different statistical distribution functions for two sets of data have been tested. The functional results confirm that the normal and log-normal of distribution. Investigating the brittleness curves indicates the possibility of lower damage in frames designed with DDBD approach. There is also a difference in the likelihood of damage to a taller height frames for the two design methods mentioned.