“…In the first one, the two horizontal components of the records are applied along two orthogonal principal axes, and According to the second procedure MIDA is performed over a sample of incident angles from 0 to 180 degrees that is DMIDA. In this study, we have rotated the axis of the coordinates of the incidence by 22.5 degrees [35,55], and the angles of 0, 22.5, 45, 67.5, 90, 112.5, 135, 157.5, and 180 are the angles of the earthquake incidence according to figure 4. final step is to adopt the 16%, 50%, and 84% fractile MIDA and DMIDA curves for developing the limit state fragility curves. It should be mentioned that according to API standard, seismic load and other environmental loads such as wave, wind, and current should not apply simultaneously to offshore structures [32].…”