The importance of the severe accident mitigation under beyond design-basis events (BDBEs) was realized to achieve the nuclear safety through the Fukushima accident. Failure mode estimation of essential components in nuclear facilities is necessary to take appropriate measures against the severe accident conditions. The failure mode of piping systems exposed to excessive seismic loading was found to be ratchet deformation followed by fatigue failure through many experimental tests in the past, whereas the failure of Test #37 of Pipe-fitting dynamic reliability program (PFDRP) conducted by EPRI was unexpected and its failure mechanism remains unclear, as it was often suspected to have been failed in plastic collapse. In the past research, the constant stress on the structure such as a dead-weight was revealed to significantly affect the failure mode and failure level of structures under seismic excitation. In this study, the constant stress components which can increase due to the ratchet deformation during a seismic excitation is focused and is analytically examined to clarify the effects on the failure mode of structures by using a cantilever structure with various dead-weight conditions and a constant cycles of sinusoidal waves which essentially represents the seismic loading with specific frequency ratios to establish the failure estimation of a structure exposed to seismic loading.