We present a simplified method to calculate the plastic ratchet of elbow-shaped pipes submitted to seismic loading and an internal pressure. This method is simplified in the sense that the value of the ratchet is obtained without the use of finite element method (FEM) calculations. Here we derive a formula and use it to evaluate the fatigue-ratcheting damage of an elbow. This approach is applicable to complex plastic response appropriately described by non-linear kinematics hardening, which is more realistic for stainless steel such as 316-L.