In this paper, by using the Armstrong- Frederick nonlinear kinematic hardening model, the ratchetting behavior of carbon steel piping elbows is described under conditions of steady internal pressure and dynamic moments out-of-plane at frequencies typical of seismic excitations. The elbows had an outside diameter of 60.3 mm and thicknesses of 3.91 and 5.54 mm. For each thickness two bend radius geometries (long and short) were studied. A pure out-of-plane bending moment applied at one end of a 90 welding elbow is reacted by a purely torsional moment at the other end. Three-dimensional elastic-plastic analyses by Armstrong-Frederick nonlinear kinematic hardening model are carried out to evaluate structural ratcheting behaviors. Initial, the rate of ratchetting is large and then it decreases with the increasing cycles. While there is practically no strain accumulation in the axial direction, the direction of highest ratcheting is along the hoop direction. The cyclic strain accumulation against response moment for each component is assessed. By Armstrong-Frederick model, the predicted ratchetting of low moments near is to the experimental results, while for the high moment, this model will over-predict the ratcheting strain.