Ratcheting is a progressive incremental inelastic deformation or strain which can occur in a component that is subjected to variations of mechanical stress, thermal stress, or both. This study concentrated on the ratcheting occurrence of the piping model under the combined effect of constant external force and dynamic cyclic vibrations. Bent solid bars represented piping models, and sinusoidal acceleration waves were loaded. Characteristics of seismic loads between load-controlled and displacement-controlled properties were studied from the viewpoint of the frequency ratio of the forcing frequency to the natural frequency of the piping model. Besides, the ratcheting occurrence conditions of the beam and the piping model were compared in one normalized diagram to display the general mechanism of ratcheting with the consideration of the effect from the difference of shape and material. Results show that ratcheting occurs easily with a lower frequency ratio in both beam and piping models. In addition, it is meaningful to use beam models to understand the ratcheting mechanism of piping models. Describing the occurrence of ratcheting using the normalized ratcheting diagram for different components is feasible.