<p>Piecewise linear elasticity represents the multiple states of a structure, where each state can be handled as a linear state as long as the switching does not occur. As long as each linear state is linear, the modal analysis can be used for the dynamic analysis, with the implementation of the switching between the states. Truncated modal analysis and the inelastic or plastic switching cause energy loss during the switching in discrete PL-elastic systems. This work introduces formulae for the quantitative analysis of this energy loss, allowing its substitution by a viscous damping ratio. It is shown that the energy dissipation during the switching can reach a significant ratio under specific conditions. The type of impact and the degree of modal truncation affect the magnitude of energy loss. Through simple examples, the evaluation of the possible outcomes is presented.</p>