Two necessary and sufficient conditions for shakedown in a structure subjected to given histories of external loads and imposed strains, in the presence of significant inertia and damping effects, are established. Structural discretization and piecewise linearization of constitutive laws are adopted. This permits to consider several hardening materials and geometric effects, in the spirit of second order theory. The statements can be regarded as a generalization to a broader context of the classical Bleich-Melan and Koiter shakedown theorems. With respect to previous work, the main novelty is the simultaneous coverage of dynamic and second order effects.