According to the basic idea of classical yin-yang complementarity and modern dualcomplementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type incremental variational principles for broken line elastoplastic dynamics of frame structure can be established systematically. The unconventional Hamilton-type incremental variational principle can fully characterize the initial-boundary-value problem of broken line elasto-plastic dynamics of frame structure. In this paper, an important integral relation was given, which can be considered as the expression of the generalized principle of virtual work for broken line elasto-plastic dynamics of frame structure. Based on this relation, it is possible to derive systematically the complementary functionals for five-field, and the functional for one-field unconventional Hamilton-type incremental variational principles and the unconventional Hamilton-type incremental variational principle in phase space by the generalized Legendre transformations were also given. Furthermore, with this new approach, the intrinsic relationship among various principles can be explained clearly.