So far, we have focused attention on the dynamic behavior of individual slender structural members. There are, of course, many practical situations in which a number of members are connected to form a truss or frame. Often, such systems are analyzed as moment frames designed to resist loads in bending. However, there are occasions in which significant axial loading occurs, and thus we augment the standard methods of structural dynamics to account for this situation. We start with revisiting the partial differential equation description of the dynamics of a slender beam with axial loading. However, we now allow for varying degrees of elastic restraint at the boundaries, because, in a typical framework, the stiffness of a joint depends (in a nonsimple way) on the effects of the members contributing to that joint. In Section 8.2, we developed some general expressions for beams with elastically restrained ends. Initially, we follow the standard approach in which a characteristic equation is developed from the governing partial differential equation. However, this is rarely a practical approach for a frame, and hence the chapter then proceeds to introduce the dynamic stiffness method. This is a systematic, FE technique that provides a powerful, matrix-based approach to solving problems in structural dynamics. We focus on frames consisting of prismatic beam members, and, because of the way in which most frames are designed to resist lateral as well as axial loads, any postbuckling, as such, will be encountered as the growth of large deflections during loading.