Inelastic buckling is the most important failure mode of a steel beam column element subjected to compression force. In order to correctly predict this phenomenon, large rotations, large displacements and the plasticity of the section along the element must be considered. Several formulations have been proposed to model problems with three dimensional large displacements and rigid body dynamics. They are usually based in the Lagrangian or the Corotational methods and are primarily oriented to solve mechanical and aerospace problems, although some applications to structural stability do exist. Independently, several formulations have been developed to model plasticity: fiber elements, plastic flow theory and lumped plasticity are popular choices. In this dissertation a novel formulation capable of solving problems with displacement and material nonlinearities in a unified way is developed. Thus, the State Space approach is selected because all the basic equations of structures: equilibrium, compatibility and plasticity are solved simultaneously and thus the global and local states are mutually and explicitly dependent. To incorporate geometric nonlinearities, the Corotational approach, where rigid body motion and deformations are described separately, is adopted. To incorporate material nonlinearities, the formulation developed by Simeonov (1999) and Sivaselvan (2003) is included. In general, the set of equilibrium, compatibility and plasticity equations constitute a system of Differential Algebraic Equations (DAE). A procedure to solve such system exists and is implemented in the package IDA (Implicit Differential Algebraic solver) developed at the Lawrence Livermore National Laboratory (LLNL), which is used to solve the problem numerically. An experimental study on "zipper frames" was conducted to assess the accuracy of the proposed formulation. A "zipper frame" is a chevron braced frame where the beam to brace connections are linked through columns, called "zipper columns". The failure mode of a "zipper frame" is the successive inelastic buckling of its braces. Three shake table tests of a three stories "zipper frame" were performed at the UB-NEES laboratory. A model of the first story of the "zipper frame" was analyzed with the new formulation and its results compared to experimental data. It is found that the new formulation can reproduce the features of the test and it is very sensitive to all the model parameters. Results are presented