The project will develop and implement a computational nonlinear mode superposition algorithm in a parallel computing environment, based on Duffing's principle of instantaneous mode superposition. This algorithm will be applied to cable-stayed bridges, which exhibits geometric nonlinearities due to cable sag, axial- flexural interaction, and inherently large displacements. These nonlinearities are most pronounced in the partially-constructed stage. The resulting applications will be used to understand the complex interactions of earthquakes, extreme winds and traffic forces and their induced structural dynamic response. The research will provide the practicing and research engineers with a tool that will help in better understanding nonlinear dynamic response behavior of large structures such as cable-stayed bridges.