Key methods include response spectrum analysis to evaluate dynamic responses under seismic loading and push-over analysis to study the structure’s behavior under increasing lateral forces. The video also demonstrates nonlinear time history analysis using real ground motion data to simulate bridge responses during actual earthquakes. A comparison of linear and nonlinear results highlights the benefits of nonlinear modeling, including improved safety and reduced shear forces. Additionally, the effects of multi-support excitation on long-span bridges are analyzed, emphasizing the importance of design review for optimal safety and performance.