The present study investigated the effects of vertical components of earthquakes on the responses of 5, 15, and 25 story steel frames by taking into account Soil-Structure Interaction (SSI). The frames were modeled on a fixed base and simulated using two shear waves velocities for the soil (100 and 250 m/s according to NEHERP soil code types E and D soils) using a cone model. The nonlinear behavior of the frames was investigated in the presence and absence of the vertical component of an earthquake and the effects of SSI were examined by comparing the results of the latter analysis with and without use of the cone model. The results showed that the vertical component and SSI can increase the axial force on columns by nearly 50%, the vertical displacement of the mid-point of the beams by nearly two-fold, drift of the stories by nearly 40%, and foundation rotation. Story shear was less affected. When soil type E and soil type D were compared, it was found that the effect of the vertical component of earthquakes on the dynamic response of the frames was generally significant.

Suspension bridges due to their long span can experience large displacement response under dynamic loading like earthquakes. Unlike other structures, their vertical vibration may make remarkable difficulty that a control strategy seems to be essential. Tuned mass damper is a passive control system that can be changed to active one by adding an external source producing the active control force called active tuned mass damper. Unlike passive systems, active ones need a controller system affecting the performance of them considerably. In this study, the efficiency of tuned mass damper and active tuned mass damper are investigated in the bridges. Two controllers, fuzzy type 2 and fuzzy type 1, are used to estimate control force of active tuned mass damper. Tuned mass damper’s parameters are optimized under wide range of ground motions. Also, fuzzy type 2 and fuzzy type 1’s parameters are optimized under the influence of three different conditions containing far-field and near-field ground motions and also combination of them. In addition, Lion Pride Optimization Algorithm is selected for optimizing section. Numerical analysis indicates that active tuned mass damper is more effective than tuned mass damper, and also active tuned mass damper does not make any instability matter of concern in active control systems. Furthermore, performance of fuzzy type 2 is better than fuzzy type 1.

Suspension bridges are structures that because of their long span and high flexibility can be prone to ambient vibrations such as ground motions. They can experience high amplitude vibrations in torsional mode during an earthquake, where a vibration control strategy seems necessary. Recently, control systems have been widely used to mitigate vibration of structures. Tuned mass damper is a passive control system. Its performance and effectiveness have been verified both theoretically and practically. In this study, a tuned mass damper system is used to mitigate the torsional vibration of a suspension bridge. The Vincent Thomas suspension bridge is selected as a case study, and its response is reduced by a tuned mass damper under ten pulse-type records from 10 major worldwide earthquakes. By using sensitivity analysis, a parametric study is carried out to optimize tuned mass damper parameters, namely, mass ratio, gyration radius, tuning frequency, and damping ratio according to the maximum reduction of the response maxima. Finally, the optimum range of each parameter that can give the best performance and provide both operational and economic justification for the implementation of the project is suggested. The numerical results indicate that the optimized tuned mass damper system can substantially reduce the maximum response and vibration time.