Nonlinear dynamic and natural frequencies of a gabled frame with elastic restraints and semi-rigid connections are investigated by using a program in OpenSees software. Natural frequencies are obtained for two states, which are flexible connections and semi-rigid supports, separately. The mode shapes of structure are also obtained for the described states. Also, the effect of connection flexibility on the dynamic responses of the frame is obtained for different values of peak ground acceleration. The members of this structure are modeled as a nonlinear beam-column element. The members of structure are assumed to be prismatic. Two equal lumped masses at the head of two columns in horizontal and vertical directions are considered as the mass pattern of structure. Note that three degrees of freedom are allocated to all nodes. Furthermore, the mode shapes of frame are obtained. Conclusively, the effects of semi-rigid connections and supports on the natural frequencies and mode shapes of structure are investigated. As results, the top level displacement and base shear responses of frame are reported.

A seismic evaluation procedure for a cable-stayed bridge based on the energy balance concept is presented. In this method, the capacity curve obtained from the modal pushover analysis of the cable-stayed bridge is converted to a modal energy capacity diagram. Then, by intersecting this diagram and the energy demand diagram for a selected ground motion, the dynamic target point is obtained. The method was employed on a cable-stayed bridge under Imperial Valley earthquakes with different peak ground motions and the seismic demands were compared with the results from modal pushover and non-linear response history analyses. It was found that this energy balance method can estimate the seismic responses under the selected ground motions with good accuracy. OpenSees software was employed for modelling and analysis of the cable-stayed bridge.

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