Vibration of Extended Frame Structures

This chapter presents the determination of the reactions of the frame, taking into account the initial phase of passage of the seismic wave. This chapter discusses the vibrations of a multistory, multi-span frame structure of considerable extent in the plan. The dynamic design model is accepted as a system with finite number of degrees of freedom. The equations of seismic oscillations of an elastic frame system taking into account extent can be obtained on the basis of the equations of the displacement method with the static horizontal shifting of supports and taking into account the inertial forces in accordance with the Dalember’s principle. In the equations of motions, it is assumed that the energy absorption of the first floor at asynchronous oscillations supports/columns is the same as with the synchronous oscillations. Equation of motion, Laplace-Carson transformation, and Equation of motion of a single-span frame, taking into account its length with arbitrary movement of the base, are discussed.