Vibrations and response to seismic excitations of flexure and shear beams on hinged end supports and a continuous deformable foundation

Sa？etak Simple formulas are derived for the fundamental periods of the free lateral vibrations and the response to sine loads of flexure beams and shear beams on laterally fix hinged end supports and a continuous elastic foundation. It is shown how the mechanical charasteristics and the response quantities of systems with flexure-shear beams can be approximated by those of a flexure or a shear beam by appropriately defining their equivalent cross-sectional stiffnesses. Applications of the developed theories in the design and analysis of some engineering structures are also dealt with and two numerical examples elucidate the procedures