Vibration and buckling of deep beam-columns on two-parameter elastic foundations

Natural frequencies and buckling stresses of a deep beam-column on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, depth change (the transverse displacement w can vary in the depth direction of beam-columns) and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a one-dimensional higher order theory for thin rectangular beam-columns subjected to axial stress is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported deep elastic beam-column. In order to assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. It is noted that the present approximate theories can predict the natural frequencies and buckling stress of deep beam-columns on,elastic foundations accurately compared with the Timoshenko beam theory and the classical beam theory. (C) 1999 Academic Press.