Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation

A new horizontally curved three-noded isoparametric beam element with or without an elastic base throughout its length, is formulated, in which the same set of parabolic shape functions in natural coordinates is used to interpolate beam geometry as well as displacements at any point of the beam. The formulation includes shear deformation effects and is also capable of accounting for torsional loading. The elastic base is assumed to offer distributed vertical reaction and torque at any point of the beam proportional to the vertical deflection and angle of twist respectively at that point. Development of the stiffness matrix is presented. A two point Gaussian quadrature rule has been followed for the necessary numerical integration. Numerical results for a few sample problems have been presented and comparison with the analytical solutions indicates the suitability of the element.