Coupled Transverse and Axial Vibrations Including Warping Effect in Asymmetric Short Beams

To model the displacement field of asymmetric one-dimensional structural elements, in which a transverse-bending motion couples with axial motion, a formulation with five displacement components is developed. The proposed formulation extends Timoshenko beam theory to asymmetric cases and adds two displacement components to estimate in-plane warping. Via Hamilton's principle, the coupled partial differential equations that govern the components of the displacement field together with the corresponding boundary conditions are derived. To validate the formulation, the lower natural frequencies of several case studies, including a monolith of Koyna Dam in India, are computed and compared with those given by two-dimensional finite-element models. To analyze the examples through the proposed formulation, standard finite-element analysis of one-dimensional elements with five displacement components is applied. In all cases, results from the proposed plane stress formulation proved to be in very good agreement with those provided by two-dimensional models. (c) 2018 American Society of Civil Engineers.