Thin-walled beams subjected to load factors and non-structural masses

The static response of beam structures to inertial loads is investigated in this work. Refined beam models are adopted for the analyses due to the ineffectiveness of classical theories in dealing with three-dimensional (3D) phenomena. The Carrera Unified Formulation (CUF) has therefore been used to develop higher-order beam theories without the need of any ad hoc assumptions on the kinematics of the model. According to CUF, the 3D displacement field is expressed as the expansion, above the beam cross-section, of the generalized displacements, which lie along the beam axis. Different classes of refined one-dimensional (1D) models can be formulated, depending on the cross-sectional functions used for the expansion of the generalized unknowns. The weak form of the principle of virtual displacements is used in this paper and 1D finite element (FE) arrays are written in the form of fundamental nuclei, which do not depend on the class of the beam theory. Both closed and open thin-walled beams are considered in the proposed analysis, and the effects of uniform as well as arbitrarily distributed load factors are investigated. Non-structural masses are also contemplated. The results are compared with those obtained using solid finite elements from a commercial FE code. Attention is focussed on the need to adopt refined models because of the inability of classical beam theories to foresee cross-sectional deformations, shear effects, and bending-torsion couplings caused by non-symmetric inertial fields.