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Higher Order Beam Theory in Linear Analysis of Beams - Axial Modes of Arbitrary Cross Sections
Abstract and Figures
Both Euler-Bernoulli and Timoshenko beam theories maintain the assumptions that neither out-of-plane (warping) nor in-plane (distortion) deformation contribute to beams response. To account for shear lag effects, the inclusion of non-uniform warping is necessary, relaxing the assumption of plane cross section. The shear flow associated with non-uniform warping leads also to in-plane deformation of the cross-section, relaxing the no-distortion assumption. For this purpose, the so-called higher order beam theories have been developed taking into account shear lag and distortional effects. In this paper, the higher order beam theory developed in a previous work of the authors is employed for linear analysis of beams of arbitrarily shaped, homogeneous cross-section, including warping and distortional phenomena due to axial, shear, flexural, and torsional behavior. The beam is subjected to general load and boundary conditions. The analysis consists of two stages. The first stage is a cross-sectional analysis, establishing the possible distortional and warping deformation patterns (axial, flexural and torsional modes by means of the sequential equilibrium scheme and the Boundary Element Method). The second stage is a longitudinal analysis where the four rigid body displacements along with the extracted deformation patterns multiplied by respective independent parameters expressing their contribution to the beam deformation are included in the beam analysis (Finite Element Method). Axial warping and distortional modes are examined. In addition, numerical examples with practical interest are presented in order to highlight the importance of axial modes in linear analysis of beams-cross-sections of class 4 (EN1993-1-1), i.e., vulnerable to axial load are analyzed.
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