Journal of Applied and Computational Mechanics, Vol. 2, No. 3, (2016), 152-173 Generalized Warping In Flexural-Torsional Buckling Analysis of Composite Beams Amalia Argyridi 1 , Evangelos Sapountzakis 2 1 Doctoral Student, School of Civil Engineering, National Technical University of Athens Zografou Campus, GR–157 80, Athens, Greece, [email protected] 2 Professor, School of Civil Engineering, National Technical University of Athens Zografou Campus, GR–157 80, Athens, Greece, [email protected] Abstract The finite element method is employed for the flexural-torsional linear buckling analysis of beams of arbitrarily shaped composite cross-section taking into account generalized warping (shear lag effects due to both flexure and torsion). The contacting materials, that constitute the composite cross section, may include a finite number of holes. A compressive axial load is applied to the beam. The influence of nonuniform warping is considered by the usage of one independent warping parameter for each warping type, i.e. shear warping in each direction and primary as well as secondary torsional warping, multiplied by the respective warping function. The calculation of the four aforementioned warping functions is implemented by the solution of a corresponding boundary value problem (longitudinal local equilibrium equation). The resulting stress field is corrected through a shear stress correction. The equations are formulated with reference to the independent warping parameters additionally to the displacement and rotation components. Keywords: Nonuniform warping, Shear lag, Shear deformation, Composite beams, Flexural-torsional buckling 1. Introduction One of the most important criteria in the design of structures subjected to compressive loading is the elastic stability of beams. In the case where the cross section’s centroid does not coincide with its shear center (asymmetric beams) the beam buckling analysis becomes much more complicated, leading to the formulation of the flexural-torsional buckling problem. Additionally, composite structural elements consisting of a relatively weak matrix material reinforced by stronger inclusions or of materials in contact, present increasing technological importance. Most representative examples are steel columns or beams totally encased in concrete, concrete plates stiffened by steel beams or fiber-reinforced materials. Usually, in the analysis of beam-like structures, Euler – Bernoulli beam theory assumptions are adopted, while in the case where shear deformations are non-negligible, Timoshenko beam theory is used by relaxing these assumptions. Nevertheless, both theories maintain the assumption that plane cross sections remain plane after deformation. This assumption keeps the formulation simple but fails to capture the well-known shear lag phenomenon [1] observed in many structural members (e.g., beams made of materials weak in shear, folded structural members, beams of box- shaped cross sections). In order to investigate shear lag effects, the inclusion of nonuniform warping [2] in beam element formulations based on the so-called higher-order beam theories is of high interest due to their important advantages over refined approaches such as 3-D solid or shell solutions. These advantages are summarized having in mind that beam models a) Require less modelling time, b) Permit isolation of structural phenomena and results’ Received December 03 2016; revised January 03 2017; accepted for publication January 03 2017. Corresponding author: Amalia Argyridi, [email protected]
Generalized Warping In Flexural-Torsional Buckling Analysis of Composite Beams
May 16, 2023
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