The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.
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On Torsion and Transverse Flexure of Orthotropic Elastic Plates
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, Calif. 92093
Reissner, E. (December 1, 1980). "On Torsion and Transverse Flexure of Orthotropic Elastic Plates." ASME. J. Appl. Mech. December 1980; 47(4): 855–860. https://doi.org/10.1115/1.3153802
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