Shear coefficients for Timoshenko beam theory

By J. R. Hutchinson. 2001

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Much ado about shear correction factors in Timoshenko beam theory (2010, background): “…extensive extant literature on finite element analyses of Saint-Venant’s flexure, viz., Mason and Herrmann (1968), Tolf (1985), Wörndle (1982), Giavotto et al. (1983), Kosmatka and Dong (1991), Schramm et al. (1994), Popescu and 1 The analogue elastostatics approach is due to Reissner (1945, 1947).”
Analysis of reinforced and thin-walled structures by multi-line refined 1D/beam models (2013, background): “Early investigators have focused on the use of appropriate shear corrections factors to increase the accuracy of classical 1D formulations, such as Timoshenko and Goodier [5], Sokolniko [6], Stephen [7], and Hutchinson [8].”
A Review of Refined Shear Deformation Theories for Isotropic and Anisotropic Laminated Beams (2001, background): “Cowper [15,16] and Murty [17,18] have given new expressions for this coefficient for different cross sections of the beam.”
Nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads (2011, background): “This approach leads to more realistic values for these coefficients, since the Timoshenko’s [29] and Cowper’s [30] definitions often lead to unsatisfactory results [31,32], while definitions given by other researchers [33,34] lead to negative values for these factors.”