Discussion: “Shear Coefficients for Timoshenko Beam Theory” (Hutchinson, J. R., 2001, ASME J. Appl. Mech., 68, pp. 87–92)

Abstract

In a recent article, Hutchinson 1 employed the Hellinger-Reissner variational principle to construct a beam theory of Timoshenko type, together with a new expression for the inherent shear coefficient κ, as Display Formulaκ=−2(1+ν)AIy2 C4+ν1−IxIywhere Display FormulaC4=−{ν(x2−y2)f1+2ν x y f2+2(1+ν)(f12+f22)}dxd yDisplay Formulaf1=−12(1+ν) ∂χ∂x+ν x22+2−ν2y2Display Formulaf2=−12(1+ν) ∂χ∂y+(2+ν)xy.