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
$κ=−21+νAIy2 C4+ν1−IxIy$
(1)
where
$C4=−∫∫{νx2−y2f1+2ν x y f2+21+νf12+f22}dxd y$
(2a)

$f1=−121+ν ∂χ∂x+ν x22+2−ν2y2$
(2b)

$f2=−121+ν ∂χ∂y+2+νxy.$
(2c)

In the above, the notation is largely...

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