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+νAIy2C4+ν1IxIy
(1)
where  
C4={νx2y2f1+2νxyf2+21+νf12+f22}dxdy
(2a)
 
f1=121+νχx+νx22+2ν2y2
(2b)
 
f2=121+νχy+2+νxy.
(2c)

In the above, the notation is largely...

1.
Hutchinson
,
J. R.
,
2001
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Shear Coefficients for Timoshenko Beam Theory
,”
ASME J. Appl. Mech.
,
68
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87
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2.
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
3.
Stephen
,
N. G.
,
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Timoshenko’s Shear Coefficient from a Beam Subjected to Gravity Loading
,”
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Stephen
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, and
Levinson
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,
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A Second Order Beam Theory
,”
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5.
Cowper
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,
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The Shear Coefficient in Timoshenko Beam Theory
,”
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6.
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
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