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# Membrane analogy

It can be shown that the differential of the equation of the deflection surface of a homogeneous membrane, subjected to uniform lateral pressure and with uniform surface tension and with the same outline as that of the X-section of a bar under torsion, has the same form as that governing the stress distribution over the X-section of a bar under torsion.

$\frac{p}{S} = 2G\frac{d\phi}{dz} = 2G\theta$