Therefore, in order to discover the stress distribution on the bar, all one has to do is cut the shape of the cross section out of a piece of wood, cover it with a soap film, and apply a differential pressure across it.
Using the membrane analogy, any thin-walled cross section can be "stretched out" into a rectangle without affecting the stress distribution under torsion.
The maximum shear stress, therefore, occurs at the edge of the midpoint of the stretched cross section, and is equal to
It can be shown that the differential equation for 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 cross section of a bar under torsion, has the same form as that governing the stress distribution over the cross section of a bar under torsion.
The curved surface surrounding the "electrodes" represents the complex increase in field strength as the electron-analog approaches the "electrode"; the upward distortion in the sheet is a close analogy to field strength.