Page 277 - Introduction to Continuum Mechanics

The Elastic Solid 261

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where/^ = ft a /2 is the polar moment of inertia of the cross-sectional area. We also note that
\xj dA = IX'dA = 0 because the area is symmetrical with respect to the axes.

Fig. 5.10

The resultant force system on the face jq = 0 will similarly give rise to a counter-balancing
couple -pO ' l p. Therefore, the resultant force system on either end face is a twisting couple
MI = M( and it induces a twist per unit length given by

This indicates that we can, as indicated in Section 5.1, determine the shear modulus from a
simple torsion experiment.