Page 349 - Introduction to Continuum Mechanics

Torsion and Tension of an incompressible Solid Cylinder 333

Thus, from Eq. (5.38.7),

With 7^.(r 0) = 0, we have

From Eqs. (5.38.4) and (5.38.8), we have

Thus,

Since r = Aj R, therefore,

Thus,

Similarly, the twisting moment can be obtained to be

ar
In Eqs. (5.38.11) and (5.38.12) <{>i and <?2 e functions of/i and /2 and are therefore functions
of/? (see Eq. (5.38.3).