Page 276 - Introduction to Continuum Mechanics
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260 Torsion of a Circular Cylinder
Thus,
Interpreted physically, we satisfy equilibrium if the increment in angular rotation (Le» twist per
unit length) is a constant. Now that the displacement field has been shown to generate a
possible stress field, we must determine the surface tractions that correspond to the stress field.
On the lateral surface (see Fig. 5.9) we have a unit normal vector n = (l/a)(x2*2 + X 3*$)-
Therefore, the surface traction on the lateral surface
Substituting from Eqs. (5.13.3) and (5.13.5), we have
Thus, in agreement with the fact that the bar is twisted by end moments only, the lateral surface
is traction free.
Fig. 5.9
On the face jtj = /, we have a unit normal n = ej and a surface traction
This distribution of surface traction on the end face gives rise to the following resultant
(Fig. 5.10)
