Example Torsion of a Circular Cylinder

6 Let us consider the elastic deformation of a cylindrical bar with circular cross section of radius a and length L twisted by equal and opposite end moments Mi, Fig. 10.1.

7 From symmetry, it is reasonable to assume that the motion of each cross-sectional plane is a rigid body rotation about the x1 axis. Hence, for a small rotation angle 0, the displacement field will be given by:

u = (0ei) xr = (0ei) X (xiei + X2e2 + x3) = - x3e2)

8 The corresponding strains are given by

1 de

2 3 dxi

0 0

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