For the hollow cylinder of Example 11.2, determine the principal stresses and the maximum...

For the hollow cylinder of Example 11.2, determine the principal stresses and the maximum shear stress at the outer surface and the increase of the outer diameter.

Example 11.2: Stresses and Deformations in a Hollow Cylinder

A thick-wall closed-end cylinder is made of an aluminum alloy (E = 72 GPa and V = 0.33), has an inside diameter of 200 mm, and has an outside diameter of 800 mm. The cylinder is subjected to an internal pressure of 150 MPa. Determine the principal stresses, maximum shear stress at the inner radius (r =a =100 mm), and the increase in the inside diameter caused by the internal pressure.

Solution:

The principal stresses are given by Eqs. 11.20-11.22. For the conditions that p2 = 0 and r = a, these equations give

The maximum shear stress, given by Eq. 2.39, is

The increase in the inside diameter caused by the internal pressure is equal to twice the radial displacement given by Eq. 11.24 for the conditions p2 = P = 0 and r =a. Thus,

The increase in the inside diameter caused by the internal pressure is 0.6006 mm.

 (11.20)

 (11.21)

 (11.22)

 (2.39)

 (11.24)