A closed-end steel cylinder (E = 200 GPa and v = 0.29) has an inside radius a = 2.00 m, wa...

A closed-end steel cylinder (E = 200 GPa and v = 0.29) has an inside radius a = 2.00 m, wall thickness h = 10 mm, and hemispherical ends. Since the state of stress is different for the cylinder and the hemisphere, their radial displacements will be different. Show that the length L/2 (see Eq. 10.48) is small compared to a so that the short length of the hemisphere can be considered another cylinder. Determine the shear force w in terms of internal pressure p1 at the junction of the cylinder and hemisphere (assumed to be another cylinder). Note that the bending moment at the junction is zero because of symmetry. Determine the maximum bending stress σzz(bending) in the cylinder, axial stress σzz, and circumferential stress σθθ at the outside of the cylinder at the location where the maximum bending stress occurs and the ratio of the maximum shear stress at that location to the maximum shear stress in the cylinder at a distance far from the junction.

 (10.48)