申論題

3. Consider a cylindrical pressure vessel subjected to internal pressure p and an external axial force F. The vessel has an inner radius r and thickness t (r ＞＞ t). The magnitude of the external axial force F is 3πr²p. Three electrical resistance strain gages are placed on the outer surface of the vessel in the manner shown in Figures 3.1 and 3.2 to measure strains. Gages A, B and C measure the extensional strains ε_a, ε_b and εc in the directions of lines Oa, Ob and Oc, respectively. (25%)

1) Find the absolute maximum shear stress at the location of the strain gages in terms of p, r and t.