고체역학 (Gere) — Applications of Plane Stress: Problem 8.3-6

8.3-6 A thin-walled cylindrical pressure vessel of a radius \( r \) is subjected simultaneously to internal gas pressure \( p \) and a compressive force \( F \) acting at the ends (see figure). (a) What should be the magnitude of the force \( F \) in order to produce pure shear in the wall of the cylinder? (b) If force \( F = 190 \text{ kN} \), internal pressure \( p = 12 \text{ MPa} \), inner diameter \( 200 \text{ mm} \), and allowable normal and shear stresses are \( 110 \text{ MPa} \) and \( 60 \text{ MPa} \), respectively, what is the required thickness of the vessel?