고체역학 (Gere) — Applications of Plane Stress: Problem 8.2-8

8.2-8 A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer that cracks when the strain reaches \(150 \times 10^{-6}\) (see figure). (a) What internal pressure \(p\) will cause the lacquer to develop cracks? (Assume \(E = 205 \text{ GPa}\) and \(\nu = 0.30\).) (b) If the strain is measured at \(125 \times 10^{-6}\), what is the internal pressure at that point?