고체역학 (Gere) — Applications of Plane Stress: Problem 8.2-11

8.2-11 A spherical stainless-steel tank having a diameter of 500 mm is used to store propane gas at a pressure of 30 MPa. The properties of the steel are as follows: yield stress in tension, 950 MPa; yield stress in shear, 450 MPa; modulus of elasticity, 210 GPa; and Poisson’s ratio, 0.28. The desired factor of safety with respect to yielding is 2.8. Also, the normal strain must not exceed \(1250 \times 10^{-6}\). (a) Determine the minimum permissible thickness \(t_{min}\) of the tank. (b) If the tank thickness is 7 mm and normal strain is measured at \(1000 \times 10^{-6}\), what is the internal pressure in the tank at that point?