Pressurized carbon dioxide is to be repeatedly filled into a hot-rolled, steel cylindrical tank ($E = 30 \times 10^6$ psi, $v = 0.29$, $S_y = 64,000$ psi, $S_u = 82,000$ psi, $\sigma_f = 170$ ksi, $b = -0.156$, $\epsilon_f = 18\%$). The tank is, with an 10-in internal diameter, length of 12-in, and thickness of 0.10-in. Determine the internal pressure that will cause fatigue at 10,000 cycles according to the Goodman failure theory ($R = 99.99\%$). Use the von Mises stress as the equivalent normal stress.
