For the cylindrical vessel with ellipsoidal heads shown in Figure P9–22a under loading p...

For the cylindrical vessel with ellipsoidal heads shown in Figure P9–22a under loading p = 500 psi, determine if the vessel is safe against yielding. Use the same material and factor of safety as in Problem 9.21. Now let a =100 in. and b = 50 in. Which vessel has the lowest hoop stress? Recommend the preferred head shape of the two based on your answers.

For modeling purposes, the equation of an ellipse is given by b²x² + a²y² = a²b², where a is the major axis and b is the minor axis of the ellipse shown in Figure P9–22(b).