What's the nature of hoop stresses on a rocket nozzle?

Question

On a rocket nozzle, are the stresses (namely hoop stresses) from pressure differentials compressive or tensile?

Obviously, in a combustion chamber, the pressure inside is greater than outside. As the exhaust velocity increases, however, Bernoulli's theorem would state that the exhaust pressure decreases:

In a flow where no energy is being added or taken away, the sum of its various energies is a constant: consequently where the velocity increases the pressure decreases and vice versa.

Is there a specific point at which the pressure and hoop stress switch directions? Is this something that nozzle design must account for? Are altitude based changes in atmospheric pressure factored into this?

Answer 1

At low altitudes, engine nozzles are overexpanded. The pressure inside the nozzle rim is lower than the ambient pressure, so there's a compressive force on the nozzle.
At high altitudes, ambient pressure has dropped to the point where it's lower than the pressure inside the nozzle rim: the nozzle is now underexpanded, and the force on the rim is outward.
The altitude at which the pressures are in equilibrium depends on the nozzle design (the expansion ratio).
The hoop stresses are bound to be a factor in nozzle design, giving a lower bound for material thickness. I can't put a number on how important this issue is though.

(image from Aerospaceweb)