# Measure stress of gas acting on a spherical container

How can I measure stress in a thin- walled sphere containing a gas? Is there a way to predict what the stress will be without actually needing to fill a sphere with gas? I am talking about hoop stress/longitudinal stress.

The thickness of the walls of the container is unknown at this point; I know the radius and the material (EVOH); the internal pressure will be 10 atm. The question then is how will I know how much stress is too much for the material to handle? Would it be the material's yield stress value? Once that is found, how will I know how much of a safety factor is acceptable?

• stress is never measured directly. You can measure strain and calculate the stress if you know the elastic modulus. Jan 7, 2017 at 2:04

Spherical vessels have a stress in the wall equal to,

$$\sigma = \frac{p r}{2 t}$$

where $p$ is the internal gage pressure, $r$ is the inner radius of the sphere, and $t$ is the thickness of the wall, where the only constraint is $r/t \geq 10$.

• I do know that this is a useful formula to use in this situation, however, the stress is unknown and thickness of the wall is also unknown. Is there a way to measure the stress in the container physically if a formula cannot be used to find the stress given the aforementioned constraints? Jan 7, 2017 at 1:59
• Are you doing this experimentally or are you trying to seek an analytical solution?
– TRF
Jan 7, 2017 at 7:31
• I am hoping for an analytical solution, but currently, I am faced with an equation with two variables. I am also open to any suggestions for how to measure the stress experimentally as well. Any suggestions for a resolution to this using an analytical solution would be preferred. Jan 7, 2017 at 21:24
• @HypnosStratagem yes, that should provide the minimum thickness (note that the equation is only valid for $t < 10r$) as long as you don't need to hold the pressure for a long time or above room temperature, which will cause creep. Jan 13, 2017 at 23:46
• No engineer in his/her right mind would solve this problem in such a convoluted way. Just draw a free body diagram for half of the the sphere plus half the pressurized gas. Resultant force on the circular "cut" through the sphere = $\pi r^2 P$ (from the gas) - $2 \pi r t \sigma$ (from the stress in the sphere = 0. Therefore $\sigma = pr/2t$. Jan 7, 2017 at 22:23