That's an odd model for me. So as the radius goes to infinity for a fixed thickness and differential the stress goes to infinity too? But take a pressurized cube with reinforced edges. You can say it's faces have infinite radius (or as small as you'd like) -- yet the stress should be finite? How do you reconcile this? Or does that work only for circles? (which would be odd since stress is a local concept to me)
I'm not sure of your background, but it is actually a pretty simple concept. To satisfy static equilibrium on a given transverse "dx" segment of a cylinder, the walls must balance the internal pressure (in this case taken as the pressure difference), so that:
Regarding your question, yes, as the radius goes to infinity, the stress goes to infinity. The area where the pressure is applied grows with r, but the cross-sectional area where the stress is applied is still (w * thickness * dx.) This equations work well for thin-walled cylindrical pressure vessels (r > 5t is general rule of thumb). For a cube, you would have to develop the equations, but keep in mind that you will have a singularity/discontinuity on the walls because of the right angle.
Ah makes more sense now, thanks for the explanation. I'm an undergrad in EE so mechanics is not my strong point.
So a planar face of a cube cannot satisfy the equilibrium equations? Interesting ... so then a cube will necessarily bulge so the radius is enough to satisfy the equations, right?
