How to determine when a vessel will fail due to pressure increase?

I am having a brainfart and cannot even think of what I need to search for.......

In short I have a container made of 16 ga. steel. It will have vaccum pressure and positive pressure. It will be cyclically loaded during operation. 25 in Hg vaccum and 25 PSI of positive pressure.

I know:

-The surface area subject to the pressure.

-The pressures (which are both positive and negative).

-The material properties of the steel.

-There are sharp corners so if memory serves me correctly there are some adjustment/increases made in pressure for these areas.

What equations do I need to look for?

Thanks!

Is this a homework problem or are you really designing something that will get built and used?

are you asking what it takes to burst it after one cycle or what is it rated for given a certain number of cycles (fatigue)

DO you have access to the ASME Code? (ASME section VIII) Vacuum is UG-28 , internal pressure is UG-27 don't forget to calculate for bulk head internal and external. if not, Roarks, or Shigley and Mischke, or Norton Machine Design will get you pointed in the right direction to get started but they only scratch the surface.

16 ga. would most likely be a thin walled pressure vessel depending on diameter. I'm assuming self supported and stationary (not over the road) whats the profile? round, elliptical?

Pressure and longitudinal bottom center line stress should be computed in combination.

buckling and vacuum should be analyzed in combination (top center line). it's not so much surface area for vacuum but unsupported length leading to buckling.

Stress concentration is important and can be calculated but if you have an FEA package to double check your hand calcs it would be a good idea to run it. I recommend designing against a published standard or buy a pressure vessel rated for the application that has been designed and proven.

Not that I'm questioning your ability, experience, or know-how but is pressure vessel design covered in Civil Engineering?

The short answer to all of this is testing.