Stress analysis on circular plate with diametral stiffeners

Hi all, I've posted here before. I am a student engineer on a work term with a consulting firm. I have been asked to perform a stress analysis on a dust collector of cylindrical shape. The maximum pressure that it can physically withstand is 6.23 psi. The top on the dust collector has twelve 2x2x3/8 angle iron (carbon steel) stiffeners welded to it for reinforcement. The dust collector body itself is made of 3/16" thick carbon steel for the tubesheet and the top plate. I am attempting to perform a stress analysis on both the plate sections between the stiffeners and the stiffeners themselves. My question is whether this can be performed analytically or is this best solved with FEA (which I don't have access to). Are there any reasonable approximations that may help give some ball park numbers? I've spent a couple of days trying different things but the numbers I get don't seem to be reasonable. Any help would be appreciated :)

FEA! Otherwise, you need to characterize the as-built material via load testing..

I figured as much. The company I'm working for doesn't own a copy of a program for FEA usage so I was hoping for a way around this problem. I'll mention this to them to see what the alternatives might be.