Stress analysis techniques without using finite elements method

I am a student engineer on a work term with a consulting that has asked me to perform stress analysis on various dust collectors under maximum stress conditions. I am to determine the maximum allowable pressure. I do not have access to a finite element analysis program and my question is whether or not I can perform a stress analysis on these systems without it. Most of the systems are cyclones and as a result of how they function are circular. Several reach high pressures and I'm examining them when they're on the brink of yield strength. They have stiffeners along the sides and a slanted cylindrical top leading into the output duct. Is there a method of performing a rudimentary stress analysis on these systems without using FEA??? Any help would be greatly appreciated as this has been a significant problem in my work books for some time now :)

Get your hands on a copy of Roark's Formulas for Stress and Strain. Back in the day before FEA, 3D modeling, etc., (You know, like when engineers designed the vehicles and weapons that fought World War II and put men on the moon using nothing more than slide rules, pencils, and paper.) every engineer worth his salt had a library. The number one book he had was Machinery's Handbook. Roark's was number two. One of the old hands around there might have one. If not, then its time to belly up to the bar and begin your own investment in your future. Amazon has them north and south of $100.