There are so many things wrong with you have written since your 14 Feb 18 10:59 post, I don't even know where to begin.
Perhaps I will start with an example:
Process: Delayed coking thermal cracking
Equipment: Coke Drum
Service: Cyclic in temperature and pressure
Fluid: Gas, hot oil, solid coke (carbon), steam, water (in that order)
Design conditions: 50 psig (at top) @ 875°F - 29.5 psig of static pressure at the bottom
Size: Range between 20' diameter and 35' diameter and 50' to 100' tan-to-tan
Situation: Many drums in this service are designed using the ASME Section VIII, Division 1 rules for pressure only. These typically last ~4 years before developing leaking cracks. Leaking cracks of hot hydrocarbon leads to fires. Those drums that are designed for the fatigue/cyclic service generally last 10-25 years before leaking cracks, but the fatigue analyses generally shows the operator where to look proactively and how often, so that they can repair the cracks before they become catastrophic.
Need I go on?
If you are unable to do the fatigue analysis requested by your client, then find someone who can. Also understand that if the fatigue analysis will govern the design of the vessel (i.e. result in a thickness or design details that wouldn't otherwise be necessary for pressure-only), then there will be a whole host of additional fabrication requirements. For example, have you given any thought to controlling the out-of-roundness/weld peaking? The Code-required value for pressure-only generally results in a fatigue life of the longitudinal seam ~1/10th that of the base cylinder. I could go on and on.
I'll finish with the same advice that I gave in another recent thread:
Find an expert. Engage them. Pay them.