This is a deadweight stress (compressive), usually considered as equally distributed on peripheral vessel thickness (excluding corrosion allowance). Not only trays, but also metal vessel weight and any insulation should be taken into account. So dead weight stress (compressive) would be σ=W/[π(D+t)t], W=dead weight (*), D=diameter, t=thickness of vessel, concerning vertical cylindrical vessels.
See Coulson and Richardson's "Chemical Engineering Vol 6", mainly example 13.3 in Chapter 13 "Mechanical Design of Process Equipment". This can be helpful for your whole task too.
(*) I think liquid hold up of trays (not a pressure load) should be also considered.