Column buckling is something worth checking in the support, but, particularly as short as they typically are, that's not the failure mode you are going to be concerned with.
The critical point is at the interface of the pipe and support - the circular projection where you are welding the two pipes together. The force due to the weight of pipe is going to cause bending in the main pipe. You can picture a piece of saran wrap, restraining it by the edges, and then pushing in the middle with your fist causing it to deflect and stretch out.
I'd have to go through my Roark book, but I don't know if he's going to have something that would essentially be a cylinder under internal pressure with a uniform load applied to the outside in a projected circle.
Since you are only looking at an axial load (i.e. along the centerline of your support), the Kellogg equation is this:
S = (1.75*f*sqrt(R*t))/(t^2) + P*R/t
f = W/(2*pi*r)
S = Bending Stress, psi
W = Axial Applied Load, lbs. (Weight in your case)
r = Radius of trunnion (support pipe), in.
pi = 3.14159
f = Load per inch
R = Radius of pipe, in.
t = corroded thickness of pipe, in.
P = Internal pipe pressure, psig
Your allowable stress is going to be 1.5*Sh, where Sh is your base code allowable stress at temperature. If you're B31.3 and using a common carbon steel like A106B or A53 B, Sh for temperatures less than 400F is 20,000 psi
Based on your description of the system, I don't expect that you have any significant circumferential or longitudinal bending loads.
I'm afraid my copy of the Kellogg paper is probably a 4th generation copy that is already in pretty poor shape. Otherwise, I'd see about scanning it and trying to post it somewhere. Perhaps one of our other distinguished members has a cleaner copy. I would expect it can be found in the sadly out of print Kellogg Design of Piping Systems. Unfortunately, I've not been able to obtain a copy of that book for my collection yet.
Edward L. Klein
Pipe Stress Engineer
Houston, Texas
"All the world is a Spring"
All opinions expressed here are my own and not my company's.