End Plate Design For a Heat Exchanger

[cpizzleo]

I am currently in the process of designing an end-plate for a heat exchanger. I know I can do what I am about to ask with FEA, but that is not feasible right now. Here are the design parameters:
Shell and tube HX, Max operating Temp=1100 F, 59 1" SS 304 Tubes, staggered pattern, 12" Shell OD (The tubes occupy 43% of the end-plate area; in other words, (# of Tubes*Dt^2)/Ds^2=.43). I found that the end-plates modulus of elasticity can be assumed to be 13% as a perforated plate with this design.

The ends of the tubes will be welded onto the end-plate which will be welded to the inside of the shell. I am concerned that the stresses on the end-plate due to thermal expansion of the pipe will lead to failure, so I am trying to find an appropriate thickness for the endplate. I did find a few good sites. One of which is:
http://www.roymech.co.uk/Useful_Tables/Mechanics/Plates.html.
The problem is I have holes that are not in the center of the end plate.

Also, I was thinking an "outside the box" solution would be to preheat the tubes when welding them to the end-plate.

 

[nvn]

cpizzleo: I do not foresee someone solving this problem without using FEA. Each tube will apply a different force to the end plate based on tube location (radius) from the end plate center, and based on end plate thickness (stiffness).

 

[Baluncore]

Maybe a sensible solution would be to put a slight bend, (or spiral), in every tube. That would convert the very high axial stress during operation into a much lower tube bending stress. End plate specifications could then be considerably relaxed.