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.