Perforated plates under out-of-plane loads

[JasonMcCool]

thread507-446756
Curious if anyone knows where forum member Dreber got the source he posted in the linked thread for checking the strength of perforated plates as a series of equivalent "cables" in tension under a uniform load. It appears the equation for ymax in his example portion of his post incorrectly has an uppercase L in place of a lowercase L based on the little screenshot of a formula and diagram included (attached is an edited screenshot with the correction). But my question is where that formula for max deflection of a cable under a uniform load in terms of span, load, cross-sectional area, and modulus of elasticity came from. I haven't found anything similar in any of my books or elsewhere online. Most references simply give cable deflection in terms of tension. With EA in there, I'm guessing this is accounting for cable stretch, but I'm having a hard time deriving it. Any ideas on a source or hints on derivation? Much thanks!

 

[GC_Hopi]

If you are doing design, there is the equivalent solid material method Link

Edit: NVM, this was already mentioned in the previous post.

 

[FEA way]

I don't know the method with equivalent cables in tension but recently I had to deal with a problem of analyzing a structural response of a perforated shell and I used the equivalent elastic properties approach mentioned by GC_Hopi. This method is used in a design of heat exchangers for nuclear power plants. You can find its description in ASME Boiler and Pressure Vessel Code, Section III.

For me the most helpful articles on this topic are:
- "Equivalent properties for perforated plates - an analytical approach" by M.M. Cepkauskas et al.
- "ASME Section III Stress Analysis of a Heat Exchanger Tubesheet With a Misdrilled Hole and Irregular or Thin Ligaments" by E. Gomez et al.

 

[RWW0002]

When in doubt.. Roark

 

[JasonMcCool]

Thanks, RWW0002! I should've bought Roark's long ago, but I'll be remedying that shortly.

GC_Hopi: Yeah, I'd already found O'Donnell's equivalent solid strength method on the IPA website, and had used that to check a perforated plate in RAM Elements with 27% of the yield strength based on the hole pattern table he developed, but the results were really questionable to me, showing the plate being overstressed by a factor of 3 under a fairly small load, so I wanted a cross-check, preferably with independent assumptions. This method, apparently from Roark's, shows the plate that I would expect to work as working, but I didn't want to rely on a method of unknown origin, especially when I was having problems deriving the formula myself. I think I'll actually go buy a sheet of perforated steel this weekend and do my own proof test and see which method is closer to reality.

FEAway: Thanks, I've added that Cepkauskas article to my catalog of resources. Always nice to see different approaches like the triangular and square patches he looks at.

Thanks for the help everyone
Jason