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Re: Finite Element Analysis

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On Oct 27, 2008, at 11:19 AM, David Francis Caballero wrote:

Can you give me an idea or reference on how to model a finite element-plate and the member connection on it-and a good reference of step by step procedure on modeling it-how to input load and support on the model.
The answer to this would be about the same if you'd asked for a step by step procedure for doing brain surgery. First, it's a much art as science. The science part is easy: plate elements loaded at the bolt holes. The art is hard and it's knowing how to interpret the results so they jibe with Code provisions. If you're just starting with FEA you've only begun to learn the easy part of the job. Which is not to say that it's impossible, but that you have to develop appropriate engineering skills. SAP2000 should do the job just fine, BTW as would any general purpose software.

I'm guessing, but it sounds like you're considering gusset plates connecting framing members like the ones that are suspected in causing the collapse of the Mississippi River Bridge in Minneapolis which killed 13 people, injured 145 more and shut down traffic in the most travelled north south artery in Minnesota and cost $400 million to replace. (My way of pointing out why you'll want to do this right…).

The first thing you'll want is a reliable listing of the concurrent loads you want each connection to carry. Each load set has to be in equilibrium, so you can't just worst case the loading using the worst member loads picked from all the load cases. If you have a dozen load cases and (say) 50 connections, your work is really cut out for you. I might consider do a simplified (elastic method described in the Steel Manual) for what you think might be the worst half of them to see how your is going and to help get you through the governing connections. You can do that with a spreadsheet.

Next model the connections one at a time. Plate elements for the gusset and beam element stubs where you'll apply the loads. Couple the beam elements to the bolt locations. Use the nodal loading at the beam element connection points to specify the bolting and to make sure your specified preload exceeds the calculated loading. The stresses in the gusset plate will include stress concentrations and very high bearing stresses. If your modeling software can handle it, you can include the bolt holes in the model and reduce the peak stresses by connecting the beam elements to the hole circumference. You'll get some peak stresses, but they'll be negligible a distance of 2-3 plate thicknesses from the hole. Stresses outside this limit (where the St Venant effect is working) can be conservatively compared to the standard code allowables. Be sure and check the overall problem for equilibrium so you'll know the loading is right. The calculated bolt loads can be used to verify that the bolt stresses including the clamping shear are within Code allowables. Use the nominal bearing stress calculated according to the steel Code for bearing. What you'll be seeing in in the plots of stress distribution are more like Hertzian contact stresses which are real, but which reduce as the bolt shanks work a little into good contact.

Make sure your mesh is fine enough so you can see how quickly the peak stresses around the holes fall off. Even so you may have some problems with high calculated stresses in the plates, and you'll have to verify that you aren't looking at secondary or peak stresses which might develop, depending on the actual design. In areas possibly subject to shear-out for example, you can estimate the actual limit load by noting how yielding spreads over the area as the load increases. There's no formula for doing it--you just have to judge how complete plastification develops.

You might also want to do a simple single bolt connection as a test problem to test your modeling details and see what approach you might take to determine the limit loads. Unless you're a lot better with FEA than you indicate, it's probably not a good idea to get into plasticity for now.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)   | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania 1864)

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