Flat Plate Displacement in Bolted Joint

[Eltron]

I am trying to determine the displacement (at the center of the end plates) for the end plates of a bolted joint. The image should give you an idea of what I'm after. As you torque the bolts down the plates deflect towards each other (more on the edges than in the center of the plate). I am assuming for the sake of calculation that the meat of the sandwich is rigid and fixed. I looked through Roark's and the interwebs without any luck, and I have already done the FEA which matches what I've measured empirically. For the sake of argument we can ignore that there are stacked end plates in the drawing attached.

I'm looking for some formulas that will allow me to determine the displacement of the end plates so I can determine how thick those end plates need to be to avoid displacement at a certain bolt torque. Make sense?

Any idears?

Dan

http://www.eltronresearch.com

Dan's Blog

 

[Tmoose]

at the very center I'd expect the sandwich to get thicker looking .
Kind of like this loading.

http://theconstructor.org/wp-content/uploads/2010/10/clip_image0189.jpg

 

[MintJulep]

Isn't it essentially

http://www.efunda.com/formulae/solid_mechanics/plates/calculators/SSSS_PUniform.cfm

 

[prex]

As the plate is quite elongated, you can treat a portion of it as a beam, long as the plate width, wide as the bolt distance and cut across the long sides in the middle. According to your assumptions the beam would be supported on the edges of the meat and loaded outside the supports by the bolt loads.
This model should get you quite close to where you want to go.
A special attention should however be devoted to corner bolts, as the corner of the plate could deflect more.

prex

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[rb1957]

the plates would arch over the "meat" ... so you'd have a 1 pitch strip loaded by a bolt near each end, reacted by a contact force at the edge of the "meat" plate ... ?

 

[msquared48]

Just see how much the plate will deflect up at the center from the force couple created at each end.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[bobslo]

I think that no "simple" formulas are available due-to the fact that this is quite complex problem. FEA is the only available tool to get out figures.

 

[rb1957]

for a strip along the Cl, it'd look like a beam loaded by end moments.

all round, it looks like a plate loaded by moments along the perimeter, ... no?

 

[Eltron]

OK. Sorry I let this one slide for so long. I got pulled away to something more urgent, and I only got back to this problem this morning. Thanks for the responses. I ended up using the beam calculations attached. I also backed it up with FEA. The deflections from the FEA and the calcs match up with three different plate thicknesses, so I'm calling it good.

Dan

http://www.eltronresearch.com

Dan's Blog