deflection, aluminum plate 2

I am trying to find out the deflection of a piece of 3/8" x 2" x 2" aluminum plate ( 6061 ) , with a point load of 225 lbs. It is supportated on all 4 sides.

Thanks
HBlake

 

[GBor]

How is it supported along the edges (simply supported or fixed) and is the point load in the middle?

 

[GregLocock]

And are the edge supports able to move in the plane of the plate?

Incidentally as it is a point load, the deflection is in fact infinite.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[johnhors]

Greg

Don't you mean stress is infinite ?

 

[TheRaptor]

johnhors,

The theoretical stress would be infinite. Not deflection. I am sure it was just a typing error by Greg.

 

[rb1957]

are you worried about very small deflections ?
a 3/8" thick piece of Al, 2" square, will deflect just about 1/2 a gnat's hair under 225 lbs ...

if you want a precise number, Roark has lots of tables, try 11.4 case 1b (7th Ed). I suspect that you could approximate the problem as a simply supported (or doubly cantilevered) beam. for the simply supported case, this would give you a maximum moment of 225*2/4 = 112 in.lbs, and a stress of 112*6/0.375^2 = 4.8ksi and a deflection, if my math is right, of 5/16*(4.8/0.1875)*(2^2/1E7) = 0.003"

 

[GBor]

Be careful what you look at in Roark's for this one. Roark's is generally useful for thin plate theory. This plate should behave more like a thick plate. It kinda' like the difference between general beam theory and Timoshenko.

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

 

[GregLocock]

Where I come from if you apply an infinite stress to a plate you'll get an infinite deflection. AKA a hole.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[prex]

Well, to come in this finite-infinite debate, this is the situation as I see it:
-theoretical bending stresses become infinite at a concentrated load
-theoretical deflections remain finite at a concentrated load
-theoretical bending stresses at a concentrated load are not realistic, because the elementary bending theory for plates is not valid, as that theory assumes that the direct stress due to load application is negligible with respect to bending stress: a different treatment is required (see Timoshenko P&S point 19)
-deflections at a concentrated load as calculated by the elementary bending theory are realistic



prex

http://www.xcalcs.com

Online tools for structural design

 

[prex]

HBlake,
though I concur with rb1957 on the low practical usefulness of your goal, you could use the calculation sheet available on the site below under Plates -> Bending+shear -> Rectangular -> Simply supported -> Conc.load
You'll see that the center deflection is 0.252 mils, where with simple bending that value is .206 mils.
rb1957 hope your fast calculated figures are incorrect, not the results of those sheets! (though there is something wrong in the bending+shear sheet that I will have to check, but this doesn't seem to fully impair the result).

prex

http://www.xcalcs.com

Online tools for structural design

 

[corus]

I'm not sure what Greg is referring to but rb1957's approximation of a simply supported plate, at all 4 sides, as a cantilevered beam isn't correct. In my copy of Roark IV ed. a load over a small area will give a stress that tends to infinity at the centre as the load area tends to zero (a point load). The deflection doesn't tend to infinity but is probably close to one estimate given of a gnat's hair. I'd ask the teacher if they can be more precise about the point load, as points don't exist in reality.

corus

 

[GregLocock]

I'm merely emphasising your point. An infinitely concentrated point load of any significant magnitude (relating tot he molecular bond strength) will punch its way through ANY structure.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[HBlake]

Thanks all for your help. I got my answer. It turns out that it was a 2 foot square and not attached to the four sides.

Hblake

 

[rb1957]

a wee bit different from the original description !!

 

[johnhors]

rb1957

What does an accurate description of the BC's count for once you have the pretty coloured result plot ? Depends what SIDE you are on.

 

[rb1957]

be nice john !