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Design - Steel Plate Loading

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swaiteen

Geotechnical
May 4, 2012
5
Hi to all,

I have a rectangular plate sitting on two parallel beams (I) which are sitting on subgrade. I'm looking at bending moments in rectangle plates (Civil Engineering Handbook 2nd Edition); some of the systems appear to resemble this concept though all equation appear to solve for ,w, (Deflection of Plate).

Any ideas on the best way to work out the maximum load for this system?



Thanks

Swaiteen
 
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This sounds like it could be looked at as a simply supported beam based on your description. Just get capacity on a per foot basis and figure out what PSF load it can take.
 
Sounds like you may be looking at a beam on an elastic foundation analysis here if you are talking about the capacity of the whole system, not just the plate.

Mike McCann
MMC Engineering
 
Hello and thanks for the reply. I have made some further developments;

I simplified the problem to a rectangular plate supported at the boundaries.
Mild Steel(E=200GPa)(650x1100x8mm)
Plate loaded uniformly (qo)
Using the governing differential equation I solved for Deflection (w).

Under load of 1000kg: w = 4.47mm
Under load of 10000kg: w = 48.56mm

For a plate of the above dimensions this appears to be practical. What do you think?

In an attempt to include the other elements in the original system I am looking at the (I) beam supports. What can I do to calculate the maximum load of an (I) beam; or shear strength of the flanges of the (I) beam? Or what do think the capacity of an (I) beam (100x50x8mm) would be?

Thanks
 
Couldn't you develop the plate loading from pg 3-155 in 13th edition? I don't see the difference between raised pattern and flat plate.

Also if you know the defelction work with that. pg 3-7 in 13th edition gives formula for max deflection. Even then you might still get complaints that the floor is moving.
 
It's not clear to me if the plate is supported on all four sides or just two sides. If it's just two sides, with uniform loading, it's just a wide beam for stress purposes, with some minor variations in deflection.

If it's supported on all four sides, then the normal bending stress derivations assume that deflections are small, not more than half the thickness or so. If deflections are over this, it doesn't mean the plae is inadequate, just that the analysis isn't valid anymore, as the plate starts developing in-plane stresses rather than bending stresses.

With it not being too clear on how the plate is supported, it's also unclear how the I-beams are loaded. If they have uniform load above and uniform support below, there isn't any significant bending, at least not in the beam sense.
 
Swaiteen:
You really have to define and explain your problem much better than you have if you want any meaningful help on it, you shouldn’t expect us to keep guessing. Show some sketches, dimensions, sizes and loads so we can get a sense of the proportions and the real problem. What are the soils conditions, Mike M’s assumption of a beam on an elastic foundation sounds about right to me. But, is it two beams side by side and fixed to each other in some way, with one load from above and at the center of the beam length, or what? Or, are the beams separated by some significant amount, and the plate spanning btwn. them? That 48.6mm of plate deflections sound pretty high to me whatever equations you used. That sounds like a whole week’s worth of deflection to me. :)
 
Hi all,

I uploaded drawings of the problem. plate (1300x840x8mm), Rectangle in between I beams (1100x650mm), I beams (50x100x8mm).

Assuming the I beams are sitting on high strength concrete. What is the max load for this system? Or what is the deflection under central point loading?

I don't want the problem solved for me just point me in the right direction.

Thank you
 
 http://files.engineering.com/getfile.aspx?folder=56cdbbb2-e33d-4d8c-bb48-0d0df6c69c10&file=Ibeams.png
How is your load dispersed over the area? (1 point in the middle, line over the center or uniform loading?)

You may consider getting a copy of roark's formula's for stress and strain. Should give you all your answers.

NX 7.5.5.4 with Teamcenter 8 on win7 64
Intel Xeon @3.2GHz
8GB RAM
Nvidia Quadro 2000
 
Sorry I missed the part where you said uniform load.

2 things:
1)Find out the allowed ground pressure for your concrete.
2)The reason most of the formulas you find are solving to deflection is because it's usually the defining factor. You'll reach an unwanted deflection before you'll reach the tensile strength limit. This may not be true in your case however, so you'll have to calculate both.



NX 7.5.5.4 with Teamcenter 8 on win7 64
Intel Xeon @3.2GHz
8GB RAM
Nvidia Quadro 2000
 
If the load is more or less uniform over the area, it looks like you could just treat the plate as a wide beam supported at two points. If the load is concentrated, you may not find tabulated solutions to match your load case.

For the I-beams, you can check the webs treating thems as short columns. If there's any possibility of lateral loading, that might control the design.
 
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