Analyze steel plate with multiple point loads?

[StructureMan44]

Is there way to analyze (find max stress and deflection) of a steel plate that is fixed supported on all four sides and has three point loads at non symmetrical positions on the surface? I did not find an applicable formula in Roark.
I could put all three loads at the center of the plate but I don't know if this is conservative.

 

[ajc2014]

The yield line method may work, altho I have never used it on something like this. What is it being used for? maybe framing below the plate is a better option.

 

[jfmann]

Consider using uniform load on entire area of plate that equals sum of point loads..........unless point loads are close to edge, that should certainly get you close.

If load are close together, and within middle half of plate........another "old school" technique would be to use beam strips......two perpendicular strips (with appropriate width) for each aggregated point load.

However, you should be able to find solution for single point load anywhere on the plate.

John F Mann, PE

http://www.structural101.com

 

[StructureMan44]

ajc2014: Thanks for the input, I'll look into the yield line method. I've attached a pdf of the configuration with 5 holes/slots for duct banks. The outer dimensions are 9'4" by 5'2" and the plate is 1/8" thick A36 with about 1000~2000lbf at each location.

jfmann: Is that conservative to add up all the point loads and make it a psf load? If so, there is a Roark formula for this and it will be much easier, thank you.

 

[jfmann]

Of course, this is just to give you basic idea of stresses using readily available method without full-fledged analysis program......and I was not considering openings in plate which greatly complicate behavior and analysis.

After looking at your diagram.......with large opening that completely disrupt plate, you have to look at continuous strips between openings that can span between supports at beams...........those large openings have effectively destroyed plate action. You might even need to reinforce plate with ribs.

However......as for basic idea; estimating analysis for bending of uniform plate (without openings).......total value for "equivalent" uniform load must be increased somewhat......depending on location of point loads relative to edges of plate. You can use proportions for simple beams as starting point.

Consider simple beam with fixed ends;

For point load (P) at midspan, moment at support is PL/8
For uniform load having same total value (wL = P).......moment at support is wL (L/12)
Moment due to point load at midspan is therefore 50-percent greater

At midspan, moment due to point load (PL/8) is 3 times greater that moment due to uniform load [wL (L/24)]

As long as point loads are spread out .....you should be able to derive reasonable value of uniform load that will provide reasonable estimate of bending stresses.

If point loads are all close together......then you could look at an estimate using single point load equal to sum of the 3 point loads.



John F Mann, PE

http://www.structural101.com

 

[TLHS]

You can do yield line for something like what is sketched, but it's likely more work than is justified for the problem and there's a real possibility that you miss checking a possible case. There will be a lot of different failure patterns.

The remaining strips are thin enough that I'd likely do my rough check by assuming it's all a beam system with imaginary beams that I sketch out over the plates. i.e. instead of treating it as two way plate action, pretend the plate is composed of a series of beams. It's conservative on both strength and deflection and only takes a minute to do. If you get crazy numbers you can try looking at it another way.

Just eyeballing it, though, looks completely inadequate. 3mm plate spanning 3m? Then you cut holes in it?

You should be framing under the point loads or using stiffeners on the plate to establish a load path. At this span size, plate isn't going to be an efficient use of materials.

Take a look at this floor plate load chart to give you some idea of reasonable spans.

http://www.gratingpacific.com/load_tables/algrip_safety/carbon_load_table.pdf

 

[jfmann]

Had not looked at your proposed dimensions and loads.......whoa.....completely untenable for 1/8-inch thick steel plate.

Spanning short direction; 62 inches.........say 12-inch wide strip between openings..........with point load at midspan......bending stress of 27,000 psi (typical allowable for A36 steel) is reached for point load of only 108 lbs for fixed-end condition (which is suspect anyway) .....clearly nowhere near your lowest load of 1,000 lbs, let alone the 2,000-lb load.

Even for plate without any openings........plate thickness would have to be more like 3/4-inch (or more, depending on allowable deflection) ........though ribs would likely be way to go.

Back to drawing board!!

John F Mann, PE

http://www.structural101.com

 

[Brad805]

I agree with TLHS that the design seems sketchy. I read it twice and still thought I must be missing something.

 

[rb1957]

maybe it's just me, but i couldn't see loads on the sketch ?

does Roark cover plate with cut-outs ? (don't think so)

strip is one approach. reinforcing the strips with stiffeners would definitely work.

another day in paradise, or is paradise one day closer ?