analysis of submerged flat plate

[frostrobn]

I'm looking for a little help in determining the proper bending equation to use in the analysis of 1/2" plate welded out around it's perimeter to a structural frame. The frame is submerged and is used to isolate a gate on a hydroelectric dam for maintenance. I was able to analyze the structural members, but what about the plate? Fixed-fixed ends using the longest dimension for (l) is way too conservative.

 

[rb1957]

Roark's no help ? ... for a rectangular plate with pinned perimeter and out-of-plane pressure ?? i imagine that it's got quite the pressure applied to it.

do you have sitffeners breaking up the plate ?

is the load carried by bearing of the plate onto the frame, or by tension in the welds (i think it's obvious which way is better) ?

is the plate welded to the frame along a single line weld, or multiple welds ? ... i picture that the frame (possibly a sq tube structure) bears against the plate so that the frame could be welded to the plate along more than one line.

 

[frostrobn]

The plate area I am trying to analyze is 4' x 6' and is welded out 100% to a frame of channel and wide flange members (it has to seal out the water). The pressure is pushing the plate against the frame. If I had a way to look at the maximum moment in the plate I could design backing members for the plate. Loading = 12 psig. Plate 1/2" A36. The entire structure slides down over an opening in a turbine intake to isolate a bypass gate.

 

[frostrobn]

P.S. Thanks for the help. I wish I had a Rourk's to look at.

 

[rb1957]

20tons of load ... from Roark 7thed, table 11.1 (reactangular flat plate, constant thickness, constant pressure) ... max stress = 0.5*q*b^2/t^2 (b is the short side) (for a plate, a/b = 1.5) = .5*12*48^2/.5^2 = 55.3ksi.

i think you're better off using the plate to distribute the pressure onto your stiffeners (1' pitch ?) ... then the stiffeners are "just" beams with a UDL (144lb/in), and maybe fixed ends ... the shear connection to the frame looks like somethig to watch (3500 lbs).

 

[miecz]

For a flat plate, try this. Be patient, it's a large pdf:

http://www.usbr.gov/pmts/hydraulics_lab/pubs/EM/EM27.pdf

 

[rb1957]

wonder why they didn't look at a plate pinned ("hinged") on all four sides ?

 

[frostrobn]

Thanks. Looks like the solution.

I agree, why would there be a hinged condition all sides? They covered everything else.

I thought there must be a fair amount of work done on this problem. I have run into this before and never felt quite comfortable with my method. My only solution was to "detatch" the plate on the long side and analyze it as a beam. Way too conservative! Thanks again.

 

[frostrobn]

Ok, I thought I was heading the right way with this. I guess I do not understand the units used by the above publication. For plates fixed on all four sides and uniform loading. Moment = Coeff. x p x a^2. What are the units? I have tried the correct table (I believe), but I can not replicate the answer that rb1957 produced using Roarks seventh edition, table 11.1, for stress after using the coefficient from the table to get the moment and then using stress = Moment/Section Modulus.

 

[rb1957]

with all sides fixed Roark's table reduces the maximum stress to .45*... (down form 0.5*...) ... does that help any ?

Roark refernces the legendry Timoshenko, "plates and shells" if you need further info.

 

[frostrobn]

rb1957, by reduction of the stress, do you mean from the maximum stress obtained when two of the sides are assumed to be detatched?

On my earlier post I was asking for assistance with the units used in the publication referenced by miecz earlier. I downloaded the publication from the Dept. of Interior and would like to use it, but I'm not sure if I am using the correct units for UDL on a plate fixed on all sides.

I can analyze the backing stiffeners correctly, it's just the plate I'm having trouble with.

I am going to dig into "Design of Weldements" by Omar today as well.

Thanks to all.

 

[rb1957]

ah, no ... i originally assumed all sides pinned, which i thought was your condition and which (strangely) isn't considered in the posted doc. the 2nd solution was for all sides fixed (and so does Roark) so i was giving you another benchmark. surely, the plate is supported on all four sides (by the frame) ... i don't see where two sides free is going in ? in any case, you're going to add stiffeners, no? ...

 

[frostrobn]

Yes, I am adding stiffeners. I am just having trouble with the analysis of the plate, specifically with the units used in the tabular coefficient tables from the publication that miecz referenced. I do not have a Roark's to reference, so I only have the a/b = 1.5 formula that you kindly offered from Roark's. But it is not valid for other values of a/b, no?

The plate is fully welded out around its perimeter (to seal out the water). I only mentioned "detatching" two sides because it is the only way I know to analyze bending in the plate, but this method is far too conservative. In design I would consider the end fixture on all sides of the plate to be fixed which lends the calculation to both the Roark's formula and to the tables referenced in the Dept. of Interior bulletin.

Thanks for the help. I am not trying to frustrate anyone. I think I'm just a little lean on reference material in this situation, that's all.

 

[frostrobn]

Omer Blodgett, "Design of Welded Structures" has the Roarke's formulas I need, Section 6.5 - 3, Table 1. Thank you.

 

[miecz]

frostrobn

I wouldn't rely on Roarke's tables for flat plates. See thread507-205764.

 

[frostrobn]

Ok, I see what you mean, miecz. Can you help me with the units that should be used in the formulas stated in the publication you referenced yesterday?

 

[rb1957]

personally, i'd stop with the flat plate (since it's going nowhere) ... i'd analyze the structure i'm going to end up with ... a stiffened panel. analyze the stiffeners as though they are beams, pinned would be reasonable. you've got a 6'x4' panel ... divide the 6' side with stiffeners, 1' and 2' pitch; each stiffener reacts 1/2 a pitch of water pressure on either side (of the stiffener datum), the frame supports these stiffeners (and the remaining 1/2 pitch on the two ends (of the 6' side). the section would be whatever stiffener you come up with and some effective plate (<1/2 pitch on either side). becareful with the shear connection between the stiffeners and the frame.

 

[frostrobn]

I agree with this approach fully. My only motive in econimizing on stiffeners is weight. This structure has to be rigged out 180' over the inlet of a dam, so crane size $$$ is a consideration.

 

[miecz]

frostrobn-

The coefficients in the tables are unitless. So, if you had a 48" x 64" plate with fixed ends all around, the maximum moment is found at x/a=0 and y/b=0.5. The coefficient for a/b=3/4 in Figure 34 is 0.0686. The moment for 12 psi is 1.90 k'/ft and the stress is 45.5 ksi. For your plate, you'd have to do some interpolation.

 

[rb1957]

my point was that once you add stiffeners you have a completely different strcuture. you're only looking at the peak stress on the flat plate, it's not something that translates onto the stiffened plate.

if you want to optimise the weight of the structure, reduce the thickness of the plate, and add more stiffeners (as the stiffeners are more effective in reacting the moment from the pressure.