Stiffened Circular Plates

[Ussuri]

I am looking at designing a stiffened circular plate under a uniform loading condition. In this situation the stiffeners will be on top of the plate instead of the more usual stiffening underneath.

I am doing some concept calculations and was wondering if anyone had come across design guidance for assessing capacity of stiffened circular plates?

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[BarryEng]

Rather than answer your problem, I will give you a method that I use.

In some cases on large pipes, I have to design dead plates for emergency shut off purposes. The load is (of course) uniform from water pressure. I first check the thickness req'd for a circular plate (& in most cases require smelling salts when I find out the req'd plate thickness). For a first quick calculation, check the dead plate size from the many flange tables on the market - for your diameter & pressure.

I then divide the dead plate into a series of squares. I want to use a series of vertical plates (ribs) so that the load is taken by a series of tee beams at right angles to each other. The steel codes (of most countries) will give you the allowance for how much width of the skin plate that you can use for the top flange of the tee (usually about 16 t) that will determine the size of the squares that you will use.

Then by ordinary basics, I design a series of tee beams (using half the loading due to the two way action) with the supports pinned. I very rarely use a fixed joint condition, even with a bolted joint due to the obvious rotational flexing of the pipe/flanges joint.

If your loading is on the side that the ribs are located, be careful of the elastic instability of the compression flange - this will determine your design of the ribs, even though the ribs (one way) are supported by the ribs in the other direction.

For very large dead plates where the edge of the rib is not supported except by the other ribs, I have (on occasions) used "half" I beams so that the I beam flange provided the support for the compression flange instability.

Also remember that the skin plate is bending in one direction & the support ribs (or half I beams) are bending in the other direction so there is biaxial bending. For a large installation you should check the von mises cirteria (reference stress = sqrt(f1^^2 + f2 ^^2 - f1 x f2). For a small installation - just use a very conservative value for bending stress.

Have I interpreted your problem correctly?

 

[miecz]

Have never stiffened a circular plate. But I have stiffened rectangular duct plates under negative pressure. If I interpret your post correctly, your situation is similar in that the composite action of the stiffened plate puts the plate in tension. If this is the case, the effective width of the plate is your full stiffener spacing. The 16t effective width limit is based on buckling of a plate in compression, and wouldn't apply to a plate in tension. Also, if you are thinking of running stiffeners in only one direction, the outstanding stiffener is in compression. So, buckling of the stiffener becomes a serious issue.

 

[Ussuri]

Thanks folks

You are both interpreting correctly, and yes my loaded side is indeed the side the stiffeners are on to the plate is on the tension side. The plate is subjected to a water pressure of 8-10 bar and will be around 6m in diameter.

My initial approach was similiar to those suggested. I have orthogonal stiffeners in two directions. I checked the plate under bending as a square fixed on all sides spanning between the stiffeners. I then checked the stiffeners as a tee section assuming the load is transferred by the 'infill' plate.

I feel this is probably conservative as the entire plate/stiffener arrangement will function as one.

 

[BarryEng]

I would do the same design process that you have detailed. Remember the biaxial bending of the skin plate over the beams that are bending in the other direction (I assume that you have continuous FW to keep crevis corrosion at bay).

On large dead plates, the main reason that I use 'half' beam sections, is that the junction of the beam to the skin plate, is two fillet welds on each side of the web of the half beam. This ensures that there is no extra bending stresses. If you use a smaller (full) beam section, the attachment of the beam to the skin plate is by fillet welds at the extremes of the bottom flange of the beam section. Any bending of the skin plate will introduce cantilever bending moments in the bottom flange of the beam.

I meant to mention that the allowable stress is different for a circular plate compared to a beam. If you look at ASCE 79 (power penstocks - big pipes for the power industry), at the ASME code, etc, you will find that the usual allowable (membrane) stress (S) is 2/3 yield.

The allowable stress for the centre of a dead plate (I think - I don't have my references with me), is 1.5 x S. This is also the condition in the Australian Standard for pressure vessels (AS1210). It is not in the general area of AS1210, but is contained towards the end of the supplement to AS1210.

Bednar (pressure vessels) also has exactly the same stress combination table as in those above.

Even so - I would still be very conservative because: -
* It is a one off design.
* The welds will probably cause some distortion to the plate & I assume that (for your size) you are not going to stress relieve the welds.
* If you require the plate to be relatively water tight, a tortionally stiff plate is what I would like.
* The plate will have to be relatively rigid to allow for handling stresses in both placing & removal.

 

[miecz]

With a six meter plate, depending on your stiffener spacing, buckling of the stiffener may be an issue, even for a grid system. I don't believe AISC covers buckling of composite beams in the "negative" moment region. I know that AASHTO does, but, of course, it's for concrete/steel systems. You may have to develop your own buckling criteria. I believe the AISI Cold Formed Steel Design Manual has some useful information on buckling of outstanding flanges attached to plates.