Rectangular plates subjected to a concentrated moment 1

[Ussuri]

Folks

I'm looking for the easy option here. Does anyone know of a reference for the anaylsis of rectangular plates with an applied moment (trunnion loading).

The old faithful Roark has a case for circular plates (6th Ed, Table 24, case 20 and 21) but no such for rectangular plates.

I could approximate by reducing the applied moment to a force couple and using the concentrated loads (one positive, one negative) and the superimposing the results, or go back to first principles and brush up on my differential equations.

Or, ask all the nice folks here if they know of a resource that would mean I didnt have to.

Cheers.

 

[dhengr]

Trunnions, their connections, their base plates, can be all sorts of things. Maybe a good sketch with dimensions, loads and their orientations, connection details, etc. would help elicit more meaningful answers or comments. For all my ranting about always relying on FEA, these kinds of problems lend themselves well to the use of FEA, since we have some trouble braking them down into simple, manageable, parts which can be superimposed with some degree of confidence.

 

[SteelPE]

I thought the AISC had a design guide that handled the design of base plates (Design Guide #1 maybe)? This design guide had examples of how to handle this situation.

 

[JStephen]

The Easy Option: Check a round plate using diameter equal to short side of the rectangular plate, then with diameter equal to long side or diagonal of the rectangular plate, and figure your case is somewhere in between those two results.

 

[shobroco]

CISC baseplate design, (like AISC) should be able to do it for you.

 

[JStephen]

In the 9th Ed. AISC, on 3-106, there is a base-plate design procedure. They assume beam bending under a couple of different load assumptions.

If your trunnion is on a base plate supported by grout or concrete, that approach is likely as good as anything. The Roark cases you referenced are with the plate supported at the edges, which is an altogether different load arrangement. Generally, with a small trunnion and large plate, I would assume that stresses were much higher near the trunnion, so checking bending across the plate width wouldn't necessarily give you a good indication of stresses near the trunnion. In that case, the Roark cases would probably be more appropriate.

 

[Ussuri]

As requested I have attached a sketch with dims and loads. Its nothing complicated, just a plate with a trunnion on it. The approach to date has been as suggested by JStephen using roarks. I just wondered if there Roark type formulae for the rectangular arrangement. In the future I see a little FE model being generated as a check.

Thanks folks.

 

[fasboater]

I hope this helps. Its out of a book called structural engineering formulas by Ilya Mikhelson. There are other formulas for uniform loads with different typs of plate connections. for example fixed, pinned, 3 sided four sided etc.

www.bowerseng.com

 

[rb1957]

that looks the same as Roark (for dist loads and pt loads) ... you can find the original reference online, google "Moody Rectangular Plates" ... there's more there than in Roark, but i don't think Moody considered pt moments.

you could always replace your moment with a couple, maybe 1" apart ? unless the load solutions assume a central load ...

 

[BAretired]

Is your sketch drawn to scale? If so, the diameter of the trunnion appears to be about 250mm. Can the moment be in any direction...or is it a vector parallel to the 1000mm side (using the right hand rule).

Are you considering the circular portion of plate within the trunnion to do a rigid body rotation, i.e. the trunnion is infinitely rigid.

If you are just looking for a safe design, you could use an approximate method of analysis but if you require an elastic solution you will have to resort to more sophisticated methods. The Navier solution comes to mind, but I would need to read up on it as I haven't used it in about fifty years.

BA

 

[Ussuri]

BA, no the sketch is not drawn to scale. Just knocked up quickly to illustrate.

I think for this case I would consider the circular section at the interface between the two to rotate the same amount as one.

I had already read up a little on the Navier solution in Timoshenko theory of plates and shells. I think it would take me some time to develop a solution from first principles. I suspect I will approximate a solution using a couple of hand calc approaches and then use a small analysis model as a comparison.

 

[BAretired]

If you are just interested in strength and not concerned about deflection, you could consider the Yield Line Method. I think that is what I would be tempted to try.

BA

 

[dhengr]

Ussuri:
That is a sketch, but confusing at conveying any real meaning, I imagined that much. I suspect that what BA meant when he asked is it to scale was, are the proportions reasonably accurate. I can see where he arrived at his 250mm trunnion dia., I made the very same guestimate, and I doubt that he was worried that it might be 240 or 260mm. But, now you leave me confused, because if it is only 60 or 80mm, that proportion change does cause one’s thinking to start to change. Furthermore, with the way you have shown your moment, and used the term rotate, I am wondering if the trunnion is loaded like you might twist it as a shaft, thus a uniform shear flow btwn. the plate and trunnion; or is it loaded as a cantilever beam with some load parallel to the plane of its base plate and causing a bending moment in the base plate, thus a shear load and a varying bending stress over the trunnion’s dia., and induced into the base pl.?

How much longer would it have taken to show correct proportions, length and dia. dimensions on the solid/hollow trunnion and a load vector out at its tip, or some point on its length. Think of how much more info. that would have conveyed. You are the one who want some help, so don’t leave us guessing at your detail. BTW, I do think your approach of some simple hand calcs. and a little modeling is the right approach, but only you really know what the loads and boundary conditions really are.

 

[rb1957]

is the moment in-plane or out-of-plane ?

can all four sides react the load, or only a pair ?

 

[Ussuri]

dhengr

The dimensions are correct, apologies for not including more. The diameter of the trunnion is 225mm. On second viewing of the sketch I see why you thought it may be an applied torsion. It is a shaft cantilevered off the plate. It is actually a tubular.

However, it is not for me to ask you guys to do the design on my behalf, which is why I did not want to provide you with all the information in case I overcomplicated things.

But since you asked. I am looking at a design of a structural pipeline bulkhead in a PLET (pipeline end termination structure). The bulkhead is a forging specfically shaped to fit into the PLET structure. The structure is the second end structure (meaning it is the last thing laid down) and is suspended from the installation vessel through a wishbone yoke onto a wire. Hanging of the back of the PLET (supported by the bulkhead) is approximately 800m of pipeline. The load in the bulkhead is the tension transferred through the pipeline back to the vessel and a moment due to the installation. The moment is a function of the the catenary action of the pipe, the hydrodynamic loading on the pipe and the structure and the motion of the installation vessel. We get the loads from the installation analysis doen by the analysts.

Just to enforce the point, I am not designing this instead i am reviewing a design and I'm trying to get into the same ballpark using some simplifications. Once again, apologies for being vague but initially all I was asking was whether anyone was aware of formulae for a rectangular plate subject to a concentrated moment.

 

[rb1957]

ok, you're reviewing someone else's design.

this bulkhead fttg has to be an industry standard, no?

Moody (Engineering Monograph 27) is still available online. he does consider a moment applied to the free edge of a plate. my 2c would be either ...

1) compare to existing designs,
2) model up something to compare with Moody, then model what you really want.

it'd be interesting to see how they calc'd the moment (rigid support or flexible support) and then see for yourself (whether the plate is rigid or flexible) ...

 

[BAretired]

First of all, it is not a concentrated moment as stated in the title. A concentrated moment would be applied at a point. This is applied over a 225mm diameter pipe welded to the plate.

I believe that a the pipe and a 225 dia. section of the plate will do a rigid body rotation under load. The magnitude of the deformation can be assumed as +1 at the top and -1 at the bottom. Any point between will deflect linearly, so the mid-section of the pipe deflects 0.

I would draw assumed yield lines and equate the internal and external energy to solve for the moment per unit length of the plate. You may have to try several patterns because Yield Line Analysis is a lower bound solution but that technique should provide results accurate enough for your problem.

BA

 

[BAretired]

It seems to me that the main force acting on the plate is the tension from the pipeline. The moment is secondary and the pipeline could be assumed pinned at the plate.

It would simplify the problem if you assume a square tube instead of a round one. The sides of the tube should be about 0.8*dia. This gives a better indication of where the yield lines should be placed.

BA

 

[BAretired]

Applied moment = 200kN-m
What is the applied tension?

How can the applied moment be known without knowing the plate stiffness?

BA

 

[rb1957]

by assuming a fixed end ... and, yes, i know what happens when you assume something.