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.

 

[BAretired]

Looks like the OP has abandoned the discussion.

BA

 

[Ussuri]

Apologies folks I have been away for a few days.

The applied loads are passed to us from the analysts. They make a number of assumptions about the stiffening effect of the structure on the pipeline during the installation, from this they provide us with the loads to be carried. The loads are determined based on the stiffness of the pipe and the structure. The analysis is carried out using a piece of software called Orcaflex.

This structure is the second end structure which means it is the last thing laid down. At one end of the structure you have the pipe running into the bulkhead, at the other end there is a yoke onto which the vessel wire is attached. So the attachment point of the yoke is the 'pin' as its purpose is to allow free rotation of the structure during the lay process. The load in the wire changes during lay, as does the angle. All of which varies the load on the bulkhead. So the wire is eccentric to the bulkhead. All of the load is transferred though the structure back to the yoke.

BA, you are correct that the loading will be a combination of the two. In this case the applied tension is of the order of 1500kN. The bulkhead forging is 150mm thick. So thin plate theory isn't really applicable anyway.

The more I think about it, the more i think that simplication isnt the way to go. Perhaps my best course of action will be to use an FEA based method as I am beginning to come to conclusion that the simplifying assumptions to allow me to do hand calcs will render them fairly useless.

 

[Ussuri]

Attached is a sketch which is hopefully clarifes my waffle above.

 

[BAretired]

I agree that your plate is not a thin plate, but I still believe that Yield Line Theory would give a good approximation of the failure load, although plates of that thickness can have unpredictable cracking when welded.

M = 200 kN-m
T = 1500 kN.

eccentricity = 200/1500 = 0.133m or 133mm

Conservatively, you could consider a point load applied at that eccentricity, then determine stresses using Roark or determine ultimate load using Yield Line. In that way, you would be considering the combination of moment and tension as one eccentric force.

BA

 

[Ussuri]

I may try a number of approximations such as yield line and plate theory just to see what figures they give me. And if supplement that with a small model I should at least have a reasonable level of confidence, assuming off course the results are comparable.

 

[BAretired]

Mf = phi*Fy*Z
For 150mm plate, Z = (150)^2/4 = 5625mm^3/mm

Mf = 0.9(300)5625 = 1.519e6 N-mm/mm or 1518kN-m per meter of plate.

Applied force, P = 1500 kN Pf = 1.5*1500 = 2250 kN

For a concentrated load at middle of simple span of 0.75m,
Mf = PL/4 = 2250*0.75/4 = 422 kN-m

Width of plate required to resist Mf = 422/1518 = 0.278m or 278mm.

If load is moved 133mm from midspan,
Mf = Pab/L = 2250*242*508/750 = 369kN-m
which is less critical than load at midspan.

Plate is adequate even on the conservative assumption of a simple span.

Using Yield Line analysis, I found the plate needs 278kN-m per meter of width for a concentrated load applied 133mm off center.







BA

 

[Ussuri]

Thanks BA, I appreciate your input.

 

[BAretired]

You are welcome, Ussuri.

BA