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Flange Strength Calculation

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SteveyB

SteveyB

Petroleum
Nov 27, 2011
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Hello,

I wonder if anyone can give me some help. I am trying to determine the strength of a flange which is subject to an external bending moment. The flange is rigidly supported at the necked portion and has a bending moment applied at the flange face. In essence it is similar to a pipe flange which has being subjected to an external bending moment. I have looked into various piping textbooks and Roark's but cannot seem to find anything. If anyone could point me in the right direction this would be most appreciated.

Thanks
 
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If you're talking simple bending of the flange, as in plate bending I would just check it old school.

Your bending moment = PL
Consider some effective width of your flange depending on how the load is applied. If it is from a pipe clamp, I would take about 3" of flange in bending.
Your section modules Sx= bd^2/6 where b=3"(assumed tributary of flange); d= flange thickness
Your bending stress is of course M/S.
Your allowable bending stress will be 0.75*Fy. If not sure about the beam run with 36 ksi for a steel beam, and allowable bending stress of 27 ksi.

Not sure how heavy your load is, but the beam itself should also be verified for possible torsional loading and additional stresses to the bottom flange from the bending applied since you're introducing bi-axial bending. If you can, apply the load to the existing beam at the 1/3 point instead of midspan and the additional check can most likely be avoided.





 
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Oh I see.. a flange for a pipe, not a beam.

If you're applying a torque to the flange, then the critical section is the pipe beyond. Apply statics to your pipe section where Sx = pi (d^4-d1^4)/32d
use same principle of M/S.
 
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The stress in the pipe may be calculated as indicated by TDengineer above. Stress in the flange will depend on how the moment is applied to the flange.

If it is applied by a weld around the perimeter, the weld will carry a variable line load. The line load will cause variable bending moments around the flange plate which will result in variable bending stress in the plate with maximum value at 90 or 270 degrees to the applied moment vector and zero at 0 or 180 degrees to the moment vector.

If the moment is applied in some other way, the above will not be true.

BA
 
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Again thanks for the responses. The moment will be applied via a bolted array. So the moment should create a similar loading as mentioned by BAretired. I am basically trying to find a method of sizing the flange. Does anybody know how to go about calculating this scenario.
 
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Is the moment applied by another flange identical to the one shown? If so, the deformation will be the same in each flange. Otherwise, the difference in rigidity needs to be considered.

The bolt array is presumably a bolt circle. The number and size of bolts needs to be specified as well as the diameter of the bolt circle.

Are the flange faces tightly abutting? If so, you will have prying action which amplifies bolt tensions and makes the analysis extremely complicated.

On the compression side of the flange, bolts will not be carrying any load. Compression will be carried by bearing on the contact surfaces of the flanges.

Analysis would be tedious and difficult by hand. It could be performed using finite element methods. There may be simplified approximations as well, but I am not aware of any.

Perhaps the mechanical guys could be of more help.





BA
 
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There was a good article on this in AISC's journal some years back:

'Design of Tension Circular Flange Joints in Tubular Structures', by: Cao & Packer. [1st quarter, 1997].

The article appears to focus on flange to flange connections, but I would assume it could be adapted for other conditions. (I'm not sure if you have pipe to pipe, or pipe to concrete, or whatever.)
 
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The components will be mounted flange to flange and bolted. I realise the strength of the flanges will increase from the combined stiffness of the bolt and adjacent flange, but generally I have no control over the mating flange. The current method we use is FEA to check the flange strength as BAretired as already mentioned, but this can be quite a tedious an long winded method. Hence I was after a manual means of checking the flange strength which would take less time to verify. It is obviously quite a complex problem and difficult to calculate otherwise there would most likely be an abundance of information available, a bit out of my league though I'm afraid.

Thanks for the reference I will also have a look at this.
 
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I'm I missing something (prolly as I read thru this pretty quickly) or is this just a baseplate with a pipe column subject to a bending moment?
If so there is a publication for monopole structures and there base plates that may be applicable. Let me know if this is your problem and I'll see if I can find the publication.

EIT
 
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One way to simplify the problem, although it may not be consistent with the prototype, is to assume that the bolt forces act alone to produce the moment, i.e. the flanges do not contact each other (perhaps soft gaskets between and washers around the bolts). The section modulus for the bolt circle can easily be calculated and from that the variable bolt forces found.

Bending in the flange could then be approximated by considering the maximum bolt force acting eccentrically to the fillet between flange and pipe. The resulting moment would act over a chord length equal to bolt spacing reduced by the factor Dp/Dc where Dp and Dc are pipe outside diameter and bolt circle diameter respectively.

The above would be a pretty crude but conservative way of checking the strength of flange.



BA
 
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The current method we use is FEA to check the flange strength as BAretired as already mentioned, but this can be quite a tedious an long winded method. Hence I was after a manual means of checking the flange strength which would take less time to verify. It is obviously quite a complex problem and difficult to calculate otherwise there would most likely be an abundance of information available, a bit out of my league though I'm afraid.

Thanks for the reference I will also have a look at this.
Click to expand...

The reference I mentioned has some design aids/charts that speeds things up. (In fact they have some in the elastic range and plastic.)

 
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I agree with BAr that assuming the forces are transmitted through the bolts only is a safe simplifying assumption. Since you have no control over the mating flange then I suppose you can assume that the mating flange is identical to your flange. Any weaker and it will fail before your flange. Any stronger and your design may not be conservative since your flange would receive something like lateral stability bracing from the mating flange.

This leads me to believe that the NRX formulations for ungrouted round base plates cannot be used unmodified or perhaps need a sensitivity study. The NRX relations for a base plate bolted to concrete likely neglect flexibility of the concrete which is like having a mating flange that is much stiffer than your flange which we have already said may be unconservative.

Somehow I think an FEA solution is the simplest approach unless you have a very specific empirical formula.

 
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How do you go about performing a yield line analysis? I would hopefully like to try and validate some of theses suggestions against FEA and see how they compare.

Thanks for the responses guys the information is great.
 
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