gusset equivalence 1

[Wantstolearn]

Here is the scenario, assume there is a pipe (any diameter) that is welded to a flat plate so that pipe protrudes on either side of the plate. Now if one end of that pipe is loaded with a load and a moment, I have been able to determine the stresses at the pipe/plate interface through a nozzle loading analysis.

I am having difficulties when we change the above scenario and install 4 gussets between the pipe and the plate (continuous weld) and apply the same loading conditions. Obviously, there is an increase in strength with the addition of the gussets. The question is how much and is there any sort of assumptions that I could make to take and "equivalent pipe diameter" which could be analized using the same process as with the non-gusseted pipe?

The overall goal of this analysis is to determine if the stresses at the nozzle/plate interface exceed the allowable stresses in the materials.

Any help would be greatly appreciated.

 

[prex]

There are too many parameters playing a role in such a problem: number of gussets, radial projection of gussets to pipe diameter ratio, thickness of plate...
My first attempt choice would simply be the circle enclosing the gussets, but, of course, with only 4 gussets and a possibly low thickness plate this is not necessarily very representative.
A comparison criterion for you problem could be to take a pipe flange with the same pipe diameter as your nozzle, a comparable pressure rating, and take the number of gussets equal to the number of bolts and the gusset enclosing diameter equal to the flange outer diameter. However, for the comparison to be complete, flange thickness should be the same as your plate, and I'm afraid this is not the case.
Note also that if you wanted to do a detailed FEM analysis of your system, you would find very high stresses at gusset tips: these wouldn't be relevant to static resistance, but would impair the fatigue resistance of the item. In fact your statement that there is an increase in strength is not necessarily true when fatigue is concerned. prex

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[RX]

What I used to do when involved with pressure vessel nozzle design was to resolve the moments and apply them as a 'pulling' and 'pushing' load onto the plate on either side of the nozzle. Thus the moment load was taken out of the nozzle, which was then analyzed using WRC 297/107 methods for the remaining shear/axial loads.
Using WRC 107 the shell plate stresses were then analyzed for the gusset loads.
This method is not exact, and technically incorrect no doubt, but it was accepted nonetheless in the absence of anything better. Having said that, I am now involved with FEA design, and that's probably the best way to analyze your situation as noted by PREX.

 

[dvd]

If you calculate the moment of inertia of the section at the plate (4 gussets radiating outward from the pipe) you could find an equivalent moment of inertia for some larger pipe and then use that pipe size in your calculations.

Bear in mind that this section property is only valid at the plate, since the gussets taper down to the pipe diameter away from the plate. You could derive an expression for the moment of inertia as a function of distance away from the plate. But there are several assumptions that you could make to speed things up, one being to use half of the gusset height in your section moment of inertia calculation and apply this moment of inertia to the length of gussetted pipe.

You could try using REGION and MASSPROP in AutoCAD, but be careful that you understand why you get the results that you do.Make sure that you calculate the properties for the pipe and not a solid circular section. You will need to subtract the inside diameter moment of inertia from your section results. Do a sample calculation using a hollow shape with known moment of inertia to make sure you do it right.

 

[Wantstolearn]

Thank you all for the replies.

DVD: I used your sort of thinking with respect to determining a larger size of pipe based on the moment of inertia. To me that seemed logical, but I would prefer if there was some reference that I could look up in order to confirm our thinking. Any suggestions?

 

[dvd]

I can't cite any references to you. If you have high cyclic loading be careful about all of the welding.

 

[prex]

I don't agree with dvd's method: this may be OK for checking the resistance of the gussets themselves or of their welds (and these are not normally critical points), but fails entirely in checking the stresses in the plate: these are mainly in thickness bending stresses, whose distribution is highly affected by the number of gussets. prex

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