How can I analyze the stresses in a closed ring girder?

[jamesm]

I could use some guidance as to how I would analyse the stresses in a ring girder similar to the one shown in the attached picture. I have found the stress in the columns that support the ring but I do not know how to find the maximum stress in the ring. The best I have been able to come up with is that the stress = reaction force from column / cross-sectional area of the ring, (σ=F/A) However I am sure that there is more to it than this.

Another thing that I want to consider is the transverse force from the friction at the slide bearing / rocker. I believe this will cause a moment where the columns are welded to the ring.

Thank you

 

[SteamKing]

It's not clear what loads are imposed on the ring girder.

Is the ring girder some sort of support, like for a pipeline perhaps?

In any event, curved girders require a slightly different analysis technique than that used for straight beams.

http://courses.washington.edu/me354a/Curved Beams.pdf

Google 'curved beams' to find similar pages.

 

[jamesm]

Thank you for the link.

The ring girder is holding up a large pipeline filled with water. The most significant loading on the ring girder will be from the weight of the contents of the pipe and a possible moment caused by the friction resisting the columns tendency to slide laterally. (as the pipeline expands and contracts due to temp. change and Poisson's effect)

I found these equations in the link that was provided. They seem to be what I'm looking for however I cannot find what should be used for the bending moment 'M' in the equations.

σ=(Mc_i)/(Aer_i) and σ=(Mc_o)/(Aer_o)

 

[SteamKing]

I think M is a pure bending moment and is as shown on p.2 of the linked document. Most of these curved beam problems use a load suspended from a hook as an example, where the pull of the load is trying to open up the eye of the hook.

This link:

http://nptel.ac.in/courses/105106049/lecnotes/mainch10.html

shows a little more development on applying a pure moment and an end load to a curved beam. I haven't found a similar set of notes about a distributed loading, however.

 

[SteamKing]

This article gives a treatment of the stresses imposed on a closed ring by a force applied across the diameter of the ring.

http://elearning.vtu.ac.in/12/enotes/Des_Mac-Ele2/Unit1-RK.pdf

See p. 58 and below for the discussion of the analysis of closed ring girders.