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
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.
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)
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.
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.