Cupola Structure Question

[Heldbaum]

Hello guys,

I have a question regarding cupola structure that I work on right now. It's a wood structure with two steel beams (compression and tension ring beams). Please see attached two diagrams, axial force and bending moments. The model is simplified for calculations' sake. Horizontal rafters as modeled as pin connected with two steel beams. Is it possible to completely eliminate bending moment in the tension collar beam, or will it always act as a beam considering the fact that load is applied to the surface etc..? Thanks

 

[Heldbaum]

Axial Force

 

[Labs763]

If I understand you correctly, I think the only way to truly eliminate out of plane bending moments is to have a perfect circle.

 

[OldBldgGuy]

I might be misinterpreting but I think you're looking at the lower rafters bearing on the ring beam at the base of the cupola. Bending in that ring beam between the corners of the cupola/hip rafters might be negligible or might be significant but without a dimensioned plan it's hard to say.

 

[Heldbaum]

Labs763 - That's what I was thinking too

OldBldgGuy - Yes it's correct, I am looking at the base of the cupola. The cupola's 'diameter' is roughly 28 feet. Each beam creating octagonal is approx. 11 feet..With the model I've created for now, I am receiving bending moment of 13k-ft which shall be accounted for.

I am just wondering if I don't miss something (boundaries conditions?) that would decrease the bending moments so only tension/compression could be accounted for..