Chord Forces in Flexible Roof Diaphragm with Large Round Opening

[enigma2]

I have a single story, flat roof structure with an irregular shape--close to an octagon, for the sake of the question. There is an interior courtyard space, open to the elements. The courtyard is round. As a result, the opening in the roof diaphragm is also round. The opening is about 25% of the overall square footage of the structure. I'm trying to determine chord forces. I know how to determine shear distribution and chord forces for rectangular openings. Any thoughts on how to do this for a circular opening?

 

[MiketheEngineer]

Need a whole lot more info - wood, steel, concrete, joists, I-beams, etc., etc Spa

 

[enigma2]

Sorry for the delayed response, I didn't get the e-mail notification. I think I have that fixed now.

The framing is steel--WF beams with 5" HSS columns. 1-1/2" metal roof deck.

 

[DST148]

There is a solved example for a rectangular opening in a flexible roof diaphragm in the Guide to the Design of Diaphragms, Chords and Collectors published by ICC.
In your case the opening is large and circular. Some idealization and simplification of the opening will be required for approximate analysis. Assume the opening is idealized as rectangular. You may treat the diaphragm as a nonprismatic simply supported beam. At the opening, there would be two beams(simplification), one on either side of the opening. The chord forces would be based on the depth of the diaphragm available on either side of the opening. The maximum moment would still be wl^2 /8, w is the uniform seismic load obtained by dividing total diaphragm load / total diaphragm area. Of course, this is a very approximate way of analyzing but should give a good estimate of the chord forces.
As part of detailing, the chords around the opening will have to be carried past the opening.