I've always wondered where the limits lie with this too. Here's what I know:
- I've done tons of large, flat roofs with 1/4" per foot, bi-directional structure sloping (deck warping). It's worked fine and, frankly, I can't imagine being market competitive without making use of that.
- I've done a handful of warped decks with 1/2" per foot, bi-directional structure sloping. Again, no problems that I'm aware of.
- Deck warping is really quite a different phenomenon as compared to straight deck bending. Bending is characterized by longitudinal, flexral stiffness. Warping is really about transverse bending of the plate elements that make up the deck profile. If a deeper deck has similar peak and trough plate widths, I would actually expect a deeper deck to be easier to warp than a shallower deck.
- From a constructability perspective, I think that it comes down to whether or not a worker can depress the deck as required with a reasonable amount of effort.
This article gives some guidance for curved deck and comes to the conclusion that 75 lbs of effort is a reasonable bar to set.
- There's no question in my mind that the act of warping the deck induces residual stresses in the deck and, probably more critically, residual stresses in the deck fasteners. I've never considered this explicitly in any of my work and have yet to see evidence of anybody else doing that either. Interestingly, the linked article does suggest consideration of residual stresses in straight deck bending applications.
- Because the nature of deck warping is different than that of deck bending, I suspect that the residual impact on the deck alone (not fasteners) is probably less important than with conventional bending. You'll have transverse flexure simultaneously with your longitudinal flexure. By the book, there will be a Von Mises style stress interaction but I doubt that would be very limiting given that these things tend to fail by way of some manner of buckling long before yield stresses become a problem.
- Back in 2003, I was quite interested in this and created a nifty MathCAD spreadsheet to study the instantaneous slope of a roof when it's warped like this. It's quite interesting. The roof surface will be sloped more like a funnel with things being very steep near the low point and surprising flat near the high point. It makes me question the wisdom of some folks enforcing 1/4" per foot on the diagonal rather than bi-bidirectionally. I'd love to show off my nifty spreadsheet but, unfortunately, it's MathCAD pre-Prime and I don't even have access to the damn thing myself. You can imagine how happy that makes me.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
