Sloped diaphragms have been discussed on the seaint list a couple of times
since early '98, and the threads may be retrievable from the seaint archives.
I've worked the problem out to my satisfaction, and shared my opinions; they
should be included in the archives. I've never seen anything published on
the matter that confirms my approach, so I suggest that you work through it
using statics and some of the following ideas to see what you come up with.
Basic to working out an understanding of sloped diaphragms is that the
diaphragm force is in the plane of the diaphragm. A diaphragm has
essentially zero rigidity perpendicular to its plane. The displacement of a
gabled roof is such that, if there were no interconnection at the ridge, the
two planes of the gable would separate vertically at the ridge. Diaphragm
displacement due to a horizontal force results in one plate having an upward
component of displacement as it deflects in its plane, the other having a
downward component of displacement as it deflects in its plane. The
resultant discontinuity at the ridge is usually not a problem because of the
diaphragms' low rigidity out of plane, so that the plates warp to at the
ridge to accommodate the tendency to separate at the ridge. Nevertheless, I
always make sure that there is some amount of vertical shear capacity at the
ridge to resist the tendency toward discontinuity -- this is more important
than the strap across the ridge that many engineers include in their design.
The shear connections at a diaphragm edge have a vertical component.
(I believe that the vertical component of force in the shear wall applied by
a sloped diaphragm, combined with the peculiarities of shear distribution in
a non-rectangular shear wall make the study of gable-end plywood-sheathed
shear walls worthy of a research project. I don't think it's clear how a
gable-end shear wall works. The inverted condition has proven to be a faulty
structural assembly -- plywood shear walls on sloped and stepped footings
were sometimes disastrous in hillside dwellings in the Northridge earthquake
At an anchored wall, the wall restraint force is the horizontal component of
the force that loads the diaphragm.