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[SEAOC] Basic Roof Rafter Analysis Question

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This may appear to be a dumb question but I'll ask it anyway (sans
I've been asked to check an existing roof structure to determine if it can
be loaded with a new full weight mission tile roof - or at worst a
lightweight equivalent (7.0 psf).
The roof is a Cedar Shake over 1x skipped sheathing and building paper. The
rafters are 2x6 DF #1 spaced at 24" o/c. The home is approximately twenty
years old. The rafters span 20 feet. They are tied by 2x6 ceiling joists at
24" o/c.
Approximately 5'-0" from the ridgeboard is a 2x6 support running continuous
for the length of the roof. The support is braced diagonally with 2x6 studs
to an interior wall located below the ridge. The interior wall appears to
be bearing - supporting the ceiling rafters (ties).
Originally there was a 32" eave at the end of the roof rafters - but this
was removed to allow for a room addition to be added.

Analyzing the 2x6 roof rafters at 20 feet clearly show that the member is
overstressed for the original shake roof. Obviously the support placed at
5'-0" away from the ridgeboard is considered as a third support. If I did
consider this to be a reaction, the rafter then becomes sufficient for a
heavy tile roof. HOWEVER, I am not comfortable with this since the 2x6
support is not bearing directly above post, but rather is framed at a 45
degree angle back to the interior wall.

My dilemma is this: The city of Los Angeles considers Cedar shake roofing
to be weighted at 5 to 6 psf (assumed wet load). I would feel more
comfortable recommending the roof for a 7.0 psf load but am not sure how to
prove the intermediate support. Space is limited to crawl into to verify
the nailing of the stud from the support to the intermediate wall.
Have any of you considered a problem such as this. Cedar is no longer an
acceptable material and the roof must be sheathed with a Class 'A' or 'B'
fire retardant material. Since the slope of the roof is around 3:12 (20 psf
live load) and the neighborhood is an intermediate class construction,
shingle is not an alternative. The owner is considering an Eagle
Lightweight roof or if justified, a heavier tile. He may be willing to
either increase framing or introduce a new intermediate support. Obviously,
I don't want to make him do more than is economically feasible.

Your comments would be very helpful on this issue.

Dennis Wish PE