rafter roof analysis design

huangyhg

rafter roof analysis / design
i have been asked to evaluate a new room addition on a house.  currently it is framed in, shingles on the roof and plywood on the exterior of the walls.  the municipality requires sealed drawings for structural adequacy.  in the current state, it is inadequate and i am looking for the best way to address it while keeping the cathedral ceiling that the owner wants.  the room is 16鈥?by 13鈥? walls are 2x4 studded, roof is 2x12 rafters on 16鈥?centers with two 2x12s at the ridge.  rafters span the long direction (16鈥?.  there are no ceiling joists, rafter ties, or anything else to resist outward thrust of the rafters.  i am looking for ideas on how to make this existing condition work while keeping as much of the cathedral ceiling as possible.  one idea i was thinking of was to design a sufficient ridge beam to place under the 2x12s at the ridge and support it with posts or columns at the ends.  any thoughts, ideas, or comments would be appreciated.
with such a small roof area you may be able to consider the diaphram action of the plywood roof sheathing as a means to transfer loads as reactions to the end walls.  you must however have a continuous chord at the ridge which you appear to have and a continuous chord at the outer edges of the roof (guter lines).
i would still try to make sure the ridge beam acts as a structural ridge so its deflection is minimized. this way you would only have vertical loads on the wall (no kick-out force) due to dl & snow load.
you could add a collar tie at each rafter, somewhat of a flatended cathedral though. you would have to adjust the height of where it is placed, this would reduce bending in the rafters and make the tie actually a compression   
please note, once you add collar ties, you will have thrust loads at the rafter end pushing out the wall. to avoid that, you need to place them very low. in that case, you won't have a cathedral ceiling
thats right, thanks for that catch.
the ridge beam solution (with end posts) would provide the most open solution.
steel cable or rods could be used for the "ceiling joists" to take the roof thrust without being to visually obstrusive.  the roof rafters appear to large enough that you could probably move the tension ties up a little from the top plate if increased headroom is a concern.
what is the roof pitch and roof loading?
what are the applied live and dead loads?
at about 15 psf dl and 25 psf ll, i'd expect 2 2x12's to come pretty close to working. what grade and species of ridge? the ridge is spanning 13 feet, (rafters span the 16 foot direction) right?.
seems like adding something immediately under the existing ridge would be best way to maintain as much of the volume. (if the ridge is flush with the rafters) if the existing ridge is dropped, could you add another board to each side?
any columns at the ends need to be continuous i'd expect due to the difficulty in bracing at least ne direction.
the post back at the original house needs to bear on something competant for the new load too.