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RE: Ridge beam/joist analysis

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If the loads to the sloped joist are vertical, and if the reactions at both ends can 
only be vertical, then you can break down the loads, and the reactions, in the 
same way.  That is, along global or local axes.  In other words, the (local) axial 
and shear stresses in the sloped joist can BOTH be resisted by the (global) 
vertical reactions at the wall and ridge beam.  Thus the tension at the ridge 
and compression at the wall referred to by the response below are addressed 
by the vertical reactions.  (Don't get me wrong, I have nothing against tying the 
system together with straps.)  Without a ridge beam, if only a horizontal 
reaction can be provided at the ridge, it's a different story, and, without collar 
ties, that horizontal thrust won't be resisted by the (vertical only) top plate 
reaction, and difficulties may ensue.  As the ridge beam deflects vertically, the 
walls must displace outward a bit; however, the ridge still provides the vertical 
reaction, so the system still works.

Jon Brody, SE
San Francisco

> Yes, the analysis is a bit against typical residential 
> practice.  Re-orienting your vectors will indicate tension at the
> ridge and compression at the wall.  The key is designing for the
> tension joint at the beam. As long as the rafter (joist) can't pull
> away from the ridge beam, the deflection of the entire system is
> limited by the deflection of the ridge beam.  Lateral deflection is
> often taken as zero, assuming an equal w on both sides of the roof
> (equal and opposite horizontal forces cancel at the ridge), leaving
> only the trigonometry of determining the lateral deflection of the
> system due to vertical deflection of the ridge, if small top-of-wall
> deflections are of concern.  Strapping, face hangers, and crossing
> rafters (above the beam) & nailing together are all ways to tie the
> system together (though toe-nailing <shiver> is the residential
> favorite).

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