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how to calculate the maximum birdsmouth depth?

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The rafter should not be notched in that way as it promotes splitting at the re-entrant corner. Much better to drop the top plate (or raise the rafter) until there is no notch. Then place blocking between rafters to fill the gap.

BA
 
End notches on the tension face should be limited to one fourth the depth of the member. So for a 2x12 you would need about 9" of lumber above the notch. The NDS section (in my 2001 ed) you comment on is for notches on the compression (top) side. If you look at section $.$.3 (in the 2001 might be the same in 2005) it comments on the tension face notches. Look in the Table of Contents under Sawn Lumber for a section on Special Design Considerations

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.
 
woodman- my NDS (05 ed) 3.4.3.2 reads: For bending members with rectangular cross section and notched on the tension face, the adjusted design shear, Vr' shall be calculated as follows...

This 1/4 rule you speak of... is that in the code somewhere or is that just a rule of thumb?
 
The 1/4 rule was in the 2001 NDS and before. Looking at the 2005 NDS it has changed. I will still stick with the 1/4 rule until I run into a problem design and need to look at the new equations.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.
 
Ben29:
BA and Woodman are right on the money with their comments. Look to minimize the birds mouth cut in this situation, not what can the max. be. Otherwise you are introducing cross grain tension in the rafter, right where the horiz. shear is also max., a sure recipe for horiz. splitting up the length of the rafter. This turns the rafter into two independent 2x4's the bottom one being unsupported at the wall. Make the vert. cut 1.5" to match the top pl. of the double top pl. on the stud wall, then a higher vert. cut on the rafter at the outside face of the wall. That’s a very complicated detail. You’ve got enough blocking in there to build another house. Why the double 2x strapping for the interior sht. rock? What are you doing to manage the rafter lateral thrust on the ext. bearing walls?
 
I really appreciate everyone's comments!

dhengr:
Thanks for your input. I'm new to wood design. This detail was approved by my boss so I just decided to go with it. The architect wants to raise the top plate without raising the rafter, thus cutting into the rafter even more than before, that that's when I got nervous and turned to you guys. This is actually the architects detail. I do not know why he needs 2x strapping. We have a steel ridge beam bearing on steel pipe columns at either end. Therefore there is no thrust in the top of the wall, correct?
 
Well, the roof pitch will encourage any snow to slide. This could induce dynamic lateral forces to the rafter.

To mitigate this, I would add strapping over the top of the ridge to connect the rafters on either side.

Mike McCann, PE, SE (WA)


 
Ben29:
There will still be trust to the ext. bearing walls to the extent that the rafters settle in their hangers or the ridge beam deflects, just imagine the geometry, the rafters don’t shorten. And, don’t make a full width/long horiz. seat cut on the rafter at the top of the wall, that is no better. You are still applying the bearing load in a way which imparts cross grain tension to the top half of the rafter, at about mid depth. Archs. do all kinds of crazy things becuase their pencils tell them to do it or their CAD programs make them do it, they have no real sound reasons, they need to fill the space with something. You have to be a bit of an educator and gently explain the errors of their ways. I would lower the double top plate to provide the 1.5" deep birds mouth on the rafter and then apply something akin to a 2x10 (2x8?) rim joist out at the outer face of the stud wall, bevel ripped on the top to match the roof SIPS. I would run the wall SIP’s up to within 1.5" of the underside of the gutter, and install a single 2x member on top of the SIPS to tie them all together, and eliminate the three 2x blocking members at the top of that wall section. You better be very confident in your gutter installer’s capabilities or you could be growing mushrooms in those walls.
 
I have done this in the past and added toenails from the rafter to the face of the double plates to add reinforcement. I have also added a 32" long 2x6 sister to the side of the rafter that was birdsmouthed properly on the plates.
 
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