Reduced wood beam depth 2

[HofOblivion]

Hi,

I designed a new 3.5"x11.25" ceiling beam in an existing house spanning almost 20 feet and the beam supports roughly 8 feet of ceiling tributary loads (10 psf of dead and live loads).
Initially, we were going to replace the existing ceiling beam with a new one and it would've been exposed and protrude below the ceiling finish.
Now, the owner wants the bottom of the beam to be flushed with the ceiling. The existing roof rafters are 2x4s and we will have to reduce depth tremendously by the support.
Flexural and shear demands aren't critical but the deflection is. Is reducing the depth by 7.75 inches even possible? Attachment for a quick sketch.

Roof slope is 7:12 if that helps any.

 

[XR250]

I believe the rule of thumb is 0.6h remaining or 7.2". That being said, your reaction is only 800 lbs. Dunno if I would worry about that.
None of this will affect your deflection in any meaningful way.

 

[jayrod12]

Since you're flushing the beam up, could you go to a 3 ply that's shallower? What does it frame into on the other end?

 

[HofOblivion]

I believe the rule of thumb is 0.6h remaining or 7.2". That being said, your reaction is only 800 lbs. Dunno if I would worry about that.
None of this will affect your deflection in any meaningful way.

The rule of thumb helps. I've mostly allowed ripping 2"~3" before, but not to this magnitude. Low reaction and minimal shear demand are why I'm even trying to determine if it's viable at all.

Since you're flushing the beam up, could you go to a 3 ply that's shallower? What does it frame into on the other end?

Shallower ply is doable. The beam sits on a post at the other end and is located in the middle of the building, so the depth is not a concern on the other end.

 

[MotorCity]

Since the rafters are only 2x4's, you could look into installing plywood gussets on each side of the joint where the rafter intersects your new beam (using blocking if needed to match member thicknesses). Create a truss of sorts and use the gussets to create a large heel. If the notch in your new beam is ok for shear and flexure, it will have negligible impact on deflection since it is so close to the support. That said, I would check with the manufacturer to see if the notch dimensions are acceptable.

 

[KootK]

Keep an eye on any uplift as that puts your notch-ish thing in tension.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.