Notched vs Tapered Timber beam shear strength 2

[Greenalleycat]

I'm dealing with a pretty common scenario in residential alterations: putting in a new timber beam that terminates at the perimeter walls
Obviously I can use steel and avoid this problem, but timber is significantly more preferred in alterations for the flexibility and ease of connecting existing structure to it
The problem is that my beam is 300mm deep in the middle and I have somewhere between 90mm and 150mm depth (TBC) at the perimeter due to the roof line closing that gap down
Pic below for reference

Notching beams absolutely destroys shear strength - using a notch calculation I don't even get close to working
So the question is: is tapering a beam the same as notching it?
Our code has a really shitty section on this that only has moment calculations from tapered beams, and only if the slope of the taper is less than 10 degrees
It has no wording on a >10 degree taper or on shear strength...so I'm not sure where that kicks us to

Anyone got any thoughts on the effects of taper vs notch on timber beam shear strength?

 

[driftLimiter]

Im not familiar with these notch shear strength calculations you mention but my understanding is that the notch profile is what significantly reduces the capacity. The sharp transition and associated stress concentration tends to split the member.

I found this but tbh there too many differential equations for me today. Perhaps this will assist in the theory part.

 

[Eng16080]

I'm guessing this U.S. code isn't applicable to you considering you're using metric, but the following snippet answers your question:

A gradual change in cross section compared with a square notch decreases the actual shear stress parallel to grain nearly to that computed for an unnotched bending member with a depth of dn.

The value "dn" noted is equal to the depth of the member at the inside face of the support. From there, per the NDS code, shear stress is: fv = 1.5 * V / (b*dn)

 

[Greenalleycat]

Perfect, I think that nails the answer.
Don't know why they didn't just include that in our code too...

The 1.5 factor I'm pretty sure is on the opposite side for us - we take the shear area as 2/3 of the gross area

Thanks mate

 

[Eng16080]

Glad to help!

 

[BAretired]

It is not really a taper versus notch. Dropping the beam down with a notch at the wall is much worse than the detail shown because of the stress riser in the sharp notch. Dropping the beam down and supporting it with a beam hanger (no notch) would seem better. If the beam can't be dropped due to limited headroom, use steel.

 

[Greenalleycat]

A notch won't work anyway as it has to follow the roof profile so it can only be a taper
Dropping down no good - talked through the option of a bulkhead with the client but it's through a living room so it would look pretty bad
I could do steel - the client and builder are open to it but the builder obviously prefers timber so I said I'd look into it
If I spec a channel they'll go with it, but I wanted to be fair and give it a go in timber first

 

[BAretired]

If shear is okay at the inside face of wall, using the depth at that point, it should be okay, but I can't prove it.

 

[WestLevel]

A notch is not good cause it puts tension perp to grain. Very bad. The notch usually starts to split just from shrinkage and then loading it will progress into the span.

This tapering is on the comp side so I am not sure this rly matters off the top of my head.

If you are concerned why not nail some plywood on the sides at the supports as shear reinforcement.

 

[Stress_Eng]

This may not be relevant, but have you had a look at shear in non-prismatic beams? It may be worth just checking.

 

[Smoulder]

No big reduction for notch on top because it doesn't fracture. It's closing not opening.

 

[SE2607]

The reference I use for these conditions is NDS 3.4.3.3:
V = 2/3 x Fv' x b x [d-(d-dn)/dn]e if e < dn
or:
V = 2/3 x Fv'/(bdn) if e > dn

where de = the depth of the section at the inside face of the support
and e is the distance between the beginning of the bevel to the inside face of the support