Nothching joist to reduce roof height

[Dereekoo]

Eurocodes I think are designed for spreadsheets rather than hand calcs. Though they can give slightly lighter sections than the BS codes if you are into pain and only use a Casio.
The BS timber code is conservative and easier for oldtimers like me to use.
OP could easily do a 35mm notch in a 147 deep joist:

No problem understanding your calcs Tony and the ouputs. But what is the rational behind reducing the allowable shear stress by the 0.76 factor to 0.53N/mm2. As you state, the allowable shear stress for C24 is 0.71N/mm2, why would this not stay the same stress per mm2 whether the depth of the wood left was 112 or 90 or even 50. Having said that I don't profess to understand the rational behind the 6.62 formula, as my spreadsheet gives a Kv factor of 0.04 in formula 6.60 if the notch is vertical and 1.27 if the notch has a 1 in 10 slope (but limited to a value of 1.0 as per formula 6.62) I cannot believe the lower factor can be anyway near right otherwise we would have notched beams failing in shear everywhere? I may have to go back to the drawing board or perhaps spreadsheeet.

 

[tony1851]

For interest, I tried to do that calculation by hand and then remembered why I try to avoid Eurocodes and gave up - life's too short!

But I think the equation for kv will be more accurate as it takes the length of the notch and the inclination of the cut into account.

The BS method, although simpler, may inherently be taking into account the factors above - particularly the square-cut local stress increase - thus giving a more conservative (ie safer) reduction factor. So to address your question; that's possibly why the allowable stress on the remaining section is reduced as the notch depth is increased.

 

[Dereekoo]

Perhaps send a screenshot of a worked formula and I should be able to work it out. If you could annotate, that would be helpful.

Tony's method very much simpler

 

[Dereekoo]

Perhaps send a screenshot of a worked formula and I should be able to work it out. If you could annotate, that would be helpful.

Slight mod to spreadsheet cell 4F, now gives a more realistic result for your case i.e. with a vertical notch, allowable stress reduced to 67% of normal figure which is still greater than the actual stress of 0.31N/mm2 given by Tony's calculation