Can I reinforce timbers by adding depth?

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I'd like to convert a lean-to roof to a vaulted ceiling. The exiting rafters are undersized as it is, but I end up with double the permitted deflection under a point load when I consider the brittle finish.

Would it work if I fix parallel timbers on the bottom of the existing, like this?:

upload_2020-3-17_11-19-46.png

The existing timbers are well within limits for shear, so does this mean the extra timbers can stop short of the bearings?

Adding parallel timbers to the sides I think is more common but they would be harder to cut and fit, and they would increase thermal bridging through the insulation.

I realise it would be ultimately up to Building Control whether to accept it, but it would be helpful to know if I could at least propose this solution.

The existing rafters are approx. 100x50mm. The span on slope is 3000mm. I'd add 47x47mm timbers to the bottom.

Thanks for any advice!
 
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In principle that would work, and as you say you don't need to take the additional timber to the ends because it's only shear
at those points.

As long as you have sufficient screws in terms of spacing and guage, it will work. BC might ask for figures, but it's fairly straight forward
to show that the screws can accomodate the shear forces arising.
 
As long as you have sufficient screws in terms of spacing and guage, it will work. BC might ask for figures, but it's fairly straight forward
to show that the screws can accomodate the shear forces arising.
Thanks for this. The screws at either end will see the most extraction force but I can specify a type that can take all the shear in a single fixing.
 
Not 'extraction' force but shear force; but you just space them closer together near the ends, so that the shear is spread over several screws.
 
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I remember doing a job like this a few years ago, so it is possible.
We used joining plates at regular intervals as specified by the structural engineer.
 

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