Nothching joist to reduce roof height

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Hi,
I'm building an extension with a flat roof and I have a question about the joists. Its a cold roof system.
The walls are coming out on the back of the house and the builder put in a steel. Normally the joists fit into the web of the steel and the other side rests on a wall plate.

The problem is that the steel has been put in 100mm too high. (I'm trying to keep the roof hieght to a minimum).

Its a 3m span and looking at the span tables I can put in 6 x 2 timber. To reduce the height, I'm thinking of notching the timber by 25mm which would be placed in the web. Then sloping the joist 1:80 for the rainwater. To ensure I have a flat ceiling internally, I will add the firring strips at the bottom of the joists. This should lower the ceiling by 75mm, which will be acceptable.

Can adding the firring's at the bottom of the joist become an issue for the inspector?
Can I cut a notch in the 6 x 2 because notches cannot be cut 0.07 from the span ?

Plese see illustration attached.
 

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Drop them down on hangers and put the furrings on top.

Furrings below are not an issue, but notching to reduce the depth at the bearing is unnecessary and reduces the effective section depth.
 
The web is 100mm deep. Part of the rsj has bricks on top (existing property), whilst the other section has nothing on top. How will I make the fixings ?
 
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Bolt a 100mm deep timber to the web of the beam and then nail joist hangers to the timber?
 
That looks perfect :) Thank you
I can drill into the rsj and put those bolts in. Looks about 2m appart, if the joists are 450mm centres.
 
That looks perfect :) Thank you
I can drill into the rsj and put those bolts in. Looks about 2m appart, if the joists are 450mm centres.

I’d go for a closer bolt spacing than 2m - M10 bolts at 900mm centres or there abouts.
You’ll want something like a Simpson strong tie JHA hanger if you’re after a long one to give you some offset for your joists
 

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