The OP here with another update. The builder convinced me to make the ceiling 2.6 and thus have no offset, but instead place the joists inside the web of 178 steel.
But he did not use a straight edge to line up the end of the joists and as you may have guessed, he cut 3 of them short! These 3 are only 5mm in the web. I maybe able to move the steel slightly in by 10mm and this will allow the joists about 15mm. As you can imagine I was not impressed
What can I do?
Is 15mm enough? - The builder said it is ok to join the shorter joists by overlapping and bolting it with another 3ft joist, will this work and what will the inspector say ?
I think it always best to place the joist (3 x 7 inch and 3m long) in the web as its stonger, wherever possible. It was suggested earlier in this thread that a piece of timber can be put inside the web lenthwise and a joist hanger added - is this a viable option, rather than the possible 15mm or joining the joists ?
Don't move the steel.
Your builder's idea is OK. Use 8mm or 10mm coach screws to connect the extension piece.
A 40mm bearing on the bottom flange would be OK.
You might need to notch either the top or underside of the timber to fit into the beam.