Based on UK building control guidelines your looking at 600mm or less spacing between joists, using 75mm x 220mm timber with a strength class of C.24.
I wouldnt use anything less than class C24 timber, but it comes back down to what the room will be used for (eg indoor gym). The smallest I would go with would be 47mm x 220mm with spacing no greater than 400mm apart.
I am no architect, but looking at the model I have to get away with 175 your talking about a gable end of less than 3.9M, so thats a massive difference. Is there no way you could drop the ceiling hight below the floor to accommodate?
I just had a quick look for unofficial guidelines, as I would tend to agree 220 is on the huge side, but even looking at this site here, its suggesting 220mm.
No problem Mike, appreciate if you could rate the service received today so I may close this case.
So I may close the case I would appreciate if you could rate the service received to date.
Please could you rate the service received so I may close the question?