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No way to get the new joists through a window? Is there no place to put a small hole through the outside wall? I've knocked holes in stucco, removed siding, taken out windows and I'm sure other techniques I've forgotten to get large material into small spaces. If I had to do it in pieces I would use the longest piece I could get up the stairs and use it to span the worst area of sag then fill in the ends. I'd use epoxy to glue them together and lots of screws.
@florida, ok in the worse case scenario you would fill in the ends rather than the location of the worse sagging. Yes, through windows, it is a may be option a the moment.
Thank you for your input
Yes, You want to keep joints as far away from the worse sag, I'd assume the middle, as possible. Actually, I'd assume the joists have probably sagged as much as they ever will. In that case, you're not trying to bear the floor load but simply level the floor and provide some support as a bonus.
I believe code says you can only sister a beam over a supporting post.
Technically a connected (proper splice plate, fixing, etc) beam should be considered as unique piece I suppose. As such I would expect to meet the code if that was the case.
From an engineering standpoint (not a code standpoint), you want to put the joint at the point of lowest bending moment.--As close to the end as possible as others have stated. For a simply supported beam, the point of maximum bending moment is at the centre.--where it also bends the most (sags) and breaks. Try standing on a board. It will break at the point of maximum bending moment, the centre, provided there aren't other weak areas like knots. FWIW, shear would only be a possible mode of failure in a laminated beam where the glue laminations fail.
Insightful. Then, assuming, no chance to have the entire beam upstairs on its entire length (preferable), a butted joint (splice plate nailed) close to the wall where the original joist sits would be the way to go. Would a calculation be required to check from where the bending moment starts changing significantly in order to know roughly the length allowed from end to connection?
I suppose a beam supported in the wall and resting on the mid wall of the house may require the joint at 1/4 of the entire length based on the typical moment behaviour.
how about a 1/4 inch thick steel plate, that might bend enough to get into position?
Can't nail the new floor to that.
fair enough