Strengthening weakened joists so can floor loft

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Hi
The building is free standing, breeze block walls, tiled roof, garage building where a roll down door was fitted at one gable end.
In order to make room for the fully retracted door, the middle 50% of the first two joists had about 2/3rds of their width cut away, Leaving just the top 1/3rd to provide the bracing.
They could have gotten away with taking less than 50%, I reckon.
All the joists are 2" by 8" and 18' long. There's 16" separation, mid-joist to mid-joist.
It's been this way for a long time and there's no visible problems with it.
But now, I'd like to floor the loft space for storage and these 2 joists are a concern.
I would not fancy putting much weight on either.
I was wondering if strengthing them with full length 2" by 4"s, one on either side of the existing joists, parallel to the top edge would be suficient to strengthen the cut away joists to carry a load?
I'd also provide support for the 2 by 4s on the wall at each end.
I don't know if I would even use any screws to join the cut away portions of the joists to the 2 by 4s for fear of weakening those sections further, I'd possibly just attach in the full width parts fo the joists?
I'd be very grateful for any criticisms or advice.
 
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I doubt that would help much. Maybe some 4x2 steel angle over lapping by 600mm either side, or some timber hangers from the ridge if they wouldn't get in the way of your storage.
 
i wonder iff 6x2" flat well scewed to one or both sides wall to wall might do ??
 
The issue as I see it is the length of the joists. In an ordinary floor an 18 ft span would require something like 10 x 2in C16 joists. OK, so you aren't going to load to quite the same extent, but even the original 8 x 2in joists weren't that strong, so adding 4 x 2in stuff is going to do very little to strengthen the existing. What you need is depth, not width. Similarly adding steel angle brackets will only add weight. It won't do much i terms of strength. TBH if you can sister the existing joists with something like 8 x 2in stuff, but lifted further up to give the required clearance beneath and if needs be by reducing/bevelling the ends to get clearance beneath the roof (assuming a pent roof) then that might work. If at all possible use a structurally graded timber (C16 is generally the lowest grade) rather than low cost carcassing (whitewood/pine) because it is stiffer and will bend less under load
 
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Thank you all very much for your replies, sorry for being slow acknowledging them.

I think I am going to go with JobAndKnock suggestion of sistering the joists and keeping the weakened joists from getting any weight at all put on them.

JobAndKnock, you put the wind up me when you mentioned that the existing joist dimensions might not be adequate for the span of the garage, this was something I'd never even considered!
So I had another look and I think I might just be OK.
While the joists are about 18' maybe a bit less, as I said, the wall to wall distance is only 16', that's the figure I should have quoted.

Also the joists themselves are 8.5" deep and just about a full 2" thick. The wood looks very good quality (to my layman's eye) so I'm hoping it's C24 quality which I think would work (according to a table here).
It suggests that with C24 wood, 47mm x 220mm (2" by 8.5" approx) and 400 mm centres (15.87") you can span 4.85m (16')
Also I sat my fat a**e on the middle of one and bounced around a little and it felt solid.
Finally when they built the garage they put a couple of Velux windows in the roof like they were planning for an attic conversion one day, so if they did that then I'm hoping they did the same with the joists!

One more question if you don't mind.
Since this is a garage and there's no insulation at all can I just lay 3/4" tongue and groove directly on the joists and use about 1.75" screws to attach it or is this a bad idea?

Thanks again
 

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