Max ceiling span using 3x2 on 400mm centers

[Dugbert]

I've just built a timber garden room inside a big workshop. I have used 3x2 for the ceiling joists on 400mm centres. I have constructed a 'warm' roof consisting of 9mm osb on top of the joists then 60mm PIR then another layer of 9mm osb (no felt or epdm, just a tarp). There is nothing on the underside (inside, ceiling) of the joists. The span of the ceiling is 3.5m. Do you think my ceiling will sag over time with a span that wide on 3x2? There is nothing stored on the roof and it is completely flat, no pitch. Thanks in advance for any answers and/or advice.

 

[Chunkytfg]

Even if you used C24 span tables show 4x2 C24 as just under 2m at 400mm centres.

I'd say it will sag very much as you seem to have gone about 3x the recommended span even for 4x2!

 

[Dugbert]

Thanks Chunky. Whoops. I'm such a doofus! I used the span tables to build the floor but didn't think to use them for the roof as there is so little weight on it (comparatively). It was only after a bottle of red that I was staring at the ceiling and it dawned on me that the joists are very thin. Then I started thinking about the span table again, hence my post. I made the floor out of C24 4x2 and it conforms to the span table. I then went down to 3x2 for the stud work in the walls to save money and just carried on with that in the roof structure. Ok, so I have some work to do. The span table suggests I will just get away with 6x2 in C24 as it allows a span of 3.57m. So I take my roof off, remove the 3x3 joists and replace with 6x2 and reinstate the roof. I elected to use joist hangers rather than sit them on top of the top plate. Will I be ok to put the 6x2's on hangers or will the 3x2 studs then buckle over time? Short of putting a supporting timber across the room with a supporting pillar in the middle of the room, is there anything else I can do other than what I have suggested? My room is 4.8x3.6m. Many thanks