This is a bit of an odd problem since my wife and my Chinese father-in-law have built an open tool shed of 15 sqm with a flat roof.
I haven't participated in the project except that I've advised the southern Chinese that the snow load can be up to 2 car weights. (They build without designing, measuring, or calculating materials, they just start building).
Apart from small details, like the roof pitch being 2.5°, the roof joists seem significantly undersized. These are 3-meter 120mm joists but all have been sawed down right in the middle to 50mm (notch for an unnecessary 90° beam that has no function but just hangs there in the roof without ground support). The joists only have ground support at the outer ends.
p=2000; [N/m^2] Snow load Stockholm
b=0.045; [m] Width of the joists
h=0.05; [m] Height of the joists (in the middle at the notched place)
L=3;[m] Length of the joists
B=0.95; [m] Typical distance between joists (it varies)
q=L*B*p; 5700 [N] Total snow weight a joist is subjected to evenly distributed on the joist.
w=b*h^2/6; 0.000018750 [m^3] Bending resistance of the joist
m=q*L/8; 2137.5 [Nm] Bending moment in the joist
s=m/w; 114000000 [N/m^2] Maximum stress in the middle of the joist.
s=114 [N/mm^2]
"According to the table, regular structural timber (standard quality) can handle 6 N/mm2 if the beam is standing edgewise and bending. (This value is the permitted stress and okay to use as max stress)."
The tool shed is therefore underdimensioned by 19 times.
My 70s veranda is underdimensioned by 3 times, and without calculating, I've worried a bit when there was 1 m of snow.
If the above is correct, and the allowed stress is 6 N/mm2, which of course includes safety margins,
Then I wonder at what stress can one expect the joist to break (nominal breaking stress)?
Another question: What would you do about the problem, any ideas?
Yep!
It will undoubtedly be broken where there's only 5 cm of material.
I don't even need to try calculating that.
Another question: What would you do about the problem, any ideas?
Tear out the notched 45x120 and replace it with a whole one, preferably 45x170.
Any other way to brace must be both more expensive and more complicated.
Yes, perhaps except for putting a couple of vertical pillars under the beam that lies in the notch.
Would probably have been more worried that the shed doesn't seem to be braced against the wind... big risk of it blowing over before the roof collapses. No cross bracing anywhere?
Would put some crosses for wind bracing, and then complemented with a couple of posts under the main beam.
Would probably have been more worried about the shed not seeming to be wind-braced...big risk that it will topple over before the roof collapses. No cross-bracing anywhere?
Would put some cross for wind bracing, and then complemented with a couple of posts under the middle beam.
Sorry, I didn't draw the entire construction. It's braced with battens that are screwed into the nearby trees.
I know exactly what I would have done. I would have said, "That will collapse this winter."
Then I would have gone inside, had a cup of coffee, and waited for winter.
...but then I'm an annoying bastard too, so that's probably not good advice.
Well, I wasn't planning on doing anything, but...
There's a problem with this, that it could collapse when someone is under the roof fetching wood or playing there.
It's also politically incorrect and a bit difficult to fence off the structure during winter so no one can actually go in there.
