The bending moment at the midpoint of the load P is M=PL/2, where L is the length.
The bending stress is S=M/W, where the section modulus W=bh^2/6. b and h are the width and height of the beam.
Therefore, S=3PL/bh^2. P in Newton and all dimensions in millimeters will give you the bending stress in Megapascal (MPa). S should be less than the bending strength of the beam.
S = 24
L = 4300 mm if you have that roof slope
b = 45 mm
h = 220 mm
24=(3*P*4300)/(45*220^2)
24=(3*P*4300)/2178000
24*2178000=3*P*4300
52272000/4300=3*P
12156/3=P
4052=P
Thus, a beam can withstand a load of 405kg in the middle with a span of 4300 mm.
If you want to know how much it can support per m^2, simply multiply 405 by the number of beams and divide by the square footage of the roof. If you use cc 600 mm, the roof can support a load of 160 kg per square meter.
