Answer
See answers.
Work Step by Step
The area per support is A = (0.040m)(0.090m)=0.0036 square meters.
Assume we need N supports.
The applied force is the roof’s weight.
With the safety factor of 12, the maximum compressive stress is 1/12th the compressive strength for wood, which is $35\times10^6\;N/m^2$.
$$\frac{F}{NA}=\frac{35\times10^6\;N/m^2}{12}$$
$$N=\frac{12F}{A(35\times10^6\;N/m^2)} $$
$$N=\frac{12(13600\;kg)(9.80\;m/s^2)}{(0.0036\;m^2)(35\times10^6\;N/m^2)} =12.69$$
We need more than 12 supports, and need the same number of supports on each side. We need 7 supports on each side.
With 6 gaps between the 7 supports, their spacing is (10.0m)/(6) = 1.66 meters apart.
