Two loads are applied to a cantilever beam with a full moment connection (like a horizontal flagpole bolted to the side of a building). One load is in a distance 2 m and the second 4 m from the fixed point but they are applied into oposite direction. The magnitude of the first as well as of the second load is random with a normal distribution. The mean of the first is 10 kN and standard deviation is 2 kN, while the mean of the second is 5 kN and standard deviation 1 kN. Clearly, the mean of the corresponding bending moment is zero.
- What is the probability that the bending moment is in absolute value less than 2 when the loads are independent?
- What is the probability that the bending moment is in absolute value less than 2 when the loads are correlated with a correlation coefficient equal to 0.8?
- Explain which probability a) or b) has to be larger and why.
