10. A bolt B holds the beam up and the bracket bear against the smooth wall at A. If the allowable horizontal and vertical loads of the bolt B are 1200 N and 220 N respectively, what are the probabilities that the actual horizontal and vertical forces of the bolt exceed their allowable forces? The beam supports two vertical forces F₁ ~ N(16, 1.0²) kg and F₂ ~ N(5, 0.125²) kg. F₁ and F₂ are independent.

Solution

Since, F₁ and F₂ follow the normal distributions that are independent, we could obtain

Therefore, we have the forces distributions as A_x ~ N(1063.4, 56.4²) N, B_x ~ N(1063.4, 56.4²) N and B_y ~ N(206, 9.9²) N. Ans.

The probability of bolt to fail in the horizontal direction is

Ans.

The probability of bolt to fail in the vertical direction is

Ans.