14. Pins B and C can only support horizontal loads of 130 lb. What are the probabilities of failure if F ~ N(100, 2.5²) lb.

Solution

Consider AC,

Consider BC,

The external force T follows the normal distribution N(100, 2.5²) lb, thus we have

Consequently, we have the distributions of the horizontal and vertical components of forces at pins B and C. B_x ~ N(120, 3²) lb, B_y ~ N(50, 1.25²) lb, C_x ~ N(120, 3²) lb and C_y ~ N(50, 1.25²) lb. Ans.

The probability of pin B may fail is

Ans.

The probability of pin C may fail is also

Ans.