1-22.  A normally distributed weight  lb is supported by two cables as shown.  The yield stress of cables is  psi and they have a diameter of 0.5 inches.  What is the probability that the weight will fall?  Assume  and  are independent variables and .

Solution:

Sum the forces: The forces F_BA and F_BC can be found by summing the forces in the x and y directions.

Since W produces a larger force in the cable AB, we use it to show:

Since  lb, and  psi are independent,  also follows a normal distribution.  .  Also,  in².

 psi

psi

Equation (1) can be written as

Ans.