1-19.    The Flying Saucer café sign has a center of mass at G which has a normally distributed load  N. It is suspended from cables AB and AC as shown.  If the allowable yield stress in both cables is  MPa, what is the required minimum diameter of the cables so that the probability of failure is less than 10^-3?  Assume  and   are independent.  ,.

Solution

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

We choose the probability of failure of AB due to the fact that it carries more of the weight:

                                                                                             (1)

Since  N, and  MPa are independent,  also follows a normal distribution.  .

 MPa                                         (2)

MPa             (3)

Equation (1) can be written as

From (1), (2), (3), and some algebra we obtain

 mm² Ans.