11. Component AB is supported by pin at A and cable BC. If the load at D follows a normal distribution of N(350,5²) lb, determine the distributions of x, y, z components of reaction at these support. And if the maximum tension of the cable is 1250 lb, what is the probability for the system to fail?

Solution

Since, the weight of load D follows the normal distribution N(350, 5²) lb, then we could obtain

Thus, we have obtained all the distributions of x, y, z components at support A and tension on cable BC. We have T_BC ~ N(1225, 17.5²) lb, A_x ~ N(-525, 7.5²) lb, A_y ~ N(1050, 15²) lb, A_z=0, M_Ay ~ N(-700, 10²) lb∙f and M_Az ~ N(-1050, 15²) lb∙ft. Ans.

The maximum tension of the cable BC is 1250 lb, then the probability that the system may fail is

Ans.