1-18.    The wall mounted television stand is supported by an arm which has a cross sectional area 625 mm².  There are two normally distributed loads applied to the stand as shown, a television  N and a receiver N.  Determine the probability of yielding failure of the arm AC if the allowable yield strength is  MPa.  Assume, , and  are independent and.

Solution

Sum the forces: The force in AC can be found by summing the forces in the x and y directions then take the moment about point B.

;       

For the probability of failure in AC:

                                                                               (1)

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

 MPa                 (2)

MPa                                                            (3)

Equation (1) can be written as

Ans.