1-17.    The supporting wheel on a hospital bed is connected to the leg with a 5-mm-diameter pin as shown.  If the wheel is subjected to a normal force N, determine the probability of failure of the pin which has an allowable shear stressMPa.  Neglect friction between the inner bed leg and the wheel shaft, and assume  and  are independent. 

Solution

Internal loading: The shear force developed on the two shear planes of the pin can be determined by the force equilibrium equation.

Average shear stress: The area of the bolt mm².

We obtain

Probability of failure:

        (1)

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

 MPa                                      (2)

MPa (3)

Equation (1) can be written as

Ans.