1-4.  The allowable average shear stress  in each of the 5-mm diameter bolts follows a normal distribution, . Along the four shaded shear planes the allowable average shear stress also follows a normal distribution, . Determine the maximum axial force  that can be applied to the joint, as shown in Fig. 1.4.1, if the probabilities of failure of the bolts and shear planes of the member are less than .

Solution

Internal loading: The shear force developed on each shear plane of the bolt and the member can be determined by solving the force equation of equilibtium according to the free-body diagrams as shown in Figs. 1.4.2 and 1.4.3, respectively.

Average Shear Stress:  The areas of each shear plane of the bolts and the members are   and  , respectively.

We obtain

Let  , the probability of failure of each bolt can be expressed as

.

We can get  and  using

Then

We can obtian that  (controls).                                                                                   Ans.

Let  , the probability of failure of shear planes can be expressed as

.

We can get  and  using

Then

We can obtian .