1-7.  A box, whose wight P follows , is suspended from wires AB and BC. If the wires have a normal failure stress of , determine the minimum diameter of each wire to make sure that the probilities of failure of the wires are less than .

Solution

Referring to the equilibrium of joint B in Fig. 1.7.2.

;

Assuming that the diameter of the wires is , and the normal stress of AB, BC are ,  respectively. Then, the cross-section area of the wires is . We obtain

,        .

Obviously, . Set , then , where

.

To make sure the probilities of failure of the wires are less than , we just have to ensure that wire AB meets this requirement. Thus, the probability of failure of wire AB is

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