5. A force acts at point C. Determine the probability of failure of the pin at A if the allowable is S ~ N(1200, 25²) N. F and S are independent.

Solution

The free-body diagram of each force member is shown below.

For point ,

Thus, the distribution of force is: .

The free-body diagram of segment is shown below.

With , we obtain the distributions of normal force , shear force , and bending moment :

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However, these results indicate a poor design. Member should be straight (from to ) so that bending within the member is eliminated. If is straight then the internal force would only create tension in the member.

Since the allowable load at pin A is S ~ N(1200, 25²), we can construct

Then we can obtain the distribution of Y ~ N(-68.5, 49.2²) N.

Therefore, the probability of failure can be calculated as

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