1-10.  The piston in an engine is subject to a random force P that follows a normal distribution of

P ~ N (10, 2²) kN. The connection rod BC has a diameter of d = 13 mm, and a length of L = 1.75 m. The length of the crank AB is R = 0.6 m. The normal stress allowed in the connection rod follows a normal distribution S_a ~ N (135, 5²) MPa. If P and S_a are independent, determine the probability of failure of the connecting rod.

Solution

Free Body Diagram

Referring to the free-body diagram

;

Finding the maximum allowable force in the connecting rod

; where

Note that the connecting rod receives the maximum force at the following instant, thus

Solving for the allowable force P

The probability of failure is . Let , then

Then,  is written as. Since normal random variables S_a and P are independent, Y also follows a normal distribution, . Thus,

= 6833 N = 6.833 kN

= 2095 N = 2.095 kN

Therefore

Ans.