2-6.  The assembly is subjected to a force P that follows the normal distribution  kN. If the initial gap  is equal to 0.26 mm before the force is applied, what is the probability that the gap is filled, given E = 245 GPa?

Fig. 2.6

Solution

Solve for the displacement of point C in terms of P. Do not consider if this displacement will fill the gap at this point.

 m²

The probability that the gap is filled is .  Let . Then,

Then, p is written as . Y follows a normal distribution, .

 = m

 = −0.04026 mm

 m = 0.01191 mm

Therefore

Ans.