6-10. A vertical random force  is acting on the beam as shown in the figure. The strain in the x direction at point C is measured and follows a normal distribution. Determine the distribution of the force . Given that the beam has a Young’s modulus of .  and  are independent.

Solution:

Section Properties

Normal Stress

Thus, from equation (3) and (4), we have

Since , we have

Thus, force P follows .                                                                         Ans.