8. The weight of a door follows a normal distribution N(95,0.3²) lb due to manufacturing variations. Its center of gravity is located at G. Determine the distributions of the reactions at the hinges if the hinge at A supports only a horizontal reaction on the door, whereas the hinge at B supports both horizontal and vertical reactions.

Solution

Since the weight of the door follows the normal distribution G~N(95,0.3²) lb, therefore, we have

Consequently, we have all three reactions distributions, A_x ~ N(30.54, 0.096²) lb, B_x ~ N(30.54, 0.096²) lb and B_y ~ N(95, 0.3²) lb. Ans.