1-11.  The loads on the beam follow the distributions of P ~ N(12, 3²) kN and Q ~ N(36, 6²) kN. The pins at A and B are in double shear, and both have a diameter of d = 15 mm. What is the distribution of the shear stress in pin B? Assume P and Q are independent.

Solution

Solve for

Pin B is in double shear, thus

Solve for area

 m²

Solve for

Because normal random variables Q and P are independent,  also follows a normal distribution, .

 MPa

 MPa

Then

 MPa