Example 1¹

Normal, Shear, & Bearing Stress

Problem: Two 1.2 kip vertical loads are applied to pin B of the assembly shown. Knowing that a 0.6 inch diameter pin is used at each connection, determine the maximum value of the average normal stress in links AB and BC. Also determine the shearing stresses in the pins and the bearing stress at C.

Solution: The links are two-force members, so a free body diagram of pin B is:

The sum of the forces must be zero, which means that the force triangle must close; therefore, I have drawn the forces long enough to do so. Using the Law of Sines,

Now I compute the normal stresses...

Next, I find the shearing stresses in the pins...

Note that a factor of two was used in each denominator since both pins are in double shear.

The bearing stress in member BC at C is:

¹ This is Problem 1.16 in Beer & Johnston's Mechanics of Materials, 2^nd Edition, McGraw-Hill.