Stresses on Oblique Planes

Problem: Please refer to Figure 1.29 on page 23 of your text. Assuming that the bolt is 5 mm in diameter and the force P = 1.2 kN, find:

a) The shearing stress parallel to the cross-sectional area
b) The shearing and normal stresses on an area within the bolt at an angle of 30^o to the shank of the bolt

a) We just need to divide the force by the area...

b) Let's derive the relation first...

Therefore, .

The area is not, of course, the same cross-sectional area used in part a: .

Dividing to get the stresses...

Notice the differences between these equations and those at the top of page 24?