# Shear Stress, Area of Projection

I am learning about shearing stress, and I am a little confused about the area of projection mentioned in my book. When it introduces it, it shows a plate with a rivet through it. The plate is of thickness t, and the diameter of the rivet, d. It shows the plate and the rivet cut in half by a plane, and reveals the rectangular area exposed as the rivet is cut, and claims that A = dt.

I am trying a practice problem where the same type of thing is going on, and asks me to find the shearing stress between the plate and the shaft. However, the solution states that A = pi*d*t. In this case, is it cutting straight through the shaft, or is it the area of half of the hole the shaft creates? Basically, why is pi included here?

BvU
Homework Helper
It's the area between the plate and the shaft: the area of a cylinder with height t and diameter d

It is the area on the plate in the shape of a through hole. You will have to imagine it without rivet in it.

JBA
Gold Member
If possible, post the figure and complete text for the practice problem.

For some reason I was thinking of bearing stress, when it was actually asking for shearing stress. It just so happens that the area must include d and t. Either way, I am starting to understand this a little more. It is asking for the stress between the plate and the shaft, which is the area of the hole that touches the collar. My confusion now is about how to picture where this will shear. Is the shaft physically connected to the collar, or does it rotate within it? In either case, how exactly would this piece break under this shear stress? I have included a rough sketch of what my book has:

JBA