Average Shear Stress on a Plate

[Colt 45 J]

1. Problem Statement
The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of the plate defined by the section lines a-a, and the average shear stress in the bolt head along the cylindrical area defined by the section lines b-b.

http://img340.imageshack.us/img340/698/solidsproblem1102.jpg

Note: I have solved the shear on the bolt head, as well as the average normal stress in the shank, it's the average shear along the plate that I am having issues with.

Homework Equations

τ = V / A
o= N / A

The Attempt at a Solution

Distribution of forces so the equivalent is 4kN

τ = 4000/(pi*(.009^2-.0035^2))
τ = 18.52MPa

The answer key (which has yet to be wrong in my experience for this textbook) says that the average shear should be 4.72MPa

Edit:
Figured out my error

τ= 8000/(pi*(.018*.03))
τ=4.716MPa

 

[pongo38]

I'm pleased you are happy with your answer, but I didn't understand why it is 4 kN, and not 8kN. If you have a moment to explain I would be grateful.

 

[Colt 45 J]

Ah originally it was because with a rectangular element it's usually double shear instead of single, in the case of the answer thank you, as I had put a typo and meant to put 8000N in instead of the 4000, the answer was calculated using the 8000 however and is correct.