Question

The circular punch B exerts a force of P = 2.8 kN on the top of the plate A. (Figure 1)

Determine the average shear stress in the plate due to this loading.

Express your answer to three significant figures and include the appropriate units.

P 4mm 12mm 2 mm

Answer 1

The average shear stress is given by Shear load/Area. This area is the area of contact when two objects slide over each other. Here in this cylindrical punch problem, the area of contact is that surface of the cylinder of 4mm diameter with the plate's thickness of 2mm. Hence the area of contact is. (2*pi*(4/2)mm*2mm)

Therefore the average shear load is $\frac{2.8 kN}{(2\pi*2mm)*2mm}$

$\frac{2.8 *10^3N}{8\pi*10^{-6}m^2}$$=0.1114*10^9 N/m^2= 0.1114GPa$