Compression Spring

For a 200 N spring load, calculate the shear stress of a 20 mm diameter helical compression spring that has a 2.5 mm wire diameter.

Hint
The shear stress in a helical linear spring is
$$$\tau =K_s\frac{8FD}{\pi d^3}$$$
where $$d$$ is the wire diameter, $$F$$ is the applied force, $$D$$ is the mean spring diameter, $$K_s$$ is the spring constant.
Hint 2
The spring constant:
$$$K_s=(2C+1)/2C$$$
where $$C=D/d$$ . (Note $$D$$ is the mean spring diameter, and $$d$$ is the wire diameter.)
The shear stress in a helical linear spring is
$$$\tau =K_s\frac{8FD}{\pi d^3}$$$
where $$d$$ is the wire diameter, $$F$$ is the applied force, $$D$$ is the mean spring diameter, $$K_s=(2C+1)/2C$$ is the spring constant, and $$C=D/d$$

In our scenario: $$C=20mm/2.5mm=8$$ and $$K_s=[2(8)+1]/2(8)=1.0625$$
$$$\tau =(1.0625)\frac{8(200N)(0.02m)}{\pi (0.0025m)^3}=(1.0625)\frac{32N\cdot m}{4.9\times 10^{-8}m^3}$$$
$$$=(1.0625)(652\cdot 10^6)N/m^2=693\:MPa$$$
693 MPa