# Calculating Bending Stress for a Cantilever Beam

Hi, I'm trying to calculate bending stress for a cylindrical beam. I'd like to have my result double checked because I got an answer that doesn't make sense to me. All of this is personal research, so I'm not very confident in my answer.

It's a cantilever beam with a point mass of 347.4 oz. on its tip. The distance from the load to the other end is 2 in., and the beam has a radius of 1/8". This is the calculation I found for bending stress:

bending stress (psi) = bending moment (lbs. in.) * distance from load to edge (in.) / second moment of inertia (in^4)

I researched the second moment of inertia to be (pi/4)*r^4 for a solid cylinder. So I plugged that in...

((21.7125 lbs. * 2 in.) * 2in.) / (pi/4 * (1/8 in.)^4)

...and got a result of about 450,000 psi. This feels like way too high a number, so I'd like to know what I'm doing wrong here. Thank you!

## Answers and Replies

JBA
Science Advisor
Gold Member
I am not sure why you doubled the load W and used the second moment of inertia.

What you will find in any engineering reference is that you should be using the formula S = W*L/Z for the max stress at the base attachment point where Z is the section modulus and for round bar Z = π*d^3 / 32 = π*(2*r)^3 / 32. By doing so you will get an answer of 28,308.7 psi.