# Beam stress analysis.

1. Feb 22, 2013

### zzinfinity

Hi,
I'm trying to calculate the maximum bending stress in a beam with a varying cross section. I found a great resource (link below) that gives examples on how to do this but am a little confused. Basically the equation used is σ=M/Sx I know what σ and M are, but I haven't a clue what Sx is meant to be. Can anyone tell me what this is? It's kind of tough to figure our a way to google "S" and get meaningful results. Thanks!

PS. What I'm trying to do, is calculate the maximum stress of a boat hull. I'm approximating it as a beam, but the cross section geometry is arbitrary. If any one has any suggestions about a better way to do this, they are certainly welcome!

2. Feb 22, 2013

### AlephZero

The general formuila is $$\sigma = \frac{My}{I}$$ where y is the distance from the neutral axis.

It looks like he is combining $I$ and the maximum value of $y$ into $$S_x = \frac{I}{y_{\text{max}}}.$$ I've never seen that notation before, but then I learned how to stress beams a very long time ago!

Edit: in one of the problems in the PDF he gives it the name "section modulus". http://en.wikipedia.org/wiki/Section_modulus. Looking at the references on the Wiki page, maybe it's used more as a civil or structural engineering term than in general mech eng.

Last edited: Feb 22, 2013
3. Feb 22, 2013

### zzinfinity

4. Feb 22, 2013

### zzinfinity

5. Feb 22, 2013

### AlephZero

Just consider I at that cross section.

But note that for a variable section beam, the maximum stress might not be at the same place as the maximum bending moment. For example I might decrease faster than M as you move along the beam, so M/I increases.

(For a constant cross section, y and I are the same everywhere along the beam so the maximum stress position is the same as the max bending moment position.)

6. Feb 22, 2013

### SteamKing

Staff Emeritus
Sx is the section modulus. This number is used in some design rules when sizing plating-stiffener combinations.