# Maximum bending stress and neutral axis

I need to calculate the maximum bending stress So let $$r$$ equal the radius $$\frac{1}{r} = \frac{M}{EI}$$ $$\sigma_{max} = \frac{Mc}{I}$$ $$\Rightarrow \sigma_{max} = E\frac{c}{p}$$

But how do I know where the neutral axis is?

The answers say it is $$\frac{c}{2}$$ which intuitively makes, but how can we come that conclusion in a more concrete manner?

I'm also confused to how you would find the second moment of area for this question should you do so?

## 1 Answer

If your beam cross section is symmetrical about Y axis that same axis is the vertical neutral axis.

If not, say your beam cross section is a T or z or just a random shape the definition of of neutral axis is were the first area moment about it taken on top and bottom are equal.

There are several ways of finding the neutral axis of a random shape.

One is to multiply small section areas by their distance from a random axis and then divide that sum by the sum of total areas of small section, area of the cross section:

$$X_n = \dfrac{x_1A_1+ x_2A_2 + x_3A_3 +\cdots}{A_1+A_2+A_3+\cdots}$$