AISC Section Modulus numbers

Question

Why does the AISC handbook only list one figure for Section Modulus for shapes such as Angle(L) steel? Shouldn't there be two? The steel is asymmetric. Is the figure given just the Delta to the bottom or something; figuring a design only needs to be concerned with Tension?

Answer 1

To quote Wikipedia:

The elastic section modulus is defined as $S = \dfrac{I}{y}$, where $I$ is the second moment of area (or moment of inertia) and $y$ is the distance from the neutral axis to any given fibre. It is often reported using $y = c$, where $c$ is the distance from the neutral axis to the most extreme fibre

The tables only show the section modulus for the fiber farthest from the centroid. This properties viewer shows L8x8x1-1/8 with $d = b = 8 \text{ in}$, $\overline y = 2.4 \text{ in}$ (from the horizontal leg), $I = 98.1 \text{ in}^4$, and $S = 17.50 \text{ in}^3$.

$$\begin{align} S_{top} &= \dfrac{I}{d-\overline y} \approx 17.50 \\ S_{bot} &= \dfrac{I}{\overline y} = 40.875 \\ \end{align}$$

One can easily get from one section modulus to another, though (but it might just be easier to calculate it with the traditional equations): $$S_{bot} = S_{top}\dfrac{d-\overline y}{\overline y}$$

It is worth stating however that the critical fiber may not be the one farthest from the centroid. While the farthest face will always have the largest (in magnitude) stress, the near face may be the controlling factor in design. After all, it may be that the lower compressive stress on the near face may lead to buckling before the higher tensile stress on the far face reaches the material's ultimate strength.

Answer 2

When using this this tool which is based on the AISC shapes database there are two values provided. If it is an equal angle section then $S_x = S_y$ and $Z_x = Z_y$, so perhaps that's why you're only seeing one value.