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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?

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  • $\begingroup$ To be explicitly clear, when you say the steel is asymmetric, you mean that the lengths (and/or thicknesses) of the flanges (horizontal and vertical) are different? $\endgroup$
    – Wasabi
    Apr 12 '16 at 2:30
  • $\begingroup$ I think they are referring to unequal leg angles. $\endgroup$
    – Ethan48
    Apr 12 '16 at 3:59
  • $\begingroup$ @Wasabi For the purposes of calculating the Ct and Cb, the distances from the Centroidal Neutral Axis of the material, to the outermost, highest stressed material, Angle(L) steel is not symmetric, vertically. The two DeltaYs will be different. And thus the Section Modulus really has two values, I think. $\endgroup$ Apr 12 '16 at 11:46
  • $\begingroup$ @Ethan48 I am referring to equal leg as well. The geometry of an equal or unequal leg angle has no line of symmetry. $\endgroup$ Apr 12 '16 at 11:47
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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.

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  • $\begingroup$ Ok, right, so in an asymmetrical shape, they just basically picked one at random, the farthest one. Because that might not be the important one, if the beam is under negative bending moment at that section. The other one might be the limiting factor. $\endgroup$ Apr 12 '16 at 16:09
  • $\begingroup$ I mean, you know, you can just pick any fiber anywhere and get the stress at that point, but the only really important ones are the Top, and Bottom, and whether each is within the Compress/Top Compress/Bottom Tense/Top Tense/Bottom allowables. So it just seems incomplete - the AISC has no idea what configuration your beam is in.... $\endgroup$ Apr 12 '16 at 16:11
  • $\begingroup$ Is that right? Am I missing something? Is there some limit or concept I am missing here? If your beam is 'contraflexed' and bending upward, and your beam is made from an asymmetrical section, the 'Farthest' fiber may not be the most stressed. $\endgroup$ Apr 13 '16 at 11:10
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    $\begingroup$ Well @AndyzSmith, the farthest fiber will always be the most stressed (as in it will present the largest stress). I agree with you that it is not necessarily the most critical. If the near edge is the one under compression, it may be that it will buckle under a stress lower than the ultimate tensile stress of the farthest edge. Or, if we were instead talking about concrete sections, the opposite may apply: perhaps the lower tensile stress on the near edge would be of greater significance than the compressive stress on the far edge. $\endgroup$
    – Wasabi
    Apr 13 '16 at 11:31
  • $\begingroup$ @AndyzSmith The fact remains, however, that this explains why the table only shows one value. It may not be a good or satisfactory explanation, but its the best I've got. There's really nothing else I can say other than "take it up with the AISC". $\endgroup$
    – Wasabi
    Apr 13 '16 at 11:34
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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.

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  • $\begingroup$ No, I am not referring to the Section Modulus based on the Y-axis centroid. I can see how an equal legs THOSE two will be the same. I am referring to the fact that an Angle steel is not symmetric, vertically or horizontally, so actually there should be TWO Numbers for BOTH Sx and Sy. So the table should have Sx(Bottom) Sx(Top) Sy(Left) Sx(Right) something like that. $\endgroup$ Apr 12 '16 at 11:49

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