Every formula in this chapter measures from the neutral axis, and in elastic bending the neutral axis passes through the centroid of the cross-section. On a rectangle or a symmetric I-shape that is mid-depth, and nobody has to think about it. Weld a cover plate on one flange, or build a tee, and the symmetry is gone. The axis moves toward the heavier side, and it has to be found before anything else can be trusted.

For a section made of two parts: $\bar{y} = \dfrac{A_1 y_1 + A_2 y_2}{A_1 + A_2}$, read aloud y-bar equals A-one y-one plus A-two y-two, all over A-one plus A-two. Name the letters once. $A_1$ and $A_2$ are the areas of the two parts in mm²; the subscripts only say which part, 1 or 2, and you choose the numbering. $y_1$ and $y_2$ are the heights of each part's OWN centroid above a datum, in mm. The datum is any reference line you like, and the underside of the section is the usual choice. $\bar{y}$, said y-bar, is the height of the whole section's centroid above that same datum, in mm, and it is the one you are solving for.

Read it as what it is: an area-weighted average. A plain average of the two heights would be right only if the parts were the same size. They rarely are, so the bigger part gets the bigger say, and $\bar{y}$ always lands between $y_1$ and $y_2$, nearer the larger area. If your answer falls outside that range, stop. An average cannot escape the numbers it averages.

Two slips cost the marks here. The first is a mixed datum: every height in the sum must start from the SAME line, so a flange sitting on a 150 mm stem has its centre at 150 plus half its own thickness, not at half its thickness. The second is stopping too soon. Once $\bar{y}$ is known, the distance $c$ to the extreme fibre is measured from it, and on a lopsided section the two faces are no longer the same distance away. The face FURTHER from the centroid governs the stress. Units guide, they do not confess: mm² times mm over mm² is mm, which is necessary and proves nothing more.