The shape of an I-beam
Why the material sits at the top and bottom and almost nowhere else.
An I-beam keeps almost all of its material in the two flat flanges at the top and bottom and almost none in the thin web joining them because material sitting far from the beam's centre resists bending far more effectively than the same material sitting near it, and putting material near the centre where it barely helps is simply wasted weight.
Why the edges do the work
When a beam bends, one face stretches and the opposite face squeezes together, and the further a piece of material sits from the beam's own centre, the more it stretches or squeezes for a given amount of overall bending, which means it does proportionally more of the work of resisting that bend. A thin strip of material sitting right at the beam's centre barely stretches or squeezes at all as the beam bends, since the centre is close to the neutral line where the transition between stretching and squeezing happens, and material there is contributing very little resistance no matter how much of it is packed in. Material sitting at the very top or bottom, furthest from that centre, stretches or squeezes the most of anywhere in the cross-section, and its contribution to bending resistance grows faster than its distance from the centre. That is the whole reason a beam's cross-sectional shape matters as much as how much material it contains.
Twice as far out, four times the stiffness
A thin strip of material contributes bending stiffness in proportion to the square of its distance from the centre. Two identical strips, one sitting twice as far out as the other, differ by a factor of four, and a strip three times as far out does nine times the work. Pulling the same two flanges apart to double the beam's depth, with only a slightly taller web added between them, makes the beam roughly four times as stiff for very little extra weight, where making a solid bar twice as deep doubles its weight along with its stiffness gain. An I-beam's designer therefore concentrates the flanges as far from the centre as the overall depth of the beam allows, while shrinking the connecting web down to whatever thickness is needed just to hold those two flanges the correct distance apart and keep them from shearing relative to each other. This is why an I-beam's overall depth, the distance separating its two flanges, is usually the single dimension a designer protects most jealously on a drawing, since losing even a small amount of that depth to fit around some other component costs far more bending stiffness than the same reduction taken from anywhere else on the section.
A hollow door that still stays flat
Knocking on an ordinary hollow interior door and hearing that unmistakable hollow sound reveals a structure built on exactly this principle. The door has two thin, solid skins on its front and back faces with very little material filling the space between them, and yet it stays flat and resists sagging perfectly well for the job it is asked to do. That works precisely because the two skins sit at the outer surfaces of the door, furthest from its centre, doing almost all of the useful work of resisting any bending force applied to the door's face, while the near-empty middle, close to the door's own centre, would have contributed comparatively little stiffness even if it had been filled solid with the same amount of timber the skins already use. A solid door of the identical overall thickness, using the same total quantity of timber spread evenly through its depth instead of concentrated at the two faces, would resist sagging less well, which seems odd until the material's distance from the door's centre is recognised as the thing doing the work.
Flanges, webs, and the parts that copy them
This is why an I-beam of a given weight is dramatically stiffer in bending than a solid rectangular bar of the same weight, since the solid bar has most of its material sitting near its own centre doing very little useful work, while the I-beam has concentrated nearly everything at the two extremes where it counts. The web only needs to be thick enough to resist shear and to stop the flanges buckling sideways relative to each other, since the flanges do the bending work. Anyone laying out a lightweight chassis member, a wing mounting, or any structural part that has to resist bending without carrying unnecessary weight is applying this same shape, however different the finished part ends up looking from a textbook I-beam. A curved wishbone, a flat mounting plate with its edges folded up into flanges, or a hollow box section are all variations on the identical idea, pushing material away from the centre and toward the surfaces doing the most work, dressed up in whatever outline the surrounding parts of the car happen to demand.