Stress concentration, and the danger in holes

Why a feature that removes material can raise local stress threefold.

Drilling an ordinary round hole through a loaded plate does not simply remove material from the middle of the part, it forces the stress that used to pass evenly through that missing material to crowd around the hole's edge instead, and the crowding is severe enough that the stress right at the rim can run to roughly three times the stress running through the plain plate on either side of it, a penalty that has nothing to do with how much material the hole actually removed.

What is really going on

A plate carrying a steady pulling force distributes that force evenly across its whole cross-section when nothing interrupts it, every part of the material sharing an equal portion of the load and none of it working noticeably harder than the rest. The instant a hole is cut through the middle of that plate, the material that used to occupy the hole can no longer carry any of the load it once shared, and that load has to be picked up by whatever material remains, which is exactly the material sitting closest to the hole's own edge. That nearby material does not simply take on a modest, evenly spread extra burden, it takes on a sharply uneven one, since the stress lines running through the plate behave less like a crowd spreading out to fill available space and more like a crowd that has nowhere else to go but through the narrowest remaining gap, all of it converging on the same small band of material right at the rim before spreading back out again on the far side. The plate as a whole might be carrying perfectly ordinary loads, well inside anything it was designed for, while the material at the very edge of the hole is quietly working several times harder than the average figure on the drawing would suggest.

The doorway-crowd comparison

A wide corridor filled with people walking at an easy, spread-out pace and then made to pass through a single doorway shows the same crowding directly. Well before and well after the doorway, everyone has room to spread out and nobody is jostling anybody else, but for the short stretch right at the opening itself, the same number of people has to pass through a much narrower gap, and they arrive shoulder to shoulder, moving faster and more urgently than they were a moment before, purely because the doorway forced them all toward the same narrow point at once. Nobody in the corridor changed how many people were walking through it, and the doorway did not add any people, it simply concentrated the ones who were already there into a smaller space for a short distance, and that concentration is uncomfortable in a way the same crowd spread across the whole corridor never was. A hole in a loaded plate does exactly this to the lines of stress running through the material, squeezing them together at the rim and letting them spread back out once they are clear of the hole, and the discomfort felt by the crowd at the doorway is a fair stand-in for the sharply elevated stress the material right at that rim actually experiences.

Why the effect does not depend on the hole's size

What makes this particular concentration worth taking seriously is that, for a simple round hole in an otherwise uniform plate, the ratio between the stress at the hole's edge and the plain stress running through the rest of the plate stays essentially the same regardless of how large or small the hole actually is. A tiny pinhole and a hole several times larger, cut through an identical plate carrying an identical load, both produce a peak stress at their own edge running to roughly the same multiple of the surrounding average, which means a designer cannot assume a small enough hole is automatically a safe one simply because it removed only a small fraction of the material. What does change with the hole's absolute size is how large an area is actually working at that elevated stress, a bigger hole spreading the concentrated stress over a bigger patch of material even though the peak multiple itself barely shifts, which is a genuinely different consideration from the peak stress question and one that matters more for how a crack, once started, goes on to behave than for whether a crack starts in the first place.

One figure worth keeping in mind

A circular hole cut into a plate under an otherwise uniform pulling load raises the stress right at the sides of the hole, the points directly across from the direction of the pull, to about three times the stress running through the undisturbed plate elsewhere, a figure that holds up remarkably well across a wide range of practical hole sizes and plate thicknesses and is one of the more reliably repeatable results in the whole subject of stress concentration.

Why this matters in practice

Because this threefold penalty applies at essentially any hole size, a part is never made safe from stress concentration simply by keeping its holes small, and a designer who checks only the plate's average stress against its rated strength, without separately checking the local stress right at every hole, vent or cutout, has quietly skipped the calculation that actually governs where the part is most likely to crack first. This matters more, not less, once the earlier articles in this set are taken into account, since a location running at three times the average stress is also a location accumulating fatigue damage at a rate the average stress figure gives no hint of, and a part that looks comfortably margined on paper against its peak expected load can still be carrying a fatigue-critical hotspot sitting directly at the edge of a hole nobody thought twice about. Rounding a sharp internal corner or adding a smooth fillet where a hole meets a flat face does real work here, softening the abruptness with which the stress lines are forced to converge and lowering the peak concentration meaningfully below the plain circular-hole figure, which is why a well-drawn part so often shows a gentle radius exactly where an inexperienced designer would have left a sharp, unforgiving edge.