Someone on the team asked me last week why the static analyst used Kt = 3 for a hole and the fatigue analyst used something different for the same hole, and which one was wrong. Neither. They’re answering different questions, on different reference areas, with different assumptions about whether the material’s allowed to yield. Almost every Kt “disagreement” I’ve ever been dragged into sorts itself out once those three things are on the table, so let me lay them out.

Gross versus net is half of it, easily. A Kt is meaningless until you say what stress it multiplies. Kt on gross area multiplies the far-field stress on the full un-drilled section and ignores the material the hole removed. Kt on net area multiplies the stress on the reduced section through the hole and has already accounted for the lost material. For an infinite plate with a small circular hole in tension the classic answer is Kt ≈ 3 on the gross far-field stress (Kirsch: σ_peak = 3·σ_∞ at the hole edge). But as the hole grows relative to the width the two part company, hard. The net-section Kt actually drops below 3, toward roughly 2 for a wide hole, while the net stress itself climbs because there’s less material left to carry the load. So a careless “Kt = 3” can be conservative or unconservative depending on which area you meant, and the two analysts arguing in the corridor are usually both right in their own bookkeeping. Quote the factor without the area and you’ve genuinely said nothing. (Loaded holes do the same thing, by the way: a hole carrying bearing has a higher edge stress than the same hole carrying pure bypass, so the effective Kt at a fastener isn’t the open-hole value, it rides on the bearing-bypass split.)

The other half is static versus fatigue, and this is the part that confuses people the most. Under static ultimate a ductile metal yields locally at the notch root and redistributes. The elastic 3× peak gets relieved by plasticity, the surrounding material picks up the slack, and the section fails when the net section reaches its strength, not when the elastic peak does. So for static substantiation of a ductile metal the net-section check often governs and chasing the elastic peak is just needlessly conservative. (For a brittle material, or anywhere local yielding isn’t acceptable, the peak still matters, which is why “is yielding allowed here” is a real question and not a formality.)

Fatigue gives you none of that mercy. Crack initiation runs on the local cyclic stress and strain at the notch root, so the fatigue analyst hangs on to the full elastic concentration. Except Kt overstates the fatigue effect, so they reach for Kf, the fatigue notch factor, which is smaller than Kt and folds in notch sensitivity:

Kf = 1 + q·(Kt − 1), with q the notch-sensitivity factor between 0 and 1.

q depends on the material and the root radius, and the direction matters: blunt notches push q toward 1 (Kf ≈ Kt), very sharp notches drop it well below 1, and at a given radius a high-strength material sits closer to Kf ≈ Kt than a soft ductile one. It’s captured empirically by Peterson’s relation, q = 1/(1 + a/r) with a a material constant and r the root radius, or by Neuber’s. The physical reason q falls below 1 is that fatigue damage responds to stress averaged over a small process-zone volume, not the mathematical point at the root, so a very sharp notch has a very small highly-stressed volume and does less damage than its elastic Kt implies.

That’s the whole reason the two numbers differ. The static analyst gets to spend plasticity to relieve the peak and the fatigue analyst doesn’t, but the fatigue analyst gets to discount the peak through notch sensitivity instead. Different physics, different factor, same hole.

One practical note on where Kt even comes from: don’t trust a single textbook value blindly. The infinite-plate 3 is a starting point and finite width, hole proximity, biaxiality, a countersink, load eccentricity all shove it around. Use the curves (Peterson, Roark) for the geometry you actually have, or a fine FE of the finite-radius feature, and remember the FE peak only means anything if the radius is modelled and the result is mesh-convergent. A sharp-cornered FE hole hands you a singularity, not a Kt.

Anyway, when two people are arguing about a Kt, I make them agree on the reference area, on static versus fatigue, and on whether local yielding is allowed, before anyone defends a number. Usually it turns out to be two correct answers to two different questions and the argument just dissolves.