The Kt questions I keep getting asked

A junior engineer asks why the static analyst used Kt = 3 for the hole and the fatigue analyst used something else for the same hole. Both are right. They are answering different questions, on different reference areas, with different assumptions about whether the material is allowed to yield. Almost every “disagreement” about a Kt evaporates once those three things are on the table.

Gross vs net is half the confusion

A stress concentration factor is meaningless until you say what stress it multiplies. Same peak stress, two different factors:

• Kt on gross area multiplies the far-field stress computed on the full (un-drilled) cross-section. It ignores the material removed by the hole.
• Kt on net area multiplies the stress computed on the reduced (net) section through the hole. It already accounts for the lost material.

For an infinite plate with a small circular hole in uniaxial tension, the classic result is Kt ≈ 3 on the gross far-field stress (the Kirsch solution: σ_peak = 3·σ_∞ at the hole edge). But as the hole grows relative to the plate width, the two diverge sharply: the net-section Kt actually drops below 3 (toward ~2 for a wide hole) while the net stress itself rises because there is less material to carry the load. So a careless “Kt = 3” can be conservative or unconservative depending on which area you meant. Quote the factor without the reference area and you have said nothing — and the two analysts arguing are probably both correct in their own bookkeeping.

The same trap appears with loaded holes: a hole carrying bearing has a higher edge stress than the same hole carrying pure bypass, so the effective Kt at a fastener is not the open-hole value — it depends on the bearing-bypass split.

Static yields the peak away; fatigue remembers it

Under static ultimate load, a ductile metal at the notch root yields locally and redistributes. The elastic peak of 3× is relieved by plasticity; the surrounding material picks up load, 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 Kt peak is needlessly conservative. (For brittle materials, or where local yielding is not acceptable, the peak still matters — so “is yielding allowed here?” is a real question, not a formality.)

Fatigue has no such mercy. Crack initiation is driven by the local cyclic stress (and strain) at the notch root, so the fatigue analyst keeps the full elastic concentration. But 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), where q is the notch-sensitivity factor, between 0 and 1.

q depends on the material and the notch root radius — sharp notches in high-strength materials approach q = 1 (Kf ≈ Kt), while blunt notches and lower-strength, more ductile materials sit lower (Kf < Kt). It is captured empirically by relations like Peterson’s (q tied to a material constant over the root radius) or Neuber’s. Physically, q < 1 because fatigue damage responds to stress averaged over a small process-zone volume of material, not the mathematical point at the root — a very sharp notch has a very small highly-stressed volume, so it does less fatigue damage than its elastic Kt implies.

That is the whole reason the two numbers differ: the static analyst is allowed to spend plasticity to relieve the peak, the fatigue analyst is not — but the fatigue analyst also gets to discount the peak through notch sensitivity. Two different physics, two different factors, same hole.

A note on where Kt comes from

For real geometry, don’t trust a single textbook value blindly. The infinite-plate Kt = 3 is a starting point; finite width, hole proximity, biaxiality, a countersink, and load eccentricity all move it. Use the curves (Peterson’s charts, Roark) for the configuration you actually have, or a fine FE of the finite-radius feature — and remember the FE peak is only meaningful if the radius is modelled and the result is mesh-convergent (a sharp-cornered FE hole gives you a singularity, not a Kt).

The takeaway

Before arguing about a Kt value, agree on three things:

1. The reference area — gross or net.
2. Static or fatigue — peak-relieving or peak-remembering.
3. Is local yielding allowed? — which decides whether the elastic peak or the net section governs.

Settle those and the “disagreement” usually turns out to be two correct answers to two different questions. The argument was never about the number; it was about which question the number was answering.