Notches: where shafts break

This is a static copy of the chapter for search engines. The interactive version has animated figures, check questions, and buttons that load the example into the calculator.

Think of the stress as flowing along the shaft like a fluid. Wherever the flow has to squeeze past a change of section, the lines crowd together and the local stress rises.

K_t: the geometric stress raiser

The theoretical (elastic) stress-concentration factor is a pure geometry number: how much higher the peak stress is than the nominal stress at that section. For a shoulder on a round shaft it depends on two ratios, D/d and r/d. ShaftLab evaluates it from Peterson’s polynomial fits rather than from a chart, so it updates as you type.

Feature	K_t bending	K_ts torsion
shoulder fillet, sharp (r/d = 0.02)	2.7	2.2
shoulder fillet, well rounded (r/d = 0.1)	1.7	1.5
end-milled (profile) keyseat	2.14	3.0
sled-runner keyseat	1.7	—
retaining-ring groove	5.0	3.0

First-iteration design estimates (Shigley Table 7-1). ShaftLab uses the computed value from the actual geometry where it can, and these where the geometry is set by a standard tool — for example a keyway cutter, which always leaves r/d ≈ 0.02 at the bottom.

Notch sensitivity: K_t is not the whole story

Materials do not feel the full theoretical peak. The sharper the notch, the smaller the volume of material at the peak stress, and the less the fatigue strength suffers. That is captured by the notch sensitivity q:

q = 11 + √a / √r K_f = 1 + q(K_t − 1)

√a is the Neuber constant, a material property that falls as the strength rises. The consequence is important and counter-intuitive:

⚠ Strong steel is more notch sensitive. For a 0.5 mm radius, a mild steel (S_ut 400 MPa) has q ≈ 0.6; an alloy steel at 1200 MPa has q ≈ 0.85. Swapping in a stronger steel and keeping the same sharp notch buys you far less than the strength ratio suggests. Fixing the notch is almost always the better move.

Which notch wins

The dangerous section is where K_f·M/W is largest, not where M is largest. A keyway sitting under a gear at mid-span, a ring groove right next to a bearing, a sharp shoulder in a region of high moment — those are the candidates. ShaftLab tabulates every notch with its K_t, q, K_f and the resulting local safety factor so you can see them ranked.

What to do about it

Give every shoulder a radius. r = d/10 if the mating part allows it. If a bearing needs a sharp corner, use an undercut, a shoulder relief groove, or a relief groove in the small diameter — all three keep the bearing seat and move the notch to a bigger radius.
Prefer a sled-runner keyway to an end-milled one where you can: 1.7 against 2.14 in bending.
Keep ring grooves out of high-moment regions. K_t = 5 is brutal; put the groove where the bending moment is small.
Do not step the diameter more than you must. D/d = 1.2 is plenty for locating a bearing.

💡 A press fit is a stress raiser too, even though there is no geometric notch: fretting at the edge of the seat gives K_f ≈ 2 for a normal interference fit. ShaftLab treats it as a direct K_f, without a notch-sensitivity correction, because there is no radius to correct with.