Stress Concentration (σmax = Kt σnom)

Nominal stress is an average, and material at a notch root does not experience averages. $K_t$ is the multiplier between the two, read off a Peterson chart for the geometry at hand. The canonical case is Kirsch's 1898 elasticity solution for a small circular hole in a wide plate under uniaxial tension, which gives $K_t = 3.00$ exactly — a 15 ksi nominal becomes 45 ksi at the two points on the hole's equator, and it does not matter whether the hole is 1 mm or 100 mm across.

That size independence is the counter-intuitive part, and it is only true for a hole in a plate large enough to be effectively infinite. What actually controls $K_t$ is the ratio of the feature's radius to the surrounding dimensions, so a sharp fillet is far worse than a generous one: opening a shoulder radius from $r/d = 0.05$ to $0.2$ can drop $K_t$ from about 2.5 to about 1.5, a 40% cut in peak stress for a change a machinist barely notices. It costs nothing and it is the highest-value edit available on most drawings.

The trap is applying $K_t$ where it does not belong. Under a static load on a ductile metal, the notch root simply yields, redistributes and shrugs — which is why a bolt hole in a steel plate is checked on net-section rupture, not on a factor of 3. Concentration matters for brittle materials, for fatigue, and for anything cold. In fatigue the effective factor is $K_f$, usually less than $K_t$ because of a notch-sensitivity effect, and the de Havilland Comet crashes of 1954 are the reason anyone learned to care: cracks grew from cutouts whose corners concentrated the fuselage hoop stress far above nominal, cycle after pressurisation cycle.