Structural Engineering & Statics
where the load goes
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Stress concentration — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Three times the stress, and it does not matter how big the hole is. The hoop stress around a circular hole in a wide plate pulled at 100 N/mm², from Kirsch's exact solution. At the sides of the hole it is 3.0 times the applied stress — 300 N/mm² — and the factor is the same for a hole of any radius, because the radius cancels. At the top and bottom of the hole it is -1.0 times the applied stress, which is compression in a plate that nothing is pushing. The disturbance dies quickly: the stress is within 5% of the applied value by 3.5 hole radii, which is Saint-Venant's principle with a number on it.

    The hole that multiplies the stress by three

    The stress at the side of a hole is three times the applied stress whatever the hole's size, and at the top and bottom of the same hole it is minus one times it — compression in a plate that nothing is pushing.

    part 1 · materials
  2. What a crack makes of a notch, against how sharp the notch is. The fatigue notch factor against the root radius, at a fixed elastic factor of 3 in a 430 MPa steel. K_t is a property of the shape and does not move along this axis at all — the dashed line — while the factor fatigue actually feels climbs toward it from below. At a 1 mm root the answer is 2.40, which is 30 per cent of the notch relieved; at 0.1 mm it is 1.38, and a notch that concentrates by 3 elastically is barely felt. Nothing has changed about the stress field: what has changed is that the peak is confined to a smaller volume than the material's own process size, so the crack starts against an average rather than against a maximum.

    The notch a crack does not feel in full

    The elastic concentration factor is a property of shape and knows nothing about size, which is what makes it so useful and so misleading. A fatigue crack starts against an average over a volume the material owns, so two notches with the same factor and different radii have different fatigue strengths — and the stronger the steel, the less of that relief it gets.

    part 2 · materials

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