Structural Engineering & Statics
where the load goes
Concept

Miners rule — where it appears

The assumption that fatigue damage from cycles of different amplitude adds linearly, each cycle contributing the reciprocal of the life it would have alone. Failure is predicted when the sum reaches one, and the rule takes no account of the order the cycles arrived in.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Three details, and no material anywhere on the plot. Stress range against cycles to failure for three detail categorys — 160, 90, 36 N/mm² at two million cycles. The lines are parallel because they share a slope of three, and the spread between them is a factor of 4.4 in stress and therefore 88 in life. Nothing on this plot depends on the strength of the steel: the same detail in a grade twice as strong lies on the same line. At a stress range of 70 N/mm² the lives are 160: 6.8e+7, 90: 4.3e+6, 36: 2.7e+5 cycles. The knee in each line is the constant-amplitude limit, past which the slope becomes five.

The load that never came near failing anything

A detail survives sixty-eight million cycles at a stress range that another detail in the same steel survives two hundred and seventy thousand of. The two lie a factor of two hundred and fifty apart, and the material is not on the plot anywhere.

materials · Fatigue Two per cent of the traffic and most of the damage. A 120-year traffic spectrum on one detail of category 71, with each band's share of the cycles and its share of the damage. The two bars have almost nothing to do with one another, and the reason is the slope of three: life goes as the inverse cube of the stress range, so a cycle twice as large does eight times the damage and a cycle a third as large does a twenty-seventh of it. The a full train band is 2% of the crossings and 58% of the damage; the smallest band is 35% of the crossings and, being under the cut-off, does none at all. The equivalent constant range that would do the same damage in the same number of cycles is 25.5 N/mm², which is the one number a designer is usually handed — and it is a cube-weighted average, so it is nearer the heaviest vehicle than to the average one.

The cycles that do not count

A fatigue spectrum has to be reduced to one number, and the reduction is a cube-weighted average rather than an ordinary one. Two per cent of the traffic does most of the damage, a third of it does none at all, and the equivalent range that comes out is nearer the heaviest vehicle than the average one.

materials · Fatigue

Named alongside it

The objects these essays reach for when they reach for this one.

Detail categoryEndurance limitFatigueStress rangeCrack growthCut-off limitCycle countingDamageEquivalent rangeFree bodyInspectionResidual stress

All concepts