Structural Engineering & Statics
where the load goes
Concept

Traffic load — where it appears

The loads vehicles put on a bridge or a deck, described by their weights, spacings and frequency rather than by one static figure. For fatigue and vibration its distribution matters as much as its peak, since a few heavy vehicles or a regular stream of them can govern.

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

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. A full train is 2% of the crossings and 58% of the damage; and three of the five bands — an ordinary lorry, a van, a car, 90% of the crossings — sit under the cut-off and do none of it 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, ninety per cent of it does none at all, and the equivalent range that comes out is nearer the heaviest vehicle than the average one.

materials · Fatigue A scatter of a few per cent in the headways and the rhythm is gone. The damping a 120 m stay at 3,500 kN, 1.01 Hz, over a deck mode at 2.01 Hz damped at 1.0 per cent needs to hold a typical history still, under identical vehicles, each giving the deck the impulse with which a random stream of them every 2.0 s on average gives it an rms of 7.1 mm, arriving every 1.987 s on average — 4 deck periods — against the scatter of their headways (coefficient of variation, logarithmic), from integrating the deck and the stay together over four 1,500 s histories at each point. Exactly regular, 0.99 per cent; scattered by 1 per cent, 0.86 per cent; by 2 per cent, 0.58 per cent; by 5 per cent, 0.13 per cent; at random, 0.05 per cent. The requirement halves at a scatter of 2.2 per cent.

The convoy that keeps the deck's time

A deck shaken by traffic is shaken by vehicles, and vehicles arrive with a rhythm of their own. The same lorries that, arriving at random, move a stay's deck by 7 mm rms and ask the stay for six hundredths of a per cent of damping, move it by 20 mm and ask for a whole per cent if they arrive every four deck periods exactly. But the rhythm is fragile in a precise way: scatter the headways by two per cent and half the danger has gone, and the timing that has to be kept is a tenth of the deck's period whatever the headway and however damped the deck. Ordinary traffic is counted by a stay, not timed; a convoy driven by a machine might not be.

dynamics · Cable dynamics

Named alongside it

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

Cable dynamicsCrowd synchronisationCut-off limitCycle countingDamageDampingDetail categoryEndurance limitEquivalent rangeFatigueFree bodyMiners rule

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