Structural Engineering & Statics
where the load goes
Concept

Axle train — where it appears

A set of loads at fixed spacings, which is what a real vehicle is and what a single moving load is not. The worst position for a train never puts its heaviest axle at the influence line's peak, because the neighbours are then off the useful part of it.

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

Influence line for the bending moment at x = 3. The bending moment at one fixed station, plotted against the position of a unit load walking across the span. The beam was re-solved at 301 load positions. The worst position is x = 3.00, giving 2.100.

The worst place to stand

A bridge is not designed for a load. It is designed for a load that moves, and for every station along it there is a different position of that load that does the most damage.

internal-forces · Influence line The worst position is not the obvious one. Three axles totalling 320 units, marched across a span of 20 in steps of 0.02. The envelope is the largest moment each station ever sees; its peak is 1160.2 at 9.88 along the span, which is 0.12 off midspan and occurs under the axle nearest the resultant rather than under the heaviest one. Barré's construction, which places midspan halfway between that axle and the resultant, independently gives 1160.3 at 9.88. The dashed curve is the envelope the same total weight would produce as one load rather than three: its peak is 1600.0, which is 38% more — spreading a load out is worth something.

The train that is worse than its heaviest axle

An influence line says where to stand one load. A vehicle is several loads at fixed spacings, and the worst arrangement never puts the heaviest one at the peak.

internal-forces · Influence line

Named alongside it

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

Influence lineMoment envelopeMoving loadPattern loadingBarre ruleBending momentMoment diagramResultant

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