Structural Engineering & Statics
where the load goes
Concept

Influence line

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
the station being watched, x = 3unit load, at its worst position2.100shaded: where a spread load must stand to make this quantity worstthe horizontal axis is where the load is, not where the beam is cut

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 12012080resultantmidspan05101520020040060080010001200station along the spangreatest moment ever seen there1160.2 at 9.88Barré: 1160.3 at 9.88

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 20 at 2δ at B = 93.33320 at 6δ at A = 93.334the shapes have nothing in commonand the two readings agree to 1e-14which is why an influence line can be measured by pushing the structure where it is easy to push

The theorem that swaps the question round

Push here and measure there; push there and measure here. The two readings are identical, for every elastic structure, whatever its shape — and that fact turns an influence line into something a model can be asked for directly.

deflection · reciprocity

Named alongside it

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

Axle trainMoment envelopeMoving loadPattern loadingBarre ruleBending momentFlexibilityMoment diagramMüller-Breslau's principleReciprocal theoremResultantStiffness

All concepts