Structural Engineering & Statics
where the load goes
Concept

Moment envelope

4 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
00.050.10.150.20.250.30.3501020304050overhang, as a fraction of the spanbest at 21% — peak 8.8sagging, mid-spanhogging, over the supportmoving the supports in by a third of the way halves the worst moment

Where to put the supports, which is not at the ends

Moving the supports of a uniformly loaded beam inward by about a fifth of its length halves the worst bending moment. The load has not changed and nor has the beam.

internal-forces · support layout moment19.6 sagging24.5 hogging30.6 if the spans were simplereactions 14.0 38.5 38.5 14.0 — the inner supports carry far more than a sharethe continuous case needed stiffness; the comparison did not

The moment over the support, and what it buys

Run a beam over its supports instead of stopping at each one, and the mid-span moment falls by a third while a new moment appears where there was none. Nothing was added but continuity.

internal-forces · continuity 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

Named alongside it

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

Pattern loadingAxle trainContinuityHogging and saggingInfluence lineMoving loadPoint of contraflexureBarre ruleBending momentMoment diagramMoment redistributionOptimisation

All concepts