Structural Engineering & Statics
where the load goes
Concept

Hogging and sagging — where it appears

The two senses of bending, one putting the top fibre in tension and the other the bottom. A continuous member does both along its length, and the reinforcement or the section has to change face where it changes sense.

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

Where to put the supports. Peak sagging and hogging moment for a uniformly loaded beam, against how far the supports are moved in from the ends. The best arrangement is where the two curves cross, and it is nowhere near the ends.

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 3 continuous spans against 3 simple ones. The bending moment in a continuous beam, solved by the stiffness method, drawn over the moment in the same spans made simply supported. The peak sagging moment falls from 30.6 to 19.6, and a hogging moment of 24.5 appears over the supports where there was none.

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

Named alongside it

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

ContinuityMoment envelopePoint of contraflexureMoment redistributionOptimisationOverhangPattern loadingReaction distributionReactionsStiffness

All concepts