Structural Engineering & Statics
where the load goes
Concept

Ratcheting — where it appears

The accumulation of a permanent change with each cycle of a load that itself returns to where it started. It is the alternative to shakedown, and it appears wherever a cycle is not reversible — a soil densifying behind a wall, a section straining a little further each time, a joint working loose.

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

Also named here as shakedown — the same set of essays touches all of them, so they are one junction rather than several.

Which of them stops moving. Three load cases on the same rectangle, each a constant moment plus a temperature profile cycled from nothing to a peak and back, over sixteen cycles. At 30% of the plastic moment with a 20°C profile it never yields at all; At 60% of the plastic moment with a 120°C profile it shakes down; At 85% of the plastic moment with a 200°C profile it ratchets, at 1.9% of the first-yield curvature per cycle. The ratcheting case never collapses and never returns: it simply arrives somewhere further round every cycle, which is a serviceability failure that no collapse calculation contains.

The structure that settles down, and the one that walks

A load that is safe applied once may not be safe applied ten thousand times. Nothing about that is fatigue — the structure never breaks, it simply arrives somewhere slightly further round every cycle, until it has arrived somewhere unusable.

materials · Shakedown The summer that is worse than the one before it. The earth pressure behind an integral abutment, summer by summer, as a multiple of the at-rest value it started at. A 60 m deck expands by 9.0 mm at each end and pushes the abutment into the backfill. Granular soil under cyclic strain densifies, so the same movement next year needs a higher pressure to achieve, and K climbs from 0.38 toward 0.90 — a factor of 2.33 on the force, reached after about a century. The design load on an integral abutment describes the bridge's whole life rather than a load case, and it is the only load in this collection that gets larger because time has passed rather than because something was added.

The summer that is worse than the last

An expansion joint is a hole in a deck that leaks salt water onto the bearings underneath it. Remove it and the thermal movement does not go away — it goes into the soil behind the abutment, twice a day for a hundred and twenty years, and granular soil under cyclic strain gets denser.

structures · Integral bridge

Named alongside it

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

ShakedownAbutmentArticulationCollapseDurabilityEarth pressureImposed deformationKinematic hardeningResidual stressRestraintSelf-equilibratingServiceability

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