Structural Engineering & Statics
where the load goes
Concept

Cyclic loading — where it appears

Load applied repeatedly rather than once, so that a structure's response depends on its history as well as on the current value. It raises questions a monotonic check cannot answer — fatigue, shakedown, ratcheting and the degradation of stiffness with each cycle.

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

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 20% of the plastic moment with a 40°C profile it never yields at all; At 50% of the plastic moment with a 150°C profile it shakes down; At 90% of the plastic moment with a 260°C profile it ratchets, at 51.0% 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 map with three regions

A structure carrying a constant load and a cycling temperature has three possible fates and only one of them is a collapse. It can stay elastic, it can yield once and then stop, or it can gain a little more deformation every cycle for ever — and the third has no failure load at all.

materials · Shakedown Yielding one way makes it easier to yield the other. Mild steel taken to a strain of 1.20% and then pushed back the other way. The stress falls by 550 N/mm² before it yields again, against a yield stress of 275 — the elastic range is twice the yield stress and not once it, which is the Bauschinger effect and is a consequence of the yield surface sliding rather than growing.

Yielding one way, and then the other

A material that has yielded in tension yields earlier in compression than it did the first time, and by an amount that is exactly what makes its elastic range twice its yield stress rather than once it. That is a property no monotonic test reports and every reversing structure depends on.

materials · Ductility

Named alongside it

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

Free bodyResidual stressBauschinger effectBuckling-restrainedCollapseDuctilityEnergy dissipationHysteresisImposed deformationKinematic hardeningLow-cycle fatigueLower-bound theorem

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