Structural Engineering & Statics
where the load goes
Concept

Collapse — where it appears

The state at which a structure has formed enough plastic hinges or released enough members to move as a mechanism under a load that no longer increases. It is what a plastic analysis computes directly, and the load that causes it is generally well above the load at first yield.

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 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 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

Named alongside it

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

Imposed deformationRatchetingResidual stressServiceabilityShakedownThermal gradientCyclic loadingFree bodyKinematic hardeningLower-bound theoremPlastic hingeSelf-equilibrating

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