Concept

Hysteresis — where it appears

The loop a force-displacement curve traces when loading and unloading follow different paths, whose enclosed area is energy that has left. A full loop is a stable yielding mechanism and a pinched one is a buckling member, and the difference decides whether a structure survives a second cycle.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

00.511.522.530510152025forcing frequency ÷ natural frequencyamplitude ÷ static deflection1% damping — 50× at the peak2% damping — 25.01× at the peak5% damping — 10.01× at the peak10% damping — 5.03× at the peak

The only thing that stops it

Drive a structure at its own frequency and the amplitude grows without limit unless something takes energy out. What takes it out is damping, and damping is the one structural property that is never designed, never drawn, and never known until the thing is built.

dynamics · damping
02468101214161820-60-40-20204060time (s)displacement (mm)a ground motion of 3.5 m/s² peakelastic, and the same frame at a 4th of its strengthelastic: peak 57.71 mmyielding: peak 65.46 mmleft 14.13 mm off plumb

The earthquake asks for a displacement

A structure a quarter as strong as the elastic demand does not deflect four times as far. It deflects almost exactly as far, yields on the way, and survives — which is why no ordinary building is designed for the force an earthquake would apply if it stayed elastic.

dynamics · ductility demand
storey shearthe link — 800 mm0.69 kN in each diagonal per kN of shearlink shear 0.47 kN · storey drift 0.008 mm · deflection magnified 5435×

The part that is meant to be weak

A braced frame is stiff and has nowhere to yield. A moment frame yields everywhere and is soft. Move the two diagonals a metre apart along the beam and the whole storey shear has to pass through the segment between them — which keeps most of the stiffness and puts every yielding in one member the designer chose.

structures · eccentric brace

Named alongside it

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

Energy dissipationCapacity designDuctilityPlastic hingeBehaviour factorBucklingDampingDamping ratioEccentric braceEqual displacement ruleFree vibrationLateral system

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