Structural Engineering & Statics
where the load goes
Concept

Permanent set — where it appears

The deformation a member keeps after a load that took it past yield has been removed. It is the plastic part of the total movement, and under a repeated load it can grow cycle by cycle or settle to a fixed value, depending on whether the member shakes down.

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

What is left when the load comes off. Mild steel taken to a strain of 0.60% and then unloaded to zero stress, at which point the strain has not returned to zero: 0.469% of it is permanent.

What is left when the load comes off

Unload a section that has yielded and it does not return to nothing. It returns to a self-equilibrating stress field it did not have before, a permanent set, and an elastic range wider than the one it started with.

materials · Unloading The force climbs back to the elastic one. The peak force of each of 40 drops of a 500 kg weight dropped 1.0 m onto a structure whose stiffness gives it 2.0 mm of static deflection under the weight, onto a structure yielding at 80 kN — half the 160 kN an elastic structure takes (dotted). Perfectly plastic, every drop peaks at 80 kN and the saving holds, at the price of the ratchet. Hardening at 2 per cent, the peak climbs drop by drop: 82 kN at the first, 91 at the fifth, 131 at the 40th; hardening at 5 per cent, the peak climbs drop by drop: 86 kN at the first, 104 at the fifth, 152 at the 40th. A hardening structure ends up carrying almost the elastic force it was made weaker to avoid.

The same weight, dropped again

A structure allowed to yield under a falling weight needs only a fraction of the strength an elastic one needs — half of it for a ductility of two and a half — because the energy goes into bending the steel rather than into force. That is the whole saving, and it is spent on the first drop. Drop the same weight again and the structure yields again: a perfectly plastic one adds the same permanent set every time and never stops, and a hardening one stops only when it has stiffened itself back up to nearly the elastic force it was made weaker to avoid, after moving more than half a metre.

dynamics · Impact factor

Named alongside it

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

AutofrettageBauschinger effectDuctilityDynamic loadEnergy absorptionImpact factorKinematic hardeningPrestressRatchetingResidual stressSelf-equilibratingShakedown

All concepts