Structural Engineering & Statics
where the load goes
Concept

Self equilibrating — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
this support 0.01 lowmoment19.6 sagging24.5 hogging30.6 if the spans were simplereactions 14.0 38.5 38.5 14.0 — the inner supports carry far more than a sharethe continuous case needed stiffness; the comparison did not

The support that moved

A redundant structure knows things statics cannot see. Settle one support by ten millimetres and a complete set of bending moments appears — in equilibrium with no load at all, and larger for a stiffer beam.

deflection · indeterminacy neutral axisI-sectionstrainalways a straight linestressthe material's own curve, sidewaysC = 322.5 kN · T = 322.5 kN · lever arm 180 mm · M = 58.1 kNm0% of the area has yielded — 0 mm from the top, 0 mm from the bottom · Mp = 72.6 kNm · shape factor 1.09

The stress that was there before the load

A rolled steel section leaves the mill carrying eighty N/mm² of stress with nothing applied to it, in a pattern that sums to no force and no moment. It is invisible to every calculation and it is the knee in every column curve.

materials · residual stress -0.6%-0.4%-0.2%0.2%0.4%0.6%-300-200-100100200300strainstress, N/mm²0.469% of the strain never came back

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 024681012141600.511.52cyclescurvature gained ÷ curvature at first yieldM/Mp = 0.30, ΔT = 20°C — elasticM/Mp = 0.60, ΔT = 120°C — shakedownM/Mp = 0.85, ΔT = 200°C — ratcheting

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

Named alongside it

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

Residual stressKinematic hardeningAutofrettageBauschinger effectCollapseColumn curveCompatibilityContinuityFirst yieldImperfectionImposed deformationIndeterminacy

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