Concept

Tangent modulus — where it appears

The slope of a stress-strain curve at the stress a member has reached, which is the stiffness available to resist any further change. Substituting it for the elastic modulus is what turns Euler's formula into an inelastic column curve, and it explains why residual stress lowers a real column's capacity.

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

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
5010015020000.20.40.60.811.2slenderness (effective length ÷ radius of gyration)the inelastic bandsquashingEulerminor axis: the core cubedmajor axis: the core itself

The column that had yielded before it was loaded

A real column sits below both of the two straight answers over the whole middle of the slenderness range, and the usual explanation — that it was not straight — is only half of it. The other half is that the flange tips had already yielded when it left the rolling mill.

stability · inelastic buckling
259 kN95299 kN83221 kN112wind 3 N/mmtop moves 100 mmleewardwindwardaxial load from the guys 801 kN · deflection exaggerated 0.5×

Held by something that goes soft

A guy is a cable, so it has no stiffness of its own — what resists a mast's movement is the guy's geometry changing, and how much of that there is depends on the tension already in it. Wind pushes the mast towards the leeward guy, which is the one losing tension.

structures · guyed mast

Named alongside it

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

BucklingColumn curveImperfectionResidual stressSelf equilibratingAnchorBeam columnCableCritical loadElastic limitElastic supportFirst yield

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