Structural Engineering & Statics
where the load goes
Concept

Geometric stiffness — where it appears

The change in a structure's stiffness caused by the forces already in it, which is negative under compression and is what buckling exhausts.

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

00.20.40.60.811.2020406080100120140160midspan sag (m)total load on the cable (kN)the design load, 150 kNsolved 0.740 m1.125 mtangent here 341.2 kN/mk₀ = 8T₀/L = 133.3 kN/mthe flat-cable law

The stiffness that comes from the shape

A cable has no bending stiffness whatever, and it still holds up a roof. What resists the load is the change of its own geometry, so its stiffness is a function of the tension already in it — and prestress buys stiffness that no change of material could.

structures · cable stiffness a half sine9.870 EI/L²exactits own sag shape9.882 EI/L²0.13% higha mid-span sag10.000 EI/L²1.32% higha parabola12.000 EI/L²21.59% highreference9.8696 EI/L²ten Ritz terms,as an eigenvalue problemevery guess is anupper boundP

Guessing the shape, and getting the load anyway

A column's buckling load can be had from a shape that is wrong everywhere, because the energy criterion is stationary at the true mode. The error in the load is the square of the error in the shape, and it is always high.

stability · stability energy

Named alongside it

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

StiffnessBuckled mode shapeCable netCompatibilityConservation of energyCritical loadEffective lengthEigenvalueEuler bucklingFlexural rigidityFunicularHorizontal thrust

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