Structural Engineering & Statics
where the load goes
Concept

Discretisation — where it appears

The division of a continuous structure into a finite set of elements, strips, stations or trial positions so that it can be computed. Where the true field lies in the family the division can represent, the answer is exact; where it does not, restricting a displacement field can only stiffen, so the error has a known sign.

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

0.511.52-0.015-0.01-0.0050.0050.010.015strips (log₁₀)error in the moment capacity2832128a tenth of a per centclosed form:x = 137.0 mmstrips: 137.0 mm

The section calculation with no formula in it

Every section result on this site is a closed form, and each was derived once for one arrangement of material. Slice the section instead, give each strip the strain a curvature puts it at, and move the neutral axis until the axial force balances — and the same twenty lines answer for a cracked section, a confined one, a prestressed one and a composite one, having been told nothing about any of them.

sections · fibre model 0123four nodes, three freedoms eachthe marked member touches six of the twelvethe global matrix, twelve by twelvethirty-six entries added in; the rest untouched

The answer that depends on how it was divided

Every computed answer in this collection came out of a structure chopped into pieces — elements, strips, stations, trial positions. The chopping is invisible in the result and it is not neutral: some divisions give the exact answer, some give one that is always too stiff, and one of them changes nothing but the cost of getting there.

deflection · discretisation

Named alongside it

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

BandwidthCompatibilityComposite actionConfinementConvergenceCracked sectionCurvatureDegrees of freedomEigenvalueEquilibriumFibre modelFlexibility

All concepts