Structural Engineering & Statics
where the load goes
Concept

Bimoment — where it appears

A self-equilibrating stress resultant on a thin-walled open section: four flange forces with no net force and no net moment about any axis. It is the quantity conjugate to warping, it appears on no ordinary diagram, and it decays over a length set by the ratio of warping to torsional stiffness.

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

+67.0 N/mm²−67.0 N/mm²+67.0 N/mm²−67.0 N/mm²I-section, ω = ±12169 mm² at a tiptop flangebottom flangeh = 295V_f = 1.69 kN each way · V_f × h = 0.500 kN·m = the torque at the built-in endM_f = 3.04 kN·m each way · M_f × h = 0.897 kN·m² = the bimomentflange plan, sideways movement ×20 against the length

The section that cannot stay flat

Twist an I-section and its cross-section dishes out of its own plane. Stop that happening at one end and the member finds a second way to resist — the flanges bend in opposite directions — and the stress resultant that describes it has units nothing else in statics has.

sections · warping 00.511.5200.20.40.60.81distance from the loaded end (depths)self-equilibrating remainder ÷ mean stressa point loadspread over h/5split in twoone depthsame resultant, same moment · one per cent left by 1.18 depths

How far a wrong load reaches

Every figure in this collection applies a load as a point, a line or a uniform pressure, and no real load is any of those. The licence is Saint-Venant's, it is usually quoted as a principle, and it is really a statement about a wavelength.

internal-forces · saint venant

Named alongside it

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

Plane sectionsWarpingAiry stress functionDecay lengthDisturbed regionEigenvalueElasticityEnd effectFourier seriesFree bodyI-sectionOpen section

All concepts