Structural Engineering & Statics
where the load goes
Concept

Load arrangement — where it appears

The pattern in which a variable load is placed on a structure, chosen to maximise one action rather than to represent a state. A continuous member has to be checked for several arrangements, and the envelope of their results is in equilibrium with none of them.

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

02468101214161820-200-100100distance along the beam (m)bending moment (kNm, sagging up)the sagging envelopethe hogging envelopeeach case exact to 3e-16 · the envelope out by 23%

The envelope is not a structure

A continuous beam whose imposed load may sit on any span has eight load cases, and every one of them is a genuine state of equilibrium. The curve the design is made against is not one of them — it is assembled from different cases at different stations, and it fails the identity all eight satisfy exactly.

equilibrium · load arrangement 0.10×0.32×3×10×00.20.40.60.81tie stiffness, relative to the one drawnthrust ÷ its rigid-tie value, and bending ÷ its worstthrustbending, to 7422 kNmas built: 2168 kN, tie stretches 68 mmfunicular wL²/8f = 2250 kN · rigid tie 2229 · the difference is the rib's own shortening

The thrust that never reaches the ground

Every arch on this site has ended at the same sentence — the foundation is where an arch is really decided. A tie changes the sentence without changing the arithmetic: the horizontal force is still there, still the same size, and it now closes on itself through a bar at deck level.

structures · tied arch

Named alongside it

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

Bending momentArchAxial shorteningCompatibilityContinuityDeckEnvelopeEquilibriumFlexibilityForce methodFree bodyFunicular

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