Structural Engineering & Statics
where the load goes
Concept

Hogging — where it appears

Bending that makes a member or a building convex upward, putting its top in tension, as over a support or on the shoulder of a settlement trough. Masonry suffers from it more than from sagging, because the top of a wall has no foundation holding it together.

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

Every section is hogged and sagged before the bridge exists. The bending moment envelope of a launched deck, section by section along its own length, taken over every position of the launch. In service each section has one sign; during the launch 100 per cent of them see both, because each passes over every pier and through every span on its way out. The worst launch moment is 42568 kNm against 40500 in service, and with no launching nose at all it would be 185977. That is why a launched bridge is a constant-depth box with symmetric flanges: the design case is not a load, it is a history.

Every section was somewhere else

A bridge pushed out over its piers subjects each of its cross-sections to a history rather than to a load case. Every one passes over every support and through every span, so the design envelope is the envelope of envelopes — and no in-service condition produces it.

structures · Launched bridge A stiff building bridges the trough it stands in. The settlement of a building 30 m long centred on the trough, over a trough 30 mm deep whose inflection points are 15 m from its centre (dashed: the ground with no building), measured from the building's settlement under its own weight, for relative stiffnesses EI/(kₛ·B⁴) of 10⁻⁴, 10⁻³ and 10⁻². At 10⁻⁴ its deflection ratio is 95% of the ground's; at 10⁻³ its deflection ratio is 66% of the ground's; at 10⁻² its deflection ratio is 17% of the ground's. The stiff building settles almost as a rigid body and leaves the trough's curvature to the ground beneath it.

The building the trough cannot bend

A tunnel leaves a settlement trough, and damage criteria are applied to the trough's deflection ratio over the length of each building above it. But a building is not the ground: it has a bending stiffness, and it takes only as much of the ground's curvature as that stiffness lets it. One number decides how much — the building's stiffness over the soil's modulus times its length to the fourth — and over two decades of it a building goes from following the trough to bridging it. Because the length enters to the fourth power, the same building is stiff when short and soft when long.

deflection · Differential settlement

Named alongside it

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

CantileverConstruction sequenceContinuityDeflection ratioDifferential settlementElastic foundationLaunching noseLoad arrangementMoment envelopeRelative stiffnessSaggingSettlement trough

All concepts