Structural Engineering & Statics
where the load goes
Concept

Wind load — where it appears

Pressure exerted on a structure's surfaces by moving air, proportional to the square of the wind speed and to a coefficient depending on the shape. It acts as suction on most surfaces of a building rather than as pressure, and the governing case is often uplift rather than lateral force.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

The windward guy tightens, the leeward one gives way. A 120 m mast on three guy levels, at a wind of 3 N/mm, with the deflection drawn 0.54 times its true size. The guys start at 160 kN each and end at 259 against 95, 299 against 83, 221 against 112 kN. The leeward guys still carry a real force — the lowest keeps 28 per cent of its partner's tension — and supply almost none of the restraint, because their tangent modulus has fallen to 54 per cent of the steel's. The mast top moves 100 mm, its worst bending moment is 554 kNm at 40 m, and it is carrying 801 kN of axial load that nothing but the guys put there.

Held by something that goes soft

A guy is a cable, so it has no stiffness of its own — what resists a mast's movement is the guy's geometry changing, and how much of that there is depends on the tension already in it. Wind pushes the mast towards the leeward guy, which is the one losing tension.

structures · Guyed mast Weight is the only thing holding it down. A body 1.6 m wide and 4.5 m tall weighing 22 kN, under a wind pressure of 1 kN/m². The wind delivers 2 kN and an overturning moment of 4 kNm about the leeward toe; the weight restores 18 kNm, a factor of 4.35. The resultant lands 0.18 m from the centre against a middle third of ±0.27 m, so the base is still wholly in bearing.

Whether it tips or slides

A free body pushed sideways has two ways of leaving, and which one it takes is decided before any load is known. The condition is a width divided by a height set against a coefficient of friction, and the weight, the wind pressure and the depth of the body all cancel out of it.

equilibrium · Overturning The arm goes in almost the same place whatever shape the wind is. The share of the tip drift removed by one outrigger on a 200 m core of bending stiffness 1.2 × 10¹⁰ kN·m² carrying 6,000 kN of wind in all, with an outrigger of 1.0 × 10⁸ kN·m per radian, against the outrigger's level as a share of the height, for the three profiles of the same total wind. uniform: best at 0.745 of the height, removing 45.6 per cent; power law: best at 0.749 of the height, removing 45.9 per cent; triangle: best at 0.757 of the height, removing 46.4 per cent. The curves lie almost on one another: the triangle, with three quarters of its load in the upper half against the uniform wind's half, moves the best level up by 1.2 per cent of the height.

The arm that ignores the shape of the wind

The outrigger arithmetic is usually done for a wind that is the same at every height, and real wind is not: it grows with height, and an earthquake's first mode loads a building as a triangle. The natural guess is that a load concentrated towards the top moves the best place for the arm. It barely does. Put the same total wind on a 200 m core as a uniform load, a power-law wind and a triangle, and the best level moves by just over one per cent of the height. What moves is the force in the arm — half as much again under the triangle — and how far the top goes, while the arm's own stiffness shifts its best level thirty times as far as the wind's shape does.

structures · Outrigger Sized for one amplitude, a nonlinear damper damps only a band around it. The damping of a structure with 2.0% of its own and a brace as stiff as the structure, against the storey's amplitude over the amplitude the damper was sized for, on a logarithmic scale, for dampers whose force goes as the velocity to the power α, each sized to the brace's best at the design amplitude. All four give 22.7% there. The linear damper gives it at every amplitude. A tenth of the design amplitude, α = 0.5 gives 6.4%, α = 0.3 1.9% and α = 0.15 1.4%; a hundredth of it, 1.9%, 1.4% and 1.4% — below the structure's own, because the locked brace has stiffened it.

The damper sized for the earthquake

A fluid damper whose force goes as its velocity to the power 0.3 is chosen because it caps the force a large earthquake can push through its brace. The same exponent makes its effective size depend on how far it strokes. Sized to its brace's best at the earthquake's amplitude, it adds 20.7% of critical damping there, 5.4% at three-tenths of it, and nothing at all at a tenth — where the brace has locked, the building is stiffer, and the motion its occupants feel meets a resonance that is as sharp as an undamped frame's. Giving half the brace to a linear damper keeps 9.3% under the wind for 1.2 points at the earthquake.

dynamics · Damping The same damper behind a lever is best at a larger motion. The damping of one storey with 2% of its own damping and a brace as stiff as the storey, with an α = 0.3 damper sized to its brace's best at the design amplitude with no amplifier, against the storey's amplitude, with the same damper behind stroke amplifiers of ratio 1, 2 and 3. A ratio f makes the damper act on the storey as one f to the power 1 + α larger — 2.46 and 4.17 times — so it locks more, and its band moves up by about f to the power (1 + α)/(1 − α): its best is near 3.8 and 7.5 times the design amplitude. At a hundredth of the design amplitude all three give 1.4%; at the design amplitude 22.7%, 6.4% and 2.3%.

The lever that moves the damper and not the band

A damper whose force goes as a low power of its speed is sized for the earthquake and locks in the wind. A toggle or scissor linkage multiplies its stroke, and it seemed it might move the band of amplitudes the damper serves down towards the wind. It cannot. Behind a lever of ratio f the same damper acts on the storey as one f to the power 1 + α larger, so its band moves up, not down; re-sized to the design amplitude, it gives the storey exactly the curve it had without the lever, and what has changed is the damper — a quarter of the size, a third of the force, three times the stroke. What would widen the band is a ratio that grows with the motion, and a toggle has one — until its links lie straight and it locks.

dynamics · Damping

Named alongside it

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

BraceDampingNon-linear responseSeries stiffnessViscous damperAnchorBeam-columnBearing pressureBucklingCableCoefficient of frictionCompatibility

All concepts