Structural Engineering & Statics
where the load goes
Concept

Torsional irregularity — where it appears

A storey whose worst edge drifts much further than the average of its two edges because its floor twists. Seismic design standards flag it when that ratio passes 1.2, and the ratio saturates: past a point a more eccentric plan reads no more irregular while its corner keeps moving further.

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

The ratio stops growing and the twist does not. For a 30 × 18 m floor with a torsional radius of 10.6 m (0.35 of its length), against the distance of the centre of rigidity from the plan's middle as a share of the length, with the accidental eccentricity of 5 per cent of the plan: solid, the codes' ratio of the worst edge's displacement to the average of the two edges; dashed, the worst edge's displacement over the translation of a plan with no eccentricity. Dotted, the thresholds 1.2 and 1.4. The ratio rises to 1.76 at an eccentricity of 0.30 of the length and then falls, to 1.72 at 0.45; the edge's movement rises the whole way, from 1.20 to 4.83. The core-and-façade plan, at 0.14, reads 1.63 and moves 1.98.

A measure of twist that divides by the twist

The seismic codes decide whether a building is torsionally irregular by one ratio: the worst edge's displacement over the average of the two edges'. For a plan with no natural eccentricity that ratio is exactly how much further the corner moves than a plan without torsion would. For an eccentric plan it is not, because the twist moves the average as well as the corner, and the ratio divides one by the other. It saturates: at a torsional radius a third of the plan's length it never passes 1.76, however far the stiffness is moved off-centre, while the corner's movement keeps growing past four times. Past a point a more eccentric plan reads more regular, and the amplifier the codes build from the ratio inherits its ceiling.

structures · Plan torsion The dynamic ratio peaks where the modes couple, and falls where the static one climbs. The standards' ratio, the larger edge's displacement over the average of the two edges', for a 30 × 18 m floor swaying with a period of 0.5 s, against Ω, the torsional radius over the floor's radius of gyration, for natural eccentricities of 2.1 and 4.2 m: from a static push at the centre of mass (dashed) and from a response spectrum combined by CQC (solid); the dotted lines are 1.2 and 1.4. At 2.1 m, static 2.05 at Ω = 0.5 falling to 1.08 at 2; dynamic 1.08 at 0.5, highest at 1.42 near Ω = 1.15, and 1.10 at 2. At 4.2 m, static 2.46 at Ω = 0.5 falling to 1.15 at 2; dynamic 1.17 at 0.5, highest at 1.55 near Ω = 1.20, and 1.19 at 2.

The floor that twists in its own time

Seismic design standards flag a twisting floor by the ratio of its worst edge's movement to the average of its two edges', and a static push saturates that ratio. Give the floor mass and shake it, and it sways and twists in two modes that share the motion. A response-spectrum analysis then reads the same ratio from combined peaks — and gives a different verdict on a third of the plans tried. Floors torsionally stiffer than they sway read worse than a push says, because the coupled modes put twist at the edges. Floors torsionally flexible read better, because combining the modes keeps how far each edge moves and forgets which way, so a twisting floor's two edges both look large.

structures · Plan torsion

Named alongside it

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

Centre of rigidityPlan torsionAccidental eccentricityCentre of massDampingModal analysisNatural frequencyResponse spectrumRigid diaphragmSeismic designStorey driftTorsional radius

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