Structural Engineering & Statics
where the load goes
Concept

Torsional radius — where it appears

The square root of a floor plan's torsional stiffness about its centre of rigidity divided by its stiffness in translation. With the eccentricity it decides how far the far edge of a floor moves when a storey force twists it.

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

Two centres, and the distance between them is a torque. A storey 30 by 18 m with its walls drawn heavy, pushed in one direction by 1000 kN. The force acts through the centre of mass and the storey turns about the centre of rigidity — the stiffness-weighted centroid of the walls, at x = 15.0 m — and the distance between the two is an eccentricity of 0.00 m before the 5% that has to be assumed anyway. The table below the plan splits each wall's force into its direct share and its torsional one. Torsion relieves the walls near the centre of rigidity and loads the far ones, so the wall in trouble is not the wall carrying the most: west wall is asked for 8% more than its direct share, and the walls at right angles to the push carry 19 kN each with nothing applied along them at all.

The corner that moves most

A lateral force is shared out in proportion to stiffness only if it passes through the centre of rigidity, which is not the centre of the plan and not the centre of mass. The distance between the two is a torque, and the wall that pays for it is the one furthest away and carrying least.

structures · Plan torsion 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

Named alongside it

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

Accidental eccentricityCentre of rigidityPlan torsionStorey driftDiaphragmEccentricityInstantaneous centreLateral systemLoad-sharingRigid diaphragmSeismic designShear wall

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