Structural Engineering & Statics
where the load goes
Concept

Plan torsion — where it appears

The twisting of a storey about its centre of rigidity, caused by any eccentricity of the applied force and worst at the wall furthest from that centre. The displacement it adds grows with distance from the centre of rigidity, so the corner furthest away moves most and is where the cladding is.

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

centre of masscentre of rigidity1000 kNwest wall500 kN direct+ 39 torsional= 539 kNeast wall500 kN direct+ 39 torsional= 539 kNsouth wall0 kN direct− 19 torsional= 19 kNnorth wall0 kN direct+ 19 torsional= 19 kNcentre of rigidity at x = 15.00 m, y = 9.00 mtorsional radius r = 17.02 m against a plan radius of 10.10 mtorsionally stiff by the usual criterion

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 0.020.1011025000.20.40.60.8floor-plate stiffness ÷ wall stiffnessshare of the storey forcethe middle wallan end walltributary arearigid plate← soft plate

The floor is a beam lying down

A floor plate spans horizontally between the walls that resist a lateral load, carries a distributed inertia load, and has chords, a web and a span-to-depth ratio like any other beam. Its stiffness decides whether the walls share the load by their stiffness or by the area of floor nearest them — and the familiar tributary answer turns out to be neither limit.

structures · diaphragm -15-10-551015020406080across the face (m from the centre)column stress (N/mm²)13 columns at 3.0 mcorner 78.513.4 in the middleplane sectionseffective width 45% · stiffness 64% of gross

The columns that lean

A framed tube carries its wind load by bending the spandrel beams between its columns, and it does it badly — the corner columns take nearly six times what the middle ones do. Tilt the columns instead, so the perimeter is triangulated, and the same shear is carried axially. The concentration falls to 1.23 and the tube recovers most of the stiffness the plan said it had.

structures · diagrid

Named alongside it

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

Lateral systemAccidental eccentricityCentre of rigidityDiaphragmLoad sharingShear wallAxial forceBracingChord forceCollectorDeep beamDiagrid

All concepts