Structural Engineering & Statics
where the load goes
Concept

Diaphragm — where it appears

A floor plate working in its own plane as a deep beam, whose stiffness relative to the walls it spans between decides how a lateral load is shared. Whether it is rigid or flexible is a comparison between its own in-plane stiffness and the walls it spans between, and the answer decides whether load is shared by stiffness or by tributary area.

Named by 3 essays across 2 fields — 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 40 N/mmas appliedbendingpure torsiondistortion=++torque 60 kNm per metre · the distortional half is 30the third and fourth cases add to the second: same torque, and one of them has none of it

The section that will not keep its shape

A box girder is closed, so torsion costs it almost nothing. What an eccentric load actually does to it is something a torsion calculation contains no term for — the rectangle becomes a parallelogram, in its own plane, along the whole length of the span.

sections · box distortion

Named alongside it

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

Accidental eccentricityCentre of rigidityEccentricityLateral systemLoad sharingPlan torsionShear wallBeam on elastic foundationBox girderChord forceCollectorCross section

All concepts