Generator

The plan-rigidity generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Two centres, and the distance between them is a torqueA 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.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

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.

3 essays call plan-rigidity. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

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 Structural form

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.

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

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.

4020080030002000000.20.40.60.81stiffness of each supportfraction of the deflection that is bendingrigid supportsare over here1%the beam drawn Deflection

The deflection that belongs to the support

A beam calculation answers a question about a beam sitting on things that do not move. Real ones sit on bearings, on other beams and on columns that shorten, and every one of those is a spring in series with the member — so a deflection is the sum of two things and only one of them is a property of the beam.

The library, page 3 of 6 — where plan-rigidity sits