Structural Engineering & Statics
where the load goes
Generator

The tributary-load 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.
Where a beam's load comes fromA 8 × 6 m panel carrying 5 kN/m², divided at 45° from the corners. The long beams take a trapezoid of 15.0 m² each and the short beams a triangle of 9.0 m²; the four areas sum to 48.0 m², which is the panel, so no load has been invented or lost. The line loads quoted are the uniform equivalents; the real distributions peak at 15.00 kN/m at midspan.15.0 m²9.38 kN/m15.0 m²9.38 kN/m9.0 m²7.50 kN/m9.0 m²7.50 kN/m8 m6 m48.0 m² divided, 48.0 m² of panel — the division closes

Where a beam's load comes from. A 8 × 6 m panel carrying 5 kN/m², divided at 45° from the corners. The long beams take a trapezoid of 15.0 m² each and the short beams a triangle of 9.0 m²; the four areas sum to 48.0 m², which is the panel, so no load has been invented or lost. The line loads quoted are the uniform equivalents; the real distributions peak at 15.00 kN/m at midspan.

2 essays call tributary-load. 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.

15.0 m²9.38 kN/m15.0 m²9.38 kN/m9.0 m²7.50 kN/m9.0 m²7.50 kN/m8 m6 m48.0 m² divided, 48.0 m² of panel — the division closes Equilibrium

The load a beam is given is a decision

Every beam calculation on this site so far has started with a load per metre, handed over as though it were a property of the beam. It is not. It is the answer to a prior question nobody draws, and two defensible answers to it differ by sixty per cent on the same floor.

 11.522.530.40.50.60.70.80.91long span ÷ short spanshare taken by the short strips6 × 8 m: 76.0%by 2 : 1 it is a one-way slab Structural form

The slab that spans both ways

A panel supported on four sides sends its load in two directions at once, and the share is decided by a fourth power — so a panel a third longer than it is wide has already stopped being a two-way slab in any useful sense. What it does at collapse is a different calculation with a different answer.

The library, page 4 of 5 — where tributary-load sits