Structural Engineering & Statics
where the load goes
Generator

The load-sharing 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 beams tied together, and the deeper one takes 89% of the loadTwo simply supported beams of 6 m, one twice as deep as the other, tied together at midspan so that they have to move as one. A load of 100 kN stands on the tie. Point stiffness is 48EI/L³, so the deeper beam is 8 times as stiff — depth cubed, nothing else — and the load divides in that ratio: 11.1 kN into the shallow beam and 88.9 kN into the deep one, 11% against 89%. Both midspan points move 5.00 mm, which is the whole of the argument: the geometry of the load never entered it. The deflection is drawn 78 times full size — the real sag is 5.00 mm on a 6 m span, about 1 in 1200.P = 100 kNthe shallow beam takes 11.1 kN11% of it — one part of the stiffness in 9the deep beam takes 88.9 kN89% of it — 8 times the stiffness of its neighbourone load, two beams, one deflection: 5.0 mm each

Two beams tied together, and the deeper one takes 89% of the load. Two simply supported beams of 6 m, one twice as deep as the other, tied together at midspan so that they have to move as one. A load of 100 kN stands on the tie. Point stiffness is 48EI/L³, so the deeper beam is 8 times as stiff — depth cubed, nothing else — and the load divides in that ratio: 11.1 kN into the shallow beam and 88.9 kN into the deep one, 11% against 89%. Both midspan points move 5.00 mm, which is the whole of the argument: the geometry of the load never entered it. The deflection is drawn 78 times full size — the real sag is 5.00 mm on a 6 m span, about 1 in 1200.

2 essays call load-sharing. 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.

P = 100 kNthe shallow beam takes 11.1 kN11% of it — one part of the stiffness in 9the deep beam takes 88.9 kN89% of it — 8 times the stiffness of its neighbourone load, two beams, one deflection: 5.0 mm each Internal forces

The stiffest path takes the load

When two members share a force the split can be argued about. When they share a displacement it cannot — stiffness settles it, and nothing about the load or the plan drawing gets a vote. The consequence is that stiffening a lightly loaded member raises its stress, and the way to unload something is to soften it.

 P = 6000 kNfrom 10 storeys abovea = 3 mstrength wants 1.94 mstiffness wants 2.55 mslope 4500 kN1500 kN13500 kNm under the column12 m Structural form

The column that stops

A load path that runs straight to the ground costs almost nothing. Interrupting one costs depth in proportion to the square root of the load times the distance it is moved — and the interruption's own deflection becomes the settlement of everything standing on it.

The library, page 2 of 5 — where load-sharing sits