Structural Engineering & Statics
where the load goes
Concept

Propped cantilever — where it appears

A member fixed at one end and simply supported at the other, so one degree indeterminate. Its prop takes a share of the load that depends on the two ends' stiffness, and if the prop moves away the member becomes a cantilever and its fixed end's moment rises.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

When the slab lets go, the stem is a cantilever again. For a 3 m stem of stiffness 67,500 kN·m² a metre, fixed at its base and propped at its top by a slab cast before the fill, backfilled in 250 mm lifts with a 60 kN/m roller: the bending moment down the stem in kN·m a metre, the base's moment positive — propped as the fill left it; after the slab has shrunk 2.08 mm away and gone slack; and with the slab tied to the stem and shrunk 4.5 mm, pulling it; dashed, the stem as a cantilever from the start. Propped, the base carries 26.6. Slack, 69.6, 2.6 times as much and close to the cantilever's 82.9. Tied, 119.9, more than the cantilever ever carried, because the slab that propped the top now pulls it.

The slab that shrinks away from the wall

A basement wall propped by its ground-floor slab before it is backfilled keeps the roller's pressure, and its slab takes it. Then the slab dries. Two millimetres of shrinkage at each end — about a year for a 30 m slab indoors — and a slab that only bears on the wall has let go of it, leaving a stem designed as propped to carry 2.6 times the base moment it was given. Tying the slab into the wall to stop that makes it worse: the slab goes on shrinking and pulls, and the base moment passes the free cantilever's.

equilibrium · Lateral pressure The seasons ride on the shrinkage. How far the slab's end has moved away from the fill since the fill was finished, over six years, for slabs 10, 20, 30 m between walls at 60 per cent humidity, swinging 3.0 K either way each year, propping a 3 m stem fixed at its base, its top held by the slab cast before its fill went up in 250 mm lifts rolled at 60 kN/m. The slab lets go of the stem at 2.08 mm (dashed). 10 m: a seasonal swing of ±0.15 mm on shrinkage reaching 1.28 mm by year six; it still touches the stem in the sixth year. 20 m: a seasonal swing of ±0.30 mm on shrinkage reaching 2.55 mm by year six; it last touches the stem 3.4 years on. 30 m: a seasonal swing of ±0.45 mm on shrinkage reaching 3.83 mm by year six; it last touches the stem 1.3 years on.

The seasons that stop reaching the wall

A ground-floor slab that has shrunk away from the basement wall it propped moves with the seasons as well, a few tenths of a millimetre at each end every year. It looks like a ratchet waiting to happen: each winter the slab presses the stem back into its fill, and each push might lock a little more pressure in. On a 30 m slab it never gets the chance — the seasons ride on a shrinkage ten times larger, and the slab last touches the wall sixteen months after the fill is finished. On a 10 m slab it touches every year for good, and the stem still loses most of its prop.

equilibrium · Lateral pressure

Named alongside it

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

CompactionLateral pressureResidual stressRetaining wallShrinkage

All concepts