Structural Engineering & Statics
where the load goes
Concept

Precast concrete — where it appears

Concrete members cast and cured away from their final position, usually pretensioned in a factory bed, then lifted into place and joined with in-situ concrete. Each part keeps its own age, creep and shrinkage, so the finished structure's forces depend on the dates its parts were cast and connected.

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

Also named here as restrained strain — the same set of essays touches all of them, so they are one junction rather than several.

Thirty years later, two concretes against one. Stress down the composite section after thirty years — a 160 mm slab cast 6 weeks after a 700 mm pretensioned beam — computed twice: with the slab as a second, younger concrete that creeps and shrinks by its own laws, and with it given the beam's concrete and age. With two concretes the slab ends at −0.15 N/mm² at its top and −0.30 at its bottom, the beam at −4.03 at its top and −7.43 at its soffit. With one, the slab is at −0.29 and −1.06, the beam at −2.22 and −8.37. The slab's own shrinkage has taken its compression away and handed it to the top of the beam, and the soffit — the fibre the prestress was designed to keep in compression — has lost 0.94 N/mm² of it. Compression is negative.

The slab that shrinks onto a finished beam

A precast beam with an in-situ slab cast on it is one member made of two concretes, and they do not age together. The slab's shrinkage is nearly the same whenever it is poured; what changes is how much shrinking the beam has left to share it with. Cast the slab at six weeks and it takes a ninth of the soffit's precompression away over thirty years. Cast it at a year and it takes a quarter, and goes into tension itself.

materials · Creep The date the joint is cast decides the sign. The moment at the pier after thirty years, for two 12 m pretensioned beams, 300 mm wide and 700 mm deep with a 160 mm slab, made continuous over the pier by a joint cast with the slab, against the beams' age when the joint and slab are cast; sagging positive, with its three parts dashed. Cast at 7 days the joint ends at +320 kN·m; at 28, +214; at 90, +59; at a year, −164. It exceeds the joint's cracking moment of 159 kN·m for any joint cast before about 45 days, and it changes sign at about 130 days. From 7 days to a year the prestress's share falls from +555 to +204, because an old beam has made most of its upward creep before it is joined; the differential shrinkage's grows from −57 to −285, because an old beam has finished its own shrinking and the slab's is then all difference; the dead load's eases from −178 to −83. The first two move the joint the same way as the beams age.

The pier that bends the wrong way

Two precast beams are made continuous over a pier by a joint cast with the deck, and the joint is designed for the hogging moment a continuous beam has there. Thirty years later it is sagging, by more than the moment that cracks its underside, because the beams were still cambering upward when they were joined. Whether that happens is decided by two dates — when the beams were cast and when the joint was — and the deck's shrinkage, which pulls the other way, is not enough to stop it.

materials · Creep

Named alongside it

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

Composite actionCreepPrestressRestrained strainShrinkageCreep coefficientIndeterminacy

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