Structural Engineering & Statics
where the load goes
Concept

Cable zone — where it appears

The band within a prestressed section where the prestressing force's line may lie without breaking a stress limit at transfer or in service. Its edges move with the moment at each section, so a straight tendon that stays inside it at mid-span can leave it near the supports.

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

The force each section may carry rises from the end, and the strands must climb under it. The prestress each section of a pretensioned beam 300 × 700 mm spanning 12 m, with eight strands of 125 kN at 220 mm below its centroid may carry at transfer without its top fibre passing −2.50 N/mm² or its bottom 18 (thick), against the distance from the end: 739 kN at 0.5 m, 1,101 at 2 m, 1,507 at mid-span, where the self-weight moment is largest. All eight strands bonded from the end give 1,000 kN once their transmission length is past (dashed), which the beam can carry only near mid-span. Debonded — six bonded from the end, one debonded for 0.50 m, one debonded for 1.00 m — their force (solid) climbs in steps that stay under the line everywhere.

The strands that are sleeved at the ends

A post-tensioned tendon can be draped up towards the centroid near the supports, where the self-weight moment that made its eccentricity safe has gone. A pretensioned strand cannot: it runs straight between the abutments of the casting bed. Choose eight strands at 220 mm below the centroid of a 12 m beam and mid-span passes every limit at transfer, while a metre in from each end the top fibre cracks. The cure is to stop some strands gripping the concrete near the ends, and how many is a trade: every strand saved at mid-span by lowering the strands is a strand to sleeve at the ends.

sections · Prestress limits Out of the bed, the beam loses its own weight's help. For the 12 m pretensioned beam, 300 × 700 mm, with eight strands at 220 mm below its centroid: its self-weight moment along its length in kN·m, sagging positive — in the casting bed, which holds it at its ends (dashed), and on bearers 1.0 m in from each end (solid). Over the cantilevers the stored beam hogs, 2.6 kN·m at the bearers; between them its moment is the bed's less a constant 31.5 kN·m, the bearers' reactions acting a metre closer in. Mid-span drops from 94.5 to 63.0. That constant is the relief the top fibre loses everywhere between the bearers: 1.29 N/mm² for each metre of inset.

The beam that leaves the bed

A pretensioned beam's debonding is designed for the moment its strands are cut, when the casting bed holds it at its ends and its own weight is the largest relief its top fibre will get. Then it is lifted by loops a little in from its ends and stored on bearers a little further in. Setting the supports a metre in takes 31.5 kN·m off the self-weight moment along the whole length between them, not just at the ends, and the schedule that passed transfer with 0.07 N/mm² to spare has room for 51 mm of it. In the yard's conditions the bearers may come in 0.57 m; a metre in needs a third strand sleeved, and past 2.2 m nothing does.

sections · Prestress limits

Named alongside it

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

DebondingPrestressPretensioningTransferBondCantileverKernLiftingSelf-weightTransmission length

All concepts