Structural Engineering & Statics
where the load goes
Concept

Debonding — where it appears

Sleeving a pretensioned strand over part of its length so that it does not grip the concrete there. It removes prestress where the beam's own weight cannot balance it, near the ends, at the cost of prestress the ends would otherwise have had in service.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

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

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 The yard's schedule has no room for the beams above. For the 12 m pretensioned beam, 300 × 700 mm, with eight strands, stored on bearers 1.0 m in from each end, debonded for the bed and the yard, with two beams stacked on it: the top fibre's stress along half the beam, N/mm², compression positive, with the stack lined up and landing 100 and 250 mm outside its bearers; dotted, the yard's limit of −3.0. Lined up, the worst is −2.98; 100 mm out, −3.24; 250 mm out, −3.63. Every beam above costs the top fibre 0.13 N/mm² for every 100 mm, at every section between the bearers.

The beam at the bottom of the stack

A precast yard stacks pretensioned beams to save space, each on bearers resting on the one below. If the bearers line up, the weight above goes straight down through them and the bottom beam never knows it is there. If they land outside its own bearers, the stack hogs the bottom beam at every section between them and takes from its top fibre relief that its debonding schedule had already spent. A schedule built for the yard leaves the bearers of a stack of three seven millimetres to be out of line. A bottom beam with a schedule of its own can be given half a metre.

sections · Prestress limits On the road the beam's top fibre has nothing left. The top fibre along the 12 m pretensioned beam, 300 × 700 mm, with eight strands, its schedule drawn for the bed and for yard bearers 1.0 m in from each end, the worst of the two bounces at each section: on its yard bearers standing still and bouncing ±30 per cent, and on a trailer carrying it 1.5 m from its front end and 2.5 m from its rear standing still and bouncing; dotted, the yard's limit of −3.0 N/mm². Yard bearers, still, −2.98 at 2.0 m; yard bearers, ±30 per cent, −3.26 at 9.8 m; trailer, still, −4.68 at 9.5 m; trailer, ±30 per cent, −4.88 at 9.5 m.

The beam the haulier holds

A pretensioned beam leaves the yard on a trailer, carried on a turntable and a bogie the haulier places, and bounced on them at road speed. The bounce works both ways: a wheel rising adds to the beam's weight over its overhangs, and a wheel falling away takes weight off — and with it the sag that was relieving the beam's top fibre between its supports. On the yard's own bearers a bounce of 30 per cent takes as much from that fibre as a stack placed 100 mm out of line. A rear overhang of 2.5 m takes five times as much. With the yard's schedule, a trailer may hold this beam only within half a metre and three quarters of a metre of its ends.

sections · Prestress limits The road is the harshest stretch of the beam's journey. The worst top fibre, at any corner of any section, of the 12 m pretensioned beam, 300 × 700 mm, with eight strands, its schedule drawn for the bed and for yard bearers 1.0 m in from each end, in N/mm² with tension negative: on the yard's bearers; on the haulier's trailer, 1.5 m and 2.5 m from its ends with a bounce of ±30 per cent; lifted by loops 1.0 m in from each end on slings at 60° with a snatch of ±20 per cent; slewed at 0.10 g; and set down on bearings sloping 1 per cent across it; dashed, the stored concrete's limit of −3.0. Yard bearers, −2.98; trailer, −4.88; lifted, −2.97; slewed, −3.13; set down, −1.79.

The beam hung from its loops

A pretensioned beam is cast in a bed, stored on bearers, hauled on a trailer and then lifted by a crane onto its bearings — and at every stage its top fibre, which the strands put in tension, has to stay inside the limit its debonding schedule was drawn for. The trailer, with a bouncing wheel and supports where the haulier put them, was the harshest stage the yard essays found. The last few metres, from the trailer to the bearings, are gentler: hung from loops at the yard's bearer positions the beam is on its bearers again, set down it is on the support its middle was designed for, and only a slew of the crane pushes it a little past its limit. Where the loops are cast decides how much margin the lift has, and the best place for them is not where the yard put its bearers but where the bed held the beam: at its ends.

sections · Prestress limits

Named alongside it

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

PrestressPretensioningTransferCantileverCable zoneImpact factorLiftingSelf-weightBondDynamic amplificationKernTolerance

All concepts