The backprop jacked tight lands on the floor below

A backprop put in snug does not stay unloaded. On a frame of 250 mm flat slabs cast a floor a week, the slab struck at seven days takes half the weight of the next wet slab when it is cast, and over the following week it creeps down onto its backprops under the weight it was carrying a moment before and hands about a quarter of its own weight to the slab below. A millimetre of slack in those backprops costs more than all the creep, because a backprop with slack does nothing until the slab above has sagged onto it.

That essay ended with the obvious remedy for slack and a question about it. Jack the backprops to a measured force when they go in and the slack is gone, and some of the struck slab’s own weight goes into the slab below from the moment of striking. Whether the preload survives the first week, or is shed back by creep so that the slab above ends up carrying what it would have carried anyway, decides whether preloading is a design choice or only a way of installing a prop.

The answer is neither of the two the question offered. The preload survives. It is the slab below that pays for it.

Where the preload goes #

The frame is the same as before: 250 mm slabs on a 7.5 m column grid, a floor every seven days at 20 °C, one level of shores under the newest slab and one of backprops under the slab beneath that. A shore carries the wet slab above it down to the slab below; when the slab it holds reaches seven days the shores are struck and backprops put in. The difference now is that each backprop is jacked, at installation, to a force equal to some fraction of a slab’s weight before it is locked off.

The figure follows one slab through three weeks. From seven to fourteen days it is the slab just struck, the one whose backprops have gone in under it. From fourteen to twenty-one it is the slab below, carrying its own backprops’ load from the slab above as well as its own. At twenty-one days its backprops are removed and it carries its own weight alone.

Jacked to 0.30 of a slab’s weight, the backprops lift that much off the young slab at once: it starts its first week at 1.22 times its weight instead of 1.52. The jack pushes down as hard as it pushes up, so the slab below takes the same 0.30 at the same instant. A week later the young slab has become the slab below, and the backprops jacked under the next slab struck push down on it in turn. It takes 1.78 times its weight at fourteen days instead of 1.48, and creeps up to 1.86.

A preload does not reduce the load in the frame; nothing can. It decides which slab carries it and when. The young slab is relieved in its first week and pays in its second, with the preload of the backprops above landing on it exactly when its own was taken away.

The preload survives the week #

The question the snug essay asked was whether the lower slab’s creep would shed the preload back, and the force in the backprops answers it directly.

The backprop carries its preload plus its share of the next wet slab, and then creep acts on it. The snug backprop starts at 0.48 of a slab’s weight — its share of the wet slab cast above — and fills to 0.71 over the week, because the young slab above it creeps onto it. The jacked backprops start higher by about their preload and fill less. At 0.30 w the force climbs only from 0.78 to 0.86; at 0.50 w it slips from 0.98 to 0.96, and that is the only preload in the range that loses anything at all.

The lower slab’s creep, which the question expected to shed the preload, is real but small. That slab is a fortnight old, half as willing to creep as the week-old slab above it, and stiffer. What dominates is the young slab, creeping down onto its backprops under whatever it is still carrying; the more of its weight the preload has already taken, the less is left for it to creep under, so the creep that filled the snug backprop is partly spent before it starts.

So the preload is kept. It is the relief it gives the young slab that is not.

The contrast with a bolt that was already stretched is instructive. A preloaded bolt clamps plates far stiffer than itself, so a load added afterwards mostly unloads the plates and the bolt hardly notices it; the preload hides the load from the bolt. A jacked backprop sits between two slabs of nearly the same stiffness, and a preload between equals hides nothing. It moves load from one of them to the other, and the only question is whether that is the direction wanted.

Half of it creep would have done anyway #

The point of preloading is to relieve the young slab, and the fair measure of that is not the relief at the instant of jacking but what is still there at the end of its week, against what snug backprops would have left it with.

Snug backprops already take 0.23 of a slab’s weight off the young slab by creep over its first week, four-fifths of it on the first day. A preload does that work immediately, on the first morning, and creep then has less to do. At the end of the week the young slab jacked to 0.30 w carries 0.16 w less than it would have with snug backprops, not 0.30. Of every preload in the figure, about half is still relief a week later and about half is load that creep would have moved into the backprops anyway.

That is not a reason against preloading — the young slab’s worst moment is the first day, when the next wet slab arrives on it, and on that day a preload relieves it by its full amount. But it means that the slab below is charged the whole preload for a relief to the slab above that is only half as large by the end of the week. A preload is a transfer that creep had already started, made faster and made larger, and the slab below is paying for both.

Which slab is overloaded #

The quantity that decides whether any of this matters is not the load on a slab but its use of strength: the load as a multiple of its weight divided by its strength at that age as a fraction of its 28-day strength. A seven-day slab at 20 °C has about three-quarters of its eventual strength, and the strength a slab has on the day is what its loads have to be compared with.

With snug backprops the week-old slab governs. It carries 1.52 times its weight on the day the next slab is cast, with 78 per cent of its strength, and its use is 1.95; a week later the same slab, carrying 1.67 a day and a half into its second week with 90 per cent of its strength, uses 1.83. A preload moves the first figure down and the second up, in very nearly straight lines, and they cross at 0.07 of a slab’s weight, where both are 1.87.

That crossing is the best preload, and it is small. A 250 mm slab weighs 6.25 kN/m², so with props on a 1.2 m grid, each carrying 9 kN of slab, a fourteenth of a slab’s weight is about 0.6 kN a prop — a firm turn of the collar, not a hydraulic jack. It reduces the frame’s worst use of strength by four per cent, from 1.95 to 1.87.

Past the crossing the slab below governs, and every further increment of preload makes the frame worse. At 0.30 w the worst use is 2.04, already above the snug frame’s. At 0.50 w it is 2.21. A large preload does protect the young slab, exactly as intended, and overloads the slab below by more than it protected the slab above, because the slab below is carrying the preload on top of the 1.48 or so a snug frame already gives it, with only a little more strength than the week-old slab had.

Creep makes the best preload smaller #

The arithmetic without creep gives a different answer, and the difference is the point of counting creep at all.

Without creep, snug backprops carry only their share of each wet slab and the young slab is left with all of its own weight. There is more for a preload to do, and the best preload is 0.13 of a slab’s weight, lowering the worst use to 1.79. With creep, the snug backprops have already done part of that transfer, the best preload falls to 0.07, and what it achieves falls with it.

A preload chosen by the rigid arithmetic — the obvious calculation, the one a temporary-works designer would do — therefore overshoots. At 0.13 w with creep the slab below is already the one governing, and the frame is at about 1.92 rather than 1.87. The error is small at that preload and grows steadily with it; the specification that asks for a third of a slab’s weight, on the reasoning that the young slab needs protecting, is well past the point where the slab below has become the problem.

The crossing also moves with the conditions that change the two slabs’ strengths. In a cold week the week-old slab has proportionately less strength than the fortnight-old one, so it governs harder, the crossing moves to a larger preload, and preloading is worth more. In a fast cycle with heated formwork it moves the other way. The best preload is not a property of the props but of how much strength each slab has when its load arrives.

Insurance against slack #

Everything so far has assumed the snug backprops really were snug. The previous essay found that they rarely are, and that slack was the largest effect of all. Here the preload finds its unambiguous use.

A snug backprop with slack carries nothing until the slab above has sagged by the slack, and a millimetre is more than half the slab’s own deflection under its weight. Over the range up to 1.5 mm the worst use climbs from 1.95 to 2.45, because the young slab carries the next wet slab almost alone. A jacked backprop has no slack by definition. Jacking it closes the gap first and then sets the force, so the slack at installation simply does not appear in the answer: jacked to 0.05 w the worst use is 1.89 whatever slack there was, and jacked to 0.30 w it is 2.04.

That is the real argument for preloading, and it needs very little force. A twentieth of a slab’s weight — under half a kilonewton a prop — buys everything that slack would otherwise cost, and a little of the balance between the two slabs as well. More than about a fifth buys nothing further against slack and begins to cost the slab below.

What a temporary-works specification can say #

The findings come out as three instructions, and each is shorter than the reasoning behind it.

Tighten every backprop, and do not jack it. A collar turned firm — a twentieth of a slab’s weight, about half a kilonewton — removes the cost of slack completely and sits close to the best balance between the two slabs. The instruction is a tightness, checked by hand on every prop after the formwork above is struck, and it does not need a gauge.

Do not specify a large preload to protect the young slab. A preload of a third of a slab’s weight protects it on its first day, keeps half of that protection to the end of its week, and puts the whole third onto the slab below a week later. On this frame that is a worse frame than snug backprops. Where the young slab genuinely needs more relief — a cold week, a fast cycle, a thin slab — the answer is a second level of backprops, which shares the load among more slabs instead of moving it from one to the next.

Check the slab below as well as the slab above. The struck slab is the obvious one to worry about, because it is the youngest slab carrying a wet one, and the checks of a construction stage are often made only there. With any preload the slab below can govern, and what governs it is a punching check at the columns, carrying 1.8 times its weight at a fortnight. The same check made on the young slab alone would pass a frame that the slab below cannot carry.

None of this is peculiar to backprops. A prop jacked against a structure is a support that carries a load nobody computed until it was installed, and the load it carries comes off something and goes onto something else. The design question is always which, and when.

The frame, by hand #

The core of the result can be had without the creep. With rigid props and no creep, a snug backprop gives the young slab its own weight plus its share of the next wet slab, which for two slabs of slightly different stiffness linked by props is a little over half: 1.52 w on the week-old slab and 1.48 w on the fortnight-old one a week later. A preload $p$ moves exactly $p$ from the first to the second, so the two loads become $1.52 - p$ and $1.48 + p$.

Dividing by the strength ratios — 0.78 at seven days and 0.90 at fourteen — gives the two uses, and setting them equal gives the best preload:

$$\frac{1.52 - p}{0.78} = \frac{1.48 + p}{0.90} \quad\Rightarrow\quad p \approx 0.13$$

with both uses at 1.79. Creep adds roughly 0.23 to the lower slab’s load and takes the same off the upper one’s within its week, but the upper slab’s worst moment is the first day, before creep has acted, so creep raises the lower slab’s use without lowering the upper slab’s. The crossing moves to a smaller preload, 0.07, and a higher use, 1.87.

Rigid jacks and a creep law fitted later #

The calculation rests on choices that limit it.

The jack sets a force and then locks. A backprop is jacked by a screw collar or a wedge, and is then a steel prop again, with the same stiffness as a snug one. A backprop jacked with a hydraulic cylinder left in place would hold its force constant instead, and creep could not add to it; that is a different device and a different answer.

Every backprop has the same preload. In practice the force achieved by turning a collar varies from prop to prop by as much as the preload itself at the small values that work best. A specified preload of half a kilonewton a prop is a specification of tightness, not a measured force, and the numbers here are an average over the panel.

The slabs are uncracked plates. A slab carrying 1.8 times its weight at a fortnight is likely cracked over its columns and is softer than drawn — though stiffer than its cracked section says — which makes the props relatively stiffer and sharpens the transfer the preload makes. The direction of every finding here is unchanged by that; its size is not.

Shrinkage is left out. A young slab drying from its faces shortens and curls against props that do not move with it, and its upward curl at the panel centre would open a snug backprop’s gap where a jacked one would simply lose some force.

The creep at a few hours old is extrapolated. The young slab’s creep in its first day does much of the work here, and Eurocode 2’s creep function is fitted to tests loaded at days and measured over weeks. How much of the half the preload loses to creep is lost on the first day depends on that extrapolation.

Still open: the preload that is removed before the cast #

Every backprop here is jacked and left. A different sequence jacks the backprops hard when the shores above are struck, to give the young slab the relief at the moment it most needs it, and then slackens them back to snug before the next slab is struck above, so that the preload never lands on the slab below. Whether that sequence keeps the young slab’s relief through its first day — when the wet slab arrives and the use of strength peaks — while handing the slab below nothing it would not have carried anyway, or whether slackening a backprop under a creeping slab simply returns its load to the young slab a week later, is a question about which slab a load is on when a collar is turned.