Structural Engineering & Statics
where the load goes
Series

Maturity — the series

6 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Seventy per cent of the strength and ninety of the stiffness. Strength and modulus against age, each as a fraction of its own twenty-eight-day value. They do not move together: E follows f to the power 0.3, so at seven days the concrete has 78 per cent of its strength and 93 per cent of its stiffness, and at three days 60 and 86. A young structure is much nearer its final deflection than its final capacity. The 20 N/mm² a striking calculation asks for arrives at 2.2 days at 20 °C, 4.6 at five degrees and 1.7 at thirty-five.

    The strength it had on the day

    Every concrete strength a design quotes is a twenty-eight-day cylinder value, and a structure is loaded long before that — formwork struck at three days, the next storey cast at seven, a prestressing force transferred at two. The number that existed at the moment the load arrived is a different one.

    part 1 · materials
  2. More props, heavier slabs — unless they go in after the weight. The heaviest load any slab carries during construction, as a multiple of its own weight, against the number of levels of props under the slab being cast. Every level a shore that carried the wet concrete and moves up with the formwork: 2.00, 2.25, 2.37, 2.44 w for one to four levels. One level of shores and the rest backprops, put in snug after the formwork is struck: 2.00, 1.50, 1.33, 1.25 w. The same number of props, differently timed: a shore enters the load path before the weight it carries and passes it down, and a backprop enters after and shares only what arrives later.

    Loaded twice over before it is a month old

    A concrete floor in a building going up a storey a week carries, in its first weeks, the wet weight of the floors being cast above it, handed down through the props. By Grundy and Kabaila's arithmetic that is twice its own weight on a single level of shores, and more with more levels — 2.25 on two, 2.37 on three — because every prop that carried wet concrete passes its load down the stack. The same props put in after the formwork is struck carry nothing until something new arrives, and the peak falls to 1.5, 1.33, 1.25. The heaviest day of a floor's life is decided by when its props went in, not how many there are.

    part 2 · materials
  3. Where in a slab's first month its heaviest load lands. The load on the sixth floor of a frame of 250 mm slabs on a 7.5 m grid cast a floor every 7 days at 20 °C, on one level of shores and one of backprops, as a multiple of its own weight, against its age. Rigid and snug, no creep: a peak of 1.51 w at 14 days; steel springs and creep: a peak of 1.71 w at 21 days; the same, 1.0 mm of slack: a peak of 1.78 w at 7 days. Snug and rigid, the slab carries its heaviest load twice, a week apart, as the struck slab and then as the one below it. With creep the second is the heavier, because in the intervening week the slab above has sunk onto the backprops; with slack, the first.

    The backprop that takes load nobody gave it

    The arithmetic of propped construction says a backprop put in snug carries nothing until the next floor is cast, and then only a share of it. Count the props as the springs they are and that barely changes, because a steel prop is about seven times stiffer than the slab per square metre. Two other things change it. The young slab just struck creeps onto its backprops within a day and hands a quarter of a slab's weight down to the one below, which then carries 1.71 times its weight rather than 1.5. And a millimetre of slack at installation — about half the slab's own deflection — gives the struck slab back everything a backprop was meant to save.

    part 3 · materials
  4. The preload lifts the young slab and lands on the one below it. The load on one slab of a frame of 250 mm slabs on a 7.5 m grid cast a floor every 7 days at 20 °C, on one level of shores and one of backprops, as a multiple of its own weight, from the day it is struck at 7 days to 28 days, with creep. With its backprops put in snug (dashed) it takes 1.52 w at the cast above it, creeps down to 1.29 by the end of the week, takes 1.48 w when the slab above it is struck and cast on in turn, and creeps up to 1.71. With every backprop jacked to 0.30 w (solid) the young slab starts its week at 1.22 w and ends it at 1.14; a week later the preload of the backprops above lands on it, and it takes 1.78 w, creeping to 1.86.

    The backprop jacked tight lands on the floor below

    A backprop put in snug shares only the load that arrives after it, and creep then pushes the young slab above onto it anyway. Jack it to a preload instead and the young slab is lifted at once — but the preload survives the week, so the lift lands on the slab below the moment the next level is struck, and about half of it is load creep would have moved within the week regardless. The best preload balances the week-old slab against the fortnight-old one, and with creep it is small: a fourteenth of a slab's weight, about six hundred newtons a prop. Anything over a fifth leaves the frame worse than snug. What a small preload does buy completely is immunity to slack.

    part 4 · materials
  5. Slackening a backprop gives the young slab back more than the preload. The load on one slab of a frame of 250 mm slabs cast a floor every 7 days at 20 °C, on one level of shores and one of backprops, as a multiple of its own weight, from the day it is struck at 7 days to 21 days, with creep. Snug, it takes 1.52 w at the cast above it. With its backprops jacked to 0.15 w it takes 1.37. Slackened to snug 1.0 day later, the backprops give it back everything they carry — the preload, their share of the slab cast above and what creep has added — and its load jumps from 1.19 to 2.00 w. Let down by the preload alone, it goes from 1.23 to 1.38. A week after it is struck the slab becomes the slab below, and the backprops jacked above it land on it whatever is done to its own.

    The preload that cannot be taken back

    A backprop jacked tight under a young slab relieves it and loads the slab below by the same amount at the same instant. The obvious repair is to slacken the backprop once the young slab is past its worst, so that the preload never reaches the slab below. It cannot work. Slackened to snug, a backprop lets go of everything it carries, not only its preload, and the young slab's load jumps from 1.19 to 2.00 times its weight. Let down by the preload alone, it gives back a load the slab below has already carried at its worst.

    part 5 · materials
  6. Every day taken off the cycle is paid for in the youngest slab. For a frame of 250 mm slabs on a 7.5 m grid at 20 °C, on one level of shores: the largest use of strength of any slab against the floor cycle, with one level of backprops snug or jacked to its best preload, and with two levels snug or jacked to theirs; dotted, a seven-day cycle on snug backprops. On one level of snug backprops the worst use is 1.95 at seven days, 2.14 at five and 2.53 at three. With the best preload, 1.87, 2.01 and 2.30. With two levels, 1.79, 1.95 and 2.31; with two levels and their best preload, 1.67, 1.78 and 1.99.

    The day taken off the floor cycle

    A frame cast a floor a week loads its slabs with the same multiples of their weight whether the cycle is seven days or four. What a shorter cycle changes is how strong each slab is when its load arrives, and it changes that unequally, costing the youngest slab more than the one below it. That is why a faster cycle makes a jacked backprop more useful rather than less, and why a frame that wants four days needs both a second level of backprops and a preload to be as safe as a week on one.

    part 6 · materials

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