The core drilled after the slab was built

A hole takes a tenth of every perimeter put a riser beside a column on the drawing, before the studs were laid out, and found that EN 1992-1-1’s shadow rule takes the same share from every perimeter the punching check uses. The control perimeter loses its share and the studs carry more; the outer perimeter loses its share and has to stand further out, and the studs with it. Because the opening was on the drawing, the rails of studs could be arranged round it and the rings extended to reach.

Most holes are not on the drawing. A building in use acquires new services — a kitchen extract on a floor that had none, a riser for a tenant’s server room, a drain from a new bathroom — and each arrives as an instruction to core-drill the slab at a stated position. Close to a column, where the services run along the gridline, that is a hole through a slab whose studs were laid out for a slab without it. The drill finds whatever is there: a stud, a rail, a bar, or nothing. This essay asks what the slab can still carry once the hole is cut, and what decides it.

The studs as they were laid out #

The slab is the one the punching essays have used throughout: 260 mm deep with an effective depth $d$ of 225 mm, carrying 12 kN/m² on 400 mm square internal columns, the frame’s moment putting the shear 300 mm off centre. On a 10 m bay the column delivers 1,182 kN, and the slab without studs is at 2.07 times its punching resistance at the control perimeter two depths out. The studs that send the check outward designed the studs it needs: twelve rails, the first ring half a depth from the face and the rest at three-quarters of a depth, until the outer perimeter — where the concrete alone can carry the shear again — stands 1.5 depths beyond the last ring.

The check asks for 1,415 mm² of studs in each ring, 118 mm² on each rail, and an outer perimeter 5.36 depths from the face, so a last ring at 3.86 depths. Nobody builds that. Studs come in stock diameters, and the smallest stock stud with at least 118 mm² is a 14 mm stud of 154 mm². Rings come in whole numbers at a fixed spacing, and the sixth ring, the first that reaches 3.86 depths, stands at 4.25. So the slab as built has 31 per cent more stud steel in each ring than the check asked for, and its outer perimeter stands at 5.75 depths, 0.39 depths further out than it needed. Neither margin was chosen. They are what is left when a check’s answer is turned into steel.

The core is checked against that slab. EN 1992-1-1’s shadow rule takes from every perimeter the part between the two tangents from the column’s centre to the hole’s outline, so the control check’s studs must carry more and the outer perimeter must stand further out. But the studs are already cast. What can be checked is whether the studs that are there, less any the hole has made useless, still carry what the control check asks, and whether the outer perimeter the built studs leave still has enough effective length.

The rail is not what decides #

A core drilled on the line of a rail cuts it; one drilled between two rails cuts nothing. That looks like the whole question, and it is the instruction most often given: drill between the rails. The next figure tests it.

The studs’ check is the easier one. A core on a rail’s line removes that rail from the check, either because it is severed or because it lies in the shadow; a core between rails, 150 mm across and one depth out, subtends 20 degrees and fits between two rails 30 degrees apart, so no rail is lost. On a rail the studs that remain are at 0.86 of what the control check asks; between rails, at 0.79. Both pass, comfortably, because the stock stud size put 31 per cent of spare steel in every ring.

The outer perimeter is the harder one, and it hardly cares where the rails are. The shadow takes the same share of the outer perimeter whether a rail runs into the hole or not, and the outer perimeter the built studs leave is fixed at 5.75 depths. With the core one depth out, the slab needs its outer perimeter at 5.73 or 5.74 depths: the built studs reach just far enough, at 1.00 of capacity. Three-quarters of a depth out the slab needs 5.80, and the outer perimeter fails at 1.01. Half a depth out, 1.02. Drilling between the rails saves the studs, which did not need saving, and does nothing for the perimeter that fails.

The room came from the rounding #

The core one depth out passes, just. The next figure asks where its room came from.

Laid out exactly as the check asked, the slab has no room for any hole. The studs would be at 1.03 of what remains and the outer perimeter at 1.06: both fail. The room the real slab has is entirely the rounding — the 31 per cent the stock stud added to every ring, which pays for the studs’ check several times over, and the 0.39 depths the sixth ring added to the reach, which pays for the outer perimeter almost exactly.

That is a margin of a kind a design never records. The check’s answer was 3.86 depths of studs; the drawing shows six rings; the calculation file says the slab passes. Nobody wrote down that it passes with 0.39 depths of reach to spare, because that number was not a decision. It is the difference between a continuous answer and the nearest whole ring, and it is all that stands between a core and a failed check.

How large a core it can take #

The next figure turns the question round: given the slab as built, how large a core can it take at each distance from the face?

About one depth out the slab can take a core of about 150 mm, on a rail or between two. Further out the room grows, because a hole of the same size subtends a narrower angle from the column’s centre and takes a smaller share of every perimeter. Closer in it shrinks. The two lines, on a rail and between rails, nearly coincide, which is the outer perimeter deciding again: it does not know where the rails are.

A 150 mm core is a small hole. A kitchen extract is 200 to 250 mm; a soil stack with its sleeve, 150 to 200. On this slab, one depth from the face, the 150 mm core is close to the largest that passes, and the next size up fails.

A margin that changes with the bay #

The room came from the rounding, and the rounding depends on how close the check’s answer happened to fall below a whole ring. The next figure shows how much that varies.

On a 7 m bay the slab needs no studs at all — it is at exactly its punching resistance without them — and any hole fails it. On a 7.25 m bay it needs two rings, and the second ring reaches half a depth further than the check needed: a 434 mm core one depth out still passes. On a 9 m bay the fourth ring reaches only 0.14 depths further than needed, and the largest core is 66 mm. Each time the bay grows enough to ask for one more ring, the new ring reaches three-quarters of a depth further than the check needed, and the room opens; as the bay grows towards the next ring the room closes again.

The studs’ own margin swings in the same way. On the 10 m bay the stock 14 mm stud gave 31 per cent more than asked; on a 12 m bay the check asks for 200 mm² a stud and the stock 16 mm stud has 201, a third of one per cent more. There a 150 mm core one depth out fails the studs’ check, at 1.02, as well as the outer perimeter, at 1.01, and the instruction to drill between the rails would not have saved it either.

Two slabs of the same design, a quarter of a metre apart in span, can differ by a factor of ten in the hole they can take. The engineer asked whether a core can be drilled beside a column cannot answer from the slab’s design; the answer is in the drawing of the studs as they were laid out, and in the arithmetic of what the check actually needed, which the calculation file may not show.

Where round the column #

The last figure maps every position round the column at which a 150 mm core could be drilled within six depths of the face, on the slab as built.

On this slab most positions are fine. The failures are a band round the column, within about a depth of the face, and the band is the same on every side and at every corner: there is no side of the column that is safe close in, and no rail that is the one to aim at. Beyond six depths EN 1992-1-1 ignores a hole altogether, and the map’s outer positions pass for that reason as much as for any margin.

On the 9 m bay the same map would be mostly open circles, and on the 7.25 m bay entirely filled. The map is a property of the slab as built, not of the design, and that is the practical instruction this essay leaves: a core beside a column is checked against the studs on the drawing of the slab as it was built, including the rounding, and not against the design’s statement that the slab passes.

What an instruction to drill should say #

The figures suggest what a building owner’s engineer should ask for before a core goes in beside a column, and it is not the slab’s design. It is three things the design does not state: the studs as laid out, with their stock size and the number of rings; the outer perimeter those rings actually leave, measured from the face; and the check’s own answer for where the outer perimeter needed to be. The difference between the last two is the slab’s room for a hole, in depths of reach, and the core’s shadow can be compared with it directly.

The same instruction should say that the frame’s moment matters. The slab here carries its shear 300 mm off centre because a moment arrives at the column from the frame, and turn the column, and the slab passes found that moment is what turns a comfortable slab into a failing one. A core on the side of the column where the moment adds shear takes its share from the most heavily loaded part of the perimeter, which the shadow rule, applying β to the whole perimeter, does not distinguish. EN 1992-1-1’s rule is symmetrical; the slab is not.

And it should say that the check’s resistance is not a strength with a known margin in it. The strength with no mechanism in it is the punching resistance’s own expression, a fit to tests with a size term that the bigger one is the weaker one explains, and its scatter about the fit is wider than the one per cent this core passes by. Passing at 1.00 is passing by the rules, and the rules’ factors are what carry the uncertainty.

A hole through a beam’s web, which the hole that costs nothing and everything followed, costs its beam by forcing the shear through two tees. A hole beside a column costs its slab by taking away perimeter the shear needed to leave by. Both are holes that look small against the member and are not small against the path the force takes, and in both cases the cost is decided by where the hole is relative to that path rather than by its area.

Checking the outer perimeter by hand #

The outer check one depth out can be followed with four numbers. The concrete alone carries $v_{Rd,c}$ = 0.658 N/mm² on this slab, and the shear to be carried across the outer perimeter is $\beta V$ = 1.149 × 1,182 kN = 1,358 kN, so the outer perimeter needs an effective length of 1,358,000/(0.658 × 225) = 9,173 mm. Without the core, that is the length of a rounded square 5.36 depths from the face: 4 × 400 + 2π × 1,206 = 9,178 mm. The built studs leave the outer perimeter 5.75 depths out, 1,294 mm, where its length is 4 × 400 + 2π × 1,294 = 9,729 mm — 556 mm more than needed. The core’s shadow, 20.3 degrees, takes 547 mm of it. What is left is 9,182 mm against 9,173 needed: 1.00, by nine millimetres of perimeter.

The shape of the arithmetic is the point. The outer check is passed or failed by the difference between two lengths of a few hundred millimetres — what the last ring’s rounding added to the perimeter, and what the core’s shadow takes from it — and either can be the larger. Neither is large compared with the perimeter, and neither appears in a calculation that stops when the slab passes.

Where the shadow rule stops #

The shadow rule is a convention. EN 1992-1-1’s tangents are a simple estimate of how much of a perimeter a hole cuts off from the column; tests on slabs with openings near columns show the loss is real, and roughly that size, but the rule’s exact numbers are not a measurement of this slab. A check that passes at 1.00 passes by the rule, not by a margin that a test would confirm.

The core is a square. A round core of 150 mm subtends a little less than a square of 150 mm, which makes the rule slightly conservative here.

The bars are not checked. A core near a column also cuts the top bars that carry the slab’s hogging moment over the column, and the flexural reinforcement ratio enters the punching resistance itself. A core that severs two of the bars in a column strip reduces the slab’s punching resistance by a little and its moment capacity over the column by more; that check is a separate one, and a drill that finds a bar should stop.

The scanner, the second core and the file #

They cannot show what the drill finds, which on most sites is decided by a scanner and a decision to move the core a few centimetres; nor the studs’ actual positions, which on a real slab are within a few centimetres of the drawing and can be checked with the same scanner. They cannot show the second core, drilled a year later by a different tenant at another column, nor the first core’s position remembered when the second is checked. And they cannot show the calculation file, which rarely records the rounding this essay found to be the whole of the slab’s room.

Still open: the slab strengthened from below after the core #

A core that fails the outer check can be paid for by extending the studs’ reach — but studs cannot be added to a slab that is already cast. Post-installed shear reinforcement, bonded bars drilled up from the soffit at an angle, can extend the reinforced zone outward by a ring or two, and carbon-fibre strips bonded to the soffit can add a little flexural steel. Whether a post-installed ring at 5 depths restores the outer perimeter a core took away, how much of the shear such bars carry when they are anchored only by bond in old concrete, and whether the reinforced zone they make is the same zone EN 1992-1-1’s outer perimeter assumes, is the question the drilled core leaves. The perimeter whose middle is not the column’s is where the outer perimeter first stopped being where the studs said, and the free body is a choice is why every one of these checks is a choice of where to cut.