The sheet says six 25 mm bars, bottom, midspan, utilisation 0.94. The schedule goes out. Three weeks later the steel fixer stops work: five bars sit across the stirrup corners and the sixth will not go in. Somebody decides in ninety seconds to force it and pour tomorrow.
The forms come off and there is a band of honeycomb along the soffit, under the heaviest bars, at the highest moment. The stone bridged across the gaps and only mortar got through. That was not a construction failure; it was a design output nobody checked numerically. Bar arrangement passes in millimetres or it does not.
Flexural design gives you an area of steel, not an arrangement. Turning 2,945 mm² into "six 25 mm bars" is a geometric claim the flexure equation never tested: it knows nothing about the stirrup, the cover, or the stones in the mix. Not every package closes the gap — many check area, minimum steel and crack-control spacing without testing whether the bars physically fit, and fewer still test it at the support, at a lap or in the joint. Check what yours actually reports. And the usual fix, a second layer, lowers the effective depth. That is a design change, not something you push downstream.
Everything below is written to ACI 318 and to the NSCP, which states the rule the same way; that is the governing code for this article and for the worked example. The minimum clear spacing between parallel bars in a layer — clear meaning edge to edge, not centre to centre — is the largest of three values: the bar diameter, 25 mm, and four-thirds of the nominal maximum aggregate size. Which one governs tells you which remedy will work.
That third value is empirical: a placeability rule written into the code, not a result derived from mechanics. The code lets it be relaxed where the licensed design professional judges that the mix and the consolidation method will place concrete free of honeycombs and voids. The code asks for that judgment; good practice asks you to back it with a trial placement and a written instruction. The other two terms carry no such discretion.
If you sign to Eurocode 2 instead, the rule takes a different form — the greatest of the bar diameter, the aggregate size plus about 5 mm, and 20 mm — which for the beam worked below gives 30.00 mm rather than 33.33 mm, so the same section fails by 3.00 mm instead of 6.33 mm and the 20 mm aggregate remedy would have to be re-checked at 25 mm. Same method, different number: run it under the code you are actually signing to.
Three things eat the width before a main bar is placed. Cover is measured to the outermost steel, which is the stirrup. The stirrup leg takes its full diameter off each face. The bend radius takes more: stirrup corners are arcs, and the governing code sets the minimum inside bend diameter for stirrup bars 16 mm and smaller at four bar diameters; larger stirrup bars need a bigger former, which costs more width. Work the tangency and the corner bar centre sits one bend radius in from the inner face of the leg, so the layer loses the bend radius less the bar radius at each face.
The width equation. Required width = two covers + two stirrup diameters + twice the bend allowance + the sum of the bar diameters + the required clear spacing multiplied by the number of gaps. Gaps are one less than bars, which is why more and smaller bars usually makes congestion worse.
Bars in contact, tied and enclosed by the stirrup act as a unit, and the code limits a bundle to four bars. For spacing and cover the bundle counts as one equivalent bar of the same total area, so its equivalent diameter is the square root of the bar count times the diameter: √2 × 25 = 35.36 mm for a pair, √3 × 25 = 43.30 mm for three, 2 × 25 = 50.00 mm for four.
Individual bars in a bundle that terminate within the span of a flexural member must be staggered by at least 40 bar diameters: releasing every bar at one section concentrates bond demand and splitting where the bundle acts like one very large bar cut off abruptly. Bars inside three-bar and four-bar bundles must develop over an increased length, and the code prohibits bundling bars larger than 36 mm in beams.
The code requires at least 25 mm vertical clear between layers, and requires upper bars to sit directly above lower bars, not staggered between them: stacked bars leave vertical channels for concrete and the poker, while staggered bars close the section into a grid stones cannot pass. Layering lowers the steel centroid, so it lowers the effective depth and the capacity. That is redesign, not redetailing.
Beam 400 mm wide, 600 mm deep. Here is the whole input list, including the three inputs most worked examples leave out and then quietly depend on.
What this check assumes. The corner bar is taken as seated on the flat of the bottom leg, past the point where the bend arc becomes tangent to it, which is why its centre lands one bend radius in from the face. Let the bar nest into the bend instead and its centre moves to 20 - 7.5 ÷ √2 = 14.70 mm, its edge to 2.20 mm, the usable width to 295.60 mm and the actual spacing to 29.12 mm: still a fail, but by 4.21 mm rather than 6.33 mm. Every sum uses nominal bar diameters, because that is what the code spacing rules are written against; the steel fixer is fighting the rib diameter, and a deformed 25 mm bar measures roughly 27 to 28 mm across the ribs, so the code check and the argument at the pour are not quite the same check. Concrete strength, steel grade and bar area are not given, so nothing here tells you whether the utilisation after Remedy A lands at 0.99 or above 1.0, only that it rises. And the margins are carried to two decimals for traceability, not because anyone places steel to a hundredth of a millimetre: with no placing tolerance stated, treat anything under about a millimetre as no margin at all.
Each face: 40 + 10 = 50 mm. Both faces: 2 × 50 = 100 mm. Net inside width: 400 - 100 = 300 mm.
Inside bend diameter 4 × 10 = 40 mm, so the radius is 40 ÷ 2 = 20 mm. Main bar radius 25 ÷ 2 = 12.5 mm. Since 20 is greater than 12.5, the outer edge of the corner bar stands 20 - 12.5 = 7.5 mm off the leg. Both faces: 2 × 7.5 = 15 mm. Usable width: 300 - 15 = 285 mm.
Bar width 6 × 25 = 150 mm. Left for gaps: 285 - 150 = 135 mm, over 6 - 1 = 5 gaps, so 135 ÷ 5 = 27.00 mm. Ignore the bend allowance and you get the figure most people quote: (300 - 150) ÷ 5 = 30.00 mm.
Bar diameter 25.00 mm; floor 25.00 mm; aggregate term 4 ÷ 3 × 25 = 33.33 mm. The requirement is the largest, 33.33 mm, governed by the aggregate. Actual 27.00 against 33.33 fails by 6.33 mm per gap, so 5 × 6.33 = 31.67 mm of width the section does not have. Even the optimistic 30.00 mm fails by 3.33 mm.
Bottom layer: 3 × 25 = 75 mm of bar, leaving 285 - 75 = 210 mm over 3 - 1 = 2 gaps, so 210 ÷ 2 = 105.00 mm each. Passes easily, with the upper three directly above at 25 mm clear. Note what that vertical gap is: 25 mm is what the code requires between layers and the check is correct on that basis, but 25 mm of clear against 25 mm stone is the same arching condition the horizontal rule exists to prevent. The code accepts it; your poker still has to earn it.
Effective depth before: 600 - 40 - 10 - 12.5 = 537.50 mm. After: bottom bar centre 40 + 10 + 12.5 = 62.50 mm above the soffit, upper bar centre 62.5 + 12.5 + 25 + 12.5 = 112.50 mm, centroid (3 × 62.5 + 3 × 112.5) ÷ 6 = 525 ÷ 6 = 87.50 mm, so the effective depth is 600 - 87.5 = 512.50 mm. Loss: 537.50 - 512.50 = 25.00 mm, or 25.00 ÷ 537.50 = 4.65 per cent. The lever arm falls by the same 25 mm, so a beam at 0.94 utilisation on one layer will not stay there.
The requirement becomes the largest of 25.00, 25.00 and 4 ÷ 3 × 20 = 26.67 mm, so 26.67 mm. Actual 27.00 mm passes — by 27.00 - 26.67 = 0.33 mm. That is a rounding artefact, not a margin: a generous bend, a bar at the top of its diameter tolerance, or 2 mm of cover drift wipes it out. Nor is it free. A smaller top size needs more paste for the same workability, so more cement and water per cubic metre, higher shrinkage and creep, higher unit cost, and a new trial mix with revised submittals.
Solve the width equation at 33.33 mm: 2 × 40 + 2 × 10 + 2 × 7.5 + 6 × 25 + 5 × 33.33 = 80 + 20 + 15 + 150 + 166.67 = 431.67 mm, rounded up to a buildable 25 mm increment, 450 mm. Check it: 450 - 115 = 335 mm usable, less 150 leaves 185, and 185 ÷ 5 = 37.00 mm, clearing 33.33 by 3.67 mm. At 425 mm: 425 - 115 = 310, less 150 leaves 160, and 160 ÷ 5 = 32.00 mm, short by 1.33 mm. The rounding is not cosmetic.
On illustrative rates, eight such beams of 6.0 m clear span: extra concrete 0.050 × 0.600 × 6.0 = 0.180 m³ each, 8 × 0.180 = 1.44 m³ at an illustrative ₱5,200 per m³ = ₱7,488; extra soffit form 0.050 × 6.0 = 0.30 m² each, 8 × 0.30 = 2.40 m² at an illustrative ₱450 per m² = ₱1,080. Total ₱8,568, or 8,568 ÷ 8 = ₱1,071 per beam. Four assumptions sit under that total and none of them is in the input list: that the full 600 mm of depth is extra concrete, with no slab thickness overlapping the beam; that the extra 0.30 m² of soffit form per beam is genuinely extra rather than displacing an equal area of slab soffit form; that the longer stirrups, the added self-weight and any re-check they force are free; and that eight beams at 6.0 m is representative of the floor.
One honeycomb patch of 0.40 × 2.0 = 0.80 m² at an illustrative ₱2,800 per m² is ₱2,240; add an illustrative ₱6,000 for access, testing and engineering time on one non-conformance report and that single patch costs ₱8,240 — 96 per cent of what widening all eight beams would have cost, and it buys nothing. Take that the honest way round: on these rates the patch comes out ₱328 cheaper than widening, so the case for widening is not a money case and should not be argued as one. The case is that the widening is priced before the pour while the patch is priced after it, when the programme has the least room to absorb a stop; that the patch leaves a non-conformance report on the record against the frame, where the wider beam leaves a drawing revision; and that the widening fixes the detail on all eight beams, while the patch fixes one soffit and leaves the other seven detailed exactly as before, waiting to be found the same way.
Midspan is the easy check. At the joint, beam top bars from two directions, beam bottom bars being anchored, the column verticals and the column ties and crossties share one block of concrete, with the confinement steel at its closest spacing. Two failures repeat: a beam bar arriving in plan at the same offset as a column vertical, so one gets bent on site and the anchorage geometry quietly disappears; and beam bars from perpendicular framing arriving at the same elevation, so the fixer drops one set lower and changes an effective depth nobody records. Before the schedule is issued, draw the worst joint in plan at full size — every column bar, tie and crosstie leg, every beam bar, at true diameter and true position. Half an hour there finds what no spacing sum will.
None of this arithmetic is hard, just tedious enough to skip under deadline. To run the width equation across a schedule of beams, or see what changes when the cover or the aggregate size does, the section and detailing utilities on the RHCES web tools page handle the repetitive part.
Usually not. Ten 20 mm bars give 10 × 314.16 = 3,141.6 mm², against 6 × 490.87 = 2,945.2 mm² for the 25 mm layout. Required spacing stays the largest of 20.00, 25.00 and 33.33 mm — still 33.33 mm, because the aggregate term does not care about bar size. The bend allowance also grows, to 20 - 10 = 10 mm per face. Required width: 80 + 20 + 2 × 10 + 10 × 20 + 9 × 33.33 = 80 + 20 + 20 + 200 + 300 = 620 mm, against 431.67 mm for six bars. Same gap, four more of them. Downsizing helps only when the bar-diameter term governs.
Not on arithmetic alone, and which term governs decides your options. If the aggregate term governs, the code allows it to be relaxed where the licensed design professional judges that the mix and the consolidation method will place concrete free of honeycombs and voids. That judgment is what the code asks for; a qualified mix, a trial placement and a written instruction are what good practice asks you to put behind it, in place of a verbal call at the pour. If the bar diameter or the 25 mm floor governs, that discretion is not offered and you fix the geometry. Either way, record the decision: a 2 mm allowance agreed on site is invisible two years later when somebody opens the soffit.