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Bar Bending Shapes & Cutting Length Formulas

IS 2502:1963 & SP:34 · IS 2502 — Standard bar shapes; SP:34 Section 5 — Bar Bending Schedule
Standard reinforcement bar shapes used in BBS (Bar Bending Schedule) with cutting length formulas. These cover 95% of shapes used in building construction. All bends assume minimum bend radius per IS 456.
IS 2502 →Try BBS Calculator →
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Standard Bar Shapes — Cutting Length Formulas
d = bar diameter, D = bend diameter (min 4d for deformed bars). Bend deduction per 90° bend = 2d. Bend deduction per 45° bend = d. Hook allowance = 9d (standard hook) or 4d (for 90° bend + 4d extension).
ShapeCutting Length FormulaDescriptionCommon Use
Straight BarL = clear span + 2×LdPlain straight bar with development length both endsSlab bottom bars, distribution bars
Straight Bar with HooksL = clear span + 2×(9d) = span + 18dStraight bar with 180° hooks both endsPlain round bars (Fe 250), older practice
Cranked Bar (bent-up)L = clear span + 2×Ld + 2×0.42D₁Bar bent up at 45° near supports. D₁ = height of crank.Slab alternate bars bent near support for negative moment
L-Shape (90° bend)L = A + B − 2d (one bend)A = horizontal length, B = vertical length, deduct 2d per 90° bendColumn starter bars, footing dowels
U-Shape (2 bends)L = A + 2B − 4dU-bar: horizontal + two verticals, deduct 2d per bend × 2 bendsBeam bottom bars into column, slab edge bars
Z-Shape (2 opposite bends)L = A + B + C − 4d + 0.42D₁Crank offset shapeStaggered bars at construction joints
Rectangular StirrupL = 2(a+b) + 2×(9d) − 3da = width, b = depth (both measured to bar centre). Standard 135° hooks.Beam and column stirrups/ties
Rectangular Stirrup (simplified)L = 2(a+b) + 24dSimplified formula including hook allowanceQuick BBS calculation
Circular Stirrup / RingL = π×D + 24dD = diameter to bar centre. Includes overlap + hooks.Circular columns, piles
Helical ReinforcementL = n × √(π²D² + p²) + hooksn = number of turns, D = helix diameter, p = pitchCircular columns, piles
Chair Bar (support bar)L = 2a + 2b + ca = horizontal legs, b = vertical legs, c = top horizontalSupporting top reinforcement in slabs
Hairpin BarL = 2A + πd + overlapA = leg length, semi-circular bend at topSlab edge, column-beam junction
Bend Deductions (per IS 2502)
Deduct from sum of outer dimensions to get cutting length
ShapeCutting Length FormulaDescriptionCommon Use
Each 45° bendDeduct 1dd = bar diameter
Each 90° bendDeduct 2d
Each 135° bendDeduct 3dUsed in stirrup hooks
Each 180° bend (U-turn)Deduct 4d
Standard hook (180°)Add 9d4d bend + 4d extension + 1d curvePlain bars
Standard 90° hookAdd 12d4d bend + 8d extensionDeformed bars (IS 456)
Minimum Bend Radius
Per IS 456 Clause 26.2.2.5
ShapeCutting Length FormulaDescriptionCommon Use
Deformed bars (Fe 415, Fe 500)Min bend dia = 4d (≤ 20mm), 5d (> 20mm)d = bar diameter
Plain round bars (Fe 250)Min bend dia = 2d
Stirrups (≤ 12mm dia)Min bend dia = 4dAt hooks and bends
Stirrups (> 12mm dia)Min bend dia = 4d
BBS Preparation Rules
Per SP:34 Section 5
ShapeCutting Length FormulaDescriptionCommon Use
Round up cutting length to nearest25 mmStandard practice
Standard stock lengths12m (most common), 6m, 9m availableMinimize wastage by matching cutting length to stock
Wastage allowance3–5% of total steel weightAccount for offcuts, damage
Overlap (lapping) steelAdd 5–8% of total weightDepends on bar length vs member length
Chair bars / spacersAdd 1% of total weight
Binding wire8 kg per tonne of steel22 gauge GI wire
Notes
• Always measure cutting length along the bar centreline, NOT along the outer face
• For cranked bars: 0.42D₁ accounts for the extra length in the inclined portion (sin45° = 0.42 × offset height)
• Stirrup dimensions are measured centre-to-centre of the main bars they enclose
• Deformed bars (Fe 415/500) do NOT need hooks — development length is sufficient (IS 456 Clause 26.2.2.1)
• Minimum straight length after a bend: 4d for 180° hook, 12d for 90° bend
• Number each shape in BBS and reference on the structural drawing
• BBS should show: bar mark, shape, diameter, number, cutting length, total length, total weight
• Weight = total length × D²/162.2 (for D in mm, weight in kg/m)
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