Development Length Calculator
A 16 mm Fe 415 deformed bar in tension in M20 concrete needs a development length of 752.188 mm, about 47 bar diameters.
752.1875 mm
Full answer, then cut to fewer decimals (not rounded):
- 752.1875 mm
- 752.187 mm
- 752.18 mm
- 752.1 mm
- In bar diameters
- 47.01171875 φ
- Design bond stress τbd
- 1.92 MPa
- Bar stress σs = 0.87 fy
- 361.05 MPa
Step-by-step solution
- τbd = 1.2 MPa (IS 456 Cl. 26.2.1.1) × 1.6 = 1.92 MPa
- Ld = φ σs / (4 τbd) = 16 × 361.05 ÷ (4 × 1.92) = 752.1875 mm
Development Length Formula
Ld = φ σs / (4 τbd)
σs = 0.87 fy; τbd for plain bars 1.2 (M20) to 1.9 (M40) MPa
Worked Example
A 16 mm Fe 415 deformed bar in tension in M20 concrete:
- τbd = 1.2 MPa (IS 456 Cl. 26.2.1.1) × 1.6 = 1.92 MPa
- Ld = φ σs / (4 τbd) = 16 × 361.05 ÷ (4 × 1.92) = 752.1875 mm
Design bond stress τbd: 1.92 MPa · Bar stress σs = 0.87 fy: 361.05 MPa
GATE tip
Check Ld at simple supports with the code condition Ld ≤ 1.3 M₁/V + L₀.
More Structural Engineering Calculators
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Singly Reinforced Beam Calculator
xu = 0.87 fy Ast / (0.36 fck b), Mu = 0.87 fy Ast (d − 0.42 xu)
xu,max/d = 0.53 (Fe 250), 0.48 (Fe 415), 0.46 (Fe 500)
Example: A 230 × 450 mm (effective) M20 beam with 942 mm² of Fe 415 steel: Moment of resistance Mu = 123.711 kN·m.
Frequently asked questions
Why is Ld often quoted as 47φ?
For Fe 415 deformed bars in M20, Ld = 0.87 × 415/(4 × 1.92) = 47φ in tension.
When is Ld increased?
IS 456 adds 25 % to τbd for bars in compression, which reduces Ld; bundled bars need 10–33 % more length.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Development Length Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/development-length-calculator/
IEEE
Scientific Converters, "Development Length Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/development-length-calculator/