Singly Reinforced Beam Calculator
A 230 mm wide M20 beam with 450 mm effective depth and 942 mm² of Fe 415 steel is under-reinforced, with a moment of resistance of 123.711 kN·m.
3 bars of 20 mm = 942.5 mm²; 4 of 16 mm = 804.2 mm².
123.71143560436 kN·m
Full answer, then cut to fewer decimals (not rounded):
- 123.71143560436 kN·m
- 123.7114356043 kN·m
- 123.711435604 kN·m
- 123.71143560 kN·m
- 123.7114356 kN·m
- 123.711435 kN·m
- 123.71143 kN·m
- 123.7114 kN·m
- 123.711 kN·m
- 123.71 kN·m
- 123.7 kN·m
- Neutral axis depth xu
- 205.3798913 mm
- Limiting xu,max
- 216 mm
- Section is
- under-reinforced (xu ≤ xu,max)
- Limiting moment Mu,lim
- 128.5130189 kN·m
- Steel percentage pt
- 0.9101449275 %
- Balanced steel Ast,lim
- 990.7104279 mm²
Step-by-step solution
- xu = 0.87 fy Ast / (0.36 fck b) = 0.87 × 415 × 942 ÷ (0.36 × 20 × 230) = 205.3798913 mm
- xu,max = 0.48 d = 216 mm
- Mu = 0.87 fy Ast (d − 0.42 xu) = 123.7114356 kN·m
Singly Reinforced Beam Formula
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)
Worked Example
A 230 × 450 mm (effective) M20 beam with 942 mm² of Fe 415 steel:
- xu = 0.87 fy Ast / (0.36 fck b) = 0.87 × 415 × 942 ÷ (0.36 × 20 × 230) = 205.3798913 mm
- xu,max = 0.48 d = 216 mm
- Mu = 0.87 fy Ast (d − 0.42 xu) = 123.7114356 kN·m
Limiting xu,max: 216 mm · Section is: under-reinforced (xu ≤ xu,max) · Limiting moment Mu,lim: 128.5130189 kN·m · Steel percentage pt: 0.9101449275 % · Balanced steel Ast,lim: 990.7104279 mm²
GATE tip
Mu,lim for Fe 415 is 0.138 fck b d², for Fe 250 0.148 and for Fe 500 0.133: handy to check an answer in seconds.
More Structural Engineering Calculators
-
Development Length Calculator
Ld = φ σs / (4 τbd)
σs = 0.87 fy; τbd for plain bars 1.2 (M20) to 1.9 (M40) MPa
Example: A 16 mm Fe 415 deformed bar in tension in M20 concrete: Development length Ld = 752.188 mm.
Frequently asked questions
How do I tell an over-reinforced section?
If xu from the force balance exceeds xu,max, the concrete would crush first; IS 456 then limits Mu to Mu,lim.
Where does 0.36 fck come from?
It is the average stress of the IS 456 stress block (0.447 fck peak over 3/7 parabola and 4/7 rectangle) times its depth factor.
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.
Cite this page
APA
Scientific Converters. (2026, October 15). Singly Reinforced Beam Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/singly-reinforced-beam-calculator/
IEEE
Scientific Converters, "Singly Reinforced Beam Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/singly-reinforced-beam-calculator/