Reinforced Concrete Beam Flexural Capacity (ACI 318-19)
The design moment of a singly-reinforced, tension-controlled rectangular concrete beam.
Example
You enter
- Concrete strength f'c (psi) 4000
- Steel yield fy (psi) 60000
- Tension steel area As (in²) 3
- Beam width b (in) 12
- Effective depth d (in) 21.5
- Required moment Mu (kip-ft, 0 = capacity only) 200
You get
- Stress-block depth a 4.41 in
- Nominal moment Mn 289.4 kip-ft
- Phi mn 260.471
- Demand / capacity 0.77 (OK)
Checked against published worked examples from: University of Memphis.
Details, formula, and sources
ScopeThe equivalent stress-block depth a = As x fy / (0.85 x f'c x b), the nominal moment Mn = As x fy x (d - a/2), and phi Mn with phi = 0.90, plus the demand/capacity ratio against an entered required moment. A 12 x 24 in beam with three #9 Grade 60 bars on 4,000 psi concrete develops 260 kip-ft -- the textbook value -- and carries a 200 kip-ft demand at 77% utilization. Singly-reinforced; the net tensile strain is checked against fy/Es + 0.003 and phi drops below 0.90 when it falls short; compression steel, T-beam action, and minimum steel are separate checks. A design aid, not a substitute for a licensed engineer's design.
Formula or tablea = As x fy / (0.85 x f'c x b); Mn = As x fy x (d - a/2); phi Mn = 0.90 x Mn (tension-controlled); util = Mu / phi Mn.
Source and editionACI 318-19 (Building Code Requirements for Structural Concrete), by name: §22.2.2.4.1 (equivalent rectangular stress block), §22.2 (nominal flexural strength), §21.2.2 (phi = 0.90 tension-controlled).
Free accessACI 318-19 is viewable through ACI's online public-access reader; the stress-block and moment-arm arithmetic is public and printed in every reinforced-concrete text.
What governsEstimate. AHJ and licensed professional govern.
API field namesfc, fy, as_in2, b, d, mu, a_in, mn_kipft, phi_mn, util
- Section basis singly-reinforced rectangular section, tension-controlled (epsilon_t >= 0.005, phi = 0.90); confirm the strain, and use a doubly-reinforced or T-beam analysis where the section calls for itACI 318-19 §21.2.2 / §22.2
- Grade 60 default fy defaults to 60,000 psi (Grade 60 deformed bar), editable for Gr 40 / Gr 80ACI 318-19
- Companion checks separate minimum steel (§9.6.1.2), shear (rc-beam-shear), deflection, and development (rc-development-length) are separate checksACI 318-19