Reinforced Concrete Beam Flexural Capacity (ACI 318-19)
The design moment of a singly-reinforced, tension-controlled rectangular concrete beam: the 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 and assumed tension-controlled (confirm epsilon_t >= 0.005); compression steel, T-beam action, and minimum steel are separate checks. A design aid, not a substitute for a licensed engineer's design.
Formula and source
a = 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.
ACI 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).
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