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Concrete Beam Flexure (ACI 318)

Singly Reinforced · φMn · ρ · As

When to use: Determine the design flexural strength φMn of a singly reinforced rectangular concrete beam per ACI 318-19. Computes the Whitney stress block depth a, neutral axis c, reinforcement ratio ρ with its ρmin/ρmax bounds, net tensile strain εt control classification, and the required steel area for the factored moment Mu.

Materials & Section
ksi
ksi
in
in
in²
kip·ft
Key Formulas
a = As·fy/(0.85·f'c·b)
φMn = φ·As·fy·(d − a/2)
φ = 0.90
ρ = As/(bd)
ρmin = max(3√f'c/fy, 200/fy)
Design Moment φMn
260.5
kip·ft
Results
Stress block a4.412 in
Neutral axis c5.190 in
Design moment φMn260.5 kip·ft
Reinf. ratio ρ0.0116
ρmin0.0033
ρmax0.0206
Net tensile strain εt0.0094
ControlTension-controlled
As required for Mu2.86 in²
φMn ≥ Mu✓ OK
ρmin ≤ ρ ≤ ρmax✓ OK
✓ φMn ≥ Mu
PASS
✓ ρ limits
PASS
References
ACI 318-19 §22.2 — flexural strength
ACI 318-19 §9.6.1 — minimum reinforcement
ACI 318-19 §21.2 — strength reduction φ