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.
Design and check singly reinforced rectangular concrete beams for flexure per ACI 318-19. Compute the Whitney stress block depth a, neutral axis c, design moment strength phiMn, reinforcement ratio rho, and net tensile strain classification to verify tension-controlled behavior.
Enter concrete compressive strength f'c, steel yield strength fy, beam width b, effective depth d, steel area As provided, and factored moment Mu. The calculator finds the Whitney stress block depth a = As·fy/(0.85·f'c·b), neutral axis c = a/β₁, and design strength φMn = 0.9·As·fy·(d − a/2). It also solves the required As for Mu using the quadratic formula.
Whitney stress block: a = As·fy/(0.85·f'c·b). Design moment: φMn = 0.9·As·fy·(d − a/2). Net tensile strain: εt = 0.003·(d − c)/c. β₁ = 0.85 for f'c ≤ 4 ksi, reducing by 0.05 per ksi above 4 (min 0.65). Tension-controlled when εt ≥ 0.005 (φ = 0.90 applicable). ρmin = max(3√f'c/fy, 200/fy).
Use for rectangular singly-reinforced beams where tension steel alone resists the applied moment. Double-reinforced beams (compression steel required) and T-beams with flanges in compression require additional calculations. Always verify the section is tension-controlled (εt ≥ 0.005) to use φ = 0.90.
A section is tension-controlled when the net tensile strain εt at the extreme tension steel is at least 0.005 when the concrete reaches its limiting strain of 0.003. This ensures ductile behavior and allows the full strength reduction factor φ = 0.90 for flexure.
ACI 318 replaces the actual parabolic concrete stress distribution with an equivalent rectangular (Whitney) stress block of depth a = β₁·c and uniform stress 0.85·f'c. This simplification gives the same resultant force and moment arm as the actual distribution.
ACI 318 §9.6.1 requires ρ ≥ ρmin = max(3√f'c/fy, 200/fy) to ensure the member is stronger than the uncracked section. The maximum ρ corresponds to εt = 0.004 (transition zone boundary); exceeding it produces a compression-controlled section with reduced φ.
Only for rectangular sections in pure tension. For T-beams where the flange is in compression, substitute the effective flange width for b when the neutral axis falls within the flange. If the neutral axis extends below the flange, a separate T-beam analysis is required.