Rebar Area Concrete Beam
Simplified estimate of longitudinal rebar area for a reinforced concrete rectangular beam.
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Reinforcement steel area in concrete beam
The longitudinal tensile steel area comes from A_s = M_d / (f_yd · z), where the internal lever arm is taken as z ≈ 0.85·d and d is the effective depth, measured from the compressed fibre down to the centroid of the steel. With CA-50 rebar, f_yk = 500 MPa and f_yd = 500/1.15 = 434.8 MPa. Take a rectangular beam of 20×40 cm with d = 37 cm and M_d = 80 kN·m: z = 0.85·37 = 31.45 cm, so A_s = 80·10² / (43.48·31.45) ≈ 5.85 cm², which works out to roughly 3 ⌀ 16 mm bars.
Always satisfy the minimum reinforcement ratio ρ_min = 0.15% · A_c that NBR 6118 requires (for fck ≤ 30 MPa); without it the section can fail brittlely the moment it cracks. And verify both states: ULS, the ultimate limit state that governs flexural capacity, and SLS, the serviceability side that covers crack width and deflection.
Applications
Sizing the longitudinal tensile reinforcement in reinforced-concrete beams, checking minimum and maximum steel ratios against NBR 6118 §17, pre-designing slabs and ribbed slabs, estimating bar count and gauge quickly for a budget, and sanity-checking what structural software spits out (TQS, Eberick, CYPECAD).
FAQ
Why z ≈ 0.85·d? The lever arm tracks the neutral-axis depth x. In under-reinforced sections (domain 2/3) z lands somewhere between 0.80·d and 0.90·d, so 0.85 is a safe middle value to lean on for preliminary sizing.
What is M_d? It is the design moment, M_d = γ_f · M_k, where γ_f = 1.4 for permanent and accidental loads under NBR 6118. Feed M_d into this formula, not the characteristic M_k.
Does this cover shear? No. It only sizes the longitudinal flexural steel. Stirrups, the transverse reinforcement, go through their own check using V_Rd2 and V_Rd3 in NBR 6118 §17.4.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.