What it calculates
Design rectangular and T-beam concrete beams to ACI 318-19 with customizable top and bottom reinforcement across unlimited spans. Checks include positive and negative flexure, shear, optional torsion, and short- and long-term deflection. Beam reactions link to connected column and footing calculations.
Who uses this calculator
Beam reactions link to connected column and footing calculations in the same project. Design rectangular and T-beam concrete sections to ACI 318-19 with customizable top and bottom reinforcement across unlimited spans. Checks include positive and negative flexural strength, shear, optional torsion, and short- and long-term deflection.
How it calculates
The Concrete Beam (ACI 318-19) calculator designs rectangular and T-beam sections to ACI 318-19 using strength design. Compared with the ACI 318-14 version, it updates concrete shear strength, the tension-controlled strain limit and the effective moment of inertia.
Flexural capacity
Positive and negative moment capacities φMn use the rectangular stress block at εcu = 0.003. For T-beams, the effective flange width engages the slab in compression for positive moment.
Mn = As × fy × (d - a/2) for singly reinforced rectangular sections
φ = 0.90 when the net tensile strain εt ≥ εty + 0.003, where εty = fy/Es. Below that, φ reduces linearly to 0.65 at εt = εty. A minimum tension reinforcement ratio of 0.0018 is checked.
Shear capacity
With at least minimum stirrups, Vc = 2λ√f'c bw d. With less than minimum stirrups or none, Vc = 8λs λ (ρw)^(1/3) √f'c bw d, where λs is the size effect factor. Vc is capped at 5λ√f'c bw d.
φVn = φ × min(Vc + Vs, Vmax) where Vs = Av × fy × d / s, Vmax = Vc + 8√f'c bw d, and φ = 0.75.
With varying stirrup spacing, the lowest capacity across the stirrup zones governs. Stirrup spacing is checked against the maximum spacing limits. The lightweight concrete factor λ is applied to Vc.
Torsion
Torsion design is optional when stirrups are included. If the factored torsion exceeds the threshold φTth, φTn is the lesser of the transverse and longitudinal reinforcement capacities.
Deflection
The effective moment of inertia is Ie = Ig when Ma ≤ (2/3)Mcr. Otherwise, Ie = Icr / [1 - ((2/3)Mcr/Ma)² × (1 - Icr/Ig)].
Ie is applied to the short-term, long-term and simplified DL+(LL or SL) deflections. Long-term deflection uses a creep and shrinkage factor from the sustained load duration, reduced by any compression reinforcement.
Each span is checked against the lesser of an absolute limit and an L/n limit. You can double the L/n limit for cantilevers.
