Reinforced Concrete Beam Design — ACI 318-19M
Beam flexural design is the daily bread of structural engineering. This page walks through the ACI 318-19M procedure (factored moment → required A_s → check), explains tension-vs-compression-controlled, and links to a free designer that gives you ɸM_n in seconds.
Formulas
| Quantity | Formula |
|---|---|
| Required nominal moment | M_n = M_u / ɸ |
| Stress block depth (singly reinforced) | a = A_s · f_y / (0.85 · f'_c · b) |
| Neutral axis depth | c = a / β_1, with β_1 from §22.2.2.4.3 |
| Tensile strain in steel | ε_t = 0.003 · (d − c) / c |
| Tension-controlled (ɸ = 0.90) | ε_t ≥ 0.005 |
| Nominal flexural capacity | M_n = A_s · f_y · (d − a/2) |
How to use it
- Enter f'_c, f_y, beam width b, effective depth d, and total depth h.
- Enter the factored moment M_u from your analysis.
- Choose singly or doubly reinforced.
- The calculator iterates to find required A_s, a, c, and ε_t.
- Check that the section is tension-controlled (ε_t ≥ 0.005, ɸ = 0.90). If not, increase d or add compression steel.
- Verify A_s ≥ A_s,min per §9.6.1.2 and A_s ≤ A_s,max (where ε_t = 0.005).
Frequently Asked Questions
Does it check shear and deflection?
Not in this calculator. Use the Beam Deflection and Reinforcement Calculator for those — and remember to check ACI Table 9.3.1.1 (or do a full deflection analysis per §24.2).
What β_1 does it use?
ACI 318-19 §22.2.2.4.3: β_1 = 0.85 for f'_c ≤ 28 MPa, then β_1 = 0.85 − 0.05·(f'_c − 28)/7, with 0.65 ≤ β_1 ≤ 0.85.
Why does the strength-reduction factor depend on strain?
ACI 318-19 §21.2.2 grades sections by their tensile strain: tension-controlled (ε_t ≥ 0.005) get ɸ = 0.90; compression-controlled (ε_t ≤ ε_ty) get ɸ = 0.65 (or 0.75 with spirals); transition zones interpolate.
Does it consider creep and shrinkage?
No. Those are serviceability concerns covered by the deflection check.