ACI 318-19 Beam Design Methodology
calcnote checks rectangular and flanged (T/L) beams per ACI 318-19, with all intermediate values exposed and a downloadable .docx calc-note. Design a beam.
Flexure (Ch. 22.2, Table 21.2.2, Cl 9.3.3.1, 9.6.1.2)
Flexural strength is computed using the Whitney rectangular stress block (Ch. 22.2) with β1 from Table 22.2.2.4.3. The strength-reduction factor φ follows Table 21.2.2 based on net tensile strain.
Minimum steel As,min per Cl 9.6.1.2 governs unless the 4/3 exception of Cl 9.6.1.3 applies (As,provided ≥ (4/3) · As,required). The net tensile strain must exceed 0.004 per Cl 9.3.3.1 for the section to be tension-controlled.
Rectangular and T/L beams are both supported. For T-beams, the neutral axis may fall within the flange (behaves as rectangular) or extend into the web (compression contribution from overhangs).
| ACI 318-19 reference | Topic |
|---|---|
| Ch. 22.2 | Flexural strength assumptions |
| Table 22.2.2.4.3 | β1 from f′c |
| Table 21.2.2 | φ factor (flexure) |
| Cl 9.3.3.1 | Strain limit 0.004 |
| Cl 9.6.1.2 | Minimum flexural reinforcement As,min |
| Cl 9.6.1.3 | 4/3 exception to As,min |
Shear reinforcement (Table 22.5.5.1, Cl 22.5.5.1.3, Cl 9.6.3.1)
Concrete shear strength Vc is computed from Table 22.5.5.1 using the simplified ρw-dependent method. The size-effect factor λs per Cl 22.5.5.1.3 reduces Vc for members without minimum shear reinforcement.
Minimum stirrups are required per Cl 9.6.3.1 when Vu exceeds φ · Vc / 2. Maximum stirrup spacing follows Cl 9.7.6.2.2. The maximum steel shear contribution Vs,max is limited by Table 22.5.1.2.
The stirrup yield strength fyt is capped at 60 ksi per Table 20.2.2.4a, and √f′c is capped at 100 psi per Cl 22.5.3.1.
| ACI 318-19 reference | Topic |
|---|---|
| Table 22.5.5.1 | Vc (simplified method) |
| Cl 22.5.5.1.3 | λs size-effect factor |
| Table 22.5.1.2 | Vs,max limit |
| Cl 9.6.3.1 | Minimum shear reinforcement trigger |
| Cl 9.7.6.2.2 | Maximum stirrup spacing |
| Table 20.2.2.4a | fyt cap (60 ksi) |
| Cl 22.5.3.1 | √f′c cap (100 psi) |
T-beam / L-beam effective flange width (Table 6.3.2.1)
The effective flange width bf is computed per Table 6.3.2.1 using the overhang-per-side formulation:
- Interior T-beam: overhang per side = min(8 · hf, sw/2, ln/8)
- Edge L-beam: overhang = min(6 · hf, sw/2, ln/12)
A direct bf override is available when the flange geometry is known. When the neutral axis falls within the flange, the section behaves as rectangular; when it extends into the web, the overhang compression contributes to capacity.
| ACI 318-19 reference | Topic |
|---|---|
| Table 6.3.2.1 | Effective flange width limits |
Crack control (Cl 24.3.2)
Maximum bar spacing is limited per Cl 24.3.2: s ≤ min(15 · (40,000/fs) − 2.5 · cc, 12 · (40,000/fs)).
The steel stress fs is taken as 2/3 · fy per Cl 24.3.2.1 (permitted approximation; no service-level cracked-section analysis).
Skin reinforcement is required when the total beam depth h exceeds 36 in. The engine flags this condition but does not design the skin bars.
| ACI 318-19 reference | Topic |
|---|---|
| Cl 24.3.2 | Maximum bar spacing for crack control |
| Cl 24.3.2.1 | fs approximation (2/3 · fy) and skin reinforcement |
Deflection (Cl 24.2.3, Table 24.2.3.5)
Effective moment of inertia Ie is computed per the Bischoff equation (Table 24.2.3.5), which replaced the Branson equation from ACI 318-14. The Bischoff formula uses a (2/3) · Mcr reduction, generally producing a lower Ie and larger calculated deflections for lightly reinforced sections.
Minimum thickness per Table 9.3.1.1 is checked first. Long-term deflection uses the multiplier from Cl 24.2.4.1. Deflection limits follow Table 24.2.2.
This check requires service loads and span length. When these are not provided, the deflection check is skipped.
| ACI 318-19 reference | Topic |
|---|---|
| Cl 24.2.3 | Deflection calculation requirements |
| Table 24.2.3.5 | Bischoff Ie equation |
| Table 9.3.1.1 | Minimum beam thickness |
| Cl 24.2.4.1 | Long-term deflection multiplier |
| Table 24.2.2 | Deflection limits |
Frequently asked questions
What beam types does calcnote support?
Rectangular, T-beam (interior), and L-beam (edge) per ACI 318-19. Effective flange width is computed from Table 6.3.2.1 or entered directly.
What changed for beam deflection in ACI 318-19 vs 318-14?
The Branson equation for effective moment of inertia was replaced by the Bischoff equation (Table 24.2.3.5), which uses a (2/3)*Mcr reduction. This generally gives a lower Ie and larger calculated deflections, particularly for lightly reinforced sections.
When is skin reinforcement required?
When the total beam depth h exceeds 36 in (Cl 24.3.2.1). The engine flags this and notes the requirement, though it does not design the skin bars.
Does the calculator design stirrups automatically?
The engine computes the required Vs from the demand Vu and the concrete Vc, then checks whether the provided stirrup size, legs, and spacing satisfy the demand. It also checks minimum stirrup area (Cl 9.6.3.1) and maximum spacing (Cl 9.7.6.2.2). The engineer enters the stirrup configuration; the engine confirms adequacy.