Beam result
14 × 24 in
4-#8
f′c 4,000 psi
fy 60 ksi
d 21.50 in
PASS
All checks pass: flexure, shear, torsion, crack control.
Longitudinal torsion reinforcement Al = 1.265 in^2 required, distributed around stirrup perimeter (at least one bar in each corner, min size #3).
Torsion requires closed stirrups (one-piece or spliced U-stirrups with 135-degree hooks) per Section 9.7.6.3.1.
Flexure check
PASS
D/C moment
0.82
- φMn (design moment capacity)
- 277.41 kip-ft
- Mu (factored moment demand)
- 228.25 kip-ft
| Quantity | Value |
|---|---|
| As (tension steel area, in²) | 3.16 |
| ρ (reinforcement ratio As / (bw·d)) | 0.0105 |
| a (equivalent stress block depth, in) | 3.98 |
| c (neutral axis depth, in) | 4.69 |
| β1 (stress block factor, §22.2.2.4.3) | 0.850 |
| εt (net tensile strain) | 0.01076 |
| εty (yield strain fy / Es) | 0.00207 |
| φ (strength reduction factor, §21.2.2) | 0.90 |
| Mn (nominal moment strength, kip-ft) | 308.23 |
| φMn (design moment strength, kip-ft) | 277.41 |
| As,min (minimum steel area, in², §9.6.1.2) | 1.00 |
| As,req (steel area required for Mu, in²) | 2.55 |
| Minimum steel check (As ≥ As,min) | Satisfied |
Whitney stress block, singly reinforced
ACI 318-19 §22.2 · §9.3.3.1 · §21.2.2
Shear check
PASS
D/C shear
0.53
- φVn (design shear capacity)
- 105.96 kip
- Vu (factored shear demand)
- 57.14 kip
| Quantity | Value |
|---|---|
| Vc (concrete shear strength, kip) | 38.07 |
| Vs (stirrup shear strength, kip) | 103.20 |
| fyt (stirrup yield strength used, ksi) | 60 |
| Av (stirrup area, all legs, in²) | 0.40 |
| Av/s (provided, in²/in) | 0.0800 |
| Av,min/s (minimum, in²/in, §9.6.3.3) | 0.0117 |
| Av,req/s (required for Vu, in²/in) | 0.0295 |
| smax (maximum stirrup spacing, in, §9.7.6.2.2) | 5.4 |
| Vs,max (section limit 8√f′c·b·d, kip) | 152.30 |
| Controlling equation (Vc) | Table 22.5.5.1(a) |
φ = 0.75 for shear
ACI 318-19 §22.5 · §9.6.3 · §9.7.6.2
Torsion check
PASS
D/C torsion (combined)
0.87
- Tu (factored torsion)
- 28.00 kip-ft
- Tu,design (design torsion)
- 28.00 kip-ft
| Quantity | Value |
|---|---|
| Torsion type (equilibrium or compatibility) | Equilibrium |
| Regime (neglect / minimum / full) | Full |
| Acp (gross area enclosed by perimeter, in²) | 336.0 |
| pcp (outside perimeter, in) | 76.0 |
| Aoh (stirrup centerline area, in²) | 215.2 |
| ph (stirrup centerline perimeter, in) | 62.0 |
| Ao (0.85 Aoh, in²) | 183.0 |
| Tth (threshold torsion, kip-ft) | 7.83 |
| φTth (factored threshold, kip-ft) | 5.87 |
| Tcr (cracking torsion = 4 Tth, kip-ft) | 31.32 |
| φTcr (factored cracking, kip-ft) | 23.49 |
| Adequacy DCR (Eq. 22.7.7.1a, RSS shear+torsion) | 0.686 |
| At/s (transverse torsion reinf., in²/in per leg) | 0.0204 |
| Al (longitudinal torsion reinf., in²) | 1.265 |
| (Av+2At)/s (combined demand, in²/in) | 0.0704 |
| (Av+2At)/smin (minimum combined, in²/in) | 0.0117 |
| smax (torsion spacing limit, in) | 5.4 |
| Min long. bar (per §9.7.5.2) | #3 |
φ = 0.75 for torsion, θ = 45°
ACI 318-19 §22.7 · §9.5.4 · §9.6.4
Crack control
PASS| Quantity | Value |
|---|---|
| cc (clear cover to tension bar, in) | 2.000 |
| fs (service stress (2/3 fy), ksi) | 40.00 |
| smax (maximum bar spacing, in, §24.3.2) | 10.000 |
| sactual (actual bar spacing, in) | 3.000 |
| Spacing check (s ≤ smax) | PASS |
Bar spacing for crack control
ACI 318-19 §24.3.2
Input summary
(values as entered)
| b (in) | 14 |
| h (in) | 24 |
| Clear cover (in) | 1.5 |
| Effective depth d (in, computed) | 21.50 |
| Tension bars | 4-#8, 1 layer |
| f′c (psi) | 4,000 |
| fy (ksi) | 60 |
| λ (lightweight factor) | 1 |
| Mu (kip-ft) | 228.25 |
| Vu (kip) | 57.14 |
| Stirrups | #4, 2 legs @ 5 in |
| Tu (kip-ft) | 28 |
| Torsion type | Equilibrium |