12x24 Rectangular Beam, 4-#8
Rectangular beam per ACI 318-19: flexure, shear, deflection, and crack control for a 12x24 / 4-#8 section. Grade 60 steel.
12 × 24 in
3-#8
f′c 4,000 psi
fy 60 ksi
d 21.62 in
PASS
All checks pass: flexure, shear, crack control.
Flexure check
PASS
D/C moment
0.70
- φMn (design moment capacity)
- 212.05 kip-ft
- Mu (factored moment demand)
- 150.00 kip-ft
| Quantity | Value |
|---|---|
| As (tension steel area, in²) | 2.37 |
| ρ (reinforcement ratio As / (bw·d)) | 0.0091 |
| a (equivalent stress block depth, in) | 3.49 |
| c (neutral axis depth, in) | 4.10 |
| β1 (stress block factor, §22.2.2.4.3) | 0.850 |
| εt (net tensile strain) | 0.01282 |
| εty (yield strain fy / Es) | 0.00207 |
| φ (strength reduction factor, §21.2.2) | 0.90 |
| Mn (nominal moment strength, kip-ft) | 235.61 |
| φMn (design moment strength, kip-ft) | 212.05 |
| As,min (minimum steel area, in², §9.6.1.2) | 0.86 |
| As,req (steel area required for Mu, in²) | 1.63 |
| 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
0.58
- φVn (design shear capacity)
- 51.38 kip
- Vu (factored shear demand)
- 30.00 kip
| Quantity | Value |
|---|---|
| Vc (concrete shear strength, kip) | 32.82 |
| Vs (stirrup shear strength, kip) | 35.68 |
| fyt (stirrup yield strength used, ksi) | 60 |
| Av (stirrup area, all legs, in²) | 0.22 |
| Av/s (provided, in²/in) | 0.0275 |
| Av,min/s (minimum, in²/in, §9.6.3.3) | 0.0100 |
| Av,req/s (required for Vu, in²/in) | 0.0055 |
| smax (maximum stirrup spacing, in, §9.7.6.2.2) | 10.8 |
| Vs,max (section limit 8√f′c·b·d, kip) | 131.30 |
| 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
Crack control
PASS| Quantity | Value |
|---|---|
| cc (clear cover to tension bar, in) | 1.875 |
| fs (service stress (2/3 fy), ksi) | 40.00 |
| smax (maximum bar spacing, in, §24.3.2) | 10.312 |
| sactual (actual bar spacing, in) | 3.625 |
| Spacing check (s ≤ smax) | PASS |
Bar spacing for crack control
ACI 318-19 §24.3.2
Input summary
(values as entered)
| b (in) | 12 |
| h (in) | 24 |
| Clear cover (in) | 1.5 |
| Effective depth d (in, computed) | 21.62 |
| Tension bars | 3-#8, 1 layer |
| f′c (psi) | 4,000 |
| fy (ksi) | 60 |
| λ (lightweight factor) | 1 |
| Mu (kip-ft) | 150 |
| Vu (kip) | 30 |
| Stirrups | #3, 2 legs @ 8 in |