48x24 T-Beam, 6-#8
T-beam with effective flange width per ACI 318-19: flexure, shear, deflection, and crack control for a 48x24 / 6-#8 section.
T-beam: bf=48.0, bw=12, hf=6.0
12 × 24 in
4-#8
f′c 4,000 psi
fy 60 ksi
d 21.62 in
PASS
All checks pass: flexure, shear, crack control, deflection.
Flexure check
PASS
D/C moment
0.83
- φMn (design moment capacity)
- 299.25 kip-ft
- Mu (factored moment demand)
- 250.00 kip-ft
| Quantity | Value |
|---|---|
| bf (effective flange width, in) | 48.0 |
| hf (flange thickness, in) | 6.0 |
| NA location (neutral axis in flange or web) | Flange |
| As (tension steel area, in²) | 3.16 |
| ρ (reinforcement ratio As / (bw·d)) | 0.0122 |
| a (equivalent stress block depth, in) | 1.16 |
| c (neutral axis depth, in) | 1.37 |
| β1 (stress block factor, §22.2.2.4.3) | 0.850 |
| εt (net tensile strain) | 0.04447 |
| εty (yield strain fy / Es) | 0.00207 |
| φ (strength reduction factor, §21.2.2) | 0.90 |
| Mn (nominal moment strength, kip-ft) | 332.50 |
| φMn (design moment strength, kip-ft) | 299.25 |
| As,min (minimum steel area, in², §9.6.1.2) | 0.86 |
| As,req (steel area required for Mu, in²) | 2.63 |
| 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
0.77
- φVn (design shear capacity)
- 51.38 kip
- Vu (factored shear demand)
- 40.00 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) | 0.0158 |
| 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) | 2.417 |
| Spacing check (s ≤ smax) | PASS |
Bar spacing for crack control
ACI 318-19 §24.3.2
Deflection check
PASS- δD (dead load)
- 0.065 in
- δL (live load)
- 0.078 in
- δLT (long-term)
- 0.208 in
| Limit | Allowable (in) | Actual (in) | Status |
|---|---|---|---|
| L/180 | 1.333 | 0.078 | PASS |
| L/360 | 0.667 | 0.078 | PASS |
| L/480 | 0.500 | 0.208 | PASS |
| L/240 | 1.000 | 0.208 | PASS |
| Quantity | Value |
|---|---|
| Ec (modulus of elasticity, ksi) | 3,605 |
| fr (modulus of rupture, ksi) | 0.4743 |
| Ig (gross moment of inertia, in&sup4;) | 24,469.7 |
| yt (centroid to tension face, in) | 15.857 |
| Mcr (cracking moment, kip-in) | 732.0 |
| n (modular ratio Es/Ec) | 8.044 |
| kd (cracked NA depth, in) | 4.286 |
| Icr (cracked moment of inertia, in&sup4;) | 8,902.1 |
| Ie,D (effective I under dead load, in&sup4;) | 15,370 |
| Ie,total (effective I under total load, in&sup4;) | 10,231 |
| λδ (long-term multiplier, §24.2.4.1) | 2.00 |
| hmin (minimum thickness, in, Table 9.3.1.1) | 15.0 |
| h ≥ hmin | Yes |
Bischoff Ie, uniform load
ACI 318-19 §24.2.3.5 · Table 24.2.2
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 | 4-#8, 1 layer |
| f′c (psi) | 4,000 |
| fy (ksi) | 60 |
| λ (lightweight factor) | 1 |
| Mu (kip-ft) | 250 |
| Vu (kip) | 40 |
| Stirrups | #3, 2 legs @ 8 in |
| Beam type | T-beam |
| hf (flange thickness, in) | 6 |
| bf (effective flange width, in, override) | 48.0 |
| L (span, ft) | 20 |
| Support | simple |
| wD (kip/ft) | 1 |
| wL (kip/ft) | 0.8 |