Design for bending for rectangular sections (concrete beam and slab: ACI 318)
Determine if compression reinforcement is needed
Nominal strength coefficient of resistance is given;1
| Rn | = | Mu / (φ*b*d2) |
| where |
|
|
| Mu | = | factored moment at section |
| d | = | depth to tension reinforcement |
| b | = | width of the compression face of the member |
| φ | = | strength reduction factor2 |
| = | 0.9 (corresponds to the tension-controlled limit) |
| IF Rn | ≤ | Rnt | THEN compression reinforcement is not required. |
| IF Rn | > | Rnt | THEN compression reinforcement is required. |
|
| where | ||||
| Rnt | = | Limit value for tension controlled sections without compression reinforcement for different concrete strength classes3 | ||
| = | ωt *(1-0.59 ωt)* f`c | |||
| f`c | = | compressive strength of concrete | ||
| ωt | = | 0.319*β1 | ||
| β1 | = | stress block depth factor 4 | ||
| = | 0.85 | for f`c ≤ 28MPa | metric units | |
| = | 0.85 - 0.05 *[(f'c - 28MPa)/7MPa] | for 28MPa < f`c < 55MPa | ||
| = | 0.65 | for f`c ≥ 55MPa | ||
| = | 0.85 | for f`c ≤ 4000 psi | US units | |
| = | 0.85 - 0.05 *[(f'c - 4ksi)/1ksi] | for 4000 psi < f`c < 8000psi | ||
| = | 0.65 | for f`c ≥ 8000 psi | ||
|
||||
Compression reinforcement is not required
The tension reinforcement ratio is given by;
| ρ | = | 0.85*f`c/fy * [1-(1- 2*Rn/√(0.85*f`c))] ≤ ρt = 0.319*β1*f`c / fy | |
| where | |||
| fy | = | yield strength of reinforcement | |
|
The area of tension reinforcement required is then given by; |
|||
| As | = | ρ*b*d | |
|
The area of compression reinforcement required is then given by; |
|||
| As` | = | Mn`/[(d-d`)* fs`] | |
|
where |
|||
| Mn` | = | Mn-Mnt | |
| = | (Mu/φ)-Mnt | ||
| Mnt | = |
nominal moment resisted by the concrete section5 |
|
| = | Rn*b*d2 | ||
|
The area of tension reinforcement required is then given by6; |
|||
| As | = |
As`* fs`/fy + ρ*b*d |
|
| where | |||
| fs` | = | MIN[Es*(εu*(c-d`)/c) , fy ] | |
| ρ | = |
ρt*(dt/d) |
|
| ρt | = |
0.319*β1*f`c / fy |
|
| εu | = |
0.0037 |
|
| c | = |
0.375*dt |
|
|
|||
Footnotes
1 Notes on ACI 318-08 Chap 7.
2 ACI 318-08 and ACI 318-11 Section
9.3
3 Notes on ACI 318-08 Section 10.3.4
4 ACI
318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 10.2.7.3
5 Notes on ACI 318-08 Section
10.3.4
6 Notes on ACI
318-08 Chap. 7
7 ACI
318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 10.2.3