Design for bending for rectangular sections (beams and slabs: 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 | |
metric units | |||
|
0.85 | for f`c ≤ 28MPa | |
|
0.85 - 0.05 *[(f'c - 28MPa)/7MPa] | for 28MPa < f`c < 55MPa | |
|
0.65 | for f`c ≥ 55MPa | |
US-units | |||
|
0.85 | for f`c ≤ 4000 psi | |
|
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 |
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