Design for bending for rectangular sections (beams and slabs: ACI 318)

Tekla Structural Designer
2021
Tekla Structural Designer

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
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