1. Analysis and Design of Reinforced Concrete Beams
King Saud University University
Civil Engineering Department
Analysis and Design of Reinforced Concrete Beams

2. Concrete Properties
1. Uniaxial Stress versus Strain Behavior in Compression  Ec o
0.45f’c fc
f’c
300
150 u

3. Concrete Properties
The standard strength test generally uses a cylindrical sample. It is tested after 28 days to test for strength, fc. The concrete will continue to harden with time.

4. Concrete Properties Compressive Strength, f’c
Normally use 28-day strength for design strength
Poisson’s Ratio, n
n ~ 0.15 to 0.20
Usually use n = 0.17

5. Modulus of Elasticity, Ec
Corresponds to secant modulus at 0.45 f’c
ACI (Sec ):
where w = unit weight
1500 kg/m3 < wc <2500 kg/m3
For normal weight concrete
(wc  2300kg/m3)= 23 Kn/m3, for Reinforced Concrete Wc= 24 Kn/m3) E (
MPa ) =
0.043 w 1 . 5 f ' (
MPa ) c c E (
MPa ) =
4,700 , f ' (
MPa ) c c

6. Concrete strain at max. compressive stress,0
For typical  curves in compression
 varies between
For normal strength concrete, 0 ~ 0.002 Ec
 o
 u
0.45f’c fc
f’c

7. Concrete Properties Maximum usable strain,  u ACI Code:  u = 0.003
Used for flexural and axial compression

8. Tensile Strength Tensile strength ~ 8% to 15% of f’c f = 0.7 f ' ( MPa
Modulus of Rupture, fr
For deflection calculations, use:
Test: f =
0.7 f ' (
MPa )
ACI Eq. 9-10 r c P fr
Mmax = P/2*a
unreinforced concrete beam

9. Tensile Strength (cont.)
Splitting Tensile Strength, fct
Split Cylinder Test
fct=2P/πDL P
Concrete Cylinder
Poisson’s
Effect

10. Steel Reinforcement
1. General
Standard Reinforcing Bar Markings

11. Steel Reinforcement Most common types for non-prestressed members:
hot-rolled deformed bars
welded wire fabric

12. Steel Reinforcement
Areas, Weights, Dimensions

13. Steel Reinforcement 2. Types
ASTM A615 - Standard Specification for Deformed and Plain-Billet Steel Bars
Grade 420: fy = 420 MPa, Dia 6 to Dia50
most common in buildings and bridges
Grade 300: fy = 300 MPa, Dia 6 to Dia 12
most ductile

14. Steel Reinforcement 3. Stress versus Strain
Stress-Strain curve for various types of steel reinforcement bar.

15. Steel Reinforcement GR 420 (less ductile)
Stress
Strain
0.20
GR 300
GR 420 (less ductile) Es 1
Es = Initial tangent modulus = 200,000 MPa
(all grades)
Note: GR300 has a longer yield plateau