1. Basic Design Principles For Reinforced Concrete Beam
Dr. M.E. Haque, PE

2. A Simply Supported Reinforced Concrete Beam -
N.A.
P = 0 A
A - A
Dr. M.E. Haque, PE

3. Three stages before collapse: 1. Un-cracked Concrete stage
2. Cracked Concrete (tension zone) - Elastic Stage
3. Cracked Concrete (tension zone) - Ultimate Strength Stage
N.A.(Zero Stress Line) P
Compression
Tension
R (Radius of Curvature)
Dr. M.E. Haque, PE

4. Typical Stress-Strain Curves for Concrete and Reinforcing Steel
Dr. M.E. Haque, PE

5. 1. Un-cracked Concrete stage
N.A.(Zero Stress Line) P
Compression
Tension
R (Radius of Curvature)
Dr. M.E. Haque, PE

6. 1. Un-cracked Concrete stageP
Compression
Tension
1. Un-cracked Concrete stage
Dr. M.E. Haque, PE

7. 1. Un-cracked Concrete Stage
ft < fr
M < Mcr
fc = ft << fc' h b d
Compression zone
Tension Zone
Strain Diagram
Stress Diagram
Tensile Stress
Compressive Stress
fc'
ft = fr = 7.5 fc' fc
ft = fc
Stress-Strain Diagram for Concrete
Dr. M.E. Haque, PE

8. At ft = fr , where modulus of rupture, fr = 7.5 fc’
C=T ; fc = ft
M = 0.5fc x (b x 0.5h) x (2/3 h)
= 1/6 fc x b x h2
fc = ft = 6M/(bh2)
C=0.5fc x (b x0.5h)
T=0.5ft x (b x0.5h)
2/3 h b
1/2 h ft fc
Stress diagram M
Section 1-1
fc = ft = Mc/Ig
where c = 0.5h
Ig = bh3/12 OR
At ft = fr , where modulus of rupture, fr = 7.5 fc’
Cracking Moment Capacity, Mcr = fr x Ig/(0.5h) = (fr x b x h2)/6
Dr. M.E. Haque, PE

9. 2. Cracked Concrete (Tension Zone) - Elastic Stage fy
0.5fy
c < 0.003
s = fs/Es
0.45fc' h b d
Compression zone
Tension Zone
Concrete Cracked
Strain Diagram
Stress Diagram
Tensile Stress
Compressive Stress
fc'
ft = fr = 7.5 fc'
fs =0.5 fy
Stress- Strain Diagram for
Concrete in Compression
Reinforcing steel in Tension Es
0.003
ft > fr
M > Mcr
fc = 0.45fc'
fs =0.5 fy
Dr. M.E. Haque, PE

10. 3. Cracked Concrete (Tension Zone) - Ultimate Strength Stageb d
Compression zone
Tension Zone
Concrete Cracked
Strain Diagram
Stress Diagram
Compressive Stress
fc'
T = Asfy  fy
Stress-Strain Diagram for Concrete in Compression
Stress-Strain Diagram for Reinforcing Steel in Tension
c = 0.003
s = fy/Es Es
0.003
ft > >fr
M > >Mcr
fs = fy
fc = entire stress block until compression failure 
Dr. M.E. Haque, PE

11. Figure 4 Manipulated Image visualization for flexural failure.
COMPRESSION
TENSION
Figure 4 Manipulated Image visualization for flexural failure.
(Digital image from Northridge Collection, Earthquake Engineering Research Center, University of California, Berkeley)
Dr. M.E. Haque, PE

12. C c T Concrete in compression 1 fc b M Reinforcing Steel in tension
Neglect concrete in tension
Concrete in compression
Reinforcing Steel in tension
Dr. M.E. Haque, PE

13. Dr. M.E. Haque, PE