basic design principles for reinforced concrete beam
DESCRIPTION
Basic Design Principles For Reinforced Concrete Beam. P = 0. A. N.A. A - A. A. A Simply Supported Reinforced Concrete Beam -. R (Radius of Curvature). Compression. P. N.A.(Zero Stress Line). Tension. Three stages before collapse: 1. Un-cracked Concrete stage - PowerPoint PPT PresentationTRANSCRIPT
Dr. M.E. Haque, PE 1
Dr. M.E. Haque, PE 2
A Simply Supported Reinforced Concrete Beam -
N.A.
P = 0
A
AA - A
Dr. M.E. Haque, PE 3
N.A.(Zero Stress Line)
P
Compression
Tension
R (Radius of Curvature)
Three stages before collapse:1. Un-cracked Concrete stage2. Cracked Concrete (tension zone) - Elastic Stage3. Cracked Concrete (tension zone) - Ultimate Strength Stage
Dr. M.E. Haque, PE 4
Typical Stress-Strain Curves for Concrete and Reinforcing Steel
Dr. M.E. Haque, PE 5
N.A.(Zero Stress Line)
P
Compression
Tension
R (Radius of Curvature)
1. Un-cracked Concrete stage
Dr. M.E. Haque, PE 6
1. Un-cracked Concrete stage
P
Compression
Tension
fc
ft
M
C
T
b
1
1
fc
ft
fc
ft
M
C
T
b
1
1
Dr. M.E. Haque, PE 7
h
b
d
Compression zone
Tension Zone
Strain Diagram
Stress Diagram
Tensile Stress
Compressive Stress
fc'
ft = fr = 7.5 fc'fc
ft = fcStress-Strain Diagram for Concrete
1. Un-cracked Concrete Stage ft < fr
M < Mcr fc = ft << fc'
Dr. M.E. Haque, PE 8
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
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
Stress- Strain Diagram for 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 Stage
ft > >fr
M > >Mcr fs = fy
fc = entire stress block until compression failure
h
b
d
Compression zone
Tension Zone Concrete Cracked
Strain Diagram Stress DiagramCompressive Stress
fc'
T = Asfy
fy
Stress-Strain Diagram for Concrete in CompressionStress-Strain Diagram for
Reinforcing Steel in Tension
c = 0.003
s = fy/Es
Es0.003
Dr. M.E. Haque, PE 11
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
fc
M
C
T
b
1
1
c
Neglect concrete in tension
Concrete in compression
Reinforcing Steel in tension
Dr. M.E. Haque, PE 13