DEPARTMENT OF CIVIL ENGINEERING
CE-2105
DESIGN OF CONCRETE STRUCTURE-I
DESIGN OF BEAM
(AS PER ACI CODE)
Course TeacherPresented ByDr. Md. Rezaul Karim Md. Jahidur Rahman
Associate Professor
S.ID- 121041
Dhaka University of Engineering &
Technology, Gazipur-1700
Content
USD(Ultimate Strength Design)
Classification of beam with respect to design system
Assumptions
Evolution of design parameters
Moment Factors Kn,
Balanced Reinforcement Ratio b
Calculating Strength Reduction Factor
Calculating
Design procedure for Singly Reinforced Beam
Design procedure for Doubly Reinforced Beam
Design procedure for T-Beam
Appendix
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Ultimate Strength Design(USD)
Assuming tensile failure condition
Additional strength of steel after yielding
ACI code emphasizes this method
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Classification of beam with respect to design system
Rectangular beam (reinforced at tension zone only)
Doubly reinforced beam (reinforced at both tension and
compression zone)
T section beam (both beam and slab are designed
together)
ASSUMPTIONS
Plane sections before bending remain plane and
perpendicular to the N.A. after bending
Strain distribution is linear both in concrete & steel and is
directly proportional to the distance from N.A.
Strain in the steel & surrounding concrete is the same prior to
cracking of concrete or yielding of steel
Concrete in the tension zone is neglected in the flexural
analysis & design computation
b
c=0.003
c
h
0.85fc
a
a/2
C
d
d-a/2
s = fy / Es
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Concrete stress of 0.85fc is uniformly distributed over an
equivalent compressive zone.
fc = Specified compressive strength of concrete in psi.
Maximum allowable strain of 0.003 is adopted as safe limiting
value in concrete.
The tensile strain for the balanced section is fy/Es
Moment redistribution is limited to tensile strain of at least
0.0075
fs
Actual
fy
Idealized
Es
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EVALUATION OF DESIGN PARAMETERS
Total compressive force - C = 0.85fc ba
Total Tensile force-
(Refer stress diagram)
T = As fy
C=T
0.85fc ba = As fy
a = As fy / (0.85fc b)
= d fy / (0.85 fc) [ = As / bd]
Moment of Resistance/Nominal MomentMn = 0.85fc ba (d a/2)
or,
Mn = As fy (d a/2)
= bd fy [ d (dfyb / 1.7fc) ]
= fc [ 1 0.59 ] bd2
= fy / fc
Mn = Kn bd2 Kn = fc [ 1 0.59 ]
Ultimate Moment- Mu = Mn
= Kn bd2
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( = Strength Reduction Factor)
Balaced Reinforcement Ratio ( b)
From strain diagram, similar triangles
cb / d = 0.003 / (0.003 + fy / Es); Es = 29x106 psi
cb / d = 87,000 / (87,000+fy)
Relationship b / n the depth `a of the equivalent rectangular stress block
& depth `c of the N.A. is
a = 1c
1= 0.85
; fc 4000 psi
1= 0.85 - 0.05(fc 4000) / 1000
; 4000 < fc 8000
1= 0.65
; fc> 8000 psi
b = Asb / bd
= 0.85fc ab / (fy. d)
= 1 ( 0.85 fc / fy) [ 87,000 / (87,000+fy)]
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For beams the ACI code limits the max. amount of steel to 75% of
that required for balanced section.
0.75 b
Min. reinforcement is greater of the following:
Asmin = 3fc x bwd / fy
or
200 bwd / fy
min = 3fc / fy
or
200 / fy
For statically determinate member, when the flange is in tension,
the bw is replaced with 2bw or bf whichever is smaller
The above min steel requirement need not be applied, if at every
section, Ast provided is at least 1/3 greater than the analysis
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Calculating
Yes
No
No
Yes
Calculating
SINGLY REINFORCED BEAM
Beam is reinforced near the tensile
Reinforcement resists the tension.
Concrete resists the compression.
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face
DESIGN PROCEDURE FOR
SINGLY REINFORCED BEAM
1. Determine the
service loads
2. Assume `h` as per
the support conditions
[As per ACI code in
table 9.5(a)]
6. Primary elastic analysis
and derive B.M (M), Shear
force (V) values
7. Compute min and b
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3. Calculate d= h Effective cover
4. Assume the value of `b` by the
rule of thumb
5. Estimate self weight
8.Choose between min and b
9. Calculate , Kn
10. From Kn & M
calculate `d required
OK
11. Check the required `d with
assumed `d
12. With the final values of , b, d
determine the Total As required
Note Below:
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Design the steel reinforcement arrangement with appropriate cover and
spacing stipulated in code. Bar size and corresponding no. of bars based on
the bar size #n.
Check crack width as per codal provisions.
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DESIGN PROCEDURE FOR
SINGLY REINFORCED BEAM BY FLOWCHART
Maximum steel ratio
Actual steel ratio
Over
reinforced
beam
Yes
Ultimate moment
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No
Under
reinforced
beam
DOUBLY REINFORCED BEAM
Beam
is fixed for Architectural purposes.
Reinforcement are provided both in tension and
compression zone.
Concrete has limitation to resist the total compression
so extra reinforcement is required.
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DESIGN
PROCEDURE
FOR
DOUBLY
REINFORCED
BEAM
Concrete
section, Area
of steel are
known
Compression bar
does not reach in
yielding
Maximum steel ratio
Actual steel ratio
rectangular
beam
No
Yes
No
Yes
Doubly
reinforced
beam
Compression and
tension bar reach in
yielding
DESIGN
PROCEDURE
FOR
DOUBLY
REINFORCED
BEAM
Reinforcement
required in comp.
zone too
Load or
ultimate
moment is
given
Doubly
reinforced
beam
Maximum steel ratio
Yes
No
rectangular
beam
T- REINFORCED BEAM
A part of slab acts as the upper part of
Resulting cross section is T shaped.
The
beam.
slab portion of the beam is flange.
The beam projecting bellow is web or stem.
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DESIGN
PROCEDURE
FOR
T-REINFORCED
BEAM
calculation
Yes
Are of concrete
section, Area of
steel are known
No
T - beam
analysis
Rectangular
beam analysis
modification
Nominal moment
Additional moment
Total moment
DESIGN
PROCEDURE
FOR
TREINFORCED
BEAM
T - beam
analysis
Moment or loading is
given
calculation
T section:
L section:
No
Area of steel in flange
Yes
Rectangular
beam analysis
Isolated beam:
Nominal moment
Additional moment
Check for
Total area of steel
Area of steel in web
APPENDIX
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AS PER TABLE 9.5 (a)
Simply
One End
Both End
Cantilever
Supported Continuous Continuous
L / 16
L / 18.5
L / 21
L/8
Values given shall be used directly for members with normal
weight concrete (Wc = 145 lb/ft3) and Grade 60 reinforcement
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For structural light weight concrete having unit wt. In range
90-120 lb/ft3 the values shall be multiplied by
(1.65 0.005Wc) but not less than 1.09
For fy other than 60,000 psi the values shall be multiplied by
(0.4 + fy/100,000)
`h` should be rounded to the nearest whole number
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CLEAR COVER
Not less than 1.5 in. when there is no exposure to weather or
contact with the ground
For exposure to aggressive weather 2 in.
Clear distance between parallel bars in a layer must not be
less than the bar diameter or 1 in.
RULE OF THUMB
d/b = 1.5 to 2.0 for beam spans of 15 to 25 ft.
d/b = 3.0 to 4.0 for beam spans > 25 ft.
`b` is taken as an even number
Larger the d/b, the more efficient is the section due to less
deflection
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BAR SIZE
#n = n/8 in. diameter for n 8.
Ex. #1 = 1/8 in.
.
#8 = 8/8 i.e., I in.
Weight, Area and Perimeter of individual bars
25
Bar
No
Wt.per
Foot (lb)
3
4
5
6
7
8
9
10
11
14
18
0.376
0.668
1.043
1.502
2.044
2.670
3.400
4.303
5.313
7.650
13.600
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Stamdard Nominal Dimensions
C/S Area, Perimeter
Diameter db
(in.)
Ab (in2)
inch
mm
0.375
9
0.11
1.178
0.500
13
0.20
1.571
0.625
16
0.31
1.963
0.750
19
0.44
2.356
0.875
22
0.60
2.749
1.000
25
0.79
3.142
1.128
28
1.00
3.544
1.270
31
1.27
3.990
1.410
33
1.56
4.430
1.693
43
2.25
5.319
2.257
56
4.00
7.091
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