Design of Concrete Structure I

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Design of Concrete Structure I
University of Palestine
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Chapter 3
Instructor
Eng. Mazen Alshorafa
3
Design of Concrete Structure I
University of Palestine
Flexural Stress
Introduction
The beam is a structural member used to support
the internal moments and shears and in some cases
torsion. C T ? M C (jd) T (jd)
Instructor
Eng. Mazen Alshorafa
4
Design of Concrete Structure I
University of Palestine
Flexural Stress
Basic Assumptions in Flexure Theory

• Plane sections remain plane after bending i.e.
  in an initially straight beam, strain varies
  linearly over the depth of the section.
• The strain in the reinforcement is equal to the
  strain in the concrete at the same level, i.e. es
  ec at same level.
• Stress in concrete reinforcement may be
  calculated from the strains using s-e curves for
  concrete steel.
• Tensile strength of concrete is neglected in
  flexural strength.
• Concrete is assumed to fail in compression, when
  ec ecu 0.003.
• Compressive s-e relationship for concrete may be
  assumed to be any shape that results in an
  acceptable prediction of strength.

Instructor
Eng. Mazen Alshorafa
5
Design of Concrete Structure I
University of Palestine
Flexural Stress
Behavior of rectangular section at ultimate limit
state in flexural

Instructor
Eng. Mazen Alshorafa
6
Design of Concrete Structure I
University of Palestine
Flexural Stress
Behavior of rectangular section at ultimate limit
state in flexural
The compressive zone is modeled with a equivalent
stress block. In the Equivalent
rectangular block, an average stress of 0.85 fc
is used with a rectangle of depth aß1c , where c
is the distance from the extreme compression
fiber to the neutral axis
Instructor
Eng. Mazen Alshorafa
7
Design of Concrete Structure I
University of Palestine
Flexural Stress
Behavior of rectangular section at ultimate limit
state in flexural

Instructor
Eng. Mazen Alshorafa
8
Design of Concrete Structure I
University of Palestine
Flexural Stress
Requirements for analysis of reinforced concrete
beams
1 Stress-Strain Compatibility Stress at a point
in member must correspond to strain at a
point. 2 Equilibrium Internal forces balances
with external forces
Instructor
Eng. Mazen Alshorafa
9
Design of Concrete Structure I
University of Palestine
Flexural Stress
Example of rectangular reinforced concrete beam
1 Setup equilibrium.
Instructor
Eng. Mazen Alshorafa
10
Design of Concrete Structure I
University of Palestine
Flexural Stress
Example of rectangular reinforced concrete beam
2 Find flexural capacity.
Instructor
Eng. Mazen Alshorafa
11
Design of Concrete Structure I
University of Palestine
Flexural Stress
Example of rectangular reinforced concrete beam

Instructor
Eng. Mazen Alshorafa
12
Design of Concrete Structure I
University of Palestine
Flexural Stress
Example of rectangular reinforced concrete beam
3 Need to confirm es gt ey
Instructor
Eng. Mazen Alshorafa
13
Design of Concrete Structure I
University of Palestine
Types of Flexural Failure
Types of Flexural Failure
Flexural failure may occur in three different
ways 1 Tension Failure - (under-reinforced
beam) 2 Compression Failure - (over-reinforced
beam) 3 Balanced Failure - (balanced
reinforcement)
Instructor
Eng. Mazen Alshorafa
14
Design of Concrete Structure I
University of Palestine
Types of Flexural Failure
1 Balanced Failure
The concrete crushes and the steel yields
simultaneously. Such a beam has a
balanced reinforcement, its failure mode is
brittle, thus sudden, and is not allowed by the
ACI Strength Design Method.
Instructor
Eng. Mazen Alshorafa
15
Design of Concrete Structure I
University of Palestine
Types of Flexural Failure
2 Tension Failure
The reinforcement yields before the concrete
crushes. Such a beam is called
under-reinforced beam, and its failure mode is
ductile, thus giving a sufficient amount of
warning time, and is adopted by the ACI Strength
Design Method
Instructor
Eng. Mazen Alshorafa
16
Design of Concrete Structure I
University of Palestine
Types of Flexural Failure
3 Compression Failure
The concrete will crush before the steel
yields. Such a beam is called
over-reinforced beam, and its failure mode is
brittle, thus sudden, and is not allowed by the
ACI Strength Design Method.
Instructor
Eng. Mazen Alshorafa
17
Design of Concrete Structure I
University of Palestine
Types of sections
Types of sections
1 Tension-controlled section When the net
tensile strain in the extreme tension steel is
equal to or greater than 0.005 when the concrete
in compression reaches its crushing strain of
0.003. 2 Compression-controlled section When
the net tensile strain in the extreme tension
steel is equal to or less than ey (ey0.002 for
fy4200 kg/cm2) when the concrete in compression
reaches its crushing strain of 0.003. 3
Transition section When the net tensile strain in
the extreme tension steel is between 0.005 and ey
(ey0.002 for fy4200 kg/cm2) when the concrete
in compression reaches its crushing strain of
0.003.
Instructor
Eng. Mazen Alshorafa
18
Design of Concrete Structure I
University of Palestine
Strength reduction factors
Strength reduction factors F

Instructor
Eng. Mazen Alshorafa
19
Design of Concrete Structure I
University of Palestine
Reinforcement Ratio Limit
Reinforcement Ratio Limit
For rectangular cross-sections, ? Minimum
Reinforcement Ratio (?min) This is to safeguard
against brittle failure fc and fy are in
kg/cm2. bw width of section and, d effective
depth of section.
d
h
As
bw
Instructor
Eng. Mazen Alshorafa
20
Design of Concrete Structure I
University of Palestine
Reinforcement Ratio Limit
Reinforcement Ratio Limit
Maximum Reinforcement Ratio (?max)
, Where As,max evaluated when et 0.004 and
eult 0.003 Cmax 0.85 fc amax b Tmax As,max
fy ? Fx0.0 ? Cmax Tmax As,max fy 0.85 fc
amax b but amax ß1 cmax From Figure and from
similar triangles, As,max fy 0.85 fc ß1 (3/7
d) b
Instructor
Eng. Mazen Alshorafa
21
Design of Concrete Structure I
University of Palestine
Summary

eult.0.003
et0.004
Flexural member Beams with axial force gt 0.1
fc Ag et 0.004 F 0.4883et
Tension-controlled et 0.005 F 0.90
Compression-controlled et 0.002 F 0.65
Transition section 0.002lt et lt0.005 F
0.4883et
et0.002
et0.005
Compression Failure
Tension Failure
Balanced Failure
?b
?max
Brittle behavior
Ductile behavior
Instructor
Eng. Mazen Alshorafa
22
Design of Concrete Structure I
University of Palestine
Design Moment
Design Moment
Design moment strength Md is obtained by
multiplying nominal moment strength Mn by
strength reduction factor F or we can solve
this expression for ? with the following results
where Md Mu
Instructor
Eng. Mazen Alshorafa
23
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1
Determine the ACI design moment strength Md (FMn
)of the beam shown in figure if fc 280 kg/cm2
and fy 4200 kg/cm2. Solution- 1- Checking
Steel Percentage i.e. ACI Code limits
are satisfied.
Instructor
Eng. Mazen Alshorafa
24
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1 contd.
2- Calculate the design moment Md

Instructor
Eng. Mazen Alshorafa
25
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2
Determine the ACI design moment strength Md (FMn
)of the beam shown in figure if fc 320 kg/cm2
and fy 4200 kg/cm2. Solution- 1- Checking
Steel Percentage i.e. ACI Code limits
are not satisfied (section is not ductile)
Instructor
Eng. Mazen Alshorafa
26
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2 contd.
another solution Compute value of
et Section is not ductile and may not be
used as per ACI Code. Compression failure not
allowed by ACI Code
Instructor
Eng. Mazen Alshorafa
27
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
Determine the ACI design moment strength Md (FMn
)of the beam shown in figure if fc 280 kg/cm2
and fy 4200 kg/cm2. Solution- 1- Checking
Steel Percentage i.e. ACI Code limits
are satisfied.
Instructor
Eng. Mazen Alshorafa
28
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3 contd.
2- Calculate the design moment Md

Instructor
Eng. Mazen Alshorafa
29
Design of Concrete Structure I
University of Palestine
Design of Rectangular Beam
Concrete Cover
Concrete cover is necessary for protecting the
reinforcement from fire, corrosion, and other
effects. Concrete cover is measured from the
concrete surface to the closest surface of steel
reinforcement
Instructor
Eng. Mazen Alshorafa
30
Design of Concrete Structure I
University of Palestine
Design of Rectangular Beam
Spacing of Reinforcing Bars
The ACI Code specifies limits for bar spacing to
permit concrete to flow smoothly into spaces
between bars without honeycomb. According to ACI,
the minimum clear spacing between parallel bars
in a layer is not to be less than the largest
of bar diameter db 2.5 cm 4/3
maximum size of coarse aggregate When two or
more layers are used, bars in the upper layers
are placed directly above layers in the bottom
layer with clear distance between layers not less
than 2.5 cm
Side cove
Clear distance
Bottom cove
Clear spacing
Instructor
Eng. Mazen Alshorafa
31
Design of Concrete Structure I
University of Palestine
Design of Rectangular Beam
Design requirements
According to ACI code, structural members are to
be designed to satisfy strength and
serviceability requirements.
The Strength Requirement
The strength requirement provides safety against
possible failure. Md design moment strength
(FMn) Mu required moment
wu
L m
Md (FMn)
Mu
Instructor
Eng. Mazen Alshorafa
32
Design of Concrete Structure I
University of Palestine
Design of Rectangular Beam
The Serviceability Requirement
The serviceability requirement ensures adequate
performance at service load without excessive
deflection and cracking. Two methods are given
by ACI for controlling deflections. The first
of which is by providing a member thickness not
less than given code minimum values, shown in
Table where l span length measured
center to center The second method is by
calculating the deflection and comparing it with
code specified values.
Instructor
Eng. Mazen Alshorafa
33
Design of Concrete Structure I
University of Palestine
Design of Rectangular Beam
The Design Equation
where As ? b d but Mu Md FMn ? is
given in terms of Mu , b , d , fc and fy by
solving for the roots of a quadratic
fc kg/cm2 fy kg/cm2
Instructor
Eng. Mazen Alshorafa
34
Design of Concrete Structure I
University of Palestine
Summary of Design Procedure
When b and d are unknown
1- Specify fc' and fy .values. 2- Compute the
factored bending moment Mu and set Mu Md. 3-
Select an appropriate reinforcement ratio between
?max and ?min (often a ratio of about 0.6
?max ). 4- Choose b and d to meet the deflection
requirement. 5- Calculate the area of steel
reinforcement As. Number of bars is to be
selected, and spacing between reinforcing bars is
checked against code specified values. Larger
size bars are used, or more than one layer of
reinforcement is chosen when reinforcement bars
are too close to each other. 6- Sketch the cross
section and its reinforcement.
Instructor
Eng. Mazen Alshorafa
35
Design of Concrete Structure I
University of Palestine
Summary of Design Procedure
When b and d are known
1- Specify fc' and fy .values. 2- Compute the
factored bending moment Mu and set Mu Md. 3-
Compute the reinforcement ratio ? using the
following equation assume that F 0.9 4- Check
Steel Percentage 5- Verify
the selected value of F (et 0.005) 6- Calculate
the area of steel reinforcement As. Number of
bars is to be selected, and spacing between
reinforcing bars is checked against code
specified values. Larger size bars are used, or
more than one layer of reinforcement is chosen
when reinforcement bars are too close to each
other. 7- Sketch the cross section and its
reinforcement.
Instructor
Eng. Mazen Alshorafa
36
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1
Design a rectangular beam for a 6m simple span if
a dead load of 2.5t/m (Not including the beam
weight) and a live load of 1.0t/m are to be
supported. Use fc 250 kg/cm2 and fy 4200
kg/cm2. Solution- a) b d are known 1-
Estimating Beam dimension and weight hmin l/16
600/16 37.5 cm assume that h 50cm and b
30cm Beam wt. 0.5x0.3x2.5 0.375 t/m 2-
Compute wu and Mu wu 1.2 D1.6 L
1.2(2.50.375)1.6(1.0) 5.05 t/m Mu
wul2/8 5.05(6)2/8 22.73 t.m
wd2.5 t/m wl1.0 t/m
6 m
wu5.05 t/m
6 m
22.73 t.m
Instructor
Eng. Mazen Alshorafa
37
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1
3- Assuming that F0.9 (et 0.005) and computing
? d 50 - 4 0.8 1.0 44.2cm (assuming one
layer of F20mm reinforcement and F8mm
stirrups) 4- Selecting reinforcing As,req.
? b d 0.0116(30)(44.2) 15.36 cm2
Use 5 F 20 mm (As, used15.71 cm2)
50
44.2
5F20
30
Beam cross section
Instructor
Eng. Mazen Alshorafa
38
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1
5- Checking solution a) Check spacing between
bars b) Checking Steel Percentage
50
44.2
5F20
30
Beam cross section
Instructor
Eng. Mazen Alshorafa
39
Design of Concrete Structure I
University of Palestine
Example Problems
Example 1
c) Check F 0.9 d) Design Check
Instructor
Eng. Mazen Alshorafa
40
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2
Design a rectangular beam for a 6m simple span if
a dead load of 2.5t/m (Not including the beam
weight) and a live load of 1.0t/m are to be
supported. Use fc 250 kg/cm2 and fy 4200
kg/cm2. Solution- b) b d are unknown 1-
Estimating the reinforcement ratio ? Use ?
0.6 ?max ? 0.6(0.01843) 0.011 assume that
own weight of beam 0.4 t/m
wd2.5 t/m wl1.0 t/m
6 m
wu5.05 t/m
6 m
22.73 t.m
Instructor
Eng. Mazen Alshorafa
41
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2
wu5.08 t/m
2- Compute wu and Mu wu 1.2 D1.6 L
1.2(2.50.4)1.6(1.0) 5.08 t/m Mu
wul2/8 5.08(6)2/8 22.9 t.m 3- Assuming that
F0.9 (et 0.005) and computing
bd2 Letting b30cm, 30 d2 61792 ? d2
2060 cm2 ? d45.4 cm
6 m
22.9 t.m
Instructor
Eng. Mazen Alshorafa
42
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2
assuming one layer of F20mm reinforcement and
F8mm stirrups. h 45.440.81.0 51.2 cm, gt
hmin l/16 600/16 37.5 cm Use 30x55 cm cross
section. dmod 55-4.0-0.8-1.0 49.2 cm 4-
Compute The new factored load and moment Own
weight of the beam 0.55 x 0.3 x 2.5 0.413
t/m wu 1.2 D1.6 L 1.2(2.50.413)1.6(1.0)
5.10 t/m Mu wul2/8 5.10(6)2/8 23.0 t.m 5-
Assuming that F0.9 (et 0.005) and computing
?mod
wu5.10 t/m
6 m
23.0 t.m
Instructor
Eng. Mazen Alshorafa
43
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2

• 4- Selecting reinforcing
• As,req. ? b d 0.00922(30)(49.2) 13.61 cm2
• Use 3 F 25 mm (As,used14.73 cm2)
• 5- Checking solution
• Check spacing between bars
• b) Checking Steel Percentage

55
49.2
3F25
30
Beam cross section
Instructor
Eng. Mazen Alshorafa
44
Design of Concrete Structure I
University of Palestine
Example Problems
Example 2
c) Check F 0.9 d) Design Check
Instructor
Eng. Mazen Alshorafa
45
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
Design the continuous beam shown in figure 1 to
support a service dead load of 3.0t/m (Including
the beam weight) and a service live load of
1.5t/m . Use fc 250 kg/cm2 and fy 4200
kg/cm2. Solution- 1- Estimating Beam
dimension hmin l/16 500/18.5 27.0 cm assume
that h 30 cm and b 80cm 2- Compute wu and
Mu From Example 2 in chapter 1, the max.
positive moment is 12 t.m and max. negative
moment 18.75 t.m as shown in figure 2.
wd3.0 t/m wl1.5 t/m

A
C
B
5.0 m
5.0 m
figure 1.
18.75 t.m
12.0 t.m
12.0 t.m
figure 2.
Instructor
Eng. Mazen Alshorafa
46
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
3- Assuming that F0.9 (et 0.005) and computing
? d 30 2.5 0.8 0.7 26.0cm (assuming one
layer of F14mm reinforcement and F8mm
stirrups) 4- Selecting reinforcing As,-ve
? b d 0.0102(80)(26) 21.2 cm2? Use 11 F 16 mm
(As, used 22.11 cm2) As,ve ? b d
0.00626(80)(26) 13.01 cm2? Use 9 F14 mm (As,
used 13.86 cm2)
11F16
30
26
80
For negative moment
26
30
9F14
80
For positive moment
Instructor
Eng. Mazen Alshorafa
47
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
5- Checking solution a) Check spacing between
bars b) Checking Steel Percentage
11F16
30
26
80
For negative moment
Instructor
Eng. Mazen Alshorafa
48
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
c) Check F 0.9 d) Design Check
11F16
30
26
80
For negative moment
Instructor
Eng. Mazen Alshorafa
49
Design of Concrete Structure I
University of Palestine
Example Problems
Example 3
c) Check F 0.9 d) Design Check
26
30
9F14
80
For positive moment
Instructor
Eng. Mazen Alshorafa