Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Lecture 04
Design of T and L Beams in
Flexure
By:
Prof. Dr. Qaisar Ali
Civil Engineering Department
UET Peshawar
drqaisarali@uetpeshawar.edu.pk
www.drqaisarali.com
Prof. Dr. Qaisar Ali
CE 320: Reinforced Concrete Design-I
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Lecture Contents
 Introduction to T and L Beams
 ACI Code provisions for T and L Beams
 Design Cases
 Design of Rectangular T-beam
 Design of True T-beam
 References
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Learning Outcomes
 At the end of this lecture, students will be able to;

Differentiate between T-beam and L-beam

Explain Mechanics of Rectangular T-beam and true T-beam

Design T- beam in flexure
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Introduction to T and L Beam
 T and L section Beams

The T or L Beam gets its name when the slab and beam produce the
cross sections having the typical T and L shapes in a monolithic
reinforced concrete construction.
T beam
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L beam
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Introduction to T and L Beam
 T and L section Beams

In casting of reinforced concrete floors/roofs, forms are built for
beam sides, the underside of slabs, and the entire concrete is mostly
poured at once, from the bottom of the deepest beam to the top of
the slab.
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Introduction to T and L Beam
 Behavior of T and L Beam

Watch the following animation attentively to understand the behavior
of T and L section beams.
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Introduction to T and L Beam
a
b
a
b
Compression
Tension
Tension
Compression
Section a-a
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Section b-b
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Introduction to T and L Beam
 Positive Bending Moment

In the analysis and design of floor and roof systems, it is common
practice to assume that the monolithically placed slab and
supporting beam interact as a unit in resisting the positive bending
moment.

As shown, the slab acts as the compression flange, while the
supporting beam becomes the web or stem.
Compression
Tension
Section a-a
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Introduction to T and L Beam
 Negative Bending Moment

In the case of negative bending moment, the slab at the top of the
stem (web) will be in tension, while the bottom of the stem will be in
compression.

This usually occurs at interior support of continuous beam.
Tension
Compression
Section b-b
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
ACI 318 Code Provisions for T and L
Beams
 Effective flange width

For T and L beams supporting monolithic or composite slabs, the
effective flange width
shall include the beam web width
plus an
effective overhanging flange width in accordance with ACI 318-19
Table 6.3.2.1.
bf
bf
bf
hf
bw
Sw
bw
𝑏 = width of web (overhanging part) of beam
𝑆 = Clear distance between adjacent beams
Prof. Dr. Qaisar Ali
Sw
bw
𝑏 = Effective flange width
ℎ = thickness of flange (slab)
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
ACI 318 Code Provisions for T and L
Beams
 Calculation of Effective flange width

for T and L beams
As per ACI 318-19, the effective flange width
shall be calculated as per Table 6.3.2.1

For T beam
𝑙
𝑏
𝑏

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For L beam
𝑏
𝑆
hf
𝑏
𝑆
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𝑏
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design Cases

In designing a T-Beam for positive bending moment, there exist
two conditions:

Case 1

The depth of the compression block
may be less than or equal to the slab
depth i.e. flange thickness (a ≤ hf).

In
such
case,
the
T-Beam
𝑎
ℎ
N.A
𝑑
is
designed as rectangular beam for
positive bending with the width of
compression block equal to bf.
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𝑏
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𝐴
𝑏
12
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design Cases

In designing a T-Beam for positive bending moment, there exist
two conditions:

Case 2

The compression block covers the
whole flange and extends into the
web portion i.e. (a ˃ hf)

𝑏
𝑎
N.A
𝑑
In such condition, the T-Beam is
designed as True T-beam.
ℎ
𝐴
𝑏
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Flexural capacity (case 1)
𝑎
𝑏
𝑎/2
ℎ
𝑑
𝑁. 𝐴
𝑙 = 𝑑 − 𝑎/2
𝐴
𝑇=𝐴 𝑓
𝑏
• For no failure,
∅𝑀 = 𝑀
• In calculating 𝐴
C = 0.85 𝑓 𝑎𝑏
,
and 𝐴
,
, use 𝑏
• Other checks remain same as that of
not 𝑏
rectangular beam design.
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Example 4.1

The roof of a hall has a 5″ thick slab with beams having 30 feet. c/c
and 28.5 feet clear length. The beams are having 9 feet clear
spacing and have been cast monolithically with slab. Overall depth
of beam (including slab thickness) being 24 in. and width of beam
web being 14 in.

Design the simply supported beam for a total factored load (including
self weight of beam) of 3 k/ft. Use
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and
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Given Data
and
/
and
𝑤 = 3𝑘/𝑓𝑡
𝑙 = 28.5′
𝑙
/
= 30′
and

5″
Required Data
19″
Design the beam as per ACI 318-19
14″
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.1: Selection of Sizes
and assume
Effective width of T- beam
is minimum of:
5″


21.5″
19″
As

14″
Therefore, 𝑏 = 94"
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.2: Calculation of loads
Ultimate load including self weight is already given
3 kip/ft

Step No.3: Analysis
/
45k
30ft
SFD
4050 in-kips
BMD
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.4: Check the behavior of section
In order to check whether the section rectangular or True T-section we
have;
Note that for T and L beams,
𝑏 is replaced by 𝑏 in equation of 𝑎
Since
Prof. Dr. Qaisar Ali
, the section can be designed as rectangular beam
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.5: Calculate Area of Steel

Step No.6: Check for area of steel
,
,
,
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,
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.7: Detailing and Drafting

Using #8 bars with bar area
Number of bars

Provide 5 #8 bars in two layers

3 in lower layer and

2 in upper layer
(3+2),#8 bars
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.7: Detailing and Drafting

Check flexural capacity of the beam as per actual effective depth
and provided steel area
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Solution

Step No.7: Detailing and Drafting
94"
5"
19"
(3+2)- #8 bars
14"
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of Rectangular T-beam
 Example 4.2 (Class activity)

Design the Beam B1 for the following moments.
B1 (15" x 24")
B1 (15" x 24")
ℎ = 6"
𝑓 ′ = 3𝑘𝑠𝑖
𝑓 = 60𝑘𝑠𝑖
𝑀 = 1764𝑖𝑛. 𝑘𝑖𝑝
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𝑀 = 1764𝑖𝑛. 𝑘𝑖𝑝
𝑀 = 3122 𝑖𝑛. 𝑘𝑖𝑝
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Design of True T-beam
 Flexural Capacity (case 2)
𝑏 −𝑏
2
𝑏
ℎ
𝑎
𝑑
𝐴
𝑏
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𝑏 −𝑏
2
=
𝑏
ℎ
𝑑
𝐴
+
𝑏
CE 320: Reinforced Concrete Design-I
𝑎
𝑏 −𝑏
2
𝑏
𝑁. 𝐴
ℎ
𝑑
𝐴
𝑏
25
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Flexural Capacity (case 2)

Calculation of

𝑏 −𝑏
2
𝒏𝟏
From stress diagram
1
1
𝑑
,
,
𝑏
ℎ /2
ℎ
𝐶 = 0.85 𝑓 𝑏 − 𝑏
𝑁. 𝐴
𝐴
𝑏
ℎ
𝑙 = 𝑑 − ℎ /2
𝑇 =𝐴 𝑓
,
,
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Flexural Capacity (case 2)

Calculation of

𝒏𝟐
From stress diagram
𝑎
𝑏 −𝑏
2
𝑏
𝑎/2
ℎ
𝐶 = 0.85 𝑓 𝑎𝑏
𝑑
𝐴
𝑏
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CE 320: Reinforced Concrete Design-I
𝑁. 𝐴
𝑙 = 𝑑 − 𝑎/2
𝑇 =𝐴 𝑓
27
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Flexural Capacity (case 2)

Calculation of

As we have
𝒔
For
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Ductility requirements
Equating horizontal forces
0.85 𝑓 𝑏 − 𝑏
For 𝑎 = 𝛽 𝑐 𝐴
Prof. Dr. Qaisar Ali
,
For 𝑓 = 40𝑘𝑠𝑖
,
For 𝑓 = 60𝑘𝑠𝑖
ℎ =𝐴 𝑓
=𝐴
,
𝑐 = 0.41𝑑 and 𝑎 = 0.41𝛽
𝑐 = 0.38𝑑 and 𝑎 = 0.38𝛽
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Ductility requirements
0.85𝑓 𝛽 𝑐𝑏
=𝐴
𝑓
,
,
(
)
which finally gives
,
,
Prof. Dr. Qaisar Ali
(
(
)
)
,
(
,
(
)
𝛽 = 0.85 for 𝑓 ≤ 4000𝑝𝑠𝑖
)
(for
)
Only valid
for
(for
CE 320: Reinforced Concrete Design-I
)
𝑓 ≤ 4000𝑝𝑠𝑖
30
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Example 4.3

Design a simply supported T beam to resist a factored positive
moment equal to 6700 in-kip. The beam is 12″ wide and is having
24″ total depth including a slab thickness of 3 inches. The center to
center and clear lengths of the beam are 25.5′ and 24′ respectively.
The clear spacing between the adjacent beams is 3 ft. Material
strengths are,
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and
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Given Data
and
/
and
𝑙
𝑙 = 24′
/
= 25.5′
and

3″
Required Data
21″
Design beam as per ACI 318-19
12″
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.1: Selection of Sizes
and assume
Effective width of T- beam
is minimum of:
3″


21.5″
21″
As

12″
Therefore, 𝑏 = 48"
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.2: Calculation of loads
We have directly given the ultimate moment

Step No.3: Analysis

Step No.4: Check the behavior of section
Since
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, the section can be designed as True T- beam
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.5: Calculate Area of Steel
,
Determine
,
and
,
,
Now,
,
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.5: Calculate Area of Steel
Hence,
,
Using #8 bar with area of bar
Number of bars
(
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bars
)
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.6: Check for area of steel
(for
,
)
,
,
(
,
,
Prof. Dr. Qaisar Ali
)
(
)
,
(
)
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.7: Detailing and Drafting
Check flexural capacity of the beam as per actual effective depth and
provided steel area
Prof. Dr. Qaisar Ali
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Solution

Step No.7: Detailing and Drafting
48"
3"
21"
(3+3+3)- #8 bars
12"
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Design of True T-beam
 Example 4.4 (Class Activity)

Design a simply supported T beam to resist a factored positive
moment equal to 6500 in-kip. The beam is 15″ wide and is having
27″ total depth including a slab thickness of 3 inches. The center to
center and clear lengths of the beam are 22.5′ and 21′ respectively.
The clear spacing between the adjacent beams is 2.5 ft. Material
strengths are,
Prof. Dr. Qaisar Ali
and
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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
References
 Design of Concrete Structures 14th / 15th edition by Nilson, Darwin and
Dolan.
 Building Code Requirements for Structural Concrete (ACI 318-19)
Figure 9
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