All the concepts of Doubly R C beam

1. PREPARED BY:
Asst. Prof. GAURANG PRAJAPATI
CIVIL DEPARTMENT
DOUBLY R C BEAM
Mahatma Gandhi Institute Of
Technical Education
& Research Centre, Navsari (396450)
ELEMENTARY STRUCTURAL DESIGN
6TH SEMESTER
CIVIL ENGINEERING

2. INTRODUCTION
 When the applied moment on the beam is more than the moment of resistance (M.R.)
of beam, the structural designer has three options:
1. To increase the depth of beam.
2. To use higher grade of concrete, to improve M.R.
3. To provide reinforcement in the compression zone of beam, to increase M.R.
 Doubly R.C. Beam:
When the applied moment on the beam is more than the Moment of Resistance of
DOUBLY R.C. Beam, the Moment of Resistance f beam is increased by providing
reinforcement in the compression zone. This type of beam is called Doubly R.C. Beam.
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3. INTRODUCTION
 The Necessity of Doubly R.C. Beam:
 When it is not possible to increase the depth of beam due to architectural purpose.
 To get more headway in the room.
 When beam is subjected to reversal of stresses.
 For pre-cast beams.
 When the loads are eccentric.
 When the beam is subjected to accidental or sudden lateral loads.
 In case of continues beams or slabs, the sections at supports are generally designed
as Doubly R C beams.
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4. STRESS DIAGRAM FOR DOUBLY R. C. BEAM [IS 456, PAGE NO. 69]
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5. STRESS DIAGRAM FOR DOUBLY R. C. BEAM [IS 456, PAGE NO. 69]
 Notation of diagram:
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b = width of beam Ast2 = Area of additional tension reinforcement
d = eff. Depth of beam Ast = Area of total tension reinforcement for doubly R C beam
D = overall depth of beam Asc = Area of compressive reinforcement
xu = Depth of Neutral Axis (N.A.) fsc = stress in compressive reinforcement
e = Effective Cover to tension steel fcc = Compression stress in concrete at the level of Compression steel
d’ = Effective Cover to compression steel fck = Compressive Strength of Conc.
Ast1 = Area of tension reinforcement required for balanced singly
R C beam
fy = Yield Strength of Steel

6. CONCEPT OF FORMULA
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 For Singly Balanced section:
C1 = Force of Compression in Concrete = 0.36 fck b xu
T1 = Force of Tension in Steel = 0.87 fy Ast1
Z1 = Lever Arm = d – 0.42 xu
 For Auxiliary section:
C2 = Force of Compression in compression reinforcement
= (fsc - fcc) Asc
T2 = Force of Tension in additional tension reinforcement
= 0.87 fy Ast2
Z2 = Lever Arm = d – d’

7. CONCEPT OF FORMULA
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 fcc = Compression stress in concrete at the level of Compression steel
up to
𝑑′
𝑑
= 0.20, fcc = 0.446 fck
 fsc = stress in compressive reinforcement
 For M.S. bars (Fe 250), fsc = 0.87 fy
 For HYSD (High Yield Strength Deformed) bars,
fsc is obtained from the following table:

8. DIFFERENCE BETWEEN SINGLY AND DOUBLY REINFORCED BEAMS
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Sr. No. Singly R.C. Beam Doubly R.C. Beam
1 Draw cross section of Singly R.C. Beam. Draw cross section of Doubly R.C. Beam.
2 In tension zone, Tension reinforcement Ast is provided.
In tension zone, Tension reinforcement Ast is provided, while In
compression zone, compression reinforcement Asc is provided.
3
In compression zone, 2 no. of 10 mm dia. Anchor bars are
provided. The anchor bars are not design to carry any
compressive force.
In compression zone, compression reinforcement Asc is provided,
which resist compressive force.
4 When Mu < Mu lim., beam is designed as Singly R.C. Beam. When Mu > Mu lim., beam is designed as Doubly R.C. Beam.
5 Its Moment of Resistance is less. Its Moment of Resistance is more.
6 Its Ductility is less. Its Ductility is more.
7
It’s not suitable where there are chances of reversal of
stresses.
It is suitable where there are chances of reversal of stresses.