Doubly reinforced beams have both tension and compression reinforcement, allowing for a shallower beam depth than a singly reinforced beam. There are two cases for the behavior of doubly reinforced beams at ultimate loading: 1) Case I occurs when both tension and compression steel yield. The neutral axis depth can be calculated and the moment capacities from compression steel, concrete, and tension steel determined. 2) Case II occurs when only the tension steel yields, and the compression steel does not yield. The strain in the compression steel must be calculated. The document discusses the behavior of doubly reinforced beams under ultimate loading conditions for both cases when compression steel does and does not yield. It provides equations to calculate forces, strains, and moment

1. Plain and Reinforced Concrete- 1
Doubly Reinforced Beams
ByEngr.RafiaFirdous

2. Plain & Reinforced Concrete-1
Doubly Reinforced Beams
“Beams having both tension and compression reinforcement
to allow the depth of beam to be lesser than minimum depth
for singly reinforced beam”
• By using lesser depth the lever arm reduces and to develop
the same force more area of steel is required, so solution is
costly.
• Ductility will be increased by providing compression steel.
• Hanger bars can also be used as compression steel reducing
the cost up to certain cost.
• For high rise buildings the extra cost of the shallow deep
beams is offset by saving due to less story height.

3. Plain & Reinforced Concrete-1
Doubly Reinforced Beams (contd…)
• Compression steel may reduce creep and shrinkage of
concrete and thus reducing long term deflection.
• Use of doubly reinforced section has been reduced due
to the Ultimate Strength Design Method, which fully
utilizes concrete compressive strength.
Doubly Reinforced Beam

4. Behavior Doubly Reinforced Beams
Tension steel always yields in D.R.B.
There are two possible cases:
1. Case-I Compression steel is yielding at
ultimate condition.
2. Case-II Compression steel is NOT yielding
at ultimate condition.

5. Behavior Doubly Reinforced Beams
Cc
T = Asfs
N.A.
εcu= 0.003
Strain Diagram Internal Force
Diagram
εs
h
c
d
b 0.85fc
a
Whitney’s
Stress Diagram
(d-d’)
fs
d
εs’ fs’
Cs
d – a/2
T = Asfs
Cs=As’fs’
Cc=0.85fc’ba
fs=Esεs
fs’=Esεs’

6. Behavior Doubly Reinforced Beams (contd…)
Case-I Both Tension & Compression steel are yielding at
ultimate condition
fs = fy and fs’=fy
Location of N.A.
Consider equilibrium of forces in longitudinal direction
sc CCT 
yscys f'Aba'f85.0fA 
 
b'f85.0
f'AA
a
c
yss 

1β
a
c and

7. Case-I Both Tension & Compression steel are yielding at ultimate
condition (contd…)
c
d'c
0.003
'εs 

εcu= 0.003
Strain Diagram
εs
c εs’
d’
B
D
E
C
A
Δ ABC & ADE





 

c
d'c
0.003'εs
1
1
s
β
β
c
d'c
0.003'ε 




 






 

a
d'βa
0.003'ε 1
s
If εs’ ≥ εy compression steel is yielding.
If εs’ < εy compression steel is NOT yielding.
(1)

8. Case-I Both Tension & Compression steel are yielding at ultimate
condition (contd…)
Cc
T = Asfy
N.A.
Internal Force
Diagram
(d-d’)
Cs
d – a/2
T = total tensile force in the steel
21 TTT 
T1 is balanced by Cs
T2 is balanced by Cc
s1 CT 
c2 CT 

9. Case-I Both Tension & Compression steel are yielding at ultimate
condition (contd…)
Cc
T = Asfy
N.A.
Internal Force
Diagram
(d-d’)
Cs
d – a/2
Moment Capacity by Compression Steel
   'dd'f'A'ddCM yssn1

 'ddT1 
Moment Capacity by Concrete













2
a
dT
2
a
dCM 2cn2
  






2
a
dTTM 1n 2
  






2
a
d'f'AfAM ysysn 2

10. Case-I Both Tension & Compression steel are yielding at ultimate
condition (contd…)
Total Moment Capacity
21 nnn MMM 
    






2
a
d'f'AfA'dd'f'AM ysysysn

11. Case-II Compression steel is not yielding at ultimate
condition
fs = fy and fs’< fy
'εE'f ss 
b'f85.0
'f'AfA
a
c
ssys 

1β
a
c and
a
d'βa
600'f 1
s


Location of N.A.

12. Concluded