Doubly reinforced beams...PRC-I

Plain and Reinforced Concrete- 1

Doubly Reinforced Beams By Engr. Rafia Firdous

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.

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

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.

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’

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'AAa

c

yss

1β

ac and

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'c0.003'εs

1

1s

β

β

c

d'c0.003'ε

a

d'βa0.003'ε 1

s

If εs’ ≥ εy compression steel is yielding.

If εs’ < εy compression steel is NOT yielding.

(1)

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

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

adT

2

adCM 2cn2

2

adTTM 1n

2

2

ad'f'AfAM ysysn

2

Case-I Both Tension & Compression steel are yielding at ultimate condition (contd…) Total Moment Capacity

21 nnn MMM

2

ad'f'AfA'dd'f'AM ysysysn

Case-II Compression steel is not yielding at ultimate condition

fs = fy and fs’< fy

'εE'f ss

b'f85.0

'f'AfAa

c

ssys

1β

ac and

a

d'βa600'f 1

s

Location of N.A.

Concluded