Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 102

fbal> fbal>

f =ε= E 13,900 × 0.00207 = 28.77 ksi f ff

2

A =× = 60.6 3.6 in

s

212 3
8

b =×+×+× +×=< 60.875 5113"16" O.K.

A
bd

3.6

s

ρ= = = 0.02208

s

16 × 10.19

f
f

87
87

4
60

87

fbal>

c
y

ρ= β 0.85 = 0.85 × ×× + 0.85 = 0.02851 1

+ f 87 60 y

f 60

28.77

( )

y
f fbal>

( )

fbal> fbal>

ρ= ρ−ρ= 0.02851 − 0.02208 = 0.0134 f s s

f

f fbal> f fbal> 2.186 in 2 A =ρ ×= ×× = bd 0.0134 16 10.19

( )

A f =× +× = 3 64 0.04 2.4in 2

f fbal>

AA
f

> brittle crushing failure

Unstrengthened beam analysis:
Assuming that steel yields:

Af
fb

×
×× ×

3.660 sy

4.67"

c = = =

0.85 β 0.85 4160.85

c 1

a = 0.85 × 4.67"3.97" =

dc
c

10.19 4.67
4.67

− −

ε= × 0.003 = 0.003 × = 0.00355 < 0.004 N.G.

s

250
3

( )

φ= 0.65 + 0.00355 − 0.002 = 0.779

or

c
d t

4.67
10.19

0.458 0.429 N.G.

= = >

1
0.458

5
3

φ= 0.65 + 0.25 − = 0.779

Even though the beam is slightly not up to ACI 318-11 (2011) provisions, con-
tinue the analysis, since it is an existing beam and it is allowed to be strengthened
by ACI 440.2R-08.

MAfd a u

3.97
2

=φ −= ××× 0.779 3.660 10.19 − = 1380.6k-in. s y

2