Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 138

Solution:

L
L

1000
1100

af
a

Plate debonding is more likely to occur than cover
delamination (Rasheed, Larson, and Nayyeri Amiri 2013).

= = 0.91 > 0.9

30

ε= 0.41 = 0.00497 < 0.9 C ε= 0.00641 fd E u

3 × 400,000 × 0.17

Determine the failure mode (whether ductile crushing or debonding):

β= 0.85

1

=β ε×
ε+ε

d 0.003 × 400

max cu f

a = 0.85 × = 127.95 mm

1

b

0.003 + 0.00497 cu fd

assuming

b ε= , since it is a research specimen (strengthening happened under
self-weight).

0

max

f
f

f
f

a
d

c b y

ρ=

max

0.85 −ρ

f s

fd fd

f = 400,000 × 0.00497 = 1, 988 MPa

fd

30
1988

127.95
350

398
300

340
1988

max

ρ= × 0.85 × − × = 0.00404

f

× 350

ρ= ××
×

3 300 0.17

= 0.001457 < ρ

max

debonding controls

f f

300 350

α+=+ fbcAf Af Af

c s s s y f fd

2

2

α= ε
ε

1
3

ε
ε

c 1

3

c

cf
c

cf
c

− = 2.50 400 − 2.50 400

c c

− −

ε= ε

c
dc

c

fd

where = 0.00497 400

cf

− − c

f

f

c − 4

ε= 1.71 4700 = 3.64 × 10 f = 0.00199

c c

f

c

( )

ε= ε −
−

cd
dc

c − 50 fd

= 0.00497 s

400 − c

f

Substituting these expressions into the force equilibrium equation,

c c

2

c 50

−

2.50 ×

− −× −

2.1 ×× +× × 30 300 c 265 200000 0.00497

2

400 c (400 c ) 400 − c

=×+× 398 340 153 1988