Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 82

Force equilibrium: =+ (5.5) CT T 0.85 f bc Af β= + AE ε

s f c 1 s y f f fe

− β

c

1

Moment equilibrium: MTjd =φ +φ Tjd =φ Afd

u s s f f s y

2

− β

c 1

+φΨε AE d (5.6)

f f f fe f

2

where ε bi is the strain in the extreme fiber of concrete substrate at the time of
strengthening.

Design solution approach by ACI 440.2R-08:

1. Assume A f

2. Assume c and i iterate to satisfy force equ il ibrium and strain compatibility

3. Compute M φ and compare it wit h − M ureq ui red

4. Adjust A f and repeat steps 1-3 until φ≥ − MM

n u required

Design solution approach by direct equations:
The design solution for this failure mode is possible to determine in closed
form (Rasheed and Pervaiz 2003):

ε

= ε+ε

0.003
0.003

d a

cu cu f f

c =

+ε = β

(5.7)

c d

f f 1

ε=ε−ε≤ε
fe (5.8) f bi fd

where ε fd is the debonding strain limit of FRP

0.85 fbaAf = + Af

(5.9)

c s y f fe

Solving for A f in Equation (5.9):

'

0.85 fbaAf

f

−

c s y

A =

(5.10)

f

fe

'

f
f

a
d

f
f

c y

ρ= 0.85 −ρ

(5.11)

f s

fe fe

A
bd

A
bd

f

s

where ρ= ρ= ,

f s

a a

MMAf =φ =φ −+φΨ d Af d −

(5.12)

u n sy f f fe f

2 2