Design Issues - Strengthening Design of Reinforced Concrete with FRP - page 76

W DL + W LL

2#3

#3 @ 6" c/c

20"

20 ft

4#6

f c = 4 ksi
f y = 60 ksi

1.5"

12"

FIGURE 4.P.1

Problem 4.2
Derive the following expression of the elastic depth to the neutral axis of the cracked
section using linear elastic cracked section analysis considering the contribution of
sectional FRP:

2

E
E

E
E

E
E

E
E

d
d

E
E

E
E

s f s f f s f

k = ρ +ρ+ 2 ρ +ρ −ρ+ρ

s f s f s f

c c c c c c

Problem 4.3
Derive the following expression for the elastic stress level in steel under service load
considering the contribution of sectional FRP. Note that this expression is given by
Equation (10.14) of ACI 440.2R-08:

kd

M +ε Ed − ( d dE − )

s bi f f f s

3

f =

ss ,

kd kd

( )

AE d − dkdAEd − + − ( d d − )

ss f f f f

3 3

Problem 4.4
Derive the following expression for the elastic stress level in FRP under service load
considering the contribution of sectional steel and FRP. Note that this expression is
given by Equation (10.15) of ACI 440.2R-08.

E
E

d d
d d

−
−

f f

f = f −ε E

fs , ss , bi f

s

Problem 4.5
Determine the elastic stress level in steel of the beam in Problem 4.1. Note that
50% of the original live load existed on the beam during strengthening. The beam
was strengthened using two plies of CFRP with the properties listed in the follow-
ing table. Compare the steel stress level to the limit set by Equation (10.6) of ACI
440.2R-08.