Background Knowledge - Strengthening Design of Reinforced Concrete with FRP - page 15

1.0

0.8

β 1 = 0.85

0.6

β 1 = 0.65

0.4

Values of β 1
for γ = 0.85

0.2

0.0 0

4 8
Concrete Strength (ksi)

12

FIGURE 2.7 Selection of β 1 variation with concrete strength. (Courtesy of ACI SP-55.)

Total compressive force C may be expressed as follows:

= Cf bc
c

(2.19)

To derive the expression of α based on Hognestad's parabola, the concept of
replacing the area under the parabola with an equivalent area of a rectangular block
with a height of α f c is introduced (Park and Paulay 1975):

ε ε

cf cf

2

ε
ε

ε
ε

∫ ∫

c c

αε=σε= f d f 2 − d ε

ccf c c c c

c c

0 0

ε 2

2 3

cf

2 3

ε
ε

ε
ε

= ε
ε

ε
ε

α= ε
ε

1
3

ε
ε

c c cf cf cf cf

(2.20)

αε = − − −

cf

2 2

3 3

c c c c c c

0

1.71 / , values of the factor (α) are shown in
Table 2.1. The equivalent rectangular block, according to ACI 318-11, has the fol-
lowing expression, as demonstrated in Figure 2.8 and Table 2.1:

For ε=
cf

0.003 and ε= fE
c c c

=γ β =γβγ = α
β

Cf ba =γ fb c

(2.21)

c c 1 1

1