Background Knowledge - Strengthening Design of Reinforced Concrete with FRP - page 16

TABLE 2.1
Variations of Factors α and γ
with Concrete Strength

εε c a f c (psi) α γ

3000 0.00164 0.715 0.84

4000 0.0019 0.748 0.88

5000 0.00212 0.748 0.94

6000 0.00232 0.736 0.98

7000 0.00251 0.719 1.03

8000 0.00268 0.701 1.08

a Equation from MacGregor (1992).

It is evident from Table 2.1 that values of (γ) noticeably exceed the ACI value
of 0.85 as the concrete strength increases beyond 4000 psi. This is attributed to
higher (α) values obtained from Equation (2.20) compared to those selected by Kaar,
Hanson, and Capell (1978) for higher f ′ c values as seen in Table 2.2.
Sources of inconsistency in α and γ results between Tables 2.1 and 2.2 are attrib-
uted to the fact that α and β 1 in Table 2.2 are selected by Kaar, Hanson, and Capell
(1978) to be a lower bound of all the scattered experimental points, whereas it is
analytically computed in Table 2.1.

ε cu = 0.003 0.85 f c

b

a/2

a = β 1 c C = 0.85 f c ba

c

d

n.a.

A s

T = A s f y

ε s > ε y

Strain Equivalent rectangular

stress block

FIGURE 2.8 ACI equivalent rectangular stress block. (Courtesy of Portland Cement
Association [2013].)