Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 109

0.9

0.8

0.7

0.6

0.5

α

0.4

0.3

0.2

0.1

0

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

ε cf

FIGURE 5.12 Linear regression plot of α vs. ε cf relationship. (First published by Engineers
Australia. Reprinted with permission.)

Plotting α and β functions in terms of ε cf , one notices that α may be approximated
by two straight lines with a breaking point at around ε cf = 0.0015 with an R 2 = 0.9931
and 0.9305, respectively, as seen in Figure 5.12.

α= 366.67 ε+ 0.0417 0 ≤ε < 0.0015

cf cf

(5.74)

α= ε+ 125 0.4042 0.0015 ≤ε ≤ 0.003

cf cf

In addition, β is seen to have a slight variation along the entire range of ε cf , as
seen in Figure 5.13:

2

β= 27.768 ε+ 0.3239 ( R = 0.9677)

(5.75) cf

0.45

β = 27.768 ε cf + 0.3239

0.4

0.35

0.3

0.25

β

0.2

0.15

0.1

0.05

0

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

ε cf

FIGURE 5.13 Linear regression plot of β vs. ε cf relationship. (First published by Engineers
Australia. Reprinted with permission.)