Constituent Materials and Properties - Strengthening Design of Reinforced Concrete with FRP - page 55

σ

f fu

E f

1

ε

ε fu

FIGURE 3.9 FRP design stress-strain curve along the fiber direction.

cracking, while in-plane shear behavior is always nonlinear. Nevertheless, this text
focuses on the behavior along the fiber direction, since FRP fibers are aligned with
the structural axis of loading in the strengthening application.
According to ACI 440.2R-08,

f fu ≡ mean ultimate tensilestrengthof20coupon specimens

ε≡
ffu

mean ultimate tensile strengthof20coupon specimens

based on ASTM D3039 and D7205.

(3.16)

f

* =−σ=

f 3 ultimate tensile strength

fu fu f

* ε=ε−σ=
ε

(3.17)

3 ultimate tensile strain

fu fu

where σ f and σ ε are the standard deviations for the ultimate strength and strain
according to ACI 440.2R-08.
Equations (3.16) and (3.17) yield 99.87% probability of exceedance

*

f = Cf = design ultimate tensilestrength

(3.18)

fu E u

*
ε= ε= C design ultimate tensile strain (3.19)

fu E u

*

f f

fu fu

E = ε = ε = design modulus of elasticityofFRP (3.20)

f

*

fu fu

where C E is the environmental reduction coefficient (ACI 440.2R-08), as seen in
Table 3.5.
For FRP plates or precured laminates, properties that are reported are those of
the composite, since fiber and resin volume fractions are well controlled. Conversely,
FRP sheets manufactured by hand wet lay-up have their properties primarily
reported based on the net fiber area, since it is more controlled than the fixed width