Constituent Materials and Properties - Strengthening Design of Reinforced Concrete with FRP - page 66

TABLE 3.15
Typical Densities of FRP
Materials Compared to Steel

Material Density lb/ft 3 (g/cm 3 )

Steel 490 (7.9)

GFRP 75-130 (1.2-2.1)

CFRP 90-100 (1.5-1.6)

AFRP 75-90 (1.2-1.5)

Along the material principal axes:

σ α

1 1

ε
ε
γ

CC
CC

0
0

1
2
12

11 12

= σ + α T

(3.21)

12 22 2 2

0 0 C

66

τ 0

12

Along the structure principal axes:

σ α

ε
ε
γ

CCC
CCC
CCC

x x

11 12 16

x
y

= σ + α T

(3.22)

12 22 26 y y

xy

τ α

16 26 66

xy xy

where the CTEs transform like tensor strains (see Figure 3.11),

α
α
α

x

2 2

−
+

CS 2

2

CS

α
α

1

y

2 2

= S C CS (3.23)

2

xy
2

2 2

+ CS − CS CS − 0

TABLE 3.16
FRP Coefficients of Thermal Expansion vs. Steel and Concrete,
× 10 −6 /°F (× 10 −6 /°C)

Direction GFRP CFRP AFRP Concrete Steel

Longitudinal α L 3.3 to 5.6

(6 to 10)

−0.6 to 0
(−1 to 0)

−3.3 to −1.1
(−6 to −2)

5.5 (9.9) a 6.5 (11.7) a

Transverse α T 10.4 to 12.6

(19 to 23)

12 to 27
(22 to 50)

33 to 44 (60
to 80)

5.5 (9.9) 6.5 (11.7)

a From Beer and Johnston (1992).