Constituent Materials and Properties - Strengthening Design of Reinforced Concrete with FRP - page 53

E

f

G =

(3.11)

( )

f

21 +ν

f

E

m

G =

(3.12) m

2 (

)

+ν

m

More-accurate determination of G 12 could be obtained using the Halpin-Tsai
equations (Jones 1975),

G
G

1
1

+ξη
−η

V
V

12 = f

(3.13)

m f

where

GG
GG

−
+ξ

1 f m

η=

(3.14)

f m

The value of ξ could be difficult to obtain, since it is a function of the fiber geom-
etry, packing geometry, and loading conditions. However, studies have shown that a
value of ξ = 1 for calculating G 12 can be approximated for a fiber volume fraction of
0.55 (Jones 1975).

3.6.5 D etermination oF ν 21 :
Once the first three parameters are estimated, the minor Poisson's ratio ν 21 is directly
calculated, as discussed in Section 3.5:

ν

= ν ν= ν

12 21 12

E

2 (3.15) 21

EE E

1 2 1

Since the ratio of

ν is accurately estimated, the minor Poisson's ratio ν 21 will yield
a lower bound solution if the mechanics-of-materials approach is followed.

E 12
1

Example 3.1

E-Glass FRP composite is made of 60% fiber and 40% epoxy matrix by volume.
Determine the in-plane orthotropic properties of the composite sheet from the
constituent properties.

ν= 0.22

f

ν= 0.37

m