Constituent Materials and Properties - Strengthening Design of Reinforced Concrete with FRP - page 50

only two independent engineering constants, which are Young's modulus of elastic-
ity ( E ) and Poisson's ratio (ν). Conversely, orthotropic laminas have nine distinct
engineering parameters, including three Young's moduli along the three principal
materials directions ( E 1 , E 2 , E 3 ), three independent Poisson's ratios (ν 12 , ν 13 , ν 23 ), and
three shear moduli ( G 12 , G 13 , G 23 ). The generalized 3-D compliance relationship of
an orthotropic sheet is

1

− ν − ν

21
2

31
3

0 0 0

E E E

1

− ν

1

− ν

12 32

0 0 0

ε
ε
ε
γ
γ
γ

E E E σ

σ
σ
τ
τ
τ

11
22

1 2 3 11

22

− ν − ν

1

13
1

23
2

0 0 0

(3.1)

E E E 33

3 33

=

1

12

12
13

0 0 0 0 0

G 13 12

1

23 23

0 0 0 0 0

G

13

1

0 0 0 0 0

G

23

where

j E . The stiffness matrix is obtained by inverting the compliance
matrix in Equation (3.1) (Rasheed 1996),

ν ν

ij
i

=

ji

E

1 −ν ν ν +ν ν ν +ν ν

23 32 21 31 23 31 21 32

E E E 000

1 1 1

σ
σ
σ
τ
τ
τ

11
22

ν+νν 1 −ν ν ν +ν ν

21 31 23 13 31 32 12 31

E E E 000 1 2 2

33

ν+νν ν+νν 1 −ν ν

= 31 21 32 32 12 31 21 12

E E E 000 1 2 3

12
13

0 0 0 G 0 0 12

23

0 0 0 0 G 0 13

0 0 0 0 0 G

23

ε
ε
ε
γ
γ
γ

11

22
33

(3.2)

12

13

23

where

=−νν−ν ν−νν−ννν 1 2 . 12 21 23 32 13 31 21 32 13