Fixed Angle Shear Theories - Unified Theory of Concrete Structures - page 247

Poisson effect

ν 12 = 0 . 2 + 850 ε sf ε sf ≤ ε y

7 a

ν 12 = 1 . 9 ε sf >ε y

7 b

ν 21 = 0 after cracking ,ν 21 = 0 . 2 before cracking

8

ν 12

1

ε 1 =

− ν 12 ν 21 ε 1 + − ν 12 ν 21 ε 2

¯

9

1 1

ν 21 1

ε 2 = ¯

− ν 12 ν 21 ε 1 + − ν 12 ν 21 ε 2

10

1 1

α 1 − γ 12
2

ε 1 cos 2 ε 2 sin 2 ¯ ε = ¯ α 1 + ¯ 2sin α 1 cos α 1

11

α 1 + γ 12
2

ε 1 sin 2 ε 2 cos 2 ε t ¯ = ¯ α 1 + ¯ 2sin α 1 cos α 1

12

Constitutive laws of materials
Concrete in compression

2 ¯

2

¯

ε 2
ζε o

ε 2
ζε o

2

f c σ = ζ − ε 2 /ζ ε o ≤ ¯ 1

13 a

1

2

(¯

ε 2 /ζ ε o ) −

1

c
2

f c

σ = ζ − ε 2 /ζ ε o ≥

¯ 1

13 b

/ζ −

(4 ) 1

5

9

1

8
f c ≤

. 1 | β |

24 ◦

ζ = 0 . √ 1 −

14

+ 400¯ ε 1

2 tan − 1

1 γ 12

β =

15

( ε 1 − ε 2 )

Concrete in tension

c
1

σ = E c ¯ ε 1 ε 1 ≤ ε cr ¯ and ε cr = 0 . 00008 mm / mm ,

16 a

f cr ε cr
¯

0 . 4

31 f c ( MPa )

c
1

σ = ε 1 >ε cr ¯ and f cr = 0 .

16 b

ε 1

Concrete in shear

c c

2

σ

1 − σ

c

τ

12 =

ε 1 − ε 2 ) γ 12

17

2(