Fixed Angle Shear Theories - Unified Theory of Concrete Structures - page 246

Figure 6.22 Mohr Circle for stresses and strains

Dividing Equation (6.90) by Equation (6.91) gives the new constitutive law of concrete in
shear as:

c
12

c c

2

τ σ

1 − σ

G 12 =

2) =

(6.92)

( γ 12 / ( ε 1 − ε 2 )

where ε 1 and ε 2 are biaxial strains.

6.1.11 Solution Algorithm
6.1.11.1 Summary of Governing Equations

The eighteen governing equations for RC 2-D elements are summarized below:

Stress equilibrium equations
σ = σ

c
1

cos 2

c
2

sin 2

c
12 2sin

α 1 + σ α 1 − τ α 1 cos α 1 + ρ f

1

c
1

sin 2

c
2

cos 2

c

σ t = σ α 1 + σ α 1 + τ

12 2sin

α 1 cos α 1 + ρ t f t

2

c c

12 (cos 2

c

sin 2 τ t = ( σ

1 − σ 2 )sin

α 1 cos α 1 + τ α 1 − α 1 )

3

Strain compatibility equations
ε = ε 1 cos 2 α 1 − γ 12

2

α 1 + ε 2 sin 2 2sin α 1 cos α 1

4

α 1 + γ 12
2

= ε 1 sin 2 α 1 + ε 2 cos 2

ε t 2sin α 1 cos α 1

5

γ t
2 =

α 1 + γ 12
2

(cos 2 sin 2 ( ε 1 − ε 2 )sin α 1 cos α 1 − α 1 )

6