Stress and strain of cracked sections - Concrete Structures: Stresses and Deformations - page 251

1000)10 −6 0.0881 m 2 A c = 0.30 × 0.30 − (930 + =

α = 200/24 = 8.33

1000)10 −6 0.1042 m 2 .

A = 0.0881 + 8.33(930 + =

The axial strain at transfer (Equation (2.33) ) is

1100 × 10 3
24×10 9 × 0.1042

ε ( t 0 ) = − = − 440 × 10 −6 .

The stress in concrete (Equation (2.35) ) is

σ ( t 0 ) = 24 × 10 9 ( − 440 × 10 −6 ) = − 10.559 MPa ( − 1.532 ksi).

The stress in non-prestressed and in prestressed steel is

σ ns = 200 × 10 9 ( − 440 × 10 −6 ) = − 88.0 MPa ( − 12.8 ksi)

1100 × 10 3 σ ps =

930×10 −6

+ 200 × 10 9 ( − 440 × 10 −6 )

= 1094.8 MPa (158.8 ksi).

(b) Changes in strain and in stress due to creep, shrinkage and
relaxation
The transfo r med s e ction to be used here is composed of A c

+ α ( A ps +

A ns ); where E s / E c ( t , t 0 )

Using Equation (1.31)

α =

24×10 9

E c =

2.4 × 0.8

= 8.215 GPa (1192 ksi)

1 +

200 α =

8.215

= 24.33.

The transformed area

A = 0.0881 + 24.33(930 + 1000)10 −6 = 0.1351 m 2 .

cial force that would be necessary to prevent strain due to
creep, shrinkage and relaxation (Equations (2.41-44) ) is

The arti fi