Stress and strain of uncracked sections - Concrete Structures: Stresses and Deformations - page 39

(b) Changes in stress and strain due to creep, shrinkage
and relaxation
The age-adjusted elasticity modulus of concrete (Equation (1.31) ) is

30×10 9

E c ( t , t 0 ) =

0.8×3 =

8.82 GPa.

1 +

The stress in concrete at the top and bottom fi bres when the strain

due to creep and shrinkage is arti fi cially restrained (Equations (2.34)

and (2.45) ) is:

( σ c restrained ) top =− 8.82 × 10 9 [3×10 −6 ( − 126 + 170 × 0.6) − 240×10 −6 ]

= 2.741 MPa (0.398 ksi)

( σ c restrained ) bot =− 8.82 × 10 9 [3×10 −6 ( − 126 − 170 × 0.6) − 240×10 −6 ]

= 8.145 MPa (1.181 ksi).

The restraining forces (Equations (2.41) to (2.44) ) are:

1.625 × 10 −3
41.84 × 10 −3

∆ N

∆

0.3545 −

creep =−8.82 × 10 9 ×3

1.625 × 10 −3 M −

− 126 1.175 N

0.1828 N-m

× 10 −6 = 10 6

− 170

∆ N

∆

0.3545

shrinkage =−8.82 × 10 9 (− 240×10 −6 )

1.625 × 10 −3 M −

0.750 N

= 10 6

− 0.0034 N-m

∆ N

∆

1120 × 10 −6 ( 80×10 6 )

1120 × 10 −6 × 0.45 (

−

relaxation =

M − 80×10 6 )

− 0.090 N

10 6

=

− 0.0403 N-m

∆ N 1.175 + 0.750 − 0.090 1.835 N

0.139 N-m

= 10 6 =10 6

.

∆ M 0.1828 − 0.0034 − 0.0403

Calculation of the properties of the a ge -adjusted transformed section is
performed in Table 2.2 using E ref

= E c ( t , t 0 ) = 8.82 GPa and α ( t , t 0 ) =

22.68 (Equation (1.31) ).