Special cases of uncracked sections and calculation of displacements - Concrete Structures: Stresses and Deformations - page 83

0.2963 m 2 25.26 × 10 −3 m 4 r c = 84.75 × 10 −3 m 2 . A c = I c = I c / A c =

The area and moment of inertia of the age-adjusted transformed
section about an axis through O are:

¯ A = 0.3811 m 2 = 37.50 × 10 −3 m 4 .

The axial strain and curvature reduction coe cient (Equations (3.17)

and (3.18) ) are:

0.2963
0.3811 =

25.26
37.50 =

η = 0.777 κ = 0.674.

Substitution in Equations (3.15) and (3.16) gives the changes in axial
strain and in curvature due to shrinkage:

300×10 −6 ) 233×10 −6

∆ ε O = 0.777( − =−

0.054
84.45 × 10 −3

−

∆ ψ = 0.674 ( − 300×10 −6 )

= 129×10 −6 m −1 (3.23 in −1 ).

The changes in concrete stress due to shrinkage (Equation (3.19) )
are:

( ∆ σ c ) top = 8.824 × 10 9 [ − ( − 300) + ( − 233) + 129( − 0.551)]10 −6 Pa

=− 0.036 MPa ( − 0.005 ksi).

8.824 × 10 9 [ 129(0.449)]10 −6 Pa

( ∆ σ c ) bot = − ( − 300) + ( − 233) +

= 1.102 MPa (0.159 ksi).

The changes in stress and strain distributions caused by shrinkage are
shown in Fig. 3.4(b).

Example 3.3 Section subjected to normal force and moment
The same cross-section of Example 3.2 (Fig. 3.4(a) ) is subjected at age
t 0 to an axial force = − 1300 kN at mid-height and a bending moment of