Stress and strain of cracked sections - Concrete Structures: Stresses and Deformations - page 256

(a) Strain and stress immediately after transfer
The calculations in this part follow the procedure presented in Section
2.3 and applied in Example 2.2. Thus, here only the results of the calcu-
lations are presented (Fig. 7.12(b) ). The stress in the bottom non-
prestressed reinforcement, σ ns = − 5.6 MPa and in the prestressed steel,

σ ps = 1030.5 MPa.

(b) Changes in strain and in stress due to creep, shrinkage
and relaxation
The analysis for this part follows the method discussed in Section 2.5
and applied in Example 2.2. The results are shown in Fig. 7.12(c). The
changes in stress in the bottom non-prestressed steel, ∆ σ ns = − 16.8 MPa

and in the prestress steel, 124.5 MPa.

After occurrence of the time-dependent changes, the distribution of
stress

∆ σ ps = −

σ ( t ) becomes as shown in Fig. 7.13(b).

(c) Changes in strain and stress in the decompression stage
The transformed area to be used here is composed of A c plus α times the

area of all reinforcements; where α = E s / E c ( t ); A c = area of concrete

section = 0.2768 m 2 :

α = 200/30 = 6.667.

Choose reference point O at the centroid of A c , at 0.303 m below the
top edge (Fig. 7.13(a) ). The moment of inertia of A c about an axis
through O 0.2768 m 2 .

The area of the transformed section, its

= 21.78 × 10 −3 m 4 ; A c =

fi rst and second moments

about an axis through O are:

A = 0.2768 + 6.667(1600 + 1200 + 400)10 −6 = 0.2981 m 2

400 × 0.253)10 −6

B = 6.667(1600 × 0.547 + 1200 × 0.447 −

= 8.734 × 10 −3 m 3

21.78 × 10 −3 6.667(1600 × 0.547 2

I = +

+ 1200 × 0.447 2 + 400 × 0.253 2 )10 −6

= 26.74 × 10 −3 m 4 .

The stress distribution in Fig. 7.13(b) may be de fi ned by the value of

stress at O and the slope of diagram: