Stress and strain of uncracked sections - Concrete Structures: Stresses and Deformations - page 51

Table 2.4 Properties of the precast section employed in calculation of stress and
strain at time t 1 = 3 days

Properties of transformed
area

Properties of area

A B I AE / E ref BE / E ref IE / E ref

(m 2 ) (m 3 ) (m 4 ) (m 2 ) ( 3 ) ( 4 )

Concrete 0.5090 0.0 0.1090 0.5090 0.0 0.1090

Non-prestressed
steel 3000 × 10 − 6

− 210 × 10 − 6

1282 × 10 − 6 0.0240

− 0.0017

0.0103

Prestressed steel 3160 × 10 − 6 1675 × 10 − 6 888 × 10 − 6 0.0253 0.0134 0.0071

Properties of 0.5583 0.0117 0.1264

transformed section A B I

N
M

− 4100 × 10 3

1400 × 10 3

− 4100 × 10 3 N

equivalent = =

− 4100 × 10 3 × 0.53 − 773×10 3 N-m

Instantaneous axial strain and curvature at t 1 = 3 days (Equation (2.32) )

are,

ε O ( t 1 )
ψ

1
25×10 9 (0.5583 × 0.1264

0.1264 − 0.0117

0.5583

=

− 0.0117 2 )

( t 1 ) − 0.0117

− 4100 × 10 3 − 289

= 10 −6

×

− 773×10 3 − 218 m −1

The above values of ε O and ψ are used to calculate the strain at any

fi bre and the corresponding stress (Fig. 2.11(a) ). The strain at the level

of prestress tendon is

− 405 × 10 −6 . The instantaneous prestress loss

is − 256 kN (6.2% of the initial force).

(b) Change in stress and strain occurring between t = 3 days and

60 days
The age-adjusted elasticity modulus of concrete (Equation (1.31) ) is:

t =

25×10 9

E c (60, 3) =

0.86 × 1.20 =

12.30 GPa (1780 ksi).

1 +

The stress in concrete required to arti fi cially restrain creep and

shrinkage (Equation (2.45) ) is: