Stress and strain of uncracked sections - Concrete Structures: Stresses and Deformations - page 57

The total restraining forces

∆ N

∆

1.937 + 2.437 − 0.221 4.153 N

= 10 6 = 10 6

M − 1.108 − 0.928 − 0.117 − 2.153 N-m

The increments of axial strain and curvature during the period t 2 to t 3
are obtained by substitution in Equation (2.40) and are plotted in
Fig. 2.12:

∆ ε O ( t 3 , t 2 )
∆ ψ

− 261

195 m −1

= 10 −6

( t 3 , t 2 )

The corresponding change in stress is calculated by Equation (2.46) and
plotted also in Fig. 2.12.

2.6 Summary of analysis of time-dependent strain
and stress
The procedure of analysis given in this chapter can be performed in four
steps. Figure 2.13 outlines the four steps to determine the instantaneous and
the time-dependent changes in strain and stress in a non-cracked prestressed
section. For quick reference, the symbols used are de fi ned again below and

the four steps summarized.

Notation
A area
B

rst moment of area
E modulus of elasticity
E c age-adjusted elasticity modulus of concrete
I second moment of area
M bending moment about an axis through O
N normal force at O
P absolute value of prestressing
t time or age of concrete
y coordinate (Fig. 2.5)
σ

fi

stress

α ratio of modulus of steel to that of concr e te at time t 0

α ratio of modulus of elasticity of steel to E c

χ aging coe cient of concrete

∆ increment