Civil Engineering Reference
In-Depth Information
ε
dec
=
strain in prestressing steel at decompression of concrete;
E
ps
=
elastic modulus of prestressed steel, taken as 200 000 MPa (29 000 ksi);
E
ps
=
tangential modulus of Ramberg-Osgood curve at zero load, taken as 214 000 MPa
(31 060 ksi);
f
pu
=
ultimate strength of prestressing steel;
m
=
shape parameter (taken as 4).
The strain in prestressing steel at decompression of concrete,
ε
dec
, is considered a known
value and can be determined as follows:
ε
dec
=
ε
pi
+
ε
i
where
ε
pi
=
initial strain in prestressed steel after loss;
ε
i
=
initial strain in mild steel after loss.
ε
dec
is approximately equal to 0.005 for grades 1723 MPa (250 ksi) and 1862 MPa (270 ksi)
prestressing strands.
The background and application of these constitutive laws are briefly described below:
1. The softened stress-strain curve of concrete in compression, Equations
7
a
and
7
b
,are
used to relate
ε
d
. This curve is shown in Figure 5.12 and compared with the nonsoftened
stress-strain curve. The expressions of the ascending parabolic curve, Equation (5.100)
or
σ
d
to
7
a
, and the descending parabolic curve, Equation (5.101) or
7
b
, are explained in
Section 6.1.6 (Chapter 6). The softened coefficient
which is expressed by Eq. (5-102) or
Eq.
8
, is plotted in Figure 5.13 as a function of the tensile strain of concrete
ζ
ε
r
,usinga
very conservative lower bound of the test data given by Belarbi and Hsu (1995). This
ζ
coefficient is applicable to normal strength concrete. However, when high strength concrete
is used, it is advisable to multiply
by the Function of Concrete Strength,
f
2
f
c
,given
ζ
in Section 6.1.7.2 (Chapter 6).
Figure 5.12
Compressive stress-strain curve of concrete
