Civil Engineering Reference
In-Depth Information
Function of concrete strength, f
2
(f
c
)
Figure 6.9
of cracking. The most important parameter to measure the severity of cracking is the tensile
strain ¯
ε
1
.
Pang and Hsu (1996) studied the behavior of 2-D elements subjected to pure shear (Figure
6.2b). The test specimens were reinforced with various amount of steel bars oriented in the 45
◦
directions (
t
coordinate). The test results of 13 panel specimens confirmed the following
equation given by Belarbi and Hsu (1995) for the softened coefficient:
−
0
.
9
ζ
=
√
1
(6.50)
+
ε
1
400¯
Equation (6.50) is valid for normal strength concrete of 42 MPa (6000 psi) or less. When the
tensile strain ¯
0.9. The constant of 0.9 was determined by the tests of two reference
panels subjected to uniaxial compression. It takes into account the size effect, the shape effect
and the loading rate effect between the testing of standard cylinders and the testing of panels.
ε
1
=
0,
ζ
=
6.1.7.2 Function of Concrete Strength
f
2
f
c
Utilizing the servo-control system on the UPT, Zhang and Hsu (1998) experimented with RC
2-D elements made of high-strength concrete of 70 and 100 MPa. They found experimentally
that the softening coefficient was not only a function of the perpendicular tensile strain
¯
ε
1
, but also a function of the concrete compressive strength
f
c
.
Fi
gure 6.9 shows that the
functi
on of con
crete strength
f
2
f
c
is inversely proportional to
f
c
and can be expressed as
5
/
f
c
(
MPa
). The groups of test data include panels with
f
c
of 42, 70 and 100 MPa.
Thus, for concrete strength up to 100 MPa, the softening coefficient
.
8
ζ
can be expressed as
ε
1
and
f
c
as follows:
a function of both
9
8
√
f
c
(
MPa
)
≤
5
.
1
ζ
=
0
.
√
1
(6.51)
+
400¯
ε
1
