Civil Engineering Reference
In-Depth Information
Similarly, when the tensile stress
σ
1
was increased with a constant compressive stress
σ
2
,
the source strain increment
ε
1
and the resulting strain increment
ε
2
were measured. The
Hsu/Zhu ratio
ν
21
was then calculated by
ε
2
ε
1
ν
21
=−
(6.28)
Strain-control procedure after yielding
Figure 6.4(b) shows a step-wise proportional loading using strain-control procedure after
yielding. When the load approached the first yielding of steel bars, a mode switch was made
from load-control to strain-control. When the compressive strain
ε
2
was increased and the
ε
1
was maintained constant, the strain increment
ε
2
and the stress increment
tensile strain
σ
1
were measured. The Hsu/Zhu ratio
ν
12
was then calculated as
σ
1
E
1
ε
2
ν
12
=−
(6.29)
where
E
1
(always positive) was the unloading modulus of the RC 2-D element because the
tensile stress
ε
1
.
E
1
was
calculated from the next reloading modulus, because the unloading modulus had been observed
experimentally to be equal to the initial linear portion of the reloading
σ
1
always decreased (i.e.
σ
1
was negative) under constant strain
E
1
was
σ
1
-
ε
1
curve.
then calculated by
(
σ
1
)
linear
E
1
=
(6.30)
(
ε
1
)
linear
where (
ε
1
)
linear
were the stress increment and strain increment, respectively,
in the linear portion of the reloading
σ
1
)
linear
and (
σ
1
-
ε
1
curve.
In the step where the tensile strain
ε
1
was increased and the compressive strain
ε
2
was
maintained constant, the strain increment
ε
1
and the stress increment
σ
2
were measured.
The ratio
ν
21
was then calculated by
σ
2
E
2
ε
1
ν
21
=−
(6.31)
where
E
2
(always positive) was either the unloading or the loading modulus of the concrete
element, depending on whether
σ
2
is positive or negative. For example, in the end level 22
to 23, the compression stress increased (
σ
2
is positive) and
ν
21
became negative.
6.1.4.2 Formulas for Hsu/Zhu Ratios
The measured Hsu/Zhu ratios,
ν
12
and
ν
21
, are plotted in Figure 6.5(a) and (b), respectively,
against the steel strain
ε
sf
. The symbol
ε
sf
is defined as the strain in the steel bars that yield first.
0
◦
(Figure 6.2a),
In panels with
α
1
=
ε
is always in tension and
ε
t
is always in compression.
45
◦
,Fig.6.2(b),
Therefore,
ε
sf
=
ε
. In panels with
α
1
=
ε
sf
could be
ε
or
ε
t
, whichever
yields first.
