Civil Engineering Reference
In-Depth Information
strain
ε
1
according to the prescribed strain history and starting
a new cycle, we can obtain the next pair of
γ
t
. By reading a new strain
τ
t
and
γ
t
. By repeating this process, a
hysteretic loop of
γ
t
can be plotted. It is clear that the calculation is very tedious
and must be performed by computer.
τ
t
and
6.3.5.2 Modifications of Material Laws
(1) In SMM Equations
13 - 17
are used to calculate the constitutive law of concrete,
β
ζ
σ
1
,
σ
2
,
τ
12
. Three adjustments should be made in CSMM. First,
including
,
,
2
σ
Equations
13
a
and
13
b
for calculating concrete compressive stresses
should
be
replaced
by
Equations
(6.100)-(6.104).
Second,
Equation
and
for
16
a
16
b
c
calculating the concrete tensile stress
1
should be replaced by Equations (6.98)
and (6.99). Third, in all the equations for
σ
c
1
c
2
, the subscripts 1 or 2 are
for tension and compression when applied to the positive direction of cyclic load.
When applied to the negative direction, however, the subscripts 1 and 2 must be
interchanged.
(2) In CSMM the equations required for the calculation of smeared steel stresses
f
, and
f
t
,
should include Equations
18
a
-
18
e
and
19
a
-
19
e
(for SMM), plus the unloading and
reloading equation, (6.108), and the limit of compressive steel stress (Equation 107).
(3) The Hsu/Zhu ratios
σ
and
σ
ν
12
and
ν
21
calculated according to Equations
and
in SMM
7
8
should be replaced by
ν
TC
and
ν
CT
, respectively, in CSMM. Hsu/Zhu ratio
ν
TC
=
1.0, and
the Hsu/Zhu ratio
ν
CT
=
0.
6.3.6 Hysteretic Loops
Conventional low-rise shear walls reinforced with vertical and horizontal steel bars in the web
(Figure 6.31a), have been shown (Derecho
et al
., 1979, Oesterle et al. 1984, Oesterle 1986) to
have lower ductility and energy dissipation capacities than RC structures that deform primarily
in flexure. Increasing the amount of vertical and horizontal steel in such shear walls did not
significantly improve their ductility and energy dissipation (Oesterle 1986). In contrast, Paulay
and Binney (1974), Mansur
et al
. (1992), and Sittippunt and Wood (1995) showed that the
hysteretic responses of shear walls improved significantly if diagonal reinforcement was used
in the web, as shown in Figure 6.31(b).
45
◦
) versus Panel CE3 (
0
◦
)
6.3.6.1 Panel CA3 (
α
1
=
α
1
=
The effect of steel bar orientation on the cyclic response of shear walls was studied by
comparing the hysteretic loops of two RC 2-D elements, CA3 and CE3 (Hsu and Mansour,
2002). Panel CA3 represents a 2-D element taken from the web of shear wall of Figure
6.31(a). In this element the
t
coordinate of the diagonal steel bars is at an angle of
45
◦
to the principal 1-2 coordinate. Such an element has been shown in Figure 6.2(b) with
α
1
=
−
45
◦
. In contrast, panel CE3 represents a 2-D element taken from the web of shear wall of
Figure 6.31(b). In this element the
t
coordinate of the diagonal steel bars coincides with
the principal 1-2 coordinate. Such an element has been shown in Figure 6.2(a) with
−
0
◦
.
α
1
=
