Civil Engineering Reference
In-Depth Information
6.3.9 Shear Stiffness
6.3.9.1 Definition of Pre-yield Shear Stiffness (
K
y
)
The pre-yield shear stiffness (
K
y
) of a panel subjected to cyclic shear is defined as:
τ
y
γ
y
K
y
=
(6.109)
γ
y
are the yield shear stress and the yield shear strain, respectively, at 45
◦
to the
principal 1-2 coordinate. In the post-cracking stage, but still below the yield shear stress, the
shear stiffness of a typical panel is found to decrease as load intensity increases and as more
cracks occur. In this pre-yield stage, the pre-yield shear stiffness
K
y
approaches an asymptotic
value defined by Equation (6.109), because the steel bars are still in their linear, elastic stage.
The positive and negative pre-yield shear stiffnesses (
K
y
and
K
y
), correspond to the positive
and negative loading directions, respectively, of cyclic shear.
where
τ
y
and
6.3.9.2 Effect of Steel Bar Angle on
K
y
Series P with panels G-45-1.2, G-21.8-1.2, G-10.2-1.2 and G-0-1.2 is designed to study the
effect of the steel bar angle (
α
1
) on the pre-yield shear stiffness of the panels, while keeping
the percentage of steel (
ρ
t
) constant at 1.2%. Figure 6.38 records the values of positive
pre-yield shear stiffnesses
K
y
ρ
,
of these four panels. It can be seen that
K
y
increases as the
α
1
) decreases. The
K
y
value of 2475 MPa for G-0-1.2 is about twice the
K
y
value of 1295 MPa for G-45-1.2. This increase of pre-yield shear stiffness from
steel bar angle (
45
◦
α
1
=
to
0
◦
is caused primarily by the decrease of the yield shear strain
α
1
=
γ
y
.
6.3.9.3 Effect of Steel Percentage on
K
y
The effect of the steel percentages (
, can be observed
by comparing the results of the three panels in the A45 series (panels G-45-0.54, G-45-1.2
and G-45-2.7), as well as those in the A0 series (G-0-0.54, G-0-1.2 and G-0-2.7). Figure
6.39 records the
K
γ
ρ
,
ρ
t
) on the pre-yield shear stiffness,
K
γ
values for panels in these two series. As expected, increasing the steel
percentage increases the pre-yield shear stiffness of the panel, because the yield shear stress
τ
y
increases almost proportionally with the steel percentage. In the case of series A45 (
α
1
=
45
◦
),
K
γ
increases from 659 MPa for G-45-0.54 (
ρ
=
0.54%) to 2094 MPa for G-45-2.7
0
◦
),
K
γ
(
ρ
=
2.7%). In the case of series A0 (
α
1
=
increases from 1415 MPa for G-0-0.54
(
ρ
=
0.54%) to 5689 MPa for G-0-2.7 (
ρ
=
2.7%).
6.3.10 Shear Ductility
Similar to the bending ductility factor defined for flexural members, the envelope shear ductility
factor is defined for 2-D elements in structures subjected to predominant shear force, such as
the low-rise shear wall shown in Figure 6.31.
6.3.10.1 Definition of Envelope Shear Ductility Factor (
µ
E
γ
)
The envelope shear ductility factor (
µ
E
γ
) in cyclic loading is based on the envelope curve
that houses the shear stress-shear strain hysteretic loops of a RC 2-D element (or panel). It is
defined as the ratio of the envelope shear strain at ultimate
γ
u
to that at the onset of yielding
