Civil Engineering Reference
In-Depth Information
γ
y
as follows:
γ
u
γ
y
µ
E
γ
=
(6.110)
In the case of an ideal elastic perfectly plastic behavior,
γ
u
and
γ
y
are easily defined.
However, for RC 2-D elements the definition of
γ
u
is somewhat subjective. The ultimate shear
strain,
γ
u
, is taken as the shear strain that corresponds to 80% of the shear stress capacity in the
post-peak descending branch of the envelope curve. The yielding shear strain
γ
y
is the shear
strain at the onset of yielding of the reinforcing bars. Since the positive and negative envelope
shear ductility factors
µ
E
γ
µ
E
γ
and
of a given panel are almost identical, only the positive
µ
E
γ
envelope shear ductility factors
are given in Figures 6.38 and 6.39.
6.3.10.2 Effect of Steel Bar Angle on
µ
E
γ
Figure 6.38 shows the positive envelope shear ductility factors
µ
E
γ
as a function of steel bar
angle (
α
1
) for series P (panels G-45-1.2, G-21.8-1.2, G-10.2-1.2, and G-0-1.2). The figure
indicates that
µ
E
γ
are 6.1 and 24 for panels G-45-1.2 and G-0-1.2, respectively. In other
µ
E
γ
α
1
decreases from 45
◦
to 0
◦
.
words,
increases by a factor of almost four as
6.3.10.3 Effect of Steel Percentage on
µ
E
γ
Figure 6.39 shows the positive envelope shear ductility factors
µ
E
γ
as functions of percentage
of steel (
ρ
t
) for panels in series A45 and series A0. When the steel ratio in a shear panel
increases from 0.54 to 2.7% in series A45,
ρ
or
µ
E
γ
reduces from 10 to 2, a reduction of 80%.
When the steel ratio in a shear panel increases from 0.54 to 2.7% in series A0,
µ
E
γ
reduces
from 36.6 to 15.5, a reduction of about 60%. In short, increasing the steel percentage in a shear
panel leads to a decrease in the envelope shear ductility factor, i.e. the hysteretic loops exhibit
a shorter envelope curve and the descending branch arrives earlier.
6.3.11 Shear Energy Dissipation
The shear resistance of a reinforced concrete element is contributed by the concrete in compres-
sion and the steel bars in tension. The concrete component experiences significant degradation
of strength and stiffness when subjected to large cyclic displacements. Therefore, the primary
source of energy dissipation must be provided by the inelastic behavior of reinforcing steel.
Improvement in the energy dissipation capacity can then be achieved by designing the rein-
forced concrete structural elements to: (1) promote large strains after yielding of reinforcement
bars; and (2) reduce the degradation of concrete in terms of strength and stiffness.
6.3.11.1 Definition of Shear Energy Dissipation
The total amount of hysteretic energy (i.e. the cumulative area of the hysteretic loops) when
the structure fails under many cycles of reversed loading should reflect three characteristics
of the hysteretic loops: (1) the pinched shape of each loop cycle; (2) the number of cycles
before failure, and (3) the ultimate shear strain as measured by the envelope shear ductility
factor (
µ
E
γ
).
