FUNDAMENTAL CHARACTERISTICS AND BEHAVIOR OF R.C. BRIDGE PIERS
SUBJECTED TO REVERSED CYCLIC LOADING
Rizkalla, S.H.l, Saadat, F.2, Higai, T.3
ABSTRACT
A
total
without
web
bridge
piers
extensive
of
reinforcements
subjected
yielding
parameters
sixteen
of
considered
longitudinal
were
to
tested
to
deflection
the
shear
study
the
specimens
behavior
large
typical
to
The
ratio,
applied
of
enough
reinforcement.
of
Each specimen was
concrete
the
span-to-depth
frequency
cycles of deflection reversals,
reinforced
reversals
longitudinal
included
reinforcement,
compressive stresses.
large-scale
cause
different
percentage
load,
and
of
axial
subjected to a multiple of three
in increments equal to the yield deflection
until failure.
Based
nondimensional
on
parametric
factor
was
studies
introduced
of
to
the
describe
of such members.
The proposed characteristic
the
maximum
ductility,
capacities,
modes
of
and
failure
the
shear
equivalent
observed
were
stress,
viscous
experimental
the
results,
fundamental
factor was used
energy
damping
behavior
to evaluate
absorption/dissipation
coefficient.
classified according
to
the
The
range
proposed factor, and also to the maximum intensity of shear stresses.
on
the
experimental
results,
an expression was
a
introduced
to
three
of
the
Based
predict
the
equivalent flexural stiffness in the post-yielding range.
(1,2)
Associate
Professor,
Graduate
Winnipeg, Manitoba, Canada.
Student,
University
of
Manitoba,
(3)
Associate Professor, University of Yamanashi, Takeda, Kofu, Japan.
2
Rizkalla et al.
INTRODUCTION
Bridge piers are commonly lightly reinforced in both longitudinal
and
transverse
different
Unlike
directions.
categories
in
terms
of
beams
shear
and
columns,
span-to-depth
they
fall
ratio,
as
into
related
to the percentage of reinforcement and level of axial compressive stresses.
The main objective of this paper is to study the behavior of typical bridge
piers when they are subjected to reversed cyclic deflections
large enough
to cause extensive yielding of the longitudinal reinforcement.
tot~l
A
without
web
of
sixteen
reinforcement
large-scale
were
tested.
reinforced
The
specimens
concrete
were
specimens
representativp.
of typical bridge piers in terms of material properties, section properties,
and
construction
The
details.
different
parameters
considered
in
this
program are the shear span-to-depth ratio (a/d), percentage of longitudinal
reinforcement
(p),
frequency
of
the
applied
load,
and
level
of
axial
compressive stresses (a).
The
experimental
as given in Table
effect
of
shear
program
was
The objective
1.
span-to-depth
divided
for
ratio,
into
subseries
aid,
on
three
I-A was
the
mode
major
series,
to examine the
of
failure
and
ductility.
For these specimens, the percentage of longitudinal reinforcement
was
to maintain a
varied
monotonic
load,
vc '
reinforcement, v y .
and
constant
the
examined
in Series
II.
III with axial compressive
prototype.
shear strength under
shear stress at yielding of the
longitudinal
In subseries I-B, seven specimens were tested to examine
the effect of the percentage
was
ratio between the
o~
steel, p.
Finally,
force
The effect of the load frequency
two specimens were tested in Series
to simulate
the actual conditions of the
3
Rizkalla et a1.
•
TEST SPECIMENS
The
pier
is
relationship
shown
in
between
Figure
The
1.
a
tested
specimen and a
dimensions
and
typical bridge
reinforcement
details
of
a typical specimen are also shown in the same figure.
The effective depth,
d,
span-to-depth
was
aid,
to
varied
allow
for
between 3.29 and 6.05.
cover
the
typical
end
block
the
foundation
used
to
in
was
of
strength of
of
30 MPa
for
to
of
shear
such members,
simulate
typical
fabrication
variation
ratio,
The percentage of steel, p, was also selected
range
designed
the
the
as
given
boundary
in
conditions
reinforced concrete bridge piers.
the
specimens
and was
was
ready-mixed
designed
from
a
Table
for
local
1.
The
provided
All
by
concrete
a nominal ultimate
concrete mix
plant.
The reinforcement used consisted of hot deformed bar grade 300 MPa.
For the
was
applied
hydraulic
two
using
jacks
specimens
an
and
in Series
especially
pin
designed
connection
cantilever in the vertical plane,
provided
by
Teflon
strips
was
III,
to
the
load
allow
axial compression
frame
for
the
as shown in Figure 2.
attached
at
the
end
equipped
of
load
with
two
of
the
rotation
A bracing system
the
cantilever
to
minimize its lateral rotation.
TESTING APPARATUS AND PROCEDURE
The vertical
reversing
loads
and
deflections were
an electric-servo closed loop MTS testing system.
downward
Py .
The
measured.
(negative
load)
corresponding
The
specimen
up
to a
deflection
was
applied using
The specimen was
loaded
load equal to the calculated yield load,
at
unloaded
the
to
location
the
of
original
the
load, Oy'
position
and
was
then
loaded upward (positive load) to a deflection equal to the yield deflection.
The specimen was unloaded and the same procedure was repeated for two more
Rizkalla et al.
4
cycles of deflection reversals, as shown in Figure 3.
deflection
was
increased
by
capacity of the specimen was
increments
less
of Oy
After three cycles, the
until
the
than the yield load,
load-resisting
indicating failure
of the specimen.
For Series II,
cycle
followed
control mode.
by a
For
the above procedures were used for the first half
fully
Series
reversed sine wave loading under the deflection
III,
the
axial
load was
applied and maintained
constant by using a pressure regulator before the application of the yield
load and the measurement of the yield deflection.
The strains of the longitudinal steel were measured using electric
resistance strain gauges.
The average steel strain was also measured using
LVDT's which were mounted on steel
studs projecting from the
reinforcement, as shown in Figure 4.
longitudinal
Using the same technique, the average
diagonal and vertical strains were measured to determine the average shear
strain.
Loads
and
deflections
at
the
end
of
the
cantilever
specimen were recorded continuously by an X-Y recorder.
was
observed
using
a
magnifying
lens,
and
sketches
part
of
the
Crack propagation
were
plotted
as
the
cracks progressed.
TEST RESULTS
Material properties and the experimental results
specimens are given in Table 2.
for the sixteen
Due to the nature of the applied reversed
loading, the diagonal shear cracks intersected each other to form an x-shaped
crack for most of the
specimens.
The
load deflection hysteresis
for a typical specimen, 1-4, is shown in Figure 5.
response
5
Rizkalla et al.
Ductility
~,
The ductility factor,
defined as the ratio between the maximum
deflection before failure, 0u, and the deflection at yielding, Oy,
for
all
decreases
the
specimens
with
the
in
Table
increase
of
The
2.
the
results
percentage
indicated
of
that
longitudinal
is given
ductility
steel
and
It is also clear that the ductility
the yield strength of the steel, pf y .
is influenced by the shear span-to-depth ratio, aid, and the tensile strength
of the concrete, f t , since all the specimens failed in shear(l).
The
parameters was
relationship
between
examined using
tested in Series I
the
ductility factor,
the experimental data
of this program.
ll,
for all
and
the above
the
specimens
Based on a multiple linear regression
analysis, the following relationship was obtained.
0)
The mean and the standard deviation values were found to be 1.00
and 0.11, respectively.
The tensile strength,
f t , could be evaluated based
on the measured concrete splitting strength, f sp ' or the ultimate compressive
strength, f~, as follows(2):
(2a)
0.6 fsp
(2b)
or
The powers of the different variables included in the parametric
relationship, Equation 1, suggest the possibility of using a nondimensional
characteristic factor, K, to predict the ductility, where
K
(3)
The relationship between the ductility factor,
characteristic factor,
K,
~,
and the proposed
for all the specimens in Series I of this program
Rizkalla et al.
6
is shown in Figure 6.
Based on a best fitting curve for the experimental
data, the following relationship is proposed:
1
0.8-0.13 K
Jl =
The
above
(4)
relationship
is
shown
also
in Figure
6 as
a
solid
line.
The
mean and the coefficient of variance values were found to be 1.00 and 9%,
respectively,
of the
clearly indicating a very high degree of predictive accuracy
Specimens in Series II are also shown in the
proposed expression.
same figure.
The
proposed
characteristic
factor,
relation
K,
ductility factor of 2.
expression
provides
suggests
which
a
minimum value
corresponds
to
To exclude the flexural
the maximum value
for
an
of
integer
2.3
for
the
value
for
the
failure mode,
K of 5.3,
the proposed
which corresponds
to
a ductility factor of 9.
MODES OF FAILURE
The
appearance
of
the
crack
configuration
failed
to
indicate
a clear trend which could be used to classify the mode of failure for such
members.
The
location
of
yielding
of
the
longitudinal
reinforcement was
the only common observation which could be used to classify the different
mechanisms.
Using
the
proposed
characteristic
factor,
K,
it was
possible
to classify the modes of failure accordingly, as shown in Figure 6.
on
the
range
of
yielding
of
of
the
the
K-values,
the
longitudinal
critical
crack
reinforcement
pattern and
could
be
the
Based
extent
predicted.
proposed classification of mode of failure can be summarized as follows:
The
Rizkalla et a1.
Mode
7
Failure
(1):
is
at
the maximum moment
of
the
longitudinal
for specimen 1-7.
Mode (2):
of
the
is
section,
to
a
large
caused by the
reinforcement
at
this
vertical
relative
movement
localization of the yielding
section,
as
shown
in Figure
7
This mode is typical for K-values between 4.8 and 5.3.
within
mainly
8
and
9
a
distance
caused
longitudinal
Figures
due
This failure mode is characterized by yielding of the longitudinal
reinforcement
failure
mainly
d
by widening
reinforcement
for
from
specimens
the
of
within
1-1
and
maximum moment
the
the
x-shaped
same
1-5,
section.
crack
distance,
respectively.
or
The
buckling
as
shown
in
This
mode
is
typical for K-values between 4 and 4.8.
Mode
(3):
The
failure
is
characterized
by
yielding
of
the
longitudinal
reinforcement within a distance 2d from the maximum moment section.
is
mainly
due
to the
initiation and widening of a
as shown in Figure 10 for specimen 1-4.
Failure
second diagonal crack,
This mode is typical for K-values
between 2.3 and 4.
EFFECT OF LOAD FREQUENCY
A total of four specimens were tested in Series II, with different
frequencies,
as
given
in Table 1.
The crack patterns at
failure
for
the
different aid categories were approximately similar to those for the similar
specimens
tested
frequency within
have
a
However,
under
the
negligible
test
static
limited
effect
results
loading
ranges
on
suggest
under higher frequencies.
the
condition.
considered
ductility
possible
in
and
changes
The
variations
this
the
load
program seemed
maximum
in
in
shear
failure
to
stresses.
criteria
8
Rizkalla et a1.
EFFECT OF AXIAL LOAD
Two
and
higher
specimens,
aid,
ranges
of
of 0.98 MPa
and
tested
presence
axial
shear
that
of
resistance
axial
3-1
in
and
representative
subjected
to
this
program.
The
stresses
ductility
compressive
as
were
compressive
and
3-3,
of
stresses
an
axial
to
no general conclusion can be made at
the
this
indicated
increase
such members(3).
It
modes
the
compressive
results
appeared
affected
of both
was
of
stress
that
the
also
the
maximum
observed
fai lure.
stage due to the
lower
However,
limited ranges
considered in this program.
ENERGY ABSORBTION CAPACITY
In
Wa ,
the
magnitude
of
the
energy
absorption
capacity,
provides a means to evaluate the response of a structure to the various
loading
on
general,
the
histories.
actual
deflection
By
area
definition,
under
increment.
the
The
this
energy
could
be
load-deflection hysteresis
relationship
between
the
determined
prior
based
to
failure
normalized
energy
absorption capacity with respect to the product of yield load and deflection,
I
"
w,
and
the
proposed
characteristic
factor,
K,
for
all
the
specimens
in
Series I could be mathematically expressed as follows:
I" = 1.82 e O . 86K
(5)
w
The
mean
and
coefficient
of
variance
values
for
the
above
relationship
are 1.02 and 14%, respectively.
The
work
index,
Iw,
introduced
by
Gosian,
et
al.
(4)
can
be
expressed as:
n
Iw =
~
Pi pi
i=l Py
oy
(6)
9
Rizka11a et a1.
where
Pi
and
0i
are
the maximum applied
load
and
deflection at
the
ith
cycle, and n represents the number of cycles prior to the failure deflection
Based
increment.
Iw and I " was
w
coefficient
excellent
on
the
examined
experimental
and
found
of variance values
agreement
between
the
of
to
results,
be
7%,
of the simplified work index, Iw, in lieu of I "
w
absorbed energy, Wa.
factor
solid
K for
line
all
obtained
respectively,
This
indices.
relationship
The
linear.
1.04 and
two
the
to
would
between
mean
indicate an
justify the
the
represent
and
use
actual
The relation between Iw and the proposed nondimensional
the
specimens
represents
the
best
in Series
fitting
I
is
curve
shown
to
the
in Figure
11.
experimental
The
data,
and can be mathematically expressed as follows:
The
mean
K
Iw =
o. 4 1
and
coefficient
(7)
- 0.07 K
of
variance of
1.01 and
9%,
respectively,
were
obtained.
To minimize the effect of the loading pattern used in this program,
an average work index, Iw
Iw
The
ave
,could be used as follows (5):
(8)
ave
relationship between
the
ductility
factor
and
the
average work
index
for all the specimens tested in Series I without web reinforcement is shown
in
Figure
12.
The
solid
line
represents
the
best
fitting
curve
to
the
experimental data, which can be mathematically expressed as follows:
~
The
mean
obtained.
web
=
1.72 IW
and
The
ave
coefficient
comparison
reinforcement
and
(9)
- 0.72
the
of variance of 1.00 and 5%,
between
the
expression
above
proposed
equation
respectively,
for
piers
by Arakawa(5)
for
were
without
columns
Rizkalla et al.
10
with 0.3 percent
proposed
lower
transverse
relationship
bound
for
reinforcement
complements
the
family
of
is
Arakawa's
curves
with
also shown in Figure 12.
The
findings
the
by
different
introducing
percentages
of web
reinforcement.
ENERGY DISSIPATION CAPACITY
In
general,
provides
a
measure
reversed
loads.
the
for
By
magnitude
the
of
inelastic
definition,
this
the
energy
performance
energy
could
dissipation
of
a
be
capacity
structure
evaluated
under
based
on
the areas enclosed by the load-deformation hysteresis loops prior to failure
deflection.
NED,
with
The
relationship
respect
to
the
between
linearized
and the ductility factor,
ll,
in Figure
line
13.
The
solid
the
normalized
applied
energy
for all the specimens
represents
the
best
energy
of
dissipation,
the
first
in Series
fitting
I,
cycle,
is shown
curve
for
the
experimental data, which can be mathematically expressed as follows:
(0)
The
and 9%,
mean
and
respectively.
the
coefficient
Thus,
of variance
are
found
to· be
1.01
for a given ductility, which can be predicted
using Equation 4, the normalized energy dissipation can be determined.
MAXIMUM SHEAR STRESS
Based
on
the
normalized with respect
to
the
characteristic
shown in Figure 14.
measured
to
data,
the
maximum
shear
the concrete tensile strength,
factor,
K,
for
all
the
specimens
stress,
ft,
in
vu '
is
and related
Series
I,
as
The solid line represents the best fitting curve for
the experimental data, which can be expressed mathematically as follows:
=
0.71
( 11)
11
Rizkalla et al.
The
high
predictive
accuracy of
this
proposed
expression
is
reflected by
the values for the mean and the coefficient of variance of 0.99 and 2.5%,
Specimens
respectively.
in Series
Based on this relationship,
web
reinforcement,
yield
load
be
the
to
are
also shown in the
of
20% of
shear
the
stresses
corresponding
modes
of
failure
intensity of maximum shear
were
also
stresses.
K-value for each failure mode,
stresses are established
figure.
for
to
the
tensile strength of the concrete
ensure reasonable performance under large deflection reversals
The
same
it is recommended that for bridge piers without
intensity
limited
II
classified
Using
the
same
to
(~=6).
according
specified
to
the
ranges
of
the ranges of the intensity of maximum shear
the
three proposed modes,
as shown in Figure
14.
The maximum shear
depends
also
on
by
work
index,
the
the
degree
Iw.
stress
resistance,
vu '
of a
structural member
of severity of the applied energy represented
The
relationship
shear stress with respect to the
between
the
normalized
Vu
tensile strength of concrete,
f
maximum
,and the
t
work
index
Figure
15.
based
on
The
solid
the experimental
line
results of series
representing
the
best
I
fitting
is shown
curve
in
to
the
experimental data can be expressed mathematically as follows:
(12)
=
The
and 6%,
shear
obtained
respectively.
stress
of
a
mean
Using
provide
energy
absorption
coefficient
this
pier without
desired deformation capacity.
to
and
of
variance
relationship it
web
reinforcement,
For example,
such
that
it
is
values
possible
vu '
for
are
1.01
to evaluate
any
level
of
assume that a pier is required
can withstand
a
deflection of
five times the yield deflection with a deflection history as shown in Figure
12
Rizkalla et al.
3,
and the
load capacity should be always more
corresponding work
would
translate
tensile
index in this case
into
strength of
a
maximum
the
concrete
approximately equal to 45, which
is
shear
The
than the yield load.
stress
according
of
to
approximately
Equation
25% of
(12).
This
the
value
could also represent the concrete contribution in resisting shear for pier
structural members with web reinforcement.
EQUIVALENT VISCOUS DAMPING COEFFICIENT
The
use
the
advantage
may
approximate
small.
The
dissipation
of
of
the
equivalent viscous
linearizing
the
other
coefficient,
capacity,
WD'
the
forms
~eq'
and
equation
of
motion.
damping
if
the
of
can
the
be
expressed
linear
~eq'
damping coefficient,
This
coefficient
dissipative
in
terms
strain energy
has
energy
of
the
stored
at
is
energy
maximum
displacement, Ws ' as follows(6):
(13)
The
equivalent
characteristic factor,
in
Figure
5.3
can
16.
be
The
K,
viscous
damping
ultimate
as
related
to
the
for all the specimens tested in Series I is shown
relationship
approximated
at
by
for
the
a
given
following
range
of K between
equation,
which
is
2.3
also
and
shown
as the solid line in the same figure:
~eq = 0.12
3/K
(14)
The accumulated equivalent viscous damping coefficient at different
deflection
in Figure
increments
17.
It
is
for
all
clear
the
that
specimens
tested
the histories
in
of all
Series
I
is
shown
these specimens can
be represented by a single curve independent of their fundamental variables,
as
shown
by
the
solid
line.
Using
linear
regression
relationship can be expressed mathematically as follows:
analysis,
the
Rizkalla et a1.
13
o• 2 2
Seq =
in
which
viscous
line
0
is
the
damping
deflection
the
concrete
loading conditions.
The
(15)
coefficient
represents
reinforced
0.15
y
- 6/o
difference
in
is
which
In
sought.
relationship
columns
at
with
the
proposed
web
the
by
accumulated
same
figure,
Gulkan,
et
reinforcement
under
equivalent
the
al.
high
dotted
(7)
for
frequency
It is evident that both curves follow the same trend.
the
response
the
reinforcement
and
above
curves
be very useful
of
the
be
The prediction of the history of the equivalent viscous damping
to
influence
may
frequency.
deemed
of web
to
to
is
effect
according
attributed
coefficient
the
limit
load
in an iterative dynamic analysis
of the response to any input excitation.
EQUIVALENT FLEXURAL STIFFNESS
The change of the overall flexural stiffness could be attributed
to
cracking of concrete,
longitudinal
steel(7).
local
reinforcement,
For
deflection
and
spalling of the concrete,
reduction of modulus of elasticity of the
calculation
at
service
flexural
stiffness,
EI,
could be predicted using
inertia,
Ieff'
the
concrete
and
by the ACI code(B).
proved to be
slippage of the
modulus
of
load
the
conditions,
effective moment
elasticity,
Ec '
as
the
of
proposed
The comparison between the computed and measured values
in good agreement up to 70% of the yield load(9).
However,
athigher load levels the scatter appears and increases as the load approaches
the ultimate load under monotonic loading condition.
Under deflection reversals large enough to cause extensive yielding
of the longitudinal reinforcement, extensive cracking of the concrete occurs
both at the top and the bottom surfaces of the beam, leading to a substantial
reduction
in
variation of
the
stiffness.
the applied load.
The
stiffness
However,
the
changes
continuously with
slope of the
secant
the
line at
14
Rizkalla et al.
any
point
on
equivalent
~,
load-deflection
flexural
stiffness,
curve
EI,
at
could
that
be
used
level.
The
to
represent
stiffness
the
ratios,
between the equivalent flexural stiffness, EI, and the effective flexural
stiffness,
I
the
EcIeff' were calculated for all
in this program.
the
relationship
the specimens
tested
in Series
Based on the multiple regression analysis of the data,
between
the
stiffness
~,
ratio,
o/oy,
aid
and
was
established as shown in Figure 18 by the solid line, which can be expressed
mathematically in the following form (3):
The mean and coefficient of variance of 0.99 and 12.9%, respectively, were
Using
obtained.
EI,
the
above
equation
the
equivalent
flexural
stiffness,
for a given reinforced concrete bridge pier at any desired deflection
level, 0, in the post-yielding range could be evaluated.
SUMMARY AND CONCLUSIONS
The
following
observations
and
conclusions
are
based
on
the
experimental program discussed in this study:
1.
The
fundamental
using
a
behavior
proposed
of
bridge
nondimensional
piers
can be
characteristic
fully
described
factor,
K,
as
follows:
K
2.
The proposed factor, K, was used to derive expressions which could
evaluate
and
the
energy
ductility,
maximum shear
absorption
capacities
stress,
and
the
energy dissipation
ultimate
equivalent
viscous damping coefficient of such members.
3.
Using
the
classify
proposed
the
characteristic
failure
mechanisms
factor,
into
K,
three
it was
possible
different
to
distinct
15
Rizkalla et al.
modes
of
to a
This
failure.
classification was
rational categorization of these
accomplished
parallel
failure modes based on the
maximum intensity of the applied shear stresses.
4.
The
load
frequency within
the
limited
range
of
this
program
is
considered to have an insignificant effect on the mode of failure,
maximum
would
shear
suggest
stress,
and
possible
However,
ductility.
changes
in
failure
the
criteria
test
under
results
higher
frequencies.
5.
The
results
of
the
two
specimens
tested
in
the
presence
of
the
axial compressive load indicated that the axial compressive stresses
affect
the mode of failure and increase the maximum shear stress
capacity and ductility.
6.
For the given loading history a relationship between the ductility
factor and the average work index,
for
the
prediction
of
the
Iw
, was deve loped to allow
ave
deformation
capacity
of
such members
subjected to various degrees of severity of the applied load.
7.
Expressions
viscous
were
damping
proposed
for
coefficient and
the
prediction
the equivalent
of
the
equivalent
flexural
stiffness
of such members in the post-yielding range.
ACKNOWLEDGMENTS
This study was carried out in the Department of Civil Engineering
at
the
University of Manitoba with
financial
assistance
Sciences and Engineering Research Council of Canada.
NOTATION
a
aid
shear span
= shear span-to-depth ratio
from
the
Natural
Rizka11a et a1.
16
d
= effective depth of the section
EI
= equivalent flexural stiffness
concrete modulus of elasticity
concrete tensile strength
fsp
=
yield strength of steel
=
concrete splitting strength
f'
concrete compressive strength
I
moment of inertia of the cross-section
c
= effective moment of inertia
work index
I
wave
=
average work index
K
= nondimensiona1 characteristic factor
n
= number of cycles prior to failure deflection increment
NED
= normalized
p
= percentage of longitudinal reinforcement
p
energy dissipation capacity
load
Pi
= maximum
Py
=
load in the ith cycle
calculated yield load
= calculated shear strength under monotonic load
maximum shear stress
shear stress corresponding to yielding of longitudinal reinforcement
at maximum moment section
energy absorption capacity
energy dissipation capacity
= strain energy stored at maximum deflection
6
=
deflection
= measured yield deflection
= maximum deflection prior to failure
17
Rizkalla et a1.
~
= ductility factor
~
=
stiffness ratio
o
=
axial compressive stresses
~eq
equivalent viscous damping coefficient
REFERENCES
1.
Higai, T. (1982):
Shear
large
reversals.
deflection
failure
of
reinforced
Technical
concrete
Report,
piers
Yamanashi
under
University,
Japan.
2.
Hwang,
L.,
and Rizkalla,
characteristics
for
S.H.
(1983):
reinforced
Effective tensile stress-strain
concrete.
Proceedings
of
the
Canadian
Structural Concrete Conference, June 1-3, Ottawa, Ontario.
3.
Saadat,
F.
(1984):
Fundamental
characteristics
and
behaviour
of
reinforced concrete bridge piers subjected to reversed cyclic loading.
M.Sc.
thesis,
Dept.
of
Civil
Engineering,
University
of
Manitoba,
Winnipeg, Manitoba, p. 273.
4.
Gosain,
for
N.K.,
Brown,
R.H.
load reversals on R. C.
and
Jirsa,
members.
J.~.
(1979):
Shear
requirements
ACI Journal, July 1977,
ST7,
pp.
1461-1476.
5.
Arakawa,
of
T.,
et
reinforced
a1.
(1981):
concrete
Evaluation
columns
under
of
deformational
cyclic
loading.
behaviour
Transactions
of
the Japan Concrete Institute, Vol. 3, 1981, pp. 391-398.
6.
Steidel,
R.F.:
An
introduction
to
mechanical
vibrations.
New York,
Wiley, 1971, Second Edition.
7.
Gu1kan,
concrete
P.,
Sozen,
structures
M.A.
to
(1974):
earthquake
Inelastic
motions.
responses
ACI
of
Journal,
reinforced
Dec.
1974,
pp. 604-610.
8.
ACI
318-77
American
(1977):
Concrete
Building code requirements
Institute,
Box
19150,
for reinforced concrete.
Redford
Station,
Detroit,
18
Rizka11a et al.
Michigan 48219.
9.
Kripanarayanan,
of
beams
under
K.M.
and
single
1972, pp. 110-117.
Branson,
and
D.E.
repeated
(1972):
load
cycles.
Short-time
ACI
deflection
Journal,
Feb.
TABLE 1.
Variables Considered in the Experimental Program
....
~
N
;>;"
Series
Spec.
No.
bxd
(mm)
Longitudinal
Reinforcement
p%
aid
Py
(KN)
Vc
(MPa)
Vy
(MPa)
Vc
Vy
Frequency
of Loading
(HZ)
Axial Compression Stress
(MPa)
III
I-'
I-'
III
Cb
rt
I-A
1-1
500x350
3-20 M
0.51
3.29
83.9
0.80
0.48
1.67
1-2
500x230
3-20 M
0.96
5.0
65.8
0.96
0.57
1.68
"
"
"
"
0.0004
None
III
I-'
1-15 M
1-3
500x190
4-20 M
1. 26
6.05
57.8
1.06
0.61
1. 74
1-4
500x190
6-20 M
1.89
6.05
83.70
1. 27
0.88
1.44
1-5
"
3-20 M
0.95
"
43.80
1.02
0.46
2.22
"
"
1-6
"
5-20 M
1.58
"
70.80
1.12
0.75
1.49
"
1-7
500x350
2-20 M
0.40
3.29
66.10
0.74
0.38
1.95
"
"
"
0.46
"
74.80
0.77
0.43
1. 79
"
"
I-B
0.0004
None
1-10 M
1-8
"
2-20 M
1-15 M
II
III
1-9
"
5-20 M
0.B6
"
140.70
0.99
0.80
1. 24
11
11
1-10
500x280
3-20 M
0.64
4.11
68.0
0.89
0.49
1.82
"
"
2-1
500x350
3-20 M
0.51
3.29
83.8
0.77
0.48
1.60
0.01
None
2-2
"
"
"
"
"
"
0.77
0.2
"
0.78
"
"
1.60
2-3
"
"
1.60
0.05
"
2-5
500x190
4-20 M
1. 26
6.05
58.8
1.10
0.62
1.77
0.1
"
3-1
500x350
3-20 M
0.51
3.29
10B.70
0.B4
0.62
1. 35
0.0004
3-3
500x190
4-20 M
1. 26
6.05
64.76
1.18
0.68
1. 74
"
"
"
0.98
0.98
......
'"
TABLE 2.
Test Results
J;d
~.
N
Series
Spec.
No.
f' c
(MPa)
fy
(MPa)
ft
(MPa)
0
K
(~)
Pmax
(KN)
Vu
(MPa)
Vu
Vy
Failure
Cycle
Yielding
Location
II
NED
;0;III
~
~
III
I-A
I-B
II
III
1-1
37
343
2.34
4.33
3.77
-103.76
0.59
1.23
-6oy/1
1d
4
37.43
1-2
35
341
2.10
3.19
6.70
- 73.43
0.64
1.12
-50y/l
LSd
3
22.37
1-3
36
343
2.28
3.17
8.56
68.29
0.72
1.18
+4oy/1
1d
3
20.64
1-4
40
341
2.58
2.4
8.40
88.64
0.93
1.06
+4oy/1
2d
2
7.57
1-5
42
341
2.40
4.54
6.90
- 52.52
0.55
1.20
-6oy/2
2d
5
69.72
1-6
~3
342
2.04
2.28
8.50
75.34
0.80
1.07
+4oy/l
2d
2
8.28
1-7
38
342
2.16
5.14
2.66
- 79.15
0.45
1.18
-8oy/2
7 114.89
1-8
38
343
2.52
5.24
2.77
- 92.15
0.53
1. 23
-90y/3
8 151.11
1-9
41
343
2.52
2.82
4.68
145.55
0.83
1.04
+4oy/1
1d
2
7.4
1-10
41
343
2.64
4.88
4.21
- 78.83
0.57
1.16
-8oy/1
ld
6
97.39
2-1
34
343
2.00
3.76
3.74
- 99.5
0.59
1.23
-4oy/2
1d
3
18.28
2-2
34
343
2.00
3.76
3.80
-107.5
0.61
1. 27
-50y/2
1d
4
39.42
2-3
35
341
2.04
3.86
3.33
-101.5
0.58
1.21
-6oy/1
1d
4
39.52
2-5
40
350
2.23
3.06
6.54
- 74.0
0.78
1.26
-6oy/2
2d
5
59.8
3-1
36
342
2.04
3.85
3.55
+122.12
0.70
1.13
+6oy/2
1d
5
46.88
3-3
41
342
2.52
3.54
8.14
- 73.62
0.77
1.13
-50y/2
2d
4
32.48
CD
M'
III
~
N
o
21.
Typical Bridge
Pier
Foundation
Anchorage
System
AppHed
~
It
, -
I.
Axial Load
I
700
~
I
I
Al
C-TOP Reinforcement
1150
Applied
Deflection
1I1:~Il-~UI-!.1~=:±====~i;t~
IU
: I
DI
11- b- 500 •.!
3~ ~f· • • ~
r.
~.;,~5~
1 •••
:gT
Sec. A-A
100
Fig. 1. Relationship Between a Typical Specimen and Bridge PierS.
Fig. 2. Test Set-Up with the Presence of Axial Load.
"'0
22.
z
o
-
t-
68y
(,)
48 y -
UJ
....J
u.
28y
o
0
I
-6a y -
~AAA~
tZ -2ay Y~l~VV
123
oQ.. -48Y UJ
o
g
....J
I
o
3
1
6
1
9
I
I
12
15
CYCLE NUMBER
Fig. 3. Load Pattern
Fig. 4. Instrumentation for Average Steel Strain.
10.0
9.0
MEAN-I.OO
STD. -0.09
~
8.0
-
C.0.V.-9%
e
SERIES I
I!J SERIES II
~ 7.0
tU
~ 6.0
>.
100
SPE~N
Ij
1-4
'83.11KNI
II, '8.4 ("'''''
JCIII.!I-6,1983
~ P,+~'7
t-
a
<I
o
0.8-0.13K
I
::l 5.0
...I
I
I
tU
:::>
40
-40
-41y
I L _ -I
r
I
o 4.0
I
41,
DEFLECTION
(mm)
.
3.0
~I
,
iii~
I
:f
I
~
,
0
:f
~
~
)(
1&1
-J
~
J:\Jt\lLl
2.0
1.0
N
2.02.3
3.0
4.0
4.75
5.3
6.0
CHARACTERISTIC FACTOR (K)
Fig. 5. Typical Load-Deflection Hysteresis.
Fig. 6. Relationship Between Ductility and
the Characteristic Factor, K.
N
W
24.
Fig. 7.
Final Crack Pattern for Specimen 1-7, 90y/3.
Fig. 8.
Final Crack Pattern for Specimen 1-1, 6 Oy/l.
25.
Fig. 9. Final Crack Pattern for Specimen 1-5, 7 Oy/1.
Fig. 10. Final Crack Pattern for Specimen 1-4, 4 Oy/1.
140
120
.
~
~
x
w
8 r
100
80~
K
lw : 0.41- 0.07K
z
~
GOr
MEAN -1.01
STD. :0.09
C. O. V.=B.9 %
0:::
0
3:
-
7'
0:::
0
I--
0 8
6 ~ 1'",.8'(1_1ve • •
5 ~=0.3%
-
:i..
0
(,)
(Arakawa, et. 01.)
Lt
>- 4
I--
40
..J
3
I-(,)
::::>
20
0
UM Specimens
Arakawa,et. 01.
2
~ p.=1.72 Iw
1/
ave
-0.72
~ =0
0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
CHARACTERISTIC FACTOR (K)
Fig. 11. Relationship Between Work Index
and the Characteristic Factor, K.
0
I
2
3
5
4
AVERAGE WORK INDEX
CI w
ave
6
)
Fig. 12. Relationship Between Ductility and
Average Work Index, Iw ave '
N
'"
>=-J-V)
V)
0.40
UJ
ex:
a SERIES I
t;
~
160
6
140r
~
a.:
120
0
(f)
(f)
a
><.!)
NED =1.8
(fL)2.19
N
C.0.V.-2.~
c:t
~
0.2~~
o
~ 0.25
80
-I
~
p----r
0.~07 J
ex:
40
~MOOE(2)
0.224
~
60
~ _.QJ.L
ft
Ko.74
~MOO£(3)
X
100
%
e
~ 0.30
a
w
STD. -0.02
:I
MEAN =1.01
STD. =0.09
C.O. V. =9.3 %
0:::
w
z
w
0.35
~
fJ')
w
z
z
t:J SERIES 11
MEAN-0.99
0.20
;1
MODE (I)
=~ ~ ~-=---
a ,.,_.
----~
..J
~
:E
0:::
FLEXURAL
20
0
Z
0
O. 15
I
2
:;
4
5
6
7
8
DUCTILITY FACTOR {fL}
Fig. 13. Relationship Between Normalized
Energy Dissipation and Ductility.
9
IL--_....I-_--'-_........L_ _.L.-_.....L-_---'-_--JL...-_""--_--'
2.0
3.0
4.0
5.0
6.0
CHARACTERISTIC FACTOR K
Fig. 14. Relationship Between Normalized Shear
Resistance and the Characteristic Factor, K.
N
"'../
--
..--
"-
0.40
r\0
0.24
::J
0.22
>
.........
Cf)
Cf)
W
CT
wQ1
0.35
....z
~
Cf)
u
ii:
l&.
0.16
0
0.30
()
Vu
0.6
(!)
ft
(Iw)O.23
::E
-:
~
0. 14
l
MEAN-1.01
a
STD.-O.Og
c.o.v.-g.l%
Z
0::
0.12
CS
::>
(J)
MEAN =1.01
STD. =0.06
C.O.V.=5.6%
0.25
<t:
~
...J
0.18
W
I
0
W
N
0.20
w
Cf)
-X~
a
.....
a:::
a:::
<t:
w
a
~
::>
0
0.10
()
(J)
:>
0.08
IZ
W
..J
0
~
5
0.20
0
w
<!
~
a:::
0.06
0.04
0.02
0
Z
0.00
0
20
40
60
80
100
120
140
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
CHARACTERISTIC FACTOR (K)
WORK INDEX (IW)
Fig. 15. Relationship Between Normalized Shear Resistance
and Work Index, Iw'
Fig. 16. Relationship Between Equivalent
Viscous Damping Coefficient and the
Characteristic Factor, K.
N
00
-
CT
~
0.25
eeq:0.22-
Z
~
0.20
MEAN :0.99
STD. :0.11
C.O.V.o:ll%
t-
!:!:!
~;~y
0.20
@
o
0
0.15
<:>
a::
:?!
«
./
--
.... ..................
---- --
4>-0.17 (: )0.18
~
/
()
en
//~e
o~
-&-1
0.05
I
(GULKAN, ET AL.)
I
~
3
0.05
----- DYNAMIC
I
...J
C.O.V-12.9%
0.10
- - STATIC
I
LLJ
STD. -0.13
IX)
eq =(I+IO (1-1/./8'1"8») 150
1
1
§
(~)o.a5
MEAN -0.99
...
'"
0.10
0
>
tz
.....
./
./
0
en
0.15
<:>
()
z
<:>
<:>
L.L.
L.L.
LLJ
C>
<:>
<:>
c:>
I
~
~
0
LLJ
o
I
2
3
4
5
6
7
8
DISPLACEMENT DUCTILITY RATIO
9
(S/S y )
Fig. 17. Variations of Equivalent Viscous Damping
Coefficient with Displacement Ductility
Ratio
c/cy.
10
o
2
3
4
5
9
678
DISPLACEMENT DUCTILITY RATIO
(8/8 y )
Fig. 18. Relationship Between Stiffness Ratio,
Displacement Ductility Ratio, o/Oy'
~
, and
N
\0