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T
.
Isaković
U
niversity of Ljubljana
,
Faculty of Civil and Geodetic Engineering
,
Jamova 2,
1000 Ljubljana,
Slovenia
e

mail:
tisak
@ikpir.fgg.uni

lj.si
Chapter
13
Recent advances in the seismic analysis and
design of RC bridges in Slovenia
Tatjana Isaković and Matej Fischinger
Abstract
An overview of the research related to the
seismic analysis and design
of RC bridges,
recently
performed at
UL FGG
is
made. F
our main topics are
addressed:
1)
Pushover based analysis of bridges
;
several recommendations
related to the use of different pushover methods are overviewed and criteria which
def
ine the applicability of single

mode methods are proposed
;
2)
Modelling of RC
bridge columns;
three types of frequently used macro

models are discussed on the
example of typical bridge columns;
3)
Estimation of the shear strength and shear
strengthening of typical RC hollow box bridge columns with substandard
constru
ction details
;
t
hree methods for estimation of
the
shear strength are
compared
;
t
he method, proposed at UCSD was found the most appro
priate
in the
investigated case
; t
he concrete jacket and
CFRP strips
successfully
prevented the
shear failure of the
streng
thened
column;
4)
Seismic isolation of RC bridges using
new semi

active device
–
magnetically controlled elastomer
(MCE)
;
t
he
efficiency
of the smart MCE bearings
in partially isolated bridges
,
subjected to earthquakes
weaker than the design earthquake
,
is
discussed and
demonstrated
.
Keywords:
RC bridges, numerical models, nonlinear analysis, seismic strengthening, shear
strength, seismic isolation, semi

active isolation
13.1
Introduction
Several
topics
related
to
the research
of
the seismic analysis and design of
reinforced concrete (
RC
)
bridges, performed at the University of Ljubljana,
Faculty of Civil Engineering
(UL FGG)
are
overviewed. They
are: 1) Pushover
based analysis of bridges, 2) Modelling of RC bridge columns, 3)
Esti
mation of
the shear strength and shear
strengthening of typical
RC
hollow box
bridge
columns using different types of jacketing, 4) Seismic isolation of RC bridges
using new semi

active device
–
magnetically controlled elastomer.
The inelastic response his
tory analysis has been used for the research purposes
for several decades. However, it is still to
o
complex to be used in the design
practice. To simplify the nonlinear seismic analysis, several nonlinear static, or so

called, pushover methods have been de
veloped. They recently became quite
popular analysis tool.
However, due to the limited understanding of their
limitations, these methods are frequently used indiscriminately. Their
indiscriminate use is particularly typical for bridges. The principles, rul
es and
2
procedures which were originally developed for buildings have often been simply
extrapolated to bridges, neglecting the major differences between these structural
systems and their seismic response.
In
Section 2
basic specifics in the application
of
the pushover methods for the analysis of bridges
are
briefly summarize
d
, and
criteria defining the applicability of the N2 method, which is included into
Eurocode
standards,
are introduced
.
To perform the nonlinear analysis, adequate numerical models are needed.
Some
experiences
obtained
at UL FGG in modelling RC bridge columns are
summarized
in Section 3
.
To establish an appropriate numerical model the adequate data about the
c
apacity of co
lumns are needed.
While the quantities defining the flexural
response are usually well defined, the shear response of columns is much more
difficult to predict. The knowledge related to this problem is still incomplete. This
is e.g. indicated by quite larg
e differences in the results of different methods
proposed for the estimation of the shear strength and stiffness of RC columns.
T
his problem is analyzed on the example of columns of a typical existing viaduct,
which includes several construction deficienc
ies. Several methods for estimation
of the shear strength are compared and evaluated by means of the experimental
results
(see Section 4)
.
There are numerous existing bridges, which were designed before the modern
principles of the seismic engineering were
established. From the nowadays point
of view, they include many substandard construction details which demand
adequate strengthening and retrofit. One of such examples is analyzed in
Section
4
. Different retrofitting techniques, including concrete and
FR
P jacketing are
analyzed on the example of a typical viaduct, built in 1970’ies.
One of the possibilities for the seismic protection of new bridges as well as for
the strengthening of existing structures is the seismic isolation. In the last part of
Chapter
(Section
5
)
a new semi

active seismic isolation device, magnetically
controlled elastomer
(MCE)
is briefly introduced and the possibilities for its use in
bridges are overviewed.
13.2
Simplified nonlinear analysis of bridges
To simplify the inelastic a
nalysis, and to make it
more
convenient for everyday
design, several simplified nonlinear analysis methods have been developed. They
are so called pushover methods. There are several methods of this type available.
The simple
st methods are so called single

mode
pushover
methods. One of the
main assumptions of these methods is that the response of a structure is governed
mostly by one predominant mode. The typical representative o
f this group is the
N2 method [1
], which is included in the Eurocode standard
s
[2], [3]
. The
specifics
in the application of this method
for the analysis of bridges
ar
e
described in
Section 2.1.
It is typical f
or long bridges (with the total length of 500 m and longer)
that
the
response can be considerably influenced by higher modes
of vibrat
ion. In those
cases, the single

mode methods are less accurate, and multi

mode pushover
3
methods can be used instead.
Some of the conclusions related to their applicability
for the analysis of bridges are shortly overviewed in Section 2.2
.
13.2.1
The N2 m
ethod
–
Single

mode
pushover
methods
The N2 method was originally developed for the analysis of buildings. Therefore
it should be modified when it is used for the analysis of bridges, since their
structural system is considerably different than that of bui
ldings (particularly in
their transverse direction). In this Section the appropriate modifications are
proposed and
summarized
. Further details can be found in [
4
]

[
6
].
The proposed modifications of the N2 method for the analysis of bridges are:
1) The
distribution of lateral forces along the superstructure
;
2) The choice of the point where the displacements are monitored to obtain the
force

displacement relationship;
3) Idealization of the force

displacement curve, and calculation of yielding
force and
yielding displacement.
1) The distribution of the “inertial” forces (lateral load) should be assumed
before the nonlinear static analysis is performed. Some of the distributions
appropriate for bridges are summarized in Fig
. 13.
1
. Note that two extreme c
ases
of the constraints above the abutments are addressed. In the Annex H of standard
E
urocode 8
/2
(EC8/2)
two possible distributions are proposed: a) distribution
proportional to the 1
st
mode of the bridge in the elastic range, b) uniform
distribution (se
e Fig
s.
1
3.1
(1)a and
1
3.1
(1)b). The first distribution can be defined
based on a modal analysis with some of the standard programs for elastic modal
analysis.
In the previous research [
5
]

[
6
] it was found that the parabolic distribution
(Fig
.
13.
1
(1)c)
is appropriate for bridges that are pinned at the abutments. This
distribution is simpler to define than that proportional to the first mode.
In many
cases
, the results of the N2 method and the inelastic response history analysis
correspond better
when the
uniform distribution is replaced by the parabolic one
.
Fig.
13.
1
Distributions of the lateral load, appropriate for bridges that are: 1) pinned at the
abutments, 2) with roller supports at the abutments
(1)
(2)
m
1
... m
i
m
n
F
1
F
i
F
n
1
i
n
i
–
1. nihajna oblika
i
= 1
x
L
x
L
i
4
4
2
2
L
X
c) paraboli
č
na
b) enakomerna
a) proporcionalna 1. nihajni obliki
i
i
i
m
F
proportional to the 1st mode
uniform
parabolic
1
st
mode
m
1
... m
i
m
n
F
1
F
i
F
n
1
i
n
i
–
trenutna
1. nihajna oblika
i
= 1
L
b) enakomerna
a) proporcionalna trenutni 1. nihajni obliki
i
i
i
m
F
proportional to the instant 1
st
mode
uniform
instant
1
st
mode
4
Table
13.1
Advantages and limitations of the pres
ented elements
Type of
Element
Advantages
Limitations
Beam

Column
Element with
Lumped
Plasticity
Simple model with small number of
elements (often one per column)
Non

linearity defined based on the
hysteretic rule with clear physical
meaning
Easy to
control
Cannot be used for the analysis of
coupled bi

directional response
Unable to estimate stresses and
strains
Fibre
Element
Able to estimate strains and stresses
Can be used for the analysis of bi

directional response
Relatively complex analysis
Seve
ral iterations are necessary to
establish the appropriate model
Control of results is more complex
MVL
Element
Relatively simple
Non

linearity defined based on the
hysteretic rule with clear physical
meanings
Able to estimate strains and stresses
Can be
used for analysis of bi

directional response
In general, several elements per
column are necessary to obtain
acceptable estimation of the
response
Appropriate number of elements
should be defined iteratively
Fig. 13.13
Typical existing viaduct with
substandard construction details
33.3 34.0 34.0 34.0 34.0 34.0 34.0
34.0 34.0 34.0 34.0 37.7 37.7 37
.7 34.0 37.7 33.3
OL S15 S16 S17 S18 S19 S20 S21
S22 S23 S24 S25 S26 S27 S2
8 S29 S30 OD
591.4
33.3 34.0 34.0 34.0 34.0 34.0 34.0
34.0 34.0 34.0 34.0 37.7 37.7 37
.7 34.0 37.7 33.3
OL S15 S16 S17 S18 S19 S20 S21
S22 S23 S24 S25 S26 S27 S2
8 S29 S30 OD
591.4
m
33.3 34.0 34.0 34.0 34.0 34.0 34.0
34.0 34.0 34.0 34.0 37.7 37.7 37
.7 34.0 37.7 33.3
OL S15 S16 S17 S18 S19 S20 S21
S22 S23 S24 S25 S26 S27 S2
8 S29 S30 OD
591.4
33.3 34.0 34.0 34.0 34.0 34.0 34.0
34.0 34.0 34.0 34.0 37.7 37.7 37
.7 34.0 37.7 33.3
OL S15 S16 S17 S18 S19 S20 S21
S22 S23 S24 S25 S26 S27 S2
8 S29 S30 OD
591.4
m
5
R
eferences
1.
Fajfar P (2000) A nonlinear analysis method for performance

based seismic design.
Earthquake Spectra 16:573

592.
2.
CEN (2004)
Eurocode
8: Design of structures for earthquake resistance. Part 1: General
rules, seismic
action and rules for buildings
.
EN 1998

1
,
Euro Commit for Stand
, Brussels,
December 2004
3.
Kanaan A.E.
,
Powell G.H.
(1973)
A general purpose computer program for dynamic
analysis of planar structures, , Report UBC/EERC

73/6, Univ. of
California, Berkeley
.
4.
McKenna F, Fenves GL (2007) Open system for earthquake engineering simulation, Pacific
Earthquake Engineering Research Center, Berkeley, California,
http://opensees.berkeley.edu
5.
Prakash V., Powell G.H., Filippou F.C.
(1993)
DRAIN

3DX: Base program users guide,
Department of Civil Engineering, Universi
ty of California, Berkeley, USA
.
6.
Vulcano A., Bertero V.V.
,
Caloti V.
(1989)
Ana
lytical model
l
ing of R/C structural walls,
Proceedings of the 9th WCEE, Tokyo

Kyoto, Maruzen, Vol. 6, pp. 41

46.
7.
Fischinger M., Vidic T., Fajfar P.
(1992)
Non

linear seismic analysis of structural walls
using the multiple

vertical

line

element model, Non

l
inear Seismic Analysis and Design of
Reinforced Concrete Buildi
ngs, Elsevier, Bled, Slovenia,
pp.191

202.
Keywords:
Bridges, RC bridges, nonlinear analysis, simplified nonlinear analysis, s
tatic nonlinear analysis,
p
ushover methods,
s
ingle mode pushover
methods,
m
ulti mode pushover methods,
a
pplicability
of pushover methods, N2 method, MPA, IRSA,
RC columns, numerical model, nonlinear
response history analysis, flexural response, macro models, beam

column elements with lumped
plasticity, fiber
element, multiple vertical line element, MVLEM, Takeda hysteretic rules,
seismic strengthening, concrete jacketing, CFRP, CFRP strips, shear strength, shear
strengthening, existing bridges, substandard construction details, experiment, hollow box
columns,
Eurocode 8, EC8/2, EC8/3, EC2, Eurocode 2, UCSD method, shear failure, buckling of
the longitudinal bars, seismic isolation, rubber bearings, elastomeric bearings, semi

active
isolation, magnetically controlled elastomers, MCE, MCE bearings, partial isola
tion, weak
earthquakes
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