1
Performance Analysis of Energy Dissipators and Isolators Placed in
Bridges to Prevent Structural Damage in Columns
Alfred Beziat1, Alejandro Mora Muñoz 2, J Geoffrey Chase3, Gregory A MacRae4, Geoffrey
W. Rodgers5, Charles Clifton6
ABSTRACT
Special energy dissipation and isolation devices can be used to avoid or minimize structural damage in
the built infrastructure. This paper analyses the impact of these devices on bridges using a spectral analysis and
standard configurations to assess their impact on peak column displacement (damage), total base shear
(foundation demand) and residual displacement (repair). A suite of 20 probabilistically scaled ground motion
records was used to ensure results compatible with performance based design approaches. The devices
considered are the High Force-to-Volume (HF2V) dissipator, Symmetric Friction Connection (SFC),
Asymmetric Friction Connection (AFC) and Linear-Elastic Isolators (LEI). The columns are assumed to remain
elastic and the column displacements and residual displacements are compared.
Energy dissipating devices yielded the greatest reduction in peak displacement when placed between
the column and the deck for periods up to about 2.5s. Above 2.5s, dissipating devices connecting ground-to-deck
provided the optimum configuration. Residual displacements when energy dissipators are placed between the
column and the deck were larger than those of the ground-to-deck connection case for periods below ~3.7s.
Above this period, frictional dissipators in the column to deck case were more effective than in the ground to
deck case. However, HF2V devices connecting ground to the deck remains the best alternative with no residual
displacements. Using the performance curves developed it is possible to select the best device and configuration,
for a reference rigid connection system of a given period, taking into account performance (dmanage),
foundation demand and residual displacement (repair).
*******************************************************************************************************************************************
1 Graduate
Assistant Researcher, Department of Mechanical Engineering, University of Besancon, France
Candidate, Civil Engineering, University of Canterbury, Christchurch, New Zealand
3 Professor, Mechanical Engineering, University of Canterbury, Christchurch, New Zealand
4 Associate Professor, Civil Engineering, University of Canterbury, Christchurch, New Zealand
5 Postdoctoral Fellow, Mechanical Engineering, University of Canterbury, Christchurch, New Zealand
6 Associate Professor, Civil Engineering, University of Auckland, Auckland, New Zealand
2 Master
Acknowledgments: The authors are grateful to the Foundation for Research in Science and Technology for funding this work
through the National Hazard Platform as part of the Low Damage Bridges project. All opinions expressed are those of the
authors.
2
1.0 INTRODUCTION
Major seismic events have significant and well known impact on the built infrastructure. In
the majority of seismic design, the primary focus is placed on buildings and life safety, using
ductility of structural elements to dissipate seismic energy. However, after an event, the
integrity and usefulness of lifelines, particularly bridges of all types, is critical to the speed of
recovery and reducing further loss of life. Energy dissipating devices that sustain no damage
or can be replaced after a major event, are useful means to enable seismically sustainable
structures [Chanchi et al. 2012]. There are many types of devices and choosing the best device
and configuration for any structure is not straightforward, as there is very limited guidance.
Four types of device were considered in this research. They are the high force to volume
(HF2V) device, the Symmetric Friction Connection (SFC), the Asymmetric Friction
Connection (AFC), and the Linear Elastic Isolator (LEI). HF2V devices are extrusion-based,
highly repeatable dissipators with weak velocity dependence [Rogers et al. 2007, 2008a,
Chanchi et al. 2012c]. Spectral analyses and design guidance have been published [Rogers et
al. 2008a] along with several damage avoidance and moment connection studies [Rogers et al.
2007, 2008b; Mander et al. 2009, Bacht et al, 2011, Desombre et al. 2011]. SFC and AFC
systems are frictional energy dissipators developed for moment connections and frames
[Danner and Clifton, 1995, MacRae et al. 2010, Chanchi et al, 2012]. LEIs are the most
common protective element, with guidance for their use in buildings in many codes [E.g.
BSSC 2003, IBC 2003].
This research analyses bridge models, consisting of columns and deck, with a suite of ground
motions to assess the impact of these devices on seismic performance. Device configurations
between the column and deck (column-to-deck) or between the ground and deck (ground-to-
3
deck) are considered. Statistics on the potential reductions in bridge response for the range of
devices and configurations are obtained and guidance on design tradeoffs for device and
configuration in a format suitable for performance based design codes is provided.
4
2.0 METHODS
2.1 Device Models:
2.1.1 Linear Elastic Isolators (LEI): LEIs were used only in the column-to-deck analysis,
with constant stiffness values of 10%, 50% and 100% of the column stiffness to represent a
range of isolator types and designs. The critical damping ratio, ξ, is 10% to approximate
isolators with nonlinear hysteretic energy dissipation [Chopra, 2005] or significant velocity
dependent energy dissipation [Cousins and Porritt, 2003]. Specific non-linear isolators, such
as lead-rubber laminated bearings were not considered to limit scope, and, a simplified
effective isolator stiffness Keff is used as an effective estimate instead [Chopra, 2005].
2.1.2 High Force-to-Volume Device (HF2V): HF2V devices are extrusion-based energy
dissipators, as illustrated in Figure 1 [Rodgers et al., 2007]. These devices are highly
repeatable and relatively velocity insensitive with force defined [Rodgers et al, 2007, 2008a]
in Equation 1 where F(t) is the damper force, Cα a constant dependent on device architecture
(usually between 5% and 10% of the mass of the deck [Rodgers et al 2008a]), v(t) the velocity
of the shaft and α the velocity component, which can be taken as α = 0.12 [Rodgers et al.
2008a] and the value of constant Cα in Equation (1) is calibrated to give the prescribed force
level, corresponding to 10% of deck weight in this research, at a reference velocity of 1m/s.
F (t )  C * v(t )
(1)
5
200
150
Force (kN)
100
50
0
-50
-100
0.0025 Hz
0.02 Hz
-150
-200
-8
-6
-4
-2
0
2
4
6
8
Device Displacement (mm)
a) Typical device cross-section (mm)
b) Device behaviour for two cyclic tests
Figure 1: HF2V device details and hysteresis loops
2.1.3 Asymmetric Friction Connection (AFC): The AFC is a special connection that dissipates
energy by sliding friction. The basic geometry is shown in Figure 2, with bolts tensioned to
Nproof load [MacRae et al. 2010] and shims between plates. Brass, bronze, cast iron and
aluminium are common choices of shim material compatible with low and medium carbon
steels [MacRae et al. 2010]. The energy dissipated is a function of displacement multiplied by
the friction induced by the bolt tension. For reference, the friction coefficient between plates
and shims is approximately µ ≈ 0.29 for brass against steel, where MacRae et al [2010] define
a procedure for obtaining a desired force for a specific connection as a function of bolt
diameter, bolt thickness and materials. Here, 10% of deck weight was used for fair
comparison with the HF2V approach.
The shape of the modelled force-displacement loop is shown in Figure 2. First, slip occurs on
the lower surface in Figure 2a (at d1) and then later on both surfaces as the bolts pull the cap
plate (after d2). The slope of the spine curve is rsp*ko = 0.007*ko [Clifton, 2005]. The slope
rsp was assumed independent of previous maximum displacement. The spine curve slope,
6
rpllv*ko after first and second slip is the same (i.e. rpllv = rsp). The unloading slope and
elastic initial slope are the same being ko.
a) Schematic representation
b) Hysteresis loop representation
Figure 2: Asymmetric Friction Connection (AFC) and hysteretic curve
In this research, the initial displacements d1 and d2 were set to 2mm and 9mm, respectively.
These values are appropriate as a general reference to observe the AFC behaviour compared
to that of other devices. To simplify the analysis, it was assumed that the loop shape did not
change with different cycles of loading. The characteristic stable sliding force Fs =
0.1*Weightdeck. Since no degradation was assumed, the results are limited to shim materials
and bolt tensioning that can guarantee this condition.
2.1.4 Symmetric Friction Connection (SFC): The SFC also uses friction to dissipate energy.
However, the three plate configuration in Figure 3 provides system symmetry and
consequently an almost rectangular hysteresis loop [Pall and Marsh, 1980; Grigorian et al.
1993]. SFC behaviour is characterised by a maximum force Fs and an elastic stiffness ko. Fs
depends on the bolt tension and shim material, while ko depends on plate area, elastic modulus
7
and connection length. The yield displacement, Δy, is taken as 4mm and Fs is 10% of the
weight deck to match those of the AFC connection to compare results for the same elastic
stiffness, defined as ko = Fs/Δy. No degradation was assumed in the loop as with the AFC.
a) Connection basic geometry
b) Elastoplastic Hysteretic Idealization
Figure 3: Symmetric Friction Connection (SFC)
2.2 Bridge Models:
The main goal of the devices is to avoid column damage by keeping the columns elastic.
Hence, columns were modelled as being linear-elastic in all cases. The two configurations
considered when implementing these devices were: 1) column-to-deck (ctd); and 2) groundto-deck (gtd). The first can be implemented in-situ, while the second entails a significant
architectural change for some typical bridge structures.
The column stiffness k1 specified in the model was calculated based on the desired rigid
system period. Its damping c1 comes from a recommended critical damping of ξ = 5% for
bridge piers on fixed spread footings with ductility µ = 1 [Priestley and Calvi, 1996]. The
mass of the deck m2 = 100,000kg and column m1 = 10,000kg are fixed parameters so that
different periods are obtained by changing only column stiffness.
8
All results are compared to that of a reference bridge with a standard fixed column-to-deck
connection. A spectral analysis approach is taken considering reference periods for bridge
with the rigid column-to-deck connection of: 0.2, 0.3, 0.5, 0.7, 1, 1.5, 2, 3, 4 and 5 seconds.
The appropriate values of stiffness k1 and damping c1 were computed for each case.
2.2.1 Column-to-Deck Models: The column to deck connection model used dissipators and
isolators between the top of the column and the deck as shown in Figure 4. Only lateral
displacements are considered, where x1 represents column displacement and x2 deck
displacement. In the rigid connection case x1 = x2.
Specific details include:
 Linear Elastic Isolator (LEI): The LEI system is linear, where the constant stiffness
k2 is 10, 50 or 100% of column stiffness (k1), and c2 relates to ξ=10%.
 High Force-to-Volume Device (HF2V): The device response is considered as an
external force between x1 and x2 based on their relative motion and Equation 1.
 Asymmetric Friction Connection (AFC): The stiffness matrix is not constant and the
parameter kt(t) represents the tangent stiffness of the AFC, which depends on relative
displacement dx(t) = x1(t)-x2(t) and relative velocity dv(t) = v1(t)-v2(t) between deck
and column. This parameter is obtained from the AFC hysteresis loop at every time
step n+1 based on values dx and dv at time step n. As seen in Figure 2, for a given
relative displacement and velocity, the kt(t) can be either ko, rpllv*ko or rsp*ko.
Modified Newton–Raphson iteration was incorporated into the numerical integration
process [Chopra, 1995].
 Symmetric Friction Connection (SFC): The basic characteristics of the SFC model
are the same as those of AFC. The main difference is that the hysteresis loop is
rectangular, resulting in only two options for tangent stiffness (k(t)=ko or k(t)=0).
9
F (t )  C * v(t )
AFC
SFC
Figure 4: Basic parameters for column-to-deck (ctd) connection case models
2.2.2 Ground-to-Deck Models: The system configuration with devices connecting ground to
deck implies a single-degree-of-freedom system (horizontal deck displacement x1(t)) as the
column-to-deck connection is considered rigid. The models are shown in Figure 5, and the
devices are treated as they were for the column to deck configuration except for the change in
their location.
10
AFC
SFC
Figure 5: Basic parameters for ground-to-deck (gtd) connection case models
2.3 Analyses:
2.3.1 Earthquake Records: The suite of medium intensity ground motion records used in this
paper consists of 20 records with a medium source distance of 16.9km and medium moment
magnitude of 6.7. They are the 20 SAC (SEAOC-ATC-CUREE) earthquake records for Los
Angeles, with a probability of excedance of 10% in 50 years (Somerville et al. 1997). The
time step is dt = 0.02s and the records were padded with zeros for a consistent duration of
100s to allow computation of residual displacements.
2.3.2 Analysis by Period: After the numerical integration of each record the maximum column
displacement (SD1) and the maximum deck displacement (SD2) are obtained. The residual
displacement (RSD) is also calculated. These values are recorded for each record, and for
each period.
The maximum column displacement reduction factor is calculated for each period as the
median of the 20 ratios SDj device/ SDj ref (j=1,2…,20) obtained from each record. Here SDj
11
ref is the reference, which is the rigid column-to-deck connection. To show the dispersion of
the reduction factors across the suite, the 5%, 25%, 50% (median), 75% and 95% percentile
values are reported for each period (and each case). The same procedure was conducted for
deck residual displacements except that these are instead normalized to SD2.
Finally, for each analysis, the base shear force normalized to total weight is calculated. It is
obtained from the median peak column top displacement multiplied by the column stiffness.
This value assesses the impact of the devices and configurations on the column foundation.
12
3.0 RESULTS AND DISCUSSION
3.1 Column-to-Deck (ctd) Connections:
3.1.1 SD1 Reduction Factor & Dispersion: For devices connecting the column to the deck, the
reduction factors for change in column displacement, SD1, and column base shear
(normalized to total weight) are shown in Figure 6. The reference period, To, on the horizontal
axis corresponds to the system with a rigid link between the column and the deck. It is clear
that for To below approximately 1.1s the best performance among the devices is obtained
using HF2V devices. Above 1.1s the most flexible isolator (LEI), with 10% stiffness is the
best solution. The performance of AFC and SFC are almost identical and only slightly less
effective than the HF2V across all periods.
For stiff columns and low periods, the period shift produced by the isolators is not big enough
to reduce the response as much as the frictional dissipators and HF2V devices, which
dissipate more energy. For flexible columns and higher periods, the spectral acceleration of
the deck is not able to trigger enough motion in the devices. As seen in Figure 6, for To=5s
neither the AFC nor SFC are dissipating energy (RF=1). The HF2V device is better (RF≈0.8),
but not near the LEI results. Hence, higher periods should prefer isolator solutions and lower
periods energy dissipating devices.
In terms of dispersion, plots with 5%, 25%, 50%, 75% and 95% percentiles are shown in
Figures 7 for HF2V devices and the 50% column stiffness LEI. Table 1 summarizes the
response of all devices for 3 specific periods: 1s, 2s and 3s. The HF2V device always has a
minimum ≈10-20% (absolute) less dispersion than the AFC and SFC, defining dispersion as
the difference between 5th and 95th percentiles. Figures 7a and 7b show different curves for
different approaches (isolation versus energy dissipation), and that the LEI has more constant
dispersion, but that it is also (Figure 7c) always greater across the suite than the HF2V device.
13
1.2
Reduction Factor
1
0.8
0.6
0.4
0.2
0
0.5
1
1.5
1.5
22
2.5
2.5
33
3.5
3.5
44
4.5
4.5
55
Rigid
(s)
Period (s)
ConnectionPeriod
Column-to-Deck Connection
Rigid Column-to-Deck
Base Shear / Weight
Base
1.4
1.2
Isolator
10%
Isolator10%
Isolator
50%
Isolator50%
Isolator
100%
Isolator100%
AFC
AFC
HF2VD
HF2VD
SFC
SFC
Rigid
Connection
RigidConnection
1
0.8
0.6
0.4
0.2
0
0.5
1
1.5
1.5
22
2.5
2.5
33
3.5
3.5
44
4.5
4.5
55
Rigid
(s)
Period (s)
ConnectionPeriod
Column-to-Deck Connection
Rigid Column-to-Deck
Figure 6: Median results for devices connecting column to deck. Top: Column displacement
SD1 reduction factor. Bottom: Normalized column base shear.
Table 1: Results for devices connecting column to deck (ctd) at periods of 1s, 2s and 3s
Period: 1s
Where:
σ
σ
SFC
0.5865
0.8447
0.5136 0.3076 0.5454
0.6502
0.5163 0.2238 0.4861
0.6913 0.4192 0.2244
HF2V
0.3521
0.8217
0.4688 0.2883 0.4460
0.7553
0.4010 0.2644 0.2970
0.7030 0.3178 0.2459
95-5 Pctil
0.0633
0.0700
0.0542
0.1514
0.2142
0.4673
0.4301
0.3584
0.5024
0.3608
= Difference between 95% and 5% percentil
= Median
0.4796
0.4692
0.3937
0.5955
0.3456
0.1544
0.1580
0.1322
0.2740
0.2083
0.5876
0.5848
0.4936
0.4058
0.1953
= Lognormal mean
σ
= Standard deviation
95-5 Pctil
0.5077
0.6574
0.4359
0.6436
0.5266
σ
95-5 Pctil
0.1983
0.1978
0.1551
0.5128
0.7227
0.2344
0.2452
0.1993
0.5143
0.4153
95-5 Pctil
0.5073
0.5376
0.4594
0.8541
0.6477
Period: 3s
0.2198
0.2265
0.1827
0.4752
0.4366
AFC
Reduction
SFC
Factor of
HF2V
Column
Displacement Isolator 50%
AFC
Normalized
Residual
Displacement
Period: 2s
0.6203
0.6088
0.4983
0.4003
0.2578
0.1597
0.1973
0.1461
0.1971
0.1962
14
Column Displacement with HF2VD for 5,25,50,75 and 95 Percentiles
1
Reduction
Reduction
Factor
Factor
Column Displacement with HF2VD for 5,25,50,75 and 95 Percentiles
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0.5
0.5
1
1
1.5
1.5
2
2.5
3
3.5
Rigid Column-to-Deck Connection Period (s)
2
2.5
3
3.5
4
4.5
5
4
4.5
5
Rigid Column-to-Deck
Connection
Period
Column Displacement
with Isolator 50%
for 5,25,50,75
and 95(s)
Percentiles
2
Column Displacement with Isolator 50% for 5,25,50,75 and 95 Percentiles
5%
25%
5%
50%
25%
75%
50%
95%
75%
95%
Reduction
Reduction
Factor
Factor
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5
0.5
1
1
1.5
1.5
2
2.5
3
3.5
Rigid Column-to-Deck Connection Period (s)
2
2.5
3
3.5
4
4.5
5
4
4.5
5
Rigid Column-to-Deck Connection Period (s)
Figure 7: Reduction factors for devices connecting column to deck. Top: Percentiles for
HF2V device. Middle: Percentiles for Isolator-50%. Bottom: Comparison of HF2V and LEI50% dispersion.
15
3.1.2 Residual Displacement & Dispersion: Residual displacements normalized to maximum
deck displacements are shown in Figure 8. When the column is stiff (below To≈1.2s) the
smallest values are obtained using HF2V. Near To=1.5s all devices have similar response, and
for longer periods the frictional dissipators have the smallest values. The last point is
explained by the fact that deck acceleration is not strong enough to generate significant
relative displacement in the frictional dissipators, and their behaviour is thus mainly elastic.
In this study, no additional devices providing restoring force in the column-to-deck
connection were considered. Without restoring force, there will always be some residual
displacement between column and deck and it is important to design the column-to-deck
connection considering the possibility of these residual displacements. Additional analyses
not shown here indicate that the difference between SFC and AFC in Figure 8 tends to
disappear if the slope of spine curve in the AFC hysteresis loop of Figure 2 diminishes.
Residual Displacement Normalized to Deck Peak Displacement
Residual Displacement / Peak Deck Displacement
0.8
0.7
0.6
0.5
AFC
HF2VD
0.4
SFC
0.3
0.2
0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rigid Column-to-Deck Connection Period (s)
Figure 8: Median of the residual displacement normalized to maximum deck displacement
for AFC spine curve with slope 0.007*ko .Devices connecting column to deck.
16
Table 1 also presents dispersion for the same 3 representative periods. The results for HF2V
and AFC show that dispersion tends to decrease for larger periods. For the SFC the dispersion
is approximately constant, with a minimum value of 0.65 at To = 2s.
3.2 Ground-to-Deck (gtd) Connection:
3.2.1 SD1 Reduction Factor & Dispersion: Figure 9 shows the reduction factors when devices
connect the ground to the deck. HF2V, SFC and AFC performance is almost the same. These
values are lower than for the column to deck case (Figure 6) for longer period structures, but
are larger for short period structures. Figure 10 shows dispersion results with the same 3
specific periods in Table 2. Dispersion for all three devices is similar, except for the AFC,
which is approximately 20% larger above To ≈ 3s.
Column Displacement (SD1) Performance. Device Connecting Ground to Deck
Column Displacement (SD1) Performance. Device Connecting Ground to Deck
1
Reduction Factor
Reduction Factor
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
SFC
SFC
AFC
AFC
HF2VD
HF2VD
0.5
0.5
Column Base Shear / Weight
Column Base Shear / Weight
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
1
1.5
1.5
2
2.5
3
3.5
2
2.5 Connection
3
3.5(s)
Rigid Column-to-Deck
Period
Rigid Column-to-Deck Connection Period (s)
1
4
4
4.5
4.5
5
5
Normalized Column Base Shear v/s Period. Device Connecting Ground to Deck
Normalized Column Base Shear v/s Period. Device Connecting Ground to Deck
SFC
SFC
AFC
AFC
HF2VD
HF2VD
No Device
No Device
0.5
0.5
1
1
1.5
1.5
2
2.5
3
3.5
2
2.5 Connection
3
3.5(s)
Rigid Column-to-Deck
Period
Rigid Column-to-Deck Connection Period (s)
4
4
4.5
4.5
5
5
Figure 9: Devices connecting ground to deck. (a) Column displacement SD1 reduction factor.
(b) Normalized column base shear.
1.2
1
0.8
0.6
0.4
0.2
0
Reduction
Reduction
Factor
ReductionFactor
Factor
1.2
1
0.8
0.6
0.4
0.2
0
5%
0.5
1.2
1.2
1.2
1
11
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
00
Reduction
Reduction
Factor
ReductionFactor
Factor
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1.2
1.2
1
11
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.20
00
Reduction
Factor
Reduction
Factor
Reduction
Factor
Reduction Factor
Reduction Factor
Reduction Factor
17
1.2
1.2
1.2
1
11
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
00
0.5
0.5
25%
50%
75% 5%
5%
95% 25%
25%
50%
1
1.5
2
2.5
3
3.5
50%
4.575%
4
0.5
0.5
0.5
1
1
11
1.5
1.5
1.5
2
2
2
2.5
2.5
3
3
3.5
3.5
4
4
Rigid Column-to-Deck Connection Period (s)
Rigid Column-to-Deck Connection Period (s)
2.5
3
5
75%
95%
95%
Rigid Column-to-Deck Connection Period (s)
3.5
4
4.5
4.5
4.5
5
5
5
Rigid Column-to-Deck Connection Period (s)
0.5
0.5
0.5
1
11
1.5
1.5
1.5
2
2
2.5
2.5
3
3
3.5
3.5
4
4
4
2
2.5
3
Rigid Column-to-Deck
Connection
Period3.5
(s)
Rigid Column-to-Deck Connection Period (s)
4.5
4.5
4.5
5
55
5%
25%
50%
75%
95%
1
0.5
0.5
0.5
1.5
1
11
2
2.5
3
3.5
4
1.5
2
2.5
3 (s)
Rigid Column-to-Deck
Connection
Period
3.5
1.5
2.5
3
3.5
1.5
22
2.5
3
3.5
Rigid
Column-to-Deck
Connection
Period
(s)
Rigid Column-to-Deck
Column-to-Deck Connection
Connection Period
Period (s)
(s)
Rigid
4.5
4
4
4
5
4.5
4.5
4.5
5
55
Figure 10: Devices connecting ground to deck percentiles. Top: Column displacement (SD1)
performance with AFC. Middle: Column displacement (SD1) performance with SFC. Bottom:
Column displacement (SD1) performance with HF2V device.
Table 2: Results for devices connecting ground to deck (gtd) for periods of 1s, 2s, 3s
Period: 1s
Reduction Factor
of Column
Displacement
Normalized
Residual
Displacement
Where:
AFC
SFC
HF2V
AFC
SFC
HF2V
95-5 Pctil
0.5717
0.6054
0.6002
0.0044
0.0057
0.0004
95-5 Pctil
0.4083
0.3786
0.3950
0.0214
0.0395
0.0010
Period: 2s
σ
0.5836
0.5953
0.6104
0.0062
0.0098
0.0005
0.1335
0.1287
0.1309
0.0063
0.0119
0.0003
0.4798
0.5338
0.5215
0.0058
0.0200
0.0003
95-5 Pctil
0.5289
0.4892
0.4916
0.0165
0.0473
0.0004
= Difference between 95% and 5% percentil
= Median
Period: 3s
σ
0.5081
0.5390
0.5286
0.0071
0.0194
0.0003
0.1608
0.1422
0.1307
0.0057
0.0152
0.0001
0.3848
0.3801
0.3791
0.0181
0.0277
0.0003
= Lognormal mean
σ
= Standard deviation
95-5 Pctil
0.5906
0.5181
0.4986
0.0777
0.2230
0.0003
σ
0.3995
0.4035
0.4018
0.0247
0.0596
0.0003
0.1905
0.1748
0.1626
0.0231
0.0724
0.0001
18
3.2.2 Residual Displacement & Dispersion: Figure 11 shows that for ground-to-deck
configurations that the column acts as a self-centring element. Hence, there is little residual
displacement for HF2V devices because force is proportional to velocity and thus, the
displacement of HF2V slowly moves back to zero. The residual displacement is small for
frictional devices, which is most likely with stiff columns and periods, To, less than 3s, above
which residual displacement can be significant with these devices.
AFC residual displacements are lower than for the SFC because of the post-elastic stiffness
and the kink in the hysteresis loop of Figure 2. These loop characteristics facilitate
displacement in the opposite direction resulting in smaller residual displacement [MacRae,
1994]. To illustrate the influence of AFC and SFC hysteresis loop shape on residual
displacement, Figures 12 and 13 show the loop for one record and the same bridge. The
impact of different devices on residual displacement is clear.
Residual Displacement / Peak Deck Displacement
Residual Displacement Normalized to Peak Deck Displacement. Device Connecting Ground to Deck
0.16
0.14
AFC
HF2VD
SFC
0.12
0.1
0.08
0.06
0.04
0.02
0
0.5
1
1.5
2
2.5
3
3.5
4
Rigid Column-to-Deck Connection Period (s)
4.5
5
Figure 11: Residual displacement normalized to maximum deck displacement. AFC spine
curve with slope 0.007*ko. Devices connecting ground to deck
19
Relative Displacement v/s Time for A-SHJ. Record #10 & Period = 0.7s
0.1
Relative Displacement v/s Time for A-SHJ. Record #10 & Period = 0.7s
0.1
0.05
X2(t) - X1(t)
X2(t) - X1(t)
0.05
0
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
-0.2
-0.2
-0.25
-0.25
-0.3
-0.3
-0.35
-0.35
0
0
5
10
5
15
10
15
20
20
25
Time (s) 25
Time (s)
30
35
30
35
40
40
45
45
Force in Connection / Sliding Force
Force in Connection / Sliding Force
Normalized A-SHJ Force v/s Relative Displacement. Record #10 & Period = 0.7s
1.5
Normalized A-SHJ Force v/s Relative Displacement. Record #10 & Period = 0.7s
1.5
1
1
0.5
0.5
0
0
-0.5
-0.5
-1
-1
-1.5
-0.35
-1.5
-0.35
-0.3
-0.3
-0.25
-0.25
-0.2
-0.2
-0.15
-0.1
-0.05
Relative Displacement
X2(t)
-0.15
-0.1 - X1(t) [m]
-0.05
Relative Displacement V2(t) - V1(t) [m]
0
0.05
0
0.05
0.1
0.1
Figure 12: AFC connecting column to deck. Record #10 (Landers Earthquake) and To=0.7s.
Top: Relative Displacement v/s Time. Bottom: Normalized AFC Force v/s Relative
Displacement.
Relative Displacement v/s Time for S-SHJ. Record #10 & Period = 0.7s
Relative Displacement v/s Time for S-SHJ. Record #10 & Period = 0.7s
0.1
Force in Connection / Sliding Force
Force in Connection / Sliding Force
X2(t) - X1(t)
X2(t) - X1(t)
0.1
0.05
0.05
0
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
-0.2
-0.2
-0.25
-0.25
-0.3
-0.3
-0.35
0
-0.35
0
1.5
1
0.5
0
5
5
10
10
15
15
20
20
25
Time (s)25
Time (s)
30
30
35
35
40
40
45
45
Normalized S-SHJ Force v/s Relative Displacement. Record #10 & Period = 0.7s
Normalized S-SHJ Force v/s Relative Displacement. Record #10 & Period = 0.7s
1.5
1
0.5
0
-0.5-0.5
-1 -1
-1.5-1.5
-0.35
-0.35
-0.3-0.3
-0.25
-0.25
-0.2-0.2
-0.15
-0.15
-0.1-0.1
-0.05
-0.05
0
0
0.050.05
Relative
Displacement
X2(t)
- X1(t)
Relative
Displacement
X2(t)
- X1(t)
[m][m]
Figure 13: SFC connecting column to deck. Record #10 (Landers Earthquake) and To=0.7s.
Top: Relative Displacement v/s Time. Bottom: Normalized SFC Force v/s Relative
Displacement.
0.1 0.1
20
3.3 Overall Comparison of Main Results:
3.3.1 SD1 Reduction Factor: Combining response curves for all devices into a single plot in
Figure 14 yields a performance curve to demonstrate tradeoffs between devices and
configurations. Below To ≈ 2.5s, energy dissipators should be placed between deck and
column, and the best performance (i.e. lowest curve) is obtained by using HF2V devices. AFC
and SFC yield slightly greater response than the HF2V devices. Above To ≈ 2.5s, the
dissipators should connect ground to deck to obtain the lowest reduction factors, and all of
them have similar performance.
LEIs connecting column-to-deck are the best solution only above To≈1.1s, and only by using
a very low, unrealistic stiffness (10% column stiffness), which can produce excessive
displacement for service level loads. The Isolator-100% does not perform as well as energy
dissipators and the Isolator-50% is effective only above To ≈ 2.5s.
0
0.2
0.4
0.6
0.8
1
0.5
1
1.5
2
2.5
3
3.5
Rigid Column-to-Deck Connection Period (s)
Isolator 100% ctd
Isolator 10% ctd
Isolator 50% ctd
AFC ctd
HF2VD ctd
HF2VD gtd
SFC ctd
SFC gtd
AFC gtd
4
4.5
Column Displacement (SD1) Performance. Device Connecting Ground to Deck (gtd) and Column to Deck (ctd)
5
21
Figure 14: SD1 reduction factor for devices connecting: column to deck (ctd) and ground to
deck (gtd)
Reduction Factor
22
3.3.2 Residual Displacement: Figure 15 shows the results for all cases. It is clear that below
To ≈ 3.7s any of the devices connecting the ground to the deck (gtd) have the lowest
normalized residual displacement. Above this period, HF2V devices connecting ground to
deck produce no residual displacement, and the frictional dissipators placed between the
column and the deck (ctd) have also small normalized values (less than 0.1).
It should be noted that the actual residual displacement can be obtained from the normalized
values of Figure 15 and peak deck displacement. For example, the value for the gtd case can
be up to 0.16*peak-deck-displacement and the maximum value for the ctd case is 0.74* peakdeck-displacement, both maximum values are reached when the SFC is used.
The residual displacements are significant for the ctd case and if the devices are not
complemented by restoring forces. Thus, any economic evaluation should consider the cost of
work to place the deck back to the original position. To mitigate this problem, self-centring
Residual Displ. / Peak Deck Displ.
elastic elements (e.g. elastomeric isolators) can be situated between the column and the deck.
0.8
SFC gtd
AFC gtd
HF2V gtd
SFC ctd
AFC ctd
HF2V ctd
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rigid Column-to-Deck Connection Period (s)
Figure 15: Residual displacement normalized to peak deck displacement for devices
connecting ground to deck (gtd) and column to deck (ctd).
23
3.4 Limitations:
3.4.1 Asymmetric Friction Connection (AFC) Robustness: Before using the hysteresis loop of
Figure 2 to model the AFC, a sensitivity analysis was conducted. Three parameters illustrated
in Figure 2b were considered: the length of the elastic displacement d1 (mm), the
characteristic point d2 (mm), and the slope factor rsp*ko. Four cases labelled A, B, C and D in
Table 3 were considered, and the SFC was included as this case coincides with an AFC with
rsp=rpllv=0 and only d1=4mm. The effect on reduction factors and the residual displacement
are shown in Figure 16.
Table 3: Sensitivity analysis of AFC connection system. Parameter values considered to
determine the influence of the hysteresis loop shape.
d1 = 1mm
d1 = 2mm
d2 = 5mm
d2 = 9mm
Slope Factor rsp=rpllv
0
0.007
A
B
C
D
The four reduction factor curves in Figure 16 are similar, showing that both the length of the
step and the slope factor do not have much effect on response. However, they have a strong
impact on residual displacement for 1s-4s periods. In this paper, d1 and d2 were 2mm and 9mm
respectively, and the slope factor was 0.007 per Clifton [2005] representing case D. Hence,
the reduction factor results are robust, but the residual displacement may vary.
24
Figure 16: Effect of AFC parameters on response. Top: Reduction factor. Bottom: Residual
displacement.
3.4.2 Effect of HF2V Shaft Elasticity on Results: The stiffness of the HF2V shaft was
considered rigid. Considering the shaft elastic adds model complexity and degrees of
freedom. Figure 17 compares the effect of the shaft elasticity using a stiffness obtained from:
E=200GPa, shaft length=50cm and three diameters (15mm, 20mm and 30mm), as well as the
rigid case. The reduction factors are effectively unchanged except for small variation at very
low periods. Hence, the HF2V shaft elasticity can be safely neglected.
25
Figure 17: Effect of HF2V shaft elasticity
26
4.0 CONCLUSIONS
Three energy dissipators (HF2V, AFC and SFC) and three linear isolators (with stiffness of
10%, 50% and 100% of column stiffness) were examined for their ability to dissipate seismic
response and mitigate damage in bridge structures, considering two different fundamental
configurations. The spectral analyses presented used nonlinear device models and a suite of
probabilistic scaled ground motions to create a series of design tradeoff curves. The main
outcomes of the research are:
 Placement of energy dissipators between column and deck (ctd) for periods below
To≈2.5s yields the lowest column displacements and damage. Above that period
devices should connect ground to deck (gtd).
 LEIs with 10% column stiffness yield lower column displacements than energy
dissipators above To≈1.1s. However, the deck displacement increases so that a more
precise analysis must be carried out to avoid excessive deformation for service level
loads. Stiffer, more realistic LEIs provide similar or lesser performance than the
energy dissipation devices.
 For periods below To≈3.7s residual displacements are much lower for ground to deck
(gtd) configurations. Above this period, column to deck connections are competitive.
 Median peak and residual displacements response curves covering both configurations
and all devices are created to summarise these tradeoffs and guide design and should
be useful in the determination of the best device and configuration in a particular
situation.
27
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