Characterization of a Roller Seismic Isolation Bearing with
Supplemental Energy Dissipation for Highway Bridges
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George C. Lee1; Yu-Chen Ou2; Tiecheng Niu3; Jianwei Song4; and Zach Liang5
Abstract: A new roller seismic isolation bearing is developed for use in highway bridges. This new bearing uses rolling of cylindrical
rollers on V-shaped sloping surfaces to achieve seismic isolation. The bearing is characterized by a constant spectral acceleration under
horizontal ground motions and by a self-centering capability, which are two desirable properties for seismic applications. The former
makes resonance less likely to occur between the bearing and horizontal earthquakes, while the latter guarantees that the bridge superstructure can self-center to its original position after earthquakes. To provide supplemental energy dissipation to reduce the seismic
responses, the bearing is designed with a built-in sliding friction mechanism. This paper presents the seismic behavior of the bearing
through analytical and experimental studies. First, the acceleration responses of and forces acting on the bearing under base excitation are
presented. Next, the governing equation of horizontal motion, the base shear-horizontal displacement relationship, and conditions for
self-centering, for the rollers to maintain contact with the bearing plates, and for rolling without sliding are discussed. An experimental
study on a prototype bearing was carried out to verify and calibrate its characteristics and the results are discussed.
DOI: 10.1061/共ASCE兲ST.1943-541X.0000136
CE Database subject headings: Seismic effects; Bridges, highway; Load bearing capacity; Isolation; Energy dissipation; Friction.
Author keywords: Seismic effects; Bridges; Bearings; Isolation; Energy dissipation; Friction.
Introduction
Currently in the United States and Japan, there are two common
types of seismic isolation bearings, elastomeric and sliding. Typical elastomeric bearings include low and high damping rubber
bearings and lead-rubber bearings. These bearings achieve seismic isolation by the low shear stiffness of the elastomers. By
using elastomers with a special compound, high damping rubber
bearings can achieve higher inherent damping than low damping
rubber bearings. In lead-rubber bearings, supplemental energy
dissipation is realized by yielding of the lead core. Typical sliding
bearings are concave sliding bearings 关e.g., the friction pendulum
bearing; Earthquake Protection Systems, Inc. 共EPS, Inc.兲 2008兴
and flat sliding bearings 共e.g., the EradiQuake bearing; R. J. Watson, Inc. 2008兲. In sliding bearings, seismic isolation is achieved
1
Professor, Dept. of Civil, Structural and Environmental Engineering,
Univ. at Buffalo, SUNY, Buffalo, NY. E-mail: gclee@buffalo.edu
2
Assistant Professor, Dept. of Construction Engineering, National Taiwan Univ. of Science and Technology, Taipei 106, Taiwan 共corresponding
author兲. E-mail: yuchenou@mail.ntust.edu.tw
3
Visiting Professor, Dept. of Civil, Structural and Environmental Engineering, Univ. at Buffalo, SUNY, Buffalo, NY. E-mail: tiechengn@
yahoo.com
4
Senior Research Scientist, Dept. of Civil, Structural and Environmental Engineering, Univ. at Buffalo, SUNY, Buffalo, NY. E-mail:
songj@buffalo.edu
5
Research Associate Professor, Dept. of Mechanical and Aerospace
Engineering, Univ. at Buffalo, SUNY, Buffalo, NY. E-mail: zliang@
buffalo.edu
Note. This manuscript was submitted on August 7, 2008; approved on
September 7, 2009; published online on October 24, 2009. Discussion
period open until October 1, 2010; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural
Engineering, Vol. 136, No. 5, May 1, 2010. ©ASCE, ISSN 0733-9445/
2010/5-502–510/$25.00.
by sliding actions. Supplemental energy dissipation is provided
by sliding friction between contact surfaces. Naeim and Kelly
共1999兲, Kunde and Jangid 共2003兲, Buckle et al. 共2006兲, and Constantinou et al. 共2007兲 provided excellent review of previous research and applications of seismic isolation bearings in the United
States, Japan, and other countries.
Here, a new type of bearing called a roller seismic isolation
bearing is developed for use in highway bridges 关U.S. Patent No.
6,971,795 共2005兲兴. The bearing utilizes rolling of cylindrical rollers to achieve seismic isolation and exhibits three distinct characteristics. First, it has a zero postelastic stiffness under a horizontal
earthquake. This means that the spectral acceleration response of
the bearing is independent of the magnitude and frequency content of the horizontal earthquake. Second, it is able to self-center
to its initial position after an earthquake ends. Third, sliding friction mechanisms are integrated into the bearing to provide supplemental energy dissipation to reduce the displacement responses.
Fig. 1 shows a simplified schematic view of the bearing. It consists of two rollers for bidirectional seismic isolation. Each roller
is sandwiched between two bearing plates. The intermediate bearing plate has V-shaped sloping surfaces at the top and underside
of the plate with the directions of the valleys of the two surfaces
perpendicular to each other. The upper and lower bearing plates
have flat surfaces in contact with the rollers. The upper plate is
secured to the bridge superstructure and the lower plate mounted
on the pier cap or abutment. Each bearing has two pairs of friction
plates. Each pair corresponds to one of the principal directions of
the bearing 共rolling direction of individual roller兲. The friction
plates are in contact with the outer surfaces of the side walls. The
side walls are attached to the four sides of the intermediate bearing plate and hence move together with it. Screws A apply normal
forces to the friction interfaces between the friction plates and the
side walls. Screws B prevent relative movements between the
friction and bearing plates. Once the superstructure moves, the
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J. Struct. Eng., 2010, 136(5): 502-510
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Fig. 1. Simplified schematic view of roller seismic isolation bearing
rollers will roll between the bearing plates and sliding friction
forces will be generated at the friction interfaces due to relative
movements between the side walls and the upper and lower bearing plates.
Tsai et al. 共2007兲 carried out a shake table study on an earlier
version of such a bearing, which does not have integrated sliding
friction mechanisms. The bearing showed a bilinear elastic hysteretic behavior with an approximate zero postelastic stiffness. An
equation was proposed to predict the maximum base shear of the
bearing. However, the interaction between the superstructure and
the roller was not considered in the derivation of the equation.
This paper first presents the theoretical background of the proposed roller bearing under base excitation. The acceleration responses of and forces acting on the bearing are derived based on
dynamic equilibrium, in which both the interaction between the
superstructure and the roller and that between the roller and the
base are considered. Next, the governing equation of horizontal
motion, the base shear-horizontal displacement relationship, and
the conditions for self-centering, for the rollers to maintain contact with the bearing plates, and for rolling without sliding are
discussed. Finally, an experimental study on a prototype bearing
is presented to verify and calibrate the characteristics of the bearing.
and 共5兲 the upper plate is attached to a superstructure that is
restrained from rotation. Conditions to maintain the first two assumptions and the applicability of the third assumption are analytically and experimentally investigated in later sections,
respectively.
Fig. 2 shows the free-body diagram of the two plates and one
roller assembly when the roller is on the left-hand side of the
lower bearing plate. Note that the sloping angle is exaggerated in
the figure for ease of presentation. A horizontal acceleration excitation ẍ3 and a vertical acceleration excitation z̈3 are imposed to
the base of the assembly. For the superstructure, the dynamic
equilibrium along the horizontal direction gives
m1共ẍ1 + ẍ3兲 + f 1 + f Ds cos ␪ sgn共ẋ1兲 = 0
共1兲
where m1 = tributary mass carried by the assembly; ẍ1
= horizontal acceleration response of the superstructure relative to
the origin O; f 1 = static friction force between the roller and the
upper bearing plate; f Ds = sliding friction force produced by the
corresponding pair of friction interfaces; ␪ = sloping angle; and
sgn= function equal to 1, 0, and ⫺1 if the variable is greater than,
equal to, and less than zero, respectively.
For the vertical direction, we have
Accelerations and Forces under Base Excitation
Superstructure
Acceleration and force responses of the bearing subjected to base
excitation along the principal directions, i.e., rolling directions of
the rollers, are derived in this section to understand the behavior
of the bearing. Since only one roller is mobilized when the bearing moves along each of the two principal directions, only one
roller and two bearing plates that sandwich the roller are considered in the derivation. A number of assumptions are made in the
derivation: 共1兲 the rollers are in contact with the two bearing
plates; 共2兲 the rollers are in pure rolling motion; 共3兲 rolling friction is ignored since it is typically very small in our application
compared to the restoring force and the sliding friction force of
the bearing; 共4兲 the lower bearing plate is fixed to a rigid base;
z1
m1 g
f Ds sgn x1 x1
f1
N1
f1
f Ds sgn x1 Rigid base
x2
m2 g
z2
f2
N2
f2
Z
O
X
z3
x3
Fig. 2. Free-body diagram when the roller is on the left
JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 / 503
J. Struct. Eng., 2010, 136(5): 502-510
Superstructure
Base shear
m1 g
N1
f2
Z
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O X
f Ds
x1
z2
f1
m2 g
z1
f Ds sgn x1 f1
N2
f Ds sgn x1 f2
z3
f Ds
fS
x2
x3
displacement
Rigid base
Fig. 3. Free-body diagram when the roller is on the right
m1共z̈1 + z̈3兲 − N1 + m1g − f Ds sin ␪ sgn共ẋ1兲 = 0
Fig. 4. Base shear versus horizontal displacement of the proposed
roller bearing
共2兲
where z̈1 = vertical acceleration response of the superstructure
relative to O; N1 = normal force between the roller and the upper
plate; and g = acceleration of gravity. The equation of dynamic
equilibrium for the roller along the horizontal direction is
m2共ẍ2 + ẍ3兲 − f 1 + f 2 cos ␪ − N2 sin ␪ = 0
共3兲
where m2 and ẍ2 = mass and horizontal acceleration response of
the roller relative to O, respectively and f 2 and N2 = static friction
force and normal force between the roller and the lower bearing
plate, respectively. For the vertical direction, we have
m2共z̈2 − z̈3兲 − N1 + f 2 sin ␪ + N2 cos ␪ − m2g = 0
共4兲
where z̈2 = vertical acceleration response of the roller relative to
O. The rotational dynamic equilibrium of the roller gives
I 2␣ − f 1R − f 2R = 0
冢
0
1
0
0
0
m1 0 0 0
0
0
0
−1
0
0 m1 0 0
0
− 1 cos ␪ 0 − sin ␪
0 0 m2 0
0
0 sin ␪ − 1 cos ␪
0 0 0 m2
0
0 0 0 0
−R −R
0
I
0 0 1 0 − R cos ␪ 0
0
0
0
0 0 0 1 − R sin ␪ 0
0
0
0
1 0 −1 0
0
0
0
−R
0
0 1 0 1
0
0
0
0
0
共5兲
where ␣, I2, and R are the angular acceleration, moment of inertia, and radius of the roller, respectively. If the roller is in a pure
rolling motion, compatibility requirements lead to
ẍ2 = R cos ␪ ⫻ ␣
共6兲
z̈2 = R sin ␪ ⫻ ␣
共7兲
ẍ1 = ẍ2 + R␣
共8兲
z̈1 = − z̈2
共9兲
Rearrange Eq. 共1兲 to Eq. 共9兲 in a matrix form gives
⫻
冢冣冢
ẍ1
− m1ẍ3 − f Ds cos ␪ sgn共ẋ1兲
z̈1
− m1共g + z̈3兲 + f Ds sin ␪ sgn共ẋ1兲
ẍ2
− m2ẍ3
z̈2
␣
f1
f2
N1
N2
=
m2共g + z̈3兲
0
0
0
0
0
冣
By solving the system of linear equations, we have, for example,
the acceleration response of the superstructure
␪
2R2 cos2 兵f Ds sgn共ẋ1兲 + m1ẍ3 + 关f Ds sgn共ẋ1兲 + 共m1 + m2兲ẍ3兴cos ␪ − 共z̈3 + g兲共m1 + m2兲sin ␪其
2
ẍ1 =
I + 共2m1 + m2兲R2 + 2m1R2 cos ␪
Since the mass of the superstructure m1 is much larger than the
mass of the roller m2, dividing both the denominator and numerator by m1 and ignoring m2 / m1 lead to
␪
− cos2 兵共1 + cos ␪兲关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 − 共z̈3 + g兲sin ␪其
2
ẍ1 =
1 + cos ␪
冣
1
␪
ẍ1 = − cos2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + sin ␪共z̈3 + g兲
2
2
In a similar manner, the solutions for all the variables are
Further simplification leads to
504 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010
J. Struct. Eng., 2010, 136(5): 502-510
冢冣
ẍ1
z̈1
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ẍ2
z̈2
␣
f1
f2
N1
N2
⎛
⎜ 再再
⎜ 再再
⎜再
再
⎝再
⎞
冎⎟
冎
冎 ⎟
冎
冎⎟
冎
冎⎠
1
␪
− cos2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + sin ␪共z̈3 + g兲
2
2
1
␪
sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 − sin2 共z̈3 + g兲
2
2
1
␪
cos ␪ − 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲
2
2
1
␪
sin ␪ − 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲
2
2
1
␪
− 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲
⬇
2R
2
1
␪
− m1 sin2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + sin ␪共z̈3 + g兲
2
2
1
␪
m1 sin2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + sin ␪共z̈3 + g兲
2
2
1
␪
m1 sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + cos2 共z̈3 + g兲
2
2
1
␪
m1 sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + cos2 共z̈3 + g兲
2
2
再
1
␪
ẍ2 = − cos ␪ 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲sgn共x1兲
2
2
共12兲
再
1
␪
z̈2 = − sin ␪ 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲sgn共x1兲
2
2
冢
⫻
冢冣冢
ẍ1
− m1ẍ3 − f Ds cos ␪ sgn共ẋ1兲
z̈1
− m1共g + z̈3兲 − f Ds sin ␪ sgn共ẋ1兲
ẍ2
− m2ẍ3
z̈2
␣
f1
f2
N1
N2
=
m2共g + z̈3兲
0
0
0
0
0
冣
冣
冎
共13兲
␣=−
再
1
␪
关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + tan 共z̈3 + g兲sgn共x1兲
2R
2
冎
共14兲
再
␪
f 1 = − f 2 = m1 − sin2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴
2
1
+ sin ␪共z̈3 + g兲sgn共x1兲
2
再
冎
共15兲
1
N1 = N2 = m1 − sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴sgn共x1兲
2
When the roller is on the right-hand side of the center of the lower
bearing plate, the free-body diagram is shown in Fig. 3.
The matrix form for the equations of dynamic equilibrium is
0
0
1
0
0
0
m1 0 0
0
0
0
0
−1
0
0 m1 0
0
0
− 1 cos ␪ 0 sin ␪
0 0 m2
0
0 − sin ␪ − 1 cos ␪
0 0 0 − m2
0
0
0 0 0
−R −R
0
I
0 0 1
0 − R cos ␪ 0
0
0
0
0 0 0
1
0
0
0
− R sin ␪ 0
1 0 −1 0
0
0
0
−R
0
0 1 0 −1
0
0
0
0
0
冎
␪
+ cos2 共z̈3 + g兲
2
冎
共16兲
Governing Equation of Horizontal Motion
Eq. 共10兲 is of great interest since it represents the governing equation of horizontal motion of the bearing 共superstructure of the
bridge兲. In our applications, sloping angle ␪ is limited to 11° to
ensure rolling without sliding of the rollers, which will be further
discussed later. Thus, cos2 ␪ / 2 ⬇ 1. Simplifying and rearranging
Eq. 共10兲 and multiplying both sides of the equation by m1 lead to
1
m1ẍ1 + m1 sin ␪共z̈3 + g兲sgn共x1兲 + f Ds sgn共ẋ1兲 = − mẍ3 共17兲
2
The second term of Eq. 共17兲 represents the restoring force f S of
the bearing. The equation can also be expressed as
m1ẍ1 + f S sgn共x1兲 + f Ds sgn共ẋ1兲 = − m1ẍ3
共18兲
1
f S = m1共z̈3 + g兲sin ␪
2
共19兲
where
Complete solutions that include both conditions when the roller is
on the left- and right-hand sides of the lower bearing plate are
Based on Eq. 共18兲, it can be seen that the maximum base shear V p
along the principal direction of the bearing is
2x
1
␪
ẍ1 = − cos2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 − sin ␪共z̈3 + g兲sgn共x1兲
2
2
x
共10兲
1
␪
z̈1 = − sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴sgn共x1兲 − sin2 共z̈3 + g兲
2
2
共11兲
Fig. 5. Relationship between displacements of the roller and the
superstructure
JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 / 505
J. Struct. Eng., 2010, 136(5): 502-510
共20兲
V p = f S + f Ds
It is clear that from Eqs. 共19兲 and 共20兲 and that the maximum base
shear is independent of the magnitude and frequency content of
the horizontal base acceleration ẍ3, which reduces the possibility
of resonance between the bearing and base excitation. In contrast,
the two common types of seismic isolation bearings previously
mentioned are typically designed to have a certain amount of
postelastic stiffness to ensure low permanent displacements after
an earthquake. In such a case, the maximum base shear is dependent on the magnitude and frequency content of the base excitation.
If both the upper and lower rollers of the bearing are mobilized, the resultant base shear will be 冑2 times the base shear
along the principal directions, that is
Vmax = 冑2f S + 冑2f Ds = 冑2V p
共21兲
This force should be considered in the design of the bridge substructure on which the bearing is seated. Fig. 4 schematically
illustrates the base shear-horizontal displacement relationship of
the bearing along the principal directions.
Note that for a pure rolling motion, the relative displacement
of the superstructure x1 is twice that of the roller x2 as shown in
Fig. 5, that is
共22兲
2x2 = x1
This means the displacement capacity of a bridge superstructure
seated on a roller bearing is twice the available travel that can be
provided by the bearing plate to the roller. This is advantageous
particularly when large displacement capacity is needed.
Conditions for Rollers to Maintain Contact with
Bearing Plates
For the rollers to maintain contact with the bearing plates, forces
N1 and N2 have to be positive, that is
再
1
N1 = N2 = m1 − sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴sgn共x1兲
2
冎
␪
+ cos2 共z̈3 + g兲 ⬎ 0
2
共25兲
When ␪ is small, the first term of the equation likely becomes
small compared to the second term and cos2 ␪ / 2 ⬇ 1. Thus, Eq.
共25兲 may be simplified and rearranged to Eq. 共26兲, which shows
that if the magnitude of the downward vertical base acceleration
is smaller than g, the rollers will maintain contact with the bearing plates
z̈3 ⬎ − g
共26兲
During an earthquake, the magnitude of the vertical acceleration
of the bearing depends on the magnitude of the vertical component of the earthquake and the overturning moments of the superstructure. If Eq. 共26兲 is not satisfied, separation between the
rollers and the bearing plates will occur. As a result, misalignment
between the rollers and the bearing plates may happen, causing a
permanent displacement when the motion of the bearing stops.
Conditions for Rolling without Sliding
Once the static friction force between the roller and the bearing
plate f developed by an angular acceleration of the roller exceeds
Conditions for Self-Centering
0.6
To maintain self-centering capability of the bearing, the restoring
force f S needs to be larger than the sliding friction force f Ds.
AASHTO 共2000兲 requires that the restoring force be greater than
or equal to 1.05 times the characteristic strength of the bearing.
This means
f S ⱖ 1.05f Ds
共23兲
Lateral force/axial force
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Fig. 6. Prototype bearing
fS
1.05
0.2
0
-0.2
-0.4
-0.6
-30
Thus, the maximum allowable sliding friction force f Dsa is
f Dsa =
0.4
共24兲
-20
-10
0
10
Displacement (mm)
20
30
Fig. 7. Results of friction test of the friction plate and the side wall
506 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010
J. Struct. Eng., 2010, 136(5): 502-510
the maximum static friction force f st that can be provided by the
contact interface, the roller starts sliding. Once the roller slides,
the bearing may exhibit a permanent displacement after earthquakes. To ensure rolling without sliding, f st must exceed f, that
is
f st = ␮sN1 ⱖ 兩f 1兩 and ␮sN2 ⱖ 兩f 2兩
共27兲
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Substituting N1 and f 1 from Eqs. 共16兲 and 共15兲, respectively, into
Eq. 共27兲 leads to
冨
再
再
冎
冎冨
1
␪
m1 − sin2 关ẍ3 + f Ds/m1 sgn共ẋ1兲兴 + sin ␪共z̈3 + g兲sgn共x1兲
2
2
␮s ⱖ
1
␪
m1 − sin ␪关ẍ3 + f Ds/m1 sgn共ẋ1兲兴sgn共x1兲 + cos2 共z̈3 + g兲
2
2
Further simplification leads to
␮s ⱖ tan
␪
2
共28兲
In a similar manner, substituting N2 and f 2 from Eqs. 共16兲 and
共15兲 into Eq. 共27兲, respectively, also leads to Eq. 共28兲. Thus, the
sloping angle ␪ has to satisfy
␪ ⱕ 2 tan−1 ␮s
共29兲
This equation shows that the upper limit of the sloping angle ␪ for
rolling without sliding increases as the coefficient of static friction
␮s increases. ␮s for steel on steel range from 0.74 for dry conditions to approximately 0.1 for greasy conditions 共Avallone and
Baumeister 1996兲. For a conservative result, ␮s is taken as 0.1.
The condition for rolling without sliding is
␪ ⱕ 11°
共30兲
Thus, the sloping angle is limited to 11° in this research.
Experimental Verification and Calibration
Prototype Bearing
To verify and calibrate the characteristics of the developed bearing, an experimental study was conducted on a prototype roller
seismic isolation bearing. The bearing is shown in Fig. 6. Both the
upper and lower rollers had a diameter D, a wall thickness t, and
a length L of 45, 11.5, and 115 mm, respectively. The design
displacement capacity of the bearing d was 50 mm. The steel used
for the rollers and bearing plates was 42CrMo quenched and tempered steel with a yield strength ␴y of 1,310 MPa. The design
vertical load capacity of the bearing p was 200 kN based on the
following equation:
PEs
D共L − d兲 ⱖ 2
8␴y
were made of steel plated with a layer of chromium to increase
wear resistance, was 0.4 based on the results from friction testing
of the two materials 共see Fig. 7兲. The loading frame and loading
protocol were the same as used in the bearing tests, which will be
presented in Sec. VIIB.
Test Program and Setup
Design parameters investigated included the following: 共1兲 sloping angles of the intermediate bearing plate ␪, 5°, and 8°; 共2兲
torques to each screw 共screws A兲 for applying normal forces to
the friction interfaces T: 0, 2.3, 3.6, and 4.5 kN mm; and 共3兲
angles between the rolling direction of the upper roller and the
direction of the applied lateral displacements ␪r 共see Fig. 8兲: 0°
共only the upper roller was mobilized兲 and 45° 共both the rollers
were mobilized兲. According to Oberg et al. 共2000兲, the torque of
each screw T has a linear relationship with the resulting normal
force to the friction interface by that screw Nb as
T = Nb共0.159t + 0.531␮td兲
共32兲
where t and d = pitch 共1.5 mm兲 and diameter 共12 mm兲 of the
screw, respectively, and ␮t = coefficient of friction between the
threads. The value of ␮t to be used in Eq. 共32兲 will be calibrated
by the test data presented later.
The test setup is shown in Fig. 9. Two vertical actuators were
used to apply a constant vertical load of 200 kN to the bearing.
One horizontal actuator was used to apply displacementcontrolled lateral cyclic sinusoidal loading to the bearing with a
peak velocity of 25.4 mm/s.
Test Results: Without Supplemental Energy
Dissipation
The results from the tests on the prototype bearing without
supplemental energy dissipation 共T = 0兲 are presented in Fig. 10. It
is seen that the bearing exhibited approximately a bilinear behavior with a fairly constant postelastic stiffness. The first linear
curve typically ends at a displacement of 1–1.5 mm. The restoring
forces measured from the tests and calculated using Eq. 共19兲 are
listed in Tables 1 and 2 for ␪r of 0° and 45°, respectively. Good
agreement is observed.
In Fig. 10, a small amount of energy dissipation is observed.
This energy dissipation was associated with rolling friction. The
coefficient of rolling friction ␮r is calculated by
Lower
roller
共31兲
Loading
direction
r
where Es = modulus of elasticity for steel, 200,000 MPa. Eq. 共31兲
was based on Eq. 14.7.1.4–1 of AASHTO 共2004兲 with a modification, reduction of L by d, to account for reduced load carrying
capacity when the bearing moves to the position corresponding to
its displacement capacity. The intermediate bearing plate was designed to be replaceable so that different sloping angles ␪ could
be tested. The friction plates were cut from molded friction sheets
for car brake lining supplied by McMaster-Carr. The dynamic
coefficient of friction between the plate and the side walls, which
Upper
roller
Fig. 8. Definition of ␪r
JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 / 507
J. Struct. Eng., 2010, 136(5): 502-510
30
30
20
10
=5°
0
=8°
20
=8°
Base shear (kN)
Base shear (kN)
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Fig. 9. Test setup
-10
10
=5°
0
-10
-20
-20
-30
-40
-20
0
20
Displacement (mm)
40
-30
-40
-20
0
20
Displacement (mm)
40
(b) r =45°
(a) r =0°
Fig. 10. Base shear versus lateral displacement for bearings without supplemental energy dissipation
␮r =
␦
R
共33兲
Test Results: With Supplemental Energy Dissipation
where R = radius of the roller and ␦ = moment arm between the
normal force at the contact and the center of the roller, which
depends on materials in contact and is 0.0508 mm for a steel
roller rolling on a steel plate 共Avallone and Baumeister 1996兲. R
of the prototype bearing was 22.5 mm. Thus, the theoretical value
of ␮r in this application was 0.0023. The rolling friction forces
f Dr measured from the tests and calculated based on ␮r of 0.0023
are listed in Tables 1 and 2 for ␪r of 0° and 45°, respectively. It is
seen that Eq. 共33兲 provides a good prediction. In addition, f Dr is
much smaller than f S, which verifies the third assumption used in
the earlier derivation.
The results from the tests on the prototype bearing with a sloping
angle of 8° and with supplemental energy dissipation are presented in Fig. 11. For each value of T, the resulting values of f Ds
and supplemental energy dissipation per cycle 共EDC兲 of the bearing are listed in Table 3. EDC was calculated up to a displacement
of ⫾25 mm. It can be seen that the strength and energy dissipation of the bearing were notably increased, showing that the sliding friction mechanism developed in this research was effective.
In addition, a fairly constant postelastic stiffness was still maintained. Also listed in Table 3 are the values of Nb and ␮t for each
test case. Nb was calculated by dividing f Ds by 0.4 共the coefficient
of friction between the friction plate and the side walls兲 and by 6
共six screws A for each principal direction of the bearing兲. With Nb
known, ␮t was then calculated by using Eq. 共32兲 to be between
Table 1. Tests of Bearings without Supplemental Energy Dissipation and
with ␪r = 0°
Table 2. Tests of Bearings without Supplemental Energy Dissipation and
with ␪r = 45°
Tests
Test case
␪r = 0 ° , ␪ = 5°
␪r = 0 ° , ␪ = 8°
Tests
Analytical
f S 共kN兲
f Dr 共kN兲
8.5
13.8
0.3
0.4
f S 共kN兲
8.7
13.9
f Dr 共kN兲
0.4
0.4
Test case
␪r = 45° , ␪ = 5°
␪r = 45° , ␪ = 8°
508 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010
J. Struct. Eng., 2010, 136(5): 502-510
Analytical
冑2f S 共kN兲 冑2f Dr 共kN兲 冑2f S
12.5
19.6
0.4
0.6
共kN兲
12.3
19.7
冑2f Dr 共kN兲
0.6
0.6
40
30
30
20
20
Base shear (kN)
Base shear (kN)
40
10
0
T=2.3
T=3.6
-10
-20
T=4.5
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T=2.3
0
T=3.6 T=4.5
-10
-20
-30
-30
-40
-40
10
-20
0
20
Displacement (mm)
40
-40
-60
-40
-20
0
20
Displacement (mm)
40
60
(b) r =45°
(a) r =0°
Fig. 11. Base shear versus lateral displacement for bearings with supplemental energy dissipation
5.
Table 3. Tests of Bearings with Supplemental Energy Dissipation and
with ␪r = 0°
Test case
f Ds 共kN兲
EDC 共kN mm兲
Nb 共kN兲
␮t
4.0
6.2
7.1
431
619
753
1.7
2.6
3.0
0.18
0.18
0.20
T = 2.3
T = 3.6
T = 4.5
6.
7.
8.
Table 4. Tests of Bearings with Supplemental Energy Dissipation and
with ␪r = 45°
Test case
T = 2.3
T = 3.6
T = 4.5
冑2f Ds from tests 共kN兲
冑2f Ds from Table 3 共kN兲
5.8
8.5
9.8
5.7
8.8
10.0
The rolling friction was much smaller than the restoring
force and hence can be ignored.
The developed sliding friction mechanism was effective in
providing stable energy dissipation and in increasing the
strength of the bearing.
The analytical model for the relationship between the torque
applied to each screw A and the resulting normal force to the
friction interface was calibrated against the test results and
presented.
The properties of the bearing, particularly the coefficient of
friction between the friction plates and the side walls, will
change over time due to wear under repeated loading cycles
and weathering due to environmental factors. Additionally,
temperature, vertical loading, loading history, and loading
rate may also have an effect on the seismic performance of
the bearing. These should be studied in future research.
Acknowledgments
0.18 and 0.2. Table 4 lists the test results with a ␪r of 45°. The
results were compared to 冑2 the values obtained from tests with a
␪r of 0°. Both the results agree reasonably well.
Conclusions
Through analytical and experimental studies, the characteristics
of a new roller seismic isolation bearing are presented. A number
of important conclusions are summarized as follows:
1. The bearing exhibits a maximum base shear independent of
the amplitude and frequency content of horizontal ground
motions and has a self-centering capability after earthquakes.
2. The maximum base shear occurs when both the upper and
lower rollers are mobilized. The magnitude of the force is the
result of the maximum base shears along the principal directions of the bearing.
3. For the rollers to maintain contact with the bearing plates, the
absolute value of the downward acceleration should not exceed approximately one acceleration of gravity.
4. To prevent sliding of the rollers, the sloping angle of the
bearing needs to be smaller than a certain value depending
on the coefficient of static friction between the roller and the
sloping surface. For steel rollers and steel bearing plates, the
upper limit of the sloping angle can be conservatively chosen
as 11°.
The writers gratefully acknowledge the Federal Highway Administration 共FHWA兲 for funding the study reported herein 共FHWA
094 Project No. DTFH61-98-C00094兲. The writers wish to express their sincere appreciation to Philip Yen and James Cooper
from FHWA for their support, advice, and encouragement and to
Andrew Whittaker and Michael Constantinou from the University
at Buffalo for their valuable comments in the development of the
bearing. In addition, the writers would like to thank Christopher
Budden and Mark Pitman at the Structural Engineering and Earthquake Simulation Laboratory of the University at Buffalo for their
help in the experimental study.
References
AASHTO. 共2000兲. Guide specifications for seismic isolation design,
AASHTO, Washington, D.C.
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Buckle, I., Constantinou, M., Dicleli, M., and Ghasemi, H. 共2006兲. “Seismic isolation of highway bridges.” Rep. No. MCEER-06-SP07, Multidisciplinary Center for Earthquake Engineering Research, Univ. at
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Constantinou, M. C., Whittaker, A. S., Kalpakidis, Y., Fenz, D. M., and
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J. Struct. Eng., 2010, 136(5): 502-510