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Characterization of a Roller Seismic Isolation Bearing with Supplemental Energy Dissipation for Highway Bridges Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 502 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 J. Struct. Eng., 2010, 136(5): 502-510 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 8y 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 + 0.531td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) Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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 Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. 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. AASHTO. 共2004兲. AASHTO LRFD bridge design specifications, 3rd Ed., AASHTO, Washington, D.C. Avallone, E. A., and Baumeister, T., III. 共1996兲. Marks’ standard handbook for mechanical engineers, 10th Ed., McGraw-Hill, London. 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 Buffalo, State Univ. of New York, Buffalo, N.Y. JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 / 509 J. Struct. Eng., 2010, 136(5): 502-510 Naeim, F., and Kelly, J. M. 共1999兲. Design of seismic isolated structures, Wiley, New York. Oberg, E., Jones, F. D., Horton, H. L., and Ryffell, H. H. 共2000兲. Machinery’s handbook, 26th Ed., Industrial Press, New York. R. J. Watson, Inc. 共2008兲. “The EradiQuake system.” 具http://www. rjwatson.com/eqs_bearing.htm典 共Aug. 1, 2008兲. Tsai, M.-H., Wu, S.-Y., Chang, K.-C., and Lee, G. C. 共2007兲. “Shaking table tests of a scaled bridge model with rolling-type seismic isolation bearings.” Eng. Struct., 29共5兲, 694–702. Downloaded from ascelibrary.org by National Taiwan University of Sci and Tech on 02/16/22. Copyright ASCE. For personal use only; all rights reserved. Constantinou, M. C., Whittaker, A. S., Kalpakidis, Y., Fenz, D. M., and Warn, G. P. 共2007兲. “Performance of seismic isolation hardware under service and seismic loading.” Rep. No. MCEER-07-0012, Multidisciplinary Center for Earthquake Engineering Research, Univ. at Buffalo, State Univ. of New York, Buffalo, N.Y. Earthquake Protection Systems, Inc. 共EPS, Inc.兲 共2008兲. “Friction pendulum seismic isolation bearings.” 具http://www.earthquakeprotection. com/product2.html典 共Aug. 1, 2008兲. Kunde, M. C., and Jangid, R. S. 共2003兲. “Seismic behavior of isolated bridges: A state-of-the-art review.” Electron. J. Struct. Eng., 3, 140– 170. 510 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MAY 2010 J. Struct. Eng., 2010, 136(5): 502-510