Bulletin of Earthquake Engineering (2005) 3:75–99 DOI 10.1007/s10518-005-0187-9
© Springer 2005
Frictional Behavior of Steel-PTFE Interfaces for Seismic Isolation M. DOLCE∗ , D. CARDONE and F. CROATTO DiSGG, University of Basilicata, Macchia Romana Campus, 85100, Potenza, Italy ∗ Corresponding author. Tel: +390971205052; Fax: +390971205052, E-mail:
[email protected] Received 17 October 2004; accepted 6 December 2004 Abstract. The widespread use of sliding bearings for the seismic isolation of structures requires detailed knowledge of their behavior and improved modeling capability under seismic conditions. The paper summarizes the results of a large experimental investigation on steel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure, air temperature and state of lubrication on the mechanical behavior of steel-PTFE sliding bearings. Based on the experimental outcomes, two different mathematical models have been calibrated, which are capable of accounting for the investigated parameters in the evaluation of the sliding friction coefficient. The first model is basically an extension of the model proposed by Constantinou et al. (1990) Journal of Earthquake Engineering, 116(2), 455–472, while the second model is derived from the one proposed by Chang et al. (1990) Journal of Engineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a function of bearing pressure and air temperature are presented for lubricated and non-lubricated sliding surfaces. Predicted and experimental results are finally compared. Key words: friction, PTFE–steel interfaces, seismic isolation, sliding bearings
1. Introduction Steel–PTFE sliding bearings have been widely used in the past to accommodate thermal movements and effects of pre-stressing, creep and shrinkage in bridges. More recently, they have been proposed as part of seismic isolation systems, to support the weight of the structure, while relying upon separate mechanisms, to provide the system with re-centring and additional energy absorbing capability. Several sliding isolation systems with restoring force have been proposed. Some of them have reached the stage of implementation, such as the Resilient-Friction Base Isolation System (Mostaghel, 1984), based on the elastic properties of rubber, the SMA Isolation System (Dolce et al., 2000), based on the superelastic properties of shape memory alloys, and the Friction Pendulum System (Zayas et al., 1987), which exploits an articulated slider moving on a spherical surface to provide restoring capability. The most important advantage in using sliding isolation systems with (weak)
76
M. DOLCE ET AL.
restoring force is that the structural response is little sensitive to variations in the frequency content of the earthquake. In Italy a different approach has been followed (Dolce, 2001). A very large number of bridges, indeed, have been equipped with elasto-plastic isolation systems, consisting of lubricated sliding bearings and hysteretic steel dampers. Such systems are able to limit the force transmitted by the deck to piers and abutments to a predefined level, almost independent from the intensity and spectral content of the seismic excitation. The drawbacks are the large dispersion in the peak displacements and the occurrence of permanent displacements after strong earthquakes. Many numerical analyses of the seismic response of structures equipped with steel–PTFE sliding isolation systems have been carried out (Mostaghel and Tanbakuchi, 1983; Fan et al., 1988). In all these studies, as well as in the current design practice, it is assumed that the friction coefficient comply with the Coulomb friction law (i.e. friction remains constant during sliding). Actually, experimental observations (Constantinou et al., 1987; Hwang et al., 1990; Mokha et al., 1990), pointed out that the friction coefficient increases more than linearly while increasing sliding velocity, while it decreases with the increase of the contact pressure. Temperature and number of sliding reversals also play a not negligible role (Tyler, 1977). An accurate mathematical model of the frictional behavior of steel– PTFE sliding bearings has been developed in (Constantinou et al., 1990). It is based on the viscoplasticity theory (Wen, 1976), and is referred to as modified viscoplastic model. Its main characteristic is the dependence of the friction coefficient on sliding velocity and bearing pressure, through an exponential analytical law. The Constantinou’s model has been implemented in the structural analysis program SAP-2000 Nonlinear (SAP-2000, 2002), as the Friction-Pendulum Isolator NLLink element. Applications of the exponential model in the analysis of a sliding isolation system have been reported in (Constantinou et al., 1990; Mokha et al., 1993; Deb and Paul, 2000), mainly with the scope of evaluating the effects of bearing pressure, sliding velocity, breakaway friction and bi-directional motion on the seismic response of base-isolated buildings, compared with the predictions of the Coulomb’s model. An interesting comparison between experimental and numerical results is reported in (Tsopelas et al., 1996), with reference to a bridge structure. The Constantinou’s model is a phenomenological model, being derived from the observation of experimental results. An evolution of the Constantinou’s model, based on the tribology theory, has been recently proposed in (Takahashi et al., 2004) to describe the frictional behavior of PTFE–steel interfaces at the microscopic level. A comprehensive program of experimental tests has been carried out at the laboratory of the University of Basilicata on steel–PTFE interfaces, in
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
77
order to fully investigate the effects of sliding velocity, contact pressure, air temperature, number of cycles and state of lubrication on the mechanical behavior of steel–PTFE sliders. Based on the experimental outcomes, two mathematical models of their frictional behavior, for conditions of interest in seismic isolation, have been developed and calibrated. The first model is basically an extension of the model proposed in (Constantinou et al., 1990), while the second model is derived from the one proposed in (Chang et al., 1990). In this paper, the main results of the experimental tests are described. Model predictions and experimental results are then compared. 2. Experimental Set up and Procedure The experimental program on steel–PTFE interfaces had two specific objectives: (i) investigating the variability of the sliding friction coefficient while varying contact pressure, velocity, air temperature, displacement amplitude and state of lubrication of steel–PTFE interfaces, (ii) developing and calibrating a numerical model of the mechanical behavior of steel–PTFE sliding bearings. 2.1. Materials The materials used were as follows: • Unfilled PTFE pads obtained from a 5.45 mm thick sheet with dimpled recesses, whose dimensions and pattern are shown in Figure 1. The function of the dimple recesses is to retain the grease and to gradually introduce it between the sliding interfaces, during wear of PTFE. • Stainless steel plates (AISI 316/L) of 3 mm thickness, polished to mirror finish, with less than 0.1 µm surface roughness. • Silicone grease, of the type normally used in the bearing manufacturing.
Figure 1. Details of PTFE dimpled recesses.
78
M. DOLCE ET AL.
2.2. Test apparatus The testing apparatus is schematically shown in Figure 2. A central steel plate is laterally finished with two polished stainless steel plates (300 mm by 45 mm dimensions) and sandwiched between two couples of 40 by 25 mm PTFE pads, with 5.45 mm thickness. The PTFE pads are placed into recesses of two lateral steel plates. The protrusion of the pads was 2.6 mm in the unloaded condition. The PTFE–steel interfaces are compressed by a 50 kN hydraulic jack and four pre-stressing steel rods. The lateral steel plates are attached to a reaction frame, while the central steel plate is driven by a 10 kN Instron dynamic actuator, with ±125 mm stroke. The dynamic actuator is equipped with a 63 lit/s controller valve, a ±10 kN load cell and a ±125 mm internal inductive transducer. The above said test arrangement is placed inside a thermal room, working in −30 ◦ C/+80 ◦ C temperature range. The air temperature is controlled by a K-type thermocouple.
Figure 2. Testing apparatus.
79
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
2.3. Test program More than 300 tests have been carried out on steel–PTFE interfaces with 9.36, 18.72 and 28.1 MPa bearing pressures, −10, 20 and 50 ◦ C air temperatures, from 1mm/s to about 300 mm/s sliding velocities, from 10 to 50 mm displacement amplitudes. Both lubricated and non-lubricated steel–PTFE interfaces were tested. In most of the tests, the motion was sinusoidal, with specified amplitude and frequency. Furthermore, a number of tests were conducted with constant velocity motion (i.e. saw-tooth displacement–time history). The two types of tests produced almost identical results for the same peak velocity of sliding. Table I summarises the whole experimental program. As can be seen, nine series of tests have been carried out. Each series consisted of 16 tests, all at the same air temperature and contact pressure. The contact pressure was progressively increased from one series to another, while keeping the temperature constant. Every three series of tests the PTFE pads were replaced by new ones.
Table I. Test program. Test Interfacesa T b (◦ C) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 a
L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P L/P
−10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50 −10/20/50
P c (MPa)
dd fe Wavef (mm) (Hz)
vg Cycles CDh (mm/s) No. (mm)
9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1 9.36/18.7/28.1
50 50 50 50 10 10 10 10 25 25 25 25 50 50 50 50
10 40 100 200 var. var. var. var. var. var. var. var. var. var. var. var.
0.05 0.2 0.5 1 0.05 0.2 0.5 1 0.05 0.2 0.5 1 0.05 0.2 0.5 1
TR. TR. TR. TR. SYN. SYN. SYN. SYN. SYN. SYN. SYN. SYN. SYN. SYN. SYN. SYN.
State of stainless steel–PTFE interfaces : L = lubricated, P = Pure. Air temperature. c Contact Pressure. d Displacement amplitude. e Frequency of loading. f Displacement profile: TR = triangular, SYN = sinusoidal. g Sliding velocity: var = variable. h Cumulative distance. b
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1000 2000 3000 4000 4200 4400 4600 4800 5300 5800 6300 6800 7800 8800 9800 10,800
80
M. DOLCE ET AL.
Triangular (saw-tooth) tests were carried out at constant displacement amplitude (50 mm), while increasing the sliding velocity from 10 to 200 mm/s. In the sinusoidal tests, the displacement amplitude was varied from 10 to 50 mm, while increasing the frequency of loading from 0.05 to 1 Hz, thus producing peak sliding velocities ranging from 1 to 300 mm/s. Five complete loading cycles were performed during each test. The cumulative distance during each series of test was approximately 10.8 m, as shown in Table I. Thus, a total distance of about 32.4 m was covered by each set of PTFE pads. The thickness of the PTFE pads was measured before testing and after their removal. 3. Experimental Results 3.1. Effect of type of test Representative frictional force-displacement loops of the single interface are shown in Figures 3 and 4. They refer to tests conducted on non-lubricated interfaces under the same contact pressure (28.1 MPa), air temperature (−10 ◦ C) and displacement amplitude (50 mm), only differing for the wave form and the loading frequency. Figure 3 compares the frictional behavior exhibited by the PTFE–steel interfaces in (a) triangular and (b) sinusoidal tests at the same peak velocity, equal to 10 mm/s (i.e. test No. 1 vs. test No. 13, according to Table I). Figure 4 refers to (a) triangular and (b) sinusoidal tests conducted at the higher peak velocities: 200 mm/s and 300 mm/s, respectively (i.e. test No. 4 vs. test No. 16, according to Table I). For the sinusoidal tests, the peak velocity is defined as the average velocity in the displacement range corresponding to force levels greater than 95% of the maximum frictional force. Two phenomena are clearly visible in the triangular tests, one at the start of sliding, the other at every motion reversal. The first phenomenon is generally taken into account through the definition of a breakaway friction coefficient, also known as static friction coefficient, to distinguish it from the sliding (kinetic) friction coefficient. The second phenomenon, generally referred to as stick-slip, corresponds to a short duration increase of the frictional force, followed by a rapid decrease. Both the observed experimental phenomena can be related to (i) a momentary sticking of the interfaces and to the (ii) acceleration impulse occurring at the start of the test and at every motion reversal, especially in the triangular tests. The examination of Figures 3 and 4 clearly highlights the dependence of the friction coefficient from sliding velocity. In each triangular test, the force–displacement loops are practically rectangular, in accordance with friction Coulomb’s law, but the friction force increases while increasing the frequency of loading in the different tests. In the sinusoidal tests, on the
81
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
(mm)
60 0 160 (sec)
0
(KN)
-60
s t ick slip
6
break-away friction
4 2 0 -60
-40
-20
0
20
40
-2
60 (mm)
-4 -6
(a)
stick slip
(KN)
(mm)
60 0 0
160 (sec)
-60
6 4 2 0
-60
-40
-20
0 -2
20
40
60 (mm)
-4 (b)
-6
Figure 3. Typical frictional force–displacement loops recorded during (a) triangular and (b) sinusoidal tests at low peak velocities (about 10 mm/s). Both tests were conducted on non-lubricated interfaces, under the same air temperature (−10 ◦ C), contact pressure (28.1 MPa) and displacement amplitude (50 mm).
contrary, the friction coefficient varies during the motion, reaching its maximum at the maximum velocity (i.e. at zero displacement). Furthermore the friction coefficient tends to decrease during continuous loading cycles, this effect being related to self-heating of the sliding interfaces. Indeed, the rate of decrease of the friction coefficient is quite negligible in the tests al low
82
M. DOLCE ET AL.
(mm)
60 0 20 (sec)
0
break-away friction
(KN)
-60
stick slip
8 6 4 2 0
-60
-40
-20
-2
0
20 4
-4
40
60 (mm)
5
-6 3
2
-8
1
stick slip
(a)
(KN)
(mm)
60 0 0
20
(sec)
-60
8 6 4 2 0
-60
-40
-20
-2 -4
0
20 4
5
40
60 (mm)
-6 (b)
3
2
1
-8
Figure 4. Typical frictional force-displacement loops recorded during (a) triangular and (b) sinusoidal tests at very high peak velocities (>200 mm/s). Both tests were conducted on non-lubricated interfaces, under the same air temperature (−10 ◦ C), contact pressure (28.1 MPa) and displacement amplitude (50 mm).
frequency (see Figure 3), while it is decidedly more pronounced (>20% in five cycles) in the tests at high frequency of loading (see Figure 4). The phenomenon comes to an end in a few cycles, due to the attainment of a new thermal equilibrium with the ambient.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
83
3.2. Effect of sliding velocity Figure 5 summarizes the results of all the tests on non-lubricated interfaces, in terms of sliding friction coefficient, i.e.: µ=
Fr N
(1)
where Fr is the frictional resistance of the sliding interfaces, and N is the normal load applied during the tests, equal to 10, 20 and 30 kN, respectively. In Figure 5, the sliding friction coefficient is reported as a function of (peak) velocity and contact pressure, for three different temperature values: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C, respectively. In the calculation of the sliding friction coefficient, reference was made to the second cycle of each test, by averaging the values of the friction force associated to both motion ways. In Figure 5, the experimental data are represented by single points, while the curves correspond to analytical laws obtained from two different frictional models, as discussed below. As can be seen, the sliding friction coefficient increases rapidly with velocity, up to a certain velocity value, beyond which it remains almost constant. This value is around 150 mm/s, regardless air temperature and bearing pressure. The difference between maximum and minimum values of the sliding friction coefficient (i.e. = µmax − µmin , see Figure 6(a)) is larger at low contact pressures, being equal to about 12% at 9.36 MPa and less than 7% at 28.1 MPa. The air temperature has little influence on . On the contrary, the percent increment θ = /µmin (see Figure 6(b)) tends to increase while increasing contact pressure, especially at medium-to-high temperatures, being of the order of 180% at 9.36 MPa, and 250% at 28.1 MPa. In view of the use of steel–PTFE sliding bearings in seismic isolation, it is worth to remark that typical design values of displacement and frequency of vibration of isolated structures are between 100–200 mm and 0.4–0.5 Hz, respectively. This means that the maximum sliding velocity, occurring in steel-PTFE bearings during an earthquake, ranges between 160 mm/s and 400 mm/s. According to the experimental results, the sliding friction coefficient is practically constant for seismic applications, but significantly different from the friction coefficient in slow movements. For the sliding interfaces considered in this study, the sliding friction coefficient ranges between 10% and 11% (depending on temperature) for a bearing pressure equal to 28.1 MPa, which is the closer experimental value to the maximum allowable contact pressure under seismic condition (i.e. 41 MPa) suggested in (AASHTO, 1999).
84
M. DOLCE ET AL.
P= 9.36 MPa
(%)
(a) 25
P= 18.72 MPa
P= 28.1 MPa
exponential
20 logarithmic
logarithmic
15 exponential
10 logarithmic
exponential
5 (mm/sec)
0 0 (%)
(b) 25
50
100
150
P= 9.36 MPa
200
250
P= 18.72 MPa
300
350
P= 28.1 MPa exponential
20
logarithmic
logarithmic
15
exponential
10 logarithmic
5 exponential
(mm/sec)
0
(c) 25
50
(%)
0
100
150
P= 9.36 MPa
200
250
P= 18.72 MPa
300
350
P= 28.1 MPa exponential
20
logarithmic
15
logarithmic exponential
10 logarithmic
5 exponential
(mm/sec)
0 0
50
100
150
200
250
300
350
Figure 5. Variation of the friction coefficient with sliding velocity, air temperature and bearing pressure, for non-lubricated interfaces. Comparison between analytical laws and experimental results. Air temperature equal to: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C.
85
(%)
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 14
-10˚C
+20˚C
+50˚C
12 10 8 6 4 2 0 9.36
18.72
28.08 (MPa)
(%)
(a)
300
-10˚C
+20˚C
+50˚C
250 200 150 100 50 0 9.36 (b)
18.72
28.08 (MPa)
Figure 6. (a) Absolute and (b) percent increment of the sliding friction coefficient in seismic with respect to service conditions, as a function of contact pressure, for three different air temperatures.
During its service lifetime, the sliding isolator acts as a usual sliding bearing, subjected to service load and thermal movements at very low velocities. The operating conditions of sliding bearing contained in various codes (AASHTO, 1999), (BS 5400, 1983), (CEN 1337, 2000) are quite different. CEN considers lubricated steel–PTFE interfaces only, while BS and AASHTO allow the use of both lubricated and non-lubricated interfaces. The maximum allowable contact pressure is assumed equal to 24 MPa by AASHTO (in absence of specific wear tests), 45 MPa by BS and 60 MPa by CEN. For unfilled PTFE sliding against stainless steel without lubrication, the service friction coefficient suggested by AASHTO (in absence of tests), for temperatures ≤ −25 ◦ C, is equal to 15% at 10 MPa and 10% at 20 MPa (or more). At 20 ◦ C, instead, the service limit state friction coefficient is assumed equal to 6% at 10 MPa and 3% at 20 MPa (or
86
M. DOLCE ET AL.
more). It is worth to observe that the friction coefficient values obtained in this experimental study, at the lowest sliding velocity (i.e. about 3 mm/s), substantially agree with the above mentioned code limits, being equal to: (i) 8.9% at 9.36 MPa and −10 ◦ C, (ii) 6.6% at 18.7 MPa and −10 ◦ C, (iii) 6.5% at 9.36 MPa and 20 ◦ C and (iv) 4.4% at 18.7 MPa and 20 ◦ C. 3.3. Effect of contact pressure As known (Mokha et al., 1990), the sliding friction coefficient of steel– PTFE interfaces reduces while increasing pressure. Based on the experimental outcomes available (see Figure 5), the rate of reduction is practically constant while increasing bearing pressure and quite insensitive to sliding velocity and air temperature. As a matter of fact, by doubling the contact pressure (from 9.36 to 18.7 MPa) the friction coefficient reduces, on average over the whole range of sliding velocities, by 24% (±3.4%) at −10 ◦ C, up to 33.4% (±2.4%) at 50 ◦ C. Similarly, by tripling the contact pressure (from 9.36 to 28.1 MPa) the friction coefficient reduces by 38.7% (±3.6%) at −10 ◦ C, up to 47.2% (±3.9%) at 50 ◦ C. It is worth to remark that the negative variation of the friction coefficient with contact pressure reduces considerably the corresponding variation observed for the frictional force when increasing the normal load. 3.4. Effect of air temperature Figure 7 reports the friction coefficient at (a) very low (i.e. 8 mm/s) and (b) very high (i.e. 316 mm/s) sliding velocities, as a function of air temperatures, for three different contact pressure values, namely: (i) 9.36 MPa, (ii) 18.7 MPa and (iii) 28.1 MPa. Experimental data (points) and model predictions (curves) are compared. The analytical curves reported in Figure 7 refer to the logarithmic model (see below), calibrated over the whole range of sliding velocities. This explains some inconsistencies between experimental and numerical data, especially at low sliding velocity. Based on the experimental results, the sliding friction coefficient decreases while increasing air temperature, according to a second-order polynomial law (i.e. µ = a · T 2 − b · T + c, with a, b, c > 0), whose expression is reported in Figure 7, for 6 pressure–velocity couples of values. As can be noted, the rate of reduction of the sliding friction coefficient is greater when passing from low-to-medium temperatures than when passing from medium-to-high temperatures. Moreover, it depends on sliding velocity, while being practically independent from contact pressure. At 8 mm/s (see Figure 7(a)), for instance, the average rate of reduction of the sliding friction coefficient with temperature is of the order of 0.77%/◦ C when passing from −10 to 20 ◦ C,
87
(%)
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
20
(P1 =9.36MPa, v1 =8mm/s): µ = 1.09E-1 - 7.31E-4*∆T + 4.3E-6*∆T2 (P2 =18.7MPa, v1 =8 mm/s): µ = 8.45E-2 - 7.31E-4*∆T + 4.3E-6*∆T2 (P3 =28.1MPa, v1 =8 mm/s): µ = 6.85E-2 - 7.31E-4*∆T + 4.3E-6*∆T2
15
in which ∆T = (T-T0) and T0 = -10˚C P1,v1
10
P2,v1
5
P3,v1
0 -10
(%)
(a)
20
20
P1,v2
15
P2,v2
50 (°C)
P3,v2
10 (P1 =9.36MPa, v2 =316mm/s): µ = 1.96E-1 – 3.95E-4*∆T + 1E-6*∆T2 (P2 =18.7MPa, v2 =316mm/s): µ = 1.42E-1 – 3.95E-4*∆T + 1E-6*∆T2 (P3 =28.1MPa, v2 =316mm/s): µ = 1.18E-1 – 3.95E-4*∆T + 1E-6*∆T2
5
in which ∆T = (T-T0) and T0 = -10˚C
0 (b)
-10
20
50 (°C)
Figure 7. Sliding friction coefficient at (a) very low and (b) very high velocities (i.e. 8 and 316 mm/s, respectively) as a function of air temperatures, for three different normal pressure values (i.e. 9.36, 18.72 and 28.1 MPa, respectively). Comparison between experimental results and model predictions.
while being of the order of 0.33%/◦ C when passing from 20 to 50 ◦ C. At 316 mm/s (see Figure 7(b)), the rates of reduction decrease by about 2.5 times. To account for the changes in the friction resistance of steel–PTFE sliding isolation systems due to temperature variations, the AASHTO defines two system property modification factors, λmax,t and λmin,t , which quantify the effects of temperature variations on the nominal value of the friction coefficient at 20 ◦ C reference temperature. They are defined as the ratio of the friction coefficient at the highest and at the lowest expected temperature (say 50 ◦ C and −10◦ C, respectively) to the friction coefficient at the reference temperature (20 ◦ C). Specific tests lacking, AASHTO provides predetermined values: λmax,t = 1.2 and λmin,t = 1, for non-lubricated steel-PTFE interfaces operating at −10 ◦ C and 50 ◦ C, respectively. The corresponding
88
M. DOLCE ET AL.
experimental values drawn from the whole set of experimental data are 1.17 (±0.09) and 0.89 (±0.054), respectively. 3.5. Effect of lubrication Figures 8 and 9 show the sliding friction coefficient for a number of significant tests on both non-lubricated (Figure 8) and lubricated (Figure 9) interfaces. Each diagram of figure 8 and 9 refers to a different air temperature: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C, respectively, as well as to a different set of PTFE pads. Each series of data, instead, refer to a different normal load, resulting in 9.36, 18.7 and 28.1 Mpa contact pressure, respectively. In each diagram the experimental data have been gathered in four groups, based on the peak sliding velocity. Each group, therefore, corresponds to tests repeated under similar test conditions, after a certain number of cycles. The displacement amplitude is generally different from one test to another, within each group. The order of execution of the tests is given by the number beside each point. By comparing Figures 8 and 9, it turns out that lubrication reduces friction coefficient by about 5 times at −10 and 20 ◦ C, and almost 8 times at 50 ◦ C. The sliding friction coefficient of lubricated steel–PTFE interfaces results always below 4%, which is the limit value for sliding isolation devices prescribed by the new Italian seismic code (Ordinanza 3274, 2003). The scatter in each group is practically negligible for non-lubricated interfaces, while it is not for lubricated steel–PTFE interfaces. For these latter, the tendency is a progressive reduction of the friction coefficient while increasing the number of cycles performed, due to the following reasons: (i) the introduction, in the sliding interfaces, of the grease contained inside the dimpled recessed, during the wear of the PTFE pads and (ii) the test sequence (see Table I), where tests wiith increasing displacement amplitude were carried out. Actually, before the start of each test sequence, grease was spread over the PTFE pads, to fill the dimpled recesses, but a certain amount of grease was also spread over the stainless steel sheets. When increasing displacement amplitude, it is reasonable to believe that more grease, from the stainless steel sheets, was introduced in the sliding interfaces. The quite negligible scatter in the experimental results relevant to nonlubricated interfaces (see Figure 8) implies that the wear of PTFE (see below) do not affect significantly their frictional behavior. For the lubricated steel–PTFE interfaces, friction is much lower and the wear of PTFE is expected to be much less than for non-lubricated interfaces. Figure 10 summarizes the results of all the tests on lubricated PTFE– steel interfaces. The sliding friction coefficient is reported as a function of (peak) velocity and contact pressure, for three different temperature values: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C, respectively. In the figure, experimental
89
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 10KN
(%)
20
2
15 6
1
10
5
17
22
20KN
7
30KN 8
11
24
27
40
43
10
13 18
23
26
34
39
42
15
28
31
44
47
30
29 45
12
14
46
33
38
50
10
50
50
10
25
10
25
50
25
50
10
12
15
40
32
30
67
77
60
155
152 (mm/sec)
0
20
8
15
10
2 1 17
5
6
13
22
29
18
7
10
23
26
34
39
42
45
(mm)
30KN
20KN
10KN
(%)
(a)
11
14
12 28
24
27
30
40
43
46
44
15 31
47
33
38
50
10
50
50
10
25
10
25
50
25
50
10
12
15
40
32
30
68
79
61
160
157 (mm/sec)
0
20
10KN
(%)
(b)
20KN
15 2
10
1
6
13
17
22
29
33
38
50 10
18
7 23
(mm)
30KN
8
11
24
27
12
15
28
31
44
47
14
10 26 40
43
30 46
45
34
39
42
10
50
50
10
25
10
25
50
25
50
12
15
40
34
31
70
80
60
162
159 (mm/sec)
5
0
(c)
(mm)
Figure 8. Effects of number of cycles on the sliding friction coefficient exhibited by non-lubricated interfaces during tests at different air temperatures, namely: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C.
data and model predictions are compared. As can be seen, the friction coefficient of lubricated interfaces follows a trend similar to that described for non-lubricated interfaces. It tends to increase when increasing sliding
90
M. DOLCE ET AL. 10KN
(%)
4
20KN
3
38 33 17 1
42
18 23
45 13
2
50
50
7
46
24
34 29
22
44
43
39
2
30KN 40
8
25
10
31
12
11
10
28
30
27
26
47
15
14
6
1
0 50
(a)
10
4
12
15
31
31
10KN
3
64
50
79
25
60
17 33 1
22 38
29
20KN
160
30KN 11
8
13
6
2
1
40
25
50
(mm)
156
(mm/sec)
(%)
10
10
7 18 2
45
10
23 39
24
26 42
15
14
28
27
40
12
30
44
31
43 46
34
47
0
4
50
10
50
50
10
25
10
25
50
25
50
(mm)
10
12
15
40
32
30
65
80
61
159
154
(mm/sec)
20KN
10KN
(%)
(b)
30KN
3
2
1
1 17
6 22
2 13
7
29
39 18 23
38 45
33
8 10 42 26
40 24
11
43 14
44 12
15
28
47
46
27
31
30
34
0
(c)
50
10
50
50
10
25
10
25
50
25
50
(mm)
10
9
15
40
31
31
66
80
62
161
158
(mm/sec)
Figure 9. Effects of number of cycles on the sliding friction coefficient exhibited by lubricated interfaces during tests at different air temperatures, namely: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C.
velocity and to reduce when increasing air temperature and contact pressure. However a greater scatter can be noted, probably due to the testing sequence and the difficulty of getting uniform distribution of lubricating grease. The behavior of the friction coefficient at −10 ◦ C is anomalous, as it increases while increasing contact pressure. Nevertheless, some interesting
91
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE (%)
(a) 4
[email protected] [email protected]
3
2
[email protected] P= 9.36 MPa 25 20
1
15 10
P= 18.72 MPa 5
0
0.000
5 0.000
1 00.000 1 5 0.000
2 00.000 2 5 0.000
3 00.000 3 5 0.000 (m m ec) /s
P= 28.1 MPa
(mm/sec) 0 0
4
100
150
200
(%)
(b)
50
250
300
350
P= 9.36 MPa 25 20 15 10
P= 18.72 MPa 5
0
0.000
[email protected]
3
5 0.000
1 00.000 1 5 0.000
2 00.000 2 5 0.000
3 00.000 3 5 0.000 (m m ec) /s
P= 28.1 MPa
[email protected]
2
1
[email protected] (mm/sec)
0 0
100
150
200
250
300
350
(%)
(c) 4
50
P= 9.36 MPa 25 20 15 10
P= 18.72 MPa 5
3
0
0.000
5 0.000
1 00.000 1 5 0.000
2 00.000 2 5 0.000
3 00.000 3 5 0.000 (m m ec) /s
P= 28.1 MPa
[email protected] 2
[email protected]
1
[email protected] (mm/sec) 0 0
50
100
150
200
250
300
350
Figure 10. Variation of the friction coefficient with sliding velocity, air temperature and bearing pressure, for lubricated interfaces. Comparison between analytical laws and experimental results. Air temperature equal to: (a) −10 ◦ C, (b) 20 ◦ C and (c) 50 ◦ C.
92
M. DOLCE ET AL.
observation can be made by referring to the average values of the friction coefficient, over the three contact pressures. The friction coefficient under service conditions (i.e. at very low sliding velocities) at 20 ◦ C air temperature is of the order of 1.5–2%. This is consistent with the values provided by AASHTO under the same conditions, ranging between 2 and 2.8%, for bearing pressures from 10 to 30 MPa. The sensitivity of the friction coefficient to temperature variations resulting from the experimental data also confirm the conservativeness of the property modification factors suggested by AASHTO. They are λmax,t = 1.5 at −10 ◦ C and λmin,t = 1 at 50 ◦ C, while the experimental data under consideration provide values equal to 1.27 (±0.09) and 0.59 (±0.07), respectively. CEN directly provides the maximum value of the friction coefficient to be used for verification of the bearing and the structure under service conditions. For expected extreme air temperatures lower than −5 ◦ C, the above said design values ranges between 3% (contact pressure ≥ 30 MPa) and 6% (contact pressure = 10 MPa), thus resulting about 2–3 times greater than the observed experimental values. Based on the present experimental study, therefore, the code recommendations concerning the effects of extreme temperatures on the sliding friction coefficient of lubricated steel-PTFE interfaces appear to be enough or even too conservative. For lubricated interfaces, the friction coefficient is much less sensitive to sliding velocity than for non-lubricated interfaces, as the values of the percent ratio θ = (µmax − µmin )/µmin is of the order of just 25% at −10◦ C and 20 ◦ C, and 40% at 50 ◦ C. 3.6. Effect of cycling Cycling produces a double effect: (i) a reduction in the sliding friction coefficient, due to self heating of the steel–PTFE interfaces and (ii) wear of PTFE. The first effect has been already discussed in 3.1. It has been found that higher sliding rates and pressures cause a larger decrease of the friction coefficient. The decay, however, follows a negative exponential trend: it becomes smaller and smaller while increasing the number of cycles. Moreover, the reduction in the sliding friction coefficient is only temporary: it returns to its original value when interrupting the cycling. As said before (see Section 2.3), the PTFE pads were changed after every three series of tests, at the same air temperature. The thicknesses of the PTFE pads were then measured, on flat areas away from dimpled recesses. As expected, the greatest wear of PTFE was observed at −10 ◦ C, for interfaces with no lubrication. In this case, the thickness of the four PTFE pads reduces by about 10%, passing from 5.4 to 4.9 mm, after having covered more than 30 m at different pressures and sliding velocities. On the contrary, the wear of lubricated PTFE was practically negligible.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
93
The wear is not a problem under seismic conditions, as an earthquake produces only a few cycles at the maximum displacement amplitudes. It could be important, instead, under service conditions. Actually, long-term tests are required by different codes and prescriptions, in order to appreciate the wear of PTFE due to slow movements resulting from both imposed thermal displacements and live loads. AASHTO, for instance, requires that at least 50% of the usable PTFE thickness must remain after completion of the wear test, consisting in 1.6 Km at the design contact pressure, air temperature of 20 ± 8 ◦ C and sliding velocity not less 63.5 mm/min. 4. Modelling of Steel–PTFE Sliding Bearings Two mathematical models of the frictional behavior of PTFE–steel interfaces have been implemented. According to Constantinou et al. (1990), the coefficient of friction at sliding velocity v, can be approximated by the following equation: µ = µmax − (µmax − µmin ) · e−α·v
(2)
in which µmax is the coefficient of friction at high velocities, µmin is the coefficient of friction at very low velocities and α is constant for a given pressure, temperature and condition of interfaces. The frictional force is then assumed equal to: Fr = µ · W · Z
(3)
where W is the normal load, Z is a dimensionless hysteretic quantity which can be calculated by solving the well-known differential equation proposed by (Wen, 1976) in random vibration studies of hysteretic systems. The alternative proposed analytical law to describe the relationship between sliding friction coefficient and velocity v is derived from (Chang et al., 1990) and is given by: µ = a + b · ln(v) v > 3 mm/s (4) µ = a + b · ln(3) v ≤ 3 mm/s where a and b are constant for a given pressure, temperature and condition of interfaces. The frictional force (Fr ) is then expressed by Equation (3). All the model parameters (i.e. µmax , µmin and α on one hand, a and b on the other hand), have been analytically expressed as a function of P (contact pressure) and T (air temperature), through a second-order polynomial model: f (P , T ) = λ1 + λ2 · T + λ3 · T 2 + λ4 · P + λ5 · P 2
(5)
94
M. DOLCE ET AL.
The coefficients λi have been obtained from a multivariate nonlinear regression, using a statistical analysis package (SPSS, 1999). The good fit of the regression, for both analytical laws, is apparent in Figure 5, which refers to non-lubricated interface. The proposed logarithmic model, however, is more accurate in capturing the experimental behavior in the low velocity range than the Constantinou’s model, which underestimates the friction coefficient in that range. For lubricated PTFE–steel interfaces (see Figure 10), the accuracy of the model predictions is decidedly worse, due to the great scatter in the experimental results. Tables II and III show the values of the model parameters for the nine combinations of bearing pressure and air temperature considered during the tests on non-lubricated and lubricated interfaces, respectively. In the tables there are also compared the experimental and analytical maximum friction forces at high peak velocities (160 mm/s, precisely). As can be seen, the error is at most equal to 5% for non-lubricated interfaces, while it ranges between 1% and 43% for lubricated sliding interfaces. It should be considered, however, the different order of magnitude of the frictional force for non-lubricated and lubricated interfaces, whose average values are equal to about 2.5 and 0.45 kN, respectively. Thus, a 5% error implies an absolute error of 0.125 kN, in the first case, while a 43% error implies, in the second case, an absolute error of 0.193 kN. In any case, the maximum frictional force provided by the model can be reliably used in seismic isolation design.
Table II. Model parameters relevant to non-lubricated interfaces, for nine different combinations of bearing pressure and air temperature values. Experimental test P (MPa)
T (◦ C)
Fra
9.36 9.36 9.36 18.7 18.7 18.7 28.1 28.1 28.1
−10 20 50 −10 20 50 −10 20 50
Constantiou’s model µmax (%)
α
(kN)
µmin (%)
1.82 1.70 1.60 2.72 2.49 2.20 3.27 2.95 2.74
8.43 6.68 6.12 6.23 4.49 3.93 4.87 3.13 2.56
19.61 18.40 17.76 13.91 12.70 12.10 11,48 10.26 9.66
0.020 0.018 0.013 0.022 0.020 0.015 0.024 0.022 0.017
Logarithmic model Fra
a
b
(kN)
Er. (%)
Fra (kN)
Er.b (%)
1.92 1.78 1.64 2.74 2.47 2.27 3.40 3.02 2.76
5 5 3 0 0 3 4 2 1
0.024 0.026 0.026 0.015 0.018 0.018 0.014 0.015 0.016
0.058 0.035 0.031 0.055 0.030 0.016 0.039 0.021 0.006
1.80 1.68 1.59 2.64 2.39 2.20 3.27 2.90 2.62
−1 −1 −1 −3 −4 0 0 −2 −4
b
Comparison between experimental and analytical maximum frictional force at high peak velocities (160 mm/s precisely) a Peak friction force at 160 mm/s maximum sliding velocity. b Percent error between experimental and numerical peak friction force.
95
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
Table III. Model parameters relevant to lubricated steel–PTFE interfaces, for nine different combinations of bearing pressure and air temperature values. Experimental test
Constantiou’s model
Logarithmic model
P (MPa)
T (◦ C)
Fra (kN)
µmin (%)
µmax (%)
α
Fra (kN)
Er.b (%)
a
b
Fra (kN)
Er.b (%)
9.36 9.36 9.36 18.7 18.7 18.7 28.1 28.1 28.1
−10 20 50 −10 20 50 −10 20 50
0.23 0.26 0.16 0.57 0.45 0.27 0.98 0.59 0.54
2.64 1.93 1.21 2.15 1.43 0.72 2.04 1.32 0.61
3.30 2.47 1.77 2.95 2.12 1.42 3.12 2.29 1.59
0.012 0.013 0.004 0.017 0.018 0.009 0.026 0.026 0.017
0.32 0.24 0.14 0.58 0.42 0.24 0.93 0.68 0.46
41 −9 −15 1 −8 −10 −5 15 −16
0.002 0.001 0.001 0.001 0.000 0.000 0.002 0.002 0.002
0.022 0.017 0.009 0.021 0.016 0.009 0.020 0.015 0.007
0.32 0.24 0.16 0.81 0.55 0.32 0.97 0.71 0.47
43 −10 −2 42 21 18 −1 19 −13
Comparison between experimental and analytical maximum frictional force at high peak velocities (160 mm/s precisely) a Peak friction force at 160 mm/s maximum sliding velocity. b Percent error between experimental and numerical peak friction force.
The accuracy of the proposed model in capturing the actual frictional behaviour of steel-PTFE sliding bearings is confirmed by Figures 11 and 12, which compare the experimental and numerical force– displacement loops of non-lubricated and lubricated interfaces, respectively. The experimental force-displacement relationships shown in Figures 11 and 12 refer to the second cycle of the tests No. 13 and 16 of Table I, at low and very high peak sliding velocities (i.e. about 15 mm/s and about 316 mm/s, respectively). Both tests have been conducted with the same displacement amplitude (50 mm), contact pressure (18.72 MPa) and air temperature (20 ◦ C). In the construction of the numerical relationships of Figures 11 and 12, reference was made to the displacement-time histories, as drawn from the experimental output. As far as non-lubricated interfaces are concerned, the accordance between experimental observations and model predictions is almost perfect, especially at low velocities. At high velocities, the numerical model is not able to capture the decay of the friction coefficient due to self-heating, as expected. Larger differences between experimental and numerical results are observed for lubricated interfaces, due to the big scatter in the experimental outcomes and to the less sensitivity of the model to velocity variation during the applied sinusoidal displacement. As previously noted, the gap between minimum and maximum sliding friction coefficient is significant for non-lubricated interfaces, while being negligible for lubricated steel–PTFE interfaces. Figures 11 and 12 clearly prove this. As a consequence, it can be said that the behavior of lubricated
96
M. DOLCE ET AL.
Figure 11. Comparison between experimental and numerical force–displacement loops of non-lubricated interfaces, at low and very high sliding velocities. Experimental tests conducted at 50 mm displacement amplitude, 18.72 MPa contact pressure and 20 ◦ C air temperature.
Figure 12. Comparison between experimental and numerical force–displacement loops of lubricated steel–PTFE interfaces, at low and very high sliding velocities. Experimental tests conducted at 50 mm displacement amplitude, 18.72 MPa contact pressure and 20 ◦ C air temperature.
steel–PTFE sliding bearings tends to be the same under seismic and service conditions, while considerable differences, in terms of maximum force and energy loss, are found for non-lubricated steel–PTFE sliding bearings.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
97
5. Conclusion A comprehensive program of experimental tests on unfilled PTFE pads sliding against polished stainless steel has been carried out. The effects on the sliding friction coefficient of (i) type of test, (ii) sliding velocity, (iii) contact pressure, (iv) air temperature, (v) conditi on of interfaces (i.e. lubricated or not) and (vi) number of cycles have been investigated. The following most important experimental findings have been obtained: (1) The coefficient of friction increases rapidly with velocity, up to a certain velocity value, beyond which it remains almost constant. Such value is around 150 mm/s, regardless air temperature and bearing pressure. The maximum velocities occurring in steel–PTFE sliding bearings under an earthquake are surely greater than 150 mm/s. Therefore, the design value of the frictional force in seismic applications can be assumed to be independent from frequency of loading and displacement amplitude. (2) The sliding friction coefficient of steel–PTFE interfaces reduces while increasing pressure. The reduction rate, however, depends on both sliding velocity and air temperature. It increases while increasing velocity and while decreasing air temperature. By referring to 20 ◦ C air temperature, 18.7 MPa contact pressure and sliding velocities ≥150 mm/s, maximum variations in the frictional force of steel–PTFE sliding bearings of the order of 30% are expected for ±50% variations of the contact pressure, regardless the state of lubrication of the interfaces. (3) The sliding friction coefficient decreases while increasing the air temperature. Its rate of reduction is greater when passing from low-to-medium temperatures, than when passing from medium-to-high temperatures. Moreover, it depends on sliding velocity, while being practically independent from contact pressure. At sliding velocities of interest for seismic applications, the reduction rate of the friction coefficient with temperature is of the order of 0.15–0.3%/◦ C, for non-lubricated interfaces. As a consequence, upper and lower bound analysis is needed, in order to evaluate the maximum forces on the structural elements and the maximum displacements in the isolation system. To this end, reference can be made to the lambda-factors (λmax,t and λmin,t ) provided by AASHTO, to estimate the values of the friction coefficient at extreme design temperatures. Based on the experimental results of the present study, the lambda-factors suggested by AASHTO lead to very accurate predictions for non-lubricated interfaces (differences less than 10%), while they result too conservative for lubricated interfaces (overestimations up to 40%). (4) The coefficient of friction tends to decrease during continuous loading cycles at high velocities, due to self-heating of the sliding interfaces. The phenomenon is exhausted in a few cycles, due to the attainment of a new thermal equilibrium with the ambient. Based on the
98
M. DOLCE ET AL.
available experimental outcomes, the overall decay of friction with continuous loading cycles is of the order of 25–30%, for non-lubricated interfaces. (5) Lubrication considerably reduces (by 5–8 times, depending on temperature) the frictional resistance of steel-PTFE sliding interfaces and, as a consequence, the wear of PTFE. In addition, the use of silicone grease strongly diminishes the gap between maximum and minimum friction coefficients and, then, the differences in the structural response between seismic and service conditions. On the other hand, the use of silicone grease increases the sensitivity to temperature variations of the mechanical behaviour of steel–PTFE sliding bearings. A mathematical model of the frictional behavior of steel–PTFE sliding interfaces has been presented, which takes into account the dependence of the frictional force on sliding velocity, contact pressure and air temperature. The proposed model describes the relationship between friction coefficient and sliding velocity through a logarithmic analytical law. The model is characterised by two parameters, which are analytically expressed as a function of contact pressure and air temperature, through a second-order polynomial equation. The accuracy of the proposed model in capturing the actual frictional behaviour of steel–PTFE sliding bearings has been verified by comparing the experimental and numerical force–displacement loops of non-lubricated and lubricated interfaces. It has been proved that the maximum frictional force provided by the model can be reliably used in the design of seismically isolated structures.
Acknowledgements The authors are indebted with Ing. Roberto Marnetto (TIS SpA), and Mr Domenico Nigro (University of Bailicata) which have cooperated in the setting up of the testing apparatus. This work has been partially funded by MIUR, COFIN 2002. References AASHTO – American Association of State Highway and Transportation Officials (1999) Guide Specifications for Seismic Isolation Design, 2nd Edition. American Association of State Highway and Transportation Officials, Washington, DC. CEN – Comit´e Europ´een de Normalisation. TC 167 “Structural bearings” (2000) EN 1337 “Structural bearings”, Part 2: Sliding elements, Brussel, Belgium. BS – British Standards Institution (1983) BS 5400: Steel, concrete and composite bridges, London, UK.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE
99
Computers and Structures Inc. (2002) SAP2000 Analysis Reference Manual, Version 8.0, Berkeley, CA. Constantinou, M.C., Caccese, J. and Harris, H.G. (1987) Friction characteristics of PTFE– steel interfaces under dynamic conditions. Earthquake Engineering and Structural Dynamics. 15(6), 751–759. Constantinou, M., Mokha, A. and Reinhorn, A.M. (1990) PTFE bearings in base isolation: modelling. Journal of Earthquake Engineering 116(2), 455–472. Chang J.C., Hwang J.S. and Lee G.C. (1990) Analytical model for sliding behaviour of Teflon-stainless steel interfaces. Journal of Engineering Mechanics 116, 2749–2763. Deb, S.K. and Paul, D.K. (2000) Seismic response of buildings isolated by sliding-elastomer bearings subjected to bi-directional motion. Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand. Dolce, M., Cardone, D. and Marnetto, R. (2000) Implementation and Testing of Passive Control Devices Based on Shape Memory Alloys. Earthquake Engineering and Structural Dynamics. (29), 945–958. Dolce, M. (2001) Remarkable design examples concerning recent applications of innovative anti-seismic techniques to bridges and viaducts in Europe. Proceedings of the 7th International Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Structures, Assisi, Italy. Fan, F.G., Ahmadi, G. and Tadjbakhsh, I.G. (1988) Base isolation of a multistory building under harmonic ground motion – A comparison of performances of various systems. Tech. Report NCEER-88-0010, National Center for Earthquake Engineering, State University of New York, Buffalo. Hwang, J.S., Chang, K.C. and Lee, G.C. (1990) Quasi-static and dynamic characteristics of PTFE-stainless interfaces. Journal of Structural Engineering 116(10), 2747–2762. Mokha, A., Constantinou, M. and Reinhorn, A.M. (1990) PTFE bearings in base isolation: testing. Journal of Earthquake Engineering 116(2), 438–454. Mokha, A., Constantinou, M., and Reinhorn, A.M. (1993) Verification of friction model of PTFE bearings under triaxial load. Journal of Structural Division, ASCE, 119(1), 240–261. Mostaghel, N. and Tanbakuchi, J.T. (1983) Response of Sliding Structures to Earthquake Support Motion. Earthquake Engineering and Structural Dynamics. 11, 729–748. Mostaghel, N. (1984) Resilient-Friction Base Isolator. Report No. UTEC 84/97, Department of Civil Engineering, University of Utah, Salt Like City, USA. Ordinanza del PCM No 3274/2003 (2003) Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica, Roma, Italy. SPSS Inc. (1999), SPSS Advanced models – Version 9.0, Chicago, Illinois. Takahashi Y., Iemura H., Yanagawa S. and Hibi M. (2004) Shaking table test for frictional isolated bridges and tribological numerical model of frictional isolator. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada. Tsopelas, P., Constantinou, M.C., Okamoto, S., Fuji, S. and Ozaki, D. (1996) Experimental study of bridge seismic sliding isolation system. Engineering Structures 18(4), 301–310. Tyler, R.G. (1977) Dynamic tests on PTFE sliding layers under earthquake conditions. Bulletin of the New Zealand National Society for Earthquake Engineering 10(3), 129–138. Wen, Y.K. (1976) Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanic Division, ASCE, 102 (EM2). Zayas, V., Low, S. and Mahin, S. (1987) The FPS earthquake protection system: experimental report. Report No. UCB/EERC-87/01, Earthquake Engineering Research Center, University of California, Berkeley.
