1 Experimental Program
1.1
Introduction
Single bearing characterization and stability tests were conducted to determine the mechanical
properties, material properties and stability curves for the four different types of elastomeric
bearings listed in Table 1-1. For the purpose of these tests, a new single bearing testing machine
(SBTM) was designed and constructed to meet the required force and displacement demands.
The tests were carried out in the Structural Engineering and Earthquake Simulation Laboratory
(SEESL) at the University at Buffalo. This chapter presents a description of the test program and
the experimental setup including the SBTM, instrumentation and data acquisition.
This chapter is organized into three sections as follows. Section 1.2 describes the elastomeric
bearings dimensions and properties. Section 1.3 presents the test program for the characterization
and stability tests. Section 1.4 describes the new single bearing testing machine (SBTM) that was
designed for the primary purpose of conducting the stability tests that can accommodate large
displacements (six to seven inches) and high axial loads up to 140 kips.
1.2
Description of Elastomeric Bearings
Table 1-1 lists the elastomeric bearings used for the stability and characterization test program.
As shown in Table 1-1 there are four different types of elastomeric bearings; three of them are
low damping rubber (LDR) and one of them is a lead rubber bearing (LR). The effective shear
modulus in Table 1-1 is the shear modulus at 100% shear strain in the rubber. Table 1-2 lists the
serial number that is used to identify each individual bearing. A total of nine elastomeric
bearings were tested, two for bearing Type 1, three for bearing Type 2, two for bearing Type 3
and two for bearing Type 4. Figure 1-1 thru Figure 1-4 present the as built dimensions for
bearing Type 1 thru bearing Type 4. Note that the only difference between bearing Type 1 and
Type 2 is the lead core of bearing Type 2.
Table 1-1 List of elastomeric bearings used in the test program
Bearing
Type 1
Low
Damping
Rubber
2
10.16
5.98
1.18
27.0
0.1180
0.1181
20
𝐷𝑒𝑠𝑐𝑟𝑖𝑝𝑡𝑖𝑜𝑛
Number of Bearings
𝑆ℎ𝑎𝑝𝑒 𝐹𝑎𝑐𝑡𝑜𝑟
𝐷𝑜 (𝑖𝑛)
𝐷𝑖 (𝑖𝑛)
𝐴 (𝑖𝑛2 )
𝐺𝑒𝑓𝑓 (𝑘𝑠𝑖)
𝑡𝑟 (𝑖𝑛)
𝑁𝑟 (#)
Bearing
Type 2
Lead
Rubber
3
12.17
5.98
1.18
28.1
0.1180
0.1181
20
Bearing
Type 3
Low
Damping
Rubber
2
10.64
6.5
1.18
37.4
0.075
0.125
25
Table 1-2 Bearing serial number list
Serial
Bearing
Bearing
Type 1
Type 2
11795
11772
Bearing
Type 3
Bearing
15180
LD-1
Type 4
Bearing
Type 4
Low
Damping
Rubber
2
5.51
5.51
0.0
25.9
0.109
0.25
12
Number
11808
11783
15196
LD-4
11792
Bearing Type 1, 2 and 4 are bearings previously used in different testing programs while bearing
Type 3 are new bearings obtained for this project. Bearing Type 1 and bearing Type 2 were first
used in the experimental studies conducted by Warn and Whittaker (2006). In these studies the
bearings were used in two different testing programs. First, under quasi-static tests, the bearings
were used to determine the influence of the lateral displacement on the vertical stiffness. In the
second test program, the bearings were used in the shake table to investigate the influence of the
coupled horizontal-vertical response on a scaled base isolated bridge model.
Bearing Type 4 was first used in the studies conducted by Kasalanati and Constantinou (1999).
In these studies the bearings were used in the shake table to investigate the response of a scaled
base isolated single span bridge model subjected to a near fault excitation. Since the current tests
are conducted ten years later, the opportunity exists to examine aging effects in the bearings.
Bearing Type 3 is a new bearing designed for the studies of the NEES Tips project. This project
includes two main experimental components at the University at Buffalo; (1) stability studies of
elastomeric bearings under quasi-static and dynamic conditions; (2) building shakes table studies
that will induce pounding against a moat wall and other limit states in seismically isolated
building. This thesis presents results from quasi-static experiments on the stability of elastomeric
bearings. Two of these Type 3 elastomeric bearings were dedicated for these studies and five
other identical bearings are reserved for future shake table studies.
Figure 1-1 Bearing Type 1 as built dimensions (Warn and Whittaker, 2006)
Figure 1-2 Bearing Type 2 as built dimensions (Warn and Whittaker, 2006)
Figure 1-3 Bearing Type 3 as built dimensions
Figure 1-4 Schematic of elastomeric bearing Type 4 (Kasalanati and Constantinou, 1999)
1.3
Test Program
The test program includes single bearing characterization test and two methods to evaluate
stability on seismic elastomeric bearings. The single bearing characterization testing program
was conducted to determine the mechanical properties and material properties of the four types
of elastomeric bearings presented in Table 1-1. Benchmark tests were conducted in between
stability test to monitor changes in bearing behavior. Stability test on the elastomeric bearings
were conducted at various shear deformations and axial forces to determine the stability curves
for each of the elastomeric bearings.
A total of nine elastomeric bearings were used for the stability tests. Each bearing is identified
with its corresponding serial number in Table 1-2. Each type of elastomeric bearing was
subjected to a particular characterization and stability test program presented in Table 1-3 thru
Table 1-10. The test program consisted of single bearing characterization test and two stability
methods named as Method 1 and Method 2. The test program sequence was as follows: first,
cyclic characterization tests were applied at different levels of shear strain, second stability
Method 2 was applied follow by stability Method 1. Benchmark unidirectional tests at 100%
shear strain with constant axial load were conducted throughout the program to monitor the
bearing mechanical properties.
Table 1-3, Table 1-5, Table 1-7 and Table 1-9 presents the characterization test program for
bearing type 1, 2, 3 and 4 respectively. The characterization tables present the following
information for each test: test number, test type, bearing type, preload 𝑃𝑜 , lateral offset Δ,
corresponding shear strain γ, frequency𝑓, data recording rate and number of cycles. Each
elastomeric bearing type has a unique characterization program.
For the stability test program each bearing was brought to the instability point at different values
of displacements and axial load. The stability tests program was organized such that the demand
on the bearing specimen increases through the program. Consequently the instability points were
plotted on a load versus lateral displacement graph to obtain the stability curve for each bearing.
For each elastomeric bearing two stability curves were obtained, a stability curve for Method
1and a stability curve for Method 2.
Table 1-4, Table 1-6, Table 1-8 and Table 1-10 presents the stability test program for bearing
type 1, 2, 3 and 4 respectively. In the test program, the characterization test is identified by the
letter A, Method 2 is identified by the letter B and Method 1 is identified by the letter C. For the
stability test program, the following information is presented: test number, test type, bearing
type, preload 𝑃𝑜 , lateral offset
, expected axial load 𝑃𝑒 , expected shear load 𝑉𝑒 , expected
displacement ∆𝑒 and the displacement rate. Expected forces and displacements correspond to the
forces and displacements at the predicted bearing instability point. These values were based on
the reduced area formulation to estimate the bearing critical load during the experiments.
1.3.1 Characterization Test
Unidirectional shear test with constant axial load were conducted to measure the shear force
response of the elastomeric bearings. Characterization test were conducted at varying strain
amplitudes and frequencies to estimate bearing mechanical properties including: shear modulus,
effective damping, dissipated energy and lead yield strength (lead rubber bearing only). A
benchmark characterization test at 100% shear strain was repeated throughout the test program to
monitor any possible degradation on the elastomeric bearing mechanical properties. Figure 1-5
shows the imposed displacements signal consisting of four cycles at constant amplitude.
Figure 1-5 Characterization test displacements signal (Warn et al., 2006)
1.3.2 Stability Test Method 1
Quasi-static stability tests were conducted to measure the critical load of the elastomeric bearings
at a constant displacement with fixed ends condition. A predetermined initial displacement is
applied and held starting from zero axial load. The axial load is increased monotonically until the
horizontal force (shear force, 𝐹𝐻 = 0) became zero or negative on the elastomeric bearing. For
this method, constant shear curves are develop to establish the instability point. This procedure is
based on a previous work by Nagarajaiah, et al. (1999). The elastomeric bearing is considered
unstable at the point where the rate of shear force with respect to the horizontal displacement is
𝑑𝐹
equal to zero ( 𝐾𝐻 = 𝑑𝑢𝐻 = 0). Figure 1-6, shows a schematic representation for the stability test
𝐻
Method 1.
P
u
Axial
Force
METHOD 1:
STEP 1
P
METHOD 2:
UH
STEP 2
P
Figure 1-6 Schematic u
representation for the stability test Method 1
Step by step procedure for stability test Method 1:
STEP 1
Shear
Force
STEP 2
I - Experimental part:
UH
METHOD 3:
1. A set of constant lateral displacements values are predefined were stability is desired prior to
the start of the test program.
2. Apply an initial lateral displacement to the elastomeric bearing with a zero axial load.
3. Apply the axial load and increase it until the elastomeric bearing shear force is reduced to
zero. A real time display of the measured shear force in the elastomeric bearing is required to
determine when the test will be stop. The test is terminated when the shear force reduces to
zero.
4. Repeat steps step 2 and 3 for all the selected lateral displacement values.
II - Data Processing:
5. A set of shear force values must be defined were stability is desired prior to processing the
data. (For the experiments in this thesis, an initial shear force of 0.5 kips was selected with
increments of shear force of 0.5 kips). The maximum value of shear force depends on the
tested bearing and the maximum lateral displacement applied. A larger number of selected
shear force values results in a better defined stability curve.
6. Plot axial load versus lateral displacement for selected values of shear force from each lateral
displacement test. These values of axial load for corresponding shear force are the
experimental results from each constant lateral displacement test.
7. Combine the results from all the lateral displacement test by combing the points with the same
shear value. A polynomial regression can be used to obtain the constant shear curve.
8. Find the maximum point for each constant curve by taking the derivative of each constant
shear curve (polynomial function). The maximum point is where the shear stiffness is zero (
𝑑𝐹
𝐾𝐻 = 𝑑𝑢𝐻 = 0) or point of instability for a corresponding axial force and a corresponding
𝐻
lateral displacement.
9. Plot the instability point in a plot of critical load versus lateral displacement.
10. Repeat steps 7 and 8 to obtain the critical load for all the constant shear curves from step.
1.3.3 Stability Test Method 2:
Quasi-static stability test were conducted to measure the critical load of the elastomeric bearing
at a constant axial load with fixed ends condition. A predetermined initial axial load is applied
and held constant while the horizontal displacement is increased monotonically until the rate of
𝑑𝐹
change of the shear force with respect to the horizontal displacement ( 𝐾𝐻 = 𝑑𝑢𝐻 = 0) or
𝐻
horizontal stiffness, reduce to zero. At the point of zero horizontal stiffness the bearing is
considered to have reached the critical load or instability point as it cannot sustain additional
load. Figure 1-7, shows a schematic representation for the stability test Method 2.
Figure 1-7 Schematic representation for the stability test Method 2
Step by step procedure for stability test Method 2:
I - Experimental part:
1. A set of constant axial load values must be defined were stability is desired prior start the test
program.
2. Apply the selected axial load.
3. From zero lateral displacement apply the lateral displacement until the elastomeric bearing
shear force shows a negative stiffness or reduction in shear force as the bearing is displaced
laterally. A real time display of the measured shear force in the elastomeric bearing is required
to determine when the test will be stopped and the axial load removed.
4. Repeat step 2 and 3 for all the selected lateral displacement values.
II - Data processing:
5. The point of maximum shear force is required from each test. The maximum point is where
𝑑𝐹
the shear stiffness is zero ( 𝐾𝐻 = 𝑑𝑢𝐻 = 0) or point of instability for a corresponding axial
𝐻
force and a corresponding lateral displacement.
6. Plot the instability point in a plot of critical load versus lateral displacement.
7. Repeat steps 5 and 6 to obtain the critical load for all tests.
Table 1-3 Bearing Type 1 characterization program
Test
1
2
3
4
5
6
Bearing
Test Type
Type
A
A
A
A
A
A
1
1
1
1
1
1
Preload
Po (kip)
13.5
13.5
13.5
13.5
13.5
13.5
Lateral
Offset
Δ (in)
± 0.59
± 1.18
± 2.36
± 3.54
± 4.72
± 2.36
Shear
Strain
δ (%)
25
50
100
150
200
100
Frequency
f (Hz)
0.01
0.01
0.01
0.01
0.01
0.10
Sampling
Rate
Rate (Hz)
1
1
1
1
1
10
No. of
Cycles
Expected
Displ.
Δe (in)
-
Displ.
Rate
(in/s)
0.0472
0.0472
5.92
0.0472
0.0472
5.58
5.24
0.0472
0.0472
4.9
4.56
0.0472
0.0472
3.87
3.19
0.0472
0.0472
2.5
0.0472
-
-
-
-
3
3
3
3
3
3
Table 1-4 Bearing Type 1 stability test program
Test
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Bearing
Test Type
Type
B
B
A
B
B
A
B
B
A
B
B
A
B
B
A
B
A
C
C
C
A
C
C
C
C
A
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Notes:
A = Characterization Test
B = Stability Test – Method 2
C = Stability Test – Method 1
Preload
Po (kip)
0
15
20
30
35
40
45
50
60
70
80
-
Lateral
Expected
Expected
Offset Axial Load Shear Load
Δmax (in)
Pe (kip)
Ve (kip)
3.54
3.54
Characterization (Test 6)
3.54
6.5
6.7
Characterization (Test 6)
6.5
5.9
6.5
5.2
Characterization (Test 6)
6.5
4.36
6.5
3.56
Characterization (Test 6)
6.5
2.05
6.5
0.76
Characterization (Test 6)
6.5
0.25
Characterization (Test 6)
1
66
2
49
3
33
Characterization (Test 6)
4
18
5
7
6
0
6.5
0
Characterization (Test 6)
Table 1-5 Bearing Type 2 characterization program
Test
1
2
3
4
5
6
Bearing
Test Type
Type
A
A
A
A
A
A
2
2
2
2
2
2
Preload
Po (kip)
13.5
13.5
13.5
13.5
13.5
13.5
Lateral
Offset
Δ (in)
± 0.59
± 1.18
± 2.36
± 3.54
± 4.72
± 2.36
Shear
Strain
δ (%)
25
50
100
150
200
100
Frequency
f (Hz)
0.01
0.01
0.01
0.01
0.01
0.10
Sampling
Rate
Rate (Hz)
1
1
1
1
1
10
No. of
Cycles
Expected
Displ.
Δe (in)
5.92
Displ.
Rate
(in/s)
0.0472
0.0472
0.0472
5.24
4.56
0.0472
0.0472
3.87
3.19
0.0472
0.0472
2.5
-
0.0472
-
0.0472
-
-
-
-
3
3
3
3
3
3
Table 1-6 Bearing Type 2 stability test program
Test
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Bearing
Test Type
Type
B
B
B
A
B
B
A
B
B
A
B
B
A
B
A
C
C
C
A
C
C
C
C
A
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Notes:
A = Characterization Test
B = Stability Test – Method 2
C = Stability Test – Method 1
Preload
Po (kip)
0
20
30
40
50
60
70
80
90
100
-
Lateral
Expected
Expected
Offset Axial Load Shear Load
Δmax (in)
Pe (kip)
Ve (kip)
3.54
3.54
6.5
6.7
Characterization (Test 6)
6.5
5.2
6.5
3.56
Characterization (Test 6)
6.5
2.05
6.5
0.76
Characterization (Test 6)
6.5
0
6.5
Characterization (Test 6)
6.5
Characterization (Test 6)
1
92
2
67
3
46
Characterization (Test 6)
4
26
5
9
6
0
6.5
0
Characterization (Test 6)
Table 1-7 Bearing Type 3 characterization program
Test
1
2
3
4
5
6
7
Bearing
Test Type
Type
A
A
A
A
A
A
A
3
3
3
3
3
3
3
Preload
Po (kip)
12.0
12.0
12.0
12.0
12.0
12.0
12.0
Lateral
Offset
Δ (in)
± 0.78
± 0.78
± 1.56
± 1.56
± 3.13
± 4.69
± 3.13
Shear
Strain
δ (%)
25
25
50
50
100
150
100
Frequency
f (Hz)
0.01
1.00
0.01
1.00
0.01
0.01
0.10
Sampling
Rate
Rate (Hz)
1
100
1
100
1
1
10
No. of
Cycles
3
3
3
3
3
3
3
Table 1-8 Bearing Type 3 stability test program
Test
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Test
Type
B
B
B
A
B
B
A
B
B
A
C
C
C
A
C
C
C
C
A
Bearing
Type
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
Notes:
A = Characterization Test
B = Stability Test – Method 2
C = Stability Test – Method 1
Preload
Po (kip)
0
10
20
30
40
50
60
-
Expected
Axial
Load
Expected
Shear
Load
Lateral
Offset
Δmax
(in)
Pe (kip)
Ve (kip)
5.25
5.25
7.0
1.98
Characterization (Test 7)
7.0
0.96
7.0
0.18
Characterization (Test 7)
7.0
0.00
7.0
0.00
Characterization (Test 7)
1
39
2
30
3
21
Characterization (Test 7)
4
13
5
6
6
1
7
0
Characterization (Test 7)
Expected
Displ.
Displ.
Rate
Δe (in)
3.00
(in/s)
0.063
0.063
0.063
2.00
0.75
0.063
0.063
0.00
0.00
0.063
0.063
-
-
-
-
Table 1-9 Bearing Type 4 characterization program
Test
1
2
3
4
5
6
7
8
9
Bearing
Test Type
Type
A
A
A
A
A
A
A
A
A
4
4
4
4
4
4
4
4
4
Preload
Po (kip)
7.9
7.9
7.9
7.9
7.9
7.9
7.9
7.9
7.9
Lateral
Offset
Δ (in)
± 1.05
± 2.07
± 3.09
± 4.5
± 1.05
± 2.07
± 3.09
± 4.5
± 3.09
Shear
Strain
δ (%)
35
69
103
150
35
69
103
150
103
Frequency
f (Hz)
0.01
0.01
0.01
0.01
0.5
0.5
0.5
0.5
0.1
Sampling
Rate
Rate (Hz)
1
1
1
1
50
50
50
50
10
No. of
Cycles
Expected
Displ.
Δe (in)
3.00
2.25
Displ.
Rate
(in/s)
0.06
0.06
0.06
0.06
1.25
0.75
0.06
0.06
0
-
0.06
0.06
-
-
-
-
3
3
3
3
3
3
3
3
3
Table 1-10 Bearing Type 4 stability test program
Test
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Bearing
Test Type
Type
B
B
B
B
A
B
B
A
B
B
A
C
C
C
A
C
C
C
C
A
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Notes:
A = Characterization Test
B = Stability Test – Method 2
C = Stability Test – Method 1
Preload
Po (kip)
0
5
10
15
20
25
30
35
-
Lateral
Expected
Expected
Offset Axial Load Shear Load
Δmax (in)
Pe (kip)
Ve (kip)
4.50
4.50
6.0
2.49
6.0
1.55
Characterization (Test 9)
6.0
0.63
6.0
0.19
Characterization (Test 9)
6.0
0
6.0
Characterization (Test 9)
1
32
2
23
3
14
Characterization (Test 9)
4
7
5
1
6
0
6.25
0
Characterization (Test 9)
1.4
Single Bearing Testing Machine
1.4.1 General
A new single bearing testing machine (SBTM) was designed for the primary purpose of
conducting stability tests on single seismic isolation elastomeric bearings. This machine was
designed to accommodate lateral displacements and axial loads required for the stability tests.
The machine consists of six main components: a steel reaction frame for the vertical actuators, a
loading beam, two 70 kips axial capacity Parker actuators for axial loading, one 50 kips axial
capacity MTS actuator for shear loading and two 5-channel reaction load cells. Figure 1-8 shows
the schematic of the single bearing machine including general dimensions and the steel sections
used. A detailed description of the SBTM is provided in Appendix C.
The vertical reaction frame of the SBTM is composed of a W 14 x 74 steel beam and four HSS
6” x 6” x ½” steel columns with steel rockers at both ends. A total of twelve steel rockers were
used on the SBTM, eight rockers were used to connect the W14 x 74 to the steel columns and the
columns to the steel base plate. Four pins were dedicated to the vertical actuators to allow the
transfer of vertical load only as the SBTM is displaced. A lateral brace in the middle of the
SBTM ensures that the top and bottom beam move together in the horizontal direction but
without any constraint in the vertical direction to avoid the transfer of load. The vertical degree
of freedom in the lateral brace was achieved by the use of two concentric tubes of different
diameters. An external tube is connected to the top beam while an internal tube is connected to
the bottom beam. The vertical actuators have rockers at both ends to ensure that the top and
bottom beam move parallel without transferring any horizontal load to the specimen under test.
The bottom beam (W12 x 79) connects the two vertical actuators on its top and the bearing
specimen under test the beam in the vertical direction. In the horizontal direction, the lower beam
is connected to the horizontal actuator. Below the bottom beam (W12 x 79) a transfer plate
connects the beam to the elastomeric bearing and two transfer plates below the elastomeric
bearings were used to connect to the two loads cells. Two five-component load cells were
required for the expected shear forces in the bearings. The five-component load cells were used
to determine the stability limits of the elastomeric bearings from combined measured shear force
of the two load cells. Two transfer plates were used to accommodate the required bearing height
to connect to the bottom beam.
Compared to previous SBTM, this setup maintains the vertical actuators vertical at all times. It
was found that this test setup give better control of the applied forces on the bearing. Figure 1-9
presents a photograph of the SBTM as assembled on the Structural Engineering and Earthquake
Simulation Laboratory.
Figure 1-8 Single bearing testing machine (SBTM)
Test Direction
Direction
Actuator
Vertical
Actuators
Bearing
Load Cells
Bearing
Figure 1-9 Photograph of single bearing testing machine (SBTM)
1.4.2 Capabilities
The SBTM is capable of imposing controlled unidirectional shear and axial load on the bearings.
The capabilities of the actuators in terms of stroke, peak velocity and peak force are listed in
Table 1-11. The bearing machine capacity is limited mainly by the maximum force of the
vertical actuators which can apply a combined axial load of 140 kips. The steel sections of the
SBTM were sized for the combined full capacity of both vertical actuators as part of a previous
experimental setup.
Table 1-11 Single bearing testing machine actuator capabilities
Actuator
(Serial No.)
Stroke
(in)
Velocity
(in/s)
Force
(kips)
Horizontal
± 12
2.95
55
±2
2.48
70
±2
2.48
70
(MTS-244.31)
Vertical East
(Parker-1C2HLT18)
Vertical West
(Parker-1C2HLT18)
1.4.3 Instrumentation and Data Acquisition
A total of twenty one data channels recorded the forces and displacements during the elastomeric
bearing characterization and stability tests. This channels collected data from four main
components, one horizontal actuator, two vertical actuators, two five-component load cells and
four linear potentiometers. Figure 1-10 presents the location of the instrumentation used to
measure the forces and displacements in the SBTM. Table 1-12 shows the lists of instruments
used during the experiments and the corresponding channel number. Table 1-12, X-direction
label and Y-direction label are used to identify the measurements taken in-plane and the out-of-
plane direction. Out-of-plane measurements were taken to monitor the performance of the test
setup.
Figure 1-10 Instrumentation Diagram
Table 1-12 Instrumentation channel list
Channel
Instrument
Quantity
ID
1
Channel
Instrument
Quantity
West
Moment - Y
ID
-
Time (sec)
12
Load Cell
2
3
4
5
Horizontal
Actuator
Horizontal
13
Displacement
Horizontal
Actuator
Horizontal
West
Vertical
Actuator
Displacement
West
Vertical
14
Force
East
Axial
Load Cell
Force
East
Shear - X
Load Cell
15
East
Moment - X
Load Cell
16
East
Shear - Y
6
7
8
9
Actuator
Force
East
Vertical
Actuator
Displacement
East
Vertical
Actuator
Force
West
Axial
Load Cell
Force
West
Shear - X
Load Cell
17
West
Moment - X
18
19
20
11
West
21
Linear
Bearing Horizontal
Potentiometer
1
Displacement
Linear
Bearing Vertical
Potentiometer
2
Displacement
Linear
Bearing Vertical
Potentiometer
3
Displacement
Linear
Bearing Out of
Plane
Potentiometer
4
Load Cell
Moment - Y
Load Cell
Load Cell
10
East
Displacement
Shear - Y
Load Cell
The SBTM and instrumentation arrangement was as follows. One horizontal MTS 244.31
actuator contains an in-line uni-axial load cell and an internal linear variable transducer (LVDT)
recording axial load and relative displacement. This actuator was operated under displacement
control to apply a desired shear deformation. Two vertical Parker actuators model 1C2HLT18
contain an in line uni-axial load cell and a Tempsonic displacement transducer recording axial
load and relative displacement, respectively. This pair of actuators applied a desired axial load on
the bearing. The vertical actuators were arranged as follows: the west actuator was working
under load control mode and served as the master actuator while the east actuator working under
displacement control mode acted as the slave actuator to keep the loading beam horizontal. The
input displacement command for the east actuator was the measured displacement of the west
actuator. The two five-component load cells worked in parallel, recording axial (N), shear (Sx
and Sy) and moment (Mx and My). Two load cells were required for measuring the expected
large forces during the stability tests. The limits for the load cells were obtained from the
Structural Engineering and Earthquake Simulation Laboratory data sheets for the loads cells that
depend on the combined axial, shear and moment applied. Four linear potentiometers (string
pots) were used. One linear potentiometer recorded the horizontal relative displacement of the
bearing, two recorded the relative vertical displacement of the bearing and one recorded the out
of plane relative displacement for quality control of the tests.
A schematic diagram of the single bearing testing machine (SBTM) control and data acquisition
system is presented in Figure 1-11. This diagram presents the individual components and
connectivity of the SBTM. In this diagram, the data flows from top down. The external power
supply lines are dotted lines whereas data lines are solid. Starting from top left to right, the first
component represents the the horizontal actuator (MTS244.31). The horizontal actuator has its
own power supply and the collected data is send to the Vishay A2 for filtering and stored in the
Megadac.
The next two other components in Figure 1-11 are the west and east Parker actuators (vertical
actuators). The west actuator was under load control while the east actuator was under
displacement control. The east actuactor under displacment control was configured to monitor
the displacement of the west actuator in order that the bottom beam remains horizontally at all
times. The power supply and data from the vertical actuators is managed by the MTS STS
controller. The vertical displacement on the vertical actuators was measured with a external MTS
Tempsonic displacement transducers. The power supply for this gages was provided by a
external Tempsonic power supply as illustred in Figure 1-11. The excitation voltage and data
collected from the five-component load cells and the four linear potentionmeters were managed
by the Vishay A2 conditioning rack. All data is stored at the Megadac and a Dell Dimension
computer was used to access the information collected by the Megadac.
Figure 1-11 Single bearing test machine data acquisition diagram
Figure 1-12 presents a schematic illustration of the single bearing testing machine (SBTM). This
figure shows how the vertical actuators (Parker 1C2HLT18) force contributes a horizontal force (
𝐹(𝑢) ) that is exerted against the horizontal actuator (MTS 244.31). The force measured by the
actuator load cell includes this component in addition to the shear force in the bearing. The
resistance force caused by the vertical actuators was estimated by equilibrium of forces at the
joint between the columns and the top beam solving for the horizontal component.
Figure 1-12 Contribution of vertical actuators to horizontal force in control channel 2
(Horizontal actuator)
For small displacements the resistance named as 𝐹(𝑢) is estimated as follows:
Assuming a small angle,
𝜃≈
𝑢
𝑙
(1.1)
𝐹(𝑢)
𝑃
(1.2)
The resistance force is estimated as:
sin 𝜃 =
From equation 1.1 and 1.2:
1
𝐹(𝑢) = 𝑃𝑢
𝑙
(1.3)
Since the horizontal actuator can apply relatively large displacement a more precise non-linear
analysis is also considered. For large displacements the resistance force 𝐹(𝑢) is estimated as
follows:
sin θ =
𝑢
ℎ
θ = tan−1
(1.4)
𝑢
(1.5)
√ℎ2 + 𝑢2
From equation 1.2, 1.4 and 1.5:
𝐹(𝑢) = 𝑃 sin [tan−1
𝑢
√ℎ2 + 𝑢2
]
(1.6)
Equation 1.3 and 1.6 estimate the correction for the horizontal actuator assuming linear and large
nonlinear displacements in the horizontal actuator. The resistance force comes from the
combined effect of the vertical axial load on the actuators and the displaced frame by an amount
(𝑢) specified by the user. Figure 1-13 presents the linear and non-linear estimated resistance
shear force ( 𝐹(𝑢) ) for the horizontal actuator obtained for a range of displacements from one to
twelve inches (the actuator capacity) and a unitary load. A difference between the estimated
force for small displacements and large displacements was observed after a displacement of nine
inches. For any given axial load (𝑃) and a specified horizontal displacement (𝑢) the linear
relation 𝐹(𝑢) = 1⁄𝑙 (𝑃𝑢) should be used to estimate the resistance force while for large
𝑢
displacements displacement (above 11 inches) the relation 𝐹(𝑢) = 𝑃 sin [tan−1 √ℎ2
+𝑢2
] should
be used to estimate the resistance force if high accuracy is desired. A difference of 1% is
expected between the linear and nonlinear relation for a corresponding displacement of 11inches.
The estimated resistance force 𝐹(𝑢) should be use to correct the measured force from the
horizontal actuator.
Shear Force - F[u] (kip)
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
Small displacements
Large displacements
0.02
0.00
0
1
2
3
4
5
6
7
8
9
10 11
12 13
Horizontal Displacement (in)
Figure 1-13 Shear force versus horizontal displacement calibration plot for horizontal
actuator
The SBTM includes redundant instrumentation for measured values of interest, particularly
between the load cells in the actuators and the five-component load cells under the bearings.
Although the uni-axial load cells in the actuators can be much more reliable since they do not
have the interaction of various force components, the horizontal actuator here was working only
within 10% of its range. In this case, the level of noise in the force measurements may be
relatively high. In addition, the vertical actuator load cell may also include forces transferred
from the loading beams. The comparison of forces measured at the actuators and load cells under
the bearings is further investigated.
Figure 1-14 and Figure 1-15 presents the SBTM machine performance for characterization test
number seven with a corresponding axial load of twelve kips and a frequency of 𝑓=0.10 Hz for
bearing Type 3. Figure 1-14a presents the axial load as measured by the load cells in the vertical
actuators and the two five-component load cells. A maximum error of five percent was observed
between the two load cells. In the analysis presented in this thesis, the axial loads measured by
the five-component load cells are used.
Figure 1-14b presents the shear force comparison between the applied load by the horizontal
actuator and the measured shear force by the two five-component load cells and the corrected
shear force by utilizing equation 1.6. A maximum error of fifteen percent was observed between
the measured horizontal actuator force and that measured load by the two five-component load
cells. An error of sixteen percent was observed between the applied axial load by the corrected
shear force in the horizontal actuator force and that measured load by the two five-component
load cells. For most part of the characterization test, the corrected shear force predicts well the
shear force measured by the load cell with the exception of the points of maximum displacement.
Further evaluation of the machine measured forces and comparison with the corrected shear
force is recommended to better estimate the shear forces at large displacements.
Figure 1-15a, presents the comparison between the measured displacement from the horizontal
actuator and the linear potentiometer used as a redundant measurement. Figure 1-15b presents
the out-of-plane displacement of the bottom beam (W12x79) of the SBTM. The out-of-plane
maximum displacement was relatively small with a maximum displacement of 0.013 inches,
based on this measured displacement it can be considered that the beam remains essentially inplane.
14
Axial Load (kip)
13
12
11
10
9
Vertical actuator load cell
8
Load cell - axial load measurement
7
0
10
20
30
40
30
40
Time (s)
a. Axial load comparison
3
Shear Force (kip)
2
1
0
0
10
20
-1
-2
-3
-4
Horizontal actuator load cell
Load cell - shear force measurement
Corrected value
Time (s)
b. Shear force comparison
Figure 1-14 SBTM performance under characterization for bearing Type 3, test 7 at 𝑃 =
12 𝑘𝑖𝑝, 𝑓=0.10 Hz (Bearing type 3 - 15180)
Lateral Displacement (in)
4
3
2
1
0
0
10
20
30
40
-1
-2
-3
-4
Horizontal actuator displacement
Linear Potentiometer
Time (s)
a. Lateral displacement comparison
Out of Plane Displ. (in)
0.15
0.10
0.05
0.00
0
10
20
30
40
-0.05
-0.10
Out of plane displacement
-0.15
Time (s)
b. Out of plane displacement
Figure 1-15 SBTM performance under characterization for bearing Type 3, test 7 at 𝑃 =
12 𝑘𝑖𝑝, 𝑓=0.10 Hz (Bearing type 3 – 15180)