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Design, manufacturing and evaluation of the performance of steel like fiber reinforced elastomeric seismic isolators
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 1 9 7 ( 2 0 0 8 ) 140–150
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Design, manufacturing and evaluation of the performance of steel like fiber reinforced elastomeric seismic isolators Ghasem Dehghani Ashkezari a , Ali Akbar Aghakouchak a,∗ , Mehrdad Kokabi b a b
Structural Engineering Division, Faculty of Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran Polymer Engineering Division, Faculty of Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this research, specimens of fiber reinforced elastomeric seismic isolators have been
Received 21 November 2006
designed, manufactured and their dynamic and mechanical characteristics have then been
Received in revised form
studied by performing vertical and horizontal (compression–shear) tests. For the sake of
17 May 2007
comparison, one steel reinforced elastomeric isolator specimen has also been designed,
Accepted 2 June 2007
manufactured and subjected to similar tests. In design of fiber reinforced isolators, the tensile and bending flexibility of the fiber cords reinforcement have been considered. Results of the experiments show that the behavior of the fiber reinforced elastomeric isolators
Keywords:
is very similar to that of the steel reinforced specimen with regard to shear deformation
Seismic isolation
and dynamic and mechanical characteristics including vertical stiffness, effective horizon-
Fiber reinforced elastomeric isolator
tal stiffness and damping. Therefore, this type of fiber reinforced isolator which has been
Vertical test
named “steel like fiber reinforced elastomeric isolators” (SLFREI) can be used in seismic
Horizontal test
isolation of structures. The advantages of SLFREI are that they are lighter and simpler to manufacture, compared to steel reinforced elastomeric isolators. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Seismic base isolation is a valuable earthquake-resistant technique for structures such as buildings and bridges. As a result of isolation, the fundamental horizontal period of structure is increased to a value away from the dominant range of periods of earthquakes. Therefore, the earthquake energy transmitted to the structure is decreased considerably. This is achieved by installing isolators which have low horizontal, but high vertical and bending stiffnesses beneath superstructure. Current systems for seismic isolation of structures usually include two types, i.e. steel reinforced multilayer elastomeric and sliding bearings. Systems that combine elastomeric and sliding bearings have also been proposed and implemented. To date many studies have been performed regarding the performance of these systems and quite a number of structures
∗
Corresponding author. E-mail address: a [email protected] (A.A. Aghakouchak). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.06.023
have been seismically isolated using these systems in different parts of the world. These structures mainly include large bridges and important buildings that contain sensitive or expensive equipment. The isolators used for this purpose are normally heavy and expensive. A few studies have also been performed on the use of steel reinforced elastomeric isolators in common residential buildings. They include design and construction of demonstration buildings such as a threestory building in Italy, a four-story one in Chile, an eight-story one in China and a four-story one in Indonesia (Taniwangsa and Kelly, 1996; Kelly, 1996). In order to apply seismic isolation for common buildings and public housing, the cost and weight of isolators must be reduced. Cost of isolators is mainly due to the process of preparing steel plates and bonding them to rubber layers. Weight of isolators is also mainly due to the same plates.
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Kelly (Kelly, 1999) suggested that both the weight and cost of isolators can be reduced by eliminating the steel reinforcing plates and replacing them with fiber reinforcement of high elastic stiffness. By introducing some fiber reinforced isolator specimens, he showed that these isolators can provide tilting and vertical stiffness in the range of steel reinforced isolators with the same diameter and the same thickness of rubber. The shear stiffness and equivalent viscous damping of the fiber reinforced specimens were about 80% and 180% of similar values for the steel reinforced isolators, respectively. Steel reinforcing plates are assumed to be rigid both in tension and bending; but fiber cords reinforcement, which are made up of many individual fibers, are more flexible in tension compared to individual fibers and completely lack bending stiffness. Moon et al. (Moon et al., 2002) designed and manufactured some specimens of fiber reinforced multilayer elastomeric isolator using different kinds of fibers such as carbon, glass, nylon and polyester. They carried out experiments to determine their mechanical characteristics and to evaluate the performance of the specimens. They also compared the mechanical characteristics of the carbon fiber reinforced isolator with a similar steel reinforced isolator. Experiments showed that performance of the carbon fiber reinforced isolator was even superior to that of the steel reinforced isolator in view of vertical stiffness and effective damping. They concluded that fiber reinforced isolators can replace steel reinforced isolators. Vertical stiffness, shear stiffness and equivalent viscous damping of the carbon fiber reinforced isolator were 299%, 94% and 256% of those of the steel reinforced isolator, respectively. In steel reinforced isolators, introduction of one or more lead plugs that are inserted into holes results in additional damping. In order to investigate the effect of hole and lead plug in fiber reinforced elastomeric isolators, Kang et al. (Kang et al., 2003) carried out vertical and horizontal tests on carbon fiber reinforced isolator specimens with and without hole and lead plug. They concluded that the hole and lead plug in fiber reinforced elastomeric isolator have little effect on effective stiffness and effective damping. Fig. 1(a) and (b) shows models of fiber and steel reinforced elastomeric isolators, respectively (Kang et al., 2003). Tsai (Tsai, 2004) derived closed form solutions for compression stiffness of the laminated elastomeric bearings of infinite-strip shape with flexible reinforcements. He considered the effect of bulk compressibility in the elastomer layer and the effect of boundary condition at the ends of the bearing. The behavior of elastomer and reinforcement layers was considered as linear elastic. He compared the theoretical solution with the results of finite element analysis. Tsai and Kelly (Tsai and Kelly, 2005) presented a beam theory to analyze the buckling load of the elastomeric multilayer isolators reinforced by thin and flexible steel plates. This theory is the extension of Haringx theory and considers the shear deformation and warping of cross-sections. The behavior of elastomer and steel reinforcement layers is considered as linear elastic. The elastomer is also assumed to be incompressible. In this research, some fiber reinforced elastomeric isolator specimens have been designed and manufactured. Their mechanical characteristics are investigated by performing ver-
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Fig. 1 – Models of elastomeric isolators: (a) fiber reinforced and (b) steel reinforced.
tical and cyclic horizontal tests. For the sake of comparison, one steel reinforced elastomeric isolator specimen has also been designed, manufactured and tested in similar conditions.
2.
Description of isolator specimens
Three carbon fiber reinforced elastomeric isolator specimens and one steel reinforced elastomeric isolator specimen have been designed and manufactured. Horizontal dimensions of all specimens have been considered exactly equal and total thickness of rubber in all specimens has also been selected nearly equal. In order to investigate the effect of the number of rubber and fiber layers in isolators and the shape factor of elastomer layers, these parameters have been varied in three fiber reinforced specimens. All specimens have steel top and bottom end plates in which four threaded holes have been considered. These holes are to be used to connect the specimens to test apparatus. Characteristics of the specimens are presented in Table 1. The fiber reinforced specimen number 3 and steel reinforced specimen are shown in Fig. 2(a) and (b).
3.
Design method and manufacture process
Design of the fiber reinforced isolator specimens has been carried out based on UBC-97 (ICBO, 1997) assuming certain parameters and according to the current method of design of the steel reinforced multilayered elastomeric seismic isolators (Naeim and Kelly, 1999; Kelly, 1997). However, the tensile and bending flexibility of the fiber cords have been taken into account using the effective parameters introduced by Kelly (Kelly, 1999), Tsai (Tsai, 2004) and Tsai and Kelly (Tsai and Kelly, 2005).
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Table 1 – Characteristics of the isolator specimens Specimen
Fiber reinforced no. 1 Fiber reinforced no. 2 Fiber reinforced no. 3 Steel reinforced
Horizontal dimensions of isolator (mm × mm) 150 × 150 150 × 150 150 × 150 150 × 150
tr (mm)
41.5 40.2 44.3 43.7
Horizontal dimensions of reinforcement layers (mm × mm) 145 × 145 145 × 145 145 × 145 145 × 145
nr
nf,s
t (mm)
tf,s (mm)
16 24 47 16
15 23 46 15
2.59 1.68 0.94 2.73
0.25 0.25 0.25 1.0
tT and B Plates (mm)
9.8 9.8 9.8 9.8
s
14.46 22.4 39.8 13.75
tr : total thickness of rubber in the isolator; nr : number of rubber layers in the isolator; nf,s : number of fiber or steel reinforcement layers in the isolator; t: thickness of each rubber layer in the isolator; tf,s : thickness of each layer of fiber or steel reinforcement in the isolator; tT and B plates : thickness of steel top and bottom end plates in the isolator; s: shape factor of elastomer layers in the isolator, i.e. the ratio of loaded area to force-free area.
In order to compare the behavior of the fiber reinforced isolator specimens with the steel reinforced ones, a steel reinforced isolator specimen has also been manufactured. In this isolator horizontal cross section and total thickness of rubber are the same as those of the fiber reinforced isolators and the number of rubber layers is equal to that of one of the fiber reinforced isolators (specimen no. 1). Due to limitations of the test rigs, the isolator specimens have been manufactured with the scale of 1/4. To manufacture the fiber reinforced isolators, initially the woven fiber warps and wefts are completely impregnated by adhesive. The raw rubber compound which has been filled
with carbon black, is also formed as sheets with desired thickness. The fiber layers and raw rubber sheets are then cut to desired dimensions and set in the mold. The woven fiber in which the directions of warps and wefts are perpendicular, is cut and set in the mold, in a way that the directions of warps and wefts of fiber layers relative to horizontal dimensions of isolator are 0/90 and +45/−45, alternatively. The steel top and bottom end plates, which have been prepared, are also set in their place in the mold. The layers and components in the mold are then subjected to a suitable pressure and temperature for a suitable period of time. The suitable temperature and time depend on the required temperature and time for the vulcanization of the rubber and the adhesive and also dimensions and volume of the specimen. The required temperature and time for the vulcanization of the rubber that depend on the curing system of the rubber compound, are obtained by performing the reological test according to the standard ASTM D2084-81. The greater the dimensions, the longer time is required to vulcanize the specimen at a certain temperature. This longer time ensures proper curing of the internal layers with lower temperatures. In this research, the specimens were shaped by compression molding at 120 ◦ C temperature and 110 min time. The pressure was needed to push the extra rubber out of the mold’s gap. The amount of the required pressure depends on the dimensions of the specimen and the mold. In this research, a pressure and heat machine was used that can impose a maximum compressive force of 300 kN.
4.
Evaluation of performance of isolators
In order to study the performance of the isolators, vertical tests and dynamic cyclic horizontal tests have been carried out.
4.1.
Vertical tests
Vertical tests have been performed on the isolator specimens to determine the vertical stiffness and effective compression modulus.
4.1.1. Fig. 2 – Some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Description of the vertical test machine
Vertical tests have been performed by dynamic tension and pressure test machine in International Institute of Earthquake Engineering and Seismology. In this machine, the specimen is
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Table 2 – Values of load in vertical tests Test number
P (kN)
1 2
67 135
P (kN) ±20 ±35
set between two grips. While the top grip is fixed, the bottom grip can move in vertical direction. The machine can impose a maximum force of 600 kN statically or 500 kN dynamically. Tests can be performed as force control or displacement control. The data acquisition and control of the machine are performed by a software on a personal computer.
4.1.2.
Vertical tests program
In order to study the effect of vertical load level on mechanical and dynamic characteristics of isolators, vertical tests have been performed in two different levels of load. In each test, initially a monotonic compressive load is applied up to a certain level of force P. Three cycles of unloading and loading with an amplitude of P are then carried out. Finally, unloading is performed in a monotonic manner. The values of forces P and P are summarized in Table 2. On each isolator specimen, test no. 1 and test no. 2 have been carried out consecutively.
4.2.
Horizontal tests
Horizontal tests are combined compression and shear tests which are carried out on isolators by applying a constant vertical load and fully reversed cycles of dynamic horizontal displacements. The tests are performed to determine the shear behavior of isolators. By carrying out the horizontal tests, the shear force–displacement loops are obtained. From these results, the mechanical and other dynamic characteristics, such as effective horizontal stiffness, effective shear modulus and equivalent viscous damping are evaluated.
4.2.1.
Description of the horizontal test apparatus
Combined compression and shear tests have been performed using a test apparatus in International Institute of Earthquake Engineering and Seismology. The test apparatus has two hydraulic actuators; one in horizontal direction and the other in vertical direction, as shown in Fig. 3. In the apparatus, force and displacement of the actuators are transferred to isolator by a horizontal beam. The beam remains horizontal during the tests. The maximum force and stroke of the vertical actuator are 1000 kN and ±150 mm and those of the horizontal actuator are 250 kN and ±150 mm, respectively. The data acquisition and control of the hydraulic actuators are performed by a software package on a personal computer. The data sampling rate in these tests have been 64 points per second.
4.2.2.
Horizontal tests program
The horizontal tests have been performed on the fiber reinforced isolator specimens no. 1 and 2 and also steel reinforced isolator specimen with different shear strain amplitudes of 50%, 75%, 100%, 125%, 150% and 175%. For the fiber reinforced isolator specimen no. 3, in addition to the mentioned amplitudes, the horizontal tests have also been carried out with shear strain amplitudes of 200% and 225%. The tests have
Fig. 3 – Horizontal test apparatus.
been repeated in three cycles for each of the shear strain amplitudes. Due to limitation of the hydraulic actuators, the horizontal loads have been applied at frequency of 0.1 Hz, for shear strain amplitudes greater than 50%. For shear strain amplitude of 100%, the horizontal tests have also been performed at frequency of 0.2 Hz, before the tests at 0.1 Hz. For shear strain amplitude of 50%, the horizontal tests have also been performed at frequency of 0.5 Hz, before the tests at 0.1 Hz. The effects of these variations of frequencies have been found to be negligible. In order to investigate the effect of vertical load level on the shear characteristics of the isolators, each horizontal test with a certain shear strain amplitude has been carried out in two different levels of constant vertical load. In the first test, a vertical load of 67 kN was applied and in the second one the load was increased to 135 kN. Also in order to investigate the effect of history of loading, the horizontal tests with shear strain amplitude of 100% have been repeated after the horizontal tests with shear strain amplitudes of 150% and 200% for the fiber reinforced isolator specimen no. 3. The fiber reinforced isolator specimen no. 3 and the steel reinforced isolator specimen are shown in Fig. 4(a) and (b), respectively while the horizontal tests are being carried out.
4.3.
Results of the tests
4.3.1.
Vertical tests
Samples of the results of the vertical tests performed on the isolator specimens are shown in Fig. 5(a) and (b) as vertical force versus displacement curves for two different levels of vertical loading. From the figures, it may be observed that parts of the curves related to cyclic unloadings and loadings are almost linear. It is also shown that the second and third cycles are almost coincident in each test. Vertical stiffness of isolator is the slope of the linear part of these curves. Effective compression modulus of isolator is calculated according to the following relationship (Naeim and Kelly, 1999): Ec =
kv tr Af,s
(1)
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Fig. 5 – Vertical force vs. displacement for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Fig. 4 – Some of the isolator specimens subjected to horizontal test: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
where Ec is the effective compression modulus, kv the vertical stiffness of isolator from test, Af,s the cross-sectional area of a reinforcement layer and tr is the total rubber thickness in isolator. The values of kv and Ec are summarized in Table 3.
4.3.1.1. Comparison of vertical stiffness of the fiber reinforced specimens and the steel reinforced isolator specimen. Table 3 shows that the effective compression modulus of the fiber reinforced isolator specimen no. 2 is very close to that of the steel reinforced isolator specimen. The effective compression modulus of the fiber reinforced specimen no. 1 is 20% less, but that of the fiber reinforced specimen no. 3 is 16% greater than that of the steel reinforced specimen. Therefore, fiber reinforced isolators with cross-sectional area and total rubber
thickness equal to those of steel reinforced isolators can create vertical stiffness equal or even greater compared to steel reinforced isolators.
4.3.1.2. Effect of shape factor of elastomer layers on effective compression modulus. Similar to steel reinforced isolators, increasing the shape factor of elastomer layers increases the value of vertical stiffness for fiber reinforced isolators too. The relationships presented by Kelly (Kelly, 1999) and Tsai (Tsai, 2004) confirm this effect. The results of this study presented in Fig. 6 show that by increasing the shape factor from 14.5 to 39.8, the value of effective compression modulus is increased by about 43%.
4.3.2.
Results of horizontal tests
Some results of the horizontal tests performed on isolator specimens are shown in Figs. 7 and 8 as horizontal force versus displacement curves for two different levels of con-
Table 3 – Values of vertical stiffness and effective compression modulus of isolators P = 67 ± 20 kN
Isolator specimen
Fiber reinforced no. 1 Fiber reinforced no. 2 Fiber reinforced no. 3 Steel reinforced
P = 135 ± 35 kN
kv (kN/mm)
Ec (MPa)
kv (kN/mm)
133.33 163.27 173.91 152.67
263.18 312.16 366.44 316.96
155.90 202.31 214.07 187.67
Ec (Mpa) 307.73 386.82 451.04 389.62
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Fig. 6 – Effect of shape factor of elastomer layers on effective compression modulus of the fiber reinforced isolator specimens.
stant vertical load of 67 kN and 135 kN. The curves are also shown for shear strain amplitude of 100% in Fig. 9(a) and (b). As shown in these figures, by increasing the number of cycles of loading, the value of effective horizontal stiffness is marginally decreased in all tests. This stress softening, which is known as the Mullins effect, occurs in the filled rubbers. This phenomenon probably reflects a breakdown of weak bonds between rubber molecules and filler particles, and at very small strains, between filler particles themselves incurred during previous loading (Gent, 2001). From the figures, it is also
found that the third cycle of loading is almost coincident with the second cycle. Therefore, the shear characteristics of isolators would not change by increasing the number of cycles after the second cycle. So the quantities related to the third cycle in each test are used to compare and study the shear characteristics of isolators.
Fig. 7 – Horizontal force vs. displacement cyclic curves for constant vertical load of 67 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Fig. 8 – Horizontal force vs. displacement cyclic curves for constant vertical load of 135 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
4.3.2.1. Shear characteristics of isolators. Effective horizontal stiffness of isolator kH,eff () is obtained using the following equation in each cycle of shear loading for a certain shear strain amplitude , a constant vertical load and a frequency
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Fig. 10 – Variations of effective shear modulus vs. shear strain amplitude for the isolator specimens for constant vertical load of 67 kN.
Fig. 9 – Horizontal force vs. displacement cyclic curves for shear strain amplitude of 100% and constant vertical load of 67 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen. Fig. 11 – Variations of effective shear modulus vs. shear strain amplitude for the isolator specimens for constant vertical load of 135 kN.
of shear loading (Naeim and Kelly, 1999): kH,eff () =
Fmax − Fmin Dmax − Dmin
(2)
where Fmax is the maximum positive shear force, Fmin the maximum negative shear force, Dmax the maximum positive shear displacement and Dmin is the maximum negative shear displacement. Effective shear modulus of isolator is calculated using the following equation (Naeim and Kelly, 1999): Geff () =
kH,eff ()tr A
amplitude are shown for different isolator specimens. In these figures, FREI is the fiber reinforced elastomeric isolator, SREI is the steel reinforced elastomeric isolator and Sp. is the specimen.
(3)
Equivalent viscous damping ratio is also obtained using the following equation (Naeim and Kelly, 1999): eq =
WD 2kH,eff ()D2
(4)
where WD is the dissipated energy in each cycle of the test equal to area of the loop of shear force–displacement: D=
Dmax − Dmin 2
(5)
In Figs. 10–13, the variations of effective shear modulus and equivalent viscous damping ratio versus shear strain
Fig. 12 – Variations of equivalent viscous damping ratio vs. shear strain amplitude for the isolator specimens for constant vertical load of 67 kN.
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Fig. 13 – Variations of equivalent viscous damping ratio vs. shear strain amplitude for the isolator specimens for constant vertical load of 135 kN.
4.3.2.2. Comparison of shear characteristics of the fiber reinforced isolator specimens and the steel reinforced isolator specimen. In Figs. 10 and 11, the variations of effective shear modulus versus shear strain amplitude have been compared for the fiber reinforced isolator specimens and the steel reinforced isolator specimen. From the figures, the following results are obtained: • The values of effective shear modulus of all fiber reinforced isolator specimens are almost equal for a certain shear strain amplitude, a constant vertical load and a frequency of shear loading. The shape factor of elastomer layers in isolator has no effect on the effective shear modulus. • For a certain shear strain amplitude, a constant vertical load and a frequency of shear loading, the effective shear modulus of the fiber reinforced isolator specimens is about 90% of that of the steel reinforced isolator specimen. In Figs. 12 and 13, the variations of equivalent viscous damping ratio versus shear strain amplitude have been compared for the fiber reinforced isolator specimens and the steel reinforced isolator specimen, from which the following results may be concluded: • Variation of values of equivalent viscous damping ratio show trends similar to that of effective shear modulus. • For a certain shear strain amplitude, a constant vertical load and a frequency of shear loading, the equivalent viscous damping ratio of the fiber reinforced isolator specimens is almost equal to that of the steel reinforced isolator specimen.
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According to the studies of Kelly (Kelly, 1999), when a fiber reinforced isolator is subjected to shear loading, bending flexibility of reinforcement fibers causes a plane cross section not to remain plane, which is in contrast to a steel reinforced isolator. On the basis of the hypothesis of Kelly (Kelly, 1999), this phenomenon that happens by an interfacial slip of single fibers against each other in the threads, as well as the tension in the threads due to vertical load, produce a significant amount of frictional damping in reinforcement fibers. This energy dissipation is added to that of the elastomer. In the fiber reinforced specimens introduced by Kelly (Kelly, 1999), due to the frictional damping, the equivalent viscous damping ratio of isolator at the shear strain of 100% had been increased from 8% (for the steel reinforced isolator with the same rubber compound) to 15%. For the carbon fiber reinforced isolator specimen manufactured by Moon et al. (Moon et al., 2002), the equivalent viscous damping ratio was 2.5 times of that of the similar steel reinforced isolator. But in the horizontal tests of the fiber reinforced isolator specimens in this research, as schematically shown in Fig. 14, even at large shear strains, plane cross sections of isolators remain almost plane. Only small regions at the edges become curved. The results of the tests show that the energy dissipation and the equivalent viscous damping of the fiber reinforced isolator specimens are almost equal to those of the steel reinforced isolator specimen. Therefore, the energy dissipation due to frictional damping is negligible in fibers. The absence of frictional damping in the fibers of the fiber reinforced specimens investigated is probably caused by the insignificant warping of the plane cross-sections and absence of interfacial slip of single fibers against each other in the threads. This may be due to the characteristics of the adhesive applied for impregnating the fiber layers and bonding them to rubber layers. The fiber layer impregnated by cured adhesive has effectively acted as a composite layer. In order to verify this hypothesis, a layer of woven fiber similar to those used in isolator specimens, was impregnated by the adhesive. It was subjected to the same conditions of the heat and pressure as the vulcanization of the fiber reinforced isolator specimens. In contrast to the original woven fiber which was completely flexible in bending and warping, it was observed that the woven fiber with cured adhesive had a fixed flat shape with a little bending stiffness. It must be noted that the presence of the steel top and bottom end plates may have also helped to prevent the warping of the plane cross sections. Considering great similarity between the dynamic and mechanical characteristics of the fiber reinforced isolators and steel reinforced isolators in this research, we have called this
Fig. 14 – Schematic deformation of plane cross sections in the fiber reinforced isolators during horizontal test: (a) without shear loading and (b) with shear loading.
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Fig. 15 – Effect of the history of shear loading on shear characteristics of the fiber reinforced isolators.
type of fiber reinforced isolators as “steel like fiber reinforced elastomeric isolators” (SLFREI).
4.3.2.3. Effect of vertical load level on the shear characteristics. Comparison of Figs. 10 and 11 and the values of effective horizontal stiffness and effective shear modulus of isolators, show that the effect of variation of vertical load in the range of 67–135 kN on these quantities is small for fiber reinforced isolator specimens and the steel reinforced isolator specimen. The variation of the values in this case is between 2% and 6%. Albeit small, it may be seen that increasing the vertical load, decreases the effective horizontal stiffness and effective shear modulus. The effect of variation of vertical load on the quantities is similar for the fiber reinforced isolator specimen no. 3 and the steel reinforced isolator specimen. By decreasing the shape factor of elastomer layers, the effect of vertical load on the quantities is increased. Comparison of Figs. 12 and 13 and the values of equivalent viscous damping ratio of isolators, show that the effect of variation of vertical load on damping is significant for both the fiber reinforced isolator specimens and the steel reinforced isolator specimen. Increasing the vertical load, results in increasing the energy dissipation and damping. In this case when the vertical load is increased from 67 kN to 135 kN, the equivalent viscous damping ratio increases by 40% for the steel reinforced isolator specimen and between 25% and 45% for the fiber reinforced isolator specimens.
Fig. 16 – Effect of the history of shear loading on effective shear modulus of the fiber reinforced isolators.
has decreased the effective shear modulus (down to 26%) and increased the damping (up to 48%). This stress softening is due to the Mullins effect in the filled rubbers. This effect may be important when the response of isolated structures during earthquakes is evaluated.
4.3.3. Ratio of vertical to horizontal stiffness of isolator specimens An isolation system must provide both sufficient horizontal flexibility to create the desired horizontal isolated period of vibration and sufficient vertical stiffness to create large enough vertical frequency (greater than the range of predominant frequencies of earthquakes) for the isolated structure. Therefore, a seismic isolator must have a very large ratio of vertical stiffness to horizontal stiffness. For a horizontal isolated period of vibration, the ratio of vertical to horizontal stiffness of the isolation system determines the vertical frequency of the isolated structure. Simply by modelling the isolated structure as a mass connected to two springs in the horizontal and vertical directions, it is concluded that (Kelly, 1997): KV = KH
fV =
f 2
1 TH
V
fH
KV KH
(6)
(7)
4.3.2.4. Effect of the history of loading on the shear characteristics. During horizontal tests on the fiber reinforced isolator specimen no. 3, the tests with shear strain amplitude of 100% have been repeated after the tests with shear strain amplitudes of 75%, 150% and 200% (three cycles in each time). Variations of shear force versus displacement are shown in Fig. 15 for constant vertical load of 135 kN. It may be observed that the history of shear deformations affects the shear behavior and characteristics. Hence, the effective horizontal stiffness and the energy dissipation are different for different tests. The values of effective shear modulus and the equivalent viscous damping ratio are compared in Figs. 16 and 17. As show in the figures, repeating the test with a certain shear strain amplitude after the tests with greater shear strains,
Fig. 17 – Effect of the history of shear loading on equivalent viscous damping ratio of the fiber reinforced isolators.
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where KV is the vertical stiffness of the isolation system, KH the effective horizontal stiffness of the isolation system at the desired horizontal displacement, fV (Hz) the vertical frequency, fH (Hz) the horizontal isolated frequency at the desired horizontal displacement and TH is the horizontal isolated period of vibration at the desired horizontal displacement.For an isolator, the above parameters may be calculated as follows: kv =
Ec Af,s tr
kH,eff () =
Geff ()A tr
(8)
(9)
Af,s ∼ =A
(10)
kv Ec ∼ = kH,eff () Geff ()
(11)
where kv is the vertical stiffness of the isolator, kH,eff () the effective horizontal stiffness of the isolator at the expected shear strain, Geff () the effective shear modulus of the isolator at the expected shear strain, A the cross-section area of the isolator and is the expected shear strain. Calculation of the ratio of effective compression modulus to effective shear modulus at the shear strain amplitude of 100% for the two different levels of vertical loads shows that the smallest ratio is for the fiber reinforced isolator specimen no. 1. It is equal to 373 for the vertical load of 67 kN (compressive stress of 2.98 MPa) and equal to 465 for the vertical load of 135 kN (compressive stress of 6.0 MPa). The largest ratio is for the fiber reinforced isolator specimen no. 3, which has the largest shape factor of elastomer layers. It is equal to 529 for the vertical load of 67 kN and equal 679 for the vertical load of 135 kN. It is evident that by increasing the compressive stress, the value of the ratios is also increased. Based on Eq. (7), by considering the value of 373 related to the specimen no. 1 and the desired horizontal isolated period of vibration equal to 2.0 s, the vertical frequency is estimated to be 9.7 Hz. If the value of 679 related to the specimen no. 3 and the desired horizontal isolated period of vibration equal to 2.5 s are considered, the vertical frequency is estimated to be 10.4 Hz. The estimated frequencies are greater than the range of predominant frequencies of earthquakes. Therefore, all the isolator specimens in this study have sufficient and suitable ratio of vertical stiffness to horizontal stiffness for seismic isolation. The ratio of effective compression modulus to effective shear modulus at the shear strain amplitude of 100% for the fiber reinforced isolator specimens shows that by increasing the shape factor of elastomer layers from 14.5 to 39.8, the ratio has increased about 44%. Comparing the above mentioned ratio for the fiber reinforced isolator specimens with that of the steel reinforced isolator specimen shows that the ratio for the fiber reinforced isolator specimen no. 2 is nearly equal to that of the steel reinforced isolator specimen. The ratio for the fiber reinforced isolator specimen no. 1 is 15% less and for the specimen no. 3 is 23% greater compared to the steel reinforced isolator specimen.
5.
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Conclusion
In this paper, specimens of multilayer elastomeric seismic isolators, which have been reinforced by layers of woven carbon fibers, as well as a specimen of similar size and shape reinforced by steel plates have been designed and manufactured. Extensive vertical and dynamic cyclic horizontal tests have then been performed on them. The study of dynamic and mechanical characteristics of the specimens shows that the behavior of the carbon fiber reinforced elastomeric isolators is very similar to that of the steel reinforced elastomeric isolators with regard to vertical stiffness and shear characteristics such as effective horizontal stiffness and damping. Therefore, the fiber reinforced isolators which have been called “steel like fiber reinforced elastomeric isolators” (SLFREI), can be used in seismic isolation of structures, while they are lighter and simpler to manufacture compared to steel reinforced elastomeric isolators. The main differences between SLFREI and fiber reinforced elastomeric isolators, previously reported in the literature, are that frictional damping is not produced in reinforcement fibers of the SLFREI and it is able to sustain very large shear strains (225%) in the presence of top and bottom steel end plates. Investigation of the effect of the shape factor of elastomer layers has shown that similar to steel reinforced isolators, increasing the shape factor of elastomer layers increases the value of vertical stiffness for fiber reinforced isolators too. In the fiber reinforced specimens, by increasing the shape factor from 14.5 to 39.8, the value of effective compression modulus has increased by about 43%. But the shape factor of elastomer layers has no effect on the effective shear modulus and equivalent viscous damping ratio. Investigation of the effect of variation of vertical load (from 67 kN to 135 kN) on the shear characteristics has shown that variation of effective horizontal stiffness or effective shear modulus in this range of vertical loads is small (between 2% and 6%) for all specimens. But the effect of vertical load on the values of equivalent viscous damping ratio is significant for both the fiber reinforced isolator specimens (between 25% and 45%) and the steel reinforced isolator specimen (40% increase). The experiments have also shown that repeating the horizontal tests with 100% shear strain amplitude after the tests with greater shear strains, has decreased the effective shear modulus (down to 26%) and increased the damping (up to 48%). This stress softening is due to the Mullins effect in the filled rubbers. This effect need to be considered in evaluating the response of the isolated structures during an earthquake with cyclic motions.
references
Gent, A.N., 2001. Engineering with Rubber, second ed. HanserGardner Publications Inc., Cincinnati, OH, USA. International Conference of Building Officials (ICBO), 1997. Earthquake regulations for seismic-isolated structures. Uniform Building Code, Whittier, CA, 1997 (Appendix Chapter 16).
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Kang, B.-S., Kang, G.-J., Moon, B.-Y., 2003. Hole and lead plug effect on fiber reinforced elastomeric isolator for seismic isolation. J. Mater. Process. Technol. 140, 592–597. Kelly, J.M., 1996. Final Report on the International Workshop on the Use of Rubber-based Bearings for the Earthquake Protection of Buildings, Earthquake Engineering Research Center, University of California, Berkeley, CA, USA. Kelly, J.M., 1997. Earthquake-resistant Design with Rubber, second ed. Springer Verlag, London. Kelly, J.M., 1999. Analysis of fiber-reinforced elastomeric isolators. J. Seismol. Earthquake Eng. 2 (1), 19–34. Moon, B.-Y., Kang, G.-J., Kang, B.-S., Kelly, J.M., 2002. Design and manufacturing of fiber reinforced elastomeric isolator for seismic isolation. J. Mater. Process. Technol. 130/131, 145–150.
Naeim, F., Kelly, J.M., 1999. Design of Seismic Isolated Structures from Theory to Practice. John Wiley & Sons, NY. Taniwangsa, W., Kelly, J.M., 1996. Experimental and Analytical Studies of Base Isolation Applications for Low-Cost Housing. Earthquake Engineering Research Center, University of California, Berkeley, CA, USA. Tsai, H.C., 2004. Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements. Int. J. Solids Struct. 41, 6647–6660. Tsai, H.C., Kelly, J.M., 2005. Buckling load of seismic isolators affected by flexibility of reinforcement. Int. J. Solids Struct. 42, 255–269.
journal homepage: www.elsevier.com/locate/jmatprotec
Design, manufacturing and evaluation of the performance of steel like fiber reinforced elastomeric seismic isolators Ghasem Dehghani Ashkezari a , Ali Akbar Aghakouchak a,∗ , Mehrdad Kokabi b a b
Structural Engineering Division, Faculty of Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran Polymer Engineering Division, Faculty of Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this research, specimens of fiber reinforced elastomeric seismic isolators have been
Received 21 November 2006
designed, manufactured and their dynamic and mechanical characteristics have then been
Received in revised form
studied by performing vertical and horizontal (compression–shear) tests. For the sake of
17 May 2007
comparison, one steel reinforced elastomeric isolator specimen has also been designed,
Accepted 2 June 2007
manufactured and subjected to similar tests. In design of fiber reinforced isolators, the tensile and bending flexibility of the fiber cords reinforcement have been considered. Results of the experiments show that the behavior of the fiber reinforced elastomeric isolators
Keywords:
is very similar to that of the steel reinforced specimen with regard to shear deformation
Seismic isolation
and dynamic and mechanical characteristics including vertical stiffness, effective horizon-
Fiber reinforced elastomeric isolator
tal stiffness and damping. Therefore, this type of fiber reinforced isolator which has been
Vertical test
named “steel like fiber reinforced elastomeric isolators” (SLFREI) can be used in seismic
Horizontal test
isolation of structures. The advantages of SLFREI are that they are lighter and simpler to manufacture, compared to steel reinforced elastomeric isolators. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Seismic base isolation is a valuable earthquake-resistant technique for structures such as buildings and bridges. As a result of isolation, the fundamental horizontal period of structure is increased to a value away from the dominant range of periods of earthquakes. Therefore, the earthquake energy transmitted to the structure is decreased considerably. This is achieved by installing isolators which have low horizontal, but high vertical and bending stiffnesses beneath superstructure. Current systems for seismic isolation of structures usually include two types, i.e. steel reinforced multilayer elastomeric and sliding bearings. Systems that combine elastomeric and sliding bearings have also been proposed and implemented. To date many studies have been performed regarding the performance of these systems and quite a number of structures
∗
Corresponding author. E-mail address: a [email protected] (A.A. Aghakouchak). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.06.023
have been seismically isolated using these systems in different parts of the world. These structures mainly include large bridges and important buildings that contain sensitive or expensive equipment. The isolators used for this purpose are normally heavy and expensive. A few studies have also been performed on the use of steel reinforced elastomeric isolators in common residential buildings. They include design and construction of demonstration buildings such as a threestory building in Italy, a four-story one in Chile, an eight-story one in China and a four-story one in Indonesia (Taniwangsa and Kelly, 1996; Kelly, 1996). In order to apply seismic isolation for common buildings and public housing, the cost and weight of isolators must be reduced. Cost of isolators is mainly due to the process of preparing steel plates and bonding them to rubber layers. Weight of isolators is also mainly due to the same plates.
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Kelly (Kelly, 1999) suggested that both the weight and cost of isolators can be reduced by eliminating the steel reinforcing plates and replacing them with fiber reinforcement of high elastic stiffness. By introducing some fiber reinforced isolator specimens, he showed that these isolators can provide tilting and vertical stiffness in the range of steel reinforced isolators with the same diameter and the same thickness of rubber. The shear stiffness and equivalent viscous damping of the fiber reinforced specimens were about 80% and 180% of similar values for the steel reinforced isolators, respectively. Steel reinforcing plates are assumed to be rigid both in tension and bending; but fiber cords reinforcement, which are made up of many individual fibers, are more flexible in tension compared to individual fibers and completely lack bending stiffness. Moon et al. (Moon et al., 2002) designed and manufactured some specimens of fiber reinforced multilayer elastomeric isolator using different kinds of fibers such as carbon, glass, nylon and polyester. They carried out experiments to determine their mechanical characteristics and to evaluate the performance of the specimens. They also compared the mechanical characteristics of the carbon fiber reinforced isolator with a similar steel reinforced isolator. Experiments showed that performance of the carbon fiber reinforced isolator was even superior to that of the steel reinforced isolator in view of vertical stiffness and effective damping. They concluded that fiber reinforced isolators can replace steel reinforced isolators. Vertical stiffness, shear stiffness and equivalent viscous damping of the carbon fiber reinforced isolator were 299%, 94% and 256% of those of the steel reinforced isolator, respectively. In steel reinforced isolators, introduction of one or more lead plugs that are inserted into holes results in additional damping. In order to investigate the effect of hole and lead plug in fiber reinforced elastomeric isolators, Kang et al. (Kang et al., 2003) carried out vertical and horizontal tests on carbon fiber reinforced isolator specimens with and without hole and lead plug. They concluded that the hole and lead plug in fiber reinforced elastomeric isolator have little effect on effective stiffness and effective damping. Fig. 1(a) and (b) shows models of fiber and steel reinforced elastomeric isolators, respectively (Kang et al., 2003). Tsai (Tsai, 2004) derived closed form solutions for compression stiffness of the laminated elastomeric bearings of infinite-strip shape with flexible reinforcements. He considered the effect of bulk compressibility in the elastomer layer and the effect of boundary condition at the ends of the bearing. The behavior of elastomer and reinforcement layers was considered as linear elastic. He compared the theoretical solution with the results of finite element analysis. Tsai and Kelly (Tsai and Kelly, 2005) presented a beam theory to analyze the buckling load of the elastomeric multilayer isolators reinforced by thin and flexible steel plates. This theory is the extension of Haringx theory and considers the shear deformation and warping of cross-sections. The behavior of elastomer and steel reinforcement layers is considered as linear elastic. The elastomer is also assumed to be incompressible. In this research, some fiber reinforced elastomeric isolator specimens have been designed and manufactured. Their mechanical characteristics are investigated by performing ver-
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Fig. 1 – Models of elastomeric isolators: (a) fiber reinforced and (b) steel reinforced.
tical and cyclic horizontal tests. For the sake of comparison, one steel reinforced elastomeric isolator specimen has also been designed, manufactured and tested in similar conditions.
2.
Description of isolator specimens
Three carbon fiber reinforced elastomeric isolator specimens and one steel reinforced elastomeric isolator specimen have been designed and manufactured. Horizontal dimensions of all specimens have been considered exactly equal and total thickness of rubber in all specimens has also been selected nearly equal. In order to investigate the effect of the number of rubber and fiber layers in isolators and the shape factor of elastomer layers, these parameters have been varied in three fiber reinforced specimens. All specimens have steel top and bottom end plates in which four threaded holes have been considered. These holes are to be used to connect the specimens to test apparatus. Characteristics of the specimens are presented in Table 1. The fiber reinforced specimen number 3 and steel reinforced specimen are shown in Fig. 2(a) and (b).
3.
Design method and manufacture process
Design of the fiber reinforced isolator specimens has been carried out based on UBC-97 (ICBO, 1997) assuming certain parameters and according to the current method of design of the steel reinforced multilayered elastomeric seismic isolators (Naeim and Kelly, 1999; Kelly, 1997). However, the tensile and bending flexibility of the fiber cords have been taken into account using the effective parameters introduced by Kelly (Kelly, 1999), Tsai (Tsai, 2004) and Tsai and Kelly (Tsai and Kelly, 2005).
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Table 1 – Characteristics of the isolator specimens Specimen
Fiber reinforced no. 1 Fiber reinforced no. 2 Fiber reinforced no. 3 Steel reinforced
Horizontal dimensions of isolator (mm × mm) 150 × 150 150 × 150 150 × 150 150 × 150
tr (mm)
41.5 40.2 44.3 43.7
Horizontal dimensions of reinforcement layers (mm × mm) 145 × 145 145 × 145 145 × 145 145 × 145
nr
nf,s
t (mm)
tf,s (mm)
16 24 47 16
15 23 46 15
2.59 1.68 0.94 2.73
0.25 0.25 0.25 1.0
tT and B Plates (mm)
9.8 9.8 9.8 9.8
s
14.46 22.4 39.8 13.75
tr : total thickness of rubber in the isolator; nr : number of rubber layers in the isolator; nf,s : number of fiber or steel reinforcement layers in the isolator; t: thickness of each rubber layer in the isolator; tf,s : thickness of each layer of fiber or steel reinforcement in the isolator; tT and B plates : thickness of steel top and bottom end plates in the isolator; s: shape factor of elastomer layers in the isolator, i.e. the ratio of loaded area to force-free area.
In order to compare the behavior of the fiber reinforced isolator specimens with the steel reinforced ones, a steel reinforced isolator specimen has also been manufactured. In this isolator horizontal cross section and total thickness of rubber are the same as those of the fiber reinforced isolators and the number of rubber layers is equal to that of one of the fiber reinforced isolators (specimen no. 1). Due to limitations of the test rigs, the isolator specimens have been manufactured with the scale of 1/4. To manufacture the fiber reinforced isolators, initially the woven fiber warps and wefts are completely impregnated by adhesive. The raw rubber compound which has been filled
with carbon black, is also formed as sheets with desired thickness. The fiber layers and raw rubber sheets are then cut to desired dimensions and set in the mold. The woven fiber in which the directions of warps and wefts are perpendicular, is cut and set in the mold, in a way that the directions of warps and wefts of fiber layers relative to horizontal dimensions of isolator are 0/90 and +45/−45, alternatively. The steel top and bottom end plates, which have been prepared, are also set in their place in the mold. The layers and components in the mold are then subjected to a suitable pressure and temperature for a suitable period of time. The suitable temperature and time depend on the required temperature and time for the vulcanization of the rubber and the adhesive and also dimensions and volume of the specimen. The required temperature and time for the vulcanization of the rubber that depend on the curing system of the rubber compound, are obtained by performing the reological test according to the standard ASTM D2084-81. The greater the dimensions, the longer time is required to vulcanize the specimen at a certain temperature. This longer time ensures proper curing of the internal layers with lower temperatures. In this research, the specimens were shaped by compression molding at 120 ◦ C temperature and 110 min time. The pressure was needed to push the extra rubber out of the mold’s gap. The amount of the required pressure depends on the dimensions of the specimen and the mold. In this research, a pressure and heat machine was used that can impose a maximum compressive force of 300 kN.
4.
Evaluation of performance of isolators
In order to study the performance of the isolators, vertical tests and dynamic cyclic horizontal tests have been carried out.
4.1.
Vertical tests
Vertical tests have been performed on the isolator specimens to determine the vertical stiffness and effective compression modulus.
4.1.1. Fig. 2 – Some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Description of the vertical test machine
Vertical tests have been performed by dynamic tension and pressure test machine in International Institute of Earthquake Engineering and Seismology. In this machine, the specimen is
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Table 2 – Values of load in vertical tests Test number
P (kN)
1 2
67 135
P (kN) ±20 ±35
set between two grips. While the top grip is fixed, the bottom grip can move in vertical direction. The machine can impose a maximum force of 600 kN statically or 500 kN dynamically. Tests can be performed as force control or displacement control. The data acquisition and control of the machine are performed by a software on a personal computer.
4.1.2.
Vertical tests program
In order to study the effect of vertical load level on mechanical and dynamic characteristics of isolators, vertical tests have been performed in two different levels of load. In each test, initially a monotonic compressive load is applied up to a certain level of force P. Three cycles of unloading and loading with an amplitude of P are then carried out. Finally, unloading is performed in a monotonic manner. The values of forces P and P are summarized in Table 2. On each isolator specimen, test no. 1 and test no. 2 have been carried out consecutively.
4.2.
Horizontal tests
Horizontal tests are combined compression and shear tests which are carried out on isolators by applying a constant vertical load and fully reversed cycles of dynamic horizontal displacements. The tests are performed to determine the shear behavior of isolators. By carrying out the horizontal tests, the shear force–displacement loops are obtained. From these results, the mechanical and other dynamic characteristics, such as effective horizontal stiffness, effective shear modulus and equivalent viscous damping are evaluated.
4.2.1.
Description of the horizontal test apparatus
Combined compression and shear tests have been performed using a test apparatus in International Institute of Earthquake Engineering and Seismology. The test apparatus has two hydraulic actuators; one in horizontal direction and the other in vertical direction, as shown in Fig. 3. In the apparatus, force and displacement of the actuators are transferred to isolator by a horizontal beam. The beam remains horizontal during the tests. The maximum force and stroke of the vertical actuator are 1000 kN and ±150 mm and those of the horizontal actuator are 250 kN and ±150 mm, respectively. The data acquisition and control of the hydraulic actuators are performed by a software package on a personal computer. The data sampling rate in these tests have been 64 points per second.
4.2.2.
Horizontal tests program
The horizontal tests have been performed on the fiber reinforced isolator specimens no. 1 and 2 and also steel reinforced isolator specimen with different shear strain amplitudes of 50%, 75%, 100%, 125%, 150% and 175%. For the fiber reinforced isolator specimen no. 3, in addition to the mentioned amplitudes, the horizontal tests have also been carried out with shear strain amplitudes of 200% and 225%. The tests have
Fig. 3 – Horizontal test apparatus.
been repeated in three cycles for each of the shear strain amplitudes. Due to limitation of the hydraulic actuators, the horizontal loads have been applied at frequency of 0.1 Hz, for shear strain amplitudes greater than 50%. For shear strain amplitude of 100%, the horizontal tests have also been performed at frequency of 0.2 Hz, before the tests at 0.1 Hz. For shear strain amplitude of 50%, the horizontal tests have also been performed at frequency of 0.5 Hz, before the tests at 0.1 Hz. The effects of these variations of frequencies have been found to be negligible. In order to investigate the effect of vertical load level on the shear characteristics of the isolators, each horizontal test with a certain shear strain amplitude has been carried out in two different levels of constant vertical load. In the first test, a vertical load of 67 kN was applied and in the second one the load was increased to 135 kN. Also in order to investigate the effect of history of loading, the horizontal tests with shear strain amplitude of 100% have been repeated after the horizontal tests with shear strain amplitudes of 150% and 200% for the fiber reinforced isolator specimen no. 3. The fiber reinforced isolator specimen no. 3 and the steel reinforced isolator specimen are shown in Fig. 4(a) and (b), respectively while the horizontal tests are being carried out.
4.3.
Results of the tests
4.3.1.
Vertical tests
Samples of the results of the vertical tests performed on the isolator specimens are shown in Fig. 5(a) and (b) as vertical force versus displacement curves for two different levels of vertical loading. From the figures, it may be observed that parts of the curves related to cyclic unloadings and loadings are almost linear. It is also shown that the second and third cycles are almost coincident in each test. Vertical stiffness of isolator is the slope of the linear part of these curves. Effective compression modulus of isolator is calculated according to the following relationship (Naeim and Kelly, 1999): Ec =
kv tr Af,s
(1)
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Fig. 5 – Vertical force vs. displacement for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Fig. 4 – Some of the isolator specimens subjected to horizontal test: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
where Ec is the effective compression modulus, kv the vertical stiffness of isolator from test, Af,s the cross-sectional area of a reinforcement layer and tr is the total rubber thickness in isolator. The values of kv and Ec are summarized in Table 3.
4.3.1.1. Comparison of vertical stiffness of the fiber reinforced specimens and the steel reinforced isolator specimen. Table 3 shows that the effective compression modulus of the fiber reinforced isolator specimen no. 2 is very close to that of the steel reinforced isolator specimen. The effective compression modulus of the fiber reinforced specimen no. 1 is 20% less, but that of the fiber reinforced specimen no. 3 is 16% greater than that of the steel reinforced specimen. Therefore, fiber reinforced isolators with cross-sectional area and total rubber
thickness equal to those of steel reinforced isolators can create vertical stiffness equal or even greater compared to steel reinforced isolators.
4.3.1.2. Effect of shape factor of elastomer layers on effective compression modulus. Similar to steel reinforced isolators, increasing the shape factor of elastomer layers increases the value of vertical stiffness for fiber reinforced isolators too. The relationships presented by Kelly (Kelly, 1999) and Tsai (Tsai, 2004) confirm this effect. The results of this study presented in Fig. 6 show that by increasing the shape factor from 14.5 to 39.8, the value of effective compression modulus is increased by about 43%.
4.3.2.
Results of horizontal tests
Some results of the horizontal tests performed on isolator specimens are shown in Figs. 7 and 8 as horizontal force versus displacement curves for two different levels of con-
Table 3 – Values of vertical stiffness and effective compression modulus of isolators P = 67 ± 20 kN
Isolator specimen
Fiber reinforced no. 1 Fiber reinforced no. 2 Fiber reinforced no. 3 Steel reinforced
P = 135 ± 35 kN
kv (kN/mm)
Ec (MPa)
kv (kN/mm)
133.33 163.27 173.91 152.67
263.18 312.16 366.44 316.96
155.90 202.31 214.07 187.67
Ec (Mpa) 307.73 386.82 451.04 389.62
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Fig. 6 – Effect of shape factor of elastomer layers on effective compression modulus of the fiber reinforced isolator specimens.
stant vertical load of 67 kN and 135 kN. The curves are also shown for shear strain amplitude of 100% in Fig. 9(a) and (b). As shown in these figures, by increasing the number of cycles of loading, the value of effective horizontal stiffness is marginally decreased in all tests. This stress softening, which is known as the Mullins effect, occurs in the filled rubbers. This phenomenon probably reflects a breakdown of weak bonds between rubber molecules and filler particles, and at very small strains, between filler particles themselves incurred during previous loading (Gent, 2001). From the figures, it is also
found that the third cycle of loading is almost coincident with the second cycle. Therefore, the shear characteristics of isolators would not change by increasing the number of cycles after the second cycle. So the quantities related to the third cycle in each test are used to compare and study the shear characteristics of isolators.
Fig. 7 – Horizontal force vs. displacement cyclic curves for constant vertical load of 67 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
Fig. 8 – Horizontal force vs. displacement cyclic curves for constant vertical load of 135 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen.
4.3.2.1. Shear characteristics of isolators. Effective horizontal stiffness of isolator kH,eff () is obtained using the following equation in each cycle of shear loading for a certain shear strain amplitude , a constant vertical load and a frequency
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Fig. 10 – Variations of effective shear modulus vs. shear strain amplitude for the isolator specimens for constant vertical load of 67 kN.
Fig. 9 – Horizontal force vs. displacement cyclic curves for shear strain amplitude of 100% and constant vertical load of 67 kN for some of the isolator specimens: (a) fiber reinforced specimen no. 3 and (b) steel reinforced specimen. Fig. 11 – Variations of effective shear modulus vs. shear strain amplitude for the isolator specimens for constant vertical load of 135 kN.
of shear loading (Naeim and Kelly, 1999): kH,eff () =
Fmax − Fmin Dmax − Dmin
(2)
where Fmax is the maximum positive shear force, Fmin the maximum negative shear force, Dmax the maximum positive shear displacement and Dmin is the maximum negative shear displacement. Effective shear modulus of isolator is calculated using the following equation (Naeim and Kelly, 1999): Geff () =
kH,eff ()tr A
amplitude are shown for different isolator specimens. In these figures, FREI is the fiber reinforced elastomeric isolator, SREI is the steel reinforced elastomeric isolator and Sp. is the specimen.
(3)
Equivalent viscous damping ratio is also obtained using the following equation (Naeim and Kelly, 1999): eq =
WD 2kH,eff ()D2
(4)
where WD is the dissipated energy in each cycle of the test equal to area of the loop of shear force–displacement: D=
Dmax − Dmin 2
(5)
In Figs. 10–13, the variations of effective shear modulus and equivalent viscous damping ratio versus shear strain
Fig. 12 – Variations of equivalent viscous damping ratio vs. shear strain amplitude for the isolator specimens for constant vertical load of 67 kN.
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Fig. 13 – Variations of equivalent viscous damping ratio vs. shear strain amplitude for the isolator specimens for constant vertical load of 135 kN.
4.3.2.2. Comparison of shear characteristics of the fiber reinforced isolator specimens and the steel reinforced isolator specimen. In Figs. 10 and 11, the variations of effective shear modulus versus shear strain amplitude have been compared for the fiber reinforced isolator specimens and the steel reinforced isolator specimen. From the figures, the following results are obtained: • The values of effective shear modulus of all fiber reinforced isolator specimens are almost equal for a certain shear strain amplitude, a constant vertical load and a frequency of shear loading. The shape factor of elastomer layers in isolator has no effect on the effective shear modulus. • For a certain shear strain amplitude, a constant vertical load and a frequency of shear loading, the effective shear modulus of the fiber reinforced isolator specimens is about 90% of that of the steel reinforced isolator specimen. In Figs. 12 and 13, the variations of equivalent viscous damping ratio versus shear strain amplitude have been compared for the fiber reinforced isolator specimens and the steel reinforced isolator specimen, from which the following results may be concluded: • Variation of values of equivalent viscous damping ratio show trends similar to that of effective shear modulus. • For a certain shear strain amplitude, a constant vertical load and a frequency of shear loading, the equivalent viscous damping ratio of the fiber reinforced isolator specimens is almost equal to that of the steel reinforced isolator specimen.
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According to the studies of Kelly (Kelly, 1999), when a fiber reinforced isolator is subjected to shear loading, bending flexibility of reinforcement fibers causes a plane cross section not to remain plane, which is in contrast to a steel reinforced isolator. On the basis of the hypothesis of Kelly (Kelly, 1999), this phenomenon that happens by an interfacial slip of single fibers against each other in the threads, as well as the tension in the threads due to vertical load, produce a significant amount of frictional damping in reinforcement fibers. This energy dissipation is added to that of the elastomer. In the fiber reinforced specimens introduced by Kelly (Kelly, 1999), due to the frictional damping, the equivalent viscous damping ratio of isolator at the shear strain of 100% had been increased from 8% (for the steel reinforced isolator with the same rubber compound) to 15%. For the carbon fiber reinforced isolator specimen manufactured by Moon et al. (Moon et al., 2002), the equivalent viscous damping ratio was 2.5 times of that of the similar steel reinforced isolator. But in the horizontal tests of the fiber reinforced isolator specimens in this research, as schematically shown in Fig. 14, even at large shear strains, plane cross sections of isolators remain almost plane. Only small regions at the edges become curved. The results of the tests show that the energy dissipation and the equivalent viscous damping of the fiber reinforced isolator specimens are almost equal to those of the steel reinforced isolator specimen. Therefore, the energy dissipation due to frictional damping is negligible in fibers. The absence of frictional damping in the fibers of the fiber reinforced specimens investigated is probably caused by the insignificant warping of the plane cross-sections and absence of interfacial slip of single fibers against each other in the threads. This may be due to the characteristics of the adhesive applied for impregnating the fiber layers and bonding them to rubber layers. The fiber layer impregnated by cured adhesive has effectively acted as a composite layer. In order to verify this hypothesis, a layer of woven fiber similar to those used in isolator specimens, was impregnated by the adhesive. It was subjected to the same conditions of the heat and pressure as the vulcanization of the fiber reinforced isolator specimens. In contrast to the original woven fiber which was completely flexible in bending and warping, it was observed that the woven fiber with cured adhesive had a fixed flat shape with a little bending stiffness. It must be noted that the presence of the steel top and bottom end plates may have also helped to prevent the warping of the plane cross sections. Considering great similarity between the dynamic and mechanical characteristics of the fiber reinforced isolators and steel reinforced isolators in this research, we have called this
Fig. 14 – Schematic deformation of plane cross sections in the fiber reinforced isolators during horizontal test: (a) without shear loading and (b) with shear loading.
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Fig. 15 – Effect of the history of shear loading on shear characteristics of the fiber reinforced isolators.
type of fiber reinforced isolators as “steel like fiber reinforced elastomeric isolators” (SLFREI).
4.3.2.3. Effect of vertical load level on the shear characteristics. Comparison of Figs. 10 and 11 and the values of effective horizontal stiffness and effective shear modulus of isolators, show that the effect of variation of vertical load in the range of 67–135 kN on these quantities is small for fiber reinforced isolator specimens and the steel reinforced isolator specimen. The variation of the values in this case is between 2% and 6%. Albeit small, it may be seen that increasing the vertical load, decreases the effective horizontal stiffness and effective shear modulus. The effect of variation of vertical load on the quantities is similar for the fiber reinforced isolator specimen no. 3 and the steel reinforced isolator specimen. By decreasing the shape factor of elastomer layers, the effect of vertical load on the quantities is increased. Comparison of Figs. 12 and 13 and the values of equivalent viscous damping ratio of isolators, show that the effect of variation of vertical load on damping is significant for both the fiber reinforced isolator specimens and the steel reinforced isolator specimen. Increasing the vertical load, results in increasing the energy dissipation and damping. In this case when the vertical load is increased from 67 kN to 135 kN, the equivalent viscous damping ratio increases by 40% for the steel reinforced isolator specimen and between 25% and 45% for the fiber reinforced isolator specimens.
Fig. 16 – Effect of the history of shear loading on effective shear modulus of the fiber reinforced isolators.
has decreased the effective shear modulus (down to 26%) and increased the damping (up to 48%). This stress softening is due to the Mullins effect in the filled rubbers. This effect may be important when the response of isolated structures during earthquakes is evaluated.
4.3.3. Ratio of vertical to horizontal stiffness of isolator specimens An isolation system must provide both sufficient horizontal flexibility to create the desired horizontal isolated period of vibration and sufficient vertical stiffness to create large enough vertical frequency (greater than the range of predominant frequencies of earthquakes) for the isolated structure. Therefore, a seismic isolator must have a very large ratio of vertical stiffness to horizontal stiffness. For a horizontal isolated period of vibration, the ratio of vertical to horizontal stiffness of the isolation system determines the vertical frequency of the isolated structure. Simply by modelling the isolated structure as a mass connected to two springs in the horizontal and vertical directions, it is concluded that (Kelly, 1997): KV = KH
fV =
f 2
1 TH
V
fH
KV KH
(6)
(7)
4.3.2.4. Effect of the history of loading on the shear characteristics. During horizontal tests on the fiber reinforced isolator specimen no. 3, the tests with shear strain amplitude of 100% have been repeated after the tests with shear strain amplitudes of 75%, 150% and 200% (three cycles in each time). Variations of shear force versus displacement are shown in Fig. 15 for constant vertical load of 135 kN. It may be observed that the history of shear deformations affects the shear behavior and characteristics. Hence, the effective horizontal stiffness and the energy dissipation are different for different tests. The values of effective shear modulus and the equivalent viscous damping ratio are compared in Figs. 16 and 17. As show in the figures, repeating the test with a certain shear strain amplitude after the tests with greater shear strains,
Fig. 17 – Effect of the history of shear loading on equivalent viscous damping ratio of the fiber reinforced isolators.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 1 9 7 ( 2 0 0 8 ) 140–150
where KV is the vertical stiffness of the isolation system, KH the effective horizontal stiffness of the isolation system at the desired horizontal displacement, fV (Hz) the vertical frequency, fH (Hz) the horizontal isolated frequency at the desired horizontal displacement and TH is the horizontal isolated period of vibration at the desired horizontal displacement.For an isolator, the above parameters may be calculated as follows: kv =
Ec Af,s tr
kH,eff () =
Geff ()A tr
(8)
(9)
Af,s ∼ =A
(10)
kv Ec ∼ = kH,eff () Geff ()
(11)
where kv is the vertical stiffness of the isolator, kH,eff () the effective horizontal stiffness of the isolator at the expected shear strain, Geff () the effective shear modulus of the isolator at the expected shear strain, A the cross-section area of the isolator and is the expected shear strain. Calculation of the ratio of effective compression modulus to effective shear modulus at the shear strain amplitude of 100% for the two different levels of vertical loads shows that the smallest ratio is for the fiber reinforced isolator specimen no. 1. It is equal to 373 for the vertical load of 67 kN (compressive stress of 2.98 MPa) and equal to 465 for the vertical load of 135 kN (compressive stress of 6.0 MPa). The largest ratio is for the fiber reinforced isolator specimen no. 3, which has the largest shape factor of elastomer layers. It is equal to 529 for the vertical load of 67 kN and equal 679 for the vertical load of 135 kN. It is evident that by increasing the compressive stress, the value of the ratios is also increased. Based on Eq. (7), by considering the value of 373 related to the specimen no. 1 and the desired horizontal isolated period of vibration equal to 2.0 s, the vertical frequency is estimated to be 9.7 Hz. If the value of 679 related to the specimen no. 3 and the desired horizontal isolated period of vibration equal to 2.5 s are considered, the vertical frequency is estimated to be 10.4 Hz. The estimated frequencies are greater than the range of predominant frequencies of earthquakes. Therefore, all the isolator specimens in this study have sufficient and suitable ratio of vertical stiffness to horizontal stiffness for seismic isolation. The ratio of effective compression modulus to effective shear modulus at the shear strain amplitude of 100% for the fiber reinforced isolator specimens shows that by increasing the shape factor of elastomer layers from 14.5 to 39.8, the ratio has increased about 44%. Comparing the above mentioned ratio for the fiber reinforced isolator specimens with that of the steel reinforced isolator specimen shows that the ratio for the fiber reinforced isolator specimen no. 2 is nearly equal to that of the steel reinforced isolator specimen. The ratio for the fiber reinforced isolator specimen no. 1 is 15% less and for the specimen no. 3 is 23% greater compared to the steel reinforced isolator specimen.
5.
149
Conclusion
In this paper, specimens of multilayer elastomeric seismic isolators, which have been reinforced by layers of woven carbon fibers, as well as a specimen of similar size and shape reinforced by steel plates have been designed and manufactured. Extensive vertical and dynamic cyclic horizontal tests have then been performed on them. The study of dynamic and mechanical characteristics of the specimens shows that the behavior of the carbon fiber reinforced elastomeric isolators is very similar to that of the steel reinforced elastomeric isolators with regard to vertical stiffness and shear characteristics such as effective horizontal stiffness and damping. Therefore, the fiber reinforced isolators which have been called “steel like fiber reinforced elastomeric isolators” (SLFREI), can be used in seismic isolation of structures, while they are lighter and simpler to manufacture compared to steel reinforced elastomeric isolators. The main differences between SLFREI and fiber reinforced elastomeric isolators, previously reported in the literature, are that frictional damping is not produced in reinforcement fibers of the SLFREI and it is able to sustain very large shear strains (225%) in the presence of top and bottom steel end plates. Investigation of the effect of the shape factor of elastomer layers has shown that similar to steel reinforced isolators, increasing the shape factor of elastomer layers increases the value of vertical stiffness for fiber reinforced isolators too. In the fiber reinforced specimens, by increasing the shape factor from 14.5 to 39.8, the value of effective compression modulus has increased by about 43%. But the shape factor of elastomer layers has no effect on the effective shear modulus and equivalent viscous damping ratio. Investigation of the effect of variation of vertical load (from 67 kN to 135 kN) on the shear characteristics has shown that variation of effective horizontal stiffness or effective shear modulus in this range of vertical loads is small (between 2% and 6%) for all specimens. But the effect of vertical load on the values of equivalent viscous damping ratio is significant for both the fiber reinforced isolator specimens (between 25% and 45%) and the steel reinforced isolator specimen (40% increase). The experiments have also shown that repeating the horizontal tests with 100% shear strain amplitude after the tests with greater shear strains, has decreased the effective shear modulus (down to 26%) and increased the damping (up to 48%). This stress softening is due to the Mullins effect in the filled rubbers. This effect need to be considered in evaluating the response of the isolated structures during an earthquake with cyclic motions.
references
Gent, A.N., 2001. Engineering with Rubber, second ed. HanserGardner Publications Inc., Cincinnati, OH, USA. International Conference of Building Officials (ICBO), 1997. Earthquake regulations for seismic-isolated structures. Uniform Building Code, Whittier, CA, 1997 (Appendix Chapter 16).
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