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This paper describes an experimental and theoretical study of the feasibilityof using fiber reinforcement to produce lightweight low-cost elastomericisolators for application to housing, schools and other public buildingsin highly seismic areas of the developing world.
EERI DISTINGUISHED LECTURE 2001
Seismic Isolation Systems for DevelopingCountriesJames M. Kelly,a) M.EERI
This paper describes an experimental and theoretical study of the feasi-bility of using fiber reinforcement to produce lightweight low-cost elasto-meric isolators for application to housing, schools and other public buildingsin highly seismic areas of the developing world. The theoretical analysis cov-ers the mechanical characteristics of multi-layer elastomeric isolation bear-ings where the reinforcing elements, normally steel plates, are replaced by afiber reinforcement. The fiber in the fiber-reinforced isolator, in contrast tothe steel in the conventional isolator (which is assumed to be rigid both inextension and flexure), is assumed to be flexible in extension, but completelywithout flexure rigidity. This leads to an extension of the theoretical analysison which the design of steel-reinforced isolators is which accommodates thestretching of the fiber-reinforcement. Several examples of isolators in theform of long strips were tested at the Earthquake Engineering Research Cen-ter Laboratory. The tested isolators had significantly large shape factors, largeenough that for conventional isolators the effects of material compressibilitywould need to be included. The theoretical analysis is extended to includecompressibility and the competing influences of reinforcement flexibility andcompressibility are studied. The theoretical analysis suggests and the test re-sults confirm that it is possible to produce a fiber-reinforced strip isolatorthat matches the behavior of a steel-reinforced isolator. The fiber-reinforcedisolator is significantly lighter and can be made by a much less labor-intensive manufacturing process. The advantage of the strip isolator is that itcan be easily used in buildings with masonry walls. The intention of this re-search is to provide a low-cost lightweight isolation system for housing andpublic buildings in developing countries. [DOI: 10.1193/1.1503339]
INTRODUCTION
The recent earthquakes in India, Turkey, and South America have again emphasizedthe fact that the major loss of life in earthquakes happens when the event occurs in de-veloping countries. Even in relatively moderate earthquakes in areas with poor housing,many people are killed by the collapse of brittle, heavy, unreinforced masonry or poorlyconstructed concrete buildings. Modern structural control technologies such as activecontrol or energy dissipation devices can do little to alleviate this, but it is possible that
a) Univ. of California, Pacific Earthquake Engineering Research Center, 1301 S. 46th St., Richmond, CA 94804
385Earthquake Spectra, Volume 18, No. 3, pages 385406, August 2002; 2002, Earthquake Engineering Research Institute
386 J. M. KELLYseismic isolation could be adapted to improve the seismic resistance of poor housing andother buildings such as schools and hospitals in developing countries.
The theory of seismic isolation (Naeim and Kelly 1999) shows that the reduction ofseismic loading by an isolation system depends primarily on the ratio of the isolationperiod to the fixed-base period. Since the fixed-base period of a masonry block or brickbuilding may be around 1/10 second, an isolation period of 1 second or longer wouldsignificantly reduce the seismic loads on the building and would not require a large iso-lation displacement. For example, the current UBC code for seismic isolation (ICBO1997) has a formula for minimum isolator displacement which, for a 1.5 second system,would be around 15 cm (6 inches).
The problem with adapting isolation to developing countries is that conventional iso-lators are large, expensive, and heavy. An individual isolator can weigh one ton or more.To extend this earthquake-resistant strategy to housing and commercial buildings, thecost and weight of the isolators must be reduced.
The primary weight in an isolator is that of the steel reinforcing plates used to pro-vide the vertical stiffness of the rubber-steel composite element. A typical rubber isola-tor has two large end-plates around 25 mm (1 inch) thick and 20 thin reinforcing platesaround 3 mm (1/8 inch) thick. The high cost of producing the isolators reflects the laborinvolved in preparing the steel plates and laying-up of the rubber sheets and steel platesfor vulcanization bonding in a mold. The steel plates are cut, sand blasted, acid cleaned,and then coated with bonding compound. Next, the compounded rubber sheets with theinterleaved steel plates are put into a mold and heated under pressure for several hours tocomplete the manufacturing process. Both the weight and the cost of isolators could bereduced if the steel reinforcing plates were eliminated and replaced by fiber reinforce-ment. As fiber materials are available with an elastic stiffness of the same order as steel,the reinforcement needed to provide the vertical stiffness may be obtained by using asimilar volume of very much lighter material. The cost savings may be possible if theuse of fiber allows a simpler, less labor-intensive manufacturing process.
If fiber reinforcement were used, it would then be possible to build isolators in longrectangular strips, with individual isolators cut to the required size. All isolators are cur-rently manufactured as either circular or square. Rectangular isolators in the form oflong strips would have distinct advantages over square or circular isolators when appliedto buildings where the lateral-resisting system is walls. When isolation is applied tobuildings with structural walls, additional wall beams are needed to carry the wall fromisolator to isolator. A strip isolator would have a distinct advantage for retrofitting ma-sonry structures and for isolating residential housing constructed from concrete or ma-sonry blocks.
The vertical stiffness of a steel-reinforced bearing is approximated by assuming thateach individual pad in the bearing deforms in such a way that horizontal planes remainhorizontal and points on a vertical line lie on a parabola after loading. The plates areassumed to constrain the displacement at the top and bottom of the pad. Linear elasticbehavior with incompressibility is assumed, with the additional assumption that the nor-mal stress components are approximated by the pressure. This leads to the well-knownpressure solution that is generally accepted as an adequate approximate approach for
calculating the vertical stiffness. The extensional flexibility of the fiber reinforcementcan be incorporated into this approach, and the resulting vertical stiffness calculated.
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 387A number of carbon fiber-reinforced rubber strip isolators were tested on a smallisolator test machine. The tests show that the concept is viable. The vertical and hori-zontal stiffnesses of the strip isolator are less than those for the equivalent steel-reinforced isolator, but still adequate, and they proved to be easy to cut with a standardsaw, in contrast to steel-reinforced isolators that are difficult to cut and need specialsaws. They were light and in use could be put in place without the use of lifting equip-ment.
Much recent discussion has focused on so-called smart rubber bearings or intelligentbase isolation systems as the new thrust in seismic isolation research. While there maybe a role for these adaptive systems for large expensive buildings in advanced econo-mies, the development of lightweight, low-cost isolators is crucial if this method of seis-mic protection is to be applied to a wide range of buildings, such as housing, schools,and medical centers in earthquake-prone areas of the world.
VERTICAL STIFFNESS OF FIBER-REINFORCED BEARINGS
The essential characteristic of the elastomeric isolator is the very large ratio of thevertical stiffness relative to the horizontal stiffness. This is produced by the reinforcingplates, which in current industry standard are thin steel plates. These plates prevent lat-eral bulging of the rubber, but allow the rubber to shear freely. The vertical stiffness canbe several hundred times the horizontal stiffness. The steel reinforcement has a similareffect on the resistance of the isolator to bending moments, referred to as the bendingstiffness. This important design quantity makes the isolator stable against large verticalloads.
COMPRESSION OF PAD WITH RIGID REINFORCEMENT
A linear elastic theory is the most common method used to predict the compressionand the bending stiffness of a thin elastomeric pad. The first analysis of the compressionstiffness was done using an energy approach by Rocard (1937); further developmentswere made by Gent and Lindley (1959) and Gent and Meinecke (1970). A very detaileddescription of the theory is given by Kelly (1996).
The analysis is an approximate one based on a number of assumptions. The kine-matic assumptions are as follows:
(i) points on a vertical line before deformation lie on a parabola after loading
(ii) horizontal planes remain horizontal
We consider an arbitrarily shaped pad of thickness t and locate a rectangular Cartesiancoordinate system, (x,y,z), in the middle surface of the pad, as shown in Figure 1a. Fig-ure 1b shows the displacements, (u,v,w), in the coordinate directions under assumptions(i) and (ii):
388 J. M. KELLYu~x,y,z!5u0~x,y!S12 4z2t2 Dv~x,y,z!5v0~x,y!S12 4z2t2 D
w~x,y,z!5w~z! (1)
This displacement field satisfies the constraint that the top and bottom surfaces of thepad are bonded to rigid substrates. The assumption of incompressibility produces a fur-ther constraint on the three components of strain, xx , yy , zz , in the form
xx1yy1zz50 (2)
and this leads to
~u0,x1v0,y!S12 4z2t2 D1w, z50where the commas imply partial differentiation with respect to the indicated coordinate.When integrated through the thickness this gives
u0,x1v0,y53D
2t5
3
2c (3)
where the change of thickness of the pad is D (D.0 in compression), and c5D/t is thecompression strain.
Figure 1. Coordinate system (a) and constrained rubber pad (b).
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 389The other assumptions of the theory are that the material is incompressible and thatthe stress state is dominated by the pressure, p, in the sense that the normal stress com-ponents can be taken as 2p. The vertical shear stress components are included but thein-plane shear stress is assumed to be negligible. Linear elastic behavior is assumed.
These assumptions and the equations of stress equilibrium lead to the pressure so-lution
p, xx1p,yy52p5212GD
t352
12G
t2c (4)
The boundary condition, p50, on the perimeter of the pad completes the system for thepressure distribution, p(x,y), across the pad.
The desired result is the effective compression modulus Ec of the pad. This is ob-tained by computing, p(x,y), in terms of the compression strain c , integrating, p(x,y),over the area A of the pad to determine the resultant load P. The effective compressionmodulus Ec is then given by
Ec5P
Ac(5)
The value of Ec for a single rubber layer is controlled by the shape factor, S, defined as
S5loaded area
free area
which is a dimensionless measure of the aspect ratio of the single layer of the elastomer.For example, in an infinite strip of width 2b, and with a single layer thickness of t, S5b/t, and for a circular pad of diameter f and thickness t, S5f/(4t), and for a squarepad of side a and thickness t, S5a/(4t).
The vertical stiffness, Kv , of a rubber bearing made of n pads is given by
Kv5EcA
tr
where the tr5nt is the total thickness of rubber in the bearing.
In this paper we are only interested in the theory for and the testing of a bearing inthe form of a long strip when the effects of the ends can be neglected and the strip takento be infinite. For an infinite strip of width 2b (see Figure 2), Equation 3 reduces to
2p5d2pdx2
5212G
t2c
which, with p50 at x56b, gives
p56G
t2~b22x2!c
390 J. M. KELLYIn this case the load per unit length of the strip, P, is given by
P5E2b
bpdx5
8Gb3
t2c (6)
Since the shape factor, S5b/t, and the area per unit length is A52b,
Ec5P
Ac54GS2 (7)
This result is reasonably accurate for shape factors in the range 5 to 15, but for largeshape factors the predicted value of the compression modulus begins to approach thebulk modulus, K, of the material, which for natural rubber is usually taken as 2000 MPa(300,000 psi). An analysis that includes compressibility is reviewed in a later section.
COMPRESSION STIFFNESS WITH FLEXIBLE REINFORCEMENT
Developing the solution for the compression of a pad with rigid reinforcement is al-gebraically simple enough to be treated in two dimensions and for an arbitrary shape.The problem for the pad with flexible reinforcement is more complicated, however; forsimplicity, the derivation will be developed for the long, rectangular strip isolator. A verydetailed derivation of the solution is given by Kelly (1999) where the influence of theflexibility of the reinforcement on the various quantities of interest is studied. In thisapproach as before, the rubber is assumed incompressible and the pressure is assumed tobe the dominant stress component. The kinematic assumption of quadratically variabledisplacement is supplemented by an additional displacement that is constant through thethickness and is intended to accommodate the stretching of the reinforcement. Thus inthis case the displacement pattern given in Equation 1 is replaced by
u~x,z!5u0~x!S12 4z2t2 D1u1~x! (8)
Figure 2. Infinitely long rectangular pad showing dimensions.
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 391w~x,z!5w~z!
The constraint of incompressibility Equation 2 remains, leading to
u0,x13
2u1,x5
3D
2t(9)
The only equation of stress equilibrium in this case is txx,x1txz,z50, and the assumptionof elastic behavior means that
txz5Ggxz (10)
which with
gxz528z
t2u0 (11)
from Equation 8, gives
txx,x58Gu0
t2
which with the assumption that txx5tzz52p provides the sole equation of equilibriumas
p, x528Gu0
t2(12)
The individual fibers are replaced by an equivalent sheet of reinforcement of thicknesstf . The internal force, F(x), per unit width of the equivalent reinforcing sheet is relatedto the shear stresses on the top and bottom of the pad by
dF
dx2txzuz5t/21txzuz52t/250
as shown in Figure 3. The shear stresses on the top and bottom of the pad are given by
txzuz5t/2528Gu0
2t; txzuz52t/25
8Gu02t
leading to
dF
dx52
8Gu0t
(13)
The extensional strain in the reinforcement f is related to the stretching force throughthe elastic modulus of the reinforcement Ef and the thickness tf such that
f5u1, x5F
Eftf(14)
392 J. M. KELLYwhich when combined with Equation 14, gives
u1,xx528G
Eftftu0
The complete system of equations is
p, x528Gu0
t2(15)
u0, x13
2u1, x5
3D
2t(16)
u1, xx528G
Eftftu0 (17)
The boundary conditions used are the vanishing of the pressure, p, and the reinforce-ment force, F, at the edges of the strip, x56b. The results for p and F from Kelly (1999)are
p5Eftf
t S12 cosh ax/bcosh a Dc (18)F~x!5EftfS12 cosh ax/bcosh a Dc (19)
where
a2512Gb2
Eftft(20)
Figure 3. Force in equivalent sheet of reinforcement.
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 393The load per unit length of the strip, P, is given by
P5Eftf
t2E
0
bS12 cosh ax/bcosh a Ddxc52Eftfat b~a2tanh a!cThis result can be interpreted as an effective compression modulus, Ec , given by
Ec5Eftf
t S12 tanh aa D (21)We note that when a0, i.e., Ef, we have Ec4GS2 as before. The formula alsoshows that Ec,4GS
2 for all finite values of Ef .
The effect of the elasticity of the reinforcement on Ec can be illustrated by normal-izing the compression modulus, Ec , by dividing by 4GS
2, giving from Equation 21
Ec4GS2
53
a2 S12 tanh aa D (22)which is shown in Figure 4 for 0
394 J. M. KELLYS2 and t/tf are certain to be large. If S is large and the influence of the stretching of thefiber is significant it will be necessary to take compressibility of the elastomer into ac-count.
COMPRESSION STIFFNESS WITH COMPRESSIBILITY OF THE ELASTOMER
When the estimated value of Ec from Equation 7 is comparable to the bulk modulus,K, of the elastomer, it is necessary to modify the approach described in the earlier sec-tion to include the influence of compressibility; the required detailed derivation for thesingle pad of arbitrary plan-form is given in Kelly (1996). The essential features of theanalysis for the incompressible pad are retained but the constraint of incompressibility(Equation 2) is replaced by
xx1yy1zz52pK
(23)
and, as shown in Kelly (1996), the equation for the pressure becomes
2p212G
t2pK
512G
t2c
and this is solved as before with p50 on the edges of the pad.For the infinite strip 2b
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 395Ec4GS2
53
b2b2
32
2b4
15512
24
5
GS2
K
and as b, i.e., S becomes very large
Ec5KF12S K12GD1/2 1
S Gshowing that K is an upper bound to Ec .
FLEXIBLE REINFORCEMENT AND COMPRESSIBILITY
In cases of large shape factors, to estimate Ec including compressibility in a mannerconsistent with the assumptions of the previous analysis the equation of incompressibil-ity Equation 2 is replaced by
xx1zz52pK
(25)
where K is the bulk modulus. Integration through the thickness leads to the amendedform of Equation 3
2
3u0,x1u1,x1
pK
5c (26)
This is then supplemented by the same equation of stress equilibrium and by theequation for the forces in the reinforcement, Equation 14. The system of equations forthe combined effects of reinforcement flexibility and compressibility is now
p, x528Gu0
t2(27)
u1, xx528Gu0Eftft
(28)
2
3u0, x1u1, x1
pK
5c (29)
Two dimensionless parameters, a and b, as defined in previous sections, determinethe comparative significance of flexibility in the reinforcement and compressibility inthe elastomer.
In terms of a and b, Equations 27 and 28 become
~p/K!,x52
3b2u0b
2 (30)
396 J. M. KELLYu1, xx522
3a2u0 /b
2 (31)
Differentiation of Equation 29 once and substitution of p and u1 from Equations 30and 31 gives
u0, xx2~a21b2!
b2u050
from which we have
u05A cosh lx/b1B sinh lx/b
where
l25a21b2
In turn, using Equations 27 and 28 gives solutions for p and u1 in the forms
u1522
3
a2
l2A cosh lx/b2
2
3
a2
l2B sinh lx/b1C1x1D
and
p/K522
3
b2
lbA sinh lx/b2
2
3
b2
lbB cosh lx/b1C2
The constants of integration are, of course, not independent of each other but arerelated through the basic equations. Substitution of the three solutions into Equation 29gives
2
3
l
b~A sinh lx/b1B cosh lx/b!2
2
3
a2
lb~A sinh lx/b1B cosh lx/b!1C1
22
3
b2
l~A sinh lx/b1B cosh lx/b!1C25c
The coefficients of sinh bx/b and cosh bx/b vanish and the result is C11C25c .
For the particular problem of the compression of the strip it is useful to consider theobvious symmetries in the solutions. Thus u0 and u1 are anti-symmetric and p is sym-metric on 2b
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 397The boundary conditions for B and C1 are that the pressure p at the edges x56b iszero and that the stress in the reinforcement Efu1,x also vanishes at the edges. Thus
22
3
a2
lbB cos l1C150
22
3
b2
lbB cosh l2C152c
giving
B53
2
l
a21b2b
1
cosh lc
C15a2
a21b2c
and the solution becomes
u053
2b
sinh lx/b
a cosh lc
u15ba2
a21b2 Sxb2 sinh lx/bl cosh l Dcand
pK
5b2
a21b2 S12 cosh lx/bcosh l Dc (32)Integration of p from Equation 32 above and use of Equation 5 gives
Ec5Kb2
a21b2 S12 tanh ll D (33)If the effect of compressibility is negligible then b0 and l5a and we have
Kb2512Gb2
t2
giving
Ec5Eftf
t S12 tanh aa D (34)which is the same as the result in the previous section. On the other hand, if the flex-ibility of the reinforcement is negligible then a0 and lb, giving
398 J. M. KELLYEc5KS12 tanh bb D (35)If the compression modulus is normalized by 4GS2, then from Equation 33 we have
Ec4GS2
53
a21b2 S12 tanh~a21b2!1/2
~a21b2!1/2 D (36)which demonstrates how the vertical stiffness is reduced by both compressibility in theelastomer and flexibility in the reinforcement.
EXPERIMENTAL RESULTS
Several fiber-reinforced bearings were constructed and tested in compression andshear. Six specimens manufactured by Dongil Rubber Belt Co., Ltd. (Pusan, Korea)were shipped in the form of strips with slightly varying dimensions as given in Table 1.The width-to-height ratio was very close to 2 and length-to-height ratio was around 7.5.Each bearing had 99 mm of rubber and was reinforced by 30 plane sheets of carbonfiber 0.27 mm thick.
The effective vertical stiffness of the bearing was obtained from a compression testconducted in the following way. The specimen was monotonically loaded up to the targetvalue of vertical pressure and then three cycles of vertical loading with small amplitudeabout this target value were performed. The shear stiffness of a specimen was obtainedfrom sets of shear cycles with step-wise increasing amplitude. These shear tests wereconducted for various values of vertical pressure and for three angles between the testingdirection and the longitudinal direction of the strip. All tests were conducted on bearingsthat were not bonded to the test machine.
Table 1. Test specimens
NameLength(mm)
Width(mm)
Height(mm)
Area(mm2) Comments
Presence of rubber cover
East West North South
DRB1 735 183 105 134505 Yes No No NoDRB2 750 190 105 142500 Yes No Yes NoDRB3 740 190 105 140600 No Yes Yes NoDRB4 365 190 105 69350 cut from 19037553105 No No Yes NoDRB5 390 190 105 74100 cut from 19037553105 Yes No Yes NoDRB6 377 183 105 68991 cut from 18337553105 No Yes No NoDRB7 377 183 105 68991 cut from 18337553105 No No No NoDRB8 730 185 105 135050 kept as sample
Notes:1) All test specimens were composed from 33 layers of 3-mm thick rubber and 30 layers of 0.27 mm fiber.2) The in-plane test machine imposed shear in the east-west direction (representing 0 direction).3) The location angle of the specimen was measured from the west direction counterclockwise (i.e., at 90 theformer west side points south).4) The rubber cover of bearing sides reduces the effective work area of the bearing in the vertical direction. Thethickness of the rubber cover varies from 5 mm to 9 mm on the long side of the bearing (north or south) andvaries from 1 mm to 3 mm on the short side of the bearing (east or west).
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 399These tests were carried out on a test machine, shown in Figure 5, designed to pro-duce in-plane vertical and horizontal cyclic loading. The vertical load was appliedthrough a stiff frame to the specimen by two hydraulic actuators. The horizontal loadwas applied by a hydraulic actuator. The test machine had a displacement capacity of6254 mm (10 inches) in the horizontal direction and a load capacity of 61,140 kN (260kips) in the vertical direction. The photograph in Figure 6 shows a global view of a testin progress.
TEST PROGRAM
Specimen DRB1 was tested under vertical load control monotonically to 1.73 MPa(250 psi) of vertical pressure and three fully reversed cycles with 60.35 MPa (50 psi)amplitude were performed, then monotonically unloaded. A similar test at 3.45 MPa(500 psi) vertical pressure with 60.35 MPa (50 psi) amplitude was performed to studythe vertical stiffness at the greater vertical load.
The horizontal test was performed under horizontal displacement control. SpecimenDRB1 was tested in cyclic shear, with three fully reversed cycles at four peak strain lev-els of 25%, 50%, 75%, and 100% (based on 99 mm rubber thickness) applied at a ver-tical pressure of 1.73 MPa (250 psi). The vertical pressure was increased to 3.45 MPa(500 psi) and the shear test was repeated. The peak value of shear deformation was in-creased by 1.5 and the test repeated. The shear tests were done for the following se-quence of the angle between the testing direction and the longitudinal direction of thestrip: 0, 90, and 45. Specimens DRB2 and DRB3 were tested under the same testprogram, but with a different sequence of the angle between the testing direction and thelongitudinal direction of the strip. For specimen DB2 this sequence was 45, 0, and 90,and for specimen DRB3 it was 90, 45, and 0.
Figure 5. Testing setup.
400 J. M. KELLYIn order not to exceed the capacity of the testing machine, a specimen was cut in twoequal halves, denoted as DRB4 and DRB5. The half-length specimens DRB4 and DRB5were used to study behavior at higher levels of vertical load and larger shear deforma-tion. The value of vertical pre-load was increased to 6.90 MPa (1000 psi) and the sheardeformation was doubled to study the behavior at a larger shear strains. The angle be-tween the testing direction in shear and the longitudinal direction of the strip was 0 forspecimen DRB4 and 90 for specimen DRB5.
The possibility of increasing of shear capacity of the bearings by stacking them (oneon top of the other) was studied by testing DRB8 and DRB9 in this way. The joint speci-men was vertically loaded up to 3.45 MPa (500 psi) vertical pressure and then was testedin shear at 50%, 100%, 150%, and 200% peak shear strains based on the single bearingthickness.
Figure 6. Test in progress.
Figure 7. Specimen DRB6 at 100% shear deformation (90).
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 401Finally, specimen DRB9 was cut in two equal halves, and these were designated asspecimens DRB6 and DRB7. They differed in that DRB6 had rubber cover at one end,whereas specimen DRB7 had no side rubber cover. They were tested under the same testprogram at three levels of vertical pressure: 0.87 MPa (125 psi), 1.73 MPa (250 psi), and3.45 MPa (500 psi). Figure 7 is a photo of specimen DRB6 under 100% shear deforma-tion testing at 90 to the longitudinal direction. The deformation with the same magni-tude at 45 to the longitudinal direction is shown in Figure 8 and the specimen under100% shear deformation in the longitudinal direction is shown in Figure 9.
DISCUSSION OF EXPERIMENTAL RESULTS
Horizontal Test Results
The manufacturer of the test isolators gave the nominal shear modulus of this naturalrubber compound as 0.690 Mpa (100 psi). The three full-length uncut specimens had anaverage area of 0.140 m2 and a total rubber thickness of 0.099 m. The horizontal stiff-ness, KH , of a conventional isolator is given by
Figure 8. Specimen DRB6 at 100% shear deformation (45).
Figure 9. Specimen DRB6 at 100% shear deformation (0).
402 J. M. KELLYKH5GA/tr
and for these values KH is
KH5970 kN/m
At 100% shear strain and a pressure of 1.73 Mpa (250 psi) the average horizontalstiffness in the longitudinal loading direction is 1280 kN/m, in the lateral loading direc-tion is 863 kN/m and at 45 is 1120 kN/m.
The hysteresis loops for the longitudinal loading direction tend to stiffen when theshear strain is increased from 100% to 150%, whereas in the lateral direction the loopsturn over so that the instantaneous tangent stiffness is negative at the larger strains. How-ever, this effect is reduced at higher pressure levels. The 45 loading does not produceeither stiffening or softening but gives values intermediate between the 0 and 90 load-ings.
The value of the stiffness at 100% shear strain in the longitudinal direction is slightlyhigher than would be expected from the nominal value of the shear modulus but in thetransversal loading direction the stiffness is lower. At 45 the stiffness is intermediatebetween the other two. If we assume that the layout of the strip isolator is orthogonalwith roughly the same number in each direction, the average between 0 and 90 is closeto the value at 45 so that the system will have the same period in any direction of move-ment.
The period, T, can be roughly estimated using the pressure and the effective shearmodulus. The period is given by
T52pAptrGg
If the average pressure over the system is 3.45 Mpa (500 psi) as in the tests and themodulus is 0.690 Mpa (100 psi) with 99 mm of rubber, we have a period of 1.4 seconds.From the code formula this would produce a displacement of 143 mm (5.64 inches) anda shear strain of 1.41. Adjusting the values to correspond to the measured stiffness atg51.5, we find that the period increases to 1.5 seconds and the displacement to 150 mm(6 inches).
This suggests that if the period of 1.5 seconds is acceptable as the target value for thedesign of the building, the strip isolators as tested would be adequate, providing that theaverage pressure can be at least 3.45 Mpa (500 psi). A longer period can be obtained byhaving one isolator on top of another. This leads to a period of 2 seconds, a code dis-placement of 200 mm (8 inches) and a g51.0. It is clear that a wide range of practicalobjectives is possible. If it is necessary to have an average pressure of less than 3.45MPa (500 psi) it is possible to use a softer compound. Compounds with shear moduli, at100% strain, down to 0.40 Mpa (60 psi) are available.
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 403Vertical Test Results
The vertical test results are shown in Tables 2, 3, and 4. Since the dimensions of thebearings are slightly different in each case it is useful to tabulate the vertical stiffness interms of the effective compression modulus, Ec , as defined by Equation 5. The full-length bearings DRB1/2/3 are quite consistent with Ec at around 414 Mpa. The two setsof half-length bearings have lower values of Ec at the same vertical pressures of testing.The pair denoted by DBR4/5 was not tested at 1.73 Mpa (250 psi) but at 3.45 Mpa (500psi) and 6.90 Mpa (1000 psi). The set denoted by DBR6/7 was tested at 0.87 Mpa (125psi), 1.73 Mpa (250 psi), and 3.45 Mpa (500 psi). At the common test pressure of 3.45Mpa (500 psi) the average of the two values of Ec of DBR4/5 was the same as that ofDBR6/7, so that we can interpret the effect of variation of the target pressure over aneight-fold range. The fact that at the same pressures the Ec values for the full-lengthbearings are higher than for the half-length bearings is most likely due to the larger in-fluence of free ends in the latter case. The theoretical analysis is developed for the in-finite length strip and for the full-length bearings the length-to-height ratio of 7.5 islarge enough that this assumption is valid. At half this value end effects can be expectedto have some influence. The vertical stiffness of an elastomeric isolation bearing is al-ways difficult to measure since the displacements at the vertical loads corresponding topractical use are extremely small and a great deal of scatter is to be expected.
Table 2. Vertical test results for 1.73 MPa vertical pressure
SpecimenNo.
Area(m2)
ImposedLoad (kN)
Average Pressure(MPa)
Average StiffnessKav (kN/M)
Compression modu-lus Ec (MPa)
DRB1 0.135 233.6 1.73 550853.9 404DRB2 0.143 233.6 1.63 602975.0 417DRB3 0.141 233.6 1.66 597053.3 419DRB4 0.069 N/A N/A N/A N/ADRB5 0.074 N/A N/A N/A N/ADRB6 0.069 120.2 1.74 251687.8 361DRB7 0.069 120.2 1.74 278983.5 400
Table 3. Vertical test results for 3.45 MPa vertical pressure
SpecimenNo.
Area(m2)
ImposedLoad (kN)
Average Pressure(MPa)
Average StiffnessKav (kN/M)
Compression Modu-lus Ec (MPa)
DRB1 0.135 467.3 3.46 791048.8 580DRB2 0.143 467.3 3.27 849319.3 588DRB3 0.141 467.3 3.31 752785.8 529DRB4 0.069 253.7 3.68 349938.19 502DRB5 0.074 253.7 3.43 352040.6 471DRB6 0.069 240.3 3.48 328721.9 472DRB7 0.069 240.3 3.48 351392.3 504
404 J. M. KELLYIt is clear, however, that there is for all test specimens a systematic increase in stiff-ness and Ec when the central value of the pressure around which the load is cycled in-creases. As the pressure is doubled the average value of Ec for the three full-length iso-lators increases by 37% to 565 MN/m2. The half-length bearing tests show an increase inEc over the complete range of pressure. The increase is not linear in pressure but tends todecrease with increasing pressure from 55% at the lowest level to 15% at the highest.This is consistent with the type of carbon fiber used in the bearings. The fiber is woven,two directional, and epoxied into a thin sheet. As the pressure increases the in-plane fi-ber sheet tension increases and tends to straighten out the fiber strands, thus increasingthe effective fiber modulus.
To assess the effect of the various parameters on the vertical stiffness it is necessaryto estimate the actual shear modulus from the tests on shear. At a vertical pressure of3.45 Mpa (500 psi) the average shear stiffness of the first three bearings when tested inthe longitudinal direction 0 is 1.278 MN/m, which with an average area of 0.140 m2
and a thickness of rubber of 99 mm implies a shear modulus of 0.904 Mpa (131 psi),which is considerably larger than the nominal modulus. This use of the longitudinal teststo provide an estimate of the modulus is warranted by the fact that this case will have theleast influence from the roll-off due to the unbonded condition.
A steel-reinforced isolator with this shear modulus, this area of rubber and this thick-ness would, if compressibility effects were ignored, have an effective compressionmodulus Ec given by Equation 5, of 3738 MN/m
2. When compressibility is taken intoaccount the effective modulus is considerably reduced as given by Equation 35. To es-timate b, we use K52000 Mpa (290,000 psi), giving b255.3 and from Equation 35 wehave 1150 MN/m2. The average measured value, 563 MN/m2, can be used to deduce theeffect of the extensibility of the carbon fiber reinforcement. For this purpose we nowturn to Equation 33 and assume that b255.3. From the results we have Ec /K50.28 andfrom the equation we determine that (a21b2)1/253.7, implying a258.4. When theknown values of the various parameters are inserted into the definition of a2 we estimateEf as 14,000 Mpa (2,000,000 psi).
There is no equipment in the laboratory to measure modulus of the carbon fibersheet directly nor has the fabricator provided a value. The result is somewhat lower thanothers quoted for carbon/epoxy sheets and the reason is not clear, but the sheets appear
Table 4. Vertical test results for extreme values of vertical pressure
SpecimenNo.
Area(m2)
ImposedLoad (kN)
Average Pressure(MPa)
Average StiffnessKav (kN/M)
Compression Modu-lus Ec (MPa)
DRB1 0.135 N/A N/A N/A N/ADRB2 0.143 N/A N/A N/A N/ADRB3 0.141 N/A N/A N/A N/ADRB4 0.069 507.3 7.35 467372.6 671DRB5 0.074 507.3 6.86 445858.5 596DRB6 0.069 60.1 0.87 175617.3 252DRB7 0.069 60.1 0.87 167190.4 240
EERI DISTINGUISHED LECTURE 2001: SEISMIC ISOLATION SYSTEMS FOR DEVELOPING COUNTRIES 405to be a very poor quality fiber with many spaces and the portion of the thickness that isfiber cannot be determined from visual analysis. It is certainly possible that the qualityof the reinforcing could be improved but it is clear that even this poor quality sheet isadequate for these bearings. An effective modulus Ec of 563 MN/m
2 at an average pres-sure of 3.45 Mpa (500 psi) implies a vertical vibrational frequency of 20 Hz, which ismore than is necessary in any isolation application. The conclusion is that although thefiber is suspected to be very low quality, and presumably low-cost, it has sufficient stiff-ness and strength for application to low-cost isolators.
CONCLUSIONS
The test results show that the concept of the strip isolator reinforced with carbonfiber is viable. The fact that the isolator can be made in long, wide sheets and cut to therequired width means that the cost of the isolator can be reduced to a level that is ac-ceptable for low-cost public housing. The tests also show that loading in the direction ofthe strip across a cut surface can be a source of delamination. In practice this should notbe a problem since the width of the manufactured sheet will be used as the length of thestrip isolator and the ends will be finished edges. Loading in the transverse direction(90), where the edges are cut, is not so severe, as the rolling of the strip tends to pro-duce lower forces in this direction. The most vulnerable direction of loading is at 45,which appears to put a very distorted pattern of displacement on the isolator and for thisreason it may be advisable to use either a better cutting method such as water jet, whichwill leave a smoother finished surface than a steel saw, or to finish the edge by a cold-bonded surface layer.
The carbon fiber appeared to be very poor quality. The fibers are laid out in only twodirections, 0 and 90, in a woven sheet with many spaces. Nevertheless the isolatorsstill functioned acceptably. It would be possible to make a much better isolator with abetter quality carbon fiber at little increase in cost.
The unresolved issue from the test program is that of overall system behavior,namely, can an isolation system made of strip isolators laid out in an orthogonal gridprotect the masonry wall superstructure above. Isolators loaded in the longitudinal di-rection stiffen with increasing displacement and those loaded across the strip will softenwith displacement above a certain threshold. The question is can the unbalanced shearbe accommodated by the wall system. Further research is needed to study this effect andthe best way to develop a reliable procedure would be to have a masonry block housemodel on isolators on a large shake table.
It is important to recall that the benefit of isolation is achieved primarily through theratio of the isolated period of the building to its fixed-base period. For a constant veloc-ity spectrum the base shear of the fixed-base building is reduced by this factor when thesame building is isolated. A masonry wall structure will have an extremely short fixed-base period, in the range of 0.10 second. A reduction of a factor of 10 can be obtainedwith an isolation period of 1 second and this is not difficult to obtain. In fact, the codeformula for isolation system displacement that has persisted through all versions of theseismic isolation codes in the United States since the earliest in 1986 would predict adisplacement of 15 cm. (6 inches) for a 1.5-second period system, and the isolators
tested here were tested to displacements of 15 cm. (6 inches) and more. However, iflarger displacements are needed, the tests showed that stacking two isolators on top ofeach other was possible, which would allow even larger displacements.
A shake table test using a full size masonry block house would help clarify details ofaccess across the isolation interface, the disadvantages if any of not having the bottomfloor slab-on-grade isolated, and the extent to which a concrete tie-strip is needed be-tween the isolators and the block wall. When these remaining uncertainties are resolvedthis valuable new technology can be implemented in many highly seismic areas in thedeveloping world.
ACKNOWLEDGMENTS
406 J. M. KELLYThe sample isolators were made by Dongil Rubber Belt Co. Ltd. of Pusan, Korea.The test program was conducted at the Structural Test Facility of the Pacific EarthquakeEngineering Research Center, University of California, Berkeley. This research workwas partly supported by the Engineering Research Center for Met-Shape and Die Manu-facturing of Pusan National University, Pusan, Korea, which is gratefully acknowledged.
REFERENCES
Gent, A. N., and Lindley, P. B., 1959. The compression of bonded rubber blocks, Proc. Inst.Mech. Eng. 173 (3), 111117.
Gent, A. N., and Meinecke, E. A., 1970. Compression, bending and shear of bonded rubber-blocks, Polym. Eng. Sci. 10 (2), 4853.
International Conference of Building Officials (ICBO), 1997. Earthquake regulations for seis-mic isolated structures, Uniform Building Code, Appendix Chapter 16, Whittier, CA.
Kelly, J. M., 1996. Earthquake-Resistant Design with Rubber, 2nd edition, Springer-Verlag,London.
Kelly, J. M., 1999. Analysis of fiber-reinforced elastomeric isolators, J. Seismic Engrg. 2 (1),1934.
Naeim, F., and Kelly, J. M., 1999. Design of Seismic Isolated Structures, John Wiley, New York.Rocard, Y., 1937. Note sur le calcul des proprietes elastique des supports en caoutchouc adher-
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(Received 13 March 2002; accepted 6 April 2002)