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Low-cost Base Isolation Devices for Residential Buildings

Habib Sadid, Ph.D., PE, Professor of Civil Engineering Idaho State University Campus Box 8060 Pocatello, ID 83209 Bridger D. Morrison, MS in Structures JUB Engineering INC 151 N 3 Ave, Suite 101 Pocatello, ID 83201

Elastomeric base isolation systems are proven to be effective in reducing seismic forces transmitted to buildings. However, due to their cost, the use of these devices is currently limited to large and expensive buildings. The application of such systems in smaller structures, such as residential buildings, depends upon the ability to reduce the cost while maintaining functionality under the corresponding lighter loads. Several lightweight and low-cost base isolation devices suitable for residential buildings were fabricated and tested for their dynamic performance. These devices were fabricated by binding alternating layers of neoprene rubber and fiberglass mesh. The fiberglass mesh was used to increase the vertical stiffness of the bearings while maintaining low lateral stiffness. The effects of axial load, rubber hardness, and the ground acceleration on the lateral stiffness of these devices were examined. Natural frequencies of the bearings were lower than that predicted by theory. The effect of the rubber hardness on the performance of the bearings was not as significant as that predicted by the theory. The dynamic testing indicated that it may be possible to produce low-cost bearings with a low horizontal stiffness for residential construction. Introduction: Base isolation, or the method of decoupling a structure from its base, and in effect from the horizontal motion produced by an earthquake. In a base isolation system, the horizontal stiffness is low enough to prevent the ground motion from being transmitted to the structure. Elastomeric bearings and sliders are widely used in the current practice. In 1909, J.A. Calantarients submitted a patent application to the British patent office for a proposed construction method which used a layer of fine sand, mica, or talc beneath a building which he called a "free joint". Calantarients believed the "free joint" would allow the building to slide in the event of an earthquake, effectively decoupling the building from the ground in the horizontal direction and reducing the damaging effects of an earthquake [1]. In 1969, the construction of an elementary school in Skopje, Macedonia, was completed, making it the first structure in the world to have base isolation constructed of rubber. At that time, the science behind elastomeric bearings was underdeveloped and not well known. As a result, the rubber bearings supporting the structure were completely unreinforced, causing the rubber bearings to bulge due to the weight of the building. In an earthquake, the building will likely "bounce and rock backwards and forwards" because the vertical and horizontal stiffness are the same [2]. The Foothill Communities Law and Justice Center in the County of San Bernardino, California, was the first building in the United States to incorporate base isolation. It was also the first building in the world to use high-damping natural rubber for its bearings. This building is four stories high with a full basement and designed to withstand an earthquake with a Richter magnitude of 8.3. This design is warranted since the building is only about 13 miles from the San Andreas Fault [1&2]. In 1992, the rehabilitation of the Mackay School of Mines at the University of Nevada, incorporated the use of a slider/elastomer combination for base isolation. This combination was used in an attempt to take advantage of the benefits of both sliders and elastomeric bearings. The sliders create a system with a long period, while the elastomeric bearings control displacements, torsion, and can produce a stiffening action if the displacement becomes large [2]. In recent times, the retrofitting of important or historical buildings has become quite popular. The U.S. Court of Appeals building in San Francisco, California has been retrofitted with sliders to protect against earthquakes. Other buildings that have been retrofitted in California are the Oakland City Hall and the San Francisco City Hall. New construction is also incorporating base isolation into the design. Both the Fire Command and Control Facility and the Emergency Operations Center in Los Angeles County were constructed using high-damping natural rubber bearings. The Caltrans/CHP Traffic Management Center in Kearny Mesa near San Diego, California is another emergency center

constructed using a base isolation system. In 1995, a hospital for the County of San Bernadino, consisting of five buildings, was supported on 450 natural rubber isolators. The office building for AutoZone in Memphis, Tennessee, was constructed using 24 lead-rubber isolators and 19 natural rubber isolators [2]. Base isolation has been incorporated in building construction throughout the world. The benefits of such isolation have become evident following earthquakes in areas where base isolation has been used. One such example is the USC Hospital located in central Los Angeles. The seven story building survived the Northridge, California earthquake. The building not only survived, but "continued to operate, while similar buildings with a conventional design collapsed." The Kobe-City earthquake in Japan tested the effectiveness of base isolated buildings there. A computer center and a laboratory building, both equipped with base isolation systems, survived the earthquake "while being surrounded by rubbles of hundreds of similar buildings on conventional footings" [3]. It has become evident in recent times that base isolation can be very effective in the event of an earthquake. The cost of installing base isolation systems has been so great that it is generally only used for emergency centers, historical buildings, and buildings housing very expensive and sensitive equipment. The high cost has limited the widespread use for all types of buildings such as housing, schools, and other types. Use of base isolation devices in developing countries has been practically non-existent due to the high costs. It is desired to reduce the cost of such systems allowing the adoption of base isolation in all types of construction in seismic prone countries. Current Practices in Base Isolation: Today, there are two main types of base isolating systems used, the slider systems and the elastomeric bearing systems. The slider systems are designed based on the concept of complete decoupling of the structure from its foundation by providing rollers between the structure and the foundation. There are some downfalls to this type of system. One major downfall is that sliders have no restorative forces. Once the building has been displaced, the structure will remain displaced. Another shortfall of sliders is their low horizontal resistance to small disturbances such as wind loads. One more downfall to using sliders is that over an extended period of time without being used, the force needed to displace the building can increase, making the sliders ineffective in an earthquake. For these reasons along with others, elastomeric bearings have become the most widely used type of base isolation system today. There are many benefits of elastomeric bearings. One major benefit is that they can be designed for higher vertical stiffness for load bearing purposes, while, maintaining lower horizontal stiffness. Elastomeric bearings have inherent restorative forces to return the structure to its original position after the effect of an earthquake. As discussed previously, elastomeric bearings that are not reinforced can cause the building to bounce and rock back and forth. Because of this, an effective system has been incorporated to increase the vertical stiffness of the bearing while maintaining the horizontal stiffness low. This method of reinforcement is usually done by the means of bounding steel plates between the individual layers of rubber. The steel reinforcement prevents bulging of the rubber and increases the vertical stiffness of the bearing. Fiber Reinforced Elastomeric Bearings: The current practice of using steel plates to reinforce the bearing has proved to be effective, but is also one of the main reasons that such bearings are so expensive and therefore, limited to only certain types of applications. Within the past few years, alternative methods of building effective elastomeric bearings have been studied. One very promising alternative is to use man-made fibers to serve as the reinforcing layers. The tensile strength of the fibers can be comparable to steel while the weight can be drastically reduced. An abstract of a seminar given by James Kelly at the University of Illinois states that in order for base isolation in the form of elastomeric bearings to become more widely used, especially for housing in developing countries, "the cost and weight of the isolators must be reduced" [4]. Kelly then explains that the majority of the weight in a bearing comes from the steel reinforcing plates. He also explains that the high cost comes from the labor involved in preparing the steel plates and rubber layers for vulcanization. By replacing the steel layers with fiber reinforcement, the weight of the bearing could be reduced dramatically. Eliminating the vulcanization process and the related preparation of the steel and rubber layers may also reduce the labor, and as a result, the cost. Another possible benefit to using fiber reinforcement is that large shapes or long strips of the bearing can be manufactured, and then individual bearings can be cut to the desired size. Finally, Kelly states a benefit that long rectangular strip bearings "would have distinct advantages over square or circular isolators when applied to buildings for which the lateral resisting system is made up of walls" [4]. Vibration Theory: In dynamic modeling of the structure and the base isolation devices, the structure is assumed to be rigid. As a result of this assumption, the entire structure and the isolating devices were modeled as a single degree of freedom (SDOF) system for which, the equation of motion is given by:

m x = - k [ x - u g ] - c[ x - u g ]

Using the following variable definitions: k = n2 , c = 2 n , and = c m m c cr The equation of motion of the system becomes

··

·

·

(1)

··

x = -

n

2 n

[x - u

g

] - 2

n

[x- u

·

· g

]

(2)

Transmissibility (T) is defined as the ratio of the displacement of the mass to the ground and is written in the following form. It is assumed that the input motion and the resulting response are harmonic. Introducing the frequency ratio as

=

the transmissibility of the system can be written in the following form.

T = ~ x ~ u g =

[( 1

(1 -

+

2

4 )

2

2

4

2

)

2

1

/ 2 2

+

]

(3)

1 / 2

For a frequency ratio, , of 0, the transmissibility, T, is equal to 1 representing static displacement. When is equal to 1, resonance occurs resulting in very high transmissibility, approaching infinity for low damping ratios. As , the damping coefficient, increases, T decreases. For = 1.4, transmissibility for all values of is equal to 1, and beyond that value of , the transmissibility is less than 1 for all values of . The goal of base isolation is to have the transmissibility less than 1. Behavior of Rubber Bearing under Compression: Kelly [2,5] provides a simplified method of designing elastomeric bearings using steel plates and fibereinforcement. Kelly's simplified version results from the analysis of Rocard [6], Gent and Lindley [7], and Gent and Meinecke [8]. The analysis of a bearing with fiber reinforcement becomes much more complex than that for a bearing with rigid reinforcement. The two properties of fiber reinforcement that adds to the complexity of the analysis is the stretching of the fibers and the non-rigid behavior of the flexible reinforcement. The fiber reinforcement used in other studies, as well as in this research, is made up of very small individual fibers grouped together in strands. The strands are then grouped and twisted into cords with larger diameters. Although the individual fibers may not be flexible in tension, the cords will allow some stretching to occur when subject to tension. This stretching of the fibers is incorporated as an additional displacement throughout the thickness of the rubber layers. In determining the additional displacement u1(r), the material properties of the fiber reinforcement become incorporated into the analysis. The modulus of elasticity, the Poisson's ratio, and the equivalent thickness of the fiber reinforcement are required to determine the additional displacement, which carries through to the compressive modulus of elasticity of the bearing. The non-rigid behavior of the fiber reinforcement eliminates the validity of the assumption used for steel reinforcement that the plane sections remain plane. In addition, the non-rigid behavior of the fiber reinforcement induces additional damping into the bearing when subject to shear. In shear, the plane cross-section of a fiber-reinforced bearing becomes curved, and the tension in the fiber bundles acts on the curvature of the reinforcing sheet. The tension causes the individual strands within the fiber bundles to slip against each other, producing a frictional damping within the bearing. This energy dissipation can be very beneficial in designing a bearing to have a specified level of damping [5]. The non-rigid behavior of the fiber reinforcement becomes important in determining the bending behavior of the bearing. The vertical stiffness and bending behavior of bearings was not the focus of this paper, and for this reason, the total analysis will not be presented here. Tsai-Kelly [9] developed equations for fiber reinforced composite bearings based on assumptions that the rubber is incompressible and the dominant stress component is equal the pressure acting on the bearing. The fiber-reinforcement is assumed to be flexible in extension, but completely without flexural rigidity. As a result, the compression modulus of elasticity of a circular bearing is given by

(1 + ) k 2t I 1 ( b ) 1 - 2 bI ( b ) 0 1 - (1 - ) I 1 ( b ) bI 0 ( b )

Ec =

f

(4)

where

k

f

=

Eftf 1 -

2

,

( b ) 2 , 4

b = S 48

I 1 ( b )

Gt , b S = 2t kf

+ ( b ) 3 16

I 0 ( b ) 1 +

b

2

: Poisson's ratio for fiber;

t : thickness of single layer of elastomer; Ef : modulus of elasticity of fiber

tf : equivalent thickness of fiber; b : radius of bearing; G: shear modulus of elastomer As b approaches infinity, Equation (4) reduces to

Ec =

(1 + ) k f 2t

(5)

Vertical stiffness of a bearing is given by

kV =

Ec A t

(6)

Where: Ec = Modulus of elasticity in the vertical direction; A = Area in which the load is applied; t = Total thickness of the bearing Although the vertical stiffness is important in determining the stability of the bearing and ensuring sufficient vertical support, the horizontal stiffness is what a structure's response depends upon in the event of an earthquake A structure's response to seismic forces depends largely upon the horizontal stiffness of the bearings. The natural frequency, and in effect, the structure's response is a function of the horizontal stiffness of the bearing. The horizontal stiffness of a bearing, for small displacement, is given by

k

H

=

AG h

(7)

Bearing Design: The contributing frequency of an earthquake ranges from 1to 4 Hz, with the most damaging frequency being around 2 Hz. The isolation bearing can be designed to protect the structure at that frequency. As it was mentioned, a transmissibility of less than one can be achieved at a frequency ratio () greater than 1.4. (For any frequency n < /1.4, T < 1.0.) If the natural frequency of the bearing is 1/3 the natural frequency of the damaging earthquake frequency, the transmissibility will be about 20 percent, or a reduction of 80 percent. This amount of reduction is very desirable since the structure will only feel an acceleration of 0.1g for an earthquake of 0.5g which is the upper limit of most earthquakes. An acceleration of 0.1g will have very minimal effect on a structure and is therefore the target maximum acceleration for a structure for the purpose of this work. Designing a bearing to have a natural frequency of 0.5 Hz will be conservative and results in a drastic reduction in the acceleration that a structure feels compared to the acceleration of an earthquake. The relatively small loads that are produced by residential and other smaller buildings makes it difficult to design a bearing with a natural frequency as low as 0.5 Hz. There are two ways to alter the natural frequency of a base isolation system. In order to lower the natural frequency, the mass that each bearing supports can be increased, or the horizontal stiffness of the bearing can be decreased. Using fewer bearings will result in a higher load per bearing, but can induce stability problems. The alternative is to use a material with a lower stiffness. The use of very soft elastomer is the focus of this research in an attempt to produce bearings with a low stiffness, and therefore a low natural frequency. Included in this research is the use of fiber reinforcement to achieve a less expensive bearing and examine the effect of fiber reinforcement in elastomeric bearings. The design for the bearings was based on one that would allow easy implementation into construction as shown below in Figure 1. A bearing size that would fit without additional design was desired to reduce the cost of implementation.

Figure 1 ­ Schematic of Implementation into Construction Sample sheets of neoprene natural rubber of five different hardnesses were tested for their mechanical properties. The different samples were uniquely named based on hardness ranging from 10 Shore A, 20, 30, 40, and 50 Shore A, with 10 Shore A being the softest sample, and 50 Shore A being the hardest sample. Cylindrical samples measuring 1.14 inches in diameter with a thickness of 0.5 inches, were cut from the sample sheets following the procedure outlined in the American Society for Testing Materials (ASTM) standard D395-98. Each sample was compressed beneath a loading cell while a set of

four Linear Variable Differential Transducers (LVDT) measured the deformation of the sample. The compression test was performed on five samples from each of the five hardnesses, totaling 25 compression tests in all. Based on the results obtained through the compression testing, two samples with the lowest shear moduli, 10 Shore A and 20 Shore A were selected for bearing design. The current practice in bearing design uses elastomer layers with steel plates added for vertical stability. The bearing design philosophy chosen for the design of prototypes was similar to that used in current practice. As discussed previously, fiberglass fabric reinforcement was chosen in place of the steel plates in an attempt to decrease the cost and complexity of manufacturing, as well as the weight of the bearing. Very little information is available on how to implement the use fiberglass reinforcement in such bearings. Several attempts were made to find a combination of adhesive and fabric that would create a good bond and provide sufficient vertical stiffness. The first attempt, using a tightly woven fabric and contact cement, was unsuccessful in bonding the fabric to the rubber. A different fiberglass mesh, one having larger openings, was chosen along with a urethane adhesive. The fiberglass mesh used is commonly used in dry-wall finishing in houses and other buildings. The urethane adhesive, LORD Adhesive 7542A/B, was chosen for its flexible bond and ability to bond well with rubber. The layers of rubber were stacked with the fiberglass mesh, oriented in alternating 90° and 45° directions, between each layer of rubber as shown in Figure 2. 3" diameter cylinders with a height of 1.5" were cut from the stacks while ensuring minimal heating. Steel channel sections were constructed to fit around a common 2" X 4" to attach to the foundation and structure as shown previously in Figure 1. The cylinder samples were then glued to the steel channels forming the top and bottom bearing plates and attachment devices. A total of four bearings were constructed from each of the two materials chosen. Each set of four bearings was attached to the horizontal shake table as shown below in Figures 3 and 4.

Figure 2 ­ Orientation of Fiberglass Reinforcing Layers

Figure 3 ­ Schematic of Shake Table Setup

Figure 4 ­ Shake Table Loaded with 800 lbs The dynamic tests performed consisted of a frequency sweep test to determine the natural frequency of the bearings. The mass supported by the bearings consisted of a steel tray and numerous steel angle irons. The angle irons were stacked on the steel tray and secured tightly to prevent any shifting during the testing. The weight supported by the bearings along with the acceleration of the table was changed for each test. The weight supported by the bearings consisted of 800, 1600, and 2400 pounds, and the base-line acceleration was alternated between 0.02g and 0.04g. Low base-line accelerations were chosen based on the previous testing attempts that resulted in separation of the bearings. Because the rubber layers were not vulcanized, the bond between each individual layer became a weak point in the bearing. Low base-line accelerations were chosen so that testing could be conducted without destroying the bearings. Test Results: Figure 5 shows the dynamic testing results for a load of 2400 pounds. Since the acceleration of the table was held constant within the limits of the equipment, the frequency at which resonance occurs can be obtained from the graph at the point where the acceleration of the mass reaches a maximum. From Figure 5, the resonance occured at 1.36 Hz. It was observed that the acceleration had no effect on the natural frequency within the limits of the equipment. Using the data above, a plot was generated to depict the relationship between the natural frequency and the load. Figure 6 shows the plot of load vs. natural frequency for the bearings made of rubber with hardness of 10 Shore A. It was discussed that a natural frequency of 0.5 Hz would produce a desirable reduction in the acceleration that a structure would experience during an earthquake. Because the natural frequencies of both sample sets were greater than 1 Hz under the chosen parameters, Figure 6 can be used to predict a range of loads required to produce a natural frequency of less than 1 Hz. In reality, the load that each bearing supports can be increased by decreasing the number of bearings used in total. Using the exponential equation for the line of best fit from Figure 6, where x is a multiple of 800 lbs, it can be predicted that a load of 11,230 lbs, or 2,810 lbs per bearing would result in a system with a natural frequency of 0.5 Hz for Sample 10. Using the same approach, it was predicted that a load of 3,370 lbs per bearing would produce a system with a natural frequency of 0.5 Hz for Sample 20. Bearings made from Sample 20 elastomer would require approximately 20 percent larger loads to produce the same desirable natural frequency as compared to Sample 10 bearings. Conclusions: The compression testing results were used to predict the horizontal and vertical stiffnesses of both sets of bearings, as well as the horizontal natural frequencies. The dynamic testing results revealed the natural frequencies of the bearings under six separate sets of parameters. The first conclusion made was that the base-line acceleration did not have an effect on the natural frequencies. Based on the natural frequencies observed, the horizontal stiffnesses were determined for both sets of bearings under all loading conditions. Comparing the experimental stiffnesses for both sets of bearings with the theoretical values shows that the experimental results are consistently lower than what was predicted by the theory. One possible reason for this discrepancy is that the shear modulus of the bearing as a whole may be smaller than the value obtained from the compression testing of the elastomer.

Although the target natural frequency of less than 1 Hz, and preferably around 0.5 Hz, was not reached, the results of this study are promising. The load required to produce a system with the desired natural frequency, as predicted from Figure 6 may be in reality a reasonable load for some types of structures while maintaining stability. The results of the experimental testing show that the effect of the elstomer hardness was less than predicted. The theory indicates that the difference in natural frequencies between the two sample sets tested should have been larger than what was observed. This leads to the conclusion that the hardness has less effect on the performance than what can be predicted using current theory.

Dynamic Testing Results - Acceleration vs. Frequency

Hardness 10, Load=2400, g=0.02

0.12

0.1

0.08

Acceleration (g)

0.06

Shake Table

Mass

0.04

0.02

0

Natural Frequency (Hz)

1. 1 88 9 2. 61 55 1 3. 14 22 4 3. 17 90 7 4. 07 62 22 7 5. 30 66 6. 7 01 97 6. 74 70 7. 4 42 72 8. 8 17 8. 6 1 89 29 9 9. 61 4 10 85 .3 3 11 31 .0 38 11 5 .7 9 12 21 .5 2 13 17 .2 1 13 69 .9 50 14 6 .6 15 3 7 .3 57 16 1 .1 1 16 27 .8 0 17 42 .5 2 18 55 .2 7 19 77 .0 6 19 21 .7 61 3

Frequency (Hz)

Figure 5 ­ Dynamic Testing Results for Hardness 10 (Test #3)

Natural Frequency vs. Load (Hardness 10)

3

2.5

2

1.5

y = 2.7792x -0.6493

1

0.5

0 800 1600 2400

Load (lbs)

Figure 6 ­ Natural Frequency vs. Load for Sample 10

Table 1 ­ Experimental Results Load / Bearing 200 lb 400 lb 600lb 200 lb 400 lb 600lb Experimental Natural Frequency 2.77 Hz 1.77 Hz 1.36 Hz 2.89 Hz 1.89 Hz 1.46 Hz Theoretical Natural Frequency 3.50 Hz 2.47 Hz 2.01 Hz 3.87 Hz 2.74 Hz 2.23 Hz

Test # Hardness Hardness 20 10 1&4 2&5 3&6 7&10 8&11 9&12

References: [1] [2] [3] [4] [5] [6] [7] [8] [9] Naeim, Farzad, Kelly, James M., Design of Seismic Isolated Structures, New York, John Wiley & Sons, Inc. 1999 Kelly, James M., Earthquake-Resistant Design With Rubber, London, Spinger-Verlag Limited 1997 "Base Isolation Earthquake Protection", Energy Research, Inc. 1998-99 Kelly, James M., "Structural Control in Developing Countries", SLC Seminar Series, March 23, 2001, MAE Center, University of Illinois, 2001 Kelly, James M., Takhirov, Shakhzod M., Analytical and Experimental Study of Fiber-Reinforced Elastomeric Isolators, PEER Report 2001/11, University of California, Berkeley, 2001 Rocard, Y., "Note sur le calcul des properietes elastique des supports en caoutchoue adherent", Journel de Physique et de Radium 1937: 8:197 Gent, AN., Lindley, PB., "The Compression of Bonded Rubber Blocks", Proceedings Institution of Mechanical Engineers., 173:324, 1959 Gent, AN., Meinecke, EA., "Compression, Bending and Shear of Bonded Rubber Blocks", Journal of Engineering Mechanics., 10(2): 48-53, 1970 Tsai, Hsiang-Chuan, Kelly, James M., Stiffness Analysis of Fber-Reinforced Elastomeric Isolators, PEER Report 2001/05, University of California, Berkeley, 2001

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