Development of multistage rubber bearing for seismic isolation of buildings.

Laminated rubber bearings are used to base isolation devices for buildings (refs. 1-4). Usually rubber bearings are designed to have a horizontal natural period of 2.0 - 3.0 seconds and horizontal displacement absorption capacity of 0.2 - 0.3 m for 980 - 4,900 kN of rated loads. But for smaller rated loads, normal laminated rubber bearings with lower horizontal stiffness have slender shapes and cannot generate enough shear displacement absorption during earthquake excitation. To overcome this problem, multistage rubber bearings were developed. The multistage rubber bearing is a laminated rubber bearing which contains small laminated rubber elements. To be stacked with stabilizing plates, multistage rubber bearings have sufficient shear displacement absorption because the laminated rubber elements will not fail due to buckling.

Multistage rubber bearing

Figure 1 shows multistage rubber bearings which are used for base isolation of light structures. These multistage rubber bearings have five stages for a rated load of 882 kN and four stages for a rated load of 1,470 kN and on each stage four element rubber bearings, which are shown in figure 2, are attached at each corner of the stabilizing plates. The horizontal stiffnesses of multistage rubber bearings were designed to have a horizontal natural period of four seconds and a horizontal displacement absorption of 40 cm when a rated load was supported. Element rubber bearings are stacked up to 48 layers for a rated load of 220.5 kN (1/4 of 882 kN) and 40 layers for a rated load of 367.5 kN (1/4 of 1,570 kN). Each layer consists of a rubber sheet made from natural rubber and an inserting plate made of mild steel. Rubber sheets and inserting plates are stacked alternately and adhered to each other by vulcanization. Table 1 shows the specifications of element rubber bearings.

[Figures 1 and 2 ILLUSTRATION OMITTED]

Table 1 - specifications of element rubber bearings

Rate load of element rubber bearings (kN)   220.5   367.5
Df: Diameter of flange (mm)                   400     480
Dr: Diameter of rubber sheet (mm)             260     340
Ht: Total height of rubber bearings (mm)      153     183
Hr: Total height of rubber sheets (mm)      100.8     128
tr: Thickness of a rubber sheet (mm)          2.1     3.2
ts: Thickness of an inserting plate (mm)      0.6     0.8
n: Number of rubber sheets                     48      40

Laminated rubber element tests (refs.5-8)

Combined loading tests

Shear stiffness, vertical stiffness and bending stiffness of element rubber bearings were measured by using a combined loading test device.

Figure 3 shows the horizontal restoring force characteristics of an element rubber bearing under a rated load of 220.5 kN. In tests, we first measured the bending moment when the element rubber bearing's diffraction angle was fixed to O red and defined as 100% in figure 3. This is equivalent to the case where the bending stiffness of the stabilizing plate was sufficiently larger than the element rubber bearing's bending stiffness. In these figures, curves with 80% indicate horizontal restoring force characteristics, vertical displacement change and rotation angle change, respectively, when an 80% of bending moment was applied to an element rubber bearing. Curves with 0% show results without restricting the rotation angle of the upper flange of the element rubber bearing. From these experimental results, it was clear that the horizontal restoring force of the element rubber bearing was decreased and its vertical displacement was increased when the bending moment for restricting the rotation angle was decreased. These experimental results suggest that for designing multistage rubber bearings, it was important that the stabilizing plate have sufficiently large bending stiffness compared with that of the element rubber bearing.

[Figure 3 ILLUSTRATION OMITTED]

Bending tests

Figure 4 shows bending stiffness of an element rubber bearing when a vertical load of 220.5 kN or 110.3 kN was supported. In this experiment, bending moment was subjected to element rubber bearing while maintaining shear deformation at a fixed value. The bending stiffnesses were defined from a change of moment from turning rotation angle zero to 0.01 rad. It was clear that the bending stiffness of the element rubber bearing was strongly dependent on horizontal displacement and would fall rapidly as horizontal displacement became larger. It was also noted that the bending stiffness slightly depended on axial force too.

[Figure 4 ILLUSTRATION OMITTED]

Biaxial test for multistage rubber bearing

Compression and shear test of a multistage rubber bearing was carried out. In this experiment, the horizontal restoring force and vertical displacement of multistage rubber bearings were measured up to the designed displacement absorption level of 40 cm under rated loads of 882 kN and 1,470 kN, respectively. Furthermore, bending stabilizing plate strains were also measured to calculate the bending moment which was generated in the stabilizing plate.

Figure 5 shows the restoring force characteristic of multistage rubber bearings. From the experimental results, they have a tendency to soften at large horizontal displacement, but it was found to be able to support a vertical load up to a required displacement level of 40 cm.

[Figure 5 ILLUSTRATION OMITTED]

Table 2 shows comparisons between the horizontal stiffness of a multistage rubber bearing which was measured directly and was predicted from the element rubber bearing's horizontal stiffness when stabilizing plates were sufficiently rigid for bending. From these results it is concluded that these multistage rubber bearings' stabilizing plates were sufficiently rigid. Figure 6 shows examples of bending strains distribution of 2nd stage's stabilizing plate of a multistage rubber bearing under rated loads of 882 kN and 1,470 kN in the transverse direction of shear deformation. From this measurement result, it was shown that the values of strains were in the elastic region up to the required displacement of 40 cm.

[Figure 6 ILLUSTRATION OMITTED]

Table 2 - horizontal stiffness of the multistage rubber bearings

                 Horizontal Stiffness (kN/m)

Rate load (kN)       Measured   Predicted
      882               225         230
    1,470               434         395

Stiffness analysis of multistage rubber bearing (refs. 9 and 10)

The maximum horizontal displacement of a multistage rubber bearing under a rated load of 882 kN were calculated by FEM analysis in which element rubber bearings were used in a beam model with non-linear stiffness, and a stabilizing plate also used to a normal beam model with linear stiffness (ref. 11). A stiffness matrix of the element rubber bearing used for analysis is shown in equation 1 (figure 6). Where [F.sub.s] is horizontal force, M is bending moment, [F.sub.z] is vertical force, [U.sub.z] is horizontal displacement, l is total height of the element rubber bearing and ?? is rotation angle.

In FEM analysis, to consider the non-linearity of the element rubber bearing's stiffness matrix, an incremental method was adopted (refs. 12 and 13). It was also assumed that each element of the stiffness matrix only depends on horizontal displacement, and each element of the stiffness matrix was established from combined loading test results for an element rubber bearing. Therefore, derivatives in this stiffness matrix were approximated as polynomial functions of horizontal displacement. [Delta] [F.sub.s]/[Delta] [Theta] and [Delta] M/[Delta] [Theta] were defined from the bending test results (figures 4 and 8). The estimated derivatives are shown in figure 9.

[Figures 8-9 ILLUSTRATION OMITTED]

In figure 5 the broken line shows the calculated horizontal restoring force characteristic and the solid line shows the measured one. these results show that the experimental results were well reproduced by this analysis from a comparison of both. Also the buckling displacement of this multistage rubber bearing was predicted from this analysis as being over 100 cm, and the safety factor for displacement of over 2.5 was sought by this analysis.

Implementation (ref. 14)

The main specifications of the base-isolated building which was supported by four multistage rubber bearings of a rated load of 882 kN and two multistage rubber bearings of a rated load of 1,470 kN are shown in table 3. Figure 10 shows the external appearance and the allocation of devices respectively. This base isolated building could withstand a long natural period of four seconds by using these multistage rubber bearings. Therefore excellent seismic isolation performance could be obtained (ref. 15).

[Figure 10 ILLUSTRATION OMITTED]

Table 3 - specification of base isolated building

Building area ([m.sup.2]                                 204
Total floor area ([m.sup.2]                              405
Story                                                      2
Total height (m)                                        10.1
Total weight (ton)                                       586
1st natural period (seconds)                            3.64
Total stiffness of multistage rubber bearings (kN/M)   1,786

Conclusions

Multistage rubber bearings which can be used for base-isolated structures/buildings have been developed. By biaxial loading tests for multistage rubber bearing and combined loading tests (shear, compression and bending) for element rubber bearings, it was that the performance of these multistage rubber bearings were within the requirement for seismic isolation designs.

An FEM method by which an element rubber bearing's stiffness matrix could be determined by combined loading tests was verified experimentally. In this method, stiffness matrices were defined in which each element had non-linear elastic stiffness. Calculated restoring force characteristics agreed with the experimental results. Furthermore, by using FEM's large deformation analysis with these stiffness matrices, the buckling displacement of these multistage rubber bearings could be predicted. The safety factor for displacement absorption under a rated axial load was also determined.

Other applications

Multistage rubber bearings also are used widely in tuned mass damper (TMD) (ref. 16), active mass damper (refs. 17-21), seismic isolation floor (ref. 22), microvibration isolation table (ref. 23) and active vibration isolation floor. Figure 11 shows a multistage rubber bearing which is installed in an active mass damper. In this case, six multistage rubber bearings with a rated load of 882 kN are equipped to support the moving mass of 470 tons. The natural period of the mass damper is 3.6 seconds and the mass ratio (the moving mass/ the first equivalent mass of the structure) is 0.034, and the height of the high rise building is 161 m. This building is a hotel and office complex. The main purpose of the installation of the active mass damper is mitigation of the vibration which are induced by strong winds and earthquake motions.

[Figure 11 ILLUSTRATION OMITTED]

References

(1.) Skinner, R.I., Robinson, W.H. and McVerry, G.H., "An introduction to seismic isolation," 85 (1993), John Wiley & Sons.

(2.) Kelly, J.M., "Earthquake-resistant design with rubber," (1993), Springer Verlag.

(3.) Soong, T.T., Constantinou, M.C., "Passive and active structure vibration control in civil engineering," (1994), Springer Verlag.

(4.) Gent, A.N., "Engineering with rubber," (1992), Oxford University Press.

(5.) Gent, A.N. and Meinecke, E.A., "Polymer engineering and science," January, 1970, vol. 10, no. 1, 48.

(6.) Stanton, J.F., "Journal of engineering mechanics," vol. 116, no. 6, June, 1990, 1351.

(7.) Gent, A., "Journal mechanical engineering science," vol. 6, no. 4, 1964, 318.

(8.) Schapery, R.A. and Skala, D.P., "international journal solids structures," 1976, vol. 12, 401-417.

(9.) Simo, J.C. and Kelly, J.M., "Engng struct.," 1984, vol. 6, July, 162.

(10.) Bathe, K.J. and Bolourchi, S., "International journal for numerical methods in engineering, " vol. 14, 1979, 961-986.

(11.) Martin, H.C., "Introduction to matrix methods of structural analysis, " (1966), McGraw-Hill.

(12.) Livesley, R.K, "Matrix method of structural analysis," (1964), Pergamon Press.

(13.) Bathe, K J., "Finite element procedure, " (1995), Prentice Hall.

(14.) Fujita, T., "Proceedings of the international meeting on earthquake protection of buildings, " 77/C (1991).

(15.) Gupta, A.K, "Response spectrum method, " (1990), Blackwell Scientific Publications.

(16.) Fujita, T, Masaki, N. and Suizu, Y. "Proceedings of the 1991 Asia-Pacific vibration conference, " 9.13 (1991).

(17.) Fujita, T., Kamada,T., Masaki, N. and Suizu, Y. "Proceedings of the tenth world conference on earthquake engineering, " 2073 (1992).

(18.) Maebayashi, K, Shiba, K, Mita, A. and Inada, Y., "Proceedings of the tenth world conference on earthquake engineering, " 2359 (1992).

(19.) Kitamura, H., Fujita, T., Teramoto, T. and Yamane, T., "Proceedings of the tenth world conference on earthquake engineering, " 2061 (1992).

(20.) Fujita, T., Kamada, T., Masaki, N. and Suizu, Y., "Proceedings of first world conference on structural control, " FA4-43 (1994).

(21.) Fujita, T., Kamada, T, Teramoto, T., Kitamura, H., Suizu, Y., Masaki, N., Kanno, T. and Kawauchi, H., "Proceedings of first world conference on structural control, " FA4-53 (1994).

(22.) Morikawa, S., Masaki, N., Suzaki, S. and Suizu, Y., "Proceedings of the international meeting on earthquake protection of buildings, " 125/C (1991).

(23.) Masaki, N., Suizu, Y, Nakayama, K, Tanaka, M., Kuroda, K. and Fujita, T., "Proceedings of the international conference in advanced mechatronics, " 791 (1989).