Author Contributions
Conceptualization, S.-J.M., T.-M.S. and G.-H.K.; methodology, S.-J.M. and T.-M.S.; validation, S.-J.M. and G.-H.K.; formal analysis, S.-J.M. and J.-S.R.; investigation, S.-J.M., T.-M.S., and J.-H.L.; writing—original draft preparation, S.-J.M. and J.-H.L.; writing—review and editing, S.-J.M. and J.-S.R.; funding acquisition, T.-M.S. and G.-H.K. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Cross-sectional shape of the LRB.
Figure 1.
Cross-sectional shape of the LRB.
Figure 2.
Input seismic data (SSE 0.3 g, 5% damping, 137 ft): (a) FRS; (b) time history.
Figure 2.
Input seismic data (SSE 0.3 g, 5% damping, 137 ft): (a) FRS; (b) time history.
Figure 3.
Schematic diagram of static test.
Figure 3.
Schematic diagram of static test.
Figure 4.
Hysteresis curve for OPT1 shear test.
Figure 4.
Hysteresis curve for OPT1 shear test.
Figure 5.
Hysteresis curve for OPT2.
Figure 5.
Hysteresis curve for OPT2.
Figure 6.
Section view of LRB after ultimate static test: (a) vertical section; (b) horizontal section.
Figure 6.
Section view of LRB after ultimate static test: (a) vertical section; (b) horizontal section.
Figure 7.
FE analysis models for simulation of dynamic test: (a) isolated dummy mass model; (b) middle portion of LRB model.
Figure 7.
FE analysis models for simulation of dynamic test: (a) isolated dummy mass model; (b) middle portion of LRB model.
Figure 8.
Analysis results of LRB simulating shaking table tests (DBE: 0.6 g): (a) steel layer; (b) rubber layer.
Figure 8.
Analysis results of LRB simulating shaking table tests (DBE: 0.6 g): (a) steel layer; (b) rubber layer.
Figure 9.
Schematics of 3D shaking table test.
Figure 9.
Schematics of 3D shaking table test.
Figure 10.
Peak response correlation affected by LRB damage: (a) resonance response in the X-direction; (b) resonance response in the Y-direction.
Figure 10.
Peak response correlation affected by LRB damage: (a) resonance response in the X-direction; (b) resonance response in the Y-direction.
Figure 11.
Correlated responses of the damaged LRB in the SSE 1-D Test: (a) displacements of the LRB without damage; (b) displacements of the LRB with damage.
Figure 11.
Correlated responses of the damaged LRB in the SSE 1-D Test: (a) displacements of the LRB without damage; (b) displacements of the LRB with damage.
Figure 12.
Schematics of the 3D shaking table test.
Figure 12.
Schematics of the 3D shaking table test.
Figure 13.
Comparison of test response spectra (SSE, 137 ft).
Figure 13.
Comparison of test response spectra (SSE, 137 ft).
Figure 14.
Effect of isolation in the acceleration response of 10 Hz beam as a secondary structure (BDBE: 0.5 g): (a) response spectra; (b) time history.
Figure 14.
Effect of isolation in the acceleration response of 10 Hz beam as a secondary structure (BDBE: 0.5 g): (a) response spectra; (b) time history.
Figure 15.
Response of 10 Hz beam structures before and after isolation system break (BDBE: 0.6 g).
Figure 15.
Response of 10 Hz beam structures before and after isolation system break (BDBE: 0.6 g).
Figure 16.
Displacement–time history of dummy mass before and after the LRB break.
Figure 16.
Displacement–time history of dummy mass before and after the LRB break.
Figure 17.
Shape of dummy mass on the totally ruptured LRB after testing.
Figure 17.
Shape of dummy mass on the totally ruptured LRB after testing.
Figure 18.
View of the LRB failure surface after break: (a) front view; (b) top view.
Figure 18.
View of the LRB failure surface after break: (a) front view; (b) top view.
Figure 19.
Slip model and equation of motion for simulation of the ruptured LRB.
Figure 19.
Slip model and equation of motion for simulation of the ruptured LRB.
Figure 20.
Displacement of sliding block under measured friction coefficients.
Figure 20.
Displacement of sliding block under measured friction coefficients.
Table 1.
Design options of the LRB for nuclear components.
Table 1.
Design options of the LRB for nuclear components.
Properties | OPT1 | OPT2 |
---|
Design Load [ton] | 1 | 1 |
Outer Diameter [mm] | 76 | 100 |
Design Hori. Freq. [Hz] | 2.0 | 2.3 |
Shape Factor, S1 | 7.6 | 9.9 |
Shape Factor, S2 | 4.4 | 5.0 |
Table 2.
Material properties of equipment LRB.
Table 2.
Material properties of equipment LRB.
Material | Properties | Value |
---|
Rubber | Shear Modulus [MPa] | 0.3 |
Bulk Modulus [GPa] | 1.96 |
Tensile Strength [ksi] | 2.5~3.5 |
Density [g/cm3] | 0.93 |
Lead | Shear Modulus [MPa] | 8.33 |
Table 3.
Comparison of designed LRB natural modes with analysis results.
Table 3.
Comparison of designed LRB natural modes with analysis results.
Mode No. | 1 | 2 | 3 | 4 | 5 | 6 |
---|
Modal analysis results [Hz] | 2.3 | 2.3 | 3.4 | 37.4 | 51.3 | 54.0 |
Design natural frequencies [Hz] | 2.3 | - | - | 36.9 | - | - |
Table 4.
Analysis results of max. equivalent stress on the rubber and steel layers.
Table 4.
Analysis results of max. equivalent stress on the rubber and steel layers.
ZPA [g] of FRS (BDBE) | Rubber Layer [MPa] | Steel Layer [MPa] |
---|
1.7 (0.4) | 3.9 | 437.4 |
2.2 (0.5) | 4.8 | 546.7 |
2.6 (0.6 g) | 5.8 | 656.0 |
Table 5.
Performance and specification of 3D shaking table.
Table 5.
Performance and specification of 3D shaking table.
Item | Performance |
---|
Size [m] | 4.0 × 4.0 |
Max Loading (Force/Moment) | 300 kN/1200 kN-m |
Frequency Range | 0.1–60 Hz |
Control Axes | 6 DOF |
Acceleration at Full Payload [g] | X | Y | Z |
1.2 | 1.2 | 0.8 |
Maximum Stroke [mm] | X | Y | Z |
±300 | ±200 | ±150 |
Table 6.
Shaking table test-I procedures.
Table 6.
Shaking table test-I procedures.
No. | Seismic Input [137 ft] | ZPA [g] of FRS |
---|
1 | OBE-X | 1.3 |
2 | OBE-Y | 1.3 |
3 | OBE-Z | 0.4 |
4 | OBE 3-Axis | - |
5 | SSE-X | 2.6 |
Table 7.
Shaking table Test-II procedures and X-dir. seismic inputs [137 ft].
Table 7.
Shaking table Test-II procedures and X-dir. seismic inputs [137 ft].
No. | LRB ID | ZPA [g] of FRS |
---|
1 | OPT-2A | 2.2 |
2 | 1.3 |
3 | 0.4 |
4 | OPT-2B | 2.2 |
5 | 1.3 |
6 | 0.4 |
7 | OPT-2C | 2.6 |