# Seismic Response of High-Rise Buildings Equipped with Base Isolation and Non-Traditional Tuned Mass Dampers

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{eff}), effective damping (C

_{eff}), initial stiffness (K

_{u}), yield force (F

_{y}), design displacement (D

_{D}) and yield displacement (D

_{y}), and effective period (T

_{eff}). The non-traditional TMDs were considered in the analysis. These control devices are characterized by a significant reduction of the stroke length, in comparison with the traditional TMDs [33]. As a result of previous analyses, the non-traditional TMDs were proposed and confirmed as much better cooperators with base-isolated structures in hybrid control systems [33]. It should be added that the effectiveness of the devices depends on how much of the passive force is added, compared to the effect of seismic isolators on which the building is resting. Thus, the effectiveness of the added TMDs can be somehow modified by changing the proportion of their contribution. A different number of non-traditional TMDs (1, 4, and 8) was considered in the study. Each TMD was modelled as the single degree-of-freedom system with spring connected to the base of building and dashpot directly connected to the ground (see [33] for details). It should be underlined that such a location of TMDs does not require any special arrangements [33]. Specifications of non-traditional TMDs for different computational cases are presented in Table 2. The TMD models are defined by three parameters: mass (M

_{TMD}), stiffness (K

_{TMD}), and damping (C

_{TMD}).

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Acceleration time histories for top story of 15-story building under the Imperial Valley (far-fault) earthquake.

**Figure A2.**Acceleration time histories for top story of 15-story building under the Loma Prieta (far-fault) earthquake.

**Figure A3.**Acceleration time histories for top story of 15-story building under the Kern County (far-fault) earthquake.

**Figure A4.**Acceleration time histories for top story of 15-story building under the Imperial Valley (near-fault) earthquake.

**Figure A5.**Acceleration time histories for top story of 15-story building under the Loma Prieta (near-fault) earthquake.

**Figure A6.**Acceleration time histories for top story of 15-story building under the Morgan Hill (near-fault) earthquake.

**Figure A7.**Acceleration time histories for top story of 20-story building under the Imperial Valley (far-fault) earthquake.

**Figure A8.**Acceleration time histories for top story of 20-story building under the Loma Prieta (far-fault) earthquake.

**Figure A9.**Acceleration time histories for top story of 20-story building under the Kern County (far-fault) earthquake.

**Figure A10.**Acceleration time histories for top story of 20-story building under the Imperial Valley (near-fault) earthquake.

**Figure A11.**Acceleration time histories for top story of 20-story building under the Loma Prieta (near-fault) earthquake.

**Figure A12.**Acceleration time histories for top story of 20-story building under the Morgan Hill (near-fault) earthquake.

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**Figure 1.**Schematic model of a building with a hybrid control system (left) and the bi-linear force–displacement relationship of the high-damping rubber bearing [34] (right).

**Figure 2.**Acceleration time histories for top story of 10-story building under the Imperial Valley (far-fault) earthquake.

**Figure 3.**Acceleration time histories for top story of 10-story building under the Loma Prieta (far-fault) earthquake.

**Figure 4.**Acceleration time histories for top story of 10-story building under the Kern County (far-fault) earthquake.

**Figure 5.**Acceleration time histories for top story of 10-story building under the Imperial Valley (near-fault) earthquake.

**Figure 6.**Acceleration time histories for top story of 10-story building under the Loma Prieta (near-fault) earthquake.

**Figure 7.**Acceleration time histories for top story of 10-story building under the Morgan Hill (near-fault) earthquake.

Building | $\mathit{M}$ (ton) | ${\mathit{K}}_{\mathbf{e}\mathbf{f}\mathbf{f}}\text{}(\mathbf{ton}/\mathbf{m})$ | ${\mathit{C}}_{\mathbf{e}\mathbf{f}\mathbf{f}}\text{}(\mathbf{ton}\text{\xb7}\mathbf{s}/\mathbf{m})$ | ${\mathit{K}}_{\mathbf{u}}\text{}(\mathbf{ton}/\mathbf{m})$ | ${\mathit{F}}_{\mathbf{y}}\text{}\left(\mathbf{ton}\right)$ | ${\mathit{D}}_{\mathbf{D}}\text{}\left(\mathbf{m}\right)$ | ${\mathit{D}}_{\mathbf{y}}\text{}\left(\mathbf{m}\right)$ | ${\mathit{T}}_{\mathbf{e}\mathbf{f}\mathbf{f}}\text{}\left(\mathbf{sec}\right)$ |
---|---|---|---|---|---|---|---|---|

5-story | 184.075 | 29.10 | 7.0 | 189.0 | 3.29 | 0.229 | 0.017 | 0.5 |

10-story | 335.348 | 53.59 | 12.8 | 348.1 | 6.06 | 0.215 | 0.017 | 1 |

15-story | 460.916 | 78.08 | 18.6 | 507.2 | 8.84 | 0.200 | 0.017 | 2 |

20-story | 596.275 | 102.57 | 24.5 | 666.3 | 11.61 | 0.206 | 0.017 | 3 |

Building | ${\mathit{M}}_{\mathbf{T}\mathbf{M}\mathbf{D}}\text{}\left(\mathbf{ton}\right)$ | ${\mathit{K}}_{\mathbf{T}\mathbf{M}\mathbf{D}}\text{}(\mathbf{ton}/\mathbf{m})$ | ${\mathit{C}}_{\mathbf{T}\mathbf{M}\mathbf{D}}\text{}(\mathbf{ton}\text{\xb7}\mathbf{s}/\mathbf{m})$ |
---|---|---|---|

5-story with 1 TMD | 0.6903 | 12.3291 | 0.6144 |

5-story with 4 TMDs | 2.7612 | 49.3162 | 2.4575 |

5-story with 8 TMDs | 5.5223 | 98.6324 | 4.9150 |

10-story with 1 TMD | 1.2576 | 21.5204 | 1.0956 |

10-story with 4 TMDs | 5.0302 | 86.0816 | 4.3824 |

10-story with 8 TMDs | 10.0604 | 172.1632 | 8.7647 |

15-story with 1 TMD | 1.7284 | 13.5266 | 1.0183 |

15-story with 4 TMDs | 6.9138 | 54.1063 | 4.0733 |

15-story with 8 TMDs | 13.8275 | 108.2126 | 8.1465 |

20-story with 1 TMD | 2.2360 | 15.0643 | 1.2223 |

20-story with 4 TMDs | 8.9442 | 60.2573 | 4.8892 |

20-story with 8 TMDs | 17.8883 | 120.5145 | 9.7783 |

**Table 3.**Earthquake records considered in the study [40].

Earthquake | Year | Magnitude | Station | Characteristics | PGA-X (g) | PGA-Y (g) | PGV (cm/s) | PGD (cm) |
---|---|---|---|---|---|---|---|---|

Imperial Valley | 1979 | 6.5 | El Centro Diff. Array | Near-fault | 0.3521 | 0.4798 | 55.32 | 33.04 |

Tabas | 1978 | 7.4 | 9102 Dyhook | Near-fault | 0.3279 | 0.4061 | 28.24 | 9.03 |

Loma Prieta | 1989 | 7.0 | Gilroy Array #3 | Near-fault | 0.5550 | 0.3674 | 43.11 | 11.83 |

Morgan Hill | 1984 | 6.1 | Coyote Lake Dam | Near-fault | 0.7109 | 1.2982 | 68.35 | 10.21 |

Northridge | 1994 | 6.7 | Sylmar Olive View Hospital | Near-fault | 0.6045 | 0.8433 | 95.38 | 21.94 |

Northridge | 1994 | 6.7 | Newhall Pico Canyon | Near-fault | 0.4549 | 0.3254 | 79.07 | 30.21 |

Parkfield | 2004 | 6.4 | Cholame #5 | Near-fault | 0.4416 | 0.3670 | 23.92 | 3.85 |

Northridge | 1994 | 6.7 | Moorpark (Ventura Fire Station) | Far-fault | 0.1931 | 0.2919 | 22.31 | 4.13 |

Northridge | 1994 | 6.7 | Saturn Street School | Far-fault | 0.4745 | 0.4386 | 35.34 | 5.96 |

San Fernando | 1971 | 6.6 | Castaic. Old Ridge Route | Far-fault | 0.3239 | 0.2681 | 19.83 | 3.29 |

Imperial Valley | 1979 | 6.5 | Calexico Fire Station | Far-fault | 0.2748 | 0.2019 | 18.52 | 9.2 |

Landers | 1992 | 7.3 | Morango Valley | Far-fault | 0.1879 | 0.1405 | 18.63 | 8.04 |

Kern County | 1952 | 7.5 | Santa Barbara Courthouse | Far-fault | 0.0871 | 0.1267 | 13.67 | 3.08 |

Loma Prieta | 1989 | 7.0 | Presidio | Far-fault | 0.0995 | 0.1999 | 20.33 | 4.98 |

**PGA**—peak ground acceleration;

**PGV**—peak ground velocity;

**PGD**—peak ground displacement; g—acceleration of gravity.

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**MDPI and ACS Style**

Naderpour, H.; Naji, N.; Burkacki, D.; Jankowski, R. Seismic Response of High-Rise Buildings Equipped with Base Isolation and Non-Traditional Tuned Mass Dampers. *Appl. Sci.* **2019**, *9*, 1201.
https://doi.org/10.3390/app9061201

**AMA Style**

Naderpour H, Naji N, Burkacki D, Jankowski R. Seismic Response of High-Rise Buildings Equipped with Base Isolation and Non-Traditional Tuned Mass Dampers. *Applied Sciences*. 2019; 9(6):1201.
https://doi.org/10.3390/app9061201

**Chicago/Turabian Style**

Naderpour, Hosein, Naghmeh Naji, Daniel Burkacki, and Robert Jankowski. 2019. "Seismic Response of High-Rise Buildings Equipped with Base Isolation and Non-Traditional Tuned Mass Dampers" *Applied Sciences* 9, no. 6: 1201.
https://doi.org/10.3390/app9061201