# Application of Mode-Adaptive Bidirectional Pushover Analysis to an Irregular Reinforced Concrete Building Retrofitted via Base Isolation

^{1}

^{2}

^{*}

## Abstract

**:**

## Featured Application

**Seismic response evaluation of a base-isolated buildings: Seismic rehabilitation design for reinforced concrete buildings using the base-isolation technique.**

## Abstract

## 1. Introduction

#### 1.1. Background

#### 1.2. Motivation

#### 1.3. Objectives

- Is MABPA capable of predicting the peak response of irregular base-isolated buildings?
- The prediction of the peak equivalent displacement of the first two modal responses is an essential step in MABPA. For this, the relationship between the maximum momentary input energy and the peak displacement needs to be properly evaluated. How can this relationship be evaluated from the pushover analysis results?
- In the prediction of the maximum momentary input energy of the first two modal responses, the effect of simultaneous bidirectional excitation needs to be considered. Can the upper bound of the peak equivalent displacement of the first two modal responses be predicted using the bidirectional maximum momentary input energy spectrum [52]?

## 2. Description of MABPA

#### 2.1. Outline of MABPA

- The bidirectional momentary input energy proposed in the previous study was applied as the seismic intensity parameter.
- The peak response of each mode was predicted from the energy balance in a half cycle of the structural response.

#### 2.2. Prediction of the Peak Response using the Momentary Energy Input

#### 2.2.1. Calculation of the Bidirectional Momentary Input Energy Spectrum

#### 2.2.2. Formulation of the Effective Period and the Hysteretic Dissipated Energy in a Half Cycle

## 3. Description of the Retrofitted Building Models and Ground Motion Datasets

#### 3.1. Original Building

#### 3.2. Properties of the Isolation Layer

^{2}for the calculation of the floor mass and the moment of inertia of each floor. Therefore, the calculated total mass ($M$) was 5412 t.

^{2}, and ${}_{s}{\alpha}_{y}$ is the yielding shear strength coefficient. In this study, the design-allowable horizontal displacement (${\delta}_{a}$) was set to 0.40 m, while the value of ${}_{s}n$ was set to 2 following the design recommendation [2]. Then, the two parameters of the isolation layer, ${T}_{f}$ and ${}_{s}{\alpha}_{y}$, were adjusted, such that the following condition was satisfied:

_{0}is the center of stiffness of the isolation layer calculated according to the initial stiffness of the isolators and dampers, while point S

_{1}is the center of stiffness of the isolation layer calculated according to the secant stiffness of the isolators and dampers considering their displacement (δ) of 0.40 m.

_{1A}and Y

_{6}are referred to as the “flexible-side frames,” while the frames X

_{6A}and Y

_{1}are referred to as the “stiff-side frames”. Note that no optimization to minimize the torsional response was made to choose the dampers in this study, because such optimization was beyond the scope of this study.

#### 3.3. Structural Modeling

#### 3.4. Ground Motion Data

#### 3.4.1. Artificial Ground Motions

#### 3.4.2. Recorded Ground Motions

## 4. Analysis Results

#### 4.1. Example of a Prediction of the Peak Equivalent Displacement

#### 4.2. Comparisons with the Nonlinear Time-History Analysis

#### 4.2.1. Artificial Ground Motion

_{3A}Y

_{3}, which is the closest point to the center of the floor mass at each level. In these figures, the nonlinear time-history analysis results are compared with the results predicted by MABPA (for complex damping ratios ($\beta $) of 0.10, 0.20, and 0.30). As shown here, the predicted peaks can approximate the envelope of the time-history analysis results, except in the case of Model-Tf34 subjected to the Art-2 series shown in Figure 20b. In addition, the predicted peak with $\beta $ = 0.10 is larger than that with $\beta $ = 0.30. When the models were subjected to the Art-1 series, the predicted peak closest to the envelope of the time-history analysis results was found with $\beta $ = 0.10 for Model-Tf34 (Figure 20a) and with $\beta $ = 0.30 for Model-Tf44 (Figure 21b). Differences in the predicted peaks resulting from the value of the complex damping were small in the case of Model-Tf34 but relatively noticeable in the case of Model-Tf44.

_{1}and Y

_{2}(the stiff side in the X direction). A similar observation can be made in the case of Model-Tf44 subjected to the Art-1 series, as shown in Figure 23, where the predicted peak with $\beta $ = 0.30 agrees very well with the envelope of the time-history analysis results, except at Y

_{1}and Y

_{2}.

_{3A}Y

_{3}and the horizontal distribution of the peak displacement at level 0 for both models according to the artificial ground motion datasets.

#### 4.2.2. Recorded Ground Motion

_{3A}Y

_{3}. The accuracy of the predicted peak displacement is satisfactory: The predicted peak approximated the envelope of the nonlinear time-history analysis results, even though some cases were overestimated (e.g., model: Model-Tf44, ground motion: UTO0416, Figure 25b). The variation of the predicted peak due to the assumed complex damping ratio ($\beta $) depends on the ground motion. In some cases, the largest peak was obtained when $\beta $ was 0.30 (e.g., model: Model-Tf34, ground motion: UTO0416, Figure 24b), while in other cases, the largest peak was obtained when $\beta $ was 0.10 (e.g., model: Model-Tf34, ground motion: TCU, Figure 24c).

_{1A}(the flexible side in the Y direction); meanwhile, in the envelope of the time-history analysis results, the displacement at X

_{1A}was the smallest. Conversely, the predicted horizontal distribution of the peak displacement in the Y direction fits the envelope of the time-history analysis in the case of TCU very well, as shown in Figure 26b. In the predicted distribution, the largest displacement occurred at X

_{1A}, which is consistent with the envelope of the time-history analysis results. The modal displacement responses at X

_{1A}and X

_{6A}(the stiff side in the Y direction) are compared and discussed further in Section 5.5.

_{3}B

_{3}on the second story, with a value of 0.12% in the case of UTO0414 (Figure 27a) and a value of 0.30% in the case of UTO0416 (Figure 27b). Therefore, the seismic performance of Model-Tf34 was excellent for the motions recorded during the 2016 Kumamoto earthquake. Figure 28 shows comparisons of the peak drift of Model-Tf44. Similar observations can be made for Model-Tf44. Comparisons of Figure 27 and Figure 28 indicate that the peak drift of Model-Tf44 was smaller than that of Model-Tf34. These figures also illustrate that the accuracy of the predicted peak depends on the column, with the accuracy in column A

_{1}B

_{1}being satisfactory and that in column A

_{3}B

_{3}being less satisfactory.

_{1A}Y

_{6}and X

_{6A}Y

_{1}) for various angles of incidence of seismic input ($\psi $). In these figures, the displacement of each isolator was calculated as the absolute (vector) value of the two horizontal directions, and the predicted peaks are shown by the colored lines. As shown in these figures, the upper bounds of the peak displacement of the isolators can be satisfactorily evaluated using the updated MABPA presented in this study.

## 5. Discussion

#### 5.1. Calculation of the Modal Responses

#### 5.2. Relationship between the Peak Equivalent Displacement and the Maximum Momentary Input Energy of the First Modal Response

#### 5.3. Comparison of the Maximum Momentary Input Energy and the Bidirectional Momentary Input Energy Spectrum

#### 5.4. Accuracy of the Predicted Peak Equivalent Displacements of the First and Second Modal Responses

_{1A}Y

_{6}shown in Figure 30c, the peak displacement at the angle ($\psi $) of −30° was close to the largest peak value. On the contrary, the peak displacement at isolator X

_{6A}Y

_{1}at the angle ($\psi $) of −30° was close to the smallest peak value.

#### 5.5. Contribution of the Higher Mode to the Displacement Response at the Edge of Level 0

_{1A}(the flexible side in the Y direction), while the envelope of the nonlinear time-history analysis results indicates that the largest peak occurred at X

_{6A}(the stiff side in the Y direction), the opposite side to X

_{1A}in the case of UTO0414, as shown in Figure 26a. Conversely, in the case of TCU shown in Figure 26b, the envelope of the time-history analysis results indicates that the largest peak occurred at X

_{1A}, which is consistent with the predicted results. In this subsection, the modal response at level 0 is calculated and discussed.

_{1A}occurs. Note that “All modes” is the response originally obtained from the time-history analysis results (${d}_{Y0j}\left(t\right)$), “First mode” and “Second mode” are the first and second modal responses (${d}_{Y0j1}\left(t\right)$ and ${d}_{Y0j2}\left(t\right)$, respectively), and “Higher mode” is the higher (residual) modal response calculated from Equation (31) (${d}_{Y0jh}\left(t\right)$).

_{1A}, shown in Figure 41a, the contribution of the higher modal response was non-negligible, even though the contribution of the first modal response was predominant. In addition, the sign of the higher modal response at the time the peak response occurred at X

_{1A}was opposite to that of the “All mode” response, with the contribution of the higher mode reducing the peak response at X

_{1A}.

_{6A}, shown in Figure 41b, the contribution of the first modal response was negligibly small and those of the second and higher modal responses were noticeable. In addition, the sign of the higher modal response at the time the peak response occurred at X

_{6A}was the same as that of the “All mode” response, with the contribution of the higher mode increasing the peak response at X

_{6A}.

_{6A}(not at X

_{1A}) in the case of UTO0414 can be explained by the contributions of the higher modal response. In the case of UTO0414, the contribution of the higher modal response was non-negligibly large.

_{1A}occurs. In the response of X

_{1A}, shown in Figure 42a, the contribution of the first modal response was predominant, while that of the higher modal response was small. Meanwhile, in the response of X

_{6A}, shown in Figure 42b, the contribution of the first modal response was negligibly small and those of the second and higher modal responses were noticeable.

#### 5.6. Summary of the Discussions

## 6. Conclusions

- The predicted peak response according to the updated MABPA agreed satisfactorily with the envelope of the time-history analysis results. The peak relative displacement at X
_{3A}Y_{3}at each floor can be satisfactorily predicted. The predicted distribution of the peak displacement at level 0 (just above the isolation layer) approximated the envelope of the nonlinear time-history analysis results, even though in some cases, the predicted distributions differed from the envelope of the nonlinear time-history analysis. A discrepancy between the predicted results and nonlinear time-history analysis may occur because of the lack of a contribution from the higher modal responses. - The relationship between the equivalent velocity of the maximum momentary input energy of the first modal response (${V}_{\Delta E1U}{}^{*}$) and the peak equivalent displacement of the first modal response (${D}_{1U}{{}^{*}}_{\mathrm{max}}$) can be properly evaluated from the pushover analysis results. The plots obtained from the nonlinear time-history analysis results fit the evaluated curve from the pushover analysis results well.
- The upper bound of the peak equivalent displacements of the first two modal responses can be predicted using the bidirectional ${V}_{\Delta E}$ spectrum [52]. Comparisons between the predicted peak equivalent displacements and those calculated from the nonlinear time-history analysis results showed that the predicted peak approximated the upper bound of the nonlinear time-history analysis results. The upper bound of ${V}_{\Delta E1U}{}^{*}$ can be approximated by the bidirectional ${V}_{\Delta E}$ spectrum.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Time-Histories of the Recorded Ground Motions Used in This Study

**Table A1.**Event date, magnitude, location of the epicenter, distance, and station name of each record.

ID | Event Date | Magnitude | Distance | Station Name | Direction of Components | |
---|---|---|---|---|---|---|

ξ-Dir | ζ-Dir | |||||

UTO0414 | 14 April 2016 | ${M}_{J}$ = 6.5 | 15 km | K-Net UTO (KMM008) | EW | NS |

UTO0416 | 16 April 2016 | ${M}_{J}$ = 7.3 | 12 km | K-Net UTO (KMM008) | EW | NS |

TCU | 20 September 1999 | ${M}_{W}$ = 7.6 | 0.89 km * | TCU075 | Major ** | Minor ** |

YPT | 17 August 1999 | ${M}_{W}$ = 7.5 | 4.83 km * | Yarimca | Major ** | Minor ** |

**Figure A1.**Two components of the recorded ground motion (UTO0414): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

**Figure A2.**Two components of the recorded ground motion (UTO0416): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

**Figure A3.**Two components of the recorded ground motion (TCU): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

**Figure A4.**Two components of the recorded ground motion (YPT): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

## Appendix B. Comparisons of the Unidirectional and Bidirectional V_{ΔE} Spectra

**Figure A5.**Comparisons of the unidirectional and bidirectional V

_{ΔE}spectra for artificial ground motion datasets: (

**a**) Art-1 series and (

**b**) Art-2 series.

**Figure A6.**Comparisons of the unidirectional and bidirectional V

_{ΔE}spectra for recorded ground motion datasets: (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

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**Figure 2.**Bilinear idealization of the equivalent acceleration-equivalent displacement relationship.

**Figure 3.**Modeling of the structural response in a half cycle used to predict the peak response: (

**a**) The effective slope (κ

_{1eff}) and (

**b**) the hysteretic dissipated energy in a half cycle per unit mass (ΔE

_{μ}

_{1U}/M

_{1U}

^{*}).

**Figure 4.**Simplified structural plan and elevation of the main building of the former Uto City Hall [44]: (

**a**) Structural plan (Level Z

_{0}) and (

**b**) simplified plan elevation (frame B

_{1}).

**Figure 5.**View of the former Uto City Hall after the 2016 Kumamoto earthquake [44]. Photographs were taken from (

**a**) the south, (

**b**) the southwest, and (

**c**) the north.

**Figure 6.**Soil profiles of the former K-NET Uto station. Figures were made from the data provided by the National Research Institute for Earth Science and Disaster Resilience (NIED). (

**a**) Primary and shear wave profile (V

_{p}: P-wave velocity, V

_{s}: S-wave velocity); (

**b**) density profile; (

**c**) soil column.

**Figure 7.**Horizontal response spectra of the recorded ground motions at the K-NET Uto station: (

**a**) Elastic acceleration response spectrum (damping ratio: 0.05); (

**b**) elastic velocity response spectrum (damping ratio: 0.05); (

**c**) elastic total input energy spectrum (damping ratio: 0.10).

**Figure 8.**Layout of the isolators and dampers in the isolation layer: (

**a**) Model-Tf34 and (

**b**) Model-Tf44.

**Figure 9.**Envelope of the force–deformation relationship for the isolators and dampers: (

**a**) Natural rubber bearings (NRBs); (

**b**) elastic sliding bearings (ESBs); (

**c**) steel dampers.

**Figure 10.**Structural modeling: (

**a**) Overview of the structural model; (

**b**) frame B

_{1}; (

**c**) frame Y

_{6}; (

**d**) modeling of the isolators (NRBs and ESBs); (

**e**) modeling of the steel dampers.

**Figure 13.**Two components of the generated artificial ground motion (Art-1-00): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

**Figure 14.**Two components of the generated artificial ground motion (Art-2-00): (

**a**) ξ direction; (

**b**) ζ direction; (

**c**) orbit.

**Figure 15.**Horizontal response spectra of the artificial ground motion (Art-1 series): (

**a**) Elastic acceleration response spectrum (damping ratio: 0.05); (

**b**) elastic velocity response spectrum (damping ratio: 0.05); (

**c**) elastic total input energy spectrum (damping ratio: 0.10).

**Figure 16.**Horizontal response spectra of the artificial ground motion (Art-2 series): (

**a**) Elastic acceleration response spectrum (damping ratio: 0.05); (

**b**) elastic velocity response spectrum (damping ratio: 0.05); (

**c**) elastic total input energy spectrum (damping ratio: 0.10).

**Figure 17.**Horizontal response spectra of the recorded ground motions: (

**a**) Elastic acceleration response spectrum (damping ratio: 0.05); (

**b**) elastic velocity response spectrum (damping ratio: 0.05); (

**c**) elastic total input energy spectrum (damping ratio: 0.10).

**Figure 18.**Nonlinear properties of the equivalent single-degree-of-freedom (SDOF) model representing the first modal response (Model-Tf44): (

**a**) The A

_{1U}

^{*}−D

_{1U}

^{*}relationship; (

**b**) the T

_{1eff}

^{*}−D

_{1U}

^{*}relationship; (

**c**) the V

_{ΔEμ1U}

^{*}−D

_{1U}

^{*}relationship.

**Figure 19.**Prediction of the peak equivalent displacements (model: Model-Tf44, ground motion: TCU): (

**a**) Prediction of the peak of the first modal response and (

**b**) prediction of the peak of the second modal response.

**Figure 20.**Comparison of the peak relative displacements at X

_{3A}Y

_{3}(Model-Tf34) for the (

**a**) Art-1 and (

**b**) Art-2 series.

**Figure 21.**Comparison of the peak relative displacements at X

_{3A}Y

_{3}(Model-Tf44) for the (

**a**) Art-1 and (

**b**) Art-2 series.

**Figure 22.**Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf34, ground motion: Art-1 series).

**Figure 23.**Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf44, ground motion: Art-1 series).

**Figure 24.**Comparison of the peak relative displacements at X

_{3A}Y

_{3}(Model-Tf34): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 25.**Comparison of the peak relative displacements at X

_{3A}Y

_{3}(Model-Tf44): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 26.**Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf34) for (

**a**) UTO0414 and (

**b**) TCU.

**Figure 27.**Comparison of the peak drift for the columns (Model-Tf34) with (

**a**) UTO0414 and (

**b**) UTO0416.

**Figure 28.**Comparison of the peak drift for the columns (Model-Tf44) with (

**a**) UTO0414 and (

**b**) UTO0416.

**Figure 29.**Peak displacement at isolators for various angles of incidence of seismic input (Model-Tf34): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 30.**Peak displacement at isolators for various angles of incidence of seismic input (Model-Tf44): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 32.**Definition of the maximum momentary input energy of the first modal response per unit mass (structural model: Model-Tf44, ground motion: TCU, angle of incidence of seismic input: ψ = −30°): (

**a**) Hysteresis of the first modal response and (

**b**) time-history of the momentary energy input.

**Figure 33.**Comparison between the V

_{ΔEμ1U}

^{*}–D

_{1U}

^{*}curve and the V

_{ΔE1U}

^{*}–D

_{1U}

^{*}

_{max}relationship obtained from the time-history analysis (Model-Tf34): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 34.**Comparison between the V

_{ΔEμ1U}

^{*}–D

_{1U}

^{*}curve and the V

_{ΔE1U}

^{*}–D

_{1U}

^{*}

_{max}relationship obtained from the time-history analysis (Model-Tf44): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 35.**Prediction of V

_{ΔE1U}

^{*}from the bidirectional V

_{ΔE}spectrum and its accuracy (Model-Tf34): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 36.**Prediction of V

_{ΔE1U}

^{*}from the bidirectional V

_{ΔE}spectrum and its accuracy (Model-Tf44): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 37.**Accuracy of the predicted peak equivalent displacements of the first two modes (Model-Tf34): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 38.**Accuracy of the predicted peak equivalent displacements of the first two modes (Model-Tf44): (

**a**) Art-1 series; (

**b**) Art-2 series; (

**c**) UTO0414; (

**d**) UTO0416; (

**e**) TCU; (

**f**) YPT.

**Figure 39.**Peak equivalent displacements of the first two modes for various directions of seismic input (Model-Tf34): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 40.**Peak equivalent displacements of the first two modes for various directions of seismic input (Model-Tf44): (

**a**) UTO0414; (

**b**) UTO0416; (

**c**) TCU; (

**d**) YPT.

**Figure 41.**Comparisons of the modal responses at the edge of level 0 (structural model: Model-Tf34, ground motion: UTO0414, angle of incidence of seismic input: ψ = −75°): (

**a**) X

_{1A}and (

**b**) X

_{6A}.

**Figure 42.**Comparisons of the modal responses at the edge of level 0 (structural model: Model-Tf34, ground motion: TCU, angle of incidence of seismic input: ψ = 60°): (

**a**) X

_{1A}and (

**b**) X

_{6A}.

**Table 1.**Floor mass, moment of inertia, and radius of gyration of the floor mass of each floor level.

Floor Level j | Floor Mass m _{j} (t) | Moment of Inertia I _{j} (×10^{3} tm^{2}) | Radius of Gyration of Floor Mass r_{j} (m) |
---|---|---|---|

5 | 677.8 | 78.37 | 10.75 |

4 | 548.5 | 62.85 | 10.70 |

3 | 543.0 | 62.50 | 10.73 |

2 | 581.0 | 67.12 | 10.75 |

1 | 1208.1 | 199.0 | 12.83 |

0 | 1853.7 | 274.9 | 12.18 |

Type | Outer Diameter (mm) | Total Rubber Thickness (mm) | Shear Modulus (MPa) | Horizontal Stiffness K _{1} (MN/m) | Vertical Stiffness K _{V} (MN/m) |
---|---|---|---|---|---|

NRB (ϕ = 900 mm, G5) | 900 | 180 | 0.441 | 1.56 | 3730 |

NRB (ϕ = 900 mm, G4) | 900 | 180 | 0.392 | 1.38 | 3420 |

Type | Outer Diameter (mm) | Shear Modulus (MPa) | Friction Coefficient μ | Initial Horizontal Stiffness K _{1} (MN/m) | Vertical Stiffness K _{V} (MN/m) |
---|---|---|---|---|---|

ESB (ϕ = 300 mm) | 300 | 0.392 | 0.010 | 0.884 | 1380 |

ESB (ϕ = 400 mm) | 400 | 0.392 | 0.010 | 1.48 | 2270 |

ESB (ϕ = 500 mm) | 500 | 0.392 | 0.010 | 2.40 | 3710 |

Initial Stiffness K _{1} (MN/m) | Yield Strength Q _{yd} (kN) | Post Yield Stiffness K _{2} (MN/m) |
---|---|---|

7.60 | 184 | 0.128 |

Earthquake of the Original Record | Ground Motion ID | Scale Factor | |
---|---|---|---|

Model-Tf34 | Model-Tf44 | ||

Kumamoto, 14 April 2016 | UTO0414 | 1.000 | 1.000 |

Kumamoto, 16 April 2016 | UTO0416 | 1.000 | 1.000 |

Chichi, 1999 | TCU | 0.5540 | 0.5718 |

Kocaeli, 1999 | YPT | 0.4293 | 0.5057 |

**Table 6.**Equivalent velocities of the maximum momentary input energy predicted from the bidirectional V

_{ΔE}spectrum (β = 0.100).

Ground Motion Set | First Mode V _{ΔE}(T_{1eff}) (m/s) | Second Mode V _{ΔE}(T_{2eff}) (m/s) | Third Mode V _{ΔE}(T_{3e}) (m/s) | Ratio (2nd/1st) | Ratio (3rd/1st) |
---|---|---|---|---|---|

UTO0414 | 0.4108 | 0.4232 | 0.7151 | 1.030 | 1.741 |

TCU | 0.7575 | 0.7319 | 0.2519 | 0.9662 | 0.3325 |

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## Share and Cite

**MDPI and ACS Style**

Fujii, K.; Masuda, T.
Application of Mode-Adaptive Bidirectional Pushover Analysis to an Irregular Reinforced Concrete Building Retrofitted via Base Isolation. *Appl. Sci.* **2021**, *11*, 9829.
https://doi.org/10.3390/app11219829

**AMA Style**

Fujii K, Masuda T.
Application of Mode-Adaptive Bidirectional Pushover Analysis to an Irregular Reinforced Concrete Building Retrofitted via Base Isolation. *Applied Sciences*. 2021; 11(21):9829.
https://doi.org/10.3390/app11219829

**Chicago/Turabian Style**

Fujii, Kenji, and Takumi Masuda.
2021. "Application of Mode-Adaptive Bidirectional Pushover Analysis to an Irregular Reinforced Concrete Building Retrofitted via Base Isolation" *Applied Sciences* 11, no. 21: 9829.
https://doi.org/10.3390/app11219829