# Response of Seismically Isolated Steel Frame Buildings with Sustainable Lead-Rubber Bearing (LRB) Isolator Devices Subjected to Near-Fault (NF) Ground Motions

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## Abstract

**:**

## 1. Introduction

## 2. LRB Isolator Devices

_{e}) and the post-yield stiffness (K

_{p}) are also defined as the equations involved with these four parameters as follows:

Model ID | Δmax (mm) | Fv (kN) | F1 (kN) | F2 (kN) | Δ1 (mm) | Δ2 (mm) | Q (kN) | K_{e} (kN/mm) | K_{p} (kN/mm) | K_{eff } (kN/mm) | λ_{eff} | Z (mm) | Dg (mm) | dg (mm) | H (mm) | h (mm) | te * (mm) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LRB1 | 400 | 3170 | 259 | 651 | 16 | 333 | 239 | 16.19 | 1.24 | 1.95 | 22.3% | 800 | 750 | 170 | 397 | 337 | 203 |

LRB2 | 400 | 5780 | 308 | 823 | 16 | 333 | 282 | 19.25 | 1.62 | 2.47 | 20.8% | 900 | 850 | 185 | 382 | 322 | 200 |

*****Total thickness of the rubber.

_{eff}) can be modelled the secant line by means of the ratio as in the following equation:

_{iso}) representing the amount of energy dissipation can be obtained from the equation as follows:

_{eff}) is proportional to the amount of energy dissipation, but inversely related to both the effective stiffness and the square displacement. This damping coefficient also depends on four key parameters, which it refers:

_{v}), and characteristic strength can be similarly affected by the size of the LRB model. In contrast, the LRB2 model exhibits slightly lower damping coefficient than the LRB1 model as expected in Equation (6). Both LRB models have the same maximum allowable horizontal displacement (Δ

_{max}= 400 mm), representing 1.2 times the length of Δ2.

## 3. Frame Model and Design

Located Area | Loads (Other) | Loads (Roof) | SDC | Site Condition | Occupancy Category |
---|---|---|---|---|---|

LA Area | DL: 4.12kPa, LL: 2.39kPa | DL: 4.50kPa, LL: 0.96kPa | D Class | Stiff Soil (Class D) | Ordinary Structures |

Story | Column * (C1) | Beam * (B1) | CBF ** | Internal Column * (C2) | Internal Beam* (B2) |
---|---|---|---|---|---|

1 | W14x109 | W24x84 | HSS6x6x3/8 | W12x87 | W24x68 |

2 | W14x109 | W24x84 | HSS6x6x3/8 | W12x87 | W24x68 |

3 | W14x109 | W24x68 | HSS6x6x3/8 | W12x87 | W24x68 |

4 | W14x109 | W24x68 | HSS6x6x3/8 | W12x87 | W24x68 |

5 | W14x109 | W18x50 | HSS6x6x1/4 | W12x87 | W24x68 |

6 | W14x109 | W18x50 | HSS6x6x1/4 | W12x87 | W24x68 |

*****Gr.50 Carbon Steel;

******Gr.B Carbon Steel for Rectangular Shape; CBF: concentrically brace frame.

## 4. Analytical Modeling

_{e}), yield force (F1), and post-yield stiffness (K

_{p}) (see Figure 2 and Figure 4b), and simply simulated by using isotropic hardening material command provided in the OpenSEES program. It was assigned to the component spring element for the purpose of reproducing the force-displacement response curve. The analytical component spring models classified herein as LRB1 and LRB2 were installed on the base-isolated frame model (see Figure 5). Each LRB spring model includes the force-displacement response presented in Figure 2. The column bases of as-built frame model without base isolation are considered to be fixed. Accordingly, LRB-isolated frame models (i.e., LRB1 and LRB2 models) have flexible end boundary conditions while as-built frame models possess fixed end boundary conditions.

_{cr}). Global buckling that indicates the peak load suddenly occurs at the middle of the brace member prior to the compressive yielding of the brace member. Moreover, other characteristic branches concerning negative stiffness after post-buckling, unloading, elastic tension reloading, and uniaxial tensile yielding (P

_{y}) are also found at the hysteretic behavior curve (see Figure 6b).

## 5. Near-Fault Ground Motions

**Table 4.**Near-fault ground motion data used for nonlinear dynamic analyses (PGA: peak ground acceleration).

Ground Motion ID | Earthquake Record | Richter Scale | Distance (km) | Duration (sec) | Max. PGA (g) | Min. PGA (g) |
---|---|---|---|---|---|---|

NF01 | 1978 Tabes | 7.4 | 1.2 | 50 | 0.90 | −0.86 |

NF02 | 1979 Tabes | 7.4 | 1.2 | 50 | 0.98 | −0.75 |

NF03 | 1989 Loma Prieta (Los Gatos) | 7 | 3.5 | 25 | 0.72 | −0.64 |

NF04 | 1989 Loma Prieta (Los Gatos) | 7 | 3.5 | 25 | 0.46 | −0.44 |

NF05 | 1989 Loma Prieta (Lex Dam) | 7 | 6.3 | 40 | 0.59 | −0.69 |

NF06 | 1989 Loma Prieta (Lex Dam) | 7 | 6.3 | 40 | 0.37 | −0.28 |

NF07 | 1992 Mendocino | 7.1 | 8.5 | 60 | 0.64 | −0.62 |

NF08 | 1992 Mendocino | 7.1 | 8.5 | 60 | 0.60 | −0.66 |

NF09 | 1992 Erzincan | 6.7 | 2.0 | 21 | 0.43 | −0.31 |

NF10 | 1992 Erzincan | 6.7 | 2.0 | 21 | 0.46 | −0.27 |

NF11 | 1992 Landers | 7.3 | 1.1 | 50 | 0.71 | −0.71 |

NF12 | 1992 Landers | 7.3 | 1.1 | 50 | 0.61 | −0.80 |

NF13 | 1994 Northridge (Rinaldi) | 6.7 | 7.5 | 15 | 0.62 | −0.89 |

NF14 | 1994 Northridge (Rinaldi) | 6.7 | 7.5 | 15 | 0.38 | −0.39 |

NF15 | 1994 Northridge (Olive View) | 6.7 | 6.4 | 60 | 0.51 | −0.73 |

NF16 | 1994 Northridge (Olive View) | 6.7 | 6.4 | 60 | 0.60 | −0.56 |

NF17 | 1995 Kobe | 6.9 | 3.4 | 60 | 1.09 | −0.73 |

NF18 | 1995 Kobe | 6.9 | 3.4 | 60 | 0.58 | −0.57 |

NF19 | 1995 Kobe (Takatori) | 6.9 | 4.3 | 40 | 0.79 | −0.51 |

NF20 | 1995 Kobe (Takatori) | 6.9 | 4.3 | 40 | 0.38 | −0.42 |

**Figure 7.**5% damped spectral accelerations for near-fault ground motions (scale factor (SF) = 1.0) and fundamental time periods for individual model cases.

**Figure 8.**Response spectral accelerations for individual ground motion data according to each model case.

## 6. Seismic Responses

**Figure 10.**Nonlinear dynamic analysis results (roof displacement vs. total base shear force curves).

## 7. Statistical Investigations

_{roof,max}) for individual frame models according to increasing scale factors are illustrated in Figure 12. The statistical lines indicating 15.9th, 50.0th (or median), and 84.1th percentile ranks are drawn in the graphs together with individual resulting data points obtained from all analysis results. As the scale factor of the ground motion increases at a fixed rate, the statistical lines for the values of the maximum roof displacements gradually ascend in the straight curves. The ranges of data scatter increase as well. The LRB-isolated frame models that permit base movements in the direction of the ground motion show larger statistical values than the as-built frame model. Furthermore, the LRB1 model has slightly higher statistical percentile lines (approximately 5%) than the LRB2 model owing to more flexible LRB properties.

_{base,max}) for individual frame models according to increasing scale factors are presented in Figure 13. The statistical values for the maximum total base shear forces are commonly proportional to the scale factors of the ground motions increasing as well. As expected, the as-built frame model is susceptible to higher base shear forces in comparison of other LRB-isolated frame models. When examining the distribution of the total base shear forces at the graphs, it can be found that the LRB base isolators lead the generation of the base shear force to alleviate considerably.

_{roof,res}) for individual frame models according to increasing scale factors are presented in Figure 14. The severe failures representing over 80mm residual roof displacements are mostly displayed at the graphs of the as-built frame model case, and generated even under the ground motions with the value of 0.6 scale factor. Therefore, the upper statistical percentile lines (50.0th and especially 84.1th percentile) for the distribution of the residual roof displacements ascend rapidly at the as-built frame model as increasing the scale factors of the ground motions. In contrast, the statistical lines of the LRB-isolated frame models show gentle ascent at the graphs of the residual roof displacements according to the increasing scale factors, meaning that these isolated frame models are little susceptible to structural damage even under strong ground motions. As compared to each frame model, the statistical values for maximum roof displacements, maximum total base shear forces, and residual roof displacements are finally summarized in Table 5. The values of each mean and standard deviation (SD) are also presented in this table.

**Figure 12.**Statistical investigations of the maximum roof displacements (Δ

_{roof,max}) for individual frame models according to increasing scale factors.

**Figure 13.**Statistical investigations of the maximum total base shear forces (ΣV

_{base, max}) for individual frame models according to increasing scale factors.

**Figure 14.**Statistical investigations of the residual roof displacements (Δ

_{roof,res}) for individual frame models according to increasing scale factors.

**Table 5.**Comparison and summary of the statistical valises for maximum roof displacements, maximum total base shear forces, and residual roof displacements.

Evaluation Item | Model ID | SF = 0.2 | SF = 0.4 | SF = 0.6 | SF = 0.8 | SF = 1.0 | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | ||

Δ_{roof,max} (mm) | As-Built | 23.7 | 50.3 | 86.8 | 56.6 | 32.2 | 47.4 | 96.4 | 166.9 | 101.2 | 49.4 | 71.0 | 127.6 | 294.8 | 148.2 | 86.1 | 91.8 | 167.7 | 430.7 | 212.4 | 144.5 | 107.0 | 200.6 | 524.4 | 287.9 | 204.3 |

LRB1 | 35.6 | 72.7 | 122.6 | 77.8 | 38.9 | 80.2 | 162.1 | 270.7 | 169.4 | 79.5 | 112.0 | 281.9 | 442.6 | 283.4 | 147.4 | 144.8 | 403.6 | 584.6 | 400.2 | 202.5 | 168.2 | 515.3 | 731.2 | 508.7 | 295.6 | |

LRB2 | 38.0 | 73.8 | 126.5 | 77.4 | 38.9 | 71.2 | 146.1 | 245.9 | 159.2 | 77.5 | 109.3 | 261.1 | 416.1 | 263.4 | 129.0 | 144.1 | 377.1 | 591.0 | 376.8 | 186.6 | 185.4 | 500.3 | 731.1 | 503.9 | 267.1 | |

ΣV_{base,max} (MN) | As-Built | 2.5 | 5.3 | 9.1 | 5.8 | 2.8 | 5.0 | 9.3 | 11.4 | 8.6 | 2.4 | 7.4 | 10.5 | 11.8 | 10.0 | 1.8 | 8.9 | 11.0 | 12.2 | 10.9 | 1.4 | 9.8 | 11.8 | 12.8 | 11.6 | 1.2 |

LRB1 | 1.5 | 2.0 | 2.5 | 2.0 | 0.4 | 2.1 | 3.0 | 4.0 | 3.0 | 0.8 | 2.4 | 4.1 | 5.4 | 4.0 | 1.2 | 2.8 | 5.1 | 6.3 | 4.9 | 1.4 | 3.2 | 6.2 | 6.9 | 5.6 | 1.5 | |

LRB2 | 1.8 | 2.3 | 3.0 | 2.3 | 0.5 | 2.3 | 3.2 | 4.3 | 3.3 | 0.9 | 2.8 | 4.5 | 5.9 | 4.4 | 1.3 | 3.2 | 5.6 | 7.2 | 5.4 | 1.5 | 3.7 | 6.6 | 7.9 | 6.2 | 1.7 | |

Δ_{roof,res} (mm) | As-Built | 0.3 | 0.6 | 6.4 | 2.8 | 5.1 | 0.4 | 5.5 | 26.9 | 13.4 | 19.0 | 0.8 | 12.1 | 72.7 | 29.1 | 43.5 | 1.8 | 32.2 | 181.7 | 65.5 | 83.2 | 3.5 | 50.6 | 269.6 | 117.2 | 137.4 |

LRB1 | 2.5 | 7.2 | 19.3 | 10.2 | 8.6 | 4.8 | 12.8 | 23.2 | 14.9 | 10.9 | 3.3 | 9.2 | 28.6 | 14.8 | 16.1 | 2.0 | 11.9 | 38.5 | 27.0 | 48.3 | 4.5 | 19.8 | 55.6 | 35.3 | 42.6 | |

LRB2 | 2.4 | 6.0 | 20.5 | 9.6 | 8.4 | 5.6 | 9.0 | 20.0 | 12.4 | 8.1 | 4.0 | 13.6 | 24.0 | 14.6 | 10.7 | 5.6 | 13.1 | 34.6 | 21.7 | 26.7 | 2.9 | 14.3 | 45.3 | 29.6 | 41.0 |

_{iso,max}) are presented in Figure 15. The LRB1 frame model presents a similar ascent slope pattern as the LRB2 frame model on the occasion of increasing scale factors, but has larger statistical values owing to more flexible behavior displayed at the LRB isolator. The ranges of data scatter indicating the degree of uncertainty are determined by the value of standard deviations. At every scale factors, larger mean values and standard deviations are found at the LRB1 frame model.

**Figure 15.**Statistical investigations of the maximum isolator displacements (Δ

_{iso,max}) for individual LRB-isolated frame models according to increasing scale factors.

_{iso,res}) are also presented for the purpose of conducting more statistical investigations required to make sure the performance of the LRB isolators in the frame building. After checking residual roof displacements presented in Figure 14, it can be affirmed that there is a little difference to corresponding residual isolator displacements. This implies that most of relative residual displacements occur at the base isolation system.

_{iso,max}) for individual LRB-isolated frame models according to increasing scale factors are presented in Figure 17. When the isolation system is fully excited by each of the NF ground motions, dissipated energy corresponds to the area of the hysteresis force-displacement loop as given to Figure 11. As expected, the graphs of the maximum isolator energies show a totally similar pattern as those of the maximum isolator displacements, including the distributional trends of data scatter. As compared to each LRB-isolated frame model, the statistical values for the maximum isolator displacements, residual isolator displacements, and maximum dissipated isolator energies are summarized in Table 6. Similarly, this table also presents the values of each mean and standard deviation (SD).

**Figure 16.**Statistical investigations of the residual isolator displacements (Δ

_{iso,res}) for individual LRB-isolated frame models according to increasing scale factors.

**Figure 17.**Statistical investigations of the maximum isolator energies (E

_{iso,max}) for individual LRB-isolated frame models according to increasing scale factors.

**Figure 18.**Statistical investigations of the maximum inter-story drift ratios (Δ

_{inter,max}) for individual frame models under SF = 0.2, 0.6, and 1.0, respectively.

**Figure 19.**Statistical investigations of the residual inter-story drift ratios (Δ

_{inter,res}) for individual frame models under SF = 0.2, 0.6, and 1.0, respectively.

**Table 6.**Comparison and summary of the statistical valises for maximum isolator displacements, residual isolator displacements, and dissipated energies.

Evaluation Item | Model ID | SF = 0.2 | SF = 0.4 | SF = 0.6 | SF = 0.8 | SF = 1.0 | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | 15.9% | 50.0% | 84.1% | Mean | SD | ||

Δ_{iso,max} (mm) | LRB1 | 11.7 | 37.4 | 79.6 | 44.0 | 31.1 | 45.2 | 115.5 | 200.1 | 118.5 | 63.7 | 73.3 | 207.5 | 286.1 | 190.0 | 84.3 | 98.9 | 263.4 | 322.9 | 237.3 | 84.4 | 137.4 | 295.9 | 335.8 | 269.6 | 78.7 |

LRB2 | 11.1 | 32.7 | 76.0 | 38.6 | 28.8 | 32.1 | 91.7 | 157.9 | 95.8 | 51.2 | 64.1 | 162.5 | 211.5 | 145.4 | 56.8 | 91.8 | 193.7 | 230.6 | 177.6 | 53.3 | 121.2 | 214.7 | 239.9 | 196.4 | 47.9 | |

Δ_{iso,res} (mm) | LRB1 | 1.6 | 7.1 | 20.8 | 10.1 | 9.7 | 2.0 | 12.5 | 26.9 | 14.2 | 13.1 | 2.9 | 10.0 | 32.6 | 14.9 | 12.9 | 3.3 | 20.4 | 55.5 | 23.4 | 19.8 | 8.3 | 19.7 | 43.5 | 24.6 | 20.3 |

LRB2 | 0.7 | 3.9 | 23.8 | 9.3 | 10.3 | 5.8 | 13.6 | 23.5 | 15.5 | 11.2 | 2.5 | 12.9 | 28.6 | 16.5 | 14.9 | 6.8 | 15.4 | 41.2 | 25.1 | 22.2 | 3.8 | 27.5 | 60.5 | 29.0 | 24.6 | |

E_{iso,max} (MN-m) | LRB1 | 0.0 | 11.0 | 44.7 | 17.8 | 22.6 | 20.3 | 67.4 | 140.4 | 77.5 | 59.6 | 41.1 | 146.6 | 229.3 | 142.2 | 80.3 | 64.7 | 216.2 | 272.8 | 192.1 | 82.4 | 90.7 | 264.6 | 286.9 | 224.4 | 77.9 |

LRB2 | 0.0 | 9.2 | 42.5 | 16.6 | 23.0 | 11.3 | 67.6 | 140.1 | 71.0 | 56.9 | 43.0 | 135.1 | 200.3 | 125.2 | 67.6 | 71.8 | 187.3 | 220.9 | 163.6 | 62.5 | 97.3 | 211.5 | 231.4 | 186.2 | 55.0 |

**Table 7.**Comparison and summary of the statistical values for maximum and residual inter-story drift ratios.

SF | Evaluation Item | Model ID | 1st Story | 2nd Story | 3rd Story | 4th Story | 5th Story | 6th Story | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

50% | Mean | SD | 50% | Mean | SD | 50% | Mean | SD | 50% | Mean | SD | 50% | Mean | SD | 50% | Mean | SD | |||

0.2 | Δ_{inter,max} (mm) | As-Built | 0.204 | 0.279 | 0.236 | 0.255 | 0.309 | 0.223 | 0.219 | 0.242 | 0.123 | 0.206 | 0.214 | 0.098 | 0.213 | 0.227 | 0.102 | 0.136 | 0.144 | 0.065 |

LRB1 | 0.538 | 0.524 | 0.115 | 0.125 | 0.125 | 0.028 | 0.058 | 0.061 | 0.021 | 0.050 | 0.055 | 0.016 | 0.055 | 0.055 | 0.020 | 0.032 | 0.033 | 0.012 | ||

LRB2 | 0.631 | 0.605 | 0.166 | 0.146 | 0.144 | 0.035 | 0.065 | 0.068 | 0.023 | 0.062 | 0.062 | 0.018 | 0.059 | 0.062 | 0.022 | 0.036 | 0.037 | 0.013 | ||

Δ_{inter,res} (mm) | As-Built | 0.005 | 0.025 | 0.061 | 0.007 | 0.025 | 0.049 | 0.009 | 0.012 | 0.008 | 0.003 | 0.005 | 0.007 | 0.008 | 0.010 | 0.007 | 0.004 | 0.005 | 0.005 | |

LRB1 | 0.050 | 0.060 | 0.041 | 0.006 | 0.008 | 0.007 | 0.009 | 0.011 | 0.005 | 0.002 | 0.004 | 0.004 | 0.008 | 0.010 | 0.004 | 0.004 | 0.005 | 0.002 | ||

LRB2 | 0.058 | 0.075 | 0.056 | 0.006 | 0.008 | 0.007 | 0.010 | 0.012 | 0.004 | 0.002 | 0.004 | 0.003 | 0.008 | 0.010 | 0.003 | 0.004 | 0.005 | 0.002 | ||

0.4 | Δ_{inter,max} (mm) | As-Built | 0.434 | 0.662 | 0.561 | 0.520 | 0.643 | 0.436 | 0.405 | 0.392 | 0.154 | 0.318 | 0.304 | 0.082 | 0.323 | 0.319 | 0.085 | 0.192 | 0.199 | 0.055 |

LRB1 | 0.727 | 0.802 | 0.287 | 0.177 | 0.182 | 0.047 | 0.083 | 0.090 | 0.028 | 0.080 | 0.082 | 0.026 | 0.074 | 0.081 | 0.028 | 0.045 | 0.049 | 0.017 | ||

LRB2 | 0.838 | 1.059 | 0.590 | 0.198 | 0.205 | 0.053 | 0.101 | 0.101 | 0.034 | 0.093 | 0.092 | 0.030 | 0.095 | 0.092 | 0.033 | 0.057 | 0.055 | 0.020 | ||

Δ_{inter,res} (mm) | As-Built | 0.030 | 0.149 | 0.227 | 0.031 | 0.115 | 0.153 | 0.017 | 0.034 | 0.044 | 0.010 | 0.016 | 0.023 | 0.010 | 0.020 | 0.029 | 0.007 | 0.012 | 0.019 | |

LRB1 | 0.084 | 0.098 | 0.066 | 0.010 | 0.014 | 0.012 | 0.010 | 0.013 | 0.008 | 0.002 | 0.007 | 0.008 | 0.008 | 0.012 | 0.008 | 0.004 | 0.006 | 0.005 | ||

LRB2 | 0.117 | 0.153 | 0.122 | 0.009 | 0.013 | 0.010 | 0.009 | 0.012 | 0.007 | 0.002 | 0.005 | 0.006 | 0.008 | 0.011 | 0.007 | 0.004 | 0.005 | 0.004 | ||

0.6 | Δ_{inter,max} (mm) | As-Built | 0.845 | 1.207 | 1.069 | 0.828 | 1.038 | 0.804 | 0.432 | 0.496 | 0.220 | 0.323 | 0.342 | 0.090 | 0.342 | 0.350 | 0.098 | 0.223 | 0.215 | 0.066 |

LRB1 | 1.204 | 1.752 | 1.719 | 0.251 | 0.251 | 0.097 | 0.122 | 0.128 | 0.052 | 0.110 | 0.113 | 0.044 | 0.108 | 0.110 | 0.042 | 0.063 | 0.066 | 0.028 | ||

LRB2 | 1.851 | 2.311 | 1.846 | 0.275 | 0.276 | 0.091 | 0.132 | 0.140 | 0.051 | 0.117 | 0.125 | 0.044 | 0.121 | 0.123 | 0.041 | 0.072 | 0.075 | 0.027 | ||

Δ_{inter,res} (mm) | As-Built | 0.143 | 0.352 | 0.525 | 0.108 | 0.273 | 0.395 | 0.027 | 0.054 | 0.077 | 0.012 | 0.027 | 0.044 | 0.012 | 0.031 | 0.050 | 0.007 | 0.020 | 0.036 | |

LRB1 | 0.162 | 0.275 | 0.337 | 0.016 | 0.022 | 0.018 | 0.012 | 0.017 | 0.011 | 0.003 | 0.009 | 0.010 | 0.009 | 0.014 | 0.011 | 0.004 | 0.007 | 0.006 | ||

LRB2 | 0.164 | 0.280 | 0.387 | 0.011 | 0.017 | 0.016 | 0.010 | 0.014 | 0.011 | 0.003 | 0.007 | 0.009 | 0.009 | 0.013 | 0.010 | 0.003 | 0.006 | 0.006 | ||

0.8 | Δ_{inter,max} (mm) | As-Built | 1.235 | 1.879 | 1.773 | 1.264 | 1.606 | 1.375 | 0.519 | 0.616 | 0.284 | 0.361 | 0.402 | 0.111 | 0.375 | 0.413 | 0.118 | 0.241 | 0.259 | 0.081 |

LRB1 | 2.689 | 3.308 | 3.165 | 0.321 | 0.349 | 0.222 | 0.163 | 0.172 | 0.073 | 0.146 | 0.144 | 0.052 | 0.142 | 0.141 | 0.049 | 0.086 | 0.086 | 0.032 | ||

LRB2 | 3.876 | 4.213 | 3.285 | 0.346 | 0.401 | 0.273 | 0.177 | 0.187 | 0.084 | 0.157 | 0.156 | 0.058 | 0.153 | 0.151 | 0.055 | 0.092 | 0.093 | 0.037 | ||

Δ_{inter,res} (mm) | As-Built | 0.370 | 0.812 | 0.939 | 0.214 | 0.635 | 0.928 | 0.051 | 0.093 | 0.113 | 0.031 | 0.048 | 0.062 | 0.030 | 0.051 | 0.067 | 0.021 | 0.039 | 0.052 | |

LRB1 | 0.436 | 0.760 | 0.856 | 0.021 | 0.058 | 0.130 | 0.014 | 0.023 | 0.019 | 0.003 | 0.011 | 0.012 | 0.009 | 0.016 | 0.013 | 0.004 | 0.008 | 0.008 | ||

LRB2 | 0.544 | 0.803 | 0.880 | 0.016 | 0.066 | 0.157 | 0.015 | 0.020 | 0.017 | 0.006 | 0.010 | 0.011 | 0.008 | 0.015 | 0.014 | 0.004 | 0.008 | 0.008 | ||

1.0 | Δ_{inter,max} (mm) | As-Built | 2.014 | 2.784 | 2.278 | 1.572 | 2.280 | 2.013 | 0.607 | 0.717 | 0.352 | 0.393 | 0.456 | 0.151 | 0.411 | 0.466 | 0.157 | 0.261 | 0.300 | 0.111 |

LRB1 | 5.220 | 5.583 | 5.065 | 0.407 | 0.593 | 0.850 | 0.218 | 0.222 | 0.098 | 0.181 | 0.174 | 0.058 | 0.177 | 0.169 | 0.051 | 0.105 | 0.105 | 0.037 | ||

LRB2 | 6.537 | 6.499 | 4.920 | 0.440 | 0.739 | 1.009 | 0.235 | 0.249 | 0.118 | 0.198 | 0.192 | 0.068 | 0.190 | 0.188 | 0.063 | 0.116 | 0.118 | 0.046 | ||

Δ_{inter,res} (mm) | As-Built | 0.790 | 1.427 | 1.515 | 0.429 | 1.179 | 1.579 | 0.104 | 0.166 | 0.184 | 0.044 | 0.080 | 0.091 | 0.031 | 0.076 | 0.093 | 0.033 | 0.067 | 0.076 | |

LRB1 | 0.815 | 1.730 | 2.713 | 0.020 | 0.234 | 0.782 | 0.017 | 0.032 | 0.041 | 0.008 | 0.016 | 0.018 | 0.012 | 0.020 | 0.019 | 0.008 | 0.012 | 0.016 | ||

LRB2 | 1.112 | 1.475 | 1.660 | 0.028 | 0.322 | 0.938 | 0.015 | 0.037 | 0.047 | 0.008 | 0.018 | 0.024 | 0.010 | 0.022 | 0.025 | 0.006 | 0.014 | 0.024 |

_{inter,max}) for individual frame models under 0.2, 0.6, and 1.0 scale factors are additionally conducted as shown in Figure 18. The as-built frame model is stable up to 0.2 scale factor, and thus has the almost same statistical percentile points distributed over the floors. In contrast, the LRB-isolated models possess the peak maximum inter-story drift ratios that occur at the first floor. The peak maximum inter-story drift ratios at the as-built frame model gradually move into the first floor after reaching 0.6 scale factor applied to the NF ground motions. The increased plastic deformations at the lower stories cause this shift. Although the LRB-isolated frame models possess larger statistical peak ratio points than the as-built frame model, the values of their other statistical ratio points (distributed over from second to top floor) rapidly decrease. A couple of data points shown at the second floor of the as-built frame model exceed 2% drift ratio limit even under 0.6 scale factored ground motions. More severe damages representing larger inter-story drift ratios are found at the first floor of the frame model under 1.0 scale factor. The LRB-isolated frame models have relatively larger maximum inter-story drift ratios distributed over the first floor due to movable base conditions. However, smaller base shear forces transferred from base isolation can cause a huge decrease in the maximum inter-story drift ratios occurring at over second floor. For instance, the median (50th percentile) peak maximum inter-story drift ratios for the LRB1 and LRB2 frame model are 0.41% and 0.44%, respectively, while that for the as-built frame model is 1.57% (see also Table 7).

_{inter,res}) for individual frame models under 0.2, 0.6, and 1.0 scale factors are shown in Figure 19. The statistical values for maximum and residual inter-story drift ratios are also summarized in Table 7. For the LRB-isolated frame models, the maximum residual inter-story drift ratios that indicate the most severe damage occurring at the column member are commonly distributed over the first floor. The 84.1 percentile line of the LRB1 frame model starts to exceed the limits for rehabilitation decision (0.5%) under the NF ground motions with 0.6 scale factor, and is slightly larger than that of the LRB2 frame model owing to the implementation of more flexible base isolation systems. In proportion to the rise in the scale factor, the extent of structural damage occurring at the first floor can be also extended with the residual inter-story drift ratio increasing. In spite, these LRB-isolated frame models exhibits excellent recentering properties characterized by the rapidly decreasing residual inter-story drifts that are distributed over upper floors, as compared to the as-built frame model. A couple of data points shown at the third floor of the as-built frame model exceed the rehabilitation decision limit after 1.0 scale factored ground motions (see Figure 19c). Furthermore, the as-built frame model undergoes complete collapse even at the second floor. It can be finally shown that base isolation systems can generally mitigate structural damage generated by the residual inter-story drift.

## 8. Concluding Remarks

- (1)
- The force-deformation responses of the LRB models can be idealized as bilinear hysteresis loops simulated based on four main parameters. Two LRB models used in the practical field construction are selected for design and analyses in this study. The LRB2 model was designed with geometric parameters having larger diameters and smaller heights in comparison to the LRB1 model. For this reason, the LRB2 model exhibits stiffer slope, larger post-yield strength, and slightly lower damping coefficient than the LRB1 model in the force-deformation response curve.
- (2)
- The prototype buildings constructed as 6 story-braced frame structures can be modeled as 2D numerical frame models because they are designed to be symmetrical to their center axes with uniform mass and stiffness distribution. The LRB isolator devices installed at the column bases of the LRB-isolated frame models were modeled as the nonlinear component springs with behavioral properties. The as-built frame models without base isolation systems had fixed end boundary conditions because their column bases were designed to be fixed.
- (3)
- A set of 20 NF ground motions were used to conduct the nonlinear dynamic time-history analyses. The average response spectral acceleration for these 20 NF ground motions was investigated to easily estimate base shear forces required for seismic frame design. The band of existing larger spectral accelerations was mostly displayed at the short fundamental time period. Accordingly, the as-built frame model with the short fundamental time period possesses relatively larger response spectral accelerations. The LRB isolator devices can elongate the fundamental time period at the entire frame structure, and effectually mitigate seismic base shear forces transmitted from ground accelerations.
- (4)
- After conducting time-history analyses with representative NF ground motion data, the seismic responses of the LRB-isolated frame models were compared to those of the as-built frame model in terms of roof displacements, base shear forces, and inter-story drifts. The relatively larger maximum roof displacements were distributed over two LRB-isolated frame models owing to flexible end boundary conditions used for simulating the behavior of the LRB isolator. In spite, these LRB-isolated frame models exhibited smaller residual inter-story drift ratios than the as-built frame model because they were subjected to the mitigated base shear forces transferred from ground accelerations.
- (5)
- All statistical lines presented herein ascend in the almost straight lines as the scale factor of the ground motion increases. The as-built frame model shows larger maximum and residual inter-story drift ratios as compared to the LRB-isolated frame models under the same seismic loading condition. This implies that the LRB isolator devices reduce the amount of generating base shear forces, thereby mitigating structural damage and permanent deformation occurring over the second floor. Finally, it is concluded based on the analysis result that seismic performance and capacity for the multi-story building structure subjected to severe NF ground motions can be upgraded by installing the LRB isolator devices.

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Hu, J.W.
Response of Seismically Isolated Steel Frame Buildings with Sustainable Lead-Rubber Bearing (LRB) Isolator Devices Subjected to Near-Fault (NF) Ground Motions. *Sustainability* **2015**, *7*, 111-137.
https://doi.org/10.3390/su7010111

**AMA Style**

Hu JW.
Response of Seismically Isolated Steel Frame Buildings with Sustainable Lead-Rubber Bearing (LRB) Isolator Devices Subjected to Near-Fault (NF) Ground Motions. *Sustainability*. 2015; 7(1):111-137.
https://doi.org/10.3390/su7010111

**Chicago/Turabian Style**

Hu, Jong Wan.
2015. "Response of Seismically Isolated Steel Frame Buildings with Sustainable Lead-Rubber Bearing (LRB) Isolator Devices Subjected to Near-Fault (NF) Ground Motions" *Sustainability* 7, no. 1: 111-137.
https://doi.org/10.3390/su7010111