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This study uses the in-structure recordings to investigate the vibration characteristics of a 51-story steel high-rise building in response to a major earthquake, typhoon and ambient vibrations. This presents an opportunity for us to compare the building behaviors, especially their modal properties under different types of excitation. First, we use a two-stage regression procedure to obtain the relations of the building response, including peak floor acceleration and velocity as a function of the wind speed and floor height of the building. Secondly, the structural dynamic characteristics of the high rise building, including the transfer functions and natural frequencies, excited by the Chi-Chi earthquake, Typhoon Aere, and ambient vibrations are also determined and compared. As a result, from the formulas for building response, the predicted peak floor acceleration is higher in the lateral (EW) component than in the longitudinal (NS) component. This is probably due to the greater stiffness of the building in the longitudinal direction than in the lateral direction. In addition, after having identified the 1
^{st}
, 2
^{nd}
, and 3
^{rd }
natural frequencies using the recorded data from the earthquake, typhoon and ambient vibrations, the ranking of the fundamental natural frequencies from low to high is the Chi-Chi earthquake, Typhoon Aere and the ambient vibrations. This means that greater excitation forces of the earthquake have resulted in lower natural frequencies than that produced by the typhoon and ambient vibrations.

Taiwan is located along the circum-Pacific seismic belt. From the historical record, many damaging earthquakes had occurred in Taiwan. Earthquakes have caused great loss of lives in Taiwan. In addition to earthquakes, typhoons are the most catastrophic weather phenomenon in Taiwan. The country has experienced 198 typhoons (tropical cyclones) in the past 43 years, averaging more than four typhoons per year [

The full-scale measurements of tall buildings during severe storms and earthquakes are still insufficient although many tall buildings have been built around the world [

In addition, Typhoon Aere passed by northern Taiwan on 24 August 2004. The measured wind data at the Taipei meteorological station and the structural array data recorded in the 51-story SK Tower in Taipei are analyzed in this paper to obtain the relations of the building response, in terms of the peak floor acceleration and velocity as a function of wind speed and story height. Furthermore, the structural dynamic characteristics of this tall building, including the transfer functions and natural frequencies of vibration, excited by the typhoon and the M7.6 Chi-Chi earthquake as well as ambient vibrations, are also determined and compared.

Not only to analyze the vibration characteristics of earthquake, typhoon and ambient vibration from a 51-story high-rise building, but also the relations of the floor acceleration and velocity as a function of the wind speed and floor height of the building would be established. The structural array data recorded at the SK Tower and the measured wind data from the Taipei meteorological station (TAP), about 850 m apart from SK Tower are used in this paper. The SK Tower is located in Taipei. It is a tall steel building in a very active typhoon region of the world. The building has 51 stories with a total height of 244.15 m at the roof (see

The structural array of SK Tower uses central recording; sensors are placed at various selected locations in the building, cables are used to send analog signals from the sensors to the central signal conditioning box. Digitization and recording are then performed at the central site. The main advantage of this system is that it is based on well proven technology [^{th}, basement 1^{th}, 3^{th}, 18^{th}, 32^{th} and 47^{th} floor and the roof. These floors are at height of −25.0 m, −4.0 m, 10.7 m, 82.4 m, 136.2 m, 193.8 m, and 205.3 m relative to the ground surface, respectively (see

An earthquake of Mw magnitude 7.6 took place in central Taiwan on 21 September 1999, local time (20 September UTC). This was the largest inland earthquake to occur in Taiwan in the twentieth century. Its strong shakings caused devastating impacts at cities and towns as far as 150 km away and destroyed several

high-rise buildings in Taipei Basin [^{2} was recorded at Channel 27, located in the roof of the SK Tower. In addition, we also recorded the ambient vibrations of the SK Tower for a 45-minute duration on 6 September 2004. The data was recorded by free running the system continuously with a gain set at 10, the record length of each segment was 62.3 s, at a sampling rate of 200 samples per second per channel.

The SK tower is also situated in one of the most active typhoon regions in the world. Typhoons attacking Taiwan mainly originate in the western Pacific Ocean. The tropical depression Aere was developed over the Pacific Ocean at about 2000 km southeast of Taipei in the morning of 20 August 2004. It intensified into a tropical storm later that afternoon. Typhoon Aere is then moved in a northwest course and attained typhoon strength on 22 August. It turned westwards on 24 August and skirted the northern coast of Taiwan the following day. Typhoon Aere caused 24 deaths and left nine people missing in Taiwan. During Typhoon Aere, the maximum 1-minute mean wind speed of 13.3 m/sec was measured by the anemometer installed at the TAP station at local time of 22:47 (TPT), 24 August 2004.

A two-stage procedure is used to estimate the floor acceleration and velocity of vibrations of the tall building. A mathematical formulation, using two independent parameters that is the wind speed and floor height in the building, is further established to estimate the floor acceleration and velocity of the tall building excited

by typhoon force.

The relationships express the peak floor acceleration and velocity of vibration of the tall building as a function of two simple parameters representing the wind speed and the floor height of the building. The following functional form is established in this study:

ln Y = a X + b H + c ± σ (1)

where Y is the peak floor acceleration (PFA) or velocity (PFV) of building vibration; X is the wind speed; H is the floor height of the building; a is a wind speed coefficient; b is a height coefficient; c is a constant; σ is the standard deviation. The coefficients a, b, and c are determined by regression from the data. In this study, the three coefficients in the above formula for predicting building vibration are determined using a two-stage regression procedure. A similar approach was used previously to obtain the strong ground motion attenuation relationships by Joyner and Boore (1993) [

Different sets of model parameters can be determined from the recorded time histories by several system identification methods, either in the frequency domain or time domain. Most common used methods are based on frequency domain [

The variations of wind speed and wind direction averaged over one-minute intervals are plotted in

In order to obtain the relationships of the peak floor acceleration and velocity versus the wind speed, and floor height, the 1-minute averaged wind speed values for an 354-minute duration, starting from 16:58 TPT, 24 August 2004 and ending at 22:52 TPT, 24 August 2004 are used in the analysis. It can be seen that the mean wind to the SK Tower, mainly blew from the north-northwest direction between 16:58 TPT, 24 August and 04:00 TPT, 25 August 2004. The wind direction then changed gradually from northwest to the south in a counterclockwise until 10:00 TPT, 25 August, as Typhoon Aere passed by northern Taiwan from east to west.

In this study, we examine the variation of Peak Floor Acceleration (PFA) and Peak Floor Velocity (PFV) of the SK Tower with respect to 1-min-mean wind speed and the height of individual floors.

Regressions on the data set, using the two-stage regression method described above, have resulted in the coefficients of the relationships for floor motion, as given in

V ( z ) V δ = ( Z δ ) α (2)

where V(z) is the wind speed estimated at desired height z, Vδ is the wind speed at boundary layer height δ, and α is the power law index. The values of α and δ for TAP station are 0.25 and 400, respectively, which were estimated by the Taiwan Central Weather Bureau based on local topographic conditions surrounding the station [

Comp. Vibration Amp. | NS-Component | EW-Component | ||||||
---|---|---|---|---|---|---|---|---|

a | b | c | σ | a | b | c | σ | |

PFA (gal) | 0.226 | 0.0072 | −3.219 | 0.468 | 0.232 | 0.0067 | −2.726 | 0.456 |

PFV (cm/sec) | 0.220 | 0.0086 | −3.845 | 0.478 | 0.215 | 0.0071 | −2.828 | 0.440 |

Remark: Building vibration model: ln ( PFA , PFV ) = a * X + b * H + c ± σ , where PFA is peak floor acceleration in gal, PFV is peak floor velocity in cm/sec, X is wind speed in m/sec, H is floor height in m, and σ is the standard deviation.

(EW) peak floor velocity for the tall building due to typhoon force, as a function of mean wind speed. The solid and dashed lines represent the same meanings as

In this study, the Chi-Chi earthquake record is used to determine the natural frequencies of the first three modes. Higher modes are not considered since they are of less significance in actual building responses [^{st}, 2^{nd}, and 3^{rd} modes of vibration in the longitudinal and lateral directions.

^{st}, 2^{nd}, and 3^{rd} lateral modes of the SK Tower are found to be 0.205, 0.500, and 0.969 Hz, respectively. In addition, the 1^{st} torsional mode is also found between 0.25 ~ 0.4 Hz in the lateral component. The corresponding results of the longitudinal component are 0.247, 0.590, and 1.060 Hz, respectively. Because the SK Tower is a steel structure, the corresponding fundamental mode period, according to the building code can be calculated as follows [

T = 0.085 h n 3 / 4 (3)

where h_{n} is the height of building from the ground. The computed natural frequency of the fundamental mode according to the building code is 0.217 Hz. When this frequency is compared with those identified from actual data, we can find that the code formula tends to underestimate and overestimate the fundamental frequency by 5.53% and 13.82% for lateral and longitudinal component, respectively, as given in ^{st} and 2^{nd} lateral natural frequencies

Mode | Source type Para. | (1) Chi-Chi Earthquake | (2) Typhoon Aere | (3) Ambient Vibrations | (4) Building Code(2001) |
---|---|---|---|---|---|

1^{st} EW | f_{1} | 0.205 | 0.210 ± 0.006 | 0.217 ± 0.005 | 0.217 |

2^{nd} EW | f_{2} | 0.500 | 0.519 ± 0.012 | 0.539 ± 0.010 | |

3^{rd} EW | f_{3} | 0.969 | 1.002 ± 0.014 | 1.027 ± 0.013 | |

1^{st} EW | δ_{1} | −5.53 | −3.23 | 0.00 |

Mode | Source type Para. | (1) Chi-Chi Earthquake | (2) Typhoon Aere | (3) Ambient Vibrations | (4) Building Code(2001) |
---|---|---|---|---|---|

1^{st} NS | f_{1} | 0.247 | 0.255 ± 0.009 | 0.267 ± 0.009 | 0.217 |

2^{nd} NS | f_{3} | 0.590 | 0.614 ± 0.018 | 0.644 ± 0.009 | |

3^{rd} NS | f_{5} | 1.060 | 1.117 ± 0.017 | 1.148 ± 0.011 | |

1^{st} NS | δ_{1} | 13.82 | 17.51 | 23.04 |

of the SK Tower as well as the 3^{rd} one is the smallest. 2) The amplitude ratios of the roof to the basement are a multiple of 26, 27, and 14 with respect to the 1^{st}, 2^{nd}, and 3^{rd} lateral natural frequencies, respectively.

After having identified the natural frequencies of the 1^{st}, 2^{nd}, and 3^{rd} modes from the Chi-Chi earthquake data, we now proceed to analyze the typhoon and ambient vibration data. These observed values and relative ratios are compared with the corresponding building code values for the 1^{st}, 2^{nd}, and 3^{rd} natural frequencies in the lateral (EW) (dark line) and longitudinal (NS) (light line) directions in

interval of sampling points [^{15}) and Δt = 0.005 sec. Accordingly, Δf = 0.0061 Hz. By comparing the modal frequencies obtained from the three different types of excitation, as given in

In the left and right side of ^{st}, 2^{nd}, and 3^{rd} mode as obtained respectively from the recorded data of the Chi-Chi earthquake (in a straight line which is made up of 1 record) and ambient vibration data (in zigzag line which is made up of 43 segments). In the middle part are showing similar results from the recorded data of Typhoon Aere (in zigzag line which is made up of 341 segments). The dashed and thick dashed lines stand for the average natural frequencies, which were calculated from total segments of records, in the lateral (EW) and longitudinal (NS) directions, respectively. From

This study uses the in-structure recordings to investigate the vibration characteristics of a 51-story steel high-rise building in response to a major earthquake, typhoon and ambient vibrations. This presents an opportunity for us to compare the building behaviors, especially their modal properties under different types of excitation. From the results presented above, we can draw the following conclusions:

1) The measured wind data and the structural array data are analyzed in this paper, using a two-stage regression procedure, to obtain the formulas for estimating the building response parameters, including the peak floor acceleration and velocity, as a function of the wind speed and floor height in the building.

2) From the formulas for building response, the predicted peak floor acceleration is higher in the lateral (EW) component than in the longitudinal (NS) component. This is probably due to the greater stiffness of the building in the longitudinal direction than in the lateral direction.

3) Moreover, we note that the regression coefficient “a” for the term of mean wind speed has higher values of the acceleration response than to the velocity response of the building. This means that the contribution of the wind force is higher to the acceleration response than to the velocity response of the building.

4) The 1^{st}, 2^{nd}, and 3^{rd} lateral natural frequencies of the SK Tower after examining the observed transfer functions are found to be 0.205, 0.500, and 0.969 Hz, respectively. The corresponding results for the longitudinal component are 0.247, 0.590, and 1.060 Hz, respectively. Accordingly, these identified natural frequencies are compared with an appropriate formula specified in the building code. It is found that the code formula tends to underestimate and overestimate the fundamental frequency of the building by 5.53% and 13.82% for the lateral and longitudinal component, respectively.

5) After having identified the 1^{st}, 2^{nd}, and 3^{rd} natural frequencies using the recorded data from the earthquake, typhoon and ambient vibrations, the ranking of the fundamental natural frequencies from low to high is the Chi-Chi earthquake, Typhoon Aere and the ambient vibrations.

6) The natural frequencies are higher for the longitudinal (NS) component than in the lateral (EW) component. This is probably because the stiffness of the building is greater in the longitudinal direction than in the lateral direction.

I thank the Central Weather Bureau of Taiwan for providing excellent structural array and wind data for the present study. I also appreciate greatly two anonymous reviewers for their valuable comments, which improved the article. This research was supported by the Ministry of Science and Technology (MOST) of Taiwan under Grant No. MOST106-2116-M-244-001.

Liu, K.-S. (2018) Vibration Analysis of a 51-Story Tower from the Recorded Data of the Earthquake, Typhoon and Ambient Vibration. World Journal of Engineering and Technology, 6, 161-175. https://doi.org/10.4236/wjet.2018.61009