Measured period of vibration of high-rise buildings
recorded on video movies opened to the public excitedby the 2011 off the Pacific coast of Tohoku Earthquake
Yutaka Nakamura1

Abstract
The long-period earthquake motion of the 2011 off the Pacificcoast of Tohoku Earthquake excited high-rise buildings with longperiod natural vibration. These situations of visible shaking can beseen on internet as YouTube as video movies recorded by the generalpublic there. Author read out period and amplitude from these movies
opened to the public and compared them to the number of the floors,
the height, and the result of the microtremor measurement before andafter the event and so on. Then author examined the relationship between the natural period and the height or the change of the natural period by the earthquake motion. As a result, it was found that it is possible to grasp a natural period and amplitude with tremendous precision from video movies, and a building with relative long natural period is said to tend to issue large deformation but it is difficult to grasp
the risk of the building only form the natural frequency. Furthermore,
there is no significant difference on the earthquake motion characteristics derived both from microtremor and earthquake motion.

_______________________________
1 System and Data Research Co., Ltd., Japan.

259

260

Yutaka Nakamura

1. Introduction
Because the 2011 off the Pacific coast of Tohoku Earthquake(hereafter the 3.11 earthquake) excited long period earthquake motion
due to the large fault rapture motion, structures with long natural period like skyscrapers are discernibly shaken. Consequently, many shaking buildings were shot at various sites and the videos can be seen on
web sites as YouTube. The author interprets the period and the amplitude of shaking buildings from these video files and considers relationships between period and height or the change of the natural period caused by the earthquake motion, comparing the result of the interpretation to the floor numbers, height or the result of microtremor before and after the earthquake.

2. Data set and interpretation method
2.1. Data set
Data set is consisted of the video files interpretable the period andamplitude with stable observing point. The period and the amplitude
are carefully interpreted based on this data set. In addition, althoughthese video files seemed to be started recording after reaching a large
motion, a clock appeared in movies shows a time around 14:50, so themain part of the long period earthquake motion seems to be recorded.
The specifications and the characteristics of skyscrapers are based on
characteristics data sheet of the database of measured dumping (edited
at 2000.10) [1] or other detail information on buildings on web sites.
Because this characteristics data sheet conceals the name of the building, that is identified from number of stories, eaves height or completed year. The buildings in video movies are also grasped the characteristics corresponding to datasheet from the name of the buildings.
2.2. Interpretation method on period and amplification(1) Direct interpretation
It is necessary for interpretation of the building motion to appear
the objects for reference. If the objects for reference can be assumed a

Measured period of vibration of high-rise buildings recorded…

261

fixed point, it is rather easy to interpret the period and the amplitude.
Here, the objects for reference was chose a structure far away orneighbor building. In case of comparing the neighbor building, relative displacement is combined from characteristics of the both buildings. Similar period or amplitude for each other causes beat. The frequency of the beat is the difference of the frequency of each building
and it is possible to fix the predominant frequency of each building
noticing that the apparent frequency is the averaged frequency of bothbuilding. It is difficult to understand clearly the beat frequency because it is rather long for building with long period. So the natural frequency easy to interpret first, and then the natural frequency of another building is estimated using the apparent frequency interpreted from
relative variability for both building and the fixed frequency.
Amplitude is interpreted roughly in 10cm seemed to be the maximum
amplitude.
(2) Indirect interpretation
The vibration of the building in the video files is very tiny and it
was often difficult to grasp it quantitatively. In such a case, potential
phenomenon for period determination were found out with repeatedly
careful confirmation of the video file. The phenomenon is, for example, sequential vibrating sound of a building, reflection on a glass wallof a building, behavior of neighboring building reflected on a wall, vibration of a movable shelf, opening and closing a door and so on. Although it was difficult to clarify the amplitude with these clues, it
seemed to be possible to estimate the period with considerable accuracy.

3. Predominant period and amplitude interpreted from video files
Totally 50 buildings between 5 stories and 70 stories were interpreted the frequency and so on from video files. The vibration frequency was interpreted for at least one direction of each building andpartly two directions, so the total number of data is more then 50. The
result of the interpretation is listed in Table 1, and examined in more
depth below.

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Yutaka Nakamura

Table 1. Predominant Vibration Excited by the 2011Off the Pacific
Coast of Tohoku Earthquake
Vibration Excited by the Quake
Analytic
Measured before Quake Noise before Quake Noise after Quake
PredominantMax.
Max. Design
Predominant Vibration '06/01/30measured '11/10/19measured
Comple- Number of Floors Height Period
Amp. Drift Ang.
PeriodPeriod in second Damp. Period
Amp.
PeriodAmp.
Structuretion
Ab.
B. Pent. in m in sec. Directioncm%
in sec. Wind Noise Quake%in sec.
times
in sec.
times
1
Shinjuku C
Oct-7954
43
216
6.00 Short: NS
50
0.23
5.65
6.00
6.00
5.85
2.1
S
54
4
3
216
Long side
5.35
4.97
4.97
4.55
4.8
2
Shinjuku N
Jun-7850
53203
5.20 Short side
100
0.49
5.42
4.80
0.39
4.94
11.2
S
50
5
3
203
Long side
4.27
3.43
0.37
3.22
6.2
3
Shinjuku AT
Jan-9544
42
189
4.50 Long: NS
90
0.48
S, partially SRC
4Shinjuku SJ
Mar-7643
62
193
4.80 Short side
150
0.78
5
Shinjuku M
Sep-7455
3210
4.25 Short side
S(2F-55F), SRC(under 1F)55
3
210
3.60 Long side
6
Shinjuku K
Jun-7147
32
170
4.50 Short: EW
80
0.47
3.85
4.30
0.50
S(3F-47F), SRC(1F, 2F),
47
3
2
170
3.85 Long: NS
40
0.24
4.30
3.10
0.80
RC(BF)
7
Asakusa C
1040
1.20 Short side
30
0.75
8
Roppongi AM
Mar-8637
4153
3.75 Short side60
0.39
S, partially SRC and RC
9
Roppongi IG
Jul-0232
2116
3.20 EW
30
0.26
SRC
10
Shinjuku JE
Sep-9728
4
1149
3.40 Long side
30
0.20
11
Shinjuku ST
Feb-9836
4
1
147
3.60 Long side
30
0.20
S
12
Shinjuku MT
Sep-9534
32
161
4.50 Short side80
0.50
S, SRC
13 TokyoCityHall1S
Mar-9148
3242
5.17 Short: EW
110
0.45
5.56
5.00
0.46
4.72
5.6 S(2F-48F), SRC(under 1F）
48
3
242
4.74 Long: NS
80
0.33
5.20
4.29
0.75
4.05
2.6
TokyoCityHall1N
48
3
242
Short: EW
5.56
5.11
10.2
48
3
242
Long: NS
5.20
4.04
5.9
14
Kanda ST
1980
14
2
56
1.50 Long side20
0.36
S, SRC(under 1F)
15
Kanda N
Mar-848
432
1.20 Short side
10
0.31
SRC
16
Akasaka SP
Mar-1116
2
64
1.91 along Road
20
0.31
S
17
Roppongi MT
Mar-03
54
6
2
238
6.00
200
0.84
18
TokyoCityHall2
Mar-9134
3
162
3.61 Short side
60
0.37
3.98
2.92
0.78
S, SRC and RC
34
3
162
Long side
3.91
2.73
0.73
19
Ikebukuro S
Apr-7860
3
3
227
Short side
6.25 6.25
1.56
S(Upper and Middle),
60
3
3
227
4.70 Long side100
0.44
5.88 4.55
SRC(Lower)
20 Marunouchi TN
Sep-0319
3
2100
5.00 Short side60
0.60
S, patiallySRC
21 Marunouchi TM
Nov-0837
42
178
5.00 Short side
S(CFT), partially SRC
22
Marunouchi ST
Apr-0735
41
165
3.10 Long side
S(CFT column)
23
Marunouchi A
Jul-71
29
4
2
110
3.00
S, partially SRC
24
Shinjuku W
Jun-9113
252
1.50 Long side
20
0.38
SRC
25
Shinjuku CT
Oct-0850
32
2043.70 NS60
0.29
S, partially SRC
26
Shinjuku LT
Jun-8931511222.70 Short: NS
60
0.49
2.99
2.60
2.80
0.90
SRC
31
5
1
122
2.70 Long side
3.00
2.38
2.55
27
Shibuya CT
Mar-01
41
6
184
4.68
S, partially SRC and RC
28
Harumi TX
Mar-01
44
183
4.40
20
0.11
29
Harumi TY
Mar-01
39
175
4.20
30
0.17
Harumi TZ
Mar-01
33
155
4.70
30
0.19
30
Yokohama LT
1993
70
3
3
282
4.54 NE60
0.21
6.02 4.60 5.22
0.70
31 Yokohama QA
Jun-9736
52
172
4.50 Short side
40
0.23
SRC
36
5
2
172
4.70 Long side
32 Yokohama MM
Mar-03
28
3
2
147
4.00
S, under ground SRC
33
Shinagawa GT
Mar-0332
3148
3.96 Long side
34
Shinagawa T
Mar-03
30
3
148
3.33
35
Shinagawa ET
Mar-03
32
3
152
4.00
S and SRC
36
Marunouchi M
Aug-0237
4179
4.30 Short side
S, under ground SRC
3741794.50 Long: EW
150
0.84
37 Marunouchi NM
Apr-0738
41
177
4.50 Long: EW80
0.45
S, under ground SRC
38
Shinjuku S
Mar-74
52
4
2
200
NE
5.07
4.44
0.74
4.79
17.8 S, partially SRC and RC
52
4
2
200
NW
5.07
4.44
0.80
4.33
15.2
39
Roppongi T
1994
9
36
1.17 Short side
20
0.56
40
Roppongi U
Nov-737
128
1.56 Short side
20
0.71
RC
41
Roppongi N
1948
7
1
28
0.54 Short side
SRC
42
Roppongi G
Sep-95
9
3
36
0.70
SRC
43
Ohfuna K
Jul-77520
0.98 Short side
15
0.75
44 Daikanyama D
Jul-05
12
48
1.50
40
0.83
45
Shinbashi Ｎ
Apr-0332
42
193
4.10 Short side
46
Shiodome R
Apr-0338
4
2
172
Long side
47
Shinbashi D
Oct-02485
1
210
6.10 Short side
120
0.57
5.40
48
5
1
210
Long side
4.60
48 Kasumigaseki K
Apr-6836
3
2
147
4.80 Short side
70
0.48
5.14
3.74
1.02
4.12
14.7
36
3
2
147
Long side
5.04
3.38
1.31
3.53
5.3
49 Kasumigaseki CGW Sep-07
38
3
1
174
4.14 EW
50 Shinagawa CST
Mar-03
29
4
1
148
3.80

No.

Building Name

3.1. Predominant period(1) Comparison of the predominant period before and after the earthquake
Microtremor measurements were conducted for high-rise buildings;
C, N and S at Shinjuku, and both of observation floors of the firstbuilding of Tokyo metropolitan city hall, between 17 o’clock and 18
o’clock on October 19, 2011, seven months after the 3.11 earthquake.
The result of the microtremor measurements are compared with that
before the earthquake found out from the characteristics data sheet.

Measured period of vibration of high-rise buildings recorded…

263

Predominant Period estimated by the microtremor
Measurement after the 311Quake in sec.

7
6
5
4
3
2
1
0
0

1

2

3

4

5

6

7

Predominant Period estimated by the microtremor
Measurement before the 311Quake in sec.

Figure 1. Comparison of the Predominant Period Before and Afterthe 3.11 Earthquake
Figure 1 show that the predominant period before the earthquake is rather longer than that after the earthquake but that is almost same level,
so it seems that the predominant frequency has not changed remarkably before and after the earthquake.
(2) Comparison between the predominant period excited by the earthquake motion and the measured predominant period before and after
the earthquake
Figure 2 compares the predominant period of microtremor before
the earthquake and that excited by the earthquake motion of the 3.11
earthquake. This figure shows that predominant period for all buildings without LT building at Yokohama is lengthened at the time of the
3.11 earthquake. It may cause a quantity of reduction of rigidity. Predominant period of the LT building at Yokohama is 5.22 seconds fromthe microtremor before the 3.11 earthquake and around 4.6 seconds
for the wind response with HMD, hybrid mass dumper. The

Yutaka Nakamura

Predominant Period estimated by the microtremor
Measurement before the 311Quake in sec.

264

7
6
5
4
3
2
1
0
0

1

2

3

4

5

6

7

Predominant Period excited by the 311 Quake in sec.

Figure 2. Comparison of the Predominant Period Excited by the
3.11 Earthquake and Before the Event
predominant period excited by the earthquake motion of the 3.11
earthquake is interpreted 4.54 seconds from the video file and it corresponds to that of the wind response, so it is concerned that HMD
worked at the time of the 3.11 earthquake.
Although the change of the predominant period of almost all the otherbuildings was less than 10%, that of both the second building of Tokyo metropolitan city hall and K building at Shinjuku was close to
20 %.
Figure 3 show the comparison between the predominant periods
measured after the 3.11 earthquake and that excited by the 3.11 earthquake. According to this figure, the periods after the earthquake seemto be short. There is a possibility that the decreased rigidity is recovered after the earthquake.
(3) Relationship between the predominant period and the height or thenumber of stories of building
Figure 4 shows the relationship between the height of the building
H (m) and the predominant period T (second) before the earthquake
derived from the characteristics data sheet.

Predominant Period estimated by the microtremor
Measurement after the 311Quake in sec.

Measured period of vibration of high-rise buildings recorded…

265

7
6
5
4
3
2
1
0
0

1

2

3

4

5

6

7

Predominant Period excited by the 311 Quake in sec

Figure 3. Comparison of the Predominant Period Excited by
the 3.11 Earthquake and that After the Event

6

0.

03

*

H

5

=

4

T

Predominant Period estimated by the microtremor
Measurement before the 311Quake T in sec.

3.11地震前の1次固有周期と建物高さの関係
7

3
2

T

1

=

0 .0

2*

H

T

.0
=0

15

*H

0
0

50

100

150

200

250

300

Height of Building H in m

Figure 4. Relationship between the Predominant Period Before
the 3.11 Earthquake and the Height of Buildings
In general, the relation ship between T and H is given in a formula below.

Yutaka Nakamura266

T  kH

On figure 4, the coefficient k below mostly scatters between 0.015 and0.03 centering on around 0.02.

7
6

H

5

0.
03

*

4

=

3

T

Predominant Period excited by the 311 Quake T in
sec.

Figure 5 shows the relationship between the height of the building H(m) and the predominant period T (second) excited by the strong motion of the 3.11 earthquake. The coefficient k basically scatters between 0.015 and 0.03 as same as the relationship between the heightof the building H (m) and the predominant period T (second) before
the earthquake, and mostly between 0.02 and 0.03. However some ofbuildings deviated from the relationship, indicating as a red marker.
The buildings with a red marker seem to be caused large deformation
more than 1/180 of averaged story drift calculated from the approximated number of interpreted maximum amplitude and the height ofthe building. The accuracy of the interpretation from the video file is
low and it seems that the error of interpretation for lower buildings islarge. Because it is clear from the video that the buildings vibrated
relative larger than neighbor buildings, it must be noticed that the

2

T

=

0

*
.02

H

T

.0
=0

15

*H

1
0
0

50

100

150

200

250

300

Height of Building H in m

Figure 5. Relationship between the Predominant Period Excited by
the 3.11 Earthquake and Height of Buildings

Measured period of vibration of high-rise buildings recorded…

267

other low buildings without a red marker have a possibility to cause
large deformation.
Figure 6 shows the relationship between the number of stories of thebuilding N and the predominant period T (second) excited by thestrong motion of the 3.11 earthquake. Most building shows longer period than that derived from an equation T=0.06N, and many of themshows longer period than that derived from an equation T=0.1N. It is
impressive that the possible deformed buildings are plotted over the
relationship T  0.1N .
Figure 7 shows the relationship between the height H and the numberof stories N of target buildings. Because there is no information of theheight for most of the target buildings lower than 20 stories, the heightis estimated by the relation below indicating in Figure 7.
H  4.0  N

Predominant Period excited by the 311 Quake T insec.

3.2. Amplitude of the earthquake motion interpreted from the movie
files
Figure 8 shows the relationship between the approximate value ofthe amplitude from the video files and the height of the buildings.
7
6

T

=

0
0.1

*

N

5
4

T=

3

6*
0.0

N

2
1
0
0

10

20

30

40

50

60

70

80

Number of Stories of Building N

Figure 6. Relationship the Predominant Period Excited by the
3.11 Earthquake and the Number of Stories of Buildings

Yutaka Nakamura

268
figure 7検討対象建物群の高さと階数の関係
300

Height of Building H in m

250
200
150

Ｔ

100

＝

4.0

*

Ｎ

50
These are estimated by using H = 4N
0
0

10

20

30

40

50

60

70

80

Number of Stories of Building N

Maximum Amplitude of Building excited by the 311
Quake in cm

Figure 7. Relationship between the Height and the Number of
Stories of the Buildings
250

200

150

100

50

0
0

50

100

150

200

250

300

Height of Building H in m

Figure 8. Relationship between the Amplitude Excited by the 3.11
Earthquake and the Height of Buildings
This figure is just for a reference because of possible large error.
Red marks indicate estimated buildings with shear deformation morethan 1/180. A low building at left end of this figure is given quite different result by a variation of 10cm. It is necessary to notice that theMaximum Amplitude of Building excited by the 311
Quake in cm

Measured period of vibration of high-rise buildings recorded…

269

250

200

150

100

50

0
0

1

2

3

4

5

6

7

Predominant Period excited by the 311 Quake in sec

Figure 9. Relationship between the Predominant Period and the its
Amplitude of Buildings Excited by the 3.11 Earthquake

Displacement Response Spectrum
Displacement Response in cm with
1% Damping

100

I
M
N
Y
U
J
S

90
80
70
60
50
40
30
20

Using 200-300 seconds length of strong motion
at the time of the 3.11 Earthquake

10
0
0

1

2

3

4

5

6

7

Un-Damped Period in seconds

Figure 10. Displacement Response Spectrum calculated from
Recorded Strong Motion of the 3.11 Earthquake at the Various Sites
near the Buildings in this Paper
low building at left end clearly behaves as biased vibration in the video file although the building is not marked red.

270

Yutaka Nakamura

Figure 9 shows the approximate value of the amplitude corresponding
to the predominant period excited. This figure gives that the longer
predominant period, the larger amplitude. Also this figure can bethought to correspond to response spectra. So the displacement response spectra is calculated from strong motion records of sites nearby
and compared in the next section.

4. Displacement response spectra using strong motion records
It seems that the displacement interpreted from video files may
reach 1/120 at the time of the 3.11 earthquake. Displacement response
spectra corresponding to the period concerned are calculated from thestrong motion records of the 3.11 earthquake to verify the validity of
the interpreted deformation, because the situation with such large deformation seems to be serious. The buildings concerned locate at
Shinjuku, Ikebukuro, Roppongi, Akasaka, Kanda, Shinagawa, Yokohama and so on. The displacement response spectra with 1% dumping
are calculated for the strong motion records of sites S, I, M, J, U, N
and Y, close to the buildings concerned. Un-damped period set to 0.5,
0.7, 1.0, 2.0, 2.5, 3.0 4.0, 5.0 and 6.0 seconds. Figure 10 shows thedisplacement response spectra. The displacement response spectra increase towards long period as 30-60cm at 4 second of period, 40-80cm
at 5 second of period and 50-70cm at 6 second of period. It agrees tothe interpreted amplitude in order. On the other hand, although thedisplacement response spectra almost agree to overall trend for all thesites, the site characteristics is also appeared, so it suggests the necessity of consideration of the site characteristics for the long periodcharacteristics.

5. Conclusion
This paper examines to grasp the dynamic characteristics of highrise buildings shaken by the earthquake motion of the 3.11 earthquakewith analyzing video files opened public. As a result, the period andthe amplitude are accurately grasped and it is possible to understandMeasured period of vibration of high-rise buildings recorded…

271

clearly the relationship between the predominant period and the heightor the number of stories. Although it is possible to say generally thatthe relative longer the predominant period of buildings, the larger the
deformation to lead damage, it is confirmed to be difficult to understand the dangerousness of buildings only from the predominant period. Also there is no significant difference of the characteristics against
earthquake motion derived from microtremor and earthquake motionof the 3.11 earthquake.
Acknowledgement
The author expresses my heartfelt thanks with respect to people who
took shaking buildings on video with quick action against abnormal
seismic motion of the 3.11eaerthquake and open to public via website
like YouTube.
References[1] Small Working Committee for Damping Data of Buildings,
Load Management Committee (2000), “Database of Measured Damping for Buildings in Japan edited at October 2000”, Architectural Institute of Japan.