JOINT CONFERENCE PROCEEDINGS
9th International Conference on Urban Earthquake Engineering/ 4th Asia Conference on Earthquake Engineering
March 6-8, 2012, Tokyo Institute of Technology, Tokyo, Japan

MEASURED PERIOD OF VIBRATION OF HIGH-RISE BUILDINGSRECORDED ON VIDEO MOVIES OPENED TO THE PUBLIC
EXCITED BY THE 2011 OFF THE PACIFIC COAST OF TOHOKU EARTHQUAKE
Yutaka Nakamura1,2)
1) President, System and Data Research, Tokyo, Japan2) Visiting Professor, Department of Built Environment, Tokyo Institute of Technology, Japan
yutaka@sdr.co.jp

Abstract: The long-period earthquake motion of the 2011 off the Pacific coast of Tohoku Earthquake excited high-risebuildings with long-period natural vibration. These situations of visible shaking can be seen on internet as YouTube asvideo movies recorded by the general public there. Author interpreted period and amplitude from these movies opened tothe public and compared them to the number of the floors, the height, and the result of the microtremor measurement
before and after 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 issaid 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 microtremorand earthquake motion.

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 beseen on web sites as YouTube. The author interprets theperiod and the amplitude of shaking buildings from thesevideo files and considers relationships between period andheight or the change of the natural period caused by theearthquake 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 theperiod and amplitude with stable observing point. The period
and the amplitude are carefully interpreted based on this data
set. In addition, although these video files seemed to be
started recording after reaching a large motion, a clockappeared in movies shows a time around 14:50, so the mainpart of the long period earthquake motion seems to berecorded.

The specifications and the characteristics ofskyscrapers are based on characteristics data sheet of thedatabase of measured dumping (edited at 2000.10) or otherdetail information on buildings on web sites. Because thischaracteristics data sheet conceals the name of the building,that is identified from number of stories, eaves height orcompleted year. The buildings in video movies are also
grasped the characteristics corresponding to datasheet fromthe 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 forreference can be assumed a fixed point, it is rather easy tointerpret the period and the amplitude. Here, the objects forreference was chose a structure far away or neighborbuilding. In case of comparing the neighbor building,relative displacement is combined from characteristics of theboth buildings. Similar period or amplitude for each othercauses beat. The frequency of the beat is the difference of thefrequency of each building and it is possible to fix thepredominant frequency of each building noticing that theapparent frequency is the averaged frequency of bothbuilding. It is difficult to understand clearly the beatfrequency because it is rather long for building with longperiod. So the natural frequency easy to interpret first, andthen the natural frequency of another building is estimatedusing the apparent frequency interpreted from relative

variability for both building and the fixed frequency.
Amplitude is interpreted roughly in order of 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. Insuch a case, potential phenomenon for period determination
were found out with repeatedly careful confirmation of thevideo file. The phenomenon is, for example, sequential
vibrating sound of a building, reflection on a glass wall of abuilding, behavior of neighboring building reflected on awall, vibration of a movable shelf, opening and closing adoor and so on. Although it was difficult to clarify theamplitude with these clues, it seemed to be possible toestimate 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 and partly two directions, so thetotal number of data is more then 50. The result of theinterpretation is listed in Table 1, and examined in more
depth below.
3.1 Predominant Period(1) Comparison of the Predominant Period Before andAfter the 3.11 Earthquake

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.
Structurecm%
in sec. Wind Noise Quake%in sec.
times
in sec.
timestion
Ab.
B. Pent. in m in sec. Direction
1
Shinjuku C
Oct-795443216
6.00 Short: NS50
0.23
5.65
6.00
6.00
5.85
2.1
S
54
43216
Long side
5.35
4.97
4.97
4.55
4.82
Shinjuku N
Jun-7850
53203
5.20 Short side
100
0.49
5.42
4.80
0.39
4.94
11.2S50
53203
Long side
4.27
3.43
0.37
3.22
6.2
3
Shinjuku AT
Jan-954442189
4.50 Long: NS
90
0.48
S, partially SRC
4Shinjuku SJ
Mar-764362193
4.80 Short side
150
0.78
5
Shinjuku M
Sep-74553210
4.25 Short side
S(2F-55F), SRC(under 1F)55
3210
3.60 Long side
6
Shinjuku K
Jun-7147
32170
4.50 Short: EW
80
0.47
3.85
4.30
0.50
S(3F-47F), SRC(1F, 2F),47
32170
3.85 Long: NS
40
0.24
4.30
3.10
0.80
RC(BF)
7
Asakusa C
1040
1.20 Short side30
0.75
8Roppongi AM
Mar-86374153
3.75 Short side60
0.39
S, partially SRC and RC
9Roppongi IG
Jul-0232
2116
3.20 EW
30
0.26
SRC
10
Shinjuku JE
Sep-972841149
3.40 Long side
30
0.20
11
Shinjuku ST
Feb-983641147
3.60 Long side
30
0.20
S
12Shinjuku MT
Sep-953432161
4.50 Short side80
0.50
S, SRC
13 TokyoCityHall1SMar-91
48
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
3242
4.74 Long: NS
80
0.33
5.20
4.29
0.75
4.05
2.6
TokyoCityHall1N
48
3242
Short: EW
5.56
5.11
10.2
48
3242
Long: NS
5.20
4.04
5.9
14
Kanda ST1980
14256
1.50 Long side20
0.36
S, SRC(under 1F)
15
Kanda N
Mar-848432
1.20 Short side
100.31
SRC
16
Akasaka SP
Mar-1116264
1.91 along Road
20
0.31
S
17
Roppongi MT
Mar-03
54
62238
6.00
200
0.84
S, SRC and RC
18
TokyoCityHall2Mar-91
343162
3.61 Short side
60
0.37
3.98
2.92
0.78
343162
Long side
3.91
2.73
0.73
19Ikebukuro S
Apr-7860
33227
Short side
6.25 6.25
1.56
S(Upper and Middle),
60
33227
4.70 Long side100
0.44
5.88 4.55
SRC(Lower)
20 Marunouchi TN
Sep-0319
32100
5.00 Short side60
0.60
S, patiallySRC
21 Marunouchi TM
Nov-083742178
5.00 Short side
S(CFT), partially SRC
22
Marunouchi ST
Apr-073541165
3.10 Long side
S(CFT column)
23Marunouchi A
Jul-71
29
42110
3.00
S, partially SRC24
Shinjuku W
Jun-9113252
1.50 Long side
200.38SRC
25
Shinjuku CT
Oct-0850
32204
3.70 NS60
0.29
S, partially SRC
26
Shinjuku LT
Jun-893151122
2.70 Short: NS60
0.49
2.99
2.60
2.80
0.90
SRC
31
51122
2.70 Long side
3.00
2.38
2.55
27
Shibuya CT
Mar-01416184
4.68
S, partially SRC and RC
28
Harumi TX
Mar-01
44
183
4.40
20
0.1129Harumi TY
Mar-01
39
175
4.20
30
0.17
Harumi TZ
Mar-01
33
155
4.70
30
0.1930
Yokohama LT199370
33282
4.54 NE
600.21
6.02 4.60 5.22
0.70
31 Yokohama QA
Jun-973652172
4.50 Short side40
0.23SRC
3652172
4.70 Long side
32 Yokohama MMMar-03
28
32147
4.00
S, under ground SRC
33 Shinagawa GTMar-03
323148
3.96 Long side
34
Shinagawa TMar-03
30
3148
3.33
35
Shinagawa ET
Mar-0332
3152
4.00
S and SRC
36Marunouchi M
Aug-023741794.30 Short side
S, under ground SRC
3741794.50 Long: EW
150
0.84
37 Marunouchi NM
Apr-073841177
4.50 Long: EW80
0.45
S, under ground SRC38Shinjuku S
Mar-745242200NE
5.07
4.440.74
4.79
17.8 S, partially SRC and RC
52
42200
NW
5.07
4.44
0.80
4.33
15.2
39
Roppongi T
1994
936
1.17 Short side
200.5640
Roppongi U
Nov-737128
1.56 Short side
200.71
RC41
Roppongi N
1948
7128
0.54 Short side
SRC
42
Roppongi G
Sep-95
9336
0.70
SRC
43
Ohfuna K
Jul-77520
0.98 Short side
150.7544 Daikanyama D
Jul-051248
1.50
400.8345
Shinbashi Ｎ
Apr-033242193
4.10 Short side
46
Shiodome R
Apr-033842172
Long side
47Shinbashi D
Oct-0248
51210
6.10 Short side
120
0.57
5.40
48
51210
Long side
4.60
48 Kasumigaseki K
Apr-683632147
4.80 Short side
70
0.48
5.14
3.74
1.02
4.12
14.7
36
32147
Long side
5.04
3.38
1.31
3.53
5.3
49 Kasumigaseki CGW Sep-07
38
31174
4.14 EW
50 Shinagawa CST
Mar-032941148
3.80

No.

Building Name

765432
10

60

12

34567

Predominant Period excited by the 311 Quake in sec.

5Figure 2 Comparison of the Predominant Period
Excited by the 3.11 Earthquake and Before the Event4321001234567

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

Figure 1 Comparison of the Predominant Period
Before and After the 3.11 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 theearthquake motion of the 3.11 earthquake. This figure showsthat predominant period for all buildings without LT
building at Yokohama is lengthened at the time of the 3.11earthquake. It may cause a quantity of reduction of rigidity.
Predominant period of the LT building at Yokohama is 5.22
seconds from the microtremor before the 3.11 earthquake
and around 4.6 seconds for the wind response with HMD,
hybrid mass dumper. The predominant period excited by theearthquake motion of the 3.11 earthquake is interpreted 4.54
seconds from the video file and it corresponds to that of thewind response, so it is concerned that HMD worked at thetime of the 3.11 earthquake.
Although the change of the predominant period ofalmost all the other buildings was less than 10%, that of boththe second building of Tokyo metropolitan city hall and K
building at Shinjuku was close to 20 %.
Figure 3 shows the comparison between thepredominant periods measured after the 3.11 earthquake andthat excited by the 3.11 earthquake. According to this figure,Predominant Period estimated by the microtremor
Measurement after the 311Quake in sec.

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

7

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

Microtremor measurements were conducted forhigh-rise buildings; C, N and S at Shinjuku, and both ofobservation floors of the first building 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 datasheet. Figure 1 shows that the predominant period before theearthquake is rather longer than that after the earthquake butthat is almost same level, so it seems that the predominantfrequency has not changed remarkably before and after theearthquake.

765432
100

12345

6

7Predominant 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 Eventthe periods after the earthquake seem to be short. There is apossibility that the decreased rigidity is recovered after theearthquake.
(3) Relationship between the Predominant Period andthe Height or the Number of Stories of Building
Figure 4 shows the relationship between the height ofthe building H (m) and the predominant period T (second)
before the earthquake derived from the characteristics data
sheet. The coefficient k below mostly scatters between 0.015
and 0.03 centering on around 0.02.

T =k×H
Figure 5 shows the relationship between the height ofthe 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

Predominant Period excited by the 311 Quake T insec.

60.

03

*

H

5=4T
32T

1=0 .02*H

T.0=015

*H

0050

100

150

200

250

Figure 4 Relationship between the Predominant Period
Before the 3.11 Earthquake and the Height of Buildings

T=

00.1

*

N

546*
0.0=
T3N

2
10102030

4050607080

Figure 6 Relationship the Predominant Period Excited bythe 3.11 Earthquake and the Number of Stories of Buildingsthat the possible deformed buildings are plotted between therelationship T=0.06N and T=0.1N.
Figure 7 shows the relationship between the height H
and the number of stories N of target buildings. Because
there is no information of the height for most of the target
buildings lower than 20 stories, the height is estimated by
the relation below indicating in Figure 7.

76

H5

*030.
=3

T

Predominant Period excited by the 311 Quake T insec.

6

Number of Stories of Building N

Height of Building H in m4703002T=0 .02*HT=

10 .05*

H = 4 .0 × N

H300

12500050

100

150200250300

Height of Building H in mFigure 5 Relationship between the Predominant Period
Excited by the 3.11 Earthquake and Height of Buildings
same as the relationship between the height of the building
H (m) and the predominant period T (second) before theearthquake, and mostly between 0.02 and 0.03. However
some of buildings deviated from the relationship, indicating
as a red marker. The buildings with a red marker seem to becaused large deformation more than 1/180 of averaged story
drift calculated from the approximated number of interpreted
maximum amplitude and the height of the building. The
accuracy of the interpretation from the video file is low andit 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 other low buildings without a red marker
have a possibility to cause large deformation.
Figure 6 shows the relationship between the numberof stories of the building N and the predominant period T(second) excited by the strong motion of the 3.11 earthquake.
Most building shows longer period than that derived from anequation T=0.06N, and many of them shows longer period
than that derived from an equation T=0.1N. It is impressive

Height of Building H in mPredominant Period estimated by the microtremor
Measurement before the 311Quake T in sec.

7200150

Ｔ

100

＝4.0

*Ｎ50
These are estimated by using H = 4N00102030

40506070

80

Number of Stories of Building NFigure 7 Relationship between the Height and the
Number of Stories of the Buildings
3.2 Amplitude of the Earthquake Motion Interpreted
from the Movie Files
Figure 8 shows the relationship between theapproximate value of the amplitude from the video files andthe height of the buildings. This figure is just for a reference
because of possible large error. Red marks indicate estimatedbuildings with shear deformation more than 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 thatthe low building at left end clearly behaves as biased

Displacement Response in cm with
1% Damping

Maximum Amplitude of Building excited by the 311
Quake in cm200

150

10050pp

IMNYUJS

90
80
70
60
50
40
30
20Using 200-300 seconds length of strong motion
at the time of the 3.11 Earthquake

10000

1234567Un-Damped Period in seconds

050

100

150

200

250300Height of Building H in mFigure 8 Relationship between the Amplitude Excitedby the 3.11 Earthquake and the Height of Buildings
vibration in the video file although the building is notmarked red.
Figure 9 shows the approximate value of theamplitude corresponding to the predominant period excited.
This figure gives that the longer predominant period, thelarger amplitude. Also this figure can be thought tocorrespond to response spectra. So the displacement
response spectra is calculated from strong motion records ofsites nearby and compared in the next section.
Maximum Amplitude of Building excited by the 311
Quake in cm

p100

250

250200Figure 10 Displacement Response Spectrum calculated
from Recorded Strong Motion of the 3.11 Earthquake at
the Various Sites near the Buildings in this Paper
response spectra with 1% dumping are calculated for thestrong 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
the displacement 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 and50-70cm at 6 second of period. It agrees to the interpreted
amplitude in order. On the other hand, although thedisplacement response spectra almost agree to overall trend
for all the sites, the site characteristics is also appeared, so itsuggests the necessity of consideration of the sitecharacteristics for the long period characteristics.
5. CONCLUSIONS

150

100

50001234567Predominant Period excited by the 311 Quake in sec

Figure 9 Relationship between the Predominant
Period and the its Amplitude of Buildings Excited bythe 3.11 Earthquake
4. DISPLACEMENT RESPONSE SPECTRAUSING 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 the strong motion records ofthe 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

This paper examines to grasp the dynamiccharacteristics of high rise buildings shaken by theearthquake motion of the 3.11 earthquake with analyzing
video files opened public. As a result, the period and theamplitude are accurately grasped and it is possible tounderstand clearly the relationship between the predominantperiod and the height or the number of stories. Although it ispossible to say generally that the relative longer thepredominant period of buildings, the larger the deformation
to lead damage, it is confirmed to be difficult to understandthe dangerousness of buildings only from the predominantperiod. Also there is no significant difference of thecharacteristics against earthquake motion derived frommicrotremor and earthquake motion of the 3.11 earthquake.
Acknowledgements:
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:
Small Working Committee for Damping Data of Buildings, LoadManagement Committee (2000), “Database of Measured
Damping for Buildings in Japan edited at October 2000”,
Architectural Institute of Japan,.