Th E ti ti f V l f thInter−noise 2007 Istanbul

The Estimation of V value of the vibration criteria curve of Void−slabsvibration criteria curve of Void slabs by the shock of the Impact ballMitsuru YabushitaYAB Corporation

Shinichiro Sato Void slab Association

Hideki HoriuchiNihon kaiser

Large span beamless oid slabs in the ho sing comple ha e come to be

p

INTRODUCTIONLarge−span beamless void−slabs in the housing complex have come to be used recently because of less restriction for floor planning. However, the natural frequency of a large−span beamless void−slab has the possibility to q y g p p yfall below 20Hz, and if it is not designed appropriately, there is a possibility of causing the vibration problem. In order to examine a new design method the vibration experiments was done with the 58 slabsmethod, the vibration experiments was done with the 58 slabs.

Study of the way for evaluation of habitability to void slab vibration byPURPOSE OF STUDYStudy of the way for evaluation of habitability to void slab vibration by dropping the impact ball to the slab.

D i h t i ti f i t b ll

Fi 2 R l i b h

Dynamic characteristic of impact ballResult of impact power measurement of different height of ball drops.

2000 12all

Dynamic characteristic of impact ball Figure2. Relation between the root of the height of ball drop and peak value of impact power.30cm

40cm50cm60cm70cm80cm90cm

100cm

1000

1500

pow

er[N

]

10cm20cm30cm40cm50cm60cm

y = 0.0056xR2 = 0.9994

4

6

8

10

t of t

he h

eigh

t of b

drop

（cm

1/2）

The impact power

p

10cm

20cm

0

500Impa

ct

70cm80cm90cm100cm

0

2

4

0 500 1000 1500 2000Peak value of impact power[N]

Squr

e ro

o d

p pcharacteristic of ball drop is stipulated by

Figure1.Relation between the height of ball drop and impact power time response

0.095 0.1 0.105 0.11 0.115 0.12 0.125Time[sec]

30

40

vel[d

B]

st pu ated byJIS(Japanese Industrial standard) A1418−2 at drop

power time response.

10

20

ower

exp

osur

e le

v

10cm20cm30cm20 0

30.0

40.0

50.0

vel(d

B)

10cm20cm30cm A1418 2 at drop

height of only1.0m.

-10

0

Impa

ct p

o 30cm40cm50cm60cm70cm80cm90cm100cm

-20.0

-10.0

0.0

10.0

20.0

Impa

ct p

ower

le 40cm50cm60cm70cm80cm90cm

Figure4.Relation between the height of ball drop and impact

Figure3. Relation between the height of ball drop and Frequency

31.5 63 125 250 500Octave band center frequency[Hz]

1.0m

-30.01 10 100 1000

Frequency(Hz)

100cm

power exposure levelheight of ball drop and Frequency characteristic of impact power.

The coefficient of restitution of ball is showed by the regression line in Figure6.

0.9

0.95

1

rest

itutio

n

y = -0.0358x + 0.8897R2 = 0.6701

0 7

0.75

0.8

0.85

Coe

ffici

ent o

f r

Figure6. Relation between the h i ht f b ll d d th

Figure5. Experiment of the coefficient of restitution of ball

0.70 0.2 0.4 0.6 0.8 1 1.2

Height of drop（ｍ）

The impact force of the ball drop is confirmed to

height of ball drop and the coefficient of restitution

of restitution of ball

The impact force of the ball drop is confirmed to be linear with ball drop height within 1.0m.

The floor vibration experiment was done with the 58 slabs of some

OUTLINE OF THE EXPERIMENT SITE

The floor vibration experiment was done with the 58 slabs of some general housing complexes. Figure 7 shows one example of the housing complex.

Monitor by FFTAnalyze computer system

Servo typeAccelerationPickup

Vibrationmeter Realtime 1/3frequency

Analyzer

DAT

Fi 7 TO t t h l b lFigure8. Measuring Instrument diagram

Floor vibration experiment method

Figure7. TO apartment houses slab plan

The experiment measured the vibration response at the center of the slab for one house unit of the

oo b at o e pe e t et od

at the center of the slab for one house unit of the building under construction.Impact source are one man person walking, two person walking, heel impact, ball drop with height 1.0m, 0.5m, 0.2m, 0.1m.The analysis items are peak of the responseThe analysis items are peak of the response acceleration, peak of the response frequency, the response acceleration of 1/3 octave band

Figure9.One person walking

Figure10.Ball drop from several

frequency at dynamic response 10msec of the real time analyzer.

heights

Result of floor vibration experimentResponse acceleration of the slab is almost proportionate to the heightResponse acceleration of the slab is almost proportionate to the height of ball drop and is shown by the regression curve in Fig.13 and 14.

Relation between the ball drop height and

Average

10

15

20

25

ban

d r

esp

onse

on（cm

/s

2）

Average

25.0

30.0

35.0

40.0

45.0

50.0

elar

atio

n（cm

/s

2）

ball drop height and response acceleration

0

5

10

0 0.2 0.4 0.6 0.8 1 1.2

Height of ball drop（ｍ）

1/3oct

Octa

ve

accela

ratio

0.0

5.0

10.0

15.0

20.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Height of ball drop(m)

Res

ponse

acc

Figure11. On peak Figure12. On 1/3 octave band at natural frequency band

R i f16352

）

Regression curve of response acceleration of slabs correspond to different height of ball

y = 13.614x0.4986

24

6

8

10

12

14

ct o

ctav

e ban

d r

esponse

ccel

arat

ion（ｃｍ

/s

2）

y = 29.991x0.5108

R2 = 0.999810

15

20

25

30

se a

ccel

erat

ion（cm

/s

different height of ball drop

Figure14. On 1/3 octave band

R2 = 0.9997

0

2

4

0 0.2 0.4 0.6 0.8 1 1.2

Height of ball drop（m)

1/3oc ac

0

5

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Height（m）

Resp

on

Figure13. On peak

Table1. The parameter of the house unit , natural frequency of slabs response acceleration and so on

ｍ ｍ ｍ ｍ ｍ2 ｍｍ Hz cm/s2

cm/s2

cm/s2

MU 501 6.70 6.30 11.17 10.72 74.84 280 23.0 30.30 9.33 3.21MU 502 6.20 6.00 11.17 10.72 69.25 280 30.7 26.66 8.15 3.49MU 503 6.00 5.80 11.17 10.72 67.02 280 25.8 27.69 8.00 3.02MU 504 6.50 6.30 11.17 10.72 72.61 280 35.9 35.34 11.41 2.73

Inside X Inside YCODE RN X Y Ball 1.0ｍX×Y Freq.Slab Thickness Ball 0.1m One person walking

g

slabs, response acceleration and so on MU 506 5.60 5.40 11.17 10.72 62.55 280 34.4 25.53 7.76 2.01MU 507 6.20 6.00 11.17 10.72 69.25 280 24.2 33.26 9.19 3.57MU 508 6.20 6.00 11.17 10.72 69.25 280 29.2 34.68 9.83 3.13MU 509 7.00 6.60 11.17 10.72 78.19 280 21.3 29.60 9.29 4.33TD 801 5.75 5.37 9.15 8.70 52.61 280 34.7 29.38 9.81 3.63TD 802 5.75 5.57 9.15 8.70 52.61 280 31.4 29.06 9.21 2.74TD 805 5.90 5.69 9.15 8.70 53.99 280 51.8 36.62 9.75 1.85TD 807 5.75 5.57 9.15 8.70 52.61 280 30.3 32.48 10.95 3.08TD 808 5.75 5.37 9.15 8.70 52.61 280 34.6 33.16 11.62 3.55TO 701 6.50 6.07 11.22 10.77 72.93 280 24.9 30.66 9.92 3.48TO 703 6.10 5.90 11.22 10.77 68.44 280 24.0 27.09 8.39 2.54TO 704 6.20 6.00 11.22 10.77 69.56 280 24.0 28.53 9.77 2.48TO 706 6.50 6.30 11.22 10.77 72.93 280 21.9 34.25 8.64 3.69AT 1301 6 50 5 90 14 15 13 70 91 98 280 33 5 29 24 8 90 2 97

Frequency characteristic of 1/3octave band response acceleration has a peak at the band

AT 1301 6.50 5.90 14.15 13.70 91.98 280 33.5 29.24 8.90 2.97AT 1302 6.50 5.90 14.15 13.70 91.98 280 36.8 31.96 9.52 2.81AT 1303 6.50 5.90 14.15 13.70 91.98 280 33.3 33.74 9.69 2.72AT 1305 6.50 5.90 14.15 13.70 91.98 280 34.2 29.80 10.24 2.69KF 903 4.80 4.36 11.22 10.77 53.86 280 41.3 41.56 10.70 2.68KF 905 7.20 6.81 11.22 10.77 80.78 280 24.5 26.66 9.44 3.10KF 906 5.80 5.61 11.22 10.77 65.08 280 37.4 36.86 11.33 4.18KF 908 5.90 5.72 11.22 10.77 66.20 280 30.7 30.45 9.70 2.48Y1 901 6.50 6.00 10.87 10.42 70.66 280 27.3 29.46 9.05 4.43Y1 902 5.75 5.53 10.87 10.42 62.50 280 39.1 41.08 12.88 3.74Y1 903 5.30 5.11 10.87 10.42 57.61 280 39.6 38.70 11.52 3.82Y1 904 5.30 5.12 10.87 10.42 57.61 280 31.9 32.16 8.98 3.41Y1 905 6.05 5.87 10.87 10.42 65.76 280 40.0 43.84 13.16 4.23Y1 906 5.30 5.12 10.87 10.42 57.61 280 30.5 31.04 8.65 3.04

p pof natural frequency of the slab and at the frequency band, peak is seemed to be proportionate to the impact power of source.

Y2 201 5.75 5.35 10.87 10.42 62.50 280 30.6 33.22 8.92 2.89Y2 202 5.30 5.10 10.87 10.42 57.61 280 28.2 25.76 7.86 2.62Y2 203 5.30 5.10 10.87 10.42 57.61 280 28.1 29.09 8.90 2.49Y2 204 5.30 5.10 10.87 10.42 57.61 280 34.3 30.51 8.59 3.13Y2 206 5.75 5.55 10.87 10.42 62.50 280 29.0 28.60 9.11 3.17Y2 207 5.60 5.40 10.87 10.42 60.87 280 25.6 26.15 8.38 2.41Y2 208 6.20 5.80 10.87 10.42 67.39 280 25.6 30.72 9.07 2.80MD 1103 4.70 4.52 11.22 10.77 52.73 280 36.9 28.89 8.77 2.13MD 1104 6.00 5.82 11.22 10.77 67.32 280 25.2 28.19 9.26 3.41MD 1105 5.15 4.97 11.22 10.77 57.78 280 38.6 39.24 10.77 2.93MA7 401 8.00 7.45 9.42 8.97 75.36 330 23.8 20.05 6.76 1.66MA7 403 7.10 6.90 9.42 8.97 66.88 280 23.2 26.50 7.94 1.93MA7 406 7.10 6.65 9.42 8.97 66.88 280 24.9 28.07 9.02 2.74MA8 501 8.00 7.45 9.42 8.97 75.36 330 21.7 18.77 6.42 1.91

Relation between the difference of impact source and 1/3octave band

MA8 501 8.00 7.45 9.42 8.97 75.36 330 21.7 18.77 6.42 1.91MA8 502 7.10 6.80 9.42 8.97 66.88 280 24.9 25.92 8.35 2.75MA8 504 7.10 6.80 9.42 8.97 66.88 280 24.0 26.50 8.47 2.41MA8 505 9.40 9.00 9.42 8.97 88.55 330 18.5 15.47 4.71 1.97MA8 506 7.10 6.55 9.42 8.97 66.88 280 24.9 26.75 9.10 3.29MB3 301 8.00 7.50 9.42 8.97 75.36 320 20.3 24.56 6.83 3.55MB3 302 6.65 6.35 9.42 8.97 62.64 280 24.9 31.01 10.35 3.76MB3 305 6.65 6.45 9.42 8.97 62.64 280 23.0 29.62 9.41 3.01MB5 301 8.00 7.60 9.42 8.97 75.36 320 21.7 20.97 6.37 2.33MB5 302 7.10 6.70 9.42 8.97 66.88 280 24.9 27.30 9.56 3.55MB5 304 7.10 6.90 9.42 8.97 66.88 280 23.0 28.44 10.10 3.42MB5 305 7.10 6.70 9.42 8.97 66.88 280 25.9 26.62 9.60 3.24MB5 306 8.00 7.60 9.42 8.97 75.36 320 21.7 23.12 6.59 3.26MD1 206 7.15 6.75 9.42 8.97 67.35 300 23.8 28.46 9.30 3.03

6 38 6 07 10 63 10 18 67 48 285 29 0 29 82 9 19 3 01Aimpact source and 1/3octave bandresponse acceleration spectrum Response 1/3octave band

acceleration spectrum among all slabs

6.38 6.07 10.63 10.18 67.48 285 29.0 29.82 9.19 3.01

0.91 0.85 1.27 1.27 10.23 14.05 6.6 5.30 1.51 0.64

AverageStandarddeviation

100.000

2 )

100.000

2 ) slabs

1.000

10.000

nse

acce

lara

tion(

0-ｐ)(c

m/s

2

1.000

10.000

nse

acce

lara

tion(

0-ｐ)(c

m/s

2

10.000

100.000

lera

tion

10.000

100.000

erat

ion

0.010

0.100

1/3

octa

ve b

and

resp

on

Ball 1.0m drop

Ball0.5m drop

Ball 0.2m drop

Ball0.1m drop

Heel excitation

One person walking

Two person walking

0.010

0.100

1/3

octa

ve b

and

resp

on

Ball 1.0m drop

Ball0.5m drop

Ball 0.2m drop

Ball0.1m drop

Heel excitation

One person walking

Two person walking

0.100

1.000

e ba

nd re

spon

se a

ccel

(0-ｐ

)(cm

/s2 )

0.100

1.000

ve b

and

resp

onse

acc

ele

(0-ｐ

)(cm

/s2 )

Figure15. On AT1301 slab

Figure16. On MB5301 slab

0.0011 10 100

1/3 octave band center frequency(Hz)

Two person walking

0.0011 10 100

1/3 octave band center frequency(Hz)

p g

0.001

0.010

1 10 1001/3 octave band center frequency(Hz)

1/3

octa

ve

0.001

0.010

1 10 1001/3 octave band center frequency(Hz)

1/3

octa

v

Figure17. ball drop 1.0m Figure18.one person walking

Correlation between response acceleration of ball drop 1.0m and othersp pThe correlation of the response acceleration of the ball drop 1.0m and one person walking is small (R2=0.06), because impulse power of

lki i d b bl lk i

y = 0.7089x225

30

35

n o

f B

all

s2) y = 0.7089x

225

30

35

n o

f B

all

s2)

0 4436

20

25

n o

f B

all

s2)

0 4436

20

25

n o

f B

all

s2)

y = 0.3066x

R2 = 0.7212

14

16

Bal

l 0.

1m

y = 0.3066x

R2 = 0.7212

14

16

Bal

l 0.

1m

y = 0.0995x

R2 = 0.06013 5

4.0

4.5

5.0

of O

ne

/s

2) y = 0.0995x

R2 = 0.06013 5

4.0

4.5

5.0

of O

ne

/s

2)

walking is seemed to be unstable even walker is same person.

R2 = 0.9539

0

5

10

15

20

25

Res

ponse

acc

eler

atio

n

0.5

m d

rop(c

m/s

R2 = 0.9539

0

5

10

15

20

25

Res

ponse

acc

eler

atio

n

0.5

m d

rop(c

m/s y = 0.4436x

R2 = 0.8482

0

5

10

15

Res

ponse

acc

eler

atio

n

0.2

m d

rop(c

m/s y = 0.4436x

R2 = 0.8482

0

5

10

15

Res

ponse

acc

eler

atio

n

0.2

m d

rop(c

m/s

0

2

4

6

8

10

Resp

ons

e ac

cele

ration

of

drop

(cm

/s2)

0

2

4

6

8

10

Resp

ons

e ac

cele

ration

of

drop

(cm

/s2)

R 0.0601

0 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Res

ponse

acc

eler

atio

n

per

son w

alki

ng(

cm/ R 0.0601

0 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Res

ponse

acc

eler

atio

n

per

son w

alki

ng(

cm/

Figure19. On 0.5m Figure21. On 0.1m

0

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

0

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

0

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

R 0

0 10 20 30 40 50

Response acceleration of Ball 1.0m drop(cm/s2)

R 0.0

0 10 20 30 40 50

Response acceleration of Ball1.0m drop(cm/s2)

0.0

0 10 20 30 40 50

Response acceleration of Ball1.0m drop(cm/s2)

Figure20. On 0.2m Figure22. On one person walkingCorrelation gCorrelation

Estimation of impulse of ball drop

y = 0.6604x

R2 = 0.9998

6.00

8.00

10.00

12.00

14.00

16.00

ve b

and r

esponse

arat

ion(c

m/s

2 )

y = 1.4462x

R2 = 0.9991

15

20

25

30

35

se a

ccel

erat

ion

（cm

/s2

）

Table2 . The response acceleration of the slabs by each exciting sources and reduced height of ball drop and reduced impulse of each exciting

Exciting sources One person walking

Two person walking

Heel impact

Average value of response acceleration 3.01 cm/s2 4.94 cm/s2 20.17 cm/s2

0.00

2.00

4.00

6.00

0 5 10 15 20 25Impulse of ball drop(N･sec)

1/3oct

av

acce

la

0

5

10

0 5 10 15 20 25

Impulse of ball drop（N･sec）

Res

pons

Figure 23. Relation between Figure 24. On 1/3 octave

ball drop and reduced impulse of each exciting sources.

Average value of reduced height of ball drop 0.012m 0.032m 0.508m Standard deviation from reduced height of ball drop 0.006m 0.016m 0.203m Average of reduced impulse value 2.22 N･sec 3.55 N･sec 14.02 N･sec Average value of response acceleration (1/3oct) 1.42 cm/s2 2.30cm/s2 9.08 cm/s2 Average value of reduced height of ball drop（1/3oct） 0.011m 0.031m 0.505m Standard deviation from reduced height of ball drop(1/3oct) 0.007m 0.018m 0.308m

Figure 23. Relation between impulses of different height of ball drop and response acceleration

Figure 24. On 1/3 octave band

g p( )Average of reduced impulse value(1/3oct) 2.16 N･sec 3.55 N･sec 14.02 N･sec

2gh)1(1( ×+=)+= mvmvm µµ Equation −1Equation of conservation of momentum Reference

Uchida’s paper: 2 35 N･sec2gh)1(1( 11122 ×+=)+= mvmvm µµ Equation 1

Estimation of ball drop impulse at height of h(m)

Uchida s paper: 2.35 N secAIJ Standard for structural caliculationof RC structure: 2.94 N･sec

hhghm ××××+×−=×)+= 1 8.925.2)8897.00358.01(21(1 µ Equation −2

Estimation of response acceleration of slab by exciting of design impulse Ir

1)85.01()8897.00358.01(

00

0 ×+×+−

×=×=hhA

IIAA r

r Equation −3

CONCLUSIONAs the impact power(impulse)of ball drop can be p p ( p ) preduced, response acceleration of walking and so on can be almost estimated by ball drop 1 0m bycan be almost estimated by ball drop 1.0m by equation−3, and used for evaluating the habitability to vibration by V value of AIJ Guide Lineto vibration by V value of AIJ Guide Line.