Wind-induced vibrations and building modes

TL;DR: In this paper, a simple theoretical model was used to calculate the frequencies of vibration of the buildings; the model was based on the assumption that there was no joint rotation in the building frames.

Abstract: This paper outlines the methods that have been used to determine the frequencies and modes of vibration of multistory buildings from their wind-induced vibrations. Three buildings of ten, thirty-eight and forty-seven stories were investigated. A simple theoretical model was used to calculate the frequencies of vibration of the buildings; the model was based on the assumption that there was no joint rotation in the building frames. A comparison of the theoretical and measured values of the frequencies showed that this simple model was a realistic representation of only the smaller building. It is concluded that a model that includes joint rotation would be more realistic for the taller buildings. Auto-correlation and power spectrum analysis of the vibration records were used to obtain an estimate of the damping characteristics of the buildings. The values obtained were 1 to 3 per cent of the critical amount of damping.

Summary

DESCI~IPTIOS OF TIIE I~UILDISGS

• Thc three buildings investigated have been c.onstructc~c1 ~vithiil the last five years-One of the buildings, the Sir Alcsaildcr Cam~~bcll Buildiilg is the headquarters of the Cunndi:ul Post Office Dcp:u.tilleilt 211 Ottawa; the other two buildiilgs, the Cnnacliail Imperial I3~1lli of Com~ncrcc Builcliitg ant1 CIll IIouhe, arc 1oc.atctl 011 Dor-c11estc.r Boulevard i~t 3101ltre~~l.
• \Trllcii the vibrntioli had becil built up to a suitable lcvel, thc motion was allon~cd to dccny and thc dampingv:\lue was again obini~icd by the logarithmic decrement mcthod.
• This assuillptioil was made, togcthcr i~ith the further assuinptioll that a11 thc Inasscs of cach floor for n give11 building were eclual.

I%ESULTS FOR I\~ODES AS11 FIEEQUENCIES OF VIBIEATIOS

• The wind records havc bceil stcacly on each occasion when readings have bccn taken froill the aiiemonleter, a fact that could be related to its isolatcd position.
• The claillpirig valucs obtained by these mcthocls arc shoxvn in Table 4 -Tllc ~ncastued and theoretical valucs of the pcriotls of tlic fulidaillclital inodcs of lateral vibration of the buildiiigs are sho~vii in the first two lilies of T~~blc 5.
• The ~ne:~surecl results in Tablc 1 show that the ratios of tlic natural frccluerlcies of vibration to the fundanlentnl freciuency :ire of the o~,cler 1, 3, 5, 7, etc. 31oclc shapes of buildings :Ire also inlportant in carthqualic engineering design l~ccause they cletermine t'lic manner in which eart'llqualic loatls are distributed thl~ougli the kicight of the st,ructure.
• One of the best ways of achicviag this knomledgc is to continue the comparison of the predictions of theory with the nleasurecl dy~ian~ic ~haractcristics of buildings.

Full text

Publisher’s version / Version de l'éditeur:
Bulletin of the Seismological Society of America, 56, 4, pp. 793-813, 1966-07-01
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Wind-induced vibrations and building modes
Ward, H. S.; Crawford, R.
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Bulletin of the Seismological Society of Americo. Vol. 56, No.
4,
pp.
793-813.
August, 1966
This paper outlines the methods that have been used to determine the fre-
quencies and modes of vibration of multistory buildings from their wind-induced
vibrations. Three buildings of ten, thirty-eight and forty-seven stories were
investigated.
A
simple theoretical model was used to calculate the frequencies
of vibration of the buildings; the model was based on the assumption that there
was no joint rotation in the building frames.
A
comparison of the theoretical and
measured values of the frequencies showed that this simple model was a
realistic representation of only the smaller building. It
is
concluded that a model
that includes joint rotation would be more realistic for the taller buildings. Auto-
correlation and power spectrum analysis of the vibration records were used to
obtain an estimate of the damping characteristics of the buildings. The values
obtained were
1
to
3
per cent of the critical amount of damping.
It is only ill the Illst few ye:irs, as strucaturcs huvc hcc~omc t:illt>r :~titl tlcoiioii~y 111s
bcconlc more import:~nt, t11:lt str~c.tur:ll designers lluvt> 1)ccii 1il:~clc to rc:diec tlic
iluportnncv of tldcr~niliilig tlic clynalnic e1l:lr:~ctcristic'h of builclillgs. Xltliougli for
m:uly year:, hu~lcliligs 11:lve bccii clc.;ig~ictl for
n
ilicl :uicl e:uthqualie lontl\, tlw :~p-
pronc.11 11:1s bccl~ hased on cluasi-static* co~ic.cpts, despite tlic obvious fncht t11:~t it is
a
tlyn:\nllc. problcni. Rcforc
tl
dyllaulic approac.li call I)c clcvelopctl very far tlicrc is
a.
licctl for more i~lfornitttion on tllc actual
:i11(1
prctlictt~tl perfor111:~1ic.cs of I)t~ildi~igs.
Siiicc the 1030'.; tlic Cons1 and C+coclctic. S111,vcy (1936) has bcc,~~ l~sillg
II
ill(1Li11-
tlucctl :uld 1n:whinc cac~tctl vibratiolih to nlc1nsurc tllc p~riocls
01'
vi1)rat ion of builtl-
ings, and si111il:u. iliforll1:it ion has been obt:~iliccl ill ,J:L~:LI~ (T:~I.;t~~ic11i Si~li:~g:~~;t,
1960). l\lost of tllc nlc:isiircnicilt to tl:ltc. have l)c,cll ol)lni~iccl by using frccluenc.y
controlled vibr:itor.: tllut cscrt :ui osc.illatilig force of
a
fc~v tons. With this llicthotl
iteady state vibratiouh at
a
~~umbcr of frcclucnc~ies arc nlc1as11red :l~icl it is the11 110s-
siblc to tletcrminc thc frccluency req)o~lsc of the struc.ttu.c. The dcvclopmcnt of
sopl1istlc.ntctl vibration gc11cr:~tors in California (I-luclso~i, 1962) has iuca~lt that tllc
~nen~rillg tccliiiiclucs ileccl iiot he too cilaboratc, si~ic*c 1Eie :unplitutlcs of vibratioli
are ronlp:lr:lt ively large.
Tlle authors liavc usctl thc incthocl of nriiicl-induc.cd vibraliol~s, n~itl
t
hey lltlve
sho11rl1 (Crawford
lid
Wartl, lS(i4) that
with
appropriate ilistrtuncl~t:it ion t~litl ~11~1-
ysis tcc~hniqucs it is possible to clctcrmillc thc dyiianlic chtwactcrist icas of builtlings
by this method. Thc object of this paper is lo rcporl
seine
further results, obtai~icd
from obscrv:~tio~is of
n
tcn-story, rcinforccd concrctc builtlitlg
:tilt1
two stecI-fr;~111cd
buildings of
3S
ant1
17
stories.
13cc2~usc of tlle late tlcvclopil~c~it of intcrcst in the dyliuinic
properties
of strur-
turcs, lhcrc has becil littlc opportunity to col.rclatc t1icorctic:~l ccalculatio~is and
nlcastuctl valucs of these properties. Bect~usc thcsc properties arc often of the utmost

'794
BULLETIS
OF
TIIE
SEISSIOLOGICAIJ
SOCIETY
OF
ASIEIIICA
importance
irl
the ~arth(l~:lli~ :111d wintl resihtant clcsig~l of
structures,
it
is impera-
tive that every opportunity should be talie~l to try to unclcrstand tho dynamic hc-
llaviour of buildi~~gs. HOUSILC~ aid 13racly
(19G3)
have studied exiitillg information,
and have co~ic.ludcd that
sonic
of the existing empiricxl formulae used
ill
builtling
codes to determine the periods of vibration of buildings can 1,c in error by as inuch
as
100
per cent.
Another c.onclusion was that soillc inoclcrn steel frame builcliilgs behave esseriti:~lly
as
if
they had rigid floor girc1el.s. Calculi~tiolls have bee11 made to t,est this assump-
tion for the buildii~gs dcscribccl
ill
this p:~prr, ancl it is sho~vil that fair agreement
was obtui~lcd for the ten-story building, but that there ~vas an overcstimatiorl of the
fundamental frequency of the order of
50
per cent for the multi-story structures.
)p
Some possible causes for the discrepancy arc discussed, and the measured values are
comparcd with sonlc of the dcrivccl formulae obt:~ined by Hous~ler and Brady.
There is
perhaps less l~no~vn about the damping properties of buildings th;~n of
t~ny other clyil:~mic c11ar:~ctcristic. Ail attempt has been made to determine damping
values froin the rccorcls of the wild-iilducctl vibrations of the building by two meth-
ods: power spectrum :ulalysis and auto-correlatioll a~lalysis.
111
one instance the rc-
sults have been compared with those obtained by inail-induced vibrations. The
incthods need to be applied to illore builclillgs before general co~lclusioris c:~n be
drawl, but the initial fi~idiiigs iiltlic~atc damp~ng values of the ordcr of
1
to
3
per cent
of criticsal.
DESCI~IPTIOS
OF
TIIE
I~UILDISGS
Thc three buildings investigated have been c.onstructc~c1 ~vithiil the last five years-
One of the buildings, the Sir Alcsaildcr Cam~~bcll Buildiilg is the headquarters of
the Cunndi:ul Post Office Dcp:u.tilleilt
211
Ottawa; the other two buildiilgs, the Cn-
nacliail Imperial I3~1lli of Com~ncrcc Builcliitg ant1 CIll IIouhe, arc 1oc.atctl
011
Dor-
c11estc.r Boulevard i~t 3101ltre~~l.
The
Posl
O.@iic.e
Ru~lrlrnq
is
266
f
by
74
ft, c~lcvcn bays by thrcc b:~ys ill pl;ul di-
mcnsio~l, ant1
147
ft
Ci
in. high. Tllcrc :we trrl floors :~bovc grouncl, including
a
pent
-
house ancl oile b:lselncilt; arlcl
t
yl~ical sto1.y height is
12
ft
1
ill. The h:~nic ;lnd floor
slabs :~i.c rciriforc~ccl conc.i3dc, and the cxtcrnal I\-:dls arc 11011-load-bc:~ri~ig 4-h~. or
8-in. bric.1; ~valls.
Tllc buildii~g rcsls
011
groups of piles
22
in.
ill
diitmdcr, e:~cl1 of
125
toils capac.it y,
that pass through
20
f
of
(21:~~
:11lc1
'LO
ft of gravel and s:lild to solid liinesto~lc rocsli.
Tllc colum~ls :we rcc-tar~gular
:LI~
oricutcd so that the stiffest usis is parallel to the
loilg clinlcnsiorl of tllc builcli~~g; the colu~nils arc s~pprosim:ltcly twicac as stiff about
this asis as they arc about the one at right angles to it. The c~olum~l stift'iic~ss is
ap-
proximately cdolistalit Roil1 the fou~~tlation lo the
fif
h
floor, where the values :we
approximately 11:llvctl a~itl Illen ~tlnniil colistailt lo the roof.
?'he
Canatlian
Insperin1
Banlc
oJ'
Co117111el*ce
Builclinq
ii
140
ft by
100
ft,
scvcil b:lys
1,y four bays iri plaii,
slid
rises
GO3
ft
above the street lcvcl. There arc
44
stories
:~bovc ground lcvcl wit11 a typical story height of
12
ft
3
ill., cxcocpt for the first floor
aiid the five ~nec~hailic.:~l floors
:L~OUI~
the fifteeilth floor level arid the top.
A
sub-
structwc thi*cc floors in tlcptll covers thc entire site of
'243
ft
by
185
ft.
1Yic building is fo~~~idctl
011
bed r0c.1;
4S
ft brlonr street level, with footi~lgs desig~~rd