Determination of the natural periods of buildings

TLDR: In this article, the first three modes of vibration of a nineteen-story building about the two major translational axes and the torsional axis of the building were determined by random wind excitation.

Abstract: Random wind excitation has been used to find the first three modes of vibration of a nineteenstory building about the two major translational axes and the torsional axis of the building. Vibration records were obtained with Willmore electromagnetic seismometers feeding into a multichannel magnetic tape recorder. A harmonic analysis was then performed with the aid of an analogue computer to determine the first few vibration modes. Concurrently with the experimental program the building modes were computed two ways using different simplifying assumptions regarding the lateral stiffness of the structure.

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Publisher’s version / Version de l'éditeur:
Bulletin of the Seismological Society of America, 54, 6, pp. 1743-1756, 1964-12
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Determination of the natural periods of buildings
Crawford, R.; Ward, H. S.
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AN
AgJyzED
Bulletin of the Seismological Society of America. Vol. 54, No. 6,
pp.
1743-1756.
December, 1964
DlrIIIIl'IO
01:
THE KAVl'UltAIJ I'EItIODS
01;
I3UII,DIS(;S
131-
R. Cna'i~n-oar)
am
I-I.
S. WAI~I)
1t:rndorn wind
excitation
lias been used to firltl thc first three
nodes
of vibration of
a
niilctcc~l-
st80ry 1)uiltling allout thc l,mo
major
transl:~tio~l:rI
~LSCS
and thc torsional axis
of
the I~uilding.
\'il~ration rccords werc obtained wit11 Willmore clcctrolnagnctic seismomct,crs fcecli~lg into
a
~nr~ltiohanncl ~rl:rgnctic tspc
recorder.
A
h:rrmonic r~nalysis
was
then
performed n.it.li thc :Lid
of a11 nn:~logue co~npul,cr
to
tlet,errni~ic thc first fc~ vil)r:~tion modes. Cot~crirrcntly wit11 the
esperi~netrt:~l progruln t,hc building
modes
were cornputcd t,\vo ways using different. si~uplifying
:rssuu~ptions regarding thc lnt,cral stiif~~css of tllc
structure.
This study was prompted by the liced for accurate informatio~~
011
the.
~~atural
pcriods of vibratioii of buildings for cotnparisoii with valucs predicted froill iiiatllc-
t~iatical modcls. Studies of this type wcrc initiated soiile ycars ago by tllc
U.
S.
Coast and Gcodctic survey but it was bclicved that inorc accuratc and extclisivc
inforination about wind-excited structures could be gained using modcrii iiirthods
of analysis. Accordingly, a trial prograin was undcrtalie~i oil one buildi~~g.
The building was a new Fcdcral Governiilcnt building, built for thc Depart~~iciit
of Public Works to house thc Dcpartincilt of Natiorial Health and Wclfare, located
at Tuniicy's Pasture in Otta'i'ira. Tlle buildii~g itsclf is situated on an csposccl parli-
lalid arca with vcry few trees or buildings nearby. Conlprisirig 19 storics (17 floors,
ground level arid basement) and shapcd like a rccta~~gular prisin, it is
140
by
88
ft
by
23.5
ft
high. The structural steel columns of the building run thc full hcigllt with
the iliaill structural changes occurrilig at thc 4th arid 14th floors. In tllc c*clitcr of
the structure is a stccl aiid coilcrcte core that llouscs thc elevator sliafts aiid stair-
ways. Of ii1oi.e iilassivc coiistructioi~ tlia~i
no st
modcrn office blocks, the 1)uilding
has 11-ill. rcinforc-ed concrctc floor slabs arid outsidc walls coiliposccl of Iic~~vy
precast co~icrctc wirido\\r scctio~~s, each wcighirig approxiinatcly 2 tons. The weight
of tllesc window sections at each floor level is horne by the floor slab itsclf so that
the outsidc walls are not cao~~sidercd as a siriglc structural uiiit. Figurc
1
shows a
general
view of thc buildi~~g; figure 2 indicates thc layout of thr struct~ur.
The Ileait of ally ~ilcasuri~ig systenl is tlic serisii~g clnilellt. Siiicc tlic pcriods of
vibration of sti~ucturcs that are of iiitcrcst lie in the same rangc as tllosc pcriods
obscrvcd in eartliclualics, gciierally in thc range
0.05
to
10
secoiids, it \\-as obvious
that a traiisduccr such as is uscd for 1-ccordi~~g carthc~uakcs could bc uscd to record
structural vibrations. Not
only is it sciisitivc ill thc correct freclucncy rangc, but
becausc of its high scilsitivity
it
is idcal for i.ccording sillall liiotioi~s of buildi~lgs
induccd by 1vi11d escitatioii.
The Willniore JIarli
I1
scisinonlctcr was uscd in this study. This is ail clectro-
inagnctic
transducer
with a fixed (.oil aiid a heavy irlagilct that acts as thc niovirig
nlass. It (*an bc set to ineasurc in either th~ vertical or horizoi~tal direction. Thc

1744
BULLETIN
OF
TIIE
SEISSIOLOGIC.1L
SOCIETY OF
ASIERICA
natural period of tile suspc~~sion ran bc
adjusted
from
0.6
to
3.0
scc, and it \vas set
at
2.5
sec to mcasurc horizontally. Whcli da~upcd
electrically
to
O.(i5
of critical
damping the velocity rcspo~lsc is flat over the desircd period ra~lgc of
0.03
to
2.0
scc.
FIG.
1.
The Xntionnl I-Iealt>ll :~ntl Flrelfal.r, Ilcad(lu:lrt,ers I3clildi1lg, Tcmney's Past,ure,
OL-
tawa.
Co~~s~rtllin(g :Li~chilecls:
13nlh:lrrie, Ilcllller a~lcl Associates,
Ot,t,axv:l;
(;rec~~spoon, Freed-
1:ultler a~ld I~IIIIIIC, Mor~t.re:~I.
Consc(/ting Sl~,r~cl~ci.cl/ E.ngi7aeci.s:
~:~rsh:~Il
:LILCI
Marshall,
h.lontrea1.
Colrsrtlling E'nyi~~ccr In
Cfhn),ye
Oj
Supc~roisio~~ clntl Con,strllrt,ion:
$11..
C;.
Pncl;, B:L~-
h:lrrie, Ilelluer and Associntes.
The electrical outputs fro111 the IITill~norc scisnlonletcr \\-cl.c fed through dc
nlnp1ifiei.s iuto a portable 7-challllcl
FA1
tapc rerordcl.. I'apcr rccaolds using a multi-
rl~annel galva~lolllctcr recolder \\.it11 direct \\-ritii~g papel. nrcrc obtai~iecl sil~lul-
tallcously with the tapc rccordings so that a chcrli could be licpt on the vibration
levels.
r
7
Ihe ~l~ag~letic tape rccordings so obtained cxolitaill tllc vibratiou data en lnassc
in the building in the fl-ecluency range of thc transducer; the problclu is to deter-
mine
the a~nou~lt of energy present at each frecluenc.y and also its origin. To this
cud a harn~o~tic
wave
al~alyscr. giving a I;ourier arlalysis of a colllplcs 11~avcCo1~11~ was