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Dynamic testing of civil engineering structures
Rainer, J. H.
https://publications-cnrc.canada.ca/fra/droits
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National Research Conseil national
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no. 865 CQP~,,&
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DYNAMIC TESTING
OF CIVIL ENGINEERING
STRUCTURES
" • - ' 'tmby
J.H.
RainerReprinted, with permission, from
Volume 1, Proceedings of the Third Canadian Conference
on Earthquake Engineering
held in Montreal, 4,s and 6 June, 1979
p. 551
-
574DBR Paper No. 865
Division of Building Research
Thie publication is being dietributed by the Division of Building R e e e a r c h of the National R e e e a r c h Council of Canada. I t ehould not be reproduced in whole o r in p a r t without permieeion of the original publisher. The Di- vieion would be glad to be of aeeietance in obtaining such permieeion.
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A l i s t of a l l publications of the Division ie available and may be obtained f r o m the Publicatione Section, Divieion of Building Research, National R e e e a r c h Council of Canada, Ottawa. KIAOR6.
DYNAMIC TESTING OF CIVIL ENGINEERING STRUCTURES
J. H. Rainer
+;::.-: ['?,ZR,?
SYNOPSIS
The use of dynamic t e s t i n g o f s t r u c t u r e s i s d e s c r i b e d i n r e s e a r c h and e n g i n e e r i n g a p p l i c a t i o n s . These i n c l u d e c o n f i r m a t i o n o f mathema- t i c a l models, d e t e r m i n a t i o n o f damping. motion stuclies under t i ind and e a r t h q u a k e s , and s h o r t - t e r m and long-term o b s e r v a t i o n o f s t r u c t u r a l behaviour under dynamic loadings. I n s t r u m e n t a t i o n requiremcnts.
s e l e c t i o n and placement o f t r a n s d u c e r s and r e c o r d i n g t h e s i g n a l s on FM, d i g i t a l and paper r e c o r d e r s a r e c o n s i d e r e d . F i 1 te r i n g , s i g n a l - t o - n o i s e r a t i o , a n a l y s i s and i n t e r p r e t a t i o n o f d a t a a r e d i s c u s s e d .
RESUME
La mise en e s s a i dynamique d e s s t r u c t u r e s e s t d s c r i t e d a n s d e s a p p l i c a t i o n s d e r e c h e r c h e e t d e g6nie. On proc'ede 1 l a c o n f i r m a t i o n d e s mod'eles mathsmatiques, B l a d e t e r m i n a t i o n d e l'amortissen.ent, 1 l'i5tude d e s mouvemencs c a u s e s par l e v e n t e t l e s tremblements d e t e r r e
e t 1 l ' o b s e r v a t i o n B c o u r t terme e t B long terme du comportement d e s s t r u c t u r e s sous d e s c h a r g e s dynamiques. Les exigence4 d ' i n s t r u m e n t a - t i o n , l e c h o i x e t l a m i s e en p l a c e d e s t r a n s d u c t e u r s e t l ' e n r e g i s t r e - ment d e s signaux s u r bandes MF, s u r p a p i e r e t s u r d a s magrbtophones d i g i t a w c s o n t examines. Le f i l t r a g e , l e r a p p o r t s i g n a l / b r u i t , l ' a n a l y s e e t l ' i n t e r p r s t a t i o n d e s donnses s o n t d i s c u t 6 s .
J . Hans Rainer obtained h i s Ph.D. from t h e U n i v e r s i t y of I l l i n o i s , Urbana, i n 1965. He is c u r r e n t l y a Research O f f i c e r i n t h e Division
of Building Research, National Research Council of Canada. H i s
r e s e a r c h p r o j e c t s have included a s p e c t s of earthquake engineering, dynamic behaviour of b u i l d i n g s and b r i d g e s , f l o o r v i b r a t i o n s , and
codes and s t a n d a r d s
.
INTRODUCTION
The l a s t decade has seen t h e f i e l d o f dynamic t e s t i n g of
s t r u c t u r e s evolve from a r e s e a r c h c u r i o s i t y t o a v a l u a b l e t o o l f o r t h e p r a c t i c i n g e n g i n e e r . The t r e n d toward more e f f i c i e n t u s e of m a t e r i a l s r e s u l t s i n s t r u c t u r e s t h a t a r e more s e n s i t i v e t o v i b r a t i o n s caused by
wind and s e r v i c e l o a d s . Dynamic t e s t i n g procedures a r e r e q u i r e d t o
a s s e s s , and a l l e v i a t e , v i b r a t i o n problems. The purpose of t h i s paper
i s t o d e s c r i b e some of t h e uses o f dynamic t e s t i n g of s t r u c t u r e s and
t o i l l u s t r a t e a s p e c t s o f t h e planning and execution of measurement pro grams.
Many p u b l i c a t i o n s have d i s c u s s e d t o p i c s r e l a t e d t o f u l l - s c a l e dynamic t e s t i n g o f b u i l d i n g s and o t h e r s t r u c t u r e s . Hudson (1)
provided a survey o f developments on dynamic t e s t i n g w i t h emphasis on t h e methods of applying f o r c e s , and an ASCE-EMD s p e c i a l t y conference d e a l t w i t h dynamic t e s t i n g and modeling ( 2 ) . Dynamic t e s t i n g of
s t r u c t u r e s i s a l s o d i s c u s s e d i n a book e d i t e d by Wiegel ( 3 )
.
Recentdynamic measurements on suspension b r i d g e s a r e r e p o r t e d i n Refs. 4 t o
7 . Numerous c o n t r i b u t i o n s on t h i s t o p i c can be found, f o r example, i n t h e Proceedings of t h e s i x World Conferences on Earthquake Engineering, t h e I n t e r n a t i o n a l J o u r n a l o f Earthquake Engineering and S t r u c t u r a l Dynamics, t h e B u l l e t i n o f t h e Seismological S o c i e t y of America, and t h e j o u r n a l s of c i v i l and s t r u c t u r a l engineering s o c i e t i e s i n many
c o u n t r i e s . Dynamic t e s t i n g can b e viewed a s one o f many n o n d e s t r u c t i v e
experimental techniques f o r observing and i n v e s t i g a t i n g t h e behaviour of s t r u c t u r e s . Although t h e method r e l i e s on p r i n c i p l e s of dynamics, useful information concerning s t a t i c p r o p e r t i e s of s t r u c t u r e s can a l s o be i n f e r r e d .
J u s t a s every e l a s t i c s t r u c t u r e deforms under t h e a p p l i c a t i o n of a s t a t i c load, e v e r y e l a s t i c s t r u c t u r e v i b r a t e s , however minutely,
under t h e a c t i o n o f f l u c t u a t i n g f o r c e s . I f damping i s small t h e s e
v i b r a t i o n s occur predominantly a t d i s t i n c t f r e q u e n c i e s t h a t correspond
t o t h e eigenmodes o f t h e s t r u c t u r e
.
Eigenmodes a r e v i b r a t i o n a l shapest h a t t h e s t r u c t u r e assumes when i t executes f r e e v i b r a t i o n ( t y p i c a l ones f o r b u i l d i n g s a r e shown i n F i g . 1 ) . The t h e o r y o f v i b r a t i o n s and of eigenmodes can be found i n standard textbooks on dynamics, e . g . , References 8 and 9 . These mode shapes, t o g e t h e r w i t h t h e a s s o c i a t e d n a t u r a l f r e q u e n c i e s , a r e a f u n c t i o n of t h e s t i f f n e s s and mass
p r o p e r t i e s o f t h e s t r u c t u r e . Information on damping c h a r a c t e r i s t i c s can a l s o be o b t a i n e d . The dynamic t e s t method i n v o l v e s d e t e c t i n g v i b r a t i o n s from wind and o t h e r f o r c e s , and e v a l u a t i n g and i n t e r p r e t i n g
REASONS FOR DYNAMIC TESTING OF STRUCTURES
Areas where dynamic t e s t i n g of s t r u c t u r e s c a n b e u s e d t o advantage a r e found i n b o t h r e s e a r c h and a p p l i c a t i o n s . Although t h i s d i s t i n c t i o n i s n o t always p r e c i s e , f o r t h e p r e s e n t p u r p o s e s r e s e a r c h r e f e r s t o i n v e s t i g a t i o n s t h a t a r e performed f o r g e n e r a l i n f o r m a t i o n r a t h e r t h a n f o r f i n d i n g t h e s o l u t i o n t o a p a r t i c u l a r problem.
Research
One o f t h e main r e a s o n s f o r p e r f o r m i n g dynamic t e s t s on b u i l d i n g s i s t o c o n f i r m methods o f m a t h e m a t i c a l modeling. Although h i g h l y
s o p h i s t i c a t e d methods o f a n a l y s i s o f b u i l d i n g s a r e now a v a i l a b l e , t h e r e a r e s t i l l p r a c t i c a l l i m i t a t i o n s on modeling d e t a i l s , and some independent v e r i f i c a t i o n of t h e v a l i d i t y o f s i m p l i f y i n g a s s u m p t i o n s i s d e s i r a b l e . There i s a l s o c o n s i d e r a b l e u n c e r t a i n t y a b o u t m a t e r i a l p r o p e r t i e s , p a r t i c u l a r l y o f s o i l and r e i n f o r c e d c o n c r e t e ; comparisons between measurements and c a l c u l a t i o n s i n d i c a t e t h e a p p r o p r i a t e n e s s o f
t h e mathematical i d e a l i z a t i o n s .
The dynamic r e s p o n s e o f s t r u c t u r e s t o d i s t u r b a n c e s such a s wind
and e a r t h q u a k e depends on damping. Damping, which i s a p r o p e r t y o f
t h e m a t e r i a l and t h e method o f c o n s t r u c t i o n , i s d i f f i c u l t t o p r e d i c t . Measurement o f damping o f s i m i l a r o r r e p r e s e n t a t i v e b u i l d i n g s e n a b l e s one t o draw g e n e r a l c o n c l u s i o n s f o r f u t u r e d e s i g n s and p o s s i b l y
i n c o r p o r a t e such p r o p e r t i e s i n recommended d e s i g n p r o c e d u r e s o r c o d e s . When s t r u c t u r e s a r e s u b j e c t e d t o extreme l o a d i n g s , such a s e a r t h - quakes, b l a s t s , and h i g h winds, " s o f t e n i n g " o f t h e system o c c u r s due t o y i e l d i n g o r l o o s e n i n g o f component e l e m e n t s . T h i s r e s u l t s i n an i n c r e a s e i n t h e n a t u r a l p e r i o d s f o r t h e s t r u c t u r e which i s r e a d i l y d e t e r m i n e d from dynamic measurements o f t h e modal p r o p e r t i e s . Measure- ments s h o u l d b e made b e f o r e t h e p r o j e c t e d e v e n t t o p e r m i t a " b e f o r e " and " a f t e r " comparison. When an extreme l o a d i n g o c c u r s , such informa- t i o n becomes v a l u a b l e d a t a i n a s s e s s i n g t h e changes e x p e r i e n c e d by t h e s t r u c t u r e . I t i s t h e r e f o r e d e s i r a b l e t h a t a l l s t r u c t u r e s i n s t r u m e n t e d w i t h s t r o n g - m o t i o n seismographs b e s u b j e c t e d t o a f u l l v i b r a t i o n
s u r v e y . A s a minimum, ambient v i b r a t i o n s s h o u l d b e monitored a t t h e l o c a t i o n s o f s t r o n g - m o t i o n i n s t r u m e n t s and t h e s p e c t r a computed.
In s e i s m i c a l l y a c t i v e r e g i o n s o f t h e world, t h e i n s t a l l a t i o n o f s t r o n g - m o t i o n i n s t r u m e n t a t i o n i n major s t r u c t u r e s such a s b u i l d i n g s , b r i d g e s , dams and n u c l e a r power s t a t i o n s , h a s become q u i t e common. Records o f s t r u c t u r a l r e s p o n s e t o s t r o n g ground motion p r o v i d e u s e f u l
i n f o r m a t i o n on l i n e a r and n o n l i n e a r b e h a v i o u r o f such s t r u c t u r e s a n d can a s s i s t i n e v a l u a t i n g t h e i r i n t e g r i t y and s a f e t y a f t e r an e a r t h q u a k e . For example, t h e Mica Creek Dam i n B r i t i s h Columbia c o n t a i n s t h r e e
s t r o n g - m o t i o n seismographs (10)
.
I n Quebec, s t r o n g - m o t i o n seismographs have been i n s t a l l e d a t t h r e e l e v e l s i n t h e D a n i e l Johnson D a m ("ManicS"), a m u l t i p l e a r c h c o n c r e t e dam, and a t "Manic 3", an e a r t h - f i l l e d dam, b o t h l o c a t e d on t h e Manicouagan R i v e r . Although t h e s e dams a r e n o t w i t h i n t h e h i g h e s t r i s k s e i s m i c zones o f Canada, t h e i r p r o x i m i t y t o a r e a s o f p r e v i o u s s e i s m i c a c t i v i t y and t h e p o s s i b i l i t y o f r e s e r v o i r -
i n s t a l 1 a t i o n o f t h e s e i n s t r u m e n t s .
The r a r i t y and s e v e r i t y o f s e i s m i c e v e n t s n e c e s s i t a t e s i n s t r u - ments w i t h f e a t u r e s such a s s e l f - s t a r t e r s , s e l f - c o n t a i n e d b a t t e r y o p e r a t i o n , rugged c o n s t r u c t i o n , and a h i g h d e g r e e o f r e l i a b i l i t y under a d v e r s e o p e r a t i n g c o n d i t i o n s . The recommendations o f t h e C a l i f o r n i a B u i l d i n g S t r o n g Motion Earthquake I n s t r u m e n t a t i o n Program, d e s c r i b e d i n Ref. 11, p r o v i d e u s e f u l guidance.
The d e s i g n o f t a l l b u i l d i n g s i s , t o a l a r g e e x t e n t , governed by t h e motion t h a t o c c u p a n t s w i l l t o l e r a t e . Measurement of motion of b u i l d i n g s and o t h e r s t r u c t u r e s under v a r i o u s wind c o n d i t i o n s i n
c o n j u n c t i o n w i t h o b s e r v a t i o n s o f occupant r e a c t i o n s can p r o v i d e u s e f u l i n f o r m a t i o n on d e s i g n c r i t e r i a f o r a c c e p t a b l e motion. I n a d d i t i o n t o monitoring t h e motions a t a few i s o l a t e d l o c a t i o n s , a f u l l determina- t i o n o f t h e dynamic p r o p e r t i e s o f t h e s t r u c t u r e i s r e q u i r e d . T h i s p e r m i t s t h e e x t e n s i o n o f motion o b s e r v a t i o n s t o o t h e r p o i n t s i n t h e s t r u c t u r e even though t h e y a r e n o t b e i n g monitored d i r e c t l y .
Under c e r t a i n c o n d i t i o n s , i t i s p o s s i b l e t o determine t h e s t i f f - n e s s o f s t r u c t u r a l components from dynamic measurements. For example,
t h e f o u n d a t i o n s t i f f n e s s o f b u i l d i n g s o r b r i d g e s founded on f l e x i b l e f o u n d a t i o n s can b e determined from dynamic measurements (12, 1 3 ) . The amplitude o f f o u n d a t i o n movement i s measured along w i t h t h e amplitudes o f t h e s t r u c t u r e t o determine t h e modes o f t h e o v e r - a l l system.
Equating t h e i n e r t i a f o r c e s o f t h e s t r u c t u r e w i t h t h e r e s i s t a n c e p r o v i d e d by t h e f o u n d a t i o n e n a b l e s one t o s o l v e f o r t h e s t i f f n e s s components o f b a s e t r a n s l a t i o n and r o t a t i o n .
A p p l i c a t i o n s
When dynamic phenomena i n s t r u c t u r e s demand a n assessment and p o s s i b l e remedial a c t i o n , knowledge o f t h e dynamic p r o p e r t i e s of t h e b u i l d i n g i s e s s e n t i a l . T h i s o c c u r s , f o r example, when e x c e s s i v e v i b r a t i o n s due t o wind o c c u r i n t a l l b u i l d i n g s o r long b r i d g e s . I n b u i l d i n g s such v i b r a t i o n s can b e c o n t r o l l e d by i n s t a l l i n g t u n e d
r e s o n a n c e dampers ( 1 4 ) , such a s t h o s e d e s i g n e d f o r t h e C i t i c o r p C e n t e r B u i l d i n g i n New York, t h e John Hancock Tower i n Boston, o r t h e CN Tower
(15) i n Toronto. The n a t u r a l frequency o f t h e b u i l d i n g mode t o b e damped h a s t o b e determined and t h i s i s o b t a i n e d from measurements w i t h g r e a t e r a c c u r a c y and c e r t a i n t y t h a n can b e a c h i e v e d from c a l c u l a t i o n s .
Some t a l l b u i l d i n g s i n c o r p o r a t e s u b s t a n t i a l damping i n c e r t a i n s t r u c t u r a l e l e m e n t s t o reduce v i b r a t i o n a l r e s p o n s e under wind l o a d s ( 1 6 ) . The long-term e f f e c t i v e n e s s o f such damping d e v i c e s can b e
a s s e s s e d by dynamic t e s t i n g . A 1 though t h e p r i m a r y concern h e r e i s w i t h t h e damping p r o p e r t i e s e x h i b i t e d by t h e v a r i o u s modes, t h e modes of v i b r a t i o n themselves have t o b e i d e n t i f i e d f i r s t .
Before remedial measures f o r e x i s t i n g b r i d g e s o r towers a r e determined o r wind t u n n e l t e s t s o f s c a l e models conducted i t i s
e s s e n t i a l t o know t h e n a t u r a l f r e q u e n c i e s , mode shapes and damping c h a r a c t e r i s t i c s o f t h e r e a l s t r u c t u r e . Dynamic t e s t i n g can p r o v i d e t h e s e p a r a m e t e r s d i r e c t l y . Monitoring t h e b e h a v i o u r o f t h e s t r u c t u r e
b e f o r e and a f t e r t h e changes e n a b l e s one t o c o n f i r m t h e e f f e c t i v e n e s s of t h e r e m e d i a l measures.
PLANNING FOR DYNAMIC TESTS OF STRUCTURES
When p l a n n i n g a dynamic t e s t , c o n s i d e r a t i o n s h o u l d b e g i v e n t o t h e p u r p o s e o f t h e t e s t , t h e i n s t r u m e n t a t i o n , equipment and p e r s o n n e l t h a t a r e a v a i l a b l e , t h e a n a l y s i s methods t o b e used, and t h e f i n a l u s e f o r which t h e i n f o r m a t i o n i s b e i n g g e n e r a t e d . I t i s q u i t e p o s s i b l e t o o b t a i n u s e f u l d a t a w i t h t h e s i m p l e s t s e t o f i n s t r u m e n t a t i o n i f i t i s a p p r o p r i a t e l y d e p l o y e d . The s c o p e o f t h e measurement program needs t o b e c l e a r l y o u t l i n e d ; t h e t e m p t a t i o n t o measure and r e c o r d " e v e r y t h i n g " s h o u l d b e r e s i s t e d .
An i m p o r t a n t d e c i s i o n t h a t needs t o b e made i n p l a n n i n g a dynamic t e s t i n g program i s t h e t y p e o f e x c i t a t i o n t h a t i s t o b e u s e d . Wind, waves, t r a f f i c and occupancy (machinery, p e o p l e movements) u s u a l l y produce measurable m o t i o n s , sometimes c a l l e d "ambient" v i b r a t i o n s and c o n s t i t u t e a c o n v e n i e n t s o u r c e o f e x c i t a t i o n . S h a k e r s p r o v i d e
c o n t r o l 1 ed f o r c i n g f u n c t i o n s and y i e l d t h e most d e f i n i t i v e r e s u l t s (1)
.
E c c e n t r i c c o u n t e r - r o t a t i n g w e i g h t s , e l e c t r o h y d r a u l i c and e l e c t r o -dynamic s h a k e r s have b e e n used a s e x c i t e r s . An e l e c t r o h y d r a u l i c s h a k e r employed i n t e s t i n g a c o n c r e t e b r i d g e i s shown i n F i g . 2 ( 1 7 ) . The t e s t i n g e f f o r t a n d c o s t o f equipment i s c o n s i d e r a b l e , however, and many owners a r e r e l u c t a n t t o have t h e i r s t r u c t u r e d e l i b e r a t e l y s h a k e n , however l i g h t l y . The v i b r a t i o n a l e f f e c t s o f h i g h winds, e a r t h q u a k e s and o t h e r a r t i f i c i a l ground motions from n u c l e a r o r 1 a r g e c o n v e n t i o n a l b l a s t s a r e o f g r e a t i n t e r e s t i n themselves and a r e f r e q u e n t l y
m o n i t o r e d , b u t t h e i r r a r e o c c u r r e n c e makes them u n s u i t a b l e f o r r o u t i n e dynamic t e s t i n g
.
Dynamic t e s t s c a n b e c a t e g o r i z e d i n t o two c l a s s e s : s h o r t - t e r m and l o n g - t e r m . These r e q u i r e d i f f e r e n t a p p r o a c h e s i n p l a n n i n g and e x e c u t i n g t h e e x p e r i m e n t .
S h o r t - t e r m t e s t s r e q u i r e a number o f days o r weeks. The f i e l d work f o r an ambient v i b r a t i o n s u r v e y f o r d e t e r m i n i n g n a t u r a l
f r e q u e n c i e s , mode s h a p e s and damping can b e accomplished i n a few d a y s . Time i s r e q u i r e d , however, t o p l a n t h e t e s t and t o assemble, check a n d c a l i b r a t e t h e equipment. C o n s i d e r a b l e time may a l s o e l a p s e w a i t i n g f o r d e s i r a b l e e n v i r o n m e n t a l c o n d i t i o n s . Of p r i m a r y concern i n t h e s e t e s t s i s t h e p o r t a b i l i t y , r e l i a b i l i t y and e a s e of o p e r a t i o n o f equipment. T y p i c a l l y , t h e s i g n a l s from a c c e l e r o m e t e r s o r v e l o c i t y t r a n s d u c e r s would b e c a r r i e d from t h e p o i n t s o f o b s e r v a t i o n v i a c a b l e s t o a temporary r e c o r d i n g s t a t i o n . The s i g n a l s a r e f i l t e r e d and
a m p l i f i e d and r e c o r d e d on a m u l t i c h a n n e l t a p e r e c o r d e r . O n - s i t e c a l i b r a t i o n o f r e l a t i v e s e n s i t i v i t y can b e performed b y p l a c i n g a l l t r a n s d u c e r s c l o s e t o g e t h e r , p o i n t e d i n t h e same d i r e c t i o n , and r e c o r d i n g t h e s i g n a l s a s would b e done i n an a c t u a l t e s t . A seven- o r e i g h t - c h a n n e l FM r e c o r d i n g system r e p r e s e n t s a b o u t t h e r i g h t compromise between p o r t a b i l i t y , e f f i c i e n c y o f i n f o r m a t i o n s t o r a g e , and c a p i t a l c o s t . Four c h a n n e l s would b e t h e s m a l l e s t u s e f u l u n i t ; a l t h o u g h 14 o r more channel FM r e c o r d e r s o r d i g i t a l r e c o r d e r s
p e r m i t a l a r g e r number o f c h a n n e l s t o b e monitored s i m u l t a n e o u s l y , t h e i n d i v i d u a l components become s u b s t a n t i a l l y h e a v i e r a n d o f c o u r s e more
c o s t l y . A measuring system used by t h e a u t h o r and co-workers i s shown
i n F i g . 3 .
I f t h e a v a i l a b l e number o f t r a n s d u c e r s o r r e c o r d i n g c h a n n e l s i s l e s s t h a n t h e r e q u i r e d o b s e r v a t i o n p o i n t s , m u l t i p l e r e c o r d i n g s e s s i o n s
a r e r e q u i r e d . A common t r a n s d u c e r r e f e r e n c e p o i n t o r s e t o f r e f e r e n c e
p o i n t s i s r e t a i n e d f o r s u c c e s s i v e s e s s i o n s . T h i s p e r m i t s t h e s c a l i n g of t h e r e s u l t s r e l a t i v e t o t h e common measuring p o i n t s . These r e f e r e n c e p o i n t s must b e chosen a t a r e l a t i v e l y l a r g e modal a m p l i t u d e and n o t
n e a r a node. For b u i l d i n g s t h e s i n g l e most s u i t a b l e p o i n t i s a t t h e
t o p o f t h e b u i l d i n g s i n c e a t t h a t l o c a t i o n a l l modes have a r e a s o n a b l y
l a r g e modal d e f l e c t i o n , a s i s shown i n F i g . 1 . The same a p p l i e s t o
t o r s i o n a l motion o f b u i l d i n g s , f o r which two a c c e l e r o m e t e r s on t h e same f l o o r a r e r e q u i r e d , o r i e n t e d i n t h e same ( o r o p p o s i t e ) d i r e c t i o n and w i t h t h e d i s t a n c e normal t o t h e i r s e n s i t i v e a x i s a s l a r g e a s p o s s i b l e . S u b t r a c t i o n o r a d d i t i o n o f t h e s i g n a l s e n a b l e s one t o
e v a l u a t e b o t h t r a n s l a t i o n a l and r o t a t i o n a l motion. Long s l e n d e r
b u i l d i n g s o r t h o s e w i t h f l o o r s h a v i n g low i n - p l a n e s t i f f n e s s r e q u i r e t h r e e o r more measuring s t a t i o n s p e r f l o o r f o r an a d e q u a t e modal
r e p r e s e n t a t i o n . For b r i d g e s i t i s a d v i s a b l e t h a t two o r more common
measuring s t a t i o n s b e c o n s i d e r e d s i n c e t h e l o c a t i o n s o f nodes a r e n o t u s u a l l y known a p r i o r i .
I n symmetrical s t r u c t u r e s i t i s u s e f u l t o a d o p t a symmetrical l a y -
o u t of t r a n s d u c e r s . T h i s sometimes p e r m i t s t h e r e s o l u t i o n of c l o s e l y
spaced modes, n o t a b l y t h o s e f o r t r a n s l a t i o n and t o r s i o n i n b u i l d i n g s and symmetrical and a n t i s y m m e t r i c a l modes i n b r i d g e s .
The l o c a t i o n o f a n e x c i t e r a l s o h a s t o b e chosen w i t h c a r e , and
i n g e n e r a l , two o r more l o c a t i o n s s h o u l d b e c o n s i d e r e d . This
minimizes t h e p o s s i b i l i t y o f l o c a t i n g on a node and t h e r e f o r e n o t
b e i n g a b l e t o e x c i t e a p a r t i c u l a r mode. On t h e o t h e r hand, t h i s a s p e c t
c a n b e u s e d t o a d v a n t a g e i n s e p a r a t i n g c l o s e l y s p a c e d symmetric and
a n t i s y m m e t r i c modes. The c o n c r e t e b r i d g e i n F i g . 4 was e x c i t e d w i t h
an e l e c t r o h y d r a u l i c s h a k e r ( F i g . 2 ) , u s i n g s h a k e r l o c a t i o n s a n d
i n s t r u m e n t s t a t i o n s g i v e n i n F i g . 5 ( 1 7 ) . Shaker L o c a t i o n 2 produced
b o t h symmetric and a n t i s y m m e t r i c modes w i t h s t r o n g i n t e r f e r e n c e b e t w e e n
t h e f i r s t two modes ( F i g . 6 ) , whereas S h a k e r L o c a t i o n 1 e x c i t e d o n l y
t h e symmetric modes ( F i g . 7 ) . The l a t t e r s t i l l shows a s m a l l amount
o f d i s t o r t i o n i n t h e f r e q u e n c y r e s p o n s e c u r v e b e c a u s e o f i m p e r f e c t
symmetry c o n d i t i o n s . T h i s i s e l i m i n a t e d , however, i n t h e s i g n a l from
t h e s y m m e t r i c a l l y l o c a t e d S t a t i o n K a s shown i n F i g . 8, which g i v e s t h e f r e q u e n c y r e s p o n s e c u r v e s f o r symmetric modes w i t h o u t i n t e r f e r e n c e from asymmetric o n e s . An a n a l y t i c a l b a s i s f o r r e s o l v i n g modal i n t e r - f e r e n c e i s p r e s e n t e d i n R e f . 1 8 .
O b s e r v a t i o n s t h a t e x t e n d o v e r some y e a r s r e q u i r e a more permanent i n s t a l l a t i o n o f c a b l e s l e a d i n g t o a c e n t r a l r e c o r d i n g s t a t i o n . For b u i l d i n g s t h e c a b l e s a r e b e s t i n s t a l l e d d u r i n g c o n s t r u c t i o n . D i g i t a l r e c o r d i n g t e c h n i q u e s a r e u s u a l l y u s e d t o p e r m i t s i m u l t a n e o u s sampling of a l a r g e number of c h a n n e l s . S i g n a l s from n e a r b y measuring p o i n t s can b e m u l t i p l e x e d a t i n t e r m e d i a t e s t a t i o n s , t h u s r e d u c i n g t h e number
o f l o n g c a b l e s t h a t l e a d t o t h e c e n t r a l r e c o r d i n g s t a t i o n . C a r e must b e t a k e n t o s h i e l d t h e c a b l e s and ground t h e components s o a s t o a v o i d p i c k u p o f e l e c t r i c a l n o i s e . D i g i t a l d a t a a c q u i s i t i o n a l s o f a c i l i t a t e s c a r r y i n g o u t some s i m p l e c a l c u l a t i o n s s u c h a s peak v a l u e s , means, root-mean-squares and s t a n d a r d d e v i a t i o n s , a n d a programmable m o n i t o r i n g program such a s h o u r l y r e a d i n g and i n i t i a t i o n of t h e
r e c o r d i n g p r o c e s s b a s e d on a p r e d e t e r m i n e d t r i g g e r l e v e l o f a s i g n a l . I t i s i m p o r t a n t t h a t some s p a r e c a p a c i t y o f c h a n n e l s , c a b l e s and o b s e r v a t i o n p o i n t s b e i n c o r p o r a t e d s o t h a t a d j u s t m e n t s can b e made a s p r e l i m i n a r y r e s u l t s a r e o b t a i n e d and t h e measuring program e v o l v e s . Only a few dynamic measuring p o i n t s need be monitored c o n t i n u o u s l y a s t h e s e p o i n t s can b e r e l a t e d t o t h e modal p r o p e r t i e s d e t e r m i n e d from a s h o r t - t e r m ambient v i b r a t i o n s u r v e y . Examples o f long-term
o b s e r v a t i o n programs a r e t h e CN Tower and Commerce Court (19) i n Toronto and Century C i t y i n Los Angeles ( 1 ) .
I t i s i m p o r t a n t t o v e r i f y t h a t t h e v a r i o u s i n t e r c o n n e c t e d
components a r e f u n c t i o n i n g p r o p e r l y and t o c a l i b r a t e t h e s y s t e m . For a long-term i n s t a l l a t i o n , c a l i b r a t i o n checks s h o u l d b e c a r r i e d o u t p e r i o d i c a l l y . B u i l t - i n c a l i b r a t i o n f e a t u r e s o f some t r a n s d u c e r s g r e a t l y f a c i l i t a t e t h i s t a s k .
The l o g i s t i c s o f c a r r y i n g o u t a dynamic t e s t program on a
s t r u c t u r e should i n c l u d e c o n s i d e r a t i o n o f a c c e s s i b i l i t y t o measuring p o i n t s , dependence on means o f t r a n s p o r t a t i o n , e . g . , e l e v a t o r s , and t h e n e c e s s i t y o f c l i m b i n g up l a d d e r s o r s t a i r s w i t h heavy equipment. T e l e m e t r y may b e employed t o a d v a n t a g e i n overcoming problems i n long
d i s t a n c e t r a n s m i s s i o n o f s i g n a l s ( 1 ) . L a s t b u t n o t l e a s t , t h e goodwill and c o o p e r a t i o n o f t h e b u i l d i n g owner o r h i s a g e n t must b e a s s u r e d and r e t a i n e d . He s h o u l d b e k e p t informed o f t h e a c t i v i t i e s a s s o c i a t e d w i t h t h e measurements, and p r i o r u n d e r s t a n d i n g must b e r e a c h e d on m a t t e r s such a s a c c e s s t o t h e b u i l d i n g , time span o f measurements, s h a r i n g o f c o s t s , and e v e n t u a l r e l e a s e o f t h e r e s u l t s .
MEASUREMENT INSTRUMENTATION
The i n s t r u m e n t a t i o n r e q u i r e d f o r dynamic t e s t i n g c o n s i s t s of s e n s o r s , s i g n a l c o n d i t i o n i n g , and r e c o r d i n g a p p a r a t u s . The c h o i c e o f s e n s o r s ( o r t r a n s d u c e r s ) w i l l depend on t h e o b j e c t i v e s o f t h e measure- ment program and t h e r e s o u r c e s a t o n e ' s d i s p o s a l . S t r u c t u r e s c a n b e measured u s i n g s e n s o r s which a r e d i s p l a c e m e n t , v e l o c i t y , o r a c c e l e r a - t i o n s e n s i t i v e . The i n t e r a c t i o n and d i v e r s e r e q u i r e m e n t s o f t h e
v a r i o u s components o f a n i n s t r u m e n t a t i o n package must b e c o n s i d e r e d i n p l a n n i n g and c o n d u c t i n g a t e s t .
The measurement of d i s p l a c e m e n t , which i s r e l a t i v e l y d i f f i c u l t , has been c a r r i e d o u t u s i n g mechanical (1) o r o p t i c a l means ( 2 1 ) . An o p t i c a l d e t e c t o r which l o c k s o n t o a c o n t r a s t i n g l i g h t - d a r k edge i s i n s t a l l e d i n t h e CN Tower t o measure t h e l a t e r a l d i s p l a c e m e n t between t h e b a s e and t h e r e s t a u r a n t l e v e l . The f o u n d a t i o n r o c k under t h e CN
Tower a l s o c o n t a i n s d e e p - s e a t e d v e r t i c a l r o d s which a r e b r o u g h t t o t h e s u r f a c e w i t h i n p i p e s . R e l a t i v e movement between t h e b a s e o f t h e r o d and t h e f o u n d a t i o n l e v e l i s o b t a i n e d b y t h i s means.
A t t h e D i v i s i o n o f B u i l d i n g Research o f t h e N a t i o n a l Research Council of Canada, a d i s p l a c e m e n t measuring d e v i c e h a s been b u i l t which c o n s i s t s o f two p a i r s o f p h o t o c e l l s mounted on a b e l t - d r i v e n
c a r r i a g e , t o b e p l a c e d n e a r t h e t o p o f a s h a f t i n t h e b u i l d i n g ( F i g . 9). Servomotors keep t h e p h o t o c e l l s "locked" o n t o a c o l l i m a t e d l a s e r beam p r o j e c t e d from t h e b u i l d i n g b a s e . The movement o f t h e b u i l d i n g i n t h e x and y d i r e c t i o n s r e l a t i v e t o t h e s t a t i o n a r y beam i s c o n v e r t e d i n t o v o l t a g e s p r o p o r t i o n a l t o t h e d i s p l a c e m e n t . One s u c h i n s t r u m e n t h a s been i n s t a l l e d i n t h e CN Tower and a n o t h e r i n t h e e l e v a t o r s h a f t o f t h e 5 7 - s t o r e y Commerce Court b u i l d i n g a l o n g w i t h o t h e r t r a n s d u c e r s shown i n F i g . 10 ( 1 9 ) . The d e t e c t o r i n Commerce Court h a s performed s a t i s f a c t o r i l y i n s t r e t c h e s o f e i g h t months o f c o n t i n u o u s o p e r a t i o n . Displacements r e c o r d e d w i t h t h i s i n s t r u m e n t a r e shown i n F i g s . 11 and 12 ( 1 9 ) . S h o r t t r i a l r u n s o f t h e i n s t r u m e n t i n t h e CN Tower showed t h a t c o n s i d e r a b l e s w i r l i n g o f t h e l a s e r beam o c c u r s due t o t h e r m a l l y i n d u c e d a i r t u r b u l e n c e i n s i d e t h e tower s h a f t . T h i s i n s t r u m e n t i s t h u s n o t i d e a l l y s u i t e d f o r t h e tower s h a f t environment a s t h e thermal t u r b u l e n c e s u b j e c t s t h e d i s p l a c e m e n t f o l l o w e r t o c o n s i d e r a b l e wear and t e a r . The major problems a s s o c i a t e d w i t h o b t a i n i n g r e l i a b l e d i s p l a c e - ment measurements a r e t h e e f f e c t s o f a i r t u r b u l e n c e on t h e patlr of l i g h t between t h e s o u r c e and r e c e i v e r a n d t h e p r o v i s i o n of a s t a b l e r e f e r e n c e p l a n e f o r t h e l a s e r beam e m i t t e r o r t h e d e t e c t i o n system of o t h e r o p t i c a l measuring d e v i c e s . To have some a s s u r a n c e o f g e t t i n g a p r o p e r r e s p o n s e from t h e d i s p l a c e m e n t t r a n s d u c e r , a c c e l e r o m e t e r s s h o u l d b e i n s t a l l e d so t h a t t h e dynamic components from b o t h methods can b e compared.
V e l o c i t y t r a n s d u c e r s g e n e r a l l y work on t h e p r i n c i p l e of a suspended mass whose motion i n d u c e s a v o l t a g e i n a c o i l
.
With t h e a p p r o p r i a t e amount o f damping t h e o u t p u t i s p r o p o r t i o n a l t o v e l o c i t y o v e r a f r e q u e n c y r a n g e above t h e i n s t r u m e n t ' s n a t u r a l f r e q u e n c y . Out- s i d e t h i s c o n s t a n t v e l o c i t y r a n g e t h e s e t r a n s d u c e r s can s t i l l b e u t i l i z e d i f s u i t a b l e c a l i b r a t i o n o f t h e i n s t r u m e n t i n t h a t frequency r a n g e i s a v a i l a b l e , o r i f t h e a b s o l u t e magnitude i s n o t of i n t e r e s t , f o r example, i n d e t e r m i n a t i o n s o f f r e q u e n c y o r mode s h a p e s . S e n s i t i v e v e l o c i t y t r a n s d u c e r s , a l s o c a l l e d "seismometers," a r e a v a i l a b l e f o r measuring i n t h e r a n g e o f m/s w i t h v e r y l i t t l e e x t r a n e o u s e l e c t r i c a l n o i s e . The s e n s i t i v i t y i n upper f r e q u e n c y r a n g e s d r o p s o f f , t h u s h i g h f r e q u e n c y v i b r a t i o n s a r e a t t e n u a t e d , l e a v i n g t h e lowf r e q u e n c y s i g n a l s r e l a t i v e l y more prominent. T h i s means t h a t sometimes r e c o r d i n g s c a n b e made w i t h o u t t h e need f o r f i l t e r i n g . They a r e
a f f e c t e d by magnetic f i e l d s , however, and have a l i m i t e d p e r m i s s i b l e d i s p l a c e m e n t r a n g e .
S t r a i n - g a u g e - and s e r v o - a c c e l e r o m e t e r s can d e t e c t s i g n a l s a l m o s t t o g , and o n l y t h e y w i l l b e d e a l t w i t h h e r e . These a c c e l e r o m e t e r s respond down t o 0 Hz, which i m p l i e s t h a t t h e y a r e s e n s i t i v e t o
o r i e n t a t i o n r e l a t i v e t o t h e e a r t h ' s g r a v i t a t i o n a l f i e l d . When a
h o r i z o n t a l a c c e l e r a t i o n measurement i s a l s o accompanied by r o t a t i o n , a c o r r e c t i o n f o r t h e r o t a t i o n a l component h a s t o b e a p p l i e d t o o b t a i n t h e t r u e h o r i z o n t a l amp1 i t u d e
.
T h i s r o t a t i o n can sometimes b e measured by s u b t r a c t i n g t h e o u t p u t from two v e r t i c a l t r a n s d u c e r s p l a c e d ac e r t a i n d i s t a n c e a p a r t . For v e r t i c a l o p e r a t i o n , a minimum t r a n s d u c e r r a n g e g r e a t e r t h a n 1 g i s r e q u i r e d and t h e c o n s t a n t v o l t a g e t h a t
r e p r e s e n t s t h e 1 g a c c e l e r a t i o n needs t o b e f i l t e r e d o u t o r e l i m i n a t e d by adding an equal d - c v o l t a g e o f o p p o s i t e p o l a r i t y . Having a t r a n s -
ducer r a n g e o f 1 g o r g r e a t e r a l s o p e r m i t s a n e a s y check on t r a n s d u c e r s e n s i t i v i t y . Turning t h e t r a n s d u c e r from f a c i n g upward t o f a c i n g down- ward produces a v o l t a g e change corresponding t o 2 g a c c e l e r a t i o n .
S e r v o - a c c e l e r o m e t e r s c a r r y c o n s i d e r a b l e h i g h frequency n o i s e on t h e o u t p u t s i g n a l which must b e f i l t e r e d o u t b e f o r e a m p l i f i c a t i o n .
Accelerometers a r e w e l l s u i t e d t o measure motion of b u i l d i n g s and long- span b r i d g e s s i n c e it h a s been observed t h a t t h e F o u r i e r o r power
spectrum o f t h e a c c e l e r a t i o n s i g n a l does n o t v a r y greatly f o r a wide range o f t h e low modal f r e q u e n c i e s . T h i s p e r m i t s t h e i d e n t i f i c a t i o n of some of t h e h i g h e r modes, whose s i g n a l s would b e r e l a t i v e l y more a t t e n u a t e d i f a v e l o c i t y s e n s i t i v e t r a n s d u c e r were used.
Bonded e l e c t r i c a l s t r a i n gauges mounted on s t r u c t u r a l members o f a b u i l d i n g , e . g . , beams, columns, r e i n f o r c i n g r o d s , can a l s o b e used t o o b t a i n dynamic i n f o r m a t i o n about t h e s t r u c t u r e . I t should b e emphasized t h a t s t r a i n gauges p r o v i d e o n l y v e r y l o c a l i z e d i n f o r m a t i o n . Comparing t h e s t r a i n gauge o u t p u t w i t h t h a t o f o t h e r t r a n s d u c e r s , however, may e n a b l e one t o r e l a t e b u i l d i n g movement t o t h e s t r a i n and s t r e s s induced i n some i n s t r u m e n t e d components ( 1 9 ) .
Dynamic measurement programs on b u i l d i n g s f r e q u e n t l y a l s o i n v o l v e t h e m o n i t o r i n g o f o t h e r f a c t o r s such a s wind p r e s s u r e , wind v e l o c i t y , and f o u n d a t i o n s t r a i n . These i n v o l v e t e c h n i q u e s s i m i l a r t o t h o s e a l r e a d y d i s c u s s e d .
SIGNAL CONDITIONING AND RECORDING
Recording o f s i g n a l s i n v a r i a b l y i n v o l v e s f i l t e r i n g t o a t t e n u a t e unwanted frequency components. Analogue f i l t e r i n g s h o u l d p r e f e r a b l y b e performed i n t h e same way on a l l c h a n n e l s s i n c e f i l t e r i n g i n t r o d u c e s phase s h i f t s n e a r t h e f i l t e r c u t - o f f f r e q u e n c i e s .
High-pass f i l t e r s a r e o f t e n used t o e l i m i n a t e d - c components o r o t h e r low f r e q u e n c i e s when t h e y a r e n o t of i n t e r e s t ; low-pass f i l t e r i n g a t t e n u a t e s frequency components above t h e r a n g e of i n t e r e s t . Such unwanted components can o r i g i n a t e from i n s t r u m e n t a t i o n n o i s e a s w e l l a s from r e a l , high-frequency v i b r a t i o n s . A common e x t r a n e o u s component i s 60 Hz which can a r i s e from e l e c t r i c a l p i c k u p o r r e a l v i b r a t i o n s produced by r o t a t i n g machinery. A f t e r f i l t e r i n g , t h e s i g n a l may have
t o b e a m p l i f i e d o r a t t e n u a t e d t o b r i n g it t o t h e optimum l e v e l demanded by t h e r e c o r d i n g equipment. Many modern r e c o r d e r s i n c o r p o r a t e a d e q u a t e
s w i t c h a b l e v o l t a g e r a n g e s , and t h i s may o b v i a t e e x t e r n a l a m p l i f i e r s . The l e n g t h o f r e c o r d i n g s e s s i o n s w i l l depend on t h e p a r t i c u l a r a p p l i c a t i o n and on t h e a n a l y s i s r e q u i r e m e n t s . Typical r e c o r d l e n g t h s f o r ambient v i b r a t i o n s v a r y from a minimum o f 10 minutes up t o 30 minutes o r more. For c r i t i c a l o r i r r e p l a c e a b l e d a t a , backup s t o r a g e o r d u p l i c a t i o n o f r e c o r d e d d a t a a s w e l l a s a n u n i n t e r r u p t i b l e power supply s h o u l d b e c o n s i d e r e d .
For FM (frequency modulation) t a p e r e c o r d e r s , t h e background n o i s e l e v e l a s s o c i a t e d w i t h t h e motions o f t h e magnetic t a p e
d e t e r m i n e s t h e s m a l l e s t u s e f u l s i g n a l t h a t can b e d i s t i n g u i s h e d . The s i g n a l t o b e r e c o r d e d s h o u l d t h e r e f o r e b e a s l a r g e a s p o s s i b l e , b u t s h o u l d n o t exceed t h e maximum v o l t a g e r a n g e o f t h e r e c o r d e r i n o r d e r t o a v o i d c l i p p i n g . The r a t i o o f t h e v o l t a g e s o f t h e maximum s i g n a l t o t h e n o i s e l e v e l o f t h e r e c o r d e r i s c a l l e d s i g n a l - t o - n o i s e r a t i o (S/N). In FM r e c o r d e r s , S/N i s t y p i c a l l y i n t h e r a n g e 50 : 1 t o 100 : 1; t h i s can b e improved somewhat by f l u t t e r compensation. Although t h i s i s a b u i l t - i n o p t i o n i n some machines, f l u t t e r compensation can b e
accomplished on playback by s u b t r a c t i n g from e a c h s i g n a l a n o u t p u t o b t a i n e d from a channel on which no e x t e r n a l s i g n a l was r e c o r d e d . T h i s f e a t u r e h a s t h e d i s a d v a n t a g e , however t h a t i t preempts one
channel on t h e t a p e r e c o r d e r . To a c h i e v e a s u f f i c i e n t l y h i g h l e v e l o f a s m a l l low-frequency component, l a r g e r a m p l i t u d e components
a t
h i g h e r f r e q u e n c i e s need t o b e f i l t e r e d o u t b e f o r e t h e s i g n a l i s
r e c o r d e d . T h i s t h e n p e r m i t s s u f f i c i e n t a m p l i f i c a t i o n t o b e a p p l i e d t o r a i s e t h e weak component w e l l above t h e t a p e n o i s e . On t h e o t h e r hand, i f t h e s i g n a l i n t o t h e r e c o r d e r exceeds t h e s p e c i f i e d maximum v o l t a g e l e v e l i t s peaks w i l l b e c l i p p e d . I f t h i s o c c u r s f r e q u e n t l y ,
s i g n i f i c a n t d i s t o r t i o n o f t h e computed spectrum a m p l i t u d e peaks c a n r e s u l t . For s i g n a l s t h a t v a r y o v e r a wide r a n g e o r t h a t a r e o f
u n c e r t a i n magnitude, it may b e n e c e s s a r y t o r e c o r d t h e same s i g n a l on two c h a n n e l s u s i n g d i f f e r e n t a m p l i f i c a t i o n s .
FM t a p e r e c o r d e r s a r e r e l a t i v e l y e f f i c i e n t i n s t o r i n g s i g n a l s t h a t have components o v e r a wide f r e q u e n c y r a n g e . Although playback of s i g n a l s i s s i m p l e , t h e r e can b e problems d u r i n g r e c o r d i n g due t o
i n t e r f e r e n c e from r a d i o s i g n a l s , i n c l u d i n g w a l k i e - t a l k i e s , t h a t a r e o p e r a t e d n e a r b y .
I n d i g i t a l r e c o r d i n g s y s t e m s t h e s i g n a l - t o - n o i s e r a t i o depends on t h e word l e n g t h a n d t h e n o i s e i n t r o d u c e d by t h e a n a l o g u e - t o - d i g i t a l c o n v e r t e r , t h e l a t t e r n o i s e b e i n g n e g l i g i b l e i n most c a s e s . Common d i g i t a l r e c o r d e r s have 1 2 - b i t words; w i t h one b i t r e s e r v e d f o r t h e s i g n t h e word l e n g t h i s (2) l 1 = 2048, a n d t h e n o i s e l e v e l i s t h e n r e p r e s e n t e d by t h e l a s t b i t . The r e s u l t i n g S/N r a t i o o f a p p r o x i m a t e l y 2000 : 1 e n a b l e s d i g i t a l s y s t e m s t o accommodate a much l a r g e r r a n g e o f s i g n a l l e v e l s t h a n FM r e c o r d e r s . D i g i t a l systems r e q u i r e t h a t t h e incoming s i g n a l b e f i l t e r e d a t l e s s t h a n t h e Nyquist f r e q u e n c y , i . e . , one h a l f t h e sampling r a t e ( 2 3 ) , The sampling r a t e i n t u r n i s
governed by t h e h i g h e s t f r e q u e n c y t h a t i s t o b e r e c o r d e d . For a n a d e q u a t e r e p r e s e n t a t i o n o f t h e s i g n a l , however, it i s d e s i r a b l e t o choose a sampling r a t e between s i x and t e n t i m e s t h e h i g h e s t f r e q u e n c y component t h a t i s t o b e f u l l y r e p r e s e n t e d . An a d v a n t a g e o f d i g i t a l d a t a l o g g i n g systems i s t h e p o s s i b i l i t y o f p r o c e s s i n g d a t a b e f o r e r e c o r d i n g i t on t a p e . Examples i n c l u d e t h e computation o f sums, d i s t r i b u t i o n f u n c t i o n s r e c o r d e d a t p r e d e t e r m i n e d t i m e i n t e r v a l s , and r o o t - m e a n - s q u a r e s . Recording c a n b e s t a r t e d o r s t o p p e d depending on a m p l i t u d e l e v e l s o r o t h e r c h a r a c t e r i s t i c s o f t h e d a t a . I n t e r f e r e n c e o f r a d i o s i g n a l s w i t h s t o r e d programs h a s a l s o been e x p e r i e n c e d w i t h d i g i t a l s y s t e m s .
The s i g n a l s from t r a n s d u c e r s can a l s o b e r e c o r d e d on p a p e r by u s i n g p h o t o s e n s i t i v e , h e a t s e n s i t i v e , p r e s s u r e s e n s i t i v e , o r i n k pen r e c o r d e r s . The f r e q u e n c y r e s p o n s e o f t h e r e c o r d e r h a s t o b e a d e q u a t e
f o r t h e frequency c o n t e n t o f t h e s i g n a l t o b e d i s p l a y e d . F i l t e r i n g may b e n e c e s s a r y . Before f u r t h e r d a t a p r o c e s s i n g can b e done on random-type s i g n a l s , t h e t r a c e s must b e d i g i t i z e d o r c o n v e r t e d t o an e l e c t r i c a l analogue s i g n a l . T h i s i s u s u a l l y v e r y l a b o r i o u s . Paper r e c o r d e r s , however, make i d e a l m o n i t o r i n g i n s t r u m e n t s i n p a r a l l e l w i t h a t a p e r e c o r d e r , t h u s p e r m i t t i n g s i m u l t a n e o u s viewing o f t h e incoming s i g n a l s . They a r e a l s o u s e f u l f o r d i s p l a y i n g t h e f i n a l s i g n a l s from s t e a d y - s t a t e v i b r a t i o n s s i n c e t h e s e u s u a l l y do n o t r e q u i r e f u r t h e r s i g n a l p r o c e s s i n g . A p o r t a b l e o s c i l l o s c o p e i s an i n v a l u a b l e t o o l f o r i n s t a n t a n e o u s examination o f s i g n a l s and m o n i t o r i n g t h e p r o p e r f u n c t i o n i n g of t h e v a r i o u s components o f an i n s t r u m e n t a t i o n system. ANALYSIS OF DATA
Before t h e a n a l y s i s o f d a t a i s begun, t h e adequacy and q u a l i t y o f d a t a have t o b e v e r i f i e d . S i g n a l c l i p p i n g , " b l i p s , " and r e c o r d gaps w i l l i n t r o d u c e d i s t o r t i o n s i n t o t h e computed r e s u l t s . Visual examina- t i o n on a s t r i p c h a r t , o s c i l l o s c o p e , o r computer-plotted t r a c e s i s a n e c e s s i t y .
The e x t r a c t i o n of u s e f u l i n f o r m a t i o n i n v a r i a b l y r e q u i r e s t h e computation o f s p e c t r a - F o u r i e r a m p l i t u d e , power, o r c r o s s s p e c t r a . The i d e n t i f i c a t i o n of a s s o c i a t e d mode shapes r e q u i r e s t h e d e t e r m i n a t i o n o f phase between t h e s i g n a l s from t h e v a r i o u s measuring s t a t i o n s . T h i s can b e a c h i e v e d b y simple a d d i t i o n and s u b t r a c t i o n of s i g n a l s and
o b s e r v i n g how t h e a m p l i t u d e s o f t h e spectrum peaks change. Frequency components t h a t a r e i n phase r e s u l t i n i n c r e a s i n g resonance peaks of an added s i g n a l ; o u t - o f - p h a s e s i g n a l s r e s u l t i n d e c r e a s i n g resonance peaks. The r e a l p a r t of t h e c r o s s spectrum of two s i g n a l s a l s o p r o v i d e s t h e phase i n f o r m a t i o n , i n - p h a s e components g i v i n g p o s i t i v e peaks, o u t - o f - p h a s e n e g a t i v e o n e s . These methods of determining phase a r e a p p l i c a b l e i f t h e frequency components a r e e i t h e r i n - p h a s e o r o u t - of-phase, i . e . , t h e y c o n s t i t u t e normal modes w i t h o n l y r e a l components. In t h e g e n e r a l c a s e where t h i s assumption cannot b e made, phase can b e computed d i r e c t l y from t h e p o l a r r e p r e s e n t a t i o n of t h e c r o s s spectrum.
Damping can b e determined by a number of methods. The half-power- bandwidth method g i v e s t h e c r i t i c a l damping r a t i o a s
where Af i s t h e width of t h e spectrum peak a t o n e - h a l f t h e peak magnitude of t h e power spectrum o r a t 0.707 t h e peak of a F o u r i e r amplitude spectrum, and f o i s t h e resonance f r e q u e n c y . T h i s i s
i l l u s t r a t e d i n F i g . 13. A u t o c o r r e l a t i o n c a l c u l a t e d from t h e power spectrum o f an i s o l a t e d resonance peak g i v e s a decaying curve from which
v
where xn i s t h e amplitude o f t h e n t h peak p a s t t h e amplitude xo of t h e z e r o t h peak. Reference 22 d e s c r i b e s t h e " P a r t i a l Moment Method," which u t i l i z e s t h e power spectrum of a s i g n a l . O t h e r methods of c a l c u l a t i n g
damping a r e p r e s e n t e d i n Ref. 23. The random decrement method (24,25) d e p i c t e d i n F i g . 14, sums f i n i t e l e n g t h s o f t h e r e c o r d s t a r t i n g from s u c c e s s i v e a s c e n d i n g and d e s c e n d i n g p o r t i o n s o f e x c u r s i o n s t h a t exceed a p r e s e l e c t e d s i g n a l l e v e l ; t h e s i g n a l must b e f i l t e r e d t o c o n t a i n o n l y one modal r e s p o n s e . The r e s u l t i s a c u r v e o f decaying a m p l i t u d e s shown i n F i g . 1 5 ( a ) ; t h e damping r a t i o i s computed u s i n g Eq. ( 2 ) . When more t h a n one c l o s e l y spaced f r e q u e n c y component i s p r e s e n t i n a s i g n a l , t h e random decrement w i l l e x h i b i t a b e a t p a t t e r n , F i g . 1 5 ( b ) ; a p p l i c a t i o n t o t h i s o f Eq. (2) can r e s u l t i n m i s l e a d i n g i n f o r m a t i o n .
P o s s i b l y t h e most d i r e c t method o f d e t e r m i n i n g damping i s from t h e f i l t e r e d impulse decay c u r v e and by u s i n g Eq. ( 2 ) . U n f o r t u n a t e l y i t i s o f t e n d i f f i c u l t t o g e n e r a t e s u c h a decay c u r v e i n major
s t r u c t u r e s . The impulse decay curve shown i n Fig. 1 6 ( a ) was o b t a i n e d on t h e Lions1 Gate S u s p e n s i o n B r i d g e d u r i n g a b r i e f b r i d g e c l o s u r e b y d r i v i n g a t r u c k i n t h e o u t s i d e l a n e , t u r n i n g s h a r p l y normal t o t h e b r i d g e and s t o p p i n g . F i l t e r i n g i s performed by making u s e of t h e F a s t F o u r i e r Transform a l g o r i t h m . The F o u r i e r t r a n s f o r m i s computed a s shown i n F i g . 1 6 ( b ) , unwanted f r e q u e n c y components a r e r e j e c t e d a s i n F i g . 1 6 ( c ) , and t h e r e s u l t i n v e r t e d back t o t h e t i m e domain. The f i l t e r e d decay c u r v e f o r t h e mode under c o n s i d e r a t i o n i s shown i n F i g . 1 6 ( d ) . Damping i s t h e n o b t a i n e d u s i n g Eq. (2)
.
The c y c l i c n a t u r e o f t h e D i s c r e t e F o u r i e r Transform h a s t o b e a c c o u n t e d f o r p r o p e r l y s o t h a t t h e r e s i d u a l v i b r a t i o n s o f t h e f i l t e r e d s i g n a l a r ez e r o o r a c c e p t a b l y s m a l l . T h i s c a n b e a c h i e v e d b y s h a p i n g f u n c t i o n s o r adding z e r o s t o t h e b e g i n n i n g and ends o f t h e o r i g i n a l s i g n a l s ( 2 6 ) .
Seldom do any two methods o f c a l c u l a t i n g damping g i v e answers t h a t a g r e e c l o s e l y . This can b e t r a c e d t o i n h e r e n t d i f f e r e n c e s i n t h e t h e o r y upon which t h e damping c a l c u l a t i o n s a r e b a s e d , e x p e r i m e n t a l o r c o m p u t a t i o n a l s h o r t c o m i n g s , o r most p r o b a b l y t o t h e f a c t t h a t t h e b a s i c a s s u m p t i o n s u n d e r l y i n g t h e t h e o r y a r e n o t f u l l y s a t i s f i e d by t h e
d a t a . S l i g h t v a r i a t i o n s i n response f r e q u e n c i e s o f a mode can make t h e c a l c u l a t i o n o f damping q u i t e m i s l e a d i n g o r i m p o s s i b l e b e c a u s e t h e r e s o n a n c e peaks a r e a r t i f i c i a l l y widened; t h e computed damping r a t i o i s t h e n l a r g e r t h a n would o r d i n a r i l y b e t h e c a s e . T h i s d i f f i c u l t y h a s been e n c o u n t e r e d w i t h dynamic measurements on s u s p e n s i o n b r i d g e s ( 4 , 7)
and t a l l b u i l d i n g s ( 1 9 ) . T h i s a r e a o f dynamics o f s t r u c t u r e s needs more a t t e n t i o n and r e s e a r c h .
O t h e r q u a n t i t i e s o f i n t e r e s t , p a r t i c u l a r l y from a s t a t i s t i c a l p o i n t of view, a r e maximum a m p l i t u d e s , means, r o o t - m e a n - s q u a r e s , and
s t a n d a r d d e v i a t i o n s . F i n a l l y it s h o u l d n o t b e o v e r l o o k e d t h a t simply f i l t e r i n g i n s e l e c t e d f r e q u e n c y bands a n d d i s p l a y i n g t h e r e s u l t i n g s i g n a l s can p r o v i d e much u s e f u l i n f o r m a t i o n on f r e q u e n c y , p h a s e , and a m p l i t u d e o f v a r i o u s modal components o f a s i g n a l .
' D a t a can b e a n a l y s e d e i t h e r on a g e n e r a l p u r p o s e d i g i t a l computer o r b y s p e c i a l purpose i n s t r u m e n t s such a s spectrum a n a l y z e r s ,
c o r r e l a t o r s , o r s p e c i a l i z e d minicomputers. Although t h e g e n e r a l
p u r p o s e d i g i t a l computer o f f e r s a wide c h o i c e o f d a t a m a n i p u l a t i o n and p r a c t i c a l l y u n l i m i t e d o p t i o n s f o r c a l c u l a t i o n s , t h e s p e c i a l p u r p o s e i n s t r u m e n t s e n j o y g r e a t p o p u l a r i t y . S i m p l i c i t y of o p e r a t i o n , r e a d y a c c e s s i b i l i t y and t h e p o s s i b i l i t y o f o n - s i t e o p e r a t i o n make t h e s e
i n s t r u m e n t s a v a l u a b l e a d d i t i o n t o any dynamic measurement system. A v i t a l p a r t o f any computational f a c i l i t y i s a l s o t h e c a p a b i l i t y o f d i s p l a y i n g s i g n a l s and r e s u l t s o f c a l c u l a t i o n s i n h a r d copy; t h e graph of a spectrum, f o r example, c o n t a i n s most o f t h e i n f o r m a t i o n t h a t i s needed.
INTERPRETATION OF RESULTS
I n t e r p r e t i n g t h e r e s u l t s o f dynamic measurements i n b u i l d i n g s must b e done i n l i g h t o f t h e e x p e r i m e n t a l p r o c e d u r e s and t h e a n a l y s i s methods employed. T h i s may b e s e l f - e v i d e n t , b u t i t cannot b e o v e r - emphasized. For example, t h e r e s u l t s from dynamic measurements
o b t a i n e d from l o w - l e v e l v i b r a t i o n s (ambient o r s h a k e r e x c i t a t i o n ) may n o t b e d i r e c t l y a p p l i c a b l e t o c o n d i t i o n s t h a t e x i s t w i t h e a r t h q u a k e s o r high winds. Where n o n l i n e a r i t i e s a r e a s s o c i a t e d w i t h h i g h
a m p l i t u d e s , changes o c c u r i n n a t u r a l f r e q u e n c i e s , mode shapes and damping r a t i o s . The problem i s complicated by t h e f a c t t h a t r e i n - f o r c e d c o n c r e t e , p r e s t r e s s e d c o n c r e t e , s t e e l , and " n o n s t r u c t u r a l " e l e m e n t s , such a s i n t e r i o r p a r t i t i o n s , d i f f e r i n t h e i r amplitude- s t r a i n dependence.
The p r e s e n c e o f f l e x i b l e f o u n d a t i o n s i n b u i l d i n g s , b r i d g e s and o t h e r s t r u c t u r e s s h o u l d a1 s o b e c o n s i d e r e d . F l e x i b l e foundat i o n s i n b u i l d i n g s i n t r o d u c e r o c k i n g and h o r i z o n t a l b a s e motion which a f f e c t
t h e mode shapes and lower t h e n a t u r a l f r e q u e n c i e s . S i m i l a r e f f e c t s o c c u r i n b r i d g e s on f l e x i b l e f o u n d a t i o n s .
Measured and c a l c u l a t e d dynamic p r o p e r t i e s o f s t r u c t u r e s
f r e q u e n t l y do n o t a g r e e c l o s e l y . P o s s i b l e r e a s o n s a r e , i n o r d e r o f r e l a t i v e importance and f r e q u e n c y o f o c c u r r e n c e : unknown o r u n c e r t a i n m a t e r i a l p r o p e r t i e s ( e . g . , s o i l , c o n c r e t e o r wood) ; f a u l t y o r
i n a d e q u a t e mathematical model f o r t h e s t r u c t u r e ( e . g . , o v e r s i m p l i f i e d o r i n a p p r o p r i a t e allowance f o r l ~ n o n s t r u c t u r a l l ' elements, expansion j o i n t s o r f l e x i b l e f o u n d a t i o n s ) ; e r r o r s i n i n t e r p r e t i n g t h e r e s u l t s ; experimental e r r o r s . The l a s t - m e n t i o n e d c a n b e minimized by
e x e r c i s i n g due c a r e and by t a k i n g some independent d u p l i c a t e
measurements
.
C o n s i d e r a b l e e f f o r t was r e q u i r e d t o a c h i e v e r e a s o n a b l e agreement between measured and c a l c u l a t e d r e s u l t s f o r t h e L i o n s 1 Gate Suspension Bridge i n Vancouver, B . C . ( 6 ) . U n c e r t a i n t i e s i n modeling t h e
t o r s i o n a l s t i f f n e s s o f t h e deck and p a r t i a l r e s t r a i n t s from b e a r i n g s and t i e r o d s r e q u i r e d an e x t e n s i v e p a r a m e t r i c s t u d y i n o r d e r t o a s s e s s t h e dynamic b e h a v i o u r o f t h e b r i d g e .
A u s e f u l i n d i c a t o r o f t h e r e a s o n a b l e n e s s o f t h e mathematical model i s t h e r a t i o of modal f r e q u e n c i e s r e l a t i v e t o t h e fundamental f r e q u e n c y . I f t h e s e computed r a t i o s a g r e e r e a s o n a b l y w e l l w i t h t h e measured o n e s , one can assume w i t h some a s s u r a n c e t h a t t h e d i s t r i b u - t i o n o f s t i f f n e s s and mass i n t h e mathematical model a r e r e a s o n a b l e . Agreement w i t h a c t u a l f r e q u e n c i e s can t h e n b e reached by s c a l i n g t h e m a t e r i a l s t i f f n e s s o r t h e mass, a l t h o u g h t h e l a t t e r i s u s u a l l y known more r e l i a b l y and t h e r e f o r e i s l e s s l i k e l y t o b e t h e major c a u s e o f
F i n a l l y , t h e i n t e r p r e t a t i o n o f damping s h o u l d b e done w i t h
c a u t i o n . A wide r e s o n a n c e peak r e s u l t i n g from s l i g h t temporal v a r i a - t i o n s o f r e s o n a n c e f r e q u e n c y can l e a d t o i n a p p r o p r i a t e l y h i g h damping v a l u e s . The same i s t r u e i f o n l y t h e f i r s t few c y c l e s of t h e a u t o - c o r r e l a t i o n o r random decrement c u r v e s a r e examined; t h e p r e s e n c e o f b e a t s , a s shown i n F i g . 1 5 ( b ) makes t h e r o u t i n e a p p l i c a t i o n o f
damping c a l c u l a t i o n s i n a p p r o p r i a t e . CONCLUS I ON
Dynamic t e s t i n g o f s t r u c t u r e s h a s emerged a s a u s e f u l e n g i n e e r i n g t o o l , b o t h f o r t h e r e s e a r c h e r and t h e p r a c t i c i n g e n g i n e e r . The method has been d e m o n s t r a t e d i n numerous c a s e s f o r s h o r t - t e r m and l o n g - t e r m o b s e r v a t i o n s .
The r e s u l t s o f a dynamic t e s t i n g program u s u a l l y r e s u l t i n s t r u c t u r a l p r o p e r t i e s such a s mode s h a p e s , n a t u r a l f r e q u e n c i e s , damping v a l u e s and maximum o r r m s r e s p o n s e l e v e l s . C a u t i o n n e e d s t o b e e x e r c i s e d , however, i n i n t e r p r e t i n g t h e r e s u l t s , p a r t i c u l a r l y t h o s e f o r damping.
P l a n n i n g and p e r f o r m i n g a measurement program s h o u l d t a k e a c c o u n t o f t h e o b j e c t i v e s o f t h e t e s t s , t h e c h a r a c t e r i s t i c s o f t h e i n s t r u m e n t s employed and t h e r e q u i r e m e n t s imposed b y t h e methods of a n a l y s i s of t h e d a t a . A v a r i e t y o f s u i t a b l e i n s t r u m e n t a t i o n f o r c a r r y i n g o u t t h e measurements and a n a l y s i s a r e a v a i l a b l e .
T h i s p a p e r i s a c o n t r i b u t i o n from t h e D i v i s i o n o f B u i l d i n g Research, N a t i o n a l Research Council o f Canada, and i s p u b l i s h e d w i t h t h e a p p r o v a l o f t h e D i r e c t o r o f t h e D i v i s i o n .
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