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Vibration criteria for long-span concrete floors
Allen, D. E.; Rainer, J. H.; Pernica, G.
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National R e s e a r c h Council of Canada Conseil national d e r e c h e r c h e 6 du Canada
VIBRATION CRITERIA FOR LONG-SPAN CONCRETE FLOORS
by D.E. Allen,
J.H. R a i n e r , and
G.
P e r n i c aReprinted f r o m
P r o c e e d i n g s , ACI Symposium Vibrations of Concrete S t r u c t u r e s
held 20 October 1977 in New O r l e a n s , Louisiana p. 67
-
78DBR P a p e r No. 858
Division of Building R e s e a r c h
SO MMA IRE
Dans cet article, les critCres provenant des vibrations
causEes par les pas dans le cas des planchers B solives d'acier de longue port6e et B dalle de bEton sont appliqu6s avec quelques changements, aux planchers en beton de longue
portle.
A
cause de leur masse relativement grande et de leur resistance B des charges exercees B court terme, les constructions coul6es sur place ne sont g6neralement passusceptibles de faire l'objet de vibration Elevges pendant
l'occupation normale des bttiments. Cependant, l'utilisation
de planchers prlcoul6s de longue portee 3 supports simples
peut entrarner des problsmes de raisonance rgsultant
d'activitEs rEpgtEes, tels la dance et le battement des mains.
Des Etudes sur place de deux planchers pr6coul6s et d'un
plancher coulE sur place ont servi pour verifier les critsres
Vibration Criteria for Long-Span
Concrete Aoors
By D. E. Allen, J. H. Rainer, and G. Pernica
Synopsis: C r i t e r i a d e r i v e d o r i g i n a l l y f o r walking v i b r a t i o n s i n long-span s t e e l j o i s t f l o o r s w i t h c o n c r e t e deck a r e a p p l i e d , w i t h some a d j u s t m e n t s , t o long-span c o n c r e t e f l o o r s . F i e l d s t u d i e s o f two p r e c a s t and one c a s t - i n - p l a c e f l o o r system a r e used t o v e r i f y c r i t e r i a and t o e s t i m a t e v i b r a t i o n parameters.
Because of i t s r e l a t i v e l y l a r g e mass and i n h e r e n t s t i f f n e s s t o s h o r t - t e n load, c a s t - i n - p l a c e c o n s t r u c t i o n g e n e r a l 1 y i s n o t prone t o u n s a t i s f a c t o r y v i b r a t i o n f o r normal human occupancy. The t r e n d toward
l o n g e r s p a n s , l e s s damping and t h i n n e r s e c t i o n s c o u l d r e s u l t i n problems i f s p e c i a l c a r e i s n o t t a k e n i n t h e d e s i g n . Also l o n g e r spans w i t h lower f r e q u e n c i e s c a n r e s u l t i n s e r i o u s resonance problems i n occupancies where r e p e a t e d human a c t i v i t i e s such a s dancing, c l a p p i n g o r stomping can o c c u r .
~ y w o r d s : beams (supports) ; concrete s
1
abs ; c r i t e r i a ; floors ; human actors engineering;1
ong span ; precast concrete; reinforced concrete; vibrations.Allen, Rainer, and Pemica
D.E. A l l e n , J . H .
Rainer
and G. P e r n i c a are r e s e a r c h o f f i c e r s w i t h t h eDivision
of
B u i l d i n g Research, N a t i o n a l ResearchCouncil
o f Canada.D.E.
Allen has been engaged i n s t r u c t u r a l e n g i n e e r i n g r e s e a r c h i n t h e a r e a s o f s t m c t u r a l s a f e t y and l i m i t s t a t e s d e s i g n , f l o o r v i b r a t i o n and f i r e r e s i s t a n c eo f
w n c r e t e s t r u c t u r e s . J . H . Rainer has been a c t i v e i n e a r t h q u a k e e n g i n e e r i n g r e s e a r c h and measurement o f b r i d g e and b u i l d i n g v i b r a t i o n . G. P e r n i c a h a s been involved i n t h e dynamic a n a l y s i s o f s t r u c t u r e s end i n t h e measurement o f f l o o r and b u i l d i n gvibrations.
V i b r a t i o n s have n o t been a problem i n t r a d i t f o n a l c o n c r e t e f l o o r c o n s t r u c t i o n under normal c o n d i t i o n s o f use and consequent1 y v i b r a t i o n c r i t e r i a have n o t been r e q u i r e d . The t r e n d toward l o n g e r s p a n s w i t h lower f r e q u e n c i e s , 1 i g h t e r p r e c a s t c o n s t r u c t j o n and fewer p a r t i t i o n s , however, may r e s u l t i n problems i n t h e f u t u r e .
nere
i s t h e r e f o r ea
need t o i d e n t i f y where v i b r a t i o n pmblerns can o c c u r and
t o
develop c r i t e r i a t o p r e v e n t u n s a t i s f a c t o r y performance.Experience shows t h a t
there
a r e
d i f f e r e n t s i t u a t i o n s i n which u n d e s i r a b l e v i b t a t i o n ~can
a r i s e and design c r i t e r i a d e r i v e d f o rone
set of
circumstances may n o t apply t o another. Sueh d i f f e r e n c e s a r i s e i n t h e n a t u r e o f t h e v i b r a t i o n source ( e . g . , machinery v s.
f o o t s t e p s ) , t h e s t r u c t u r a l response (e.g., t h e damping e f f e c t s o f n o n - s t r u c t u r a l components and humans) and i n t h e s e n s i t i v i t y o f s p e c i a l equipment o r o f humans engaged i n d i f f e r e n t a c t i v i t i e s . T h i s paper w i l l b e concerned p r i m a r i l y w i t h walking v i b r a t i o n si n
long-span f l o o r s i n o f f i c e , r e s i d e n t i a l arid s i m i l a r "quiet" human occupancies.CRITERIA FOR CONTINUOUS VIBRATION
A c o n s i d e r a b l e amount o f t e s t i n g h a s been c a r r i e d o u t on t h e r e a c t i o n o f humans t o continuous s i n u s o i d a l v i b r a t i o n ( 1 ) . The r e s u l t s shown by t h e hatched a r e a s i n F i g s . 1 and 2, i n d i c a t e t h a t humans v a r y c o n s i d e r a b l y i n t h e i r r e a c t i o n and a r e most s e n s i t i v e i n t h e frequency range o f 2 t o 8 H z .
Against t h i s background of h u m r e a c t i o n Figure 1 shows accept- a b i l i t y c r i t e r i a f o r " q u i e t t t occupancies, e . g . . r e s i d e n c e s , o f f i c e s , s c h o o l s , given i n t h e IS0 d r a f t
for
v i b r a t i o n i n b u i l d i n g s (2) and i n " S t e e l S t r u c t u r e s f o r Buildingstq, CSA S t a n d a r d 516.1-1974 (3).
F i e l d t e s t d a t a are a l s o shown i n Fig. 1 f o r continuous v i b r a t i o n o f s h o r t d u r a t i o n , e . g . . due t o t r a f f i c o r ongoing walking v i b r a t i o n , which i n d i c a t e agreement w i t h the CSA c r i t e r i o n o f 0.5% g a c c e l e r a t i o n . V i b r a t i o n s become more annoying the l o n g e r t h e y l a s t a d t h i s a c c o u n t s f o r t h e d i f f e r e n c e between the CSA c r i t e r i a and IS0 c r i t e r i a which are f o r continuous { e . g . , due t o machinery) a s well a s i n t e r m i t t e n t v i b r a t i o n .Figure 2 shows IS0 (2) and USSR (4) c r i t e r i a f o r " a c t i v e u
bng-Span
Concrete
Floors
f i e l d t e s t o b s e r v a t i o n s c a r r i e d o u t by t h e a u t h o r s . I t appears t h a t f o r "active" occupancies, t h e c r i t e r i a go up by a f a c t o r of 5 t o a b o u t 2.5% g. For v e r y s e n s i t i v e occupancies, e.g., o p e r a t i n g rooms and f l o o r s s u p p o r t i n g s e n s i t i v e measuring d e v i c e s , t h e c r i t e r i a should b e m o r e s t r i n g e n t t h a n t h o s e given i n Fig. 1 .
The c r i t e r i a shown i n F i g s . 1 and 2 a r e q u i t e g e n e r a l b u t a s y e t a r e n o t d i r e c t l y a p p l i c a b l e i n d e s i g n , e x c e p t p o s s i b l y f o r d e s i g n by performance t e s t i n g . One reason i s t h a t t h e l o a d i n g , p a r t i c u l a r l y t h a t
due t o walking, i s n o t amenable t o simple s t r u c t u r a l d e s i g n c a l c u l a - t i o n s . The o t h e r reason i s t h a t t h e c r i t e r i a do n o t t a k e i n t o account v i b r a t i o n decay (damping) which h a s been found t o b e p a r t i c u l a r l y important f o r walking v i b r a t i o n s .
CRITERIA FOR WALKING VIBRATIONS
Problems w i t h walking v i b r a t i o n s have r e c e n t l y o c c u r r e d i n new forms of long-span c o n s t r u c t i o n , p a r t i c u l a r l y long-span s t e e l j o i s t f l o o r s w i t h t h i n c o n c r e t e deck and open f l o o r p l a n . The t r a d i t i o n a l s t i f f n e s s r u l e s , such a s l i m i t i n g d e f l e c t i o n under l i v e load t o span/ 360 o r l i m i t i n g r a t i o o f span t o depth o f a s u p p o r t i n g s t e e l beam t o 20, have r e s u l t e d i n u n s a t i s f a c t o r y v i b r a t i o n s i n a number o f c a s e s .
Experience w i t h walking v i b r a t i o n s i n long-span f l o o r s h a s shown t h a t discomfort i s caused p r i n c i p a l l y by v i b r a t i o n a t o r n e a r t h e fundamental frequency and t h a t annoyance i s s t r o n g l y a f f e c t e d by damping
-
t h e l e s s t h e damping t h e more t h e v i b r a t i o n s from s u c c e s s i v e f o o t s t e p s merge t o g e t h e r and t h e more annoying i s t h e v i b r a t i o n . V i b r a t i o n s i n t h e h i g h e r modes g e n e r a l l y damp o u t q u i c k l y and do n o t c a u s e discomfort.S u b j e c t i v e e v a l u a t i o n s o f many e x i s t i n g f l o o r s have been r e l a t e d t o t h e f l o o r v i b r a t i o n r e s p o n s e a s measured by t h e h e e l impact t e s t (up on t h e t o e s , down on t h e h e e l s ) , t h a t i s t o t h e measured frequency, damping and peak a c c e l e r a t i o n from h e e l impact a f t e r f i l t e r i n g o u t t h e h i g h e r modes. C r i t e r i a r e l a t e d t o t h e s e f l o o r p r o p e r t i e s a r e shown by t h e hatched l i n e s i n Fig. 3 f o r "quiet" occupancies ( r e s i d e n c e s , o f f i c e s , e t c . ) . These c r i t e r i a a r e based on a v a i l a b l e f i e l d t e s t r e s u l t s (5). and a r e an e x t e n s i o n t o t h o s e proposed by Lenzen i n 1965
( 6 ) . Most o f t h e f l o o r s were o f s t e e l j o i s t and beam c o n s t r u c t i o n w i t h c o n c r e t e s l a b , b u t t h e c r i t e r i a should b e a p p l i c a b l e t o any type of long-span f l o o r c o n s t r u c t i o n . They w i l l s u b s e q u e n t l y b e a p p l i e d t o c o n c r e t e c o n s t r u c t i o n .
The c r i t e r i a i n Fig. 3 a r e , however, r e s t r i c t e d t o s p a n s g r e a t e r t h a n 25 f t (8 m) and f r e q u e n c i e s l e s s than 10 Hz; t h e y a r e n o t
a p p l i c a b l e t o short-span o r l i g h t f l o o r s . The main reason f o r t h i s
i s
t h a t humans a c t a s shock a b s o r b e r s which a r e e f f e c t i v e i n damping o u t walking v i b r a t i o n s i n l i g h t f l o o r s , b u t n o t i n heavy f l o o r s . The c r i t e r i a f o r l i g h t , short-span f l o o r s a r e r e l a t e d more t o t h e m t i o n caused b y r e p e a t e d s t a t i c d e f l e c t i o n than t o v i b r a t i o n response i n t h e fundamental modes. C r i t e r i a r e l a t e d t o s t a t i c d e f l e c t i o n under p o i n t l o a d a r e t h e r e f o r e more a p p r o p r i a t e f o r d e s i g n . Short-span c o n c r e t e s l a b s a r e g e n e r a l l y v e r y s t i f f t o suddenly a p p l i e d p o i n t load and,
Allen,
Rainer,
and
Pemica
consequently, walking v i b r a t i o n s a r e n o t a problem.APPLICATION OF VIBRATION CRITERIA
TO CONCRETE STRUCTURES
Table
1 c o n t a i n s case s t u d i e s o f t h r e e t y p e s o f long-span c o n c r e t e c o n s t r u c t i o n : p r e c a s t double T f s i n a p a r k i n g a r e a , p r e c a s t s t a n d s i n astadium and a c a s t - i n - p l a c e two-way beam and s l a b o f f i c e f l o o r . The f i r s t two r e p r e s e n t " a c t i v e t ' occupancies and t h e t h i r d a "quiet" occupancy. Table 2 c o n t a i n s measured v i b r a t i o n c h a r a c t e r i s t i c s
for
d i f f e r e n t tests c a r r i e d o u t on t h e s e f l o o r s . Peak a c c e l e r a t i o n s
f r o m
normal use a c t i v i t y , i . e . , walking o r d r i v i n g , a l o n g w i t h a s d j e c t i v e assessment o f v i b r a t i o n a c c e p t a b i l i t y , a r e i n c l u d e d i n F i g s . 1 and 2. Measured h e e l impact a c c e l e r a t i o n f o r t h e o f f i c e f l o o r , p l o t t e d i n Fig. 3, f a l l s s l i g h t l y below t h e c r i t e r i o n for 3% damping; i n t h i s c a s e t h e v i b r a t i o n , which was b a r e l y n o t i c e a b l e t o most people, annoyed o n e s e n s i t i v e person l o c a t e d n e a r the i n t e r s e c t i o n o f two walkways. Such c a s e s a r e b e t t e r r e s o l v e d by r e l o c a t i o n than by using c o n s e r v a t i v e d e s i g n c r i t e r i a .
To use t h e v i b r a t i o n c r i t e r i a o f F i g . 3 f o r f l o o r d e s i g n , one has t o e s t i m a t e fundamental frequency, f , damping and h e e l impact
a c c e l e r a t i o n , a
.
These parameters w i l l now b e d i s c u s s e d .Fundamental frequency f o r simply- supported one-way systems i s e s t i m a t e d from t h e beam formula:
f = 3 1 F (= 0 . 0 0 4 9 6 i n S I u n i t s ) w L where E = t h e modulus o f e l a s t i c i t y , p s i (gPa), I = t h e moment o f i n e r t i a , i n . (mm4), w = t h e dead weight, l b / i n . (kN/m), L = t h e span, i n . (m)
.
For the p r e c a s t
T's,
t h e c a l c u l a t i o nis
s t r a i g h t f o w a r d . For t h e p r e - c a s t s t a n d s , which are t i e d t o g e t h e r t o p r e v e n t t w i s t i n g o f t h e unsymmetric c r o s s - s e c t i o n s , t h e frequency was determined a b o u t t h e minor p r i n c i p a l axis, i . e . , v i b r a t i o n t h a t is normal t o the p l a n e o f t h e s t a n d s . For t h e c a s t - i n - p l a c e beam and s l a b system, t h e c a l c u l a - t i o n of frequency was based on a n assumed simply-supported T s e c t i o n with f l a n g e w i d t h equal t o t h e t r i b u t a r y area o f the beam. As seen i n Table 2, the assumption o f simple support g e n e r a l l y u n d e r e s t i m a t e s t h e frequency, even f o r p r e c a s t elements. Although more s o p h i s t i c a t e d a n a l y t i c a l t e c h n i q u e s a r e a v a i l a b l e t o determine frequency, t h e s ea r e
g e n e r a l l y n o t warranted u n l e s s resonance i s l i k e l y t o b e a problem. Damping depends p r i m a r i l y on the presence o f n o n - s t r u c t u r a l components such a s p a r t i t i o n s . The damping r a t i o s suggested for j o i s t f l o o r s
131
a r e 3% ofc r i t i c a l
f o r t h e bare f l o o r , 6% f o r f u l l y f i n i s h e d f l o o r w i t h open o f f i c e f l o o r p l a n . and 1 2 % f o r f u l l h e i g h t p a r t i t i o n s .The measurements i n Table 2 i n d i c a t e t h a t the damping r a t i o f o r f u l l y contintmus c a s t - i n - p l a c e c o n c r e t e f l o o r s i s o f the o r d e r of 2 to 3% and
Long-Span Concrete
Floors
f o r i n t e r c o n n e c t e d p r e c a s t beams i s about 4 % . F u r n i t u r e , c e i l i n g , rug, low p a r t i t i o n s , e t c . used i n open o f f i c e f l o o r p l a n s i n c r e a s e t h e damping r a t i o by about 1 t o 3%. F u l l h e i g h t p a r t i t i o n s i n c r e a s e t h e damping r a t i o by a f u r t h e r 2 t o 4%. Non-structural elements, such a s p a r t i t i o n s , t h e r e f o r e appear t o b e l e s s e f f e c t i v e i n i n c r e a s i n g t h e damping r a t i o o f c a s t - i n - p l a c e c o n c r e t e a s compared w i t h j o i s t f l o o r s . T h i s can b e a t t r i b u t e d t o t h e g r e a t e r mass and l e s s o p p o r t u n i t y f o r f r i c t i o n a l damping i n t h e connections.
Peak a c c e l e r a t i o n from h e e l impact f o r long-span s t r u c t u r e s can b e e s t i m a t e d by c a l c u l a t i n g t h e fundamental mode response o f an e q u i v a l e n t
I
simply-supported beam t o a h e e l impulse, (67 W a s ) . The r e s ~ i l t i n g a c c e l e r a t i o n is c l o s e l y approximated by ( 5 ) : I , ( F i g , 4 ) , o f 15 l b - swhere M i s t h e e q u i v a l e n t mass o f a simple o s c i l l a t o r , which i n t h i s c a s e is 0.64 times t h e mass o f t h e beam. I f t h e beam mass i s r e p l a c e d by W/g where W i s t h e weight i n k i p s (kN) and g
is
t h e a c c e l e r a t i o n due t o g r a v i t y , t h e na (%g) = 1 3 . 3 f / W (= 59 f/W i n S I u n i t s )
I
I
T h i s formula can b e used f o r i s o l a t e d beams o r narrow b r i d g e s . I t can a l s o b e used f o r f l o o r systems i f a r e a s o n a b l e e s t i m a t e i s made o f t h e " e f f e c t i v e " width o f " e f f e c t i v e " number o f a d j a c e n t elements t h a t p a r t i c i p a t e i n r e s p o n s e t o h e e l impact.For j o i s t f l o o r s , t h e e f f e c t i v e width was taken a s 0.64 (60 t c ) where tc i s t h e c o n c r e t e s l a b t h i c k n e s s and 60 tc r e p r e s e n t s t h e d i s t a n c e between nodal l i n e s o f v i b r a t i o n ( 5 ) . For c a l c u l a t i n g a, i n Table 2, i t was assumed t h a t f o r t h e p r e c a s t T ' s and s t a n d s t h r e e elements were l o c a t e d between t h e nodal l i n e s o f v i b r a t i o n . For t h e c a s t - i n - p l ace beam system, t h e t r i b u t a r y width supported by t h e beam (20 f t ) was taken a s t h e e f f e c t i v e width. More a c c u r a t e methods o f e s t i m a t i n g e f f e c t i v e width a r e c o n t a i n e d i n Ref. 7 .
An a c c u r a t e c a l c u l a t i o n o f f l o o r response t o h e e l impact, p a r t i c u l a r 1 y f o r c a s t - i n - p l a c e continuous c o n s t r u c t i o n , can b e v e r y d i f f i c u l t . In g e n e r a l , however, continuous c o n s t r u c t i o n should b e assumed t o b e simply-supported, o r n e a r l y s o , s i n c e i n t h e fundamental mode a d j a c e n t f l o o r p a n e l s v i b r a t e i n o p p o s i t e d i r e c t i o n s . Also, approximate e s t i m a t i o n s o f response parameters a r e g e n e r a l l y adequate f o r a s s e s s i n g v i b r a t i o n comfort.
Allen, Rainer, and Pemica
RESONANCE PROBLEE
I f t h e frequency o f t h e f l o o r i s c l o s e t o t h e frequency o f t h e d i s t u r b a n c e , l a r g e o s c i l l a t i o n s can b u i l d up. Dancing, c l a p p i n g and o t h e r s i m i l a r r e p e t i t i v e human a c t i v i t i e s can c r e a t e p e r i o d i c f o r c e s i n
t h e frequency range 1 t o 4 Hz. A commentary t o t h e National Building Code o f Canada (8) t h e r e f o r e recommends t h a t f l o o r s s u p p o r t i n g such a c t i v i t i e s should n o t have n a t u r a l f r e q u e n c i e s l e s s than a b o u t 5 Hz, (8 Hz i n t h e c a s e of dance f l o o r s s i n c e some resonance can b u i l d up i f t h e dance b e a t corresponds t o every second c y c l e o f n a t u r a l frequency). The Netherlands code (9) recommends t h a t f l o o r s should n o t have
f r e q u e n c i e s 3 Hz o r l e s s f o r walking (walking f o o t s t e p s o c c u r a t about 2 Hz), and n o t l e s s t h a n 5 Hz f o r jumping; t h e s e l i m i t a t i o n s may b e waived i f t h e p e r m n e n t l o a d i s 5 kPa (100 p s f ) o r m r e f o r f l o o r s l a b s o r 150 kN (35 k i p s ) o r m r e f o r f l o o r beams.
The w o r s t frequency f o r dance f l o o r s i s i n t h e neighborhood o f 1 1/2 t o 3 Hz; a number o f t h e s e have been b u i l t i n r e c e n t y e a r s and have experienced l a r g e u n s a t i s f a c t o r y v i b r a t i o n l e v e l s . Figure 5
( c a s e 28 of Tables 1 and 2) shows an example o r resonance measured i n a p r e c a s t grandstand ( n a t u r a l frequency 2 1 / 2 Hz and dead weight >
100 p s f ) d u r i n g a rock and r o l l c o n c e r t where a c c e l e r a t i o n s up t o 34% g b u i l t up during c l a p p i n g and stomping.
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 Building
Research, National Research Council o f Canada and i s p u b l i s h e d w i t h t h e approval of t h e D i r e c t o r o f t h e D i v i s i o n .
REFERENCES
1 . H a r r i s , C.M. and C.E. Crede. Shock and Vibration Handbook, Vol. 111, Ch. 44, p . 22, McGraw H i l l , 1961.
2.. D r a f t Recommendations f o r V i b r a t i o n s and Shock L i m j t s f o r Occupants o f B u i l d i n g s , IS0 TC108, 1974.
3. Guide o n F l o o r V i b r a t i o n s , Appendix G t o S t e e l S t r u c t u r e s f o r B u i l d i n g s , CSA Standard S16.1-1974. Can. S t a n d a r d s Assoc., Rexdal e O n t a r i o .
4. Environment Standards f o r t h e Design o f I n d u s t r i a l E n t e r p r i s e s ( i n Russian) SN 245-1971, GOSSTROI, USSR.
5 . Allen, D.E. and J . H . Rainer. V i b r a t i o n C r i t e r i a f o r Long-Span F l o o r s . Can. J . Civ. Eng., Vol. 3 , No. 2, June 1976.
6. Lenzen,
K.H.
Vibration of S t e e l J o i s t s . AISC Engineering J o u r n a l , No. 3, Vol. 3, p . 133, 1966.7. Galambos, T. V. V i b r a t i o n o f S t e e l J o i s t - C o n c r e t e S l a b Floors. Techn., Dig. No. 5, S t e e l J o i s t I n s t . , Arlington, Va, 1973.
Long-Span Concrete
Floors
73
8. S e r v i c e a b i l i t y C r i t e r i a f o r D e f l e c t i o n s and V i b r a t i o n s .
Commentary A, Supplement 4 t o National Building Code o f Canada 1977. Nat. Res. Council o f Canada, Assoc. Com. Nat. Bldg. Code, Ottawa.
9. Regulations f o r t h e C a l c u l a t i o n o f Building S t r u c t u r e s
-
General C o n s i d e r a t i o n s and Loading ( i n Dutch). TGB 1972. NEN 3850.Nederlands N o r m a l i s a t i e - I n s t i t u u t , R i j s w i j k .
Table 1
-
F i e l d S t u d i e s o f Long-span Concrete F l o o r Systems1 f t = 0.305 m 1 p s f = 0.048 kPa
Table 2
-
V i b r a t i o n C h a r a c t e r i s t i c s f o r Cases i n Table 1Frequency, Hz Measured
.
Peak
From Measured Peak Acceleration,Heel Impact, % g
Case
.
-
Damping,.
% g, FromMeasured Calculated (1) % C r i t i c a l Measured C a l c u l a t e d (2)
I 1 A 5.4 4.0 3-4 1.6 0 . 8 ( 1 . 1 0.5 (walking) 1.7 ( d r i v i n g ) 1 B 9 . 3 9.2 4-4.5 2.8 2.8 (2.8) 0.7 (walking) 3.4 ( d r i v i n g ) 2A 4.8 2.6 4-5 1.1 1 . 2 ( 2 . 2 ) O . S ( w a l k i n g ) 2B 2.6 2.2
- -
--
--
34 (rock & r o l l ) 3A 7.2 5 . 3 2-2.6 1.2 0 . 8 ( 1 . 1 0 . 3 (walking) 38 6.7 5.3 3- 5 1-1.5 0.8 (1.0) 0.3 (walking) 3C 7.7 5 . 3 6.3-6.9 0.9 0 . 8 (1.2)----
Notes: (1) Assumes simple s u p p o r t .
Long-Span
Concrete
Floors
'OOr----l
F I E L D TEST D A T A F O R S H O R T - T E R M C O N T I N U O U S V I B R A T I O N : J O I S T F L O O R S ' ~ ' 0 S A T I S F A C T O R Y U N S A T I S F A C T O R Y R/C F L O O R ( C A S E 3 ) B O R D E R L I N E C S A ~ 1 6 . 1 ' ~ ) ( S H O R T TERM V I B R A T I O N ) : O F F I C E S , R E S I D E N C E S A N D S C H O O L S,-.
1 ~ 0 " ' ( C O N T I N U O U S O R I N T E R M I T T E N T V I B R A T I O N ) : O F F I C E S R E S I D E N T I A L 1 2 4 6 1 0 2 0 F R E Q I J E N C Y , H z F I G U R E I H U M A N R E S P O N S E C R I T E R I A F O R C O N T I N U O U S V I B R A T I O N : " Q U I E T " O C C U P A N C I E SWen,
Rainer,
and
kmica
l o o
7
F I E L D TEST D A T A FOR SH0FiT'-TERM C O N T I N U O U S V I B R A T I O N
F R E Q U E N C Y , H z
F I G U R E 2
H U M A N RESPONSE C R I T E R I A FOR C O N T I N U O U S V I B R A T I O N : " A C T I V E " O C C U P A N C I E S
---
C R I T E R I A F O R W A L K I N G V I B R A T I O N S A S G I V E N B Y H E E L I M P A C T TEST-
C R I T E R I A F O R C O N T I N U O U S V I B R A T I O N F R E Q U E N C Y , H z F I G U R E 3 A N N O Y A N C E C R I T E R I A FOR F L O O R V I B R A T I O N S : ' " Q U I E T " O C C U P A N C I E SAllen,
Rainer,
and
Pemica
-
-
2-
4 0 0-
-
lil U =2
300-.
2 0 0--
I = 15 1b.r 100-
a l o 20 S O 4 0 S O 6 0 TIME. mt FIGURE 4HEEL IMPACT (REF. 9 )
FIGURE 5
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