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An Approach to a vibration standard for buildings
Rainer, J. H.
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An Approach to a Vibration
Standard for Buildings
by J.H. Rainer
A N A L Y Z E D
Appeared in
C.S.C.E. 1986 Annual Conference
"Specialty Conference on Computer Applications" Toronto, Ontario, May 12-16, 1986
Proceedings, Vol. 4, Structures, 19p. (IRC Paper No. 1387)
Reprinted with permission
Price $2.00 NRCC 26052
SHOUT ABSTKACT
A framework i s p r e s e n t e d f o r e s t a b l i s h i n g a v i b r a t i o n s t a n d a r d f o r b u i l d i n g s . I t s major components comprise a d e s c r i p t i o n of t h e s o u r c e f u n c t i o n , t h e r e s p o n s e d e t e r m i n a t i o n a t t h e r e c e i v e r , and t h e c r i t e r i a of a c c e p t a b l e v i b r a t i o n a p p l i c a b l e a t t h e r e c e i v e r .
C e t t e communication propose d 1 6 t a b l i r une n o u v e l l e norme de v i b r a t i o n p o u r l e s b z t i m e n t s q u i s e r a i t p r i n c i p a l e m e n t c o n s t i t u g e d'une d e s c r i p t i o n de l a s o u r c e d e v i b r a t i o n , d'une mgthode pour c a l c u l e r l a rgponse du r s c e p t e u r e t de c r i t s r e s d e v i b r a t i o n a c c e p t a b l e s au n i v e a u du r s c e p t e u r .
AN APPROACH TO A VIBRATION STANDARD FOR BUILDINGS
RAZNER
,
J.
HansABSTRACT
It is proposed that a new vibration standard for buildings be subdivided in terms of source, transmission path, and receiver. Vibration problems would be classified according to methods employed to effect a solution. Detailed descriptions could then be allocated for common vibration sources and criteria applicable to buildings.
The vibration source is described as a force or displacement function; this includes excitation from people and machinery within buildings, traffic and construction activity propagated through the ground outside buildings, and fluid flow and impulse forces transmitted by air; or water. The properties of the transmitting medium are described by the frequency response function, which can be calculated or obtained experimentally (in some cases wave
propagation methods may be required). Response calculations are carried out according to standard mathematical techniques in the time or frequency domain. The appli~able~criteria are associated with the receiver of the vibrations, that is, the occupants of buildings, the contents, or the structure itself. Criteria, if available, are taken from national or international standards; others may need to be developed. A list of topics needing further study.is provided.
1. INTRODUCTION
Vibrations occur everywhere in the natural and man-made environment. The earth trembles as a result of a rupture in its crust, a volcanic eruption, sea waves pound the shore, and wind moves water, trees and buildings.
Machinery and people in buildings cause floors to vibrate, and rail and road traffic can shake entire buildings, often to the annoyance of occupants. But unperceived vibrations may also be detrimental to the proper functioning of such contents of buildings as sensitive instruments or certain industrial processes. While vibrations are rarely a safety hazard (with the obvious exception of large earthquakes and high winds), they can result in loss of function or serviceability ranging from simple annoyance to loss of economic benefits
.
Problems with vibrations in buildings have generally been treated on an ad hoc basis after the problem has been encountered. As structures become lighter with the more efficient use of materials, however, vibration sources increase. At the same time, demands for vibration limits become more
stringent and incorporation of vibration criteria into the design process becomes more important. A number of organizations, therefore, have recently addressed aspects of vibration problems in buildings and other structures. Among them are 65MDB Committee of RILEM, Task Group V/4 of CEB, and Working Group WG2 of ISO/TC98/SC2. The approach presented here has been prepared for submission to the IS0 working group, "Vibration Criteria for Serviceability of Structures." It is desirable that the outline of such a standard should be presented to interested investigators, researchers, and other users so that they will be encouraged to contribute their expertise as well.
Vibration problems tend to be very complicated, and some may not be amenable to a full quantitative solution with a given set of resources. Simplifying assumptions and empirical methods often have to be employed.
Methodologies and specialized techniques for the prediction of vibrations will continue to be developed so that a standard in this field will continue to be updated periodically.
2. OBJECTIVES OF A VIBRATION STANDARD
The objectives of a vibration standard for buildings are many. It should:
1) be able to deal with all cases within its scope;
2 ) reflect the current state of knowledge;
3 ) be sufficiently flexible to accommodate developments in the near
future and act as a catalyst for the development of improved methods or techniques;
4 ) be useful: usefulness depends on the particular perspective of the users of the standard, who include
a) international or national standards-writing bodies, b) vibration engineers,
c) building designers and practitioners, d) consumers or users of the end product.
It can readily be appreciated that the degree of detail and sophistication required in a standard varies for each category. Nevertheless, a common framework should be useful.
An important role of the proposed standard is to standardize the source function for different actions and the criteria that apply to various
receivers. The word "action" derives from the International Standard
ISO/DIS 2394 (1) and is used as a general term to describe the source (forces or loads, deformations, temperature changes, etc.).
For the purposes of this proposed standard the term "building" is used in the sense defined in the 1985 National Building Code of Canada: "any structure used or intended for supporting or sheltering any use or
occupancy."
3. OUTLINE FOR A VIBRATION STANDARD
3.1 Serviceability Limit State
As most vibration problems in buildings do not involve the immediate safety of the structure, the applicable design basis is the serviceability limit state (2); the materials usually behave elastically, and in current practice the load factors and resistance factors for this limit state are
taken to be 1.0 (3). This implies that the given loads and criteria are
treated as known deterministic quantities. Thus, no specific allowance is made for variability of dynamic loads, material properties, or the criteria
be desirable to account for such variables, but neither the necessary simple methodology nor the required data on variability of loads (the structure and
the criteria) are as yet available, although guidelines for their development have been addressed ( 1 , 2 ) .
3.2 Structure of Proposed Vibration Standard
The structure of the proposed standard is outlined in Table 1. In
physical terms the problem concerns a vibration source that affects a receiver (i.e., a person or an object) at some distance from the source; this vibration can be acceptable or objectionable. The prediction model thus needs to
include 1) the source, 2) the transmitting medium from the source to the receiver and the determination of the resulting vibrations there, 3) the applicable criterion at the receiver. Using these major subdivisions, it is desirable to proceed in two stages.
Stage 1 is a general statement of principles for the proposed standard. It consists of a classification of available methods and the type of
information required to solve vibration problems in buildings. It should prove useful to standards-writing bodies and other users by pointing out consistent sets of data that need to be considered. It could serve as an inspiration for development of new methods of solving vibration problems.
Stage 2 provides specific values for the various sources of vibrations and applicable criteria for the receivers in buildings. This would be of major interest to designers and analysts in solving vibration problems during
the design process or in retrofitting existing buildings. 3.2.1 Stage 1: Classification
The classification scheme for vibration problems leads from the general type of solution to a simplified one, then to the approximate one. Three categories are formed according to type of information available or desired, as outlined in Table 2.
Category A comprises a general statement of a prediction model. The source description can be a function of time and space, possibly dependent on the response of the supporting medium or structure. This concerns dynamic sources, either stationary or moving, that interact with the supporting medium
and thereby modify the forces applied to the structure. Examples are sprung vehicles moving on flexible structures or on the ground.
Determination of the response at the receiver employs methods of mechanics and mathematics; in practice, however, they may be difficult to carry out. The receiver may be in a fixed location or in a number of
locations. For the latter, a probable worst case response would need to be established.
The criteria that apply to the receiver need to be determined by
experimental or theoretical means or selected from existing international or national standards.
Category B comprises cases in which the source is stationary in space, or can be considered stationary. Various possible combinations of source descriptions, response determinations at the receiver, and applicable criteria are presented in Table 2. They need to be consistent in terms of variables employed at each step, from source to receiver to applicable criteria. Simplified models based on principles of mechanics such as equivalent
single-degree-of-freedom models are included. The conditions that need to be satisfied in such simplified models should be described.
Category C encompasses cases that can be classified as empirical and
are generally based on correlations with observed behaviour rather than on principles of mechanics. Examples include simple blasting criteria for the onset of building damage, and floor vibration criteria for walking (4,5). Empirical criteria should have well-defined scope, should confirm field observations, and state limits or ranges of applicability. The reliability and variability of the results should be determined whenever possible.
Although the listing of prediction models is generally in decreasing order of sophistication, it does not necessarily follow that the same rank ordering applies to the appropriateness of application to a specific problem or to the order of the degree of accuracy of the results that can be expected. Simple methods can often be more effective than highly sophisticated ones, although the latter may sometimes be necessary.
3 . 2 . 2 Stage 2: Specific Design Inf ormation
Source functions or dynamic actions: Source functions are specific to particular situations, including activity, machinery, traffic, small
earthquakes, wind, and impulse sources such as blasting (Table 3 ) . For some of these, specific quantitative values exist, but for others they need to be developed.
Response calculation: Determination of the response at the receiver arising from an action at the source can be complicated, and mathematical modelling of the problem generally requires skill and judgement. Methods of vibration analysis are available that employ differential equations, numerical techniques such as finite element methods, or modal analysis. Simplified methods such as equivalent singledegree-of-freedom oscillators are
particularly useful in the design phase when such approximations are
appropriate. The mathematical model needs to account for special features such as damping devices or vibration isolators for either components or the entire building. These analytical techniques would not be standardized unless the method of solution were to form part of an empirical procedure. Brief descriptions of analysis methods are presented in Table 4.
Vibration criteria: Vibration criteria, which are associated with the receiver, can be divided into three major classes: human occupancy, building contents, and building structure. Each can be further subdivided as
summarized in Table 5. The criteria pertaining to various receivers are taken from available standards, but their applicability to a specific situation has to be carefully assessed. The suggested criteria at this early stage of development are illustrative only and may not assure satisfactory performance in all situations.
4. REMEDIAL MEASURES
A vibration standard should concern itself with measures to alleviate unacceptable vibration levels in existing buildings. This would involve the following steps:
1) assessment of existing vibrations;
2) conrparison with acceptable criteria and establishment of desired vibration levels;
3) implementation of necessary changes; 4 ) verification of effectiveness of changes.
The recommendations, except for the criteria, would be advisory only.
4.1 Assessment of Existing Vibrations
This aspect usually involves vibration measurements taken at or near the source or the receiver and analysis and interpretation of the results. Such a program can vary from simple determination of vibration levels by means
I
of a hand-held vibration meter (or observing the effects of vibrations) to full-scale determination of modal properties involving dynamic excitation tests. In general, such work must be carried out by specialists. Few standards for measurement of structural vibrations exist, although some are
, now being developed at national and international levels.
4.2 Comparison with Criteria
If the criteria of acceptability have a rational basis, they can be
used in assessing existing vibrations. Care must be taken not to misuse those associated with a specific type of excitation or environment, or those forming part of an empirical procedure, e.g., criteria associated with the heel impact
I test for assessment of floor vibrations, or criteria associated with onset of
blasting damage for structures. Analysis of existing vibration levels and the I
desired criteria will indicate the necessary changes in vibration levels and
vibration characteris tics.
!
I 4.3 Implementation
Once the desired reduction in vibration levels has been established, the method of achieving it has to be devised. This can take the form of
I
additional damping, changes in the frequency of excitation and the resonancefrequency of the structural system, moving or removing the source or receiver, and adding (or removing) stiffness and mass. The effect of possible remedial measures needs to be carefully assessed so as not to cause inadvertent
I
deterioration in the vibration environment.4.4 Verification
Verification of the effectiveness of any recommendations is important.
4.5 R e t r o f i t
Where t h e d e s i g n a g a i n s t v i b r a t i o n i s n o t c l e a r l y a p r a c t i c a l one o r t h e u n c e r t a i n t i e s a r e t o o g r e a t , i t may be d e s i r a b l e t o proceed on t h e u n d e r s t a n d i n g t h a t f u r t h e r measures may have t o be t a k e n i f t h e v i b r a t i o n behaviour of t h e f i n i s h e d s t r u c t u r e s h o u l d prove u n s a t i s f a c t o r y . T h i s can be a n a c c e p t a b l e d e s i g n s t r a t e g y . By p r o v i d i n g a p p r o p r i a t e a c c e s s r o u t e s o r mountings f o r p o s s i b l e damping d e v i c e s one can o f t e n s i m p l i f y t h e
implementation of needed r e t r o f i t measures.
5. VIBRATION DESIGN GUIDELINES
The f o l l o w i n g examples i l l u s t r a t e how e x i s t i n g v i b r a t i o n g u i d e l i n e s can f i t i n t o t h e proposed scheme.
5.1 F l o o r V i b r a t i o n s from Coordinated A c t i v i t y
The f o r c e s F ( t ) g e n e r a t e d by c o o r d i n a t e d a c t i v i t y such a s jumping, d a n c i n g , and e x c e r c i s e s c a n be e x p r e s s e d by ( 6 , 7 ) : F ( t ) =
1
a n wp sin(21mf + (n) n where a n = dynamic l o a d f a c t o r , w = weight of p e o p l e , P f = f r e q u e n c y of e x c i t a t i o n , $ = phase a n g l e , n = i n t e g e r r e f e r r i n g t o t h e harmonic component.Suggested v a l u e s of a and w a r e g i v e n i n Commentary A , Supplement No. 1 t o n P
t h e N a t i o n a l B u i l d i n g Code of Canada 1985 (6).
The r e s p o n s e h a s t o be e v a l u a t e d a t t h e a c t u a l l o c a t i o n , o r
h y p o t h e t i c a l r e c e i v e r . A g e n e r a l d e s c r i p t i o n of t h e dynamic f l o o r p r o p e r t i e s would c o n s i s t of t h e frequency response f u n c t i o n ( 8 ) , b u t f o r a f u l l s o l u t i o n of t h e v i b r a t i o n s i g n a t u r e t h e c o n v o l u t i o n between f o r c i n g f u n c t i o n and e n t i r e impulse r e s p o n s e f u n c t i o n of t h e v i b r a t i n g s t r u c t u r e i s r e q u i r e d . For most p r a c t i c a l problems, however, knowledge of t h e n a t u r a l f r e q u e n c y and damping of t h e e q u i v a l e n t single-degree-of-freedom o s c i l l a t o r of t h e l o w e s t few modes s u f f i c e s ; o f t e n o n l y t h e fundamental mode needs t o be c o n s i d e r e d . The method p r e s e n t e d i n Commentary A ( 6 ) employs t h e l a t t e r s i m p l i f i e d approach.
C r i t e r i a t h a t e x p r e s s t h e l i m i t s of a c c e p t a b l e v i b r a t i o n s a r e n o t a l w a y s w e l l d e f i n e d . Not o n l y does a c c e p t a b i l i t y change w i t h t y p e and d u r a t i o n of v i b r a t i o n , but i t a l s o depends on t h e environment i n which t h e v i b r a t i o n s a r e p e r c e i v e d . This i s r e f l e c t e d i n t h e c r i t e r i a p r e s e n t e d i n References 6 and 7, where 5% g r a v i t y i s s u g g e s t e d f o r a c c e p t a b i l i t y i n a c t i v e o c c u p a n c i e s ; f o r normal r e s i d e n c e s 0.5% g i s s u g g e s t e d f o r w a l k i n g v i b r a t i o n s o c c u r r i n g on a n i n t e r m i t t e n t b a s i s ( 4 ) .
Other c r i t e r i a have r e c e n t l y been p r e s e n t e d : ANSI S3.29-1983 ( 9 ) , BS 6472 ( l o ) , and t h e d r a f t s t a n d a r d ISOIDIS 263112 (11). I n terms of t h e proposed s t a n d a r d , t h e s o u r c e f u n c t i o n would be g i v e n by i t e m l b , Table 3, and t h e c r i t e r i a by s o u r c e l b , Table 5, under Occupancy. Concerning t h e
c l a s s i f i c a t i o n of t h e s o l u t i o n method, S t a g e 1, t h i s v i b r a t i o n g u i d e l i n e would c o r r e s p o n d t o i t e m B1 i n Table 2, f o r which t h e f r e q u e n c y r e s p o n s e f u n c t i o n i s t h e s i m p l i f i e d , e q u i v a l e n t single-degree-of-freedom o s c i l l a t o r model f o r t h e f l o o r . 5.2 V i b r a t i o n s of F o o t b r i d g e s A method of d e t e r m i n i n g t h e adequacy of v i b r a t i o n s of f o o t b r i d g e s o v e r highways i s c o n t a i n e d i n t h e 1983 O n t a r i o Highway Bridge Design Code
Commentary (12) and i n t h e B r i t i s h Standard BS 5400 (13). A s o u r c e f u n c t i o n , F, i n newtons i s s u g g e s t e d , F = 180 s i n wt It i s n o t , however, u s e d e x p l i c i t l y . I n s t e a d , a r e s p o n s e c a l c u l a t i o n f o r a c c e l e r a t i o n , a , i s employed a s f o l l o w s : where f = f i r s t n a t u r a l f r e q u e n c y , w = maximum s t a t i c s u p e r s t r u c t u r e d e f l e c t i o n (m) due t o a v e r t i c a l S c o n c e n t r a t e d f o r c e of 700 N, K = c o n f i g u r a t i o n f a c t o r t o a c c o u n t f o r c o n t i n u i t y , a = a c c e l e r a t i o n ( m / s 2 ) ,
+
= r e s p o n s e a m p l i f i c a t i o n f a c t o r , i n g r a p h i c a l form.The r e s u l t i n g a c c e l e r a t i o n i s compared w i t h t h e a c c e p t a b i l i t y c r i t e r i o n . For example, BS 5400 ( 1 3 ) s p e c i f i e s f 4 q (m/s2) f o r highway f o o t b r i d g e s , whereas OHBC ( 1 2 ) s p e c i f i e s h a l f t h a t v a l u e . For f o o t b r i d g e s t h a t connect b u i l d i n g s o r c a r r y p e d e s t r i a n s w i t h i n b u i l d i n g s , however, more s t r i n g e n t r e q u i r e m e n t s s i m i l a r t o t h o s e a p p l i c a b l e t o f l o o r s a r e needed.
T h i s p r o c e d u r e can be r a t i o n a l i z e d t o conform t o t h e proposed s t a n d a r d where t h e s o u r c e f u n c t i o n f o r w a l k i n g may be found i n Table 3, i t e m l a ) , t h e c r i t e r i a i n T a b l e 5 u n d e r Occupancy and s o u r c e l a ) . The method of r e s p o n s e c a l c u l a t i o n would be c a r r i e d o u t a c c o r d i n g t o Table 2, i t e m B l . Again, a n e q u i v a l e n t single-degree-of-freedom model i s used a s a s i m p l i f i e d f r e q u e n c y r e s p o n s e f u n c t i o n t o r e p r e s e n t dynamic p r o p e r t i e s of t h e span. The b a s i s f o r t h i s r a t i o n a l i z a t i o n h a s been d e s c r i b e d (14). 5.3 B l a s t i n g C r i t e r i a f o r Basement Walls From t h e amount of e x p l o s i v e , W , p e r i g n i t i o n d e l a y a t t h e s o u r c e , t h e peak p a r t i c l e v e l o c i t y , V, a t a c e r t a i n d i s t a n c e , R , c a n b e p r e d i c t e d a c c o r d i n g t o t h e e m p i r i c a l r e l a t i o n where a , b , and c a r e c o n s t a n t s .
T h i s s h o u l d n o t exceed a s p e c i f i e d peak p a r t i c l e v e l o c i t y , commonly t a k e n a s 50 m m / s f o r o r d i n a r y b u i l d i n g f o u n d a t i o n s ; f o r more d e t a i l e d c r i t e r i a , see
R e f e r e n c e 15. For h i s t o r i c b u i l d i n g s s m a l l e r v a l u e s are i n d i c a t e d . Because of t h e l a r g e p o s s i b l e s c a t t e r i n t h e r e s u l t s , a m o n i t o r i n g program i s
f r e q u e n t l y employed.
I n terms of t h e proposed s t a n d a r d t h i s i s a n e m p i r i c a l p r o c e d u r e and t h u s f a l l s under c a t e g o r y C , Table 2. The s o u r c e d e s c r i p t i o n i s g i v e n i n T a b l e 3, i t e m 4a, t h e c r i t e r i a i n T a b l e 5, i t e m 4a, f o r t h e v a r i o u s t y p e s of r e c e i v e r . For o t h e r t h a n basement w a l l s , s t r u c t u r a l a m p l i f i c a t i o n f a c t o r s need t o be a p p l i e d t o t h e ground motions i n o r d e r t o o b t a i n t h e v i b r a t i o n l e v e l s a t t h e v a r i o u s r e c e i v e r l o c a t i o n s i n t h e b u i l d i n g .
6. FURTHER RESEARCH NEEDS
Although there is available considerable information suitable for use in establishing a vibration standard for buildings, some areas require more study. These are indicated below, subdivided for the proposed standard.
6.1 Source Functions or Dynamic Actions
1. Forces generated by human activities; additional information has
recently become available (16-18).
2. Source functions for various types of road and rail traffic.
3. Dynamic wind loading functions for buildings.
6.2 Response Calculation
1. Improved methods for modelling the ground as a propagating medium
for vibrations.
2. Ground-building coupling effects.
3. Simplified methods of evaluating transmission of vibrations within
buildings. 6.3 Criteria
1. Verification of applicability of proposed standards (ISO, ANSI) for
different occupancies and vibration characteristics (duration, composite signals, etc.).
2. Vibration criteria for certain classes of building contents (e.g.,
electron microscopes, photographic processes, computers, etc.). Some
are available from manufacturers or from previous experience (19,20), but they have not been codified. For other situations existing criteria are perhaps too sweeping (21) or unavailable.
3. Evaluation of fatigue behaviour of common building materials, old and
new. Fatigue may be important for large numbers of loading cycles. 4 . Further rationalization of empirical criteria such as those for
blasting and construction activity.
6.4 General
1. Integration of the various components into a coherent vibration
2. Design-oriented methods f o r c e r t a i n v i b r a t i o n problems.
3. Development of a p p r o p r i a t e l o a d and r e s i s t a n c e f a c t o r s f o r t h e s e r v i c e a b i l i t y l i m i t s t a t e .
7. SUMMARY AND CONCLUSION
A framework h a s been p r e s e n t e d f o r t h e e s t a b l i s h m e n t of a v i b r a t i o n s t a n d a r d f o r b u i l d i n g s . The major components i n c l u d e a d e s c r i p t i o n of t h e s o u r c e f u n c t i o n , t h e r e s p o n s e d e t e r m i n a t i o n a t t h e r e c e i v e r , and t h e c r i t e r i a of a c c e p t a b l e v i b r a t i o n a p p l i c a b l e a t t h e r e c e i v e r . A f t e r a broad
c l a s s i f i c a t i o n based on t h e t y p e of i n f o r m a t i o n needed, s p e c i f i c s u b d i v i s i o n s of t h e t y p e s of s o u r c e a r e c o n s i d e r e d : p e o p l e , machinery, t r a f f i c , s m a l l e a r t h q u a k e s , impulse s o u r c e s , and flow-induced v i b r a t i o n s . R e c e i v e r s c o n s t i t u t e occupants and c o n t e n t s of b u i l d i n g s , and t h e b u i l d i n g s t r u c t u r e i t s e l f . S p e c i f i c examples of e x i s t i n g v i b r a t i o n g u i d e l i n e s a r e p r e s e n t e d i n t h e c o n t e x t of t h e proposed s t a n d a r d , and a r e a s a r e i n d i c a t e d f o r which a d d i t i o n a l i n f o r m a t i o n i s needed.
8. ACKNOWLEDGEMENT
Acknowledged a r e f r u i t f u l d i s c u s s i o n s w i t h S. Kraemer, D.E. A l l e n , and members of t h e I n t e r n a t i o n a l S t a n d a r d s O r g a n i z a t i o n , working group
ISO/TC98/SC2/WG2.
T h i s paper i s a c o n t r i b u t i o n from t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n , N a t i o n a l Research Council of Canada.
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Table 1. GENERAL DESCRIPTION OF VIBRATIONS IN BUILDINGS Physical State
Vibration source Supporting structure or
transmitting medium Receiver
-
Mathematical Model Source description: Action Dynamic model: Mathematical model of dynamic properties for supporting and transmitting medium Determination of response at receiver: Response calculation at receiver by analytical or numerical methods Adequacy of vibration environmentI
C o m p l a i n t
I
Applicable criteria: Comparison of response with serviceability' limit stateTable 2. CLASSIFICATION OF METHODS FOR EVALUATING VIBRATIONS FOR THE SERVICEABILITY LIMIT STATE
Source Description Dynamic Model Determination of Response Criteria
Category A
Force or displace- ment source is a function of time and space, may depend on the response of the supporting medium Category B Force or displace- ment source is a function of time I 1. Dynamic force P 0 functions I 2. Dynamic dis- placement functions 3. Amplitude or power spectrum of source 4. Source vibration level (rms, peak) 5 . Energy imparted at source Category C Specific source descriptions
Dynamic model of continuum in Evaluation of response at
1, 2, or 3 dimensions (wave receiver (solution of
propagat ion, continuum differential equations,
dynamics ) numerical methods)
Discretized representation of Evaluation of response by
transmitting medium (F.E.M. numerical methods
method, lumped parameter etc.)
Frequency response functions, Numerical solutions,
impulse response function Closed form solutions,
Convolution integral
Transfer function H, Numerical solutions,
frequency amplification Closed form solutions,
function Convolution integral
ication function
IHI
or Amplitude or powerspectrum of response
Amplification factors Response level (rms,
peak
Propagation or attenuation Closed form or numerical
laws in medium solutions
Empirical method of response evaluation
Appropriate response criteria
Peak or rms criteria
Peak or rms criteria
Narrow band or broad band criteria
Response criteria in rms or peak levels
Acceptable energy levels or vibrations at receiver Empirical criteria
Table 3. DYNAMIC ACTIONS OR SOURCE FUNCTIONS FOR BUILDING VIBRATIONS
Source Inf ormat ion
1. People: a) walking, running b) coordinated activity c) isolated jumps 2. Machinery: a) rotating b) reciprocating c) repetitive impacts 3. Traffic: a) exterior to building b) interior to building 4. Impulsive Source: a) seismic and paraseismic b) structure borne c) air pressure d) water blasts 5. Fluid flow wind
Time history; sinusoidal force functions
Time history; sinusoidal force functions Time history; triangular force pulse;
amplitude Pma,, duration td; impulse
Sinusoidal force function
Sinusoidal force components, spectrum Force pulse; repetitive pulses;
impulse
Force or deformation time history; source spectrum
Force or deformation time history; source spectrum
Displacement-time history; source functions; ground motion spectrum; peak ground motion values; energy release
Force or displacement time history; impulse; peak levels
Source spectrum; time-pressure variation Energy release at source
Wind spectrum; statistical properties of source function; vortex generation
Table 4: SOME METHODS OF VIBRATION ANALYSIS
Supporting or Transmitting
Medium Method of Analysis
Structures or structural Superposition of normal modes of vibration;
components equivalent singledegree-of-freedom response;
force vibration response using frequency response function; impulse response; wave propagation methods; empirical methods; random vibrations
Ground and ground-structure Attenuation laws of continuum mechanics; wave
interaction propagation; discretization methods (F.E.M.,
lumped parameter); modal response to
band-limited excitation; frequency response functions; modal response using actual or simulated ground motions or response spectra; simplified methods (impulse response,
equivalent S.D.F.); empirical methods
Fluids Random vibration methods; wave propagation
methods; aerodynamic admittance functions; interaction of vortex shedding with structural response; simplified methods; empirical
Table 5: SUGGESTED VIBRATION CRITERIA Source R e c e i v e r - - -- Occupancy - - - B u i l d i n g C o n t e n t s - - - B u i l d i n g S t r u c t u r e s Beams Walls S e n s i t i v e H i s t o r i c
Quiet Regular Active S e n s i t i v e Normal Foundation F l o o r s e t c . P a r t s B u i l d i n g s
1. People: a ) walking b ) c o o r d i n a t e d a c t i v i t y c ) i s o l a t e d jumps 2. Machinery: I P a) rotating \D I b ) r e c i p r o c a t i n g c) i m p a c t i n g 3. T r a f f i c : a ) exterior h ) i n t e r i o r 4. Impulse Source: a) p a r a s e i s m i c b ) s t r u c t u r e borne c ) a i r p r e s s u r e d ) s e i s m i c e) w a t e r blasts 5. F l u i d Flow: (wind, w a t e r )
Curve Curve 2-4 Curve
1 o r 50 o r
e m p i r i c a l Ref . 6
Curve Curve
16 128
Curve Curve Curve
1 2-4 50 I n s t r u m e n t o r
p r o c e s s Maximum stress o r s t r a i n ( i n c l u d i n g
c r i t e r i a o r f a t i g u e ) ; e m p i r i c a l c r i t e r i a
Curve Curve Curve p r e v i o u s
1 4 50 e x p e r i e n c e
Curve Curve Curve
1 16 128
T h i s paper i s being d i s t r i b u t e d i n r e p r i n t form by t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n . A l i s t of b u i l d i n g p r a c t i c e and r e s e a r c h p u b l i c a t i o n s a v a i l a b l e from t h e I n s t i t u t e may be o b t a i n e d by w r i t i n g t o t h e P u b l i c a t i o n s S e c t i o n , I n s t i t u t e f o r R e s e a r c h i n C o n s t r u c t i o n , N a t i o n a l Research C o u n c i l of C a n a d a , O t t a w a , O n t a r i o , K l A 0R6. Ce document e s t d i s t r i b u 6 s o u s forme de t i r k - 3 - p a r t p a r 1 ' I n s t i t u t de r e c h e r c h e e n c o n s t r u c t i o n . On peut o b t e n i r une l i s t e d e s p u b l i c a t i o n s de 1 ' I n s t i t u t p o r t a n t s u r les t e c h n i q u e s ou l e s r e c h e r c h e s e n matisre d e bdtiment e n e c r i v a n t b l a S e c t i o n d e s p u b l i c a t i o n s , I n s t i t u t de r e c h e r c h e en c o n s t r u c t i o n , C o n s e i l n a t i o n a l d e r e c h e r c h e s du Canada, Ottawa ( O n t a r i o ) , KIA 0R6.
