BUILDING SCIENCE SERIES 47

Structural Deflections.

A Literature and

State-of-the-Art Survey
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Structural Deflections.

A Literature and

State-of-the-Art Survey

^O\[d\i-0^ ^\f,f\C€. - National Bureau of Sta:n(Sard$

' ^ ' ^ MAY S 1374 T, V. Galambos, P. L. Gould,

M. K. Ravindra, H. Suryoutomo,

Civil and Environmental Engineering Department

Washington University

St. Louis, Mo. 63130

and

R. A. Crist

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued October 1973
Library of Congress Catalog Number: 73-600282

National Bureau of Standards Building Science Series 47

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 47, 104 pages (Oct. 1973) CODEN: BSSNBV

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.29/2:47). Price S1.25
6l Conversion Units

In view of the present accepted practice in this country for building

technology, common U. S. units of measurement have been used throughout

this paper. In recognition of the position of the United States as a signatory

to the General Conference on Weights and Measures, which gave official

status to the metric SI system of units in 1960, assistance is given to

the reader interested in making use of the coherent system of SI units

by giving conversion factors applicable to U. S. units used in this paper.

Length

1 in 0.0254 meter (exactly)

1 ft 0.3048 meter (exactly)

Mass

1 lb (Ibm) = 0.4536 kilogram

Force

1 kip 4448 newton

Stress

1 psf 47.88 newton/meter 2

iii

TABLE OF CONTENTS

Page

SI Conversion Units iii

1. Introduction 1

2. Background 2

3. Static Deflections 7 3.1 General 7

3.2 Effects of Deflections on Structures 7 3.3 Quantitative Limitations on Deflections 8

3.4 Computation of Deflections 10

3.5 Field Observations 11

4. Dynamic Deflections 12

4.1 General 12

4.1.1 Current Design Practice . 12

4.1.2 Forcing Functions 14

4.1.3 Structural Systems 15

4.1.4 Natural Frequency 16

4.1.5 Damping 17

4.1.6 Damage to Structures 18

4.1.7 Vibration Isolation 19

4.2 Floor Vibrations 20

4.2.1 Introduction 20

4.2.2 Analytical and Experimental Studies on Floor Systems . 20

4.2.3 Experiments on Steel Joist Floor Systems (Lenzen). . . 22

4.2.3.1 Dynamic Response Experiments 22

4.2.3.2 Damping 24

4.2.3.3 Conclusions 25

4.3 Drift 26

4.3.1 Effects of Lateral Loading on Structures 26

4.3.2 Quantitative Limitations on Drift 27

4.3.3 Calculation of Drift 28

V
4.3.4 Measurements of Drift Deflection 29

4.4 Human Perception and Response to Motion of Structures 31

4.4.1 Previous State-of -the-Art Reviews 33

4.4.2 Physiological Responses 34

4.4.3 Subjective Responses of Humans 34

4.4.4 Observed Human Response 36

4.4.5 Vibration Clauses in Standards 39

4.4.6 Comparison of Data for Human Response to Structural

Vibrations 41

4.5 Discussion 49

5. References 50

Appendix A, Summary of Vertical Deflection Limitations in U. S. Codes and Standards 67

Appendix B, Summary of Vertical Deflection Limitations in Foreign

Codes and Standards 79

Appendix C, Steel Floor Joist Vibration Formulas Developed by Lenzen . 93

vi
Structural Deflections

A Literature and State -of -the -Art Survey

T. V. Galambos, P. L. Gould, M. K. Ravindra, H. Suryoutomo

,

and

R. A. Crist

A literature survey and state-of-the-art study was compiled using

approximately 225 primary source documents, research papers and texts.

Over 800 documents were scanned to arrive at the primary source documents.

The problem of structural deflections is discussed and reviewed in its

component areas of static and dynamic deflections as related to forcing

functions and structural characterisitics . Also the interactions of major

structural deflections with building structures subsystems and human

occupants is reviewed. Emphasis is placed on serviceability limit states

of deflections. Detailed comparisons of human response to structural

vibrations are also made. This report is broad in scope and covers the areas of analysis, design and experimentation.

Key Words : Analysis; deflection; design; dynamic; experimental; human

sensitivity; loading functions; specifications; static; structural engineering;

subsystems; vibration.

1. Introduction

This literature survey and state-of-the-art study* encompasses a broad area of the structural engineering field; deflections of building

structures. Other types of structures such as tov\rers , bridges, etc. are briefly mentioned but primarily in the context of information that

may be applicable to building structures. This study was compiled using

approximately 225 primary source documents, research papers, and texts.

Over 800 documents were scanned to arrive at the primary source document.

The report was assembled considering building structure deflection

in a sequence that would be used when considering the solution of a structural

deflection problem, i.e., separation of static and dynamic deflections

and then considering each of these as a three component problem of load--

structural characteristics - -response (deflection]. This sequence is

developed and defined for the respective components throughout the report.

Also the interactions of major structural deflections with building structures

subsystems and human occupants is reviewed.

In this report an attempt is made to identify serviceability criteria

for the present practice of building construction, to determine the theoretical

and experimental basis for these requirements and to evaluate the range of

applicability of the existing criteria. Primary emphasis is on the

identification and documentation of existing serviceability provisions. The

bibliographical listings are not necessarily a listing of all available

literature but rather a listing of what vas considered by the authors to

be the most pertinent. This report is broad in scope and covers the areas

of analysis, design and experimentation.

* Research sponsored by the Office of Policy Development and Research,

Department of Housing and Urban Development, V/ashington , D. C. 20410.
2 . Background

In design and construction in the past, deflections have been

relatively small compared to member sizes or average building size, thus,

they have not been a dominant concern for the structural designer. Within

this decade the rapid increase of building construction costs have been

pressing the industry for more economical methods of construction; new materials have become available which result in low effective material

modulus and overall reduced structural stiffness; and more sophisticated and

accurate methods of design and analysis are being used. For these reasons deflections have become more significant than in the past with respect to

design control. Serviceability limit states have become progressively

more important. With an emphasis on serviceability, the structural designer

is confronted not only with a more complex situation of designing for

deflection as well as strength, but, he is also required to solve an interdisciplinary problem. Serviceability of a building structure has

a direct correlation to the comfort of the occupants of a structure.

The aspects of human comfort as related to structural deflection involve

the knowledge of psychologists, bioengineers , the medical profession,

only to name a few. Professionals with diverse backgrounds such as structural

engineers and psychologists have to find a common ground of communication

so that problems can be rationally approached. New vocabularies in each

field have to be mastered and understood.

Structural deflections are difficult to discuss unless they are broken down to more specific subjects. For this report serviceability

is of primary concern. A serviceable structure is a structure which

meets the needs for which it is intended in everyday use. Deflections

of a structure at a serviceable level are not generally those deflections

which occur at a collapse or an ultimate limit state. Some brief mention

of deflections at ultimate limit states will be made in this report with

respect to ductility as it applies to life safety and earthquake loading.

However, most of the emphasis ^^rill be on serviceability referenced to

small recurrence interval loadings and to continued functional use of

a structure.

The problem of deflections in building structures as viewed in this

report is divided into components as shown in figure 1. The primary

division is the separation of static and dynamic deflections. Traditionally,

many dynamic structural design problems were reduced to a pseudo dynamic

problem by use of "equivalent" static loads. Advancement of technology

now permits the actual consideration of the dynamic structural problem.

The primary difference between the static and dynamic problem is the

consideration of the dimension of time in the dynamic case. Dynamic

deflections corresponding to dynamic loads are time dependent, i.e.,

they have a describable time history. Strictly speaking for the general

case, all loads and deflections are time dependent and thus dynamic.

Hov;ever, in the more practical sense, if time parameters of loading and

structural characteristics are considered, a difference can be made betxveen

the static and dynamic cases. A static load, thus causing a static deflection,

is one which is sloA'/ly applied and released. Slowly refers to the duration

of time of application and release of load compared to the natural period

of the structure. If the ratio of load application or release duration

to natural period is large, the load and corresponding deflection can

be considered static. Conversely, if the ratio of load application or release duration to natural period is small, the load and corresponding

deflection are dynamic and the dimension of time has to be considered.'

It also can be stated that in the dynamic case, inertial forces are significant

and must be considered to create dynamic equilibrium. An order of magnitude

estimate for static and dynamic loads which cause corresponding static

and dynamic deflections in building structures can be given. Dynamic

loads are applied and released in the order of seconds or less whereas

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static loads are applied or released in the order of minutes or greater

Another type of dynamic, i.e., time dependent load, has to be considered

in a greater order of magnitude time domain. Long term, in the order

of months and years, deflections due to sustained (static) loading attributed

to creep of the constituent materials of the structure are important to

the serviceability of a structure. These deflections are more accurately

understood by the study of the constituent materials. The subject of

creep deformations is important but due to the scope of this work has*

not been emphasized in this report.

Once the differentiation is made between static and dynamic deflections,

it becomes clear why traditional deflection design requirements are inadequate

in a general sense. The structural design practice has been dominated

by deflection criteria such as ; the vertical deflection of a beam or floor for a given load shall not exceed the span divided by 360, or the

horizontal deflection of a high-rise structure subjected to a lateral

load shall not exceed 0.002 times the total height of the structure.

In the case of the requirement for floors and beams where occupants are responding to a time dependent deflection, the L/360 criterion has little

rational justification. It has been adequate in the past because of

the relatively stiff floors using high effective modulus materials. Now

that new materials (lower moduli and higher stresses) and more flexible

systems are being used, the dimension of time has to be considered in

the deflection criteria. In the case of the lateral deflection criteria,

pseudo dynamic loads (equivalent static loads) have been used to calculate

deflections from structural analysis methods which did not consider the

dynamic properties of the structure and did not consider all elements

of the structure which contribute to its stiffness. This causes a twoway confusion. The loading is not realistic and the analysis model of

the structure is inaccurate, thus, a deflection criterion on this basis

has as its only rationale that it has been adequate through experience.

When past experience is somewhat nullified by changes in structural design

methods and materials, the deflection criteria then becomes inadequate.

These two typical deflection requirements have been used as a panacea

for a very complex aggregation of design considerations. They should

not be expected to be broadly applicable.

Further breakdoim of each of the static and dynamic deflection

problems can be made. Considering the static deflection problem, possibly

the less complex of the t^vo , the problem can be stated in engineering

terms as shown on figure 1.

ipj= [K][yj

From a given load,[p] , and given structural characteristics, [K] , a system

deflection, (yj , can be determined. Alternatively, with two of the three

components of the problem known the other can be determined. The fourth

component of this engineering statement is interaction with the occupants

of the structure and the subsystem, (figure 1). It is by far the most

complex and difficult to define of tlie four components. The subsystems

considered are the partitions, windows, doors, mechanical equipment,

etc. Human response is expressed in subjective terms such as "desirable"

and "undesirable" A^?hich are difficult to define. Even though the subsystem

response is objective, it has not been clearly defined in the past what

system response characteristics affect the function of the subsystems.

The dynamic deflection problem is shown on figure 1. It can be expressed

in block diagram from as

F(t) G(t) Y(t)

In general terms, the major components are; the dynamic load or forcing

function, F(t), the structural characteristics or transfer function.

4
G(t), and the system response, Y(t). If two of the three components are known, the other can theoretically he determined. Analysis leading to

design involves a designated forcing function and a calculated transfer

function to determine the system response. Measurements of system response

(deflection of a structure in service) allow a reverse process, i.e.,_

the structural characteristics can he determined if the forcing function

is known or the forcing function can he inferred if the structural

characteristics are known.

The forcing function can be random or transient such as that created

by foot traffic or vehicles. Steady state loading is generally caused

by reciprocating mechanical equipment; wind load is both random and transient

but it is referred to here separately because of its importance. Earthquake

loading is also random and transient, however, as previously mentioned,

this type of loading will not be considered extensively. It is applicable

to the ultimate limit state more than the serviceability limit state.

The possibility should not be overlooked that small recurrence interval,

low intensity earthquakes could be considered in the category of serviceability.

Dynamic structural characteristics involve the identification of

the natural frequency of a structure (mass and stiffness) and damping.

The dynamic structural characteristics are more complex than just determining

the natural frequencies of a structural frame. The dynamic structural

characteristics are the properties of the entire structure which interact

(in the mechanical as well as the mathematical sense) with the forcing

function to result in a structural system response. Non - structural elements

(partitions, walls, etc.) have a significant effect on these properties.

Also it is possible that the interaction of the structure and its foundation

may effect the structural characteristics. The system response is a time

dependent deflection.

Similar to the static deflection problem, there is an interaction

of the dynamic system deflections (figure 1) with the human occupants

(human response) and subsystems. Human response is considered in three

general divisions, whole body vibration, audial and visual. Whole body

vibration is a general category which does not designate the specific

cues that sense whole body vibration. Specific cues are the local excitation

of internal organs, inner ear, skin, bone, muscle, etc. Human sensitivity

(figure 1) has been found to cover a wide range of motion parameters

such as acceleration, velocity, damping and total duration of vibration

exposure. The classification of human response parameters in terms

of quality of response start at a perception threshold and cover a range

to an intolerable or damaging level of vibration. The environment of

a human while responding to vibration is another important variable affecting

the quality of human response to vibration. Visual response to vibrations,

such as the sway of high-rise structures observed from one structure

to another or the local motion of equipment within a structure, affects

the human response. Audible response to vibrations such as the creaking

of a structure or the banging of elevator counterweights is also a factor

to be considered in human response.

Subsystem response is a parallel area of concern in the dynamic

interaction problem. The system deflections must allov; for the proper

functioning of the subsystems. Measures of the proper functioning of

the subsystem are local damage and serviceability.

This breakdown of the structural deflection problem is principally

concerned with serviceability. It has divided the problem into its major

categories to lead to a rational approach of the problem. Some of these

categories have been studied extensively and major contributions have

been made to the technology. Other areas have had fragmented or limited

study and require further research and assimilation. Subsequently, this

report v/ill elaborate on the details of this problem breakdown as shown

5

i
in figure 1. As the literature is reviewed, it will be evident where

gaps of knowledge exist. These points will be discussed individually

within each section.

It is appropriate to point out how a rational understanding of the

structural deflection problem shown in figure 1 can lead to a properlydesigned structure with respect to deflections. The understanding and

solution of the interaction problems lead to allowable deflections. The

iteration loop of design applicable to deflections is then completed.

It is formed by three major components; structural characteristics, specified

load, and allowable deflection.

Many different deflection criteria would be required for satisfactory

behavior if all probable loading situations are considered for a particular

structure. Several are evident from figure 1.

Static system deflection is controlled to limit:

human response to static deflection

subsystem response to static deflection

Dynamic system deflection is controlled to limit:

dynamic whole body vibration

audible perception of motion

dynamic visual perception to motion

dynamic subsystem response.

Although these are not all that are possible, they appear to be

the major categories. Each case can result in a deflection requirement.

It is possible that each structure is unique with respect to which of

these cases will be significant. Categories may be combined as more is

learned of each. Again, it is evident why a single deflection specification,

which was derived from tradition without rationale, cannot be expected

to result in adequate deflection criteria.

6
3. Static Deflections

3 . 1 General

This section covers the computation, measurement and the assessment

of the effects of static deflection on structural systems and subsystems.

Those deflections which are associated with lateral building movement

are discussed separately in Section 4.3. Appendices A and B include

a summary of various code requirements with explicit reference to the

respective codes.

3. 2 Effects of Deflections on Structures .

The possible undesirable effects of excessive structural deflections

have been noted by Allen [2]*, These effects include 1) cracking of

primary structural members which may provide a means for the transmission

of unwanted sound, moisture and cold air and promote corrosion, as well

as being unsightly; 2) cracking or crushing of non-structural components

such as partitions; 3) lack of fit of doors and windo\\rs ; 4) walls out

of plumb; 5) eccentricity of loading due to rotation; 6) unsightly droopiness;

and 7) ponding. Allen suggests that many deflection-caused problems

can be alleviated by alternate design solutions such as flexible joints,

etc

.

The American Concrete Institute (ACT) Committee 435 report [1] lists

the following reasons for limiting deflections: 1) Sensory acceptability

(visual, tactile, auditory); 2) Serviceability of structure (surfaces

which should drain water, floors v/hich should remain plane, members supporting

sensitive equipment): 3) Effect on nonstructural elements (walls, ceilings,

adjacent building elements supported by other members); 4) Effect on structural elements (deflections causing instability of primary structure,

deflections causing different force system or change in stresses in some other element, deflections causing dynamic effects). In this report

examples of each of the items noted are given along with deflection

limitations

.

A comprehensive examination of the effect of deflections on st:fuctures

is coi;Ltained \n the report. Deformations, Committee No. 4 of Comite

Europeen du Beton [8]. In this report, the effect of deflections on structures are separated into deflections which do and do not effect

the overall stability of structures. Those deflections which affect

the structural stability are further classified into 1) static; and 2)

dynamic effects. Those deflections which do not affect structural stability

are classified as 1) psychological or esthetic effects; 2) effects which

may produce damage in other non load-bearing structural units; 3) indirect

effects on the stability of other structural members or structures; and

4) effect of deflections on the serviceability of the structure.

The American Institute of Timber Construction Standard [19] states

the reasons why a deflection limitation requirement is desirable: 1)

Possible damage to attached or connected materials such as plaster and

roofing; 2) Effect on the function of the completed structure such as

* Numbers in brackets refer to literature references. References are grouped in the respective report sections and are listed in alphabetical

order in each section.

7
vibration and springiness; 3) The acceptable final shape or position

of the completed structure or nenber such as roof pitch and pockets

affecting drainage or interior appearance; and 4) Effect on door clearances

or effect on sash and glass lielow a member.

For wood floor structures, Vermeyden [20] had traced the requirements

for deflection limitations to a prevention of 1) sagging or cracking

of ceilings and jamming of doors; and 2) discomfort. He discusses the

effect of long-term deflection as well as instantaneous elastic deflections.

With regard to aluminum structures , the Report on the Structural

Use of Aluminum by the Institution of Structural Engineers [14] states

that the deflection of a member shall not be such as to impair the strength,

functioning or appearance, or to cause damage to the finish of any part

of the structure.

Some structural deflection phenomena are o^^ten long-term time-dependent

and consequently may become evident only after some years. As such,

the construction sequence, inelastic material properties, climatic effects

and pattern of usage may determine if a given structure ivill suffer from

deflection induced problems. Furthermore, when the designer considers

the relative importance of deflection criteria in building design, he

should discern between those factors which can lead to catastrophic failure,

such as ponding and corrosion, as opposed to those items which simply

cause inconvenience, such as jammed windows. A quantifiable method of

discerning between failure and unserviceability type criteria has been

noted by Davenport [7] .

3 . 3 Quantitative Limita tions on Deflections . Quantitative limitations on deflections are most often given in terms

of a fraction of the span length, L. A summary of this type of limitation

is given by Allen [3] . In this commentary on the various standards pertinent

to the National Building Code of Canada, 1970, various types of roof, floor

and wall members are considered along with the most used construction

materials, timeber, reinforced concrete, steel and aluminum. The general

range of values is from L/18n to L/360. These deflection limitations refer

to dead load, live load, creep and ponding deflections when applicable.

Represenative specific values are given in Appendix B. An early study (1948) of the behavior of houses was done by Whittemore

et al at the National Bureau of Standards [21] . Insight of these authors

was expressed through the realization that the the L/360 limitation was quite arbitrary. Absolute limitations of deflection for various types

of loading (compressive, transverse, concentrated, impact and racking)

and elements (walls-load and non-load bearing, floors and roofs) are given. As an example, for transverse loading on floors, 2-inches of

deflection is allowed for a 40 Ib/ff^ superimposed static load. Also

a permanent set, for the same condition, of 1-inch is allowed. The rationale

for these large allowable deflections is that the actual loading on the

floor may not be more than 8 Ib/ft^. Many qualifications would have to

be made before this type of criteria could be used.

A comprehensive summary of deflection limitations for reinforced

concrete construction is provided in the ACI Committee 435 report [1].

In this report, deflection limitations are given for the various classifications

noted in the previous section. The limitations are given in the usual

fraction of span but, in addition, absolute deflection limits are specified with respect to the effect of deflections on non-structural elements.

Also, the rationa:ie of using the depth/span ratio as an indirect quantitative

index of allowable deflection is developed. A notable feature of the

suggested limitations is the specification of the portion of the total deflection upon v/hich each limitation is based.

8
A great many state and local codes in the United States incorporate

the Building Code Requirements for Reinforced Concrete, ACI 318-71 [2];

the Specification for the Design, Fabrication and Erection of Structural

Steel, AISC [11]; the American Institute of Timber Construction Specification,

AITC [19] ; the Specifications for Aluminum Structures [4] ; and the Standard

Specifications and Load Tables of the Steel Joist Institute, SJI [16].

These standards thus should reflect the general state-of-the-art practice

with respect to these building materials. The pertinent deflection limitations

are summarized in Appendix A and are discussed in the subsequent paragraphs.

The model codes summarized in Appendix A also incorporate these provisions.

A comparative review of the model codes is give by Buchert, Mulner and

Rubey [6] . The ACI Building Code gives deflection limitations in terms of a fraction of the span for the following member types: 1) Flat roofs not

supporting or attached to non -s tructural elements likely to be damaged

by large deflections; 2) Floors not supporting or attached to non- structural

elements likely to be damage by large deflections; 3) Roof or floor construction

supporting or attached to non-structural elements likely to be damaged

by large deflections ; and 4) Roof or floor construction supporting or attached to non -structural elements not likely to be damaged by large

deflections. As a second means of controlling deflections, minimum thickness

requirements are provided for solid one-way slabs , ribbed one-way slabs

and beams which are not supporting or attached to partitions or other

construction likely to be damaged by large deflections. Also, miminum

thickness requirements are provided for nonprestressed two-way construction.

The AISC specification states that beams and girders supporting

floors and roofs shall be proportioned with due regard to the deflection

produced by the design loads but only specifies a quantitative limitation

of L/360 for members supporting plastered ceilings. Ho\>:ever, in the

commentary, guidelines are suggested for the depth/span ratio as a function

of the yield point stress, F as a means for controlling deflection.

For fully stressed beams and^girders in floors , the suggested value of

the depth ratio is F /800 while for roof purlins F /lOOO (excluding flat

roofs) is given. ^ ^

Another deflection-related phenomenon treated in detail by the AISC

specif icication is ponding, defined therein as the retention of water

due solely to the deflection of flat roof framing. The code provisions

are based on the spans and moments of inertia of both the primary and

secondary members and of the steel deck supported on secondary members.

These relations are based on equations given by Marino [12]. In addition,

graphical design aids are provided in the commentary when a more exact

determination of required flat roof framing stiffness is required. The

AISC specification also limits the total bending stress to 0.80 F in

primary and secondary members due to the weight of the ponded water plus

dead and gravity live loads. It is noted that stresses due to wind or seismic forces need not be included in a ponding analysis.

The AITC specification requires the simultaneous satisfaction of

deflection limitations of L/240 for total load and L/360 for live load.

The Specification for Aluminum Structures suggests the use of the

effective width concept when deflection at design loads is critical.

The SJI specification give deflection limitations of L/360 for floors

and roofs with plastered ceiling attached or suspended and L/240 for

other roofs.

A comparison of European standards and specif icatipns for , reinforced

cpncrete is provided by the Committee 4 report of Comite Europeen du

Beton [8] where information from Austria, Belgium, Switzerland, Germany,

9
Denmark, Spain, England, Italy, Portugal, Poland, Sweden, Turkey and

Yugoslavia is presented. The information from this report regarding allowable

limits of deformation is included in Appendix B.

A survey of European and North American practice for timber members

is provided by Vermeyden [20]. In addition to the Dutch regulations

for the limiting deflections of wood beams, he also surveys those from

Germany, Switzerland, Austria, Denmark, France, Great Britain and Canada.

He notes that in all cases the limitations are based on elastic deflections

but that total load is used in some cases while live load is used in

others. The specific deflection limitations contained in this paper

are summarized in Appendix B. Another literature survey with similar information to that contained

in Vermeyden's report was conducted by Onysko [13]. Deflection limitations

from this report are given in Appendix B.

3 . 4 Computation of Deflections

When numerically computed values of deflections are specified and

presumably correlated with the presence (or absence) of certain undesirable

effects in buildings, it is preferable to have a rational and standardized

basis of computation. The possibility for achieving this standardization

is dependent on the complexity of the structural framing system including

connections, foundations and the materials of construction.

With respect to the problems introduced by complex framing systems

and the ensuing representation by the mathematical model for which the

deflections are computed, an example of the poor correlation between

computed and observed deflections of a structural frame is reported by

Wiss and Curth [22]. Section 4.3 discusses the available computer-based

techniques of structural analysis which enable improved m.athematical

models of structures to be considered.

The problems introduced by constituent material considerations are principally encountered in the computation of deflections for reinforced

concrete members and structures. These problems are enumerated in great

detail in ACI Committee 435 report [1] and appear to be a result of several

factors: 1) the assumption that concrete carries no tension for strength

calculations which may be unduly conservative for deflection calculations;

2) the assessment of the end restraint introduced by monolithic construction;

3) the non-linear material behavior in the working load range prior to

and beyond cracking; 4) the historical sequence of loading including

construction and load test sequences; 5) the contribution of the transformed

are-a of the reinforcing steel to the stiffness in uncracked sections

and the contribution of the compression steel to the stiffness in cracked

sections; and 6) long-term deflections due to shrinkage and creep. The

difficulties involved in considering any one of these factors makes the

precise determination of deflections in reinforced concrete structures

a somewhat academic exercise which suggests that limitations on computed deflections should be rather broad.

With respect to European practices, a comparative study of various

assumptions for elastic modulus, effect of sustained loading ai;id effective

momeijit of inertia is contained in Committee 4 report of Comite Europeen

du Beton [8] along with some suggested overall methods of computing deflections.

For timber structures, creep under sustained load must also be considered

in addition to elastic deformations. A method for computing deflections

in timber structures including creep effects is pronosed by' Vermeyden

in
With regard to structures constructed nf structural steel or aluminum,

it appears that the accepted methods of elastic analysis ^re applicable

with the basic assumption of linear elastic behavior in the working load

range. Some further elaboration, however, is needed for steel structures

designed by the method of plastic design. Since this method considers

the structural behavior at the collapse load and many of the deflection

limitations found in the various codes are based on structural serviceability

at working loads, the determination of deflections prior to the formation

of the "last hinge" and collapse will not usually be sufficient to check

serviceability criteria. This aspect of plastic design has been investigated

by the Joint WRC-ASCE Committee on Plasticity Related to Design [10].

Some correlations between working load and ultimate deflections are reported.

It appears that an additional elastic analysis under service loads would

be required if the approximate deflections calculated by the method suggested

in the report exceed the prescribed deflection limitations.

Since deflection limitations are becoming an increasingly important

consideration in the design process, some authors have proposed design

methods in which the structural members are directly proportioned to

satisfy deflection requirements and then checked for strength, a procedure

opposite to that is usually follo^^^ed. Such methods are proposed by Stevens

[17] and Blakey [5]. Certainly these methods are rational and can provide

safe and serviceable structures; however, this has revealed that the

presently available limitations on deformations are not nearly as precise

as those on strength and it does not seem logical to base a design on such criteria at the present time.

3. 5 Field Observations . A comprehensive survey of existing data for 98 buildings, 58 with

no damage and 40 of which have been damaged as a consequence of foundation

settlement is reported by Skempton and MacDonald [15]. Although the

authors are concerned with foundation settlement induced deflections,

this vsTork has bearing on other types of deflection, especially the tentative

values for damage limits. The types of damage are classified as follows:

1) structural (involving the frame) ; 2) architectural (involving only

the panel walls, floors or finishes); and 3) functional. From the study

of frame buildings with infill panels, it is evident that architectural

damage such as cracking of wall panels is likely to occur at distortions

smaller than those which cause structural damage. It appears that these

authors found that a limiting differential settlement of L/300 represents

a reasonable value which, if exceeded, is likely to result in architectural

damage. This criteria is based on the data obtained from the observed

settlements and additional unpublished test data.

Supporting data to the previously cited conclusions by Skempton

and MacDonald is given by Thomas [18] with a particular emphasis on brickwork.

An investigation into the causes of large deflections of electrically

heated concrete floors is described by Jenkins, Plowman and Haseltine

[9]. The deflections are attributed to aggregate shrinkage, slab creep,

and creep with the latter being the most significant. It was recommended

that compression reinforcement be used in slabs and that the allowable

span/depth ratios given in the British Standard Code of Practices; The

Structural Use of Reinforced Concrete in Buildings, CP 114 (1957) be

revised. The CP 114 (1969) (Appendix B) designates a deflection limitation

for simply supported beams of L/d <_ 20.

11
4. Dynamic Deflections

4 . 1 General

Dynamic deflections, as previously discussed, are a result of a dynamic

load acting on a structure or element. Dynamic loads extend over a broad

range of time durations. They can be transient and short in duration,

i.e., less than the natural period of a structure or cyclical and long

in duration, i.e., steady state. Depending on the relationship between

the time characteristics of the loading function and the natural period

of the structure, the structure may deflect less than if the same load were applied statically or it may deflect many times the deflection of

the same load applied statically (resonance).

The review of the literature for dynamic deflections is first covered

in a broad scope by discussing current design practice, and then discussing

forcing functions, structural systems, dynamic structural characteristics,

damage to structures and vibration isolation. Because of the importance

of particular areas of dynamic deflections, detailed discussions will

be made on the specific areas of floor vibrations, drift, and human perception

and response to the motion of structures.

4.1.1 Current Design Practice . An excellent state-of-the-art report which includes an extensive

list of references has been presented by Steffens [30]. Since Stef f ens

report covers most of the available literature on the subject of structural

vibration up to 1964, this report will focus mostly on the work done

after 1964.

Present structural design practice to prevent destructive or disturbing

vibrations varies in sophistication from suggestions of simple arbitrary

deflection limits to recommending a dynamic analysis of the structure.

The specifications of the American Institute of Steel Construction

[29] read "Beams and girders supporting large open floor areas free of

partitions and other sources of damping, where transient vibration due

to pedestrian traffic might not be acceptable, shall be designed with

due regard for vibration."

No specific recommendations for design considering vibrations have

been given either in the American National Building Standard [24] or

in the ACT Building Code [23].

Perhaps the National Building Code of Canada [28] is the most progressive

of all present codes in this respect, however, no clear guidelines are given. Following are some of the clauses in it relating to vibrations.

Structural members shall be designed so that their

deflections and vibrations under expected service loads

will be acceptable with regard to

a) the intended use of the building or member

b) possible damage to nonstructural members and

materials

c) possible damage to the structure itself.

12
The reference velocity pressure, q, for the design

of structural members for deflection and vibration shall

be based on a probability of being exceeded in any one year of 1 in 10 (as against a probability of 1 in 30

for the design of structural members for strength)

.

Buildings whose heiglit is greater tlian four times

their minimum effective width or greater than 400 ft

and other buildings whose light weight, low frequency

and low damping properties make them susceptible to

vibration shall be

a) designed by experimental methods ^or the danger

of dynamic overloading and vibration ^nd the

effects of fatigue, or

b) designed using a dynamic approach to the action

of wind aust.

'''heoretical models have been proposed for the dynamic analysis of

structures. The adequacy of theoretical models has been discussed by

Ward [31] in relation to the investigation carried out by the National

Research Council of Canada. Many uncertainties exist in input to analysis,

for example, the dynamic structural characteristics. In addition, the

limits that constitute excessive vibrations which cause minor structural

damage and physical disturbance are yet to be defined quantitatively.

'''raditionally , 'n typical civil engineering structures, resonance

has riot been a dominant problem. Whenever resonance was a possibility

due to machinery housed in the structure, proper care in machinery operation

and in the design of the structure eliminated its occurrence. Resonance

of structural floors caused by people moving on the floors is claimed

not to occur if the natural frequency of the floor is greater than about

5 Hz [28] . This conditon is satisfied by most floor systems but may

be a t>roblem for long-span and low frequency systems.

For low-rise buildings the structural response to wind is not as significant as for high-rise buildings. Hence most research efforts

have been directed to the study of wind effects on tall buildings.

The dynamic response of structures to earthquakes has been extensively

studied. The recommended practices in various countries for seismic

design are discussed by Beles and Ifrim [25], Korchinsky [27], FerryBorges and Ravara [26] , Wiegel [32] , Wiggins and Moran [33] and in the

commentary of the National Building Code of Canada [28] . The various

earthquake design provisions concern principally the ultimate limit states

rather than the serviceability limit states and thus this topic will

not be extensively considered in this report.

Structural response to other types of dynamic excitation such as sonic booms, shock waves and traffic are special situations and as such

they must be considered individually.

Minor damage due to the sway of tall buildings and physical discomfort

due to transient floor vibrations have been considered in present design

practice through simple static deflection limitations.

13
4.1.2 Forcing Functions . Most dynamic loading sources that cause structural vibrations are classified in t\io groups, natural and man-made. Dynamic loads resulting

from wind and earthquakes belong to the first group. Man-made sources

of vibration are sonic booms, air shock waves, machinery, traffic and

disturbances caused by construction processes.

The effects of wind, particularly the turbulent characteristics

of it, are important in the design of tall structures, suspension bridges,

etc. Present practice makes use of a dynamic approach [37, 38, and 39] or model testing in wind tunnels for large structures. The nature of

wind and its treatment in design are discussed by Ferry-Borges [34]

Davenport [35], and Scruton and Flint [36].

The problem of seismic structural vibrations has received much attention.

Present practice allows routine design using seismic coefficients [24,

28 and 42]. For tall buildings and for buildings with irregular layouts,

design based on dynamic analysis is recommended. A survey of present

knowledge in earthquake engineering is given by V/iegel [43] . The interaction

of structure-foundation system in the seismic response of structures

is discussed by Parmell et al [40] and more recently by Sarrazin et al

[41]. Sarrazin's approach is more general than Parmelee's by using nondimensional parameters and root mean square response to a white noise input

simulating an earthquake environment. Also Sarrazin assumes a different

geometry in the mathematical model. The essential feature of earthquake

resistant design is to determine the maximum response and its direction

for a chosen forcing function representing an earthquake. The validity

of the analysis depends on the accuracy of the choice of the design earthquake

and of the structural r)arameters such as damping, ductility (resistance

function) and the natural period of the structure. It should again be

emphasized that consideration of earthquake loading relates primarily

to the ultimate rather than the serviceability limit states.

The nature of the sonic boom problem and its effect on structures

has been discussed by Hubbard [44] , Lo\\rery and Andrews [45] , McKinley

[47] and others [46, 48, and 49]. Although it was regarded that general

structural damage due to sonic boom was unlikely, these studies were undertaken after a series of allegations of damage to window glass.

As a result of McKinley 's study [47], it was suggested that windowpanes

designed to resist wind pressures of 10 psf are not likely to break when

exposed to booms from jets operating under control. The reported damage

[45, 46, and 47] may have been caused by a number of other reasons such

as improper fitting of panes to the frames and rusting of metal window

frames

Blasting operations produce earth vibrations that are imposed upon

structures and buildings. Crandell [51], Wiss [55] and others [50, 52,

53 and 54] have studied the effects of such vibrations on structures.

Resonance appears to be unlikely; minor damage such as plaster cracking is

often incorrectly attributed to this source of vibration. Wiss [55]

has indicated safe limits on the sizes of explosives charges to preclude

damage to nearby structures.

In a report of the Australian Bureau of Mineral Resources, Geology

and Geophysics, Anthony [56] points out that the vibrations from machinery

are not likely to cause damage beyond a radius of 20 feet. Many economically

feasible methods are available for isolating the structural components

from machinery- induced vibrations. Novak [57] has studied the influence

of the non-linear properties of soils on vibrations of machine foundations.

14
Vibrations from traffic have limited effects on adjoining structures

as a study by the British Railway [58] has shown. The Australian report

[56] indicates that the traffic movements (including trolleys and trains)

are not likely to cause damage beyond a radius of about 40 feet.

4.1.3 Structural Systems . The effects of vibrations on low-rise buildings have been studied

mainly in the context of earthquake loadings. However, transient vibrations

due to moving people are important regardless of building height. A

literature review of the performance of wood-joist floor systems is made

by Onysko [59] wherein the problems of dynamic loading leading to floor resonance and human sensitivity to vibration are discussed. Section 4.4

of this report is devoted entirely to the review of the literature on these topics.

Tall buildings are subjected to vibrations from both wind and earthquake

loadings. The natural frequencies of tall buildings are likely to be

lower than 1.0 Hz [66]. This low frequency, and the fact tliat the modern

tall buildings tend to have low damping, make the effect of both wind

and earthquake loadings significant. Davenport [62 and 63] has suggested

design criteria for all buildings for wind loading. These criteria attempt

to account for most of the significant wind effects, namely, collapse,

damage to masonry and finishes, damage to windows and cladding, fatigue

damage and comfort of occupants. Dynamic analysis taking into account

wind custs and model testing in a boundary layer wind tunnel simulating

the actual terrain are the only sophisticated design approaches available

today. The response of tall buildings to turbulent wind action consists

of a fluctuation about a mean deflected position with oscillations usually

occurring at a frequency equal to the fundamental frequency of the building.

Davenport [621 and Chang r60] have given expressions for the maximum

acceleration in terms of the vibrational characteristics of the building.

Robertson [67] has also stressed the importance <^f ^he establishment

of rational acceptance standards for huilding sway. Goldberg and Herness

[64] have formulated a method of calculating the '^ormal modes and associated

natural frequencies of multistory buildings considering both shear and

bending deformations in the floor and stiffening walls. ^nme dynamic

deflection measurements "^f multistory buildings have been reported by

Korchinskiy [66]

.

Vibration of towers have been examined by Chiu et al [61] and Ishizaki

and Katsura [65] . The procedure followed by these authors is to formulate

a mathematical model of the tower and to study the effects of variations

•'"n vertical wind profile, mean wind velocity and its standard deviation.

The effects of slenderness and flexibility of multis tr inger steel

highway bridges has been studied with respect to strength and serviceability

by Wright and Walker [69]. A conclusion reached v^as that a more flexible

bridge tends to be stronger in resistance to yielding of a stringer.

Flexibility of bridges was related to pedestrian comfort and it was found that substantial changes in flexibility only moderately affected

human response.

Tajimi et al [68] report the vibration characteristics of a nuclear

reactor enclosure structure. The structure was analyzed for factors

such as natural period, damping etc., to check the validity of staticdesign earthquake coefficient. Subsequent field measurements have sho^^?n good agreement with the analytical results.

A thorough description of the state-of-art in foundation vibrations

is given by Whitman [72], The theory idealizing the foundation as a

1 5
mass supported by an elastic half-space is gaining increasing support

over the traditional approach of a single degree-of -freedom , mass-springdashpot system. The major problem still remains of estimating the constitutive

relationships for the soil to be used in the elastic half -space analysis.

V/hitman includes a complete list of pertinent references. Hsieh [70]

has presented a method of analyzing the coupled modes of vibration of

a foundation resting directly on soil using a mathematical model with

six-degrees of freedom. Theoretical ivork and background information

on foundation vibrations is contained in the book by Richart, Hall and

Woods [71].

4.1.4 Natural Frequency . The natural period or its reciprocal, the natural frequency, of

a structure is one of the fundamental parameters used in the determination

of the response of a structure to dynamic loads. Various techniques

are known by which a building structure may be caused to vibrate to determine

its natural period of vibration. Some examples of these are: firing

attached rockets [80] , pulling the structure with a cable and then releasing

it , and having a person move his body back and forth in synchronism with

the natural period of vibration of a structure [75]. Alternatively,

the response of the buildings at certain frequencies of artificially

applied forced •>''ibration or from random wind excitation [74] may be studied

to determine the natural period of the buildings. Janney and Wiss [77],

and Rea , et al [81] have also reported dynamic tests on structures to

determine the natural period.

As a result of experiments, Steffens [30] presents several empirical

formulas which make it possible to calculate the natural period of a building from its dimensions. The height of a building appears to be

the most significant parameter governing the natural period of a building.

The natural period varies from 0.1 second for low buildings to 10 seconds

for very tall buildings. Davenport [63] has reported that the natural

period of the Empire State Building in New York is about 8 seconds.

The Uniform Building Code [42] and the American National Standards

Institute [24] recommend that the natural period of a building be calculated

using the simple relationship

O.OShj^

or for moment-resisting space frames,

T = 0.10 N

where

T = natural period in seconds

h = height of the structure

n

°

D = dimension of the building parallel to the lateral force

and

N = number of stories.

Blume [73] has proposed a pseudo-stiffness procedure to determine the

natural periods, modes and stiffness taking the joint rotations and soilstructure interaction into account. Keintzel [78] has considered the

16
effect of structural types (high walls without openings, frames and high

walls with openings or frames filled with masonry) on the natural periods.

Rubinstein [83] and Rubinstein and Ilurty [82] have considered the effect

of joint rotation and axial deformation on the periods of multi-story

framed structures. They recommend that all joints within a given floor

level should be assumed to undergo equal rotation and that the axial

deformation in the columns may be neglected. Considerable reduction

in computation time is achieved with a small sacrifice in accuracy

(6 percent)

.

Actual measurements of natural periods of tall buildings have shown

that the empirical formulas may provide a reasonable estimate of the

natural period. Wiss and Curth [84] compare the measured natural period

of a 56-story building with those determined by equations from the Uniform

Building Code [42] or ANSI A58.1-72 [24]. The structure contains a shear

wall core to the 42nd floor and floor slabs and unbraced columns above

the 42nd floor.

Formula Long Direction Stort Direction

seconds

T=0.1N 5.6 5.6

0. 05h

n

Measured 3.7 4.0

Determination of the natural periods of vibration of structural

elements such as beams, floors and slabs is fairly straightforward either

theoretically or experimentally. Steffens [30] gives expressions for

natural periods of different types of beams under concentrated and uniformly

distributed loads. He reports that the natural periods of steel beams

will be in the range 0.02 to 0.20 seconds, and for floors and slabs the

range is 0.03 to 0.10 seconds. For wood-joist floor systems, Dnysko

[59] observes natural periods of 0.16 seconds, "''acobsen r76] has theoretically

determined the natural periods of uniform cantilever beams considering

flexure and shear in a beam and the elastic yielding of a rigid support.

Masur [79] has given a theoretical solution for the natural frequencies

of rigid frames .

4.1.5 D amping . Observations of the free vibration of a real system reveals '•hat

the amplitude of vibration decays with time. This ^-ehavior is attributed

to the action of damping in the system. The damping forces act in opposition

to the motion, doing negative work on the system ~nd dissipating energy

from the system.

There are three major categories of damping. If it is assumed that

the damping is proportional to velocity, it is known as viscous damping

and the amplitudes of successive free oscillations reduce in geometric

progression. If the damping is the result of solid body friction, then

the amplitudes of successive free vibrations decrease in arithmetical

progression. This is known as Coulomb ^riction damping. Tn a real structure,

some of the energy loss may be attributed to the internal friction of

the material. This is called structural damping. Although it is difficult

to predict the magnitude of various types of damping, experiments suggest

[88] that damping increases as the driving force increases. It was also

noted that damping in each mode of vibration was proportional to the

resonant frequency of the corresponding mode.

17
Another type of damping which is important in structures is the

aerodynamic damping which is considered in the dynamic response o£ structures

from wind loadings. This damping is sometimes negative which causes

an instability of the structure known as "galloping." Some of the reported

failures of icecovered transmission cables and suspension bridges are caused by galloping. Fortunately, for typical building structures

aerodynamic damping is negligible in comparison with the mechanical

damping associated with structures (viscous, coulomb and structural).

However, it is possible that local problems caused by galloping can exist

for isolated members such as columns, braces, struts and truss systems.

Damping of a real system is a complex phenomenon involving all mechanical

damping types. It is common practice to approximate the damping of a structural system by equivalent viscous damping.

Steffens [30] has discussed various factors and coefficients used

for damping. Of these, the critical damping coefficient (c ) and the

damping ratio (D) are important. The critical damping coefficient, c^,

is defined as the least value of the damping coefficient, c, required

to prevent oscillation of a system. The damping ratio relates the actual

damping to the critical damping value, i.e., D = c/c^, Steffens has

also given the damping ratios for steel, rubber, concrete and other materials.

Davenport [62] suggests the following values of damping ratio, D,

for tall buildings:

Concrete 0.01 < D < 0,02

Steel 0.005 < D < 0.01

Englekirk and Matthiesen [85] report that a damping ratio of 0.035 was measured in the vibration test of an eight story reinforced concrete

building. Nielson [88] found the damping ratio to be between 0,005 and

0.01 for a nine-story steel frame building. Reed [89] reports the largest

range of damping for tall structures, 0,004 < D < 0.07, which he obtained

from a survey of the literature. Jennings and Duroiwa [86] and Laxan

[87] have conducted experimental investigations to study the effect of

intensity and history of motion and soil interaction on the damping characteristics of structures. Damping of structural elements can be improved by

coating their connecting surfaces with a thin layer of plastic material

or by inserting mechanical damping devices [87],

Steffens [30] has outlined the methods of determining damping in

any given elastic system. Analysis of the results of free vibration

tests or examination of tlie response of the structure (at given frequencies)

to forced vibration will give an approximation of the damping of a structure.

4.1.6 Damage to Structures . Damage of structures from vibrations may range from collapse to

minor damage such as cracking of plaster and window glass or interference

with the operation of equipment.

Comparatively few cases have been reported in the literature where

severe vibration, except for earthquakes, has been the most likely cause

of structural damage, although complaints alleging damage to structures

as the result of vibrations are made frequently. Steffens [30] has

dealt with this topic in detail. He concludes that structural damage

due to dynamic response is likely only under earthquake conditions. He

also points out the inadequacies of the mathematical models used to determine

the response of structures to dynamic loads (i.e., earthquake loads),

uncertainties regarding dynamic characteristics of the structure (i.e.,

damping) and the uncertainties in loadings (e.g., lack of strong motion

18
data). Some or all of these Factors contribute to the observation that

buildings designed to withstand an acceleration of 0.1 g (g = 32.2 ft/sec ) are often found to be almost unharmed by accelerations as large as 0.3

g. Analysis of the strong motion data from the San Fernando Earthquake

of February 1971 [95], where accelerations up to 1 g were recorded, may

shed some light on the actual eartliquake resistance of buildings.

Minor damage such as cracking of plaster, window glass and damage

to brickwork are often incorrectly attributed to severe vibration [90,

91 and 92] . It was pointed out in these references that to cause damage

to plaster ceilings by vibration, amplitudes have to be in the order

of 0.1 in. or accelerations should be in the order of 1 g. These amplitudes

are not often experienced for structures in service even with blasting,

T)ile-driving or forge-hammer operations. The probability of fatigue

damage due to low level vibration is very small for most structural materials.

As the loading causing vibration (e.g. wind and earthquake") and

the response of the structure are stochastic in nature, design has to

be based on a specified but nonzero risk. Davenport [62] has suggested

a set of recurrence intervals for various unserviceability limits such

as breakage of windows and cladding, comfort of occupants and structural

fatigue for tlie design of tall buildings to resist wind.

Various criteria [90 and 91] for assessing the vibration damage

of structures have been suggested. Koch [93] has classified the intensities

of vibration and their probable damaging effects on structures. Investigation

on vibration effects of blasting has yielded some information as to the

safe charges of blast and criteria for damage [94]

.

4.1.7 Vibration Isolation . The reduction and isolation of harmful vibration as a result of

operation of industrial plant and machinery can be achieved [96] by correct

siting of machinery, proper balancing and the use of antivibration mountings

or special foundations . Isolation of structures from vibration can be atained by the provision

of trenches, using sand and gravel under the foundations, using suitable

building materials and type of construction, inserting special antivibration

pads under beam supports and column bases or mounting the complete building

on a suitable spring system. Steffens [30] has described each of these

methods and has cited a number of cases where each method was used in

practice

.

Den Hartog et al [97] have described a method to isolate a large

structure from shock vibration by suspending the foundation system within

an underground cavity. Vibration isolators are used to reduce the effect

of machine vibrations on buildings and Eberhart [98 and 99] has theoretically

examined the vibration transmissibility of different types of foundations.

Nelson [100] and Waller [102] have described the use of rubber bearing

pads and viscoelastic material to damp structural vibration.

Waller [101] has emphasized the significance of the damping characteristics of a structure in controlling its vibration. He has described the use of vibration absorbers in the 260 meter high chimney at Drax Power

Station, England. He suggests the possibility of using this technique

to control vibration in tall buildings.

19
4.2 Floor Vibrations.

4.2.1 I ntroduction . Floors are flexible structural systems and they will vibrate when

excited by a dynamic force. When the excitation ceases, ^he vibration

will then dampen and cease. Floors may be excited by human activity,

by machinery located on the floor, or any other activity which could

impart direct dynamic forces to the floor. Indirect excitation may be

transmitted to the floor from the structural frame which may be vibrated

by an earthquake, wind, vibrating machinery or various transportation

vehicles

.

Most problems with vibrating floors occur when the vibrations are nerceptible or annoying to the occupants. Because human sensitivity

to motion is very keen, the stresses and deformations corresponding to

perceptible vibrations are relatively small and no structural distress

is expected. A possible exception to this could be floors which support

machinery where distress may be caused by fatigue or resonance. Steady

state vibratory forces may create stresses which cause fatigue failures.

Resonance should be avoided where floors are exposed to steady state

forcing functions

.

The floor vibration problem has the following aspects: 1) Determination

of what is oerceptible and annoying vibration to human occupants (Section

4.4); 2) development of adequate mathematical models to represent the

floor systems ; 3) development of procedures to analyze and design acceptable

floor systems with respect to vibration; and 4) determination of economically

feasible repair procedures for unacceptable floors.

4.2.2 Analytical and Experimental Studies on Floor Systems . Floor systems are treated as 1) beam and girder assemblies, 2) grid

systems, 3) isotropic plates and 4) orthotropic plates. The study

of the vibration of beams, grids and plates is a part of mechanics and

the fundamentals are treated in any number of texts on the theory of

vibrations. With finite element procedures and computers, structures

or structural elements can be analyzed as long as the system and its

dynamic load are realistically defined. The search of the literature

indicates that there is an adequate number of references on olate or grid vibrations available so that the major aspects of the analysis of

floor vibration can be determined.

The following specific problems have been treated analytically

in the literature:

1) Beam and girder systems [105, 106, and 120].

2) Rectangular slabs and plates with various edge

conditions [108, 109, 112, 114, 116, 117, 120, 122

and 123]

.

3) Stiffened plates [110 and 118].

4) Orthotropic plates [113] . 5) Beams and slab system [118],

6) Slab on rigid and elastic columns [115].

7) Grid systems [120] . 8) Sandwich plates [103, 107 and 124].

9) Plates not rectangular in plan [108, 111 and 119].

10) Tapered plates [104] .

In addition, plate and beam vibration solutions are tabulated in a Russian handbook [121]. Solutions for buckled plates, prestressed plates

and beam-and-slab bridges are also given in the literature. A great

20
many types of vibrating plate problems have been solved, but they are concerned with applications in other technologies (aircraft space vehicles,

etc.) than building technology.

Bleich [105] considers the floor system to be made up of a set

of beams and girders orthogonally connected to each other. Two subsystems

are considered; the beams supported by infinitely stiff girders which

frame at right angles to the beams and the girders which support infinitely

stiff beams. He shows that by combining the dynamic properties of the

subsystems (which are now simple beams for which solutions are available)

,

the dynamic properties of the total grid system can be obtained. Finally,

a set of simultaneous equations are developed and the determinant of

the coefficients of the equations gives the desired natural frequencies.

Rogers [120] gives the complete dynamic solution (i.e., natural

frequencies and mode shapes) to three problems: 1) Floor systems with

a central girder and simply supported iDeams framing into this girder

at right angles; 2) rectangular, simply supported isotropic elastic

slab; and 3) orthogonal gridwork. He also describes Bleich's method

[105] thoroughly. Examples are worked for each case and the procedure

is readily usable for design calculations.

Burckhardt [106] presents nomographs and charts to rapidly determine

the natural frequencies of floor beams. The floor is idealized and represented

by beams of uniform, stiffness with various end conditions.

Mackey and Ying [115] present a method of analysis for floor systems,

considering floors as plates resting on supporting columns. The fourth

order partial differential equation involved is solved by the normal

mode method. A simple frequency equation in terms of the number of "symmetrically situated" columns is derived and some typical cases are solved

numerically. The stiffness of the floor system on elastic interior columns

is also discussed and mode shapes due to free and forced vibrations are briefly considered.

Floor systems are idealized by Lenzen, Dorsett and Sokolowski [113] as rectangular orthotropic plates, and solutions are presented for the

free undamped vibration (natural frequencies) , for the case of forced

harmonic vibration, and for static loading. The theoretical results are compared with experimental results and a simplication involving the concept

of "effective number of joists" is advanced.

Steffens [30] gives a broad review of many vibration problems. The

subjects of floor vibration and frequency of beams and slabs is covered.

Steffens notes that tests in Norway (1958) on timber joist floors resulted

in the recommendation that the deflection of the floor should not exceed

0.034 in. under a concentrated load of 220 lbs. Most domestic floors were stated to have resonant frequencies in the range of 10 to 30 Hz.

Excessive floor vibrations can be reduced by changing the properties

of the floor system. Approximate natural frequency formulas are given

for beams. Reference is made to the literature for natural frequencies

of slabs.

Ohmart [118] determined the response of a solid web steel beamconcrete slab floor system to dynamic impact by considering the floor

system as stiffened simply supported rectangular plate. The floor section

was treated as a system of discrete elements, i.e., a plate and beams.

A series of beam and slab test floors were constructed and tested to

verify the theoretical analysis. Excellent comparisons between theory

and experiment were obtained for the fundamental natural frequency and

fair correlation was observed for the maximum displacement.

21
From the current state-of-the-art o£ dynamic analysis it appears

that many practical and relevant problems have been solved and that techniques

exist to solve most problems. There are two things missing: 1) design

aids to assist the design engineer in computing frequencies and amplitudes

and 2) the treatment of the problem of the combined structural frame

and floor systems.

4.2.3 Experiments on Steel Joist Floor Systems (Lenzen) . Theoretical treatments of the dynamics of plates and floor systems

generally use idealized models of the systems and boundary conditions.

In reality, floor systems are highly complex with boundary conditions

which are often difficult to define. They are constructed of diverse

elements such as, slabs, beams, girders, joists, flooring, partitions,

insulation, ducts and ceilings all of v.'hich interact in a complex manner.

In buildings designed for human occupancy such as offices, stores, schools,

hospitals, etc., vibrating floors infrequently caused problems with the

types of construction used up until a few years ago. Recent availability

of high strength steels at a cost almost equal to that of the cost of

ASTM A36 steel has resulted in mucli lighter structural floors. For example,

the most popular open web steel joists are the H-series bar joists which

are made of steel with a minimum yield stess of 50 ksi. Lighter floors,

larger areas without partitions and ligliter ceilings have resulted recently

in some floors with unsatisfactory vibrations. B'^th the AISC Specifications

ril] and the National Building f^f^de of Canada r28] require that annoying

vibration of floors be avoided without defining what annoying vibration

is and without cruiding the designer to the appropriate design computations.

Steel j oist -concrete slab floors are one of the lightest forms of

floor construction. ^he Steel Joist Institute has sponsored a significant

amount of research on this problem at the University of Kansas under

the direction of Lenzen [125 through 132] which was nerformed in the

period 1959 to 1970. Some of this work has been reported in a series

of reports in the University of Kansas "Studies in Engineering Mechanics."

Since considerable research nn the topic of steel ""oist-concrete floors was performed by Lenzen, it is necessary to examine this work in detail

to give it proper perspective in the state-of-the-art in floor vibrations.

4.2.3.1 Dynamic Response Experiments . The first phase of the floor vibration work performed for the Steel

Joist Institute is given in reference 129. A test floor consisting of

a 2 1/2 in. thick slab resting on six steel joists about 15 ft. long

and spaced at 20 in. on center was constructed. Three sets of steel

joists, 8, 10 and 12 in. deep, were used in the study. The joist ends were simply supported and the slab edge, at right angles to the longitudinal

axis of the joists, was free. The dynamic excitation of the floor was achieved by subjecting it to; 1) steady state vibration and 2) impact

vibration caused by dropping an iron ball or a human heel drop. The

heel drop was performed by a man standing on his toes, relaxing, thus

allowing both heels to impact the floor. The measured natural frequencies

indicated that the slab and joist acted as a composite system even though

no intentional shear connecting devices were present. It was shown that

the natural frequency of such floors can be predicted adequately by considering

the beam to consist of the steel joist and an effective concrete slab.

The report also discusses the measured frequencies in 46 different floors

in service and construction. Various degrees of conformance with theoretical

predictions were noted. Human response to vibrating floors was also

discussed and is presented in Section 4.4 of this report.

22
Lenzen [129] discussed various features of damping and artificial

damping devices. A test floor, with a clear span of 24 ft., joist spacing

of 24 in., joist depth of 12 in., and with 9 joists was constructed to

study damping devices. The efficiency of insulation, bridging, prestressing

and a variety of cable installations in increasing damping was found

to be negligible, but external mass -spring-dashpot devices were found

to be excellent in enhancing the damping characteristics of the floor

system. Lyons [131] gives a detailed account of the investigation of the

structural and external damping devices used by Lenzen.

Floors in twenty buildings with composite and non-composite slabs

on solid web steel beams were subjected to impact with a mechanical impact

device and with a human heel drop [128] . The dynamic response of the

floor system (amplitude, frequency, damping) was recorded and analytical

studies were made of the dynamic properties of the floor system, A great

deal of data on framing, floor dimensions, records of response etc.,

are given in the report. In two of the twenty buildings it was noted

that the occupants complained of annoying vibrations of the floors. The

other floors appeared to have sufficient damping and it was suggested

that spray-on fire proofing may contribute to damping. The comparison

of the measured and predicted amplitudes due to impact indicated that

the T-beam anology is not a good method for these floors and an orthotropic

plate model is suggested for a better analysis. The report [128] contains

a great deal of data which might be used for a more in-depth analysis

in the future.

The second phase of the Steel Joist Institute sponsored research

project on floor vibration at the University of Kansas is given in reference

127. A test floor, larger than and different from the other floors, was constructed and subjected to a variety of tests. The floor consisted

of a concrete slab and 25 joists 32 ft. long and spaced at 24 in. on center. All four sides of the floor were simply supported. Excitation

of tlie floor system consisted of a sliaker producing steady-state vibration

or a mechanical device producing impact. Relatively long duration impact

was also produced by a human jumping on the floor. Static and dynamic

deflections and strains as well as accelerations were measured.

Dynamic properties of the test floor were determined by experiment

for the following configurations:

11 2 in

.

slab, simple bridging

21 2 in

.

slab, no bridging

3) 2 in

.

slab, full bridging

4) 4 in

.

slab, full bridging

5) 4 in

.

slab , no bridging

61 4 in

.

slab, only half the floor acting

7) 4 in

.

slab, only ^^alf the floor acting and ends of

slab removed

.

The conclusions from these tests were the following:

11 The slab and joist floor system acts ^^s a "nit, i.e., the floor

must be considered to be composite even though no mechanical shear f'onnectors were t)resent

.

2) Bridging does not affect the dynamic characteristics of these

floors

.

3) The concept of an "effective floor size" was experimentally

demonstrated. Floors larger than the effective '^loor size behave essentially

the same way as if their size were equal to this ^rea.

4) Addition of mass and stiffness by increasing the slab thickness

results in changed dynamic characteristics. Reduction of amplitude is

greater than the increase of the frequency, thus human response was stated

to be more favorable.

23
5) Cracked floors and slabs witli cut-outs have unfavorable vibrational

performanc'e

.

6) "Beating" which is noticeable and unpleasant occurs in light

floors

.

In addition to the experiment results, formulas for the determination

of the effective floor size, the impact amplitude and the frequency are given, and it is shown that close agreement exists between the experimental

observations and the theoretical predictions. The theory is based on the assumptions of orthotropic plate behavior [113].

The dynamic response of three concrete slab-steel joist floor systems

was studied at the structures laboratory of the University of Kansas

(to be published). The largest of these had a length of approximately

33 ft and the floor was approximately 50 ft wide with joists running

longitudinally along the 33 ft length. A simple support was provided

on all four sides of the rectangular floor. The other floors were 15

ft and 24 ft long and about 12 ft and 20 ft wide with the joists running

along the lengths of the slabs. The two sides supporting the joists were simple supports and the other two edges were free.

The three joist-slab floor systems were subjected to a great many

tests to study the effects of the following variables on the dynamic

response: slab thickness, joist size and depth, end conditions, beamversus-slab action, bridging, dynamic damping devices, dynamic excitation

devices, ceilings, joist spacing and presence of humans.

Parallel with the experimental program, an analytical study was performed to investigate the theoretical dynamic response of three steel

joist-concrete slab floor systems. Various analytical models were used,

and the most sophisticated of these considered the floor system to be

an orthogonally anisotropic composite plate.

Another phase of the research performed by Lenzen (to be published)

was on the problem of damping by artificial means, i.e., the use of damping

devices. Many internal and external damping systems were investigated.

It was found that the most effective device was an external friction

system which proved to be the predecessor of various such devices now commercially available.

In the previous unpublished work a comparison was made of the laboratory

results to many (both vibrationally adequate and inadequate) floor systems

in service and under construction. This work indicates that there was

a correlation between the human response studies, the field observations,

the laboratory tests and the analytical studies. This interplay yielded

considerable insight into the problem of vibrating floor systems.

4.2.3,2 Damping .

In view of the importance, considerable effort was devoted by Lenzen

[129] to determine the damping characteristics of steel j ois t -concrete

slab floors. Because of the complexity of this problem, no conclusive

results were obtained, however, certain observations were made:

1) Bridging of all types v;ill not improve the damping characteristics

and thus the presence or absence of bridging in the final floor makes

no difference as far as vibration abatement is concerned.

2) Addition of superimposed dead \\ieipht did not improve the response

of the floors . 3) Multiple sizes and types of joists did not improve the response.

24
4) People were excellent dampers and the presence of groups of

people on a floor, as contrasted to only one or. two people, effectively

damped the vibrations.

5) An increase in slab thickness improved the vibration characteristics

of a floor by increasing the effective stiffness of the composite section,

thus reducing the amplitude. The corresponding increase in frequency

was not large, thus this is an effective means of avoiding undesirable

vibration if no additional damping is nresent from partitions.

6^ Normal construction provided sufficient damping through such

features as walls, partitions, flooring, floor covering, ceilings, etc.,

so that transient vibrations were usually in the non-perceptible ^r barely

perceptible range.

71 If unusual conditions existed, such as large school rooms or churches, in which enough damping was not inherent in the construction,

damping could be provided by 'lamping units available commercially. In

such cases a ''areful analysis "^f the vibration problem may be warranted.

8) Any loss of the integrity of the concrete slab increased the

vibration. Cutting av/ay the slab from the ends of the --oists was especially

undesirable. A severely cracked slab could reduce the stiffness of the

composite joist-slab section by as much as 20 percent.

9) The floor system may not be the only cause nf its objectionable

vibration. Joists supported by flexible beams can interact with the beams

therefore the interaction of the total system must be considered. The

problem can be avoided by providing stiffer support beams.

4.2.3.3 Conclus ions . The extended scope of the research on the dynamic behavior of steel

j oist -concrete slab floor systems performed by Lenzen provides some data

for an understanding of vibrating floors.

One of the achievements of the research was that it was possible

to correlate theoretical predictions of dynamic behavior with the correspondin

measured behavior in the laboratory and in the field. The correlation

was excellent with respect to the laboratory test floors , where good

knowledge of all parameters existed, and it was also satisfactory in

the tests made on most floors in the field. Such satisfactory correlation

gives confidence to the analytical determination of tlie dynamic parameters

of floor systems in the design stage.

The combined experimental and analytical studies led to tlie following

insights into the dynamic behavior of joist-slab floor systems:

11 Tinder human impact loading all joist-slab floors act ^s composite

floors, even though no positive shear connection is provided and the

strength is governed by only the joists. The reason for this is that

under the -relatively small loads and deflections friction bet\\!een the

slab and the joist provides 'Essentially composite behavior. This composite

action results in an increase in the stiffness '^f the floor system. Positive

verification of the composite behavior under vibratory loads was provided

only for normal -weight concrete, altliough the same is estimated '•o be

true for light-weight concrete slabs, fimited tests showed, however,

that no increase in stiffness can be expected from gypsum concrete floors.

2) The joist-slab floor system acts a two-way plate system under

vibratory loads. Since the stiffness is different in each direction,

i.e., the stiffness of the composite section ^long the length parallel

to the joists and the stiffness of the slab alone perpendicular to the

joists, the analysis of dynamic behavior was achieved by assuming an orthotropic plate. Such an analysis verified the experimentally observed

existence of an "effective floor area" which participated in the vibratory

motion after impact. For floor areas larger than this effective area

it was found that only the effective floor area was actively participating

25
in vibration. Equations for determination of the effective floor area,

the frequency and the amplitude are given in Appendix C. While the dynamics of floor systems have been explained by developing

analytical models, the reaction of humans to vibrating floors is not

easily quantified. Human reaction depends on many parameters. This

topic is discussed in Section 4.4 of this report.

4.3 Drift.

The term drift is used to describe the lateral deflection of a building

generally when subjected to a lateral loading such as wind and earthquake

or to thermal gradients such as from solar heating. This section on drift covers the topics of effects, limitations, calculation and measurements.

It is apropos to clarify the use of terms referring to the direction

of motion of a structure with respect to the wind direction. Three

commonly used pairs of terms appear in the literature and are summarized

here.

Motion perpendicular Motion parallel

to wind to wind

across-wind along-wind

lift drag

transverse longitudinal

Drift deflections are of primary concern in the design of tall buildings.

The many aspects of the design of tall buildings has been the subject

of a joint effort of the American Society of Civil Engineers and the

International Association for Bridge and Structural Engineering on the

Planning and Design of Tall Buildings. A conference held at Lehigh University,

August 1972, produced conference proceedings which assembled this effort.

Specifically, drift deflections are considered in the proceeding references

[134, 135 and 136] of this conference. The major aspects of these references

are covered within subsequent discussions in this section of other more detailed references.

4.3.1 Effects of Lateral Loading on Structures . The undesirable effects of excessive structural deflections have

been classified into four broad categories in the ACI Committee 435 report

[133]: 1) sensory acceptability; 2) serviceability of the structures;

3) effect on non-structural elements; and 4) effect on structural elements.

Of these, drift limitations are given only regarding the category of

effect on non-structural elements.

In the ACI Committee 442 report [156] , lateral deflection is considered

as a serviceability criterion for the lateral load design of high-rise

buildings. Particular attention is called to the effect of drift on the stability and cracking of members.

Davenport [139 and 141] , has included among the major factors governing

design for wind: 1) failure due to instability of the frame; 2) failure

due to yielding with excessive permanent deformations; 3) failure due

to widespread damage to exterior cladding; 4) unserviceability due to

excessive deflections causing cracking of walls and degradation of the

structural skin and mechanical systems; 5) excessive sway accelerations

26
causing discomfort of occupants; and 6) breakage of windows. All of these

may be related to the drift of the structure.

I'/ith respect to seismic loading, Hisada [146] has classified the

problems associated with drift as: 1) restriction of damage to the non- structural components such as glass panels, curtain wall panels, plaster

walls and other partitions; and 2) protection from motion sickness or discomfort

.

Reed [155] presents a summary, as well as new data, for response

of high-rise structures to wind loading and human response to this type

of motion. Structural response to v/ind loading is discussed here and

human response is discussed in Section 4.4 of this report. Reed presents

calculation methods and analytical models from various other authors.

Consideration is given to the identification of the wind loading on the

structure and structural characteristics such as damping and natural

frequency. A comprehensive and broad coverage of various methods and

models are given. Emphasis is given to a probabilistic approach to the

forcing functions as well as the structural response. Reed observed,

from an examination of previous data and calculations and his calculations,

that total displacement in the drag direction is often greater than total

lift displacement, whereas at the same time lift acceleration is greater

than drag acceleration. Also it has been observed that lift deflections

are sometimes greater than drag deflections. This points to the important

fact that there is a very high probability that structural motion normal

to the wind is greater than the along-wind component. Reed considers

both the across-wind and along-wind components in his study.

Reed found that drift deflections have been limited to a range of

0.0015 to 0.0030 times the total height of a structure depending upon

whether the buildings were masonry or curtain-wall towers. The lower

allowables were applied to the curtain-\\rall type structures. Acceleration

calculations and measurements motivated observations that: lift accelerations

may be 2 to 4 times the drag comnonent , analytically nredicted drag accelerations

are 2 to .3 times the field or wind tunnel measurements, and tv?ist motions

are of the same magnitude as lift components. Reed points out that acrossivind or lift response is a significant consideration in determining drift

deflection or response. Details of this phenomenon have been studied

by Novak, Davenport, Wooten, Scruton, Vickery, and Clark [150, 151, 162,

and 165] . It is not the intention of this survey to present the methods

for prediction of lift response, but rather to draw particular attention

to the subject when lateral vibrations induced by wind loading are being

considered for high-rise structures.

4.3.2 Quantitative Limitations on Drift .

In numerous building codes, standards, recommended design procedures,

as well as in textbooks and research reports, the limitations on drift

are specified as a fraction of the total building height. The value

of the fraction appears to be loosely correlated v;ith observations on

the performance of structures designed and constructed v;ith theoretical

drift limitations. Values ranging from 1/200, mentioned by Khan, [147]

to 1/1200 noted by Frischmann and Prabhu [145] are given in the literature.

Fleming [144] has provided a summary of early work in this area. The origin of this now familiar form of limitation \-fas attributed

to Spurr [158] according to Frischmann and Prabhu [145]. From 1930 to

the present, the acceptable value has decreased somewhat. This is probably

due to the changing technology of liighrise building construction which

has seen the progressive elimination of masonry partitions and other

elements which added considerable stiffness to the structure. These

27
components traditionally have not been included in the mathematical model

used to compute the drift deflection.

A recent survey of seismic design codes by Hisada [146] revealed

that drift limitations are specified for design earthquake loads in

the Mexican and New Zealand seismic codes. Allowable values of drift

deflection from 1/400 to 1/500 are given with an increase of twice the

value if adequate clearances for all non-structural components are provided.

In the commentary of the Uniform Building Code [160] a value of 1/200

is recommended. In Japan there is no limitation given in the Building

Standard Law [146] but 2 cm per story is usually taken as the limit of

the drift computed by dynamic analysis for high-rise buildings. Provisions

on the separation of buildings to avoid contact during earthquake loading

are given in seismic codes in the U.S.S.R., Venezuela, t-1exico and Portugal

[146] and U.S.A. [160] . The ACI Committee 442 report [156] comments that a deflection limit

of 1/500 recommended by ACI Committee 435 [133] has resulted in the design

of modern buildings that appear to have been satisfactory with respect

to the following effects of sway under wind loading: 1) the stability

of the individual columns as well as the structure as a whole; 2) the

integrity of nonstructural partitions and glazing; and 3) the comfort

of the occupants of buildings. It is pointed out that the method of

computing the drift as well as the assumptions used in the calculations

vary considerably among practicing engineers. This aspect is discussed

further in Section 4.3.3 of this report.

Another limitation, reported by Philcox [153], that has been correlated

with performance is the height-depth ratio of the building which is

limited to 10 for a single shear wall and to 15 for a core. The depth

is apparently the dimension parallel to the wind direction.

It has also been recognized that limiting the total deflection

at the top of a structure may not be adequate. An additional limitation

of 0.15 inches per story is given in the ACI Committee 435 report [133].

Davenport [139] reported that cracking of partitions in a 40 story building

may occur if the drift exceeds 0.25 in. per story.

Since the limitations for drift essentially reflect an attempt to

provide factors of safety for both collapse and serviceability criteria,

it is likely that no single limitation is adequate. Davenport [139]

has noted that the risk of incurring collapse should be extremely small

and much less than the risk, of unserviceability . Also, he notes that

a distinction should be made between a structure which gives warning

of collapse and one which collapses suddenly. He suggested mean occurrence

rates per annum for the following: 1) catastrophic failure; 2) incipient,

non-catastropic failure; 3) window breakage, wall cracking; and 4) excessive

acceleration. It would appear that future performance criteria should

include probabilistically-based considerations of damage and risk.

4.3.3 Calculation of Drift . As noted in the preceding section, the drift limitations expressed

as a fraction of the overall building height have seemingly become more restrictive in recent years. This is attributed to a reduction in the

stiffening provided by the non-structural elements. Also, the tremendous

improvements in design and analysis techniques, facilitated by the computer,

have influenced the correlation between actual building performance and

design calculations. Assumptions previously implicit in the mathematical

models are now explicitly included. Large, Carpenter and Morris [148]

enumerate the contributory elements to the theoretical drift as; 1) web

drift (bending of girders, bending of columns, deformation of connections

28
and bracing) ; and 2) chord drift (direct lengthening and shortening of

columns). Also, the so-called secondary moments due to the direct column

loads acting through the lateral displacements (P-Delta effect) can be

important

.

All elementary methods of rigid frame analysis permit the computation

of deflections due to the bending of the girders and columns assuming

fully continuous connections. The effect of so-called semirigid connections

and secondary moment has been examined by Williams and Badland [163].

The deflection due to column shortening can be readily computed [143]

.

With the computer-based analysis techniques available, the modeling of

a structure to include most of the structurally effective components

is possible and it is expected that improved mathematical models should

provide for closer correlation between observed behavior and design calculations.

With reference to the relative contributions of the web drift or shear racking and the chord drift or column shortening portions of the

total drift, Khan [147] has shown that the web drift can be controlled

and set to a predetermined magnitude by providing adequate column and

girder stiffness at each floor. Because it is principally a function

of the overturning moment, the chord component is more difficult to affect

without simply increasing the column areas. Secondary moments and the corresponding additional deflections have

been examined with respect to limit design methods. Modern standards

[159 and 137] consider the secondary moment in the design of beam- columns

.

The computation of sway deflections in unbraced frames including secondary

moment effects is discussed by Driscoll [143] .

4.3.4 Measurements of Drift Deflections . Probably the first scientific measurements of the drift of a tall

structure were performed by Custave Eiffel on the top of the Eiffel Tower

between 1893 and 1895. His summarized results are given in English by

Parmelee [152]. Among other observations, Eiffel noted that high velocity

gusts (iniplying short duration) had a smaller effect on the displacement

of the top than those caused by the lower velocity continuous wind and

that the measured displacements were less than the computed values. This

he attributed to a lack of reality in the analysis assumntions . Parmelee

[152] also reports that in 1894 the deflection of the >Tonadnock Building

in Chicago, a sixteen story bearing wall building, was measured during

a windstorm. The deflections were observed by transits and checked by

observing the oscillation of plumb-bobs suspended in the stairway shaft.

The two observations agreed well and gave an east and west vibration

amplitude of 1/4 to 1/2 inch.

In order to verify a popular design method devised by vSpurr [158] , a scale model of a 55 story three-panel symmetrical bent was constructed

and tested at Ohio State University, The static load test results, presented

by Large, Carpenter and Morris [148], verified that the Spurr method

was accurate for the design of regular symmetrical bents, but that the

method was inadequate for irregularities such as fixed column bases,

tall basement stories and two-story entrances. This is still an important

result even for contemporary design since the Spurr method is based on

a prescribed drift.

The continuous observations of the Empire State Building in New

York are described by Rathburn [154]. Among these observations are a record of the pressure distributions on the structure and the movements

of the top of the building.

29
The velocity and direction of the wind were obtained from an anemometer

1263 ft. above the street. The author questioned the accuracy of the

anemometer for recording the velocity of the wind because of the presence

of the building itself and the other buildings in the area. The pressure

and pressure distribution of the wind was studied by thirty manometers.

Pressure distribution at the 36th, 55th and 75th floors are given for

a 90 MPfl, NNW wind, 50 to 60 MPII NW wind and no wind. A lack of correlation

in the measurements was indicated.

The motion at the top of the building was found to consist of two

types: 1) a mean deflection from the vertical under the action of a steady

wind; and 2) an oscillating motion under gusting which had different

periods in each axis of the structure. The motion was studied using

a vertical collimator on the 6th floor to observe a target on the 86th

floor. Also a plumb-bob was suspended from near this target to near

the sixth floor. The author reported that the collimator proved to be

very useful in studying the vibrations while the plumb-bob was more useful

in obtaining the mean deflections.

The reported plumb-bob observations are grouped into three classes

based on the wind velocity: 1) less than 20 MPII 2) 20-30 MPH ; and 3) more than 30 MPH. The maximum deflection in the east direction under

90 MPH, NNW wind was 10.7 inches. It was noted that the building did

not return to the original position at rest indicating the considerable

amount of inelastic material surrounding the structural frame. An interesting

conclusion was that the rigidity of the building including the masonry

exterior was stated to be approximately 350 percent more than the structural

steel frame.

Investigations conducted by the National Research Council of Canada

directed primarily toward measuring the natural periods of buildings

are summarized by Wiss and Curth [164] . They also comment on the work

of Rathburn [154]. Using these studies as background, they describe an investigation designed to measure the dynamic response of a high-rise

concrete frame building to wind loading. The authors designate the steady

component of the total measured lateral deflection as drift and the oscillations

as vibration.

Seismic type instrumentation was selected to make motion measurements.

A suitable system for measuring the vibrations in a high-rise building

is stated as: 1) the natural period of the unit should be adjustable

bet^veen 15 sec. and 70 sec; and 2) the unit should be capable of measuring

horizontal displacements up to 10 in. single amplitude [164]. A horizontal

seismic pendulum was developed for the purpose of measuring the vibrations

and a vertically hung pendulum was designed as a tiltmeter to measure

drift. Two perpendicular horizontal pendulums and a two -component tiltmeter

were placed in the concrete frame structure at the NE corner of the 55th

(top) floor. An identical set of instruments was located at the SW corner

of same floor. Tiltmeters were also located on the 42nd and 3rd floors.

Data were recorded for a period of 30 days using an oscillograph.

The average daily winds ranged from 5 mph to 20 mph vvrith daily peak gust

velocities between 14 and 48 mph (U.S. Weather Bureau data). Measured

wind velocities above the top of the building ranged from 0 mph to 70

mph during the recording period. A number of difficulties due to temperature

fluctuations were encountered in calibrating the instruments and are reported. The largest magnitude of the vibration recorded was a peakto-peak displacement of 1.0 in. during the 70 mph wind velocity at the

top of the building. The drift at the 70 mph wind speed was not directly

determined because of the time characteristics of the high wind velocities

compared to the pendulum. The authors developed a formula for determining

the drift based on changes in velocity from 10 mph to 20 mph. The extrapolation

of data with the formula resulted in an estimated drift of 1.5 in. for

the 70 mph wind.

30
Also, a comparison was made between the drift computed by the structural

designer and the corresponding value calculated by the formula based

on the test data [164]. The structural designer computed a deflection

of 8.9 in. at the top which corresponded to wind velocity at the top

of 103 mph as calculated from the equivalent static pressure specified

in the Chicago Building Code. Using the 103 mph velocity in the drift

formula, a drift of 3.3 in. was calculated which is 27 percent of the

value computed by the structural engineer. It was noted that the building

had shear and core wall elements as well as columns to resist the wind

loading which made it difficult to calculate drift deflections. It appears

that an inaccurate mathematical structural model and loading function

lead to an inaccurate drift calculation. Also, the accuracy of measurement

devices needs to be considered as pointed out by Dalgliesh and Ward [138]

in a discussion of Wiss and Curth [164] research.

Mackintosh [149] has reported that for frames tested with large

lateral loadings, the difference in measured plastic compared to elastic

drift due to beam flexure is much greater than would be expected.

An interesting set of aeroelastic wind tunnel studies to assess

the relative aerodynamic merits of different building shapes is reported

by Robertson [157]. Aeroelastic models of six building shapes (triangle,

modified triangle, square, cross, 2:1 rectangle and circle), each with

the same floor area, height, density and frequency of transverse vibration, were studied in a simulated city environment of a boundary layer wind

tunnel. Envelopes of peak deflection (static plus dynamic) at the top

of the models are plotted and the circular cross -section appears to have

the least overall deflection while the triangle and the 2:1 rectangle

have the largest deflections in the principal directions. No analysis

of these results are presented in the reference.

Davenport et al [142] describe the analysis of measurements made

of drift deflections for the 100 story John Hancock Center in Chicago.

They also determined natural periods of vibration for the two principal

axes of the structure. A comparison was made between actual dynamic

deflections and those predicted by the "gust loading factor" approach

given by Davenport [140] and Vickery [161] . Measurements of the fluctuating

response were reported to agree with the gust load factor approach. The

fraction of critical damping was approximately constant for the two axes

of the structure at 0.009 and 0.006 for a wide range of deformations

from fractions of an inch to one inch. The largest movements were found

to be normal to the wind direction.

^

•

^ Human Perception and Response to Motion o f St ructures

.

The study of human response to motion is part of a general area which is often termed human engineering. Humans are subject to motion

during most of their lives while walking, travelling, working and even sleeping. Some motion causes pleasure and a feeling of well being, while

other types of motion cause annoyance, discomfort, sickness, or even

death. There is considerable literature available on the general subject

and the limits of various levels of response such as perception, annoyance,

tolerance, etc., to various types of motion in ships, planes, cars, trains,

space vehicles, etc., are well known.

A special area of the general study of human response to motion

is human response to the motion of building structures. The state of

knowledge in this area is by no means complete. In fact, not really enough

is known to be able to make definitive suggestions to the designers

and builders of structures. This section describes pertinent references

and makes comparisons of various vibration criteria.

31
Deflection and vibration may disturb or hamper the functional performance

of the subsystems of a building, i.e., elevators j.amming, machinery or instruments functioning improperly, windows popping out, etc. The resulting

human cost is annoyance, discomfort and inconvenience resulting in economic

loss. If the tolerance of the subsystems and humans is knovm , the structure

may be designed so that deflections are not likely to be large enough

to cause more than very infrequent malfunction or human discomfort.

"Large" deflections and "violent" vibrations may also impair the

safety of the structure and result in its failure or collapse. With

the usual ductile structures used in modern construction, the deformations

corresponding to this limit state are several orders of magnitude larger

than those human occupants are willing to tolerate on a day-to-day basis.

Of course, the ultimate limit states involving deflections must be considered

in design. Thus, the human responds to deflections and vibrations which

are usually much smaller than those which result in collapse.

A seldom discussed aspect of human response to deflection and vibration

of structures is fear from collapse if motion is experienced. People

generally believe that structures are rigid and that visible or felt

deformation portends failure or at least an unsafe situation. This psychological factor leads to various degrees of fear or discomfort which exacerbate

the physiological effects of motion.

Awareness of static deflection is based on the sense of vision (sagging

ceiling or floor, cracked plaster or cracked walls). Adverse reaction

results if the deflection can be sensed by vision. How much deflection

can be detected by eye? Perhaps the traditional rule of L/360 is related

to this effect. Could psychological research give an answer. There was

no indication of an answer in the literature which was examined.

Awareness of vibratory deflection is based on the kinesthetic senses

and on vision. Visual effects are direct, i.e., a floor is seen to vibrate,

and indirect, i.e., chandeliers sway or relative motion is observed.

Vibratory motion is sensed by the human kinesthetic perception through

the inner ear, or by other parts of the body. Severe vibration can also

be accompanied by noise, although even small vibrations may result in

audible effects, i.e., tinkling glassware in a display case.

A great deal is kno\>:n about the response of humans to vibratory

motion, but the present knowledge of human reaction to the motion of

buildings is still quite rudimentary. Huignard [169] in a review paper,

had the following to say about the subject in 1971:

The human sensitivity to mechanical vibration extends

both above and below the range of hearing and is indicated

by a variety of receptor organs distributed throughout

the body. In the most sensitive range (below about

30 Hz) , the threshold of sensation may be as low as

1 cm/sec^. The social reaction to traffic induced

vibration of structures, however, may be modified by

many physical and psychological factors. Much of the

published work on the human response to vibration has

been concerned with relatively intense and continuous

vibration such as is felt in vehicles or near industrial

machinery, and most of the existing recommendations as to criteria and limits of human exposure to vibration

are related to those fields. It is suggested that

there is need for more basic research into the factors

determining human reactions to vibration of relatively

low intensity, of the kind induced in buildings and

other structures excited by traffic or industrial

operations outside.

32
4.4.1 Previous Statc-of -tlie-Art Reviews . Ihman reaction to vibration is important and worh has been done

on this subject. Reviev/s of the state-of-the-art ]iave been nade from

various points of viev/. Right such reviev/s are given in this section.

Each of these is relatively short and the benefit of another compilation

combining all of these is rather doubtful, tluis only a brief statement

is made about each

.

Historically significant reports related to these state-of-theart reviews are given in the list of references [167, 171 through 174,

176, 179 and 181]. These are listed for the convenience to the reader

if specific details are desired.

Cope [166] reviewed the status of knowledge on the response of humans

to moving vehicles. He gives 19 references and the report was published

in 1960. The reviews by Hornick and Lefritz [170] and by Richards [177]

deal with the same subject.

Chapter 44 in the Shock and Vibration Handbook, 1961 Edition, by

Coldman and vonCierke [168] presents available data, tlieoretical background

and design information mainly for human response to steady state vibrations

The most up-to-date and pertinent review, as far as response to

motion of buildings is concerned, is by Cuignard [169]. He points out

the need for fundamental research in this area, noting that most of the

information on human response to vibration v/as developed for much greater

vibratory intensities than is tolerable on a day-to-day basis for buildings

occupied by neople.

The report of Onysko [175] is a broad review of structural requirements

of wood joist floor systems including the requirements for strength

and deflection. Th.e date of the report is January 1970 , and 97 references

are listed and discussed. From a structural designer's point of view

this is the m.ost significant literature review for floors of those cited

]iere. Onysko discusses the code requirements, the background for code

provisions, past research and current problems. The following quote

from this report indicates the conclusion reached that more research

is needed.

Wliile it }\3.s been demonstrated that deflection under

a concentrated load correlates reasonably well v/ith

acceptability, this criterion alone does not yield the

necessary guidance to provide acceptable floors. It

has been seen that the vibration of floors affects

their acceptability. TIius , it may be expected tliat a performance specification founded on hum.an perception

to vibration will provide the necessary guidance. It

is in this area that work is necessary, not only to

define how the variables affect acceptability, but

also to indicate hovi floor designs might be im.nroved.

Stef^^ens [178] discusses the various scales used for measuring human

reaction to vibration, but dv/ells m.ainly on the effects of vibration

on the structure itself. He lists 172 references covering the tim.e period

from about 1900 through 196 5, but only a few of these refer to work on

hiiman response. The references are mostly English and German, although

som.e Japanese and East European ivork is covered. There is a notable

absence of Russian literature.

.33
The review by Wric^ht and Green [180] specifically cover the state

of knowledge of human response to motion up to 1959. The various scales

of response are described and 70 references are cited.

The clear conclusion from these eight reviews is that there is by

no means enough known to formulate valid rules on performance criteria

regarding human response to vibration for the design of building structures.

4.4.2 Physiological Responses . Many studies have been performed to examine the response of the

human body and its subsystems to different types of motion. The references

listed for this section [182 through 197] should be considered to be

representative samples rather than as a complete list. The work has

concentrated on the dynamics of human organs and the body as a whole,

and physiological reactions to relatively severe vibrations and motions.

Much has been learned about the reaction of humans to motions encountered

in moving and vibrating vehicles; however, this work is only indirectly

applicable to motion of building structures.

4.4.3 Subjective Responses of Humans . The references of this section deal with the human subjective response

to vibration. Typically, human subjects were placed on devices which

provided a controlled and programmed vibratory environment. The test

subjects then answered questions about what they felt and how they reacted.

Generally the human test subjects were subjected to sinusoidally vibrating

situations, thus the results apply essentially to long term vibration

(steady-state) and not necessarily to transient vibrations which are also

encountered in building structures. These studies demonstrate that the

scales of human response as developed by Reiher and Meister [212] and

Goldman [204] are valid for defining response to steady-state vibration

which can be expected in vehicles or in structures with vibrating machinery.

V/hether or not these scales are valid for designing structures subjected

to random and transient dynamic loading for human occupancy has been

repeatedly questioned.

The majority of the references listed in this section [198, 199,

201, 202 , 205 and 207 through 211] have been reviewed by V/right and Green

[180] or Steffens [178], therefore, they will not be reviewed here. Four

references have not been reviewed in the previously mentioned surveys

and will be discussed here in some detail. These references are significant

because they were the only ones which report work performed specifically

to measure the response of humans to building vibration.

The research by Blume [200] measured the response of occupants in

buildings which are subjected to vibrations originating from underground

nuclear blasts. Tests used eight subjects on a suspen(led platform (pendulum)

to determine the threshold level of horizontal motion perception. These

tests were correlated with motion perceptions reported by observers in

high-rise buildings in Las Vegas, Nevada, during underground nuclear

tests. Threshold of perception was presented as a curve relating acceleration

to period. A statistically derived equation for the acceleration at

the threshold of perception v;as given as mean perception threshold (g) =

0.00245 + 0.00025 x frequency

where g is the aceleration of gravity. The standard deviation about

the mean expression line was 0.0012 g. The range of applicability of

34
Blume's equation is for a frequency ran,'Te of .33.3 I!z to 0.2 Hz or, in

terms of period, from 0.03 sec. to 5 sec. The ranges of the formula

were put together as a composite from results presented earlier by Goldman

and von Gierke [168] in the high frequency range, from results of the

pendulum tests on eight subjects in the laboratory C^ediiim frequency),

and from results of the Las Vegas building observations (low frequency)

.

The results of Blume's work give further information on the response

of humans to low frequency, low amplitude horizontal vibration. The mean acceleration at the threshold of perception range from 0.0025 g to

0.0108 g over the whole applicable frequency domain. This compares with

the range of 0.004 g to 0.0075 g reported by Khan and Parmelee [206], but

the latter did not correlate their findings with frequency. Blume also

notes that there is significant difference between individuals and that

the body attitude is less significant. This is essentially the same conclusion as that reached by Khan and Parmelee. No physiological and

psychological data were given on the eight subjects. The number of subjects

was small and no consideration was given to the effect of damping and

duration of vibration.

Khan and Parmelee [206] and Chen and Robertson [203] studied the

response of humans to wind gust induced vibrations in tall multi-story

structures. Khan and Parmelee made three sets of observations. The

first concerned an analytical study of the maximum acceleration of four

tall buildings (two 50 story, one 60 story and one 100 story buildings)

under gusts deviating 20 percent from the maximum wind veloctiy for 5 sec. Maximum accelerations were found to vary from 0.002 g to 0.004

g. The second report concerned tests on 30 human subjects on a rotating

platform. Body posture (standing, sitting, lying), face direction (four

orthogonal directions relative to direction of acceleration) and acceleration

were the variables. It was found that body posture and face direction

had less effect than differences between individuals. The barely perceptible

level of acceleration was found to be from 0.004 g to 0.0075 g, and 0.02

g was disturbing to all subjects. The final set of observations contained

acceleration data taken in one building (860 Lake Shore Drive, Chicago;

a 26 story apartment building) at one location (top story) during a wind

storm. The maximum acceleration measured during a 70 mph wind was 0,0042 g. Chen and Robertson [203] tested 112 subjects to determine the threshold

of horizontal m.otion perception. Tests \'/ere performed in a horizontally

oscillating room at periods of 5, 10 and 15 seconds. The folloAving

variables were considered: period, body orientation (four directions

with respect to direction of motion), body movement (standing, v;alking,

sitting) and exnectancy level (t^iree levels; total ignorance of the test,

expectation of motion, and previous experience of motion in test chamber).

The data from the subjective responses of the test subjects were analyzed

statistically and they A-.'ere presented in the form of curves relating

cumulative frequency to perception thresholds in g's. All of the test

variables were found to be significant. This contrasts with Blume's

observation that body posture was not significant. However, Blume's

subjects did not move and all can be assumed to have expected the motion.

Clien and Robertson demonstrated that the perception threshold in g's

is highest for walking subjects and the lovrest for sitting subjects.

It appears that perception thresholds are smaller when subjects are anticipating

motion or have experienced it previously.

Additional tests have been performed by Wiss , Janney and Elstner,

in cooperation with Parmelee on many subjects to study the effect of

damping. This worlc has not been published, however, findings relating

amplitude, frequency and damping to human perception and response have

been developed.

35
4.4.4 Observed Human Response .

The references 213 through 220 are representative of research relating

to the ability of test subjects to see, track and respond in a vibrating

environment. This work is' especially significant for transportation

vehicles, but the motions are more severe than those expected in a building

structure, thus are only indirectly applicable.

The previously referenced research on human response to motion was performed essentially on subjects in a laboratory controlled environment.

Some of the results were planned to be used in the design of buildings.

Data on observed human response to motion of structures in service, which

is necessary to make a successful transformation from laboratory controlled

human response scales to building design, is difficult and expensive.

Lenzen (to be published, refer to Section 4.2.3.1 of this report)

built several full scale concrete slab-steel joist floor systems. He

tested subjects standing or sitting in chairs on the test floors as these

floors were excited by impact, and then recorded the impressions and

reactions of the test subjects. Also data on subjective responses were obtained by interviewing people who had experienced vibrating floors

in actual buildings in service and during construction. The human response

characteristics were coordinated with dynamic analyses of the corresponding

floor systems and limits of human tolerance were established. Mo documentation

as to subjective response was presented, only conclusions are given.

Lenzen concluded that the most important parameter affecting the response

of humans to transient motion is the rate at which the amplitude of deflection

due to the initial impact is damped out. It was demonstrated that if

the deflection amplitude decayed to about 20 percent of its initial value

at impact in five cycles or less, the human subjects felt only the initial

impact. Perception to oscillations and unpleasant reactions were nonexistent.

If the vibration persisted for more than five cycles , the oscillations

were felt.

In the case v;here no inherent structural damping exists due to partitions

or other items, Lenzen [225] suggested a modification of the Reiher and

Meister [212] human response curves for a design guide of floor systems.

These curves are also presented in the review report by Wright and Green

[180] . The deflection amp litude - frequency domain is subdivided by curves

into subdomains of "not perceptible, slightly perceptible, distinctly

perceptible, strongly perceptible, disturbing and very disturbing." The same subdivisions are retained by Lenzen, but the deflection amplitude

scale (ordinate) is referenced to the initial amplitude upon impact,

and the magnitude of the amplitude is increased to 10 times the Reiher

and Meister scale. This increase was made to empirically account for

transient vibration rather than steady state. The boundary line between

the slightly perceptible and the distinctly perceptible domains was taken

to be the design limit for floors supporting human activity. Furthermore,

this limiting line was shifted upward parallel to its original position

a distance equal to 20 percent of the original distance between the original

lines representing the two boundaries of the distinctly perceptible

region. This shift is assumed to empirically incorporate the fact that

all floor systems possess some damping.

While the modification of the Reiher and Meister human response

curves to account for transient vibration in a damped structure appears

to be somewhat arbitrary, a great deal of circumstantial evidence was presented for justification. This evidence is taken from interviews

of people subjected to vibrations of floors in the laboratory and in

the field, and from dynamic analyses of floor systems which had been

judged as satisfactory or unsatisfactory in service.

36
It is difficult to drav; quantitative conclusions from the Lenzen

vibration work, but qualitative aspects of the problem become apparent

from studying his results: 1) the important differences between transient

and steady state vibration; 2) the importance of damping; and 3) the

difficulty of transforming human response in the laboratory to actual

field requirements. Observations of unsatisfactory floors in the field were subjectively correlated with interview data on laboratory floors.

Onysko [175], in his literature survey, reviews in considerable

detail studies made by Russel [226], Hansen [224] and Vermeyden [228] on the human subjective response to wood- joist floors. These sought to

discover whether or not the test floors were acceptable to the test subjects

when the floors were subjected to various load intensities. It was quite

difficult to determine what the tests results meant. It appeared that

a relationship between deflection and occupant comfort was developed.

These results were then used to develop allowable deflection criteria.

Chang [221] gives a graph which can be used to ascertain human comfort

in buildings subjected to wind loading, but it is not clear from the

paper where this information comes from and how it was developed. An

article by Crandell [222] gives curves for human and structural response

to vibration. He notes that safe vibrations for structures are two orders

of magnitude larger than the vibrations felt by humans. Davenport [223]

considers the dynamic response of a tall building and attempts a correlation

with thresholds of human response.

Reed [227] recently studied high-rise structures with respect to

wind loading and human comfort. Linear and angular acceleration were identified as the response parameters for humans in tall buildings. Timerate of change of acceleration (jolt or jerk) may also be significant.

This suggests that acceleration response is a function of frequency.

The fundamental natural frequencies observed of tall structures ^^^as found

to range from .07 to .3 Hz. Items other than motion were observed to

be significant and to influence human response, such as, noise, structural

creaking and groaning, local motion of fixtures within a structure and

the world moving outside. The latter refers to perceptible relative

visual motion as viewed from one structure to another. An important

observation is made that perceptible motion is not necessarily annoying

motion. A review is made of the cues which manifest external human response,

i.e., human mechanisms which transduce vibration to human perception.

Reed's experimental program included a subjective survey of human

response to the motion of tv/o high-rise buildings located in widely separted

geographic areas of the United States each subjected to strong winter

storms. Motion measurements were taken in one of the structures and were inferred for the other from wind tunnel studies and calculation.

Table 1 gives the pertinent information for each structure, the storm

data and the structural response. The height of both buildings is approximately

550 feet and the fundamental natural frequencies were approximately 0.17

Hz. The average magnitudes of notion were 0.002 g (rms , root-mean-square)

and 0.005 g (rms) during the storm peaJcs ivhich lasted 20 to 30 minutes.

The structures and storm intensities Avere very sim.ilar. Occupants of

the structures were surveyed by personal interviews regarding their response

to the motion of the structures during the storms. A large portion of

those interviewd rated motion sensation and motion sickenss sym.ptoms

as significant. The motion sickness symptom was rated the highest of

the two. The interviews indicated that a learning mechanisms is possible,

i.e., there is an ability of people to adapt to the motion of high-rise

structures.

Perception of motion was studied by Reed on a probabilistic basis

from structures in service by determining the percent of people objecting

37
TABLE 1

Summary of Building Information for Wind Loading Response

to High-Rise Structures [227]

Statistic Building A Building B

Height 550' + 550' +

O Li UL-uUI ctJ. Sys tem resisting frames

First natural

period

5-6 sec. 6-7 sec.

Age < 10 yr. < 10 yr.

Building

density

9 - 10 pcf 9 - 10 pcf

Environment Urban, near ocean Urban, near ocean

Building type Office Office

Average number

of occupants

2800 2800

Length of

perceptible

lllU LXUll LI Li 1 XJI^ work day

6 hr 5 hr

Length of storm

peak

30 min 20 min

Average rms

iiiocion levex

during entire

perceptible

period

0.001 g (rms) 0.002 g (rms)

Average rms motion level

during storm

peak

0.002 g (rms)

38

0.005 g (rms)
to the motion resulting from a storm when c^ivcn the number of storms

that could occur in one year. Typical results ranged from 9.4 to 25.6

percent of the people objecting to 2 to S storms per year. This approach

is proposed to be superior to the extrapolation of laboratory experiments.

Reed's research is based on all environmental and psychological factors

that interact with motion response. A general conclusion made for the

structures studied is that people are sensitive to notion and do not

consider nerceptible motion acceptable except on rare occurrences. I'/hen applied to the desij;n prolilcm, a probabilistic approach is taken which

relates a perceptible acceleration magnitude to a desirability of its occurrence. It x^ias found througli interviews with owners, developers and

engineers that a reasonable limit of 2 percent of the occupants of a structure

could object to motion in one year without interferring significantly

with the overall operation of a structure. This objection rate is then

related to a return period of a severe storm for the given acceleration

level of tlie structure investigated.

4.4.5 Vibration Clauses in Standards . Traditionally the possible problems with vibrating buildings were avoided by specifying live load (superimposed static load) deflection

limits in structural standards. This topic was discussed in detail in

Sections 3. and 4.3. Generally this has v/orked through experience with

respect to human response to structural vibrations. The application

of these specifications made computations quite simple such that load

tables of allowable live loads for presumably adequate structural systems

could be compiled. The codes generally do not distinquish between various

uses of the buildings, except that the Dutch Code TAR 1955 [extracted

from 20] for wood floors has a live load deflection limit of 1/500 of

the span for floors not subject to considerable vibration while a limit

of 1/800 of the span is prescribed for floors subject to considerable

vibration

.

With the increased use of high strength materials, larger spans

and generally more flexible construction, it became apparent that the

simple live load deflection limits did not always suffice. Khan and

Parmelee [206] report some buildings which were found to be unsatisfactory

in high velocity gusty windstorms (horizontal deflections) , and Lenzen

[128] occasionally refers to unsatisfactory floors. It appears that

the live load deflection limits as specified in codes provide a guide

for satisfactory performance for vibratory loads encountered in buildings

most of the time, but that this is not an infallible procedure. As a result, modern standards [29] do require that

Beams and girders supporting large open floor areas

free of partitions or other sources of damping,

where transient vibrations due to pedestrian traffic

might not be acceptable, shall be designed with due

regard for vibration.

Similar provisions are contained in the Canadian Standards [28] where

the Commentary also contains an approximate formula for computing peak

acceleration due to wind gusts, and a perceptible acceleration of about

0.01 g is indicated. The Guide Criteria for the Design and Evaluation

of Operation Breakthrough Housing Systems [230] recommends that

39
transient vibrations induced by human activity should

decay to 0.2 of their initial displacement-amplitude

within a time not to exceed 1/2 second.

Futhermore, steady state vibration is to be isolated, or, where this

is not possible, a human perception curve (deflection amplitude versus

frequency), based on the Lenzen modified Reiher and Meister [225] curves,

should be satisfied.

The International Organization for Standardization currently has

a draft standard, Guide for the Evaluation of Human Exposure to WholeBody Vibration ISO/DIS 2631 [231] which is within committee for review

and approval. This guide is written with a general approach for application

to many vibratory environments. As quoted from the Guide, it is applicable

to

Vibrations transmitted to the body as a whole through

the supporting surface; namely, the feet of a standing

man, the buttocks of a seated man, or the supporting

area of a reclining man. This kind of vibration is usual

in vehicles, in vibrating buildings and in the vicinity

of working machinery.

The Guide is applicable to a frequency range of 1 to 80 Hz for steady

state, periodic vibrations, random vibrations with a distributed frequency

spectrum and continuous shock excitation if the energy is contained within

the 1 to 80 Hz band. Vibration directions are three dimensional and

apply to the human for the foot -to -head , right -to - left side and backto-chest orientations. All allowable vibrations are given in terms

of frequency and rms (root -mean-square) acceleration. Therefore, interpretations of the given allowable vibrations can be made for vertical floor

vibrations and transverse or drift deflections. An adjustment formulation

of the Guide applicable to building structures has been proposed by

Splittgerber [229 and 232]. Several classifications of commercial and

residential occupancies are categorized. These categories are: 1) hospitals

and sanatoriums ; 2) private homes situated in a district with prevailing

residential buildings; 3) private homes situated in a district in which

residential buildings and industrial plants are mixed; and 4) private

homes situated in a district with prevailing industrial plants. An allowable

vibration level is designated for night and day occupancy for each of

these four occupancy classifications. Generally the night time allowable

are lower than the day time. Vibration allowables were established for

vibratory inputs of steady state, interrupted (less than 2 hours without

pause) and short time ( 1 to 3 transient vibrations in a 24-hour period).

One band of acceptable vibration is designated with the subjective title

of "reduced comfort boundary to avoid considerable annoyance to occupants"

[223].

The Guide [231] is strictly qualified in that it may not be extrapolated

outside the frequency band of 1 to 80 FTz. Belo^^^ 1 Hz symptoms of kinetosis

(motion sickness) appear which do not relate to frequency, intensity

and duration of vibration exposure in a manner to that of the higher

frequency vibrations. Above 80 Hz local factors such as precise direction

of vibration and area of application become significant factors. These

qualifications are significant with respect to indicating regions of

vibration frequencies which manifest significantly different human responses.

It is apparent that codes and standards are moving cautiously toward

a specific set of requirements with regard to human response to structural

motion. This, of course, is necessary, but certainly not enough guidance

40
is given to the designer to be reasonably sure of avoiding annoying

vibration. Until more is known about this difficult topic, this dilema

will be present and the designer must use his best judgement.

4.4.6 Comparison of Data for Human Response to Structural Vibrations . The literature review has revealed several sources of information

from which the structural designer can obtain guidance for the control

of deflections to minimize discomfort of building occupants. The information

is diverse and many times does not give consistent results when the various

data are compared.

For comparison purposes two categories can be formed: 1) human response

to vertical vibrations, 2) and human response to horizontal or lateral

vibrations. Vertical vibrations refer to floor vibrations and lateral

vibrations refer to drift deflections such as that induced by wind load.

The literature is not consistent in presenting the magnitudes of

vibration thresholds and sensitivities. Thus a base parameter of rootmean-square (rms) acceleration will be used so that comparisons can be

made. Some data is presented in the form of deflection or half amplitude

deflection. This data was transformed to rms acceleration by

^peak = 47T^f^A (1)

where

A = half amplitude deflection

f = frequency, Hz

and

I = — a , rms peak C2)

General vibration specifications such as the ISO Guide [231] present allowable

vibrations in dB (decibel) levels above or below a basic specified acceleration,

The dB is a power ratio defined as

IdB = 201og (3)

where the a^ (i = 1 , 2) are the basic or allowable acceleration magnitudes

Human response to structural vibrations changes depending upon the

vibration time history, i.e., steady or transient. Steady state has an explicit definition of continued sinusoidal vibration or random vibration

that can be described in a continuous manner. Transient vibrations have

been ambiguously described in the literature. Each author has a separate

definition, none of which appear to have a common denominator. Comparison

of steady state vibration sensitivity from several sources will be made

which apply to vertical floor vibrations induced by forcing functions

eminating from mechanical equipment, etc. Transient vertical vibrations

in floors will then be considered. Finally attention will be given to

transient horizontal (lateral) vibrations induced by wind loads.

41
The ISO Guide [231] is presented in rms acceleration units. The allowable

magnitude o£ acceleration as proposed by Splittgerber [232] is given as

a dB (decibel) level above or below a basic ISO Guide acceleration allowable.

Figure 2 shows the allowable upper and lower boundaries for steady state

vertical vibration for day and night occupancy of private homes situated

in a district with prevailing residential buildings determined from the

ISO Guide and adjusted according to Splittgerber. For this particular

vibration classification, no differentiation was made between day and

night occupancy, however, a differentiation is made for other housing

classifications between day and night. The vibration levels for these

boundaries shown on figure 2 are for a foot-to-head orientation, a , applicable

to the standing or sitting human. ^

Also shown on figure 2 are the perception band v\;idths from the original

work of Reiher and Meister [212]. These perception bands range from

a perception threshold to an unpleasant level. The data from Reiher

and Meister is in the form of half-amplitude deflection, thus it was transformed

to rms acceleration by equations (1) and (2) . Another set of curves from

Goldman [204] are shown on figure 2 to complete the steady state vibration

comparison. Goldman's curves are average perception levels from a perception

threshold to unpleasant and represent much of the data on human perception

to the time of Goldman's report (1948). The bounds of curves on figure

2 represent the rms acceleration and frequency ranges over which they were established by the respective authors. The Goldman summary data

and the Reiher and Meister data compare consistently which is not unexpected

as the Reiher and Meister data was included in the Goldman summary. However,

the Goldman data does extend over a broader frequency range. The ISO

Guide with the Splittgerber adjustment falls below the perceptible range

of both Goldman and Reiher and Meister for f > 4 Hz. This indicates that

for this frequency range the ISO Guide requires that floor vibrations

not be perceptible assumming the Goldman and Reiher and Meister data are valid. For 1 < f < 4 Hz the ISO Guide is below the Goldman average perceptible

curve and trends in a similar manner to the Goldman curve. Reiher and

Meister data do not extend to this frequency range. Data for steady state

vertical vibrations appear consistent within the various subjective classifications, i.e., perceptible, unpleasant, etc., and trend in a similar manner

with respect to frequency versus acceleration.

As previously mentioned, transient vibrations have been ambiguously

defined in the literature. The adjustments recommended by Splittgerber

for the ISO Guide, which are applicable to vertical transient vibrations,

use two different states of transient vibrations , interrupted and short

time. Also a differentiation is made between day and night occupancy.

Figure 3 shows three different bands of allowable vertical transient vibration

for the ISO Guide - Splittgerber references; short-time day, interrupted

day, and short-time and interrupted night. Each of these decrease in

allowable acceleration level in the respective order listed.

Lenzen [127] uses another definition of transient vibration which

considers the characteristics of one single transient pulse rather than

an aggregation of pulses over a given period of time such as Splittgerber.

Lenzen's transient vibration specification is a modification of the original

Reiher and Meister work [212] for steady state vibrations. All levels

of Lenzen's perception bands are shown on figure 3. Lenzen's data is

in half -amplitude displacement and was transformed to rms acceleration

according to equations (1) and (2). Lengths of curves represent the frequency

range over which his modification extends. The trends of the ISO Guide

Splittgerber and Lenzen data for f > 8 Hz are similar; however, for f <

8 Hz there is a divergence of the two. That is, the allowable perception

level increases for the ISO Guide with respect to Lenzen's allowables

as frequency decreases. The allowable short-time day ISO Guide specification

for f > 8 Hz corresponds to Lenzen's slightly perceptible range which

does appear to be a consistent relation; however, at f = 1 Hz the Lenzen

42
Legend

Goldman [209]

Reiher and Meister [212]

ISO, Splittgerber

[231, 232]

C7> C

tM o

<

a:UJ

_j

LlI o

o

<

CO

10

7

5

3

2

I 7

5

10"

5 7 10 T"

5 7 IOC T

7 - 5

UNPLEASANT^ / UNPLEASANT (RANGE) 7—5^

/

-DAY AND NIGHT (RANGE)

WEAKLY

PERCEPTIBLE

(RANGE)

J L 2 3 5 7 10 2 3 5 7 I0(

Figure 2.

FREQUENCY, f, Hz

Human Response Thresholds, SteadyState Vertical Vibration

43
I

Legend

Lenzen [127]

ISO, Splittgerber

[231, 232]

C7>

<

1x1 _J

Ixl O

<

cc

10

7 -

5 —

10

2 3 5 7 10 2 3 5 V 100

1— 10

r

- 7

5

-SHORT-TIME, INTERRUPTED

NIGHT (RANGE)

J L

I I J L 5 7 10 2 3

FREQUENCY, f, Hz

3

2

10- 5 7 100

Figure 3, Human Response Thresholds,

Transient Vertical Vibration

44
allowable is an order of magnitude (1 x 10) below the ISO Guide - Splittgerber

allowable for a similar perception range. Except for f < 4 Hz , the ISO

Guide-Splittgerber interrupted day and short-time, interrupted nightfall approximately an order of magnitude below the Lenzen slightly perceptible

range. No definite conclusion can be drawn except that, relatively speaking,

either Lenzen 's allowables are too high for slightly perceptible boundaries

or the Splittgerber allowables are too restrictive for the interrupted

day and short -time, interrupted night boundaries.

Horizontal vibrations are considered with respect to wind loading

on high-rise structures. The vibration direction induced in the human

is generally considered as side-to-side or back-to-chest for a standing

or sitting human. The horizontal vibrations are considered transient

for these comparisons however, each author's definition of the nature

of transient vibration is different. Transient vibration infers that

the structure is responding to either gust loading or the short time (such

as the Splittgerber designation) lateral vibration as it oscillates from

the excitation of the rise and fall of the peak of a storm activity. All

data are compared on a basis of frequency and rms acceleration. Inhere

data were in the form of peak acceleration or deflection, transformations

were made consistent with equations (1) and (2).

Blume [200] compiled data from others and their own experiments.

They determined a median for a perception threshold for horizontal vibration.

Blume's tests exposed the subjects to an oscillatory motion of which the

total duration was not designated, however, it was observed that the subjects

responded to the initial acceleration peak. This threshold is shown on figure 4 with boundaries of +^ s , the unbiased estimation of the standard

deviation. The data compilation covers a large frequency range of .2

< f < 30 Hz. Most high-rise structures fall in the lower portion of the

band of f <^ 1 Hz. For this lower region of the data, the threshold of

perception is approximately constant with respect to frequency. The median

threshold is between 0.0015 and 0.002 g (rms) and the estimated standard

deviation is approximately 0.001 g (rms).

Splittgerber [232] recommends adjustments to the ISO Guide for horizontal

vibrations similar in manner to the way in which they were applied to

vertical vibrations. Horizontal vibrations or accelerations, a , refer

to back-to-chest and right-to-left side orientation with respec^'^o vibration

input to the human. These levels of allowable vibration are shown in

figure 4 for short-time day and interrupted day for private homes situated

in a district with prevailing residential buildings. The short-time day

would be applicable to gust loading response, whereas the interrupted

day would be applicable to response from the rise and fall of the peak

of a storm activity. The ISO Guide-Splittgerber alloA^?able vibrations

are not applicable for f < 1 Hz . The trends of the ISO and Blume data

appear consistent and the bounds are similar and coincident for some of

the band width of allowables. The ISO Guide-Splittgerber short-time day

allowable is approximately one order of magnitude higher than the Blume

data and the ISO Guide-Splittgerber interrupted day allowable. The ISO

Guide-Splittgerber allowables indicated that humans are less sensitive

to short time vibrations than the longer exposure period of an interrupted

vibration

.

Chen and Robertson [203] presented low frequency threshold human

response data for horizontal vibrations for .067 < f < 0.2 Hz. The mean

of the perception threshold (50th percentile threshold) is shoAm on figure

4 with boundaries of plus and minus the unbiased estimated standard deviation.

The Chen and Robertson data is offset on the acceleration axis by a factor

of approximately 2 with respect to the Blume data and the Chen and Robertson

data are higher. The trend of their data is divergent from the trend

of the Blume data, this is, for decreasing frequency, the perception threshold

is decreasing for the Blume data and increasing for the Chen and Robertson

45
Legend — ISO Splittgerber

[231, 232] — Blume [200] — Chen and Robertson

[203]

© Reed [227]

FREQUENCY, f , Hz

Figure 4. Human Response Thresholds,

Transient Horizontal Vibration

46
data. The two sets of data do not overlap but are adjoining, therefore,

it is impossible to determine any transitional trends for the connecting

frequency ranges. The Chen and Robertson data indicate an estimated

standard deviation of approximately 0.001 g which is similar to the estimated

standard deviation of the Blume data.

Reed [227] presented an approach to human perception that was different

from all other literature reviewed. Perception levels were determined

from structures in service. Two discrete points were determined from

these high-rise structures subjected to strong storms. Several different

subjective evaluations resulting in various terms referring to motion

perception were made. A nuisance -comfort evaluation was made through

personal interviews. It was found for the two structures that 37.6 percent

of the people felt that the motion was a nuisance and/or uncomfortable

for the lower level acceleration, 0.002 g, (figure 4) and 60.5 percent

felt the motion to be a nuisance and/or uncomfortable for the higher level

acceleration, 0.005 g (figure 4). It should be noted that one point

of the Reed data falls on the median of the perception threshold of Robertson

data and the other point of the Reed data falls close to the median of

the perception threshold of the Blume data. However, Reed's discrete

points do not agree with the Chen and Robertson and Blume data in that

the latter two are perception thresholds whereas the Reed data is an uncomfortable region. Subjective classifications are difficult to conclusively

compare, however, these do appear to be inconsistent.

The data for the low frequencies, f < 1 Hz, for the horizontal vibration

is insufficient to determine whether it Ts inconsistent or that there

is a change of trend of acceleration response. In a gross sense, the

data could indicate an increase in perception level as frequency decreases,

a similar trend as that indicated for the transient and steady state vertical

vibrations at the lower frequencies (figures 2 and 3). Much information

needs to be obtained for perception thresholds of horizontal vibrations

for f < 1 p{z . This frequency region will be difficult to interpret due

to the predominance of kinetosis (motion sickness) which both the ISO

Guide [231] and Reed [227] have observed.

Chang [221] presented data and specifications for human response

to horizontal vibrations; however, these data are not used here for

comparisons as their basis is questionable. Chang's acceleration sensitivity

levels were determined from tests performed by Parks and Snyder [211]

for 1 < f < 27 Hz for subjects strapped to a seat and subjected to vertical

vibrations. Transformation of this narrow band vertical vibration data

to broadband horizontal vibration specifications is questionable. Reed

[227] also points out that a review and re- interpretation of Parks' and

Snyder's report resulted in a large change in the threshold values at

f = 1 Hz for vertical vibrations. This draws even more question to the

Chang specification.

An overall comparison is made (figure 5) of perception levels for

transient vertical, transient horizontal and steady state vertical

vibrations. Extreme boundaries of similar perception thresholds were determined from figures 2, 3 and 4. Each of the three classes of vibrations

with the respective extreme boundaries were then plotted on figure 5. The boundaries are broad; trend similarly in some areas and are divergent

in others. Divergence of extremes occur in all three vibration categories

for f < 5 Hz. Divergence is especially evident for the transient vertical

vibrations. Acceleration perception levels for transient vertical vibrations

are higher compared to steady state by an order of magnitude. The acceleration

levels generally translate down without a change in frequency (figure

5) from transient to steady state thresholds. Generally comparing transient

vertical and transient horizontal vibrations, the perception level for

horizontal is approximately one order of magnitude below the vertical.

47
CM

H < Z

Z H O iiJ 2 -

Z LiJ (E < Qc m trH O

X ^>

o

J L

to CVJ

I I I

I I I 'O

in ro CVJ o

r- If) ro CM

~ O

lO

ro

CM

O

lO

ro

CM

- N O

z

in yj

ro

CM

— in

ro

CM

A'xd'Zd '6'NOIiVd31300V SViH

48
There is also a general trend of a shift of the frequency to the left

for the horizontal with respect to the vertical transient vibrations.

That is, there is both a reduction of acceleration as well as frequency

for a given threshold of perception for transient horizontal vibration

as compared to transient vertical vibration. The "appendage" of transient

horizontal vibration response (figure 5) for f < 0.2 Hz trends similar

to the transient vertical vibration response.

The broad band of variance for threshold levels, trends of human

response with respect to frequency, and discontinuities and gaps in data

demonstrate the need for considerable study in the domain of human response

to structural vibrations. Considerably more questions arise in the area

of human response to transient vibrations than to steady state vibrations.

Definition of a transient load in itself is a very complex and difficult

task. These comparisons were not intended to compile all available data,

but to present selected data and research representing a broad expanse

of time from 1931 to the present.

4 . 5 Discuss ion . The problem of designing building structures for deflection which

are as economical as the state-of-the-art of construction permits and

are satisfactory with respect to serviceability, funtional ity , and aesthetic

and human requirements is composed of three parts: 1) the definition

of the excitation (forcing function) ; 2) the definition of the structural

charactertistics and 3) the definition of the deflection or response requirements. These three are vitally connected and one cannot consider each

individually without regard to the other two. Each of the three parts

of the problem are random variables and a truly satisfactory answer cannot

be obtained without a probabilistic formulation, coupled with cost optimization.

Methodologies for such a solution exist, although a realistic practical

solution is still far off. Some parts of the puzzle are already available:

wind loads and gusts have been defined probabilistically, dynamic analyses

of complex structures have been performed and some indication of human

response to motion is known. Many pieces are still missing: what should

the forcing motion be for human activity on a floor system; what is the

statistically quantified human response to damped vibration; what is the

actual dynamic character of a building as compared to what can be modeled;

what role does the psychology of fear have in the human response to motion

of buildings, etc.?

Much needs to be determined about human response to motion in buildings.

But more importantly, a definition of the total problem must first be

formulated, each missing piece must be identified, and then it must be

decided to what extent it is worthwhile to get a complete answer to each

question

.

By examination of the literature in the area of human response, it

is clear that previous work is either inapplicable, i.e., it is concerned

with motions well above that acceptable in buildings or incomplete (no

psychological evaluation), inadequate consideration for damping, no clearly

defined test conditions, etc. It is possible to obtain the required answers with a good deal of effort in a broad research program involving cooperation

between psychologists, physiologists, engineers, builders and statisticians.

Ultimately such a program is necessary to provide an adequate and

scientifically based guide for the totally functional building structure.

49
5. References

Static D efl ej^'tj_ons

1. ACT Connittee 435, "Allowable r)e:Plections" , Proceedings

American Concrete Institute, Vol, 65, Paner Mo. 65-31,

1068, pp. 433 -44-1 .

2. ACT Conmittee 318, Buildi ng Co d e Re g^uire ments for Reinforced

Concrete (ACI 31 8 - 717) , American Concrete Institute,

Detroit, Michigan, 1971.

3. Allen, D. E., "Serviceability Criteria for Deflections

and Vibrations", Building Structures Section, Division

of Building Research, National Research Council of Canada,

NBC of Canada, Supplement No. 4, Commentary Mo. 4, 1970,

pp. 597-598.

4. Aluminum Construction Manual , Specifications for Aluminum

Structures , The Aluminum Ass~ociation , Mew York City,

Nov. 196 7.

5. Blakey, F. A., "Deflection as Design Criterion in Concrete

Buildings", Transactions of the Civil Engineering , Institution of Engineers, Australia, Vol. C. E. 5, No. 2,

Sept. 1963, pp. 55-60.

6. Buchert , K. P., Mulner, W. , and Ruhey, H. , "Application

of Turn-Key Construction to Industrialized Urban Housing

in Missouri - Summary Report", Mizzou Housing Project .

7. Davenport, A. C, "Tlie Treatment of V'ind Loading on Tall

Buildings", Proceedings of Symposium, Univ. of Southampton,

April 1966.

I t t 8. Deformations , Report No. 4, Comite Europeen du Beton,

"5th Session, Vienna, April, 1959 .

9. Jenkins, R. A. S., Plowman, J. M. , and Haseltine, B. A.,

"Investigation Into the Causes of the Deflexion of Heated

Concrete Floors Including Shrinkage", Structural Engineer , Vol, 43, No. 4, April, 1965, pp. 105-116.

10. Joint WRC - ASCE Committee on Plasticity Related to Design,

"Commentary on Plastic Design in Steel: Deflections,"

Progress Report No . 7 , Proceedings ASCE, Vol. 86, No. EM 2,

Paper 2454 , Apr. , 1960 , pp. 141-160.

11. Manual of Steel Construction , American Institute of Steel

Construction, Seventh Edition, New York, 1970, pp 5-35,

5-36.

12. Marino, F. J., "Ponding of Two-Way Roof Systems", Engineering

Journal , American Institute of Steel Construction, Vol. 3,

No. 3, July 1966, pp. 93-100.

13. Onysko, D. M. , "Performance of Wood-Joist Floor Systems",

Forest Products Laboratory Information Report np-X-24 , Canadian Forestry Service, Department of Fisheries and

Forestry, January, 1970, Ottawa,

50
14. Report of Structural Use of Aluminuin , The Institution of

Structural Engineers , London , Jan., 1962.

15. Skempton, A. W., and MacDonald, D. H. , "The Allowable Settlement

of Buildings", Proceedings , Institution of Civil Engineers

London, Vol. 5, Part 3, Paper No. 50, Dec, 1956, pp. 727-762.

16. Standard Specifications and Load Tables , "Open I'/eb Steel

Joists and Longspan Steel Joists"'^'"^ Steel Joist Institute,

Arlington, Virginia, 1970 Edition.

17. Stevens, L. K. , "Direct Design by Limiting Deformations",

Proceedings , Institution of Civil Engineers, Vol. 16, July,

1960, pp. 13 5-258.

18. Thomas, F. G., "Strength of Brick Work", S tructural Engineer , Vol. 31, No. 2, Feb., 1953, pp. 35-46, No. 7, July, I960,

pp. 187-189.

19. Timber Construction Manual , American Institute of Timber

Construction, Washington, D. C, First Edition, John Wiley

and Sons, Inc., New York, 1966.

20. Vermeyden, P., "Strength and Stiffness of Wood Joists",

Heron, Vol. 9, No. 2, 1961.

21. Whittemore, H. L., Cotter, J. B., Stang, A. II. and Phelan, V. B. "Strength of Houses", Application of Engineering Principles to

Structural Design, U. S. Dept. of Commerce, National Bureau

of Standards, Building Materials and Structures Report BMS 109,

April 1948.

22. Wiss, J. F. and Curth, 0. E., "Wind Deflections of Tall

Concrete Frame Buildings", Proc. ASCE Vol. 96, No. ST7,

July, 1970.

Dynamic Deflections

Current Design Practice

23. ACI Committee 318 "Building Code Requirements for Reinforced

Concrete", (ACI - 31 8 - 19 71 )

,

' Detroit , Mich.

24 . American National Standard " Building Code Requirements for

Minimum Design Loads Tn Buildings and Other Structures ",

A 58.1 - 1972, American National Standards Institute,

New York, N. Y.

25. Beles, A. A. and Ifrim, M. D., "Elements of Earthquake

Engineering" (Elemente de Seismologie Inginereasca) Bucharest,

Editura Technica, 1962, 247 pages.

26. Ferry-Borges , J. and Ravara , A., "Earthquake Engineering - Seismic Design of Reinforced Concrete Buildings", Laboratorio

Nacional de Engenharia Civil, Lisbon, 1969.

27. Korchinskiy, I. L. "Method of Designing Buildings for Seismic

Forces", Earthquake Engineering Research Institute , 1960,

pp. 10-15.

28. National Building Code of Canada , National Research Council of

Canada, Ottawa 19T0~.

51
29 . Specification for the Design, Fabrication and Erection of

Structural Steel for Buildings , American Institute of Steel

Construction, New York, February 1969.

30. Steff ens , R. J., "Some Aspects of Structural Vibration",

Vibration in Civil Engineering , Proceedings of a Symposium

Organized by the British National Section of the International

Society for Earthquake Engineering, Editor, B. 0. Skip,

Butterworths , London 1966.

31. Ward, H. S., "Dynamic Characteristics of a Multistory Concrete

Building", Proc. Inst. Civil Engrs . Vol. 43, Aug. 1969,

pp. 553-572.

32. Wiegel, R. L. (Editor) "Earthquake Engineering", Prentice Hall,

Englewood Cliffs, N. J., 1970.

33. Wiggins, Jr., J. H. and Moran, D. F., "Earthquake Safety in

the City of Long Beach Based on the Concept of Balanced Risk",

J. H. Wiggins and Company, September 1971.

Forcing Functions - Wind

34. Ferry-Borges , J. "Dynamic Loads (in Particular Wind and

Earthquake Loads)", Preliminary Publication , Eighth Congress,

International Association For Bridge and Structural Engineering,

New York, 1968, pp. 663-686.

35. Davenport A. G. "Wind Loading on Tall Buildings", Proceedings of

Design Symposium, Northwestern University, Illinois 1970,

pp. 109-123.

36. Scruton, C. and Flint, A. R. , "Wind-Excited Oscillations of

Structures", Proceedings , Institution of Civil Engineers,

Vol. 27, Apr. 1964, pp. 673-702.

37. Scruton, C. "A Brief Review of Wind Effects on Buildings and

Structures", Journal of The Royal Aeronaut ical Society , London , May 1966

.

38. Wind Effects on Buildings and Structures, Proceedings of a Symposium held at the National Physical Laboratory, June 1963,

Her ^tajesty's Stationery Office, London, 1965.

39. Wind Loads on Buildings and Structures, Proceedi ngs of a Technical Meeting, Building Science Series 30, National

Bureau of Standards, U. S. Department of Commerce, Washington,

D. C. , November 1970

.

Forc ing Functions - S eism ic

40. Parmelee, R. A., Perelman, D. S., Lee, S. L., and Keer, L. M.

,

"Seismic Response of Structure -Foundation Systems", Jo urnal of

the Enginee ring Mechani cs D ivis ion , ASCE, Vol. 94, No7 EM6

,

Dec. 1968 , pp. " 1295-1315.

41. Sarrazin, M. A., Roesset, J.M., and V'hitman, R. V., "Dynamic

Soil-Structure Interaction, Journa l of the S tructural Division , ASCE Vol. 98. No. ST7 , July 1972.

^'^ • Ui"ti form Building Cod e, International Conference of Building

Officials, Los Angefes , 19 70

.

52
43. V/iegel, R. L. (Hditor) "Earthquake Engineerinr;" , Prentice Hall,

Engiewood Cliffs, N. J. 1970.

^ ° cijig Functions - Sonic R oom

44. Hubbard, H. II. ^'Nature of the Sonic Boom Problem", Journal

of the Acoustical Society of America, Vol. 3^ , Mo. S,

Part 2, 1966, pp. S-1-59.

45. Loivery, R. L. and Andrev/s , D. K. , "Acoustical and Vibrational

Studies Relating to an Occurrence of Sonic Boom Induced

Damage to a IVindow Class in a Store Front", Contract NAS

1 -5813 Andrews Associates, Inc., Oklahoma City, 1966, p. 37.

46. ''ayes, W. H. and Edge, Jr. P. M. , "Effects of Sonic Boom and

Other Shock Waves on Buildings", Materials R esearch and

Standards , Vol. 4, No. 11, Nov. 1^F47 pp . 588-593.

47. McKinley, R. 1/. "Response of Glass in V/indows to Sonic Booms",

Materi als Research and Standards , Vol. 4, No. 11, Nov. 1964,

pp". T94-6no

.

48. Newberry, C. W. "Response of Buildings to Sonic Boom",

Journal of Sound and Vibration , Vol. 6, No. 3, Nov. 196 7,

pp . 406-418

.

49. U'iggins, J. II., Effects of Sonic Boom, J. II. Wiggins Co.,

Paios Verdes Estates, Calif., July 1969.

Forcing Functions - Shock I'/ave

50. Blasting Up in Builtup Areas, Journal of South African Mining

and Engineering, Vol.' 72, No. 3579, Sept. 8, 1961, pp. 569-573.

51. Crandell, F. J. "Cround Vibration due to Blasting and its

Effect on Structures", Journal of the Boston Soc. of Civil

Engineers 36, 1949, pp. 222/245.

52. Edwards, A. T. and Northwood, T. D., "Experimental Studies of

Blasting on Structures", Engi neer , Vol. 210, No. 5462, Sept.

30, 1960, pp. 539-546.

53. Langefors, U., Westerberg, H. , and Kilhstron, B., "Cround

Vibrations in Blasting" , Water Power , Vol. 10, No. 9, 10

and 11, 195 5.

54. Leet , L. D. "Vibration from Construction Blasting", Explosive

Engineer , Vol. 38, No. 1 and 2, 1960.

55. Wiss , J. F. "Effect of Blasting Vibrations on Buildings and

People", Civil Engineering , Vol. 38, No. 7, July 1968,

pp. 46-48.

Forcing Functions - ^lachinery

56. Anthony, P. J. "Survey to Determine Likelihood of Damage by

Industrial Vibrations:, Sur . Min . Res. Australia, 1965.

57. Novak, M. "The Vibrations of Massive Foundations on Soil",

International Association for Bridge and Structural Engineering,

Zurich, Vol. 20 , 1960 , pp. 263-28l'.

53
Forcing Functions - Traffic

58. "Measuring Vibration in Building Constructed over RailwayLine", Civil Fngineering (I^ondon) , Vol. 56, No. 656 , March 1961,

pp. 345'^3T7".

"'^

Structural Systems - Houses and Apartmen ts

59. Onysko, D. M. "Performance of I'/ood-Joist Floor Systems;

A Literature Review", Information Report nP-X-24, Forest

Products Laboratory, Ottawa, Ontario, January 1970.

Structural Systems - Tall Buildings

60. Chang, F. K. "Wind and Movement in Tall Buildings", Civil

Engineering , ASCE, Vol, 7,7, pp. 70- 72 , August 1967.

61. Chiu, A. N. L. , Sawyer, D. A. and Crinter, L. E., "Vibrations

of Towers as Related to V/ind Pulses", Journal of Structural

Division , ASCE, Vol. 90, Part 2, Oct. 1964 ,' pp. 137-158.

62. Davenport, A. G. "The Design of Multistory Buildings Against

Wind", Fi nal Report , Eighth Congress, International Association

for BriSFe and Structural Engineering, Mew York 1968,

pp. 687-692.

63. Davenport, A. C, "The Treatment of Wind Loading on Tall

Buildings", Proceedings of a Symposium held at the University

of Southampton , Apr fl 1966 , Pergamon Press, New York 1967.

64. Goldberg, J. E. and ITerness , E. D., "Vibration of Multistory

Buildings Considering Floor and IVall Deformations", Bulletin,

Seismological Society of America, Vol. 55, No. 1, Feb. 1965,

pp. 181-200.

65. Izhizaki, 1^. and Katsura, J. "On the Vibration of a Cylindrical

Tower Structure Induced by Strong V/inds", Bulletin of the

Disaster Prevention Research Institute, Kyoto University,

Japan, Vol. 19, Part 2, No. 155, Nov. 1969, pp. 19-23.

66. Korchinsky, I. L. "Vibration of Tall Buildings", Earthquake

Engineering Research Institute, 1960, pp. 56-72.

67. Robertson, L. E, "On Tall Buildings", Proceedings of a Symposium held at tlie University of Southampton, April 1966 , Pergamon Press, New York 1967.

68. Taj imi , H. , Ichino, I. and Cotoh, H. , "Aseismic Design of

Reactor Enclosure of the Japan Power Demonstration Reactor

(JPDR) and its Actual Behavior for Earthquake", Bulletin

of the JSME, Vol. 9, No. 34, May 1966, pp. 294-299.

69. Wright, R. N. and Walker, W. H. , Vibration and Deflection of

Steel Bridges, Engineering Journal, American Iron and Steel

Institute N. Y., N. Y., Vol. 9 No. 1, January 1972.

Structural Systems - Foundations

70. Hsieh, Tso Kung "Foundation Vibrations", Proc eedings , Institution of Civil Engineers, Vol. 22, June 1962^"

pp. 211-226.

54
71. Richart, F, E., Jr., Hall, J. R. Jr., and Woods, R. n.,

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214. Buckhout , R. , "Effect of Whole Body Vibration on Hum.an

Perf orm.ance" , Journal of the Human Factors S ociety, Vol. 6,

No. 2, April l^T^. - -

-

215. Dennis, J. P., "The Effect of Whole Body Vibration on a Visual Performance Task", Ergonomics , Vol, 8, No. 2, Apr. 1965.

64
216. Frazcr, T. M. , Hoover, C. N., Ashe, W. F., 'Tracking Performance

During Low Frequency Vibration", Ae rospace Medicine, Vol. 32,

1961/

217. Holland, C. L,, "Performance Effects of Long Term Random

Vertical Vibration", Journal of the Human Factors Society , Vol. 9, No. 2, Apr. IWT.

218. Hornick, R. J., "Effect of Whole Body Vibration in Three

Directions Upon Human Performance", Journal of Engineering

Psychology , Vol. 1, No. 3, 1962.

219. Lange , K. 0,, Coermann, R. R. , "Visual Acuity Under Vibration",

Journal of the I'uman Fact ors Society, Vol. 4, No. 5, Oct. 1966.

220 . Simons, A. K., Hornick , R. J., "Effects of the Vibration

Environment in Mobile Systems on Human Performance",

Ergonomics , Vol. 5, No. 1, Jan. 1962.

Response to Building Vibration

221. Chang, F. K. , "Wind and Movement in Tall Buildings", Civil

Engineering , Vol, 37, Aug. 1967.

222. Crandall, F. J., "Will 'ly Blasting Damage Property?", Engineering

News Record , Vol. 144, May 4, 195 0.

223. Davenport, A. G., "The Treatment of Wind Leading on Tall

Buildings", Proceedings of a Symposium held at Southampton,

April 1966.

224. Hansen, H. , "Deflection Characteristics of Wood Joist Floors",

Nat. Res. Council Technical Translation, NRC - TT883, Ottawa,

1960.

225. Lenzen, K. H. , "Vibration of Steel Joist -Concrete Slab Floor

System -Final Report", Studies in Engineering Mechanics No. 16 , Center for Research in Egnineering Science, The Univ. of

Kansas, Lawrence, Kansas, Aug. 1962.

226. Russell, W. A., "Deflection Characteristics of Residential

V/ood Joist Floor Systems", Housing Res. Paper 30, HHFA,

Washington, D. C. , 1954.

227. Reed, J. W. , "Wind Induced Motion and Human Discomfort in

Tall Buildings", Structures Publication No. 310, Civil

Engineering Dept., M.I.T., Nov. 1971.

228. Vermeyden, I. P., "Strength and Stiffness of Wood Joists",

Heron, Vol. 9, No. 2, 1961.

Vibration Clauses in Standards

229. Duetsche Normen , Enschutterungen im Bauwesen, Einwirkungen

auf Menschen in Cebauden, DIN'4150, Blatt 2, July 1971.

230. Design and Evaluation of: Operation Breakthrough Housing

Systems. U. S. Department of Housing and Urban Development,

National Bureau of Standards Report 10 200, September 1970.

65
"Guide for the Evaluation of Human Fxj^osure to Whole-BodyVibration", Draft International Standard ISO/DTS 26.31,

International Orf^anization for Standar^U zation , May 1972 . Snlitt fTerl:)er , H. , "Die Pinwirkuns^ von F.rschutterunren auf

den Menschen in Hebauden", (The Pffects of Vibrations on People in Structures), in German, Zeits chrift Technische

Ub erwachun.q , Bd 10 (1969) No. 9, S TT^?^.

Private correspondence, Dr. H. Splitt<Terber to Dr. P. Crist,

July 1972.

66
APPENDIX A

Summary of Vertical Deflection Limitations

in

U. S. Codes and Standards

National Standards

Model Codes

State and Local Codes

67
MAT I ON AL STANnARnS

CD o i> o IT) •H • H 4-' o M r—

J

<D tx E O

d) •i-i 1—

1

o o

O I—

1

0

1 1 CD o •H

CJ •"^

J

1 r-* t-H E E

*^ r—

J

E nJ * 1^ ri Q

IP, Cj ^ + •H

c_ O 1^ T> u CJ o H o •H O

*-> I—

I

M • r-i O O t—

t

E o O c: o O O C ^3 •H

t=: ' ' C- w o •H PI c C o

t/) c <D cC •H ctJ P. o c •M >^ f—

1

J-I (/) u •H U

r—

i

Jh J-i cti o

C- c c 1—

t

"M o I—

I

o c c '-i-i t/) c U~- •H

•H O I—

1

a> c <D Oj CO a- P= M-J t-H

<—

•

t/) c

,

rH n; O '—

1

CO

C- •H

E—

'

to

u: M • H

•H <D H

P-i •H .—

(

o o O o

1—

1

cc \o CO

I—

(

tn

to CO o

r—

1

<—

I

CO •H -a o > +-> ci u

a; E ' rH •H ct <U +J <D C <D

c/: cc o C

c<

<

H

4-1 D

+-> •H

!->

If) c

<D

+-1 <DU

O

C

o !=; u 1-1 o

•H

+-1 rt CO u

U <-H

• Hu

0)

68
NATIONAL STANDARDS

M

cS

<D iH /2 M-H u

rH 0

1—

<

o ••->

t/i OS

1/1 I/) iH C

cr; - o H •H .J^ v< to +J +-> nj •H

t/1 to O +J &

tj^ CD •(-( • H c E 13

CJ •H U •H

1—1 (D O t-H 0 H ;3 t-H C U

to i-i OJ u 4; c M to •H n- 0

t:' CD r! 03 C to

OJ (/) o a O CC rt o c I-H O to 0

r-l 10 c

t^ C 1/) rH !h •H u

(/; CJ (U C rt a; 0 t-l rt X > tA O > IJ > 0 •H

I—1 -M -H t—

1

o o H I-H (D l-J C-, O 00 u H i-J U C

CO

E-< n

1—

1

2:c O

1—! \D o O 0

vC VO U (SI E

-J C

+->

rC t3 o

O </) -3 ca c .I-H +-> •H c o u (/) rH c

O >—1 -H H (U •H

•H a> +-> o C 0 (U to

4-J O T-f E • H f-l U +-> 13 p a; • H 3 to W (=! H • H t/1 r—

1

>

JS C <1> Z C +-> ^ o (1) W

t/1 O 4-J o •H l-> ^-| < i=; +J \0 M CO to 0

O (L) 0) o 0) <f) C~i •f-i +J (_)•»-»> H (-> U r-( o o t-C < ^. o •t-J •H •H H >—1 +-1 CO U 4-> • H

O 'H O •H !h •H 1—1 ^1 M o u

•)-' i/i p; a-. (-1 (/) (=; ^ a) c

c/: c o i-H t/) o p. p.-t-' 0

1—1 .H C 1-1 •H g in C CO •H

4_) - o 0) 4-1 O C O AS u c M •H D fI-H U t-i O S-i u !-i - rt tn !-) W .H 4-) >H OJ •H M >s Id <D to H

" ^ Ifl in <D C .-H OC+J C cues (D C >-i e o <u E O -H +J C < u 2; H < U 5c c/: I-! I-H 1—1

69
MODEL COnF.S

bec ^.

<D bo •H <D c rH 4_) c •H •H t/1 3 4-> (D Ct) ^1 CJ 1—1

(/I

O >

<u P, •H

•H fx 1—(

(U

i-H c 3

,C o (/) CO •H E « •H 4) •H

(D o +J t/i >-i W. I—(

(/I

u <U •H o

<r. i/l (-1 3 VI M- p. c re <-i-i o J-i If. p. O o (-> 3 c (/) (h c 1—I

(/) i-i •H f-i

C I/) o U-i E- 1—1 OJ •H o u O •rt •(-> 4-) (/I E

i-i o X)

u 1 <D <+J !-i u c E

13 £i ^ t;

(L> <D o « P E cJ o « t-J t-J u o o 3 4) C O iH > l/l l/l <u 1-1 £ IT, E c I—1 u o nj 03 <-> UI f—l o s- 1—! 1—1 in o •H lA 13 OJ CC c c P p. rt > C rt o > +-> r-{ p c C 1—1 •H •H U O o H o

rt CH I—1 c -J

H

*^1—1 c c o o o o o C 00 o \P 1—1

T-l \-J '

'

U-c

<; < 1 CJ C 1—i c c o

(J t3 o 1 •H 1 o u c CJ c a) r-^ o

0) <D a-. E o bp U I-H < CTi

(-> <D f—I

•H 1—1

13

1—( o o o 13 C • H (D •H o o 3 13

CJ +J ea o

c/: Id •H CJ

P-; o .-( 13 c u C -i-i f-, c •T-t •H (J nJ c; u w u •13 O 13 •H c •H +-1 1—)

•d

•H i-t (/) ,—1

•H 3 •< CJ •H

i-H o Ph CJ 3

•H cq P3 3 i-l O c c/: P5 CS e

•H

U o r

O -13 •H

O JO

H t-i

U

H 3 M C. c (/) •iH o +J 10 3 VC • H PQ D o CT) P U ec PC Ln 1—1

r)

70
.STATH AND LOCAL COnP.S

O

o

•H

C/j c

E-* o f

o o

t— F

t

o +->

• 10 u

to c fH O <+- t' <+j c Q Q Q *— m O H o I-H M-i o (I It. o o

c; t; o CJ o IT, i a' (U I—

1

Cj u u !h •H aj <L c> *^ o

b.: >- 4-1 l-J C o W. i

t/i •H "f t-j ct 1- s K •M

,1^ dl f. t-< o r-H i-H >H ir, rt C c

O V. .-( i-H c I-H rt 0-

or

U

-J

Ptno

•Hw

•H>o

p.u

•H

<4-l H

U

0)p.

to

c o

cc

I-H

.-3

MHo

o te

/—

\

CSJ p +-> c. •H vo rH u 0-

.

1-H

<L) •H

to T3

CJ O i-H E o

u ,M tJ> u

c a. I-H u w i-H O

I-H

• H < •H •5

l-) 3 t-H 13 o c U •H U •H w •H n H M

Uh *-> (-' U K

o !-i O U •H r« O <u o o

tn t) X. c; H c

rt T3 u 10 c ^: o o rt o < u < CJ u

71
STATn ANn LOCAL CODES

H

(U +J

U)C8 iH

PiM

p

^1o

cx

u

O

O

• H

'v3

O

c

o

o

<S) (D

O .-I O '-r. cj O 4-1 Sh ^c^ -h

0) 4-J •H e !-.

(/) cti O

CD O +->

O o

O

u

(U o

E ^

ri

in <D o

O <D

H cd , 4-> •H e c o

O

•p e O O

CvJ •H f-i tD C O -1-1

O

C O f-i P O

•H +J G

U cfxi

•H p

3 O

I/) CS r-(

<U !-> <U E P, >

•H O O

4-" U i-H

I X

C (U O - 4-' iH <D U

U 3

C i-H +-> P, w

U 4-> O r p. b!.

!=: o O I-H •ri

4-1 u C

d) oi

<4-: +J

P, CO i-H

ns p

P O

U c3 P 4J ^ •H 4-) 03

(/I 0) u o

o p

-Pie Id

(D C

E CD

P

(UE

•H

cr

cu

ShP

O

o

0) iH

!hO O

E >

O tc, 4J ,-1 > rt O

O P CD <JJ

O <D P,--!

P-'4-'

10P

3 aj

I 1-1 10 p +J +J

4-1 ni M- O !-( (U

p; •Ti LT) P.+j

<D

01

!h

0) p'

OJp

o

c

u

p. w

4-1 P

CDE>

ou

p.e

72
STATU .vm Lnr\]^ cmns

tob o

03 •H

U

<L> 0) +J t3 u

to rt c

CtJ o !-. iH

p

r-H rH

O ' ' St

<U

es bc > •H

(=; •H rr-J i-Hp

•H r-H 03 • H o

^-> o E 0)

H

!-, r-H

O o o +-1

O 1—1 o in t—t u

p. •H CJ

u 10 i-i p_ T3 > c3 O Sh ;3 •H .—( c o O •I-I

1/1

U rH 1—1(U

H o I—1w. <u U di O i-i M-l C

t/l

X +-1CO

+-> c (U

O (/5U

O t;U

(/) :3 +J o

•H rt !h s- 13 o 1/1 >H O c O (U (L o !-> E 03 <D 4-> U c i-H c f- ^> V. tA, o

(I •H o o C 03 +-> o iH u o >-. 1—1

t—11/1 o • H rt (=; o P- p. 03

1—1 <D

O o 1—1

p. i-H p- U u O P,

00

O c

t—I HU

P!

COP3

05Eo

<4-^

C to o• HW

•H>o

p.

P,

Same oc

tH

ino 3 I-H rH P

l-H iH rH O O P o o >

•H 03 iH

n

(-> P i-H 03 03 •H

+-> rH •H > •H

ci V) <u 3

tc

p

C +->

O o o ^1 i-J u p; > p 1+^ r-* o; O U ••-> c p CO H o) 1—1 o CTl •H m P 1/1 u o •H CD o c <L) P Cl rH

iH 3 ^ o 0} 3 O C-. u l/l Id 6 U 1-1 •H to o

1/1 iH 03 rH 4)

u

•H t-C w. 03 1-J

O

O •H

03 P p P, o P< P P P •H H (—1 •H m rt 03 3 <D

p rtu <D (U P O to iH •H 1—1 rH •H <vi P P •H in •H o •H •H iH P P P in >

c. P 3 3 O C-. •H •H P •H 1) rH eq K > 1—1 o p; co

73
STATE AND LOCAL CODES

to

c

o

•r-( o

+-> •H U +-< Q

3 u

^-c D o l-J ^^ o o t/l M

1—

1

d I/l

' <4-i

onW

1

1

U

C;

ns O

o

of •H

I/) T-t o 0) o ^3 o

u t) I/) o in <D <D

(D U ^-i e

<D •H 0 <u

in 1—

1

+J M •l-i C (D I/) W

•H ^-> E a rt

ir> lU 1—

1

I—

1

u rt (/I p. P- 1—1 o 1—1 to

i-l

CO

O

VD

<4-< O

>

o

E

CD M

>

o

u

D

C

ou

<

Cu

t/1 U

(1)

o

2-

O

o

Ou

3

(L)

OU

>

E<

74
STATi; AND LOCAL CCiDF.F, o

13u

+-> tn0

oa oM

t3 T3

CD (-> (U o

rt <t) c o O M p.

-J I/) M- E

rt

O

H

4-> o I—( c

(/) 4-> )-( (/) O t/l (D H rt 0) E

iH •H

rs (->

O

O

C

4->

rJ o e

4-J o 1—1 e C O !-

^' 

1—(

COHw o o

•n- 00

-J

•H ,—1 o X rt 0)

03 -t-J

C I—1

+-i E O o

t/i

H

u CD !h 0) 13 bo H O (/I C

U- rH o •H

Jh •H 13 E <D 3 •!-> f-t O (Nl O +J 13 rJ • H

i-H >4-l •H

u 3 V 1 }-< a SO li ca

fi c p. t-i o o p. 03 •H o c •H 1—1

03 P 3 *->

O o o rH +->

"4-1

C in 1—1 o o I—1

IIU

n- •H <4-l •H

CJ <D c <+-, o o u Tj o C •I-H .H O •H E

i-H

M i-H i-H (-> o u u Wi 3 U <D u m 03 !- H • H +-> •H t—1

1—1 c (U I/)

t/1 E t/) p. o E P

P, 3 o P- •H 03

O

k: rt E Si ri •-> in

(i> o (/) 13 13 b.C O bC O C u P

•H Yo

u li c 13 p r—1 o 1—1 o <U •H • H 53 •r-l +-> 3 +-> Q o cr. u

<4-l 3 0)

1—1 o S-i 1—1

4-1 03 4J P.

(/) }-> cu (/)

H c flJ 4-> P 4-" o P 03 o 1—1 c u <U 4-" u 3 c e: CT, o p o P O

•H 4-> c •H 4-1 CT. 13 c 13 0) i-l

t-H (D •H t—1<u •H 1—(

4-1 •H 1-1 3 J3 U u 3 X: ?-< « 03 3 « 03 o <D o U !-. U J2

>• •H +J E <U •H <b E

1—1 Ul o 4-J i-H 4-> <L) 03 P, P u 03 P, 03 O 5 4-1 P-, o aj 4-> P, 4-> (D LO < G to < to

75
STATE ANn LOCAL COnHS cu

(/) •H

(1) 4-1 oi +-> bl GC no

<D

p.. sio o 1 ) hp t

t/) ct 4_) o

,—1

Q !-.

u

i-H C3 tc

O t/1 C)

i-J 1—1

rt c 0 _J

<+- , , to

Q •H E c o •M 1

•H +J

O c to in +-1 c •H «' c O c

•H £ •H

C

u o M +-> !-< 'c •M c >

in

u 1—1

i-H o •H

O

u o .-J c c P y- c C r—1

+-1 o £

+-> c. t: J- Pu

(/. •H re c

c: 1/1 l/l (/; ° c; o 1—< c CJ 1

t5

p E

<j c ri !^ o o

•H 1—1 O

O o w, !- o o X c O CD o (Li tr o M E o •l-J > C) 'i o > re O rj H !- o C o C •H o c

+-> e 1—I U a. o

E-UW

-J

bO3u o o iH C H

MCt Ut

10

re tr LO

(DE c

re cu o

1—1 C,

O - a) i-l u £ 13

re

O c U 1—1 o o

•H o to

+-> rH u E- •H O 3 £ >

^1 13 1—1 •M H

(/) re 3

(U 1 c ea c o o d u o

•H c +-> Ti

+-> b.0 re ^3- o re C o •4-) vO >- c O •i-i 4-1 •H

H

T3 > 1—1 13

1—1 <D 0) o 1—1 H I—1

S-i •H 3 X- ti S- re 3

la rt

C 4)

u « o u •H ^ O ^ <D • H --1 6 CO Q.) l-J I—1

>, \o (-> I-J re P. 0) u l-J ai re •M P^ S o •H 1-1 _o I-J < o c c

76
STATE AND LOCAL CODLS

CO

c

O 3

i-H fo M

l« M

<D O

+J o c de

CD (/) v< o

> rJ u

• H u

1—1 o

<u o

C

tc • •H

•H t—

1

in 1—

i

o

10 (U t-i H

O OJ o OJ M P.

•(-> (= u

u^^ rt >.

P. 1—1 0 O <D 0 u

tr. I—

1

ai o

i-l >M c o

e: to 0) >-i H M P- U o rH U cT o ^ 10

1—1 cr (-1 C •H

•H o f= < cn 1—< a M •H

C

C3 o

iH

to o u c 0

1—1 (D 4-1

if) <D II •xl to ,—

1

1—

I

o c (1) O p. O

to t/1 c u to o o r- CO • H +-> C 'H

1-1 Cj C <4-^ >-i +-> 1—

j

1—

1

> r. C p. c t/^ •H u o

1—1 o e +-'

• H iH to o 4:: <u ct

(-> E P--I-' u 1—1 O c ft ct p. U H cd •H 0 D <+- 0 1 u 00 e t/) 0 M- +-> o 1 I 0

M +-> +-> c

t/! O c c cr

cS c o c

cc c: c c

<D 1—1 CT. I—

(

6

cS

(/I J

fc.0 •H

iH

r-iO c c

VC

C-. Vi CTj rH C 1-1o

(D •H O O c u (_)

C-O c c o

•H u

CTi

1—1 1—1 i-i < H •H

e: ec (/; o

o O (/I >. •H H 3 +-> ^ O H c c rr u

P.

OJCOc

o

P-c

c

77
STATE AND LOCAL CnnnS

COcu

tn in

1—1 c u ( o 0

•H •H 0 c +-) .-1

^-> ar1—1

uo

T> p. c rH b". O o <+- C T3 o H O •H c c i-j +-1 M

<D

u !-i +J o 0 in

(= ^ to

•H !h C- c u t/1 rt •H C rt != 1-1 .—( o +-> c •H • •H ^-> u U (D

4-1

a (J rt

U !-. 0

<D (1) 13 1—1 Si •H 0 M f 0 Stn c rt 0 0) > C O F. 1—1 •f-J •H o i- a' M-l IT, i—l u rt o

(L> rt rt I—1 C o If, o Cl. tc o c c M E •H o £ c rt (A. I—1 c (-> 0

(7) +J rt PC rt < 0 Uc 4-1 <4- d; 1 C 't- 0

P^O > M- 0 C C U - C -H 0 0)0 0

ui

C 0 <D (3 r--

(/) "C 0 cri 1—i 0 rH

rt .r;u 1-1

U 1—1 4-) <D rt

in fx c t-C

C c

4-J -H -iH • C 0

-3 rt 'd

U 4-> •H

u • H

C c; c (=: 13 4-1 rt in 0 -H a) 1—1 1/1 •H 0 1—1 VO

tn c 4-1 p. <D c D rt ED U CO P5 •H

rt

C t-i (U i-i

u

d) -H c ^ 0 U •H 4-)

I--", PC +j 1+^ +j M-j

H I 0c

in

rt PC c

•H 0 tn c rt

rt •1-!u

13

1—i

0) 1—1 •H 0)

p) rt

DC

LO PC < c

13

ts •H (U 4J <u C in

10 > U 0

UU at 0 4; ^^ •H H 4-» in 0

in iH

p; •H

di "p.e 0 <

_o

U < CD P3 to •H

H Oi

t/i (3 in in I—1 0 in 0 •H C C

(U 13 0 0 c >N 1—1 u u <D

4-> (3 4-1 •H in in T3 •H OJ •H 3 •H •H 0 U P3 U

78
APPENDIX B,

Summary of Vertical Deflection Limitat

in

Foreign Codes and Standards

79
c

|2 be rt

l/l o

to ,0

M

rtO o <D 1—1

t—1

10 UU •H•M

!-<

rt rt <D of u Ut CO c C- 4-) X. o E U

•H •M

H

O (U

t:: p. +-»

u

r3 <L> rt c C TJ 4-' rt (U O

•HE

(is > •H CD t—1

<D

4-)

H o 4-1

U "4- 4-> (D >c O • H c U-

(D to rt > t/l U

O c rt II II £, o I—1 u m O O O rt to LO VC * to p V 1 V 1 V ! o c U •rt 0 Ph p

—J I—] c O to

"7" 4-J <D ,P '—'

to o E /-^ Pi

U

C 4-' <D * * rt o •H rt E <D <D

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92
APPENDIX C

Steel floor joist vibration formulas were developed by Lenzen [113].*

The steel j oist - concrete slab floor system was assumed to act as a two-way

plate system under vibratory excitation from human activity. Only an equivalent number of joists, N, are assumed to participate in the vibration,

where

where

where

N =

n =

N =

X . =

n X.

1 + 2 T. cos IT -j^

i = 1 o Cic)

1, 2, . . .n, number of joist in floor under consideration

equivalent number of full effective joists

= distance from the center joist to the joist under consideration

= distance from the center joist to the edge of the effective

floor, where

V - 3 YTe L ^o 3

L =

D = X D =

1/4

(2C)

(3C) length of joist and e = (D^/D^)

flexural stiffness perpendicular to the joist (slab only)

flexural stiffness parallel to the joists (composite section).

The flexural stiffness perpendicular to the joists is the stiffness

of a unit width of the concrete slab or

where

^c '

12

= modulus of elasticity of concrete

(4C)

t = slab thickness

The flexural stiffness parallel to the joists is determined from the

formula

E I Dy

(5C)

where I is the moment of inertia of a composite section consisting of one steel jSist and the concrete slab of width, b, where b is the effective

slab width which usually is equal to the joist spacing. is determined

by converting the slab to an equivalent steel element by reducing its

width, b, to bg = b E /E.

* Numbers in brackets refer to literature references. References are grouped in the respective report sections and are listed in alphabetical

order in each section.

93
The floor will behave dynamically as a simply supported equivalent

flexural beam consisting of N joists, thus its dynamic properties can be

determined much more easily than the dynamic properties of an orthotropic

slab. The beam has an equivalent flexural stiffness of

"equ

= N I (6C)

and an equivalent mass of

equ (7C)

where w is the weight per unit length of one joist and the slab of width

equal to the joist spacing, and g is the acceleration due to gravity.

The natural frequency of the equivalent beam can be determined from

the flexure formula for a beam

fn = 2L

(8C)

equ 2L

Human response to vibrating floors depends not only on the frequency

of vibration but also on the amplitude of the deflection due to impact.

Lenzen used: 1) an impactor, consisting of a cylindrical steel weight

of 3155 lbs in a vertical frame; and 2) a heel drop on the floor by a human. These two methods of excitation gave distinctly different responses

in the floors. The first impact, due to the mechanical impactor, was approximated by a rectangular pulse having a force of 794 lbs and a duration of 0.01 seconds, (F = 794 and ti = 0.01). The corresponding

maximum amplitude at the center of the effective floor area is given

as where

and

where

4 F L

IT N E I

4 F L

for t < t^ C9C)

TT N E I

sin IT f tj for t > tj n a o ci (IOC)

= first maximum amplitude, in.,

F = force of rectangular impulse, lbs.,

L = length of joist, in.,

N = equivalent number of full effective joists

= moment of inertia of one joist and its slab, acting compositely,

in

6 E = modulus of elasticity of steel, E = 29 x 10 psi

f = natural frequency (eq. 8C)

94
= duration of impulse

= time to occurrence of maximum amplitude,

t = o

1 TT

(llC)

The impact due to the human heel drop was approximated by a triangular

impulse of duration, t, and maximum force, F, and the values of t^ = 0.05

seconds and F = 606 Ids were used. The maximum amplitude at time t^ is

2 F L

TT E N I.

C2 for t < t,

o — d (12C)

where

TT f.

tan

-1

(2 - fn ^d)

(13C)

and

2 F L

TT E N I \ 2 TT f t 1 c \ n d

r2 [1 - 2 TT fj^t^ sin 2 ti f^t^ - cos 2 tt f^t^J + [2 tt f^t

7^1

-n"d nM- -n^dfor t„ > t,

o a (14C)

where

t = o (--1 tan

1 - cos 2 TT fj^t^

sin2TTft,-2TTf„t, no. n d

(15C)

* U. S. GOVERNMENT PRINTING OFFICE : 1973—542-650/59

95

rORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS BSS-47

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Structural Deflections* A Literature and State -of -the -Art

Survey

5. Publication Date October 1973

6. Performing Organization Code

7. AUTHOR(s) T. V. Galambos; P. L. Gould; M. K. Ravindra;

H. Suryoutomo; R. A. Crist

8. Performing Organization

9, PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No. 4618381

11. Contract/Grant No.

12. Sponsoring Organization Name and Address Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

13. Type of Report & Period Covered

Final - 1972

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A literature survey and state-of-the-art study was compiled using 233 primary source

documents, research papers, and texts. Over 800 documents were scanned to arrive

at the primary source documents. The problem of structural deflections is discussed

and reviewed in its component areas of static and dynamic deflections as related

to forcing functions and structural characteristics. Also the interactions of

major structural deflections with building structures subsystems and human occupants

is reviewed. Emphasis is placed on serviceability limit states of deflections.

Detailed comparisons of human response to structural vibrations are also made.

This report is broad in scope and covers the areas of analysis, design and experimentation.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Analysis; deflection; design; dynamic; experimental; human sensitivity; loading

functions; specifications; static; structural engineering; subsystems; vibration,

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Pn UNLIMITED.

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