Department of Civil and Environmental Engineering Stanford ...rm315dh3494/TR50_Moncarz_Krawinkler.pdfThe research reported herein is part of the project "Scale Modeling and Testing

Department of Civil and Environmental Engineering

Stanford University

THEORY AND APPLICATION OF EXPERIMENTAL MODEL ANALYSIS IN EARTHQUAKE ENGINEERING

by

Piotr D. Moncarz

and

Helmut Krawinkler

Report No. 50 June 1981

The John A. Blume Earthquake Engineering Center was established to promote research and education in earthquake engineering. Through its activities our understanding of earthquakes and their effects on mankind’s facilities and structures is improving. The Center conducts research, provides instruction, publishes reports and articles, conducts seminar and conferences, and provides financial support for students. The Center is named for Dr. John A. Blume, a well-known consulting engineer and Stanford alumnus. Address: The John A. Blume Earthquake Engineering Center Department of Civil and Environmental Engineering Stanford University Stanford CA 94305-4020 (650) 723-4150 (650) 725-9755 (fax) earthquake @ce. stanford.edu http://blume.stanford.edu

©1981 The John A. Blume Earthquake Engineering Center

THEORY AND APPLICATION OF EXPERIMENTAL

MODEL ANALYSIS IN EARTHQUAKE ENGINEERING

by

PiOtr D. Moncarz

and

Helmut Krawinkler

The John A. Blume Earthquake Engineering Center

Department of Civil Engineering

Stanford University

Stanford ~ California 94305

A Report on a Research Proj ect Sponsored by the

NATIONAL SCIENCE FOUNDATION

Grants ENV75-20036 and ENV77-14444

June 1981

Abstract

ABSTRACT

This report summarizes part of a four year study on the feasibility

and lim! tations of small-scale model studies in earthquake engineering

research and practice. The emphasis is placed on dynamic modeling theo-

ry, a study of the mechanical properties of model materials, the develop-

ment of suitable model construction techniques and an evaluation of the

accuracy of prototype response prediction through model case studies on

components and simple structures. Steel and reinforced concrete struc-

tures are considered in this study.

The basics of similitude theory and its application to the modeling

of dynamically excited structures are reviewed and similitude laws for

various types of models are developed. These models include true replica

models in which all physical quantities are properly simulated, and va-

rious kinds of adequate models in which the violation of specific simili-

tude laws does not affect appreciably the response prediction.

Adequat~ simulation of material properties was found to be the most

important aspect or model research, particularly under dynamic excita-

tlons. Materials for modeling of steel structures (structural steel and

copper alloy 510) and reinforced concrete structures (wire-reinforced mi-

croconcrete) are investigated under low and high strain rates and with

due regard to cyclic load effects. A comprehensive set of material data

inis assembled for direct use model studies, and systematic material

procedurestesting developed for the investigation of alternativeare

model mterials.

Problems encountered in the construction of models are identified

and are made for the fabrication and joining of modelrecommendations

Abstract

elements for steel well as for microconcrete mix designstructures as

practices, fabrication of model reinforcement and fabrication and curing

of reinforced m1croconcrete elements.

The adequacy of the simulation of prototype response is evaluated on

hand of a series of tests on models for which prototype test data are a-

The correlation between model and prototype response is judged~ailable.

Whenevergood excellent, depending on the type of structure.toas

discrepancies in the response are observed, the causes are identified and

earthquakeevaluated to the limitations of model research inassess

used for this purpose are cantileverengineering. The test specimens

beams made of steel, phosphor bronze and microconcrete, and simple single

degree of freedom structures made of steel and phosphor bronze which are

tested on a shake table.

The research has demonstrated that model analysis be used incan

many cases to obtain quantitiative information on the seismic behavior of

cannot be analyzed confidently by conventionalcomplex structures which

techniques. Methodologies for model testing and response evaluation are

developed in the project and applications of model analysis in seismic

response studies on various types of civil engineering structures (buil-

dings, bridges, dams, etc.) are evaluated.

ACKNOWLEDGEMENTS

The research reported herein is part of the project "Scale Modeling

and Testing of Structures for Reproducing Response to Earthquake

Excitation" conducted under the sponsorship of the National Science

Foundation. The authors are grateful for the financial support of

NSF which made this project possible. The continued encouragement of

Dr. S. C. Liu of NSF is especially acknowledged.

The authors gratefully acknowledge the continuous participation

of the principal investigator of this project, Professor James M. Gere,

as well as the advice provided by Professor Holt Ashley on modeling

theory and by Professor Cedric W. Richards on materials research.

The skillful help of the graduate students Maher A. Bader, Nathaniel

G. Cofie, Bahman Lashkari-Irvani, Russell S. Mills and Mahmud Zohrei

in various phases of the experimental research is much appreciated.

The use of experimental and computer facilities was provided

by the John A. Blume Earthquake Engineering Center, Professors James

M. Gere and Haresh C. Shah, Directors. The technical staff of the

Center is acknowledged for an excellent job done in the fabrication

of test specimens and instrumentation.

iii

-:) " I ,.1 'c I ,

TABLE OF CONTENTS

ACKNOWLEDGEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. iii

TABLE OF CONTENTS iv

CHAPTER

1 INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . 1

2 OBJECTIVES AND SCOPE 7

3 LITERA TURE REVIEW 9

4 DYNAMIC MODELING THEORY 18

4. 1 Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 General Discussion 194.3 Dimensional Analysis 264.4 Similitude Relationships and Types of Models 344.5 Physical Models For Shake Table Studies 38

4.5. 1 True Replica Models 384.5.2 Adequate Models 464.5.3 Distorted Models 554.5.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 EV ALUATION OF MODEL MATERIALS 60

5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.2 Mechanical Properties of Interest 625.3 Material Tests - Experimental Facilities 67

5.3. 1 Testing Equipment 68

5.3.1.1 Uniaxial Load Test Facilities 685.3.1.2 Component Test Facilities 725.3.1.3 Load History Control 74

5.3.2 Instrumentation 755.3.3 Data Acquisition and Reduction System 78

5.4 Testing Program 80

6 MATERIALS FOR MODELS OF STEEL STRUCTURES 84

6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.2 Stress-Strain Characteristics of Structural Steel 856.3 Suitable Model Materials 88

6.3. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 886.3.2 Structural Steel as a Model Material 92

iv

1" : I I I

CHAPTER

6.3.2.1 Strain Rate Effects 936.3.2.2 Size Effects 97

6.3.3 Copper Alloys 98

6.3.3. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.3.3.2 Preliminary Study on Cartridge Brass .. 101

6.3.4 Phosphor Bronze (CA 510) 104

6.3.4.1 Stress-Strain Characteristics 1046.3.4.2 Annealing Results 1066.3.4.3 Strain Rate Effects 1066.3.4.4 Cyclic Behavior 110

6.3.5 Lead and its Alloys 114

7 MATERIALS FOR MODELS OF REINFORCED CONCRETE STRUCTURES 117

7.1 Simulation of Concrete 117

7.1 . 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.1.2 Design of Microconcrete Mixes 119

7.1.2.1 Basic Requirements Imposed onMicroconcrete as Model Material 119

7.1.2.2 Levels in the Simulation of ConcreteProperties 121

7.1.2.3 Control of Properties through MixProportioning and Use of Additives 124

7.1.3 Scale Effects in Microconcrete 133

7.1.3.1 Size Effects 1337.1.3.2 Strain Rate Effects 137

7.2 Simulation of Reinforcement 145

7.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.2.2 Fabrication of Model Reinforcement 1477.2.3 Size and Strain Rate Effects in Model

Reinforcement 152

7.3 Bond Simulation 154

8 MODEL COMPONENT TESTING 159

8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

8.2 Models of Reinforced Concrete Cantilever Beams 160

8.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160iI

v

.[~ , I I.[.. , I I I

CHAPTER

8.2.2 Specimens 161

8.2.2.1 Specimen Fabrication 1668.2.2.2 Test Setup and Instrumentation 171

8.2.3 Simulation of Prototype Response (1/d=3.1).. 1758.2.4 Simulation of Shear Failure Mode (1/d=2.0).. 1828.2.5 Simulation of Flexural Failure Mode (1/d=6.9).. 1848.2.6 Effects of Cycling Frequency 1868.2.7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

8.3 Models of Steel Cantilever Beams 192

8.3.1 Steel vs. Phosphor Bronze Cantilevers 1948.3.2 Effect of Cycling Frequency 196

9 TRUE REPLICA MODEL STUDY OF A STEEL STRUCTURE 200

9.1 Model Description, Instrumentation and Testing Program 2009.2 Results and Conclusions 203

9.2.1 Elastic Tests 2039.2.2 Inelastic Tests 207

10 FEASIBILITY AND LIMITATIONS OF MODEL TESTING IN EARTHQUAKEENG INEERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

11 SUMMARY AND CONCLUSIONS 220

REFERENCES. . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 227

APPENDIX

A Control of Microconcrete Strength Properties 245

B Hysteresis Loops of Reinforced Microconcrete Beams 250

vi

I ! I I I

Chapter 1 Introduction

CHAPTER 1

INTRODUCTION

Experimental techniques have always been vital part of advanceda

engineering design. Whenever the current theoretical knowledge reaches

its limit, an experiment provides an alternative in the evaluation of the

adequacy of the proposed design. The final design of innumerable ad-

vanced structures is based on the results of experimental analysis. At

present, mathematical methods are capable of predicting the response of a

structure to environmental effect, providing the complete functions of

material characteristics, geometric delineation and boundary conditions

available. The time and temperature dependance of such functionsare

often results in a complexity surpassing the feasibilities of mathema-

tical approach. Consequently, the experiment remains the only alterna-

tive. The interrelation between the complexity of the analyzed struc-

value of the structure (re-ture, the ratio of the cost of design to the

lative cost) and the applicable analysis techniques is presented schema-

tically in Fig. Ref. 1)..1 (after Hossdorf, With the improvements in

numerical techniques and theoretical knowledge, the line of analytical

capability moves to the right, thus including a larger number of struc-

tures in the left portion of the figure. This progress does not indicate

a decrease in the number of structures located to the right of that line,

as the demands posed on the design are increasing with the technological

progress.

Considering the high cost of experimentation as compared to conven-

tional computer analysis, the scope of experimental work is usuallyor

limited to fundamental research and the study of complex input and res-

ponse phenomena which cannot be modeled mathematically with confidence.

.1


1

Limit of analytical capability -I~ 1

~ I~ ,~ " Conventional analysis I

Q . """' I

cc ,~ " I

w~ " Problem frequency ~ Computer analysis~ " 1

QI , I>.,oj'

I~ .

co,I.-1 .

: '. I

'. I

'. I

"-

I

"-i- Model analysis

I

1

I

I

""" 1

' I ° °-

I ' °-

I

Degree of difficulty

Conventional Computer Model

Figure 1.1 Application of Various Methods of Structural Analysis (Ref. 1)

2

I, I I


In most cases, experimentation is carried out to fulfill one of the

lowing three basic objectives:

(1) models of force-deformation charac-Develop or verify analytical

teristics of materials, individual elements and structural subas-

semblies.

(2) for complex environmentalEstablish realistic loading criteria

effects such as wind or earthquakes.

(3) specific structuresStudy the behavior of structural systems or

under simulated loading conditions. The purpose of such experi-

mentation may be the verification of analytical studies, the de-

of the integrity and safety or structural systemsmonstration

levels of environmental disturbances, or a generalunder various

response characteristics of structural systems withstudy of the

controlled variation of input and response parameters.

on either unscaled prototypesExperimental work can be carried out

or scale models of elements, subassemblies and complete structures.

places in the results of experimental studiesconfidence the profession

Very few doubtsappears to be proportional to the selected scale factor.

are raised regarding the reliability of experimental results of prototype

tests or one-half scale On the other hand,to one-third model tests.

(in order of 1:5 and smaller) are oftensmall scale model tests the

viewed with considerable skepticism. This skepticism is often unwar-

in the materials and the load application areranted when scale effects

properly accounted for and the instrumentation system is adapted to the

it is desirable to keep thesize of the test specimen. Nevertheless,

scale factor close to one whenever feasible.

In earthquake engineering, where post-elastic response characte-

3


against failure are of primary interest, the analysisristlcs and safety

of many structures requires the application of experimental methods. Ex-

per imen tat ion may be performed in the field or in a controlled laboratory

test versatility and control precisionlimitations,environment. Cost

Inmake laboratory testing most applicable to experimental analysis.

earthquake engineering, laboratory experimentation on complete structures

cases, limited to testing of scale models, often at ratheris, in most

small scales.

analysis in earthquakeA powerful tool was provided to experimental

engineering through the development of closed-loop shake tables and high

are available a smallspeed data acquisition systems. In the U.S. there

number of medium size tables (larger than 10 ft. x 10 ft.). With few ex-

andcept1ons, such component equipment testing and testing of veryas

small prototype structures, experimentation on such tables is limited to

models. There are obvious advantages to theone-half or smaller scale

one-third scale).use of large scale models (one-half to For instance,

structures, andsmall rolled sections can be used for models of steel

concrete)prototype material (reinforcing bars and be used forcan

Nevertheless, such structures are models andreinforced concrete models.

unless modeldo not fully simulate the behavior of an actual structure

motion, material, and force simulation aretor groundsimil1 tude laws

taken into consideration.

be clas-The majority of shake tables available in the U.S. have to

sified as small tables 10 ft. x 10 ft. and smaller}. of these ta-Host

bles are used primarily for demonstration pruposes, qualitative studies,

or component testing. It that they are not fully utilized forappears

forreplica modeling of actual structures at small scales. The reason

4


this limited utilization 1s that modeling problems increase with a

decrease in scale and that insufficient information is available in the

literature on the possibilities and limitations of small scale replica

modeling.

To fully utilize available laboratory facilities tor mitigation ot

hazards of eqrthquakes, it 1s necessary to develop a general capability

for constructing, at different scales, replicas of actual buildings, bri-

dges, dams, etc., and for reproducing adequately the manner in which they

respond, absorb and dissipate energy, and ultimately fail under pres-

cribed earthquake excitation. If such a capability can be developed it

should be possible to use small shake tables in a cost efficient manner

viable and reliable research tool in the field of earthquake engi-as a

neering. Among the many topics on which model tests on shake tables

should provide useful information are the following:

1. High-quality. small-scale models can be used as complement for

and/or an alternative to analytical investigations. This need is

especially urgent in connection with complex structures, where

mathematical models are difficult to construct and to verify

2. Models are especially useful for comparative studies or cont-

rolled parameter variations, since it is relatively easy to alter

their configurations systematically.

3. Replica models enable the investigation of earthquake-related

phenomena which cannot be studied on actual prototype structures.

Such phenomena include rate of loading effects, dynamic response

characteristics under realistic seismic excitation ranging from

low amplitude vibrations to excitations inelasticproducing

orresponse and failure, failure mechanisms, effects andmass

5


stiffness irregularities, torsional effects, overturning effects,

dynamic instability and idealized soil-structure interaction

effects.

4. The demonstration or integrity and sarety under various levels or

earthquake inputs--if it is ever to be accomplished prior to the

erection of an actual structure--could be achieved with a

replica model.

advancement in knowledge of all aspects ofAt this time or rapid

earthquake engineering it is necessary to examine carefully the place dy-

namic model testing could occupy in the field oC earthquake engineering

dynamicresearch. It can be said that experimental research with

application is in its infancy compared to quasi-static experimentation

and analytical studies, and there 1s little doubt that it will playa

more significant role in the years to come.

A study of the feasibility and limitations of small-scale model tes-

tins in earhtquake engineering was the subject of a four-year NSF spon-

sored study which in part is summarized in this report. In the first re-

port 00 this study, Mills et. ale (Ref. 58) present a comprehensive dis-

cussion of shake table performances and or modern data acquisition sys-

A model study of a three-story steel frame structures is also des-tern.

cribed in Ref. 58.

This report emphasizes general aspects of dynamic modeling theory,

model material behavior and the accuracy of prototype response prediction

through small-scale model tests. In conjunction with Ref. 58 this report

1s intended to provide a state-of-the-art assessment to researchers and

practicing engineers who want to utilize small-scale model tests in

earthquake engineering research and practice.

6

Chapter 2 Objeot1Yes and Scope

CHAPTER 2

OBJECTIVES AND SCOPE

The main objective of this work is to asses the feasibility of model

and detailedtesting in earthquake engineering and to provide systematic

and modusinformation on procedures involved in the design, execution,

This goal is approached by pla-dynamic model experiments.operandi ot

the emphasis on dynamic modeling theory, model material studies, mo-

case studies performed on components andfabrication techniques, and

research concentrates on models of steel and re-Thesimple structures.

inforced concrete structures.

The scope of the work presented in this report is summarized in the

following paragraphs.

The emphasis 1s placed on the synthesis1. Dynamic Modeling Theory.

and extension of modeling theory into the domain of time-dependent, non-

Various types of models arelinear response of structures and materials.

within the constraints of material,explored which be constructedcan

but still permit an adequate predictionsimula tionmass, and earthquake

of prototype behavior.

1s placed on the 1dent1t1-2. ~el Material Stu~es. The emphasis

cation of material properties affecting the reliability of prototype res-

A systematic approachponse prediction based on small scale model tests.

Various types of material tests and ofto material studies is developed.

steel,equipment are explored. Material studies ontestingnecessary

phosphor bronze, microconcrete and model carried outreinforcement are

including studies of the uniaxial stress-strain behavior of the materials

under various strain rates and of the cyclic behavior of steel and phos-

phol' bronze.

7

Chapter 2 Object! yes and Scope

Small-scale mo-

dels of structural elements and simple structures are fabricated and tes-

ted to develop suitable model construction techniques and to study the

accuracy of prototype response prediction. Cyclic loading tests are car-

made of steel, phosphor bronze and mi-ried out on cantilever specimens

The simulation of prototype response is evaluated with duecroconcrete.

the speed of loading (cycling frequency). Forregard to the effect or

the microconcrete specimens, tests are performed with cycling frequencies

from 0.0025 Hz to 10 Hz and, with beams of different span-to-depth ratios

to investigate the simualtion of different failure modes from flexure to

pure shear. The results of a shake table study on a simple steel struc-

ture and its phosphor bronze model are evaluated by comparing displace-

ments, accelerations and story shears in the prototype domain.

One of the major concerns of this work is to present the information

in as complete a form as possible, incorporating throughout the text re-

suIts of studies reported by other researchers. In addition, an exten-

sive list of U.S. and foreigh literature is compiled.

8

Chapter 3 L1terarure Review

CHAPTER 3

LITERATURE REVIEW

purpose of this chapter is to acquaint the reader and prospec-The

art in model analysis and withtive model builder with the state of the

the background informationmaterial that containsreferencerelevant

necessary for successful modeling of structures in seismic el'tVironments.

been used in civil engineeringSince for many years replica models have

and alternative to design and analysis, it is recognizedas a complement

review is incomplete and limited to those publica-that this literature

or thistions which were found particularly helpful in the development

past studies onidentifyingEmphasis 18 placedresearch project. on

either areespecially those whichbuilding structures and materials,

dynamic modeling or contain information which can be uti-concerned with

lized for dynamic model studies.

written on the subject orbooks

model analysis, that by Hossdorf (Ref. 1) provides an excellent introduc-

go deeply into anyone aspect of modelIt does nottion to the subject.

healthy perspective of theanalysis but touches many aspects and gives a

The book by Mulleranalysis in structural engineering.place of model

treats the topics of model materials and instrumentation in a(Ref. 2)

that by Fumagal11 (Ref. 3) contains a lar~e numberthorough manner, and

buil-interesting model case studies, particularly those concerningof

dings and dams.

One of the first comprehensive series of papers on structural models

Referencesa RILEM symposium in 1959 in Madrid, Spain.was presented at

papers of this symposium relevant to this4 and 5 contain of thesome

9

Chapter 3 Literarure Review

research project. References 6 to 11 are summary papers on general prob-

lems of modeling of structures in the elastic and inelastic range.

Many studies are reported in the literature on modeling or rein-

forced concrete structures. Much of the progress on this subject is pre-

sented in papers compiled in Refs. 12 to 14 and is summarized in Ref. 15.

Specific topics in static modeling of reinforced concrete structures and

structural elements are discussed in Refs. 16 to 29.

Scale modeling of structures made of materials other than reinforced

or plain concrete has received surprisingly little attention in the past.

Reference 30 presents the results of researcha project on modeling of

concrete masonry blocks and structural elements. Detailed information on

fabrication and testing (under static loading conditions) of small scale

models of steel structures and their components, using steel as a model

material, is presented in Ref. 31.

Dynamic Model Studies: The references mentioned so far are not spe-

cirically concerned with dynamic modeling problems but contain oomprehen-

sive background information on the subject of model analyeis in structu-

ral engineering. The literature search disclosed that quite a few model

experiments on structures under simulated dynamic loads and earthquake

motions have been carried out in the past (Ref's. 32 61).to However,

much or this work was concerned with elastic behavior only. The case

studies reported in the literature on modeling of structures to failure

generally lack a thorough discussion of the ofconsequences inadequate

material simulation and orten do not take full advantage of the potential

of dimensional analysis in deriving appropriate modeling laws.

Physical models for elastic earthquake response prediction were used

10


fifty Ruge (Ref. 32) presented a comprehensivemuch years ago.as as

dynamic modeling theory in 1934, and in Ref'. 33 heelasticpaper on

described a detailed model study on the earthquake resistance of elevated

water-tanks which included a feasibility study of various model materials

and brass to simulate steel and a discussion(mercury to simulate water

Even earlier, dynamic studies on modelsof feasible model distortions.

cylindrical tanks, and multistory buildings had beenor wood panels,

table at Stanford University (Refs. 34, 35). Theoarried out on a shake

masses in the building models were lumped at story levels and represented

by vertical ball-supports, while the buildin8by steel plates kept apart

frame and wall rigidities or the prototype were represented by horizontal

coiled springs.

study on dynamic modeling or steel andA thorough and comprehensive

reinforced concrete structures was carried out in the early sixties at

HIT (Refs. 36 to 39). The purpose of this study was primarily the inves-

As such, the source oftigation of structural response to blast loading.

excitation and or the relevant response characteristics are quitemany

different from earthquake loading, but much of the modeling theory

material studies and fabrication techniques presented in these research

directly utilized for model studies in earthquakereports becan

orengineering. Other useful information from model studies structures

subjected to blast loading can be found in Refs. 40 to 43.

scale models forIn the United States, the use of large and small

seismic response investi~tions in the inelastic mate~ial domain became

earlyacceptable alternative to analytical studies only in thean

towardsseventies. In most studies directedcases these were

for specific structural systems (e.g.,verification of analytical models

11

Chapter 3 Literature Review

earthquake response phenomena (e.g.,reinforced concrete shear walls) or

overturning and uplift problems). such cases, distortions of seismicIn

configurations (to suit available shake tablestructuralinput ofor

the use of established material and modelcapabilities permitor

accepted since the physical modeltechniques) often bestruct1on can

results are compared to analytical results and not to prototype behavior.

in the research laboratories at the University oftablesThe shake

have been used ex-Illinois and the University of California at Berkeley

The University or Illinois facilitystudies.tensively for such model

studies of reinforced con-has been used primarily for small scale model

Much of this research work is summarizedcrete building structures.

found in Refs. 45paper by Sozen (Ref. 44); more detailed results can be

to 49.

small soale model studies per-Reference 50 provides an example or

behavior or reinforced concretetheformed at Cornell University on

structures under seismic excitation.

6x6 m (2Ox20 t't)The U.C. Berkeley facility which is built around a

shake table is used primarily for testing of structures which may be con-

large-scale pseudo-models. The structural elements aresidered to be

usually made of prototype structural material (s_ll hot rolled steel se-

small reinforcing bars) and floor mas-ction or concrete reinforced with

ses are simulated with a sufficient number of concrete blocks to simulate

roughly oneIn size, the structures begravity-induced stresses. may

motion usually is notThe seismic inputhalf that of actual structures.

scaled according to model similitude laws, and intentionally so since the

not meant to be replica models of actual structurestest structures are

12

Chapter 3 Literarure Rev1e1

but physical representations or mathematical models. The drawback or

this kind of experimentation is that a one-to-one correspondence with a

prototype structure cannot be established; the advantage is that

structural detailing be simulated much difficultycan without and

material behavior is well known which increases the confidence in test

results and permits reliable analytical correlation. References 51 to 56

discuss specific studies or this type carried out at the U.C. Berkeley

shake table.

Actual replica models are also tested at the U.C. Berkeley facility.

An excellent example is the 1:30 scale model of' reinforced concretea

high curved (Ref. 57).overcrossing This model built of mioro-was

concrete and closely follows dynamic similitude laws. Great care was ta-

ken in precise simulation or all details at expansion joints which were

known a priori to be subjected to damage caused by multiplesevere

impaotin~ in both torsional and translational modes. To maintain body

forces similitude, the mass of the model was increased to 30 times the

self-weight by adding lead blocks.

More recently, a shake table study on a 1:12 scale steel model of a

three story, one bay steel frame structure completed by Mills et.was

a1., (Ref. 58) on the Stanford University shake table. The 1:6 scale mo-

del ot a 1:2 scale pseudo-prototype tested at Berkeley (Ret. 51) wae used

to directlycompare the results obtained from the tests of the pseudo-

-prototype and its model. Reference 58 includes a comprehensive descrip-

t1on or the evaluation of the shake table performance, of the instrumen-

tation, and of data acquisjtion and reduction systems. The report discu-

sses in detail the modeling techniques for steel structures and presents

guidelines for a rational comparison of experimental data from model and

13

Chapter 3 Li terarure Review

prototype tests.

It should be noted that much valuable information on dynamic mode-

ling can be drawn from publications in fields other than structural engi-

neering. References 59 to 61 are examples of oolleotions of informative

Although much of the theory and dimensional analysis developedpapers.

herein will useful, it has to be recognized that the referencesprove

tend to focus on response within the elastic range of material behavior.

The use of physical models in earthquake engineering has been much

more extensive in Europe than in the United States and Canada. For ins-

tance, the Istituto Sperimentale Modelli e Strutture in ItalyBergamo,

the Laboratorio Nacional de Engenharia Civil in Lisbon, Portugal, and the

Institute for Research and Testing in Materials and Structures in Ljub-

elaborate and well-equipped model laboratoriesljana, Yugoslavia, have

which Referencesare used for research work in earthquake engineering.

62 to 84 desoribe some of the dynamio model studies oarried out at these

and other laboratories and contain information on modeling ot' buildings,

bridges, dams, nuclear reactor components and containment vessels.

Several model studies on seismic behavior of building structures and

containment vessels were also oarried out in industrial and university

laboratories in Japan. Some of these models were pseudo-models (as des-

cribed previously) and References 85 towere actual scale models.some

88 are examples or this work.

Dynamic Modeling Theory: Applications of dynamic modeling theory are

discussed in many of the aforementioned references. The basis for the

development of model similitude lawa can be found in many books concerned

with the theory of similitude and dimensional analysis, of which Refs. 89

11..


Dimensional analysis as an analyticalto 98 are a representative sample.

tool for the derivation of model similitude laws is largely attributed to

and Rayleigh (Ref. 100). Specific(Ref. 99)of Buckinghamthe work

aspects of modeling theory as applied to civil engineering problems

A comprehensive discussion of the physi-105.discussed in Refs. 101 to

dimensionaltheirentering a structural problem and ofquantitiesasl

dependence is present in Ref. 38.

The interrelated subjects ofModel Materials and Model Fabrication:

--

and modelscaling effects in material simulation,material selection,

fabrication have been the subject of many studies and are widely reported

a large number orremainsNevertheless, thereupon in the literature.

unanswered questions some or which are the subject or this study.

associatedGood summaries on available model materials and problems

material simulation and model fabrication can be found in Refs. 106with

made orwith elastic and ultimate strength models",, concernedto

plastics, cementitious and metallic materials.

information on the use of miorooonorete andSpecific and detailed

gypsum mortar and the simulation of reinforcement in models of reinforced

14,25,29, 36, 39 and 106conrete structures are presented in Refs. 12,

119 provide guidelines on the43 and 1111References 14, 39, toto 123.

mechanicalstrength andvariousmixes forof' mlcroconcretedesign

mix proportions, mixing andgrading,Appropriate aggregateproperties.

(Ref. 118) points outMaiseldiscussed.curing techniques are

or microconcretemechanical propertiesor changing thepossibility

(E-modul1 ,

additives,

15


References 18,smooth silicone resin. 39, 117, and 122 discuss the

effects of speed of testing on the compressive strength or microconcrete.

effects in modelReference 123 provides state-of-the-art report on size

References 18, orconcretes. 21, 39, 117, 118 and 124 present results

individual case studies concerned with size effects. References 125 to

144 provide information on mix design, testing, mechanical properties,

References 18, 43, 117, 118,and load rate effect on prototype concrete.

140 and 145 techniques used in model reinforcement fabrication.present

Ref. 146 presents results of a study on strain rate effect on the tensile

behavior of model reinforcement. Ref. 147 discusses the problem of crack

and deformation similitude in reinforced concrete which was investigated

by means of bending tests of similar beams at different scales. Referen-

concrete behavior (pro-ces 147 to 150 provide information on reinforced

totype and model) under dynamic loading conditions.

Much less information than on reinforced concrete 18 available on

the feasibility of using steel or other metallic materials to simulate

prototype structural steel. The study summarized in Ref. 31 and the re-

cent study by Mills et. al., (Ref. 58) treat in detail the problems of

element fabrication and member joining encountered when steel is used as

a model material for steel structures. Strain rate effects in low carbon

steel are discussed in Refs. 151 to 153. Size effects on tensile and

flexural behavior of structural steel investigated by Richards inare

Refs. 154 and 155. The properties of phosphor bronze and its feasibility

model material for steel structures under dynamic loads areas a

discussed 1n Ref. 38. Ref'. 157 1s excellent text on basic materialan

behavior.

~~ Instrumentation ~ Dyn!mic ~ Facilities: It 1s evident

16


that the instrumentation system for measurement of pertinent response pa-

rameters must be adapted to the size of models be tested. Re-the to

on the instrumentation system and feasible measuring devicesquirements

are discussed in Refs. 58, 158, 159. use or minicomputers inand The

summarized inmeasurement, analysis and control of experimentation is

Refs. 58, 160, 161 and specific problems associated with recordingand

and interpretation of dynamic test results are discussed in Ref. 162.

The problem of simulating an earthquake environment in the field and

sponsored workshop in Sanin the laboratory was the subject of NSFan

(Ref. 163) contain valuableFrancisco. The proceedings of this workshop

1n earthquake enginee-information on the role of experimental research

experimental facilities.ring, on experimental needs, and on existing

Several other publications that discuss earthquake simulation systems and

speoifio simulation problems are listed in Refs. 16~ to 169.

17.

Chapter 4 Dynaaic Modeling Theory

CHAPTER 4

DYNAMIC MODELING THEORY

4.1 DEFINITIONS-

in an experiment can be divi-The phvsioal quantities or isportanoe

variables and parameters, these being either dependent or~-ded into

pendent.

phys1-The independent Quanti.ties are automatically assigned by the

cal characteristics or the problem.

The dependent quantities are those measured during the experiment.

A variable is a quantity which spans a continuous range of values in

a single problem (e.g., time in a dynamic problem).

is what Bridgman (Ref. 89) calls a d1men-An independent parameter

sional constant.

in nature, thatA dependent par..ter 1s a result, usually global

typically represents a single experimental measurement.

MllpleA physical quantity can be measured by comparing with aa

This known reference amount is calledknown amount or the same quantity.

a~. For the complete specification of any physical quantity, both the

unit used and the number of units contained in the sample must be given.

The unit or any physical quantity can be expressed as a combination

such basic quantities as force andbe expressed in or units ofterms

length).

powers or basic Quantities (described inQLmensions are products of

basic units), and as such relate the units of measurement of any physical

18

Chapter - Dynamic Modeling Theory

quantity to the selected basic units.

which does notA dimensionally homoy,eneous equation is an equation

equationdepend on the fundamental units of measurement. Such con-an

eachthe sum of products ot powers of physical quantities andslsts of

term in the sum has the same dimension.

of powers of physical quanti-~-Factors are dimensionless products

products describes a physicaldimensionlesscC8Plete !.!l orties. A

such renders it independent onphenomenon in a dimensionless form and as

selected units.

A dimensional aatrix is an arrangement or numbers conta1n1n~ d1men-

sional exponents of physical quantities expressed in terms of basic quan-

It comprises as many columns as physical quantities in the funo-titles.

quantities.basictional relationship or a problem and as many rows as

displacement of anFor instance, if the functional description tor the

dimensional Mtrixproblem is given by u = u(x,y,z;l,v,P), theelastic

has the followlnB fora:

independentparameters

!dependentIvariable

independentvariables

pEu x y z \J

0 0 0 0 1 0 1Force F

01 , 1 t -c 0Length R.

4.2 GENERAL DISCUSSION

model analysis in earthquake enRlneering Is the pre-The ~rpose of

structures from laboratorydiction or the dynamic response or prototype

include all pertinenttests 00 physical models. This prediction may

parameters or it may be limited to selected parameters such 8.5response

19

Chapter ~ Dynamic Modeling Theory

natural frequencies and mode shapes. The desired range or prediction may

be limited to the linear elastic response or it may comprise the complete

response history to failure including material and geometric nonline-

arities. In the or single parametercases and elastic response

prediction several model design requirements can often be relaxed which

makes model analysis a simpler but also less powerful tool.

In this chapter modeling theory is discussed in generala sense

which makes it suitable tor all types of model studies and is then ap-

plied to specific cases which are most useful in seismic investigation.

Modeling theory establishes the rules according to which the geometry,

mateial properties, initial conditions, boundary conditions and environ-

mental effects (loading) of the model and the prototype have to be rela-

ted so that the behavior of one can be expressed as a function of the be-

havior of the other. The theory which leads to the development of a com-

plete set of correlation functions (sometimes referred to scalinga8

laws) defining the model-p~ototype correspondence is that of similitude.

The Oxford English Dictionary defines similitude as: "the quality

or state of being like resemblance, similarity, likeness. Now somewhat

rare." Among the ideas associated with similitude analogies,are:

dimensional invariance, homoge-analysis, dimensionless numbers, group

netty, inspectional analysis, local similarity, looal solutions, ~-,!.!!!.&, scaling~, self-similarity, separation of variables, similarity

rules, symmetry, transformations.

which modelThe theory of similitude, upon desi~ and analysis is

based, may be developed by dimensional analysis. Dimensional analysis as

a powerful analytical tool is developed from a consideration of the di-

20

Chapter 4 Dynamic Modeling Theory

mensions in which each of the pertinent quantities involved in a physical

phenomenon is expressed. The principles of dimensional analysis are well

established in the literature and are summarized in Section 4.3 as far as

needed for the development of a general modeling theory. For de-more

as Refs. 1tailed information the reader is referred to the books listed

and 89 to 98 and the technical publications listed as Refs. 38 and 99 to

105.

To develop the necessary mathematical relationships between the cha-

from the premiseraoteristios of a prototype and its model, let us start

that physical phenomenon be expressed by dimensionallyevery can a

homogeneous equation of the type

Q1 = F(Q2,Q3, Qn) (4-1)

where 1s the total number of physical quantities involved 1n then

phenomenon. In thi8 expre88ion q, i8 a dependent quantity and to qnq2

are the variables and parameters which q, depends.on According to

Buckingham's Pi theorem (Seotion 4.3), every dimensionally homogeneous

equation can be written in the form

1Tl = f(1T2,1T3, 1Tn-N) (4-2)

dimensionless or powers of the physicalproductswhere ~1 to ~n-N are

The number N isquantities q, to qn. the rank of the dimensional matrix

which 1s usually equal to the number of basic units needed to describe

the physical quantities.

Since Eq. (4-2) is identical to Eq. (4-1), it describes the same

physical phenomenon and, because or its dimensionless form, must be

equally valid for prototype and model if similitude is to be achieved. A

sufficient condition for complete similitude is therefore

21

I

Chapter - D,n8mic Modeling Theory

(4-3)

and

(1T2)p..O)n-N p

- (1f2).

(4-4)

('IT - (1Tn-N)m

equation and!qua tion (~- 3) is often referred to as the prediction

Eq'S. (4-4) constitute the design conditions for the model. Methods tor

deriving the dimensionless products are summarized in Section 4.3

to taoe.There are two major dittioul ties the model analyst has

to exercise extreme ~re in specifying the right nuaber orFirst he has

physical quantities which enter Eq. (4-1). wh1ch have 1n81-Quantities

gnitioant etteot on the response parameters of interest will impose unne-

model, while ne~lectins a significant quantitycessary restraints on the

Secondly, the experimenter i8 often facedcan yield incorrect results.

reproduce at modelwith almost unsurmountable problems when he tries to

Eq'S. (4-4). In particular, thescales the design conditions posed by

conditions besimulation or material properties and loading may an

theextremely difficult or impossible task. The latter orten leads to

more or the design conditionsdesign or distorted models in which one or

it theNevertheless, such models may still be adequateare violated.

the violations in the desi~torprediction can be corrected to account

conditions.

The speoificatlon of all important quantities on the right hand side

underor Eq. (4-1) does require some insight into the physical problem

that is known about the behavior or theIn general, thestudy. more

22


prototype and of the laws which describe it, the easier it is to design

the model, but the less necessary the model is. Considering the level ot

confidence in model results and the effort invested in desl~, testing

and data analysis, models are most useful when the general features of

the prototype behavior are known but specifics such &S complex geometry

or material nonlinearities render it difficult to obtain quantitative

information by analytical means.

The physical quantities which may enter a structural problem are

difficult to enumerate in their entirety but are for most cases contained

in on~ or the following four groups (Refs. 38, 90).

Geometric Properties: Geometry includes all the space relationships

which may influence the results. All distances or lengths and all angles

that are pertinent must be represented. For geometrically similar models

a location vector is sufficient to describe any point 1n the structure

In dynamic problems the vector will depend not only on the space ooor-

dinates but also on the time t. Alternatively, the location vector may

be specified at a time to and the geometry at time t may be defined by

+ +the location vector r and a time dependent displacement vector u(t).0

Material Properties: In general, these properties may vary from

point to point in space and with time and temperature. A I18terial has

thermal, mechanical, electrical and magnetic properties, although the la-

tter two usually be neglected in structural problems. Thermalcan

properties or interest be specific heat, coefficients of thermalmay

conductivity and linear expansion, and emissivity. The mechanical pro-

perties are the specific mass, and the material properties defining the

state of stress and strain in the material. These properties may be time

23


and temperature dependent (e.g., creep and relaxation), vary from point

to point (inhomogeneity), and be direction dependent (anisotropy). They

also describe the interaction between different directions (Poisson's

ratio) and the interaction between neighboring points (e.g., strain

gradient effects). A complete discussion of these properties is beyond

the scope of this report, but to show the complexities involved in a

thorough material state description, the uniaxial stress-strain relation

proposed by Harris et al. (Ref. 38) is reproduced below:

( -to T de:) (-to T de: I ) \0' r,t, 'at = 0'0 r,to' o"at 0 + 1

~ (e:-e:)n { n I ~ (t-t)j n+j.L.. £- ~ t ,T ,k + L . loa 0' . + (4-5)n=l n. ae:n (0 0 at 0) j=l J. ae:natJ t=t \

0

~ 9.. ~ (ae: de:I ) k } I~ ~- 2~~~ I +:2: -at" - 4 0 __1':'--[~ ] -9..=1 9... ae:naT9.. - k=l k. (k\ k ae:n 0'-0'0

T-To a at;

where t and T are the time and temperature variables, respectively, and

the subscript 0 denotes a reference value. It should be noted that

material damping, which is of importance in seismic studies, is included

in this state equation, although for low level excitations it is often

isolated and specified separately as a coefficient of damping.

It is evident from Eq. (4-5) that compromises in material simulation

must be accepted in model studies since no two materials are alike in the

time and temperature domain. Even the use of prototype material is a

compromise because of size scaling and the dependence of material

properties on time rate effects. Material simulation is discussed in

24

t , IT

Q\apter - Dynaalc Modeling n.ory

more detail in Chapter 5.

by initialInitial Conditions: - These conditions can be described

stress iO and Tot at time to.and temperature functions, c In many cases,

the specification and siaulation of 0: and T0 0 will be an extremely dlt't'l-

cult task due to their dependence on fabrication and construction proce-

dures and previous loading histories. In the design or models this will

necessitate a faithful reproduction of fabrication and construction pro-

cedures those have a significant effect on the initial condi-whenever

tl~8. In conditions beinitialreinforced concrete structures may

strongly affected by and shrinkage while 1n steeleffects,creep

structures residual stresses due to welding and erection stresses have to

be considered. For steel as a prototype material it may be necessary to

trace the history back to meMber fabrication which is usually the source

of significant residual stresses.

Such influences may be

orprescribed displacements wich may be time dependent as 1n the case

seismic ground motions, prescribed temperature variations, surface forces

the boundaries or the structure, and body forces caused by theon

gravitational tield ot the earth or generated by artiticial mean8 8uch a8

magnetic fields.

For most structural problems the pertinent physical quantities can

be selected from these four groups. Based on a physical understanding of

the problem, it is the task of modelthe analyst to choose those

quantities which will significantly atteot the response quantities to be

measured during the model experiment. The experimenter may be interested

in tracing the complete history which be described byresponse may

25


stress, strain or displacement functions, or only in specific quantities

such as the failure load which may be characterized by material failure

or buckling phenomena.

To aid the model analyst in selecting model design and response

quantities, an extensive but certainly incomplete list of physical

quantities and their dimensional description is presented in Table 4.1.

Before we can utilize Eq's. (4-1) and (4-2) to derive appropriate

similitude realtionships for dynamic model studies, it is necessary to

briefly summarize the fundamentals of dimensional analysis which is done

in the next section.

Before entering this discussion, a different approach to modeling

theory than that of dimensional analysis should be mentioned, namely, mo-

del analysis based on system response equations. In several cases the

differential equation representing the response of a stucture is known,

although the solution of it cannot be obtained analytically. By trans-

forming the variables of such an equation and also of its boundary and

initial conditions into a dimensionless form one obtains a set of dimen-

sionless parameters defining the relation between the model and the pro-

totype. Although some authors call this method a forcing of the model to

be an analog computer for solution of the equation, a careful use of it

can help in elimination of certain otherwise very rigid requirements

obtained from the dimensional studies.

4.3 .DIMENSIONAL ANALYSIS

Dimensional analysis is an analytical method by which a dimensio-

nally homogeneous equation, containing physical quantities and describing

26

i '\

~apter 4 Dynamic Modeling Theory

equationphysical phenomenon, is converted into equivalenta an

containing only dimensionless products (~-factors) of powers or the phy-

sical quantities. Since these dimensionless products describe the same

physical phenomenon and are independent of the units of measurement, they

is bemust be equal in prototype and model if complete similitude to

achieved.

Dimensional analysis is based on the Buckingham!! Theorem (Ref. 99)

a dimensionally homogeneous equation can be reduced towhich states that

a complete set or independent dimen-a functional relationship between

sionless products (n-faotors). number of independent dimensionlessThe

total or physical Quantities involvedproducts is equal to the number

theminus number of fundamental quantities needed to desoribethe

dimension8 of all physical quantitie8.

The simple rule tor the determination or the number or independent

dimensionless products has been shown to tail occasionally (Ref. 89) and

in more formal mathematical terms (Ref's. 91, 94)has been reformulated

is equal toas: the number of dimensionless products in a complete set

the total number of physical quantities involved minus the rank of their

(The rank of a matrix is order of the largestdimensional matrix. the

submatrix whose determinant is nonzero).

determine complete set of dimensionless products itIn order to a

should be noted that the units of any physical quantity can be expressed

as a combination or units or basic or fundamental quantities. The choice

of basic quantities is largely an arbitrary one but 1s governed by prac-

tical considerations of physical phenomena and simplicity of measurement

Different fields or science may choose different basic quantities. In

27

Chapter 4 . Dynamic Modeling Theory

or basic quantities are those of massengineering, the most common sets

M, length L, time T and temperature 9 (called the HLTO system) or force

FLTQ system). Several authors (Refs. 38, 105)F, L, T and 9 (called the

for convenience heat basio quantity, disregarding itsuse as a

Rocha (Ref. 103) and Beaujoint (Ref. 105) discussequivalence to energy.

the usefullness or strain as a basic quantity and assign it a basic unit

This idea 1s discussed in Section 4.5.3.

Table 4.1 presents a set of commonly used physical quantities in en-

gineering mechanics and their dimensional description in the ML TQ and

FLTQ systems. It should be noted that several quantities in this table

dimensionally such as pressure, stress and modulus orequivalent,are

Also, it is often necessary to distinguish between certainelasticity.

quantities through their physical meaning although they bemay

As an example wedimensionally and quantitatively equivalent. can use

each of them, kinetic, potential, damping,terms whereenergy one

hysteretic Or' recoverable strain energy may have a distinctly different

Thus, commonly used physical derivations ofmeaning to the investigator.

quantities are included in the table where feasible.

The basic quantities can be used building blocks since theas

dimensions or all other physical quantities can be expressed as products

of or basic quantities. When the dimensions or physicalpowers

quantities are properly arranged in a dimensional matrix it is reasonably

simple to extract dimensionless products by comparing individual

quantities as to their dimensional dependence. Although systematic

tormethods generating a complete set or productsdimensionless are

presented books, it equally well be achieved byin most text can

inspection if the following rules and guidelines are considered:

28


TABLE 4.1

PHYSICAL QUANTITIES AND THEIR DIMENSIONS

29


TABU 4.1 (continued)

D1.-ns1ons inT e S 15 tIIS

M e

'O1MnS10ns in.. FL Te Syst8S

- -Description

in terms of otherphysical quantities

Sym-bolPhysical Quantity

F L~ T e

1I

1-2 -2 0Specific weight 1 -3~ 0 0l'

1 -4~ 2 0 1 -3 0

0

0

0

Mass density p

11 2 0 0Mass .Mass ~t of

Inertia all.2 1 0 0I.:v

-- 1. 0 2

I [£/2(1 + v)pJ~

1[(l-v)£/(l-v-2v

0 1 00 -1 0

itVs

Vp

.' 0 ~-1 0'() 04-1 0 0

Velocity

s-Wave Velocity

P-Wave Velocity

Angular Velocity

Acc.leration a0 1 -2 00 -2 0

Acceleration ofGravity 9

. 0 0 0 -2 00 01-2Angular Acceleration

Coefficient ofViscous ~ing 1 0 -1

-1

01 0c Fo'vT/(dv/dy) 1 -z~ 1 0

0

1 -1 0'J1

0 2 -1 0:

Dynamic Viscosity

Kin_tic Viscosity WP

2..,

0v

Kinetic Energy

Potential Energy

KE:

F4

Cy2t

a£.13

PE

DE

HE2 -2 00 0 1

DallPing Energy

Hysteretic Energy

Recoverable Strair;Energy ad3. K82RSE

HHeat c.. kiTe1 1 0M 1 o. 1 0~nt.. my

Fv ,-1 0 1 2 -3 0

1

Power p

0 0 0 0 0T~eratu" e

0 0, 0 I .16/18

H/T18

0 0 .}Coefficient of

Thermal Expansion ~

-1Thermal Conductivity k

-2 0 2 ~ -2 ~ -1c H/~ 0Specific Hut

Coefficient ofHeat Transfer H/T,,2e 11 -~ .~ o. -3'h

30

Chapter 4 Dyna!Dic Modeling Theory

1. The dimensionless products are composed of products of powers of

the physical quantities and should involve not more than N-1 quantities

in anyone product, where N is the number of basic quantities.

2. The dimensionless products must be independent, i.e., none of

the products can be obtained as a product of powers of other products.

3. Independence is easy to verify if the dimensionless products are

generated such that each product involves a quantity which does not

appear in any other product.

4. The dimensional matrix should be arranged such that the response

quantity of interest (dependent variable) is listed first, followed by

independent variables and then parameters.

5. Dimensionless products should be generated such that quantities

are eliminated from left to right in the dimensional matrix.

Guidelines 4 and 5 are important for the design and control of the

experiment. Since complete sets of dimensionless parameters are not

unique, one will be more useful than others in model analysis.

Buckingham has pointed out that we obtain maximum amount of experimental

control over the dimensionless products if the original physical

quantities that can be regulated in the experiment each occur in only one

dimensionless product (Ref. 91). Thus, a warning must be issued against

a superficial use of dimensional analysis. It is a powerful tool but its

usefulness for specific model analysis problems is entirely in the hand

of the user. Here, it may not be out of place to cite two of the

"fathers" of dimensional analysis:

Dimensional analysis yields an amount of information dependenton the skill and experience of the analyst.

-Po W. BuckinghamEncyclopedia Britannica1964 ed.

31

irt{'i1~iI1; t'i)_'!\I~~t!!!¥f;:{,i1/~


Dimensional analysis proves to be an exceedingly powerful weapon,althou~h I should add the warning, based on bitter experience ofmy own as well as a critical study of other people's work, thatit is also a blind, indiscriminating weapon and that it isfatally easy to prove too much and to get mo~e out of a problemthan '8S put into it.

-G. K. BatchelorQuart. J. Roy. Meteor. Soc.,

1959

dimensionlessThe ~neratlon or complete set or independenta

inspectional analysis 18 illustrated in the followingparameters by

Let us consider the problem of bending orsimple example. elastic a

rectangular cantilever beam which is affected by the following physical

qantities:

geometric properties: b, h, t

material properties: E, v

papplied load:

The response quantity ot interest 18 the deflection <5 under the load,

(b,h, 1, I,v, P). All quantities can be expressed in terms or1...,15.leads to the following dimensionalthe basic quantities F and L which

llatrix:

matrix is 2, hence we have 1 - 2 = 5 independent dimen-'nle rank of the

sionless products. It is convenient to form one product that contains

the response qusntity to the first power and relate it to what seems to

be the most relevant independent quantities. Additional products that

can be written down immediately those which p;iven by dimen-are are

32


sionless quantities, in this case v, and those which are formed by ratios

of quantiities having like dimensions. The remaining products becan

formed by trial and following the aforementioned guidelines. For the

beam this procedure gives

(4-6)<5 b h PI = f v, t' I' 2

ER.

to see that these factors are independent since each one con-It is easy

tains a quantity which is not involved in any other factor.

reveal that the solution isInsight into the physical problem may

independent on certain parameters that would at first sight appear signi-

be dropped).fioant (i.e., for slender beam the dependence oouldon "certainThe knowledge the problem 18 linear with respect tothat

For example,simplify the functional relation.furtherparameters can

the deflection isusing linear theory or elasticity one can state that

directly proportional to the load applied and inversely proportional to

the breadth of the beam, hence the corresponding factors be takencan

outside the function:

(11-7)6 p ( h

)"1 ~ m £1 "I~ v

is'ntis linear dependence upon certain dimensionless parameters very

helpful when model distortions have to be considered (see Section 4.4).

In some cases the complete set of dimensionless products obtained by

experimenter's desire torinspeotional analysis not satisfy themay

In such cases a different set of productsoptimum experimental control.

simple transformation techniques. Thesecan he generated by means of

dimensional analysis andtechniques are presented in most textbooks on

need not be repeated here.

33


Several dimensionless products have gained traditional status in en-

gineering and are commonly used in defining physical problems. Table 4.2

presents a set of such "popular" dimensionless products.

4.4 SIMILITUDE RELATIONSHIPS AND TYPES OF MODELS--The necessary conditions for complete similitude between model and

prototype can be derived through the following procedure:

1. Write down all physical quantities on which the solution of the

phenomenon under study depends significantly.

2. Develop a suitable and complete set of independent dimensionless

products from these physical quantities (Eq. 4-2).

3. Establish equality between prototype and model for each of the

independent dimensionless products (Eq's. 4-2 and 4-4).

The third step defines the design conditions for the model and the

prediction equation (or equations) for the dependent response quantity

(or quantities) which relates the measured model response to the proto-

type behavior. As such, this step establishes the scaling laws for all

physical quantities or products of physical quantities. Usually, these

scaling laws are expressed as ratios of the numbers of units needed to

describe identical quantities in model versus prototype. In this report

these ratios are designated with a subscript r added to the description

of the physical quantity, i.e., t = t ~t = 0.1 means that one unit ofr m p

length measurement (e.g., in.) in the model corresponds to ten equal

units of length measurement in the prototype.

One important observation can be made from the fact that all physi-

cal quantities can be expressed in terms of basic or fundamental quanti-

34

l, I , I

Chapter 4 Dynamic Hodeling Theory

TABLE 4.2

DlMENS I <If LESS pR(XMJCTS

{a} Named Dimensionless Products

y - surface tension [Fl-l]Bfot Number

Bond NlDnber

Cauchy N~r

Einstein NllAber

Euler r~wnber

Fanning Number

Fourier Nwnber

Froude Number

Grashof Nunmer

Mach NlDnber

Newton N..mer

hL/k

pg,,2/y

pv2/E

v/c

TW - shear at the wall

v - kinematic viscosity

c - speed of sound

R - aerodyn. reacti onexperienced by a body

~P/py2

TJ(l8)y2)

kt/pC12

y2/19

"'*\I

Y/c

R/pR,2y2

ht/k

Cu/k

p/pv2

v2/1f

Nusselt's NU1Ii)er

Prandtl's NUllmer

Pressure Coefficient

f - force per uni t mass

2j)V 1/y

Reech Number

Reynolds Number

y - surface tensionStrouhal NlDber

Weber ~Iuni>er

(b) Dimensionless Products CommonlyEncountered in Structural Engin-eeri ng Problems

35

tv/" ortvp/~

lAIR./v

Chapter 4 Dynarnic Modeling Theory

ties (e.g., FLTQ or MLTQ). Since these basic quantities are independent

on each other, it is evident that as many scales can be selected

arbitrarily (within physical constraints) as there are basic quantities

needed to describe the problem. For instance, in a static problem which

has F and L as basic quantities, two scales can be selected arbitrarily.

In a dynamic problem which may be described by M, Land T, three scales

can be selected arbitrarily. However, in this case it is usually

necessary to select gr = , (g is the acceleration of gravitv) which

reduces the choice of arbitrary scales to two. The scales of all other

physical quantities are then expressed in terms of the arbitrarily

selected ones and can be obtained from the dimensionless products.

It should be noted that the choice of arbitrary scales is not

limited to basic quantities; any set of independent quantities may be

selected for this purpose. The number of independent quantities is

always equal to the number of basic ones, and their independence can be

checked through the formation of the Jacobian whose determinant must be

nonzero (Ref. 38), i.e.,

d(Ql,Q2,ooooqr) of a (4-8)d (kl,k2'o 0_0 okr)

where r is the number of independent quantities, q, to qr are the

selected quantities whose independence is to be checked, and k, to kr are

the basic quantities.

To illustrate the determination of scaling laws, let us take the

beam example of Section 4.3 whose dimensionless products were written as

0 ( bh P)"]i = f V, "]i'"I' ~ (4-6)

E.Q, repeated

If we freely select a length scale ~ and a scale for the modulus ofr

36

,,£ I i 1


elasticity Er' complete similitude requires that

similarity)evident from geometric and p = Er r

dimensionless Quantity be equal for model and prototype. Themust

In many practical situations the fulfillment of all design conditons

will be an impossible task. Under those circumstances it is a matter of

features which may be alteredjudgement and experience to isolate those

such that model construction becomes feasible but the response prediction

is not encumbered with an excessive amount or error.

(Ref. 90)In these kinds of models, Murphy distinguishes between

Adequate models are those where the pre-

by thediction equation is not affected (except for the error introduced

disregard or violation or a design condition) and design conditions may

problem reveals that thebe violated when insight into the physical

results will not depend signiti~antlY on the violated design oondition.

For instance, in the above example, cross-sectional similarity may not be

signitioantly thecritical if shear deformations do not contribute to

deflection 0 . In this case, the moment of inertia 1s adequate to

describe the cross section and band h can be distorted accordingly. As

another example, in certain dynamic problems the effects of gravitational

forces may be small compared to those of inertia forces and consequently

certain design conditions may be disregarded (see Section q.5.2).

models the distortion inActual distorted those whereare one

dimensionless either leads to a distortion of the predictionproduct

equation or is accounted for by introducing compensating distortions in

37


other dimensionless products. In the first case the prediction equation

needs to be modified by a prediction factor 0 defined as

(7TI)0 = p (4-9)

(7TI)m

where 7T1 is the dimensionless product defining the prediction equation.

The prediction factor can be determined through physical insight into the

problem or by means of a series of auxiliary experiments. For instance,

in the example problem defined by Eq. (4-6) it is evident that 0 is

inversely proportional to b thus if b is distorted by a factor a , the

prediction factor is given by 0 = 1/a.

For more information on the determination of 0 and compensating

distortions the reader is referred to the book by Murphy (Ref. 90). An

alternative method for the evaluation of compensating distortions is

presented in Section 4.5.3. There, the distorted physical quantity is

introduced as an artificial basic quantity.

4.5 PHYSICAL MODELS rQ.!! ~ ~ SrUDIES

4.5.1 ~ !eplica Models

Suppose the task is to reproduce, at model scale, the time history

-rof stress components aij(r,t) in a replica model subjected to a time his-

tory of vector imposed acceleration a (t). Recognizing that the distri-

butions of stress and of material in the prototype and model must be

identical, dimensional analysis can be applied by calling a a typical

stress, p a typical density, and E some representative stiffness

property. Then the stress distribution may be written as

38

1. I' I . .II I I I II ,


-+-cr.. = crS..(r,t) i,j = 1,2,3

J.] J.]

where Sij is dimensionless.

With the greatest degree of simplification, the typical stress can

be expressed through a functional relationship of the form

-+- -+-cr = F(r,t;p,E,a,g,t,cro,ro) (4-10)

-+-

where cr and r refer to initial conditons. Evidently, the omission of0 0

all material properties with the exception of E implies that similarity

of material properties is tacitly assumed.

Utilizing dimensional analysis, a complete set of dimensionless

products can be generated from the dimensional matrix of the quantities

in Eq. (4-10). The products presented in Table 4-2 should be usef1:11 for

this task. The resulting dimensionless relationship could be of the

following form

-+-

c-+- ~ cr r~ = f.!:..!. ! '. ~ ~ ~ ~E (t' t p' g' E' E' t ) (4-11)

If gravitational contributions to stress histories must be accounted

for, the two terms containing the gravitational acceleration g ver~, much

so restrict the model analyst's freedom in selecting model materials and

scale factors. Since there is almost no practical way that g can be

changed between model and prototye, the value of gr usually must be taken

equal to one. Consequntly, from the dimensionless product a/g (Froude'~

Nu!!!b~!:, usually written as v2/tg) it follows that

a = g = 1 (4-12)r r

If this relationship is substituted into the design condition

39

!~ I I I


(g~p/E)r = 1, it follows that

(~)r = ~r (4-13)

This scaling law places a severe limitation on the choice of suitable

model materials.

Equation (4-13) is sometimes expressed in terms of one-dimensional

wave propagation velocities, as follows:

vr = 'i{flr = 1[i-; (4-14)

and is then referred to as the Couchy condition (based on Couchy's Number

pv2/E).

There are alternatives to the use of dimensional analysis as a way

of arriving at the Froude and Cauchy criteria. For instance, one can

examine the internal and external forces to which a structure of a given

geometry is exposed. The most important of these are inertia, gravita-

tional, and restoring forces (FI' Fa' and FR' respectively). Their rela-

tionships to material density, stiffness, length, and applied

acceleration may be expressed as

Fr 'V p~3a

F '\i ~3G P g

2 2FR 'V cr~ = E:E~

In these expressions cr and E: are representative measures of stress and

strain.

Independent of scale, FI and Fa must bear instantaneously a fixed

40

it Ii'


field, the following parame-ratio, as also must FI and FR- In a one-g

ters result from this requirement:

Froude's Number

.P.!:.!.E

2.e!-

E

3F I .e!...!. '"'" 2

e:ER.Cauchy's Number-

FR

numbers produces a parameterCauchy'sFroude's andbetweenThe ratio

replica model reproduce the full-scaleIt it is required that81 9.pg. a

EqS. (4-12) and (4-13) can be de-values of those numbers, for fixed g,

Thus, Eq. (~-13) is a necessary condition tor simultaneous repli-rived.

cation of restoring forces, inertia forces and gravitational forces.

otherfrom theobtaineddesign conditionsAdditional are

theFor instance, it follows fromor Eq. (4-11).dimensionless terms

second term on the right-hand side that

t(4-15)

bethey must

From thisequal in the prototype and model structures.instantaneously

typical structural displacements are relatedobservation it follows that

bya - R.r r

that geometric nonlinearity in structural behaviorThis relation ensures

is property simulated.

41


Table 4.3 shows in column (1) the scaling laws for several physical

quantities for a true replica model. In this the independentcase

quantities are chosen to be ~, E and g, and gr 1s taken equal to one.

Only one--but almost unsurmountable--difficulty exists in this true

suitable model materialreplica modeling, namely, the selection or a

Exact material simulation far beyond simulation of modulus ofgoes

elasticity, Poisson's ratio and strain; theoretically it should include

all pertinent material properties discussed in Section 4.2, such as those

defined by Eq. (~-5). Since two materials 1n nature are exactlyno

alike, material simulation will always introduce errors in the prediction

The importance of these errors, or in many cases their insigni-values.

ficance, the subject or material study which is discussed inare a

Chapter 5.

In the simplest case, similarity 1s tor the uniaxialnecessary

stress- strain curve for the range of strains of interest. Since tJ"ue

replica modeling requires that E : 1 (since e; is dimensionless), ther

stress-strain curves of model and prototype materials should be identical

except for constant stretching by the ratio E IE in the £-directionp ma

(see Fig. 4.1).

Materials difficult to find,with shape-similar (]- e: diagrams are

1n the E-direct1on (E.particularly if no distortion = 1) is permitted.r

Under certain conditions, strain distortion (Er~ 1) provide anmay

interesting alternative to true replica modeling, idea which 1san

discussed in Section 4.5.3.

True replica models are extremely difficult to realize because of

problems in material simulation. Nevertheless, for certain length scale

42

M

..W-l

.!

~~~--'zVi

!. I~ ~.BIs-eA.

~C

~~eoX

.u-'Q.!QI

2--

litlit

is-'Z..--~i'"---II)......-:

~$¥

";GI

Z

1ftGI~0

>->

~,~

s-...s-o

...~

-Q

C

"';s....'A

;~ -;; 1-

c.

~

I;,-

---

-In-

:5cocOi

~

.. I .P s.. of s.. .PI.... ~ .., -1

...-t

.Z' .P.... - ~... Q,.P ~

...1 '"Q: ~ '"Q: u.. - GI

loa - loa -- . - ~

.,~ ~ ~

... ... ...- - -I s.. s.. s..

I.s..~~~-~~~

i~

..~I ..~ -..,. -

of ... .p... _I8\ et

50 50 50 50 50.. ~ > ~

4_~

.888- ->. v >"'~ ~~ ... ~s.. s..41 - "41 GI= v .~~ ~0" 0 >GI aJ41 ~ IOU vs.. 41 s..v V~ "'. ..

~u~

";.

~

~"'Q:

'"-

7~'"

-

... ... ... ... ~. Q. .., 0 w

~I.. -I -

~-litCQI

~ c

-

lit oalit s..

I ~

et'-""\.-'"

~I-

-,

litlit

flit

'" "'I'" '"

'"'

I.. 1..1'" '"

C'I.- ~ ~I - W W

~ I ~ I I ~C'I'"8t ~W~ ~W ~~

~W ~w w '-8t 8tW w '-8t '- '-

~ .. w WM

I- l-I W

...~>.

i0'" '"- u'"

"'u ~4IU~- ~ c ..1 '" u a-

.. 4I~ III... a ~~ """~

&.- &.Q. &. &.-

'01602!!O', ~

«~

...- N,.,Co - ... 81 81'" 81 ... ..-

...~

o.pter -

N tOtI- l-

I- of .... I- I-

-., ~

...

N '- '-'- w Wt '- '-

.., ~

N M50 50 50

~ ~ ..

~0

o,n..lc &deling Theory

fI~c~

~0Ia~-'"II>C-

. II'" .c- -8 >.i .a

cU II

- '"0

'" .c.. U

-GI GI

'-

'- ....GI -0C GI

- C- -

'- ~0 II

-0C'iN~'" .",~"'O

.!,.:~c'-

"'0>.- II. U ~

~GlUIa~'"

CGlCJ..GI.c

U~~« ~

Chapter ~ Dynamic Modeling Theory

(1factors = Er/Pr>' suitable materials for the modeling of metallicrtestingstructures can be found (see Chapter 5) and a pilot program on

simple models of this type is discussed in Chapter 9.

Stress-Strain S18ilitude Require8entsFigure 4.1

In many cases it is possible to find acceptable alte~natives to true

replica modeling which are based on compromises that minimize the errors

Several or alternatives are discussed inin response prediction. these

the problemsSections ~.5.2 and ~.5.3; or them will solve allnone

but all are believed to be suitable torencountered in dynamic modeling

model studies concerned with particular paramet~rs andofcertain types

structural configurations.

To overcome the difficulty of simul-~ Testing ~ !. Centrifuge:

p;ravitationaltaneously reproducing restoring forces, inertia forces and

forces, one could try to increase the effective value of g in the modelm

by mounting a shake table inIt might be possible to achieve thistest.

a suitable orientation on the cab of a large centrifuge. Also, it would

have to be possible to bring leads from the cab so that required data can

Let it further be hypothesizedbe recorded and processed on the outside.

44

Chapter 4 Dynamic Modelins Theory

created over the entirethat a uniform, parallel acceleration field is

model and, during centrifUge operation, that there would be no difficulty

Thus,in applying the required earthquake Aooeleration A to the model.II

given "controllable gravity". it follows from (gtp/E)r = 1 thAt

(*)g R, -r r r

choose the same materials tor model and proto-couldAs an example, one

type; thus:

1r.r

g er

last requirement might prove impractical. Itsmall models, thisFor

would 0811 tor both very high rates or rotation in the centrifuge and for

very high imposed acceleration levels am since ar = gr . 1/tr8

In order to put this results in perspeotive, let us look at the NASA

the "Ames ResearehAmes Research Center twentY-R centri ruge described in

Facilities Summary, 1914". This facility can provide lon~-time exposure

No smaller thanot up to 20g tor a payload ot up to 1200 (earth) pounds.

a twentieth-scale model of the same material could therefore be accomoda-

weight or this lIOde 1, theWith 8 roughly 1000 1bs. limit theted. on

that could be modeled is limited toweight or prototype structurea

1000 x (20)3 Ibs., or about 8,000 kips.

it is possible that a centrifuge might be employedAlternatively,

Thus, one might choose phosphor bronze, whichwith reduced E/p models.

On the 20-R facility, one could thenhas roughly haIr the £1 p or steel.

model, at 1/40 scale, structures or steel that weiRht up to 64,000 kips.

45


4.5.2 Adequate Models

All physical models which violate any of the design conditions dis-

cussed in the previous section could be called distorted models. How-

ever, if the effect of a distortion in one dimensionless product is such

that it does not require an adjustment of other dimensionless products or

of the prediction equation, then it appears appropriate to separate such

models from truly distorted models. In this report such models are

called adequate models.

The need for such models is based on the desire to theuse same

materials as in prototypes. However, the types or models discussed in

this section not limited materials; 1nare to the use of prototype

certain cases the use of different materials make such models evenmay

more powerful tools.

There are two distinot "distortions" leading to two types of models

which should very useful ror model studies or certain olasses orprove

structures on shake tables.

1.

Equation (4-13) for true replica modeling requires that model mate-

rials have a small modulus or large mass density or both. Since such Ina-

terials dlt't'loult to find,are it appears attractive to augment the

density or the structurally effective material with additional material

which is structurally not effective. This easily be achieved incan

lumped mass systems but may also be feasible for distributed mass systems

as is discussed below.

(!.) Lumped ~ Systems: For oftypes typical buildingmany

46


seismically effective massstructures it is acceptable to represent the

the floor levels (lumped masses).by a series of masses concentrated at

be decoupled from theIn this case the seismically effective mass can

relaxes theof' structurally effective material whichdensity the

dimensional requirement that (Kip) must be equal to I. .rrCauchy's requirement for proper simulation or inertial forces and

restoring forces can then be written as

(~ (~'\9.2E ,I

(4-16).m p

which tor g = 1 becomesrM,.

In this equation, H represents the lumped masses at the floor levels.

to be added to the seemingly trivial termA word or caution has

"lumped mass." Such masses are those which are seismically ~ ~ struc-

mass which is attached to structuralturallyeffective. In reality, any

Masses at floor levels.will affect the structural response.components

will certainly affect the stress distri-such as a concrete slab system,

structural elements and in many cases will be part of thebutton in the

must be taken in positioning such "lumpedGreat carestructural system.

gravitationalmasses" in models to simulate realistically the effects of

simulationand inertia forces. In the distributed massmay cases

discussed in (b) is preferable.

the structurally effective mass is small andNevertheless, when a

representation of the seismically effective mass by lumped masses is fea-

r r

47


model tests this often requires excessive weights which may render such

tests impractical. The weight requirements may be reduced when model ma-

terials with small stiffness properties (E) are used (see EQ. 4-16).

(~) ~istributed ~ Systems: For many types of structures a correct

simulation of the mass distribution in space is essential and a simpli-

fied lumped mass system cannot be accepted. A simple way of testing

adequate models of such structures would be to decouple the mass density

Po of the structurally effective material from an additive P1' which is

to be built into the model but has no counterpart in the prototype. Thus

the full-scale density and stiffness would be represented by (po)p and

Ep' whereas those for the model would be (po)m + P1 and Em' respectively.

This modification would alter Cauchy's requirement as follows:

19m= [~]pWith one-g testing this relation leads to

PI Er(po) + (p> = rr 0 P r

or

PI = [ f- - (po) ] (po) (4-17)r r p

For instance, for a 1/20 scale model using prototype material

(Er = (po)r = 1) the density will have to be increased by a factor of 19.

In a small-scale model, it takes considerable imagination to see how the

material that increases the density by P1 might be incorporated.

Much work needs to be done on this sub,1ect, since it is very

48

I :1


difficult to effectively separate the seismically effective mass from the

structurally effective material. There are, however, instances whE~re it

seems quite practical. For instance, in structures consisting of s:lender

load-carrying members, the scheme for addin~ mass could be to atta(~h to

each member suitable amounts of lead or other soft high density matE~rial,

arranged in such a way that it contributes negligibly to the strength and

stiffness but augments the weight and inertia. The spacing of these

added masses should be maximized, so as to facilitate the manufacture

while still adequately approximating a distributed inertia.

The modeling law for such distributed masses can be obtained by

replacing the mass per unit volume Po with some representative ma~JS per

unit length Vo' When lead or other material with running mass ~1 is

attached to the model members, Cauchy's requirement then is altered to

[~~]m= [~Jp

With one-g testing this leads to

1.11(V) + ( ) = E R,

or V rr0 p

or

~ = [ E R, - (~) ] (V) (4..18)1 rr or op

Using the same material in model and prototype would make Er = 1 and

( 2 2~o) = R, (from p = V It). This leads to the requirementr roo

VI = (t r - R, 2)(V ) (4-19)r 0 p

This law mayor may not be practicable, because it calls for adding a!21

of mass. For instance, for linear elements of a 1/20 scale model of

identical structurally-effective material, (~o)m is 1/400 of (~o)p

49

I 1

Chapter 4 ~namic Modeling Theory

whereas ~1 is 1/21 of (~o)p hence 19-times as massive per unit len~ths as

the basic model structure.

It appears that the practical realization of this scheme for small

scale models in many cases will call for using reduced E/P model mate-o

rials. The use of such materials (wh.ich need not obey the requirement

(E/p)r = ~r) will require a lesser amount of added ~1 which might enable

the model designer to reach much more desirable compromises in the choice

of materials and added weights.

As an example, the combination of lumped masses and model materials

other than those of the prototype could prove to be useful in case of

truss type structures such as transmission towers, drilling towers, radar

stations, etc. For instance, in the case of a radar station it would be

improper to neglect the weight of the members and account only for the

radar screen weight; on the other hand lumping of the masses at the

joints or at the best at a few points along each member seems to be

sufficiently precise. Use of a model material of lower E/p than that of

the prototype material will help to keep those masses down to manageable

sizes. Construction of this kind of model seems to be relatively simple

provided the joint area is not of critical importance.

The modeling laws summarized in column (1) of Table 4.3 apply to the

cases discussed in (a) and (b) with the exception of the requirement

(E/p)r = ~r' For the case of identical prototype and model material

(E = 1) the modelin g laws are shown in column (2) of the table.r

Models with "artifical" mass simulation have been used extensively

in the past for static and dynamic model studies. References 45 to 58

are examples of the application of st.!ch models in the field of earthquake

50

I


engineering. Particularly, multistory buildings and bridge structures

appear to be well suited for these types of studies. Such model studies

are expected to result in a good prediction of prototype behavior

provided that mass distribution is properly simulated, the ground motion

is reproduced according to the laws of similitude, model design and

construction is done according to prototype procedures, and last but

perhaps most important, a thorough material study has proven the ad,equacy

of material simulation. It is expected that model tests with

"artificial" mass simulation will remain ~ very important sour,ce of

information on structures whose stress and displacement histories h:ave to

be simulated in the elastic and inelastic range and whose materials are

difficult or impossible to simulate by other than prototype-like

materials, such as in the case of reinforced concrete structures.

.?:. ~ Tests Without Si!!!ulation .C;?!: Gravity Forces

Considering at this time only building structures, it appears that

for certain types of structural configurations the stresses indul~ed by

gravity loads are small and maybe negligible compared to stress his1t.ories

generated by seismic motions. In this case (a/g)r need not be equal to

one, which allows considerably more freedom in selecting model materials

and scaling parameters.

The scaling laws can be derived from the remaining dimensionless

products of Eq. (4-11), with g in g~p/E replaced by a. If ~ and E as

well as p of a specific model material are selected as the independent

quantities, the scale factors shown in column (3) of Table 4.3 can be

derived. If prototype material is used (i.e., Er = Pr = 1), all scale

factors can be expressed in terms of ir' see column (4) in Table 4.:3.

It is important to note that the scale factors for many physical

51

I; I I


quantities are different from those for true replica models which will

affect the shake table input, the model design and the response predic-

tion. For instance, when prototype material is used (column (4) in Table

4.3), with t = ~ and a = ~-1, a reproduction of actual seismic motionsr r r r

on commercially available shake tables may cause problems. This again

invites the use of other than prototype materials with (E/p) smallerr

than one. For instance, if brass is used for the simulation of steel,

(E/p) r is approximatelv 0.5 which results in t = 1.41~ ' v = 0.71 , and" r r r

ar = 0.5~;1. With these values, seismic motions become more easily

reproducible on shake tables.

A building system which may be suitable for this type of model

testing is a K = 0.80 buildin~, i.e., a structural system where the

lateral load resisting system consists primarily of shear walls which

carry little vertical loads except through boundary elements. In slender

shear walls the level of stress due to vertical loads in the boundary

elements will usually be small and will not affect the response of a

shear wall to a significant degree. Clearly, even a K = 0.80 building

will not be replicated "precisely" through a model of this type since the

stress level in the moment resisting space frame surroundin~ the shear

walls is not properly simulated. However, considering the low stiffness

of this frame compared to the shear wall, from such model tests one can

expect reliable information on shear walls far into the inelastic range.

Considering steel structures, let us look at a multistory braced

frame without moment resisting connections. In most types of bracing

systems the stresses in the bracing members due to vertical loads will be

negligible compared to those induced by lateral loads. Thus, the

response of bracing members will be replicated through model tests of the

type discussed herein. However, a simulation of the load-deformational

52

ii! 'I


response of the structure will require proper modeling of, at least, the

vertical elements of braced bays.

4.2.Let us investigate a braced frame of the type shown in Fig.

Figure 1& . 2 Braced Frame

Assuming uniform distribution of dead load WD(psf)

triangular lateral load distribution.

and live load

WL(psf> and approximatea an

analysis shows that the ratio or axial column loads due to seismic and

gravity forces above leveli is given asn

1: j{j-i)

j-i+l-Ii~ j

j-l

( ~Pc i

where ct is a seismic coefficient defined by base shear V = a WD8

For the ground floor (i = 0) this equation reduoes to

n

r j2- ~ ~~ 1h j-!

nr j

j-l

I'~

PG -aW;;+~b0

53

Chapter JI Dynamic Modeling Theory

For braced frames with b = 2h and wL = 0 (a rational assumption for model

tests) one obtains the force ratios given in Table 4.4

Table -.-

n5 10 20 30

1-0 5.5a la.Sa 2a.Sa 3D.Sa

5 7.1a

13.4a 24.4a10

14.4a20

Assuming the seismic coefficient ~ to be of the order of 0.1 to 0.3,

significantit can be seen that the effect of gravity loads becomes less

one to believe that awith an increasing number of stories. This leads

replication of gravity loads may sometimes not be necessary for this type

or frame.

or the kind described here appear attractive since theyHodel tests

containmentreactormterial. Nuclearpermit the use of prototype

quiteanother type of structure where such tests appearvessels are

loads are small compared to theor gravityfeasible since the effects

It usuallyeffects of internal pressurization and s.evere ground motions.

or not thewhetherjudgement decideis up to the model designer's to

introduced by neglecting gravity effects are acceptable. It theerrors

lar~e, true model distortion is evident and either thetooerrors are

products have to be modifieddimensionlessprediction equation or other

geometric nonlinear1tiesWhen materialto compensate for the error. or

are involved in the problem, this will be an extremely difficult task.

with linear elasticHowever, when the model test is only concerned

seismic effects andbehavior, gravitatinal effects can be decoupled from

54


can always be neglected in the derivation of similitude law. Thus, the

scaling laws in columns (3) and (4) of Table 4.3 can always be used for

linear elastic problems, regardless of the importance of gravity effects.

This makes model design for linear elastic tests very simple sin,ce the

only material contraints are that of a linear elastic range characterized

by E and, where needed, similitude of Poisson's ratio v and ma'terial

damping properties.

4.5.3 Distorted Models

The use of truly distorted models for seismic studies of nonlinear

problems is rather limited since it rarely will be possible to find

adequate corrections to the prediction equation or other ph~'fsical

quantities, to account properly for the violation of an important design

condition.

One could attempt, for instance, to design a model where g]~avitv

effects are only partially simulated through the addition of "artif:lcial"

masses to reduce the error introduced when all gravity effect:~ are

neglected. Such a "mixed" model would be governed by similitude laws

which are a compromise of those listed in columns (2) and (3) of Table

4.3. Thus, the scale factors for the quantities governing the seismic

input to the model (t, v ' a) will need to be re-evaluated throu~hr r r ~

physical insight or an auxiliary testing program.

Alternatively, one could try to properly simulate spatial geometry

of the structure but distort the geometry of the cross section such that

gravitational and inertial forces produce the correct level of stress in

each member as well as correct dis p lacement similtitude (cr = ~). Usin~r r ~

prototype material for the model one arrives, from E E ~ 2 = p ~ 3, at

rrr rr

55

.oT~ I


the following similitude laws:

A =.R,3 As =.R,3r r' r r

I = .R,5, J =.R,5r r r r

This shows that simultaneous replication of axial load, shear,

bending and torsional effects will not be possible. However, the

possibility exists to change the shape of the cross section such that

close similarity between A, As, I and J may be achievable.

Both of these alternatives will have limited applicability and are

not pursued further in this project. However, another type of

distortion, namely strain distortion, shows certain promise for small

scale model studies provided that no geometrical nonlinearities are

expected.

The requirement of identical strains in model and prototype

(£r = 1, see Fig. 4.1) is often difficult to fulfill from the standpoint

of availability of suitable model materials. It is much easier to find

shape-similar materials if a stretching by £ ~ 1 in the £ -direction isr

permitted as is illustrated in Fig. 4.3.

To account for strain distortion in cases where small displacement

theory holds true throughout the experiment (i.e., no secondary effects

are involved), Rocha (Ref. 103) proposed the introduction of an artifi-

cial fundamental quantity D for strain measurement. When this term is

included in the dimensional matrix in the addition to M, Land T, and a

dimensional exponent of 1 is assigned to the quantities dependent on £,

the following dimensionless functional relationship can be obtained:

56

, '\

Chapter 4 Dynaa1c Modeling Theory

+(] r

a.&.!e. 0 0i' IE' iE"' '1£

+ ifl' t EIi' I p; (4-20)...Q:..-'l

EE

= 1, the following similitude laws can then be derived:

1

For 8r = gr

(~)r

-~e:r r

(4-21)

_A~.Y~r-r

t r

and

4, .1&r-rThese and other similitude laws derived from Eq. (4-20) are shown in

column (5) or Table 4.3.

Em£pF1&Ure -.3 Streu-StraiD Diacraa - Strain Distortion

As the development of these similitude laws is based on the somewhat

fundamental strain quantity and assumes linearorphilosophical idea a

on this fundamental quantitydependence of selected physical quantities

fordistortionfurther study is needed to prove the feasibility of this

Assuming that the similitude laws of column (5)inelastic model studies.

prove toof Table 4.3 adequately account for strain distortions, it may

of problems where Reometrlc nonllnearltiesmodelingbe very useful for

57


are known to be insignificant. The restrictive requirement {E/p)r = ir

for materials for true replica models can then be relaxed to

(E/ p) = i /~ which Permits considerabl y more freedom in the choice ofr r r '

suitable model materials. For instance, it may be possible to fabricate

small scale models of steel structures made of certain copper alloys

(Er~0.5, Pr=1) without artificial mass simulation, presuming that it is

possible to anneal the alloys such that they have a yield strength of

(cr) = (if ) E ~ = (cr ) E t /(E/P) -=:-L for P -::: 1. However, this alsoym yprr yprr r r r

implies that ~ -=:- 2~ (for E ~ 0.5) and 8 ~ 2~ 2 which will requirer r r . r r

very sensitive instrumentation.

Other types of inadvertently caused model distortions often have to

be considered, primarily those caused by inadequate material simulation

such as distortions in Poisson's ratio, hysteretic energy dissipation,

strain rate effects, etc. Such unintentional distortions are sources of

errors and can rarely be accounted for through modifications 1n the

dimensionless functional relationship of the problem. These errors are

discussed in more detail in Chapter 5.

4.5.4 Summary

Dimensional analysis has been used to derive modeling laws for

various types of model tests of structures subjected to seismic motion.

At the outset it has to be realized that an exact replication of all

parameters affecting the response of structures under dynamic actions can

rarely ever be achieved. The emphasis in this study is directed towards

identification of important parameters and possible types of model tests

which allow, as exact as possible, replication of these important

parameters.

58

" I


generallyof the modelin~ laws presented herein areAlthough most

studies of prototypesapplicable, emphasis was placed primarily on model

The model test resultsas steel.of homogeneous isotropic material such

and lead one to believe that manyobtained in this study are encouraging

Asteel structures can be modeled with sufficient accuracy.of'types

whichfinal answer can only be obtained through a series of model tests,

needs to be pointedItcan directly be compared with prototype studies.

this study, only primary structural elements have beeninout that,

nonstructuralstructural andinteraction betweenoonsider-ed and no

elements is included.

the right type of model for the intended purpose andorThe choice

the degree or approximation that must be accepted are of primary concern

complex thr-ee-general ormost ato the model analyst. In the case

are equallyinertia effeotsgravity anddimensional structure, where

the ideal choice provided that areplica model~istrueimportant, a

adequateIt this is not possible,suitable model material can be found.

often be achieved by means of ~ t!!tsmodel testsaccuracy in can

showsIn cases where prior knowledge

seismicgravitational effects are sufficiently small compared tothat

feasibleeffects, ~ test~ without simul~~ion ~ gr!yity forces are

believed to be theThese three types of model studies arealternatives.

phenomena bymost suitable ones for the replication of seismic response

means or small shake tables.

59

Chapter 5 Evaluation of Hodel Materials

CHAPTER 5

EVALUATION OF MODEL MATERIALS

5.1 INTRODUCTION

Providing the right model material whose properties wellare

documented in the literature and which properly simulates the behavior of

the prototype material has always been a major obstacle to the acceptance

of model tests as verification of prototype response, and has raiseda

continuous suspicion as to the reliability of model results. Thistest

holds particularly true for dynamic tests to failure which are of primary

interest in experimental work in earthquake engineering.

The demands placed on a model material can easily be defined but the

search for a suitable material and a verifioation of its suitability are

formidable task. similaritya Ideally, a model material should provide

of all material properties disoussed in Seotion ~.2, i.e., the listed

thermal and mechanical properties should be identical to those of the

prototype material after the application of scaling laws. In the simple

case of a unixial stress-strain relationship (see Eq. 4-5) this requires

similarity of the derivatives of stress with respect to strain, time, and

temperature, and of' strain with respect to time. Fortunately, in

practical modeling problems, similarity 1s only required tor those

material properties which affect significantly the response quantities of

interest in the study. An a priori knowledge of these relevant material

properties, derived from physical understanding or the problem, is

important for every model study since it may simplify the search tor a

suitable model material.

Even then, satisfactory model material will be difficult to find

particularly for dynamic studies in the inelastic domainresponse

60

Chapter 5 EYaluation or Hodel Materials

model material must be readily available, reasonably inexpen-Firstly, a

be easily adaptable to structural shapes andsive and, above all, must

fabrication of member connectionsmust allow a simulation of prototype

that no two materials are alike and compro-realizemustSecondly, one

Even a prototype materialmises in material simulation must be accepted.

time and lengthwill not simulate mechanical properties properly in the

It is imperative, therefore,domain due to strain rate and size effects.

to isolate the material properties which must be simu-in a mde 1 study,

Also, errors encounteredlated and those which can be compromised. the

due to improper simulation of material properties must be evaluated as to

their importance in response prediction.

Sinoe this study is oonoerned primarily with dynamio models of steel

emphasis in material modeling isand reinforced concrete structures,

placed on the simulation of structural steel, concrete and steel reintor-

cement.

SuccessfUl studies on ultimate strength models of steel prototype

structures have been reported by several researchers who used either pro-

totype material (i.e., Refs. 31, 58, 85, 86) or non-ferrous metals (i.e.,

Ref. 38). Results of material tests on structural steel and on copper

alloys performed in this study are reported in Chapter 6.

For modeling of' subjected to inelasticconcrete structures

deformations it is hardly ever possible to use anything but concrete-like

Thematerials such as microconcrete, cement mortar or gypsum mortar.

static properties of model concrete and model reinforcement wellare

documented in the literature (Refs. 18, 36, 117, 120, 145,39, 115 to

147), while much less is known about the properties under dynamic test

146, 149).conditions (Refs. 39, 122, A significant portion or this

study is devoted to modeling of reinforced concrete. Techniques adopted

61

Chapter 5 Evaluation of Model Materials

in the fabbrication and testing of microconcrete and reinforcing wire are

discussed in Chapter 7 together with the results of static and dynamic

tests of these materials. Chapter 8 provides a discussion on the fabri-

cation, testing and test results of reinforced microconcrete beams. Both

static and dynamic behavior are considered.

In this chapter, the properties which are expected to affect the

dynamic response in the elastic and inelastic range are identified and

their simulation requirements are briefly summarized. A material testing

program is discussed which should provide the information necessary for

the evaluation of the pertinent material characteristics. The chapter

includes also a section on laboratory equipment and instrumentation nee-

ded for the implementation of such a program.

5.2 MECHANICAL PROPERTIES OF INTEREST-When it is necessary to simulate the complete load-deformation res-

ponse of a structure from zero load to failure, ideally the following ma-

terial properties should be simulated:

1. Stre~s-Strain Diagram ~ Unixial ~ Tests: If no strain dis-

tortion is allowed this will require point by point equality of the ratio

alE, in prototype and model material, where E is the modulus of elasti-

city or some other representative stiffness property, and a is any elas-

tic or post-elastic stress value on the a-£ diagram. In other words, the

stress-strain curves of model and prototype materials should be identical

exce pt for a stretchin g by the ratio E IE in the 0 - direction (seep m

Fig. 4.1). This requirement is often difficult to fulfill as will be

shown in the case of individual materials. However, exact simulation of

the monotonic stress-strain behavior may not be of the utmost importance

62

. I ,," ,


in cases where the material (whether single or composite) is known to be

subjected to inelastic stress reversals. In seismic response studies the

requirement that the amount of energy dissipated bV the material be

properly simulated is of primary importance. Ideal simulation would mean

that at all strain amplitudes the shape and area of hysteresis loops

should follow the modeling law. Again, this may be difficult to achieve

entirely, but prototype and model materials should have similar strain

hardening or softening tendencies and shape similar hysteresis loops in

the strain range of interest.

It should be observed that a simple tension test or a cyclic load

test of the prototype and model material is a model study bV itself, and

hence should fulfill similitude laws such as strain rate scaling and

scaling of the geometry of the specimens. The importance of this obser-

vation will become apparent in the next few points.

2. Poisson'~ Ratio: In the discussion of modeling theory it was

stressed that all dimensionless quantities should be equal for model and

prototype. This applies also to Poisson's ratio unless the error intro-

duced by a distortion of v is negligible or can be accounted for through

modification of other physical Quantities. Approaching the modeling

theory through the equation of state defining the response of the pro-

totype enables the investigator to approximate the error involved in the

misscaling of v. For instance, Hossdorf (Ref. 1) shows that for a bar

subjected to a considerable amount of torsion, the ~ Quantity v could be

replaced by a different dimensionless product of the form:

EI I~ = ~ = (1 + V)J;

Thus, the prediction error for torsional response will not be propor-

63

:1 I I I 1

Chapter 5 Evaluation or Hodel Materials

tional to the respective v values, but will be proportional to the 1 + v

tions of related physical quantities can be illustrated in the example or

plate (Ref. 96).the vibration of simply supported The governinga

equation for small transverse bending vibration of a thin plate is

a4w

-;;;.-+

11 2 2a w p 3(1 - v ) a w+2:---

ayll ax2ay2 E h2 at2

a4w

2For true dynamic replica modeling it must hold that (RIP) = 1 and t =r r r2 2 2lr' thus, dimensional homogeneity will require that «1 - v )/h )r = 1/lr

This condition permits the derivation or a separate scale for the half

thickness h of the plate as h = 1 .f( 1 - v 2) I.r r V\ I - v J r

Hence, in many practical cases it is possible to evaluate the in flu-

ence of Poissons's ratio on the load-deformation response of the struo-

ture. When found to be of a minor importance (probably in a majority or

building structures), a compromise in the modeling of v is acceptable.

3. Material Damping: The importance of parameter in materialthis

simulation depends on the definition given to this term. Damping in

structures subjected to severe earthquakes will be caused, amongst other

factors, by anelastic material damping the energy dissipated by a ma-

terial within a hysteresis loop without permanent strain offset), actual

hysteretic offset),damping (associated with permanent strain anda

interfaces between structural materials (e.g.,friction type damping at

at bolted connections) and between structural and nonstructural elements.

The anelastic material damping depends greatly upon the stress or

strain amplitude (Refs. 170, 171) and although its value can be of signi-

64


ficance in the elastic cycles, once the linear range of material behavior

is exceeded, it is small compared to other damping contributions and is

not investigated further in this study. Hysteretic damping at strain

amplitudes beyond the yield level is a matter of shape and size of the

hysteresis loops which can be compared directly between prototype and the

model material. As such, this covers material damping in steel but not

necessarily material damping in materials and composites which exhibit a

nonlinear range between the proportional limit and the designated yield

strength. This range may be a source of si~nificant difference in

damping between the prototype and model materials. It will be necessary,

therefore, to evaluate this damping in model materials, at various stress

levels, by means of the damping tests discussed in the next section.

Simulation of friction-type dampin~ is a problem which may greatly

affect the response of structures but is not included in this material

study. Actual model tests are necessary to evaluate structural damping

as a whole and to provide answers regarding the adequacy of the

simulation of this type of damping.

4. Strai~ ~ Effects: It is well known that high strain rates

will affect the cr-E diagram. For structural steel they will cause a

distinct increase in the yield strength, a negligible increase in the

tensile strength, and a decrease in the ductility of the material. For

concrete, they will cause a significant increase in compressive strength

(f'), a noteworthy increase in initial stiffness (E), and a decrease inc

the strain at f'.c

The understanding of such phenomena is of importance for two main

reasons: first, to estimate the dynamic properties of the prototype

material based on the values obtained in static tests, and second, to

account for different strain rates in the prototype and in the model. To

65

, I I 1


illustrate the second problem, the empirical formula derived by Nagaraja

(Ref. 151) for mild steel is presented:

(a )d / (a) =, + 0.762 £°.26y y s

. . -1where E represents the strain rate ln sec.

Since the strain rate in the model test will be scaled by the factor

1/t , the increase in yield strength due to strain rate effects for anr

ideal model material should follow the rule

. o 26(a )d / (a) =, + 0.762 (t E) .Y Y s r

This expression shows that the use of prototype material is not ideal for

model tests; it will exhibit too large a yield strength, although only by

a small amount except for very high strain rates.

5. ~-~ Effects: In theory, simulation of initial conditions

will require the tracing of all time-history events affecting the proto-

type from the time of construction to the time at which the dynamic event

takes place. These events will include, amongst others, time-dependent

material effects such as creep, shrinkage and increase of compressive

strength of concrete. A study of these phenomena was not part of the

reported research and only a short discussion follows in subsequent

sections.

6. ~ Effects: The increase in strength with decreasing size of

specimens has been studied by various researchers for both steel and

concrete materials. Nevertheless, only fragmentary data can be found in

the literature on size effects of mild steel and even less precise infor-

mation is available on these effects for concrete. In part, the size

effects can be accounted for by carrying out the material studies on spe-

cimens comparable in size to the smallest dimension of model structural

elements. Specific size effects, such as strain gradient effects and

effects related to fabrication (e.g., weldments), can hardly ever be a-

66

!

I I 'I~ I I

Chapter 5 Evaluation of Hodel Haterials

voided and deserve attention in the evaluation of model test results. In

particular, a simulation of crack initiation and propagation at weldments

cannot be achieved at reduced scales and should not be attempted in model

tests.

that high1. Ductility: Sufficient evidence is available to prove

Size effects willstrain rates will decrease the ductility of materials.

characteristics. Within structural elementsalso change the ductility

the changes in ductility characteristics of metal model materials should

characteristics atthebe of negligible consequence; however, fracture

connections (in particular at welds) are size dependent (see previous pa-

deformation capacity ofragraph) which in turn may affect the inelastic

In model elements of reinforced concrete structures themodel elements.

element ductility will depend not only on the ductility of the component

materials but also on the bond characteristics and fabrication details as

is discussed in Chapter 8.

8. of' models or steelElements

model material by means of machining,structures may be fabricated from

casting, extruding, rolling, welding, soldering, glueing. Possibleor

processes mustchanges in material characteristics through any of these

Suitable fabrication techniques are discussed inbe closely controlled.

detail in Ref. 58.

5.3 MATERIAL TESTS - EXPERIMENTAL FACILITIES

In order to perform a successful model material study, a specialized

testing system must be developed which consists of suitable testing faci-

The following pa-lities, instrumentation and a data acquisition system.

ragraphs summarize the experience gained and the observations made during

67

Chapter 5 !Yaluation or Hodel Material.

or suitable testingthis study with regard to the three components a

system.

5.3.1 Testing Equipment

Under this heading such elements as testing machines, support frames

The main objectives in the design orgripping devices are included.and

application capacitytesting equipment are to provide the necessary load

and simple gripping orand control over the applied force and reliable

will dependThe desired characteristics of the systemthe specimen.

greatly on the type or tests to be performed and also on the geometry and

strength of the specimens.

5.3.1.1 Uniaxial Load Test Facilities

This group includes facilities for monotonic tensile, 8Onotonic com-

The tests can be performed either at staticpressive and cyclic tests.

or at dynamic rates.

the relativeof tests 1sOne of the major problems in this type

of the speci-stiffnessstiffness of the testing system compared to the

the ability ot the system to respond fast enoughmen, and simultaneously

strokeinformation provided by the control device (strain, orto the

is or particular importance when a rapiddevice). Thisforce control

change in specimen stiffness is expected (upper yield in mild steel, com-

pressive strength in concrete) and specimen behavior beyond that point is

High rate loading plaoes partioularly high demands on theor interest.

To ove~oome the problemresolution capacities of the testing facilities.

stiff concrete specimens with a rapid strength losscaused by relatively

stirrenin~ or the testing system have beenartificialat r', methods orc

68


employed by various researchers (Ref. 126 to 130). Wang, et. al.,

(Ref. 126) used a case hardened steel tube which was compressed

elastically together with the concrete specimen and which prevented a

rapid change in the resistance capacity to the applied load after the

ultimate capacity of the concrete specimen had been reached. This

approach requires a testing machine of load capacity much higher than

that of the specimen tested and is limited to strains below the

proportional limit strain of the steel sleeve.

A solution to the problem of insufficient stiffness of the testing

machine could be provided by an "ideal" closed-loop system (soft system)

which would respond instantaneously to the signal of the controlling

device. These conditions are becoming increasingly attainable with the

increasing sophistication of electronically controlled testing equipment.

It should be stressed that even the simplest material test cannot be

designed without a close correlation with the capacities of the testing

equipment.

~ ~ ~, the uniaxial load tests were carried out on an MTS

10,000kG (98kN, 22 kips, model 810.015) closed-loop testing system. The

load in this uniaxial system is applied through the movement of an hyd-

raulic actuator. This movement is controlled electronically either

through an LVDT monitoring displacement of the actuator (stroke control),

a load cell monitoring load applied to the specimen, or a clip extenso-

meter monitoring average strain (displacement between two points) in the

specimen (strain control). Each of the controlling devices is suitable

for different types of tests. Load control is used in cases in which no

sudden change in the stiffness of the specimen occurs, thus usually for

elastic tests. Stroke control can be used for displacement control tests

69

II \ 1


on relatively soft specimens. This control is unsuitable for relatively

stiff specimens, as the monitored displacements include the deformations

within the testing system (machine frame and actuator displacement, load

cell and gripping device deformation). In those cases and in cases in

which strain control is desired, an extensometer can be used for the

control of the test.

All the tests on metal specimens were strain controlled, and compre-

ssion tests on microconcrete cylinders were controlled by the extenso-

meter monitoring the change in distance between the plattens.

For simple tension tests of steel specimens, standard MTS hydraulic

tension-compression grips were used for gripping the test specimens since

small preloads and misalignment inherent in the use of this grip proved

to be of no significant influence. However, the problem of testing mate-

rials of lower strength than that of steel, the use of small specimens

necessitated by scaling of length, and the need for cyclic testing with

excursions into the compressive range required better alignment than

could be achieved with the standard MTS grips. This problem was solved

through the fabrication of a special "self aligning" Woods metal grip

similar to that developed by Morrow (129). A sketch of this grip is

presented in Fig. 5.1 and a test specimen embedded in the grip and

mounted on the MTS system is shown in Fig. 5.2.

The gripping procedure was as follows:

1. Thread and lock the specimen into the load cell attached to the MTS

crosshead and into the inner part of the grip.

2. Heat the fusible alloy in the grip by running saturated steam through

the heating-cooling spiral in the outer sleave of the grip. (Fusible

alloys = easily meltable alloys whose eutectic temperatures are below

70

I .III ! I I


the melting temperatures of the alloying constituents; Woods metal

used is the product of alloying 50% of bismuth, 25% of lead, 12.5% of

tin and 12.5% of cadmium with the resulting melting temperature of

about 10oC, and with positive volume change in the cooling process).

3. Lower the crosshead till contact develops between the parts of the

grip.

4. Activate the MTS actuator under load control to produce a minimal

compressive load.

5. Cool the alloy by running cold water through the spiral.

6. Switch the control to the extensometer attached to the specimen.

5.3.1.2 Component Test Facilities

As will be discussed later, component tests are often necessary to

permit a reliable correlation between prototype and model response, and

to aid in an evaluation of the feasibility of specific model materials.

~ ~ st~d!, the pseudo-static and dynamic behavior of components

was studied by means of subassembly tests of the type shown in Fig. 5.3.

These tests were carried out on the MTS testing machine utilizing a

specially designed erector-type rigid test frame which is shown in

Figs. 5.3 and 5.4. The frame was constructed in such a way as to permit

its translation and rotation respect to the MTS machine and to allow the

testing of specimens of different confi~urations. For the specimen shown

in Fig. 5.3, ball bearing hinges were fabricated to provide low friction

support for the column of the subassembly. Monotonic or cyclic loads can

be applied to the tip of the cantilever beam by means of the MTS

actuator. Lateral support of the beam is provided by pairs of teflon

padded vertical rails attached to the test frame at specified locations. I

72

11 1

Chapter 5 Evaluation or Hodel Materiala

Figure 5.3 View or CoGponent Test Setup

Figure 5.4 Test Fra88 for Co8ponent Testi~

73


A different type of subassembly which was tested in this support frame is

shown later in Fig. 8.2.

5.3.1.3 Load History Control

The capability for the reproduction of various load histories is of

basic importance in material test studies. Mills, et. al., (Ref. 58)

discuss wave forms which may be used to control material tests. The

subsequent paragraphs present a summary of the major points of that dis-

cussion.

Three basic functions are commonly used for the test history con-

trol, namely ramp function, triangular wave and sinusoidal wave. Each of

these waves can be used with shifted origin thus resulting in cycles with

positive or negative mean load, displacement or strain. Numerical, com-

puter-generated random histories can be converted to analog form «,onti-

nuous voltage output) and used for test control.

As rate of loading is of considerable importance in material testing

for dynamically loaded models, it is necessary to evaluate this parameter

for consistent correlation between the tests. Ramp loading and triangu-

lar wave forms provide constant testing rate throughout the entire time

history. Sinusoidal waves result in a rate varying from a maximum near

the axis of symmetry to zero at the peak of the wave, and thus only a

mean rate can be estimated. Despite this disadvantage, a sinusoidal wave

form proved to be very suitable for cyclic studies. It provides a smooth

change of the direction of the loading and also resembles more closely

the loading history which the specimen undergoes within the structure

during a dynamic motion.

!n this s~~dy, ramp functions were used for the control of monotonic

74

f I

Chapter 5 Evaluation or Hodel Materials

testss and sinusoidal functions used tor thewere control of cyclic

material and component tests.

5.3.2 Instrumentation

Standard instrumentation for experimental model analysis is

discussed by MilIa, et. al., (Ref. 58). In this section, only a brief

review of the instrumentation used in this study is given with the empha-

sis on the instrumentation developed for special measurements in material

and component tests.

In addition to the previously mentioned instrumentation belonging to

the standard equipment of the MTS testin~ machine, e.g., linear variable

differential transducers (LVDT) for displacement control, load cells ot

various sensitivity depending upon the load applied, and clip extensome-

ters for the ormeasurement small length changes which permit an

assessment of average strain, the following instruments were used in this

study:

0 LVDTs used to measure deflections in component tests

0 strain gages used to calibrate the instrumentation and to measure

localized strains in flexural metal elements

0 mercury gage extensometers used for the measurement of average

strain in compressed concrete cylinders

0 mercury gage extensometers for the measurement of average curva-

ture in component study of reinforced microconcrete cantilever

beams.

dent in material studies. In the studies on model materials and compo-

75


nents an additional demand is imposed, namely that the instrumentation be

(Ref. 58),Mllls, et. a1., usedor minimal size. mercury gap;esa

panel distortion in the tests of small(Fig. 5.5) for the measurement or

lowsubassemblages. The exhibitscale beam-to-column verygages .balan-(0.3 ohm) and therefore have to be used either with aresistance

opposite arm of the bridge or with precisioncin~ mercury in thegage

For standard signal conditioners, the resistance of the gagesresistors.

of a four arm bridge is recommendedtherefore the1s too low and use

with the remaining two arms supplied by higher resistance (e.g., 120 ohm)

pretenslonedprecision resistors. The should be used in agages

Each gage must betheir linear behavior.condi tion in order to ensure

Forprovide the calibration constant.calibrated individually to

instance, for 20 mm (0.75 in) long mercury gages and the signal condltlo-

ner set at 1 mVIV, the oalibration constant was 1.2 to 1.5 V/mm. The 08-

libration was done using an HTS testing machine with an extenaometer used

tor the control ot the displacement.

The measurement of strains in compressed concrete cylinders presents

Glued-on strain gages provide only localized intor-a major difficulty.

meaningless if a crack develops under the gage.mation which may become

large num-In addition, this method is inefficient in studies in which a

of specimens is to be tested, due to the high cost and large amountbel'

preparatory work involved. usedof In this study, tour clip gages were

the average strain over a gage length of 50 mm (2 in.) at 900to measure

The ~~s (Fig. 5.6) developed inintervals around the specimen. were

the laboratory, with mercury ~ages used to monitor the change in the gage

lenp;th.

The mercury gages proved also to be very useful for the measurement

16


MERCURY IN SILASTIC TUBING0.040 In. dl..eter0.015 iD. vall thickness

PLUGSHRINK-TUBING

r~UNTI NG BLOCK

~ I,

L-_!---./~ '.-

PtJUNTING PIN 1 "-~F:~{T).e ~ SOLDERED LEADWIRE

58)Figure 5.5 Silaatlc Mercury Ga~ (Ref.

Fisure 5.6 View of Setup for Microconcrete Compression Test

77

Chapter 5 Evaluation or Model Materials

or relative displacements between two points in a structural element.

For instance, in the study of reinforced concrete components the measure-

ment of the rotation of a specific cross-section or the beam with respect

to the column face was necessary. This was done by measuring the change

in distance between the column face and a frame attached to the beam at

the cross-section in question (Fig. 8.5). The measurements donewere

using mercury gages.

5.3.3

All the aforementioned instrumentation is or electronic nature and

the measurements are obtained i~ terms of voltage, thus allowing a conti-

nuous record of' the data. Although graphical recording i8 of importance

primarily for an immediate test evaluation, digital registration of the

data is needed for final data reduction. A properly designed data acqui-

sittion system permits a rapid and continuous recording or data from a

large number of channels (instruments) simultaneously. Once the data 1s

recorded, its reduction in terms of numerical analysis can be performed.

The data acquisition system used in this study allows a recording or data

from 32to channels at the rate of 42000 dataup points/second. An

extensive data reduction package is available in the computer library of

the laboratory. Figs. 5.7 and 5.8 present schematically the experimental

facilities and data reduction package available at Stanford. A detailed

description of the data acquisition and reduction system 1s presented 1n

Ref. 58.

78

Chapter 5 Evaluation or Hodel Haterials

'isure 5.7 Testing Facilities at Stanford Structural Laboratory

Fisure 5.8 Baaio Data Reduction Package (Ref ~ 58)

79


5.4 Testing Program

The testing program carried out in this study included the following

tests for prototype and model materials:

1. ~ Strain ~ Monotonic~: Standard ASTM tension tests

were carried out on steel prototype material and on reduced size speci-

mens (geometrically scaled in proportion to the model length scale lr) of

model materials. In most cases the tests were carried to failure to in-

vestigate similitude at all ranges of deformations. Various sources sug-

gest different strain rates as being representative for a static loading

test. Since a perfectly isothermal test (Ref. 173) is not within the

range of engineering investigations, a low yet feasible strain rate of

2x10-4/sec. has been selected as a static strain rate. Compression

tests on steel specimens were also performed to provide a comparison for

the compressive branch of the skeleton curve obtained from cyclic load

tests.

In the material study of model concretes, compression tests were

carried out on 50x100 mm (2x4 in.) microconcrete cylinders to investigate

the strength of microconcretes obtained from various mix proportions and

cured for various lengths of time.

2. ~ S~r~!n ~ Monotonic~: This series of tests with va-

rious strain rates was carried out to supplement the data on strain rate

effects available in the literature for steel and microconcrete and to

investigate strain rate effects in phosphor bronze and its adequacy in

satisfying Eq. (5-1). The tests were carried out with constant avera~e

strain rates over the mid-section of the metal specimens (extensometer

attached to the specimen), and over the entire height of the

microconcrete cylinders (extensometer controlling the distance between

80

f I


the plattens). Ramp functions were used for the control signal of the

extensometer.

3. Cyclic ~~: Low strain rate cyclic load tests were

carried out on metal specimens with a gage length equal to twice the

section diameter. These stocky specimens were required to prevent

buckling in the strain range of interest. The selected load histories

consisted of symmetric cycles with increasing strain amplitude a as

shown in Fig. 5.9. The three selected loading histories permit an

evaluation of strain hardening or strain softening tendencies, a

comparison of shape-similarity and area of hysteresis loops and an

assessment of the stability of hysteresis loops of equal strain

amplitudes (see loading history #3). The tests were carried out under

strain control with sinusoidal input wave. Cyclic loading test~1 with

random loading histories and high strain rates would be desirable but

were not within the scope of this study.

~cQ ~ eq"i; £y "f7

12. /2 12-

9 1 9

6 6 6

3 3 3

'*' oJI. -#

3 :3

, , 6'

9

1 I 12-

(t) (2) (3)

Figure 5.9 Cyclic Load Histories Used in Metal Specimen Tests

4. Material Dampins: The anelastic material damping can be evalua-

ted at various stress levels from free vibration tests in torsion or ben-

ding by means of standard laboratory equipment. This was done for the

81

~ I

Chapter 5 Evaluation o~ Hodel Materials

metal materials studied. metal ma-The actual hysteresis damping in the

terlals be deduced from cyclic load tests for loops with variouscan

strain amplitudes. An equivalent viscous damping can be calculated from

the expression proposed by Jacobsen (Ref. 174), i.e.,

~w-w

Beq

1:-

21T

where 6eq = equivalent viscous damping coefficient

A W = dissipated work per cycle

W = work capacity per cycle

There alternative ways to measure material damping (Refs. 170,are

175) which are not pursued further in this project since the knowledge of

damping or the integrated structural system is of more importance that

that of an isolated material segment. Thus, the emphasis in this study

measurement of the damping in complete models through free andwas ~

forced vibration tests on the shake table, with dampingthe charac-

teristics fromextracted the decay of free vibration or from spectral

analysis of forced vibration records (Rer. 176).

5. ~~onent Te~: It must be emphasized that material tests alone

are not suffioient to permit a reliable correlation between prototype and

model response and an evaluation of the feasibility of specific model

materials. Such important phenomena size effects, strain gradientas

effects, and simulations of local instabilities and stress concentrations

at bolted or welded connections can only be studied through component

test with known quasi-static load application. Also, simple component

tests have shown that apparent dissimilarities in material behavior may

often have little effect on the response of structural elements. Conseq-

uently, certain dissimilarities such as the absence of an upper yield

point and of a yield plateau in model materials for steel structures may

82


sometimes be acceptable.

The tests described in this chapter are time consuming but, once a

inbe carried out mostmethodology has been developed, they can

integral ofwell-equipped structural laboratories. They form partan

purpose of providing theevery successful dynamic model study, for the

necessary to select a suitable model material and to assessinformation

the reliability of the prototype response predicted from model tests.

8~

Chapter 6 Materials for Models of Steel Structures

CHAPTER 6

MATERIALS FOR MODELS OF STEEL STRUCTURES

6.1 INTRODUCTION

Despite the extensive use of steel in structural design the number

of model studies performed on steel structures 1s remarkably small oom-

pared to the number of model studies performed reinforced concreteon

structures. The reason for the scarcity of model studies on steel struc-

mathematical techniquestures may be that larger confidence is placed in

Structural analysis methods based onapplied to this type of structures.

the theory or elasticity are widely accepted 1n steel design. Local

nonlinearities (connections, local instabilities) oan be accounted for by

applying experience gained in innumerous laboratory tests performed on

full scale structural components and subassemblages. This is not so in

the case or reinforced concrete structures. Early nonlinearities appe-

.ring in the behavior or this composite material always imposed serious

questions reliability of standard structural analysis methods.theon

The complex nature of force transfer within the material and between the

members required extensive study, not only of the components but also or

entire structural modelsystems, and hence perpetuated studies on

concrete structures.

Under earthquake excitations and other dynamic loading events (blast

loading, extreme wind, impact loading, etc.), energy dissipation through

In these oases,inelastic deformation may become of primary importance.

inadequate and experl-available mathematical modeling techniques may be

mental model analysis may provide much additional information. Harris,

et. a1., (Rer. 38), have performed an experimental study on model mate-

84

Chapter 6 Haterials ror Models or Steel Structures

In Refs. 31, 85,rials for dynamic models of steel prototype structures.

86 and 143, case studies on models of steel prototypes are reported.

6.2

one-to-one simulation of the scaled stress-strain diagram is de-A

maDded by similitude laws (Section 4.5.1) for monotonic as well as cyclic

Therefore, a brief review or the uniaxial stress-load application.

-strain characteristics of structural steel is presented in the following

paragraphs.

schematic diagram of an engineering stress vs.Fig. 6.1 presents a

strain curve for structural steel (low carbon steel subjected to monoto-

The yielding ~henomenon is associated with thenic tension till failure.

yield),initial yielding of metal at a stress concentration point (upper

bands)the propagation or plastioally derormed metal bands (Luder'sand

development or thealong the lover yield plateau. The initiation and

amount or interstitial atoms preventin8 theyield bands depends upon the

dislocations (impurity pinning) tree propagation. Carbon atomsfrom a

present in the structural steel crystalline exemplify interstitial atoms.

Under normal testing conditions, the drop in strength from upper to lover

yield is of the order of 10 to 20' for An explanationstructural steel.

necking andof the physical phenomena associated with strain hardening,

rupture is presented, tor instance, in Ret. 157.

cyclicstress-strain diagram for structural steel underA typical

load application is shown in Fig. 6.2. Compared to the monotonic stress-

-strain diagram, a description of the cyclic characteristics is complica-

the occurence ot cyclic work hardening, Bauschingerted considerably by

Manyempiriosleffects, mean stress relaxation and other memory effects.

85


bCI)CI)uJIt:

~

O'"yu

O'"yl

F1iUr8 6.1 Stress-Strain Diagram fro. Tension Test of Structural Steel

S'."I.

Figure 6.2 Cyclic Stress-Strain Disgram for Structural Steel

86


models have been proposed in the literature for a mathematical evaluation

with great success toappliedbeenof these phenomena, but havenone

Under load histories with symmetric strainfully random load histories.

amplitudes it can be observed that the peak stresses and hysteresis loops

The lineequal strain amplitude.cycles orstabilize after fewa

at various strain amplitudes isconnecting the peaks of stabilized loops

This curve and theas the cyclic stress-strain curve.often referred to

this study toused insymmetric hysteresis loopsshape of the are

characterize the cyclic stress-strain behavior.

structural steel,of'An experimental study on the cyclic behavior

Laboratory at Stan-Structureswhich has been recently completed at the

cyclicford (Ref. 156), provides valuable data for a comparison with the

symmetricThe th,-ee basicbehavior or other than steel model materials.

Ref. 156 are listedstrain histories with zero mean strain adopted from

'~was added in this study tohistoryin Table 6.1. The test with load

amplitude provide information on thee8tablish whether three cycles per

final (stable) hysteresis loops.

Tabl,6.1

Cyclic Load Histories

AmplitudeCyclic LoadHistory No.

Cycles perAmplitudeFirst Incremental

steel-1

3.3

12

2242

1131

1234

81


6.3 SUITABLE ~ MATERIALS

6.3.1 ~roduction

One of the major difficulties in the modeling of steel structures is

the choice of a satisfactory model material. Ideally (~replica ~-

~), the material should satisfy the similitude requirement stating

that the specific stiffness scale ratio should be equal to the geomet-

rical scale, i.e, (E/p) = 1 (see Section 4.5.1). This rule eliminatesr rthe use of prototype material for true replica models. Due to the

specific nature of the stress-strain diagram of structural steel, it is

very difficult to find non-ferrous materials with behavior similar to

that of steel.

A preliminary search for a suitable model material may be based on

the monotonic stress-strain characteristics but must then be supplemented

with information on the cyclic stress-strain behavior. Table 6.2, which

is taken from the Material Selector Issue of Material Engine~ring, pro-

vides a convenient tabulation of specific stiffnesses of a wide variety

of materials. Besides the required E/p ratio, the material must satisfy

the condition that the yield strength to modulus ratio, cry/E, be the same

as that of the prototype material (uniqueness of strain scaling, see

Section 4.5.1). For A36 structural steel, cr IE is approximately equal toy

0.0012. This requirement poses severe problems for thermoplastics

because of their inherently low elastic moduli. Most thermoplastics

studied were found to have much higher yield strengths compared to their

E values than steel (for example, for polypropylene cry/E = 0.02). Con-

sequently, to make use of these plastics ways would have to be found of

drastically reducing their yield strengths while not affecting the

88

, , I


Table 6.2

Specific Stiffnesses Elf

E/~. 10fin

Material. Ratio Material. Ratio

8erylllum 657 BerylliumCopper 64SillconCarbide 607 ZirconiumandltsAlloys 598oronCarbide 483 Yellow8rasses(cast) 58~~,yllia. 413 NickeISilvers 57AlumlnaCeramics 420 Phenolics. Shock Resistant 56MIca,Natural 337 Silicon8ronzes 56Mica,Synthetic 281 Red8rass.85% 54Titanium Carbide Cennet. ... ' ".' 248 Commercial 8ronze. 90%.. ~ 54PolycrystaUineGlass 219 Leaded Brasses 53TunlSlen.Titanium Carbide Cermet 192 GildinR, 95% 53Zircon 188 PhosphorBronzes 53TunISIen CarbideCermet 185 Copper.. "..."..." ,., ,.,..." 53BoronNitride 163 TinandAluminumBrasses 53StandardElectricaICeramics 143 CartndgeBrass.70% 52Glass. Alumino-Silicate 140 LowBrass,80% 51Ruthenium 136 Leaded Tin Brorues(cast) 51Glass.FusedSilica 129 TeliuriumCopper 50Mica,Glass.Bonded 129 MuntzMetal., 50MolybdenumandltsAlloys 127 Yellow Brass 49Glass.96%Silica 124 Columbium 48Glass. Borosilicate... 123 Leaded Red Brass (cast)..., 47Sleatite... . . .. . ... ... 120 Tantalum. . . . . . . . .. 45Cobalt.BaseSuperalloys 120 Uranium 43Nickel.BaseSuperalloys 112 Hafnium 43TitaniumandltsAlloys III Metamines 42Glass, Soda Lime... ... '" III Carbon.. ... .' '.."..'." '...' '." 41HighTemperatureSteels III Palladium 39UltraHighStrenithSteels 107 Ureas 34Ingot Irons 106 Polystyrenes.Glass.Filled 33CarbonSteels(cast) 106 ReinforcedPlastics.Polyester 33Wroughtlron 106 Graphite 31PearjiticMalieablelrons 106 Pewter 29Carbon Steels. . . . .. . ...,.".,.."., ,.. . . . 106 Silver. . . . . . . . . . . . . . . . . .. . .. ... ".,..,.. ."...,...". 29AIIoySleejs 106 PhenyleneOxide.30%Glass-Filled 29NitridingSleeIs 106 Tln.Lead.AntimanyAlloys 29StainlessSteels(ca5t) 106 Platinum 27AluminumandltsAlloys 105 DiallyIPhthalate 25Age HardenableSlainlessSteels 104 GradeATin 25HeaIResistantAlloys(cast) 104 Thorium 24FerriticStainlessSleels 104 Phenolics,GP , 23MartensiticStainlessSteels 104 Polyvinyl Formal 19Iron.8aseSuperalloys(Cr.Ni.Co) 103 ModitiedPolystyrenes 18Free.CuttingSteels 102 Gold 17Iron.BaseSuperaJloys(Cr.Ni) 102 Polyesters(cast) 16MagnesiumAlloys 102 Polystyrenes.GP 16AusteniticStainlessSteels 100 Acrylics,GP 14Nodularlrons(cast) : 100 Phenolics(cast) 12Osmium 98 PolyvinyIButyral 12Reinforced Plastics. Phenolic 96 Nylon66 12Malleablelrons(cast) 96 EthyICeliulose,GP 10RhodIum 94 ~lon6 10Cobalt 94 enylene Oxide, 5E.100 9.5NickelandltsAlloys 93 Acrylics,Hightmpact 9Cordiente. .. . . ... . ... .. . . . 93 Acetal. . ... . ... .. . ... . . . . .. . ... ..,."..,. ... . . 9Iridium 91 ABSResins 9Vanadium 87 Ethyl Cellulose, High Impact 9NickelandltsAlloys(cast) 86 Polycarbonate 9Phenolics. Electncal... . . . . .. . . ." . . . 85 Nylon 610. . . . ... . . .. .. . . ... . . . 8Tungsten 84 Polypropylene 6Glass.LeadSilicate 82 Nylon1! 6Monel 82 CeliuloseNitrate 5LowExpansionNickeIAlloys 81 LeadandllsAlloys 5Gray Irons (cast)... . . . . .. . ... .. . . 77 CFE Fluorocarbons. . . . . . . . . .. . .. .. . . 5ColumbiumAlloys 74 Polyethylenes. LowDensity 1Cupro.Nickels """"""'.'.".".'."'" 68 TFEFluorocarbons. 1AlumlnumBronzes(cast) 66 PolyvlnylChloride,Nonrigid "".'."""."""'..' 0.07. .. SpeelDC .tiffIlCM. or .tlffn_weigbt rati.-. were obtained by dividing ruo<Julua or eluticity ia teoaion (pai) by denaity (Jb/cu in.). SpecIDcalJy,th.

bigb., vallI. uf a rang. or typiCal valua wu divIded by thA, material'. deaoity.

89

I I


elastic properties. Fig. 6.3 (after Ref. 38) presents the stress-:strain

curve for ethyl cellulose (ethyl ether of cellulose), and Fig. 6.4 shows

the comparison of the idealized stress - strain curve to that of

structural steel. The specific stiffness ratio is equal to about 1/63,

the modulus of elasticity ratio is equal to about 1/160 and the ratio of

yield stresses is equal to about 11.!.Q. The two last ratios indicate!, that

in order to satisfy the true replica model requirements, the yield

strength of this material would have to be lowered by the factor of 16,

which is impractical. Another possible difficulty with the thermoplas-

tics is their high Poisson's ratios compared to steel and other metals.

Metallic materials with E/p ratios higher than that of structural s~teel,

such as lead alloys and copper alloys, on the other hand, cain be

heat-treated to develop appropriate a IE ratios.y

In view of the above considerations in the preliminary study, the

effort was concentrated initially on both lead and copper alloys and on

one specific copper alloy, namely phosphor bronze (CA 510) in the final

study.

For adeq~ate mod~ls (see Section 4.5.2) the requirement that

(E/p)r = lr need not be fulfilled. Thus any material that fulfills the

material similitude requirements can be used for such model studies. The

obvious choice is clearly the prototype material, i.e., structural steel.

Suitable copper alloys are often desirable alternatives due to their

smaller stiffness which reduces the weight requirements for artificial

mass simulation.

Whatever the choice of a model. material, it must be emphasized that

certain material characteristics cannot be simulated at model scales.

.1:8

90

j I


~

41504000

... 3000Q.-

(/)U)..,a:'<i) 2000

000

~ 2 4 5 6 '1 8 9 10STR.A:IN, -'0

If "2 '3 14 15 1116

Figure 6.3 Stress-Strain Diagram from Tension Test of Ethyl Cellulose (Ref. 38)

,...:;Q)(.)

t~

f

STRAIN %

F~re 6.- Comparison or Tensile Stress-Strain Diagraas or StruQural Steel and Ethyl Cellulose

91


This holds true particularly for fatigue and fracture properties, whether

the model material is nonferrous or structural steel as in the prototype.

Even in the latter case the size and distribution of initial flaws and

the fracture properties as well as crack propagation rates cannot be

simulated due to size effects.

6.3.2 Structural Steel ~ ~ ~ ~aterial

\;ithin certain limitations, structural steel is the best suited ma-

terial for models of steel structures with artificial mass simulation or

without simulation of gravity forces. The identical shapes of the

stress-strain diagrams of the model and prototype materials, and the

ability to closely simulate prototype connections (bolted or welded) are

the major advantages. Nevertheless, the question remains as to the sig-

nificance of the increase in the strength of the model material caused by

the higher strain rates (tr) as compared to prototype material. Thus,

much emphasis is placed in this study on a thorough evaluation of strain

rate effects in structural steel. The importance of size effects is dis-

cussed in a subsequent section. When strain rate and size effects are

quantitatively known for the selected length and time scale, it is reaso-

nably simple to account for specific aspects of these effects by either

modifying the gravity loads and seismic input or, perhaps more appropria-

tely, by suitable heat treatment reducing the yield strength to the

desired value. In this study, A36 structural steel was used for all the

experiments. The modulus of elasticity of the material used in the tests

is E = 212.3x103 MPa (30.5x106 psi) and the specific gravity is 7.6930.

92

! ,


6.3.2.1 Strain Rate Effects

Considerable research has been devoted to the influence of the speed

of testing on the yield stress and the ultimate strength of mild steel.

Manjoine (Ref. 152, 1944) reports a study in which mild steel was

tested in tension at strain rates from 10-8/sec. to 103/sec. The

reported increase in yield stress for this range is 83% and for the range

from 10-5/sec. to 10-1/sec. the increase is 31%. These high values might

have an inherent error due to the inadequate strain rate control.

Manjoine also observed that the yield stress increases with the increase

in strain rate until the limit when the ultimate stress (which is inde-

pendent of strain rate) is reached without yielding.

Garner (Ref. 153) presents a compilation of data from 9 sources for

-4yield strength obtained at strain rates varying from 10 /sec. to

103/sec.

More recently (1966) Nagaraja (Ref. 151) performed a study on strain

rate effects on the yield strength of structural steel. The empirical

formula derived in this study for rates till 1.4x10-3/sec. is

(crY)d/(cr) =1 + 0.762 EO.26, y s

or, using the yield stress obtained at a strain rate of E = 2x10-~/sec.

as the normalizing value:

cry/(cry)2x10-4 = 0.923 + 0.703 eO.26 (6-1)

Pirotin and East (Ref. 189) presented the following relationship for

strain rate effect on the yield strength of stainless steel (after norma-

lization for t = 2x10-4/sec.) :

cry/(cry)2x10-4 = 0.920 + 0.44 to.2 (6-2)

~ ~~, tensile tests were performed on structural steel at

strain rates from 10-5/sec. to 10-1/sec. A set of 24 specimens was ma-

93

i I


chined out of A36 steel square bar stock and stress relieved at 600oC for

one hour after machining. The central section or the specimens was 45 mm

(1.15 in.) long with a diameter of 9.52 mm (O.375 in.) and with smooth

transition from the ends. The specimenssquare mounted in thewere

testing machine with the help or hydraulic grips.

The tests were performed under constant strain rate controlled by a

25 mID 1 in.) gage length MTS extensometer attached to the central por-

tion of the specimen. Ramp function (constant strain rate) was used as

the controlling signal. The tension tests were terminated when the ave-

raged strain reached 3 percent. The measurements made during the test

(load, average strain) were recorded continuously by the computer data

acquisition system (Section 5.3.3).Fig. 6.5 displays two typical stress-strain diagrams obtained for

low and high strain rates. The high strain rate exhibits twocurve

anomalies. First, the lack of sharp transition from lowertoupper

yield, and second, the strong stress fluctuation along the lower yield

plateau. Both the phenomena are believed to be independent of real ma-

terial behavior and to be caused by the inability of the testing system

to control such rapid load changes (0.09 sec. till yielding).

All the lower yield stress values were normalized with respect to

the average value obtained for the strain rate of 2x10-4/sec. (300 MPa,

43.5 ksi). The results of the testing program summarized in Tableare

6.3 and the normalized data points with a fitted curve are displayed in

Fig. 6.6. The mathematical representation or this curve is or the

following form:

(6-3)

94

Chapter 6 Materials tor Models of Steel Structures

~Zi CE~2~10/5e . ksiMPa

-" ,-c41. C£#2~1U .,se

300 40(/)

~Q::~

C.I)

200

0

100

3.2.%

f.o.STRAIN

Figure 6.5 Tensile Stre..-Strain Diagrama for Structural Steel Tested at Low and

High Strain Rate

Table 6.3

Sum8ary of Result. for Strain Rate Ittect

on the Lover Yield Stress or Structural Steel

NO!'malizedYield Stress

Strain hte No. ofSpecs.

Coefficientof Variation

Average LowerYield Stress

J1/sec. MPa ksi--0.9810.987, .

300.6302.7306.5

43.1I 43.~

44.,1

0.5

0.4

313

,

1x10-::>1x10-42x10-4

2x10-41x10-35x10-32x10-21x10-1

II3323

297.9310.8322.5333.0350.3

113-

115.

116

118.

50

1.21.51.10.11.1

1.1.0431.0821.1181.17c

95

,011 :16

,21,08.77,30,81

Chapter 6 Haterials for Models of Steel Structures

b-

~IIGI..

rt)

~..~='..()='~..rt)

'"'0

IIII..~~"...II>-~!

.3..c..c0..0

~'"'J81

41..

~

c..

~

..

rt)

~\0

t~I&.

~I~

~

<JQJ

~~'-

':'>C- lJJ

h"C{Q::

~~~V)"0-

It)

'c-

C\J~ q~

-: 0')c

~.o Jxc).. av ).. ,9

~ D ,.of)

96


This curve and curves obtained by other researchers are plotted in

Fig. 6.7. These curves show that in model studies, in which steel is

used as model material, differences in the yield strength between the

prototype and model can reach 3% of the value for 1:15 models with simu-

lated gravity forces (t = 1 -1/2), and up to about 6% for models inr r

which gravity forces are neglected (tr = lr). Whether those relatively

small differences in the initial yielding value are acceptable without

adjustments has to be decided separately for each individual case.

t

- - - - - - - - Manjaine

Nagaraja'ro 1.1 Garner

:.: ~t:J >- C\J this study

~>-

\D

f.

--~,-

0.9I

STRAIN RATE (f/sec.JFigure 6.7 Results from Various Sources on the Strain Rate Effect on the

Lower Yield Stress of Structural Steel

6.3.2.2 Size Effects

Conflicting opinions are expressed in the literature on size effects

of mild steel and other materials. However, there is considerable expe-

rimental evidence of size effects on the yielding of mild steel

(Refs. 154, 155). The effects are explained by the difference in stress

gradients of large and small specimens. Richards recorded and evaluated

statistically size effects in round steel bars subjected to axial tension

97

, i I

Chapter 6 Materials ror Models or Steel Structures

bendingsubjected to(Ref. 154) rectangular steel beams pureand

concluded that the yield stress can be related to the(Ref. 155). He

volume of the test specimens and can be expressed by the equation

ifif =-~Y y1/m

y1 is the yield stress for awhere V is the volume of the test specimen, 0

for specificspecimen of unit volume, and m is a material constant the

For the steel used in his investigation (a commercial qua-type of test.

carbon content or 0.18 percent)lity killed structural mild steel with a

Richards found m to be equal to 58 for and equal tothe tension tests

that the size effect inThus, it is evident11.7 for the bending tests.

bending is much more pronounced than in axial tension and may be si~iti-

cant for small scale models.

be partially accounted for by the use or eater!alSize effects can

in size to the smallest dimension of model struo-comparablespecimens

tural ele88nt.

6.3.3 Copper Alloys

6.3.3.1 Introduction

which render themalloys have mechanical propertiesMany copper

In addition, theseof steel structures.quite useful for model studies

eas1lyare readily available in bar and plate stock, can bealloys ma-

of individual elementschined into structural shapes, and permit joining

a manner very similar to steel. However, it must be pointed out thatin

heat effects from welding affect different alloys in different ways which

single most important criterion in the search for amake weldab111ty the

suitable copper alloy for modeling of welded struotures.

98


The E/p for most copper alloys is of the order of one half or that

for steel, hence these alloys can be used for 1:2 scale true replica mo-

dels. Probably more important is their application for models with arti-

ricial mass simulation since their elastic stiffness is approximately

only haIr that or steel. Small scale steel models will often require ex-

cesssive amounts of additional mass which may either cause model fabrica-

tion problems or place excessive demands on the weight and dynamicmay

force requirements for small shake tables. When copper alloys are used

as a model material, the weight requirements are cut in half and the dy-

namic force requirements are also reduced.

Although general information mechanical properties of copperon

alloys can be found 1n many material handbooks (134 to 136), detailed

data on stress-strain behavior and other relevant properties discussed in

Section 5.2 were not available, which necessitated a testing program on

several promising alloys. The alloys investigated in the course of this

material study (copper alloys No. 260, 510,614, and 655, see Table 6.->

exhibited quite different properties. However, all tested alloys or1~i-

nally had strength properties which were much too high to satisfy the s1-

militude condition (ay/E>r

cess had to be carried out

= 1. Thus, trial and error annealing pro-a

to reduce the nominal yield strength to the

desired value.

The results of high strain rate (3x10-2/sec.) tension fortests

three or these alloys in the non-annealed condition and for cartridge

4080Cbrass annealed at are presented in Fig. 6.8. It is evident that

AHPCO 8 and Everdue 1010 show undesirable stress-strain characteristics

tor a simulation of steel while cartrld~e brass and CA 510 appear to be

well suited tor this purpose.

99

Chapter 6 Materials for Models ot Steel Structures

Table 6.4

Copper Alloys Investigated Prel1minarly in this Study

Standard

DesignationColIDDercial Name Chemical Composition Form a t De 1 i very

CA 260Cartridge Brass 70J Cu, 30J Zn 6 mm ('/~ in.)

half-hard plate

Ampco Grade 8 CA 614 91% Cu, 7% AI,2% Fe

6 mm (1 JI in.)

half-hard plate

Everdur 1010 CA 655 97% Cu, 3% Sn 12 mID (1/2 in.

half-hard rod

!Phosphor Bronze CA 510 9~.8J Cu, 5J Sn,O.2J p

12 mm (1/2 in.)half-hard rod

1 - Cartridge Brass Annealed at 408 C, 2 - AHPCO 83 - Copper Alloy 510, 4 - EVERDUR 1010Strain Rate 3*10-2/sec.

I(J)

MPakai

50

300

40

!oj

~ 30E-o

C/)

200

20

100

10

0,000.002 0.03 0.040.01 0.02

ST&AjN

Figure 6.8 Stress-Strain Dia~ams for Copper Alloys Tested at High

Strain Rate (t: 2.4x10-2/sec.>

100


6.3.3.2 Preliminary Study on Cartridge Brass

This alloy attracted special attention because of its availability,

reliable chemical composition (70% copper and 30% zinc with possible

impurities of less than 0.1% lead and iron), and promising mechanical

properties. The material was purchased in the form of half-hard, 1/4 in.

thick plate. The properties of the delivered material were:

E = 1.12x105 MPa (16,300 ksi), a = 386 MPa (56 ksi), and p = 84 kN/m3y

(0.31 lb/in~). Since this alloy was used to model structural steel with

a measured yield strength of (ay)p = 293 MPa (42.5 ksi), it had to be

annealed to (a) = E (a ) = 159 MPa (23 ksi). Guidelines forym r yp

appropriate annealing temperatures were obtained from graphs presented in

Ref. 177 and 178 which are reproduced for this alloy and fo~ CA 510 in

Fi~. 6.9. Also shown in this figure are the yield strengths obtained in

this study from a series of tension tests on cartridge brass specimens

annealed for one hour at different temperatures. An annealing tempe-

rature of 408oC was found suitable to reduce the yield strength to the

desired value. The test results obtained from low and high strain rate

. ( 0-4 -2 )tens1on tests 2x1 /sec. and 3x10 /sec. of cartridge brass annealed

at 408°C are shown in Fig. 6.10. The following observations can be made

from this figure:

(1) The material exhibits a large linear elastic range, but shows a

gradual decrease of stiffness beyond the proportional limit until it

stabilizes at a strain hardening stiffness of about 2.5 percent of

the elastic stiffness. This transition range between proportional

limit and "yield strength" was observed, to a lesser or larger de-

~ree, in all copper alloys investi~ated.

101

I I

102

ssa.lJS

Chapter 6 Materials for

=

~~

'0..."

~"0

~

I.

...0

s:...."u"l~~fuCt)"

~

!

0...

.\D

f

".....

....Ici~-e,.;!

'E.

~...

i...

.!

la of' Steel Struct

.,

.,

~.w~,.oj...

~

~

'g.

.

~

~

...0.ca..,0

f

"

~

.,

t

B

~

~

i

0-.\D

f

~


(2) The strain hardening stiffness decreased very slowly below 2.5 per-

cent in the strain range of interest. When compared to structural

steel, this strain hardening causes a relatively higher strength

beyond yielding under monotonic loading, promising even higher har-

dening under cyclic loading due to the highly annealed condition of

the material.

(3) From the high strain rate test (curve B) it is evident that the

strain rate effects are comparable to that of steel (see Fig. 6.5).

Thus, is can be concluded that annealed cartridge brass is a material

that reproduces reasonably well the strength and stiffness properties of

structural steel, at least under monotonic loading. However,

unacceptable material properties developed in the heat-affected zones at

welded connections. As can be seen from Fig. 6.9, continuous decrease in

yield strength (grain growth) is associated with high temperature

treatment. Even though the heat exposure due to welding is of short

duration, over-annealing in a small region of the base material could not

be prevented. Hence, cartridge brass should not be used for models of

welded structures where yielding in the base material at welds is

expected. Brazing may be an alternative in some cases, however, it would

have to be done at temperatures below the desired annealing temperature

which may not permit the attainment of sufficient strength, particularly

at connections where high inelastic deformations have to be tolerated.

The problems associated with welding necessitated the investigation

of copper alloy other than cartridge brass, and phosphor bronze was

chosen for this purpose.

103

6 Materials for Models or Steel Structures

6.3.4 ~osphor Bronze (f! 2!Q.)

This alloy selectedwas mainly because of its specified excellent

weldability (Ref. 179). CA 510 is promising since its yieldvery

strength in the fully annealed condition is about 140 MPa (20 ksi

(see Fig. 6.9) which is in the range of the desired yield strength and

therefore, over-annealing due to welding should not prooblempose a

provided 8 too long exposure to the high welding heat can be avoided and

thus large crystal growth can be prevented.

6.3.4.1 Stress-Strain Characteristics

Due to the content of interstitial atoms of phosphor in the crystal-

line structure, the general stress-strain behavior of phosphor bronze re-

semb1es that of structural steel where cool atoms fulfill a 8imila~ ~ole.

Not only does phosphor bronze exhibit a straight line behavior 1n its

pre-yielding range but, as has been observed in several tests, also upper

Fig. 6.11and lower yield can be identified in the tensile test diagram.

displays results of' tensile test of CA 510, annealed for 1 hr.a at

5200C, and Fig. 6.12 provides comparison between the stress-straina

lines for structur8l steel and annealed phosphor bronze and cartridge

brass. The similarity between the stress-strain diagrams for structural

steel and CA 510 is noteworthy.

The modulus the annealed phosphor bronze 18

E = 126.2x103 MPa The measured specific gravity 1s

8.8744. Thus, for the phosphor bronze and structural steel used in this

study, the ratio ot' specific stiffnesses is (E/p)~ : 1:1.92, and the

ratio of elastic stiffnesses is Er = 1:1.61.

All the material tests phosphor bronze performedon were on

104


Poksi

20

U)~lJj fOO

~U)

fO

0 O.Of 002 0.0.3

STRAINFigure 6.11 Tensile Stress-Strain Diagram for Half-Hard Phosphor Bronze (CA510) Annealed at

520oC/1 hr. and Tested at Low Strain Rate (t = 2.4x10-4/sec.)

15

--- ------ ~

':"c f.O """"", ".",..,."...,...'

It;

-~\!) - Structural Steel~ '."" Phosphor Bronze (CA5/0J0.50 - - - Cartridge Brass

000 O.Of 0.02 0.03STRAIN

Figure 6.12 Tensile Stress-Strain Diagrams for Structural Steel, Annealed Phosphor Bronze

and Annealed Cartridge Brass Normalized with Respect to their Individual Yield

Stress 105

!i ,III ' I \


specimens scaled by 1 = 1:2 which approximately matches the E/p ratio orr1 : 1 . 92.

6.3.4.2 Annealing Results

Once the moduli of elasticity of the prototype and model materials

scale ratio for the yield stress can be derived fromare established the

temperatures from 500°C to 675°C (930°, to 1250°'), and tested in tension

HTS Results or this shown inthe closed-loop system. studyon are

5200C (968oF) wasFig. 6.9. An annealing temperature or chosen as

appropriate tor this study.

6.3.4.3 Strain Rate Er~ects

A study of the strain rate effect on the yield strength of phosphor

correlation orbronze was performed to provide information allowing the

static and dynamic test results, and to compare the magnitude or the

effect in prototype and model materials.

A series of 15 annealed tension specimens wae tested at strain rates

varying from 1.4x10-5/eec. to 1.4x10-1/sec. The strain rates chosen fo~

this study were based on applyin~ a time scale factor t or 1 :o.J2"1to ther

study (see Table 6.3).rates used in the steel This factor was based on

the true replica scaling law correlating steel prototype and CA 510 model

materials. The E/p ratio for these two materials is of the order of 1:2,

= 1/f2'.hence t r

106

Chapter 6 Materials for Hodel$ of Steel Structures

Table 6.5. Fig. 6.13The results of this study are summarized 1n

displays individual data points

value at strain rate 2.8x10-4/sec.

normalized with respect to the average

Theand a curve fitted between them.

equation or this curve is

(6-4)

the material, and exhibit only a minor decreasethe initial stiffness or

510 behaves in a manner veryin the strain hardening stiffness, thus CA

similar to structural steel.

provide a comparison between the curves for structuralIn order to

tor CA 510 both the curves are shown in Fig. 6.14. The lowersteel and

strain rate effect exhibited by phosphor bronze will be partially accoun-

Th18 181ftted for by the higher strain rates occurr1n8 in the model.

particular true in the gravity neglected models for which t = lr and notr

model studies or~ as tor true replica models. Only tor large-scale

high strain rate phenomena (impact) the difference in yield strength may

be significant since the time scale ratio 18 small to provide atoo

sufficient "shift" of the phosphor bronze curve to the left on the strain

rate axis.

T.ble 6.5

SUmmary of Results for Strain Rate Effect

on theY1eld Stress of Phosphor Bronze

Strain Rate No. ofSpecs.

Average YieldStress at 0.002

Coefficientof Variation

NormalizedYield Stress

1/eec. MPa Jkai

1.4x10-52.8x10-46.9x10-31.4x10-1

4533

158.9161.9166.2178.2

23.0423.4824.1025.85

0.9821

1.0261.101

3.31.61.52.1

107

The obtained stress-strain results do not exhibit a noticeable change in


'"

~In.to)tI~f~to0

s:g,f)0

f'-0

G

~

f...~

'0rot.

...tI

s:..

c0

...0

~'-~

II...

IIc

f...

~

,r,~

.

\0

EQ..

.(..,)QJ;

~~'--

~'q::'Q:r;c:~

~~;tI)

C\J~ ~~ 0)

c:>

-.-8'cp.DJx AQ/..(9

~D?/

108


t)to!~.0~

III

~0.ca-ft0

f

-g.!VJ

.~..0

f..VJ

...0

ft~

t..VJ

'0.>-..c..

8..0

~...II!

.~

:

~..04

f~VJ

...0

~0ft

..04

~

i

8

#.-0.0

f

jJ&.

0-

~10-

~(,.)QJ

~~'-

I~- ~'q::Ct~~~<I')

~0-

It)

'a1-

C\J~

-...: c.~ 0)c

109


6.3.4.4 Cyclic Behavior

A series of cyclic tests was performed to provide comparison data

for the simulation of cyclic behavior of structural steel.

The three loading histories used in cyclic tests of structural steel

(see Table 6.1) were implemented using the same strain increments

(E t 1). It was found that, unlike the case for structural steel,y,s ee

three loops per amplitude did not lead to a stabilization of the

hysteresis loops. Therefore, two additional load histories were carried

out, namely load histories No. (2) and No. (3), but with twelve cycles

per amplitude rather than with three. Even with this relatively large

number of cycles the material, strongly softened by the annealing

process, did not reach totally stable hysteresis loops although the peak

stress difference between the last loops was very small. The first and

last loops at various load amplitudes for three different load histories

are presented in Fig. 6.15.

Fig. 6.16 shows cyclic stress-strain diagrams for structural steel

and phosphor bronze for loading history No.1 (Table 6.1). Both the

diagrams are normalized with respect to the yield stress of the materials

and with E t 1 , which was used to control the strain increments.y,s eeComparing the two dia~rams in Fi~. 6.16 it is evident that the

annealed phosphor bronze work-hardens considerably more than the structu-

ral steel. For strain amplitudes less than or equal to 7Ey,steel' the

stress-strain hysteresis loops are similar in shape and enclosed area,

but for larger strain amplitudes the similitude becomes rather unsatis-

factory. The lar~e and history dependent work-hardening of annealed

phosphor bronze is more evident from Fig. 6.11 which shows skeleton

curves for various deformation histories. For structural steel the

110

(1 1

Chapter 6 Materials for Models or Steel Structures

II)

~~II)

001 002-(1.02 -ODI 0STRAIN

I/)

~l-I/)

-OD2 -001 0

STRAIN

00f 002

Fisure 6.15 First and Last Loops at various Strain A8plitude rro. Cyclic Tests or Phosphor

Bronze

ill

m

Chapter 6 Materials for Models of Steel Struct

-~'-"

'GfQ)'"CI)

tU~

.au:3~'"CI)

-A-

QJN

~0""

~

""0

.g,Q)0

~

'0QJ

.-4tV

8<

tItI~rn

.~:s~0:s~~rn

~0

.,C-O0..I

n~n~~"..n>.

=

c~.~~rn

In.,tI~

~

~0

581~;a-s

\0....\0

f'iI~

I)H~0~

IQ

~

.8Q.~0

.c,.,

~~

.113

Chapter 6 Materials for Models of Steel

'(I~

.30...-4

~U

~0

..r..

~r..

~.,8r..

~

~.cg.~0

.c~

-g.

.-4

::...C/)

.-4.r..~

...0

~...C/)

~0

81"

t~

u

c0

~.,

"

~

t-o-.

\0"r..

~..ra.

..tI

004~0

.....

004:c

tures


or cyclescurves are similar regardless of' the number perskeleton

largeramplitude, while annealed phosphor bronze exhibits significantly

work-hardening for twelve cycles per amplitude than for one cyole.

Figs. 6.16 6.17 point out theandpresented indiagrams

phosphor bronze for simulation of thelimitations of the use of annealed

number ofProvided that theot structural steel.cyclic behavior

inelastic deformation cycles is small, satisfactory simulation appears to

response history demands a large number of largepossible. It thebe

phosphor bronze as model material may givedeformation cycles, annealed

of' structuralmisleading information on the energy dissipation capacity

This'simulationsuperior work-hardening properties.steel due to its

Section 8.1 Chapter 9 whichinin andproblem is discussed further

and shakepseudo-static component testspresent experimental data on

table tests.

6.3.5

steelit is desired to test a small scale replica model ot aWhen

simulation is not feasible, the choice orstructure, and artificial mass

materials is very limited because of the requirement thatsuitable model

Table 6.2)(see only(E/p)r = Ire In a review of available materials

These materials can easily beits alloys showed some promise.lead and

extruding but havestructural shapes through casting orformed into

such as high creep and damping, whichcertain material characteristics,

pose difficulties in material simulation.

ratio less than one-twentieth(99.9~ Ph) has an E/pChemical ~nonlinear at lowthat of steel. However, its stress-strain curve is very

114

Chapter 6 Materials ror Models or Steel Structures

stresses, and the material i8 subjected to large creep deformations and

high damping losses. Consequently, it has not been considered further in

this studies.

steel. For the measured modulus, the desired yield strength to simulate

A36 steel would be 24.8 MPa (3.6 kat). The tension test on this material

(see Fig. 6.18) showed too low a yield strength, but a suitable hardening

or chemical treatments could be used to increase its yield strength to

the desired level. Hore research on this material is needed to asses its

feasibility as a model material.

!I2! ~ (82.4~ Ph, 5.9~ Sn, 11. 7~ Sb) readily availableis a

of that of steel. Thematerial with an E/p of approximately one-tenth

E-modulus is 2.8x1010 Pa C-.Ox106 )measured psi which would require a

yield strength or 34.5 MPa (5.0 kai) to simulate A36 steel. The stress-

-strain diagram for this material (see Fig. 6.18) shows that the measured

however annealing at 200oC didyield strength 18 somewhat too high,

reduce the yield strength to approximately the desired value. However,

the shape or the stress-strain diagram differs significantly from that or

steel, and it will be extremely difficult to reconcile these differences

to a satisfactory level through chemical mechanical har-treatment or

dening.

Material damping 1s another problem which must be considered in the

of type metal a model material. This a~pect was investigateduse as

through damping tests on a torsion pendulum apparatus. These tests have

shown that damping in type metal is highly dependent on frequency, tempe-

rature and stress level. At 20oC it varied from O.5J for high frequency

115

Chapter 6 Materials tor Models or Steel Structures

and low stress (cast material to more than 2' for low frequency and hiSh

stress levels approaching yielding (rolled material). It was observed

that the damping in rolled type metal consistently higher than inwas

cast material by an amount of 40 to 901 at different stress levels.

Due to the time dependent behavior of lead alloys and the early non-

concluded that leadlinearity in their stress-strain behavior, it was

materials. Their wouldalloys cannot be modelrecommended as use

which rendersnecessitate complicated chemical or mechanical treatment

them unfeasible for most practical applications.

F1Iu~ 6.18 Stress-Strain Diagrams tor Lead Alloys -- Low and High Strain Rates

116

Chapter 7 Materials for Models of R/C Structures

CHAPTER 7

MATERIALS FOR MODELS OF REINFORCED

CONCRETE STRUCTURES

7.1 SIMULATION OF CONCRETE

1..1.1 In~~oQ!J:ction

Scale models of plain and reinforced concrete structures have gained

as has been shown 1n manyacceptance as a tool of structural analysis,

publications and symposia devoted to this topic, e.g., Refs. 12, 13, 14.

As with other types of structural models, of concrete struc-those

tures can be divided into two fundamental groups: elastic models and ul-

timate strength models.

overall structuralconstructed study theElastic Models toare

The mate-behaviour and force distribution in the linear elastic regime.

rials used for elastic model tests must fulfill the basic requirements of

the theory of elasticity, namely linear stress - strain relationship, in-

Because of their high workabi-variant Poisson's ratio, and homogenity.

both thermosetttlnglity, the most commonly used materials are plastics,

polyesters) and thermoplastic (acrylics, polivynyl chloride(epoxies,

(Ref. 14)PiC). provides a review of this type of models andMirza a

comprehensive list of specific references.

Strength ~dels are constructed to provide not only infor-Ultimate

mat ion on the structure in its virgin stage, but also its behaviouron

The necessity of 81-throughout the entire loading history till failure.

prototype material in its entireUlUlation of the behaviour of the11.7

Chapter 7 Materials for Models or R/C Structures

potential modelnumber orsignificantly limits thestrength range

materials which will satisfactorily reproduce concrete behaviour. Gypsum

limitedand concrete made with aggregate ofmortars,cementplasters,

orvariousbeen used with degreessize known as microconcrete have

(e.g., Refs. 62 to 64 and 71) as well asMany reports of ISMESsuccess.

use of cement and pumice(Ref. 3) thediscussFumagB 111 in his book

17)(Ref. givesBurggrabepractical DK>del analysis. amortars in

the model andschematic presentation of the relation between the size of

the choice of the model material {Table7.1b

Table 7.1

Size or Models and Suitable Hodel Materials

The minimum dimension of the model is by no means the only criterion

material, and such factors as the characterin the decision on the model

mixtures), creep foror railure of the material (more brittle in mortar

tests with sustained loadings, etc., can be of decisive importance

Although gypsum has been used successfully for elastic model analy-

ratio and straightPoisson'ssis because of its high workability, low

strengthapplicability to ultimatestress - strain relationship, its

strainThe reason is that the nonlinear stress -limited.studies 18

region exists in wet gypsum only, and the strength of wet gypsum is lower

that demanded for concrete modeling. Gypsum also possesses exces-than

ofstrength and low bond to the reinforcement in the casesive tensile

16,18,107).reinforced gypsum models (Refs.

118

Chapter 7 Materials for Models or R/C Structures

bybeen reportedstudies on gypsum-sand mixtures haveSuccessful

White and Sabnis (Refs. 120,121), and by Zelmn et. al. (Ref. 111).

Pumice mortars provide the often welcome low E modulus (Ref. 17) but

to the reinforcement causes considerable problemsbondinsufficient

in small scale models (Ref. 107).

Microconcrete, made mainly of the same materials and with the same

gained the widestconcrete, hasdesign philosophy as in the prototype

acceptance of all the aforementioned model materials.

attention will be focused mainly on thisIn the subsequent sections

material.

~esign of Microconcr~~e Mixes7.1.2

mixes have beenmicroconcreteSeveral approaches to the design or

developed, and their applicability depends cn similitude requirements for

other modelthe particular study, the model construction technique and

of theunderstandingWith the increase in thedesign considerations.

develop-of microconcrete and of their control, and with theproperties

and evaluation of properties, theof new methods of quality control

satisfactory fUlfillment of similitude requirements,final goal, namely

can be attempted more successfully than ever.

Basic Requirements Imposed on Microconcrete as Model Material7.1.2.1

Modeling of plain, reinforced and prestressed concrete structures is

presented in Chap-subjected to the general laws of similitude which are

In Refs. 15,36, and 117 these laws are presented with particular4.

119

Chapter 7 Materials for Hodels of R/C Structures

stress on ~odeling of concrete.

requirefor uniaxial stress - strain relationshipSimilitude laws

respect to strain, and ofof stress withaffinity of the derivatives

to time (Chapt. 4). These criteria are subjected tostrain with respect

to the significance of a given material propertyaccordingmodification

to the studied problem

goal in the most basic mix design is to achieve a pres-The first

Fullstrength (f') at a given age of the concrete.ccribed compressive

affinity of the stress - strain relationship for compressive tests is re-

demand thatlaws for model materialsBasic similitudequired next.

same as in the prototype. It has beenmodel be thestrains in the

relaxedSection 4.5.3) this requirement could be(see thatsuggested

(t ~ 1) using appropriate modification factors.rof concrete is of basic importance in theWhenever tensile strength

the ratio or compressiveul timate behaviour of the structure, over

tensile strength should be equal in model and prototype.

strongly influenced by the1sThe initial stiffness of a structure

proper simulation of(E),elastic modulus of the material demanding a

This would be achieved with full r - e line simulation.this property. c

Studies concerned with shear transfer in the post-cracking stage de-

interlock mechanism which at thismand a closer look at the aggregate

fully even in the prototype domain. Since thisunderstoodtime is not

mechanism depends on surface roughness and crack width, significant simu-

lation problems have to be expected.

for which long-time events are of significant impor-For structures

This isrequirements are to be taken into account.additionaltance,

true in oarticular when the prototype initial conditions need to be simu-


lated. In theory, simulation of initial conditions will require the tra-

cing of all time history events affecting the prototype, from the time of

construction to the time at which the dynamic event takes place. These

events w111 include, amongst others, construction sequence, curing me-

thods, time dependent material effects (creep, shrinkage, increase in

compressive strength of concrete), as well as damage accumulation due to

previous events

Modeling of combined creep and shrinkage effects is a virtually im-

possible task because of incompatibilities in time scaling. Simulation

of creep requires equal time in model and prototype (t = 1) while simula-r

tion of shrinkage requires large time scaling. Creep and shrinkage de-

pend strongly also on the size and grading of the aggregates which are

not reproduced at model scales. Considering these problems it is usually

a futile exercise to attempt modeling or creep and shrinkage phenomena,

particularly since they often have reasonably small influence on thea

ultimate strength behavior under oyolio loading. It appears to be more

appropriate to control the initial conditions in the model experiment by

minimizing shrinkage and creep of'through sealing the model structure

(for instance, by applying of shellac)coats and avoiding long-time

pre loading prior to the dynamic test

It is to be expected that, with the increasing understanding of con-

stitutive relations for multi-axial strength of prototype concrete, an

increasing effort will be made to accomodate this knowledge in microcon-

crete design and testing whenever justified.

7.1.2.2 Levels in the Simulation of Concrete Properties

Simulation of the properties of a heterogenous material such as con-

121

Chapter 7 Materials ror Models or R/C Structures

crete presents a particular difficulty due to the complexity of the in-

of such a material can be performed at diffe-Studiesfluence factors.

levels:

a) atomic and molecular

b) inter-structural

c) macroscopic or phenomenological

It is seldom given to the designer to influence the atomar structure

of microconcrete, except for the use of a specific cement type, aggregate

and chemical additives, all of which influence the chemical reactions

and the gel-aggregate force developmentoccurring in the gel formation

Considering the complexity or hydration and hardening processes, it is

expected that intervention by the mix designer at the atomicto be

and molecular level will be feasible.

of concrete properties at the inter-structural level wouldScaling

require not only the appropriate scaling or the aggregate size but also

scaling of the pore sizes in the gel, and void sizes in the aggregate

the last requirement might be partly satisfied by the nature ofAlthough

only slightly influenced bysmall aggregates, the gel pore size becan

the use of finer cements (i.e. Type III)

Gradeline design for the model aggregate based on length scale re-

quirements is feasible only as far as the large aggregate size is con-

cerned (Refs. 18, 39). Shifting of the entire sieve line according to

the length scale of the model requires adjustments, as the lower limit of

aggregate size usually has to be increased from that dictated by

(Refs. 13, 114) limit the orsimilitude. It is customary to amount

aggregate passing U.S. No.100 sieve (0.15 mm) to than 10%.less Due to

(A/Wthe high specific area of finer aggregate, the amount or water

ratio) achieve desired workability increases rapidly withtonecessary

122

Chapter 7 Materials for Models of R/C Stru~tures

the decrease of the average aggregate size, thus increasing the amount of

cement (CIA) necessary to achieve the required compressive strength which

in turn results in a too high tensile strength of the concrete.

The above speculations show that a phenomenological approach to the

mix design, supported by the knowledge of the effects or inter-structural

changes, might be the most appropriate, it not the only realistic one.

In the design of prototype concrete one of the objectives is to find a

grading which would result, for available aggregates, in the best worka-

bility at the lowest water content. This can be achieved, within limits,

by minimizing the specific surface area. It has been found that, provi-

ded the specific surface area of the aggregate (coarse + fine) 1s kept

constant, a wide difference in grading will not affect the workability

appreciably, and this provides or designing gradinga means a gap

(Ref. 1lf3). Abram's law (Ref. 144) suggests that, provided the concrete

is fully compacted, the compressive strength is not affected considerably

by the aggregate shape, surface texture and the aggregate grading. The

above information does not imply that concrete properties are totally

insensitive to aggregate grading, but that an extensive effort in the

simulation of the grading curve of prototype mix might not be justified.

On the other hand, for simulation of the concrete - reinforcement stress

transformation inter-structuralzone, similarity at this iszone

important. This is shown by the schematic stress transfer diagram of

Fig. 7.1 (from Ref. 119).

Line I - I represents the tensile crack, line II - II represents the

shear crack, and line III - III either bond or compression failure. The

development or crack line II-II and in particular crack line III - III

depends strongly upon the structure of the aggregate matrix. Ferthermore

123

Chapter 7 ..ter1als I'or Models 01' R/C Structures

ratio of the size ofthe bond failure III-III depends strongly upon the

reinforcement ribs to the size of the surrounding aggregate

...6

'4+6" .

. , ,tI" 11

. ..';'

. Q (1.oC).;-~ ,. ("'" r

-Ill-

...Q- 111"'. ~\"'\St . r,..T _.~

"')f:3r$:," l.!-II

"'" '-"i .c.i::;:: . :

O ~.

. . .'. . .-- .. -I I

F1&Ure 1.1 Stress Transfer 1n Re1nforced Concrete (Ref. 119)

Control of Properties through Mix Proportioning7.1.2.3and Use or Additives

Several attempts have been made to present definite guidelines for a

i.e. Rets. 14, 114). It hasmix with desired final strength properties

the properties or the cementto be expected that, due to differences in

in the compactionabsorption or the aggregate,uaed . in the water

or the finalother mix design details, the propertiestechniques and

product may be quite different from the one predicted from the guidelines

Nevertheless, these general guidelines can be very useful in(Ref. 43).

Figure 7.2 presents sieve lines used bythe initial mix proportioning.

and theTable 1.2 lists mix proportionsinvestigators, andvarious

compressive strength of the concrete resulting from their application.

range ofof or wide~ ~ ~ the strength m1croconcrete a

124


ASTM Alternative Sieve Designation10 20 50 fOO4

" " .,

\\t)\

os.(I)(I)'

&

~50~~(.),~

\\2 -~-

&\\

3 ~ e-~.

4

,,. 5 _.*.~

6 e05. f. 0.5 0./

Sieve Apertures (mm)

Figure 7.2 Sieve Lines Used by Various Researchers

Table 7.2

Hicroconcrete Mixes Used in Various Studies

t'c

Age r'c

AgeC : A : W Reference c A : W Reference

days I Mfa ksi MPa ksidays

1 :4.0 :'1:3.75:1 :3.25:1:2.75:1:2.50:1 :2.25:

1121283114148

2.53.0-.05.06.07.0

Mirza(Ref. 2)

1:5.0 :0.80 2.83.54.2

4.6.5.2

5.25.96.8

11-28

11'-

11428

I 19! 2-29

,32 ;

36 I,136

41: -7

White(Ref. 43)

-~ 1:3.5 :0.60

1:3.0 :0.60383911351

14 5.55.76.17.4

Gran,Bruce(Ref. 23)

15202836

2.22.94..15.2

Fuss(Ref. 22)

1:11.- :0.81:3.6 :0.11:3.6 :0.51 :2.11 :0.5

63236363

39455561

5.76.58.08.9

Harris,et. a1.,

(Ref. 30)

125

1. White (Geneva Filter Sand)

2. Burssrabe (Light Agsregate)

3. Gran. Bruce (Silicone Sand)4. Mirza (Cruahed Silicone Sand),

~ 5. Hai..l (Silicone Sand)~, 6. KarTis. et. al. (Ithsc:a Sand)

.83

.72

.60

.55

.50

.40

1:3.75:0.721:3.25:0.60

1:2.75:0.551:2.50:0.50

1:5.-0:1.201:11.32:1.001:3.110:0.831:2.68:0.70


aggregate to cement to water (A:C:W) ratios was investigated. This was

done for two reasons. First, to evaluate the properties of microconcrete

of different mix proportions, and second, to supplement the existing data

on strain rate effects on the compressive strength of microconcrete

All the material studies on microconcrete properties were performed

on 50 x 100 mm (2 x 4 in.) cylinders, using Type 3 (High Early Strength)

cement

ASTHThe maximum aggregate size (MAS) was established to be passing

sieve #8 (2.4 mm), and the grading line for the aggregate to matchwas

closely the grading line recommended by White in Ref. 25 (Fig. 7.3).

ASTM Alternative Sieve Designation'0 20 50 '004

'V A~ All. u.#d0.4 L.L.2 0.5 LL3Q.3 LL.JO0-

.5;.

~~" ;0-

~"u...

~

. ~-::..~ 6,1Id.L'"

~'I I ~II~IOJ

Si~ APel"IIIes (mm)

Ca> .,Individual Sands (b) Final Grading Line

Figure 7.3 Sieve Line of Aggregate Used in This Study

Locally available (Lone Star, Monterey, California) sea sand (Lapis

Lustre) used as aggregate.was The thoroughly washed sand is sold in

Lapis Lustre #3 (MAS below 2.4 mm), 12sacks in narrow gradation ranges.

(HAS below 1.7 mm), and #30 (HAS below 0.811 mm) with individual grade

lines as shown in Fig. 7.3a were mixed in proportions 0.4:03:03 to obtain

a grade line as shown in Fig. 7.3b.

126

50

i

I

The mixing of the microconcrete was done manually by first combining

the weighed aggregate and cement and then gradually adding of water. The

was placed in the oiled steel cylinder molds in two layers, each or

them compacted by 20 strokes of 12 mm (0.5 in.) rod. After smoothing of

surface of the concreteupper the molds were covered to prevent

moisture loss and left undisturbed for 24 hours. Subsequently, the molds

the fog room (95J RHwere stripped and the specimens were transfered to

at about 200C).

At the age of approximately two weeks, the specimens were capped and

then returned to the fog room. The capping was done using a melted sul-

phur capping compound and a precision jig (Fig. 7.4).

One day before testing, the specimens were submerged in lime-satu-

rated water, and kept in this solution until about 45 minutes before the

beginning of the actual test. This time span was needed for mounting of

the specimen in the testing machine and attaching of the instrumentation.

The testing performed on a closed-loop MTS testing machine,was

utilizing control of displacement rate. Because of the importance of the

strain built-up in the testing system, displacement rates were controlled

through an extensometer monitoring the distance between the plattens,

rather then using conventional stroke control.

Average strains were obtained from displacement measurements at the

central 50 mm (2 in.) of the specimen. The measurements were done with

four clip extensometers attached 90 degreeat angles to the specimen

(Fig. 7.5). averaged and theThe four obtained strain-time records were

combined with theaverage was stress-time record resulting in one

stress - average strain plot. The results obtained in this study are

summarized in Table 7.3, Figs. 7.6 and 7.7.

127

Chapter 7 Materials ror Hodels or R/C Structures

F!sure 7.11 Capping Ji&

Figure 7.5 Co8presaion Speci-.n with Attached Extensoaeters

128

~~:3~e

~~

'ie

~

e...

t0

~0i

.e-81

...

.D

~

c0

...ftft

f

,~

-LIII ~ ~

~...~

I;

-..,&,

-M .

~O"w:

:a

c

t')

..~

'" .0 m

v. 4)~.s-

-0a,

. I-~.~~8~U 0

. ~"'."'>

8'0'" .0 ~

0

j!

IV- I " I_~"_I;" I

Mii

..

-~-3

If~

c~

~

...,

~ .~0.'"..

.oU'##--NN

"'4"'~~

o..ot-c

~2;;t

"'O\~Nt-0\~0'0

. . . .~N,"cr

_OC,"-. . . .

.r--oc,"

129

-~.

&-:.0.00

00. .

It\It\.. ..

.--

Cbaoter 7 Materials ror Models or R/C Structures

~.Q'on..,

011\011\et-t-\D

. . . .0000.. .. .. ..

0000. . . .---~

.. .. .. .....~~~

~N~NN

.., ""~, 'r

-~O-. . . .

-N\OON~"IM

t--t--OCW\t-... . . .CW\CW\tW\:'t"

N-In\o. . . .

-,""-~

1'"

~11'".

to;"'"

.-

'"f"\

....

~,")G\

11\011\1-1-.0

000.. .. ..II\II\In

. . .MMM.. .. ..

-.,-.-

t-t-t----

""r'"I~

0-11\. . .

I-O~"'~~

-t-1l\o m

. . .I""~#

GO\N. . .~"'O

..,.

m...,

0.Q:

~

0-

0:"~

0-

~ .~It\~cY\..

....

c.N

M

....oD~

P\

~In

~

I';"'

~'"

~

In

~'"


ksi

t~:~~5~~~::5~'~ "'"30.4.0

3.0~ 20.1G.J ~

.Q:J-:CJ)

20individual ex1ensomefe,.s

fQaverage---

1.0

0.00.002ao 0.001

STRAINFigure 7.6 Four Stress-Strain CurYes r~om Compression Test with Four Extensometers

Figure 7.7 Average Stress-Strain CurYes for Three Specimens Tested at the Same Speed

130

Chapter 7 Materials tor Models ot R/C Structures

Figure 7.6 shows four individual stress-strain records which,

averaged, give the stress-average strain relationship for one test speci-

men (shown in dashed line in the figure). Figure 7.7 shows three stress-

stress-average strain curves for four individual specimens, the average

-strain line derived from those curves (dashed line), and a stress-strain

line based on the theoretical equation presented by Popovics in Ref. 188.

The equation was developed for prototype concrete, and the stress-strain

line is based on the compressive strength f' of the concrete.c

All the Figs. 7.6tests summarized in Table 7.3, 7.7 wereand

6 -5

performed with an average strain rate of .3x10 /sec.

Fulfillment of the requirement of simultaneous similitude of f~

ft presents a much higher degree of difficulty (Refs. 14,18,39,114,118)

As discussed previously, the finer the aggregate used (SEllerwas

maximum aggregate size), the lower 1s the A/W ratio necessary to provide

the desired workability. Low A/W ratios result in low A/C ratios

retain the W/C ratio needed for desired f~), thus producing a mix with a

sometimes much higher tensile/compressive strength ratio than in proto-

type concrete. Thus, it often may be necessary to reduce the tensile

strength of microconcrete.

The schematic presentation of stress transfer in the composite mate-

rial shown in Fig. 7.1 suggests that by decreasing the adhesion between

the aggregate and the cement gel, the strength along the tensile crack

line I - I will be influenced to a much higher degree than the compres-

siTe or direct shear strength. Maisel (Ref. 118) proved this observation

by testing mixes with different aggregate types, namely relatively rough

and porous light aggregate (inflated schist), relatively smooth sands or

various origin, and aggregate coated with water-repellent, hard

13~

Chapter 7 Materials tor Models or R/C Structures

previously, this type of a table may be used as amentionedAs ws

the agreement between the results will depend theandguideline, upon

the materials and the technique used in the study onsimilarity between

which the table is based and those used in the current study.

0.7f~~

~LEGEND

~ MICROCONCRETE

. THIS STUDY. JOHNSON& MIRZA. HARRIS, et 01

PROTOTYPE CONCRETE/1 EFSEN,GLAR80a ARKAZANAx ZELGER+ GRIEB, WERNER0 BROOMS

l

2 3 4 5 6 7COMPRESSIVE STRENGTH (ksi)

8

Figure 7.8 Split Ten.ile StrenRth Ys. Co8pr..sive Strength rrom Various Studi.. (Rer. 29)

1.1.3 ~ Effects ~ Microconcrete

7.1.3.1 Size Effects

In general, size effect may be defined as a change in a characteris-

tic material property of a specimen due to the change of its size

Although there are a number of recognized sources of size effects in

concrete, there is no general theory which includes them all. The theory

or the failure of brittle materials through propagation or cracksa

flaws size effects by assigning a constant flawinitiated at explains

133


to differential curing effect. The influence of the specific area of the

aggregate on the magnitude of size effects was also studied by using mi-

xes with different aggregate size. There was no noticeable difference in

size effects observed between the finer and the coarser aggregate mixes.

Figure 7.9 Influence of Specimen Size on the Figure 7. 10 Unconfined Compressive Strength vs,

Compress1Te Strength (Ref. 118) Specimens Volume (Ref. 39)

In Ref. 18, Harris, Sabnis and White present a comparison between

the size effect in prototype concrete and in microconcrete (FiS. 7.11)

Although the trend of strength decrease with the increase of specimen

size is evident for both the materials, it is much stronger for microcon-

crete as can be seen from curve A (prototype concrete) and the shifted

curve M (microconcrete).

In a previously mentioned study (Ref. 39), third-point loaded beams

of span to depth to width ratio of 12:2:1 were tested to study the size

effects on the tensile strength in flexure. The results of these tests,

summarized in Fig. 7.12 indicate that the flexural tensile strength is

rather sensitive to specimen size, and is most sensitive to the change in

the volume of the specimen.

In Ref. 21, Mirza presents results of a series or split cylinder

tests using specimens of different dimensions but of otherwise identical


density per unit volume (volume effect). It cannot account for the

influence of the specimen curing and testing conditions on the extent of

the size effects. Other commonly quoted of size effects insources

microconcrete are differential drying throughout the volume of a specimen

as a function of the distance from the surface, faster curing of smaller

specimens (both effects often are referred to as the differential curing

effects), increase of quality control with decreasing specimen size

changes in strain gradient in flexural tests

Sabnis and Mirza present in Ref. 123 a review or the state-of-the-

-art on the question of size effects in microconcrete. The paper

includes an extensive list or literature concerned with this problem.

Selected results or important research in this area are discussed

below.

In 1963 Harris et. al. (Ref. 39) presented the results of an exten-

siye study on size effects in microconcrete. Compression cylinders of

height to diameter ratio of 1:2 were used to study the influence of spe-

cimen size and curing age on the unconfined compressive strength ft.c All

the specimens were compacted manually by rodding and cured in a moist

room (95J RH) until tested. Figure 7.9 shows the results obtained for

two mixes with different aggregate sizes and for varying specimen sizes.

For both mixes the smaller samples had a higher compressive strength and

reached almost full strength in a shorter time than the larger ones (see

individual points for the 1x2 in. specimens for W:C:A mix of 0.1:1:3.6

and along the 1/4x1/2 in. curve for 0.725:1:3.6 mix). The observed flat-

tening of f~ VB. volume of stressed concrete curves (Fig. 7.10), tor

the concrete ages, indicates that part of the observed size effect is due

135


.-

,U'C.

~III.>

......~

~

Figure 7.11 Size Effects on Compressive Strength of Prototype Concrete

and Hicroconcrete (Ref. 18)

Figure 7.12 Variation of Flexural Tensile Strength with the Size of Specimen (Ref. 21)

1.36


Figure 7.13 Effect or Loading Rate on Co8Pressive Behavior or Prototype Concrete (Ref. "2)

Fisure 1.1- Strain Rate Effect on the Unconfined Compressive Strength of Conc~t. and

Microconcrete (Ref. 39)

139

Once f~ was exceeded, the strain energy release in thestrains up to £'.c

relatively soft themachine could not be controlled throughtesting

extensometer feedback and a sudden increase in strain rate was evident.

the recorded stress-strain curves couldThus, the decreasing branches of

not be relied upon and are omitted in Fig. 7.15 which shows stress-strain

obtained for various strain rates and for two mixes of differentcurves

The plots were obtained in the way described in Sec-strength.ultimate

clearly shows the expected increase in thetion 7.1.2.3. This figure

ultimate strength (f') and in the initial stiffness (E), and the decreasec

maximum stress (E.~ with the increase in thethein the strain value at

strain rates

The results of the study are summarized in Table 7.4.

displayed inf' - £ data points for individual specimens arec

The

the points theFigs. 7.16 a and b.

strength values at £ These values were

at each testing strain rate torstrengthused to normalize the average

four test series (Fig. 7.17). The close correlation of these pointsall

A secondof different strength is noteworthy.obtained for concretes

data points shown in this figure, derived from aorder curve through the

regression analysis based on least square method, has the following form:

+ 0.0145 (log ~)2, .

f' / f' 4 = 1.4776 + 0.1815 log £C c2x10-

(1-1)

the more than one hundred strain rate tests carried out inBased on

this study, this empirical equation, which is independent of f', is bestc

with a change insuited to describe the change in compressive strength

strain rate

.1'1

iaiac, c'" I


MPo

640

4~~~(I)

20

2

00.000

00.00/

STRAINaOO2

MPa

6 4012

3

54

~l4j~(I)

20(1) £ - 2*10-2 I sec.

(2) £ - 1*10-2 I sec.

(3) £ - 5*10-3 I sec.2

(4) £ . 6*10-4 I sec.

(5) E: . 6*10-5 I sec.

00 I I I ,~0.000 0.001 Q002

5TR AIN

FigUre 7.15 Stress-Strain Curves tor Two Different Strength Hicroconcretes Compressed Onder

Various Strain Rates

142

Chapter 7 Haterials ror Models or R/C Structures

Table 7.4

Results Summary for Strain Rate Effect

on Compressive Strength of Hicroconcrete

Figure 7.16 Results or the Study or Strain Rate Erfect on Compressive Strength or Four

Dirrerent Strength M1croconcretes

143


"b

'bGI

...

~~

...~~

...rn

I)~

"...

f0c000~0

;j"-0

.c

...~

5i'-

...rn

"~

I)

:~

J

iN...

..~Z

t-.

t-

f

.;Ik.

~C)

~~

b

b

b~aN)

.~

C)~

.~

aC\J

.~a0)a

aQ

144

~

<.JQ;

~~'-

~~Q::hU)

X~:J j,

Chapter 7 Mat.rials for Models of R/C Structures

studies onFigure 7.18 provides a summary of the results of several

strain rates on the compressive strength of microconcreteofthe effect

(Harris, et. a1., Ref. 39; this study), and prototype concrete (Jones and

comparison of theRichart, Ref. 141; Hatano and Tsutsumi, Ref. 142). A

in this study pro-obtainedresults obtained by Harris and the results

regression line expressed with Eq.thevides additional confidence that

andoriginstor microconcretes or various(7-1) representativeis

effect on the compressive strength of proto-The strain ratestrength.

Quantitativetype concrete is of similar magnitude as for microconcrete.

be made due to the fact that data on truly strain ratestatements cannot

controlled tests of prototype concrete was not found.

SIMULATION OF REINFORCEMENT1.2

1.2.1 Introduction

The modeling of concrete reinforcement has attracted a considerable

amount of attention, and' techniques allowing the manipulation of reinfor-

ductility have been presented by many researchersstrength andcement

accepted methods of fabricationThis section summarizes the most widely

reinforcement and discusses theor modelcontrol or propertiesand

reinforcement used in this study.

microconcrete as modeling material, havingofThe wide acceptance

properties close to those of the prototype concrete, limits thestrength

reinforcement to those matePlal with strength similar tochoice of model

In theprototype reinforcement, thus to steel. casesstrength orthe

subjected to scaling, materials otherwhere the strength of concrete 1s

Copper alloys provide wire or lowerconsidered.than steel becan

145


"-b~

f)>

oMf)f)f)

ke0

u

c0

81..0~

"-"-rat

~...

~

coM.~..r/J

C0

f)~()~='

r8

~0~:

8s;.

'""

f).....~f)~

~

'""0

>-~

.Ir/J

0>-

.t-~~

~c..

b

'PC)

~:~:

GI...GIs-(}~0(}0s-(}...2:

'Q~e

GI...tIs-(}~0

u

0

.c

..~~tIs-

..ff)

... ~~~

hU)

~:)II)II)~

~~\...(.Jc::0(.J

h"-~

b~aN)

.~

a~

.~

aC\J

.~

a0)a

C)C).~

/'

146

~(jQJ

,v)~,'-:

Chapter 7 Materials tor Models ot R/C Structures

E-modulus if so desired. However, caution should be exercised in the use

ot these materials as the adhesive forces between andconcrete copper

alloys are negligible (Ref. 117).

The subsequent discussion will be devoted to steel wires, due to the

predominant use of this material as model reinforcement.

7.2.2

bond simulation imposes special re-The concrete - reinforcement

quirements on the surface characteristic of the wire used.

Bond stress development may be assured either through adhesive for-

or through wire surface deformation achieved either through chemical

treatment or, more commonly and with higher reliability, through mecha-

nica1 deformation of the wire.

Burggrabe (Ref. 117) presents results obtained with zinc-galvanized

wire. He found that the use of zinc plating in the case of chrome rich

(O.1Jcement Cr) results in a strong chemical bond between the wire and

cement. In the case of cement with much lower content of chrome, a

thin film of zincoxide can develop, providing a viscous layer between the

steel and the concrete.

A simple and reliable method of providing and controlling bond

strength 18 deform soft Theto steel wire through cold-rolling.

deformation may be applied by pulling the wire through a set of knurling

wheels (Fig. 7.19). A detailed description of a knurling apparatus can

be found in Refs. 18 and 40. Types of deformations and their effect on

bond simulation are discussed in Section 7.3

147

s,t

o~ 1.1~9~wm pell0~ PI00 9q~ JO q~BU9~~S 9q~ uodn spuadap enl~A pa~1sap ~

eq. ~e~ot o. A~8S£aOeU 'e~n.e~adwe.~U11eeuue ptetA91D1':1. ~uw~suoo~.

'&Ul1~~U11eeuue ~ue~suoo ~e e~n~e~edW9~ ~U11e9UUe 9~ BuJ1&9UUe .JO

-0 pUS Q s OG-L .sS1a JO SeA~nO eq1 q11~ UKOqS ss Su11seuue 1Uen

eti~ JO edstis eti~ -basqns 4~no~4~ pattO~~UO~ aq u~~ wv~~~JP uJ~~~s-ssa~~s

I.l~UeOtJ '&&.l~&Po~ 'pue q~Bue~~s PletA e~.l~ttt~onp pssvs~oap awos

-.ui.s u. PUg ~u1od-PLa.A pauIJap LLa~ ~ ~noq~.~ q~Sua~~s PLa.A pas~a~oul

iU1Uap.leqsesneo BUtTT~ PToO e~ U1 iu1..1nseol lee..s eq..10>{.JOM

-(£n -J9H) S9Jn~~AJnO 9~euJmJt9

o~ 1ttnjssaoons pasn u9aq ssq OStS S9ASatS ~q~1~U"J:a.ll"paW.lOjap9q~

JO ~9~9meIP 9q~ s9ml~ ~L ~9~9We1P JO ~uam~ea.l~ ~eaH"e.l1'" pem.l°Jepeq1,

eq~ q~~~ ssaoons poo~ s~JodaJ (9~~"J9H) 19S1~ esn.snIP JO steeqJ'. JO

ai~et Al~ua1o1JJns Jo StaeqM ju1t~nU~ iu1sn AQ paonpa~ 9QUe;)W91Q -e.1

-o.Jd S14J..emos~eqmno eiso iUlo~oJule~ eq1 Jo eis1Qmesss eq1 se~sw ~e1s1

sesse~~s tenp1se~ dn ~t1nq ~ enp '8U1PuaqiUt~tnS9.J IS001mO.IJ qOJqp.

awnsse 01 spua1 a~1~ 941 ss9~0~d Bu1ttO~-PtO~ a41 ~a1JV e.ln~eA.lnO e

~8tUeqOaw SUtt~n~ 6L. L ~nSTA

C:~~~~illnElli~

sa~n~on~~s J/H Jo staPOW ~oJ StaT~~-W L ~a~d.QJ

Chapter 7 Materials for Models 01' R/C Structures

0.062 in. diam.

0.072 in. diaDI.

0.08 in. diam.

1 1/2Time in Hours

1 21/21/2 1

(a) Relative Yield Strength VB. AnnealingTi.

at 538°c (1000oF) (Ret'. 18)

Yield Strength va. Annealing Temperature (t = 1 hr. Change in Stress-Strain Curve Through(b) (0)

for Cold Drawn 1020 Steel Wire (Ref. 113) Heat Treatment (Ref. 43)

Figure 7.20 Effects of Heat Treatment on the Strensth of s.&ll Scale Reinforcement

149


specimen and on the diameter of theamount of cold work applied theto

Thus, a trial annealing by varying temperature or time has tospecimen.

43) used quenching followed by tempe-Gran and Bruce (Ref.be performed.

wire at various temperatures (quenching: heat beyond A3 tem-ring of the

brittle hard marten-obtainperature equal about 9100C, cool rapidly to

site structure; tempering: heat the specimen to temperature in the range

of 2O0oC to 360oc and cool slowly to obtain ferrite-cementite composition

They report that thehigh ductility).andof relatively high strength

between 410 MPa (59 kat)yield strength manipulated in this way ranges

and 620 MPa (90 ksi) depending upon the tempering temperature.

~ ~ study soft steel wire of diameter 2.0 mm (0.08 in; Gauge 14)

reinforcement consisting of No.9 rebarswas used to simulate the main

annealed form 1n c011s orblack(28.6 mm). The wire was purchased in a

about 2000 m (6000 ft) length.

(37 kat),255 MFaThe yield strength of the wire as delivered was

414 MPa (60 ksl, Grade 60abovewhereas the desired yield strength was

in strength to 440 MPa (63.7 ksi, Fig.reinforcement). The increase

was achieved through cold rolling of the wire with a set of knurls,7.21

The ultimate strain of1ndentatlon~.ofproducing two orthogonal sets

The resulting effective0.08 0.12.andthe deformed wire was between

an indentation1.98 rom (0.018 in.) withdiameter of the wire "d" was

of'"w" of about 0.13 rom (0.005 in.), and indentation spacing "s"depth

e/d = 0.37 satisfy theThe ratios wId = 0.06 and0.74 mm (0.029 in.).byspecifiedprotrusion height and maximum protrusion spacingminimum

A microscope enlargement of theASTM Standards, Section A615 (Ref. 187).

Heat treatment of the deformed wiredeformed wire is shown in Fig. 7.22.

Indesiredclose to thethe strength one.omitted wassincewas

150

Chapter 7 Materials ror Hodels or R/C Structures

~e~..

."0 ""010 10 J()Sf_AlII Ii"

Figure 7.21 Effect of Defor..tion on Stress-Strain Behavior of Reinforcing Wire Used

in this Study

Figure 7.22 Detor8ed Wire Gage ,. (d . 288; 0.078 in.) ( SEM 44X )

151


retrospect, it must be said that quenching and tempering would have been

desirable to improve the strain hardening characteristics of the deformed

wire.

To simulate the shear reinforcement, which consisted of stirrups or

4 bars (12.7 rom), black annealed Gauge 20 wire (0.88 rom = 0.035 in.),

available in small coils in hardware stores under t~e commercial name of

Bandi-Wire, was used. The wire, as purchased, has a shiny smooth black

scale on its surface, thus promising a very low bond to the concrete.

Due to the small diameter of the wire, chemical surface rougheningvery

chosen rather than mechanical deformation. The following treatment

procedure was employed:

for 2immerse the wire minutes0 in 10 J HCL solution to remove the

smooth scale present on its surface,

0 subsequently immerse the wire for 45 seconds in 30~ H2SO4 solution to

roughen the surface of the wire, and

0 wash the wire thoroughly under a stream of tap water.

The procedure resulted in lowering of the strength of the wire by 6~ thus

indicating a change in the Test of foureffective area by that amount.

treated wires resulted in a coefficient of variation of the ultimate

strength of 0.015, hence the process results in a uniform area decrease

No noticeable change was observed either in the wire ductility or

its stress-strain characteristics due to the above treatment.

Fig. 7.23 presents microscope ot the wire surfaceenlargements

before and after the treatment.

1.2.3 ~ ~ Strain Rate Effects in Model Reinforcement

Despite extensive studies the yield and ultimate strength Oron

152

Chapter 7 Ma~er1als for MOdels of R/C Structures

....0..'tI

.cu

~II

...~

<

'0C.

II

~

~.!

.

c...

In,...

q

0"

JCO

.

0

"'0..

0N

1/~.

0

t)

~...

=-

Q.:I~~

or-!~11)

~0

t)0

~~:I

11)

,...~t-t)~:I~

...fa.

'0Q)

~.c~~~

.-I

.-IIII()

m.cu

~ucu

~r-IQIQI~CI)

aN

QIbO~cu

t-' ><00C\I

~V)

..c

!..~

'0QJ~cdQJ~~

g

153

Q)~

~

~Q)

~cdQ)

~

,..>-

ccC'

~tJ:'-


wires subjected to various treatments, little attention has been paid in

the literature theto effect or the wire diameter on its properties.

This is justified as the strength of the wire used in each individual

study is manipulated separately to obtain the desired values

Very limited information is available on the elastic stiffness of

small wires. Maisel (Ref. 118) observed a modulus of elasticity of about

20% lower for 2mm wire than could be expected from the base material

properties. A survey of data presented by Harris et. a1. (Ref. 18), and

Starrier and Sozen (Ref. 146) shows also a decrease in the stiffness

value. Maisel suggests that a major portion or this decrease should be

attributed to the initial bends formed along the wire which act as

springs.

Strain rate effects in model reinforcement were extensively studied

by Staffier and Sozen (Ref. 146). Results for two sizes Of laboratory

deformed and heat treated wires summarized in Fig. 7.24.are

increase in yield stress at higher strain rates is similar to thatvery

reported in Section 6.2.1 for structural steel. Comparing Fig. 7.24 with

Fig. 7.17, it can be seen that the strain rate effects are lower for

model reinforcement than for microconcrete.

7.3 BOND SIMULATION

Proper simulation of the force transfer between concrete and the re-

inforcement poses a major problem at model scales. The force transfer

will affect not only the resistance against pull-out but also the spacing

between direct tension cracks and the occurence of secondary failure me-

chanisms such as longitudinal splitting along bars close to the surface

In this section, only those aspects of force transfer will be discussed

154

Chapter 7 Materials ror Hodels or H/C Struetures

Figure 7.2' Strain Rate Effect on the Lower Yield St~th of Model. Reinforce..nt (Ref. "6)

~2000wire diameter d - 1.6uepull-out length 1 - lSd

I~~~l~:::::~:

~1500 -

"fir,""

-z-~~

~ 1000

~

E-t

9~5- 500~

00 0.2 0.4 0.6

SLIP AT UNLOADED END

0.8(~)

1.0

Figure 7.25 Effect of Surface Preparation on the Bond Characteristics of Reinforcement Wire

(let. 118)

lSS

Chapter 7 Materials tor Models ot H/C Structures

which are concerned with resistance against pull-out as determined from

simple pull-out tests.

The surface preparation of the reinforcement, together with the

embedment length, will determine the bond characteristics of the wire.

This is illustrated in Fig. 7.25, in which results of pull-out tests of

smooth, galvanized, and deformed wire are displayed (from Ref. 118).

Smooth wire can provide only a small amount of bond based mainly on

adhesion between the steel and the wire

Zinc-galvanized wire permits the development of relatively high bond

stresses, however, once a maximum bond-stress is reached, a deterioration

of the composite action occurs.

Deformed wire presents the most realistic and reliable solution to

the bond problem. Even then, certain compromises are necessary since a

perfect affinity between the prototype and model bond layer becannot

achieved in practice.

c*} short indentations -- gel shear action(b) long indentations -- compressive arch action

tf1tFigure 7.26 Inf"luence of" Shape and Spacing of Wire Defot"llations on Bond Mechanism (Ref

The shape and spacing of the surface deformation significantly In-

fluences the bond behavior (Fig. 7.26). Burggrabe (Ref. 117) found that,


using 3 mm diameter wire, the bond strength was 2.8 times higher for

1 mm apart than for a threaded rod with the same depthwide ribs spaced

rather than 1of thread, and 1.5 times higher for ribs spaced 3 mm apart

(Ref. 18) stressed the major differences between theHarris et. a1.mm.

or prototypesurface character of most laboratory deformed wires and

surface with indentedreinforcement, the first or which usually has a

The im-internal valleys, whereas the second has external protrusions.

by a properbe diminished, however,portance of these differences can

spacing and shape of the knurls. Nevertheless, it can be expected that a

or the force transfer betweenbetter simulation or all characteristics

be achieved through protrusions on thereinforcement and willconcrete

Actual cold-rolling of wires which pro-wire rather than indentations.

duced protrusions of the type shown in Fig. 7.19 was used sucsessfully at

the University or Stuttgart (Ref. 118).

bond characteristics of the model reinfor-A limited study theon

used in this study was performed by Bader (Ref. 29). The resultscement

are shown inof pull-out tests on wires with different embedment length

corresponding bond shown inFig. 7.27. The ultimate stresses are

Fig. 7.28 the results obtained by other researcherstogether with

satisfactorymodel and prototype reinforcement. The showscomparison

bond strength of the reinforcement used.

157

Chapter 7 Haterials for Models of H/C Structures

LEGEND'.00

:-VI~ ~ooo

DE'ORMED 8ARS

+ QQS IN. JAR «F. 1M$ STUD!'

. .,as . , lOr. CAST

. .'85 ; . TOP ,6 .," ; # lOT.

. ...5 , , TOP ". _7 ., ~ "

. .7 ., TOP "0 0.', IN. ; PLA'N CORHELL

. O~. ., M , T

. 00062. . «F. CORNELL

. 0004" . PLA'N I

. 0.0.'. ,. DE~. #

I (

a,'

;" / ./1

\11I ..

i

\~,400 \

IIIIII~-...WI

Q~Q-

~...~!...

5

~~-~~

PLAIN eARS\708010 .sO

EM8EDOEO LEN"TH"0

/ DIAMETER'0'°

RATIO

Fi~re 7.26 Bond Strength for Reinforcement Used in This and Other Studies (Refs. 29 and 39)

0.00'.J..

GAGE No. 14 WIRE T.0.08

INDENTA TIONSAVERAGE AlAXIIAVAI BOND STRESS

Lib

0.029.,...

,.,-,., 0' wire

\ L/O a 20"Vi'

I~STRESS PSO

L/o- 10900

10~011.9013~0780

4

6'

e

10

20

Iu~~Q...

#

D.O2.9~~0.029# -+-40.30' -+-00029#

liD . 10-~--8~,'-""-:-~~~"",:", ~\\ ~..p~~

0,20 0.2'0.10 0.15

SLIP A NO £LONGATION

0.0'

COIASINED (INCHES)

Fl~re 7.27 Results or Pull~t Test or Wire Used in This Study (Ref. 29)

158

,..

"

.

00

00

00

Chapter 8 Model Component Testing

CHAPTER 8

MODEL COMPONENT TESTING

8.1 INTRODUCTION

in Chapters 6 and 7 provide informa-The material studies described

tion on the material (metal or concrete) behavior under various load his-

of the behavior of a complete structure or struc-tortes. Understanding

tural model requires additional information on the behavior of structural

true forelements and structural subassemblies. This, in particular, is

beam-to-column connections incomplicated structural details such as

interaction in joints andsteel structures or concrete - reinforcement

structural compo-members of reinforced concrete structures. Testa or

nents also provide a direct calibration of structural component response

be detected neither at theload. Phenomena whichto the applied can

a complete dynamic test of the structurematerla~ test 1eft1 nor through

Detection or crack initiationcan be studied,through component tests.

the component, post-and study of the subsequent change in strength or

otand localized yield effects are examplesbehavior-yield component

such phenomena.

performed on reinforced microconcreteIn this study, tests were

steel and phosphor bronze cantilever beams.

159

Chapter 8 Hodel Component Testing

8.2

8.2.1 Introduction

To evaluate the adequacy of material simulation in the case of com-

posite materials, testing of structural elements is necessary. This, in

particular, is true for reinforced concrete models because of the compli-

cated nature of the concrete - reinforcement interaction. It is an un-

fortunate fact that even the tightest material control does not assure

similitude of all possible failure modes. These modes may be affected by

crack and bond similitude, cyclic loading effects, confinement and multi-

axial states of stresses in concrete, stress and strain gradient effects,

and otherfabrication accuracy considerations. Several of thesemany

aspects are not fully understood in prototype structures and to aeven

lesser degree in models.

~ ~~, the simulation of inelastic cyclic response characte-

r1st1cs and cycling rate effects for beam elements were investigated.

this purpose eighteen 1:14.4 scale models of a previously tested can-

tilever beam (Ref. The first test series (2 beams) was186) were tested.

concerned with the simulation of the prototype response using its proper-

ly scaled load history. The prototype failed in a combined flexure and

shear mde. The second series (12 beams) was tested to study the effects

of different cycling frequencies on the strength, stiffness and hystere-

sis behavior of beams subjected to high bending moments and small shears

third series (4 beams) was concerned with the simulation of failure

modes controlled primarily by shear rather then flexure.

The model beams for the three test series had identical material and

geometrical properties and differed only in the shear span to depth ratio

160


lId indicated in Part 1 or Table 8.1.

8.2.2 Specimens

or model and prototype response, theTo permit a direct comparison

an element for which the materialchoice of a prototype was limited to

response characteristics were well documented.properties and the cyclic

study reported in Ref. 186 was chosen for this purpose.Beam No. 46 of a

is shown in Fig. 8.1, and a summary of its geometry andThe prototype

material properties is presented in the third column of Table 8.1

at Stanford (see Pragraph 7.7.2). Figs. 8.2previous studies performed

and 8.3 show the external dimensions of a model specimen, which consisted

of two beams joining into a column stub, and details of the reinforcement

respectively.layout, The fifth column of Table 8. 1 provides a summary

Figs. 8.4 and 8.5 show assembled cages and casting forms,of these data.

respectively.

made of three types of wire whoseThe model reinforcement cage was

properties are summarized in Table 8.1

1) main reinforcement - Gauge 14 black annealed wire, deformed in the la-

bora to ry by cold-knurling (see Paragraph 7.2)

Gauge 202) beam and column stirrups - black annealed and 18 wire was

used for beam and column stirrups, respectively (Bandi-Wire, available

in hardware stores). The wire was annealed and chemically roughened

after stirrup fabrication

161

Chapter 8 Hodel CO8ponent Te-sting

FORMWORK

~A-A

, AI ~ ~~':!:~5,4 [=:D(lxi-fIB) -=:::s. ~

~

C""""'" ~: - .

~-.

Figure 8.2 Hodel Geometry and Formwork

162

Chapter 8 MOdel Component Testing

table 8.1 Su88ary or Prototype and Model Properties

I«)DILPRoroTYPEPARAMETERS

Model ~111Prototype Do81n

t geo.try

- (111.)1

"'9 (11'.0)

1981 (18.0)

"39 (56.6)

1316 (51.8)

306.~

137.6

99.9

91.-

lId I

lId I:

lId I

lId.

1981 (18.0)

137 (29.0)

381 (15.0)

6" (25.25)

95 (3.15)

3811 (6.00)

131 (28.8)

366 (1...)

6U (25.28)

89 (3.52)

3835 (S.95)x

50.8 (2.00)

25.' (1.00)

".6 (1.16)

6.2 (0.2->

19 (O.029>x

- (iD.)

- (in.)

- (ia.)

- (ia.)

_2 (iD~)

b

b

d

d'

A . A'. .

Oeuse ,. knurledwire

2 _in re1ntor~t f9 bara

1.98 (0.018)

'13 (59.9)x

'39 (63.T)X

1.27 (0.29)

1.35 (0.30)

-(in.)

Mfa (ai)

Mfa (ai)

d (kips)

kl (kips)

28.6 (1.12)

'61.9 (61.0)

110.2 (103.2)

265.3 (59.6)

'aT.8 (102.')

28.5 (1.12)-

tl

tu

PI

Pu

263.8 (59.3)

280.. (63.0)

Ga.. 20 cb~ca1l7I roughened wire

3 stirrup ties ,- bars

0.88 (0.033)xx

3'5 (so.O)x

"3 (59.9)x

0.189 (0."2)

0.22' (0.050)

1.9 (0.31)

0.0" (0.275)

0.051 (0.323)

12.1 (0.5)

'13.1 (60.0)

661.9 (96.0)

52.' (11.18)

83.8 (18.85)

152 (6.00)

0.689 (3.927)

1.103 (6.283)

12.0 (0.5)4

ty

tu

Py

Pu

39.3

-6.-

11-

0.692

0.815

.

2Py/.

2P ,.v

-(in.)

HPa (k81)

HPa (kal)

kB (klps)

kB (klps)

- (In.)kK'- (klps/ln.)

kB'- (klps/ln.)

- 8ioroooncreteomorete

31.9 (5.50)

-.- (0.63)

11.6

27.5 (3.99)

3.1 (0.'5)

11.3

t' MPa (ka1)c

ti MPa (k81)

t'lt's 100t c

valuea baaed on approxiate d1a8eter ot the wire

diameter atter ohem1cal treatMnt

163

(12.08)

:5.-2)

:3.93)

[3.60)

6.9

3.1

2.2'2.0

(8.8)

(10.')

{'.S)

(3.952)

('.651)

~~ ~9~1e ~ 8s: e =~ ~ q)(.!) ""' -

1,u~<1~ ~ ~c ~ -e: tt-n~:oi tr---rr~ S2 ~! "--err ~ ~ tt---ttc ~ -- II II!,&: 0 II II~ K> <\! II II~ ~ ~ II II~ ~ - II IIi ~ -8? II II

II II~ ~ II II

~ -e-: ~ II II~ II (I.<.. II IIbiJ n rr~ Tf---if~ n:::tt-~ rr-:--rr~ II : II~ ... II : II

~~w~ .~~

<~~(:I)~w~

~~~-.;oJ..J~

~l~""

.1Q)!

"

r"=";-

,"1"H"t, " +.'TM, "'

..~

~~

0)",. I~'0'-"c;Il"

-t/))c

C\J

II

<J>'

- -J" ::.'.II IIII IIll:::tt ~+f--+t -

+t---HI[ II IIII IIII IIII II

"III~ V)II II ~ ~

11 III I -4-e:II I C\JII IIII IIII IItt--1fTr--1TIT-TT

:::::!

~

~~~.I~w:"".;;:~.~ (,I,J -"-'9~(/jl~

~

Q::)

d3

~~~Uj~:5~G

~I

~

~h~~V)~~~

164

I-

r

~

.

,-LV""Q"

I..J

-t- ... ...

-1..1Il_LI_.1~.i. 'i-,' -.-;-.-t

JtJ-Loiu

IFft

w

(O~Z )~

TcL'i ~-n ji 1 (£'9}'0) -- -'- .~L."

fr'--' I '. I I

-

t~

ftf

I

"p-

r' :L


0)~

h

i

-I,

I

0

1(..)

r- -fII

-w~:..L

CD~tt)

...c:

I0

~~c:

.~

.'0

i

rr:«)

t~fa.

L+~""'1I I' I+ ...,'"" ,-... ' . . I

t-;-


Figure 8.4 Assembled Reinforcement Cages

Figure 8.5 Casting Forms

165

Chapter 8 Model Comoonent Testing

8.2.2.1 Specimen Fabrication

Due to the cold-knurling process, the main reinforcement was assu-

radius of about 5 m, which required a special ar-ming a curvature of a

rangement for the assembly of the reinforcement cage. The wires were

precisely located holes, anchored at onethreaded through templets with

strength at the other endend, and tensioned to about 1/3 of their yield

turn buckles as shown in Fig. 8.6. The spacing of the wiresby means of

was also controlled by intermediate spacers (see Fig. 8.7). Details of

reinforcement cages, with all longitidunal and transverse reinforcement

in place, are shown in the photographs of Fig. 8.8.

The beam stirrups were fabricated in the following steps:

wire tightly on a machined steel bar of a cross section1) spooling the

equal to the internal stirrup dimensions,

(600°C 11120p) 2 hrs.)2} stress relieving ot residual torstresses

built up during the unwinding of the coil ot wire and during thethe

rewinding around the steel core,

into individual3) sliding the wire off the steel core and cutting it

stirrups while accounting for the hooks still to be formed, and

to remove the shiny and smooth scale4) chemically treating the stirrups

and to roughen the wire surface (see Paragraph 7.2).

was threaded through the closedThe min beam and column reinforcement

stirrups the joint area, where the column stirrups had to beexcept in

opened and reclosed after being positioned.

Since the strength or the stirrup wire was lower than that required

orthe scaling of the prototype properties (Table 8.1), the spacingby,

an equivalent amount of shear rein-the stirrups was altered to provide

Chapter 8 Model Component TestlnR

Figure 8.6 Setup for Reinforcement Cage Assemblage

Figure 8.7 Control of Wire Location in Reinforcement Cage

161

Chapter 8 HOdel Component Testing

Figure 8..8 Details of Reinforcement Cage

168

.c. I


for cemen t per unit length:

sm

where s is the stirrup spacing, 1 the length scale ratio (1:14.4), andr

Py the yield force of the stirrup.

the calculated spacing for a beamThe stirrups were spaced at 8 m

length equal to twice the beam depth and at 28 thereafter to reduce them

control thefabrication effort. Machined plexiglass combs were used to

spacing.

were attached to the main reinforcement by tighteningThe stirrups

them together with Gauge 24 wire at every third crossing along the main

reinforcement (Figs. 8.7, 8.8). The tightening required some practice in

Finally, at each suchorder not to bend the relatively weak stirrups.

adhesive (GR-R-1P, Alpha Cyanocrylate adhe-node a very small amount or

slip-freesiye by GC Electronics) was applied, which resulted in a

nection between the stirrups and main reinforcement, thus providing the

for further handling after removalrigidity of the cage necessary

assembling table.

assemble oneIn average, it took less than three working days to

reinforcement cage.

The forms for casting of the specimens were made out of wood covered

with PiC foil to prevent wood warping and adhesion between the forms and

the concrete, and out of aluminum angles of depth equal to the width or

the beam (Figs. 8.2 and 8.5). The beams were cast horizontally as in the

case of the prototype. The positioned in the forms usingcages were

spacers and stiff horizontal stainless steel wires passing through the

aluminum angles.

.169

Chapter 8 Model Co8ponent Testing

C:A:W ratio otThe microconcrete used tor the specimens had a

1:3.5:0.12, with aggregate grading and cement type as reported in Section

7.1.2.3 for mixes used in this study.

orAll the specimens were cast together using a single batch conc-

A total or 35 accompanying 5Ox 1 00rete. (2x4 in.) cylinders were cast

at the same time.

The mixing was done using a two-speed 0.5 tt.3 (0.003 m3) mechanical

mixer. The procedure used (as recommended in Re~. 18) was as tollows:

1. Place the entire quantity of mix water in the bowl of the mixer.

2. Add cement, mix tor 30 seconds at slow speed, add aggregate, mix

30 seconds

3. Stop mixer for 50 seconds. Scrape any mortar stuck to the sides down

into the batch,

4. Mix ~or 60 seconds at slow speed.

The concrete was poured into the forms and vibrated into place by tou-

ching forms with a pneuatic hand vibrator. Once the concretethe

upper edge of the beam form, a plexiglass stopper (Fig.reached the

placed in position to prevent the flow ot the concrete duringwas

casting of the higher located portion of the column.

After the casting was completed the forms were covered with PVC foil

24 hours.to prevent moisture loss, and left undisturbed tor Then the

connected byforms were stripped (by dismantling the formwork which was

screws) and the specimens were placed in a fog room (20oC, 95~ RH)

To equal moisture content in all specimens at the time otassure

well prevent shrinkage cracking, all specimens weretotesting, as as

Ref. 18.sealed using clear shellac spray, as it was recommended in

coating 1s proof, transparent and highly brittle, thus providingwater

170


the possibility of crack observation during the test. The sealing was

accompanying cylinderaccomplished by removing the test beams and

specimens from the fog room after 5 weaks, allowing their surface to dry

for about 40 minutes and then spraying the surface with the first coat or

The coatedshellac. Subsequently, two additional coats were applied.

specimens were then stored in a constant temperature room (20oC) till the

day of testing.

8.2.2.2 Test Setup and Instrumentation

HTS closed-loop testing machineThe tests were performed using the

with the adjustable testing frame shown in Fig. 5.4.

The test setup and part or the instrumentation shown inare

photos of Fig. 8.10. The cyclic loads were applied8.9 and in the

In order toto the column stub by means of the MTS hydraulic actuator.

avoid force redistribution between the two beams of a test specimen, the

column stub was rigidly connected to the hydraulic actuator.

The supports of the beams were provided by linkages consisting or

spherical rod-end bearings with a load cell mounted between themtwo

8.10) . two linkages allowed preciseA turn-buckle in each of the

adjustment of the length of the linkages.

braced against lateral out-of-plane mo-The ends of both beams were

The bracing was provided through teflon-lined, rigidly supportedvement.

in Fig. 8.9).plates (not shown A very small gap was left between the

teflon and beam faces. Closing of this gap was not observed in any test,

thus out-or-plane bending did not occur

The instrumentation of the test consisted of the following:

1. LVDT of the hydraulic actuator measuring the column displacement. In

171

Chapter 8 Hodel

I~

f.§

.

t Testing


Figure 8.10 Views of Experimental setup and Instrumentation

173


also used for test control.most of the cases the actuator stroke was

In this manner, both beams subjected to equal displacementwere

but were permitted to undergo different load histories whenhistories

unequal strength properties existed in the two beams.

force the end or each beam2. Two load cells measuring the at

One of the load cells was used for the test control inindependently.

sub-yielding cycles of the high shear tests.

Qt tor the measurement or3. Two three pairs mercury gaugesor

displacements at the top and bottom sides of rectangular rigid frames

in Figs. 8.9 and 8.10. Fromwhich were attached to the beam as shown

the rotations and average curvaturesthe displacement measurements

over a predetermined distance were deduced. The use of mercury gauges

measured betweenis discussed in Chapter 5. Average curvatures were

(0.41 in.10.5 mm andthe column face and two sections located at

30.5 mm (1.20 in.) from the column face.

Signals of all the instruments were recorded in digitized form by a

Several X-Y recorders registering the load-deflection andminicomputer.

load-average curvature measurements were also used in the low frequency

tests to allow visual control of the test. In the high frequency tests

load-displacement histories were registered on oscilloscope screens.

coated with shellac (see previous section) onAll beamsthe were

which a grid identifying the location of the main reinforcement and stir-

rups was drawn with a felt pen.

The cracks were observed with the help of a magnifying glass, marked

with a felt pen, and recorded photographically.

174


Simulation g! Prototype Response (!/~ = 1.1)

In order to evaluate the adequacy of a small-scale model of a beam

element subjected bending and high shear, two beams (one specimen)to

subjected to the properly scaled prototype loading history

(Ref. 186). The loading history ot the prototype beam is shown sche_ti-

cally in Fig. 8.11.

The loading velocity was controlled through a ramp function with the

speed of loading based on the assumption that the time of first loading

to yielding is 100 seconds.

Load-displacement or the prototype fromresponse is reproduced

186 and presented in Figs. 8.12 , with the load points corresponding

to the ones marked in Fig. 8.11.

In order to compare these results on a one-to-one basis with the re-

sults obtained for the model beams, appropriate scale factors were ap-

plied to the measured model Comparisons of severalresponse values.

load-displacement hysteresis loops of the prototype and model response

are presented in Figs. 8.13 and 8.14. Table 8.2 provides a comparison of

tangent stiffnesses in different cycles in the prototype and model beams.

For the cycles below and slightly beyond yielding of' the main

reinforcement, the shapes or the hysteresis loops are similar in model

simulationand prototype and an accurate or the prototype response was

achieved with the smll-scale model. However, at the first large

(Point 26)amplitude reversal and thereafter, a significant strength

deterioration is evident in the model response which did not occur in the

prototype. 'ni1s phenomenon must be attributed largely to the lack of

strain hardening in the main of'reinforcement the model beam. It 18

175

Chapter 8 Hodel Comppnent Testing

~~z0I-UbJ-J""4JaQ.I- .

BEAM 46

Figure 8.11 Prototype Loading History

Table 8.2 Tangent Stiffness of Prototype and Hodel Bea8a

+ Prototype Domain

176


,"

~ "+ ",o?" ~?

.I ~ ~~

.,

~~->.Q.

~0t.J

,

BEAM 46

-'"~...

- I I I I I I0.3 0.4 0.5 0.6 0.7 0.8 0.9

TIP DEFLECTI~ 8 (IN)

It I . 1-.0.9 .,0.8 41 -4t ..o,s .;Qc4 -o~ -02 ...

~'"

"'~//~~ ",J':"//~ ~~ -40

",'"

-

~'

I-E&80 ~p

tW)L.

Ca> Up to Yielding or Reinrorce..nt

FilUre 8.12 Prototype Load Displacement Response

177

120

80

40

r


Figure 8.13 Comparison of Model and Prototype Load-Displacement Response for Cycles

up to Yielding of ReinforC888nt (Prototype Domain)

160r-..CI)

~ 120~"-

Q. 801

60024 3D

~~'-

Q..

~

400h~~=::~~:;=J . ~

200 II~ /,1

i'T 40

p 16/,

0 2.0<5 (IN)...

;'/,.

-200 ""

'"

~

..

~

"1/-400 ..0.-

f: i -- - l-- ---

26 prototypemodel32

-600-/60.1-

I I I II I 81 III I I

-60 -40 -20 0 20 40 606 (mm)

Figure 8.1- Comparison of Model and Prototype Load-Di.plaOeMDt Response for Cycle.

beyond Yielding of Reinforcement (Prototype Domain)

178

-40/y


believed that, with reinforcement which is heat-treated to develop the

necessary strain hardening ability, also the larger amplitude loops could

be successfully reproduced

Figure 8.15 presents the load-average curvature (or moment-curvature

after multyplying of the vertical axis by a constant) response of the mo-

del over a length of 438 mm (17.3 in. (prototype domain). The curvature

record shows a symmetrical behavior corresponding to the symmetrical

displacement history. This indicates that the inelastic tip deflection

is caused primarily by a symmetric pattern of cracks concentrated in the

close vicinity of the column. Figure 8.16 shows the load-curvature

relationship length or 152 mm (6 in. for the prototype.over a

Superimposed are the peak values of the curvatures measured at the same

location in the model. It can be seen that the peak values differ consi-

derably between model and prototype. The unsymmetric peaks in the proto-

type are attributed to the strain hardening in the reinfor-prototype

cement which led to a redistribution of strains which had no counterpart

in the model due to lack of strain hardening.

In retrospect, the importance or simulating the strain hardening

characteristics in model reinforcement cannot be overemphasized. It is

well established that the post-yielding cyclic response characteristics

or f1exural elements are largely controlled by the mechanical properties

of the reinforcement. Strain hardening will permit an increase in the

bending resistance and will also cause a spreading of flexural (and also

shear) cracks into the beam proper

Figures 8.17 a and 8.17 b present the crack pattern in the prototype

and in the model, respectively. Here again the lack of strain hardening

179


Figure 8.15 Model Mo8ent-Curvature Response

3D+

~J.-=rr

Figure 8.16 Co8par1son of Model and Prototype MomeDt-Curvature Response

180


(a) Prototype

(b) ~el

Figure 8.17 Views of Prototype and Model Crack Patterns

181


in the model reinforcement is or visiblea Although theinfluence.

cracks in the vicinity ot the column similar,are no cracking in the

model beam regions located further away from the column observedwas

Since there was no increase in the beam capacity with increasing displa-

cement amplitude (no strain hardening), the cracks did not propagate

beyond the initially cracked Difficulties inzone. detecting small

cracks in the microconcrete specimens may have contributed to the limited

extent of cracking indicated in Fig. 8.11 b.

8.2.4 Simulation of Shea~ Failure Mode (!/~ = ~.Q)

Four of the beams were tested with very small shear to depthspan

ratios to examine the feasibility of small-scale model tests of beams

failing in a mode controlled primarily by shear. Two of the cantilever

beams were loaded at a distance of 2.0d from the column face and two at a

distance of 2.24d

Figure 8.18 shows the load-displacement hysteresis loops for one of

the beams with lId = 2.0. The applied load history consisted of three

cycles at a displacement amplitude slightly beyond yielding of the rein-

for cement and three subsequent cycles of twice this amplitude. Prototype

test data are not available for a direct comparison of response behavior,

but the model test results exhibit all the characteristics expected from

a high shear test. The first load reversal led to a set of nearly ortho-

gonal diagonal cracks which in subsequent cycles caused the well-known

pinching of the hysteresis loops evident in Fig. 8.18.

At the large displacement amplitude, the second and third cycles led

to a rapid deterioration in strength and stiffness. This deterioration

was caused primarily by a decrease in the aggregate interlock along the

182

Chapter 8 Hodel Co8POnent Testing

-2 -1 0 , 2of ~fofype domain (in.) 1--- ~I ,~-

:-..S;tj

~"'Gq,

~~eQ..

~-r!2 p

Q';q:C)-J

00~~.~t)

§15-~0e:

-2 -tOO

-4 -' I - I I ~del d~mo;n ('!'m)- 04 -2 0 2 4

DISPLACEMENT

FigUre 8.18 Load-D1splac..ent Response fro. Test with lId. 2.0

Figure 8.19 View or Crack Pattern from H1gh Shear Test

183


major diagonal cracks. Considerable crushing of the concrete occurred

be in Fig. 8.19 which shows the crackalong these cracks, as can seen

pattern at the end of the applied load history. This crack pattern ap-

pears to be representative or prototype cracking although the spacing or

the major shear cracks probably is larger than that of a prototype. The

spacing of shear cracks in prototype or the dimensions shown ina

Fig. 8.1, but with different lId and shear reinforcement (Ref. 186) than

that used in the model beams, is approximately equal to one-fifth of the

beam height whereas it is on the average one-quarter of the beam height

in the model beam.

8.2.5

In order to explore the feasibility of simulation of a predominantly

flexural roode of couple of cantilever beams was tested withfailure a

shear span to depth ratio equal to 6.9

The loading history to which the cantilevers were subjected consis-

ted of 3 cycles at a displacement amplitude slightly beyond yielding of

the reinforcement and subsequently 3 cycles at twice this amplitude.

Figure 8.20 shows load-displacement hysteresis loops obtained in

this test. There is no shear pinching effect, and the observed strength

deterioration can be attributed entirely to the lack of work hardening

exhibited by the main reinforcement. The crack pattern developed in the

beams (Fig. 8.21) entirely of flexural nature, although, as in thewas

previous tests, all the cracks of visible size were concentrated in the

region relatively close to the column stub.

184

Chapter 8 Hodel Co8ponent Test1n8

Displu..-a;-,wf cI ( in-)

-s 0 5. . T' , . , I . ',. . .~- 1_,- ' ,pr~~ d~

-as 0.0 0.5F. , . . ! I ~~ 1- I=::::'--I"8:-::;:::i J cf -

I F==!--I , JSO~

rl"~

- ~-::==2~ J~200 ~. -!p.

.~--'-

~

~0

I i~0

I o.o~-

c:~E0

1:)

"Ii~0E

~~~Q.'baa

,.J

~.,~lo.o 100

;,/W:/ .--="" "" \ - ;11"';

,-02-200 -1.0 r50

. t . )

. -In .

,-a,} Cycle of. - - - 2-.- D#s~-:

3-,. A~moM' dlNrlain .

I I I I J J-- - 10

prototype domo;,L . J . J'..' J . I-100 0 100

Displac~nt cf (mm)

Figure 8.20 Load-Displacement Response t~ Teat with lId. 6.9

Figure 8.21 '1- of Crack Patt8r'ft tI'O8 R1ih Flexure Test

185

'.0

Chapter 8 Model Component Testin~

Ca) Cycling Frequency 0.0025 HzDisplacement clrin.)

-5 0 5'tic' I , I I I I I . I I I

p'ototy~ domain-0.5 0.0 0.5

,~ "". I I -!-"_I ~ .' 'dOnIa.I l= :J!~cfi! rrouua In - ,

200 .~,.o ~.s F=~--.~ t- - .S I .~ 50e: I ~ P "' c" - -- ~ 0.2 e:I ~ .g ; 1 - ,#'" - - 117 .g .g

II '- ~,'I" " ' -.. 1e:: I~ -t q.

,~ 0 0 ~~ I e: e: I ~

i ~O.O ' -:- : o.o~

i~'-Q,.'b~~

.,.J

~~a.~~~

.,J

~.0u

"/ ....

.<).2-200 -'.0 ..,

- - f.a,} Cyc,..,O- - - .2'-114 Dispi«--'-- - - - - ;J-,.4 A,.p"'w.

mode'ldomoin. r~,""I' . I. I I I I j

.c-lO 0 10. prototyp~ domain

,1;,\;,:;. t . t. -, . I.' -100 0 100

Disp/oc~ment cJ (mm)

(b) Cycling Frequency 10 Hz

Displacement r!'in.)-5 0 5, 'r'" , I ' , , '-" ,

prototy~ domain-as 0.0 .

i-' '" " '-'- -'~. ~f.1i=::==~~3 Q.$-.S, ~-- .Jd moMI ,"

0 .e T.g:t0e

:-="".s-

0O.2e

.g..Q.~0e

O.O~

200;I

.s.C)s

.g

":tC)s

so!pi~'-Q..

"b2...,

~~Q."1:J00

..,J

~0 IC()

1-0.2-20u -1.0 -so'-.'} CYC,.M. - - - 2-.d Ois,,_--

-- - - -- .5-,d AM,,"'"mode/domain

".~" I I ~ I I I I 1'0 I

prototype domoint,- I - ,-, - ,-100 0 100

Displacement c1 (mm)

Figure 8.22 Comparison of Load-Displacement Responsefor Be8IU Tested at Different Frequeneies

187

.g

.! I

..9:0~o.o


1.0~C\I~(lCI

~~t)0

.,..J

~4.1

.~-..t)

~0

~

-1.0

Figure 8.23 Load-D1splacement Response tor Tbree D1fferent Cyclin4 Frequencies

Figure 8.24 Influence of Cycling Frequency on the Peak Load at a D1aplace8ent &.pl1tude

188

o.0


control at high frequencies did cause some differences

measurements performedAll the hysteresis loops obtained from the

the twelve beams are presented in Appendix B.during the oftests

normalizedload-displacement history, andeach beam a normalized a

Table B.1 summa-bending moment-average curvature history are presented.

rizes the measured maximum load values vs. displacement amplitude.

Figure 8.24 presents the quantification of the influence of cycling

the two displacement amplitudes.frequency on the average peak loads at

the average peakThe average load values are normalized with respect to

the change for the first cycle of the second

NP21 indicate the significant difference in the

fourth line (~1) reflects

Namplitude. Lines P11 and

frequency (0.0025 Hz) and atstrength of the beams tested at the static

Hz).dynamic frequencies (2 Hz and 10 The difference between the two

10s8 of strength, from the smaller to the larger amplitudelines shows a

of approximately 13~ for the lowest frequency, about 1~ t'or the second

for the highest frequency. There is nofrequency and some minimal gain

significant difference between the strength deterioration rate for cycles

of the same amplitude carried out at different frequency levels

described for the lowest frequencyThe crack patterns of the beams

Section 8.2.5 Itwere also studied for the higher frequencies.1n

crack pattern was basically independent ofalthough theobserved that,

the cycling frequency, there was a difference in crack sizes. In the

frequency test, pieces of concrete around the major crack at the column

189


face spalled off whereas in the high frequency tests the crushed concrete

pieces did not fallout. This may explain the large difference between

the peak load values for the first cycle or the small and the large

amplitude in a low frequency test, and the relatively small difference in

Nthe high frequency tests. Line P" indicates that the effect of material

strain rate accounts for a 5~ strength increase by increasing the cycling

frequency from 0.0025 Hz to 10 Hz, and thus is small relatively to the

effect of cycling frequency on the post-cracking behavior ot concrete

particles located in the cracked area

8.2.7 Conclusions

Because of the lack of strain hardening in the model reinforcement,

only a limited assessment of the simulation or the various failure modes

(flexure, Also,flexure-shear, and shear) can be made from this study.

prototype test results available only tor the beam failing in aare

flexure-shear mode. For this case, the stiffnesses in the various cycles

closely ade-simulated at model scales and the strength values are

quately reproduced in the early post-yield range. The tests on specimens

small lId ratios show the characteristic pinching of hysteresis

loops while the tests specimens with large lId exhibit the expectedon

fat hysteresis loops controlled by the stress-strain characteristics of

the reinforcement. Considering the complex mechanisms that are involved

in shear transfer (aggregate interlock, dowel action, contribution of

shear reinforcement, etc.), the results of this limited test series are

not tully conclusive but are indicative that most or these complex

mechanisms be simulated with reasonable success at small modelcan

scales. In all cases, strength deterioration in the inelastic range

190


occurred at a rate which exceeds that expected in the prototype. It 1s

likely, although it cannot be proven at this time, that much or all of

this discrepancy is caused by the lack of strain hardening in the model

reinforcement used in this study. Further research with more accurately

scaled stress-strain characteristics of the reinforcement is needed to

verify this conclusion.

The study of the cycyling frequency effect indicated that the ma-

terial strain rate effects, as discussed in Sections 7.1.3 and 7.2.3,

pear to have relatively little effect the strength of the specimens.on

or larger importance seems to be the effect of deformation rate on

post-cracking behavior of the concrete which restrains dislocation or

concrete particles in high frequency tests. This phenomenon causes

doubts in the accuracy of dymamic response prediction from psuedo-static

load tests

1~1


8.3 MODELS OF STEEL CANTILEVER BEAMS

In this study, tests carried out on two metal cantilevers, anwere

1:1.92 model of it made of CA 510A36 structural steel cantilever and a

annealed phosphor bronze. The tests were performed to provide informa-

of two single-degree oftion an the load-deformation behavior of columns

This information was neededfreedom models tested the shake table.on

phosphor bronze model, in which temperature effectsparticularly for the

The studydue to the column welding process were of particular concern.

thewas also performed to investigate the effect of cycling frequency on

load-deformation behavior of the specimens.

selectedFor ease of fabrication, rectangular cross sections were

The dimensions of the cantilevers were based on thefor the specimens.

models studieddimensions or columns ot single-degree or freedom

subsequently on the shake table. The steel columns were fabricated from

13x19 mm (1/2x3/4 in.) hot rolled flat bar. The mill scale wasa

final dimensions of the cantilever were: hxbxl =machined off, and the

distance from the12.3x18.3x279 mm (O.484xO.719x11.0 in.), 1 being the

face of the column to the point of load application corresponding to one

half of the column height. The phosphor bronze columns were machined

from 13 mm 1/2 in. diameter half-hard rod. The scaling ratio from the

bronze columns is. based on true replicasteel columns the phosphorto

= (E/p)r.model rules demanding that 1 In this study, the ratio wasr

1:1.92. Thus, the dimensions of the phosphor bronze cantilever were:

hxbxl = 6.4x3.5x145 mm (O.252xO.374x5.7 in.).

The cantilever beams were welded to a rigid steel column. In the

case of the phosphor bronze, small alumnimum bronze plate was weldeda

face of the column, and then the cantilever was welded tofirst to the

192


that plate. This procedure was chosen to minimize the heat input to the

cantilever, and thus to minimize the over-annealing of the material.

welding was done using tungsten innert gas (TIG) technique.

The cantilevers tested in the frametest described inwere

Section 5.3.1.2 and shown in Figs. 5.3 and 5.4. Figure 8.25 shows

schematically the test setup. The instrumentation consisted of a

cell measuring the tip force applied to the cantilever, a LVDT measuring

the vertical displacement at the force application point, and two pairs

01' strain gages measuring strains on the top and bottom surface ot a

cross section. The first pair was positioned at a minimal distance from

the welded joint, and the second at a position where no material yielding

was expected. The measurements from the latter pair were used to obtain

a reliable moment-strain calibration for the shake table study.

////// //-"I~~!ifJ / / J~~'J'!/ / // / / ////////_///~;"// /// //////~(/ /f/ // I I.-

"1fT

!l-t1' 0-'I ,

~LoodC~IIL.L.U

~~~

~A

!

~S Ing ram~

Actuator

Figure 8.25 Experimental Setup tor Cantilever Test

193


for the steel, whereas the phos-resulted in very slim hysteresis loops

phor bronze loops exhibited a significant amount of plastic deformation.

discrepancies must be attributed to the effect of overheating nearThese

The welding process caused athe phosphor bronze specimen.the ~lds of

loss of strength in excess of the desired reduction in strength which was

controlled through subsequent annealing.

post yielding cycles, the peakfewWith the exception of the first

the different displacement amplitudes and also the hysteresisforces at

attri-loops for the two specimens matched rather closely. This can be

buted to the high work hardenings of the phosphor bronze which first

eliminated the effect of the lower yield strength.latersened and

vertheless, in dynamic response studies the lower yield strength and fat-

phosphor bronze will lead to dissimilarities inter hYsteresis loops of

These dissi-first few inelastic cycles.the response, at least for the

the premature yielding inDlilarities may not be large, however, since

partially counterbalanced by the greaterphosphor bronze 18 energy

dissipation capacity represented by the fatter hysteresis loops.

These simple cantilever tests as well as the material tests indicate

for models of welded steelthat phosphor bronze is not an ideal material

major problems are represented by the excessivestructures. The

of annealed phosphor bronze (see Section 6.3.4.4) and byhardening

Itstrength in the heat affected zones at weldments.excessive loss or

these two effects counteract each other to a degreeethatis fortunate

material. This 18which may make phosphor bronze an acceptable model

demonstrated by the shake table study of a simple steel structure and ita

phosphor bronze model discussed in Chapter 9.

195

Chapter 8 Model Component Test1nl

in

0.50.0.

zoo

100

Q..c0~

Po-

fo4

1b0kN 0.0

-100

.200

2010-0-

mm-10

TIPDEFLECTION . -~ .

F1iUre 8~26 Co8P8r1aoD of Load-D1aplaoement Response of Steel and Annealed Phosphor

Bronze Cantilevers (Steel Cantilever Do8a1D)

~rrect ~ QIcling ~requency8.3.2

itther, at whichThe questions which have

structures.in the case of dynamically loaded

frequencytesting

on the fatigue life of the component?

and fast

numericalofbaeietesting program, thus providing athecycles in

196


hysteresis loopsFigure 8.27 showsresponses.comparison between theThecantilever.static and dynamic cycles of the phosphor bronze

from

the averagecorresponding tostatic cycles were conducted at 0.01

strain rate of 2.4x10-4/sec. The dynamic tests were conducted at 2.8 Hz

-2corresponding to the average strain rate of 7.5x10 /sec.

Hz

in.

o. s0-0.5.0.300.

zoo.

lO.

100. -Q

-<0~

PI~...

o.o.kN

- 1,0.

1- 40

- 300.1.0100

mm':10-20

TIP DEFLECTtON

Figure 8.21 Comparison or Hysteresis Loop. tor Static and Dyna8ic Cycl..

ot ADnealed Pboaphor Bronze Cantilevers

except ot the somewhat higher peak valueidenticalThe loops are near ly

can be accounted for almostThisexhibited by the high frequency loop.

The hysteresishardening ot the material.high workby theentirely

It should be noted, however, that theloops.in low and high frequency

197


control. Thus, thetests were carried out with sinusoidal displacement

strain rates close to the peak force and displacement values are approa-

ching regardless of the cycling frequency. The lack of influencezero,

of the cycling frequency the or the cantilevers is in anon response

agreement with the findings by Almuti (Ref. 191)

The effect of cycling frequency on the fatigue-crack-growth rate has

been studied by others in conjunction with the material toughness and fa-

tigue behavior. In Fig. 8.28, Rolfe and Barsom (Ref. 201) present a sum-

mary of cyclic studies performed on A36 steel at frequencies from 0.1 to

100 Hz. The figure indicates that the cycling frequency does not

influence the fatigue behavior of the material (in environment)benign

Figure 8.29 (Ref. 201) indicates the independance of the fatigue behavior

or the shape of load function used to control the test.

the data presented in Figs. 8.28It should be noted, however, that

and 8.29 were obtained in the range of elastic nominal stress cycles and

it is not known whether the conclusion drawn from this set of data can be

extended to the regime of plastic fracture mechanics.

198

Chapter 8 Hodel Co.ponent Testing

F1pre 8.28 Etteot or Cycliq Freq8DOJ' ~ Crack

Growth Rate. (from Ref. 201)

,I'iI

ii

6

&

4

5

4

.U>-..i~.~Z'a...0'a

W~~X....0~~

~uc~u 3

210 20 30 40 50 60 80 100

STRESS -INTENSITY- FACTOR RANGE. b.K I. k.i .r;ii'C'h"""

Pigure 8.29 Effect ot the Shape ot Load Function on Crack Growth Rates (rro. R.t. 201)

199

3

2

10-5

8

6

Chapter 9 True Replica Hodel Study of a Steel Structure

CHAPTER 9

TRUE REPLICA MODEL STUDY OF A STEEL STRUCTURE

A study on a simple structure subjected to earthquake excitation was

Section 4.5.1necessary to evaluate experimentally the laws-presented in

for true replica models, and to subject the steel and phosphor bronze

studied at the material level (Chapter 6) and component level (Chapter 8)

to a true earthquake test.

9.1

freedom system was selected as aFor simplicity, a single degree of

The tested structures consistedtest structure. of four rectangular co-

lumns connected by welding to a rigid top plate and to base plates rigid-

ly attached to the shake table (Fig. 9.1). are stronger inThe columns

uniaxial motion and are braced at mid-the direction orthogonal to the

structures were testedheight to prevent motion in that direction. Two

on a shake table, one made of steel and one made of phosphor bronze

4s!!ak~ fable ~motion

Figure 9. 1 Longi tldunal and Transverse View ot The Model

The steel model is used a pseudo-prototype structure for theas

allowing numerical comparison of the resultsphosphor bronze model, thus

200

Chap~er 9 True Replica Model Study of a Steel Structure

both the models. The overall dimensions of theobtained from tests on

pseudo-prototype are based on the size of the shake table available at

Stanford, and on cost considerations. The steel model can be viewed as a

1:4 scale model (with artificial mass simulation) of an actual structure

the dimensions as specified in Table 9.1. This structure was

designed to resist the N-S component of the 1940 El Centro acceleration

record at level close the yield of the columns. The materialtoa

properties of the steel used in the pseudo-prototype and of the phosphor

(CA 510)bronze used in the true replica model summarized inare

Table 9.2. The dimensions of the phosphor bronze model derived byare

applying the scaling rules for true replica models (section 4.5.1) to the

pseudo-prototype dimensions. The following are the inverse values of the

in Fig. 9.2The instrumentation used in the experiment 18 shown

The shake table accelerometer and LVDT provide a record of the input

attached to the top plate of themotion, the accelerometers and LVDT's

The accelerometer orientedmodel provide a record of the model response.

in the direction transverse to the direction of shake table motion prov-

ides information as to whether any significant transverse movement takes

place. The two relative motion LVDT's permit an estimate of any rotatio-

nal DDtion. Strain gages attached to the columns within their elastic

calculation orrange provide a strain history record thus allowing the

shear forces experienced by the columns. This is done using the formula

v = (M. + M2} / h, in which h is the distance between the instrumented

201

Chapter 9 True Replica Model Study or a Steel Structure

Table 9.1

Dimensions of the Prototype,the Steel and Phosphor Bronze Models

Table 9.2

Properties or Model Materials

LVDT's

SIDE VIEW /"7~~!!~~-~-.n; ,- ~--~~f~ -"\.8-cf

2 st~tn.!~_('c0Ull1.s I COII8I\ :;

I "t

I "" : ,.' I

P LAN VIEW ">~~~-~~~

Figure 9.2 Schema tic View of the Instrumentation

20.2

Chapter 9 True Replica Hodel Study of a Steel Structure

cross section, and M1 and H2 are the moments recorded at the two cross

sections. The moments were recorded directly by using the moment-strain

calibrations obtained from the cantilever tests (Section 8.3).

testing program was designed to provide maximum information on

the correlation of the behavior of the pseudo-prototype and its model at

the 1940 Elvarious levels of dynamic excitation. The N-S component or

Centro earthquake chosen as a basic input motion. The record waswas

scaled for the pseudo-prototype using a length scale or1 = 1:4 and arand for the CA 510

= 1 :{i-:68' = 1: 2.77.

model using

For both the'r

structures, = 1.a The models were subjected to two time histories,r

consisting of 60% and 177% (shake table limitation) of the displacements

obtained from the 1940 El Centro record

To establish the dynamic elastic characteristics of the structure

free vibration tests Thewere performed prior to the shake table tests.

natural frequencies and damping values of the models are established from

the free vibration time record and from the mean spectral density func-

tion obtained from Fourier analysis of the record. The free vibration

tests repeated after the entire testing history to evaluate thewere

changes in the dynamic elastic characteristics of the structure

9.2

9.2.1 Elastic Tests -

free vibration tests for the pseudo-prototype and its model

yielded the following results (in the pseudo-prototype domain) :

203

9 True Replica HOdel Study or a Steel Structure

pseudo-prototype model

natural frequency 4.45 Hz. 4.60 Hz.

O.134J O.137~percent or critical damping

The slight discrepancy (3~) between the natural frequencies of the pseu-

do-prototype and the model is mainly attributed to the difference in

column stiffnesses due to the different height of the weld. A difference

of this order of magnitude may already some effect on the elastichave

response and makes directly overlaid time histories more difficult to

review.

Figure 9.3 shows the first 20 seconds of the shake table displace-

ment response to 60~ of the El Centro record scaled for the pseudo-proto-

type and the model and represented in the pseudo-prototype domain

Although the records are very close, some dissimilarities can be observed

at the peaks of the displacements, where the very small displacement

fluctuations are not reproduced at the model level. These dissimilari-

ties, which are caused by stiction problem at the shake table bearings

are a source of discrepancies in the response of the two test structures.

Figures 9.4 and 9.5 show a comparison of the story displacement and

acceleration response between the steel pseudo-prototype and the phosphor

bronze model. The plots represent the response to the 60J El Central

motion in the pseudo-prototype domain. {4For the time window shown

seconds in the pseudo-prototype domain, i.e., 8 seconds in the prototype

domain), the responses are rather similar except that the peak responses

are consistently larger, by a few percent, for the phosphor bronze model.

Considering that the two structur-es respond elastically and that the

measured damping is almost identical, this discrepancy must be attributed

primarily to problems in reproducing the input motion at the two model

204

Chapter 9 True Replica Model Study of a Steel Structure

~.00.0

\C.0 .0N.0

N.9

~

t!r

~.

9

.~ 00#'

.

9 .0N iQ)

"8

eQ)Nd0k

.0

k0

'8.m0

'8...III

a

ioS

g..i

f;..c

~

g-\D

~...

I~

~

I

!Co.

Q

.!.

.D.

104

j

.0-

f

!..

-~'08Qj~'-'

~~::~_.~~-~

-~

X

1-4

E-I

~ -~--

-=---

- -_:

,'IC=:

I I I I~~-~-I : .". II 0

s. . . . .0 0 0 0 0

S N.-4 .-4 NI I

J.N~W~:>V'ldSla

205

Q)~:t;-o0k~I0

-gQ)co~

Q)Q)co


in...~.'.'.'. ~

0.4w.

....M*MU-C..I.....~

A0.2:So

'" :.... . . . ..1\0. A' "(.~~~. '" 0.0o.

~-I

~

\.f i Yi -\:' . ,.'.. . .

. .

000.2~i~.

~"

"

.'

.'

0'f

>.'.'.'-.

~1

-0.4'"to. - - - - - pho8phor bronae model

8teel p8eudo -prototype

4.03.01.00.0 2.0(seconds)TIM E

Figure 9.4 Displacement Response or the Structures to 63J £1 Centro Motion

(Pseudo-Prototype Do~)

Figure 9.5 Acceleration Response or the Structures to 63~ El Centro Motion

(Pseudo-Prototype Do81n)

206

Chapter 9 True Replica Model Study or a Steel Structure

scales. This conclusion is substantiated further by larger discrepancies

in the respnoses in later stages of the motion (not shown in the figures)

which must have been caused by spurious signals in the shake table

motion.

9.2.2

Figure 9.6 presents the first 20 seconds of the shake table dlspla-

cement response to 177~ of' the El Centro record scaled for the steel

pseudo-prototype and phosphor bronze models. The discrepancies between

the two records are smaller than these observed in the lower amplitude

test (Fig. 9.3).

Figures 9.7 and 9.8 provide the comparison of the displacement and

acceleration responses of the pseudo-prototype and its model tor the

first four seconds in the pseudo-prototype domain. In the time domain,

the displacements compare well for the first three seconds while the ma-

ximum floor acceleration are in general lower for the inelastic cycles in

the phosphor bronze model. The differences in the response are more evi-

dent from Fig. 9.9 which shows the column shear vs. story displacement

response for the first four seconds. As was expected from the material

and component tests (Chapters 6 and 8) the yield strength of the phosphor

fatterbronze model is smaller and its hysteresis loops are than in the

steel structure. Nevertheless, the comparison of the column shear--story

displacement response is quite satisfactory as for the number of major

inelastic excursions and their force and displacement amplitudes

The low amplitude response after the first three seconds and the

subsequent inelastic response did, however, exhibit considerable discre-

207


Q.QN

C-.4

J.~..8

~

0.

an~

~

!g~s:

f..c:~

~MI:.-L~

i~..

0 .~

-G)'0~0C.JQIG)

'-'

~'x.H~

0

,.t.ofQ

~.D.!.oX

a

~0-

t

j..

0.In

0.0

.tN:iN:i~V'IclSla

208

Chapter 9 True Replica Hodel Study of . Steel Structure

0.0 1.0 3.0 4.0

TIKZ2.0

(..~da)

Figure 9.7 D1splao8Mnt Responae ot the Structures to 1771 11 Centro Motion

(Pseudo-Prototype DC8ift)

.

.A1.0 !!

A

:.~

.0..to-c-M 0.0.,MUU

v

~ ~v-1.0 f

v

0.0 1.0 3.0T I K I

Z.O

(Me-de)

Figure 9.8 Acceleration Response or the Structures to 177J £1 Centro Motion

(Pseudo-Prototype Do8iD)

209

~ - - - - pho.pbor bronse model

.teel p.eudo - prototype

Chapter 9 True Replica Hodel Study ot a Steel Structure

in.

0.0 ,0;0.50.5.1.0200

0.5 100

«

:5:con

z

~-'0u

lb0kM 0.0

-100

/;-0.5 .teel p.egdo - prototype

frIt, II

-20 -10 0 It 20-

MIl

- 'c DRIFTin.

-1.0 -0.5 0.0 0.5

-200

1.0

200

0.5100

~

~%VJ

ZX=--'0u

lb0kll 0.0

"/

-100-0.5

phosphor bronze model

-200-20 -10 0 10 20

l1l1I

Figgre 9.9 Shear-Displacement Response of One COlu.n to 177S El Centro Motion

(Approximately Firat Four Seconds or the Motion; Pseudo-Prototype Domain)

210


pancies. In part, these discrepancies must be attributed to the afore-

mentioned differences in the material behavior but, more likely, much of

the response difference is caused by difficulties in reproducing the

input IIK>tion at different model scales. This statement is supported by

the observation that similar response discrepancies did occur at similar

times in the elastic test.

In conclusion, this series of shake table tests demonstrated that

phosphor bronze is an adequate but not ideal material for models of steel

structures. Based on the results obtained within the first four seconds

of' the inelastic shake table test, it appears that good simulation ot

overall characteristics can be obtained from phosphor bronzeresponse

models. The major problem encountered in such models is the decrease in

yield strength in heat affected zones at weldments. A closer simulation

of the inelastic response can be expected when welding is not required or

when inelastic deformations occur in ~egions removed from weldments.

211

Chapter 10 Feasibility and Limitations or Hodel Studies in Earthquake Engineering

CHAPTER 10

FEASIBILITY AND LIMITATIONS OF HODEL TESTING

IN EARTHQUAKE ENGINEERING

The results of the study presented in this report and in the previ-

ous report by Hills et. al. (Ref. 58), together with research performed

by others permit an assessment of model analysis as a tool in earthquake

engineering

Tests carried out at Stanford and other places have demonstrated

that the dynamic response ot structural building systems (frames, shear

wall structures, etc. can be simulated quite accurately at model scales.

However, the quality of response prediction depends strongly on the accu-

racy of material simulation {particularly in reinforced concrete), sui-

table fabrication techniques that properly simulate initial and boundary

conditions, accuracy in simulating important details, reproducibility or

dynamic input (performance spectrum of earthquake simulator), resolution

or instrumentation system and speed of data acquisition system. It must

also be recognized that model tests not be feasible when damage ormay

failure is initiated by certain localized phenomena such as weld fracture

in steel structures or bond failure in reinforced concrete structures

Although no experience exists at this time, it appears quite feasi-

ble to incorporate realistic floor slab systems and nonstructural ele-

ments (partitions, walls, stair cases, elevator shafts, etc. in careful-

ly designed models. Hodel studies may also be utilized to study specific

problems in earthquake engineering, such as overturning and uplift, dyna-

mic instability and effects of stiffness and mass irregularities.

Experiments with true replica models (column 1 of Table 4.2) have

212

Chapter 10 Feasibility and Limitations of Hodel Testing in Earthquake Engineering

proven feasible for dynamic studies steel structures, using certainon

copper alloys which permit approximately a 1:2 scale ratio. Copper alloy

510 (a phosphor bronze) was found to be a suitable material which permits

satisfactory welding and, with appropriate heat treatment, reproduces wi-

thin certain limits the desired stress-strain properties. Experiments on

predict rathersimple welded models have shown that true replica models

accurately the maximum response. Welding in critical region poses a pro-

blem since the strength of phosphor bronze in the heat affected zone may

be reduced to a value less than that dictated by model similitude.

(EILead alloys which possess specific stiffnesses allowing soa-

ling in the order of 1:10 to 1:20 have been found in the initial study to

be of limited because or several undesirable material propertiesuse

(early nonlinearity, excessive damping, high creep).

Although the usefulness or a true replica copper alloy scale model

the scale limitation to a 1:2 ratio, the utilizationis debatable due to

a much smaller stiffness than steel, is ofof such an alloy, which has

much value when combined with artificial mass simulation since it permits

a significant reduction of the weights which have to be added to the mo-

2= E 1 ).r r(H This idea is particularly attractive for structures inr

Spacewhich the mass distribution along linear members is of importance.

trusses, transmission towers and antennas, long span and cable stayed

bridges can serve as an example of this type of structures.

Models with artificial mass simulation the obvious choice whenare

gravity effects cannot be neglected and prototype material is used in the

model. carried out at Stanford onA detailed shake table study has been

in. high 1:6 scale model (Ref. 58) of a steel frame prototype tested

previously at U.C. fromThe structural shapes were machinedBerkeley.

213

Chapter 10 Feasibility and Limitations of Hodel Testing in Earthquake Engineering

all primary frame connections were fully welded usingandA36 bar stock

Subsequent heat treatment of the finished modelthe TIG heliaro process.

performed to relieve initial stresses and to satisfy scaledframe was

The model structure was subjected toprototype construction tolerances.

the prototype input motions and the measured modelscaled versions of

the prototype domain forscaled back toresponse quantities were then

prototype response prediction.

between true prototypecomparison carried outA detailed was

This comparisonresponse and the response predicted from the model test.

done for strains, joint distortions, story displacements and accele-

rations and integrated energy terms (input energy vs. dissipated energy).

In all cases very good agreement was observed between model and prototype

differences between the results are attribu-test results. Some local

and an unavoid-table primarily to discrepancies in table input motions

able oversizing of welds in the model.

not only proved the possibility of reliable prediction ofThe study

prototype response with tests performed on small scale models, but also

effort involved in both thegave an insight into the relative cost and

major cost difference is in the size of the required tes-studies. The

very significant, a1-Also, the saving in material 1sting facilities.

the benefit or it is decreased by the rather high cost of custom-though

data acquisi-The cost of instrumentation and-made structural shapes.

prototype and model tests since the larger effort1s about equal1n

instrumentation for model tests is balancedin developing more sensitive

by its smaller size and the reduced cost of instrument support frames

models ofShake table experimentation on a variety of small scale

reinforced concrete structures, utilizing artificial mass simulation with

214

Chapter 10 Feasibility and Limitations of Model Testing in Earthquake Engineering

lumped masses of the floor levels, has been carried out for several years

(Refs. 46, 48).at the University of Illinois Although these model

structures did not simulate specific prototypes, they have resulted in a

wealth of detailed information the seismic of reinforcedon response

concrete structures. Much of the presented data in good agreementare

with mathematical models testsused for prototype structures. Other

(Ref. 23) have demonstrated that even localized crack patterns can be si-

mulated in small scale models. Strain rate effects in model concrete and

structural components were investigated in this study and are discussed

in Chapters 7 and 8

Discretely distributed additive masses, rather than lumped masses,

will be required in models of structures where mass distribution in space

1s of importance. This is the case in problems of frame-floor slab in-

teractlon, walls subjected to transverse excitations and in many towers

and antennas. Caution must be used in separating the added masses from

the structural material in such a way that they will not influence the

stiffness characteristics of the material.

Scale model investigations are of much interest for the verification

of the seismic safety and integrity of large man-made structures whose

failure would be of Components of nuclear reactorssevere consequences.

and containment vessels are appropriate examples. For the latter, the

gravity effects are often negligible compared to effects or internal

pressurization and severe ground motion. Thus, the modeling requirements

of column 3) of Table 4.3 may be utilized. In this case the major prob-

lem is in the reproduction of the scaled seismic input which requires an

earthquake simulator with high frequency reproducibility (since t = 1 )r r

and large dynamic force capacity (since ar = 1-1 )r . Piping systems can be

215

Chapter 10 Feasibilit"yand Limitations of Hodel Studies in Earthquake Engineering

through artificial mass simulation, by adding lumped tomodeled masses

reactor and discretely distributedot thethe structural components

masses to the piping system.

studies on bridge structures have been performed forDynamic model

more recently also on shake tables (Rer. 57). Because of thesome time,

effects, artificial mass simulation is usually re-importance of gravity

possible the use of model material of reducedquired. However, where

stiffness (E

the JOOdel.

simulated inin which strength properties were intentionally onlytest

anticipated while the design was simplified inregions where damage was

Clearly, this simplification must be done with due regardother regions.

to simulation of dynamic characteristics to transmit the effectsproper

condi-The simulation or boundaryto the regions of potential damage.

will often pose a significant problem and, when small scale modelstions

seismicthe pertinentbe difficult to reproduceused, it mayare

frequency range on conventional earthquake simulator.

the field of damThe need for model studies is well established in

Ideally, this requires the modeling of the dam (concrete orengineering.

embankment), the reservoir water and the geomechanical boundary condi-

Practical considerations make the use of water desirable as modeltions.

in turn requires model materials of very low stiffness andfluid which

for P = 1).r

for the dam (since E It is possible tostrength = 1= crr r rof concrete dams butdevelop suitable materials for small scale models

not for earth dams

table study ofNiwa and Clough (Ref. 192) have performed shakea

1:150 models of segments of arch and gravity dams.

216

They used mixturea

Chapter 10 Feasibility and Lim1 tations or Model Testing in Earthquake En~ineering

prediction.

One major problem requires consideration in all model studies

regardless of scale, namely the simulation of boundary conditions. In

dynamic model studies a proper simulation of boundary conditions may be

more essential than in staticeven model studies. Taking seismic

response studies on shake tables example, supporting the modelas an

structure rigidily on the table will not allow tor the rocking and

translational motion at the foundation-soil interface and for the energy

dissipation by hysteretic action and radiation ot waves in the supporting

medium. It is quite feasible to support model structures on a medium

that simulates these phenomena to various degrees (Ref.193). The largest

difficulty will be encountered in simulating wave radiation which depends

on the wave propagation and requires scaling otvelocity, v a

v for a true model. Since the stl~~ne8s o~ the sup-r

porting medium must be scaled in the same manner as the stiffness of

structural material (usually E = 1) this will necessitate very highardensity medium.

Within the limitations discussed in this chapter, it can be conclu-

ded that testing of small scale models of steel and reinforced concrete

structures can result in a reliable prediction or the overall response or

prototypes, provided that:

1) Similitude laws are satisfied in the design or the model, in the

choice ot the model material, and in the scaling of the input

motion.

2) Care is exercised in the fabrication of the model, in particular in

areas of special importance such as joints and weldments.

218

Chapter 10 Feasibility and Limitations of Hodel Testing 1n Earthquake En~1neer1ng

The testing facility is capable of precise reproduction of the pre-3)

is sensitive enough to monitorscribed motion, the instrumentation

acquisition system is capable orthe measured values, and the data

10-the output of the measuring devices withoutorregistration

troduotion or data distortions.

achieved inA simulation of localized failure modes becan

crack propagation of weldments).{e.g.,in othersoases but not

simulation of localized failure modes, theregarding thedoubts exist

be complemented with prototype component tests.model study should

response history of the component, as obtained from a shake table test of

history applied in theloadingthethe model structure, can serve as

prototype component test.

219

Chapter 11 Summary and Conclusions

CHAPTER 11

SUMMARY AND CONCLUSIONS

The major goal of this research project was to develop a methodology

for small scale modeling of structures in earthquake engineering studies,

and to evaluate the feasibility and limitations of model analysis in dy-

namic response studies.

Dimensional analysis can be utilized to derive similitude laws for

dynamic models. In studies involving material and/or geometric nonline-

arities, the simultaneous simulation of gravity and inertia effects poses

a major problem. If both effects have to be simulated fully, similitude

requires the use of model materials with specific stiffnesses (Elp which

proportion as the length.scale in the same An alternative, which per-

mits the use of prototype material for many practical cases, is provided

by adding lumped masses to the structure. beThese lumped masses must

structurally ineffective and should be distributed in a fashion that per-

mits adequate simulation of all important gravitational and~ :inertial ef-

fects. In linear elastic model studies and in other cases in which gra-

vity effects can be neglected, a different set of similitude laws can be

derived which permits the use of prototype materials without the addition

of lumped masses. The use o.t distorted models may provide acceptable

response predictions in some cases but necessitates either several model

studies at different scales considerable insight into-the physicalor

phenomena to permit an evaluation of the response distortion.

Adequate simulation of material properties was found to be the most

difficult and important aspect of small scale modeling. Similitude of

the monotonic stress-strain behavior alone is insufficient for dynamic

22()


studies. Cyclicresponse response properties, strain andrate size

effects, damping characteristics and other time and temperature dependent

effects must be considered. Laboratory testing programs sui table for an

evaluation of these properties are proposed in this report and the test

facilities and instrumentation used in this study for a comprehensive ma-

terial testing program are discussed in detail.

Modeling of steel structures can be performed using either ferrous

or non-ferrous materials. Material tests on structural steel and copper

and lead alloys were performed as part or this study. Monotonic and cyc-

110 load tests were carried out as well as a series of strain rate tests.

The monotonic stress-strain curves o~ steel and annealed phosphor bronze

show a remarkable similarity. In the cyclic tests, phosphor bronze re-

veals a higher work hardening than structural steel. Considerably more

cycles are needed to obtain stable cycles in phosphor than inbronze

steel. Thus, the peak stress reached by phosphor bronze at a prescribed

strain amplitude depends strongly on the previous cyclic history, as

revealed by cyclic tests with various histories. This phenomenon occurs

also in structural steel, but to a much smaller degree. It is concluded

that in earthquake studies, where usually only a small number of cycles

extends into the inelastic range, this phenomenon should not have a major

effect on the model response unless the deformation history leads to a

very unsymmetric cyclic response

The strain rate tests revealed that an increase in strain rate leads

to an increase in the yield strength but has no noticeable effect on the

elastic and post-elastic stiffness properties of the monotonic stress-

-strain curve. Empirical curves and their analytical equations are deve-

loped which give the relationship between strain rate and yield strength

221


Annealedfor A36 steel and annealed phosphor bronze. phosphor bronze

strain rate.considerably less sensitivity to the change in theshows

scale models made of phosphor bronze, this differenceHowever, in small

partly accounted tor by the increased strain rates duewill be at least

to the scaling of time.

For small-scale models of concrete structures, microconcrete offers

properties usingsimulation of concretepossibility of' olosethe a

or compressiveprototype-like material. It was found that a wide range

strengths and or tensile/compressive strength ratios can be achieved with

mix design praoti-appropriate mix proportioning. This report discusses

designs used inces and presents strength data for a large number of mix

this study and in model studies by other investigators.

close to 200 cylinder specimens wasinvolvingAn extensive study

to evaluate the stress-strain behavior ot various mixes ot mi-performed

croconcrete and the effect of strain rate on the compressive strength and

The tests were performed using a close cont-the stress-strain diagram.

thus allowing reduction of therol over the speed of platten movement,

having to account for the effect of relative stifrness8s ofda ta without

Average strain measurements werespecimen.the testing machine and the

Thetour clip extensometers developed tor this purpose.obtained from

strain rate study revealed that the relative magnitude or the strain rate

is essentially inde-effect on the compressive strength of microconcrete

It was found that the strainot the mterial.pendent of the strength

rate effect in microconcrete is of a similar magn1 tude as in prototype

A second order logarithmic equation for strain rate effect onconcrete.

the compressive strength of microconcrete is derived.

for model studies of reinforced concrete structuresReinforcement

222

Chapter 11 SUmlBry and Conclusions

amplitude show the importance or proper simulation or post-yield charac-

teristics of the reinforcement. The lack of strain hardening in the mo-

del reinforcement used in this study resulted in a faster strength de-

terioration in the model than in the prototype beam.

The tests with varying shear span to depth ratios have shown that

characteristicsresponse (load-dispacement hysteresis loops, crack

pattern) for various failure modes can be reproduced satisfactorily with

small scale models. The spacing of major cracks in flexure and in shear

1s somewhat larger in models than in prototypes, but the crack patterns

in critical regions of similar configurationare in both domains.

However, the lack or strain hardening in the model reinforcement has a

considerable effect on the size and on the distribution of cracks away

from the critical region.

Tests at various cycling frequencies were carried out to evaluate

the differences in the structural ot elementsresponse subjected to

pseudo-static and elements subjected to dynamic cycling histories. It

was found that the material strain rate effects have a relatively small

influence the component behavior.on However, the spalling out of the

crushed concrete is much smaller in high frequency tests, thus reducing

the strength deterioration as compared to pseudo-static tests. This

phenomenon affects the reliability of dynamic response prediction based

on the results of pseudo-static tests. The relatively small difference

The feasibility of simulation of the behavior of welded steel struc-

tural element with scale models made of' phosphor bronze studiedwas

through a series of tests of steel and annealed phosphor bronze canti-

224

Chapter 11 s.-ry and Conclua10D8

presents a majorThe large heat sensitivity of phosphorlevers. bronze

the yieldIn theseproblem in the welding heat affected zone. zones

reduced to a value less than thatstrength ot the base material bemay

However, this effect 1s counteracted byrequired by material similitude.

Thus, in the earlythe large work hardening of annealed phosphor bronze.

strengthinelastic cycles phosphor bronze cantilevers exhibited s_ller

Res-values but in the latter cycles rather similar loops were obtained.

ponse to cycling under different frequencies revealed a negligible dif~e-

steel andstatic and dynamic cycles for both structuralbetweenrence

Thus, the effects of material strain ratesannealed phosphor bronze. on

orthe structural response response or metal structures 1s shown to be

negligible importance in seismic response studies.

A shake table study of a s~ple steel pseudo-prototype structure and

was carried theannealed phosphor bronze model out to assess

phosphor to modelling of welded structures.applicability of' annealed

the simu-Within the limitations discussed in previous paragraph,the

lation or the inelastic response (story shear and displacement) was quite

It can be expected that results of similar quality will besatisfactory.

Thus, phosphor bronzeobtained with more complex model structures. mo-

dels can provide satisfactory simulation of overall response characteris-

tics but will result in distortions in the prediction or local stress-

-strain histories

sulllDarized as followsThe experience gained from this study can be

aspects of model research are a thorough knowledge ofThe mst important

and-.terlal much diligencemodeling theory, a comprehensive study,

patience in faithfully reproducing all pertinent details and oharaoteris-

or theof the prototype and, last but not least, the recognition

Chapter Summary and Conclusions

shortcomings and limitations of model research. It is an unfortunate

that very few inelastic dynamic response phenomena can be reproduced

"precisely" at model scales. True replica models require materials with

specific stiffnesses (E/p) which are much less than those of the proto-

type materials, but no two materials in nature are exactly alike. Arti-

ficial mass simulation permits the use of prototype material but introdu-

distortions in the force simulations. Thus, there 1s no ideal model

their- "dis-test but there are many adequate model tests, provided that

tortions" are recognized, evaluated and found to be acceptable. In order

to Bake this judgement, much experience in model research and a thorough

understanding of the physical phenomenon under study is needed. If a 1Do-

test is performed without due regard to its limitations, it may

easily lead to erroneous information and may discredit an otherwise quite

reliable experimental analysis technique.

226

References

REFERENCES

1.

2. Huller, R. K., Handbuch ~ Modellstatik, Springer Verlag, Berlin,Heidelberg, New York, 1971.

3.

4. "Models of Structures--RILEM Symposium," Bulletin RILEK, No. 12,1961.

5. Oberti, G., "Large Scale Hodel Testing of StructuresElastic Limit," ~l]._etin RILEH, No.7, July 1960.

Outside the

6. Rocha, M., "Structural Model Techniques--Some Recent Developments,"Chapter 16 in Stress Analysis, edited by O. C. Zienkiewicz and G.S. Holister, John Wiley and Sons Ltd., 1965.

7 Oberti, G. and Castoldi, A., "New Trends in Model Research on LargeStructures," ISHES Publication No. 53, Bergamo, Italy, 1977.

8. Oberti, G., "Model Contribution to the Design and Safety Control ofLarge Structures," ISMES Publication No. 89, Bergamo, Italy, 1977.

9. Litle, W. A. and Hansen, R. J., "Use of ModelsDesign," Journal ~ Boston Society Q.!: ~ Engrs.,2, April 1963.

in StructuralVol. 50, No.

10. Breen, J. E., "Fabrication and Tests o.fProceedings, ASCE, V. 94, ST 6, June 1968.

Structural Models,"

11.

12.

13. Proceedings of Symposium on "Models inCanadian Chapter of the ACI, Montreal, Oct.

Structural Engineering,"1972.

227

References

14. "Structural Concrete Models--A State-of-the-Art Report," compiledand edited by M. S. Mirza, Dept. of Civil Engineering, McGillUniversity, Montreal, Oct. 1972.

15. ACI Committee 444, "Models of Concrete Structures--State-of-the---Art," Report No. ACI 444R- 79, Concrete Intern~t_!.onal, Jan. 1979.

16. Brock, G., "Direct Models as an Aid to Reinforced Concrete Design,"~ineering 187, No. 4857, pp. 468,470, 1959.

11. Fumagalli, E., "The Use of Mbdels of Reinforced Concrete Struc-tures," Magazin of Concrete Resear_c- h, No. 12/35, 1960.

18. Harris, H. G., Sabnis, G. M. and White, R. H., "Small Scale DirectModels of Reinforced and Prestressed Concrete Structures," Dept.of Structural Engineering Report 326, Cornell University, Sept.1966.

Magura, D. D., "Structural Model Testing - Reinforced and Pres-tressed Mortar Beams," f£! Journal, Vol. 9, No.1, Jan. 1967.

Harris, H. G., Sabnis, G. M. and White, R. H.,mate-Strength Models for Concrete Structures,"SESA Annual Meeting, Oct. 1967.

"Small Scale Ulti-paper presented at

21. Mirza, M. S., "An Investigation of Combined Stresses in ReinforcedConcrete Beams," Thesis presented to McGill University in partialfUlfillment of the Ph.D. requirements, Montreal, Canada, 1967.

22. Sabnis, G. M. and White, R. N., "Behavior of Reinforced ConcreteFrames Under Cyclic Loads Using Small Scale Models," Journal 2r ~American ~o_n_crete Institute, Sept. 1969.

Chowdhury, A. H. and White, R. N., "Inelastic Behavior of SmallScale Reinforced Concrete Beam-Column Joints Under Severe ReversingLoads," Report No. 342, Department of Structural Engineering,Cornell University, Ithaca, New York, Oct. 1971.

White, R. N. and Chowdhury, A. H., "Behaviour of Multi-Storey Rein-forced Concrete Frames Subjected to Severe Reversing Loads,"Symposium on the Resistance and Ultimate Deformability ofStructures Acted on by Well Defined Repeated Loads, InternationalAssoc. for Bridge and Structural Engineering, Lisbon, 1973.

228

References

White, R. N., "Modeling Techniques for Reinforced Concrete Struc-tures," Department of Structural Engineering, Cornell University,Ithaca, New York, March 1976.

26. Chowdhury, A. H., White, R. N. and Scott, N. R.,Models for Reinforced Concrete Structures,"Vol. 20, No.1, Nov. 1976.

Harris, H. G. and Mushivitch, J. C., "StudySub-Assemblies - Validation of Small ScaleTechniques," Department of Civil Engineering,Oct. 1977.

of joints andDirect Modeling

Drexel University,

28. Godden, W. G., "Model Analysis and Design of Prestressed ConcreteNuclear Reactor Structures," Nuclear Engineering ~ Design,North-Holland Publishing Company, Amsterdam, 1969.

Bader, M. A., "Shear and Moment Transfer in Thick-Walled ReinforcedConcrete Cylinders," Ph.D. Dissertation, Stanford University,Stanford, California, Sept. 1980.

30. Becica, I. Y. and Harris, H. G., "Evaluation of Techniques in theModeling of Masonry Structures," Department of Ci vil Engineering,Structural Model Laboratory, Report No. M77-1, Drexel University,Philadelphia, June 1977.

Little, W. A., Foster, D. C., Oakes, D., Falcone, P. A., Reiner, R.B., "Structural Behavior of Small-Scale Models," Steel Research forConstruction, Bulletin No. 10, AISI, April 1968.

32. Ruge, A. C., "The Determination of Earthquake Stresses in ElasticStructures by Means of Models," Bulletin P.r Seismological SocietIQf America, Vol. 24, 1934.

Ruge, A. C., "Earthquake ResistanceTransaction ASCE, Vol. 103, 1938.

or Elevated Water-Tanks,"

34. "Vibration Research at Stanford University,"Seismological Society 2!: America, Vol. 19, No.1,

229

References

35. Jacobsen, L. S., "Dynamics ofProceedings, I Modelli NellaLincei, Rome, Italy, 1956.

Structural

Tecnica,Models

Academiain U.S.A.,"

Nazionale Dei

36. Antebi, J., Smith, H. D., Sharma, S. D., Harris, H. G., "Evaluationof Techniques for Constructing Model Structural Elements," ResearchReport R-62-15, Department of Civil Engineering, MassachusettsInstitute of Technology, May 1962.

31. Smith, H. D., Clark, R. P. and Mayor, R. P., "Evaluation of HodelTechniques for the Investigation of Structural Response to BlastLoads," Report No. R63-16, Massachusetts Institute of Technology,Feb. 1963.

38. Harris, H.G., Pahl, P. J. and Sharma, S. D., "Dynamic Studies ofStructures by Means of Models," Research Report R-63-23, Departmentof Civil Engineering, Massachusetts Institute of Technology, Sept.1962.

Harris, H. G., Schwindt, P.C., Taher, I., Werner, S. D., "Tech-niques and Materials in the Modeling of Reinforced Concrete Struc-tures Under Dynamic Loads," Research Report R63-24, Department ofCivil Engineering, Massachusetts Institute of Technology, Dec.1963.

Murphy, G. and Young, D. F., "A Study of the Use of Models toSimulate Dynamically Loaded Underground Structures," TDR 62-2, AirForce Special Weapon Center, 1962.

Young, D. F. and Murphy, G., "Dynamic Similitude ofStructures," Proceedings, ASCE, Vol. 90, EM3, June 1964.

Underground

Dobbs, N. and Cohen, E., "Model Techniques and Response Tests ofReinforced Concrete Structures Subjected to Blast Loads," ACI,~-~, Models for Concrete Structures, 1970. ---

43. Gran, J. K. and Bruce, J. R., "ScaleVertical Shelter Structures," ProjectMenlo Park, California, June 1979.

ModelingReport,

.Techniques for HISRI International,

44. Sozen, M. A., "Earthquake Simulation in the Laboratory," Preprintsof the NSF Workshop on Earthquake Resistant Reinforced ConcreteBuilding Construction, Berkeley, July 1977.

230

References

45. Otani, S. and Sozen, M. A., "Behavior of Multi-StoryConcrete Frames During Earthquakes," Civil EngineeringStructural Research Series No. 392, University ofUrbana, Nov. 1972.

ReinforcedStudies,

Illinois,

46. Otani, S. and Sozen, M. A., "Simulating Earthquake Tests of R/CFrames," Journal of the Structural Division, ASCE, Vol. 100, ST3,Proc. Paper 10435:- Mar. 1974.

47. Sozen, H. A., Aristozabal, J. D. and Lybas, Y. H., "Multi-StoryWalls Subjected to Simulated Earthquakes," Proceedings, 6th WorldConference on Earthquake Engineering, New Delhi, India, Jan. 1977.

4~. Aristozabal, J. D. and Sozen, M. A., "Behavior of Ten-StoryReinforced Concrete Walls Subjected to Earthquake Motions," CivilEngineering Studies, Structural Research Series No. 431,University of Illinois, Urbana, Oct. 1976.

49. Lybas, J. M., "Response of Reinforced Concrete Coupled-Wall Systemsto Earthquakes," Ph.D. Thesis submitted to the Graduate College,University of Illinois, Urbana, June 1977.

Chowdhury, A. H., and White, R. N., "Multi-Story Reinforced Con-crete Frames Under Simulated Seismic Loads", Vi~ratiQn of ConcreteStructures, ACI Special Publication SP-60, 1980.

51. Clough, R. W., Rea, D., Tang, D. and Watabe, M., "Earthquake Simu-lator Test for a Three Story Steel Frame Structure," Proceedings,5th World Conference on Earthquake Engineering, Vol. I, Rome,Italy, June 1973.

Clough, R. W. and Tang, D. T., "EarthquakeSteel Frame Structure, Vol. I: ExperimentalNo. 75-6, Berkeley, California, 1975.

Simulator Study of aResults, EERC Report

53. Clough, R. W. and Hidalgo, P., "Design of a Shaking Table Test fora Reinforced Concrete Frame Structure," Proceedings, 5th WorldConference on Earthquake Engineering, Vol. I, Rome, Italy, June,1973.

54. Hidalgo, P. and Clough, R. W.,Reinforced Concrete Frame,"California, 1974.

"Earthquake Simulator Study of aEERC Report No. 74-13, Berkeley,

231

References

Clough, R. W. and Huckelbridge, A. A., "Preliminary ExperimentalStudy of Seismic Uplift of a Steel Frame," EERC Report No. 77-22,Berkeley, California, 1977.

Clough, D. and Clough, R. W., "Earthquake Simulator Study of Cy-lindrical Liquid Storage Tanks," presented at the ASCE Annual Con-vention, San Francisco, October, 1977.

Williams, D. and Godden, W. G., "Experimental ModelSeismic Response of High Curved Overcrossings,"No. 76-18, Berkeley, California, 1976.

Studies onEERC Report

Hills, R. So, Krawinkler, H. and Gere, J. Mo, "Hodel Tests onEarthquake Simulators-Development and Implementation ofExperimental Procedures, Report ~.~, The John A. BlumeEarthquake Engineering Center, Department of Civil Engineering,Stanford University, Stanford, California, June, 1979.

Colloquium on "Use of Models and Scaling in Shock andASHE Winter Meeting, Philadelphia, Pennsylvania, Nov.

Vibration,"1963.

59.

the Symposium on Aeroelastic and Dynamic ModelingAir Force RTD-TDR-63-4197, Part I, 1964.

60. Proceedings ofTechnology, U.S.

Modeling1980.

61. Bannister, R. L. and Aneja, I. K., "Before-the-FactSolves Turbomachinery-Foundation Problems," Power, August,

Lauretta, E., "Dynamic Behavior of Large Structures Studied byMeans of Models," Prelim. Publication, 7th Congress, IABSE, Rio de

Janeiro, August, 1964.

63. Casto1di, A., "New Techniques of Model Investigation of the SeismicBehavior of Large Structures," presented at the ASCE NationalStructural Engineering Meeting, San Francisco, April 1973.

64. Oberti, G. and Lauretta, E., "Structural Models for the Study ofDam Earthquake Resistance," Transactions, 9th InternationalCongress on Large Dams, Vol. 4, 1967.

Oberti, G., "Development of Aseismic Design and Construction inItaly by Means of Research on Large Model Test," ~ PublicationNo.6, Bergamo, Italy, June 1957.

232

References

66. Oberti, G. and Lauretta, E., "Dynamic Tests on ModelsStructures," ~ Publication No. 19, Bergamo, Italy, June 1962

or

67. Lauretta, E., "Dynamic Features of a Recent Italian Arch Dam,"~ Publication No. 24, Bergamo, Italy, October 1964.

Lauretta, E., "Theoretical Considerations and Experimental Researchon the Behavior of Tall Buildings During Earthquakes," ~Publication No. 28, Bergamo, Italy, January 1965.

69. Oberti, G., "Results and Interpretation of Measurements Hade onLarge Dams of All Types, Including Earthquake Observations," ~Publication No. 29, Bergamo, Italy, Jan. 1965.

Oberti, G. and Lauretta, E.,Dam Earthquake Resistance,"Italy, ~ 1967.

"Structural ModelsISMES Publication

for theNo. 33,

Study ofBergamo,

Lauretta, E. and Castoldi, A.,Nuclear Reactor ContainmentItaly, 1968.

"DynamicBuilding,"

ModelsReport,

of PECBergamo ,

Tests onISHES

72. Castoldi, A., "New Techniques of Model Investigation of the SeismicBehavior of Large Structures," ISMES Publication No. 56, Bergamo,Italy, April 1973.

Castoldi, A. and Casirati, M., "Experimental TechniquesDynamic Analysis of Complex Structures," ~ PublicationBergamo, Italy, 1976.

for theNo. 74,

Baste11ani, A., Casto1di, A. and Ionita, H., "Numerical AnalysisCompared to Model Analysis for a Dam Subjected to Earthquakes,"ISMES Publication No. 83, Bergamo, Italy, Sept. 1976.

75. Baglietto, E., Casirati, M., Castoldi, A., Miranda, F. andSammartino, R., "Mathematical and Structural Models of Zarate-BrazoLargo Bridges," ISMES Publication No. 85, Bergamo, Italy, Sept.1976.

76. Borges, F. J. and Pereira, J., "Dynamic Model Studies for DesigningConcrete Structures,"!£!, ~-~, Models for Concrete Structures,1970.

233

References

Borges, J. F., "Dynamic StructuralReport, IABSE 7th Congress, 1964.

Studies Models," Finalon

18. Borges, F. J. and Ravara, A., "Structural Behavior of PanelStructures under Earthquake Actions," .Proceedings, RILEM Symposiumof the Effects of Repeated Loading of Materials and Structures,Mexico, 1966.

19. Bostjancic, J., "Model Materials Suitable for Dynamic Tests ofModels in the Plastic Range," Preprints, Vol. No.9, 6th WorldConference on Earthquake Engineering, New Dehl1, India, Jan. 1977.

80. Mihai, C., et a1., "On the Static and Seismic Behavior of a Struc-tural Mbde1 of an Industrial Storied Hall," Preprints, Vol. 9, 6thWorld Conference on Earthquake Engineering, New Deh1i, India, Jan.1977.

81. Barkov, Y. V. and Glina, Y. V., "Theoretical and ExperimentalInvestigations of Precast and Monolithic Frameless Buildings onLarge-Scale Reinforced Concrete Models," Proce~din5s, 5th WorldConference on Earthquake Engineering, Rome, Italy, June 1973.

82. Shaishmelashvili, V. N. and Edisherashvili, N. A., "ExperimentalStudies of Dynamic Characteristics of Multy-Story Steel FrameBuildings Large-Scale Models with Difference Vertical Bracings,"Preprints, 5th World Conference on Earthquake Engineering, Rome,Italy, June 1973.

83. Irwin, A. W., "Static and DynamicStructure," The Institution of CivilPaper No. 7486, April 1972.

Hodel Shear Wall

Proceedings, 51,Tests onEngineers,

a

Berriaud, C. and Tigeot, Y., "ParaseismicStructures," Closed~, 3, 6, 1973.

Testing or Model

Okada, H., Takeda, T., Yoshiaka, K., Omote, Y. and Nakagawa, K.,"Experiment and Research on the Response of Steel Model StructuresSubjected to Impact Horizontal Loading and to SimulatedEarthquakes, Proceeding~, 5th World Conference on EarthquakeEngineering, Rome, Italy, June 1973.

Kato, B. et. a1., "Dynamic Collapse Tests of Steel StructuralModels," Preprints, 5th World Conference on Earthquake Engineering,Rome, Italy, 1973.

234

References

Suzuki, T. et a1., "Experimental Study on PCRV-Support SructuresUnder Simulated Earthquake Motion," Preprints, 2nd InternationalConference on Structural Mechanics in Reactor Technology, Vol. 4.

88. Takeda, T. and Yamaguchi, T., "Dynamic Hodel Test and Analysis forPrestressed Concrete Containment Vessel," Report of the TechnicalResearch Institute, Ohbayashi-Gumi, Ltd., 6, Ohbayashi-Gumi, Ltd.,Tokyo, 1972.

89. Bridgman, P. W., Dimensional Analysis, Yale University Press, 1920,2nd Edition, 1931.

90. Murphy, G.,1950.

Similitude !a Engineering, Ronald Press, New York,

91. TheQ!:Y 2! Models, Wiley,

92. Huntley, H. E., Dimensional Analysis, McDonald, London,York, 1961.

Dover, New

Sedov, L. I.,TranslationYork, 1959.

94. Birkhoff, G., Hydrodynamics:! ~ ~ Logic,Similitude, Princeton University Press, 1950, 1960.

Fact and

95. Ipsen, D. C., Units, DimensionsMcGraw-Hill, NeWYOrk, 1960.

and

Hudson, D. E., "Scale-Model Principles,"V_~bration Handbook, McGraw-Hill, 1967.

27,Chapter Shock and-

Pankhurst, R. C., Dimensional Analysis ~~ Scale Factors, Reinhold,New York, 1964.

Skoglund, V. Y., Similitude, Theory ~ Applications, InternationalTextbook Company, 1967.

Buckingham, E.,1914.

"On Physically Similar Systems," ~. Review 4,

235

References

Rayleigh, Lord, "The Principles of Similitude," Nature 95,Preprint in Scientific Papers 6, Dover, New York, 1964.

1915,

Ashley, H., "General Considerations on Scaling," National Academy.2f Engineering Workshop.Q!! Simulation.2f Earthquake Effects .Q!!

Structures, Proceedings, San Francisco, Ca., Sept. 1973,

Goodier, J. N. and Thomson, W. T., "Application ofPrinciples to Structural Models," NACA, Technical NoteJuly 1944.

SimilarityNo. 933,

Rocha, H., "DimensionnementAnnales de 1'I.T.B.P., 1952.

Experimental des Constructions,"

Borges, J. F., "Statistical Theories of Structural Similitude,"RILEH international Colloquium on Models of Structures, Madrid,June 1959.

Beaujoint, N., "Similitude and Theory of Models," Bulletin RILEMNo.7, June 1960.

Fumaga11i, E., "Materials for Scale Models and Devices of Loading,"Bulletin RILEM No.8, Sept. 1960.

Roll, F., "Materials for StructuralVol 94, ST 6, June 1968.

Models," Proceedings, ASCE,

108. Mirza, M. S., White, R. N., Roll, F. and Batchelor,"Materials for Dircet and Indirect StructuralState-of-the-Art Report on Structural Concrete Models,M.S. Mirza, Department of Civil Engineering, McGillMontreal, October 1972.

B. de V.,

Models,"edited by

University,

Mirza, M.S., White, R. N., and Roll, F., "Materials forModels," Proceedings, ACI Symposium on Models ofStructures, Dallas, March 1972.

StructuralConcrete

110. Carpenter, J. E., Roll, F., and Zelman, M. I., "Techniques andMaterials for Structural Models," Models for Concrete Structure~,Special Publication No. 24, ACI, 1970.

Zelman, M. I., Heidebrecht, A. C., Tso, W. K. and Johnston, W. A.,"Practical Problems and Costs of Fabricating Multi-Story Models,"Models for Concr~te StructW'es, Special Publication No. 24, ACI,1970.

236

References

112. ModelingVol. 79,

Ferrito, J. M., "An Evaluation of the Accuracy of Material HodelRepresentation of Reinforced Concrete, " ~ ~ES~ Spring Meeting,Paper No. A-4, San Francisco, California, May 1973.

114. Fuss, D. S., "Mix Design for Small-Scale ModelsStructures," Technical Report ~, Naval CivilLaboratory, Port Hueneme, California, Feb. 1968.

of ConcreteEngineering

Johnson, R. P., "Strength Tests on Scaled-Down Concretes Suitablefor Mbdels, With a Note on Mix Design," ~gazine of Con~re_teResearch, Vol. 14, No. 40, March 1962.

Tsui, S. H. and ~rza, M. S., "ModelStructural Concrete Series, No. 23, McGillNovember 1969.

Hicroconcrete

Un1ver1sty,Mixes,"

Montreal,

Burgrabe, A. H., "Hikrobeton fuer Hode11statische Untersuchungen,"Berichte des Institutes fuer Hode11statik der UniversitaetStuttgart, Heft Mr. 1, 1972.

Maisel, E., "HikrobetonBerichte des institutesStuttgart, 1979.

fuerfuer

modelstatische Untersuchungen II,"Hodellstatik der Universitaet

Steffens, K., "Entwicklung eines Kunstharzmoertels zur Nachbildungdes Werkstoffes Beton bet Hodellversuchen fuer Stahlbeton-tragwerke," Lehrstuhl fuer Hassivbau, TU Hannover.

120. Sabnis, G. M. and White, R. N., "A Gypsum MortarMode1s,"!Q! Journal, Vol. 64, No. 11, Nove. 1976.

tor Small-Scale

Gypsum Mortars,"White, R. N. and Sabnis, G. H., "Size Effects inJournal of Materials, V. 3, No.1, March 1968.

122. Ferrito, J., "Dynamic Tests of Model Concrete."R-650, Naval Civil Engineering Laboratory,California, Nov. 1969.

TechnicalPort

ReportHueneme,

237

References

Sabnis, G. M., Mirza, S. M., "Size Effects in Model Concretes?,"ASCE Journ~l of the Structural Division, June 1979.

123.

Litle, W. A. and Paparoni, M., "Size Effects in Small-Scale Modelsof Reinforced Concrete Beams," ACI Journal, Vol. 63, No. 11,Nov. 1966. -~-

Wang, P. T., Shah, S. P. and Norman, A. E., "Stress-Strain Curvesof Normal and Lightweight Concrete in Compression," !£! Journal,Proceedings, Vol. 75, No. 11, Title No. 75-62, Nov. 1978,

pp.603-611.

125.

Brock, G., "Concrete: Complete Stress-Strain Curves," En~ineering(London), Vol. 133, No. 5011, May 1962, p. 602.

126.

Barnard, P. R., "Researches into the Complete Stress-Strain Curvefor Concrete," Magazine of 9~ncrete Research, (London), Vol. 16,No. 49, Dec. 1969, pp. 203-210.

Strain RateMo. 5557,

ConstantVol. 214,

"Stiff(London)t

Turner, P. W. and P. R. Barnard ,

Testing Machine," !h! EngineerJuly 1962, pp. 146-148.

"Strength and CompleteConcrete Tested in Uniaxial

Conditions," Materials and(Paris), Vol. 5, No. "3O,'

Sangha, C. H. and Dhir, R. K.,Stress-Strain" Relationships forCompression Onder Different TestStructure~/Research !!!£ TestingNov.-Dec. 1972, pp. 361-370.

Popovics, S. and Sandor, "A Review of Stress-Strain Relationshipfor Concrete," ACI Journal, Proceedings, Vol. 67, No.3, Mar. 1970,pp. 2113-2118. - -

130.

Kaar, P. H., Hanson, N. W. and Capell, H. T., "Stress-StrainCharacteristic or High Strength Concrete," Douglas McHenryInternational Symposium on Concrete and Concrete Structures, Sp-55,ACI, Detroit, 1978, pp. 161-185.

131.

Sinha, B. P., Gerstle, K. H. and Tulin, L. G., "Stress-Strain Rela-tions tor Concrete Under Cyclic Loading," ACI Journal, Vol. 61,No.2, Feb. 1964. -

132.

238

References

Ramsley, D. and McHenry, D., "Stress-Strain Curves forStrained Beyond the Ultimate Load," Laboratory ReportU.S. Interior Department, Bureau of Reclamation,March 1947.

ConcreteNo. SP-12,

Denver,

Hughes, B. P. and Chapman, G. P., "The complete Stress-Strain Curvefor Concrete in Direct Tension," Bulletin RILEH, No. 30,March 1966.

Rusch, H., "Physikalische Fragen der Betonpruefung,"-~, Vol. 12, No.1, 1959.

Zement - Kalk

Rusch, H.,StructuralJuly 1972.

"Research Toward a General Flexural Theory forConcrete,"!£! Journal, Proceedings, Vol. 32, No.1,

Raphael, J. M., "Big Tujunga DamConcrete in Dam," Structural ResearchCalifornia, Berkeley, June 1975.

Strength andLaboratory,

ElasticityUniversity

oror

Raphael, J. M., "The Nature of Mass ConcreteMcHenry International Symposium on ConcreteStructures, ill Publication ~-.22, Detroi t , 1978.

in Dams, It Douglasand Concrete

139. " Recomended Practice for Evaluation of Compression Test Results of

Concrete," !Q! Committee~, ACI, Detroit, 1965.

Mirza, S. A., Hatzinikolas, M. and MacGreor, J. G., "StatisticalDescription of Strength of Concrete," Journal 2r ~ Structural Di-vision~, June 1979.

141. Jones, P. G. and Richart, F. E., "The Effect of Testing Speed onStrength and Elastical Properties of Concrete," ProQeedings~,Vol. 36, Part II, 1936, pp. 380-391.

Hatano, T. and Tsutsumi, H., "Dynamic Compression and Failure ofConcrete Under Earthquake Load," Technical Report £-22Qi, TechnicalLaboratory of the Central Research Institute of the Electric PowerIndustry, Tokyo, Sept. 1959.

143. 1, 3rd Ed., AppliedOrchard, D. F., "Concrete Technology," Vol.Science Publishers Ltd., June 1979.

239

References

144.

Staffier, S. R. and Sozen, M. A., "Effect of Strain Rate on YieldStress of Model Reinforcement," University of Illinois, CivilEngineering Studies, Structural Research Series No. 415, Urbana,

February 1975.

Sabnis, G. M. and White, R. H., "Small Scale Models ot ConcreteStructures Subjected to Dynamic Loads," Preprints, 6th WorldConference on Earthquake Engineering, Vol. 9, Hew Delhi, India,

Jan. 1977.

Frames toNo. 108,

Hayerjak, R. J., "A Study of the Resistance of ModelDynamic Lateral Load," University of Illinois Publication

Aug. 1955.

150.

151.

Strain and Temperature on. !p;plie~ ~chanic~, Dec.152. 2!.

153.

Test of Mild Steel,"TensionRichards, c. W., "Size Effect in the

~oceedings, ASTM, 1954.154.

240

191tj:.

No.7, Paris, June 19bO.

References

Richards, C. W., "Effect or Size on theBeams," Proceedings, ASTH, 1958.

Yielding of Mild Steel

Zohrei, H., "Cyclic Stress-Strain Behavior of A36Engineering Thesis, Civil Engineering Department,University, Stanford, California, Dec. 1978.

Steel,"Stanford

Hayden, H. W., Moffatt, W. G. and Wulff, J., ~Properties .2f. Materials, Vol. III, "MechanicalWilley & Sons, Inc. New York, London, Sydney, 1965

158. Dove, R. C. and Adams, P. H.,Motion Measurement, CharlesOhio, 1964.

Sabnis, G. M., "Instrumentation in Structural Models,.State-=-of-the-Art Report on Structural Concrete Models, edited byM. S. Mirza, Department of Civil Engineering, McGill University,Montreal, Oct. 1972.

160. Mills, R. S. and Krawinkler, H., "The Use of Minicomputers for Con-trol and Data Handling in Dynamic Tests," Proceedings, Internatio-nal Instrument Society of America, Anaheim, California, May 1979.

Selander, C. E. and Carpenter, L. R., "Application or theMinicomputer in Measurement, Analysis and Control or StructuralTesting by BUREC," Preprint No. 295O, ASCE Convention, SanFrancisco, Oct. 1977 .

Ives, K. D., "Considerations tor Instrumentation ot Typical DynamicTests," Experimental Mechanics, 13, May 1973.

163. "Earthquake Environment Simulation," Final Report and Proceedingsof a Workshop on Simulation of Earthquake Effects on Structures, inSan Francisco, Sept. 1973, published by National Academy ofEngineering, 1974.

164. Penzien, J. Bouwkamp, J. G., Clough, R. W. and Rea, D.,"Feasibility Study of Large-Scale Earthquake Facility," EERC ReportNo. 67-1, Berkeley, California, 1967.

165. Stephen, R. H., Bouwkamp, J. G., Clough, R. W. and Penzien, J.,"Structural Dynamics Testing Facilities at the University ofCalifornia, Berkeley," EERC Report No. 69-8, Berkeley, California,1969.

241

References

Rea, D. and Penzien, J., "Dynamic Response or a 20 x 20-rt ShakingTable," Paper No. 180, Proceedings, 5th World Conrerence onEarthquake Engineering, Rome, Italy, June 1973.

Takahashi, Y., Rea, D. and Abedi-Hayati, S., "Effects ofSpecimen Reaction Loads of Shaking Tables," Preprints, 5thConference on Earthquake Engineering, Rome, Italy, June 1973.

TestWorld

Lauretta, E. and Castoldi, A., "Earthquake Simulation by a ShakeTable," 4th World Conference on Earthquake Engineering, Santiago,Chile, 1969.

Tsutsumi, H., "Vibration Research in CRISPI by Means ot ShakingTable, Some Recent Earthquake Engineering Research and Practice inJapan, Japanese National Committee, International Assn. tor

Earthquake Engineering, Tokyo, May 1973.

170. Particular

Damping,Lazan, B. J., "Energy Dissipation in Structures, withReference to Material Dumping," Colloquium on StructuralASHE, Atlantic City, N.Y., Dec. 1959.

111. Sherby, O. D., "Anelastic Properties of Solids," DepartmentMaterial Science, Stanford University, California, 1973.

or

Manual .Q!l ~ ,9%018 Fatigue Testing, ASTH STP 465, ASTM, 1969.

173. Richards, C. W., EngineeringBelmont, California,1961.~

Material Brooks/Cole,Science,

174. Jacobsen, L. S., "Damping in Composite Structures," Proceedings,2nd World Conference on Earthquake Engineering, Tokyo, Japal1,1-960.

175. Internal Friction, Damping, and Cyclic Plasticity, ""InternalFriction, Damping, and Cyclic Plasticity," ASTH Symposium, Chicago,June 1964, Special Technical Publication No. 378, ASTH, 1964.

176. Kircher, C. A., "Ambient and Forced Vibration Analysis or FullScale Structures," John A. Blume Earthquake Engineering CenterReport No. 27, Stanford University, No. 1977.

177. ~ Metals Handbook, Vol. 1, ASH, 1973.

242

References

!!!2r ~igest, Engineering Alloys Digest, Inc., Upper Montclair, New

Jersey.

"Standards Handbook, Wrought Copper and Copper Alloy Mill Products,Part 2--Alloy Data," Copper Development Association Inc., N.Y.,1973.

Institute ofMassachusettsCrandall, S., ed., Random Vibrations,Technology Press, 1958. --

~ SpectralNewland, D., ~Analysis, Longman,1975.

of ArtificialDiv., Vol. 90, ~1,

Housner, G. and P. Jennings, "GenerationEarthquakes," Proceedings, ASCE, Engr. Mech.

Feb. 1964.

Histories and ResponseDiY., Vol. 100, EM4,

Scanlan, R. and Sachs, K., "Earthquake TimeSpectra," Proceedings, ASCE, Engr. Mech.

Aug. 1974.

Matins for Design Purposes,"Div., Vol. 98, EH2, April 1972.

Tsai, H., "Spectrum--Compatible~oceedings, ASCE, Engr. Mech.

184.

Steel FrameNo. 75-36,

Tang. D. T., "Earthquake Simulator Study of aStructure," Vol. II: "Analytical Results," EERC ReportUniversity of California, Berkeley, California, 1975.

Popov, E. P., Bertero, V. V. and Krawinkler, H., "Cyclic Behaviorof Three R. C. Flexural Members with High Shear," Report~. EERQ1£-2, Earthquake Engineering Research Center, CollegeEngineering, University of California, Berkeley, California,

1972.

ofOct.

14, "Concrete and Mineral187.

Aggregates"

Popovics, S., "A Numerical ApproachCurve of Concrete", University of~search, Vol. 3, 1973.

188.

243

Rererences

Pirotin, S. D. and East, G. H. Jr., "Large Deflections, Elastic--Plastic Response of Piping: Experiment, Analysis andApplication", Transactions of the 4th International Conference onStructural Mechanics in Reactor Technology, vol. F, Paper F3/1, SanFrancisco, California, 1977.

!!!.

Almuti, A. M., "Post-Elastic Response or Mild Steel Beams to Staticand Dynamic Loading", University or Michigan, Civil EngineeringDepartment.

Niwa, A. and Clough, R. W., "Shaking Table Research on Concrete DamModels", EERC Report No. 80-05, University of California, Berkeley,California, Sept. 1980.

Kinoshita, K. and Kushida H., "Experimental Study on VibrationalCharacteristics of The Structures with Embeded Foundations",Proceedings, 5th World Conference on Earthquake Engineering, Rome,Italy, June 1973.

244

Append1x A

APPENDIX A

CONTROL OF MICROCONCRETE STRENGTH PROPERTIES

This appendix presents a summary of results of an experimental study

throughcontrolledwhose strength propertiesmicroconcretes wereon

additives, and through aggregatechemicaldifferent mix ingredients,

The studyresulting in smooth and moisture sealed aggregate.treatment

the results are reproduced was performed at the Institute torfrom which

118) .Model Mechanics at the University of Stuttgart, W. Germany (Ref.

The results are ordered withThe summary is presented in Table 1.2.

compressive stength f' for each specimen age. The compressivec

obtained from tests on erismatic specimens and the tensile

declining

strength 1e

The modulus of elasticity is1s obtained from flexural tests.strength

based on initial specimen stiffness.

Each specimen series is characterized by code designations providing

ingredients, andage, mix proportions,information the specimenon

The key to the code is given in Table A.1, and theaggregate treatment.

0~(/)(/)

~w0~zwu~~~

SIEVE APERTURES mm

Figure 1.1 Sie.e Lines ot aggrecates Used

245

Appendix A

Table A.1

Note:1) Aggregate/Cement Ratio is constant for all the specimens

and equals A/C = 22) The largest aggregate size is 2 mm unless specified differently3) Compression tests were performed on prismatic specimens of

width to height ratio of 1:44) Tensile strength was obtained from bending tests5) Aggregate sieve lines are given in Fig. A.1 and are identified

in code designation C6) The code key consists of code designations ABCDE

CodeDesignation

A

(days)Age of Tested Specimens

7142128424768

123456a6b

W/C RatioCode

DesignationB

0.550.600.650.700.750.500.610.67

123456a6b60

CodeDesignation

CAggrega te Type

2345

6a

6b

SandLight aggregate (inflated shist) not sievedLight aggregate; sieve lines 2 and 3aLight aggregate (fraction 1), sand (frs. 2,3,4)Light aggregate (fr. 1), sand (frs. 2,3),river sand (fr. 4)No frs. 1 and 2, sand or mixture of light aggregateand sand (fr. 3), sand or light aggregate (fr. 4)Light aggregate (fr. 1), light aggregate or

sand (fr. 2), sand (frs. 3,4)Light aggregate (frs. 1-4), sand (fr. 5; 2-3 mm)

60

246

Appendix

ContinuationTable A.

CodeDesignation

CAggregate Type

6d6e

6t

Sand (frs. 1,2), light aggregate (frs. 3,4)Light aggregate (fr.1), blast furnace clincker

(frs.2,3,4)Light aggregate (frs. 1,2), light aggregate or blastfurnace clincker (fr. 3), blast furnace clincker (fr. 4)

CodeDesignation

DAggregate Treatement

016a6b

+ 108.4 g/kg cementNon-treatedCoated with silicon resin solutionAs 1 but with 216.8 g/kg cementAs 1 but with 54.2 g/kg cement

CodeDesignation

ECement type, additives

0 Portland cement, no additivesHydro-cement, no additivesHydro-cement with air entrainment:2

2a2b202d2e2t

92 mm3/kg cement110 1!ID~/kg cement115 D113/kg cement

130 1IID3/kg cement

55 mm3/kg cement

30 mm /kg cement

with a minimal amount of oil coatingon aggregate fractions 2,3,4 :

55 mm3/kg cement80 mm3/kg cement

2g2h3IIlIalibIIclid5

Hydro-cement with retarderHydro-cement with workability i~prOVing additives

50 mm liguefier Ikg cement70 mm~ liquefier Ikg cement90 mm liquefier Ikg cement

110 mm3 liquefier Ikg cement

With oil coated aggregate

+ resin used for impregnation of concrete formework;in W. Germany known under the commercial name of Pluvoil

247

Appendix A

249

Appendix B

APPENDIX B

HYSTERESIS LOOPS OF REINFORCED MICROCONCRETE BEAMS

This appendix presents load-displacement and moment-average curva-

ture response curves of beams tested in the study of the cycling frequen-

oy effeots (Section 8.2.6).

Table B.1 summarizes the results ot this study in terms or relative

The load valuepeak load at each cycle tor each ot the specimens tested.

used for normalizing of the results was taken as the average peak load of

ot the beams tested at a frequency of 2 Hzthe first excurssion

and curvatures are the averagenormalizing values tor the displaoements

of the peak values for all the beams at the first amplitude. The speci-

identified in the table and in the tigures by a set ot threemens are

digits, the first of which denotes the testing frequency (0.0025 Hz,

10 Hz),and the second denotes the specimen number at a frequency,

the third the beam number in the specimen.

250

-.~~.-4

~

~

.

.

~~

i.I.

-=..

'iN

......~Ii;'0

i

~w

~

gw

i'"..

J0t1

g

':.J.;

I'"~

~

~

~..

p;

...

~004~5

I

~ .~i~t.) .~O~ZrI)

. .

ef

I=~,

B£

=a.,

.;Po~Q

~~

~'"

;;'"

~...

""

..

;:.

~

~..

I

;:...

t..

~

;:,

~

fr.

D;o

.-.-

~ ~ 2:0 G\ ~

. . .- ~

.0 I'-I'- It\~ C:

-N..~

.. \0t- .. ~t- ~ ~. . ,

~ ;: 'II :.to: co. ~ ~

~

-eto:

ca-

t-;

~0

~~

00

c;0

-.-

~-

~.(\I

N.-.

U\-~

MO-O-In ~ ~ ~ ~

, , .

.. V\ -t- 00 mt- t- t-

~ §

...\Q'D;

000

~0

.N.

&t\ 0\- ~0\ e

, .

0 .0m 00- 0-. .

~~

~'"'

000.0

C0'

~

~~

~~.,..

"' I "'\G '" ~'"

0: ~O;

~a>.

f":N

e.

~oGt- .

It\0

~

Go~

to::

- - N - 1 fW\O fW\ N oc fW\ OCIt\

0: e ~ ~ eo

w::.

~:o:>w

QzC .~t;

#.

g~

\0N'-0\0

..,e-':1~

~Il\0..t-O

NIO1--=0. ,

".0

~~

II\~

~8;

~8. ....

NN

~S;

~~0

lSl

V\c0:

;.~

.-.N

R;0.

0-0.-

0-.0-0-II' C"\ \Q II'O-O-~~. . ,

~~

0'.-0

t- ~ t-... 0 t-0\ 0\ ~- .

r- 0# .r- c

~ ~ 20\ 0\ 0;. .

\D\Dco.

,1; ~~ ~

-.C\4

..0:

..~~,

#' ~ 0,.., 0 0\0\ 0\ ~. .

N....

0\ In0 ~0 0\

. .~

0- V\V\ 0-0- ~. -

~

0- \Q- to.

~ ~

to. 0In In~ ~

N

.~N

~~

\D-~

'"to-

~

C\I.'"

~

M-.~

\Da-m

N

~

~I~~

-to-o:

In

~

~

.-&

In..~

19\.0to;

"' I ~O ;' ::~

Oln.In0\0, .

-=-fO'\~-0\0. .

00-

o:~

t- In "' I . ~-t-lne0\ e e e

. . '"

NV\O\N~O, .

~:I~ .-<>>k3

~~-< .~~

11\0\ 1 '" o. ~

0\0 ~

NOO.~O

0\0\000\0

~~

..~

~~

~-.

-.

,.,

\1\

~

InN~

-~ N~ ~

M t-o- ...~ 0'.

, .

-~

=e,

-~

0-N~

0\ .c 0N C"1 .-0 0 0

. . .- ~

0\ ~ 00 0 ..0\ 0\ 0

. . ...

...00\

..0~

~

~N

~...

to. ...., N

~ ~- ~

-It\0:

~ t-o ~0\ ~, .

f'" 11\ ..= - == ~ =, , ,

\Q\Q

cc,

-D-D

~

~~

t- ~ t-- m -~ ~ ~

ff'\

.-0:

.~f".

N

~~

.....Q\.

-e~

oD 0\Il' ~0\ ~. -

.., .., I N" 0 .. "'..,

0\ ~ ~O. , ..

~0:

~...,

-0.~

~~

0-\D0-

...I¥\

~

1- 1 0.00 - 0.-~ ID.~

~0:

-f"\~

~-0.

'"'~

V\-~

~~>>M

&1ZC .M'"~,!11

N-~~.-

OV\#N0\0

~

I;~0\0. .

\01\:~N~C

om0\0

~.g;~

~-~~

...~

~8. .

ON

~~

1-.0

~o.

'"

!e>-~c

..-N

--

~0

Z

.Z

Q.

zoX

~~

Z'0

IM0

an

~z~ot)c-ot)..,

.

#

.~f

'"I0';c-'"N

0.Z..

AJ)pend1x B

Appendix B

~C\I~Q..°

~~tJ0

-J

"t)q"

.~~

~0

~

1.0 -...:x:;~«\10

~

--

~E:~~~"-'"'t)E:~

~

0.0\

'-

"'\, .'1

~

\..11- ;:I'~~

-f:--""'"

f-.'} CYCN .,.- - - Z"H DiJploc.w

~r~ ~-/.0

I I II I ~ It I t I

5 0 5

Normalized Average Curvature

Figure B.1 Moralized Load-Displace_nt aoo MoMnt Curvature Response or Beam Tested

ul.der Freq...enay 0.0025 Hz (Spec18n 1. 1. 1 )

252

-2.0 - ".0 0.0 1.0 2.0

Appendix B

I===~s~! ~ d1.0

p~C\I~Q..a

~~t)()

..,J

"t)'"

.~-t)

~()

~

I-s' } Cycle at 0 - - - ""ad Disploc--'

.- - - - -.J-rd A,.",'N*/.0

2.0-2.0 - ".0 0.0 f.ONormalize.d Displacement cJ/ cJ:v.

i~~ ~3rpf.O

~--=== ~~

:x:~(\10

~/'

,~

0.0

1.0- I-at } c,c,..,. - - - 2-84 Dis,,---

. - - - - - .t-rd A8pi1"fwft

..1 ~INormalized Average Curvature "fV ~Qv.

Figure B.2 Nor8B11zed Load-Displacement and Moment Curvature Response of Beam Tested

under Frequency 0.0025 Hz (Specimen 1.1.2)

253

o.0

-c:Q)E

~~Q).-~0

E.

Appendix B

~:=~~~~ t ~ d/.0

p

--I;-

~C\I~QO

~;

~~

~t:J0

-J

~Q./.~-t:J

~0

~

-1.0- - '-a'} CY~1e at.- - - 2"M Ojs,,--'

",",I A.j~

L L- I I I - ~ - I ~ I,.. 1_-;I;; J

-2.0 -".0 0.0 1.0 2.0Normalized Displacement d/ cr:v.

~ " "cJ

' I

4)..QUP1.0...:r:.>,<\10

~

~

-c:;QJE

~

~"-~0E.,

~

0.0

I-sf- - - 2-.d.t-rd-1.0

C1CM ., 0

OisplOc.-tA.,,'Iwde

l~ilt~t I I~5 0 5

...t .b.. I~ 'f.1av;

FigUre B.3 Normalized Load-Displacement and Moment Curvature Response or Beam Tested

under Frequency 0.0025 Hz (SpeciBen 1.2.1)

254

/;;'

o.0

Appendix B

jcf,i:=:~s3itL-

.--~

"

""I

,(,...~ 4

If ".I~ ,~I/'.

L,.,...

- /.0 '-at }c,c,. 8f.. - - - D;s,'.~Jo..- ~

I I I I I : I I I IJ-2.0 - ".0 0.0 1.0 2.0

Normalized Displac,ement cr/ cf:v.

1.0...:t:;~C\I~

~

"

~

!1J1

0.0


Figure B.4 Normalized Load-Displace88nt and Ho8ent Curvature Response of Be.. Tested

under Frequency 0.0025 Hz (Spec188n 1.2.2)

255

,--.I- - - - -It'

Appendix B

I===~s~ ! ~ cf ~

::; "

,--- v:

«,',.

p

~

-,,,

'1/1/

,.I

...

-,"

--

~

----~ - -'-.' } CI~"". - - - ~.I DI",-,--,

-,",I A~

l-1 I 1 I ~ - I .1- I ~I ;:~

-2.0 - f.O 0.0 1.0 2.0Normalized Displacement cJ/ cJ:v.

1.0 --~C\I~

~

~

i- - - - -'-

::1-~E:

~"'t>

~"---0

e

~

0.0

ff ,,' /,./,

~

- 1.0

-

5 0 5

Normalized Average Curvarure

Flsure 8.5 Mormalized Load-DlsplaC888nt and Ho88nt CurYature Response ot 98.. Tested

under Frequency 2 HZ (gp.c18eD 2.1.1)

256

, 11

-J;7/

Appendix B

~:~~~3 t ~ cfI"~C-':=-=Z

/]1.0

p

~

~C\I~~

~

-1,1-...

~tJQ

...J

"t)QJ

.~-tJ

~Q

~

//

'"'t /'~,"/t=: - .- -e,

- '-st

---2-"

~rd- /.0Cyc" 0' 0Oi$"OC--'A,.,'i~

L-__L I 1 I _&- I ~I" I-;;~ J-2.0 -foO 0.0 f.O 2.0

Normalized Displacement d/ d:v.

/M

t.O-4j.qzt. p

~...~>'C\lC)

~

--"/'--,

~QJE

~

~

~'---t)

E~

0.0

Cycl~ at GOisplGC--'A,.plifu.

'-at- - - Z-.d,J-,d1.0

~ T


Figure B.6 lor8alized Load-Displacement and Moment CUrvature Response of Beam Tested

under Frequency 2 Hz (Specimen 2.1.2)

251

o.0

Appendix B

1.0...:x:~<\10

~

~~~"'tJ

~'--..;;0E

~~

0.0

- /.0


Figure B.7 Mo1'811zed Load-Displace_nt and MoMnt Curvature Reaponse or Be- Tested

under Frequency 2 Hz (Speo1-.n 2.2.1)

258

-2.0 -".0 0.0 1.0 2.0

Appendix B

1==:~~s3 ! ~ cJ1.0 ~ ~ry-- -- - - .

- .

-; .p~

C\I~Qt»

~

~

-~t)0

-J"tJQJ

.~~

~0

~

"'1'/

./-.".

4---=~- /.0

Normalized Displacement d/ d~v.

/~

1.0-~- -il

'., ""1, I,

",II/

',/--

4~ pN

:C;>,C\lc

~

~

~

-~

~

~q,E

~"t:J

~.-"0E,

~

0.0

',1 - -

.il --1'- - -- #.0 '-.st}Cyele of.

.- - - Z-.d Oi - - - - - - ~rd A8PiJlwde

5 () 5

Normalized Average CurvatureFigure B.8 Moralized Load-Dlsplaoe_nt and Ho_nt Curvature Response of Beall Tested

under Freqdency 2 Hz (Specimen 2.2.2)

259

0.,0

""/

I-st }C,eM ., 0- - - 2-.d Olsploc--'. - - - - - .5-rd Aap/,-w.

L- 1 I 1 I. I .1- I _1_--1

-2..0 -f.O 0.0 1.0 2.0

Appendix B

~

J:=:~~~:3 ! ~ cf1.0

p~C\I~Q.,°

~" ,..f ... c ~

~

;//4'/

"g()

.,.J

"2.~~

~()~

,,?...

'/I"'/-~--

-1.0

1.0 0--~---fit

:t-;):(\j~

~-~E~"'t)

~"-0E~

:<::

-,,-I0.0

,,

,,'/,/

/1

--- -- II:.c.=~::...;:::;;.tf~~ '-.'} CICIe.,. - - - 2"" Dj~".c-.r

.J-rd A.~1.0

L. ~. -, I J I ~ I II I I

5 0 5


Figure B.9 Moralized Load-Displac.-nt and I1oMnt Curvature Response of Be.. Tested

under Frequency 10 Hz (Spec18en 3.1.1)

260

o.0

I-a'} CycM".J - --2-" Di.~

-- - - - - .,.,.d A_".,.de

I I I I I ~ I I I _1_1-2.0 - 4.0 0.0 1.0 2.0

Appendix B

i;:=~~3! ~ cJ1.0 ..d~'~::.:~~.:] . .-

p~t\I~QO

~

-#

/"':... ;r

...,.

.,I~~"g()-J~"

.~""i5

~()

~

-1.0- - '-5t } C1~,.ota - - - 2-" DI~"a~--

,,",.d AI8p/I~

L---1- I I I -. - I~I- I-;;J~.. ~-2.0 -f.O 0.0 1.0 2.0

Normalized Displacement d/ d:v.

~~~ ~..-~~=:=..:::Ii-II-iZLP

~~--=- - -=-= ~1.0

...

:t:>,C\lo

~

/....../'

,...

..."1/,'

I.', ,}J-c:~E

~

~N"-~0

E

~:<::.

0.0

'-sf} C1C~ ata- - - 2-ad Displac_'.- - - - - .J-rd A,.plitv«-1.0

~


Figure 8.10 Mor8alized Load-Displacement and Moment Curvature Response of Beam Tested

under Frequency 10 Hz (Specl_n 3.1.2)

261

o.0

If

Appendix B

i:'L~ Jfij;=:=3 r

p1.0 ~..;.- - -'

..,

...:t)O"'0

~

/" ,,"/

I /,.."'~,

'1

]e~~QJ,..."-

~E,

~

(/0.0

ff-st } C,~" .,.

- - - 2-84 DI.,/oc--'~r4 AIY""'-*

-1.0

IIII .;. I I J I5 0 5

..1 ~1Normalized Average Curvature CfV ~av.

Figure B.11 Moralized Load-D1spla~nt and Mc.-nt CurTature Response or Be- Tested

under Frequency 10 Hz (Speci88n 3.2.1)

262

~ -2.0 - ".0 0.0 1.0 2.0

bJ_;-l

Appendix B

1=:=~~~3 t ~ cf

P1.0 -- -

~t\I~~

~

:,

'/~ ,, -...

///

'I'/

~t)()..oJ"t)4.1.~~

~(:)

~

,,' ", ,I" ;" ,/ ( ' "'/

,,' ,/(' " :/ "'/ /

I I '/I' ;!f "" " , "-, /, ' ~ -,'--=-:- -=-=-:J~.~ :~~~~~ ~..

L-' -~~ _I-1.0

1.0 ..:-=- - ~ ~'""'

j

J

~

=z;;~C\la

~

-If,

~e:~~'-0..0;

0

e:~

~

,0.0

,,,,

l ;;:, /I

,-.,} Cy~~.,. - - - 2-8d 01.,,---

-- - - - -.J-rd A.,""N*-1.0)

I I I t I; f I I I I5 0 5

Normalized Average Curvature ct\I$:w.Figure B.12 Nor8l1zed Load-Displace8nt anG Ho8nt Curvature Response or Beam Tested

under Frequency 10 Hz (Speo18en 3.2.2)

263

o.0

-2-0 - 4.0 0.0 1.0 2.0

- - '..'} C,e,..,. - - - ~N 01",---

~,.. ~

t I I I I : I I I I I

Documents

Department of Civil and Environmental Engineering Stanford ...rm315dh3494/TR50_Moncarz_Krawinkler.pdfThe research reported herein is part of the project "Scale Modeling and Testing