U

2\, q- q

SEISMIC DESIGN OF
UNRtr,INFORCED MASONRY
STRt]CTT]RES

by

Gregory Mark Klopp B.E.(Hons.)

A thesis submitted to the Faculty of Engineering at The University of Adelaide for

the Degree of Doctor of Philosophy-

Depaftment of Civil and Environmental Engineering,

The University of Adelaide.

January, 1996
CONTENTS

LIST OF'FIGURES v
LIST OF TABLES .
v111

ABSTRACT x

ACKNOWLEDGMENTS.................. xlll
I.INTRODUCTION.. .......1

2 LITERATURE REVIEW 7

2.1 Period Fonnulae 9

2.2 Full-Scale Buikling Tests t7

2.3 Dynarnic Loading Tests on Bricks V/alls and Structures 24

2.3.2 Out-of-Plane Tests 29

2.3.3 Sumrnary 30
2.4Data from an Unreinforced Masonry Building Subjected to
Earthquake Ground lt4otion 32
2.4. 1 Description of tlie B uilding ............... 32
2.4.2 Observed Behaviour .......... 33

2.4.3 Computational S tudies. 35

2.4.4 Conclusions...... 36

2-5 Brickwork Properties............ 37

2.5. 1 Axial Cornpressive Strength 37

2 -5 -2 Flexvral S trength 42
2.5.3 Shear Strength 45

2-5 -4 Bitxial S tress Behaviour 41

2.5.5 Stiflìress 49
2.6 Finite Elernent Modelling of Brlckwork 52
2.7 Earthquake Design Models for Brickwork 56

2. 8 Floor Flexibility/Stiffness 59

lt
 Contents

2.9 Appropriatc R,lor Unreinforced Masonry 61

3. FIELD TESTING 66

3.1 Inl.roducl.ion 66

3.2 Development ot Testin g Methodology .'.-... - -.-.. 61

3.2. I Sotrrce of Viblation.-.....-.... 67

3.2.2Data Collcction on Site 67

3.2.3 Digttisation ancl Filtering of the Data ...------ -----------70

3.2.4 Cot'wersion of the Data to the Frequency Domain -----------"""'7L

3.2.5 Examination of the Data 12

3.3 TesLing Progtam

3.3.1 Tlie Physics Builcìing Annex 12

3.3.2 -lhe En gineering B Lrilding Annex 73

3.3.3 General Testing Prograrn 73

3.4 Expected Fonn of Period Formula 74

3.5 Comparison with Perjod Fonnulae.. .-----.--"""""77

3.6Implications 90

4 DYNAMIC TESTS ON BRICK PANELS 94

4.1 Introduction..... 94

4.2DeveIopmenl. of Testing lr4ethodology......------- """""""""'95

4.2.I Laboratory Test Set-trp """96
4.2.2 Bnck Maso n ry Panels 98

ion.........-.
4.2.3 Instrumenta ""' 100
4.3 Testing Program ."""""'102
4.4 Resuls 103

4.5 Discussior-r of Results 108

4.6 Determination of ar-r Eft-ective Young's Modulus 111

4.7 Summary of Laboratory Tests """"'Ll4

5 MODELLING OF BUILDINGS........ --...-----.116

5.1 Introduction........- """"" 116

5.2 Response Spectrurn Analysis Details """"'-""'- 118

5.3 IMAGES3d Model Details. r20

5.4 Preliminary Analyses Results 124

5.4.1 Plate Element TYPo 124

5.4.2 Young's Modulus of Brickwork r25

Geornetry
5.4.3 Wall ----.----""""127
5.5 Modal Analyses Resuls ----.."""""'-129
5.6 Response Spectrum Analyses Results 132

5.6.1 2-Storey Commercial Building (EE2) 134

lll
 Contents

5.6.2 2-Storey Commercial Building (EE3) 135

5.6.3 2-Storey Cornmercial Building (EE4) 136

5.6.4 3-Storey School Buildirrg (CBC) ""'-'I31

5.6.5 2-Storey Social Club Building (IAC) """"""""" 138

5.6.6 3-Storey Commercial Builcling (LTI) """"""""" 139

5.6.7 2-Storey Commercial Building (NSC) 140

5.6.8 2-Storey Retail Building (STP) r42

5.6.9 5-Storey Universiry Building (OLW) r43
5.6.10 2-Stoley Apattrnent Building (KIDA) 145

5.6.11 2-Storey Apartment Building (KIDB) 145

5.7 Sumurary r46

6E,QUIVALE,NTSTATICFORCEANALYSISOFBUILDINGS r49
6. 1 Introduction......... r49
6.2CodeBased Analysis ""'149
6.3 Results of Static AnalYsis r52
6.3.1 Natural Periods r52
6.3.2 Base Shcar r52
6.3.3 Distribution of the Base Shear """""' 155

6.3.4 ConnecLiott Forces......-- 156

Etlècts
6.3.5 Out-of-Plane """"' 159
6.4 Summary of Code Base<l Analyses """""""""'164
6.5 Refined Code Based Analysis. """"' 165
168
7 SUMMARY AND CONCLUSIONS
7. 1 Surnmary......---.--- 168

7.3 Future Work t73

APPENDIX A - SAMPLING THEOREM........... .............T74
APPENDIX B - BUILDING DETAILS ..........175
185
APPENDIX C - REGRESSION ANALYSIS
189
APPENDD( D - TYPICAL ROOF LOAD CALCULATIONS
APPENDX E - COMPARISON OF ADE,LAIDE RESULTS TO
CALIFORNIAN RESULTS ............191
195
APPENDIX F - OVERTURNING AND UPLIFT CALCULATIONS
APPENDIX G - CALCULATION OF SHEAR AND BENDING
COMPONENTS IN LABORATORY WALL SPECIMENS 198

1V
LIST OF F'IGTiRtrS

Figure 2.3.1 Mengi and McNivcn test set-up 25

Figure 2.4.1Plan of the Gilroy Firehouse- 33

Figure 2.5.1 Orientation of bending for rcsults in Table 2.5-8- 45

Figure 2.6.1 Finite element subdivision 53

Figure 2.6.2 Finite eletnent details. 54

Figure 2.7 .I Energy path tbr a masonry building resisting seismic loads 56

Figure 2.9.1 General Structural lìesponse- 62

Figure 3.2.1 Eftect of accelerometer location on tecorded modes. 69

Figure 3.3.1 Physics Annex Results 73

Figure 3.4.1 Shear Deflection of a Beam 76

Figure 3.5.1 Concrete and Timber Floor System Connections to Walls. 78

Figure 3.5.2 Plot of Period versus Building Heigl-rt, h - All Data. 79

Figure 3.5.3 Plot of Period versus Building Heigl'rt, h - Concrete Floor

Systems 80

Figure 3.5.4 Plot of Period versus Building Height, h - Timber Floor

Systems. 80

Figure 3. 5.5 Plot of Period versus +

JD
Al1 Data. 81

h
Figure 3.5.6 Plot of Period versus - Concrete Floor Systems 81
JD
h
Figure 3.5.7 Plot of Per-iod versus Timber Floor Systems- 82
;u
Figure 3.5.8 Plot of Period versus Number of Stor-ies, N - All Data. ......................82
Figure 3.5.9 Plot of Period versus Number of Stories, N - Concrete Floor
Systems. 83

Figure 3.5.10 Plot of Period versus Number of Stories, N - Timber Floor

Systems. 83

Figure 3.5.11 Plot of Period versus h3la - AU Data. 84

Figure 3-5.lzPlot of Period versus h3la - Concrete Floor Systems 84

 List of Figures

3/o
Figure 3.5.13 Plot of Period versus h - Tirnber Floor Systerns. 85
1
Figure 3.5.14 Plot of Period versLìs l.rlo - All Data. 85
J,\
1
F'igure 3.5.15 Plot of Per-iod verstìs It3la - Concrete Floor Systems. ..............86
JA"
I
Figure 3.5.16 Plot of Period versus It3lo - Timber Floor Systems. 86
JA"
Figure 3.5.17 Plot of Periocl versus hJB - All Data. 87

Figure 3.5.18 Plot of Periocl versus hJB - Concrete Floor Systems. 8l

Fig ure 3.5.19 Plot Periocl versus hJB - Timber Floor Systems. 88

Figure 3.5.20 Plot of Period versus NJB t+16.4(f *fll - Atl Data.............88
\B D)]
Figure 3.5.21Plot of Period versus N B 1+16 -(+.*)] - Concrete
Floors 89

1+ 16. .(
11
+-
Figure 3.5.22 Plot of Period verslrs NJB - Timber
B D )l
89

Figure 4.1.1 Definition of Shear Stiftness 95

Figure 4.2.1 Shaking table test set up............. ----..-----------.---91

Figure 4.4.1 Tensile failure and rocking of wall panels.-'--.. ...-.--------...- 104

Figure 4.4.2Induce-d shear force versus in-plane displacement -'Walls 1, 2

and 3. ...........105
Figure 4.4.3 Induced shear force versus in-plane displacement - Walls 4, 5,
6 and 7............... ............106
Figure 4.4.4Induce-d shear force versus in-plane displacement - Walls 8, 14
and 15....._. ....107
Figure 4.4.5 Induced shear force vetsus in-plane displacemenr Walls 9, 10,
II,I2 and 13. ..-.---.--....'- 107

Figure 4.6-1 Mathematical models of the test specimens tL2

Figure 4.6-2 Compadson of Number of Elements. ...'---.--.... ----------.'..-- 113

Figure 4-63Effective Young's Modulus for wall specimens- --.....---'..- 114

Figure 5.1.1 Concrcte Floor to'Wall Connection Details-.---- ----..---------ll7
Figure 5.2.1 ASl 110.4 Design Response Spectrum- --......-- 119

Figure 5.4.1 Two Storey Apartment Building - Connection Force

Comparison : Single Wall versus Twin Wall. ----I29
Figure 5-5.1 Plot of the ratio of the results of the ambient vibration tests to
the results of the IMAGES3D analyses. r32
Figure 6.3.1 Plot of component acceleration versus relative height. 160

VI
 List of Figures

Figure 8.1 Plans of buildings EE2, EE3, and EE4. t76

Figure 8.2 Plan of building WARD """""""""L77
Figure 8.3 Plan of building CBC......... """"""' 178
Figure 8.4 Plan of building IAC.......... """"""'I19
Building 8.5 Plan of building LTI.......... .----.--"""":""""" 180

Figure 8.6 Plan of building NSC 181

Figure 8.7 Plan of building STP r82

Figure 8.8 Plan of building OLW 183

Figure 8.9 Plan of KIDA and KIDB 184

Figure C.1 Plot of data and regression line 185

Figure E-l Typical cantilever shear beam -.--'.""I92

Figure F.l Typical shaking table test specirnen- ---.-."""""' 195
Figure G.l Laboratory Wall Specirnen Number 4 199

vll
LIST OF TABLtr,S

Table 2.4.1 Measured Brick Properties frorn the Gilroy Firehouse. ..-....32
'Wall 34
Table 2.4.2 Surnmary of Norninal Stresses.

Table 2.5.1 Compressive Strength of Brick- - 37

Table 2.5.2Conpressive Strengtl'r of Mortar 38

Table 2.5.3 Compressive stfength of mortar compared to sand gradation 39

Table 2.5.4 Compressive Strength of Brickwoft- ---.---.-.-- 40

Table 2.5.5 Modulus of Rupture of Brick- 42

Table 2.5.6 Tensile Strengtl-r of Mortar.- 42

Table 2.5.7 Tensile Strength of Brickwotk- .---.-.--.-. 43

Table 2.5.8 Modulus of Rupture of Brickwork. 44

Table 2.5.9 Shear Strength of Brickwork. 47

Table 2.5.l0Internal fiiction Coefficient, m, of Brickwork 47

Table 2.5.11Friction coefhcients for the shear capacity of brickwork. 48

Table 2.5-12 Shear Strengths of brickwork with membtanes 48

Table 2.5.13 Young's Modulus of Clay Bricks 49

Table 2.5-14 Young's Modulus of 50

Table 2-5.15 Young's Modulus of Brickwork 51

Table 2.9.1 Values of tlie parameters of the bi-linear relation for the
response modification factor, R 65

Table 3.3.1 Results of ambient tests 75

Table 3.5.1 Deøils of Period Formulae Comparison-..-----.---..- 91

Table 4.3-1 Shaking Table Test Plogram---...----... 103

Table 4.5-l Calculated in-plane stiffness from laboratory tests- 108

Table 4.5.2 Compatison of Frequency of Excitation and Single or Double

Leaf on Shear Stiffness. ------.--...-..--. 109

Table 5-4-1 Two Storey commercial Building (F,F,2) - trffect of Horizontal

Plate Type on Modal Properties. -----125

vlll
 List of Tables

Table 5-4-2Two Storey Apartme¡t Building (KIDA) - Effect of Young's

Modulus of the unreinforcecl masonry walls on tlie modal frequencies- 126

Table 5.4.3 - Results for 110 mm Twin Element Model (KIDA)..... ....128
Table 5.5.1 - Results of Modal Analyses on Buildings 130

Table 5.5-2 - Cornparison of Experirnentally Determined Natural

Frequencies to those Detennined from Modal Analyses- 131

Table 5.6.1 Response Spectrurn Analysis Resuls : Building EE2 t34

Table 5.6.2 Response Spectrurn Analysis Results : Building EE3 136

Table 5.6.3 Response Spectrurn Analysis Results : Building EE4 r37

Table 5.6.4 Response Spectrurn Analysis Results : Building CBC 138

Table 5.6.5 Response Spectrurn Analysis Results : Building IAC r39

Table 5.6.6 Response Spectrurn Analysis Results : Building LTI 140

Table 5.6.7 Response Spectrurn Analysis Results : Building NSC 1,4r

Table 5.6.8 Response Spectrurn Analysis Results : Building STP.......-.. r42

Table 5.6.9 Response Spectrurn Analysis Results : Building OLW t44
Table 5.6.10 Response Spectrum Analysis Results : Building KIDA t45
Table 5.6.11Response Specrrum Analysis Results: Building KIDB t46
Table 6.3.1 Summary of base sliears by static and dynamic analyses. t54
Table 6.3.2 Storey Shear ResulS frorn static and dy¡amic analyses.- 156

Table 6.3-3 Summary of naximum connection forces t57

Table 6.3.4 Summary of Out-of-Plane Tensile Stresses for 4S1170.4 and
Response Spectrum Analyses. """"' 163

construction.--------
Table 8.1 Details of EE2,EE3, and EE4 --------."'-"I76
Table 8.2 Details of V/ARD constntctiorl----.--..-'..-- "'-"""'177
Table 8.3 Details of CBC construction' 178

Table 8.4 Details of IAC construction.- 179

Table 8.5 Details of LTI construction..-.....-..-..- -.-.."""""' 180

Table 8.6 Details of NSC construction- 181

Tabte 8.7 Details of STP construction. t82

Table 8.8 Details of OLW constrLrction. -.....---.-.. """"""" 183

Table 8.9 Details of KIDA and KIDB construction 184

Table E.1 Comparison of Adelaide to Berkeley Results 194

IX
ABSTRACT

Unreinforced masonry buildings have generally perfonned poorly in earthquake.s.

This thesis reports on a study into the behaviour and design of unrcinforced masonry
buildings when subjected to forces induced into the structure from earthquake
ground motion.

The study involved the monitoring of ambient vibrations in a number of unreinforced

masonry buildings in Adelaicle to identity their dynamic properties for use in later
analyses of the building's response to eatthquake induced forces. The dynamic
properties of the buildings, specilìcally the natural period, were then compared to
estimates of the dynamic properties given by formulae included in various earthquake
design codes. The suitability of these formulae for use in the design of unreinforced
masonry buildings for earthquake induced forces was then examined.

Shaking table tests were then conducted on fifteen unreinforced masonry wall
specimens to determine tl-re stiffness of the walls when subjected to dynamic
excitation. The tests were conducted to examine the variability of the stiffness of the
walls with variation in the excitation fiequency, compressive stress level, and size of
panel. The test results fonn the panels were then used in conjunction with a finite
element model of the wall specimens to determine a Young's Modulus for
unreinforced masonry walls for use in dynamic analyses-

The results from the fîrst two parts of the study were then used in the modelling of
the buildings from the ambient vibration tests. The Young's Modulus values

determined from the results of the shaking table tests were used as the basis for the
Young's Modulus of the brickwork elements in the models of the buildings. Modal
analyses were undertaken of the building models and the results compared to the
results of the ambient vibration tests. The building models were then used in
response spectrum analyses in accordance with The Australian Standard "Minimum

X
 Abstract

design loads on structures - Part 4: Earthquake Loads", 451170-4-1993 to

determine the predicted respor.tse of the buildings to the Australian design magnitude
earthquake. Exarnined respolÌses were tlÌe wall stresses, floor to wall connection
forces, base shears, and storey shears. These results were compared to the predicted
response of the buildings to the Australian design magnitude earthquake determined
from equivalent static force analyses.

The results of the two types of analyses lbr predicting tlie response of a structure to
earthquake excitation were then used as the basis of suggested modihcations to the
451170.4 equivalent static force design procedures for u.se with unreinforced
masonry buildings.

XI
ACKNOWLtr,DGMtrNTS

The author wishes to acknowledge the assistance, guidance and encouragement

given by his supervisor, Dr. Michael Griffith, throughout this project. The work was
made possible through his dedicated interest in the project and guidance during the
preparation of the manuscriPt.

The author also wishes to acknowledge tl're late Dr. George Sved for his ideas and
suggestions throughout the project. His experience in hnite element modelling, in
pafticular of unreinforced masonry, contributed greatly to the success of this part of
the research.

The experimental work conducted as part of this research was undertaken with
assistance and guidance from Mr. Bruce Lucas and Mr. Stan Woithe from the
Instrumentation Laboratory, Mr. Colin Haese and his staff in the Engineering
Workshops, and Mr. Wemer Eidarn and his staff in the Structure's Laboratory of the
Department of Civil and Environmental Engineering and the author gratefully
acknowledges their contribution to the project.

This project was funded by the Australian Research Council-

x111
 !ql

1. INTRODUCTION

Eartliquakes are one of the most clevastatirìg of all natural disasters. Striking without
warning, they kill and injure people, destroy buildings, and disrupt power and water
supplies.

One of most vulnerable fonns of construction to damage in earthquakes is

tl-re
unreinforced masonry. The 1989 Newcastle, Australia, earthquake was a recent
event that demonstrated this vulnerability. Page et al (1990) noted that the majority
of damage in Newcastle was to older load bearing masonry construction or to non-
structural masonry. Page et al, however, also noted that a large number of small and
large unreinforced masonry buildings pelformed well during the earthquake-

With the generally poor perlbflnance of unreinforced masonry buildings when

subjected to earthquake glound motion and evidence suggesting this that these
buildings do not have to perform poorly, there is pressure on the engineering
community to design and detail unreinforced masonry buildings to perform well in
earthquakes. This study was devised to help engineers design and detail unreinforced
masonly buildings that have an acceptable performance in earthquakes.

The general aim of this study was to investigate the susceptibility of unreinforced
masonry buildings when subjected to earthquake ground motion, with special
reference to the design magnitude earthquake in Adelaide and to provide an engineer
with the tools necessary to provide unrcinforced masonry with an acceptable level of
performance under earthquake ground motion. The aim was achieved through an
examination of the suitability of the earthquake design provisions included in The
Australian Standard "Minimum design loacls on structures - Part 4 : Earthquake
loads" 4S1170.4-1993 for use with unreinforced masonry construction common to
Australia. The study was limited to unreinforcad clay brick masonry. Unlike previous
studies which concentrated on a single building, this study looked at eleven buildings

1
 Chapter I : Introduction

in orcler to try and ascertain trencis frorn the predicted seismic behaviour of these

buildings.

Ge¡erally earthquakes are consiclerecl to be the ploblern of areas on tectonic plate

boundades, Calilbrnia, Japan, ancl New Zeal¿nrl, for example. For buildings not in
al.eas on the tectonic plate boundaries earthquake loading may not be considered in
the design process. While buildings constructed in areas near the tectonic plate
boundaries are more likely to expedence a large magr-ritude eartliquake, to ignore the
possibility of buildings in areas not near the tectonic plate boundaries experiencing
earthquake ground motion coulcl be disastrous. Again, the 1989 Newcastle
earthquake demonstratecl that arcas not on tectonic plate boundaries are not immune
I'rom t¡e dangers of earthquakes. There are dil-terences fur the properties of the
earthquakes that occur at the tectonic plate boundules, interpktte eatthquakes, and
those tlrat do not, intapl.ate eathquakes. Wliile not directly part of this study, the
properties of intraplate plate earthquakes will be considered when examining the

earthquake design provisions of AS II10-4-

Wien examining the rlevelopment of unreinforced masonry it becomes apparent that

its development followed a clil'lerent path to the other materials used in the
construction of buildings and structures. The sophisticated use of unreinforced
masonry has been found to date back 3000-4000 years (Fìill (1984)) and the frst
codihed rules for its use were by the Roman architeclengineer Vitruvius (Armytage
(1961)). While structural engineering progressed rapidly in the 19th and 20th
centuries, with the problems of bending and elasticity having been solved and the
new principles of structural engineering being readily applied to the new building
materials, iron, steel, and concrete, masonry buildings were still built using the basic
rules developed 500 years earlier. In tlie late lgth and 20th centuries, isolated series
of tests on masonry walls and piers were undertaken, though it was not until the
1950's that significant information was available to allow development of building
codes based upon science and structural engineering theory. A new design approach
for masonry was developed in Europe to cope with high rise residential buildings
'War.
constructed in the period after the Second World No longer was each wall
considered separately. Instead each wall was recognised as being part of the whole
building. These new design approaches usually dealt with vertical and wind loads-

As has already been noted at the being of this section, unreinforced masonry has
generally performed poorly in earthqutkes and this poor performancc was
highlighted recently in Australia in the Newcastle, 1989, earthquake (magnitude 5.6).

2
 Chapter I : Introdtrctiott

Australia previously experìencecl earthquake <Jarnage to unreinforced masonry

builclings during a rnagnitucle 6.9 event in Mcckering in 1968. Beresford (1969)
observed that of fifty-two builciings with masonry walls of various types ancl quality,
only one survived with damage that v/âs ecollomically repairable. Yet, of twenty-
seven tirnber l'ramccl buildings, only two sustainecl worse than minor damage.

The Australian experience of unreinl'orced masonry perfonning poorly in earthquakes

is not unique. Unitecl States earLhquakes such as Long Beach, 1933, Anchorage,
1964, V/hittier Nanows, L987, Loma Pdeta, 1989, and Nortliridge, 1994 also
highlight the vulnerability ol unreinfbrcecl masonry buildings to earthquake ground
morion. Stuclies after the Whittier Narrows (Deppe (1988) and Comerio (1992)) also
tbund that strengrhenecl unreintbrced masonry buildings generally had acceptable
performance. Ealthquakes in Canada, Iran, and Japan also confirmed the generally
poor perfonnance of unreinforced masonty when subjected to seismic actions.

Bruneau (1994) and Boussabah and Bruneau (1992) described the possible failure
modes for unreinlbrcecl masonry buildings when subjected to earthquake induced
loading:

(1) Lack of Anch.orage: The lack of anchorage of the floors and roof to the walls
results in the exterior walls behaving as cantilevers over the total height of the
building. This can result in flexural stresses at the base of the walls that can
cause out-of-plane t-ailure. Another possibility is the overall failure of the
structure as a result of the floors and roof sliding from their supports;

(2) Anchor Failure: Tlie anchor between the walls and the roof or floors can fail
This can be through a fäilure of the anchor or rupture at the connection points;

(3) In-Plane Fa.ilures: In-plarie failures of the walls may be induced by excessive
bending or shear. In-plane shear failures are common and are usually evidenced
by double diagonal (X) shear cracking- However, shear cracking, unless very
severe, does not usually prevent the wall from continuing to carry gravity load.
Unreinforced masonry facades with numerous window openings can also have
short piers and spandrels fail in shear. Flexural failure is also possible in those
elements, especially in slender unrcinforced masonry columns. The cracking in
both ends of an unreinfbrced masonry element transfotms it into a rigid body of
no fufther lateral load resisting capacity;

J
 Ch.apter I : Itúroduction

(4) Ottt-of-Plane Failt.tre.s : The anchors between the horizontal elements of a

structure ancl the walls provicle out-of-plane support to the walls- These
suppol.ts allow the walls to behave as one-storey liigh panels excited at each
end by the movement in the horizontal diaphragms. Unreinforced masonry
buildings are especially vuhierable to out-of-plane flexural failures and unlike
in-pla¡e shear failures, these failures prevent the wall from continuing to carry
gravity loads. This type of failure also includes parapet failures where the
parapet, if unrestrainecl, acts as a cantilever. Tliey are also subject to the largest
amplilicatiol of the base acceleration (being the tallest part of tlie building)-
Multiwythe walls which are improperly bonded to each other are also very
vulnerable to otlt-ot:plane f ailure;

(5) Contbìnecl In-Plane and Ou.t-of-Plane Effects : As the principal direction of

loading seldom coincides witl'r the prìncipal axis of buildings unreinforced
masonry walls are generally subjected to combined in-plane and out-of-plane
effects. As in-plane shear cracking occurs, the resultant triangular cantilever
wedges have a con.siderably weaker out-of-plane strength than the original
uncracked walls. It is cliltìcult to identify this type of failure on site and the
failures are generally attributed, incorrcctly, to only out-of-plane forces; and

(6) Diaphragnt Related Fail.ures: The failure of the diaphragm is rarely observed
following earthquakes. In most cases, damage to the diaphragm itself would
not impair its gravity load canying capacity. The failure of the diaphragm can,
however, induce darnage at the wall corners from the in-plane rotation of the
diapl-rragrn's ends.

The study was broken into thlee main parts:

(1) A study of the dynamic properties of twelve existing unreinforced masonry

buildings using an ambient vibration freld testing technique. The dynamic
properties were used to calibrate finite element models of the buildings for use
in paft (3) of tl-re studY;

(Z) A shaking table testing program aimed at determining the dynamic shear
stiffness of a typical unreinforced brick masonry wall panel. The effect of four
variables on the shear stiffness were examined. The results were used in the
finire elemenr modelling of the buitdings from part (1) of the study in part (3);
and

4
 Chapter I : Introductiott

(3) The ll¡ite elernent rnodelling of eleven of the buildings from part (1) of the
study- The l-rnite element models were then used ilr response spectrum analyses
using the cJesign resporÌse spectrum frorn AS I 110.4 for Adelaide. These results
were comparecl to the results of an equivalent static force design of the
buildings identilying dill'erences ir the results of tlie two approaches. From this
comparison a simplitiecl design methodology was developed based on the static
force method.

A literature review of various aspects of earthquake design, unreinforced masonry

construction, ancl the cornbination of both is undeftaken in Chapler 2. The areas
examined include period fonnula, full-scale building tests, dynamic load tests on
unreinforced rnasonry, rcal earthquake data from unrcinforced masonry buildings,
strength and stiflness properties of unreinforced masonry, finite element modelling of
brickwork, earthquake design models for unreinforced masonry buildings, floor
flexibility, and response modification factors used in simplified earthquake design
procedures. The r.easons for studying these areas are described in the appropriate
section of Chapter 2.

Key aspects of the arnbient vibration tests are desclibed in Chapter 3. These include
the development of the testing methodology, and the testing program to measure the
natural frequencies of twelveunrcinforced masonty buildings in Adelaide. The
suitabiliry of the various period formulae from the literature review for use with
unreinforced masonry buildings are then discussed-

Chapter 4 describes the shaking table testing phase of the study. The test set-up,
testing procedure, testing program, and results of the shaking table test program are
discussed. The reasons for choosing the four variables for the program and the
construction of the test specimens are noted. The resulting dynamic shear stiffness
values are comparcd to the values obtained by other researchers. The wall panels are
then modelled using finite elements to establish an effective Young's Modulus for use
in later hnite element modelling work. The Young's Modulus was compared to those
obtained by other researchers in Australia and overseas-

The results from Chapters 3 and 4 were then used to build hnite element models of
the buildings studied during the ambient vibration tests. These are described in
Chapter 5. The development of the models to accurately represent the behaviour,
based upon modal analyses, of the buildings is discussed. The models were then used
in response spectrum analyses to determine the response of the buildings to the

5
 Chapter I : Introduction

Australian design earthquake response spectrum for Adelaide. In particular, the

results were examinecl to detennine whetl-rer trends ilr the pattern of failure exist, and
if so, in which aspect of the rcspolÌse.

Chapter 6 presents the rcsults of

equivalent static force analyses which were
performed on each of the buildings in accordance with AS 1170.4. The results of the
equivalent static force analyses are compared to the results of the response spectrum
analyses from Chapter 5, in particular the rcsults that influence the six failure modes
described above, and refinernents and simplifications of the code based design
procedure are suggested.

Chapter 7 summaúses the results of the study and makes recommendations as to

further research that is required-

6
}LITERATURE REVIEW

In this chapter a review of previous work carried out by other researchers into

various subjects that are of relevance to this study is presented. Those subjects are:

(1) Period Formulae - An examination of previously published period formulae for

use with unreinforced asonry structures in an earthquake analysis procedure;

(2) Futl-Scale Building Tests - A review of tests conducted on actual buildings in

order to determine their dynamic properties. The review encompasses both the
ambient vibration method chosen for this study and the forced vibration testing
method;

(3) Dynamic Loading Tests on Brick Walls and Structures - A review of dynamic
loading (both shaking table and otherwise) tests conducted on unreinforced
masonry walls and building models to both examine the results for input to an
earthquake analysis procedure for unreinforced masonry and to guide the

determination of a testing methodology for use in this study;

(4) Data from an Unreinforced Masonry Building subjected to Earthquake Ground

Motion - A study of the reported data from an unreinforced masonry building
subjected to the 1989 Loma Prieta Earthquake to provide some indication of
the actual deformations and stresses experienced by an unreinforced masonry
building in an actual earthquake;

(5) Brickwork Properties - A review of the material properties of unreinforced

masonry including strength and stiffness values for use in an earthquake
analysis procèdure for unreinforced masonry;

7
 Chapter 2 : Literature Review

(6) Finite Element Modelling of Brickwork - A review of hnite element modelling

of unreinforced masonry conducted by other researchers to guide the finiæ
element modelling conducted as part of this research;

(i) Earthquake Design Models for Brickwork - A review of previously published

models for the design of unreinforced masonry buildings subjecæd tó

earthquakes to either adopt for use, or guide the development of an earthquake
analysis procedure for unreinforced masonry;

(S) Floor Flexibility/Stiffness - A review of previous studies into the effect of floor
flexibility on the performance of unreinforced masonry buildings in earthquakes
and the importance of floor flexibility in the hniæ element modelling of
unreinforced masonry buildings; and

(9) Appropriate \ for Unreinforced Masonry - A study of a the \ factors used in

various codes throughout the world and proposed by researchers for selection
for an earthquake analysis procedure for unreinforced masonry-

There were some areas that have an effect on the performance of unreinforced
masonry buildings that were not examined as they were considered not to be within
the scope of this study. These subjects included soil-structure interaction, the use of
sliding joints in unreinforced masonry buildings to reduce the earthquake induced
forces, and the use of reinforcement to increase the strength of masonry buildings.

8
 Chapter 2 : Literature Review

2.1. PERIOD FORMULAE

An examination of the equilibrium equations for a dynamic multi-degree-of-freedom

system (Clough and Penzien (1993)) reveals that the natural period of a structure is
an important factor in determining the response of that structure to earthquake
ground motions. As such, it plays an important role in the determination of the
induced earthquake forces in the various earthquake design procedures (time history,
response spectra, and equivalent static force). In this section various period formula
contained in several earthquake design codes or provided by researchers from around
the world are described and evaluatecl for use to determine a reliable estimate of the
natural period of an unreinforced masonry building. The symbols used by the various
codes and researchers have been standardised for ease ofcomparison.

The Australian Standard "Minimum design loads on structures - Part 4 : Earthquake

Loads" 4S1170.4-1993 included two different formulae to determine the natural
period of a building for use in an equivalent static load design-

h
(2.t.1)
46

for the fundamental translational period, and:

h
-- (2.t.2)
58

for the period in the orthogonal direction, where:

T = The natural period of the building, in seconds; and

h = The height of the building, in metres.

Itwas expected that form of period formula suitable for use with an unreinforced
masonry building was one in which the period is proportional the building's height
(Equation 3.4.6) and both Equations 2.I.I and2.l.2 are of this form.

9
 Chapter 2 : Literature Review

The original Australian earthquake code Australian Standard "SAA Earthquake

Code" AS2l2l-I979, included the formula:

0.09h (2.r.3)
T_
JD

for the determination of the natural period of a building , where:

D The plan dimension of the building in the direction under

consideration, in metres; and

h and D are as detlned above. The code then noted that the natural period can be
determined by Equatio n 2.I.3 except when the total horizontal force is resisted by a
moment resisting frame and then the natural period can be deærmined by:

T =0.010N (2.r.4)

where T is as dehned above, and N is the number of storeys in the building. These
formulae are for use in an equivalent static load design. Based upon Equation 3-4-6 it
would appear that Equation2.L.4 is of reasonable form for a shear walled building as
the number of storeys can be seen to be proportional to the buildings height- The
extra depth term in Equation 2.1.3 would suggest that the mass is not proportional to
the depth and based upon Equations 3.4.1 to 3.4.6 would not seem to be of the
correct form for use with an unreinforced masonry building-

Comparing F,quations, 2.1.1 and 2-l-2, with Equation2-1.4, it can be seen that with
a Story height of about three metres, a reasonable estimate for a modern multi-storey
building, the three formulae will give approximately the same natural period.

The "Tentative provisions for the development of seismic regulations for buildings"
(ATC (1984)) included the formula:

T = Crh3/a (2.t.s)

for moment resisting structures and for all other buildings:

T- (2.t.6)

10
 Chapter 2 : Literature Review

where T is as previouslY defined,

CT 0.035 for steel framed structures and 0.025 for concrete framed
structures; and

h and Dare as for Equation 2-1.3 except that in this case the units are feet-
Conversion of Equation 2.1.6 to SI units yields Equation 2-l-3. Equation 2.1-5 is
similar to Equations 2.1.1,2.1.2, and2-l-4 in that the period is a function of the
height of the building, though not a linea¡ function as would be expected of a shear
walled building as discussed in Section 3.4.

The "Recommended Lateral Force Requirements and Tentative Commentary" of the

Seismology Committee, Structural Engineers Association of California (SEAOC
(1988)) and "The Uniform Building Code" (UBC(1991)) provided, for the static
lateral force proÇedure, Equation 2-1.5 except with:

CT = 0.035 for steel moment resisting space frames;

= 0.030 for reinforced concrete moment resisting space frames;
and

= 0.020 for all other structures-

Further, as an alternative for structures with concrete or masonry shear walls:

CT _JÇ
0.1
(2.r.7)

where:

(2.1.8)

with:

L=o.s (2.t.e)
ho

11
 Chapter 2 : Literature Review

where:

4 The eflective horizontal cross sectional area, in square feet, of a

shear wall in the first storey of a structure; and
De The length, in feet, of a shear wall element in the flrst storey in
the direction parallel to the applied forces-

Itshould be noted that the shear wall masonry building mentioned in these codes
could be a reinforced masonry building. The use of the coefficient as dehned in
F,quation 2.1.1 would result in the depth of the building appearing in the
denominator of the period formula. Referring to Equation 3.4.1 it can be seen that
the square root of the shear area could appear in the denominator, but the depth
would then be expected to appear on the top line of the equation-

SEAOC provided a second method for the determination of the fundamental period,
their "properly substantiated analysis". Based upon the structural properties and the
deformation characteristics of the resisting elements it used the formula:

n n

T=2 )*,õi )-[ g)r,¡, (2.1.10)

i=l t=l

The values of f, represent any lateral force distributed approximately in accordance

with any rational distribution. The elastic deflections, õ, , are calculated using the
applied lateral forces, { . The period determined using this method is not allowed to
be less than eighty percent of that obtained using the Equation 2.1.6- The calculation
of the natural period by this method is suiæd to engineered structures but is not well
suited for a simplihed design procedure-

Aoyama (1981) srated the formula provided in the Japanese building code for the
"hrst phase design" for earthquake forces:

T = (0.02+0.01cr)h (2.1.11)

where T and h are as defîned for the AS 1170.4 formulae and:

cx, Ratio of the height of storeys, consisting of steel columns and

girders, to the entire height, h.

T2
 Chapter 2 : Literature Review

For the case of unreinforced masonry buildings cr = 0 and Equation 2.1-11 becomes
similar to Equarions 2.1.1 and 2.I.2 from 451170.4. As with these equations,
Equation Z-L.n would seem to be of the correct form for shear walled buildings.

Housner and Brady (1963) derived a form of equation to be used specifically with
shear walled buildings. It was assumed that the plan dimensions of the building were
sufficiently large compared to the height to ensure the building acted as a shear beam
with negligible bending. The resulting formula:

T = ChJB (2.r.r2)

i¡cludes the term B which is the breadth of the building normal to the direction of
vibration, h which is the height of the building, and C which is constant and is in a set
of units consistent with h and B. This is the form of equation that would be expected
for a unreinforced masonry building and Housner and Brady used the same
justification for its form as was used in Section 3-4.

Housner and Brady then discussed the determination of the natural period of space
frame buildings. While this is not directly related to shear walled buildings, the form
of the equations may provide a basis for a formula for use with the buildings included
in this study. Three types of space frame buildings were considered:

(1) where the stiffness of a storey is proportional to the weight above that storey;
(2) where the stiffness for each storey is the same and is proportional to the total
number of storeys; and
(3) where the stiffness of each storey is the same and is independent of the total
number of storeys.

For the first two cases the formula:

T = CJñ- (2.r.13)

was derived. For the third case the formula:

T=Ch (2.1.r4)

was derived. T, C and h are as in Equation 2.1.12. The absence of any plan
dimension in both equations was again explained by the terms being common to both

13
 Chapter 2 : Literature Review

the mass term and the stiffness term and subsequently cancelling out when combined-
Borh of these equations are of the form that is expected for shear walled buildings,
being proportional to the buildings height, and Equation 2.1.14 is in fact exactly as
would be expected with the period being proportional to the buildings height
(Section 3.4).

Housner and Brady went on further to compare Equations 2-l-3,2.1-12, and 2'1'13
to the measured periods of a number of steel and reinforced concrete shear walled
buildings along with a fourth equation which turned out to have the best fit to the
data:

T = CNJB 1+16 411*fll (2.r.ts)

\BD))

The variables are all as previously defined. The difference between the standard
deviation of the equation with the best fit, Equation 2.1.15, and the equation with the
worst fit, Equation 2.1.3, was twenty-five percent. Housner and Brady then
concluded thatto achieve a significant improvement in the fit of the equation it
would be necessary for the wall stiffness to appear explicitly in the equation and
consequently provided the Japanese equation:

r = c{4+h(1-4d)} Q.t.L6)

where T, c, and h are as previously defined by Housner and Brady and:

d Total storey length of wall divided by the total area of all floors.

Because d makes an allowance for the actual length of walls, Housner and Brady
concluded that Equation 2.1.16 came closer to allowing for the true stiffness of the
wall. The units in Equation 2.1.16 are not consistent, however, and no guidance was
given as to what units should be used for d-

Muria-Vila (1990), in a study involving ambient vibration testing of unreinforced

masonry buildings in Mexico City, found, by fitting a curve to test data, the empirical
relationship:

T = 0.039N (2_r.17)

t4
 Chapter 2 : Literature Review

where T and N are as defined previously. This equation gives a period only thirty-
nine percent of that calculated by Equation 2-I.14. Equation 2.1.17 is also of the
form expected of a period fonnula for a shear walled unreinforced masonry building-

Stafford-Smith and Crowe (1986) approached the problem of determining the natural
period by different means. Rather than provide simple formulae for natural period a
"hand method" was presented. The method was developed for tall structures having
uniform properties through their height. The structures could consist of rigid frames,
coupled walls, wall-frames, and braced frames. It is the coupled wall type that is
most relevant for this study. A coupled wall consists of two shear walls in the same
plan connected by beams along the height of the walls. The beams have known
stiffness, length, and spacing. The basis of the method is that all the types of
structures lisæd above behave as members of a family of shear-flexure structures
whose static deflections can be predicted by coupled wall theory. The method
involves sixteen lines of simple calculation and would be suitable for an engineered
structure. This would limit its use for the unreinforced brick buildings in this study as
the aim was to provide a simplified design approach. The method was tested against
a series of computer analyses of coupled wall buildings and was within two percent
of the period estimated by the computer model. The UBC formula, Equation 2-l-5,
underestimated the same periods by an average of fifty-one percent.

Monge (1984) presented a method to determino the fundamental period of a tall

building using a continuum model. The model was based on the hypothesis that the
shear force in any vertical substructure of a building, such as a wall or rigid frame, is
proportional to the first derivative and the second derivative of the displacement of
the building multiplied by stiffness coefhcients. Monge stated that the natural period
could be calculated by hand in three hours using this method. The results from this
method compared favourably with the results of matrix modal analysis, the Rayleigh
method, and the UBC.

Cheung and Kasemset (1978) developed a model for determining the modal
frequencies of a shear wall frame structure using the frniæ strip method. Two
methods were proposed. In the first method the shear walls and frames were
idealised as an assemblage of finite strips of varying thicknesses. In the second
method the shears walls were idealised as hniæ strips while the frame elements were
regarded as a number of long columns. The proposed methods showed good
agreement with a frniæ element analysis in the determination of the modal

frequencies.

15
 Chapter 2 : Literature Review

Mukherjee and Coull (1974) and Coull and Mukherjee (1978) presented a method
for the determination of the natural frequencies and mode shapes for a shear walled
building, specifically those with complex geometric layouts. The method derived
governing dynamic equations from energy principals using Masov's theory of thinned
walled beams. The method can incorporate foundation flexibility in the determination
of the natural frequencies. The method was compared with the results from

experimental investigations of two model structures. The authors concluded that the
comeiation between the experimental results and the results from the proposed
method was generally good.

In Chapter 3, the suitability of the above formulae for estimating the natural period
of unreinforced masonry buildings was examined. This was done by comparing the
periods given by the formulae to the measured values for sixteen unreinforced
masonry buildings in Adelaide. The methods proposed by Stafford-Smith, Crowe and
Monge, Cheung and Kasemset, and Coull and Mukherjee were not considered
further in this study because of their complexity. Recall the criterion of a simple
approach to the design of unreinforced masonry buildings for earthquake induced
forces. They were included here only to show that more refined methods are
available for the determination of the natural periods which do not require a finite
element analysis, even if a structure has a complex geometry.

L6
 Chapter 2 : Literature Review

2.2 ßTJLL- S CALE BUILDING TESTS

Testing of tull-scale structures has long been recognised as a convenient method of

¿etermining for the first time or conhrming the dynamic properties of structures (for
example Iba¡ez and Shanrnan (1973)). Tests have been conducted in many part.s of
the world and on many different types of structures. The use of both ambient
vibrations and vibrations induced by purpose made shaking machines to determine
the dynamic properties have been reported. The mathematical justification behind the
use of ambient vibration testing for the identification of structural system parameters
is beyond the scope of this thesis but can be found in Gersch and Martinelli (1979)
and Gersch and Brotherton (1982)-

Tests conducted using a purpose made shaking machine to induce vibration in a

structure, or forced vibration tests, were reported by Nielsen (1966)' Reay and
Shepherd (Ig7l), Petrovski et al (1973), Chen et aJ (1977), Foutch and Jennings
(lgi7),Ohta et aI (1971), and Muto et al (1984) for reinforced concrete buildings;
by Meyyappa and Craig (1984), and Ohta et al for steel framed buildings; and by
Stephen and Bouwkamp (1977) for a reinforced masonry building. These tests were
used to determine the accuracy of existing mathematical models and/or to determine
parameters for new mathematical models of existing structures-

Briceno et al (1973) used pull back tests to study the dynamic response of a

reinforced concrete building with different levels of non structural elements presenl

Ward (1977) observed "It is convenient that the dynamic component of the wind
acting on a bluff body can be considered to approximaæ a 'white noise' input to a
multi-storey building. This means the lateral wind-induced vibrations of these
structures can be interpreted in such a way that their natural periods, mode shapes
and equivalent damping values can be measured". This dynamic component of wind
results in ambient vibration of the structure.

Torkamani and Ahmadi (1988), and Kwok et al (1990) determined the natural
periods of sreel framed buildings from tests conducted without inducing additional
vibrations in the buildings, ambient vibration tests. Kwok et al, and Mendoza' et al
(1991) undertook ambient vibration tests on reinforced concrete, and Muria-Vila
(1990) on unreinforced masonry buildings, and Gates and Smith (1984)' Nigbor
(1984), and Brownjohn et al (1987) determined the dynamic properties of bridges

I7
 Chapter 2 : Literature Revíew

using ambie¡t vibration tests. Diehl (1986) used ambient vibration tests to veriÛ a
mathematical model of a multistorey building-

Taoka et al (1973), and Williams (1984) determined the natural periods of reinforced
concrete buildings by both a forced vibration test and an ambient vibration test-
Boukamp and Stephen (1913) used both methods to determine the dynamic
properries of a sreel framed building, while Maguire et aI (1984) performed both
types of tests on a chimney structure, and williams on a bridge.

Forced vibration tests are the traditional method of undertaking full-scale testing- An
oscillating force is applied at a single frequency and the frequency varied until a
resonancecondition is reached in the structure. Conducting ambient vibration tests
have some significant advantages over forced vibration as recognised by Stubbs and
Mclamore (Ig73) and Torkamani and Ahmadi "...the duration of testing and amount
of labour needed in vibration generator tests are much greater than for ambient
vibration tests". Gates and Smith noted "Ambient vibration testing is an economical
means of testing structures for their dynamic response characÛeristics", and
Brownjohn et al observed "The advantage of relying on this type of input (ambient)
is that the test procedure is considerably simplified, as the only equipment required
during the test is for data acquisition". Brownjohn et al also noted the disadvantage
of ambient vibration testing "....the excitation is a non-stationary random process"-
However, Bouwkamp and Stephen, when comparing the results obtained during their
forced and ambient vibration tests, noted that "The natural frequencies determined
from the forced and ambient vibrations agree very closely". Maguire et al noted that
"The results obtained from both ambient and impulse tests on the BRI chimney are
presented in (their) Figure 5. The natural frequencies obtained from the two tests are
similar,...". It would seem that both ambient vibration tests and forced vibration tests
are legitimate methods of obtaining the dynamic properties of structures. Both
methods were therefore considered for adoption in this project.

A concern raised by a number of researchers with the use of forced vibration tests,

and especially ambient vibration tests, was the applicability of the results at the low
levels of excitaúon during the tests to the higher levels of excitation associaæd with
earthquakes. V/ard observed, when discussing ambient vibration tests, that "The
wind-induced vibrations in tall buildings are small, and it can be argued that the
results from this type of study are not relevant to earthquake resistant design"-
Foutch and Housner (1977) noted that during the San Fernando earthquake buildings
acted as non linear softening dynamic systems - "It was noted that the fundamental

18
 Chapter 2 : Literature Review

periods of vibration of virlually all instrumented buildings were longer than those
determined before the earthquake during ambient vibration tests at much lower levels
of excitation.".

In a study into the identification of the modal parameters from forced vibration tests
on a small model structure, Soucy and Deering (1989) noted a "slight, but steady"
decrease in tlie natural frequency as the force level increased-

Nielsen noted "By exciting some of the modes at different amplitude levels it was
found that the resonant frequency decreased slightly as the force level was increased,
the shift in frequency being typically that of a 'softening spring' ". The lowest
translational mode frequency decreased by a maximum of one percent for a seven
and a quarter times increase in force. The second lowest mode frequency decreased
by one and a half percent for a seven times increase in force. Foutch and Housner, in
a follow up to the work of Nielsen, compared the results of the forced vibration
testing to recordings of the behaviour of the structure during an earthquake and
found "....the natural periods of vibration of the building were longer during the
earthquake than they were either before or after the event". The explanation given by
Foutch and Housner, however, rather than the building acting as a softening spring is
that "-...changes observed during the earthquake could be the result of the loss of
stiffness due to cracking of the encasing concrete of the columns". It was noted that
the damage sustained by the structure during the earthquake was repaired afær the
event. An important warning in the conclusion of Foutch and Housner should be
noted for all full-scale dynamic tests "A prediction of the fundamental period of
vibration of a particular structure may be 20 to 30 percent different from that
observed during an earthquake".

Ohta et al also reported a difference in the fundamental natural period obt¿ined from
vibration tests and the fundamental natural period observed during earthquakes. The
period during earthquakes was 1-13 times the natural period measured during
vibration tests. Chen et al observed that "The increase of the period of the
undamaged structure with increasing amplitude of response,.., indicates the structure
has stiffness properties of a non linear softening spring system". Their results showed
a twenty-five percent decrease in the frequency for a change in the roof velocity from
just above zero to twenty cm./sec. The frequency converged to a constånt value as
the roof velocity (and hence force level) increased. It was also observed that the
mode shape remained constant regardless of the force level of the test. Foutch and
Jennings observed "it is not uncommon for the natural periods of a building to

l9
 Chapter 2 : Literature Review

lengthen by 20 to 30 percent during the large amplitudes of vibration experienced

during response to strong motion"-

Gates and Smith compared the natural periods determined from ambient vibration
tests to those detennined under earthquake conditions and under large force
conditions for two of the bridges in their study. For the bridge subjected to a force
vibration tests with large force levels it was found that the natural frequencies
decreased by a maximum of eleven percent and by an average of hve percent from
ambient vibration tests to large scale vibration tests. The bridge subjected to
earthquake excitation had a reducúon in frequency of a maximum of eighty-five
percent from ambient vibration tests to earthquake conditions in the longitudinal
direction. For the vertical and translational direction the maximum reduction was
thirty-seven percent for the first mode. The authors explained the signifrcant
difference in response between the ambient and earthquake results as a result of the
non-linear response of the soils at the bridge abutments-

In contrast, however, Petrovski et al found the level of excitation did not have any
effect on the first mode frequency, but the second mode frequencies decreased as the
levels of excitation increased. A change of one percent in frequency was noted for
fifty-nine percent increase in force level- Also noted was the fact that the mode shape
was unaffected by changes in force level. Reay and Shepherd concluded from thei¡
comparison of results of a force vibration test and theoretically calculated dynamic
characteristics that "...the dynamic from the small
characteristics determined
amplitude vibration tests undertaken by the authors are applicable to signifrcantly
higher strain levels".

Examination of the changes to the natural frequency due to changes in the level of
vibration applied to a structure would suggest that the results of vibration tests at
low levels would be of little use when considering the response to earthquake forces.
However, when the errors in determining the frequency (experimental errors) are
taken into account, the effect of the force level may not be as great. Further, the
position of the structure's frequency on a response spectrum curye, especially on the
constant acceleration region, could result in the change in frequency being
insignificant. Finally, it was unanimously observed by those researchers which
compared the results of tests conducted at high levels of excitation to those
conducted at low levels of excitation, that there is an increase in the natural period
(or decrease in the natural frequency) with an increase in the level of excitation- An
examination of the design response spectrum, Figure 5.2.I, shows that an actual

20
 Chapter 2 : Literature Review

period lower than the design period will either result in the design force being the
same, if both are on the constant acceleration region of the design response
spectrum, or a lower design force if they are not, which results in a conservative
design force.

Gates and Smith raised a further problem with ambient vibration tests. Ambient
vibrations could contain a predominant exciting force. When field data is obtained it
is verydifficult to identify and remove these unwanted frequencies from the response
of the structure. A possible solution to this problem is also given by the authors.
They suggest that to eliminate any dominant exciúng force frequencies from the
recorded response of the buildings multiple data be recorded and the results
averaged. No other researchers mentioned this potential source of errors.

Hoerner and Jennings (1969) discussed the problem of the modes of vibration of a
structure being close together and subsequently interference occurring between two
adjacent modes. While the discussion was for forced vibration tests, some of the
conclusions can be applied to ambient vibration tests. It was shown that there is no
interference on the flrst mode and this was shown mathemaúcally as well as with an
empirical example. For allmodes except the first, the possibility of modal
interference was real and a method of separating the modes from the results of tests
containing modes that have interference was presented. It can therefore be assumed
that as long as the modes are excited the modal frequency and shape can be
determined by either full-scale ambient or forced vibraúon testing.

Hoerner and Jennings also mentioned the important consideration of the location of
the sensors of the vibration and in forced tests the location of the exciter. They
observed that the "generators usually are located in the upper portion of the structure
so that the exciting force will be away from any nodes of the lower modes of
vibration,..". Chen et al found that the location of the vibration exciter had "a
significant influence" on the deflected shape of the building undergoing testing.
Nielsen noted that for the forced vibration tests conducted on a nine storey steel
frame that "The exciter was located away from the center (sic) of the floor so that
both translational and torsional modes could be excited.' and further stated that "The
main problems in gaining the most information from forced vibration tests are (1) to
locate the vibration exciters far enough away from nodal points of the desired modes;
and (2) to locate the vibration exciters such that interference between the response of
modes that have frequencies close together is eliminated-"

2l
 Chapter 2 : Literature Review

Kwok et al noted that the accelerometers in their series of ambient vibration tests
effects
were located, if possible, at the shear centres of the buildings so that torsional
were eliminated an<l only lateral modes were recorded- Bouwkamp and Stephen
observed for their forced and ambient vibration tests "..for the t¡anslational
motions
so as
the accelerometers were located near the center (sic) of the floor and orientated
to pick up the appropriate North-South or East-West accelerations. For recording
(sic) of
the torsional motion accelerometers were properly oriented near the center
two opposite walls."

Diehl further simplif,red the ambient vibration method by restricting the location of
the instrumentation to the roof, orientated so that both torsional and lateral modes
were identified. Using this method, five modes were recovered for a structure,
"----the mode
sufhcient to verify a mathematical modet. Diehl further observed that
ranking comes close to the 1,3,5 frequency sequence for structures dominated by
other
shear deformation,..". This ratio of modal frequencies was not mentioned by
researchers.

Other important information provided by the authors of various studies into full-scale
testing included Maguire et al noting "One of the greatest sources of error is
(sic)
(transient)
any digitalty computed spectrum results from the fact that the measured
signal is not periodic in the measurement period chosen and therefore violates a
prime requirement of the FFT. This results in the true spectral estimate at a particular
frequency being modihed by power leaking from other frequency components
Leakage can be significantly reduced by'windowing'the sampled time history record,
ie shaping it to become periodic". Also mentioned was the problem of aliasing, the
use of a too small sampling rate resulting in the structural frequencies being recorded
as a lower frequency. (see Appendix A - Sampling Theorem)'

Ohta et al used a 'Hanning' window to modiff the data in their forced vibration tests
of various buildings to modify the data to a periodic record. Torkamani and Ahmadi
also used the 'Hanning' window. Further, they noted that they recorded 102-4
seconds of data at 40 samples per second, and a FFT was performed on 4096
points

of their record. Brinceno et al used a sampling rate of 200 samples per second-
Nigbor mentioned the use of low pass filæring to remove the frequencies from the
record that are of no interest to the researchers. High pass filtering was performed on
the record to remove the DC offset-

22
 Chapter 2 : Literature Review

Either the ambient vibration test or the forced vibration test could have been used in
this study. In Chapter 3 - Field Testing - the method adopted, and the reasons for
that choice are discussed.

23
 Chapter 2 : Literature Review

z.3DYNAMIC LOADING TESTS ON BRICKS

WALLS AI\D STRUCTURES
The 1970s saw a significant increase in the amount of research conducted on the
earthquake performance of unreinforced masonry walls. Some of the research
involved the dynamic testing of unreinforced masonry walls in the laboratory and this
research is reviewed in this section. While this study is limited to unreinforced
masonry, where the experimental test methods used on other materials are relevant
to the current study they are included in the review-

2.3.1 In-Plane Tests

Researchers at the University of California at Berkeley have undertaken a number of

tests on unreinfo reinforced (i.e- reinforced only at critical sections)
walls and scale-model buildings, including some shaking table tests

Cyclic shear tests on masonry double piers were reported by Mayes et al (1976a),
and Mayes er al (1976b) and on single piers by Hidalgo et al (1978) and Chen et al
(19TS). Four failure modes were observed in the tests; shear failure, shear failure
with vertical cracks, shear and flexure failure, and flexure failure with crushing of
compressive side. The unreinforced masonry panels failed by the fust type, shear
failure. All of the double piers experienced some type of ductile behaviour. A trend
towards more ductile behaviour as bearing stress was increased was noted. However,
the lateral displacement decreased with the increase in bearing stress so that the
increased ductiliry was offsetby an increased induced shear force. The ultimaæ
strength of the panels was found to increase with increased amounts of
reinforcement, or increased bearing stress. The shear stiffness of the piers was found
to increase not only with increased bearing stress but also with an increased rate of
loading.

Further tests on single piers were conducted at Berkeley and reported by Hidalgo et
at (1978), Hidalgo et al (1919), and Chen et al (1973). From the unreinforced
masonry piers tested it was found that for a height to width ratio of t'wo, a flexural
mode of failure occurred. For a height to width ratio of one, the unreinforced
masonry specimens failed in shear-

Further dynamic testing of unreinforced clay brick masonry walls was canied out at
Berkeley and reported in Mengi and McNiven (1989) and McNiven and Mengi

24
 Chapter 2 : Literature Revíew

(1989). The shaking table tests conducted as part of this study (Chapter 4) were
based upon the tests reported by Mengi and McNiven. The test set-up used
for these

tests at Berkeley is shown in Figure 2.3-I-

[-ead Ingots Irad Ingots

Bonding

2x
Single I-eaf Walls Bracing

!
Earthquake Motion Shaking Table

Figure 2.3-1 Mengi and McNiven test set-up-

(from Mengi and McNiven (1989))

The authors noted that the experiments were designed to produce pure shear in the
wall so that the shear modulus was established. The most significant observation
from the testing program was that "the values of the shear modulus which we
(McNiven and Mengi) establish when the masonry is responding to dynamic forces
are radically different from those when the masonry is responding to static forces".
This has serious implications if the results of static tests are used to model the
dynamic response of masonry buildings-

In 1984, similar tests conducted on unreinforced concrete block masonry were

reported by Mengi et al (1984) and Sucuoglu et al (1984)-

The last tests conducted at Berkeley of interest to this study were a series of shaking
table tests on model masonry buildings. These tests were reported on by Gulkan et al

25
 Chapter 2 : Literature Review

(Ig19),Clough et al (1979), Gulkan et al (1990), clough et al (1990), and Manos et

at (1983). The test specimens were a square afrangement of four wall panels. The
authors noted the i¡fluence of workmanship on the properties of the masonry
components. The load path shown in Figure 2.1-l was observed for the buildings in
these tests. The requirements for the diffelent components of the model buildings
were summarised as:

(1) Out-of-plane walls must have sufficient flexural strength to resist inertia forces
due to their own self mass when acting as vertical beams supported top and
bottom;

(Z) In-plane walls must have the capacity to resist the inertia forces of the entire
roof system plus the top half of the out-of-plane walls; and

(3) The roof structure must be strong enough to transmit the roof forces and the
out-of-plane wall forces to the in-plane connecúon by membrane action.

Conclusions from the tests included that the "frequency characteristics of the
earthquake input are not a major factor in its tendency to induce damage in a
masonry house" and that "no signihcant deterioration in the overall performance can
be seen" when the model buildings were orientated on the shaking table such that in-
plane and out-of-plane responses were induced in the walls simultaneously.

In Italy, Benedetti and Benzoni (1984) undertook laboratory shaking table and static
load testing on model stone masonry buildings for use with a non-linear finite
element model. It was found that the failure of the buildings occurred at levels of
base acceleration four to six times greater than the design level base acceleration for
most of Australia.

Arya (1980) reported on a series of tests conducted on reinforced and unreinforced

masonry wall specimens at the University of Roorkee in India from 1961 to 1978.
The observations from these tests included:

(1) That the cracking of masonry largely occurred as a consequence of tension;

(2) Application of compressive load at the time of curing increased bond strength;

26
 Chapter 2 : Literature Review

(3) plain masonry walls, when tested as shear walls, had shear strengths 70 percent
of the theoretical values; and

(4) Unreinforced masonry walls had no reserve strength beyond the hrst crack
load

eamaruddin et al (1984) described further research conducted

at the University of
Roorkee aimed ar determining the possible advantages of providing sliding joints in
masonry walls at their bases. It was observed in these tests that the workmanship
plays an important part in determining the strength of a masonry structure.

Research on the earthquake behaviour of brick masonry has also been undertaken in
Europe. In Germany, Konig et al (1988) reported on shaking table and quasistatic
tests conducted on unreinforced masonry walls- It was found that the crack pattern
strongly depended on the axial load level.

In Slovenia, Tomazevic (1987) and Tomazevic and Zarnic (1984) reported on the
earthquake simulator testing of a l/7-scale 4-storey masonry building model- The
tests were conducted to examine the feasibility of the storey mechanism model, noted
in Section 2-7,to model masonry buildings subjected to earthquake excitation. It was
concluded that the hrst natural mode was predominant in the response of the model
to earthquake excitations.

Tomazevic and Weiss (1994) reported on the shaking table testing of two 3-storey
plain and reinforced masonry 1/5 scale building models. Considering only the
unreinforced masonry model it was found that at the ultimaæ state horizontal cracks
developed at the joints between most walls and slabs. The model collapsed at the
attained maximum response, showing no ductility.

Tomazevic and Velechovsky (1992) reported on the testing of a Il7 scale model
masonry buildings after finding that this was the most practical upper limit for the
modelling for the modelling of masonry.

Also in Europe, in a joint research program between Macedonia and Italy,

Jurukovski et at (1992) reported on three 1/3 scale 4-storey buildings tested on a
biaxial shaking table. The aim of the testing program was to examine the
effectiveness of
strengthening techniques. The traditionally constructed model
experienced intensive damage to the hrst floor, including the collapse of complete

27
 Chapter 2 : Literature Review

walls, slight damage to tl're second floor, and almost no damage to the top two
floors.

Magenes and Calvi (lgg2) conducted cyclic tests on unreinforced masonry walls in
Italy. The tests were conducted to determine the effects of aspect ratio and vertical
compression. Two failure modes were found for differing levels of axial stress- A
frictional failure of the mortar joints was observed for lower axial stress levels and
tensile cracking of the bricks was observed for higher axial stress levels-

In Britain, shaking table tests were conducted on twin unreinforced masonry wall
specimens using a'test set-up similar to that used at Berkeley and shown in Figure
2.3.I and reported in Pomonis et al (1992). Pomonis et al concluded that the
frequency content of the ground motion proved to be an important factor, along with
the actual amplitude of the motion, in determining the response of the walls-

Shing et al (1989) reported on the testing of sixæen reinforced masonry specimens

under dynamic shear forces at the University of Colorado- From the results of these
tests it was concluded that the stiffness of a wall panel does not alter with the
position of the induced displacements-

Cyclic in-plane loading tests were conducted on unreinforced masonry walls at the
University of Illinios at Urbana-Champaign by Abrams (L992). Abrams noted that "it
appeared as though the previous loading and damage had little to do with the
subsequent behaviour". It was also found that the walls continued to resist sizeable
Iateral loads while deflecting beyond well beyond the linear range of response'

Jankulovski and Parsanejad (1994) undertook a similar study at the University of

Technology, Sydney. It was found that the hysteresis behaviour of the walls varied
within a broad range- The masonry walls exhibited a sizeable capacity for non-linear
deformation and energy dissipation. The elastic limit for the horizontal displacement
was about 0.2 percent of the height of the wall-

Similar tests were conducted in New Znaland by Priestley and Bridgeman (1974) on
reinforced masonry walls. While the tests were not directly relevant to unreinforced
masonry it was found that satisfactory ductility could be obtained by the provision of
reinforcing steel in masonry walls.

28
 Chapter 2 : Literature Review

2.3.2 O at-of-Pl ane Tes ts

It has been found by research on model structures with walls in both orthogonal plan
directions that the walls subjected to out-of-plane forces are just as crucial to the
satisfactory performance of unreinforced masonry buildings under seismically
induced loads as the in-plane walls- This has been recognised in a number of research
projects where the out-of-plane behaviour of masonry walls under cyclic load.s has
been investigated.

Bariola et al (1990) reported on the out-of-plane response of unreinforced clay brick

walls during a shaking table test series. The walls were te.sted as cantilevers and
failed by rocking as a rigid body after the bending strength of the base of the wall
was exceeded.

Kariotis et al (1985) and Adham (1985) reported on a series of full-scale tests

conducted on unreinforced masonry wall specimens to study the out-of-plane
dynamic stability as part of a larger research program conducted in the United States
aimed at mitigating the seismic hazards in existing unreinforced masonry buildings-
The failure of the wall specimens was not sudden, but was characterised as a slow
drift into instability during reversal of the dynamic motions of the ends of the walls-

Also in the United States, Davidson and Wang (1935) conducted cyclic laæral load
tests on masonry wall panels. Both reinforced and unreinforced masonry wall
specimens were tested and the unreinforced masonry specimen was found to absorb
no energy and failed during the first cycle. The theoretical maximum moment for the
specimens was found to be considerably greater than the measured maximum
moment-

In New Znaland, Priestley et al (1979) reported on a series of out-of-plane tests

conducted on masonry veneer panels. It was found that preformed horizontal and
diagonal cracks had no apparent influence on the ultimate performance of the
veneers.

29
 Chapter 2 : Literature Review

2.3.3 SummarY

The results of the previous research into the behaviour of unreinforced masonry
construction can be summarised as:

(1) Unreinforced masonry walls exhibited some ductility;

(2) Ductility improved with increased bearing stress;

(3) Ultimate strength increased with increased bearing stress;

(4) The ultimate flexural strength determined from dynamic tests was less than or
. equal to the ultimaæ strength values from pseudo-static tests. This result was
different to what has been observed for steel and concrete, where increased
loading rate increases the flexural strength;

(5) Shear stiffness increased with increased bearing stress and an increased rate of
loading;

(6) Height to width ratios of unreinforced masonry wall panels influenced the
failure mode;

(i) The dynamic shear stiffness was radically different to the static shear stiffness;

(S) The influence of the workmanship was significant;

(9) Typicat single storey masonry houses are so rigid that they do not develop
complicated dynamic response mechanisms. The frequency cha¡acteristics of
the input motion are not a major factor in the ændency to induce damage;

(10) The required strength of a wall to resist combined in-plane and out-of-plane
loads was not significantly different to that required to resist the in-plane and
out-of-plane actions independently;

(11) Out-of-plane strength was the critical design parameter. Shear stiffness was
important in determining the forces induced in the structure;

30
 Chapter 2 : Literature Review

the
(I2) Unreinforced masonry walls have little reserve bending strength beyond
no
first crack load. Walls subjected to out-of-plane loads fail abruptly and have
energy absorPtion;

(13) Unreinforced masonry wall damage increased with increased in input energy'

whether applied by one shock or in a series of smaller shocks;

(14) Crack patterns depended on the axial load level;

(15) The hrst mode response dominated the overall response of an unreinforced
masonry building subjected to earthquake motion; and

(16) For walls subjected to out-of-plane loads, the theoretical upper bound of the

centre displacement can be momentarily exceeded'

3l
 Chapter 2 : Literature Review

z.4DATA FROM AN UNREINFORCED

MASONRY BUILDII{G SUBJECTED TO
EARTHQUAKE, GROUI{D MOTION

A significant number of buildings around the world have been instrumented so that
their performance in earthquakes can be monitored. Unfortunately, very few of
these

are unreinforced masonry buildings. However, one such unreinforced masonry

building is a historic hrehouse in Gilroy, California and reported in Tena-Colunga
brick
and Abrams (1992) and Abrams (1993). The Gilroy firehouse is a two-storey
the
building typical of construction in the turn of the century in California and across
United States. Lateral load resistance is by unreinforced masonry bearing walls and
timber diaphragm floor and roof systems. The building survived the 1906 San
Francisco earthquake and was instrumented as part of the California Strong Motion
Instrumentation Program. The data recorded by the instrumentation was a result of
the 1989 Loma Prieta earthquake (Gilroy is within 15 km of the epicentre of the
Loma Prieta earthquake).

2.4.1 Description of the Building

The Gilroy firehouse was initially constructed as a box, consisting of four exterior
brick walls. A back room was later added to the building. The south and the west
walls of the building contain several openings, while the west, north, and the interior
walls are almost solid. The centrs of the in-plane wall stiffness is offset from the
centre of mass and therefore some torsional response would be expected during an
earthquake. The plan of the building is shown in Figure 2'4'l'

The total wall thickness of 305 mm is made up of three wythes of brick. Mortar bed
joints were 13 mm. Bricks were removed from the building and their properties were
measured. The results are shown in Table 2-4-I-

Table 2.4.1 Measured Brick Properties from the Gilroy Firehouse

(from Abrams (1993)

17.5 kN/m3
13.8

modulus of 1.79 MPa

com ive strength 37.0 MPa

32
 Chapter 2 : Literarure Review

North

stair

12.2m

three wythe
brick wall
(typical)

original firehouse addition

72.9m 6.1m

Figure 2.4.1Plan of the Gilroy Firehouse-

(from Tena-Colunga and Abrams (1992)

In-situ shear strength tests were also canied out. It was found that the shear strength
of the brickwork was 0.59 MPa-

2.4.2 Observed B eh aviour

Damage to the building from the Loma Prieta earthquake was limited to diagonal
cracking emitting from the top exterior cornef of a window on the second floor.
Cracking at the wall-ceiling interface was noted on the second floor level. No other
structural damage was noted.

The horizontal accelerations were measured in three directions in the roof- The east-
west acceleration was measured at the top of the interior wall and at the centre of the
roof diaphragm. The recorded peak acceleration at the interior wall was 0.419 and at
the centre of the roof diaphragm was O-79g. These accelerations corresponded to

33
 Chapter 2 : Literature Review

of 0'559
amplification factors of 1.4 and 2.7 respectively. A north-south acceleration
was recorded at the centre of the roof diaphragm, coffesponding
to an amplihcation
factor of 1.9.

was noted by Abrams that the sequence and frequency content of

It the east-west
that the
wall motion was remarkably similar to the ground motion which suggested
of
wall acting within its plane was "quite stiff'. The Fourier spectra of the response
the structure lead to the determination of the dominant apparent period of the
structure as 0.45 seconds. When a critical damping value of five to
ten percent was

assumed, excellent agreement was found between response Spectra

maxima and

measured response values. This suggested to Abrams that linear response spectra are
a viable means for estimating peak response, provided a reliable
estimate of building

period can be found, as \Mas noted in Section 2'1'

Nominal shear and flexural stresses were estimated from the measured floor
accelerations using masses derived from the estimated structural weight-
The

horizontal acceleration at the top of the walls was assumed to be equal to measured
acceleration at the top of the interior wall in the east-west direction- This
assumption
were
was acknowledged by Abrams as being "rather crudg" and the nominal stresses
2.4.2'
only indicative of the approximate range. The stresses are shown in Table

Table 2.4.2 Summary of Nominal Wall Stresses-

(from Abrams (1993))

Watl Shear Stress Flexural stress Gravity Stress

(MPa) (MPa) MPa)
South 0.26 0.43 0.30

Central 0.24 o.7r 0.28

North 0.09 0.27 o.r7

East 0.24 0.54 0.28
'West 0.15 0.31 0.20

as the
The shear stresses in Table 2.4.2 were calculated using the entire wall section
moment
shear area, the flexural stresses were calculated by dividing the overturning
by a section modulus based upon gross, uncracked sections. Gravity stresses were
based upon minimum vertical dead loads alone'

34
 Chapter 2 : Literature Review

Based upon the stresses reported in Table 2.4.2, it was reasonable that the walls of
the Gilroy hrehouse did not crack. The difference between the ænsile
flexural stress

and the gravity stfesses were nearly all less than the (United States)
code allowable

values. The central wall had the highest tensile stress (0.43 MPa) which
was about
codes of
1.3 times the allowable values given in the va¡ious United States masonry
practice.

2.4.3 Computational Studies

As well as measuring the response of the firehouse to the Lnma Prieta earthquake,
Tena Colunga and Abrams also undertook computational studies into the
performance of the building.

Firstly, a discrete multi-degree-of-freedom system was used to analyse the building

for each horizontal direction. Dynamic degrees of freedom were assigned to lumped
masses at the centroid of each wall and at the centre of the diaphragms
for the floor
and roof. Soil flexibility was modelled by generalised translational and rotational
springs at the base. Tena Colunga and Abrams concluded from the results of several
analyses that the dynamic response is sensitive to variations in diaphragm
stiffness'

wall stiffness, mass discretization, and damping assumptions- It was found that the
measured acceleration histories at the roof could be "replicated reasonably
well"

using the discrete mulú degree-of-freedom model, provided that diaphragm stiffness
and soil flexibility were estimated accurately-

Secondly, a 3-dimensional finite element model was used to predict the behaviour
of
thebuilding. The hnite element model was confined to the linear range as the
building was found to be largely uncracked afær the earthquake. The hniæ element
model was used to determine the mode shapes and frequencies. Further, it was used
to undertake earthquake analyses using :

(1) Equivalent static forces (obtained from the multi degree-of-freedom dynamic
discrete model);

(2) Response spectrum (from recorded ground motions); and

(3) a time-sæp integration of 20 modal coordinates using the measured ground

motions-

35
 Chapter 2 : Literature Review

Tena colunga and Abrams reported good correlation between

the three methods of
model
analysis. It was further concluded that the discrete multi degree-of-freedom
response spectrum
may be suitable for estimating peak lateral forces and that a linea¡
is suitable once modes of vibration are identihed'

2.4.4 Conclusions

upper limits to
Abrams concluded that the ground motion at Gilroy represented the
Similarly,
that which would be expected to experienced in the eastern united States.
Loma Prieta earthquake would be at the upper limits of ground motion
that a
the
building in Australia might be expected to experience. As such, it suggests
that

unreinforced masonry can be designed to perform satisfactorily for the

design level

earthquakes in Australia.

The
Abrams further noted the importance of wetl tied roof and floor diaphragms'
importance of this observation cannot be underestimated based upon
the
the importance
observations in a number of earthquakes. Also noted by Abrams was
of a large ratio of wall to floor area-

36
 Chapter 2 : Literature Review

2.5 BRICK\ryORK PROPERTIES

In order to model the behaviour of unreinforced masonry buildings under earthquake

induced loads it is necessary to have an understanding of the properties of the clay
brick unit, mortar, and the two phase material that results when brick units and
mortar are used to construct a wall. In this section, the strength and stiffness
properties of these two materials and the combined material, as reported in different
studies, are examined. It should be noted that mean values of the properties are
usually reported and that for masonry, the Scatter can be large.

2.5.1 Axial Compressive Strength

Brickwork is usually designed for the axial loads applied to the structure, and

therefore several studies have been conducted to investigate the axial strength of
brick, mortar, and brickwork.

Considering first the clay brick unit, the results of tests conducted in Australia and
overseas are summarised in Table 2.5-I-

Table 2.5.1 Compressive Strength of Brick.

Details Rese¿¡drer
Compressive Strength

(MPa) (Origin)

E3.2 Full size normal brick with 3 cores (Ar¡^st¡alia) Base and Baker (1973)

66.3 Full sizo normal brick with ! corgg-.(4gq[3þ)- Base and Baker (1973)

36.3 Normal brick (Australi a) Pase (1978)

22.9 3 core clay bricks (Auslralia) Jankulovski and Parsaneiad (199)

32.9
'Wire cut 3 hole brick (8rl!4!D- Hendry (1973)

31.8 Wire cut 5 hole brick (Britain) Hendrv (1973)

19.7 Normal brick spe¡imers (ItalY) Masenes and Calvi (1992)

r40 Maximum commercial (United States) Grimm (197Ð

Itcan be seen that the compressive strengths of commercially available clay brick
units range from 20 MPa to 140 MPa. The variance in the strength is due to the
differences in manufacturing techniques and raw materials from one country and
manufacturer to the next.

37
 Chapter 2 : Literature Review

Compared with the brick units, mortar has a considerably lower compressive
strength. It is the weak link in the compressive strength of brickwork. The results
of
the compressive testing of mortar are summar-ised in Table 2-5.2. The mortar mix
ratio refers to the ratio of cement to lime to sand in the mortar mix- A mortar mix
ratio of 1:1:6 (1 part cement: 1 part lime: 1 part sand) corresponds to the typically
used mix in Adelaide from the Australian Standard, "SAA Masonry Code" 453700-
1988.

Table 2-5.2 Compressive Strength of Mortar-

Mortar Details Researche¡

Compressive Slrength

fMPa) Mix Ratio (Origin)

l:0.4:5 28 rlay strength (Australia) Ba-se and Baker (1973)

8.7

:1:6 Standard Australian mix (Australi a) Paee (1978)

3.2 1

3.3 1 :1:6 (Au.stralia) Jankulovski and Parsaneiad (1994)

7.2 1:1:6 (Britain) Hendrv (1973)

76.7 1:0.25:3 (Britain) Hendry (1973)

r<< 4 and? Cement - lime ratio (United State'¡) Grimm (1975)

t4.o I Cement - lime ratio (tjnited States) Grimm (1975)

4.3 0:1:3 (Italy) Masenes and Calvi (1992)

36.9 l:O.25:3 28 dav st¡enÊth runited Statqs) Mayes and Clor¡eh (1975a)

17.1 l:1:6 28 dav frensth (United Statqs) Mayes and Clor¡gh (1975a)

2.5 1:4:15 28 day strenslh (United States) Maves and Clor¡sh (1975a)

Not surprisingly, the compressive strength of the mortar decreases with a decreasing
proportion of cement in the mix. Mayes and Clough (1975a) also noted that the
compressive strength of mortar is also a function of the gradation of the sand
component of the mix. Table 2.5.3 shows the effect of the sand gradation on the
compressive strength of the mortar based upon a 1:1:6 ratio-

Itcan be seen when comparing Table 2.5-2 to Table 2.5.3 that the effect of sand
gradation is not as signif,icant as that for the mortar mix ratios. The mortar mix ratio
has a large effect on the compressive strength and for the mortars considered the
lowest is an order of magnitude below the maximum'

38
 Chapter 2 : Literature Review

Table 2.5.3 Compressive strength of mortar compared to sand gradation

Mortar Details Rese¿¡cher

Compressive Strength

(MPa) Mix Ratio (Orisin)

13.0 1:1:6 fine grain (Jnited Statas) Mayes and Cloueh (1975a)

16.9 l:1 :6 mqtium train (United States) Mayes and Clough (1975a)

18.7 l:1:6 coarse grain (Jnited Statas) Maves and Clcx¡sh (1975a)

76.4 l:1 :6 coar.se to find blenri (Jniterl Statas) Maves and Clcueh (1975a)

15.8 l:l:6 fine to coa¡se blend (Jnited States) Maves and Clcueh (1975a)

Now considering the combined brick-mortar material, an initial assumption may be

that the brickwork strength is limited by the strength of the mortar. However, this is
not the case. As Grimm (1975) explained, the uniaxial compressive strength and
modulus of elasticity of mortar are considerably lower than that of the brick unit and
the Poisson's ratio is higher for mortar than the brick unit. Therefore, under an axial
compression, the unrestrained lateral strain in the mortar would be greaÛer than that
of brick. Between the brick and mortar exists shear and friction resistance and this
acts to restrain the mortar. This results in the mortar being in triaxial compression
while the brick is in axial compression and lateral tension. Therefore, the uniaxial
compressive strength of brickwork exceeds the uniaxial compressive strength of the
mortar. As the tensile strength of brick is low, the typical mode of failure of brick
masonry in compression is by vertical longitudinal splitting. The reported brickwork
compressive strengths are summarised in Table 2.5.4. The "good" masonry refened
to by Jankulovski et al (1994) was described as laboratory made specimens.

Mayes and Clough (7975a) reported on two attempts to quantitatively predict the
compressive strength of masonry prisms, one based on stress analysis considerations,
the other on strain considerations. Both of the methods are approximate and have
several limitations, including the assumption that there is perfect bond benveen the
brick and mortar. Mayes and Clough also noted that the prism shape and the platen
restraint provided by the compression testing apparatus influenced the compressive
strength of a brickwork specimen and that results from one series of tests may not b
directly comparable with other tests by other researchers.

comparing the results in Table 2-5.4 with the results in Table 2.5.2 it can be seen
that the effect of mortar type on the brickwork compressive strength is less than the
effect on the mortar compressive strength- The order of magnitude of difference in
mortar compressive strength is not reflected in the brickwork compressive strength

39
 Chapter 2 : Literature Review

joint thickness is of
which has a upper value twice the lower. The effect of the mortar
the same order as the effect of the mortar type'

Table 2.5.4 Compressive Strength of Brickwork'

Details Rese¿rcher
Compressive Strength Mortar

(MPa) Mix Ratio (Origin)

"Ccnd" masonrY (Aust¡alia) Jankulovski et al (1994)

15.0

4.0 "Pcrrr" masonry (Australia) Jankulovski et al (1994)

(Au.stralia) Jankulovski and Pa¡saneiad (1994)

76.1

Prism stren¡llt (Unite(l Slâfes) Grimm (1975)

7.1

44.8 Prism strength States) Grimm (1975)

40.0 l:O.25:.3 Brickwork Þrism (Jnited States) Maves and Clor¡sh (1975a)

37.9 l:0.5:4.5 Brickwork prism (United States) Maves and Clor¡eh (1975a)

26.9 1:1:6 Brickwork ¡nism runited States) Maves and Cloueh (1975a)

20.0 l:2:9 Brickwork prism (United States) Maves and Clorsh (1975a)

45.2 6.4 mm Mortar ioint (United States) Maves and Cloueh (1975a)

40.3 9.5 mm Mortar ioint (United States) Mayes and Clor¡gh (1975a)

13.7 12.? mm Mortar ioint (United State's) Maves and Cloush (1975a)

27.9 15.9 mm Mortar ioint (IJnited States) Mayes and Clor¡eh (1975a)

21.7 19.1 mm Mcxtar ioint (United State.sl Maves and Clor¡eh (1975a)

9.2 1:0:3 (India) Arya (1980)

6.0 1:0:6 (India) Arva (198o)

1:0:12 (fndia) ,A,rya (1980)

5.3

5.8 1:2 Lime-surkhi rnortar (India) Arva (f980)

5.2 l:2 Lime-cinde¡ mortar (Inclia) Arya (1980)

4;l Clay mud riolar (India) Arva (1980)

7.9 lltalY) Masenes and C¡lvi (1992)

6.0 ûtalv) San Bartolome et ú 1992\

5.3 Rrll scale specimens (Slovenia) Tomazevic and Weiss (1994)

While masonry piers are used in practice as columns, the more normal method of
carrying compressive loads in unreinforced masonry buildings is through walls.
Brooks (1980) examined the behaviour of unreinforced masonry walls under vertical
loading. Brooks noted that load tests on walls have indicated that there are two
distinct types of failure mechanism. For short walls the failure pattern is a vertical
ænsile splitting at right angles to the compressive strain. Tall walls or walls loaded at

40
 Chapter 2 : Literature Review

large eccentricities may fail in tension across the bed joints due to the flexural acúon
associated with out-of-plane buckling. The failure mechanism for short walls is
similar to that of the masonry pr-isms described earlier. Brooks noted that the
compressive strength of a brick wall increases with increasing brick compressive
strength, mortar compressive strength, increased bond strength, and reduction in
joint thickness, all of which Mayes and Clough showed increased compressive
strength of brickwork prisms, and by the use of solid bricks rather than cored bricks-
If the failure of the wall is by buckiing the brick and morta¡ compressive strengths

are not important in the determination of the maximum load carrying capacity of the
wall.

pande et al (lgg4) discussed the derivation of the equation for the compressive
strength of masonry as given in the Eurocode "Design of Masonry Structures", EC6-
The EC6 equation is:

r* = r(rí)"(r-)P (2.s.r)

where

f- = Characteristicmasonrycompressivestrength;
f- = Average mortar compressive strength;
fb = Normalised unit compressive strength, which was defined as the
compressive strength of the masonry unit modified by a

moisture factor and a shaPe factor;

K = 0.4;
cx, = 0.75; and
p = 0.25.

Evaluating Equation 2.5.1 with the range of values for compressive strength of the
brick and mortar materials as already discussed in Tables 2.5.1 and 2.5.2 (bnck
compressive strength from 31-B MPa to 83.2 MPa and mortar compressive strength
from 2.5 MPa to 36.9 MPa) yields a range of values for the compressive strength of
brickwork from 6.7 MPa to 27.2 lr/.Pa. The reported values of the compressive
strength in Table 2.5.4 range from 4.7 MPa to 45.2 MPa, which is a larger range
than that estimated by EC6.

4l
 Chapter 2 : Literature Review

2.5.2 Ftexural Strength

The actual flexulal strength of the components in brickwork have not been widely
reported. Reported values of the modulus of rupture of brick are reported in Table
2.5.5 and reported values for the tensile strength of mortar are presented in Table
2.5.6.

Table 2.5.5 Modulus of Rupture of Brick.

Modulus of Rupture Details Researcher

(MPa) (Orisin)

4.'1 Five hole wire cut hrick (Britain) Hen<lw (1973)

5.6 Tlree hole wire cut brick (Britain) Hendrv (1973)

-

Table 2.5.6 Tensile Strength of Mortar.

Tersile Strength Morta¡ Details Researche¡

(MPa) Mix Ratio (Orisin')

2.1 1:0.25:3 28 day (IJnited States) Mayes and Cloueh (19?5a)

1.0 1:0.5:4.5 28 dav lljnited States) Maves and Cloush 11975a)

o.4 1:l:6 28 dav (United States) Maves and Clor¡eh (1975a)

1.2 1:l:6 (Britain¡ Hendrv (1973)

1.8 7:O.25:3 (Britain) Hendrv 11973)

'When
considering brickwork there is two values related to the strength in flexural
and/or tension. The flexural tensile strength, also known as the modulus of rupture,
is determined from bending tests. The tensile strength is a measure of the strength of
the brickwork in tension, usually determined from a test such as the bond wrench
test.

Grimm (1975) reported that the flexural tensile strength of brick masonry is a
function of the tensile bond strength of mortar to brick, mortar cement ratio, morüar
bed joint thickness, and orientation of the mortar bed joints with respect to span.

Base and Baker (1913) observed that three modes of failure are possible in
brickwork subjected to flexure across perpend joints:

42
 Chapter 2 : Literature Review

(1) Bending failure of the bricks;

(2) Failure of bond in bending on tho perpend joint; and

(3) Failure of bond in torsional shear on the bed joints

Base and Baker noted that in tests of brickwork subject to flexure the modulus of
rupture decreased with increasing span. Three hypothesis were given:

(1) Any horizontal restraint of the rollers would have given rise to arching action
which would have had greater effect on tho shorter spans;

(2) Deep beam action was approached on shorter spans; or

(3) With high moment gradient, in the shorter spans only two joints were subject
to maximum or near maximum moment.

Reported values of the tensile strength of brickwork are presented in Table 2-5.7 -

Table 2.5.7 Tensile Strength of Brickwork-

Mortar Details Researcùe¡

Tensile Strength

Mix Ratio (Oriein)

MPa)

0.10 "Poor" masonrY (Aust¡alia) Jankulovski er al (1994)

1.0 "Good" ma-sonry (Australia) Jankulovski et al (1994)

1.2 (Australia) Jankutovski and Parsaneiad (1994)

0.69 1:0:3 (India) Arva (1980)

o.24 1:0:6 (India) Arva (1980)

0.04 1:O:12 (India) Arva (1980)

0.09 7:2 Lime : surkhi (India) Arva (1980)

o.06 lz2 Lime: Cinder (India) Arya (1980)

0.o3 Clay mud (ndia) A¡va 119801

0.07 ûtalv) Magenes and Calvi (192)

0.5 (Slovenia) Tomazevic and Vy'eiss (1994)

The moduli of rupture of brickwork reported by a number of researchers are

presented in Table 2.5.8-

43
 Chapter 2 : Literature Review

Table 2.5.8 Modulus of Rupture of Brickwork-

Mortar Details Researcler

Modulu of Rupture

(MPa) Mix Ratio (Oriein)

Flexural failure in Þerpentls (Australia) Ba-se and Baker (1973)

2.5

o.34 (Jnite{l States) Grimm (1975)

3.4 runited States) Grimm (1975)

o.62 1:1 :6 0 <lesrees - FiÊure 2.5.1 (Britain) Hendrv (1973)

o.2z l:1:6 45 degreas - Figure 2.5.1 (Britain) Hendry (19?3)

0.08 1:l :6 90 rlegrees - Fisure 2.5.1 @ritain) Hendrv 11973)

o.94 1 :0.25:3 O desrees - Figure 2.5.1 @ritain) Hendrv (1973)

o.49 1:O.25'.3 45 <legree"s - Figure 2.5.1 @ritain) Hendry (1973)

0.20 I :0.25:3 90 desree,s - Figure 2.5.1 @ritain) Hendry (1973)

2.70 l:O.25:3 Normal to bed ioint @rilain) West et al (1977)

l:O.25:'3 Parallel to bed ioint (Britain) West et al (1977)

o;73

2.74 1:1:6 Normal to bed ioint @ritain) West et al (1977)

o.77 1:1 :6 Pa¡allel to bed ioint (Britain) West et al (19?7)

rù/est et al (1977)
1.86 7:2:9 Normal to bed ioint (Britain)

o.57 7:2:9 Parallel to hed.ioint (Britain) V{est et al (1977)

1.59 (Italy) Masenes and Calvi (1992)

Itcan be seen from Table 2.5-7 that the ænsile strength of the brickwork is very
small compared to the compressive strengths given in Table 2.5-4.

Hendry (1973) also reported on the results of tests to determine the modulus of
rupture of brick walls using two types of mortar. These results are shown in Table
Z-5.1-The angles given were the direction of bending and are shown in Figure 2-5-1

It can be seen that the modulus of rupture was signifrcantly higher for bending
parallel to the bedding planes than for bending perpendicular to the bedding joints.

Itcan be seen that there is considerable variation in the magnitude of the moduli of
rupture and the tensile strengths reported by the various researchers. This can be
partially explained by the difference in maærial properties from test to test. As
research was done at different times in different countries there is no likelihood of
the materials having identical properties to allow direct comparison. The other
important factor is the workmanship. The workmanship involved in the construction

44
 Chapter 2 : Literature Review

of brickwork has a significant influence on its properties and this can explain some
of
the differences in the properties measured by the various researchers.

0 degrees bending

90 degrees bending

Figure 2-5.1 Orientation of bending for results in Table 2-5.8

2.5.3 Shear Strength

In order to establish the seismic resistance of a shear wall structure such as an

unreinforced masonry building the shear strength of the resisting elements is needed.
Ghazali and Riddington (1988) and Riddington and Ghazali (1990) described an
hypothesis for the shear failure of masonry walls. It was noted that the widely
accepted explanation for the strength of a masonry joint is that it is derived from a
combination of bond shear strength and friction between the brick and the mortar-
The ultimate shear strength is then expressed by:

Í, =To+[ro" (2.s.2)

where shear strength, to is the bond shear strength between brick

t, is the ultimate
and mortar, p is the coefficient of intemal friction at the brick mortar interface, and
o" is the axial compressive stress. The results of tests have shown that the rate of

45
 Chapter 2 : Literature Review

increase inshear strength starts to reduce at higher compression stresses. This

decrease often occurs at around 2 MPa compressive stress. This would suggest
that

the coefficient of fiiction reduces with increasing compressive stress- Riddington

and

Ghazali p¡oposed that the shear failure in the mortar-brick inærface is initiaæd by
joint slip at compression stresses below approximately 2 MPa, but at higher stress
levels, shear failure is initiated by tensile failure within the mortar. This hypothesis
was supporled by hnite element modelling and shear testing. Yokel and Fattal (1976)
also advanced the hypothesis of shear failure proposed by Riddington and Ghazali.
The hypothesis was again in good agreement with test results.

Mayes and Clough (1975b), in a literature review on the shear strength of masonry,
reported on a proposal to predict the shear strength of a masonry assemblage that
identified three failure modes. The first two are similar to those identified by
Riddington and Ghazali and Yokel and Fattal. The third failure occurs for an axial
compressive stress higher than that which defînes the second type of failure, tensile
failure. The third mode is governed by a Mohr type failure, where the shear strength
is equal to Poisson's Ratio multiplied by the compressive stress. The proposed failure
mechanisms were supported by the results of laboratory testing. Mayes and Clough
also noted that an increase in mortar strength resulted in an increase in the shear
strength of masonry. Further, they provided evidence from other investigations that
supported the hypothesis for shear strength given in Equation 2-5-2, where an
increase in the bearing load increases the shear strength-

The results of tests to determine the shear strength of brickwork walls are
summarised in Table 2.5.9. The results from tests to determine the coefficient of
inærnal friction, V, are presented in Table 2.5-ß-

Most brickwork walls built in Australia include a damp proof membrane at the base.
This membrane results in no bond shear strength and the shear resistance is only
derived from frictional resistance based on the axial load. Page (1994) conducæd a
series of tests that determined the shear capacity of membrane type damp proof
courses. The tests were conducted with the damp proof course placed on the brick
and the mortar placed on top and with the damp proof course in the middle of the
mortar layer- The results of these tests are shown in Tables 2-5.L| and2-5-L2-

page concluded that the friction coefficients are all greater than the default value of
0.30 specified in Australian Standard, "SA¡{ Masonry Code" 453700-1988 except
for the Polyethylene Bitumen Coated Aluminium-

46
 Chapter 2 : Literature Review

Table 2.5.9 Shear Strength of Brickwork.

Mortar DeLails Rese¿¡cher

Shear Slrengtlt

(MPa) Mix Ratio (Origin)

o.'l "Gocxl" nra.sonry (Australia) Jankulovski et al (1994)

0.1 "Poor" masonry (Atr.ûalia) Ja¡rkulovski et al (1994)

1.0 (Australia) Jankulovski and Parsanejad (1994)

0.35 (B ritain) Rid(linston and Ghazali (199O)

1.19 @ritain) Ridrlinston and Ghazali (199O)

0.21 llralv) Masenes and Calvi (1992)

0.4 (I-Jnited States) Grimm (1975)

4.1 (Jnited S(ate,s) Grimm (1975)

0.8 (ltaly) San Bartolome et al (1992)

Table 2.5.L}Internal friction Coefficient, Þ, of Brickwork-

Inte¡nal Friction Mortar Details Researdter

Coefficient, P Mix Ratio (Origin)

o.4 (United Stâtes) Yoket and Faltal (1976)

0.6 (United States) Grimm 11975)

1.33 runited States) Grimm (1975)

0.68 Suggested value (United States) Grimm (19?5)

Comparison of the shear strength of brickwork with membranes to that of normal

brickwork reveals that the shear strength of brickwork with the membranes is
considerably lower than normal brickwork (two orders of magnitude in some cases).
This lower shear strength occurs at the critical location in the load path for lateral
loads, the base of the building where the total lateral load is transferred to the

ground.

2.5.4 Biaxial Stress Behaviour

It is obvious that masonry elements are rarely subjected to only one type of load at
any time. Walts are genera[y in a complex state of stress produced by in-plane
loading and/or out-of-plane loading. This loading is normally cyclic, such as wind
and earthquake induced loading. Thus, the wall experiences cyclic biaxial sftess
states which can be tensile and/or compressive-

47
 Chapter 2 : Líterature Review

Naraine and Sinha (1991 and 1992), Page (1981), and Dhanasekar et al (1985a and
1985b) all examined the bi-axial stress behaviour of unreinforced masonry walls- This
is generally beyond the scope of this study and will not be investigated further-

Table 2.5JLFriction coefhcients for the shear capacity of brickwork.

(from Page (1994))

Danp [toof Course TYPe In Plane Out of Plane

In Joint On Brick In Joint On Brick

o.4t o.49 0.50 o.47

Standa¡d B itumen Coated

Alurninium

0.60 o.4l o.57 o.48

Su¡rer Bitunren Coated

Aluminium

o.26 o.26 0.31 0.35

Polyethylene Bitumen Coated

Embossed Polydrene o.68 o.59 o.59 o.56

Embossed Polytltene 0.?1 0.58 0.60 o.59

(Supercourse 750)

Table 2.5-12 Shear Strengths of brickwork with membranes-

(from Page (1994))

Dampkoof Course TYPe In Plane Or¡t of Plane

In Joint On Brick In loint On Brick

Standard B itumen Coated o.18 0.01 o.72 0.00

Aluminium

Super Bitumen Coated 0.10 o.07 0.03 0.01

Polyethylene Bitumen Coated 0.o8 0.(X o.07 0.05

Embcsed Polythene 0.09 o-o2 0.07 0.02

Ernbæsed PolYthene 0.10 0.03 o.11 0.02

(suoercourse 750)

48
 Chapter 2 : Literature Revíew

2.5.5 Stiffness

In order to develop mathematical models of brick masonry walls it is important to

have the value of the stiffness of the maærials making up the structure. Brickwork
walls can be modelled as one-phase or two-phase materials and therefore the stiffness
properties of both the one-phase material and both phases of the two-phase material
are examined.

Reported values for the Young's Modulus of clay bricks ¿ue presented in Table
2.5.r3.

Table 2.5.13 Young's Modulus of Clay Bricks

Details Resea¡che¡
Young's Modulus

(MPa) (origin)

9,750 (Australia) Brooks et al (19?9)

18,000 Used in 2 oha-se finite element mqlel (Au.dralia) Payne et al (1990)

16.000 (Australia) Brooks and Pavne (199O)

- Ba-se and Baker (1973)
24,750 (Australia)

5.920 Loadine parallel to bed ioint (Australia) Paee 11978)

7,550 Loading perpendicular to bed ioint (Au-stralia) Paee (1978)

14,700 (Australia) Zhuse et al (1993)

27,000 Wire cut brick (Britain) Riddington and Ghazali O99O)

10.400 Sinsle frossed pressed common brick (Britain) Riddineton and Ghazali (199O)

The reported Young's Modulus of mortar are presented in Table 2.5-14

The values of Young's Modulus of brickwork determined from experimental work

and/or used by researchers in the modelling of brickwork elements are summarised in
Table 2.5.t5.

The Choice of Young's Modulus of brickwork is not easy. Priestley (1985) used a
young's Modulus of 1,000 MPa in a sample calculation for the earthquake resistance
of unreinforced masoffy. Robinson (1986), in a discussion of Priestley, suggested a
more appropriate Young's Modulus of 10,000 MPa based on the fact that most of
the deformation of a brick wall is in the mortar which makes up only a small
percentage of the total height of a wall. Priestley countered that Robinson offered no

49
 Chapter 2 : Literature Review

from
proof of the 10,000 MPa value and that 1,000 MPa is backed up by test results
the Uniæd States and New Tnaland-

Table 2-5.l4Young's Modulus of Mortar

Mortar Details Resea¡che¡

Young's Modulus

(MPa) Mix Ratio (Oriein)

8,300 1:1:6 (Australia) Brooks et al (1979)

1:1:6 (Australia) Payne et al (1990)

8,000

6.000 Typical range (¡usq4ia) Brooks a¡d Payne (1990)

10,000 Twical range (Australia) Brooks and Pavne (1990)

7,400 (Australia) Zhuse et al (1993)

1:0.4:5 (Australia) Base and Baker (19?3)

8.1 30

1:0:3.5 @ritain) Riddington and Ghazali (199O)

9,100

The values given for the Young's Modulus of brickwork by va.rious researchers in
Table Z-5-I5 shows the large variability in the properties of unreinforced masonry- It
was this variaúon in properties that was the motivation behind the shaking table tests
conducted as part of this research and discussed in chapter 4-

Finally, the Poisson's Ratio of brickwork given byresearchers ranged from 0-11 to
0.25

50
 Chapter 2 : Literature Review

Table 2.5-15 Young's Modulus of Brickwork

Morta¡ Details Resea¡chet

Young's Modulus

(MPa) Mix Ratio (Oriein)

ComDression (Aust¡al ia) Base and Baker (1973)

15,120

21,200 Bending vertically (Aurralia) Base and Baker (1973)

19.240 Bendins horizontally (Australia) Base and Baker (1973)

2.000 "Good" masonry (Atlsúâlia) Jankulovski et al (1994)

900 "Pcnr" masonrY (Australi a) Jankulovski et al (f994)

(Aust¡alia) Paee et al (1985)

5

13,240 From 2 pha-se modelling (Australia) Zhuse et al (1993)

1.000 Used in calculation (New Zealand) Priestley (1985)

10,000 Di-scussion of above (New Zealand) Robinson (1986)

2.991 (Italy) Masenes and Calvi (1992)

1.510 (Peru) San Balolome et al (1992)

4.500 (Slovenia) Tomazevic and Vleiss (1994)

17,750 Pemendiorlar to bed ioint (Brilain) Duarto and Sinha (1992)

1 3,500 Pa¡allel to bed ioint (Britain) Duale and Sinha (1992)

13.910 runited States) Anand and Yalamanchili (1988)

1,000 (ItalvÂJnited States) Catvi et al (19%)

1.652 l:0:3 Staric (India) Arva (1980)

1.16 I 1:0:6 Static (India) Arva (198o)

1.O85 7;O;12 Static (lndia) Arva 11980)

2.266 l:0:3 Dvnamic llndia) Arva (1980)

1,638 1:0:6 Dvnamic Ondia) Arva (1980)

1,422 7:O:72 Dynamic (India) Arya (1980)

51
 Chapter 2 : Literature Review

FINITE ELEMENT MODELLING OF

2.6
BRICKWORK
Brickwork is a two phase material. When researchers and designers modelled
brickwork panels using the finiæ element method it was usual to have a model that
separated the two phases of the brickwork. The model would therefore consist of a
mortar phase, divided into many elements, and a brick phase, also divided into many
elements. This led to models of br-ickwork panels having a large number of elements,
increasing the size of the model and the úme taken to analyse the problem. In this
section finite element models for the two phase modelling of brickwork, as well as
various methods for modelling brickwork as an equivalent one phase model to
overcome the problem of model size and complexity, are examined.

page (1978) looked at a two phase finite element model for masonry walls subjecæd

to in-plane loads. A finite element model was modified to take into account the
specific properties of masonry. The material properties and characteristics were
obtained from a laboratory testing program. The masonry wall was modelled using a
continuum of plane stress elements with superimposed linkage elements simulating
the mortar joints. The bricks were modelled using conventional plane stress elements
with isotropic elastic properties. A typical hniæ element subdivision is shown in
Figure 2.6.1.

Because of the joint elements being extremely thin, the pairs of nodes, (1,3) and
(2,4), are specified by the same coordinates of nodes A and B and the thiclness, t, is
used in computing joint element properties. The ûechnique used to add the joint
element stiffness to the total structural stiffness was originally used in reinforced
concrete and rock mechanics. The joint element stiffness was determined by
minimising the potential energy with respect to the element displacements. An
iterative process was then used to model material non-linearities, solving until
convergence is achieved after checking the solution against failure criterion.

Another two phase fïniæ element model was developed by Sved et al (1982). This
model differed from the Page model in that it only used standard finiæ elements.
Brickwork that was part of a typical wall element was subdivided into small brick-
mortar "modules" as shown in Figure 2-6.2.

52
 Chapter 2 : Literature Review

v
t
3 1 4

1 2
L J
I
L

JointElement
A Þ

b
a

t-
Brick Element

Figure 2.6.1 Finiæ element subdivision.

(from Page (1978)).

The properties of a single module were used to analyse the behaviour of a whole
panel by the investigation of the load-deformation characteristics of a module with
the brickwork in the uncracked and cracked state. The stiffness values obtained from
the module were substituted into differential equations describing the behaviour of
plates of variable thickness. For the uncracked condition the elements making up the
module were coupled at the brick-morta¡ interfaces, and uncoupled whenever tension
stresses occurred at the brick-mortar interfaces. The model had good agteement with
the properties of a brickwork wall panel determined from an experimental æst

program.

Shing et aI (lgg2) used both a one phase model and a two phase model in the finite
element analysis of masonry wall panels. The one phase model used a smeared crack
model to simulate distributed tension and compression failure of masonry units. This
is an approach that has been used for reinforced concrete members. It has the

53
 Chapter 2 : Literature Review

advantage of computational efficiency. The study concluded that the failure of

reinforced and unreinforced masonry wall panels, with and without conhning frames,
can be adequately modelled with a combination of smeared crack and inærface
elements- The later was used to model the separation of a confining frame and

masonry wall. The results were verified by an experimental program.

AtAt ArAo

BrBo

DrDo

(a) briclovork in st¡etcher bond O) finite element details

Figure 2.6.2 Finite element details.

(from Sved et al (1982)).

page et al (1985) described a one phase finiæ element model that incorporated
material characteristics taken from biaxial stress tests on masonry panels. The model
reproduced the inelastic deformations typical of brick masonry and used a failure
criterion that included the orientation of the jointing planes and the state of stress.
Page et al noted an advantage of the one phase model is that a relatively course grid
could be adopæd which led to computational advantages when analysing a large wall
panel. The finite element results were compared to the results from an experimental
test program on five infilled steel frames. The predicted results from the finite
element model for the load-deflection behaviour, the modes of failure, failure loads,

54
 Chapter 2 : Literature Review

and local stress-strain behaviour were all in good agreement with the experimental
results.

Zhuge et al (1993) used a one phase finite element model to model masonry walls-
The model was based on convenúonal four node plane stress rectangular elements-
An equivalent elastic modulus was derived for the one phase material based on the
formula:

E6 = cEs +(1-c)Er'r 0.5 < c < 1.0 (2.6.t)

where Eo is the equivalent elasúc modulus for a one phase material, E" is the elastic
modulus of brick, and Enn is the elastic modulus of mortar. To test Equation 2-6-1
and to determine a suitable value of "c" a wall was modelled two phase material
as a

using the appropriate material properties- A one phase model was then run with an
elastic modulus derived from Equation 2.6.1 with various values of "c"- Good
agreement between the two phase model and the one phase model was obtained
when c = 0.8.

Anand and Yalamanchili (1988) used a one phase model for the brickwork
component of a composite masonry wall (a composite masonry wall consists of a
brick leaf, and concrete block leaf separated by a grouted cavity). The frniæ element
model was used to examine the behaviour of the composite wall when subjecæd to
earthquake induced forces. A2016 node, 1547 element grid was used to model the
three phases of a 3.05m x 3-05m composite wall. The results of the f,rnite element
model were not confirmed by experimental data.

Itcan be seen from the research discussed in this section that the finite element
modelling of masonry can take two paths. First, a two phase model, where the
masonry unit and the mortar are treated as separate materials and the finiæ element
mesh is constructed so as to allow for the individual materials. The alærnative
method is to adopt a single material to represent both the masonry unit and the
mortar phase of the masonry construction. This later method has the advantage of
being considerably less computer intensive than the two phase model as a courser
mesh can be adopted. The one phase method has been adopted successfully by Shing
et al (lgg2), Page et al (1985), Zhuge et al (1993), and Anand and Yalamanchili
(1e88).

55
 Chapter 2 : Literature Review

2.7 E^RTHQUAKE DESTGN MODELS FOR

BRICKWOR
There have been previous attempts by researchers to model the behaviour of
masonry buildings under earthquake induced loadings. While most have focused om
reinforced masonry buildings, some have studied unreinforced masonry buildings. In
this section some of the models proposed by previous researchers are presented.

priesrley (19g5) ourlined the traditional method of seismic analysis of unreinforced

masonry buildings. It was noted that ductility considerations were traditionally
inappropriate in the design of unreinforced masonry. Further, it was stated that the
seismic capacity of unreinforced masonry was not govemed by material strength
but

rather by stability and energy considerations. Priestley also provided the energy path
for an unreinforced masonry building subjected to earthquake excitation (Figure
2.1.D.

energy input path

+
l-

=\

ground motion, a,

Figure 2.7 -I Energy path for a masonry buitding resisting seismic loads.
(from Priestley (1985)

56
 Chapter 2 : Literature Review

Jankulovski et al (lgg4) presented a simple approach for the non-linear

dynamic

response analysis of an unreinforced masonry building- The basic assumption

of the
model was that the vertical elements are connected at the floor and roof levels
by a

rigid diaphragm.

Kwok and Ang (1987) reported on research conducted at The University of Illinios
at Urbana-Champaign on the seismic damage analysis and design of unreinforced
masonry buildings. Kwok and Ang hrst noted that collapse of an unreinforced
masonry wall element was equivalent to failure. It was further noted that under cyclic
loading walls can resist lateral loads through friction mechanisms even after severe
cracking. Two aims of the seismic design of masonry buildings were noted:

(1) Prevention of catastrophic collapse of a structure; and

(Z) Damage should not be concentrated in any particular storey but should be
uniformly distributed among the various stories'

Kwok and Ang then simplified the procedure such that it became the basis for a

modified equivalent lateral force procedure as used in many earthquake codes-

Mengi et al (1984), research conducted at Berkeley, developed a linear

in
the
mathematical model for the in-plane behaviour of brick masonry walls based on
experimental program already reported in Section 2.3. Two models for masonry
were used; a two phase mixture model (MM) and a one phase effective modulus
model (EMM). It was concluded for ground motions with a lower frequency content
than the first modal frequency of the wall element" the EMM should be used. If,
however, the frequency content of the ground motion is higher than the first modal
frequency of the wall element, the MM should be used'

Further work on the modelling of unreinforced masonry by researchers at Berkeley

(1989). As
was reported by Mengi and McNiven (1989) and McNiven and Mengi
with Mengi et al a testing program was undertaken (Section 2.3). A linea¡ isotropic
model was used to model the unreinforced masonry.

Wesley et al (1980) used the "reserve energy" technique for the analysis of the
collapse capacity of unreinforced masonry wall structures. Wesþ et al identifred the
collapse mechanism of unreinforced masonry walls as cracking occurring at the base

57
 Chapter 2 : Literature Review

of the wall followed by rigid body rocking of the wall-roof system as an inverted
pendulum.

A brief summary of several proposed modelling methods for reinforced masonry

buildings follows.

Tomazevic (1987) looked at the dynamic modelling of horizontally reinforced

masonry buildings by the storey mechanism model. Good correlation was
found

between the storey mechanism model and the results of a scale-model testing
program. Tomazevic and Sheppard (1987) used the storey mechanism model to
model masonry buildings damaged in earthquakes and found that the behaviour
of
these buildings was best described by the storey mechanism model-

eamaruddin et al (1985) developed a mathematical

model of a multi-storey
reinforced brick building. Another study of reinforced masonry was conducted by
of a
Soroushian et al (1988). The main emphasis of the study was the determination
model for the hysteretic behaviour of a reinforced masonry shear wall. The building
was idealised as a single degree of freedom system'

The work of Goel and Chopra (1990) examined a number of one-storey buildings
with asymmetric plans. It was found that the linear elastic response of a one-storey
asymmetric plan system depends on the lateral and torsional vibration frequencies
of
the corresponding symmetric plan system.

In summary, it can be seen that some researchers used an equivalent linear model to
simulate the non-linear behaviour of unreinforced masonry. This was accomplished
by various methods such as the "Reserve Energy" technique- In Section 2.9 it will be
seen that another method of achieving this type of model is the use of a response
modification factor, Some researchers only modelled the in-plane elements of the
\.
structure to simplify the model. Single and two phase models were used by
researchers with no conclusive proof that either was better. It would seem
that a
give
single phase masonry material model using an equivalent linea¡ elastic model can
a reasonably accurate model for unreinforced masonry buildings subjected to
earthquake excitation.

58
 Chapter 2 : Literature Review

2.8 FLOOR FLEXIBILITY/STIFFNE SS

The stiffnesses (EA) and the related flexibilities of floor and roof diaphragms play an
important part in the determination of the overall stiffness of a building and the
distribution of the forces and the moments in the building.

In this section a review was conducted on various studies into the effect of the

horizontal-vertical element connection on the properties of a building. Also, a review

of studies into the sensitivity of the structural behaviour to floor/roof stiffness was
also undertaken.

Moon and [æe (Igg4) reported on a study to investigate the effects of in-plane floor
slab flexibility on natural periods, mode shapes, seismic base shear, and the
distribuúon of seismic base shear. The study involved two structures, a 6-bay 5-
storey building, and a 10-storey building with set back- Two types of structural
system were considered for each building, a frame system, and a frame plus shear
wall sysrem. The buildings were each modelled with a rigid floor diaphragm (no in-
plane floor flexibility, EA = inhnity) and a semi-rigid floor diaphragm (some in-plane
floor flexibility).

Moon and Lee found that for frame type structures that in-plane floor slab flexibility
did not have a significant effect on the natural period of structures. For the frame
plus shear wall structures the inclusion of in-plane floor slab flexibility increased the
natural period of the structure. Moon and I-ee concluded that the period for the
semi-rigid floor diaphragm was up to 2.5 times that for the rigid floor diaphragm. In-
plane floor slab flexibility also led to mode shifs for the buildings.

In order to compare the seismic behaviour of the two types of floor slab flexibility,
Moon and [æe undertook modal analysis of the structures using the Applied
Technology Council (ATC (1984)) design spectra. For the frame type structure, the
effect of floor slab flexibility on the base shear was not significanl For the frame plus
shear wall structures, floor slab flexibility reduced the seismic base shear. This was
attributed to two things:

(l) Increase in period associated with the in-plane floor slab flexibility results in
the structure being on the descending portion of the design response spectra
(see Figure 5.2.1); and

59
 Chapter 2 : Literature Review

(2) Decrease in the effective weight for the lower modes'

It was also found that the use of rigid floor diaphragms in models of low rise building
structures with end walls can result in underestimation of the storey shea¡s and
column axial forces.

Adham and Ewing (1973) studied the effect of roof diaphragms of va¡ious stiffness
on the behaviour of unreinforced masonry buildings. Three floor diaphragm stiffness
values were used, with diaphragm stiffness values in the ratio 20:4:1. It was
found

that the natural period of the structure increased with increasing period, similar to
what was found by Moon and L,ee. Simila¡ base shear conclusions to Moon and I-ee
were also found bY Adham and Ewing-

Itcan be seen that the stiffness of the horizontal elements of the structure play an
important part in the determination of the response of a structure to earthquakes- In
the laær parts of this study, the influence will be investigated further to determine the

effects of the properties of the horizontal elements-

60
 Chapter 2 : Literature Review

2.9 APPROPRIATE, Rf FOR UNREINFORCED

MASONRY

An important consideration in the equivalent static load approach to earthquake

design is the choice of the structural response factor, or response modification factor,

\ This is a factor included in the calculation of the base shear, and subsequently, the
loads applied to the various levels of a structure to simulate earthquake induced
inertia forces, that allows for structural over-strength, damping, and the ability of a
structure to support load into the inelastic behaviour range of its materials. It is a
factor that varies with material type and the structural system.

Prior to examining the va¡ious recommended and proposed values of \ an

examination of the meaning of R, is presented. The explanation is based on Uang
(1ee1).

Figure 2.9.1 shows the structural response idealised by a elastic-perfectly plastic

curve. The structural ductility factor is defined as:

Fr
(2.e.r)

where the deformation is expressed in terms of inter storey drift, Å. Because of this
ductility (or energy dissipation capacity), the design force can be reduced to C, by a
ductility reduction factor, Ru.

Cv (2.e.2)

This reducúon factor is usually computed with an equivalent viscous damping ratio,
usually five percent of critical. C, is then reduced to C. by an over-strength factor, Ç),
such that:

C, 9. (2.e.3)
o

and C, is the minimum required design base shear ratio corresponding to the first
significant yield levet defined by Uang (1991) as a level beyond which the first
plastic hínge forms and the global structural response starts to deviate signíficonþ
([IBC
from the elastic response- Codes such as the "Uniform Building Code"

61
 Chapter 2 : Literature Review

(1991)) specifies the seismic force level for allowable stress design by reducing
further the C, level to the C* level by a factor Y. The \ factor in the Australian
Standard "Minimum design loads on structures - Part 4 : Earthquake Loads"
451170.4-1993 incorporates the ductility reduction factor, the over-strength factor,
and a correction for the assumed hve percent critical damping.

C"o

Actual
Response
R,C,
Idealized
Response
cy

_ü. CS
QC"
YCo, C,"

Â*4 \, Â.,'

Storey Drift,
^

Figure 2-9.1 General Structural Response.

(from Uang (1991)

451170.4 specifles an Rr of 1.5 for use with any unreinforced masonry lateral load
resisting system when used with the equivalent static load design approach and the
response spectrum method. This is the smallest \ allowed in 451170/ and only
considers over-strength and damping and assumes m¿ìsonry buildings do not exhibit
any ductile behaviour. The maximum & in 4S1170.4 is 8.0 for reinforced concrete
and steel moment resisting frames. Hutchinson et al (1994) noted that the \
factors

in 4S1t70.4 are taken from the "Uniform Building Code" and a¡e modified to reflect
the ultimate limit state condition used in the Australian loading codes and a slight

62
 Chapter 2 : Literature Review

difference between the two codes in the proportion of live load included in the

overall weight of the structure-

The ',NEHRp Recommended Provisions for the Development of Seismic Regulations

for New Buililings Part 1" (NEHRP (1991)) has a \, or in the case of the NEHRP
an R factor, of I.25. The "NEHRP Recommended Provisions for the Development
of Seismic Regulations for New Buildings Part 2: Commentary" (NEHRP (1991))
described the R factor as taking into account damping and ductility. There
i.s no

mention of over-strength. This factor is close to the 4S1170.4 factor and with the
inclusion of over-strength the NEHRP factor would increase and could become
closer to the AS 1170.4 value. The other earthquake code used in the united States
is

the ,'Uniform Building Code" and it is from this code, as noted previously, that the
AS 1170.4 R, values are taken (Hutchinson et al (1994))'

In the 1985 National Building Code of Canada (Zhu et al (1989)) the equivalent
static load approach uses a form of equation that is different to the usual form found
in most of the world's earthquake codes and subsequently the factor that is the
equivalent of 4S1170.4's R, is not directly comparable to the values from other
codes. The factor, K, is 2.0 for unreinforced masonry buildings. Rainer (1987)
calculated an equivalent R (or factor based on the "Tentative provisions for the
Ç
development of seismic regulations for buildings" (ATC (1984) for a K = 2.0 of
2-27 whichis considerably greater than the 'A.S1170.4 value which means a lower
elastic force demand and an assumed higher level of ovef-strength, damping and/or
post-elastic behaviour. Rainer, noting this discrepancy' suggested that the 1985
Canadian Code be changed to a R factor and brought in line with the ATC'

The 1990 National Building Code of Canada (Tso and Naumoski (1991) and
Chandler (1991)) changed from the K factor of the 1985 code to a form of
the
equivalent base shear formula that is similar to the form used by AS1l7O.4 and
ATC. There is one major difference between the response mdification factor, R,
from the Canadian code and \ used in 4S1170.4. The R in the Canadian code is the

ratio of the elastic strength to actual strength (Tso and Naumoski) and is therefore
only a ductility factor. Another factor is used to take into account over-strength- Rr
is both the over-strength and ductility factor. Tso and Naumoski report that the over-
strength factor has an assigned value of 0.6 and that R varies between 1 for a
non-

ductile system to 4 for a ductile system. Combining these two factors into an
effecúve ¡ç for a non-ductile system, such as unreinforced masonry, yielded a & =
1.667, very close to the 4S1170-4 value.

63
 Chapter 2 : Literoture Review

The regulations for the seismic design of buildings in Mexico City were discussed by
Fukura (1991). A reduction factor for the ductility of structures is included in the
Mexico City design requirements and for unreinforced masonry structures such as
those in this study a reducúon factorof 1.0 is specifred (under structure type - other
structures). The largest reduction factor in the Mexico City code is 6-0- This is
just
similar to the factor in AS1L70-4 where the \ = 1-5 reflects no ductility and is
an over-strength and damping factor.

The Chilean seismic code, as reported in Moroni et al (1992)' has a more

sophisticated approach to the determination of a seismic force reduction factor than
the previously noted codes. A formula is given in the Chilean code that uses a factor
dependant on the soil conditions, To, the period of the structure, T, and a parameter,

\, related to the structural ductility. The formula is given as Equation2-9.4.

T
R=1+ T
(2.e.4)
0.10T^
"
+
Ro -1

Moroni et al did not give values of To or Ro.

Riddell et at (1989) proposed the use of a response modification factor that is

partially consistent with the Chilean code in that it uses the building's period as a
variable. A bi-linear response modiñcaúon factor is proposed which consists of a
linearly increasing response modification factor from 1.0 at a period of 0, to a
maximum value depending on a ductility factor, p. The curve then remains constant
for increasing period. The period at which this maximum first occurs also depended
on p. The response modification factor was expressed as:

R=1+R
T
-1r for0<T<T* (2.e.s)

R= R* for T ) T' (2-9-6)

where the values of R* and T* are given in Table 2.9-I fot various values of p-

The use of a structural response factor that is period dependant was also noted in
Hutchinson et al (1994) as a way of correcting reported increased ductility demands
in short period structures.

64
 Chapter 2 : Literature Review

Table 2.9.1 Values of the parameters of the bi-linear relation for the response
modification factor, R
(from Riddell (1989))

Ductility factor, P, for a

sin gle-degree-of-freedom R- T. (seconds)

system
2 2.0 0.1

3 3.0 o.2
4 4.O 0.3

5 5.0 0.4

6 5.6 0.4

1 6.2 o.4

8 6.8 o.4

9 7.4 0.4

10 8.0 o.4

It can be seen that the response modification factor in the Australian earthquake
code, 4S1170.4, has a similar value to the other earthquake codes around the world
that have a similar approach to design. It is suggested by some researchers, however,
that the structural response factor should be period dependant. For unreinforced
masonry buildings the periods may be found to be in a small range (Chapær 3) and a
constant value of the structural response factor may still be appropriate'

65
3. FItrLD TESTING

3.1- II{TRODUCTION
As outlined in Secti on 2.L, earthquake design requires reliable estimates of the
natural period of a structure to calculate an earthquake design force. The
appticability of existing earthquake code formulae for the natural period when
applied to unreinforced masonry buildings was examined. The natural periods of a
series of buildings were measured and the results compared to the periods
determined by period formulae from building codes and proposed by other
researchers. These period formulae have already been discussed in Section 2-1.

The only way to determine the actual natural period of a structure, as opposed to
that determined by some form of mathematical modelling, is to measure it. In order
to conduct tests on existing unreinforced masonry buildings it was fust necessary to
devise a testing methodology that was reliable, non-destructive, and had minimal
impact on the occupants, as well as addressing the problems higtrlighted by other
researchers and noted in Section 2-2.

The procedure to be used was broken down into five components:

(1) Source of vibration to record;

(2) Data collection on site;
(3) Digitisation of the data;
(4) Conversion of the data to the frequency domain; and
(s) Examination of the data.

While each component was dealt with separately, the interaction and compatibility of
the components was carefully considered.

66
 Chapter 3 : FieldTesting

3.2 DEVELOPMENT OF TESTING

METIIODOLOGY
3.2.1 Source of Vibration

The source of the vibration to be recorded and subsequently analysed to determine

the natural frequencies was the first part of the testing procedure to be considered-

Initially, the use of a small dynamic oscillator was considered, located either in the
building, or on the ground near the building. This is the same method employed by
various authors in forced vibration tests. However, it had three main disadvantages:

(1) Setting up and removal time on site;

(2) Disruption to occuPants; and
(3) possibility of damage, or blame for damage to the building due to extra stresses
induced in the structure as part of the test-

These three disadvantåges ruled out forced vibration testing for this project.

It was decided to use ambient vibration as the source for the vibration measurements
of the buildings. This immediately overcame the three disadvantages of the forced
vibration method listed above- Ambient vibrations have been used successfully by a
number of researchers to obtain a reasonable estimation of the natural period, as has
previously been noted in Section 2.2. No external vibration source was required and
the on siûe set-up consisted of only the basic instrumentation required for the
recording of the building response-

3.2.2 Data Collection on Site

The measurement of vibration can be achieved by the measurement of one of three

physical actions:

(1) Displacement;
(2) Velocity; or
(3) Acceleration.

Ideally the measurement of vibration \ryas to be achieved by the use of existing

departmental resources, provided no compromises in the quality of the data was

61
 Chapter 3 : FieldTesting

resources- No
encountered. This ensured the most optimum use of the project's
ruled out'
equipment existed for the measufement of velocity so this was immediaæly
Both displacement and acceleration have been used by previous researchers without
problem.

To measure the displacement of a structure the use of a displacement transducer is

require¿. The displacement is measured relative to a fixed datum. This datum
would

need to be very stiff to ensure it will not move relative to ground. While this
would

present no problem in a laboratory, the setting up and dismantling of such a frame on

siæ would counteract the main advantages of using ambient vibration, namely,
the

ease with which tlie tests could be set-up and conducted'

Hence, acceleration proved to be the best solution. Absolute acceleration was

measured by attaching accelerometers directly to the building. The accelerometers

chosen were the KISTLER 3054 model. These accelerometers have an upper
acceleration limit of fifty times the acceleration of gravity and a lower limit of 0-0005
times the acceleration of gravify. While it was not expected that the upper limit
would be reached, the recorded accelerations were expected to be around the lower
limit so all recorded accelerations were compared with the lower limit to ensure the
results were within the linear operating range of the accelerometers.

'Plasti-
The accelerometers were attached to the buildings using plastic mounts and
Bond, two part adhesive compound. The mounts were easily removed after the
completion of the test by gentle hammering. This also removed the 'Plasti-Bond' and
left no trace of the test having been conducted. The accelerometers could be
mounted on any material usually found on a building, concrete, masonry, timber, or
steel. This ensured that the location of the accelerometers was not compromised by
any difhculties in attaching them-

The positioning of the accelerometers was critical. Incorrect positioning could lead
to the localised modes of the building elements being recorded with the desired
overall building modes (refer Figure 3.2.L). Separation of the two types of modes
from the combined recording would be impossible. To overcome this problem the
accelerometers were placed at the floor and roof levels of the building as these were
node points of the local vertical modes of vibration of the walls (a node is a point of
no relative displacement for the mode shape - see points labelled (2) in Figure 3-2-I)
and ensured that these local modes were not present in the recorded data- The
horizontal location of the accelerometers was at the corners of the building as these

68
 Chapter 3 : FieldTesting

were node points of the local horizontal modes of vibration for the walls and
again
the
ensured that these vibrations were not present in the recorded data. By recording
present in
data from the corners of the buil<Jing, torsional modes were expected to be
data
the data. These modes were identifiecl because of their presence in the recorded
of both axes.

(1)

(2)
plan (3)
(3)
Q)
(b) torsional mode
local mode of wall
(1) subject to out ofPlane
bending (A) accelerometers at Positions
denoted by (1) measure modes
(A) and (B)
accelerometers at positions
overall building
denoted by (2) measure mode
mode (B)
(B) only
accelerometers at positions
denoted by (3) measure torsional
elevation modes
(a) lateral mode

Figure 3.2.lBffect of accelerometer location on recorded modes.

Accelerometers were also placed in both directions at the ground level of the
buildings to identify the exciting vibrations in the recorded data. This ensured that
the exciting frequency was easily identified in the upper level records

Itwas necessary to position the accelerometers in a vertical line so that the mode
shapes of the building could be determined. This was easily accomplished along the
corners of the building. The data for one direction was recorded simuløneously so
that the magnitude of the exciting force was constant for all levels of the building and
the relative magnitudes at each level were compatible-

69
 Chapter 3 : FieldTesting

The accelerometers were connected to a seryo-amplifier operating in the 0'2 g

per

volt range. This setting was found by trial and error during initial tests to result in the
best resolution of the data for the levels of excitation experienced under ambient
vibration conditions. After the attachment of the accelerometers to the building the
gain of the servo-amplihers was adjusted to 'zero' the output. This meant adjusúng
the gain until the acceleration was centred about zero volts. While it was not possible
to exactly 'zero' the accelerometers, the 'zero' level was set within t 10 millivolts-

Two of the major requirements for the data collecúon and recording device were
reliability and portability. One possible solution would have been the use of analogue
tape recorders as used by previous researchers. A better alternative was provided by
the computer program 'Chart' with the'Maclab'data collection device running on an
Apple Macintosh SE personal computer. 'Chart' is a computer simulaúon of an
analogue chart recorder. This system provided the capacity to record up to eight
channels of data, which was more than sufhcient for the unreinforced masonry
buildings in Adelaide. The data was recorded on a 3.5 inch computer floppy disk for
further processing.

3.2.3 Digitisation and Filtering of the Data

To be abie to undertake further processing of the data afær it was collected on siæ
the data was converted from an analogue to a digital format. The 'Maclab' system
digitised the dat¿ prior to recording and therefore no further actions were required-

Wittr the acceleration data being recorded with respect to time, the 'Sampling
Theorem' (Appendix A) was invoked. As the periods of interest were low, because
of the high stiffness and relatively low height of the unreinforced masonry buildings,
the frequencies measured were expected to be in the 2 to 10 Hertz range so a low
pass filter with a cut-off of 20 Hertz was used. To keep the frequencies of interest
and the filæring frequency well below the Nyquist frequency of the digitising device
a sampling rate of 100 Hertz was adopted (resulting in a Nyquist frequency of 50
Hertz). The filter used was a 5 pole Butterworth filær-

As will be explained later, 20.5 seconds of data was recorded. At 100 Hertz this
resulted in at least 2048 (2k) points of data being available for conversion to the
frequency domain.

70
 Chapter 3 : FieldTesting

3.2.4 Conversion of the data to the frequency domain

A Fourier transform was used to convert data in the time domain to the frequency
domain. Various algorithms exist fur different computer packages for the Fourier
transformation of clata. Three readily available in the Civil and Environmental
Engineering Deparlment were considered for use in this study.

(1) Hewlett Packard Structural Dynamics Analyser;

(2) 'Maclab Scope' program; and
(3) 'Lab-Workbench' computer software-

However, after consideration of the compatibility between the format of the recorded
data and the format required for the input of the data to the three alternatives, as
well

as the format of the output data from the Fourier transformation, it was decided to
use 'Lab-Workbench'.

'Lab-Workbench' is a UNIX based data collection and manipulation program. It is

run on a MASSCOMP real time UNIX computer and is controlled from a graphics
terminal using a flow chart and icon system. The transfer of the data from Maclab to
MASSCOMP was relaúvely simple. The data was saved in text mode in the 'ChaÍ'
program and transferred to the UNIX operating system via the 'Macintosh' program
'MacKermit'. This program transferred the data serially while alæring the data format
to UNIX. There is no restriction on the number of channels to be transferred
simultaneously. A file similar to that produced by the 'Lab-Workbench'
header
program when storing data was created using the UNIX system editor 'vi'. This
allowed the use of the 'playback' module in 'Lab-Workbench' to load the dat¿- The
'power spectral density'module was used to change the data from the time domain to
the frequency domain. The output of the 'power spectral density' module was saved
in the same format as the input data. At the time of testing, no "haId" copy output
from the MASSCOMP was possible. It was necessary to transfer the data from the
UNIX sysrem ro a MS-DOS PC and load the data inûo either of the spreadsheæt
'Excel' or the program 'C-Plot' for output in graphical form to a laser printer- This
transfer was completed using the standard'Ethernet' computer connection.

The 'Lab-'Workbench' provided a sharp and clear power spectrum of the data. From a
trial and error approach with various lengths of input data it was found that 2048
points per channel provided the sharpest image. While less points provided the
power spectrum peaks at the same frequency with the same magnitude, the peala

1T
 Chapter 3 : FieldTesting

were more easily disti.guishable with 2048 points. More points had no significant
effect on the resolution of the output. As outlined in Section 2.2itis necessary
to use

a window to make the data periodic. The options included in the program for
windowing were all tried and, while none were signihcantly better than the others'
the Blackman-Hanis window was adopted for tliis study'

3.2.5 Examination of the Data

The power spectra of the data were examined. Firstly, the peaks in each spectrum
were identified as the natural frequencies of the building. A peak was always
present

at the 0 Hertz point representing the DC offset of the accelerometers. Even though
tlre accelerometer output was 'zetoecl' prior to the test, a small voltage at zþfo
acceleration was always present. The lateral and torsional modes were identified
from the data as discussed in Section 3.2.2- If a peak was common to both axes of
mode
the building it was not possible to determine whether the mode was a torsional
or a combined torsional and lateral mode-

In order to estimate the mode shapes for each of the buildings in this study, the
magnitude of the response spectrum peaks for each frequency at each level were
normalised and plotted against the height of the building.

3.3 TESTING PROGRAM

3.3.1 The Physics Building Annex

The first unreinforced masonry building to be tested was a five storsy annex to the
physics Building on the University of Adelaide's North terrace campus. The results
of this test indicated that the fundamental natural frequency of this building was 3'1
Hertz (see Figure 3.3.1). This result was promising because the annex is located
more than 500m from any street and was expected to be subject to very low levels of
ambient vibration. Thus, the method was established as being capable of deærmining
the structural periods for buildings subject to low levels of excitation-

An estimaæ of the normalised hrst mode shape was also determined (see Figure
3.3.1) based upon the power spectral density values at each floor. It was not possible
to determine the second mode shape because the power spectrum data did not
include enough information to estimate the point at which the mode shape crossed
the vertical axis-

72
 Chapter 3 : FieldTesting

Roof 1.00

no result lst Mode

5th Floor
at 5th floor

4th Floor 0.34

3rd Floor 0.13

2nd Floor 0.08

lst Floor 0.02

3.1 5.9
Frequency (Hertz)
(a) Power Spectrum O) Normalized Mode ShaPe

Figure 3.3.1 Physics Annex Results

3.3.2 The Engineering Building Annex

After the physics Building Annex test, the annex of the Engineering Building at the
University of Adelaide was also tested- This building is a steel moment resisting
used
frame. It was chosen because it contained a gantry crane. The gantry cfane was
to impart a pulse excitation to the structure by running it into its end stops- This
caused a pulse excitaúon and the structure responded at its natural frequencies-
The

results from the pulse excitation tests were compared to the results from an ambient
vibration test on the same structure- The natural frequencies determined by both tests
agreed, hence providing further confidence that the ambient vibration tests were
suitable to obtain period estimates.

3.3.3 General Testing Program

Ambient vibration testing was conducted on hfæen unreinforced masonry buildings,

inctuding the physics Building annex, in the Adelaide central business distict
and

meüopolitan area using the method outlined above. The data was recorded

73
 Chapter 3 : FieldTesting

there was
concunrently for both directions of the building, except in one case where
insufhcient accelerometers, on the MACLAB system'

The raw data was transferred to the MASSCOMP system. After calibraúon, the data
from three buitdings was found to be below the lower limit of the accelerometers and
were discarded from the data set. All three buildings were single storey- One building
in the remaining twelve, a city social club (IAC), has two results included in the final
data set because it was considered to have two parts with differing dynamic
properties and the accelerometers were placed to record the vibration modes
associated with each part seperately.

The thirteen results from the twelve buildings not eliminated from the testing
program are given inTable 3.3.1 along with various parameters associated with the
period formulae given in Section 2.1. Full details, and plans of the buildings are given
in Appendix B.

3.4 EXPECTED FORM OF PERIOD FORMULA

The naturat period of a structure is a function of the ratio of the structure's mass to
its stiffness (Ctough and Penzien (1993)). Assuming that the deflection of an
unreinforced masonry building, or any panel or shear walled building, is
predominantly a result of the shear deflection of the walls then the deflection of the
building could be expected to be of a simila¡ form to the equation for the shear
deflection of a beam, Equation 3-4.I, as shown in Figure 3-4.I. This makes the
simplifying assumption that the earthquake induced load acts at the top of the wall
only, and hence, the wall has a straight deflected shape-

Ph
(3.4.1)
^=k AG

where A is the shear deflection, P is the force, h is the height, A is the cross sectional
area, G is the shear modulus, and /< is a constant-

The shear stiffness of a wall, K, is given by:

r=3 (3.4,2)

74
 Chapter 3 : FieldTesting

Table 3.3.1 Results of ambient tests

Plan Buitrling Íleight, Building Ptan Measured

h (melres) Dimensioos, Period, Floor Type

Building Description v
D* and D, T, and T, Conc¡ele/Timber
L_-"'
(mehqs) (.seconcLs)

2 storey vacant ctty

7.8 3.9 x'1.3 0.208 and 0.200 timber
commercial building
t-t
2 storey vacant city
7.8 '1-i x12.2 0.278 and 0.20O timber
comrnercial builtìing
(EE3)
2 storey vacant citY
7.8 7.3 x 12.2 0.27O and 0.200 timber
commercial building
(EE4)
I storey suburban
3.9 20.6 x 11.5 0.057 and * timbe¡
residence
rWARD)
3 storey school
8.8 lO.9 x32.4 O.182 and * conqete
bui'lding
(CBC) l-l
1 storey city
3.6 19.8 x 14.5 0.073 and 0.0?2 conqete
social club
(IAC)
2 storey city
social club
IIAC)
3lorey city
I 6.5

13.0
19.8 x 36.1

23.5 x29.O
O.092 and 0.089

0.313 and 0.270

concfele

concf€le
commercial building
GTD
2lorey city
commercial building
INSC)
2 storey city retail
r 8.0 11.4 x 28.8 0.099 and * concfete

9.3 l0.O x 27.O 0.135 and 0.133 timbe¡

building
(STP) ¡
5 storey universitY
19.1 12.2x48.8 0.323 and * coDcrìe¡e
building
(olw) E
2 storey suburban
4.6 5.5 x 15.0 0.139 and O.137 concf€te
apartment building
(KIDA) t¡
2 storey suburban
4.6 5.5 x 20.0 O.139 and O.139 concfele
apalment building
(KIDB) t¡
* denotes resutt not available for lltis direction.

75
 Chapter 3 : FieldTesting

P
Ka>

Figure 3.4.1 Shear Deflection of a Beam-

The shear area is proportional to the depth of the building, D, so that:

rc*2h (3.4.3)

where G and k are constants in Equation 3.4-I.In addition, the mass of the building
is proportional to the breadth, B, depth, D, and height, H so that substituting into the
equation for natural Period gives:

BDh (3.4.4)
Jæ
Dlh

So that it could be expected that a period formula for unreinforced masonry, or any
panel type building, would take the form:

T ". h',Æ (3.4.5)

76
 Chapter 3 : FieldTestíng

To take this analysis further, it could also be assumed that the stiffness of the
building would be proportional to its breadth, B, as a wider building would be
expected to have more walls parallel to the direction of interest which would
contribute to the shear stiffness. Hence, Equation 3.4.5 would reduce to the period
being proporlional to the building's height:

T".h (3.4.6)

3.5 COMPARISON \ryITH PERIOD FORMULAE

The tested buildings were divided into two categories; those buildings where the
floor was a concrete slab and those where the floor was timber. The distinction was
considered important because of the detail of the connection between the floor and
the wall for the two types of floor system were expected to lead to different types of
behaviour between the wall and the floors. Considering the concrete slab floor
system first. The typical connection detail for the buildings in the study with concrete
floors is shown in Figure 3.5.1(a). It can be seen that rotation would not be expected
to occur between the floor and wall for this type of connection. The typical
connection detail of a timber floor to a masonry wall is shown in Figure 3.5.1(b). It
can be seen that rotation can occur between the wall and the floor for this type of
connection. The building's type of floor system is included in Table 3.3-1.

As previously stated, the aim of this part of the research project was to ascert¿in the
accuracy of various formulae for the estimation of the natural period of unreinforced
masonry buildings for use in earthquake design. To accomplish this, the natural
periods determined from the field tests were plotted against the various parameters
from the period formula discussed in Section 2.1.

Three linear regressions were carried out for each of the forms of period formula:

(1) Using all the data;

(2) Using the data from the buildings with concrete floor systems; and
(3) Using the data from the buitdings with timber floor systems.

The linear regressions were performed so that the resulting regression line passed
through the origin (0,0) of the plot (Appendix C). The confidence intervals
corresponding to the va¡ious period formulae were also calculated- It can be seen

71
 Chapter 3 : FieldTesting

tlrat for the Australian design response spectrum (Figure 5.2-l) an underestimation of
the fundamental natural period will result in a design earthquake force either equal
to, or less than, that corresponding to the actual fundamental natural period. For this
reason the calculated confidence intervals were single sided. That is, a 30 percent
confidence interval meant that per-iod formula predicted a fundamental natural period
less than or equal to the actual fundamental period for 30 percent of the data- The
resulting plots of the parameters from the various forms of the period formulae
against the measured periods can be seen in Figures 3.5-2 to 3.5-22. The various
period formulae are also plotted on the appropriate graphs along with the regression
cuwes. The results are summarised ilr Table 3.5.1 along with the values of R2 (a
measure of the fit of the form of the formula to the measured data) for each of the
forms of the period formula and for each of the three sub-sets of data.

concrete slab restrained timber floor able to

by masonry rotate on wall

\ L s lL al
I /llr

deformed
deformed
shape
shape

(a) Concrete Floor System (b) Timber Floor System

Figure 3.5.1 Concrete and Timber Floor System Connections to Walls.

The frst form of period formula to be compared was that found in The Australian
Standard "Minimum design loads on structures - Part 4 : Earthquake Loads"
4S1170.4 (Equations 2.1.I and 2.1.2). The three comparisons are shown in Figures
3.5.2,3.5.3, and 3-5-4. Next form of period formula to be compared was that found

78
 Chapter 3 : FieldTesting

in The Australian Standard "SAA Earthquake Code" AS2l2l @quation 2'1'3)' The
three comparisons ate shown in Figures 3-5.5, 3-5-6, and3-5-7 -

The alternarive fonn of period formula from 452121 (Equation 2-I-4) was compared
next. The three compadsons are shown in Figure 3.5.8,3-5-9, and 3-5.10. The next
comparison was for the form of equation used in the "Tentative provisions for the
development of seismic regulations for buildings" (ATC(1984)), Equation 2-l-5-
Tlrese compadsons are shown in Figures 3.5.11,3-5.12, and 3-5-13- The revised
form of the ATC formula (Equations 2.1.5 and 2.1.7) was compared to the measured
periods in Figures 3.5-14,3.5.15, and 3.5.16. The next form of period formula
compared was the expected form of period formula for a masonry building (Equation
3.4.5). The comparisons are shown in Figures 3-5.I7,3.5.18, and 3.5-19- The hnal
form of period formula compared was that given by Housner and Brady (1963)'
Equation 2.1.15- The comparisons are shown in Figures 3-5-20,3.5.21, and3-5-22-

AS1170.4, T:*
0.8
AS1170.4, T:+
JapaneseCode, T=0.02h
0.6

regression, T:å
Period /-'
- -¿-- -
0.4
(seconds) -'-1"--- -'
\--/': -- --'{
X --l'
/
X:/ -/
-z- "'
0.2
X
..b{=>-¿
";- x
t; ¿^:t¿
lx
,5F X

0.0
.r'4
0 5 10 15 20

Height, h (meftes)

Figure 3.5.2 Plot of Period versus Building Height h - All Data-

79
 Chapter 3 : FieldTesting

- AS 1 170.4 and resression, t:I

0.8
46

- ASl ll0.4,T:+
58

0.6 - Japanese Code, T = 0.02h

Period 0.4
--
(seconds)
X ¿- --'K
yl
0.2
X ,'7*-=-;
X
- rX4
0.0
0 5 10 15 20

Height" h (metres)

Figure 3.5.3 Plot of Period versus Building Height, h - Concrete Floor Systems-

- 4S1170.4, r:) 46
0.8
-AS1 170.4, T:+
58

0.6 - Japanese Code, T =0.02h

regression, T:+
4t
Period 0.4
(seconds)
X --/-2'-- "2
--11>: -- -
--:'2
0.2 -1"-
-.í7
--t
./- t' --
-')?
X

0.0
-tr-ê
0 5 10 15 20

Height h (met¡es)

Figure 3.5.4 Ptot of Period versus Building Height, h - Timber Floor Systems.

80
 Chapter 3': Field Testing

0'09h
0.8 AS212l..JD
1=
regtessron, 'l': 0.079h
JD
0.6

.¿¿
Period
-/'¿.
0.4 -/
(seconds) ' --' ./ X
X
X x
X X
0.2 4 X
XX {X X
X X X
.t'#-
0.0
0 2 4 6

:h
JD

h
Figure 3.5-5 Plot of Period versus
5 - All Data.

0'09h
0.8
.
AS2l2l.1= ,./D
0.082h
tegresston, ,:-JD
0.6

Period 0.4
(seconds)
x -' -'j-'
.¿
X
x --._-
-' .-
0.2 -X
XX i
X X X

0.0
0 2 4 6

:h
JD

h
Figure 3.5.6 Plot of Period versus
6 - Concrete Floor Systems.

81
 Chapter i : FieldTesting

ASZI2:, t:H
0.8
regression, t:#
0.6

Period 0.4
(seconds)
-x.-'
X- -/. X
0.2
xa X

, *'-
0.0
0 2 4 6

:h
JO

h
Figure 3.5.7 Plot of Period versus - Timber Floor Systems.
.,6

- AS2l2l,T=0.lN
0.8
- Muria-Vila, T=0.039N
regression, T=0.079N
0.6

Period 0.4
(seconds) X
.x
X X

0.2 x
-xx
/ ;d
0.0
0 2 4 6

Number of Storeys, N

Figure 3.5.8 Plot of Period vefsus Number of Stories, N - All Data.

82
 Chapter 3 : FieldTesting

- 452121, T=0.lN
0.8
- Muria-Vila, T=0.039N

regression, T=0.068N
0.6

Period 0.4
(seconds)
.x
X

0.2 tx
-X'
X

0.0
2 4 6
0

Number of Storeys, N

Figure 3.5.9 plot of Period versus Number of Stories, N - Concrete Floor Systems.

- AS2L}L,T=0.lN
0.8
- Muria-Vila, T=0.039N

regression, T=0.097N
0.6

'/ '/
-'/
Period 0.4 -'/
(seconds) .'/ .:?
'/
o.2

-----4-'--
0.0
2 4 6
0

Number of Storeys, N

Figure 3.5.10 Plot of Period versus Number of Stories, N - Timber Floor Systems-

83
 Chapter 3 : FieldTesting

UBC, T = 0.049h3/a
0.8
regression, T : 0.037h3/a

0.6

Period 0.4
.X
(seconds) -f
X X

0.2 \-{
-"x X
X
X
XX
? -'¿
0.0
0 2 4 6 8 l0

h3/¿

Figure 3.5.11 Plot of Period versus h3/4 - AU Data.

- UBC, T=0.049h3/a
0.8
regression, T = 0.035h3/a

0.6

Period 0.4
(seconds) .X
- -X-'
X

0.2
-'x x
'-- .X X
z.-i'-
0.0
2 4 6 8 10
0

h:/¿

Figure 3.5.tzPlot of Period versus h3/a - Concrete Floor Systems.

84
 Chapter 3' : Field Testing

UBC, T = 0.049h3/a
0.8
regression, T : 0.040h3/a

0.6

Period O.4
(seconds)
x._ -

-. -
-*_-
0.2
zx
- "-/
-- X
0.0
0 2 4 6 8 10

]n3l4

Figure 3.5.13 plot of Period versus h3/a - Timber Floof Systems.

0.8

0.6

Period 0.4
(seconds)
x
X
0.2 X x
-x
xx- Xã
./- - 'ry X
-i
/- ;>r
0.0
0 2 4 6

:h1l¿
JA"

1
Figure 3-5.L4 Plot of Period versus h3l+ - All Data.
',Ã;

85
 Chapter 3 : FieldTestíng

0.8

0.6

Period 0.4
(seconds)

0.2

-&x
-/-
-rr<-1-
0.0
2 4 6
0

:h3/¿
JA"

Figure 3.5.15 Plot of Period versus h3/a - Concrete Floor Systems.

0.8

0.6

Period 0.4
(seconds)
x
./
0.2 ./x.z' X x

./-/ - n'.-"i
.
---X'
0.0
0 2 4 6

:h3/¿
JA"

Figure 3.5.16 Plot of Period versus hïl+ - Timber Floor Systems.

86
 Chapter 3 : FieldTesting

regression, T = 0.023hJ8
0.8

0.6

Period 0.4
(seconds) X
X
x.{
0.2 >?. ./ X X
x< ,"* X

.x^ x
X

0.0
0 l0 20 30 40

hJB

Figure 3.5.I7 Plot of Period versus h.,Æ- - All Data.

regression, T = 0.02lhJB
0.8

0.6

Period 0.4
(seconds)
Y X
X..
0.2 X
x< /xx
X X

0.0 ^
0 10 20 30 40

hJB

Figure 3.5.18 Plot of Period versus h.Æ- - Concrete Floor Systems.

87
 Chapter 3 : FieldTesting

regression, T = 0.025hJ8
0.8

0.6

Period 0.4
(seconds)
X/
0.2 N X
X X

4
0.0
10 20 30 40
0

hJB

Figure 3.5.19 Plot Period versus h.Æ-- Timber Floor Systems-

regression, T=0.01NJ8 r+rc.q(L+L

0.8 \Bd )

0.6

Period 0'4
(seconds) x./ X
XX
0.2 X¡ x .-/ X
><x. / xxx
*{* xx
-.-x
0.0
0 20 40 60

N^Æ- r+re.¿É+11
\B d)

Figure 3.5.20P1ot of Period versus NJB 1+16. ,(+.*)] -AuData

88
 Chapter 3 : FieldTesting

regression, T : 0.0088NJ8 r+ re.¿l!+11

0.8 \B d)

0.6

Period 0.4
(seconds) X
X
x
0.2 /' x
x-/X X
X {'
XXX
0.0
20 40 60
0

NJB r+re.¿11+1ì
\B d)

Figure 3.5.2LPIotof Period versus NlÆ' 1+16.4(+.*)] - concrete Froors.

regression, T = 0.01 l+16. .(+.å)

0.8

0.6

Period 0.4
(seconds)
X

0.2 Xy. I
,/x X

/"
0.0
0 20 40 60

N.Æ- r+ro.¿f1+l
\B d)

Figure 3.5.22 Plot of Period versus

.*rc.q(!*1ll - Timber Floor.
\B D))

89
 Chapter 3 : FieldTesting

3.6 IMPLICATTO¡{S

Examination of the fit of the forms of period formulae to the measured data (R2)

noted in Table 3.5.1 revealed that the form of equation:

T*hJB (3.6.1)

had no fit to the data regardless of which of the three data sets was considered- This
contrasts with the discussion in Section 3.4 where this form of equation was the
expected form of period formula (Equation 3-4-5) for unreinforced masonry
buildings.

The form of equation:

T""N B t+rc.+(L*fll (3.6.2)

\B D))

also has poor fit to the data for the three sets of data. Both of these formulae
(Equations 3.6.1 and 3-6-2) were, therefore, considered unsuitable for the estimation
of the natural period of an unreinforced masonry building.

The lrve remaining forms of equation have very similar fit (54.2 percent to 49
percent) when all the data is considered- When considering only the data for the
buildings with concrete floor systems, the five remaining forms of equation had
improved fit to the data (55-2 percent to 72.2 percent) and three of the forms of
equation stood out from the other two with significantly improved fit:

T ". h3/a (3.6.3)

T".N (3.6.4)

and

T".h (3.6.5)

with fits of 72-2 percent, 67.7 percent, and 67.1 percent respectively.

90
 Chapter 3 : FieldTesting

Table 3.5.1 Details of Period Formulae Comparison

Data Set
AllData I C-oncrete FIoor TimtrcrFlou
Form of Fornula
Line¿¡
Regression Line k = o.o227 k -- o.o277 k = o.o244
T=kh
AS11?0.4 52.5% 50.o% 60.v%

2.1.1
76.O% 73.O% 't7.5%
AS1170.4
Rluation 2.1.2
Japmese &3% 59.O% 65.OEo

Eouation 2.1.11
R2 (ranking) 53.l%o 67.17o 9.1%
(2) (3) (3)

h Linear
T k
JT Regression Line k = o.o79 ,t = 0.082 k = o.o75

4S2121 34.5% 55.2% 513%

Equation 2.1.3
R2 (ranking) 529% 55.2Vo 51.3%
(3) (5) (1)

Linear
T=tN Regression Line t = 0.079 È - 0.068 k= 0.097
AS212l 23.OVo 8.51o 46.9%

Equation 2.1.4
Muria-Vil¿ 92.5% 89.O% 92.5%

Equation 2.1.17
R2 (ranking) 49.O% 67.7% 3.4%
(5) (z',, (4\

Line¿¡
r =*n3/a Regression Line k = o.o37 & = 0.035 t = 0.040

I.JBC t6.o% t7.vh 30.M

Equation 2.1.5
R2 (ranking) 54.27o 72.2% 1.4%
(1) (1) 15)

T-b- h3l4 Linear

JA" Regression Line ll = 0.099 t = 0.101 t = 0.096

UBC 775% 78.O% 73.t%

2.1.7
R2 (ranking) 51.2% 61.2% 18.9%
(4) ø\ Q\
Linear
r =rhJB Regression Line k=o.o23 k=O.O2l t = 0.025

R2 (ranking) o.o% o.o% o.t%

0\ 0l t6)

Linear
T= 1+16. .(+.+)l Regression Line È = 0.010 t= 0.o@ f, = 0.015

R2 (ranking) 18.5% 28.1% o.o%

(6) (6) Í7)

91
 Chapter 3 : FieldTesting

In Section 3-4, the derivation of Equation 3.4.5 was taken further and it was
determined that a reasonable form of equation for the estimation of the natural
period of unreinforced masonry buildings would be an expression where the period
was proportional to the building's height. Two of the best performed of the period
formulae are for formulae where the period is proportional to the buildings height, or
the number of storeys, which is generally related to the buildings height- However,
the best performed of the forms of period formulae when all the buildings were
considered, or when the data for the buildings with concrete floor systems were
considered was a formula where the period is a function of the height only, but not
directly proportional.

For the case of the buildings with timber floor systems, the fit of the data was worse
than when either of the other two data sets were considered. The fits of all the forms
of period formulae bar:

(3.6.6)

were very low (all less than 20 percent). Equation 3.6.6 has the best ht for this data,
by a large margin, of 51.3 Percent.

It can be seen then that the two types of unreinforced masonry buildings, that is
buildings with concrete floor systems and buildings with timber floor systems, have
different requirements for a formula for the reliable estimation of the natural period-
The concrete floor system buildings require a formula that has the period as a
function of the building's height and the timber floor system buildings rcquire a
formula that has the period as a function of the building's height and its depth-
Therefore, it could be necessary to split the buildings into two categories and provide
two equations for the determination of the natural period'

Further examination of the performance of the various period formulae conøined

with the various earthquake codes reveals that, in general, the formula from
AS1170.4, Equation z.IJ, performs as well as any of the other equations
considered. The formula corresponds to the linear regression line for the data from
buildings with concrete floor systems and, as already discussed, has a high level of fit
to the data- The period formula associated with Equation 3.6.3, that is Equation
Z-1.5, only corresponds to the 11 percent confidence inærval for the data, and is
therefore unsuitable for use in design. The formula provided by Muria-Vila (1990)'
Equation 2.I.I7, corresponds to the 89 percent confidence interval for the data-

92
 Chapter 3 : FieldTesting

It has already been discussed that the only form of period formula suitable, of those
considered in this study, for use with unreinforced masonry buildings with timber
floor systems is that shown in Equation 3.6.6. The formula from AS2LZL, Equation
2-l-3, corresponds closely to the linear regressed line for the data.

In summary, it can be seen that for unreinforced masonry buildings generally, and
specihcally unreinforced masonry buildings with concrete floor systems, the period
formula provided with AS1I70-4 provides a reasonable estimate of the natural period
for use in earthquake design. Further, an examination of the measured periods from
the buildings in the study and the design response spectrum from AS1l7O-4 (Figure
5-2.L) reveals that the periods for all but one of the buildings correspond to the
constant acceleration region of the response spectrum and, as such, the estimate of
the period becomes a moot point when calculating equivalent static force design
approach earthquake loads in accordance with 4S1170.4.

93
4 DYNAMIC TESTS ON BRICK
PANELS

4.1 II\TRODUCTION
One of the properties required for an accurate structural model, and generally not
examined in detail in previous work, is the dynamic in-plane stiffness of unreinforced
masonry walls. The in-plane súffness is as defined in Figurc 4.1.L. The dynamic
stiffness depends upon:

(1) The geometrical layout and size of the components making up the structure;
and
(2) The Youngs Modulus and Poisson's Ratio.

The geometrical properties are readily available for a given structure. However, the
determination of material properties presents more of a challenge- As was explained
in Sections 2.6 and 2.7, an equivalent modulus, or single phase model, for the brick
and mortar unit can be used rather than using the respective moduli for the brick
units and the mortar to create a model of an unreinforced masonry structure. It has
already been seen in Section 2.5 that there is a large variation in the reporûed values
for the Young's Modulus of brickwork and very few Young's Moduli from dynamic
tests have been reported- In order to undertake the modelling of the unreinforced
masonry structures in Chapter 5 it was decided to perform dynamic tests of
unreinforced masonry wall panels to determine an appropriate Young's Modulus for
the dynamic loading of Adelaide brickwork.

94
 Chapter 4 : Dynamic Tests on Brick Panels

t- ^ --l
induced shear force 1
tlrough cent¡e of
mass, v

V=kA
k = in-pla¡re stiffness

Figure 4.1.1 Definition of Shear Stiffness

4.2 DEVELOPMENT OF TESTING

METHODOLOGY
The discussion of results of previous in-plane dynamic testing of unreinforced
masonry panels in Section 2.3 highlighæd three variables as critical to the stiffness of
a wall panel:

(1) Axial compressive stress ;

(2) Workrnanship; and
(3) Rate of loading.

The dynamic testing undertaken as part of this research was required, therefore, not
only to determine the in-plane stiffness of a masonry wall panel but also to study the
influence of axial load and the rate of loading. It was also decided to vary the height
of some specimens since the in-plane stiffness is also a function of the geometry of
the panel tested-

95
 Chapter 4 : Dynamic Tests on Brick Panels

One method to determine the in-plane stiffness of a masonry panel is by a static load
test. This involves applying a monotonically increasing in-plane force to the top of
the watl panel and measuring the corresponding panel displacements. The in-plane
stiffness can then be determined from the load-deflection plot for this test. Mengi and
McNiven (1989) and McNiven and Mengi (1939) noted, however, that the dynamic
from the static shear modulus (Section 2'3). As
shear modulus was radically different
earthquakes induce dynamic loading in a structure, the dynamic modulus was
required for a more accurate structural model. Hence, it was decided to conduct
dynamic tests of masonly panels to establish appropriate dynamic ìn-plane stiffness
values.

The dynamic tests were conducted on the earthquake simulator in The University of
Adelaide's Structural Engineering Laboratory. This was considered to be the easiest
way to apply dynamic in-plane loading to a masonry panel. This approach had the
added advantage that it also more accurately modelled the true nature of earthquake
induced forces.

4.2.L Laboratory Test Set-uP

The test configuraúon was chosen so that the masonry test panels were subjected
only to in-plane shear, and allowed variable axial loads. Mengi and McNiven (1989)
and McNiven and Mengi (1989) had already devised a test set up that achieved this,
as shown in Figure 2.3.1- Hence, a similar arrangement \ryas adopted for these tests.

The Adelaide test set-up is shown in Figure 4.2.1. The panel size was dictated by the
size and capacity of the shaking table. The University of Adelaide's Structural
Engineering Laboratory's shaking table consists of a 1400 mm by 2200 mm sæel
plate mounted on bearings on a concrete base. The plate is orientated such that a
hydraulic actuator provides motion parallel to the plate's 1400 mm side. The actuator
is controlled by an 200 kN INSTRON load/displacement hydraulic testing machine.
The actuator can be controlled such that it applies a specified displacement
(displacemenr control) or specified load (load control). The INSTRON control panel
has pre-defined analog signals which are used to drive the hydraulic actuator with
sinusoidal, pulse wave, square wave, static, or any arbitrary displacement or load
pattern, such as an earthquake ground motion. The mærimum veftical load capacþ
of the shaking table, as governed by the bearings, is 66 kN. The maximum horizont¿l
displacement is * 125 mm.

96
 Chapter 4 : Dynamic Tests on Brick Panels

M20 mass holding

down bolls accelerometers
rigid frame ext¡a roof mass
to laboratory timber roof beams
strong floor 5- 140x35F5
Ð

POT
50x50x5ASEA
frame to base
6 mm rod
fixed at DCDT
top comer f .D

timber st0p bolted

M20 bolt. to lifting fem.rles
tfueaded rod
welded to 1350Lx450Wx
shaking table 100 D reinforced
concrete base

shaking table shaking table base 25 mmtube

movable plate cast in bæe

(a) side elevation

timber roof beams M20 holding down bolts

ext¡a roof mass
masonite ¡- accelerometers
)- J
"roof'
6 mm diagonal rod fixed
at top comer
DCDT

DCDT
50x50x5ASEA
frame to base
reinforced
timber stop concrete ba.se

bearings shaking table

shaking table base

(b) end elevation

Figure 4.2-1 Shaking table test set up-

91
 Ch.apter 4 : Dynamic Tests on Brick Panels

A roof stfucture was placed on top of the wall panels. It consisæd of a 3 mm thick
masonite sheet with four 100 mm deep x 35 mm wide timber "beams" evenly spaced
across the walls. The roof structure was attached to the wall panels to prevent sliding
by four M8 Ramset "Dynabolts" in each wall panel. The roof structure had a mass
of
21.5 kg. Adclitional mass was placed on the roof structure to more accurately
represent the axial stresses in a real wall (see Appendix D for the calculation of a
realistic level of stress). The additional mass consisted of a number of 400 Newton
steel weights. The weights were attached to the roof structure by M20 bolts.

To prevent sliding of the wall panels along the concrete bases a timber stop was

attached to tl-re end of the concrete bases and "dental paste" was placed benveen the
stop and the wall Panel.

4.2.2 ßrick MasonrY P anels

Single and double leaf specimens were tested as both types of construction are used
in masonry buildings, double leaf on outside walls, and single leaf on inæmal walls.
The original test specimens were 13 courses high and hve bricks long (Figure 4-2-l
only shows the nine course specimen). For reasons given in Section 4.4, nine course
high specimens were also tested. Full details of the test specimens are given in
Section 4.3. The specimens were constructed individually on concrete bases that
allowed the panels to be moved within the laboratory by gantry crane. The concrete
bases were artached to the shaking table by six M20 holding down bolts. As adopted
by Mengi and McNiven (1989), the panels rù/ere tested in pairs. Each pair of æst
panels were identical and symmeüically positioned on the table to minimise the

amount of torsion induced in the specimen.

The panels were constructed from standard commercially available nominal 110 mm
x 70 mm x 90 mm clay bricks purchased from an Adelaide brick manufacturing
company that uses clay quarried in the Adelaide Hills. The bricks used were typical
of those used in the Adelaide metropolitan area on a variety of building projects
ranging from family homes to cladding on multi storey commercial buildings- The
mortar used was a standard mix used in Adelaide and around Australia consisting of
one part portland cement, one part lime, and six parts building sand as specified in
the Australian Standard, "SAA Masonry Code" 453700-1988. Sufficient water was
added to ensure a workable mix. Brick ties were used on the double leaf specimens
in accordance with 453700 and typical practice'

98
 Chapter 4 : Dynamic Tests on Brick Panels

The bricklaying and mixing of mortar was done by an experienced Adelaide

br-icklaying contractor in one week. It was stressed to the bricklayers that the
workmanship was to be of the same standard as used in practice on a building site.
Subsequently the mortar was batched using shovels and water was added until the
bricklayer felt the mix was "right". While this lead to larger variations in the
properties of the masonry thanif a tight quality control had been imposed on the
mixing of mortar and brick laying, it was decided to make the investigation on
realistic examples of brickwork. Comparison of the quality of the brickwork
construction of the laboratory test panels to that observed on building sites in
Adelaide lead to the conclusion that the laboratory test panels were ropresentative of
the range of quality observed on site, and would be in the middle to upper part of the
quality range, with respect to joint thickness, grooving of mortar, and consistency of
the finished wall.

The panels were constructed in the structure's laboratory of the Civil and
Environmental Engineering Department near the shaking table so as to limit the
amount of handling púor to testing. The panels were cured in the laboratory for 35
days prior to testing and were subject to ambient temperature and humidity during
curing. Prior to testing, the panels were painted white so that cracks could easily be
identified. Sixteen reinforced concrete bases were built and a total of thirty-one wall
panels were constructed in two barches. The iniúal series of panels were all double
leaf and thirteen courses high. Subsequently, four courses were removed for the
reasons outlined in Section 4.4. The hnal series of panels consisted of single and
double leaf panels, nine courses high-

Brick and mortar specimens were tested to determine their individual properties.
Randomly selected brick units were tested in a compression testing machine- The
units were placed with a thin layer of dental paste on their top and bottom to provide
a more even load distribution. The units were loaded and unloaded three times while
the force-displacement relationship was recorded on a chart recorder. The
displacement was measured using a Direct Current Differential Transducer (DCDT)
and the force using a force transducer. The average Young's Modulus for the bricls
was 1400 MPa, with values ranging from766 MPa to 3065 MPa. The compressive
strength was 43 MPa. Comparing the Young's Modulus determined here with the
values published by other researchers (Section 2.5.5) it can be seen that the Young's
Modulus deærmined here was substantially less than that given by other researchers.

99
 Chapter 4 : Dynamic Tests on Brick Panels

Three mortar specimens were made while the walls were being constructed- The
mortar specimens were made using standard 100 mm concrete cylinders. The mortar
specimens were tested immediately after the wall tests were conducted using the
standard procedure for determining the Young's Modulus for concrete. The average
young's Modulus for the mortar specimens was 1079 MPa, with values ranging from
840 Mpa to 1680 MPa. Similar to the brick values, the Young's Modulus determined
from the laboratory tests was signitìcantly less than that published by other
researchers (Section 2.5.5) -

The final test conducted on the brick and mortar was to take a part of the failed walls
and to subject them to a bond wrench test. The tests were conducted on random
samples of brickwork from different panels. The average bond strength was 0-04
Mpa with values ranging from 0.02 MPa to 0.07 MPa. Again, these values are less
than those published by other researchers (Section 2.5-2).It can be concluded that
the brickwork used in these tests had properties significantly different to brickwork
used overseas and in other parts of Australia-

4.2.3 Instrumentation

In order to determine the in-plane stiffness of the panels it was necessary to measure
the displacement of the top of the panel relative to the base. Recall that the definition
of in-plane stiffness adopted for this study uses the total base shear divided by the
top displacement relative to the base (Figure 4.1.1). To measure the relative
displacements Linear Voltage Displacement Potentiometers (POTs) were attached to
a rigid frame connected to the laboratory floor and were mounted to the frame in line
with the top and mid height of each of the wall panels. A frfth POT was mounted on
the frame in line with the shaking table to measure its displacement relative to the
laboratory floor. The difference between the displacements of the top POTs and the
shaking table displacement was the displacement of the wall panel relative to its base-
The pOTs v,'ere Honston Scientihc model 1850-050 types with a maximum
displacement of 500 mm. The POTs v/ere powered by a 10 volt DC power supply
unit and the output was a voltage.

The main diff,rculty with this method was the relatively low level of relative
displacement expected in the walls. Using the results of Mengi and McNiven (1989)
and McNiven and Mengi (1939) as a guide to the in-plane stiffness of a panel, it was
estimated that the expected relative displacement at the top of the panel was 0-12
mm for a 0.5g acceleration. This was less than 0.02 Vo of the maximum absolute

100
 Chapter 4 : Dynamic Tests on Brick Panels

level
displacement of the POTs. The ability of the POTs to measure this small
displacement was questionable (A compadson of the results of Mengi and McNiven
(1989), and McNiven and Mengi (1989) to this study was undertaken in Appendix
E). To overcome this problem a second rigid frame was attached directly to the
reinforced concrete bases that the walls were constructed on. This rigid frame moved
with the shaking table so that there was no relative displacement between the frame
and the shaking table. Attached to this frame were four Direct Current Differential
Transducers (DCDTs) which measured the top and mid height wall displacements
relative to the base for both wall panels. The DCDTS were + 10 mm and
*5 mm
Sangamo Schlumberger models and usecl the same 10 volt power supply as the
POTs.

The in-plane shear distortion of the panels was also measured using 6 mm diameter
steel rod positioned diagonally on each wall panel, the rods were fixed at the top
corners of both panels. Guides were placed along the length of the diagonal of the
wall panels with the rod free to move in the guides. At the opposite corner of the
panels DCDTs were mounted to measure the in-plane distortion as the rod moved
with the top of the wall.

Finally, horizontal acceleration at the top and mid height of the wall panels, and the
horizontal acceleration of the shaking table were measured using Kistler Servo-
Accelerometers model305A. In later tests, an accelerometer was also placed on the
reinforced concrete base to measure the acceleration in the vertical direction to
ensure the t¿ble was not rocking on the bearings when the panels started to rock.
The accelerometers were powered by a servo ampliher and the output was low pass
filæred with a Butterworth hlter of 20 Hefiz in order to ensure compliance with the
Sampling Theorem (ApPendix A).

The instruments were calibrated before and after the fust series of æsts and before
and afær the second series of tests. No changes were observed in any of the
calibration factors.

The voltage outputs from the instruments were recorded using the Civil and

Environmental Engineering Department's Real Time Unix Masscomp computer- The

computer has an inbuilt analogue to digital converter so the output from the
instruments could be fed directly to the computer's input channels. "Labworkbench",
the computer package discussed in Chapter 3 with respect to data processing, was
also used here, to sample the data. The data was sampled at 100 Hertz and 2048

101
 Chapter 4 : Dynamic Tests on Bríck Panels

points for each channel were collected. It was found from previous work that 2048
points was the optimum amount of data for Fourier Transformation. To facilitate
post processing, the data was transferred to the "DADiSP" program on an IBM
compatible personnel computer. "DADiSP" was used to apply calibration factors to
the data and any otlÌer pfocessing required. The data from "Labworkbench" was
transferred to a personnel computer as text files using an ethernet card and were read
directly into the "DADiSP" program after writing a standard input heading hle-

"DADiSp" used a system of workbooks to display and process data. A workbook

consisted of a number of windows each containing a data set. Each data set w¿ls
manipulated by performing functions on its window or a series of windows, similar
to a spreadsheet. A default workbook was written to receive the data from a test and
to calibrate it. The data was then plotted on a laser printer.

4.3 TESTING PROGRAM

As explained in Section 4.2.2, the walls were constructed in two series of sixæen
panels. This meant eight tests per series. However, one of the fust series of panels
was damaged while being placed on the simulator and only seven tests were
conducted during the hrst test series. Test pairs numbered one to seven comprised
the first series of tests and test pairs numbered eight to fifteen comprised the second
test series. The panels were tested by moving the shaking table horizontally in a

sinusoidal fashion such that the base motion could be described by the equation:

ur(t) = A sin(zæft) (4.3.1)

The frequency (fl) of the base motion was varied from panel to panel. The amplitude
(A) of base motion \ryas first applied at a low level and subsequently increased until
failure occurred in the panel. Details of the testing program are shown in Table 4-3-l-
The sine wave frequency (f) refers to the frequency of the sinusoidal displacement of
the shaking table. The superimposed load is the weight of the extra mass placed on
the roof.

r02
 Chapter 4 : Dynamic Tests on Brick Panels

Table 4.3.1 Shaking Table Test Program.

V/all Test Pair Number of Double or Superimposed Sine Wave

Number Courses Single Leaf Load Frequency (f)

(D/S) (kN) (Hertz)

1 13 D 4.8 1.0

2 13 D 4.8 2.0

J 13 D 4.8 1.0

4 9 D 4.8 1.0

5 9 D 4-8 2.0

6 9 D 4.8 5.0

1 9 D 4.8 0.625

8 9 D 4.8 1.0

9 9 S 2.4 0.625

10 9 S 2.4 1.0

11 9 S 2.4 2.0

t2 9 S 2.4 5.0

13 9 S 6.4 1.0

t4 9 D 0 1.0

15 9 D 6.4 1.0

4.4 RESULTS

The first test panel was tested and found to fail by rocking. Rocking was defined as a
vertical tensile failure of the panel in the mortar-brick inærface at the first mortar
course level or at the mortar-concrete base inærface (Figure 4.4.1). This type of
tensile failure occured at both ends of the panel and moved inward as the shaking of
the base continued. After experiencing this failure, the panel began to rock as a rigid
body about its base.

After the fust panel failed in this manner it was thought that the failure may have
been caused by the panel overtuming. However, subsequent calculations of the
overtuming moment and resistance to overturning indicated that uplift should not
occur (see Appendix F). Prior to the onset of rocking the panel was subjected to a
sinusoidal base displacements of A = t 11 mm, 19 mm, 34 mm,49 mm, and 65 mm'
Rocking commenced at A = ll0 mm. The test was continued after the onset of

103
 Chapter 4 : Dynamic Tests on Brick Panels

rocking but this data did not give a measure of the in-plane stiffness and was
subsequently discarded from the data set. In addition, some of the initial tests had
very small relative displacement of the walls. If the values in the data were below the
resolution of the instrumentation the results were not used for the calculation of the
dynamic in-plane stiffness. In order to calculate the in-plane stiffness it wa-s first
necessary to calculate the induced shear force. This calculation was based upon the
measured accelerations at base, mid, and full height levels of the wall. Figure 4.4.2
shows the shear force (V) plotted against the top wall displacement (A) for test panel
number 1.

tensile failure in the tensile failure in the

bond between the bond between the
mortar and the brick mortar and the brick
and moves inward with and moves inward with
continued shaking continued shaking

_---) c-

(a) initial cracking of panels

-1

"rocking" of the wall

panel - rotation of the
ì---
panel about the comer
of the first brick-mortar \-
layer with continued
t-
shaking of bæe

(b) "rocking" failure of panel

Figure 4.4.1 Tensile failure and rocking of wall panels.

While undertaking the first test it was noted that manual control of the amplitude of
base displacement to which the model was subjected was difficult The boarseness'
of the displacement control for the shaking table made small changes in the table
displacement difficult to achieve. This problem was expected to be magnified when
dealing with the panels to be tested at a higher frequency.

104
 Chapter 4 : Dynamic Tests on Brick Panels

10 _ o- V/all 1

of -- - Wall2
rocking
^-
8 Wall3
-rr--

6
Shear
Force, V
(kN)
4 rocking
dA

2
onset of
,,'/ rocking
0
0.0 0.1 0.2 0.3 0.4 0.5

Relative displacement af top of wall, Å (mm)

Figure 4-4.2Induced shear force versus in-plane displacement - Walls 1,2 and3-

The second panel was tested using the same set-up as the first panel but subjecæd to
a higher frequency base motion. The adverse effect in the ability to control the table
manually of the increased frequency was conhrmed when the panel was only able to
be subjected to two base displacements, A = t 12 mm and +21 mm, prior to the
onset of rocking. Rocking commenced at A = *30 mm. Figure 4.4-2 shows the
induced shear force plotted against the top relative displacement for wall panel
number 2.

was decided for the third panel to try to prevent the onset of rocking to gather
It
more stiffness data. The test used similar parameters to the first panel. Holes were
drilled through the bottom course of both leaves of the panels at each end. Sæel rods
were placed through the holes and grouted in place. The rods were then fxed to the
concrete bases using a timber bracket. A test was then conducted to determine the
onset of rocking. It was found that rocking started at A = t80 mm, 10 mm more
than for the frst panel. This increase was small and the rods were not used on the
later panels. The induced shear force versus the in-plane displacement in the panel
for this wall is also shown in Figure 4.4.2-

105
 Chapter 4 : Dynamic Tests on Brick Panels

Another method to prevent the onset of rocking was tried with the fourth panel- In
this test, the top four courses of the panel were removed. The aim was to lower the
centre of mass of the panel to reduce the tensile force induced in the edges of the
panel from the horizontal inertia force. This panel was also tested using the same
parameters as the first and third panels. Prior to the onset of rocking this panel was
subject sinusoidal displacements varying between A = +20 mm and 80 mm'
to
Rocking commenced at A = * 83 mm. It was then decided to remove the top four
courses of the remaining hve pairs of walls from the frrst constructed batch and to
have the second batch constructed to nine instead of thiræen courses- The induced
shear force plotted against the panel's in-plane displacement is shown in Figure 4-4-3-

t6
o Wall4
- -
F
7 onset of
rocking
- o- - Wall5
t2 --o-- Wall6
o

- ^- -
WallT
Shear
Force,V 8
f , ' onset of
G}D rocking
¿-- -_-- ----'
t,e
---
4 -- - -
onset of
rocking
0
0.0 0.1 0.2 0.3 0.4 0.5

Relative displacement at top of wall, Â (mm)

Figure 4.4.3 Induced shear force versus in-plane displacement - Walls 4,5,6 and 7.

Panels five to seven were then tested using the par¿Lmeters as described in Table
4.3-l.Alt of the panels failed by rocking. The second of panels was then tested
baûch

and again all of the panels failed by rocking. The induced shear force plotted against
the top relative displacement for panels five to fifæen are given in Figures 4.4-3 to
4.4.5.

106
 Chapter 4 : Dynamíc Tests on Brick Panels

10 of
onse t.

rockinc
--n
LT
8 /^
r/r'
Shear
6
4. onset of --o-- WallS
Force, V oI rocking
Wall 14
(kN) - ^-
4 {
- ct- - Wall 15

0
0.0 0.1 0.2 0.3 0.4 0.5

Relative displacement at top of wall, Â (mm)

Figure 4.4-4Induced shear force versus in-plane displacement -'Walls 8, 14 and 15

10

p
8 Wall9
' 'onset
of - ^-
d rocking Wall l0
-o--
6
of
Shear
Force,
(kN)
V il onset
rocking
--->T-
-x-
o- -
Wall

Wall 12
11

4 -
I onset of
rocßng-'
¿- - - o- - Wall 13

2
onset of
rocking

0
0.0 0.1 0.2 0.3 0.4 0.5

Relative displacement at top of wall, Â (mm)

Figure 4.4.5 Induced shea¡ force versus in-plane displacement- Walls 9, 10, ll, L2
and 13.

rc]
 Chapter 4 : Dynamic Tests on Brick Panels

4.5 DISCUSSION OF RESULTS

As noted in Section 4.1, the tests were conducted in order to determine the dynamic
in-plane stiffness for unreinforced masonry wall sections. The measured in-plane
stiffness values are listed in Table 4.5.1 and were calculated from the induced shear
force and in-plane displacement data given in Figures 4-4-2 to 4-4-5 using the
regression analysis technique as dehned in Appendix C for htúng a curve that passes
through the origin. The dehnition of in-plane stiffness used was that shown in Figure
4.I.1. Also lisæd in Table 4.5.1 was the ratio of induced shear force to the panel
weight at the onset of locking for each panel. The values in Table 4.5.1 are for one
panel of the pair of panels tested. That is, for the double leaf tests the stiffness is for
two leafs of brickwork and for the single leaf tests the stiffness is for one leaf of
brickwork.

Table 4.5.1 Calculated in-plane stiffness from laboratory tests.

Ratio of Induced
Wall Test Pair Axial Stress Shear Stiffness, Shear Force to

Number (MPa) k (kN/m) Panel Weight at

rocking

1 0.032 61,500 0.651

2 0.032 44,600 0.861

3 o.032 30,150 0.689

4 0.026 52,400 0.868

5 0.026 102,400 t.256

6 0.026 80,250 0.947

7 0.026 54,100 0.735

8 0.026 149,600 o.771

9 0.026 68,400 0.944
10 0.026 28,250 o.377

11 0.026 37,650 1.001

12 o.026 59,900 1.475

13 0.044 62,200 0.7t9

t4 0.015 99,350 1.168

15 0.029 163,300 0.648

108
 Chapter 4 : Dynamic Tests on Brick Panels

It can be seen from Table 4.5.1 that the measured in-plane stiffness values vary over

a large fange. This is most evident in the comparison of Wall 4 to Wall 8, a control
specimen included in the second batch for which the test parameters were the same-
V/all 8 had almost three úmes the in-plane stiffness of Wall 4. This variability was
attributed to a cornbination of workmanship and material variability. The variability
in the properties of the brick units and mortar was noted previously in Section 4-2-2-

Tlre first of the parameters noted in Section 4.2 to be examined were the frequency
of excitation and the eftèct of single and double leaf. The axial stress was kept
constant for the comparison at 0.026 MPa. The comparison is summa¡ised by the
data in Table 4.5.2.

Table 4.5.2 Comparison of Frequency of Excitation and Single or Double Leaf on

Shea¡ Stiffness.

Frequency of Single Leaf Shear Double Leaf Ratio of Single to

Excitation (Hertz) Stiffness (kN/m) Shear Stiffness Double Stiffness
(kN/m)

0.625 68,400 54,100 1.26

1 28,250 52,400 & 149,600 0.54 & 0.19

2 37,650 102,400 0.37

5 59,900 80,250 0.75

Average 48,550 87,750 0.55

It was expected that the in-plane stiffness of the double leaf walls would be ¡wice
that of the single leaf watls as the in-plane stiffness was assumed to be proportional
to the wa1l's cross sectional area for shear type deformation and proportional to the
width of the wall for bending type deformation. The average values of the in-plane
stiffness seemed to show this. The ratio of 0.55 was very close to the expecæd value
of 0.5, especially considering the variability in materials and workmanship already
discussed. The individual ratios vary considerably, but this was not surprising
considering the variability in panel properties, As only one panel of each type was
tested, individual comparisons were dangerous. This was best illustrated by the
comparison of results at 0.625 Hertz, where the single leaf wall was stiffer than the
double leaf wall. What was important, however, was that the overall trend of in-
plane stiffness follows the expected pattern of t'wice the in-plane stiffness for a
double brick panel compared with a single brick panel.

109
 Chapter 4 : Dynamic Tests on Brick Panels

The eflect of the excitation fiequency on the in-plane stiffness was more difficult to
determine because of the variability in materials and workmanship. It has already
been noted that the in-plane stiffness of the 0.625 Hertz specimens were inconsistent
with the expectation that a double leaf specimen would be twice as stiff as a single
leaf specimen. Whether the single leaf specimen was at the upper limits of the
possible range of in-plane stiffness, or the double leaf specimen was at the lower
limits, or a combination of both is difhcult to determine. If the data from the 0-625
Hertz test is momentadly ignored, the single leaf specimens suggested a trend of
increasing in-plane stiffness with increasing frequency of excitation. However,
inclusion of the 0.625 Hertz data meant this trend could have been a result of the
variability of the materials and workmanship. Examination of the data for the double
leaf specimens also did not lead to a definite conclusion. Careful selection of the data
for the double leaf specimens could have in fact resulted in the conclusion that there
was a trend of decreasing in-plane stiffness with increasing excitaúon frequency-
Therefore, the only conclusion that could be reached, based on the test data, was that
there was no clear trend in the effect of the excitation frequency on the in-plane
stiffness in the range of testing frequencies,0-625 to 5 Hertz. To establish definiæ
statistically valid trends, a much larger number of æst specimens would be required-

The third variable considered was the level of axial stress in the walls. The axial
stress was varied for a set of specimens tested with an excitation frequency of 1
Hertz.It was expected that the specimens would show a trend of increasing stiffness
with increasing axial stress as was noted by other researchers (Section 2-3). There
were two results for the double leaf specimens tested with an axial stress of 0-026
Mpa. Firstly, using the result from the panel with the higher stiffness (149,6001Ò{/m)
and comparing with the results from the other panels with the same excitation
frequency and geometry there was a trend of increasing in-plane stiffness with
increasing axial stress levels. If, however, the other panel tesæd with 0.026 MPa
axial stress was used in the comparison the trend was no longer observable. Again,
the variability of the materials and workmanship seemed to mask any trends in the
relationship between axial stress and in-plane stiffness.

The hnal parameter checked was the specimen panel height. The frst three panels
were, as already noted in Table 4-3.L, thirteen courses high and the rest of the test
specimens were nine courses high- If the walls were acting as a simple cantilever
shear beam it would be expected that the stiffness values were inversely proportional
to the panel heights and in this case that would mean the thirteen course panels
would have lower values of stiffness than the nine course panels, in the ratio of nine

110
 Chapter 4 : Dynamic Tests on Brick Panels

to thirteen, 0.69. Comparing the thirteen course panels to the nine course panels
tested with excitation fi'equencies of I and 2 Hertz, it was seen that there was no
observable trend in the stiffness of the panels. It would seem that any trend is masked
by the variability in the materials and workmanship-

In summary, it would appear the main parameter affecting the dynamic in-plane

stiffness of unreinforced masonrywall panels was material and workmanship

variability. This variability and its effect on the properties and behaviour of
unreinforced masonry has been recognised by many previous researchers as noted in
Chapter 2.'lheeffects of material and workmanship variability masked the effects of
other parameters. From the tests conducted as part of this research the expected
trend of a double leaf wall having double the stiffness of a single leaf wall was

confirmed and the trend of increasing stiffness for increasing axial stress was partially
observed. Any trends in in-plane stiffness with panel height and excitation frequency
could not be identified from these tests- Further testing, with a larger number of
panels, is required to ascertain these trends. The main objective, however, of this

testing was to determine the in-plane stiffness of the wall panels for latter use with a
mathematical model of masonry walls and this was accomplished.

4.6DETE,RMINATION OF AN EFFECTIVE
YOUNG'S MODULUS

In order to determine the effective Young's Modulus of brickwork to be used in the

later modelling of unreinforced masonry buildings, the shaking t¿ble test results were
used to calibrate a mathematical model of the laboratory wall specimens. A single
leaf laboratory wall specimen was modelled using the IMAGES3D finite element
program. The geometrical parameters and material densities were all based on data
obtained from the laboratory test specimens. An in-plane load was applied through
the centre of mass of the wall panel (including the roof mass). The combined
brickwork material was assumed to have a Poisson's Ratio of 0.2 and the Young's
Modulus was varied until the in-plane stiffness of the model of the laboratory wall
panel matched the range of in-plane stiffness values determined from the shaking
table æsts (7,538 to 40,825 kN/m for a single leaf of wa11)-

Three different finite element grids were used to determine the sensitivity of the
model to the number of elements. As the walls were rectângular, the chosen grids
consisted of rectangular elements having the same number of elements vertically and

111
 Chapter 4 : Dynamic Tests on Bríck Panels

horizontally.Gridsof 1x L,4x4, and 16x 16elementswereused.The 1x l grid

did not allow for the load to be applied at the centre of mass which was calculated to
be 540 mm from rhe bolom of the nine course (760 mm high) panels for 12 x
400 N

superimposed roof load. This centre of mass was close to 75Vo of the total height
and on the 4 x 4 and 16 x 16 grids the horizontal load was applied to the nodes along
the line representin g757o of the panel height, that is the 4th row of nodes for the 4 x
4 grid and the l3th row of nodes for the 16 x 16 grid. The 4 x 4 grid model was also
tested with the horizontal load applied at the top of the panel for comparison to the 1
x 1 grid. The models are shown in Figure 4-6-l-

roof load applied across nodes roof load applied across nodes
horizontally
J, J .t
induced load

1x 1 grid 4x4 gnd

horizontally
roof load applied across nodes induced load
applied at both
horizontally levels to determine
induced load --) effect

16 x 16 grid

Figure 4.6.1 Mathematical models of the test specimens.

Itwas decided to load the panel with the load induced in wall panel 4 just prior to
the onset of rocking, 3550 N. The 3,550 Newton load was resisted by four single
leafs so that the load applied to the model panels was 890 N'

The hrst modelling parameter to be studied was the number elements used in the
grid. This was carried out by comparing the results of analyses for the three models
with a constant Young's Modulus. The comparison is shown in Figure 4.6.2- It can

tt2
 Chapter 4 : Dynamíc Tests on Brick Panels

be seen that the number of elements had little influence on the in-plane stiffness-
Considering a Young's Modulus of 2,000 MPa it can be seen the difference
in in-
plane stiffness between the three models was 6,800 kN/m which is less than the
influence of the workmanship and material variability and could be considered to be
insignihcalt from a practical point of view. A 4x4 element grid was used for all
subsequent models.

150,000
16x16
.a
.1 .a
---4x4
---- lxl z /t'
./,;
z './
100,000 z
/-./
In-plane ./;
Stiffness
(kN/m) /2
50,000 /z
.z

0
0 500 1,000 1,500 2,000

Young's Modulus (MPa)

Figure 4.6-2Comparison of Numberof Elements-

The 4x4 model was used to determine the sensitivity of the results to the position of
the applied horizontal load- The load was applied first at the top of the wall and then
at 75 percent of the wall's height, corresponding to the centre of mass. The load was
applied at the top in one case to permit direct comparison of the results to those from
the model which, by necessity, was constrained to have its horizontal load
lxl
applied at the top of the wall. It was noted that the in-plane stiffness values
determined from the top loaded model varied significantly from those deærmined
from the centre of mass loaded model. Hence, care was taken in all subsequent
modelling to ensure that the inertia forces would be concentrated at nodes very near
to the centre of mass.

113
 Chapter 4 : Dynamic Tests on Brick Panels

The 4x4 model was then used to study the sensitivity of the results to values for
young's Modulus. The results of these analyses are given in Figure 4-6-3- The
measured values of in-plane stiffness, given in Table 4-51, for the double leaf
specimens were divided by two to give an estimate of the in-plane stiffness for a
single leaf wall. It can be seen that for the measured values of the in-plane stiffness,
the corresponding values of Young's Modulus were220 to 1250 MPa. These values
were then used in mathematical models of real buildings as an effective Young's
Modulus for the composite brick and mortar material.

1500

1000
Effective
Young's E"u = 680 MPa
Modulus,
Een
(MPa) 500

0
123456 789101112t31415
Wall Specimen Number

Figure 4.63Bffective Young's Modulus for wall specimens-

4.7 SUMMARY OF LABORATORY TESTS

From the laboratory tests conducted as part of this research it was seen that the in-
plane stiffness and the Young's Modulus of an unreinforced brick masonry wall vary
considerabty with workmanship and material variability. The variation of these
properties due to workmanship and materials tends to mask any relationship between
the frequency of excitation, axial stress level, and wall height with the in-plane
stiffness. Only the expected relationship between the number of leafs and the in-plane

rl4
 Chapter 4 : Dynamic Tests on Brick Panels

stiffness could be conf,rrmed from the tests. In order to ascertain any relationships
number
between the frequency of excitation, axial stress level, and wall height a large
of tests would need to be conducted and average results used to minimise the effects
of workmanship and material variability-

The results from the laboratory tests were used to calibraæ a mathematical model
which relates the range of values for in-plane stiffness to a range of values for an
effective Young's Modulus for a combined brick and mortar material'

The range of values determined for the brickwork Young's Modulus, 22O to 1250
MPa, are of the order expected for brickwork based upon some of the work reported
in Section Z.s.s,for example Arya (1980), Jankulovski et al (1994), Priestley (1985)'
San Bartolome er al (1992), and Calvi et al (1994). It should be noted, however, that

there was no consensus between other researchers who have conducted tests on
unreinforced masonry walls as to an effective Young's Modulus and as many
researchers whose results agree with the order of magnitude of Young's Modulus
determined from these tests disagree and suggest and/or measure a Young's Modulus
an order of magnitude greater.

115
5 MODtr,LLING OF BUILDIì{GS

5.1 INTRODUCTION
As was noted in the introduction, part three of this study involved an examinaúon of
the force and stress demands placed on unreinforced masonry buildings when
subjected to the design earthquake ground motion. The major weaknesses of
unreinforced masonry construction when subjected to earthquake ground motion
have already been identihed in Chapter 1 as connection failure between the walls and
the floor and roof diaphragms, in-plane (shear) failures in the walls, and out-of-plane
(bending) failures in the walls. In order to study these weaknesses the following
model responses were examined in detail:

(1) Base shear;

(2) Storey shears;
(3) Connection forces and corresponding required connection friction coefficients;
(4) In-plane and out-of-plane wall stresses; and
(s) Deflections.

The connection forces and corresponding connection friction coefficients are relaæd
to the interaction between the unreinforced masonry walls and the roof and floor
diaphragms. Whilst the roofs often had a mechanical connection to the 1ryalls, usually
due to the need to hold the roof down under wind loading, the concrete floor to wall
connections normally relied on friction between the floor and wall to transfer lateral
loads. On the other hand, timber floors were usually connected to the walls with a
type of mechanical connection. Two connection details between the concrete floors
and the unreinforced masonry walls were observed in the buildings in this study. The
two types of connections are shown in Figure 5.1-1.

116
 Chapter 5 : Modelling of Buildings

storey shear storey shear

resisted by resisted by
interaction interaction
of floor and of floor and
inner leaf both wall
leafs

(a) Type I - concrete floor on (b) Type II - concrete floor on

inner leaf only both leafs

Figure 5.1.1 Concrete Floor to V/all Connection Details

From Figure 2-7 .I it can be seen that the storey shear is transferred from the floor
and roof diaphragms to the in-plane walls. The main difference between the two
types of concrete floor to wall connections, shown in Figure 5.1.1, is how this storey
shear is transferred. For Type I connections, the storey shear is transferred by friction
from the concrete floor to the inner leaf of the two leaf wall. For Type II connections
the storey shear is transferred by friction from the concrete floor to both leafs of the
double leaf wall. The use of a Type I or Type II connection also has an important
implications on the level of vertical load that contributes to the frictional resistance of
the induced horizontal earthquake load.

The typical connection for a timber floor to a masonry wall was shown in Figure
3.5.1. It can be seen that the shear from the floor system is transferred into the inner

It7
 Chapter 5 : Modelling of Buildings

leaf of the double leaf wall similar to the connection in Figure 5.1.1 (a), although the
loads will be concentrated at rafter locations and not uniformly distributed along the
wall.

The response spectrum method (Clough and Penzien (1993)) was chosen to carry
out the earthquake analyses for the unreinforced masonry buildings. The choice of an
appropriate response spectrum has an important bearing on the validity of the resulls
of the analysis. In the absence of actual Australian earthquake strong ground motion
data it was decided to use the design response spectra included in The Australian
Standard "Minimum design loads on structures - Part 4 : Earthquake Loads"
451170.4-1993 as the basis for the dynamic analyses. The use of this design
response spectrum also permitted easy comparisons to be made between the results
obtained from the code's equivalent static force provisions and the results of
response spectrum analyses.

5.2 RESPONSE SPECTRUM ANALYSIS

DETAILS
The AS1Il0-4 response spectrum is shown in Figure 5.2.I. It can be expressed
mathematically as:

1'2L1S
ç=
^1.t t <2.5a (s.2.r)

where S is a site factor, taking into account the soil profile; a is an acceleration
coefficient; and T is the natural period of the building. The response spectrum is then
multiplied by the ratio:

I (s.2.2)
Rf

to account for the importance of the structure (I) and the ductility and over-strength
of the building material (R¡ - see Section 2.9).

Four variables from Equations 5-2.L and 5.2-2had to be defined prior to undertaking
the analysis. It was considered that unreinforced masonry is unlikely to be used for
buildings that have post disaster functions, such as hospitals. Hence, the importance
factor, I, was chosen to be 1.0. The site factor, S, was taken as 1.0 corresponding to

118
 Chapter 5 : Modelling of BuíIdings

a hrm soil site. The response modification factor, Rr, was taken as 1.5 in accordance
with the recommendations for unreinforced masonry buildings in AS1170-4- This low
value assumed that an unreinforced masonry building had little ductility (see Section
2-9) and so is greater than 1 mainly due to a small amount of over-strength. The
ground acceleration coefficient, a, was taken to be tliat which 4S1170.4 specifies for
Adelaide, South Australia, that is a = 0.1g, and is the highest ground acceleration
specihed for any Australian capital city.

Normalized
Acceleration
2
C r.25
<2.5
a Tz/t

forS=1
I

0
0 1 2 3 4 5 6

Period (seconds)

Figure 5.2.1 AS1I7O.4 Design Response Spectrum.

The use of a commercial analysis package to undertake the response spectrum

analysis was decided upon in the interests of reliability and time. The computer
package chosen to undertake the analysis was the IMAGES3D program already used
to model the wall specimens from the laboratory testing as described in Section 4.6.

119
 Chapter 5 : Modelling of Buildings

5.3 IMAGES3D MODEL DETAILS

As was already noted in Section 4.6, IMAGES3D is a finiæ element based structural
analysis program. As with other finite element programs, the structure to be analysed
must be delined in terms of nodes, elements, and geometrical and maærial properties
of the structure. The package then automatically assembles a stiffness matrix for the
structure. In order for dynamic analyses to be performed, IMAGES3D also
assembles a mass matdx so that the dynamic equilibrium equation can be solved.

There were three parameters that could be varied in the IMAGES3D models of the
unreinforced masonry buildings. The parameters were:

(1) Type of plate element used;

(2) Young's Modulus of the brickwork; and
(3) Wall geometry.

Two types of plate element are available with IMAGES3D. A "membrane" plate is a
plate element with two degrees-of-freedom at each node of the element representing
the in-plane distortion of the element. The other type of plate element available, the
"membrane plus bending" plate, has three additional degrees-of-freedom at each
node representing the out-of-plane displacement of the element and the bending
about the two in-plane axes. As out-of-plane bending failure is common in
unreinforced masonry walls the "membrane plus bending" plate type elements were
chosen to model the unreinforced masonry walls. Concrete floors and metal deck
roofs can behave similarly so that "membrane plus bending" plates were also used to
model the concrete floors and metal deck roofs. Timber floors were considered to
act mainly as a diaphragm, with very little bending stiffness. Therefore, it was initially
decided to model timber floors using "membrane" plates. This assumption was tested
on one building (East End Market Building 2 - EEZ) where the timber floors were
also modelled with "membrane plus bending" plates to examine the effect of the extra
stiffness provided by the "membrane plus bending" plates had on the structural
response and it was found that there was little difference between the two types of
plates.

The variability of the Young's Modulus of brickwork has already been discussed in
Section 2.5 and Chapter 4. Any value from the range of values for the Young's
Modulus of brickwork determined from the shaking table testing could be used for
the building models. One of the buildings in the study (two-storey apartrnent building

t20
 Chapter 5 : Modelling of Buildings

- KIDA) was used to determine the sensitivity of the modal properties (frequency,
mode shape, and effective modal mass) and the earthquake response, determined by
the computer model, to the value of Young's Modulus.

The unreinforced masonry buildings in this study had double leaf (two 110 mm leafs)
external walls. Simply defining the elements modelling the external walls to have the
same thickness as the wall would yield incorrect results.It was decided that the shear
stiffness of the walls was the most important aspect of the model to have correct as
the in-plane stiffness of the unreinforced masonry walls was considered to be the
major component of the overall structural stiffness of the building. It was therefore
decided to set the wall thickness It 220 mm for the correct evaluaúon of the wall
area and shear stiflhess (GA). However, this had implications for the wall bending
deformations. A 220 mrn thick element has the same cross-sectional area as two 110
mm thick elements. Since shear and axial stresses in the wall are proportional to the
cross-sectional area of the element then the axial and shear stresses calculaæd by
IMAGES3D for a single 220 mm thick element model should be the same as for two
110 mm thick elements.

The bending stresses, however, will not be calculated conectly for a single element
model. For example, consider two walls, one consisting of two plate elements of
thickness "d", and the other consisting of a single element '2d" thick. The moment of
inertia, I, for the twin "d" thick wall model is:

I,o,u, (s,3.1)

Dividing by the depth to the neutral axis gives the bending modulus, z:

bd3
2x
12
L_ (s.3.2)

which reduces to:

bd2
(s.3.3)
3

t2l
 Chapter 5 : Modelling of Buildings

Considering the "2d" thick single wall, the moment of inertia ls

(s.3.4)

dividing by the depth to the neutral axis, d, gives the bending modulus, z:

u(z¿)3
12 (5.3.5)
d

this reduces to:

2bd3
(s.3.6)
3

which is twice the value for tlie twin "d" wall model. Applying this to the models of
the buildings in this study it can be seen that the buildings modelled with the single
220 mm thick wall elements will have twice the bending modulus of the same
building modelled with twin 110 mm thick elements. This will lead to the single 220
mm thick element models having half the bending stress of the twin 110 mm thick
element model. As the twin wall model more accurately represents the real situation
of the buildings, that is two independently acting walls, then the bending stress
results from the models, using single 220 mm thick wall elements, need to be
doubled to accurately model the buildings. The bending deformations for the "2d"
elements will be one-quarter of those for an equivalent model with two "d" walls.
Basically, for ease of modelling, single 220 mm elements were used to model the
double leaf brick walls, but the bending stresses were doubled to reflect the actual
bending stresses expected. The same building used for the comparison of different
values of Young's Modulus (KIDA) was also used to confirm the effects of using a
single 220 mmwall element model by comparison with a model of the building using
two parallel 110 mm elements to represent the double leaf walls.

The comparisons described above for the three variable parameters in the models of
the buildings are reported in Section 5.4.

t22
 Chapter 5 : Modelling of Buildings

Further details of the models of tlie buildings included:

(1) The resrrai¡r provided by the foundation of the building on the building
structure was modelled by restraining the displacement of the nodes at the base
of the building in the thlee global axes, that is, pinned suppoß;

(2) Tle properties of the materials used in the horizontal elements of the buildings
were taken as the typical values used in design. These properties were:

Concrete Young's Modulus 30,000 MPa

Poisson's Ratio 0.3
V/eight Density 24 kNim3

Steel Young's Modulus 200,000 MPa

Poisson's Ratio 0.2
Weight Density 79 kN/m3

Timber Young's Modulus 8,000 MPa

Poisson's Ratio 0.3
Weight Density 11kN/m3

Ceiling Young's Modulus 10,000 MPa

Poisson's Ratio 0.3
Weight Density 17 kN/m3

(3) The material properties used for the masonry walls were also taken from
typical design values. The Poisson's Ratio was taken as 0-2 and the weight
density was taken as 19 kN/m3. The Young's Modulus was determined from
the comparison noted previously for building KIDA and detailed in Section
5.4; and

(4) The thickness of the concrete floor slabs were taken to be actual thickness of
the slabs- Timber floors were modelled using an effective thickness to take into
account the floor boards and flooring joists-

After each model was defined, IMAGES3D was used to carry out modal analyses of
the structures. The modal analyses identified the natural periods of the structure, the
mode shapes, the modal participation factors, and the effective modal masses. Where

t23
 Chapter 5 : Modelling of Buildings

possible, sufficient modes were identihed in each of the two major horizontal axes
such that 90 percent of the total mass was reptesented in each direction. The 90
percent value corresponded to the requirements of the AS 1 170.4.

In many cases, IMAGES3D calculated a number of local modes as well a-s the
desired global building modes. To minimise the number of local modes determined
by IMAGES3D, and therefole maximise the number of global modes, the weight of
the horizontal building elements, such as floors, roof, and ceiling, were not generated
by the program from the defined weight densities for these elements. Instead,
weights were defined ill the global horizontal directions only at each floor level. This
eliminated many of the local modes in the horizontal elements which did not
contribute to tlie overall behaviour of the building with regard to earthquake induced
forces.

After each modal analysis was canied out a response spectrum analysis was

performed using the modal analysis data and the design response spectrum from
4S1170.4 (Section 5.2). The modal maxima were combined using the CQC method
(Wilson et al (1981)), assuming hve percent damping. The results of the modal
analyses are given in Section 5.5. The results of the response spectrum analyses are

given in Section 5.6.

5.4 PRELIMINARY ANALYSES RESULTS

As noted in Section 5.3, the effect of the variation of three parameters on both the
results of the modal analyses and the response spectrum analyses is reported in this
section.

5.4.L Plate Element Type

The flrst aspect of the IMAGES3D models to be checked

was the use of
"membrane" or "membrane plus bending" plates to model úmber floors. A two storey
city commercial building (EE2) was chosen for this test- The model was fust
analysed with the floor diaphragm modelled using "membrane plus bending" plates.
The model was then re-analysed with the floor diaphragm modelled using
"membrane" plates. The results are shown in Table 5.4.I.

124
 Chapter 5 : Modelling of Buildings

It can be seen from Table 5.4.1 tliat the change of the type of element used in the
floor plates frorn "membrane" to "membrane plus bending" had little effect on the
main lateral modes in each direction. Tliere is a third short direction lateral mode that
is very close to the second lateral mode (7.8 Hertz) and has an effective modal mass
of 4 percent of the total mass for the "membrane plus bending" plate model. It was
concluded from this exercise that only "membrane plus bending" plates would be
used in all of the subsequent analyses.

Table 5.4.1 Two Stoley Commercial Building (EEz) - Effect of Horizontal Plate
Type on Modal Properties.

Modal Frequency (Hertz) and Effective Modal Weights

Element Type (Vo Lotal mass)

lst Short I 2nd Short ll r.t Long

il
membrane 5.1 7.6 7_5

Q73q') (8.08") 03.97o)

"membrane plus 4.8 7.7 7.5
bending" (l4.9Vo) (2.I7o) (74.0Eo)

5.4.2 Young's Modulus of Brickwork

The value of Young's Modulus for unreinforced masonry which was used in the
models for all of the unreinforced masonry buildings was obtained by hnding the
value of Young's Modulus which resulted in a natural period which matched the
measured value of one building from the ambient vibration tests (Chapter 3). The
chosen Young's Modulus was selected to be in the upper half of the range of
Young's Modulus to reflect the fact that walls constructed on future buildings which
had earthquake induced forces considered as part of the design would also have a
reasonable level of supervision in the construction of the walls and therefore, have
stiffness properties in the upper part of the range. The second to last building in
Table 3.3.1 was used for this purpose as it was one of the first buildings modelled.
The results of the modal analyses for different values of Young's Modulus are shown
in Table 5.4.2.

It can be seen from Table 5.4.2 that the Young's Modulus used for the unreinforced
masonry walls of a building has a significant effect on the modal frequencies of the
building. The modal frequencies calculated using a Young's Modulus of 1500 MPa
were almost three times larger than those calculated using a Young's Modulus of 200

125
 Chapter 5 : Modelling of Buildíngs

Mpa. A value of Young's Modulus of 1065 MPa was found to give a reasonable
estimate of the natural period in the short direction. This value was subsequently
used in all future models of the buildings.

Table 5-4-2Two Stoley Apartment Building (KIDA) - Effect of Young's Modulus of

the unreinforced masonry walls on the modal frequencies-

Mode Young' s Modulus, E (MPa)

200 s00 1065 1500

1st 4.9 1.7 11.1 1 3 1

(lateral short)

2nd 6.9 10.8 15.1 18.4

(torsional)

3rd 7.4 tl.7 r7.0 20.r

(lateral long)

It should be noted that the modal fiequencies determined by the modal analyses for
all of the values of Young's Modulus considered all corresponded to a modal period
of less than 0.35 seconds and when the design earthquake response spectra to be

used in the analysis was considered (Figure 5-2-l) the periods all corresponded to the
constant acceleration region of the design earthquake response spectra and the
choice of a Young's Modulus between 220 MPa and 1,250 MPa (the range derived
from the laboratory tests) would have no effect on the induced design earthquake
force calculated using the design response spectrum for this two storey building.

In order to determine the effect of adopting a Young's Modulus value corresponding

to that given by a number of researchers (Section 2.5) that was an order of
magnitude greater than that determined from the shaking table tests one of the
buildings in the study (OLW) was analysed with the adopted Young's Modulus of
1,065 MPa and with a Young's Modulus of 20,000 MPa. For a Young's Modulus of
1,065 MPa the first lateral mode frequency in the short direction was 2.4Hertz, for a
Young's Modulus of 20,000 MPa the frequency increased to I0-7 Hertz. The
3.IHertz which was close to that predicted
measured frequency (Table 3.3.1) was
by the IMAGES3D model with a Young's Modulus of 1,065 MPa. The frequency

126
 Chapter 5 : Modelling of Buíldings

predicred by the IMAGES3D model with a Young's Modulus of 20,000 MPa was
more than three times Sreater than the measured frequency.

Also varied was the Young's Modulus of the reinforced concrete floor to deærmine
its effect on the modal properties. The comparison was undertaken using building
KIDA, with the Young's Modulus of the unreinforced masonry walls equal to the
value adopted for use in this study, 1,065 MPa. When the reinforced concrete floor
was given a Young's Modulus of 30,000 MPa, the value adopted as standard for thls
study, a modal fiequency of 11.1 Hertz was obtained for the first mode (a short
direction lateral mode). Wren the Young's Modulus was increased to 60,000 MPa
(an unrealistically high value for concrete) the first modal frequency was 1l-2Hertz-
Hence, was concluded that the value of the Young's Modulus adopted for the
it
horizontal elements had little effect on the overall modal properties of the
unreinforced masonry building and the values adopted for the properties of the
materials used in the horizontal elements were acceptable for use in this study.

5.4.3 Wall Geometry

The final check undertaken on the IMAGES3D models before the commencement of
the modelling program was to examine the effect of modelling double leaf walls with
a single 220 mm thick plate elemenl The two storey apartment building (KIDA)
used in the comparison of the effect of the Young's Modulus on the modal properties
was used in this compaúson. As has already been described in Section 5.3, the
building was modelled using the 220 mm plate elements for the double leaf walls- A
second model of the building was completed with two 110 mm thick elements
replacing the single 220 mm thick elements of the frst model for the double leaf
walls. The use of two 110 mm thick walls ensured that IMAGES3D correctly
calculated the bending stiffness, shear stiffness, and bending modulus for the walls.
The results for the 220 mm thick single element model are given in Table 5.4.2- T\e
results for the twin 110 mm thick element model are given in Table 5.4-3.

In the short direction the two models gave similar results (11-1 Hertz compared with
l0-7 lJrertz). In the long direction the twin element model was cha¡acterised by a
number of modes close together (15.1, 15.4 and 15.4 Hertz). The single element
model had a mode at a similar frequency, 17.0 Hertz, with a low effective modal
mass (5.5 percent).

721
 Chapter 5 : Modelling of Buildings

The results of a response spectrum analysis on the twin wall model were compared
to the results of a response spectrum analysis on the single wall model' The
compadson was camied out for the first mode in the short direction. The hrst
comparison was for base shear. For mode one of the single wall model the base shear
was 161 kN. For tlie twin wall model, the first mode base shear was 157 kN, a
difference of 2.5 percenr. This difference was considered to be negligible in light of
the variability of the properties of unreinforced masonry as reported in Chapter 4 and
in Section 2.5. The next result compared was the connection force that was
experienced at the connection of the floors to the walls of the building. The
aparrmenr building had a connection detail similar to Figure 5.1.1(b). The out-of-
plane connection forces were very low (< 0.3 kN/m) in both cases. The in-plane
connection forces were consiclerably greater than the out-of-plane connection forces
for both models. In the case of the twin wall specimen, the connection force was
assumed to be divided evenly between the two concurrent wall elements. The
connection forces are shown in Figure 5.4.1, where the connection forces in each of
the concurrent walls for the twin wall specimen were summed to obtain a total
connection force for comparison to the single element model. It can be seen from
Figure 5.4.1 that the connection forces are essentially the same for both models-

Table 5.4.3 - Results for 110 mm Twin Element Model (KIDA)-

Modal Frequency (Hertz) and Effective Modal Weights

(Vo totzl mass)

lst Short ll rrt r-one I zno ,one | ¡r¿ rone | ¿,h ton*
Twin 110 mm rc.1 14.4 15.1 15.4 t5.4
V/all Model (88.47o) (2.IVo) 6.07o') (6.6Eo) 47.37o

The last response to be compared was the wall stresses. The results for the twin 110
mm wall model and the single 220 mmwall model were compared to determine if the
ratio of the bending stress would be approximately half. It was found that the single
220 mm model bending stresses were indeed hatf those of the twin 110 mm wall
model as was expected. Hence, single 220 mm thick element models were used to
model the double 110 mm thick watls for all buildings in the study. However, the
calculated bending stresses were adjusted to compensate for the overestimate of the
bending stiffness and section modulus.

128
 Chapter 5 : Modelling of BuíIdings

2.9 kN/m 2.9 kN/m

1.5 kN 1.5

1.8 kN
kN/m

1 .4 KN 7.3

9 kN/m kN/m
kN/m tt.2

base shear 161 kN base shear 157 kN

(a)single 220 mm thick wall model (b) twin 110 mm thick wall model

Figure 5.4.1 Two Storey Apartment Building - Connection Force Comparison

Single Wall versus Twin Wall-

5.5 MODAL ANALYSES RESULTS

After the comparisons described in Section 5.4 were completed, modal analyses were
performed for each of the buildings in Table 3.3.1. The results of these analyses are
listed in Table 5.5.1.

The descriptions given for the buildings in Table 5.5.1 correspond to the descriptions
given to the same buildings in Table 3-3-1-

The frst mode frequencies for the buildings were compared with those determined

from the field experiments (Chapter 3) and are presented in Table 5.5.2.

r29
 Chapter 5 : Modelling of Buildings

Table 5.5.1 - Results of Modal Analyses on Buildings-

Mcxlal Frequency (Hertz) ard Perceniâge of

Building Description
Direction Peræntase of Total Mæs Total
Mqle 1 Mcxle 2 I Mcxle 3 I Mode4 Mass

2 storey vacant city slrort 4.8 1;Ì 7.8

('14.99/) (2.1E") (4.o%\ 8t.o%

ænrmercial builtling
(EE2) long 7.5
(74.OE )
'l4.Ùio

2 storey vacant citY .short 6.8 1.4

(48.OVo) (23.3Vo) 7l.3Vo
commercial building
long 1.6 '7.7 7.9 8.1
(EE3)
(8.s%) (5.',|Eo', (6.7Vo) (64.9V") 85.87o

2 lorey vacant city slrort 6.6 1.4

(22.57o) (58.9V') 81.4%
æmmercial builtling
(EE4) long 7.6 1.9 8.2
('7.3c/o'l 6.O9"\ ('ll;7E'\ 85.Mo

3 storey scltool slìort 5.9

(88.7Eo) 88.7%
building
(CBC) long 7.O 7.6 79.4
1r.o%) 07.97o\ (lo.3Eo) 93.ZVo

2lorey city short ro.7

(89.7Eo) 89.7%
social
club long 11.5 19.3
(83.9V") (lO.OVo) 93.91o
(IAC)
3 storey citY short 4.3 1 1.1
(9.1Eo\ 85.2%
commercial builtling Q5.4Eo)

GTT) long 5.1

(74.91"\ 763qo

2 storey city slìort 6.5 7;7

('l8.\Eo) (e.e%) 88.7%
corìmercial buikling
(NSc) Iong 10.4 11.3
(79.6c/o\ (77.7Vo\ 91.3%

2 storey city short 4.2 4.9 9.1

(47.\Vo) (12.3Vo) (6.67o) 86.7%
retail building
(STP) long 9.5
(81.4Vo\ 81.4%

5 storey universitY short 2.4 6.8

office building Q6.3Eo) (19.sEo, 95.8%

(oLrM) long 3.5

(81.9E') 81.9%

2 storey suburban short 1 1.1

apartmeDt building (9o.4%) 90.4%

(KIDA) long t5.7 rt.o

(5.sEo) (86.4%'l 91.9%

2 storey suburban slìort 5.2 8.2

apaftment building (8t.9Vo) Q.L%o) u.G%

(KIDB) Iong 8.8 9.2
(46.4Vo) ll8.2%\ il.6%

130
 Chapter 5 : Modelling of Buildings

Table 5.5.2 - Comparison of Experìmentally Determined Natural Frequencies to

those Determined from Modal Analyses'

Direction Measured FrequencY IMAGES3D FrequencY

Buikling De.scriPtion
(Iìertz) Olertz)

slrort 5.O 5.1

2 storey vacant cltY
long 4.8 7.5
commercial building

city short 3.6 4.8

2 storey vacant
long 5.O 7.5
commercial buikling
GE3)
short 3.7 6.8
2 storey vacant citY
Iong 5.0 7.6
conrmercial builtling
(EE4)
slrort 5.5 5.9
3 storey scltcnl builcling
't.o
(CBC) long

2 storey city .short r3.9 to.7

social club long 1r.5

ûAC)
city commercial short 3.2 4.3
3 storey
long 3.7 5.1
building
GTD
short 10.1 6.5
2 storey city commercial
long 10.4
building
(NSC)
2 storey city short 7.4 4.2

retail building long 7.5 9.5

(STP)
office short 3.1 2.4
5 storey universitY
long 3.5
building
(oLIù¡)
short 7.2 11.1
2 storey suburban apartment
building long 7.3 15.7

ßIDA)
short 7.2 5.2
2 storey suburban apartment
long 7.2 8.8
building
(KIDB)

Comparison of these results are probably best aided by a plot of the form of Figure
5.5.1. From this it can be seen that there is no clear trend in the data. In some cases
the ambient vibration tests determined a lower frequency than the IMAGES3D
analyses and in some cases the ambient vibration tests resulted in a higher frequency
than the IMAGES3D analyses. For most buildings the measured and calculated
frequencies were within 25 percent of each other although the overall correlation
was probably only fair. In certain cases the agfeement was very good (OLW, KIDB,
EE2, and CBC).

The modal properties were then used in the response spectrum analysis conducted on
the unreinforced masonry buildings and described in Section 5.6.

131
 Chapter 5 : Modelling of Buildings

2.0

1.5
Ratio of
frequency +25 V"
from ambient
tests to 1.0
frequency from
IMAGES3D -257o
aralyses
0.5

0.0

Figure 5.5.1 Plot of the ratio of the results of the ambient vibration tests to the
results of the IMAGES3D analyses.

5.6 RESPONSE SPECTRUM ANALYSES

RESULTS

As noted in Section 5.2, the unreinforced masonry buildings were subjected to a

response spectrum analysis using the design earthquake response spectrum from
4S1170.4 for a firm soil site in Adelaide (S = 1.0, a = 0.1 and \ = 1.5).

The results from the previous modal analyses were used as the basis for the response
spectrum analyses and the modes given in Table 5.5.1 corresponded to the modes
used in these analyses. Each building was analysed for earthquake effects in the

directions of both major plan axes of the buildings.

Itwas found from the analytical results that the buildings tended to behave as
described by Priestley (1985) (Section 2.7). T};re induced earthquake force was
resisted by in-plane shear in walls running parallel to the direction of the earthquake

r32
 Chapter 5 : Modelling of Buildings

ground motion. The primary response of the walls at right angles to the seismic input
was in bending.

The results of the response spectrum anaiyses are examined here ín the order in
wlrich tlie buildings were presented in Tables 5.5.1 and 3.3-l- The dimensions of the
buildings are given in Table 3.3.1 and details in Appendix B- The main building
responses examined were:

(1) The base shear;

(2) The storey shear;

(3) The maximum and average connection forces along the in-plane walls and the
friction coeff,rcient, p, required to resist that connection force (the roof
connections do not rely on friction so no friction coefficient was given for the
rooflevels); and

(4) The conected wall bending stresses. The bending stresses are given about a

horizontal axis and a vertical axis-

The required fricúon coefficients were compared to those determined by Page (1994)
and described in Section 2.5. The friction coefhcients given in Page are for wall.s
with a damp proof membrane and it would be expected that brickwork without a
membrane, such as that which would exist at the floor connection, would be able to
achieve even greater friction coefficients than those published by Page. The bending
stresses were compared to those given in Section 2.5 by various researchers to
determine if a tensile failure might be expected.

Also presented for the buildings in the study was the total sway of the buildings and
the corresponding average shear strain, y (total sway divided by the height of the
building). The shear strain was presented so that it could be compared to the shea¡
strain corresponding to a shear failure in the walls. The shear strain corresponding to
shear failure was calculated by taking the failure shear stress and dividing by the
shear modulus, G. The shear modulus was calculated from the Young's Modulus, E,
used in this study, 1,065 MPa, and the assumed Poisson's Ratio, 0.2- The range of
shear strength presented by Jankutovski et al (1994), 0.1 MPa to 0.7 MPa, was used
to calculate the range of shear strains corresponding to failure. The calculated range
was 270 microstrain to 1900 microstrain. For reasonably good levels of

r33
 Chapter 5 : Modelling of Buildings

workmanship it would be expected that the shear strength would be in the upper part
of the shear strength range and correspondingly, the upper level of the shear strain
range.

5.6.1 2-storey Commercial Building (F.EZ)

The firsr building was a 2-storey commercial building (EE2). It had a timber floor
anil a timber truss and metal deck roof. The results for the response spectrum
analysis are shown in Table 5-6.1-

Table 5.6.1 Response Spectrum Analysis Results : Building EE2

Short Direction Long Direaion

Mcxle I Mcxle 2 I Mode 3 I "qc

Mode I
103 -11 9 104 -98
Base Shear ftN)
(W = self weiglrt of the (0.12w) (0.olw) (0.01w) (0.r2w) (0.llw)

Storey Slrear (kN)

1st Floor 99 4 -6 99 93

Roof 55 -l 6 55 50

In-plane Connection Force -

Maximum (kN/m) and P
lst Floor 72;7 0.5 -0.8 12.8 6.4

P=o.71 ¡r = 0.03 tr = 0.04 P = 0.?1 ¡t=O.25

Roof 7.1 -0.1 0.8 'l.t 2.8

In-plane Connection Force -

Avuage (kN/m) and P
1st Floor 12.7 0.5 -0.8 12.8 6.4

F = 0.71 P = 0.03 p = 0.O4 Ir = 0.71 ¡t=O.25

Rcxrf 7.1 -0.1 0.8 7.1 2.8
'Wall Shesses (MPa) -

horizontal and velical

lstFloor - Hori 0.015 0.009 0.019 o.o32 0.012

- Vert 0.059 o.o25 o.o52 0.100 0.038

Roof -Hori o.032 0.o08 0.015 0.040 0.053

- Vert o.M2 0.021 0.043 0.078 o.o77

The connection force was evenly distributed between the two in-plane walls. The
required friction coefhcients are all generally achievable in practice, based upon the
results of Page (1994). The only required friction coefficient that may cause a
problem in practice and lead to a possible failure at the connection of the floor to the
wall was for mode I in the short direction. It should be noted, however, that this
buitding has timber floors and the connection of timber floors to walls was generally
achieved with a positive connection between the floor joist and wall by use of a
mechanical fastener, such as bolts. The out-of-plane connection forces were all less
than 1 kN/m and were not considered to be a problem-

134
 Chapter 5 : Modelling of Buildings

The most common form of damage to unreinforced masonry buildings when

subjected ro earrhquake excitation is due to out-of-plane failure of the walls- This
building had an average axial compressive pre-load due to self weight of 0.11 MPa
for the walls between the roof and the first floor and 0.18 MPa for the walls between
the hrst floor an<l the ground. It can be seen that the none of the bending stresses
given in Table 5.6.1 woul<l be expected to cause a wall bending failure in a properly
constructed building, especially when taking into account the axial compressive
stresses.

The last important response of the buildings to earthquake excitations is the sway.
The building sway in the short direction was 2.1 mm and 1.1 mm in the long
direction, both small enough not to initiate pounding with adjacent buildings- The
corresponding shear strains were 260 microstrain and 100 microstrain respectively.
These shear strains were both less than the expected range of shear strain
corresponding to a .shear failure in the in-plane walls based on the work of
Jankulovski et al (1994).

5.6.2 Z-Storey Commerci al Building (EE3)

The second building analysed was part of the same development as the first. It had
similar details but was larger and had an internal double leaf wall. The results of the
response spectrum analysis are shown in Table 5-6-2-

As with the first building, the friction coefhcients required to resist the in-plane
connection force for this building were all smaller than should be able to be achieved
in practice. In this case the extra (interior) wall resisting the earthquake induced
forces in the short direction resulted in a smaller connection force in the walls and a
subsequent lower friction coeffi.cient demand than the first building-

The axial compressive self weight stress in the walls of this building were 0.175 MPa
for the walls from the f,rrst floor to the ground and 0.102 MPa for the walls from frst
floor to the roof. From the results in Table 5.6-2, it can also be seen that there is
unlikely to be an out-of-plane wall failure due to bending about a horizontal axis-
However, the bending stress about a vertical axis in the walls was nearly equal to the
stress that would cause failure. This aspect of the performance of the walls will be
examined further in Chapter 6 when the requirements of the 451170.4, and the
Australian Masonry Code, 453700, are examined. It can be seen then that the walls

135
 Chapter 5 : Modelling of BuíIdings

of this building may experience out-of-plane failures, which are catastrophic, and

would lead to collapse.

Table 5.6.2 Response Spectrum Analysis Resuls : Building EE3

Sho¡t Direction I-ons Dke.-tion

Mcxtetlvcxlez lcQC t'¡cbl I vcxle2 | io*", I vcdea I cQC

Base Shar (kN) 128 -62 t7t 23 l5 18 151 118

(W = self weiglrt of tlre (0.07w (0.04w) (0.10w) (0.01w) (0.01v/) (0.0rv/) (0.09v/) (0.07w)

buikli ng)
Storey Shear (kN)
lst Floor 132 46 163 -32 19 -tl 124 83

Rcnf 55 25 72 -14 -8 4 49 34

In-plane Connætion Force -

Maximurn (kN/m) and P
lst Floor 6.8 2.8 8.7 - 1.1 -o.7 -o.7 5.9 4.2
p= p= tt= p=0.M F= p= ¡t=O.23
Rmf o.25 0.10 o.32 0.06 -o.4 o.04 o.33 1.5

3.1 1.1 3.8 -o.7 -o.4 2.4

In-plane Connection Force -

Average (kN/m) and ¡r
1st Floor 6.0 2.4 1.6 - 1.1 -o.7 -o.7 5.9 4.2
tl= ¡!= p= p = 0.04 p= ¡t=O.23
Roof o.2z 0.09 0.28 0.06 -0.4 0.04 0.33 1.5

2.7 1.0 3.4 -o;1 -o.4 2.4

Wall Stresses (MPa) -

horizontal and vertical
lstFloor - Hori 0.080 o.o'14 o.137 -0.055 -o.M2 -o.045 0.103 0.040

- Vert o.r85 0.171 0.315 -0.150 0.109 0.116 o.290 o.622

Roof -Hori 0.101 0.064 o.t4'l -0.049 -0.036 -0.039 0.075 0.186

- Vert o.233 0.143 0.336 -0.141 0.102 0.105 0.201 0.514

The sway for this building, determined by CQC, was about 2 mm for both directions
of excitation, well within limits that would prevent pounding between adjacent
buildings. The corresponding shear strains were 260 microstrain in both directions
and as with the first building in the study, these shear strains are not expected to lead
to in-plane failures in the walls-

5.6.3 2-Storey Commercial Building (EE4)

The third building analysed was the last building from the same development as the
f,rst two and it had the same details as EE2 and EE3 as well as an inærnal double
leaf wall. The results are shown in Table 5.6-3-

This building had a very similar layout to building EE3, with the main difference
being the internal wall which was offset from the centre-line of the building. This led
to some torsional response in the building. Again, the required friction coefficients

136
 Chapter 5 : Modelling of Buildings

should be able to be met in practice. The self weight axial compressive stresses for
tliis building were the same as those for the previous building. The only bending
stress that may cause a failure in the walls was bending about a vertical axis in the
short direction above the hrst floor. The sways for this building were the same as the
previous builcling, about 2 mm. The conesponding shear strains were the same as for
building f,,p],260 microstrain, and again were not expected to lead to any in-plane
failures in tlie walls.

Table 5.6.3 Response Spectrum Analysis Results : Building EE4

Slrort Dire¿lion Lons Diredion

Mcxtel I Itno'"t I aq. Mcxle I I "*"i I ".',"¡ I CQC

Base Shear (kN) -59 r56 189 19 76 190 164

(W = self weiglrt of ilte (0.03v/) (0.09v/) (0.1lw) (0.01r{) (0.01vù) (0.1lw) (0.09v/)

builrlinc)
Storey Shear ftN)
1st Floor 68 120 t6t -19 140 109

Rcnf 24 59 73 -12 54 42

In-plane Connection Force -

Maximurn (kN/rn) and P
1st Floor 3.4 6.7 8.7 -1.0 -o.7 6.5 5.3
p = 0.12 ¡t,--O.25 P=O32 P = 0.06 [r = O.04 p = 0.36 )L=O.29
Roof 1.6 2.9 3.9 -0.6 -o.4 2.7 2.O

In-plane Connection Force -

Average ftN/m) and ¡r
lst Floor 3.0 6.1 7.9 -1.0 -o.7 6.5 5.3
p = 0.11 ¡t=O.22 ¡r = 0.28 tt = 0.06 tt=0.(X P = 0.36 tL=O.29
Roof 1.4 2.6 3.4 -0.6 -o.4 2-'l 2.O

rùr'all Strasses (MPa) -

horizontal and vertial
lstFloor - Hori 0.069 0.090 0.135 -o.M7 -0.050 o.o92 0.05?

- Vert 0.171 o.247 0.355 -o.125 -0.130 o.263 0.159

Roof -Hori 0.079 o.o74 o.129 -0.M1 -o.u2 0.0út 0.048

- Vert o.197 0.182 0.321 -0.1 18 -0.1 16 o.172 0.1 35

5.6.4 3-storey School Building (CBC)

The fourth building analysed was a 3-storey school building. It had concrete flat slab

floors, metål deck and steel beam roof and was not symmetrical. The results for the
response spectrum analysis are shown in Table 5.6.4.

The connection forces in this building required friction coefficients that should be
able to be met in practice- The bending stresses were also sufhciently low that an
out-of-plane wall failure was not expected. The building responded torsionally as
there was a wall present in the long direction of the building on the ground floor that
v/as not present in the upper floors- Because of this, it is the only building which

131
 Chapter 5 : Modelling of Buildings

could have a problem with out-of-plane connection forces. The calculated out-of-
plane connection force in the second storey was 2'4 kN/m'

Table 5.6,4 Response spectrum Analysis Results : Building cBc

Short Direction Long Direclion

Mcxle I Mcxle I Mcxle2 | v**¡ | cQC
r00 -659 -94 608
Basc Slrear (kN) -8 12
(0.12v/) (0.01v/) (0.0ew) (0.01v/) (0.09rw)
(W = self weìglrt of tlre
buildins)
Storey Shear ftN)
812 -100 658 95 60't
lst Floor
2nd Floor 553 -83 463 44 416

Rcrlf 745 -23 125 46 120

In-plane Connection Force -

Maximum ftNfn) an<I P
lst Floor )^, -3.3 tt.2 1.3 9.5
p = 0.38 p = 0.07 ¡r - O.23 p = 0.03 ¡r = 0.20
13.1 -,, < 11.6 -1.1 10.2
2nd Floor
¡t = O.26 p = 0.10 ¡t-- O.47 t¡ = 0.04 ¡r = 0.41

Rcrcf 4.4 -0.9 3.8 -7.2 3.5

In-plane Connection Force -

Average ftN/m) and ¡r
27.3 -7.2 8.4 1.2 7.8
lst Floor
p = 0.34 p = 0.o3 F = 0.18 p = 0.03 lL=O-77
'1.5 -o.7 7.O
2nd Floor I r.1 -0.9
tL=O.22 tr = 0.O4 p = 0.31 P = 0.03 þ=o.29
3.3 -o.7 1.4 -o.7 1.3
Roof
Iùr'all Stresses (MPa) -
horizontal and vertical
0.009 0.001 -0.002 0.001 o.002
lstFloor - Hori
- Vert 0.045 o.005 -0.010 0.004 0.009

0.001 0.002 -0.002 0.000 o.002

2nd Floor - Hori
- Vert 0.005 0.010 -0.007 0.001 0.008
o.000 0.003
Roof -Hori 0.002 0.003 -0.o04
o.011 o.o15 -0.020 0.001 0.015
- Vert

The sway of rhis building was 2 mm in the short direction and 1 mm in the long
direction. The corresponding shear strains were 230 microstrain and 110 microstrain
respectively. Neither of these corresponded to the level of shear strain expected to
correspond to an in-plane failure of the walls.

5.6.5 2-storey Social Club Building (IAC)

The fifth building rù/as a 2-storey building with a concrete suspended floor slab and a
one storey area which houses a social club in the city- The results of the response
spectrum analysis are given in Table 5.6-5-

138
 Chapter 5 : Modelling of Buildíngs

Table 5.6.5 Response Spectrum Analysis Results : Building IAC

Short Direction Long Direction

Mcxle 1 Male 1 Mcxle 2 | .q.
-522 62 523
Base Shear (kN) -558
(W = self weiglrt of üte (0.11\M) (0.10w) (0.01w) (o.l0v/)

Storey Shear ftN)

556 524 -51 5?'5
1st Floor

Roof 1ll 133 41 140

In-plane Connection Force -

Maximum (kN/m) and ¡r
1st Floor 9.6 8.4 -o.7 8.4

¡r = 0.60 P = 1.01 p = 0.08 F= l.0l

Rcnf 2.9 4.8 1.5 5.1

In-plane Connection Force -

Average (kNÍn) and P
lst Floor 6.0 4.6 -0.5 4.6
p=o.31 p = 0.55 F = 0.06 p = 0.55

Roof 2.8 4.6 1.5 4.9

\ùr'all Stresses (MPa) -

horizontal and vertical

lstFloor - Hori 0.035 0.002 0.002 0.003

- Vert 0.018 0.o10 0.003 0.011

Roof -Hori 0.073 0.003 0.003 0.004

- Vert 0.010 o.015 0.o06 0.016

The connection force requirements for this building were complicated by the fact that
the upper floor only covers part of the ground floor plan. This resulted in a fairly low
compressive stress in the ground floor walls and high friction coefhcient
requirements (p > 1). In the long direction, a failure was predicted benveen the floor
and wall for in-plane forces. The bending stresses were all low enough that out-of-
plane wall failures were not expected. The sway of the building in both directions
was less than 1 mm due to the large plan area and low height providing a very stiff
structure to resist the lateral loads. The corresponding shear strain in both directions
was 150 microstrain; well less than that required for an in-plane wall failure.

5.6.6 3-storey Commercial Buitding (LTI)

The sixth building analysed was a 3-storey commercial building that had concrete
floors, unreinforced masonry stair and lift shafts, and a metal deck roof. The results
of the response spectrum analysis are given in Table 5-6-6-

The friction coefficients (p) required to resist the in-plane forces in this building were
all less than 0.5. The out-of-plane bending stresses were also low and would not h
expected to result in a tensile failure in the brickwork. The low stress levels may be

r39
 Chapter 5 : Modelling of Buildings

The
due ro the r-elatively (to the other buildings in the study) small storey height-
problem
sway in both directions was less than 3.0 mm and would not be considered a
to adjoining buildings. The conesponding shear strains were both 230 microstrain,
which was not expected to correspond to a shear failure in the in-plane walls-

Table 5.6.6 Response Spectrum Analysis Results : Building LTI

SIrort Dirætion Long Direction

Mcxle 1 Mcxle 2 CQC Mcxle I

-1480 190 1490 1470
Bæe Shear ftN)
(0.10w) (0.01v/) (0.10vi) (0.10w)
(W = self weight of dte
buiklins)
Storey Sheu (klr)
1st Floor 747 4 -190 1484 t4lo
2nd Floor 14 10 -t24 t414 1406

l 003 t32 1013 989

3rd Flcxrr
309 l06 128 291
Roof
In-plane Connection Force -
Maximum (kN/m) and P
Floor 2't.7 -3.4 27.9 20.6
1st

IL = O.24 p = 0.03 lL=O.24 ¡r = O.1'l

26.2 -2.O 26.3 19.8

2nd Floor
p = 0.34 p = 0.03 P = 0.34 lL=O.24
19.7 2.1 19.8 14.9
3rd Floor
p = 0.50 p = 0.05 F = 0.50 ¡r - 0.34

Rcxrf 6.6 2.2 7.O 5.4

In-plane Conneciion Force -

Average (kN/m) and ¡r
23.9 -3.1 24.1 17.5
lst Floor
þ=o.2r tr = 0.03 tL=O.21 p - 0.14

2nd Floor 22.8 -2.O 22.9 16.7

p = 0.30 p = 0.03 p = O.30 p = o.20

16.3 2.3 16.5 I 1.8

3rd Floor
P = 0'41 tt = 0.06 p=O.42 lt=O.27
5.0 1.7 5.3 3.5
Rcnf
Wall Strasses (MPa) -

horizontal and vertical

0.003 0.001 0.003 0.005
lstFloor - Hori
- Vert o.o12 0.003 o.otz o.o24

0.002 0.001 0.002 0.001

2nd Floor - Hori
- Vert 0.o03 0.002 0.oo4 0.003

0.002 0.001 0.002 0.007

3¡d Floor - Hori
0.006 0.002 0.006 o.004
- Ve{t
0.002 0.005
Roof -Hori 0.002 0.001
0.004 0.002 0.004 0.oo5
- Vert

5.6.7 2-Storey Commercial ßuilding (NSC)

The seventh building analysed was a 2-storey commercial building with a suspended
slab that is part reintbrced concrete and part timber and a metal deck roof- The
results of the response spectrum analysis are given in Table 5-6-7 -

140
 Chapter 5 : Modelling of Buildings

Table 5.6.7 Response Spectrum Analysis Results : Building NSC

Short Dirætion Lone Diredion

Msle 1 Mqle2 CQC Mcxle I | ú*"t I .q.

-61 506 386 -57 353
Base Slrear (kN) -481
(0.12v/) (0.01v/) (0.12v/) (o.o9w) (0.0|ù¿) (0.08!w)
(rJy' = self weiglrt of ilre
buil<ling)
Storey Shcar (kN)
445 2l 451 -361 35 340
lst Floor
82 '18 10 1)
Rcnf 80 7

In-plane Connection Force -

Maximum (kN/rr) and ¡r
lst Floor 15.7 1.5 16. I -6.6 0.8 6.1
p = 0.54 tt = 0.03 O.2l
¡r = 0.53 F = 0.05 ¡t=O.23 lL =

Rcxrf 4.5 o.2 4.6 -1.7 0.1 1.6

In-plane Connection Force -

Average ftN/m) and ¡r
1st Floor 73.5 1.3 13.9 -6.3 0.8 5.8
p=o.47 lr = 0.O3 p = 0.20
p = 0.46 tr = 0.O4 ¡t=O.22
Rmf 3.4 0.1 3.4 -1.6 o.1 1.5

rùr'all Snesses (MPa) -

horizontal and vertial

lstFloor - Hori 0.017 o.o32 0.040 o.018 0.031 0.045

- Vert 0.057 0.145 0.169 0.05r 0.117 0.154

Roof -Hori 0.054 0.026 0.066 o.M2 o.o27 0.063

- Vert o.237 0.115 0.283 o.180 0.096 o.252

This building's connection force requirements should be able to be met in practice.

However, the calculated bending stresses were of concern. For both directions of
ground motion the bending stresses in the walls between the first floor and the roof
were high for bending about a vertical axis. The contribution of the self weight axial
stresses to the resistance of these bending stresses is less than that for the bending
about a horizontal axis. An out-of-plane wall failure in the upper walls of this

building v/ould therefore be a possibility.

The sway of the building (<3 mm) will not cause problems to adjacent buildings in
either direction. The corresponding shear strain was 370 microstrain for both
directions. Unlike the other buildings examined so far, this exceeded the lower bound
of the range of shear strain that corresponded to a shear failure in brickwork based
on the ,ù/ork of Jankulovski et al (1994). It is therefore possible that this buitding
could experience an in-plane wall shear failure-

t4l
 Chapter 5 : Modelling of Buildings

5.6.8 2-storey Retail Building (STP)

The eighth building analysed was a 2-storey retail building which had a suspended
timber grou¡d and upper floor and a metal deck roof. The results of this analysis are
given in Table 5.6.8

Table 5.6.8 Response spectrum Analysis Results : Building STP

Sl¡ort Direction Long Direction

Mcxle I I Mcxle2 | uo¿"¡ Mode 1

Base Shear (kN) -241 138 33 246 4@

(0.07v/) (0.o4vf) (o.o|w) (0.07w) (0.r2w)
(W = self weiglrt of tlte
buildine)
Storey Slreu (kN)
24r t62 -32 254 409
Ground Flær
1st Floor 241 142 tz 245 351

50 -67 -16 74 139

Roof
In-plane Connection Force -
Maximum (kN/m) and ¡r
13.0 -10.6 -1.6 14.5 7.6
Ground Floor
lL= 0.32 tL = O.27 P = 0.04 p = 0.36 tt = O.2l
13.0 -8.6 0.6 13.6 6.6
1st Floor
v=0.62 p = 0.41 P = 0.03 It = 0.65 P = 0.35
Rcnf 3.5 -3.7 -0.8 4.5 2.7

In-plane Connection Force -

Average (kN/rn) and P
12.5 -8.4 -1.3 13.2 7.6
Ground Floor
p = 0.21 P = o.o3 p = 0.34 ¡t-O.21
¡r = O.32
12.l -7.3 0.3 12.4 6.5
lst Floor
p = 0.58 p = 0.35 p - 0.ol p = o.59 ¡r = 0.34

Roof 2.8 -3.3 -o.7 3.8 2.6

Wall Stresses (MPa) -

horizontal and vertical
0.308 o.236 0.030 0.436 0.003
GroundFloor- Hori
- Vert 0.050 0.102 0.056 0.139 0.005
0.009 1.046 0.005
lstFloor - Hori o.778 o.523
- Vert 0.401 o.263 0.013 0.535 0.003

Roof -Hori o.469 o.256 o.ol1 o.592 0.005

- Vert 0.167 0.035 0.031 0.183 0.008

The connection force requirements for this building should be able to be met in
practice. The connection forces that required a friction coefhcient of about 0.6 may
be of some concern and may lead to an in-plane connection failure. The axial
compressive stresses due to the buildings self weight were 0-092 MPa for the wall
between the roof and the hrst floor, 0.116 MPa for the walls between the fust floor
and rhe ground floor, and 0.211 MPa for the wall from the ground floor to footing
level. The plan of this building given in Appendix B shows that for two corners of
the building the floor does not meet the wall. This meant that the walls were

r42
 Chapter 5 : Modelling of Buildings

spanning from the roof to the floor (9300 mm) which was a span considerably
gfeater than the other buildings in the study. It can be seen from the results given in
Table 5.6.8 that the upper level walls risk out-of-plane failure when the building was
excited in the short direction. The span of the out-of-plane walls for earthquake
excitation in the long direction were the floor to floor height, and coupled with the
short horizontal span resulted in bending stress levels that would not be expected to
lead to failure.

The short direction had a large sway, about 8 mm, which, though large compared the
majority of buildings in the study, would not be expected to result in pounding
problems. The long direction sway was 0.6 mm. The corresponding shear strains
were 860 microstrain and 60 microstrain respectively. The shear strain in the short
direction could be expected to lead to an in-plane failure of some walls.

5.6.9 S-storey University Building (OLW)

The ninth building analysed was a 5-storey university office building which had
reinforced concrete flat slab floors and roof. The results of the analysis are given in
Table 5.6.9.

This building was the tallest in the study. The required friction coefficients for the in-
plane connection forces were all less than 0.6- This was due to the building having a
high self weight, including a concrete roof. The only connection force that may be of
concern in an earthquake was for the hfth floor in the long direction, where a friction
coefficient of about 0.6 was required. Prior to analysis, it was thought that the height
of this building would lead to the possibility of out-of-plane failures in the upper
floors. This turned out to not be the case. This was due to the regular spacing of the
inærnal walls that kept the span of the out-of-plane walls small enough that the
bending stresses remained low.

Naturally, for the tallest building the sways were relatively large, 4 mm in the long
direction, and nearly 10 mm in the short direction. The corresponding shear strains
were 520 microstrain and 209 microstrain, respectively. A shear failure in the short
direction was a possibility if the wall shear strength was in the lower part of the
range.

t43
 Chopter 5 : Modelling of Buildings

Table 5.6.9 Response spectrum Analysis Results : Building olw

Short Direction Long Direaion

Mqle 1 Mqìe 2 CQC Mcxle 1

868 321 8 -3647

Base Sher (kN) -3 105
1v/) (0.03v/) (0.12v/) (0.1 3v/)
(W = self weiglrt of tre (0.1

buikling)
Storey Shear ftN)
3014 -836 3122 3641
1st Floor
2875 -566 2926 3381
2nd Floor
2593 -t't9 2598 2961
3rd Floor
2137 153 2r44 2351
4tlt Floor
7495 314 1530 1559
5th Floor
233 '720 703
Roof 679

In-plane Connection Force -

Maximurn (kN/rn) and P
lst F'loor 35.9 -1 1.5 f7.6 33.6
p = 0.40 p = 0.13 ¡t=O.42 tL = O.42
21.7 -4.1 22.1 22.O
2nd Floor
F = 0.30 F = 0.06 p = 0.30 [r = O.34
19.5 -1.3 19.5 19.9
3rd Floor
¡r = 0.34 ¡r = 0.02 P = 0.34 P = 0'40

t5.9 1.2 16.0 16.2

4th Floor
p = 0.39 ¡r = 0.03 p = 0.40 ,t=O.47
I 1.1 2.4 11.4 11.6
5tlr Floor
F = 0.46 F = 0.10 p=o.47 F = o.59
5.5 1.8 5.8 6.1
Roof
In-plane Connection Force -
Average ftN/m) and P
20.9 -6.1 21.7 22.4
lst Floor
)r=O.24 p = o.o7 ¡r=O.24 F = o.2E

10.7 -2.O 10.9 13.2

2nd Floor
P = 0.15 p = 0.03 F = o.15 lt = 0.2O
3rd Floor 9.6 -o.6 9.6 11.3

¡r = 0.01 p = o.17 ¡r = O.23

jL = O.l7
4th Floor 8.0 0.6 8.0 8.7
p = 0.20 p = 0.01 p = 0.20 tt=O.25
5.6 1.2 5.7 5.7
5th Floor
lL=O.23 F = 0.05 þ=o.23 tL=O.29
2.7 0.9 2.9 2.1
Roof
Wall Stresses (MPa) -
horizontal and vertical
0.008 0.004 0.010 0.010
lstFloor - Hori
- Ve{t o.M2 0.015 o.M4 0.043

Hori 0.012 o.0L2 0.017 0.001

2nd Floor -
0.010 o.005 o.011 0.009
- Vert
o.014 o.otz 0.018 0.001
3rd Floor - Hori
0.009 0.003 o.009 o.003
- Vert
41h Floor - Hori o.018 0.007 0.o19 0.000
0.002 0.003 o.004 0.002
- Vert
o.o24 0.001 o.o24 0.001
5th Floor - Hori
0.oo3 0.001 0.003 0.oo3
- Vert
Roof -Hori 0.030 0.009 o.o32 0.m0
0.003 0.002 0.oo3 0.002
- Vert

t44
 Chapter 5 : Modelling of Buildings

5.6.10 2-Storey Apartment Building (KIDA)

The tenth building analysed was a 2-storey apartment building- This building
consiste<l of a reinforced concrete flat slab and a metal deck roof. The results of the
analysis are given in Table 5.6-10.

Table 5.6.10 Response Spectrum Analysis Results : Building KIDA

Short Direction Long Direction

Mqle 1 Mcxle 1 Mcxle 2 coc
Base Shear (kN) -1 6l to -153 747

(0.1 3v/) (0.0rÌ¿) (0.12rw) (0.12tù/)

(W = self weiglrt of lJre

buiklins)
Storey Shear (kN)
741 -10 136 130
lst Floor
25 23 22
Roof 1

In-plane Connection Force -

Maximum ftN/m) and ¡r
I 1.3 - 1.I 5.3 4.7
lst Floor
p = 0.60 P = 0.06 p = 0.28 F=O.25
2.9 -0.3 1.1 0.9
Rcnf
In-plane Connection Force -
Average (kN/m) and P
9.9 -0.6 4.4 4.1
lst Floor
tt = O.52 P = 0.03 tL=O.23 lL=O.21
2.1 -0.1 o.7 0.6
Rcnf
Wall Snesses (MPa) -
horizontal and vertical
lstFloor - Hori 0.014 0.002 0.014 0.0r5
- Vert o.036 o.004 0.o31 0.034
0.018 0.020
Roof -Hori 0.013 0.002

- Vert 0.M5 0.005 0.054 0.057

The connection force friction coefhcient requirements for this building were all less
than 0-6. The out-of-plane bending stresses were all small so that an out-of-plane
failure was not expected. Sways of less than 0.5 mm were calculated and these
corresponded to shear strains of 109 microstrain for both directions. Shear strains of
this level \¡/ould not be expected to lead to an in-plane failure in the walls-

5.6.11 2-storey Apartment Building (KIDB)

The last building analysed was part of the same development as the previotts
building. The difference between the two buildings is that KIDB was longer and had
a staircase at one end- The results of the analysis are given in Table 5-6.11-

r45
 Chapter 5 : Modelling of Buildings

Table 5.6.11 Response Spectrum Analysis Results : Building KIDB

Short Dirætion Long Direclion

Mo<ie 1 Mcxle 2 I .q. Mode I Mode 2 I .q"

-276 2'16 -156 -67 212
Bæe Shar ftN)
(0.1?v/) (0.00w) (0.17vv) (0.09w) (o.04ur) (0. l 3v/)
(\il = self weight of dte
building)
Storey Shear (kN)
1st Floor 234 4 234 139 37 173

63 0 63 29 10 38
Rcnf
In-plane Connection Force -
Maxinrum (kN/m) and ¡l
13.8 -0.3 13.8 3.7 1.2 4.8
1st FIoor
p = 0.78 ¡r = 0.02 F = 0.78 ¡t = 0.20 tt = 0.06 tL=O.25
6.1 1.1 0.3 1.4
Rmf 6.1 -0.1

In-plane Connection Force -

Average ftN/rn) and ¡r
1st Floor 12.8 o.l r2.8 3.4 l.l 4.4

P=O.72 ¡r = 0.01 p=o.72 F = 0.18 P = 0.06 P=O.32

4.0 -0.1 4.O 0.9 o.2 1.1
Roof
Wall Strsses (l\tfPa) -
horizontal and velical
o.o29 0.020 0.036 0.040 0.130 0.166
lstFloor - Hori
0.096 0.073 o.123 0.057 o.294 0.348
- Vert
0.099 0.173 0.050 o.2r9
Roof -Ilori 0.062 0.075
o.272 0.053 o.220 0.3 85 0.086 0.464
- Vert

This building may have problems achieving the required in-plane friction coefhcients
at the first floor level for excitation in the short direction. Bending stresses for
bending about a vertical axis \r/ere also near the value where tensile failure could
become a possibility, especially in the long direction.

The sway for both directions was calculated to be about 2 to 3 mm' This
corresponded to shear strains of 430 microstrain to 650 microstrain. Both of these
exceeded the lower bound of the expected range of shear strains that corresponded
to shear failure in the walls.

5.7 SUMMARY

A single phase finiæ element model was used to model the dynamic behaviour of
eleven unreinforced masonry buildings. The dynamic properties of the buildings were
esrimared using single22O mm thick elements to model twin 110 mm thick walls-
The only response property to be incorrectly modelled by this procedure was the wall
bending stress, which was doubled to obtain a more accurate value of bending stress.

r46
 Chapter 5 : Modelling of Buildings

It was found that the in-plane connection force requirements could generally be met
by fiiction. This conclusion was based upon the results of Page (1994)' The
predicted failure mechanism for an in-plane failure was that the connection force at a
particular point of the wall exceeded the capacity of the floor-wall connection- This
resulted in the floor trying to slide along the wall at this location. Because the floor is
a rigid diaphragm, the floor cannot slide at this point until the rest of the floor-wall
connection slides. So rather than a local failure, an in-plane connection force failure
can not occuf until the whole floor-wall connection reaches its capacity. This meant
that rhe fi-iction from the weight of all of the parts of the building contributing to the
dead load on these walls was available to resist the total storey shear on that wall-

For new buildings it would be expected that a reasonably high level of workmanship
would be present in the unreinforced masonry walls and that the shear strength of an
unreinforced masonry wall in a new building would be at the upper end of the 0-1
Mpa to 0.7 MPa range reported by Jankulovski et al (1994). In-plane wall shear
failures would then not be a likely failure mechanism in an unreinforced masonry
building subjected to earthquake excitation based upon the results of these buildings-
However, if the shear strength of the walls was at the lower part of the range of
shear strength then there is the possibility of some in-plane wall failures. However,
in-plane shear type wall failures are generally do not lead to collapse.

A failure mechanism that is more likely is an out-of-plane wall failure, particularly in

the upper walls were the self weight is the lowest and the acceleration, and hence the
inertia force, is the greatest- Five of the buildings in the study had bending stresses
that would suggest that an out-of-plane failure was a possibility based upon the
ænsile strengths reported in Section 2.5. Unlike in-plane wall failures, the out-of-
plane failure of walls are generally a collapse condition.

No correlation was observed between the building height and the possibility of an
out-of-plane failure from the results of the response spectrum analyses. However, it
was obvious that as the height of a buildings increased, so will the induced
acceleration, and hence, the induced inertia force. Also important in predicting the
possibility of an out-of-plane wall failure was the floor-to-floor height, and the
horizontal span of the walls. Obviously, the greater the span of the wall between
suppoß, the greater the out-of-plane deflections and bending moment induced in the
wall by the earthquake ground motion, and the greater the bending stress.

r41
 Chapter 5 : Modelling of Buildings

The sway of all the buildings in the study was sufhciently small that the buildings
would not be expected to pose a problem for neighbouring buildings through
pounding. This was the result of the buildings having a very large shear stiffness due
to the in-plane walls.

Comparison of the results of this study to the results gained from a real earthquake
acting on an unreinforced masonry building, as outlined in Section 2.4, ftom Tena-
Colunga a¡d Abrams (1992) and Abrams (1993), was difhcult because the ground
acceleration at the f,rrehouse studied was 0.299, almost three times that used in this
study, and is further complicated by the fact that an & factor of 1.5 was used in the
response spectrum analYses.

Nevertheless, a comparison of the shear and bending stresses in Table 2.4.2 for the
hrehouse showed that the bending stresses and shear stresses (and hence, connection
forces) obtained from the response spectrum analyses canied out in this study were
of a simila¡ order of magnitude for the base acceleration and in many cases, about
one third of the firehouse values.

Itwas concluded that the calculated responses of the buildings in this study to the
earthquake ground motion represented by the response spectrum provided a
reasonable prediction of the behaviour of the buildings to earthquake ground motion.
These results will be further compared to the requirements of 4S1170.4 in the next
chapter.

148
6 trQUIVALENT STATIC FORCE
AI{ALYSIS OF' BUILDINGS

6.1 INTRODUCTION

To achieve the overall aim of this project, that is to evaluate and, if necessary' refine
the current simplihed methods for tlie earthquake analysis of unreinforced masonry
buildings, it was f,rrst necessary to examine a number of existing methods available to
the designer. In Australia, this meant the design procedures given in The Australian
Standard "Minimum design loads on structures - Part 4 : Earthquake Loads"
AS 1170.4- Lg93. The code contains two methods 'for th-e analysis of a structure
when

subjected to earthquake induced forces. The first method is an

qquivalent static load'

approach and the second method is by a dynamic analysis- The second method allows
the use of either â¿response spectrum analysis (Chapter 5) or a time history analysis.

This chapter presents the results of an investigation where the -equivalent static load
was used to analyse the buildings from Chapter 5. These results are then
1plro_ach
compared to the results of the response spectrum analyses described in Chapter 5.
From this comparison was concluded that the equivalent static load approach
it
required rehnement to take into account the particular properties of qqreinforced
masonry and unreinforced m buildings.

6.2 CODE BASED ANALYSN

All the buildings in the study were analysed in accordance with the equivalent static
force procedures in AS1 110.4. All the buildings were classified asþy-¡le I structures
except for the hve-storey university ofhce building (OLW) and the two-storey city

r49
 Chapter 6 : Equivalent Static Force Analysis of Buildings

social club (IAC) which are both Type II buildings, because of the office
building's

height and the social club's potential for holding a large number of people'

The AS1 110.4 equivalent static force base she4r is given by the formula:

V=I (6.2.r)

where

(6.2.2)

and I is an importance factor, S is a site factor, taking into account the soil profltle, a
is an acceleration coefficient, T is the natural period of the building, and \ is a
response modification factor (Section 2.9). GEis the gravity load, given by:

G, = G +V"Q (6.2.3)

where G is the dead load, Q the live load, and ry" is a live load combination factor
from the Australian Standard "SAA Loading Code - Part 1 : Dead and live loads and
load combinations" AS 1 170. 1- 1989-

The variables, a, S, and were all taken to be the same values as used for the
I,
(a =
response spectrum analyses in Chapter 5; that is, for a firm soúsiæ in Adelaide
0.10g, S = 1.0, and I = 1.0)-

The earrhquake design category given in 4S1170.4 for Type I buildings with as =
0.1 is category B_, and for the lype II buildings is category'C. The requirements for
category B and C buildings are very_ similar for. non-ductile constrì¡ction, such as
unreinforced masonry. The buildings are required to be designed by either the
equivalent static force method or by dynamic analysis'

There is a further requirement for buildings that are f=o-Ur o! morg storeys-high- That
is, unreinforced masonry is not allowed to be used for the earthquake force resisting
mechanism for these buildings. This requirement meant that the five storey university
office buitding in this srudy does not comply with the current earthquake code and
the analysis procedures do not apply to it. However, for completeness, the equivalent

150
 Chapter 6 : Equivalent Static Force Analysis of Buildings

static force analysis was also canied out for this building for comparison to the
results of the response spectrum analysis presented in Chapter 5.

The c¿þulated:_bage sheaqwas applied to the building using the procedures given in
451170.4. The rnethod used the fonnula:

& =c*v (6.2.4)

to distribute the base shear up the building. F* is the force applied at level x and

c* (6.2.s)

io
i=l
,,hl'

where G** and Gri are the ns of the load G, at levels x and i respectively,4
and h, are the -d$!_q1.9 from the base to levels x and i respectively, and n is the total
number of storeys. k is a period dependant exponent that for periods less than 0-5
seconds (alt of the buildings in this study) is equal to 1-0-

The torsional effects created in the buildings due to centre of mass and the centre of
slrear not being coincident were also evaluated using the provisions in AS1l70-4-
The static eccentricity, that due to the distance between the centre of mass and the
centre of shear, was calculated and then the design eccentricity was calculated using
the procedures in 451170.4. Torsion tends to increase the force to be resisted by
individual members of a structure compared to the case where only lateral modes are
considered.

4S1170.4 also specifies a minimum wall anchorage requirement for the connection
of walls to floors and the roof. The minimum anchorage is 10(aS) kN per metre run
of wall. This requirement applies to the out-of-plane resistance of the wall-floor
connection rather the in-plane connection force. 10(aS) is equal to 1 kN/m for all the
buildings in this study. For the in-plane connection force no other requirements a¡e
included. Through a simple analysis of the structure, assuming the structure acts as
described by Priestley (1935) (Figure 2.7.1), it would appear that the storey shear
should be distribuæd to the in-plane walls in proportion to their stiffness with an
additional correc tion for eccentricity.

151
 Chapter 6 : Equivalent Static Force Analysis of Buildings

6.3 RESULTS OF STATIC ANALYSIS

In this section the results of the equivalent static force procedure are presented and
compared with the results of the response spectrum analyses reported in Chapter
5'

The response quantities compared were:

(1) Natural periods;

(2) Base shear;
(3) Distribution of base shear;
(4) Connection forces; and
(s) Out-of-plane effects.

6.3.1 Natural Periods

The hrst result to be investigated was the natural periods calculated using Equations
2.1.1 and Z-I.2. It was noted that the periods calculated from these equations
corresponded to the constant acceleration region of the Design Response Spectrum
(Figure 5.2.1) for all buildings except the hve-storey ofhce building, OLW' This
resulted in the design base shears for these buildings being equal in both directions-
Further, the constant acceleration region of the Design Response Spectrum is
expressed as the upper limit in Equation 6.2-1, so that the acceleration in this region
is independent of the site factor, S. Hence, the soil type under the building does not
effect the calculated design base shear for these buildings. The soil type under the
building only changes the length of the constant acceleration region as it effects the
building period at which the upper limit to the acceleration is reached-

6.3.2 Base Shear

The calculated design base shears from the equivalent static load method are

compared to the base shears calculated from the response spectrum method in Table
6.3.r.

4S1170.4 specifies rhat the base shear determined by a response spectrum analysis
must not be less than the base shear determined from the equivalent static force
approach if the building is classed, in accordance with the code, as "irregular". If the
building is classed as "regular", then the base shear calculated by the response
spectrum method should not be less than 90 percent of that determined from the
static force approach in the code. The only exception to this requirement for regular

t52
 Chapter 6 : Ecytivalent Static Force Analysis of Buildíngs

buildings is if the fesponse Spectfum analysis was performed using the natural
periods for the builciing detennined from the period formulae included in the code
(Equations 2.1.1 and 2.1.2)- In this case, the base shear calculated by the response
spectrum method should not be less tl.ran 80 percent of that determined from the
static force approach in the cocle. The code also states that the base shear determined
from the response spectrum method need not exceed the 100, 90, and 80 percent
levels described above. The buildings that the code considers "regular" are denoted
by "reg" in the Building description column of Table 6.3.1 whilst those considered
"irregular" are denoted by "imeg". The minimum allowable base shear for a response
spectrum analysis (90 or 100 percent) is also shown in Table 6.3.1 under the values
for the AS I 170-4 determinecl base shear for each building. Also shown in Table 6-3- 1
is the percentage of the required minimum base shear for each of the base shears
calculated by the base shears expressed as a percentage of the required minimum
base shear under the response spectrum base shear values-

For the buildings in this study the base shear detennined using the response spectrum
method never exceeded the values determined using the equivalent static force
approach. In fact, the response spectrum results for all the buildings in this study
would be required to be factored up to the minimum levels of base shear (either 100
percent for irregular buildings or 90 percent for regular buildings) specified in
4S1170.4. However, for the purpose of comparison, the response spectrum results
were not altered. There was a large discrepancy in the difference in the base shears
from the two types of analyses between the buildings. In some cases, notably KIDB,
the response spectrum base shear and the 4S1170.4 base shear were very close, in
orhers, such as STP and LTI, the 451170.4 base shears were considerably higher

than the base shear from the rcsponse spectrum analysis. In the case of STP the code
base shear was three times the response spectrum base shear in the short direction. It
was expected that the differences will be least when the participating mass all
occurred in a single mode and greatest when it occurred in a large number of modes-
This was best illustrated with building KIDB where, for the short direction, the
majority of the mass was in one mode (Table 5.5.1) and the response spectrum
analysis predicted 94 percent of the 451170.4 base shear compared to the long
direction wherc the mass was spread amongst mulúple modes and the response
spectrum analysis predicted a base shear J2 percent of that determined by 4S1170.4.

153
 Chapter 6 : Equivalent Statíc Force Analysis of Buildings

Table 6.3.1 Surnmary of base shears by static and dynamic analyses.

B¿se Slrear (kN)

Building Short Direction Long Drection

Dascription AS1170.4 1993 Re.srxlnse Soectrum AS1170.4 1993 Resrnnse SÞectrr¡m

2 storey vactnt c¡ty

comnrercial building 154 IM 154 98

I ggn7o2
= 739 (7 57o)j 9gEo = 739 0t%\
2 storey vacant citY
771 318 118
commercial building 318
(41Vo\
(EE3) - ree 96o7o =286 (6OEo) 9OVo =286
2 storey vacant citY
æmmercial building 318 189 318 164

(€84) - res (66V"\ 9Ùclo = 286 (577o\

9OVo =286
3 forey scltool
building 1343 812 1343 608

ICBC) - inee TOOc/o = 1343 (6OVo\ TMVo = 1343 ØSVo\

2lorey city
social club 951 558 951 523
(59%\ (55V"\
ûAC) - ines 7NV" = 957 7OO7o = 957
3 storey city mmmercial
building 2955 1490 2955 1470
(LTI) - reg (56Vo) 9OVo =266O (5s%',,
9OVo =266O
2 storey city commercial
building 771 506 771 353
(NSC) - ree 9OVo = 694 (73Vo\ n%- 694 (5|V"'l

2lorey cily
rerail building 759 246 759 409
gOEo (367o'l -- 683 (6Mo\
(STP) - ree = 683 9OVo

5 storey university offiæ

building 4544 3218 5094 3U7
toÙEo = 4544 (7l%o) lo07o = 5@4 02%\
2 slorey suburban
apalment building 224 t6l 2U L47
(727o\ lúVo=224 (667o\
IKIDA) - ines TOOcIo =224
2 storey suburban
apamnent building 294 276 294 212
(KIDB) - irree lûVo=294 (947o\ IOO% =294 Q2%\

1 Th" buildings denoted "reg" were classified as regutar according to AS11?O.4. The buildings denoled "irreg" we¡e classified

as irregular according to AS 1 170.4.

2 Mini-unt base shear for a reqronse E)ecfrum analysis. The base shear was required to be a minimum d 90% d that

determined from an equivalent static loa<l approach for a regular building and 10O% for an ir¡egular building.

3 2
Th" base shear from the re,sponse sp€ctrum analyses expressed Às a perc€trtåge <f rhe required minimum base strear (see

above).

t54
 Chapter 6 : Equivalent Static Force Analysis of Buildings

6.3.3 Distribution of the Base Shear

The third building response to be cornpared was the distribution of the base shear up
the height of the building. This was compared by looking at the storey shear for the
buildings and assuming that the connection type was that shown in Figure 5.1.1(b) as
Type II and behaved as described in Section 5.1. As the base shears for the two types
of analyses were different it was inconsistant to compare the absolute values of the
storey shears. Wliat was compared was the storey shear expressed as a percentage of
the base shear. For the AS 1170.4 analyses the distribution of the base shear up the
height of a building was calculated using Equation 6-2.4. This equation relied on the
distribution of the mass of the building and the building's storey heights.

Subsequently, the force clistribution was the same for the long and short directions
using the 4Si170.4 approach. The results for the code and response spectrum
analyses ate shown in Table 6.3-2-

In tlre majority of cases the 4S1110.4 analyses had a greater percentage of the base
shear applied to the upper levels of the buildings than did the response spectrum
analyses. This was not the case for OLW in both directions and IAC in the long
direction. For OLW this could be due to the assumption that the mode shape, and
hence the shear force distribution, was based on a linear function. That is, in
Equation 6.2.5 k = 1.0. For the taller OLW building this assumption may not hold as
more bending could be present in the mode shape than would be expected in the
other buildings where their height is low compared with their plan dimensions and
shear type deflection would tend to dominate the mode shape. For the IAC building,
the upper floor only covered part of the lower floor and this may be contrary to some
of the assumptions implicit in the use of Equation 6-2.5. Generally, however, it
should be noted that a building designed according to the requirements of 4S1170.4
would have a greater percentage of its base shear applied higher up the building and
would, therefore, predict that the upper walls experienced higher connection forces
and shear stresses than the same building analysed using the response spectrum
method for the same base shear. Similarly, the overturning moments calculated from
the results of the code based analyses would be greater than those determined from
the results of the response spectrum analyses.

155
 Chapter 6 : Equivalent Static Force Analysis of Buildings

Table 6.3.2 Storey Shear Results from static and dynamic analyses

4S1170.4 Storey Re.sponse Spectrum Storey Shear as

L(ution Shear æ peræntage of Base Shear

Building
percentage of Ba-se Short Direction Long Direction
Description
Shear

2 storey vacânt city

roof to l-st floor 0.63 o.52 0.51
commercial building
(EE2) - ree 1-st to ground lo0 0.95 0.95

2 storey vacant cltY

rmf to lst flmr 0.58 o-42 o.29
comnrcrcial building
(EE3) - ree 1st to !.rounrl 1.00 0.95 0.70

2 storey vacant city

rcxrf to l.st flmr 0.58 0.39 o.26
comnre¡cial builtling
(EE4) - reg 1.st to eroun(l 1.00 0.85 0.66

3 slorey sclrool roof to 2nd fl(K,r o.22 0.18 0.20

building 2nd to lst floor o.74 0.68 0.68

(CBC) - inee lst to Eround 1.00 1.00 t.o0

2 storey city
social club roof to lst floor o.2t o.20 o.27

(lAC) - ineg l.st to crounrl 1.00 1.00 1.00

3 storey city roof to 3rd floor 0-33 o.22 o.20

commercial 3rd to 2nd floor o.73 0.6E o.67

building 2nd to 1.st floor 0.96 0.95 0.96

(LT[) - res 1.^t to cround 0.99 l.o0 1.00

2 storey city comnrercial

building roof to lst floor 0.40 o.l6 0.20

(NSC) - reg lst to ground 1.00 0.89 0.96

2 storey city roof to lsl floor 0.35 o.30 0.34

retail building lst to ground 0.87 l.OO 0.86

(STP) - ree ground to ba.se 1.00 1.00 1.OO

5 torey roof to 5tlr floor 0.13 o.22 0.19

university 5tI to 4dr floor o.42 o.48 o.43

office building 4ùr to 3rcl floor 0.65 o.67 0.65

(OLW) - ineg 3rd to 2nd floor 0.83 0.81 0.81

2nd to l.st floor o.94 0.91 0.93

lst to Around 1.00 o.97 1.OO

2 storey suburban
apartrnent building roof to lst floor 0.39 0.16 0.15

1st to ground 1.00 o.88 0.88

2 storey suburban
apartment building roof to lst floor 0.39 o.23 0.18
(KIDB) - irres lst to ground 1.00 o.85 0.82

6.3.4 Connection Forces

Whilst the greater 451170.4 analysis base shears ensured the average connection
force for a level of a building is greater than or equal to the average connection force
calculated by a response spectrum analysis, the maximum connection forces
calculated from the 451170.4 analysis may not have been equal to or greater than
the response spectrum analysis value. The difference between the average and the

156
 Chapter 6 : Equivalent Static Force Analysis of BuíIdings

maximum connection force in the 4S1110.4 analysis was due to torsional effects-
The ratio of the maximum connection force to the average connection force
calculated using the torsional requirements of AS1l7O.4 are shown in Table 6-3-3-
Where rhe plan of the building changes with height (such as building IAC and
building CBC) the calculations were done for the floor level that had the maximum
torsional response. Tlie ratio of maxirnum connection force to average connection
force from the response Spectrum analyses are also shown in Table 6-3-3-

Table 6.3.3 Summary of maximum connection forces

Sllort f)irection Long Direclion

Ratio of nraxinrum to averflge geometric R¡tio of maximum to average geometric

connection force eccenlricity connection force eccenhicity

AS1170.4 Ras¡xrnse (percentage AS1170.4 Response (perceoøge

1993 Spectrum of width of 1993 Spectrum of width of

buikline)l buikling)

2 storey vacant city

commercial buikling 1.05 1.00 0 l.o5 1.OO

2 storey vacant city

1.09 1.14 1.6 1.O5 1.00 0
commercial building

2 storey vacant city

1.10 1.10 2.4 r.05 1.00 0
commercial building
IEBI) - res
3 storey school
building 1.13 I .13 3.4 r.00 t.2t 24.7

(CBC) - inee
2 storey city
1.16 1.60 4.5 1.O8 1.82 1.0
social club
(lAC) - ineg
3 storey city commercial
building 1.05 1.32 o 1.05 r.54 0

(LÏ) - reg
2 forey city commercial
building t.t2 1.35 3.8 1.05 r.07 0

INSC) - ree
2 storey city
retail building 1.05 r.18 0 1.O5 1.(X 0
(STP) - res
5 storey university ofüce
building 1.06 2.O3 o.4 t.o7 2.90 o.6

(OLIW) - irree

2 storey suburban
apartment building 1.16 r.38 4.7 1.10 1.50 4.0

2 storey suburban
apalment building 1.09 1.53 2.O t.o7 1.27 3.4
(KIDB) - irree

I geometric ecæntricity is the difference between the sltear centfe and tlle centre of mros

r57
 Chapter 6 : Equivalent Static Force Analysis of Buildings

For the buildings where the centre of mass and the shear centre coincide 4S1170-4
specifies a minimum "acciclental" eccentricity of frve percent of the plan dimension
of
the building in the direction perpendicular to the direction under consideration- This
resulted in the maximum connection force being five percent greater than the average
connection force for tl-rese buildings when the building only has two external walls-
The response spectrum analysis did not take into account this "accidental"

eccentricity and as such had maximum connection forces equal to the average where
the contributing modes were purely lateral.'When a torsional response was included
as one of the modes that are combined using the CQC æchnique then the maximum
connection force will be greater than the average connection force-

For the buildings where the shear centre and the centre of mass did not coincide the
ratio of maximum connection force to average connection force for the response
spectrum analysis results \ilas greater than that for the 4S1I10.4 results. This
suggested that the 4S1170.4 analysis procedure may have underestimaæd the effect
of the torsional component of the response of the buildings to earthquake ground
motion. The maximum connection force was nearly three times greater than the
average connection force for the OLV/ building. Building IAC, which had the largest
eccentricity of all the buildings in the study, had the next largest increase in
connection force of up to eighty percent. The increase was generally less than hfty
percent of the average connection force for the rest of the buildings in the study.

Table 6.3.3 also gives the geometric eccentricities for the buildings in the study- This
was the distance between the shear centre and the centre of mass expressed as a
percentage of the width of the building. It can be seen in Table 6.3.3 that there
seemed to be no conelation between the geometric eccentricity of the building and
the differences between the ratio of the maximum connection force to the average
connection force for the two analysis methods examined.

Comparing the lower maximum connection force to the higher base shea¡ predicted
by the 451170.4 analysis method to the response spectrum method it could be seen
that the higher base shear for the 451170.4 analysis would, for the majority of the
buildings in the study, ensure that the connection forces calculated by the 4S1170-4
method would be greater than the maximum connection forces calculated by the
response spectrum analyses. The only exceptions were for building OLW and for
building KIDB in the short direction.

158
 Chapter 6 : Equivalent Static Force Analysis of Buildings

6.3.5 Out-of-Pl ane Effects

The last structural response to be compared and one of the most critical was the out-
of-plane wall bending. It has already been seen in Chapter 5 that applying earthquake
induced forces to some of the buildings in the study resulted in stress levels in the
upper walls exceeding the estimated tensile capacity of the brickwork.

The analysis of earthquake forces on out-of-plane walls is given in Section 5.2 of

4S1170.4. The inertia force to be applied to a wall is given by the formula:

Fo = aSa"a*C"lIG" < 0-5G. (6.3.1)

where:

a = Acceleration coefficient, as per Equation 6-2.I;

S

ac = Attachment amplification factor, a variable that takes into

account the flexibility of the connection between the component
and the building. For the case of out-of-plane walls it would be

equal to 1.0;
ax = The height amplification factor as given in Equation 6-3-3;
C"t = Earlhquake coefficient for architectural components- For non-
ductile out-of-plane walls it is 1.8;
I = Importance factor, as per the one in Equation 6.2-l; and
G" = Weight of the component.

For a firm soil site in Adelaide Equation 6.3.1 simplifies to:

Fp=0.18a*G"<0.5G" (6.3.2)

The height amplification factor is given as:

u, = t+fr (6.3.3)

where h" is the height above the base of the structure at which the component is
attached and ho is the total height above the base of the structure. Dividing Equation
6.3-1 by the weight of the component yields the acceleration applied to the
component. The acceleration of an out-of-plane wall versus the height of the wall

159
 Ch.apter 6 : EEdvalent'static Force Analysis of Buildings

in
above the base of the wall (expressed as a percentage of the total height) is plotted
Figure 6.3-1.

0.4

0.3

Fo
(e) 0.2
Gc

0.1

0.0 0.2 0.4 0.6 0.8 1.0

h,
ho

Figure 6.3.1 Ptot of component acceleration versus relative heighf

Examining Figure 6.3.1 can be seen that for an out-of-plane wall attached to the
it
building at ground level the level of acceleration applied to the building is 0.18 g
compared to 0.1 g for the building structure and the maximum level of acceleration
that an out-of-plane wall can be subjected to is 0.36 g. This acceleration is to be
applied through the centre of mass of the wall.

The analysis of a brick wall subjected to out-of-plane forces can be undertaken by

two simple merhods. Firstly, the wall can be analysed as a plate element subjected to
a point load at the centre of mass of the wall. The wall could then be taken to be in
either one or two way bending, depending on the height to width ratio of the wall
panel. The height is the storey height and the width is the width between points of
support for horizontal bending. Traditionally, one way action is deemed to be
applicable when either the height or the width is twice the perpendicular dimension.
Design tables can then be used to determine the bending moments and bending
stresses in the wall.

160
 Chapter 6 : Equivalent Static Force Analysis of Buildings

The second method requires tl're wall to be broken down into .smaller sub walls- The
design acceleration is then applied through the centroid of these new sub walls- As
the number of sub walls approaches inhnity the out-of-plane forces become a
distributed load over the area of the wall, a similar situation to that of lateral wind
loading on the wall. The Australian Standard, "SAA Masonry Code" 453700-1988
has provision for the determination of the lateral wind load capacity and this can then
be used to detemine whether the wall's capacity is exceeded-

The vertical bending capacity of an unreinforced masonry wall is given in 453700 as

the lesser of:

M"u = Crf'n,t Zo+f uZo (6.3.4)

and

M* =3.0c,rrf'rnr Z.l (6.3.5)

where:

c* = A capacity reduction factor given as 0-6;

f mt = The characteristic flexural tensile strength of masonry, given as

0.2 MPa for masonry not subjected to axial tension;

zd = The section bending modulus; and
fd = The minimum design compressive stress on the bed joints of the
masonry at the cross section under consideration-

The horizontal bending capacity of an unreinforced masonry wall is given in 453700

as the lesser of:

M* =2.oc*Kpm[t.*)r. (6.3.6)

M¿, = 4.oc,"KpJ-f;¿d (6.3.7)

and

Ma, = C-(0-44f'ut f, * 0-56f' ú)zd (6.3.8)

161
 Chapter 6 : Equivalent Static Force Analysis of Buildings

where, in addition to the definitions for tetms given for Equations 6.3.4 and 6-3-5:

ç A perpend spacing factor;

fut The characteristic lateral modulus of rupture of the masonry
units; and
fz The ratio of the lateral section modulus of the masonry units per
millimetre of height to the lateral section modulus of the
perpend joints per millimetre height.

For rhe walls of the buildings in this study, the 4S1170.4 out-of-plane forces were
calculatecl and the resulting forces were compared to the capacity of the walls as
calculated in accordance with 453700. Only the top walls were checked as these
were subjected to the highest accelerations and hence the highest out-of-plane forces
(the a* factor is maximised for the top wall). The a, factor from F.quation 6.3.1 was
calculated for the mid height of the wall, as the wall is connected at two points to the
building; at its top and base- It was considered then that the wall element would be
subjected to the average of these two accelerations, which for the linear function
shown in Figure 6.3.1, is equal to the force calculated using the mid height of the
wall.

The majority of the walls in the buildings in the study acted in predominantly one
way vertical bending as the restraints in the horizontal direction were usually widely
spaced. The results of the 4S1170.4 and 453700 evaluation of the performance of
the out-of-plane walls, summarised in Table 6.3.4, revealed that all of the walls
acting in one way bending would be expected to fail in the event of the design
magnitude earthquake. The only walls not expected to suffer out-of-plane failure
were in OLW, for excitation in the short direction, in KIDA and KIDB for excitation
in the long direction, and :ri_EBz for excitation in the long direction. The OLW walls
did nor fail because of the significant number of cross walls in this building making
the walls act in two way bending. The KIDA and KIDB did not fail because they
have height to width ratios that allow them to act in two way bending- The EE2
walls also did not failure because the height to width ratio ensures two way action.

In comparison with the results of the response spectrum analysis (Section 5.6), it can
be seen that rhe 451170.4 equivalent lateral force analysis predicted more of the
buildings experience out-of-plane bending failures. This could be due to the
to
requirements of 453700 introducing a capacity reduction factor, C-, that was not
used in the evaluation of the bending stresses in the response spectrum analyses. This

r62
 Chapter 6 : Equivalent Static Force Analysis of Buildings

lowered the allowable tensile stresses and subsequently increased the number of walls
that were likely to expedence out-of-plane failures. It should be noted that according
to the AS1170.4 analysis the level of accelerationexpected in the top level of the six
srorey OLW building is the same as that for the 451170.4 analysis of the two storey
KIDA builcling (Fo is not propoftional to the total height of the building - see
Equation 6.3.3).

Table 6.3.4 Summary of Out-of-Plane Tensile Stresses for ASlll0.4 and Response
Spectrum AnalYses.

Maxinrunr Out-of-Plane Tensile St¡ess (including dead load stress)

(MPo)

AS I 170.4 AnrlYses Ras¡xrnse S¡æctrum Analysæ

Short Direction Long Direction .Short Direclion Long Direction

2 storey vactnt c¡ty

0.201 0.08 0.10 o.o'17
commercial building

2 storey vacant city

commercial building 0.201 0.181 0.34 o.62

2 storey vacant city

cornmercial building 0.201 o.t sl 0.36 o.16

lEE4) - ree
3 storey school

buil<ling o.2t o.25 0.05 o.o2

(CBC) - irree
2 storey city
sæial club 0.28 0.30 0.07 0.02

IIAC) - inee
3 storey city commercial
building 7.40 1.40 0.01 o.o2

ILTD - rec
2 storey city comrnercial
building 0.37 o.52 0.28 o.25
(NSC) - ree
2 storey city
retail building 0.33 0.51 1.05 o.o1

ISTP) - ree
5 storey university ofÍrce
building o.o5 o.75 0.04 0.04
(OLW) - irree
2 storey suburban
apartment building 0.151 0.11 0.05 0.06
(KIDA) - inee
2 storey suburban
apartment building 0.151 0.11 0.22 0.46
(KIDB) - ineg

1 Value exceeds AS370O design stress (C-f *,) but not AS370O tensile strength (f-1)

163
 Chapter 6 : Equivalent'static Force Analysis of Buildings

6.4 SUMMARY OF CODE BASED ANALYSES

Comparing tlie two sets analyses for each building it was seen that generally the code
based method predicted higher levels of force and stress than the response spectrum
method.

The first aspect of the code based analysis procedure to be examined was the natural
period. The natural periods calculated by the code based formulae and the response
spectrum analysis have already been discussed in Chapters 3 and 5-

For all of the buildings in the study, the 4S1110.4 code based analyses resulted in a
greater base shear than that obtained from the response spectrum analyses. A simila¡
situation occurred for the storey shears, except for two buildings where the response
spectrum analyses distributed a larger proportion of the base to the upper floors than
the AS1170.4 analysis. One of these cases was the OLW building. The other case
was for a building that had an extremely irregular plan (IAC) and a smaller upper
floor than lower floor. The larger base shear predicted by the code based analysis
ensured, however, that the storey shears calculated by 4S1170.4 were greater than
the storey shears calculated by the response spectrum method for all but two
buildings.

The connection force calculations for the in-plane walls were based on the storey
shears. Hence, the average connection force, being the storey shear divided by the
total length of in-plane walls on a floor, was always greater for the 451170.4
analyses than the response spectrum analyses. However, the average connection
forces were increased due to torsional effects to create local maximum forces. Two
of the buildings in the study had a greater maximum connection force from the
response spectrum analysis than the 4S1170.4 analysis, even taking into account the
greater base shears associated with the code based analyses. One was the OLW
building which, as discussed previously, had a greater number of storeys than is
allowed by the code for unreinforced masonry building. The other was the KIDB
building, where the maximum connection force was thirty percent greater for the
response spectrum analysis than the code analysis even though the base shear
associated with the response spectrum analysis was six percent lower than the code
base shear force.

164
 Chapter 6 : Equivalent Static Force Analysis of Buildings

The last comparison made was for out-of-plane failures of the walls. In all cases the
AS1170.4 analyses resulted in larger values of stress than the response spectrum
analyses.

6.5 REFII\ED CODE BASED ANALYSIS

From this work, it appeared that the analysis procedure in 4S1170.4 was sufficient
to ensure a conservative design for the majority of unreinforced masonry buildings. It
was, however, complicated by the fact that it was applicable for a wide variety of
building types and as such has a number of variables that for the case of an
unreinforced masonry building were constants. In order to simplify the requirements
of the code a number of refinements could be considered. The results for the OLW
building were ignored in this section as the building did not comply with the
requirement of the code that limited unreinforced masonry buildings to be less than
or equal to three storeys.

Firstly, considering the code formula for base shear and the effect of the building's
natural period on the calculated base shear (Equation 6.2-l). Every unreinforced
masonry building in the study had natural periods for both major axes, from both the
ambient vibration tests (Chapter 3) and by calçulation by the code period formulae
(Equations 2.I.I and2.I-2), that placed them in the constant acceleration region of
the design response spectra (Figure 5.2-I)- This resulted in the base shear for the
buildings in the study being independent of the site factor, S, since the only effect S
had on the constant acceleration region of the response spectrum curve was to
extend the length of the plateau from T = 0.35 seconds for S = 1.0 to T = 1 second
forS=2.

Assuming that all unreinforced masonry buildings have a natural period that places
them on the constant acceleration region of the design response spectrum resulted in
a simplification of the base shear formula. The design base shear of a unreinforced
masonry buildings became independent of the natural period of a building, T, the site
factor, S, and the design coefficient, C. Further, for unreinforced buildings the
response modif,rcation factor, IÇ, is 1.5. The base shear formula from 451170.4
(Equation 6.2.1) then reduced to:

V = 1.667IaGe (6.5.1)

165
 Chapter 6 : Equivalent Static Force Anolysis of Buildings

This compared with the requirement for a "domestic" structure in the code where the
design base shear is 0.15G, which meant that an unreinforced masonry "domestic"
srrucrure (as defined in 4S1170.4) is allowed to be designed for a slightly lower base
shear force than an unreinforced masonry "general" structure.

Whether the use of unreinforced masonry construction is suitable for buildings that
have a post disaster function given the poor performance of unreinforced masonry
builclings in past earthquakes is beyond the scope of this study. However, it can be
seen from the results of the response spectrum analysis and from reports of the

performance of recently built unreinforced masonry construction that it is possible to

design and detail an unreinforced masonry building to perform adequately in design
magnitude earthquakes in regions of low to moderate earthquake hazard. Whether it
is possible to design and detail unreinforced masonry buildings economically to be
able to function after an earthquake is another matter that requires further
investigation. In the meantime, the importance factor, I, can be retained as a variable
in Equarion 6.5.1 and the formula could possibly be used for AS1170.4 Type III
structures.

The distribution of the base shear force up the height of the building for subsequent
design can be undertaken using Equation 6-2.4. For unreinforced masonry buildings
k= 1.0 as atl of the measured and calculated building periods were less than 0.5
seconds. Equation 6.2.4 then reduces to:

C \x (6.s.2)

where C*, Ggi, and h, are as defined for Equation 6-2-4-

The storey shears are distributed to the walls as in-plane connection forces and shear
stresses using general structural mechanics. Whether the storey shears are
transmitted through the floor slabs into the walls or down the outside walls without
using the floor slab depends upon whether the detail at the floor-wall connection was
Type I or Type II from Figure 5.1-1. The increase in some of the wall shear stresses
and the in-p1ane connection forces due to torsion in the building response can be
taken into account by increasing the average connection force and shear stresses by
thirty percent. This brings the torsional effects requirements for unreinforced
masonry buildings in tine with the general requirements for 4S1170.4 Type I regular
structures with shear resisting elements without static eccentricity. A limit to the type

166
 Chapter 6 : Equivalent Static Force Analysis of Buildings

of structure that can be analysed using this requirement would be needed to prevent
buildings such as IAC from being analysed using this simple rule, though the rule
could be less restrictive than AS 1170.4's "regular" and "irregular" distinction-

The out-of-plane connection force can be calculated using the AS1170-4 equation
(lgaS kN/m run of wall). As was already noted the acceleration applied to the
buildings in the study are independent of the site factor, S. This meant that the results
for the response spectrum method will not change with a change in the site factor
and the out-of-plane connection force will be independent of the site factor- This
meant that the site factor, S, could be removed from the connection force formula
for consistency with the calculated base shear. Applying this to the connection force
formula resulted in:

force = 10a kN per metre of wall (6.5.3)

where a is as was dehned for Equation 6-2.1- However, as will be discussed in

Chapter i, the removal of the site factor from the base shear formula may be
inappropriate based on the observations in recent earthquakes. On this basis, the site
factor probably should be kept in Equation 6.5-3-

The out-of-plane bending forces in the walls can be best determined using the
4S1170.4 requirements. The out-of-plane inertia force on an unreinforced masonry
wall is given by:

ro = r sa[r.*)" c
(6.s.4)

where the variables are as defined for Equations 6.3.1 and 6.3.3- The capacity of the
wall to resist this out-of-plane force can be checked using the lateral wind loading
requirements of 453700.

This procedure should ensure that an unreinforced masonry building is accurately

designed for the forces induced in the structure by an earthquake that can be
represented by the design response spectra. Whether the shape of the current design
response spectra is appropriate for Australia and whether the constant acceleration
region of the response spectra should be independent of the siæ factor for non-
ductile structures are questions that require further attention.

r67
7 SUMMARY AND CONCLUSIONS

7.1 SUMMARY

The overall aim of this project was to provide the tools for an engineer to use with
confidence to design an unreinforced masonry building to perform accept¿bly when
subjecæd to earthquake ground motion-

This was accomplished by firstly undertaking a series of ambient vibration tests on

unreinforced masonry buildings in Adelaide. The ambient vibration tests involved
recording the vibrations induced in a structure due to wind, traffic, and other
common low levels of excitation- The recorded vibrations were then converted from
the time domain to the frequency domain using a Fourier Transform. From frequency
domain plots, the natural periods were identihed. The measured natural periods of
the buildings were then compared to the natural periods estimated using period
formulae from various earthquake codes from around the world, including The
Australian Standard "Minimum design loads on structures - Part 4 : Earthquake
Loads" 4S1170.4-1993. It was found that none of the period formulae considered
had a very high level of fit. Of particular interest here were the formulae included in
the Australian Earthquake Code (Equations 2.1.1and2.I.2). The fit the ambient test
data, R2, to these forms of period formula were 67 percent for buildings with
concrete floors, 9 percent for the buildings with timber floors, and 53 percent for all
the buildings in the study. This level of fit was as good as for any of the other period
formulae examined. It
was further noted that using the measured periods in
conjunction with the Aust¡alian Earthquake code requirements and the design
response spectrum (Figure 5.2.L) meant that the periods of all buildings were in the
constant acceleration region of the design response spectra-

168
 Chapter 7 : Sumtnary and Conclusions

The next part of the study involved undertaking shaking table tests of unreinforced
brick masonry wall panels to determine a realistic value for the dynamic in-plane
shear stiffness of a brickwork wall panel. This stiffness was subsequently used in
hnite element modelling of the buildings from the first part of the study- The
experimental test procedure was based on that used in a similar study on block and
brick masonry in the United States. The shaking table tests were used to study the
effect of axial stress, rate of loading (the excitation frequency), and panel geometry
of the on the dynamic in-plane stiftness. It was found from the tests that increased
axial compressive stress increased the dynamic in-plane stiffness. This confirmed
results of other researchers. Unfortunately, material and workmanship variability
between the panels masked any relationship between the dynamic in-plane stiffness
and fiequency of loading. The observed clianges in the dynamic in-plane stiffness
with changes in testing panel geometry were not consistent with classical structural
theory, possibly due to material and workmanship variability. Finally, the dynamic in-
plane stiffness of the panels were noted to be consistent with the values from shaking
tests conducted in the United States.

The shaking table test panels were then modelled using the frnite element method.
The walls were modelled as a one phase material model (brick and morta¡ combined
as one type of maærial) rather than a two phase (brick and mortar as individual
phases) model. The finite element model was calibrated to establish an effective
Young's Modulus for a one phase material model for use in subsequent one phase
modelling of the buildings from the first part of the study. The most important result
from the shaking table tests was that the calibrated value for Young's Modulus (1065
MPa) was considerably less than that commonly accepted for design in Australia.
This has also been observed by Australian and overseas researchers where values of
Young's Modulus for brickwork of approximately 1000 MPa have been reported.

The results from the first two parts of the study were then used in the final part of
the study where response spectrum analyses of the buildings from the first part of the
study were carried out. The stiffness for the walls of the buildings were based on the
results of the shaking table tests noted above. The buildings were modelled using the
finiæ element method. Double leaf walls were modelled using an equivalent single
leaf plate element. Equivalent stiffness properties (Young's Modulus, Poisson's
Ratio, and wall thickness) were calculated for the single element to model the
properties of a double leaf wall, namely the cross sectional area, and the bending and
shear stiffness. It was found that, without modihcation, the bending stiffness was
overestimated by a factor of two.

169
 Chapter 7 : Sumntary and Conclusions

The buitding models were subjected to a response spectrum analyses using the design
response spectrum from Tlle Australian Standard "Minimum design loads on
structures - Part 4:
Earthquake Loads" AS1110.4-1993. The base shears, storey
shears, bending stresses, connection forces, and drifts of each building were then
examined. It was found that, in general, the required connection strength between the
floor slab and the walls of each building could be provided, in practice. The
calculated shear stresses were also found to be within the generally accepted
capacities for unreinforced masonry walls. However, the maximum wall bending

stress results suggested that some out-of-plane failures could be expected in the
upper walls of some buildings. This was consistent with the observations of
earthquake damage to many of the damaged unreinforced masonry buildings in past
earthquakes.

The results of the response spectrum analyses were then compared to the results of
equivalent static force analyses undeftaken using the static force analysis procedures
given in ASII71.4. It was found that the 451170.4 procedures were generally
conservative with regard to the results of the response spectrum analyses- The

4S1170.4 estimates of the building periods placed all buildings, except the six storey
building, in the constant acceleration region (for S = 1) of the design response
spectrum as did the measured periods. It was therefore concluded that for seismic
design based upon the design response spectrum in 4S1170.4, the natural period
calculation for an unreinforced building is not necessary. It was also noted that soft
soil effects are implicitly deemed not to be important in the constant acceleration
region of the design response spectrum since the design base shear calculations are
independent of S in this region-

Evidence from recent earthquakes, including the 1989 Newcastle Earthquake

(Newcastle Earthquake Study(1990)) suggested that the soil type does play a
significant part in deærmining the level of force to which a structure in an earthquake
is subjected. The exclusion of soil effects from the determination of the base shea¡
may be acceptable for ductile structures. As a ductile structure is loaded, cracking
occurs, resulting in a decrease in structural stiffness, an increase in building period,
and therefore, a reduction in the induced design load as the change in period
decreases the applied acceleration as it moves to the right on the design respgnse
spectrum and off the constant acceleration region. For a brittle structure, such as am
unreinforced masonry building, cracking denotes a failure of the structure and the
period shift cannot occur. This point may need to be investigated further-

170
 Chapter 7 : Summnry and Conclusions

While the ASl 170.4 procedure was found to give consistently larger estimates for
base shear, storey shear, and bending stress values obtained from the response
spectrum analyses, the code based analysis was not always conservative with respect
to the response spectrum analyses in accounting for torsional effects- Even taking
into account the larger base shear values which were obtained from the code
analysis, the maximum connection forces in some buildings were greater for the
response spectrum analysis than for the code based analysis'

In liglit of the above results, refinements to the 451170.4 equivalent static force
analysis procedure were considered. It was based on the following assumptions:

(1) The response spectrum from the code was appropriate for use in Australia;

(2) The buildings were founded on hrm soil sites such that the site factor was at
least 1.0 (the rehned procedure could be used for a siæ factor that is less than
1.0 as the procedure then becomes conservative); and

(3) The appropriate response modification factor for unreinforced masonry, &,
was 1.5

The amended design base shear value was then given by Equation 6.5.1 and is

reproduced below:

V = 1.667IaG, (6.5.1)

where I, a, and G, are as defined in AS1110.4. The base shear can be distributed up
the building according to the fotmula given in 451170.4 using k = 1-0 (Equation
6.5.2)- The torsional component of the response can be catered for by increasing the
maximum calculated connection force by 30 percent.

The out-of-plane connection force was found to be accounted for using a modified
connection force requirement from AS1ll0.4:

force = 10a kN per metre of wall (6.5.3)

r7l
 Chapter 7 : Sumtnary and Conclusions

The out-of-plane bending stresses were also calculated based on the formula given in
4S1170.4. The formula was simplihed to Equation 6.5.4 shown below:

Fp=l' 8,I t+!Å c

(6.s.4)
ho

This procedure should ensure an improved level of performance for the majority of
unreinforced masonry buildings in Australia.

7.2 CONCLUSIONS

The results of this study suggest that it is possible to design and detail unreinforced
masonry buildings to perform to an acceptable level during the moderate levels of
earthquake excitation expected in Australia. However, attention to detail and
supervision of the workmanship during construction are clea¡ly important to ensure
that a masonry building will perform as intended during earthquake excitation.

Some of the major hndings of this study are:

(1) The natural period of most unreinforced masonry buildings is such that it falls
in the constant acceleration region of the design response spectrum;

(Z) The dynamic stiffness of an unreinforced masonry brickwork wall is an order of

magnitude less than the accepted value used in design for static forces.
Experimental results indicate values of Young's Modulus, E, of approximately
1000 MPa would be aPProPriate;

(3) A hniæ element model using a single "equivalent" element can be used to
model double leaf brick masonry walls;

(4) The design procedure included in The Australian Standard "Minimum design
loads on structures - Part 4 : Earthquake Loads" 4S1170.4-1993 can be used
for the design of unreinforced masonry buildings for earthquake induced
forces. The torsional requirements of the code may need to be increased by
about 30 percent to account for increased wall stresses due to the torsional
response of the building; and

t72
 Chapter 7 : Summnry and Conclusions

(5) The design procedures in AS1I10-4 can easily be simptifred to reflect the
particular properties of unreinforced masonry and unreinforced masonry
buildings.

7.3 FUTURE WORK

The results of this study can be applied to the design of unreinforced masonry
buildings to improve its perforïnance when subjected to earthquake excitation-
However, further research is needed in some areas to further improve the
understanding of the performance of unreinforced masonry buildings in earthquakes
and to allow more accurate models of the behaviour to be developed.

In terms of masonry, further work is required to verify the design strength for use in
seismic design. The dynamic stiffness of a wall panel has been found in this study to
be less than the static stiffness. Whether similar effects are evident for the strength of
masonry walls under dynamic and static loading requires further investigation.
Experimental investigations to determine the expected strength of typical floor-to-
wall connections under in-plane and out-of-plane loading is also required.

For the earthquake part of study, much work is needed to develop a design response
spectrum for Australia based on Australian intra-plate earthquake data. Until a
staústically significant set of actual intraplate earthquake ground motions are
obtained. however, this can not be done. In the meantime, the whole area of
Australian earthquake research and design is heavily dependant on the assumption of
the type of ground motion that can be expected-

The use of the site factor, S, in the 451170.4 needs examination. For example, an
unreinforced masonry building on soft soil, according to the current code, must be
designed for the same base shear, and hence connection forces, out-of-plane forces,
and shear stresses as the same building constructed on a stiff clay. This does not
seem to be consistent with observations of earthquake damage around the world.

173
APPENDIX A. SAMPLING
THEOREM

The sampling Theorem can be stated as:

"It is necessary to take more than two poittts per cycle of the highest significant
frequency component in a signa.l in order to recover that
signal"

This means that if a signal f(t) is sampled at úmes t = -2T, -T, 0, T, 2T, and so on, at
arate of 1Æ = f, samples per second, the frequency components of the signal greater
than f!2 = Il2T cycles per second cannot be distinguished from the frequencies in
the range of 0 to f/2 cycles per second-

r74
APPENDIX B - BIJILDING DETAILS

In this appendix the details of the buildings studied in Chapter 3 and subsequently

modelled in Chapters 5 and 6 are presented. The plans of the buildings are shown in
Figures 8.1 to 8.9. The dimensions given in the plans are in millimetres. The plans
are not necessarìly to scale. The information on the buildings was gained from site
visits and from the archives of the City of Adelaide where the building plans and
building submissions are stored.

175
 Appendix B : Building Details

B.L EAST END MARKET BUTLDTNGS (F.F'z, EE3,

AND EE4)

The three buildings from the East Encl market complex are shown in Figure 8.1

llexibte arclt links at roof level A-l

DE3 7300

þ--l
6200 '1530 4610 6?00 5500 3900

Al
nrcta[ (leck
3910

ce ili ng
39r0
ü nrber lloor
39r0

cross scstion A-A

Figure 8.1 Plans of buildings EE2, EE3, and EE4-

The East End Market buildings were constructed in the early 1900's from clay brick
with a srone work facade- The three buildings were linked by a flexible masonry arch
link at the roof level. It was cousidercd that the tinks would not be stiff enough to
provide a signifrcant restraint to the walls of tlie buildings. All three buildings were of
sirnilar construction, the details of wl'rich are given in Table 8.1.

Table 8.1 Details of EE2, EE3, and EE4 construction-

Number of 2
Construction of Suspended Timber joist with 140 mm thick timber floor
Floors boards
Construction of Roof Timber frame with metal decking
Construction of External Walls Double leaf brickwork without articulation
Construction of Internal Walls Single leaf brickwork without articulation
Footing Type Concrete strip footings
Soil Clay
Stair and Lift Details Timber stairs in EE2 and EE3, metal stairs in
EE.4

r16
 Appendìx B : Building Details

B.}WARD RESIDENCE (WARD)

The plan of the Ward Residence is shown in Figure B-2.

11000

TA

LA 19000

roof- conlìniucs 10 900 aboveceilitrg

SætionA-A

Figure 8.2 Plan of building WARD

The Ward Residsnce was constructed in 1881. An addition was added to the rear of
the house at a later date. The details of the construction are given in Table 8.2.

Table 8.2 Details of WARD construction.

Number of S S 1

Construction of SusPended none

Floors
Construction of Roof Timber frame with metal
Construction of External Walls 13 inch bluestone for original building and
double leaf brickwork without articulation for
extension
Construction of Internal Walls Single leaf brickwork without articulation
Footing Type None on the original building, raft footing on
the exterision.
Soil Type
Stair and Lift Details none

t]7
 Appendix B : Building Details

8.3 CHRISTIAN BROTHERS COLLEGE

BUILDING (CBC)
The plan of the classroom block CBC is shown in Figure 8.3

wal I onl y pres ent or

from ground to r0800
10800
ûßt floor

8 175

balcony 2725
rcinforced concrcle
bâlcony wi llì stcel
col mms stai r
A_J

nrcl¡l deck roof

2900
reinforced concrcle floor
2900
rci nforced concrcte floor
2900

Sætion A-A

Figure 8.3 Plan of building CBC

The Christian Brothers College classroom is a typical 1960's Adelaide building. It

consists of a flat concrete slabs supported by masonry walls. One of the main walls of
the building is present from the ground floor to the flrst floor only. Above this, the
wall is replaced by windows. The details of the building are given in Table B.3.

Table 8.3 Details of CBC construction.

Number of s 3
Construction of Suspended Flat 150 mm thick reinforced concrete slabs-
Floors
Construction of Roof Metal deck with steel
Construction of External V/alls Double leaf brickwork without articulation.
Construction of Internal Walls leaf brickwork without articulation
Footing Type Raft footing.
Soil Type Clay
Stair and Lift Details Reinforced concrete.

178
 Appendíx B : Buildíng Details

B.4IRISH AUSTRALIA CLUB BUILDING (IAC)

The plan of the Irish Australia Club building is shown in Figure 8.4.
TA
33000

13400

4250
-i
'1250
1000 9000 3000 7250
wall over
LA
nlet¡l <leck roof
2S00
Éi nforced concrcte fìoof
3600

SætionA-A

Figure 8.4 Plan of building IAC.

The Irish Australia Club building consists of two parts. The front part of the building
is a 2 storey building, and the rear part is a single storey meeting hall. The details of
the building are given in Table 8.4.

Table 8.4 Details of IAC constmction.

Number of Storeys 2
Construction of Suspended Flat 160 thick reinforced concrete slab.
Floors
Construction of Roof Metal deck with steel
Construction of External Walls Double leaf brickwork without articulation.
Construction of Internal V/alls Single and double leaf brickwork without
articulation
Footing Type Raft footing
Soil Type
Stair and Lift Details Reinforced concrete.

179
 Appendíx B : Building Details

8.5 LEIGH TRUST INCORPORATED BUILDTNG

(LTr)
The plan of the Leigh Trust Incoryorated building is shown in Figure 8.5
rcinforced concrete colmlN
5750 ctrs left to right and
4500 ctm lop to botlom

melrl deck
rooI
æiling
16000

corcrcte
slabs

1470 3000

2940
. TA.
4500
r470

1000 3000 4500 4500 5000 12000

SætionA-A
Ln

Building 8.5 Plan of building LTI

The t eigh Trust Incorporated building consists of a box structure with internal
reinforced concrete columns supporting a flat concrete slab. The interior also has
two stair wells and a lift shaft. As part of a refurbishment in 1986 the building was
checked for earthquake performance using the then current Australian Standard

"SAA Earthquake Code" As2l2l-l919.The details of the construction are given in

Table 8.5.

Table 8.5 Details of LTI construction.

Number of Storeys 3 plus basement

Construction of SusPended Flat 100 thick reinforced concrete slab.
Floors
Construction of Roof Metal deck with steel
Construction of External Walls Double leaf brickwork without articulation.
Construction of Internal Walls none
Footin S

Soil
Stair and Lift Details Solid 125 mm walls on the lift shaft and stair
wells with reinforced concrete stairs.

180
 Appendix B : Building Details

8.6 NOLAN SHANNON COMPANY BUILDING

(NSC)

The plan of the Nolan Shannon Company building is shown in Figure B-6-

400

nret¡l deck roof

4000

L J ti nlber floor
4000

9600 Sætion A-A

Figure 8.6 Plan of building NSC

The Nolan Shannon Company building is a 1950's or 1960's warehouse type

structure. A fire in the 1980's resulted in the rebuilding of part of the upper floor in
concrete. The details of the building are given in Table B-6-

Table 8.6 Details of NSC construction.

Number of 2
Construction of Suspended Flat 110 ttrick reinforced concrete slab and
Floors traditional timber floor and
Construction of Roof Metal deck with timber framing.
Construction of External V/alls Double leaf brickwork without articulation.
Construction of Internal Walls leaf brickwork without articulation.
Footing Strip
Soil Type Clay
Stair and Lift Details Timber stairs.

181
 Appendíx B : Building Details

ß.7 SAINT PAULS BOOKSHOP (STP)

The plan of the Saint Pauls Bookshop is shown in Figure B'7

7000 3000

4500
nelal deck roof
3720
timber floor
3720
16000 ti mber floor
1860
3720

_J

Sætion A-A
6500
void in

Figure 8.7 Plan of building STP

The Saint Pauls Bookshop consists of timber suspended floors that have voids at one
corner that result in the wall not having lateral support at these locations. The
building also has a basement that is only partly underground. The details of the
building are given in Table 8.7.

Table 8.7 Details of STP construction.

Number of 2plus basement

Construction of Suspended Timber joist and floor board.
Floors
Construction of Roof Metal deck with timber
Cons truction of External Walls Double leaf brickwork without articulation.
Construction of Internal Walls none

Soil Type
Stair and Lift Details Timber stairs.

r82
 Appendix B : Building Details

8.8 OLTPHANT WrNG BUILDTNG (OLW)

The plans of the oliphant wing building is shown in Figure B-8.

rcinforced
cofErete
roof 3200
24/00

3200

rei nforced 3200

corcrcte
floos 3200

8500
3200

3200
L I
15900

Section A-A

12200

Figure B.8 Plan of building OLW

'Wing building is a reinforced concrete flat slab on unreinforced

The Oliphant
masonry wall building designed tn 1961. The building has an external staircase
midway along is length and a reinforced concrete lift shaft at one end. The roof is
also reinforced concrete- The details of the construction are given in Table B-8.

Table 8.8 Details of OLW construction-

Number of 6

Construction of SusPended 180 mm thick reinforced concrete flat s1ab.

Floors
Construction of Roof 180 mm thick reinforced concrete flat slab.
Construction of Exærnal Walls Double leaf brickwork without articulation.
Construction of Internal V/alls Sin leaf brickwork without articulation.
Srri
Soil Cla
Stair and Lift Details Reinforced concrete stairs and reinforced
concrete lift shaft.

183
 Appendix B : Building Details

8.9 KIDD UNITS (KIDA AND KIDB)

The plan of the Kidd Units is shown in Figure 8.9

6800 8200

KIDA

5000
constrrction gap

8200
metal dech roof

rci nforced concrcte

2300
t_ IA
lloor
2300
KIDB ó800

SætionA-A
5500

Figure 8.9 Plan of KIDA and KIDB

The Kidd Units are two separate structures. The balconies meet but are separated by
a construction joint. The two structures are of identical construction. The type of
construction is typical of a number of units and aparünent buildings in Adelaide- The
details of the construction are given in Table B-9-

Table 8.9 Details of KIDA and KIDB construction-

Number of 2
Construction of SusPended 110 mm thick reinforced concrete flat slab.
Floors
Construction of Roof Metal deck with timber
Construction of External Walls Double leaf brickwork without articulation.
Construction of Internal Walls Double leaf brickwork without articulation.
Raft
Soil
Stair and Lift Details Reinforced concrete stairs

184
APPENDIX C - REGRESSION
ANALYSIS

A regression analysis was performed on a set of data by minimising the square of the
vertical distance between the data points and the regression line. The data was
assumed to have non-constant vadance. The weighting and regression analysis was
based upon that contained in Ang and Tang (1975).

Yi X
X
X

aj Y=bx
X
X
6yj X
X
X
X

X
xj

Figure C.1 Plot of data and regression line

185
 Appendix C : Regression AnalYsis

Figure C.1 shows the linear regression line passing through the origin, y=bx, plotted
along with a set of data. The vertical distance between the jth point of the data and
the regression line is denoted as aj . The conditional variance about the regression
line may be a function of the independent variable (x coordinate). The normal
approach to the regression analysis is modihed to take account of the variation in the
conditional variance. The variation may be expressed as:

Var(Y lx)- o'g'(*) (c.1)

where g(x) is predetermined constant, and o is an unknown constant. In the case of

this study it was assumed that the conditional standard deviation of the period (y
axis) was assumed to increase linearly with the x value:

Var(Y lx)=62*z (c.2)

Thus:

1
wi =-; (c.3)
X:

To minimise the square of the vertical distance between the data point and the curve
results in minimising:

(c.4)
q )*,u,

substituting

(c.s)
q Ëå,t,-bx,)'
j=t ^l

The minimum of q occurs when:

9=o (c.6)
db

and hence

(c.7)
ål=-å#,,r,-bx,)=o

186
 Appendix C : Regression AnalYsis

-bx,) =o (c.8)
åi,r,
v.
a-nb=0
) x. (c.e)
j--t
I

Therefore:

(c.10)

An unbiased estimate of the unknown ot is:

S
I w (v
n-2
- b*, )'
(c.11)

Hence, an estimate of the conditional variance is:

sl,* = s'g'(x) (c.r2)

and

sr,. = sg(x) (c.13)

V/ith the conditional standard deviation used in this case:

S
Ylx SX (c.14)

To calculate the confidence intervals, the students 't' distribution was used (Kreyzig
(1933) and Ang and Tang (1975)). A one sided confîdence interval was chosen, as
explained in the text. The equation for the confidence interval line wa.s then:

y=bx-t*,o-2sy/* (c.1s)

To measure the fit of a regressed line to the data the reductions in the original
variance of T, R2, was calculated:

187
 Appendix C : Regression AnaIYsís

ST,.
R' = (1- ) (c.16)
S?

where:

1
si -D' (c.17)
n-1 I(v,

Because of the dependence of the conditional variance of T on the value of the x

coordinate it was decided to calculate R2 at the mean value of the period so as to
compare different regressed lines.

188
APPENDIX D - TYPICAL ROOF
LOAD CALCULATIONS

A typical roof would result in loads of the order of:

ceiling 0.22 (Gyprock)

tiles 0.51 (Terracotta - including framing)

0.97 kPa (D.1)

being applied to the walls that support it. A typical roof would span six metres
between supports giving a load per unit length of wall of:

3 m x 0.79 kPa = 2.4 kN/m (D.2)

The laboratory wall panels are L-2 metres long

2.4 kN/m x I.2 m = 2.9 kN (D.3)

As there are two wall panels being tested:

2.9 kN x 2 = 5.8 kN roof load (D.4)

The wall panels should therefore have a superimposed load representing the roof
load of 5.8 kN. The result if the roof was spanning eight metres and each wall
therefore supported four metres of roof would be:

4 m x 0.79 kPa = 3.2 kN/m (D.s)

189
 Appendix D : Typical Roof Load Calculotions

3.2 kN/m x L.2 m = 3.8 kN (D.6)

3.8kNx2=7.6kN (D.7)

so that the superimposed roof load increases to 7.6 kN'

panels represented the lower half a wall there would be superimposed load
If the wall
from the upper part of the wall applied. If a double leaf wall was 2.4 metres high then
the superimposed load would be:

l.2m (high) x 19 kN/m3 x0-22 m (thick) = 5-0 kN/m (D.8)

For two walls, 1.2 m long:

5.0 kN/m x 1.2 m x2 = 12 kN superimposed load (D.e)

These calculations were used to determine reasonable levels of superimposed load to

apply to the wall panel specimens for the shaking table tests'

190
APPtrNDIX E - COMPARISON OF'
ADELAIDE RESULTS TO
CALIFORNIAN RESULTS.

As was noted in Chapter 4, the test set-up used for the laboratory tests in this

research was similar to the test set-up as used by Mengi and McNiven (1989) at the
University of California at Berkeley for tests on unreinforced clay brick masonry. It
was therefore possible to use the results from the Berkeley tests to predict the order
of magnitude of the expected results fiom the tests conducted in Adelaide.

It is hrstly assumed that the behaviour of the wall as a result of the induced
horizontal shear force was that of a cantilever shear beam. This was based on the
calculations in Appendix G that show that the majority of the deflection of the wall
panels was made up of the shear deflection component than the bending deflection
component (two thirds of the total was shear deflection). A typical cantilever shear
beam is shown in Figure E.1.

The disptacement of the shear beam is of the form:

L- k-PL (E.1)
AG

where P, L and A are as dehned in Figure E.1, G is the shear modulus, /< is a
constant, and  the deflection of the beam. As the test set-up used in both the
Adelaide and Berkeley tests was the same it was assumed that k was constant for
both tests. Similarly, as both tests were carried out on clay brick masonry it was
assumed that the shear modulus for both tests were equal. The panels used in the
Berkeley tests were two single leaf 190 mm thick, 244O mm long and 1830 mm high

191
 Appendix E : Comparison of Adelaide Results to Caliþrnian Results

clay masonry walls. This compares to the four 110 mm thick, 1175 mm long by 760
mm high clay masonry panels used in the Adelaide double leaf tests-

applied load, P

cross section
A

panel length, L

Figure E.1 Typical cantilever shear beam

The applied load was also different for the two tests- For earthquake simulator tests
the applied load was an inertial load which was a linear function of the base

acceleration and the vertical mass. Without information regarding the distribution of
horizontal acceleration along the height of the wall it was assumed that it was
constant for both tests even though, as will be seen later, the Berkeley tests had a
significantly greater proportion of the total vertical mass at the roof level. The total
mass for the Berkeley tests consisted of. 12,729 kg of roof superimposed mass and
3,292 kg of mass due to the wall panels. The Adelaide tests, specifically the tests
with typical roof load applied, 12 x 400 N, had 510.8 kg of roof superimposed mass
and 650.8 kg of wall mass.

192
 Appendix E : Comparison of Adelaide Results to Caliþrnian Results

For a similar level of base acceleration, then the ratio of the displacement of the
Adelaide test to the Berkeley test became:

Àno.'"'n. (8.2)
-
^"o0",r, Bøkeley

substituting in from PreviouslY:

1161.8x0.76
Á on.t",u" 0.517
- 1602lx1.83 (E.3)
uo*,",
^ 0.9296

and evaluaúng:

Âon.,.,n" (E.4)
= 0.054
ro*",",
^

It was expected that the maximum acceleration applied to the model speÆimens
would be 0.5 g as this would be a conservative upper limit for any design earthquake
in an area of low seismicity such as Australia. At a maximum acceleration of O.472 g
for the Berkeley tests, which \¡/as for the EI Centro, 1940, earthquake tecord, the top
displacement was 2-118 mm. Applying EquationE-4 to this result yields an expected
displacement for the top of the panels in the Adelaide tests of 0-12 mm-

For the Adelaide single leaf specimens with the same axial stress as the double leaf
specimens it was found that the load, P, was halved as was the cross sectional area.
These two factors cancel when substituted in Equation 8.2 and led to the same ratio
as Equation E.4.

After the tests were compleæd it was possible to compare the results of the Adelaide
tests to the Berkeley tests. None of the Adelaide tests had a peak acceleration that
matched any of the reported Berkeley results. Subsequentþ, the expected ratios of
deflections need to be corrected for the differing peak acceleration. As the applied
load p is proportional to the base acceleration, the peak acceleration appears on the
top line of Equation E-1. Further, the Berkeley tests were expected to have a centre
of mass relatively higher than the Adelaide tests due to the larger proportion of mass
at roof level for the Berkeley tests. The induced shear force for the walls was applied

193
 Appendix E: Contparison of Adelaide Results to Caliþrnian Results

through the centre of mass so the L term in Equation E'l was

affected by the
tests was found
difference in the centre of mass. The centre of mass for the Berkeley
height- The centre of
to be 1,640 mm from the base. This was 89 percent of the panel
percent of the height'
mass for the Adelaide tests was 547 mm from the base, 72
Modifying Equation E.4 with the ratios of the centre of mass yields:

Åo0.,",0' (E.5)
= o-054 x0'72
o' 89
^"o*.,",
evaluating

Âo0",",0' (8.6)
= 0.043
^uo*",.,

ratios are:
Comparing the actual results from Berkeley to Adelaide, the expected

Âoo",u,o. âr¿.1"t¿"
- Q.g43 (E.7)
aBok.l"y
expæted
^"o*.t",

and the comparison is given in Table E'1

Table E.l Comparison of Adelaide to Berkeley Resulrc

âAdrl"idt Àoo.,u,o" aBok"l.y actual expected

(mm) (g) ^"our',
(mm) Âoo",o,u" Àoo',o,0'
(e)

^uo*"t' ^"*aot
0.026 0.149 o.629 0.041 0.053
0.184
0.033 0.285 0.966 0.034 0.039
0.264

in the
The results show that the order of magnitude of the displacements measured
in the
Adelaide tests are consistent with those of the Berkeley tests. The difference
expected results compared to the actual results can be attributed
to factors such as
workmanship, actual distribution in the acceleration, and the maærial
properties

(mortar composition, thickness etc)-

t94
APPE,NDIX F . OVERTURI{ING AT{D
UPLIFT CALCULATIONS

Overturning and uplift were checked for a typical 13 course wall panel from
the

shaking table test program. The typical wall panel is shown in Figure F'1'

roof mass
q=0.259 z--z

5s0
i v,

a*=0-228t--= wall mass

+ #Hw

5s0 Iv*
A
ar=0.188 ¿--

590 590

Figure F.1 Typical shaking table test specimen'

The mass of the masonry component of the wall test specimen (single leaf) was given
by:

V* = 0.1lm x 1.lm x 1-18m x 19 kN/m3 - 2-7 kN (F,1)

195
 Appendix F : Overturning and Uphft Calculations

and the mass of the roof (per leaf of brickworþ was given by

Y,= !2J.5 kg x 9-81 m/s2 x 10 3 - 1.3 kN (F.2)

Calculation of the earlhquake induced horizontal loads using the accelerations shown
in Figure F.1 gave:

H*=2.7 kN x 0.229 = 0.6 kN (F.3)

and

H. = 1.3 kN x 0.259 = 0.3 kN (F.4)

For overtuming, taking moments about point A shown in Figure F'1, lustly
calculating the moment that causes overturning:

I H,y, = 0.6 kN x 0-55m + 0-3 kN x 1.lm = 0'7 kNm (F.5)

and calculating the moment that resists overturning:

I V,z, = 2.7 kN x 0.59m + 1.3 kN x 0.59m = 2-4 kNm (F'6)

Therefore the factor of safety against overturnlng was:

2.4 kNm õ a (F.7)

= J.+
0.7 kNm

Overturning was therefore not a problem. Calculating the potential for uplift
(ænsile

failure in the bottom mortar layer). The overturning moment, Equation F'5, was
divided by the bending modulus, z, to determine the tensile stress at opposite corner
to point A in Figure F.1. The bending modulus was given by:

110 x 11802 .
z=-:25.5 x 106 (F.8)
6

the tensile stress then becomes:

= 0.03 MPa (F.e)

196
 Appendix F : Overturning andUplifi Calculations

was given
The resisting stress due to the self weight of the wall and the roof on top
by:

2700 + 1300
rr
-c = = 0.03MPa (F.10)
110 x 1180

due to
The ænsile stress due to overtuming was the same as the compressive stress
the self weight of the panels and the roof. The factor of safety against
uplift was the

tensile strength of the brickwork-

r97
APPtr,NDIX G. CALCULATION OF
SHEAR AND BENDING
COMPONENTS IN LABORATORY
WALL SPECIMEI{S

In order to determine the component of shear deflection in the total deflection of the
laboratory wall specimens calculation of the expected static bending and shear
components of the total deflection of the laboratory wall specimens was undertaken.
It was assumed that the four leaf wall was a simple cantilever beam of thickness
equal to four times the thickness of one wall panels'

Considering the laboratory test specimen number 4. A cantilever beam consisting

of
a point load at the free end, a uniformly distributed load along the length of the
beam, and a triangularly distributed load varying from zeÍo at the support to
maximum at the free end. The applied acceleration ranged from 0.1849 at the base,
linearly increasing to O.247 g at the free (top) end. The test set up is shown in Figure
G.1.

The properties used to determine the components of the deflection were:

length = 1175 mm
height = 760 mm
width = 4x110mm=440mm
density = 19 kN/m3

198
 Appenrlix G : Calctú,ation of Shear and Bending Components in Laboratory WaIl
Specimens

a.=0'259 roof mass 510 kg

1.2 kN
\\
triangular / /
distributed--) -)
load ---7\ --7\
0.6 kN/m
ac =0.229
max -) I
UDL
wall mass 1.8 kN/m
1000 kg/m height
ì-)
ll
)-)
a" = 0.189 )l

(a) wall specimen G) idealized can[ilever

beam

Figure G.l Laboratory Wall Specimen Number 4

G.1 BENDING COMPONENT

The bending component of the deflection was made up of three parts superimposed-
The equations used for each part of the deflection were taken from Gere and
Timoshenko (1987).

The deflection at the end of the cantilever due to the point load at the end of the
cantilever was given bY:

PL3
ô - (G.1)
3EI

where p is the point load, L is the cantilever length, B is the Young's Modulus, and I
is the second moment of area of the cross section. The deflection to the end of the
canúlever due to the uniformly distributed load along the cantilever length w¿ts given
by:

199
 WaII
Appendix G : Calctilation of Shear and Bendfug Components in Inboratory
Specimens

wLo (G.2)
õ
8EI

where w is the distributed load per unit length, and L, E, and I are as
previously

defined. The third part of the bending deflection, that due to the triangularly
distributed load was given bY:

- l lo[-a (G.3)
I2OEI

where q is the maximum value of the triangular load per unit length, and L, E,
and I
are as previouslY defined-

Substituting the values for the laboratory wall specimen number 4 yields an end
bending deflection of:

4.6 (G.4)
ô
E

where E is in MPa and the deflection is in millimet¡es'

G.2 SHEAR COMPONENT

As with the bending component, the shear component of the total deflection is made
up of three parts superimposed. The deflections due to the point load and the
uniformly distribured load are given in Roark and Young (1989). For the point load
at the free end of the canúlever beam the deflection at the free end of the cantilever
was given by:

õ=FPL (G.s)
AG

where p is the point load at the end of the beam, L is the length of the beam, A is the
cross sectional area, G is the shear modulus, and F is a factor depending on the form
of the cross section, for rectangular cross sections F = 615. The deflection at the free
end of the cantilever was given bY:

200
 Appendix G : calcttlation of shear anrl Bending components in Laboratory wall
Specimens

^ 1 --wl-'?
o=ro (G.6)
nc

where F, A, G, and L are as previously dehned and w is the uniformly distributed

formula
load per unit length. For the triangularly distributed load no shear deflection
was used
was found so the unit-load method as described in Gere and Timoshenko
to determine the deflection. The resulting equation for the deflection for a
the free end
triangularly varying distributed load on a cantilever with the maximum at
was:

1p9Ú (G.7)
ô=
3AG
value of the
where F, L, A, and G are as previously defined and q is the maximum
triangularly distributed load per unit length-

yields a
Evaluating Equations G.5 to G.7 for the laboratory wall specimen number 4
total shear deflection in millimetres of:

^ 3.66
|=- (G.8)
G

modulus
where G is the shear modulus in MPL The lgungls Modulus and the sþear
of a material arc related by the formula:

(G.e)

E and G are as previously dehned and v is the Poisson's Ratio. Using a Poisson's
ratio of 0-17 (the averags of the Poisson's Ratio for the brick and mortar phase as
in
reported in Section 2.5) the shear component of the deflection can be expressed
terms of the Young's Modulus. The shear deflection then became:

_
ò--
8.56 (G.10)
E

20r
 Appendix G : Calculation of Shear and Bending Components in Inboratory WaIl
Specimcns

G.3 COMPARISON OF DEFLECTIONS

play a
From Equations G-4 and G.10 it can be seen the bending deflection does not
significant part in the overall deflection of the laboratory wall specimens- Just over
one third of the total deflection was due to bending. In a wall in a real building,
however, it would be expected that the length is very much greater than the height
and the shear component of the deflection would dominate to an even greater
degree.

202
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2t5
 O(ì9(T\
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501 5
-- >-

ADDENIDUM

This addendum contains further information and clarif,rcation as suggested by the

assessors.

The shaking table tests were conducted using the most common brick type
manufactured in Adelaide which were a nominal 230 mm x 70 mm x 90 mm. The
size given on page 98 is incorrect. The actual sizes varied from 230 to 236 mm long
by 109to I 13 mm wide. The height was generally a uniform 70 mm. Table AD.l
gives further information regarding the size of the wall test panels described in
Chapter 4 and expands upon the information in Table 4.3.1.

The "Masonry Wall Panel Width" was the total width of masonry making up one of
the two walls of the test panel pair. For the double leaf specimens it was the width
of two brick leafs but not the cavity, and for the single leaf wall pairs was the width
of one leaf of brickwork. The length of the wall panels were 1125 mm for all tests.

The shear forces calculated for the test wall panels and described on page 104 were
determined using the approach outlined in Appendix F (Equations F.1,F.2, F.3, and
F.4). The associated masses are given in Appendix F as V* and \ .

The cracking patterns observed in the masonry wall panels are as described in
Figure 4.4,1. Stiffness calculations were based on measurements made prior to the
onset of rocking.

The effects of stocþ piers and openings in wall panels was not examined as part of
this research project.
 Table AD.1 Shaking Table Test Panel Details

Wall Test Pair Number of Height of Double or Masonry

Number Courses Panel Single Leaf Wall Panel
(mm) (D/s) widrht
(mm)
1 l3 I 135 D 180

2 13 1 135 D 180

J t3 1 135 D 180

4 9 795 D 180

5 9 795 D 180

6 9 795 D 180

7 9 795 D 180
8 9 82s D 180

9 9 79s S 90
10 9 795 S 90

11 9 795 S 90

t2 9 79s S 90

13 9 79s S 90
t4 9 195 D 180

l5 9 795 D 180

The bending stresses given in Tables 5.ó1 to 5.6.11 are the earthquake induced
bending stresses and do not include any dead load.

Equations 6.2.4 and6.2.5 are intended for use with rigid diaphragm systems