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DEVELOPMENT OF LOAD AND RESISTANCE FACTORS FOR REINFORCED CONCRETE STRUCTURES IN TURKEY

A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF MIDDLE EAST TECHNICAL UNIVERSITY

FATİH KÜRŞAT FIRAT

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF DOCTOR OF PHILOSOPHY IN

CIVIL ENGINEERING

SEPTEMBER 2007

Approval of the thesis:

DEVELOPMENT OF LOAD AND RESISTANCE FACTORS FOR REINFORCED CONCRETE STRUCTURES IN TURKEY

submitted by FATİH KÜRŞAT FIRAT in partial fulfillment of the requirements for the degree of Doctor Of Philosophy In Civil Engineering, Middle East Technical University by, Prof. Dr. Canan Özgen __________________ Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Güney Özcebe __________________ Head of Department, Civil Engineering Prof. Dr. M. Semih Yücemen __________________ Supervisor, Civil Engineering Dept., METU Examining Committee Members: Prof. Dr. M. Yaşar Kaltakcı __________________ Civil Engineering Dept., Selcuk University Prof. Dr. M. Semih Yücemen __________________ Civil Engineering Dept., METU Assoc. Prof. Dr. H. Şebnem Düzgün __________________ Mining Engineering Dept., METU Assist. Prof. Dr. Erdem Canbay __________________ Civil Engineering Dept., METU Assist. Prof. Dr. Murat Güler __________________ Civil Engineering Dept., METU

Date: 07/09/2007

I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last Name: Fatih Kürşat Fırat Signature :

ABSTRACT

DEVELOPMENT OF LOAD AND RESISTANCE FACTORS FOR REINFORCED CONCRETE

STRUCTURES IN TURKEY

Firat, Fatih Kürsat

Ph. D., Department of Civil Engineering

Supervisor: Prof. Dr. M. Semih Yücemen

September 2007, 293 pages

In this dissertation, a study is conducted to develop a probability based load and

resistance factor design criterion for structural members considering the local

conditions of Turkey. The Advanced First Order Second Moment (AFOSM)

procedure is utilized as the probabilistic method of analysis. Various sources of

uncertainties associated with concrete compressive strength, yielding and ultimate

strength of reinforcing steel bars and the dimensions of beams, columns and shear

walls are analyzed and quantified. The resistance statistics for different failure

modes of different types of reinforced concrete structural members are computed by

using the resistance parameters within the framework of reliability analysis.

Structural load effects of dead, live, wind, snow and earthquake loads are analyzed

considering the uncertainties in these loads.

For different load combinations, the safety levels corresponding to the current

design practice are evaluated in terms of the reliability indexes for reinforced

concrete beam, column and shear wall design in flexure and shear, and also column

design in combined action of flexure and axial load. Depending on this evaluation

and the reliability index values reported from other countries, target reliability

indexes are selected for different load combinations and different failure modes of

structural members. Finally, a new set of load and resistance factors corresponding

to selected target reliabilities and levels of uncertainties are proposed for each

different failure modes of the structural members considered in this study,

separately.

Keywords: Uncertainty, Load and Resistance Factors, Reliability, Reliability Index,

Safety Level, Structural Member, Load Combination

YÜK VE DAYANIM KATSAYILARININ TÜRKİYE’DEKİ BETONARME YAPILAR İÇİN

BELİRLENMESİ

Fırat, Fatih Kürşat

Doktora, İnşaat Mühendisliği Bölümü

Tez Yöneticisi: Prof. Dr. M. Semih Yücemen

Eylül 2007, 293 sayfa

Bu tez çalışmasında, Türkiye koşullarına göre istatistiksel yöntemler kullanılarak

betonarme yapı elemanları için yük ve dayanım katsayılarına dayalı bir tasarım

kriteri geliştirilmiştir. “Geliştirilmiş Birici Mertebe İkinci Moment” (GBMİM)

metodu istatistiksel analiz metodu olarak kullanılmıştır. Beton basınç

dayanımındaki, beton çelik çubuklarının akma dayanımındaki ve kolon, kiriş ve

perde duvar boyutlarındaki değişik belirsizlik kaynakları incelenmiş ve bu

belirsizlikler sayısallaştırılmıştır. İncelenen yapı elemanlarının değişik göçme

durumları için, istatistiksel dayanım parametreleri “güvenilirlik analizi”

çerçevesinde hesaplanmıştır. Sabit, hareketli, kar, rüzgar ve deprem yüklerindeki

belirsizliklerin sayısallaştırılması ve bu yüklerin yapıya olan etkisi ile ilgili bir dizi

analizler yapılmıştır.

Türkiye’deki geçerli tasarım kriterine uygun olarak değişik yük kombinasyonları

için emniyet dereceleri, güvenilirlik indeksleri dikkate alınarak, bazı göçme

durumlarına göre ayrı ayrı incelenmiştir. Bu göçme durumlarıyla ilgili olarak, basit

eğilme ve kesme etkisindeki kiriş, kolon ve perde duvarların yanısıra eksenel basınç

ve eğilme altındaki kolonlar dikkate alınmıştır. Bu çalışmada hesaplanan emniyet

dereceleri ve yabancı kaynaklarda verilen hedef güvenilirlik indeksleri göz önünde

tutularak, yeni hedef güvenilirlik indeksleri farklı yük kombinasyonları ve farklı

göçme durumları için belirlenmiştir. Son olarak, belirlenen hedef güvenilirlik

indekslerine uygun, yeni yük ve dayanım katsayıları her bir yapı elamanının her bir

göçme durumu için ayrı ayrı önerilmiştir.

Anahtar Kelimeler: Belirsizlik, Yük ve Dayanım Katsayıları, Güvenilirlik,

Güvenilirlik İndeksi, Emniyet Derecesi, Yapı Elemanı, Yük Kombinasyonu

ACKNOWLEDGMENTS

I would like to express my deepest appreciation to my thesis supervisor Prof. Dr. M.

Semih Yücemen for his professional guidance, support, criticism, and

encouragement. It was a great pleasure for me to work with him.

I owe special thanks to Assist. Prof. Dr. Erdem Canbay and Assoc. Prof. Dr. H.

Şebnem Düzgün for their helpful suggestions and guidance throughout the study.

I also would like to send my thanks to Turkish Meteorological Department,

Ministry of Public Works and Settlement, Turkish Chamber of Civil Engineers,

General Directorate of State Hydraulic Works, Techno-test, Vetaş and Armada

firms, Habaş, İçdaş, Ekiciler, Çolakoğlu, Egeçelik, Kroman and Yeşilyurt iron and

steel factories, and the materials laboratories of METU, ITU and Selçuk University

for providing the data used in this study.

Special thanks are due to Ali Faik Ulusoy, Seval Pınarbaşı, Mustafa Can Yücel,

Yusuf Baran and Ayşem Karadağ for their great friendship and help.

Finally, I am deeply grateful to my wife Emine and my daughter Ayça for their

endless support and altruism. I also would like to convey my deepest thanks to my

parents Nurcihan and A.Turan Fırat for their support and encouragement.

TABLE OF CONTENTS

ABSTRACT ..........................................................................................................iv

ÖZ …………………………………………………………………………………..vi

ACKNOWLEDGMENTS................................................................................... viii

TABLE OF CONTENTS.......................................................................................ix

LIST OF TABLES...............................................................................................xiv

LIST OF FIGURES .............................................................................................xxi

LIST OF SYMBOLS .........................................................................................xxiv

CHAPTERS

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

1.1 GENERAL VIEW....................................................................................1

1.2 REVIEW OF RELATED WORK.............................................................3

1.3 AIM AND SCOPE OF THE STUDY.......................................................5

2. STRUCTURAL RELIABILITY MODELS ......................................................8

2.1 THE CLASSICAL RELIABILITY THEORY..........................................8

2.2 FIRST ORDER SECOND MOMENT METHOD ....................................9

2.2.1 Mean Value Method ....................................................................10

2.2.2 Advanced First Order Second Moment Method ...........................12

2.3 MODELING AND ANALYSIS OF UNCERTAINTIES........................14

3. QUANTIFICATION OF UNCERTAINTIES RELATED TO

RESISTANCE PARAMETERS .....................................................................17

3.1 CONCRETE ..........................................................................................17

3.1.1 Evaluation of Data.......................................................................19

3.1.2 Uncertainty Analysis of Concrete Compressive Strength .............22

3.2 REINFORCING STEEL BARS .............................................................25

3.2.1 Evaluation of Data.......................................................................28

3.2.2 Uncertainty Analysis of Reinforcing Steel Bars ...........................30

3.3 DIMENSIONS.......................................................................................33

3.3.1 Data Collection and Analysis.......................................................34

3.3.2 Beam Width and Depth ...............................................................36

3.3.3 Beam Effective Depth .................................................................38

3.3.4 Column Width and Depth ............................................................40

3.3.5 Column Effective Depth ..............................................................42

3.3.6 Shear Walls .................................................................................44

3.3.7 Reinforcement Area.....................................................................46

4. MODELING OF CAPACITY OF REINFORCED CONCRETE

MEMBERS IN DIFFERENT FAILURE MODES..........................................48

4.1 CAPACITY OF REINFORCED CONCRETE BEAMS IN

DIFFERENT FAILURE MODES ..........................................................48

4.1.1 Flexural Capacity of Beams.........................................................49

4.1.2 Shear Capacity of Beams.............................................................57

4.2 CAPACITY OF REINFORCED CONCRETE COLUMNS IN

4.2.1 Combined Action of Flexure and Axial Load for Columns ..........64

4.2.2 Shear Capacity of Columns .........................................................72

4.3 CAPACITY OF REINFORCED CONCRETE SHEAR WALLS IN

4.3.1 Flexural Capacity of Shear Walls.................................................75

4.3.2 Shear Capacity of Shear Walls.....................................................78

5. MODELING OF LOADS...............................................................................80

5.1 INTRODUCTION..................................................................................80

5.2 DEAD LOAD ........................................................................................83

5.3 LIVE LOAD ..........................................................................................85

5.3.1 Arbitrary Point-in-Time Live Load (Lapt).....................................86

5.3.2 Maximum Live Load (L) .............................................................89

5.4 SNOW LOAD........................................................................................91

5.4.1 Roof Snow Load..........................................................................93

5.4.2 Ground Snow Load, Pko ...............................................................95

5.4.3 Annual Extreme Roof Snow Load ...............................................97

5.4.4 Maximum Roof Snow Load (S)...................................................99

5.4.5 Mean to Nominal Ratios of San and S.........................................101

5.5 WIND LOAD.......................................................................................102

5.5.1 Analysis of Wind Speed ............................................................104

5.5.2 Maximum, Yearly Maximum and Daily Maximum Wind Loads106

5.6 EARTHQUAKE LOAD.......................................................................110

5.6.1 Determination of Total Equivalent Lateral Earthquake Load......113

5.6.1.1 UBC-1994 ...................................................................114

5.6.1.2 TEC-2006....................................................................116

5.6.1.3 Case 1..........................................................................121

5.6.1.4 Case 2..........................................................................124

5.6.1.5 Case 3..........................................................................127

6. ASSESSMENT OF THE SAFETY LEVELS INHERENT IN THE

CURRENT DESIGN PRACTICE ................................................................132

6.1 INTRODUCTION................................................................................132

6.2 LOAD COMBINATION......................................................................133

6.2.1 Turkstra’s Rule..........................................................................134

6.2.2 Safety Criterion .........................................................................135

6.2.3 Load Statistics ...........................................................................136

6.3 RESISTANCE STATISTICS ...............................................................139

6.4 COMPUTATION OF RELIABILITY INDEXES.................................141

6.4.1 Reliability Indexes for Reinforced Concrete Beams in the

Flexural Failure Mode ...............................................................142

6.4.1.1 Gravity Loads ..............................................................142

6.4.1.2 Gravity and Wind Loads ..............................................145

6.4.1.3 Gravity and Earthquake Loads .....................................147

6.4.2 Reliability Indexes for Reinforced Concrete Beams in the Shear

Failure Mode .............................................................................149

6.4.2.1 Gravity Loads ..............................................................149

6.4.3 Reliability Indexes for Reinforced Concrete Columns in the

Combined Action of Flexure and Axial Load Failure Mode.......155

6.4.3.1 Gravity Loads ..............................................................155

6.4.4 Reliability Indexes for Reinforced Concrete Columns in the

Shear Failure Mode ...................................................................159

6.4.5 Reliability Indexes for Reinforced Concrete Shear Walls in the

Flexural Failure Mode ...............................................................160

6.4.6 Reliability Indexes for Reinforced Concrete Shear Walls in the

Shear Failure Mode ...................................................................161

6.4.7 Assessment of Target Reliability Indexes ..................................162

7. SELECTION OF LOAD AND RESISTANCE FACTORS...........................171

7.1 INTRODUCTION................................................................................171

7.2 LOAD AND RESISTANCE FACTORS CORRESPONDING TO

THE SELECTED TARGET RELIABILITIES .....................................172

7.2.1 Load and Resistance Factors for Reinforced Concrete Beams in

the Flexural Failure Mode..........................................................173

7.2.2 Load and Resistance Factors for Reinforced Concrete Beams in

the Shear Failure Mode..............................................................179

7.2.3 Load and Resistance Factors for Reinforced Concrete Columns

in the Combined Action Failure Mode.......................................185

7.2.4 Load and Resistance Factors for Reinforced Concrete Columns

in the Shear Failure Mode..........................................................191

7.2.5 Load and Resistance Factors for Reinforced Concrete Shear

Walls in the Flexural Failure Mode............................................197

7.2.6 Load and Resistance Factors for Reinforced Concrete Shear

Walls in the Shear Failure Mode................................................197

7.3 OPTIMAL LOAD AND RESISTANCE FACTORS ............................198

7.4 MODIFIED OPTIMAL LOAD AND RESISTANCE FACTORS ........202

7.5 RECOMMENDED LOAD AND RESISTANCE FACTORS ...............209

8. SUMMARY AND CONCLUSIONS............................................................213

REFERENCES ...................................................................................................221

APPENDICES

A. STATISTICAL PARAMETERS OF 7 AND 28 DAY COMPRESSIVE

STRENGTH DATA ACCORDING TO CONCRETE CLASS

AND REGION……………………………………….…………………….. 229

B. STATISTICAL PARAMETERS OF BCIII(A) REINFORCING

STEEL BARS USED in TURKEY……………………………………………234

C. ANNUAL MAXIMUM SNOW DEPTHS FOR DIFFERENT

LOCATIONS………………………………………….…………..…….….....253

D. ANNUAL MAXIMUM WIND SPEEDS FOR DIFFERENT

LOCATIONS………………………………………………………………….256

E. DAILY MAXIMUM WIND SPEEDS OBSERVED DURING THE YEAR

2004 IN DIFFERENT LOCATIONS…………………………………………259

F. FIGURES SHOWING THE VARIATION OF RELIABILITY INDEX

OBTAINED ACCORDING THE TURKISH DESIGN PROVISIONS…...…272

G. FIGURES SHOWING THE VARIATION OF SAFETY LEVEL

CORRESPONDING TO THE RECOMMENDED LOAD AND

RESISTANCE FACTORS……………………………………..……………..280

CURRICULUM VITAE……………………………………………….…………293

LIST OF TABLES

Table 3.1 Statistical parameters of compressive strength data according to years

for Turkey .......................................................................................................21

Table 3.2 Statistical parameters of 28 day compressive strength data according

to concrete class for Turkey.............................................................................21

Table 3.3 Statistical parameters of 7 day compressive strength data according to

concrete class for Turkey.................................................................................21

Table 3.4 Different country standards related to reinforcing steel bars...................27

Table 3.5 Mean value and c.o.v. of yield strength of BCIII(a) reinforcing steel

bars produced by different steel and iron plants in Turkey ...............................28

Table 3.6 Mean value and c.o.v. of ultimate strength of BCIII(a) reinforcing

steel bars produced by different steel and iron plants in Turkey .......................29

Table 3.7 Mean value and c.o.v. of elongation of BCIII(a) reinforcing steel bars

produced by different steel and iron plants in Turkey.......................................29

Table 3.8 Statistical parameters of yield strength of BCIII(a) reinforcing steel

bars according to years ....................................................................................29

Table 3.9 Results of the statistical analysis of beam external dimensions for .........38

Table 3.10 Results of the statistical analysis of beam internal dimensions before

the placement of concrete ................................................................................39

Table 3.11 Results of the statistical analysis of column external dimensions for

different regions ..............................................................................................42

Table 3.12 Results of the statistical analysis for the column internal dimensions ...44

Table 3.13 Results of the statistical analysis of shear wall external dimensions

for different regions.........................................................................................45

Table 3.14 Results of the statistical analysis of reinforcement areas ......................47

Table 4.1 Statistics of the basic variables involved in the calculation of flexural

and shear capacities of reinforced concrete beams ...........................................49

Table 4.2 Mean to nominal ratios and coefficients of variation of the beam

flexural capacity (b=200 mm and b=300 mm) .................................................56

flexural capacity (b=400 mm and b=1000 mm)................................................57

shear capacity..................................................................................................62

Table 4.5 Statistics of the basic variables involved in the calculation of the

combined action and shear capacities of columns ............................................64

Table 4.6 Mean to nominal ratios and coefficients of variation of the axial and

flexural capacities for eccentrically loaded columns (b/h=0.6) .........................68

flexural capacities for eccentrically loaded columns (b/h=1)............................69

flexural capacities for eccentrically loaded columns (b/h=2)............................70

flexural capacities for eccentrically loaded columns (b/h=0.5) .........................71

and shear capacities of shear walls...................................................................75

Table 4.11 Mean to nominal ratios and coefficients of variation for the flexural

capacity of shear-walls ....................................................................................77

Table 4.12 Mean to nominal ratios and coefficient of variations of resistances

for shear-walls in the shear failure mode..........................................................79

Table 5.1 Statistics of dead load (from Ellingwood et al., 1980)............................85

Table 5.2 Statistics of arbitrary point-in-time live loads for offices reported in

different studies (from Ellingwood et al., 1980)...............................................87

Table 5.3 Results of arbitrary point-in-time live load surveys for office buildings

which was reported in different studies (from Kumar, 2002a)..........................89

Table 5.4 Statistics of maximum live loads as reported in different studies............90

Table 5.5 Statistical parameters of the annual extreme ground snow load..............97

Table 5.6 Statistical parameters of the annual extreme roof snow load ..................99

Table 5.7 Statistical parameters of the 50-year maximum roof snow load............101

Table 5.8 Statistical parameters of the mean to nominal ratio for annual extreme

and 50-year maximum snow loads.................................................................102

Table 5.9 Mean values and coefficients of variation of wind speeds for different

locations........................................................................................................106

Table 5.10 Mean values and the total uncertainties of wind loads for different

locations........................................................................................................108

Table 5.11 Mean to nominal wind load ratios and associated total uncertainties

for different locations ....................................................................................109

Table 5.12 Type I distribution parameters of mean to nominal wind load ratios

for different locations ....................................................................................109

Table 5.13 Geographical coordinates and seismic zones of selected locations,

and corresponding peak ground acceleration values for different return

periods ..........................................................................................................111

Table 5.14 Parameters of Type II distribution for peak ground acceleration for

different locations..........................................................................................112

Table 5.15 Mean value and total variability of peak ground acceleration for

different locations..........................................................................................113

Table 5.16 Seismic zone factor in UBC-1994......................................................115

Table 5.17 Response modification factor (RW) for reinforced concrete buildings

in UBC-1994.................................................................................................116

Table 5.18 Effective ground acceleration coefficients (A0) in TEC-2006.............118

Table 5.19 Spectrum characteristic periods (TA, TB) in TEC-2006 ......................119

Table 5.20 Structural system behavior factor (R) in TEC-2006 for cast-in-situ

reinforced concrete buildings.........................................................................120

Table 5.21 Mean to nominal ratios of earthquake load in terms of different local

site classes and building heights (RW=8, Ra(T)=7) .........................................122

site classes and building heights (RW=6, Ra(T)=6).........................................125

site classes and building heights (RW=6, Ra(T)=6).........................................126

Table 5.27 The average mean to nominal ratios of earthquake load obtained

from UBC 1994 and TEC-2006 for different locations...................................130

Table 5.28 Mean to nominal ratios of earthquake load for different locations

where both values are computed based on TEC-2006 ....................................130

Table 5.29 Statistical parameters of the mean to nominal ratio for earthquake

load ...............................................................................................................131

Table 6.1 Statistics of dead, live, wind and earthquake loads...............................138

Table 6.2 Resistance statistics for different reinforced concrete members in

different failure modes...................................................................................140

Table 6.3 Relative frequency distribution of the ratio of a given load to dead

load ...............................................................................................................142

Table 6.4 Reliability indexes and design situations for the flexural failure mode

of reinforced concrete beams subjected to D+L combination .........................143

of reinforced concrete beams subjected to D+S combination .........................144

of reinforced concrete beams subjected to D+Lapt+W combination ................146

of reinforced concrete beams subjected to D+L+Wapt combination ................147

of reinforced concrete beams subjected to D+Lapt+E combination..................149

Table 6.9 Reliability indexes and design situations for the shear failure mode of

reinforced concrete beams subjected to D+L combination .............................150

reinforced concrete beams subjected to D+S combination..............................151

reinforced concrete beams subjected to D+Lapt+W combination ....................152

reinforced concrete beams subjected to D+L+Wapt combination ....................153

reinforced concrete beams subjected to D+Lapt+E combination......................155

Table 6.14 Reliability indexes and design situations for reinforced concrete

columns in the combined action of flexure and axial load subjected to D+L ..156

columns in the combined action of flexure and axial load subjected to D+S...156

columns in the combined action of flexure and axial load (for D+Lapt+W).....157

columns in the combined action of flexure and axial load (for D+L+Wapt) .....158

columns in the combined action of flexure and axial load (for D+Lapt+E) ......159

Table 6.19 Reliability indexes for reinforced concrete columns in the shear

failure mode ..................................................................................................160

Table 6.20 Reliability indexes of reinforced concrete shear walls in the flexural

failure mode ..................................................................................................161

Table 6.21 Reliability indexes of reinforced concrete shear walls in the shear

failure mode ..................................................................................................162

Table 6.22 Reliability indexes corresponding to the current design practice and

the target reliability indexes for different load combinations and different

structural members according to different studies ..........................................163

Table 6.23 Current and the target reliability indexes for different load

combinations considering beams in the flexural failure mode ........................165

combinations considering beams in the shear failure mode ............................166

combinations considering columns in the combined action failure mode........167

combinations considering columns in the shear failure mode .........................168

combinations considering shear walls in the flexural failure mode.................169

combinations considering shear walls in the shear failure mode.....................170

Table 7.1 Optimal load and resistance factors for reinforced concrete beams in

the flexural failure mode................................................................................199

Table 7.2 Optimal load and resistance factors for reinforced concrete beams in

the shear failure mode....................................................................................200

Table 7.3 Optimal load and resistance factors for reinforced concrete columns in

the combined action failure mode ..................................................................200

Table 7.4 Optimal load and resistance factors for reinforced concrete columns in

the shear failure mode....................................................................................201

Table 7.5 Optimal load and resistance factors for reinforced concrete shear walls

in the flexural failure mode............................................................................201

Table 7.6 Optimal load and resistance factors for reinforced concrete shear walls

in the shear failure mode................................................................................202

Table 7.7 Modified optimal load and resistance factors for reinforced concrete

beams in the flexural failure mode.................................................................203

beams in the shear failure mode.....................................................................204

columns in the combined action failure mode ................................................204

columns in the shear failure mode..................................................................205

shear walls in the flexural failure mode..........................................................205

shear walls in the shear failure mode .............................................................206

Table 7.13 Load and resistance factors in USA and Jordan for beams in the

flexural failure mode .....................................................................................206

Table 7.14 Load and resistance factors recommended by Kömürcü and

Yücemen (1996) for beams in the flexural failure mode.................................207

Table 7.15 Average load factors for all structural members in different failure

modes............................................................................................................207

Table 7.16 Load and resistance factors and corresponding reliability index

values for different structural members and failure modes for φ=1.0..............208

Table 7.17 Recommended load factors for all structural members in different

failure modes for Turkey ...............................................................................210

Table 7.18 Recommended load and resistance factors and the corresponding

reliability index values for beams in the flexural failure mode .......................210

reliability index values for beams in the shear failure mode ...........................210

reliability index values for columns in the combined action failure mode ......211

reliability index values for columns in the shear failure mode........................211

reliability index values for shear walls in the flexural failure mode................211

reliability index values for shear walls in the shear failure mode....................212

LIST OF FIGURES

Figure 2.1 Reliability Index β2 (from Thoft-Christensen and Baker, 1982) ............13

Figure 3.1 The map showing the locations of iron and steel plants founded in

Turkey (from http://www.dcud.org.tr/indextur.htm).........................................26

Figure 4.1 Stresses and forces in reinforced concrete beams..................................50

Figure 4.2 Beam sections of T and L shapes (Ersoy and Özcebe, 2004) ................52

Figure 4.3 Stresses and forces in reinforced concrete columns...............................66

Figure 4.4 a) Lateral loads b) Isolated wall c) Shear diagram d) Moment

diagram ...........................................................................................................74

Figure 5.1 The map showing the locations of selected cities..................................83

Figure 7.1 Variation of the load and resistance factors for RC beams in the

flexural failure mode (Turkey; D+L; βT=3.0).................................................173

flexural failure mode (Bursa; D+S; βT=3.0) ...................................................174

flexural failure mode (Turkey; D+S; βT =3.0) ................................................174

flexural failure mode (Canakkale; D+Lapt+W; βT =3.0)..................................175

flexural failure mode (Turkey; D+Lapt+W; βT =3.0) .......................................176

flexural failure mode (Canakkale; D+L+Wapt; βT =2.7)..................................177

flexural failure mode (Turkey; D+L+Wapt; βT =2.7) .......................................177

flexural failure mode (Ankara; D+Lapt+E; βT =1.75) ......................................178

flexural failure mode (Turkey; D+Lapt+E; βT =1.75) ......................................178

shear failure mode (Turkey; D+L; βT =3.0)....................................................179

shear failure mode (Bursa; D+S; βT =3.0) ......................................................180

shear failure mode (Turkey; D+S; βT =3.0)....................................................180

shear failure mode (Canakkale; D+Lapt+W; βT =3.0)......................................181

shear failure mode (Turkey; D+Lapt+W; βT =3.0)...........................................182

shear failure mode (Canakkale; D+L+Wapt; βT =2.7)......................................183

shear failure mode (Turkey; D+L+Wapt; βT =2.7)...........................................183

shear failure mode (Ankara; D+Lapt+E; βT =1.75)..........................................184

shear failure mode (Turkey; D+Lapt+E; βT =1.75) ..........................................184

Figure 7.19 Variation of the load and resistance factors for RC columns in the

combined action failure mode (Turkey; D+L; βT =3.2) ..................................185

combined action failure mode (Bursa; D+S; βT =3.2).....................................186

combined action failure mode (Turkey; D+S; βT =3.2) ..................................186

combined action failure mode (Canakkale; D+Lapt+W; βT =3.2) ....................187

combined action failure mode (Turkey; D+Lapt+W; βT =3.2) .........................188

combined action failure mode (Canakkale; D+L+Wapt; βT =3.0) ....................189

combined action failure mode (Turkey; D+L+Wapt; βT =3.0) .........................189

combined action failure mode (Ankara; D+Lapt+E; βT =1.75).........................190

combined action failure mode (Turkey; D+Lapt+E; βT =1.75).........................190

shear failure mode (Turkey; D+L; βT =3.0)....................................................191

shear failure mode (Bursa; D+S; βT =3.2) ......................................................192

shear failure mode (Turkey; D+S; βT =3.2)....................................................192

shear failure mode (Canakkale; D+Lapt+W; βT =3.2)......................................193

shear failure mode (Turkey; D+Lapt+W; βT =3.2)...........................................194

shear failure mode (Canakkale; D+L+Wapt; βT =3.0)......................................195

shear failure mode (Turkey; D+L+Wapt; βT =3.0)...........................................195

shear failure mode (Ankara; D+Lapt+E; βT =1.75)..........................................196

shear failure mode (Turkey; D+Lapt+E; βT =1.75) ..........................................196

LIST OF SYMBOLS

A Cross sectional area

A Peak ground acceleration

A0 Effective ground acceleration coefficient

A1 Influence area

As Reinforcement area

Asw Cross sectional area of stirrups

A(T1) Spectral acceleration coefficient

b Member width

C Coefficient related to the fundamental period of vibration of the structure

C1,C2 Tabulated coefficients of Type I distribution

Ce Exposure factor for snow load

Ci Influence coefficient of load “i”

Cs Snow load coefficient

Ct Thermal factor of snow load

c Air density constant

c Distance from the neutral axis to outer compressive fiber in a T cross-section

cb Depth of neutral axis at the balanced case in reinforced concrete cross

section

D Dead load effect

Df Failure domain

Ds Safety domain

d Depth of the member

de Effective depth of the member

E Earthquake load effect (the lateral seismic base shear)

Es Modulus of elasticity of steel reinforcement

FX,fx Cumulative distribution function (CDF) and probability density function of

variable X, respectively.

fc Concrete compressive strength

fct Tensile strength of concrete

fs Steel stress

fy Yield strength of steel bars

fyw Yield strength of shear reinforcement

G Gust factor of wind load

g(x) Limit state function

HN Building height

h Ground snow depth

h Member depth

I Importance factor

k Shape parameter of Type II distribution

k1 A dimensionless coefficient which is a function of strength of concrete

L Live load effect of maximum live load

lw Horizontal length of a shear wall

M Safety margin

Mr Bending moment capacity

N Correction factor

N Axial load

Pf Probability of failure

Pko Ground snow load

P(E) Probability of event E

Ps Survival probability (reliability)

pi The weight assigned to the ith load situation

R Generalized resistance

R Rate of loading

R Structural system behavior factor

Rw Response modification factor for the earthquake load

Ra(T1) Seismic load reduction factor

S Snow load effect

S Site coefficients of soil properties

S(T) Spectrum coefficient

s Spacing of stirrups

T Fundamental period of vibration of a building in a specified direction

TA,TB Spectrum characteristic periods

t Depth of the flange thickness

U Effect of factored load

u The scale parameter of Type I distribution

V Wind speed

V Total design base shear

Vc Shear resistance of concrete

Vd Maximum design shear force

Vr Shear strength

Vw Resistance of shear reinforcement

W Wind load effect

W Weight of structure

X Basic random variable

Χ Mean value of X

Χ′ Nominal value of X

X∗ Design value of X

Χ The model used to estimate X

Xapt Arbitrary point-in-time value of X

xi Distance between neutral axis and ith steel layer in reinforced concrete cross

section

Z Seismic zone factor

z Normalized parameter

α Direction cosine

α The local parameter of Type I distribution

β Reliability index

xxviii

βT Target reliability index

Γ(.) Gamma function

γ Generalized load factor

∆ Prediction uncertainty

δ Basic variability

εcu Ultimate strain in concrete

η Stress distribution coefficient

λ,ζ Parameters of lognormal distribution

µ Mean value

ν Characteristic parameter of Type II distribution

ρ Average density of snow load

ρ Steel ratio

ρb Balanced steel ratio

ρ′ Compression reinforcement ratio

σ Standard deviation

σs Steel stress

φ(.) Tabulated probability distribution function of the standard normal variate

Ω Total variability

ϕ Generalized resistance factor

AFOSM Advanced First Order Second Moment Method

APT Arbitrary point-in-time

a.p.t. Arbitrary point-in-time

C.D.F. Cumulative distribution function

c.o.v. Coefficient of variation

FOSM First Order Second Moment Method

JCSS Joint Committee on Structural Safety

LRFD Load Resistance Factor Design

RC Reinforced Concrete

TEC Turkish Earthquake Code (Specification for Structures to be Built in

Earthquake Areas)

CHAPTER 1

INTRODUCTION

1.1 GENERAL VIEW

Due to the uncertainties in the properties of building materials and rising

construction costs, the structural design engineers have been working mainly on the

subject of safe, functionally reliable and economical structures. Structures and

structural elements must satisfy the following requirements with appropriate levels

of reliability:

-They should be serviceable till the end of their economic life (serviceability

limit state requirement).

-They should withstand extreme or frequently repeated effects taking place

during their construction and economical lifetime (ultimate limit state

requirements).

-They should not be damaged by natural hazards and accidental events like

earthquakes, floods, hurricanes, fires and explosions.

Thereby, modern structural design codes should provide a simple, economical and

safe way for the design of engineering structures. Design codes not only make easy

the work of engineers but also optimize the resources of society. Traditionally,

design codes take design equations as the basis, and the reliability of a given design

can be checked by a simple comparison of resistances and load effects. Due to the

fact that loads and resistances are subjected to uncertainties, structural design must

be made in the presence of uncertainties. Additionally loads and strengths of

materials are subjected to random variability due to the complex environmental and

structural mechanisms that govern them. Moreover, the data required for the

structural design are obviously not certain with 100 % confidence. These

uncertainties in structural design are taken into consideration by using probabilistic

methods. Therefore, in recent years, the trend in code development is evolving

towards the use of probabilistic techniques as a basis for developing design criteria.

The traditional approach does not take these uncertainties sufficiently into

consideration and their logical basis is not sufficiently developed. However, the

uncertainties in structural design are considered fully in probabilistic approach. In

this approach, loads and design parameters are treated as random variables and

safety is to be realized by using a tolerable risk or reliability index. Reliability level

can be chosen to reflect the consequences of failure. Besides, the reliability of

complete structural system is determined by considering the reliability of individual

structural system components. The combined effects of different potential failure

modes are also taken into consideration while applying this procedure. Additionally,

this method provides a way to update the present standards with additional

knowledge in a systematic way.

The safety formats of design codes, i.e. design equations, characteristic values, and

load and resistance factors may be chosen so that the level of reliability of all

structures designed according to relevant structural design codes and specifications

is uniform and independent of the choice of material properties, loading types,

operational conditions and environmental surroundings, within the scope of the

structural reliability methods (probabilistic methods). This procedure, covering the

choice at the preferred level of reliability or target reliability, is commonly referred

to as code calibration (Faber et al., 2003).

1.2 REVIEW OF RELATED WORK

First quarter of the 20th century is the beginning of introduction of the probability

concepts in the assessment of structural safety. ACI Building Code introduced the

ultimate strength design in which the design was based on ultimate limit states

using loads increased by load factors and strengths reduced by strength reduction

factors in the early sixties of the 20th century. These important factors were

established upon an elementary statistical analysis carried out by using the

incomplete data and insufficient information. Remarkable studies in this discipline

began in the late sixties and a growing interest has been shown in structural

reliability since then.

Wide ranging studies have been performed during seventies to derive load and

resistance factors for steel structures. These load factors differ from the ones used in

the concrete structures. Recognizing the possible confusion in design offices due to

use of different set of load and resistance factors in the design of steel structures and

reinforced concrete structures, ACI Building Code Committee passed a motion in

1976 endorsing the idea of almost identical load factors for all materials in a manner

that is agreed upon by all committee members.

So as to propose a set of universal load and resistance factors to be utilized in the

design of buildings, the Centre for Building Technology at the National Bureau of

Standards brought Drs. Cornell, Ellingwood, Galambos, and MacGregor together in

1979. The outcomes of this study were published in several papers (Ellingwood et

al., 1980; Galambos et al., 1982, Ellingwood et al., 1982). The basic set of load and

resistance factors was incorporated in the 1982 ANSI A58.1.

Rackwitz (2000) studied the code-making process by using the total cost

minimization as the decision tool to assess the target reliability. In his study, the

maintenance and reconstruction costs were also taken into consideration. Aktas

(2001) studied the structural design code calibration using reliability based cost

optimization, in which predefined target reliability levels were not used.

The Liaison Committee, that coordinated the activities of six international

associations in civil engineering created a joint committee on structural safety

(JCSS) in 1971. This committee’s basic goal was improve the general knowledge

related to structural safety. Thus, JCSS has developed a model code in 2001. This

code is related to only probabilistic design and gives no information about

mechanical models like buckling, shear capacity, flexure failure.

The study of Nowak and Szerszen (2003a,b) documents the calibration of the

Building Code Requirements for Structural Concrete (ACI 318). Their study is

presented in two articles. The first article addresses the topic of statistical model for

resistance (i.e. the models of strength of materials). The developed resistance

models served as a basis for the selection of resistance factors (strength reduction

factors). Accordingly, the second article focuses on the reliability analysis and

selection of resistance factors.

In Turkey, the probabilistic design approach is not well known. Therefore, there is

not much research related to the probabilistic design. Nonetheless, there are a few

studies, such as Keskinel (1971), Yücemen and Gülkan (1975), Gündüz (1988) in

which simple probabilistic concepts were used, but the conception utilized is far

from developing a reliability based design code. In this area, the first significant

research was done by Yücemen and Gülkan in 1989. In their research, a set of

reliability-based load and resistance factors were proposed for the reinforced

concrete beams. Later, Kömürcü (1995) developed a reliability-based design

criterion to be used in reinforced concrete beams in the flexural failure mode by

considering the local conditions and the design practice in Turkey, which is the

most comprehensive study conducted in this field in the past.

The research work presented in this dissertation is to a certain extent a follow up of

the research work conducted by Kömürcü (1995). However, in the present research

compared to the study of Kömürcü (1995), much more comprehensive data sets are

compiled with respect to the basic resistance and load variables, and also the load

statistics are computed for many different cities. Additionally, more recent and up

to date codes are taken into consideration in this dissertation. The most significant

difference is the fact that Kömürcü (1995) has considered only reinforced concrete

beams in the flexural failure mode whereas in this study, reinforced concrete beams,

columns and shear walls in the flexural and shear failure modes as well as

reinforced concrete columns in the combined action of flexure and axial load failure

mode are taken into consideration.

1.3 AIM AND SCOPE OF THE STUDY

This study aims at developing a set of load and resistance factors for the design of

reinforced concrete structural elements by considering the local conditions of

Turkey and by utilizing probabilistic methods. Resistance and load parameters are

assumed as random variables in this study. The data necessary for the assessment of

these parameters are collected in Turkey and are unified with the data published in

the international literature.

In this study, structural load effects resulting from dead, live, wind, snow and

earthquake loads are evaluated. For calibration purposes, the ratios of mean to

nominal load values are determined. Probability based resistance criterion for the

design of reinforced concrete beams, columns and shear walls in the flexural and

shear failure modes as well as the design of columns in the combined action of

flexure and axial load failure mode are examined by using the First Order Second

Moment Method (FOSM). In order to propose a set of load and resistance factors,

the Advanced First Order Second Moment Method (AFOSM) is adopted as the

structural reliability model.

The present building codes in Turkey were developed without taking various

sources of uncertainties into consideration in a direct way. In this study, various

sources of uncertainties associated with the load and resistance parameters are

analyzed and quantified based on the data available in Turkey and in the foreign

literature. The proposed criterion and the resulting load and resistance factors will

form a rational basis for the reflection of the effects of uncertainties directly on the

design.

After this chapter, the relevant structural reliability models and a probabilistic

method to be used for the assessment of uncertainties are introduced in Chapter II.

In Chapter III, the mean to nominal ratios and the total variabilities of basic

resistance variables, namely compressive strength of concrete, yield strength of

reinforcing steel bars and dimensions of the structural elements are quantified using

the local data and reported results. In Chapter IV, using the values proposed in

Chapter III, the mean to nominal ratios and the total uncertainties of resistances for

different failure modes of three basic types of reinforced concrete structural

members, namely beams, columns and shear walls, are computed within the

framework of structural reliability. In Chapter V, the load modeling is carried out

with the published data in the literature and the local data collected in Turkey. In

Chapter VI, reliability based resistance criterion for the failure modes of reinforced

concrete structural members are examined, and target reliabilities are selected. In

Chapter VII, a set of new load and resistance factors for different failure modes of

beams, columns and shear walls are computed according to AFOSM method by

using two computer programs prepared for this purpose. Finally, the summary and

conclusions of this dissertation are provided in the last chapter.

In Appendix A, statistical parameters of 7 and 28 day compressive strength data

according to concrete class and region are given. Appendix B displays the statistical

parameters of reinforcing steel bars used in Turkey. In Appendices C, D and E, the

meteorological data related to annual maximum snow depth, annual maximum wind

speed and daily maximum wind speed for 12 different locations are given,

respectively. The reliability index values for load combinations considered in this

study are displayed in graphical forms in Appendix F. Lastly, in Appendix G,

figures showing the variation of safety levels corresponding to the recommended

load and resistance factors are given.

CHAPTER 2

STRUCTURAL RELIABILITY MODELS

2.1 THE CLASSICAL RELIABILITY THEORY

The problems related to the reliability of structural engineering systems may be

considered as a problem of capacity against demand. When the safety of structure is

considered, the strength of the structure, R, should be adequate to resist the lifetime

maximum applied load, S. If the reliability of a single member is taken into account

for introducing the basic concepts of the structural reliability theory, the member

failure occurs when "R<S", or equivalently when "M<0", where M is the safety

margin (M=R-S). The probability of failure, Pf, is defined by the following

relationship:

Pf = P(R≤S)=P(R-S≤0)=P(M≤0) (2.1)

where P (.) represents the probability of occurrence of the event in brackets.

In the case of independent and normally distributed R and S with mean R and S ,

standard deviation, σR and σS , the failure probability is given in Eq. (2.2):

−φ−=

σφ−=

M1P (2.2)

where φ(.) is the probability distribution of the standard normal variate and M is the

mean value of the safety margin.

However, in practice, resistance (R) and load (S) are dependent on other basic

variables, e.g. the material properties, geometrical quantities and load effects.

2.2 FIRST ORDER SECOND MOMENT METHOD

The reliability of a structure can be determined as the probability of operating its

proposed function. In order to obtain a generalized formulation, a mathematical

model is first derived concerning the resistance and load variables according to the

limit state under consideration (Ellingwood et. al., 1980). Let M=g( Χ~ )=g(Xi,...,Xn)

be the limit state function, in which Χ~ =(Xi,...,Xn) is the vector of basic variables

concerning the structure. The failure surface can be described by Eq. (2.3). In this

equation, positive values of g indicate safe sets of variables (the safe region) and

non-positive values of g indicate unsafe sets of variables (the failure region) (Toft-

Christensen and Baker, 1982).

0)X,...,X(g)X~

(g n1 == (2.3)

If the safety margin M is linear and basic variables are normal, the reliability index

β1 is defined by:

β1 = µM / σM (2.4)

where β1 is a nonparametric measure of safety, µM and σM are the mean and

standard deviation of M, respectively. The higher the value of β1 is, the safer the

structure will be.

If the safety margin M is linear in the basic variables X1,…,Xn as expressed below:

M=a0+a1.X1+…an.Xn (2.5)

where, a0, a1,…,an are constants, then the mean and variance of M can be obtained

from the following equations:

µM= a0+a1.µ1+…an.µn (2.6)

σM2=a1

2.σ12+…+an

2.σn2+∑ ∑

= = ≠1 1i j ji

ρij.ai.aj.σi.σj (2.7)

Here, the last term is related to the correlation between any pair of basic variables

and ρij is the correlation coefficient between Xi and Xj.

For the case of a linear safety margin, M, the calculation of the mean safety margin

(µM), the standard deviation of safety margin (σM) and also the reliability index (β1)

is easy. In the case of nonlinear failure functions, the mean value method and

advanced methods are used, which are explained briefly in the following sections.

2.2.1 Mean Value Method

When the safety margin M is nonlinear in Χ~ =(X1,…,Xn), then approximate values

for µM and σM can be obtained by using a linearized safety margin. The safety

margin can be expressed by the following formula:

M =g( Χ~ )≅g (X1,X2,...,Xn) (2.8)

If Eq. (2.8) is expanded in a Taylor series about ((X1,...,Xn) =(µ1,...,µn) and if only the

linear terms are kept, then:

M =g( Χ~ )≅ g(µ 1,…,µ n) + )(

µ−Χ

∂∑

where 0

∂ is evaluated at (µ 1,…,µ n).

Approximate values ofµ M and σM are determined by:

µ M ≅ g(µ 1,…,µ n) (2.10)

σ2M= ),(Cov

0j1i 1j 0i

∂∑∑

(2.11)

where Cov(Xi, Xj) is the covariance between Xi and Xj.

Ellingwood et al. (1980) stated that the mean value method has the following two

basic shortcomings:

-If the failure function is nonlinear, significant errors may be introduced at increasing

distances from the linearized point by neglecting higher order terms.

-The mean value method fails to be invariant to different mechanically equivalent

formulations of the same problem. In effect, this means that reliability index depends

on how the limit state is formulated. This is a problem not only for nonlinear forms

of failure functions but even in certain linear forms, e.g., when the loads counteract

one another.

2.2.2 Advanced First Order Second Moment Method

Due to shortcomings in the FOSM and the mean value methods, Hasofer and Lind

(1974) proposed a new reliability index denoted by (β2). The process of calculating

β2 is generally referred as the advanced first-order second-moment (AFOSM)

method.

In this method, first the basic variables Xi's are converted into the standardized

variables, Zi's, including zero means and unit variances, as shown below:

Χ−Χ= , ni ,...,2,1= (2.12)

The failure surface in the X-coordinate system is mapped into a failure surface in

the z-coordinate system. The failure surface in the z-coordinate system divides the z

space into a failure region and a safe region. Reliability index β2 is defined as the

shortest distance from the origin to the failure surface in the z-coordinate system.

The design point is defined as the point having the shortest distance to the origin on

the failure surface. In Figure 2.1, the reliability index, β2, and the design point are

illustrated for the case of two basic variables.

The definition of reliability index, β2 can be formulated as:

22 min

iizβ (2.13)

Figure 2.1 Reliability Index β2 (from Thoft-Christensen and Baker, 1982)

When the failure surface is nonlinear, the searching of the design point and the

calculation of the reliability index can be carried out by the iterative algorithm.

According to the iterative procedure, the design point (z*i,…,z*

n) on the failure

surface is determined by solving the following system of equations (Thoft-

Christensen and Baker, 1982):

( ) 2/12i

∑ ∂∂

∂∂−=α , i=1,2,…,n (2.14)

2iiZ βα=∗ (2.15)

0)z,...,z(g ni =∗∗ (2.16)

where αi’s are directional cosines that minimize β2. The derivatives are evaluated at

the design point. Since the computed design point is related to standardized

coordinate system, the basic variables on the design point must be converted to

original variable space. This procedure can be carried out by using the following

formulation:

).1( iiii Ωβα−Χ=Χ∗ (2.17)

where iΩ is the coefficient of variation reflecting the total uncertainty in Xi. The

load and resistance factors, γi, corresponding to a prescribed reliability index, β,

may then be determined by the following expression:

ii (2.18)

where Χ′ is the nominal or design value of the ith load or resistance parameter

specified in the code ( Ellingwood et al., 1980)

If all of the Xi’s are independent, normally distributed random variables and the

failure function g is linear in *iΧ , then the reliability index, which may be related to

the probability of failure (Pf), can be determined by using FOSM method described

above. This relationship between β and Pf is given in Eq. (2.19):

)P1( f1 −φ=β − , )(1Pf βφ−= (2.19)

2.3 MODELING AND ANALYSIS OF UNCERTAINTIES

The assessment of safety and reliability in the probabilistic approach first of all

requires the quantification of uncertainties, which can be achieved by the

assessment of standard deviation, variance or coefficient of variation (c.o.v.) of

basic variables. In the evaluation of structural reliability, it is highly important to

quantify the uncertainties as accurately as possible. The model for each limit state

contains a specified set of basic variables, e.g. material and geometrical properties,

physical quantities that characterize actions and environmental loads. The

evaluation of reliability must include the uncertainties related to these basic

variables as well as the prediction models.

Uncertainties in civil engineering problems can be divided into two main groups:

aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty is due to

inherent variability and this type of variability, which is a state of nature, cannot be

controlled or reduced. On the other hand, epistemic uncertainty is due to lack of

knowledge and can be reduced by additional information and data. Prediction,

modeling and statistical errors are sources of epistemic uncertainty. The

uncertainties related to discrepancy between laboratory conditions and in-situ

conditions are examples for prediction uncertainty. Modeling uncertainty is owing

to simplifying assumptions, indefinite boundary conditions on unknown effects of

other variables that are not included in the model. Statistical uncertainty is due to

the limited number of observations utilized in the estimation of the mean of a basic

variable. Engineering judgment has an important role in reducing epistemic

uncertainties. Comprehensive uncertainty analysis requires inputs from experience-

based professional engineering judgments.

The different sources of uncertainties can be modeled by using the following

relationship for a basic variable (Ang and Tang, 1984):

iiiΧNΧ = (2.20)

where:

iΧ : the true (but unknown) value of the ith basic variable

iΝ : a random correction factor to account for epistemic uncertainties

iΧ : the model used to estimate Xi

The mean of Ni will be denoted by iΝ and its coefficient of variation byi

X∆ , which

respectively quantify the mean bias and epistemic uncertainty. Χ is the mean of iΧ

and its coefficient of variation is denoted by iΧδ , which also quantifies the inherent

variability, i.e. aleatory uncertainty. According to FOSM method, the total

uncertainty can be formulated as fallows:

∆+δ=Ω (2.21)

If Ni is expressed as the product of component correction factors as

in2i1iiN,...,NNN = , then based on FOSM method the following relations can be

written for i

Ν and iΧ

∆ , assuming all Ni’s mutually independent:

in2i1ii ,...,ΝΝΝ=Ν (2.22)

in2i1ii

X,..., ∆++∆+∆=∆ (2.23)

CHAPTER 3

QUANTIFICATION OF UNCERTAINTIES RELATED TO RESISTANCE PARAMETERS

3.1 CONCRETE

The quality control of concrete is quite important for achieving safety in reinforced

concrete structures. The following properties can be taken into account for the

quality of concrete from the viewpoint of mechanical characteristics:

-Compressive strength,

-Durability against physical and chemical effects,

-Time dependent deformations, i.e. creep and shrinkage.

Furthermore, the following properties can be sought for concrete produced in some

circumstances in addition to the three basic properties given above:

-Impermeability,

-Abrasion resistance,

-Unit weight,

-Resistance in flexure and tension.

The most appropriate way to evaluate the quality of concrete is through the

statistical analysis of data. Taking into consideration the properties listed above, the

mean value of the samples obtained must be high, while the coefficient of variation

must be as low as possible.

There are a number of factors that affect the quality of concrete, and these factors

can also affect each other considerably. To obtain good quality concrete, the

following recommendations can be made:

-The materials like sand, gravel, cement and admixtures, which constitute

concrete, should be of good quality.

-Concrete should be a carefully dosed mixture of cement, aggregate, water

and admixtures for the class of concrete desired.

-The technology used should be good.

-Knowledge and ability of personnel who performs actual production should

be sufficient to obtain good quality concrete in the stages of production.

-The techniques of production and maintenance should be arranged for the

concrete class selected, and the environmental conditions should be adjusted in the

application of these techniques.

In common construction sites in Turkey, it is well known that the conditions

required for high quality production were not efficiently taken into account until the

last few years and the issue of production of good quality concrete was not given

notable importance. Due to irresponsibility, unconsciousness and lack of control

and supervision in production of concrete, poor quality of production was generally

observed. Even for a concrete class sampled from the same construction site, it was

a reality that there were significant differences among the concrete samples

produced.

One of the aims in this section is to shed some light upon the quality of concrete

production in Turkey. The most important property that affects the quality of

production is compressive strength, which contributes to other properties

proportionately. Therefore, the quality control of concrete is examined by using the

compressive strength tests utilizing the standard cube specimens (Dislitas et al.,

2006). Considering the compressive strength of concrete and its variation according

to regions and years, the quality of concrete production is investigated from a

statistical point of view.

3.1.1 Evaluation of Data

Laboratory test results of 150x150x150 mm cube specimens, which are obtained

from different laboratories located in different cities of Turkey, form the database

considered in this study. The data that belong to 2000, 2001, 2002, 2003, 2004 and

2005 years are analyzed comprehensively. Besides, the data that belong to earlier

years are also taken into consideration for the sake of comparison.

The data used in this study, which are sampled from Ankara, Istanbul, Konya,

Corlu, Trabzon, Erzurum, Kayseri, Samsun, Bursa, Izmir, Gaziantep, Denizli,

Antalya and Malatya regions are obtained from the following institutions:

-The laboratories of Turkish Chamber of Civil Engineers (IMO) in Istanbul,

Konya and Antalya offices,

-The materials laboratory of Middle East Technical University (METU)

Department of Civil Engineering,

-The materials laboratory of Istanbul Technical University (ITU)

Department of Civil Engineering,

-The materials laboratory of Selcuk University (SU) Department of Civil

Engineering,

-The laboratories of Ministry of Public Works and Settlement in Malatya,

Trabzon, Erzurum, Kayseri, Samsun, Bursa and Gaziantep offices,

-The laboratory of General Directorate of State Hydraulic Works (DSI)

Konya office,

-The laboratory of Techno-test firm,

-The laboratory of Vetas construction materials firm,

-The laboratory of Armada concrete and construction materials firm.

In the following tables (Tables 3.1-3.3), an idea can be obtained about the quality of

concrete produced in Turkey. Just a certain building firm or a ready mixed concrete

production plant is not taken into consideration, and compressive strength test

results used are obtained from different construction sites. Since compressive

strength test results are not evaluated for each construction site separately, high

values of coefficient of variation are obtained for Istanbul region. However, in

Ankara, Konya, Corlu, Trabzon, Erzurum, Kayseri, Samsun, Bursa, Izmir,

Gaziantep, Denizli, Antalya regions, the values of c.o.v. are obtained for each

construction site individually. Therefore, all of the regions except Istanbul are taken

into account during the calculation of c.o.v. for Turkey, while all regions are

considered during the calculation of mean values of concrete classes. The results of

data analysis are summarized in Tables 3.1-3.3.

Statistical parameters of 7 day and 28 day compressive strength data are given

according to regions mentioned above in Appendix A. In Tables 3.1-3.3 and

Appendix A, fck is the nominal value of the concrete compressive strength and

“number of the values under the limit” refers to the number of samples whose

compressive strength is less than “fcmin= fck-4” N/mm2, as specified in TS EN 206-1

(2002).

As indicated in Table 3.1, the comparison of the mean compressive strength values

for the years 1994-1995 and the subsequent years covering the interval between

2000-2005, reveals that in Turkey, the mean compressive strength has increased

considerably over the years. Comparing the overall weighted average compressive

strength values it can be said that the 28 day compressive strength is 1.23 times

higher than the 7 day strength, as it is seen in Table 3.2 and Table 3.3. It is also to

be noted that the c.o.v. of the 7 day compressive strength (0.132) is 1.26 times more

than the c.o.v. of the 28 day compressive strength (0.105).

Table 3.1 Statistical parameters of compressive strength data according to years for

Turkey

Number of samples

(N/mm2)

Coefficient of variation

Number of values under the limit

Percentage of values under the limit (%)

94/95 417 20.60 --- 58 13

2000 732 26.97 0.142 40 5.46

2001 535 30.97 0.107 23 4.30

2002 465 31.21 0.104 10 2.15

2003 644 30.78 0.131 36 5.59

2004 1283 28.87 0.123 30 2.34

2005 615 29.97 0.120 24 3.90

concrete class for Turkey

Concrete

Number of samples

fck, cyl

(fck,cub)

(N/mm2)

C14 137 14 (18) 20.04 0.143 1 0.83

C16 755 16 (20) 25.11 0.144 13 1.73

C18 739 18 (22) 25.82 0.120 23 3.11

C20 5817 20 (25) 28.46 0.104 118 2.7

C25 2767 25 (30) 32.48 0.100 53 2.81

C30 870 30 (37) 40.07 0.079 14 2.47

Overall 11085 29.87 0.105 222 2.65

concrete class for Turkey

Concrete Class

Number of samples

fck, cyl (fck,cub)

(N/mm2)

Mean (N/mm2)

C14 24 14 (18) 14.32 0.159

C16 418 16 (20) 20.26 0.154

C18 538 18 (22) 18.69 0.153

C20 3091 20 (25) 23.04 0.132

C25 1701 25 (30) 26.85 0.129

C30 463 30 (37) 32.63 0.100

Overall 6235 24.20 0.132

3.1.2 Uncertainty Analysis of Concrete Compressive Strength

After conducting a statistical analysis on the collected data, the mean value of cubic

compressive strength of overall concrete is obtained as 29.87 N/mm2 and c.o.v. of

compressive strength as 10.5% by considering the whole data set (Table 3.2). If the

cubic compressive strength of overall concrete data is converted to the standard

cylinder strength value, then cf and δfc are found to be 24.87 N/mm2 and 10.5 %,

respectively. Here, cf denotes the compressive strength and δfc stands for the c.o.v.

of fc, which is a measure of basic (inherent) variability in the compressive strength

of concrete. When the most common construction conditions in Turkey are

considered, these values can be taken directly as representative of whole Turkey.

On the other hand, in practice, the strength of concrete in a structure may differ

from its specified design strength. The major sources causing these differences are

variations in material properties, proportions of concrete mix, variations in mixing,

transporting, placing and curing methods and variations in testing procedures

(Mirza et al., 1979).

Some factors, which cause additional uncertainty besides inherent variability, will

be considered in the following paragraphs. Mostly, since there is no adequate local

information, these factors are quantified within the scope of the international

literature.

The strength of concrete in a structure is lower than the strength of control cylinder

molded from the same concrete. This difference results from the effects of different

curing and placing processes, the segregation of concrete in deep members, the

effects of difference in size and shape and the effects of different stress conditions

in the structure and in the specimens. Due to these factors, the actual core strength

of concrete is lower than the laboratory measured strength in most of the situations.

The average ratios of core strength to standard cylinder strength reported in

different studies varied within the range of 0.74 and 0.96 with an overall average

value of 0.87 (Mirza et al., 1979). Likewise, in another study conducted by

Ellingwood and Ang (1972), this ratio was stated to range from 0.83 to 0.92. In

order to compensate for the difference between the in-situ actual strength and the

strength obtained from control cylinders, a correction factor, N1, will be introduced.

Based on the reported ranges, the mean value of the corresponding correction

factor, 1N , is taken as 0.86, which is the average of the above ranges. The c.o.v. of

N1 is denoted by ∆1. Ellingwood and Ang (1972) recommended a value of 0.16 for

∆1. In the study performed by Mirza et al. (1979), it was proposed that ∆1=0.1.

Here, the value of ∆1 will be taken to be 0.13 as the average of these two values.

The apparent strength of concrete rises as the rate of loading increases. The increase

in strain with time because of the micro cracking and creep causes the decrease of

observed strength of concrete. To account for this effect, the correction factor, N2,

with a prediction uncertainty, ∆2, is introduced. Mirza et al. (1979) used the

following empirical relationship to express the mean value of N2 in their study.

2N =0.89(1+0.08 log (R)) (3.1)

where R is rate of loading (psi/sec). Using the value of 1 psi (6.895 kN/m2 per

second) for R, 2

N is found to be 0.89. Kömürcü (1995) suggested the value of 0.88

N with no prediction uncertainty, i.e. ∆2=0. Based on other studies, Mirza et

al. (1979) stated that the prediction uncertainty associated with N2 can be ignored,

and if the rate of loading, which is approximately 234.43 kN/m2 per second for

standard cylinder test, is decreased to 6.895 kN/m2 per second, then apparent

strength of concrete decreases by a value of 12%. In this study, 2

N is taken as 0.88

which is a conservative estimate, and prediction uncertainty, ∆2 is neglected.

Thirdly, the specimens are obtained from a special concrete batch rather than

obtaining them randomly from the actual mix. Standard testing procedures may not

be applied; for example, testing on the specimens may not be carried out at the

correct time by properly calibrated machines. In other words, due to human factor, a

prediction error may occur. As a result, to be on the safe side, a correction factor, N3

is introduced with a mean of 0.95 and a prediction error, ∆3 of 0.05 (Kömürcü,

1995).

The in-situ value of compressive strength of concrete can be modeled according to

Eq. (2.20) as follows:

cfc f.Nfc

= (3.2)

where fc is the in-situ value of compressive strength of concrete, cf is the

compressive strength of the cylindrical specimens tested at the laboratory, and

fcN is overall bias in fc.

The overall mean bias in fc is computed as 321fc N.N.NN = =0.86x0.88x0.95=0.72

and the mean value of the in-situ compressive strength of concrete will be

cf =0.72x24.87=17.87 N/mm2. Here, C14, C16, C18, C20, C25 and C30 concrete

classes, which are given in TS 500 (2000), are taken into consideration. The

weighted average value of concrete class used in Turkey, which is obtained from

the third column of Table 3.2, is found to be 21.55 (in other words, the weighted

average concrete class is “C21.55”). Regarding this weighted average, the nominal

compressive strength is taken as 5.1

55.21=14.37 N/mm2. Hence, the ratio of mean to

nominal compressive strength, i.e. c

90.17 will be equal to 1.25.

On the other hand, the total prediction uncertainty due to these three sources of

uncertainty will be 222f 05.0013.0

c++=∆ =0.14. The inherent variability in

compressive strength based on laboratory test results and the total prediction error

are combined to find the total variability, which becomes

18.014.0105.0 22

=+=Ω . In a similar study, the total uncertainty was taken as

0.21 by Kömürcü and Yücemen (1996). Likewise, Real et al. (2003) used three

different values for the overall variability of concrete in their study as 0.10, 0.15,

and 0.20. The value computed here is consistent with the values given in these

previous studies.

The normal distribution was used for concrete compressive strength by the majority

of researchers (Mirza et al., 1979). Yücemen and Gülkan (1989), Kömürcü (1995)

and Nowak and Szerszen (2003a) also used the normal distribution for the

compressive strength of concrete. In this study, a statistical analysis of collected

data based on the Chi-Square and Kolmogorov- Smirnov tests also supported the

normal distribution at a significance level α=0.05; consequently a normal

distribution for the compressive strength of concrete is used herein.

3.2 REINFORCING STEEL BARS

Turkish iron and steel sector, the base of which was established in the 1930’s, plays

an important role in the industrialization and development of Turkish economy. Iron

and steel production was first started in Kirikkale, which is now known as

Mechanical and Chemical Industry Corporation (MKEK). The first integrated plant,

Karabük Iron and Steel Works (KARDEMIR) began to operate in Karabük in 1937.

In order to meet the demand for flat products, the second integrated plant, Eregli

Iron and Steel Works (ERDEMIR) started production in 1965. In 1977, Iskenderun

Iron and Steel Works (ISDEMIR), Turkey’s third integrated steel mill, came on line

to meet the demand for long products and semi-finished products. The Turkish iron

and steel industry has shown great progress in the last fifteen years in terms of

quality and capacity and has been one of the growing iron and steel industries in the

world. Currently, Turkish iron and steel sector ranks 11th among the 64 steel-

making countries in the world and 3rd in Europe. In 2003 steel products were

exported to more than 130 countries in the world (Turkish Iron and Steel Producers

Association, 2004).

Figure 3.1 The map showing the locations of iron and steel plants founded in

Turkey (from http://www.dcud.org.tr/indextur.htm)

In Figure 3.1, the locations of iron and steel plants founded in Turkey are shown.

Since steel products are exported to more than 130 countries in the world, most of

these steel and iron plants prepare their products according to different standards as

specified by different countries, and some of these steel products are also sold in the

domestic market. Furthermore, Turkey also imports steel from different countries.

Therefore, the quality of steel used in construction sites is affected negatively in

terms of coefficient of variation, since there are a lot of different types of steel in

the domestic market. Some country standards concerning reinforcing steel bars are

given in Table 3.4.

Table 3.4 Different country standards related to reinforcing steel bars

(from Özsoy, 2001)

Country Standard Class

Minimum Yield Strength ( N/mm² )

Minimum Ultimate Limit Strength ( N/mm² )

Yield/ Ultimate Strength

Minimum Elongation ( % )

Turkey TS 708 (1996)

III a IV a

420 500

500 550

1.1 1.08

12 (Ø8-Ø28) 10 (Ø32-Ø50)

England BS 4449 (1997)

Gr 460B 460 - 1.08 14

Germany DIN 1986 BSt 420 S BSt 500 S

420 500

500 550

1.05 1.05

Norway

NS 3576-2 (1997) NS 3576-3 (1997)

B500B B500C

500 500

1.08 1.15

ASTM A615 / A616M (1996)

Gr 40 Gr 60 Gr 75

300 420 520

500 620 690

11 ~ 12 7 ~ 9 6 ~ 7

Within the scope of this study, the local data on reinforcing steel bars are obtained

from the production reports of the following steel and iron plants:

-Habas iron and steel plant,

-Icdas iron and steel plant,

-Ekiciler iron and steel plant,

-Colakoglu iron and steel plant,

-Egecelik iron and steel plant,

-Kroman iron and steel plant,

-Yesilyurt iron and steel plant.

3.2.1 Evaluation of Data

In Turkey, BCIII(a) reinforcing steel bars are widely used. Therefore, the test

results on 24875 BCIII(a) reinforcing steel bar specimens with different bar sizes

ranging from 8 mm to 26 mm are obtained from the test reports. After the analysis

of data, the mean and c.o.v. of yield strength, ultimate strength and elongation

values are determined for each steel and iron plant. Additionally, the statistical

parameters of yield strength, ultimate strength and elongation based on civil

engineering material laboratories of ITU, METU and SU are investigated. The test

reports of university laboratories do not belong to a specific steel and iron plant, i.e.

the reinforcing steel bars tested in university laboratories are obtained from

different firms. The values based on civil engineering material laboratories of only

ITU and METU are arranged according to years. The results are presented in Tables

3.5 to 3.8, and the detailed results are given in Appendix B. In Table 3.8 and in

Appendix B, “number of the values under the limit” refers to the number of

reinforcing steel bars yield strength of which is less than “fy= 420 N/mm2”, as

specified in TS 708 (Steel Bars for Concrete).

Table 3.5 Mean value and c.o.v. of yield strength of BCIII(a) reinforcing steel bars

produced by different steel and iron plants in Turkey

Plant Habas Icdas Ekiciler Colakoglu Egecelik Yesilyurt Kroman Overall

Number of samples

9619 1400 2390 530 1073 3024 1673 19709

Yield strength (N/mm2)

530.01 516.79 480.94 473.63 489.71 464.4 460.71 503.46

0.034 -- 0.047 0.048 0.052 0.036 0.035 0.038

Table 3.6 Mean value and c.o.v. of ultimate strength of BCIII(a) reinforcing steel

bars produced by different steel and iron plants in Turkey

Plant Icdas Ekiciler Colakoglu Egecelik Kroman Yesilyurt Overall

Number of samples 1400 2390 530 1073 1673 3024 10090

Ultimate strength (N/mm2) 621 563.81 617.95 631.45 675.68 593.1 609.1

Coefficient of variation -- 0.047 0.065 0.057 0.040 0.043 0.045

Table 3.7 Mean value and c.o.v. of elongation of BCIII(a) reinforcing steel bars

produced by different steel and iron plants in Turkey

Plant Icdas Ekiciler Colakoglu Egecelik Kroman Yesilyurt Overall

Number of samples 1400 2390 530 1073 1673 3024 10090

Elongation (%) 18.32 18.78 19.25 19.02 23.69 21.7 20.46

-- 0.076 0.094 0.097 0.105 0.081 0.087

Table 3.8 Statistical parameters of yield strength of BCIII(a) reinforcing steel bars according to years

Years Number of samples

Required yield strength (N/mm2)

Mean value of yield strength (N/mm2)

Standard deviation (N/mm2)

1998-1999 846 420 491.89 72.31 0.147 122 14.4

2000 877 420 490.16 58.82 0.12 84 9.6

2001 911 420 502.16 62.26 0.124 64 7

2002 897 420 498.35 47.84 0.096 35 3.9

2003 770 420 492.78 59.13 0.12 49 6.4

2004 532 420 491.06 44.19 0.09 25 4.7

Overall 4833 420 494.76 58.38 0.118 379 7.8

3.2.2 Uncertainty Analysis of Reinforcing Steel Bars

The sources of variation in the yield strength and the ultimate strength of steel bars

are listed as follows:

-Variation in the strength of material itself,

-Variation in the cross-sectional area of the bar,

-Effect of rate of loading,

-Effect of bar diameter on mechanical properties of bars,

-Effect of the strain at which yield is defined.

The variability of yield strength of reinforcing steel bars depends on the nature and

source of the data. The variation in the yield strength within a single bar is

comparatively small, while the in-batch variation is insignificantly higher.

However, the variability of samples obtained from different batches and sources

may be high due to the fact that the quality measures change for different

manufactures and different bar sizes. When the data are taken from different

producers, an increase in coefficient of variation from 5% to 8% is observed for

individual bar sizes (Mirza and Macgregor, 1979). In the literature related to yield

strength of reinforcing bars, the basic variability in general ranges from 1% to 4%

for individual bar sizes supplied that the bars are produced by the same

manufacturer (Kömürcü, 1995). However, these values change from 2% to 7% for

individual bar sizes in Turkey. Here, the basic (inherent) variability in the

reinforcement yield strength for individual bar sizes is taken to be 3.8% as an

overall value of the data obtained from steel and iron plants, i.e. δfy=0.038 (Table

The observed strength of a test specimen is affected considerably by the strain rate

and the rate of application of the load: the lower the rate of loading, the lower the

apparent strength. Since tests on reinforcing steel bar specimens are generally

performed at much greater strain rates than those encountered in structures

subjected to static loads, they are inclined to overestimate the yield strength (Mirza

and Macgregor, 1979). Ellingwood and Ang (1972) estimated the mean bias, 1N ,

accounting for this effect as 0.9. On the other hand, the prediction error, ∆1, due to

this discrepancy was assumed to be negligible (Kömürcü, 1995). In this study, the

mean bias is also taken as 0.9 and the prediction error is neglected.

Yield strength of reinforcing steel bars may be determined corresponding to upper

or lower yielding points or at a specific strain. These upper or lower yielding points

and specific strain values affect the yield strength. Mirza and Macgregor (1979) did

not include this effect in their study. Ellingwood and Ang (1972) used the value of

5% of prediction error in order to account for this effect. Kömürcü (1995) suggested

a value of 9% for the associated prediction error. Here, prediction error, ∆2, is taken

to be 5% as an average of these values, and a correction factor, N2, is introduced

with a mean value of 1.00.

On the other hand, the reality that most of the structures are built with reinforcing

steel bars produced in different iron and steel plants in Turkey has to be considered

as a prediction uncertainty. We mainly have two types of data related to reinforcing

steel bars, first of which are acquired from iron and steel plants separately. The

second type of data is obtained by test reports of reinforcing steel bars evaluated at

university laboratories. The average total inherent variability in the yield strength of

reinforcing steel bars of different steel and iron plants is computed to be 11.8 % and

the average inherent variability, i.e. within group variability of steel and iron plants

is found to be 3.8 % as an overall value. In connection with this study, the

maximum value of prediction uncertainty for structures which are built with

reinforcing steel bars of different iron and steel plants will be 0.112 based on Eq.

(2.21); that is, the maximum value of group variability between plants in addition to

within group variability is 11.2 %. If the structure is built with reinforcing steel bars

produced by only one plant, this value can be taken as 0. Here, the prediction error,

∆3, is taken to be 0.056 as an average value of 0 and 11.2%, and 3N will be taken

as 1.00.

Mirza and Macgregor (1979) stated that the use of different bar diameters like Φ8,

Φ28 did not have a significant effect on the yield strength. At the end of data

analysis, it is seen that there is no significant difference among bar diameters from

the point of view the yield strength of reinforcing steel bars. Therefore, the effect of

bar diameter on yield strength is neglected.

After conducting a statistical analysis on the collected data, the yield strength is

computed to be 501.37 N/mm2 as a weighted average value obtained from the data

supplied by iron and steel plants and university laboratories. In connection with this

study, the overall mean bias is computed as 321fy N.N.NN = =0.9x1x1=0.90.

Using this value, the mean yield strength will be equal to 0.9x 501.37= 451.23

N/mm2. The nominal yield strength for BCIII(a) is 365 (420/1.15) N/mm2 as

given in TS 500 (2000). Consequently, the ratio of mean to nominal yield strength

is 1.24 (i.e. fy ff ′ =451.23/365=1.24).

Kömürcü and Yücemen (1996) assigned a value of 0.14 for the total variability of

the yield strength of reinforcing steel bars. Real et al. (2003) stated that the total

variability in reinforcing steel bars change from 0.05 to 0.10 in their study. In this

study, the overall prediction error for reinforcing steel bars is computed to be

08.0)056.005.00( 222yf =++=∆ . By combining the inherent variability and

overall prediction error, the total variability in the yield strength of reinforcing steel

bars is computed as 09.0)08.0038.0( 22yf =+=Ω .

The sources of variation in the ultimate strength of reinforcing bars are the same as

those causing variation in the yield strength (Mirza and Macgregor, 1979). By using

the data values obtained from iron and steel plants and university laboratories, the

weighted average of the ultimate strength is computed as 615.96 N/mm2. The

overall mean bias of ultimate strength of reinforcing steel bars is computed as

321fu N.N.NN = = 0.9x1x1=0.90 and the mean ultimate strength will be equal to

0.9x 615.96= 554.36 N/mm2. The nominal ultimate strength for BCIII(a) is 435

(500/1.15) N/mm2 as given in TS 500 (2000). The ratio of mean to nominal ultimate

strength is 1.27 ( uu ff ′ =554.36/435=1.27). For ultimate strength, the overall

prediction error is computed to be 08.0)056.005.00( 222uf =++=∆ . Here, the

basic variability in the reinforcement ultimate yield strength for individual bar sizes

is taken as 4.5 %, which is a weighted average value obtained from steel and iron

plants (Table 3.6). Combining the inherent variability and overall prediction error of

ultimate strength, the total variability in the ultimate strength of reinforcing steel

bars is calculated to be 09.0)08.0045.0( 22uf =+=Ω .

As for the distribution of the yield strength of reinforcing steel bars, Kömürcü

(1995) used the lognormal distribution for reinforcing steel bars. Nowak and

Szerszen (2003a) and Topcu and Karakurt (2006) recommended that normal

distribution is suitable for the reinforcing steel bars in their study. Here, the normal

distribution will be used for the yield strength of reinforcing steel bars. The

statistical analysis of the collected data also supports this selection.

3.3 DIMENSIONS

The dimensional characteristics of reinforced concrete members constructed at the

site sometimes do not match with those calculated in the design stage of the

structure. These geometrical discrepancies and imperfections are generally observed

in certain dimensional properties which are listed below:

-the cross-sectional shape and dimensions,

-the vertical and horizontal position of columns, beams, floors and

foundations,

-the levels of reinforcing bars, ties and stirrups.

Geometrical discrepancies may occur during different stages of the construction

process, which mainly depend on shape, size and quality of forms used. Concreting

and vibrating operations generally create the geometrical discrepancies.

Additionally, the strength of concrete, the dimension of orientation (depth, width)

and the position of the cross-section (mid-span, support) may affect geometrical

deviations. For these reasons, the degrees of geometrical discrepancies vary from

country to country, region to region and even from structure to structure, and these

differences are mainly dependent on the quality of construction techniques,

equipment and training of the site personnel.

Udoeyo and Ugbem (1995) used normal and lognormal distributions for the errors

on the dimensions in their study. On the other hand, a number of researchers have

recommended the normal distribution (Mirza and MacGregor, 1979). Yücemen and

Gülkan (1989) and Kömürcü (1995) also used the normal distribution in their

studies, which were conducted for Turkey. Since it is simple to use normal

distribution as the probability model, the normal distribution is used here to

represent the distribution of errors pertaining to dimensions of reinforced concrete

members, consisted with the previous studies mentioned above.

3.3.1 Data Collection and Analysis

Unfortunately, almost no local study concerning the geometrical discrepancies has

been performed in Turkey. Furthermore, the process of collecting and reporting data

for geometrical discrepancies has not been standardized. Therefore, the comparison

of the results of measurements is difficult in order to derive quantitative conclusions

for Turkey. As stated before, engineering judgment plays a critical role in

quantifying the epistemic uncertainties. Using the idea and inputs obtained from

experience-based professional engineering judgment, some additional prediction

uncertainties (epistemic uncertainty) related to the dimensions can be quantified.

Moreover, epistemic uncertainties in beam dimensions are compared to epistemic

uncertainties in dimensions of other structural members, within the scope of the

engineering judgment in cases where there is a lack of information.

Accordingly, the results of the uncertainty analysis mentioned above on

dimensional properties will be compared against the results reported in other

countries. In order to quantify the geometrical discrepancies and uncertainties as to

dimensions of reinforced concrete members, the data belonging to aleatory

uncertainty are obtained by measuring the dimensions of structural members after

the removal of forms. On the other hand, additional prediction uncertainties having

relatively small values (in terms of c.o.v) in the dimensions must be estimated. The

main characteristics of these additional prediction uncertainties can be defined as

follows:

-The increase in the variability of dimensions parallel to the decrease in the

design value (i.e. value of the dimension specified in the design),

-The complexity of direct measurement of effective depth,

-The unfixity of forms,

-Problems of vibration and concreting operations.

In spite of the fact that the variability in dimensions changes with different design

values, the same variability will be used for all of the design values considered in

this study. The prediction error associated with this effect will be assumed to be 2%.

The actual dimension may be affected due to unfixity of forms, problems of

vibration and concreting operations, i.e. the quality of workmanship and the

construction techniques affect the variability. In order to account for this effect, a

prediction error of 2% is introduced. The total prediction error due to these sources

of uncertainty will be ( ) ( )( )22

bw02.002.0 +=∆ =0.03. On the other hand, considering

the effective depth of column and beam, it is very difficult to measure the effective

depth directly, and we used the depth of structural member and relevant steel cage.

A c.o.v. of 6% is assigned to this prediction error resulting from the indirect

measurement of effective depth. This value seems to be high; however, Ellingwood

et al. (1980) and Kömürcü (1995) took this prediction error also as 6% in their

studies due to the high probability of change in the position of bars during placing

of concrete. Accordingly, the total prediction error (i.e. epistemic uncertainty) in the

effective depth of beams and columns will be ( ) ( )( ) 07.0)06.0(02.002.0 222

bw=++=∆

Considering the above characteristics of epistemic uncertainties related to

dimensions, Ellingwood and Ang (1972) quantified the total prediction uncertainties

as 0.02, 0.02 and 0.05 for width, depth and effective depth of beams, respectively.

On the other hand, Kömürcü (1995) quantified these uncertainties for width, depth

and effective depth of beams as 0.03, 0.03 and 0.07, respectively. In this study,

owing to similarities of quality of workmanship, construction systems and operating

techniques in beam, column and shear wall dimensions, the prediction uncertainty

will be taken conservatively as 0.03, 0.03 and 0.07, as computed above, for the

width, depth and effective depth of these structural members, respectively.

In the following sections, the basic variabilities and total uncertainties will be

evaluated separately in addition to prediction uncertainties.

3.3.2 Beam Width and Depth

Variations in beam width and depth dimensions influence the weight, strength and

deflections. Variations in beam width and depth generally depend on concreting and

vibration operations and unfixed forms. Furthermore, the quality of workmanship

and the construction techniques influence the beam width and depth dimensions.

In order to investigate the width and depth dimensional variations of beams, a total

of 3725 measurements were carried out in all of the building sites. Results are given

in Table 3.9. The nominal (specified) beam external dimensions were usually

between 250 to 500 mm for width and 300 to 1150 mm for depth. The mean to

nominal ratio changed within a range of 0.980 and 1.011 with an overall mean value

of 0.998 for beam width, and 0.967 and 1.012 with an overall mean value of 0.996

for beam depth. The basic variability changed between 3.1% and 8.3% and the

overall mean value was equal to 4.5% for the beam width; whereas for the beam

depth, the basic variability changed between 1.3% and 6.6% and the overall mean

value was equal to 2.5%.

Combination of the basic variability and the overall prediction error results in the

total variability on the beam width and depth, which are )03.0045.0( 22bw +=Ω =

0.054 and 04.0)03.0025.0( 22

bd=+=Ω , respectively.

The average of mean to nominal ratio is found to be 0.998 and 0.996 based on the

analysis of the collected data for beam width and depth, respectively. This ratio is

pointed out as 1.0 by Yücemen and Gülkan (1989) and Kömürcü (1995) for Turkey.

Table 3.9 Results of the statistical analysis of beam external dimensions for

different regions

Region

Dimension

Number of observations

Design value (mm)

Mean of mean to nominal ratio

Mean of basic variability

Width 515 200-600 1.007 0.046 Istanbul

Depth 580 300-850 0.998 0.022

Width 363 200-500 0.999 0.040 Ankara

Depth 345 500-1000 0.999 0.021

Width 247 200-600 0.996 0.042 Konya

Depth 224 300-900 0.998 0.021

Width 306 200-600 0.995 0.046 Adana

Depth 356 400-1150 0.991 0.030

Width 226 200-500 0.995 0.044 Malatya

Depth 215 350-800 0.994 0.027

Width 165 200-600 0.988 0.053 Ordu

Depth 183 350-800 0.994 0.031

Width 1822 250-600 0.999 0.045 Overall

Depth 1903 300-1150 0.996 0.025

3.3.3 Beam Effective Depth

Effective depths of reinforced concrete beams are directly dependent on the position

of the top and bottom reinforcing steel bars, which are influenced by several factors,

e.g. external dimensions, chair heights, concrete placing operations and lack of

transverse support. In addition to these, the position of beam reinforcement changes

as a result of conflicts with other exterior bars at beam to beam or beam to column

intersections. Besides, the exterior bars of beam may be formless due to unsuitable

stirrups or truss bars and also, the stirrups are opened as people walk on the beam

for concrete placing.

Since the direct measurement of the effective depth of a beam is rather difficult, the

depth of the steel cage and the beam depth are taken into consideration together.

Effective depth of a beam can be calculated by using Eq. (3.3). The dimensions of

the steel cage were measured before the placement of concrete. The specified d*

ranged from 300-600 mm and the basic variability was found to be 0.023, as shown

in Table 3.10.

bbbe += (3.3)

where:

dbe: beam effective depth

db: beam depth

db*: depth of steel cage

The distance between the outer sides of the steel cage and the external dimensions

of beam can be treated as perfectly correlated variables. Based on the collected data,

the mean of mean to nominal ratio of the beam effective depth is found to be 1.00,

and the average basic variability in the beam effective depth is computed as 0.024

by using Eq. (3.3).

Table 3.10 Results of the statistical analysis of beam internal dimensions before the

placement of concrete

Dimension description

Design value (mm)

Steel cage depth (db*) 415 300-600 0.998 0.023

Depth (db) 1903 300-1150 0.996 0.025

The total prediction error and the basic variability in the effective depth are

combined to find the total variability; yielding 074.0)07.0024.0( 22bed =+=Ω .

Ellingwood and Ang (1972) suggested the total prediction uncertainty as 0.086. In

similar studies conducted by Yücemen and Gülkan (1989) and Kömürcü (1995),

total variability in the beam effective depth was found to be 8%.

3.3.4 Column Width and Depth

Variations in reinforced concrete column external dimensions affect the load

carrying capacity of columns. These variations are results of concreting and

vibration operations and unfixed forms. The most important problem on column

concreting and vibration operations is the opening of molds during the casting of

fresh concrete. This causes an increase in external dimensions due to the weight of

concrete and the vibration effect. The pressure caused by the concrete pump

machine also expands the external dimensions of columns. In the light of this

explanation, the quality of workmanship and the construction techniques stands out

as a significant property.

A total of 4216 measurements were taken for columns in all building sites. Results

are given in Table 3.11. The nominal column external dimensions were usually

between 200 and 800 mm for width and between 350 and 1200 mm for depth. The

mean to nominal ratio ranged from 0.932 to 1.027 with an overall mean value of

1.007 for column width, and ranged from 0.922 to 1.033 with an overall mean value

of 1.013 for column depth. The basic variability was found to be 1.8%-9.3% and the

overall mean value was equal to 3.2% for column width whereas, for the column

depth, the basic variability changed between 1.2%- 7.2% and the overall mean

value was equal to 2.4%.

Since the actual external dimensions of columns are greater than nominal external

dimensions due to the opening of molds during the casting of fresh concrete, a

correction factor, N, is introduced to take into consideration this effect. In order to

find the value of N, 42 observations were carried out in the construction site. First,

the forms constructed with exact interior sizes were chosen and measured before the

placement of concrete. Then, after the removal of forms, measurements of columns

were again taken. At the end of observations and measurements, a mean value for N

is recommended as 1.02 whereas the prediction error associated with N is not

considered. The mean of mean to nominal ratio are corrected by these correction

factors yielding to: 1.02x1.007=1.02 and 1.02x1.013= 1.03 for width and depth,

respectively.

When the basic variability and the overall prediction error are combined, the total

variability in the column dimensions becomes 044.0)03.0032.0( 22cw =+=Ω for

width and 038.0)03.0024.0( 22cd

=+=Ω for depth.

Table 3.11 Results of the statistical analysis of column external dimensions for

different regions

Region

Dimension

Design value (mm)

Width 580 350-800 1.018 0.027 Istanbul

Depth 596 400-1200 1.019 0.020

Width 431 300-600 1.009 0.029 Ankara

Depth 441 400-1200 1.020 0.024

Width 315 200-600 1.00 0.029 Konya

Depth 313 400-1200 0.999 0.029

Width 304 250-600 1.002 0.038 Adana

Depth 311 400-1000 1.016 0.019

Width 252 300-600 1.013 0.030 Malatya

Depth 237 400-1200 1.015 0.021

Width 215 350-600 0.984 0.048 Ordu

Depth 221 400-800 0.996 0.039

Width 2097 250-800 1.007 0.032 Overall

Depth 2119 400-1200 1.013 0.024

3.3.5 Column Effective Depth

Effective depth of a reinforced concrete column is directly related with the position

of the steel cage which is considerably affected by overall depths and widths of

columns. At the same time, the exterior bars of steel cage may be out of position

due to formless stirrups. In addition to these, the position of column reinforcement

can be affected by the conflicts with other exterior bars at column to column or

beam to column intersections.

Due to difficulties of direct effective depth measurement, the distance between the

outer sides of the steel cage was measured as well as column depth, but

measurements of steel cage were taken before concrete placing. The specified d*

ranged from 300 to 700 mm and the basic variability changed from 1% to 4.2%

with an average value of 2.7%. The results for steel cage depth and column depth

measurements are given in Table 3.12. Effective depth of columns can be calculated

by the following relationship with the help of these results:

ccce += (3.4)

where:

dce: effective depth of column

dc: column depth

dc*: depth of steel cage

The depth of steel cage and the external dimension of the reinforced concrete

columns can be treated as perfectly correlated. Based on the column external

dimension and the steel cage depth, the mean of mean to nominal ratio and the

average basic variability of the column effective depth are found to be 1.01 and

0.025, respectively.

It is necessary to combine the basic variability in the effective depth and the total

prediction error in order to find the total variability. Thus, the total variability in the

effective depth of a column becomes 074.0)07.0025.0( 22ced =+=Ω .

Table 3.12 Results of the statistical analysis for the column internal dimensions

Dimension description

Design value (mm)

Steel cage depth (dc*) 555 300-700 1.005 0.027

Depth (dc) 2119 400-1200 1.013 0.024

3.3.6 Shear Walls

Concreting and vibration operations and unfixity of forms influence the variations

in shear wall external dimensions. One of the main problems on shear walls like

columns is the opening of molds during casting of fresh concrete which causes an

increase in dimensions due to the weight of concrete, vibration effect and

disturbance caused by concrete pump machine.

To examine the variations of external dimensions on shear walls, 2942 dimensions

were measured. Results are given in Table 3.13. As the nominal shear wall widths

were 200, 250 or 300 mm, the nominal shear wall depths usually varied between

1200 and 1500 mm. The mean to nominal ratio ranged from 0.932 to 1.027 with an

average value of 1.003 for width and 0.922 to 1.033 with an average value of 0.998

for shear wall depth. The basic variability was found to be 2%-7.6% with an

average value of 4.7% and 0.4%- 2.7% with an average value of 1.4% for shear

wall width and shear wall depth, respectively.

Table 3.13 Results of the statistical analysis of shear wall external dimensions for

different regions

Region

Dimension

Design value (mm)

Width 348 200-300 1.006 0.045 Istanbul

Depth 366 1200-4400 1.00 0.014

Width 257 200-300 1.004 0.043 Ankara

Depth 252 1350-5000 0.998 0.014

Width 235 200-300 1.004 0.054 Konya

Depth 238 1200-3000 0.999 0.014

Width 284 200-350 1.001 0.048 Adana

Depth 270 1200-4000 1.001 0.012

Width 195 200-300 0.998 0.051 Malatya

Depth 199 1450-2500 0.995 0.015

Width 141 200-300 1.006 0.044 Ordu

Depth 157 1200-1800 0.995 0.018

Width 1460 250-350 1.003 0.047 Overall

Depth 1482 1200-4400 0.998 0.014

As a result of the opening of molds during casting of fresh concrete, actual shear

wall width is greater than the nominal value. A correction factor, N, is introduced

to take this effect into consideration. Since the depth of shear wall is considerably

greater than other dimensions, the ratio of increase in this dimension is quite small;

therefore, the correction factor related to shear wall depth is ignored. In order to

find the value of N, a total of 36 observations were carried out. First, the forms

constructed with exact interior sizes were chosen and measured before the

placement of concrete. Then, after the removal of forms, measurements of shear

wall widths were again taken. At the end of the observations and the measurements

carried out only for shear wall width, a mean value for N is recommended as 1.05

and the prediction error associated with N is ignored.

If we correct the mean of mean to nominal ratio; 1.05x1.003=1.05 is found for the

shear wall width. On the other hand, as it is seen on Table 3.13, the mean of mean

to nominal ratio in shear wall depth is equal to 0.998 based on the analysis of the

collected data.

When the basic variability and the overall prediction error are combined, the total

variability in the shear wall width and depth, respectively, becomes:

056.0)03.0047.0( 22sw =+=Ω and 033.0)03.0014.0( 22

sd =+=Ω

3.3.7 Reinforcement Area

The basic variability in the reinforcement area of any structural element can

be computed from the variability in the individual bar area assuming that there is a

perfect correlation among the bar areas. Except for the fabrication errors, the other

errors do not considerably affect the variability of reinforcement bar areas. In

Turkey, BCIII(a) type reinforcing bar is widely used. Thus, test results on 1587

BCIII(a) reinforcing bar specimens with different bar sizes from 8mm to 22 mm

were obtained. After the analyses of the data, the mean of mean to nominal ratio,

standard deviation and mean of basic variability of each bar size were determined.

The results are presented in Table 3.14.

Table 3.14 Results of the statistical analysis of reinforcement areas

according to bar sizes

Bar size

Standard deviation

8 185 1.01 0.16 0.02

10 172 0.99 0.10 0.01

12 256 1.00 0.15 0.013

14 126 1.01 0.15 0.011

16 185 1.00 0.13 0.008

18 106 1.00 0.19 0.011

20 284 0.99 0.26 0.013

22 112 0.99 0.26 0.012

25 96 1.03 0.31 0.012

Overall 1522 1.00 0.20 0.012

As it could be seen from Table 3.14, the ratio of mean to specified values of

reinforcing steel bar areas and the basic variability in reinforcement area is equal to

1.00 and 1.2%, respectively, based on the overall data. Prediction uncertainties arise

from fabrication errors, and the mean areas of smaller diameter bars are less

predictable (Ellingwood and Ang, 1972). To account for the additional sources of

variability, Ellingwood and Ang (1972) and Kömürcü (1995) used a total prediction

error of 3% in their studies. Here, the total prediction uncertainty will also be taken

as 3%. Thus, the total uncertainty of reinforcement area, quantified in terms of

c.o.v., equals to 03.0)03.0012.0( 22As =+=Ω .

CHAPTER 4

MODELING OF CAPACITY OF REINFORCED CONCRETE MEMBERS IN DIFFERENT FAILURE

In the previous chapter, various sources of uncertainties associated with concrete

compressive strength, yield strength of reinforcing steel bars and the dimensions of

beams, columns and shear walls are analyzed and quantified. Based on these

uncertainties, the resistance statistics for flexural and shear failure modes of

reinforced concrete beams, columns and shear walls as well as columns in

combined action of axial load and flexure failure modes are computed within the

framework of reliability analysis in the following sections.

4.1 CAPACITY OF REINFORCED CONCRETE BEAMS IN DIFFERENT FAILURE MODES

Beams are structural members whose main function in a structure is to carry

transverse loads that create flexural moments and shear forces. Due to monolithic

nature of reinforced concrete structures, beams can be subjected to axial loads and

torsional moments as secondary loads in addition to transverse loads. In this study,

only flexural and shear capacities are treated since they are usually the most critical

parameters that govern the beam design. The statistics of basic variables concerning

the flexural and shear capacities of beams are summarized in Table 4.1.

Table 4.1 Statistics of the basic variables involved in the calculation of flexural and

shear capacities of reinforced concrete beams

Parameter Nominal (Specified) value

Mean to nominal ratio

Inherent variability

Prediction error

Total Uncertainty

Compressive strength of concrete (fc)

21.55 MPa 1.25 0.105 0.14 0.18

Yield strength of BC III (fy)

365 MPa 1.24 0.038 0.08 0.09

Beam width (bw) 250-600 mm 0.998 0.045 0.03 0.054

Beam depth (h) 300-1150 mm 0.996 0.025 0.03 0.04

Effective depth (dbe)

250-1100 mm 1.00 0.024 0.07 0.074

Reinforcement area (As)

100-4000

mm2 1.00 0.012 0.03 0.03

4.1.1 Flexural Capacity of Beams

When beams are under the influence of flexure, bending strains are produced. It

should be noted that under positive bending moments, tensile strains are produced

in the bottom of the beam while compressive strains are produced in the top of the

beam. Accordingly, these strains produce tensile stresses in the bottom of the beam,

and compressive stresses in the top of the beam. Hence, both tensile stresses and

compressive stresses must be resisted by beams in a suitable manner.

The skill in determining the sense of bending is highly critical in the design of

reinforced concrete members. The concrete must be embedded with steel on the

tension side since the tensile strength of concrete is very low compared with its

compressive strength. The absence of properly placed steel will most likely cause

structural failure (Meyer, 1996).

By using the equivalent rectangular stress block approach, the nominal flexural

strength of a rectangular reinforced concrete beam can be determined. A typical

rectangular beam cross-section with strain, stress and force distribution diagrams

are shown in Figure 4.1. The equivalent rectangular block of intensity 0.85fc and

depth, a, as shown in this figure. The depth of the equivalent stress block “a” can be

determined by the following equation (TS 500, 2000):

a= k1c (4.1)

where:

k1: a factor of function of strength of concrete that takes a value of 0.85 for C16,

C20, C25, a value of 0.82 for C30, and a value of 0.79 for C35 (TS 500, 2000)

c: distance from the neutral axis to the outer compressive fiber.

Figure 4.1 Stresses and forces in reinforced concrete beams

0.85fc 0.003

Cross-section

Strains Stresses Internal forces

(d-a/2)

Neutral axis

In a reinforced concrete beam, flexural failure may occur in three different ways:

a) Balanced failure: This type of failure occurs when yielding of tension steel

and crushing of concrete in the extreme concrete fiber take place at the same

time; for this reason, the behavior is brittle. The amount of steel required to

produce this condition, which is a borderline case, is large.

b) Tension failure: This type of failure occurs when the balanced steel ratio is

higher than the steel ratio of the cross section. Such beams are said to be

underreinforced.

c) Compression failure: This type of failure occurs when the concrete in the

compression zone crushes before the steel in the tension zone yields; that is,

if a beam has a larger amount of steel than that required to create the

balanced condition, compression failure occurs. The beams showing this

type of failure are said to be overreinforced.

Since compression failure is dominated by concrete, the behavior of an

overreinforced beam is brittle and sudden. For this reason, overreinforced beams are

forbidden in design codes. In order to determine whether a beam is underreinforced

or overreinforced, balanced case should be investigated first. It is to be noted that

the equivalent rectangular stress block approach assumes a value of εcu=0.003 for

the strain in the extreme compression fiber at ultimate stage in the all types of

failure (TS 500, 2000). The balanced steel ratio, ρb, and the existing steel ratio, ρ,

can be computed from Eq. (4.2) and Eq. (4.3), respectively.

0.85fρ b

= (4.2)

s= (4.3)

where cb is the depth of neutral axis at the balanced case. In the case of double

reinforced beams, (ρ-ρ′ ) should be checked against balanced steel ratio ρb to

control whether the beam is overreinforced or underreinforced. Here, ρ′ is the

compression reinforcement ratio.

Reinforced concrete floor systems usually consist of beams and slabs that are placed

monolithically. Typically, a certain portion of a slab which is adjacent to a beam

becomes a part of the beam. This part of the slab that behaves together with the

beam against the flexural moment gives rise to a beam section of T or L shapes as

shown in Figure 4.2. In reinforced concrete structures, the most commonly observed

beams are this type of beams. Therefore, in this study, flanged beams are treated as

reinforced concrete beams.

Figure 4.2 Beam sections of T and L shapes (Ersoy and Özcebe, 2004)

Since flanged beams ensure a large compression area in the compression zone of

the beam, they can carry high compression force with this portion of the section

without necessitating additional steel reinforcement in this zone. Flanged beams are

advantageous owing to that the shifting of the centroid of the compression zone

toward the compression face raises the moment arm, which leads to a great benefit

in terms of moment carrying capacity of the beam.

The neutral axis of a T beam may be either in its flange or in the web (i.e. the part

of the T beam below the slab) depending upon the strength of materials, the cross

sectional properties and the amount of reinforcing steel bars (Nilson et al., 2004). If

the depth of the flange thickness is greater than the compression block, k1c (i.e.

t≥k1c), then the analysis of a flanged beam is identical to the analysis of a

rectangular beam. The depth of the flange thickness is rarely less than the depth of

the compression block except in precast beams (Ersoy and Özcebe, 2004). For this

reason, in this study, the analysis of the flanged beam is carried out in the same way

as the analysis of a rectangular beam.

Using the equivalent rectangular stress block approach, the ultimate moment

capacity, Mr, of a flanged beam where “t≥k1c” can be computed by using the

following equations:

ckdfAM 1

ydsr (4.4)

b0.85f

1 = (4.5)

In order to compute the mean to nominal ratio and the total variability for the

flexural capacity of a beam, a code is written in MathCAD 12 in accordance with

FOSM method, and beams with various dimensions and with different

reinforcement areas are analyzed using this code. Besides, the beams whose depth is

much smaller than its width are considered. The results are given in Tables 4.2 and

4.3. It is to be noted that, in these tables, the mean to nominal ratios of the flexural

capacity of the beams are computed by substituting the in-situ and nominal values

of the basic variables into the following equation (a bar “ - ” over a basic variable

stands for the “true” mean and a prime “ ′ ”denotes the nominal value):

′′

′′−′′′

r (4.6)

From Tables 4.2 and 4.3, it can be seen that rr M/M ′ =1.24 as an average value for

the studied cases. The corresponding value was suggested by Ellingwood et al.

(1980) as 1.14 and 1.05 for Grade 40 and Grade 60 steels, respectively. In a similar

study, Kömürcü and Yücemen (1996) reported a value of 1.19 for the flexural

capacity of beams. In the following chapters, a value of 1.24 will be used in the

reliability calculations.

Considering the total uncertainties of the basic variables involved in the flexural

capacity of a beam, the overall standard deviation, Mrσ , is calculated by utilizing the

FOSM format. For the flexural capacity of a beam, based on Eq. (2.11), the

standard deviation equation can be rewritten as follows:

∂= (4.7)

After the computation of standard deviation by using Eq. (4.7), the total variability

in terms of coefficient of variation is calculated by dividing the standard deviation

to the mean value. As given in Tables 4.2 and 4.3, the total variability varies from

0.119 to 0.141 with a weighted average value of 0.12. In addition, it is necessary

that the analysis uncertainty (i.e. epistemic uncertainty resulting from the difference

between actual behavior and estimated behavior predicted by analysis) should be

included into the overall uncertainty. For this reason, Ellingwood et al. (1980) and

Nowak and Szerszen (2003a) used the values of 0.046 and 0.06, respectively in

their studies. Here, the analysis uncertainty is taken as 0.06 in order to be on the

safe side. Thus, the total uncertainty in the flexural capacity of a reinforced concrete

beam becomes 13.0)06.012.0( 22

rM =+=Ω .

Ellingwood et al. (1980) used the values of 0.14 and 0.11 for Grades 40 and Grades

60 steels, respectively. Yücemen and El-Etoom (1986) reported MrΩ to be 0.16.

Kömürcü and Yücemen (1996) also calculated this value as 0.16 in their study.

Despite being slightly smaller, the value found in this study is consistent with the

values reported in the studies mentioned above.

Table 4.2 Mean to nominal ratios and coefficients of variation of the beam flexural

capacity (b=200 mm and b=300 mm)

b (mm)

d (mm)

(mm2) rM

rM′′′′ ΩM

100 1.24 0.120

200 1.24 0.120

400 1.241 0.119

600 1.241 0.119

800 1.241 0.121

200 1.240 0.120

400 1.240 0.119

800 1.241 0.120

1200 1.241 0.119

2000 1.242 0.132

200 1.240 0.120

400 1.240 0.119

900 1.241 0.119

1200 1.241 0.120

2000 1.242 0.126

400 1.240 0.119

800 1.241 0.120

1600 1.242 0.128

360 2400 1.244 0.152

400 1.240 0.119

800 1.241 0.119

1600 1.242 0.123

460 2400 1.243 0.134

400 1.242 0.120

800 1.242 0.119

1600 1.242 0.121

560 2400 1.242 0.127

Average value 1.241 0.123

Table 4.3 Mean to nominal ratios and coefficients of variation of the beam flexural

capacity (b=400 mm and b=1000 mm)

b (mm)

d (mm)

(mm2) rM

rM′′′′ ΩM

800 1.242 0.119

1600 1.242 0.119

2400 1.242 0.121

3200 1.242 0.123

800 1.242 0.120

1600 1.242 0.119

2400 1.242 0.120

3200 1.242 0.121

800 1.242 0.120

1600 1.242 0.119

2400 1.242 0.119

3200 1.242 0.120

800 1.242 0.119

1600 1.242 0.119

3200 1.242 0.122

4000 1.242 0.125

800 1.242 0.120

1600 1.242 0.119

3200 1.242 0.120

4000 1.242 0.122

800 1.242 0.120

1600 1.242 0.119

3200 1.242 0.119

4000 1.242 0.120

4.1.2 Shear Capacity of Beams

Reinforced concrete structural members are usually subjected to shear besides

flexural and axial loads. In the classical sense, not only shear but also torsion

produces shear flows in structural members. While shear strength of concrete is

lower than its compressive strength, it is considerably larger than its tensile

strength. In fact, shear by itself does not usually create any critical condition in

reinforced concrete members. Nevertheless, the principal tensile stresses caused by

shear can produce an important problem in reinforced concrete members, as the

tensile strength of concrete is very low (Ersoy and Özcebe, 2004).

If there is inadequate shear reinforcement in a structural member, structural

collapse, which is brittle, can occur owing to the principal tensile stresses. In order

to prevent this type of failure, structural members should be provided with adequate

shear reinforcement so that these members can reach their ultimate limit state by

flexure, but not by shear. Therefore, in the design of structural members, the

following equation should be satisfied:

dr VV ≥ (4.8)

where:

Vr: shear strength of the member,

Vd: maximum design shear force to be calculated based on convenient load factors

and combinations.

TS500 (2000) defines the shear strength of a structural member as the sum of the

resistance of concrete and the resistance of the shear reinforcement. The resistance

of concrete, Vc, which is commonly taken as 80% of the cracking shear strength of

concrete and the resistance of shear reinforcement, Vw, can respectively be

calculated by using the Eq. (4.9) and Eq. (4.10), as specified in TS500 (2000):

)dbf65.0(80.0V wctdc Ψ= (4.9)

AV ywd

sww = (4.10)

where:

fctd: design tensile strength of concrete

fywd: design yield strength of shear reinforcement

Asw: cross-sectional area of stirrup

s: spacing of stirrups

If a reinforced concrete member is subjected to axial stresses in addition to shear

resulting from the applied axial forces or imposed deformations, such as shrinkage

and temperature change, the magnitude and direction of the principle tensile stresses

can change. A stress analysis indicates that axial tensile stresses lower the diagonal

cracking resistance whereas axial compressive stresses increase it. The value of Ψ

given in Eq. (4.9) can be found from the following formulas for beams subjected to

axial tension or axial compression besides shear, respectively:

N3.01+=Ψ (4.11)

N007.01+=Ψ (4.12)

It is worth noting that Nd has to be entered (-) in Eq. (4.11) and (+) in Eq. (4.12).

When Nd/Ac<0.5 N/mm2, one can take Ψ as 1.0.

Based on the discussion above, shear strength of a reinforced concrete beam can be

calculated by using the following relationship:

Ψ+= dbf52.0dfs

AV wctdywd

swr (4.13)

In order to find the mean to nominal ratio and the total variability of the shear

capacity of a beam, a code was developed in MathCAD 12 according to FOSM

format. Various cases with different reinforcement areas and dimensions are taken

into account by using this code, and the results are presented in Table 4.4. The mean

to nominal ratio of the shear capacity of a beam is obtained by substituting the in-

situ and nominal values of the basic variables into the following equation:

Ψ′′′′+′′′

′dbf52.0df

dbf52.0dfs

wctdywdsw

r (4.14)

From Table 4.4, one can infer that for the studied cases rr V/V ′ has an average

value of 1.24. This value was indicated by Ellingwood et al. (1980) as 1.09. In a

similar study, Nowak and Szerszen (2003a) reported the value of 1.23 for the shear

capacity of the beam. In the following chapters, a value of 1.24 will be used in the

reliability calculations.

Considering the total uncertainties of the basic variables involved in the shear

capacity of a beam, the overall standard deviation, Vrσ , is calculated on the basis of

FOSM procedure. For the shear capacity of a beam, by using Eq. (2.11), the

standard deviation equation can be rewritten as follows:

V2fctσ

V2fywσ

(4.15)

If the standard deviation of the shear capacity is divided by its mean value, the total

variability in the shear capacity of the beam is obtained. From Table 4.4, it can be

seen that the total variability changes within a range of 0.116 to 0.157 with a

weighted average value of 0.14. On the other hand, the actual behavior of shear

capacity of a beam is different from the estimated behavior predicted by structural

analysis. Ellingwood et al. (1980) and Nowak and Szerszen (2003a) assigned 0.115

and 0.10 in their studies, respectively as the c.o.v. to account for this effect. In this

study, the epistemic uncertainty resulting from the effect mentioned above (analysis

uncertainty) will be taken as 0.10 as reported in the study of Nowak and Szerszen

(2003a) due to fact that it is a more recent study and contains up to date data and

information in comparison with the study of Ellingwood et al. (1980).

Consequently, the overall uncertainty in the shear capacity of a beam will be

17.0)10.014.0( 22

rV =+=Ω .

Ellingwood et al. (1980) reported VrΩ to be 0.17. Nowak and Szerszen (2003a)

used a value of 0.11. In spite of the fact that there is significant difference between

the results obtained from studies conducted by Ellingwood et al. (1980) and Nowak

and Szerszen (2003a), the value found by Ellingwood et al. (1980), which is the

same as that also computed in this study, is on the safe side. Therefore, a value of

0.17 will be used for the overall uncertainty of the shear capacity of a beam.

Table 4.4 Mean to nominal ratios and coefficients of variation of the beam shear

capacity

(mm) h

(mm) d

(mm) Asw

(mm2) s

(mm) r

′′′′

50 180 1.244 0.132

78.5 180 1.243 0.122

100 280 1.243 0.126

50 145 1.244 0.132

100 145 1.243 0.119

100 230 1.244 0.127

100 330 1.244 0.136

100 400 1.244 0.138

200 200 1.242 0.116

50 280 1.245 0.157

78.5 280 1.245 0.144

100 280 1.244 0.136

78.5 220 1.244 0.137

100 280 1.244 0.136

200 400 1.244 0.147

100 330 1.245 0.146

78.5 320 1.246 0.157

200 320 1.243 0.125

78.5 200 1.245 0.142

100 250 1.245 0.142

200 350 1.243 0.132

78.5 100 1.245 0.142

100 150 1.245 0.147

200 200 1.244 0.135

4.2 CAPACITY OF REINFORCED CONCRETE COLUMNS IN DIFFERENT FAILURE MODES

Columns are vertical structural members which are designed to support load-

carrying beams. The height of a column is generally considerably larger than its

cross-sectional dimensions. These structural members transfer loads from the roof

or the upper floor to the lower levels, and then to the soil through foundations.

Since columns are compression members, failure of one column in a critical region

can lead to progressive collapse of the adjoining floors resulting in total collapse of

the entire structure. Structural column failure is of major importance in terms of not

only economic but also human loss. Hence, extreme care should be given to design

a column with a higher reserve strength compared to beams and other horizontal

structural elements, especially since compression failure provides little visual

warning (Nawy, 2005).

Columns can be classified into four general types as tied columns, spiral columns,

composite columns and concrete-filled pipe columns, generally according to the

forms used and the arrangement of reinforcing steel bars (Atimtay, 1998):

- In tied columns, which are usually in rectangular, square or L shape and rarely in

circular shape, the longitudinal reinforcement bars are held in position by

intermitted lateral ties,

-In spiral columns, which are usually in circular, and rarely in rectangular or square

shape, the longitudinal reinforcement bars are enveloped by a continuous helix of

steel bar or wire,

-In composite columns, which are usually in rectangular, square or circular shape,

steel profiles are thoroughly encased in concrete, which is also reinforced with both

longitudinal and spiral reinforcement,

-Concrete filled pipe columns are manufactured by filling steel pipes with concrete.

Macgregor and Wight (2005) indicated that over 95 percent of the columns in the

buildings located in nonseismic regions are tied columns. In spite of the fact that

spiral columns are also used where increased ductility is needed, tied columns are

the most commonly used type of columns due to their lower construction costs

(Nawy, 2005). In Turkey, the number of the rectangular tied columns is

considerably more than the number of the other column types. For this reason, in

this study, rectangular tied columns will be studied. The statistics of the basic

variables concerning the flexural and shear capacity of reinforced concrete columns

are summarized in Table 4.5.

Table 4.5 Statistics of the basic variables involved in the calculation of the

combined action and shear capacities of columns

Prediction error

Total Uncertainty

21.55 MPa 1.25 0.105 0.14 0.18

365 MPa 1.24 0.038 0.08 0.09

Column width (bw) 250-800 mm 1.02 0.032 0.03 0.044

Column depth (h) 400-1200 mm 1.03 0.024 0.03 0.038

Effective depth (dbe)

350-1150 mm 1.01 0.25 0.07 0.074

1400-6400

mm2 1.00 0.012 0.03 0.03

4.2.1 Combined Action of Flexure and Axial Load for Columns

A great majority of columns as a part of monolithic reinforced concrete structures

are not subjected to only uniaxial loading. Due to asymmetrically placed floor

loads, initial crookedness of the column, and the possibility of lateral loads, such as

wind load and earthquake load, flexural moment, shear and sometimes torsion take

place in addition to axial compression in structural columns. In fact,

nonhomogeneous nature of concrete creates an eccentricity even when only an axial

load is applied to the geometric centroid of the cross-section. This is why, most of

the design codes avoid column designs with no moment, and assign a minimum

eccentricity in order to stay on the safe side (Ersoy and Özcebe, 2004). Therefore,

not only axial forces but also moments, namely the combined action of flexure and

axial load, are taken into consideration for the columns considered in this study.

The design of an eccentrically loaded column necessitates the determination of two

basic quantities: (i) the moment that can be resisted for a specified axial load and

(ii) the axial load that can be carried for a specified moment.

The same basis concerning the stress distribution and the equivalent rectangular

stress block utilized for beams are equally applicable for columns (Nawy, 2005).

As stated above, most of the columns in structures are tied columns, which are of

rectangular cross-sections. A typical rectangular column cross-section with strain,

stress and force distribution diagrams are shown in Figure 4.3. For rectangular

sections, the equivalent rectangular stress block approach leads to the following

equations for the calculation of axial load, Nr, and moment capacity, Mr:

1isisib1cdr Ackf85.0N (4.16)

1isisi

11cdr xA

hckf85.0M ∑

−= (4.17)

ssi fc

1E003.0 ≤

+=σ (4.18)

where:

Asi: steel area in the ith layer

σsi: steel stress in the corresponding steel area in ith layer

Es: modulus of elasticity of steel reinforcement

xi: distance between neutral axis and ith steel layer

Figure 4.3 Stresses and forces in reinforced concrete columns

As mentioned above, all columns in a structure should be designed with respect to

the combined action of flexure and axial load. All possible load combinations

should be taken into consideration in the structural analysis. For each load

combination, a pair of N and M values is computed. Then, the plot of M versus N

obtained from these three equations for a given cross-section represents the strength

envelope called interaction diagrams or interaction curves. Most of the structural

codes limit the axial load on a column and also specify a minimum eccentricity. The

column design should be carried out for the most critical Nd and Md combinations

0.85fc 0.003

Cross-section

Strains Stresses Internal forces

Neutral axis

which are determined from the analysis.

In order to obtain the values of mean to nominal ratio and total variability for the

combined action of axial and flexural capacity of a column, a code was written in

MathCAD according to FOSM. With the help of this code, the mean to nominal

ratio and total variability are computed for different cases with various

characteristics by using both the nominal and in-situ values as discussed before. For

different design cases, the statistics of mean to nominal ratios associated with the

combined action of flexure and axial load capacity of reinforced concrete columns

are summarized in Tables 4.6 - 4.9. From these tables, the mean to nominal ratio of

axial capacity of a column is observed to vary from 1.212 to 1.263 with a weighted

average of 1.25 whereas the mean to nominal ratio of flexural capacity vary from

1.145 to 1.276 with a weighted average of 1.22. Accordingly, the mean to nominal

ratio of the combined action in columns will be taken as 1.24, which corresponds to

the average of these two values. In similar studies, Ellingwood et al. (1980)

recommended a value of 1.10 for axially loaded columns while Nowak and

Szerszen (2003a) reported the value of 1.26 for this ratio.

As shown in Tables 4.6-4.9, the total variability changes in a range of 0.058 and

0.162 with a weighted average value of 0.12 for the axial capacity of a column

whereas for the flexural capacity of a column, the total variability ranges from

0.059 to 0.107 with a weighted average value of 0.07. To be on the safe side, the

total variability in the combined action of the axial and the flexural capacity of

columns will be taken as 0.12, which corresponds to the total variability in the axial

capacity of the column. In addition, it is to be noted that, a value of 0.046 for the

analysis uncertainty is reported by Ellingwood et al. (1980) in their study whereas

this value is reported as 0.08 by Nowak and Szerszen (2003a). Here, the analysis

uncertainty will also be taken as 0.08. Thus, the overall uncertainty for the

combined action of axial and flexural capacity of a column will be

14.0)08.012.0( 22ca =+=Ω .

flexural capacities for eccentrically loaded columns (b/h=0.6)

Design case Axial force Moment

ρ c r

′ ΩN

′ ΩM

c=1.5h 1.262 0.162 1.147 0.066

c=h 1.258 0.163 1.272 0.106

c=0.75h 1.260 0.160 1.170 0.073

c=0.5h 1.262 0.142 1.240 0.067

c=0.25h 1.260 0.097 1.240 0.068

c=cb 1.262 0.14 1.240 0.067

c=1.5h 1.254 0.149 1.147 0.065

c=h 1.246 0.148 1.271 0.106

c=0.75h 1.235 0.136 1.173 0.073

c=0.5h 1.261 0.113 1.240 0.068

c=0.25h 1.252 0.074 1.240 0.068

c=cb 1.255 0.116 1.240 0.067

c=1.5h 1.246 0.136 1.148 0.065

c=h 1.237 0.134 1.271 0.106

c=0.75h 1.222 0.121 1.172 0.073

c=0.5h 1.257 0.097 1.240 0.068

c=0.25h 1.249 0.063 1.240 0.068

c=cb 1.250 0.100 1.240 0.067

c=1.5h 1.240 0.125 1.148 0.065

c=h 1.228 0.124 1.271 0.106

c=0.75h 1.212 0.109 1.172 0.073

c=0.5h 1.255 0.087 1.240 0.068

c=0.25h 1.247 0.058 1.240 0.068

c=cb 1.246 0.089 1.240 0.068

Average value 1.248 0.118 1.218 0.075

As2 9.0h

′′,

=λ dıı

flexural capacities for eccentrically loaded columns (b/h=1)

ρ c r

′ ΩN

′ ΩM

c=1.5h 1.260 1.160 1.148 0.065

c=h 1.258 0.164 1.274 0.107

c=0.75h 1.252 0.157 1.174 0.074

c=0.5h 1.265 0.135 1.240 0.068

c=0.25h 1.258 0.100 1.240 0.068

c=cb 1.262 0.142 1.240 0.068

c=1.5h 1.249 0.142 1.147 0.065

c=h 1.245 0.147 1.274 0.107

c=0.75h 1.235 0.137 1.174 0.074

c=0.5h 1.259 0.108 1.240 0.068

c=0.25h 1.252 0.074 1.240 0.068

c=cb 1.255 0.116 1.240 0.068

c=1.5h 1.241 0.127 1.147 0.065

c=h 1.235 0.134 1.274 0.107

c=0.75h 1.223 0.121 1.174 0.074

c=0.5h 1.257 0.097 1.240 0.068

c=0.25h 1.249 0.063 1.240 0.068

c=cb 1.25 0.100 1.240 0.068

c=1.5h 1.234 0.115 1.147 0.065

c=h 1.226 0.123 1.274 0.107

c=0.75h 1.213 0.110 1.174 0.074

c=0.5h 1.253 0.082 1.240 0.068

c=0.25h 1.247 0.058 1.240 0.068

c=cb 1.246 0.089 1.240 0.068

Average value 1.246 0.158 1.219 0.075

dı As1

′′,

=λ dıı

flexural capacities for eccentrically loaded columns (b/h=2)

ρ c r

′ ΩN

′ ΩM

c=1.5h 1.260 0.160 1.145 0.063

c=h 1.257 0.113 1.207 0.084

c=0.75h 1.253 0.158 1.181 0.075

c=0.5h 1.266 0.139 1.240 0.067

c=0.25h 1.258 0.100 1.240 0.067

c=cb 1.263 0.141 1.240 0.067

c=1.5h 1.248 0.141 1.145 0.063

c=h 1.244 0.147 1.206 0.084

c=0.75h 1.237 0.137 1.181 0.076

c=0.5h 1.261 0.113 1.240 0.067

c=0.25h 1.259 0.080 1.240 0.068

c=cb 1.259 0.117 1.240 0.067

c=1.5h 1.240 0.126 1.145 0.063

c=h 1.233 0.133 1.206 0.084

c=0.75h 1.225 0.122 1.181 0.076

c=0.5h 1.257 0.097 1.240 0.068

c=0.25h 1.249 0.063 1.240 0.068

c=cb 1.253 0.100 1.240 0.068

c=1.5h 1.233 0.115 1.128 0.063

c=h 1.224 0.122 1.206 0.084

c=0.75h 1.216 0.111 1.181 0.076

c=0.5h 1.255 0.087 1.240 0.068

c=0.25h 1.247 0.058 1.240 0.068

c=cb 1.247 0.088 1.240 0.068

Average value 1.248 0.115 1.208 0.071

As1 8.0h

′′,

=λ dıı

flexural capacities for eccentrically loaded columns (b/h=0.5)

ρ c r

′ ΩN

′ ΩM

c=1.5h 1.262 0.160 1.158 0.059

c=h 1.264 0.162 1.276 0.099

c=0.75h 1.245 0.158 1.160 0.068

c=0.5h 1.253 0.138 1.231 0.065

c=0.25h 1.245 0.106 1.234 0.064

c=cb 1.257 0.144 1.233 0.066

c=1.5h 1.252 0.141 1.158 0.059

c=h 1.256 0.146 1.276 0.099

c=0.75h 1.231 0.138 1.159 0.068

c=0.5h 1.240 0.111 1.231 0.065

c=0.25h 1.233 0.078 1.234 0.064

c=cb 1.247 0.119 1.233 0.066

c=1.5h 1.244 0.127 1.158 0.059

c=h 1.25 0.133 1.276 0.099

c=0.75h 1.217 0.122 1.159 0.068

c=0.5h 1.232 0.094 1.231 0.065

c=0.25h 1.228 0.066 1.234 0.064

c=cb 1.239 0.162 1.233 0.066

c=1.5h 1.238 0.115 1.158 0.059

c=h 1.244 0.122 1.276 0.099

c=0.75h 1.207 0.111 1.159 0.068

c=0.5h 1.227 0.083 1.231 0.066

c=0.25h 1.224 0.059 1.234 0.064

c=cb 1.234 0.091 1.243 0.066

Average value 1.24 0.12 1.216 0.070

As2 9.0

′′,

=λ dıı

4.2.2 Shear Capacity of Columns

Shear strength of a column can be computed in the same way as done in the case of

beams. However, for the shear capacity of a column, the values of axial load, Nd,

which appears in Eq. (4.12) is considerably larger than that used for the shear

capacity of a beam.

In order to acquire the values of mean to nominal ratio and total variability for the

shear capacity of a column, a code was developed in MathCAD complying with

FOSM format. Using this code and the statistical parameters compiled in Chapter 3,

the mean to nominal ratios and total variabilities are computed for various cases

with different reinforcement areas, dimensions and axial loads. The mean to

nominal ratios and total uncertainties are almost the same with those presented for

beams in Table 4.4. Therefore they are not given here once again.

The mean to nominal ratio of the shear capacity of a column is found to be 1.24 by

using both nominal and in-situ values as stated in the case of the shear capacity of a

beam (Section 4.2.2). For the beams, this value was indicated as 1.09 by

Ellingwood et al. (1980) and as 1.23 by Nowak and Szerszen (2003a). In the

following chapters, a value of 1.24 will be used in the reliability calculations.

It is observed that the total variability in the shear capacity of a column varies from

0.116 to 0.157 with a weighted average of 0.14 (Table 4.4). Although, the values of

axial load, Nd, acting on a reinforced concrete column are considerably more than

those acting on a reinforced concrete beams, the value of total variability does not

change significantly. On the other hand, the actual behavior of shear capacity of a

column is different than the estimated behavior predicted by structural analysis. In

order to account for this effect, Ellingwood et al. (1980) and Nowak and Szerszen

(2003a) used a value of 0.115 and 0.10, respectively in their studies. Here, the

analysis uncertainty will be taken as 0.10. As a result, the overall uncertainty in the

shear capacity of a column will be 17.0)10.014.0( 22

rV =+=Ω .

4.3 CAPACITY OF REINFORCED CONCRETE SHEAR WALLS IN DIFFERENT FAILURE MODES

Large lateral loads acting on a reinforced concrete structure, such as seismic loads

or very high wind loads are mostly resisted by shear walls, which may be

constructed between column lines or may be combined into stair wells and elevator

shafts. Shear walls are vertical structural members whose cross-sectional dimension

ratio is greater than 7. The additional function of shear walls is to decrease the

possibility of damage to the non-structural members that most building contain

(Nawy, 2005). As stated by Paulay and Priestley (1992), “individual shear walls

may be subjected to axial, translational and torsional forces; to the extent to which a

wall will contribute to the story torsion, story shear forces and resistance of

overturning moments depends on its geometric appearance, orientation and location

within the plane of building”.

When shear walls are placed in advantageous positions in a building, they can be

very efficient in resisting lateral loads (Park and Paulay, 1975). In a structural

system, shear walls can be used together with a frame system. There are also

structural systems in which vertical load carrying elements are only shear walls.

Shear walls are considerably stiffer than regular frame elements, and thus can

absorb or respond to greater lateral forces, while controlling interstory drift.

Therefore, structures constructed with shear walls are significantly effective

compared to rigid frames from structural integrity, damage control and structural

safety point of view. (Nawy, 2005)

The use of shear walls becomes imperative in certain types of high-rise buildings if

the interstory deflections caused by the lateral loading have to be controlled. Shear

walls can both provide adequate structural safety and give a great prevention against

costly non-structural damage during a moderate seismic excitation (Park and

Paulay, 1975). Shear walls act as cantilever beams fixed at the base of the structure

in order to transfer lateral loads, such as earthquake load and wind load, to the

foundation. In a shear wall, gravity loads produce uniform compression over the

cross-section while flexure creates compression on one face of the wall and tension

on its opposite face. Flexure and shear have maximum values at the base of the

shear wall which vary over its height as shown in the Figure 4.4. The statistics of

basic variables concerning the flexural and shear capacity of a reinforced concrete

shear wall are summarized in Table 4.10.

Figure 4.4 a) Lateral loads b) Isolated wall c) Shear diagram d) Moment diagram

e) Axial loads

a) b) c) d) e)

and shear capacities of shear walls

Prediction error

Total uncertainty

21.55 MPa 1.25 0.105 0.14 0.18

365 MPa 1.24 0.038 0.08 0.09

Shear wall width (bw) 250-350 mm 1.05 0.047 0.03 0.056

Shear wall depth (w

l ) 1200-4400

mm 0.998 0.014 0.03 0.03

1500-7500 mm2 1.00 0.012 0.03 0.03

4.3.1 Flexural Capacity of Shear Walls

The diagram shown in Figure 4.4.c. indicates that shear walls, which can be

subjected to very high moments, must be designed to resist the moment at their

base. Additionally, the axial compressive force caused by gravity loads act on the

base section. In order to take into account the effects of both forces in combination,

an interaction diagram can be developed. Because of its large cross-sectional area,

the axial compressive load on a shear wall is often considerably smaller than the

one which would cause a balanced failure condition, in other words, in low-to-

moderate rise structures, the axial load is generally quite low; consequently, the

moment capacity is usually increased by the gravity forces in shear walls (Park and

Paulay, 1975). Therefore, it is conservative to consider only the moment at the base

in comparison with the axial compressive force. The moment capacity of a shear

wall can be computed from the following equations (Ferguson et al., 1988):

wydstrl

z1lfA5.09.0M (4.19)

( )( )ydstcdw1

fA/hflk85.02/1l

z+= (4.20)

where:

wl : the horizontal length of the shear wall

h: the thickness of the wall

Ast: the horizontal reinforcement area

In order to calculate the mean to nominal ratio and total variability of the flexural

capacity of a shear wall, different cases with varying characteristics of shear walls

are taken into account through another code written in MathCAD 12 according to

the FOSM format. The results of mean to nominal ratios and total variabilities for

the shear wall flexural capacity are given in Table 4.11.

The mean to nominal ratio of the flexural capacity of a shear wall is found to be

1.24 by using both nominal and in-situ values as explained before; and also, the

total variability in the flexural capacity of a shear wall is found to vary from 0.092

to 0.097 (Table 4.11). Correspondingly, in this study, the total variability will be

taken as 0.09. Again, the total variability in shear wall flexural design should be

combined with the analysis uncertainty. Accordingly, the analysis uncertainty

should be estimated. Ellingwood et al. (1980) used a value of 0.046 for beams and

columns in order to include this type uncertainty, whereas Nowak and Szerszen

(2003a) recommended the values of 0.06 and 0.08 for beams and columns,

respectively. On the other hand, the analysis uncertainty in the shear capacity of a

beam is given as 0.10 by Nowak and Szerszen (2003a) in their study. In the analysis

of shear walls, the assumption of “plane section remains plane after deformation” is

considered similar to the beam analysis. The studies, however, have showed that

this assumption is not correct if the height to width ratio of the cross-section is

excessively high. Therefore, in this study, the analysis uncertainty of the flexural

equation for shear walls is taken larger than the values taken for the flexural

equation of beams. Accordingly, in this study, the analysis uncertainty is set equal

to 0.10.

As a result, the total variability in the flexural capacity of a shear wall and the

analysis uncertainty for the equation of flexural capacity of a shear wall are

combined to find the overall uncertainty; yielding 13.0)10.009.0( 22M r

=+=Ω .

Table 4.11 Mean to nominal ratios and coefficients of variation for the flexural

capacity of shear-walls

bw (mm)

(mm) As

(mm2) r

′′′′ ΩM

200 1500 3500 1.241 0.092

200 2800 2500 1.240 0.094

200 2000 4500 1.241 0.092

200 3500 7500 1.242 0.092

250 1500 3500 1.241 0.093

250 1500 4500 1.242 0.092

250 1500 7500 1.242 0.092

250 2500 7500 1.242 0.092

250 4400 7500 1.241 0.093

300 1500 1000 1.240 0.096

300 1500 1500 1.241 0.095

300 1500 2500 1.241 0.094

300 1500 3500 1.241 0.093

300 2800 1500 1.240 0.097

300 1500 2500 1.241 0.094

300 1500 3500 1.241 0.093

300 2800 1500 1.240 0.097

4.3.2 Shear Capacity of Shear Walls

Shear walls behave like fixed supported beams, and the design of shear walls can be

carried out in the same way as beams (Park and Paulay, 1975; Celep and Kumbasar,

2005).

Shear capacity of wall cross sections, Vr, can be calculated by using the following

equation, as specified in TEC-2006 (Specification for Structures to be Built in

Earthquake Areas, 2006):

)ff65.0(AV ydshctdchr ρ+= (4.21)

where:

Ach: gross section area of the shear wall

ρsh: ratio of horizontal web reinforcement of shear wall to the gross area of shear

wall web [(ρsh)min=0.0025]

On the other hand, the shear force, Vd, should satisfy the conditions defined below:

rd VV ≤ (4.22)

cdchd fA22.0V ≤ (4.23)

In order to calculate the mean to nominal ratio and the total variability of the shear

capacity of a shear wall, various dimensions with different reinforcement areas are

analyzed using a code written in MathCAD 12 according to the FOSM formulation.

The results are given in Table 4.12.

As observed in Table 4.12, the analyzed cases indicate a value of 1.24 for the mean

to nominal ratio of the shear capacity of shear walls by using both nominal and in-

situ values as stated before, and also the total variability in the shear capacity of

shear walls is found to vary from 0.085 to 0.103, with a weighted average value of

Nowak and Szerszen (2003a) recommended a value of 0.10 for the analysis

uncertainty for the shear capacity of a beam in their study, based on the research

conducted by Ellingwood et al. (1980) and engineering judgment. Here, the analysis

uncertainty will also be taken as 0.10; in other words, in order to account for the

analysis uncertainty of the shear capacity of a shear wall, the same value that is used

for the shear capacity of a beam will be used. Consequently, the overall uncertainty

in the shear capacity of a shear wall will be 14.0)10.010.0( 22Vr

=+=Ω .

Table 4.12 Mean to nominal ratios and coefficient of variations of resistances for

shear-walls in the shear failure mode

bw (mm)

lw (mm)

′′′′ ΩM

200 1500 0.0025 1.244 0.102

200 2000 0.0040 1.243 0.094

200 3000 0.0055 1.243 0.091

200 4000 0.0040 1.243 0.094

200 5000 0.0055 1.243 0.091

250 1500 0.0030 1.243 0.098

250 2000 0.0040 1.243 0.094

250 3000 0.0048 1.243 0.092

250 4000 0.0032 1.244 0.097

250 5000 0.0025 1.244 0.102

300 2000 0.0026 1.244 0.101

300 3000 0.0033 1.244 0.096

300 4000 0.0040 1.243 0.094

300 5000 0.0050 1.243 0.091

300 6000 0.0025 1.244 0.102

CHAPTER 5

MODELING OF LOADS

5.1 INTRODUCTION

The information on the design loads is one of the main components in structural

engineering for the analysis of structures. The loads acting on a structure can take

on a wide variety of forms. They are usually considered as primary or secondary

loads. Secondary loads are due to temperature changes, construction eccentricities,

shrinkage of structural materials, settlement of foundations, or other such loads.

Primary loads include the own weight of the materials from which the structure was

built, the occupants and the furniture, various weather conditions, loading

conditions that the structure is experienced during construction and environmental

loads. In this study, only five major loads, namely dead, live, wind, snow and

earthquake will be considered as the primary loads.

Dead load can be defined as the weight of the permanent elements of a structure.

These elements are always present; therefore, the dead load will nearly remain

constant unless any major changes are carried out in the building.

Imposed or live loads include all the movable objects in a building, such as people,

furniture, machines and fixtures, partitions and other non-structural elements.

The degree of snow load effect depends on the climate of a region. Some countries

and regions have snowfall for six months of the year or more while some have little

or no snowfall during a year. Structures have to be designed to withstand the

appropriate snow load consistent with the weather conditions of the regions in

which they are located.

Wind load is the lateral pressure on the structure due to wind blowing in any

direction. Wind loads play a much more important role in modern construction than

they did in the past. In modern construction, where a steel framework is used, wind

loads primarily affect the strength and stability of the building.

The importance of earthquake loading is related to its likelihood of occurrence and

possible magnitude in any given region. Structural engineers mainly deal with the

local effects of large earthquakes in regions where the ground motions appear to be

intense enough to lead to the structural damage. Earthquake load is assumed to be

lateral load acting in any horizontal direction on the structural frame due to the

dynamic action of earthquakes. The structure can be designed considering the

maximum shear force at the base of structure. In the earthquake resistant design, the

reliability-based design criteria is required to include the characteristics of

earthquake load, structural capacity and structural response, which are all random in

nature and involve uncertainties.

Any type of structural load becomes meaningful if it leads to a load effect.

Assuming a linear relationship between a load and its effect, the following formula

gives the load effect, Si, on the basis of its corresponding structural load, Li,

(Ellingwood et al.1980):

iiii LNCS = (5.1)

where:

Ci: influence coefficient

Ni: modeling parameter

Li: structural load

It should be noted that in this formula, the parameters on the right hand side of the

equations, i.e. Ci, Ni, and Li are assumed to be statistically independent. According

to the FOSM method, the mean and coefficient of variation for any load type can be

computed from the following formulas, respectively:

iiiiLNCS = (5.2)

2CiSi ∆+∆+∆=Ω (5.3)

In the following sections, structural load effects resulting from dead, live, wind,

snow and earthquake loads will be evaluated. The published data in literature and

the local data compiled in Turkey constitute the main sources of information in the

evaluation of the load statistics. For calibration purposes, the ratio of mean to

nominal load values should be determined. The nominal values of loads will be

obtained from TS 498 (Design Loads for Buildings). It is worth mentioning here

that although the dead and live loads acting on a structure are independent of the

geographical location of the structure, environmental loads, such as snow, wind and

earthquake loads are highly dependent on the location of the structure. Accordingly,

for the assessment of statistics of environmental loads, different cities, which will

represent the whole Turkey, are chosen. In this selection, cities with the highest

critical environmental load are given priority. Also, cities with larger populations

are preferred. Another criterion in this selection is that these cities be located in

geographically different regions of Turkey. For the snow depth and wind speed, the

data are obtained from the meteorological stations that are in the centers of these

cities. The locations of these cities are shown in the following map:

Figure 5.1 The map showing the locations of selected cities

5.2 DEAD LOAD

Dead loads result from the weight of the structural elements, such as beams,

columns, slabs, and non-structural permanent fixtures like roofing, surfacing and

covering. The main characteristics of dead load can be described as follows (JCSS

Probabilistic Model Code, 2001):

-Throughout the life of the structure, dead load remains constant and the

probability of occurrence of dead load at an arbitrary point-in-time is one.

- The variability of dead load with time is generally negligible.

- The uncertainties related to dead load are normally small in comparison

with other types of loads.

Taking the above statements into consideration the following factors cause

variability in dead load:

- The errors and tolerances in the measurement of dimensions,

- The differences in the actual and nominal unit weights of the construction

materials,

- The tributary area method which represents a rough approximation of the

real situation.

In addition to the factors listed above, the variability in dead load also results from

the variability in the weight of the non-structural items, such as roofing, partitions.

The most important variability in dead load is due to weight of these non-structural

components. Therefore, Ellingwood et al. (1980) expressed that the material that

constitute the structural system has a very weak influence on variability of dead

Concerning the uncertainties in dead load, the following sources of variability can

be taken into consideration: variability within a structural member, variability

between different structural members of the same structure and variability among

various structures (JCSS Probabilistic Model Code, 2001).

Most of the investigators indicated that the probability distribution of dead load

should be normal and assumed that the ratio of mean to nominal dead load, DD ′ , is

unity. Some of the values on the mean to nominal ratio and the coefficient of

variation as reported by different reliability based design studies are listed in Table

5.1. It is observed in Table 5.1 that the variability in dead load ranges from 5% to

10%. In his study, Kömürcü (1995) assumed that normal distribution is suitable for

dead load. He took the mean to nominal ratio of dead load, and total variability as

1.05 and 0.10, respectively. It is assumed that DD ′ =1.05 and ΩD=0.10 as the

approximate average value of these studies, and normal distribution is taken for the

dead load. Here, D and D′ denote the mean and nominal value of dead load,

respectively, and ΩD stands for the total uncertainty in dead load.

Table 5.1 Statistics of dead load (from Ellingwood et al., 1980)

References DD ′′′′ ΩD

Galambos and Ravindra, 1973 1.0 0.08

Allen, 1976 1.0 0.10

Elingwood, 1978 1.0 0.10

Lind, 1976 1.05 0.09

Lind et al., 1978 1.0 0.05

Ellingwood et al. 1980 1.03 0.10

5.3 LIVE LOAD

Most of the live load research works were conducted about two decades ago and the

development in the understanding of live loads has been hampered by the

insufficiency of live loads survey data (Kumar, 2002a). Live loads on floors of

buildings include the weight of furniture, equipment, stored objects, movable

partitions, and persons and their possessions. At the same time, rare events expected

in the lifetime of structure, such as gathering of persons or moving of objects which

may occur during reorganization or redecoration, cause to this type of load. Any

structural or non-structural elements like covering, extraordinary equipment or

partition walls are not included in live loads. The live load can be separated

according to categories of usage, such as domestic and residential activities, office

areas, shopping areas, hotels, hospitals, restaurants, dance halls where people may

concentrate in number.

A wide variety of loading possibilities, which the structural engineers may not

predict, can occur within the lifetime of a structure. In addition, live loads vary in

time and space in a random manner. On the other hand, owing to the correlation

between room use and the room area, unit floor loads are strongly correlated with

the room area. “The total live load on a floor area may be thought of conveniently

as consisting of a sustained component which remains relatively constant within a

particular occupancy, referred to as the arbitrary point-in-time live load, and an

extraordinary component which arises from infrequent clustering of people above

and beyond normal personal load, or from activities such as remodeling”

(Elingwood et al., 1980).

It is rational that unit floor loads are insignificantly affected by geographical

locations, height of storey, sector, age and traditional habits in countries. Although

there are differences among the results which are based on UK, USA, Australian

and Indian surveys, the overall characteristic and variation of live loads are very

similar. (Kumar, 2002b)

5.3.1 Arbitrary Point-in-Time Live Load (Lapt)

A number of load surveys which were analyzed by using probabilistic load models

have been conducted in different countries. Although most of the studies have

focused on office buildings, some data on residence, retail establishments and other

occupancies were also taken into consideration. A summary of results obtained

from the analyses of load survey data is shown in Table 5.2.

In addition to studies given Table 5.2, the arbitrary point-in-time live load

intensities for office buildings obtained from different studies are compared in

Table 5.3. The differences among the live load survey results of various studies are

due to a number of typical reasons, e.g. sample size of surveys, time interval

between different surveys, methodology of data collection, cultural backgrounds of

social groups using relevant buildings, such as occupancy duration and properties of

devices used in the buildings.

Table 5.2 Statistics of arbitrary point-in-time live loads for offices reported in

different studies (from Ellingwood et al., 1980)

18.58 m2 92.9 m2 464.5 m2

929 m2

Reference

LLapt′ ΩLapt LLapt

′ ΩLapt LLapt ′ ΩLapt LLapt ′ ΩLapt

McGuire and Cornell (1973)

0.24 0.89 Varies 0.52 Varies 0.41 Varies 0.40

Ellingwood and Culver (1977)

Chalk and Corotis (1979)

Allen (1976) 0.16 0.70 Varies 0.48 Varies 0.38 Varies 0.36

Sentler (1975) 0.15 0.59 Varies 0.26 Varies 0.20 Varies 0.18

Mean of ΩLapt 0.80 0.50 0.45 0.40

According to Table 5.3, the average arbitrary point-in-time loads for office

buildings are 0.609 kN/m2, 0.58 kN/m2, 0.51 kN/m2, 0.488 kN/m2 for surveys

conducted by Mitchell and Woodgate (1971), Culver (1975), Choi (1992) and

Kumar (2002a), respectively. In this study, the arbitrary point-in-time live load will

be taken as 0.55 kN/m2 for office buildings, which is the average of the values

reported in the studies mentioned above. On the other hand, the average basic

variability of arbitrary point-in-time live load is taken as 0.78 based on Table 5.3.

The c.o.v. in live load effect should include the uncertainties in the analysis which

converts the equivalent uniformly distributed loads to a load effect and errors in the

load modeling. The uncertainty due to the transformation of the equivalent

uniformly distributed load to a load effect is assumed to be ∆C=0.05, and the

modeling uncertainty is taken as ∆N=0.10 (Ellingwood, et al., 1980). The total

prediction error due to these two sources of uncertainty will be

22 05.010.0 +=∆L =0.11. As a result, the total uncertainty in arbitrary point-in-

time load becomes 79.078.011.0 22 =+=ΩL . As it is seen in Table 5.2, the mean

of total variability in arbitrary point-in-time live load, ΩLapt ranges from 0.8 to 0.4

depending on the area with an average value of 0.60. In this study, taking into

consideration the values associated with the arbitrary point-in-time load, the total

variability, ΩLapt, will be taken as 0.70 as an average value of total variabilities

obtained from Tables 5.2 and 5.3.

In the Turkish Code of design loads for buildings, i.e. TS 498 (1997), the nominal

live load, L′ , is given as 2 kN/m2 for housing or terrace room and corridors, stores

up to 50 m2, hospital rooms and offices. Thus, the ratio of arbitrary point-in-time

load to nominal live load is 0.2752

Lapt==

The normal, log-normal and gamma distributions were tested by different

researchers to describe the distribution of live load. The normal distribution did not

show a good fit. Among the three distributions studied, the use of gamma

distribution seems to provide a reasonable probabilistic model for live load (Corotis

and Doshi, 1977). Accordingly, the gamma distribution is taken as the probability

distribution for the arbitrary point-in-time live load in this study.

Table 5.3 Results of arbitrary point-in-time live load surveys for office buildings

which was reported in different studies (from Kumar, 2002a)

Survey

Bounds of room floor area, A (m2)

Mean live load (kN/m2)

Standard deviation

Mitchell and Woodgate (1971)

2.4 5.2

14.0 31.2 58

111.3 192.4

0.66 0.64 0.62 0.61 0.59 0.58 0.56

0.65 0.53 0.43 0.34 0.30 0.26 0.21

0.98 0.83 0.69 0.56 0.51 0.45 0.38

Culver (1975)

A≤4.7

4.7<A≤9.3 9.3<A≤27.9

A>27.9

0.83 0.63 0.44 0.42

0.82 0.60 0.31 0.43

0.99 0.95 0.70 1.02

Choi (1992)

5<A≤10 10<A≤20 20<A≤40 40<A≤80

0.50 0.62 0.55 0.45 0.43 0.51

0.66 0.64 0.47 0.53 0.45 0.41

1.32 1.03 0.85 1.18 1.05 0.80

Kumar (2000)

8<A≤16 16<A≤24 24<A≤32 32<A≤40 40<A≤48 48<A≤56 64<A≤72 72<A≤80

0.68 0.60 0.50 0.50 0.47 0.45 0.45 0.46 0.46 0.31

0.41 0.32 0.36 0.29 0.26 0.24 0.25 0.15 0.19 0.20

0.60 0.54 0.72 0.58 0.55 0.53 0.56 0.33 0.41 0.65

5.3.2 Maximum Live Load (L)

Maximum live load which is used for design purposes is composed of lifetime

maximum sustained load and extraordinary load. The lifetime maximum sustained

load is the maximum of the various sustained loads which are normally present as a

consequence of everyday activity, and this type of load is dependent on the rate of

change of occupancy. Crowding of people or stacking of furniture causes additional

loads which act at a moment during the lifetime of building except for sustained

load. This type of loading is defined as extraordinary load.

Loads acting on a structure at any point in-time can be defined by load surveys, but

the determination of the maximum load which may be expected to act on the

structure at any time during its lifetime is impossible with these load surveys

performed during a limited duration of time. In addition to survey data of arbitrary

point-in-time loads, the frequency of occupant changes and extraordinary load

events must be predicted. Ellingwood et al. (1980), Kömürcü and Yücemen (1996)

and Kumar (2002a) used Type I extreme value distribution to describe the

distribution of maximum live load. Type I extreme value distribution is also

preferred in this study. Some of the results obtained from the studies related to

maximum live load for office buildings are shown in Table 5.4. In spite of the fact

that the results in Table 5.4 are derived for offices, examination of data for a

number of other occupancies covering multistory residences and retail

establishments shows similar properties (Ellingwood et al., 1980).

Table 5.4 Statistics of maximum live loads as reported in different studies

(from Ellingwood et al., 1980)

18.58 m2 92.9 m2 464.5 m2 929 m2

Reference LL ′ δL LL ′ δL LL ′ δL LL ′ δL

McGuire and Cornell (1973)

Ellingwood and Culver (1977)

Chalk and Corotis (1979)

Sentler (1975) - 0.26 Varies 0.18 Varies 0.14 Varies 0.12

In the studies performed by Ellingwood et al. (1980) and Kömürcü (1995), the

uncertainty due to the transformation of the equivalent uniformly distributed load to

a load effect is assumed to be ∆C=0.05, which is the same value for Lapt, and

uncertainty in the load modeling is taken as ∆N=0.20. Here, the value of ∆C and ∆N

are also taken as 0.20 and 0.05, respectively. The basic variability, δL, is taken to be

0.17 as the average of the values reported in Table 5.4. Accordingly, in the case the

prediction uncertainties and inherent variability are combined, the total uncertainty

in maximum live load, L, will be equal to 27.005.020.017.0 222 =++=Ω L .

Kömürcü (1985) took mean to nominal ratio of maximum live load as 1.00. Also, in

another study, Nowak and Szerszen (2003b) proposed this ratio to be 1.00. In this

study, the mean to nominal maximum live load ratio is also taken as 1.00.

5.4 SNOW LOAD

Snow loading is one of the main reasons of structural performance failures which

can cause significant economic losses in certain regions; therefore, structural

engineers should anticipate snow action on structures (O’Rourke and Wreen, 2004).

In some cases, the drifted snow on roofs may cause severe damage and even

collapse of structures in Turkey if the design snow load is less than its real value

(Durmaz and Daloglu, 2005). Buildings, particularly roofs can be affected by snow

in numerous ways; the important ones can be listed as follows:

- Snow load can cause the collapse of roofs due to heavy accumulation.

- The drifting around buildings can obstruct people and vehicles to access

inside.

- Snow slides from sloped roofs and skylights can endanger pedestrians.

- Ice and ice dams cause water leakage under roofs.

- Snow melting causes gathering of water at low or irregular areas on a roof.

Although all snow problems should be paid attention, in this study, the snow load

on roofs, which is probably the most important problem in terms of human safety

and economic properties will be taken into account. Design snow loads for roof

structures are based on a number of parameters. These parameters include

geographical location, roof type and slope, building configuration, air temperature,

amount of sunshine, thermal building conditions and roof exposure to wind. In

addition to these parameters, amount and type of snowfall, sliding snow, snow

drifts, unbalanced snow loads, building characteristics and surrounding environment

must be considered (Jeff Quell, 1998; Schiever, 1978). To be aware of how they

affect snow loads is important both in evaluating the validity of calculated snow

loads for a special roof at a specific site and in determining the characteristic ground

snow load.

Among the parameters that influence design snow loads on roofs, the wind effect is

probably the most important one because the wind exposure usually causes the

snow drift. Winds incline to decrease snow loads on the windward side of a roof

and raise snow loads on the leeward side. In addition, terrain features, rooftop

projections, parapet walls and adjacent buildings can all cause snow drifts on roofs.

Extra snow can also be accumulated on roofs equipped with satellite dishes and

solar collectors. On the other hand, impact snow loads resulting from snow sliding

off or falling from a higher roof cause additional snow load. The roof surface

temperatures, the slipperiness of the roof surface and rooftop obstructions influence

the amount of sliding. Since most structural failures associated with snow loads

came into existence due to overloads, such as snow drifts and sliding snow, for the

convenient design of the roof, and in some cases, the removal of snow drifts is key

to the integrity of the roof structure( (Jeff Quell, 1998).

If a building is adjacent to a small building, it is important to understand that the

small building may be exposed to more severe snow action. On the other hand, the

design snow load on an existing roof structure may be changed by building

additions and alterations, or by the construction of a new building which is adjacent

to the old structure.

In the structural engineering problems, snow loads are generally an important

design factor if:

-The building is constructed in regions that are cold and snowy.

-The building is adjacent to a higher existing building.

-The building has a relatively large roof.

-The building has an unusually shaped roof.

The principles and methods used to calculate the design snow loads are determined

in the model building codes, or can be clearly described by the local building codes.

The application of these building codes by a design engineer determines the design

snow load for each building separately (Jeff Quell, 1998).

5.4.1 Roof Snow Load

According to standards, roof snow load required for structural analysis is defined as

the product of a design ground snow load and different conversion factors that

transform the ground snow load to roof snow load. This transformation procedure

can be carried out by using the following formula (ASCE/SEI 7-05, 2006):

k0te .I.P.Cα.CS = (5.4)

where:

S: roof snow load

α: basic reduction factor

Ce: exposure factor

Ct: thermal factor

I: risk factor

Pko: ground snow load.

The basic reduction factor, α, takes into account the redistribution of the snow on

the roof caused by wind, in other words, α results from wind effect on snow

accumulation. It was proposed to be 0.47, 0.6 and 0.7 by Q’ Rourke et al. (1982),

Kömürcü (1995) and ASCE/SEI 7-05 (2006), respectively. In this study α will be

taken as 0.6, which is approximately the average of these three values.

The thermal coefficient, Ct, accounts for the roof’s thermal special features. If a

structure is heated, thermal energy moving smoothly through the roof should cause

a change in roof snow load. The structures can be mainly divided into heated

structures, heated structures with ventilated roofs in freezing and cold climates and

unheated structures. According to ASCE/SEI 7-05 (2006), the corresponding

thermal factors range from 0.85 to 1.2 for heated structures. Since the heated

structures are considered as a basis for design in this study, thermal factor will be

taken as 1.0.

The exposure factor, Ce, depends on the location of both structure and roof, as well

as theirs surrounding (O’Rourke et al., 1982). Ce in ASCE/SEI 7-05 (2006) ranges

from 0.7 to1.2 for the separate classifications with an approximate average value of

1.0, which will be also valid in this study.

The aim of the importance factor, I, used in snow load analysis is to increase design

loads for cases where the consequences of failure are greater than normal, and is to

decrease design loads for structures where consequences of failure are less than

normal. It ranges from 0.8 to 1.2 ASCE/SEI 7-05 (2006). In this study, importance

factor value will be taken as 1.0.

As a term, all of these conversion factors can be defined as snow load coefficient,

Cs, and, Eq. (5.4) can be rewritten as “ k0s .PCS = ”. This coefficient is consequently

calculated as 0.6. The total variability in snow load coefficient, ΩCs, which results

from the above conversion factors is assumed to be 0.23 (Ellingwood et al., 1980;

Kömürcü and Yücemen, 1996).

5.4.2 Ground Snow Load, Pko

In Turkey, snowfall generally increases from west to east and from south to north; it

also increases with altitude of the site from the sea level (Ayaroglu, 1991). The

ground snow load is determined from the basic meteorological data, and naturally

shows diversity according to the geographical location of the building sites.

Therefore, site specific case studies determine design ground snow load.

Accordingly, the annual maximum snow depth is obtained for Ankara, Izmir, Bursa,

Antalya, Gaziantep, Samsun, Malatya, Erzincan, Canakkale and Hakkari.

Considering the earthquake effect, Istanbul region has two different seismic zones,

seismic zone I and seismic zone II; some of the buildings in Istanbul are located in

seismic zone 1 whereas other buildings are located in seismic zone II. Therefore,

two centers for Istanbul are classified as Göztepe located in seismic zone I and Sile

located in seismic zone II. Another reason to consider this classification is that

Istanbul has the largest population among the cities in Turkey; naturally the number

of buildings is quite more than an ordinary city. Also snowfall is expected for only

three or four months in most of the cities in Turkey; we do not mention any snow

loads in the other months for these locations. Furthermore, snowfall may not be

seen in some years for specific locations. Therefore, years in which there is no

snowfall are not taken into account and for locations where there is regular

snowfall; 0.01 m snow depth values are ignored. On the other hand, 1.00 m snow

depth value in the Gaziantep region, which deviates from the mean by more than

3σ, is treated as an outlier, and is not taken into consideration. The modified data is

given in Appendix C.

The average values of the maximum snow depths for Ankara, Izmir, Bursa,

Antalya, Gaziantep, Samsun, Malatya, Erzincan, Canakkale, Hakkari,

Göztepe/Istanbul and Sile/Istanbul are found to be 0.127 m, 0.02 m, 0.188 m, 0.015

m, 0.16 m, 0.142 m, 0.250 m, 0.207m, 0.107 m, 1.057 m, 0.146 m, 0.147 m,

respectively. The matching variabilities in annual snow depth values for these cities

are computed as 0.54, 0.63, 0.71, 0.47, 0.66, 0.88, 0.51, 0.52, 0.85, 0.50, 0.66, and

0.76, respectively.

The ground snow load can be determined by using the following equation:

h.ρPk0 = (5.5)

where:

h: depth of snow on the ground (m)

ρ: average density of snow (kN/m3)

The value of snow density is determined by using its water equivalent (O’Rourke et

al., 1982, Rusten et al., 1980). Snow density is space and time dependent; while

snow depth grows, snow density, which also rises with time, will naturally increase.

TS 7046 (Bases for Design of Structures-Determination of Snow Loads of Roofs)

and Ghiocel and Lingu (1975) proposed the following empirical relationships

between snow depth, h (m) and snow density, ρ (kg/m3):

1.5h200.e300ρ −−= (5.6)

Considering the mean snow depths, mean snow densities can be computed for

Ankara, Izmir, Bursa, Antalya, Gaziantep, Samsun, Malatya, Erzincan, Canakkale,

Hakkari, Göztepe/Istanbul and Sile/Istanbul by using Eq. (5.6). By putting in the

mean values of annual maximum snow depth, anh , and the mean values of snow

density, ρ , in Eq. (5.5), the mean value of the annual extreme ground snow load,

Pko, for different locations are computed. The total variability in ground snow loads

is calculated by using the variability in maximum snow depths and the variability in

snow density according to Eq. (5.7). The results are summarized in Table 5.5.

ρP ankoΩΩΩ += (5.7)

Table 5.5 Statistical parameters of the annual extreme ground snow load

Parameter

Location

(kN/m3)

(kN/m2)

Ankara 1.35 0.12 0.127 0.54 0.171 0.55

Izmir 1.06 0.03 0.02 0.63 0.021 0.63

Bursa 1.49 0.18 0.188 0.71 0.280 0.73

Antalya 1.04 0.02 0.015 0.47 0.016 0.47

Gaziantep 1.43 0.16 0.16 0.66 0.229 0.68

Samsun 1.38 0.20 0.142 0.88 0.196 0.90

Malatya 1.62 0.15 0.250 0.51 0.405 0.53

Erzincan 1.53 0.15 0.207 0.52 0.317 0.54

Canakkale 1.30 0.16 0.107 0.85 0.139 0.86

Hakkari 2.59 0.11 1.057 0.50 2.738 0.51

Göztepe/Istanbul 1.39 0.16 0.146 0.66 0.203 0.68

Sile/ Istanbul 1.40 0.18 0.147 0.76 0.206 0.78

5.4.3 Annual Extreme Roof Snow Load

The mean annual roof snow load, anS , can be computed for Ankara, Izmir,

Gaziantep, Samsun, Malatya, Erzincan, Canakkale, Hakkari, Göztepe/Istanbul and

Sile/Istanbul by using the appropriate values of the parameters Cs and ankoP .

Statistical parameters of the annual extreme roof snow load are shown in Table 5.6.

It is observed that the lognormal distribution shows a reasonable fit to the data

according to Minitab and BestFit computer programs for the annual maximum snow

depth of different locations. The Chi-Square and Kolmogorov- Smirnov tests results

for Lognormal, Normal, Extreme-value (Type I), Gamma, Weibull, Rayleigh

probability distributions are given in Appendix C. The distribution of ankoP can also

be taken as lognormal and regarding the distribution of component variables Cs

andankoP , the distribution of San could be approximated by a lognormal distribution

like its component ankoP (Ellingwood et al., 1980). The parameters of the

corresponding lognormal distribution are computed from the following general

equations (Ang and Tang, 1984):

)1ln( 2Ω+=ζ (5.8)

1ln ζ−µ=λ (5.9)

Table 5.6 Statistical parameters of the annual extreme roof snow load

Parameter

Location

(kN/m2)

anSζζζζ

anSλλλλ

Ankara 0.103 0.60 0.555 -2.427

Izmir 0.013 0.67 0.609 -4.528

Bursa 0.168 0.77 0.682 -2.017

Antalya 0.009 0.52 0.489 -4.83

Gaziantep 0.137 0.72 0.646 -2.197

Samsun 0.118 0.93 0.789 -2.449

Malatya 0.243 0.58 0.538 -1.560

Erzincan 0.190 0.59 0.547 -1.810

Canakkale 0.083 0.89 0.764 -2.781

Hakkari 1.643 0.56 0.522 0.36

Göztepe/Istanbul 0.122 0.72 0.646 -2.313

Sile/ Istanbul 0.123 0.81 0.710 -2.348

5.4.4 Maximum Roof Snow Load (S)

Maximum roof snow load, S, can be defined as the 30-year maximum value for

Canada and Russia, and the 50-year maximum value for Europe and U.S.A.

(Durmaz and Daloglu, 2005). In this study, a 50-year maximum value will be used

for maximum roof snow load.

The probability distribution of maximum roof snow load is based on the

distributions of Cs and mainly on ankoP , which is lognormally distributed. Type II

extreme value distribution for S is used on the basis of the fact that the limiting

distribution for a series of lognormally distributed variates is the Type II extreme

value distribution of largest values (Ellingwood et al., 1980). Considering that the

initial distribution of a random variable is lognormal with parameters, ζ and λ , the

distribution of the largest value of a random variable converges to the Type II

asymptotic form with following parameters (Ang and Tang, 1984):

=SSS λ

2ln(n)2

ln4πlnln(n)ζ2ln(n)ζ

S ev (5.10)

2ln(n)k = (5.11)

The mean value and variability of S are obtained substituting the above parameters

in the following equations:

11ΓvS (5.12)

SS −

= (5.13)

where Γ(.) stands for the gamma function.

Table 5.7 Statistical parameters of the 50-year maximum roof snow load

Parameter

Location

S (kN/m2)

Ankara 0.283 5.044 0.329 0.31

Izmir 0.039 4.593 0.046 0.35

Bursa 0.558 4.099 0.679 0.41

Antalya 0.022 5.718 0.025 0.27

Gaziantep 0.432 4.328 0.519 0.39

Samsun 0.454 3.543 0.577 0.50

Malatya 0.652 5.194 0.754 0.30

Erzincan 0.516 5.118 0.598 0.31

Canakkale 0.309 3.662 0.389 0.48

Hakkari 4.295 5.356 4.938 0.29

Göztepe/Istanbul 0.385 4.328 0.462 0.38

Sile/ Istanbul 0.425 3.938 0.523 0.43

5.4.5 Mean to Nominal Ratios of San and S

The statistical parameters of an

S /S′ and S /S′ can be found after determining the

nominal snow loads. The nominal snow load, S′ , can be obtained from TS 498

(1997). Results of mean to nominal ratios of San and S are shown in Table 5.8 for

the different locations considered.

Since the distribution of San is lognormal San/S′ will have a lognormal distribution.

However, S/S′ has a Type II distribution because Type II distribution is used for

maximum snow load, S.

Table 5.8 Statistical parameters of the mean to nominal ratio for annual extreme and

50-year maximum snow loads

5.5 WIND LOAD

The assessment of wind load and reliability of structures under the influence of

wind has been receiving growing interest during the last few decades. However, a

number of significant issues as to wind load still remain unsolved (Minciarelli et al.,

2001). Structural engineers should make certain that the structures subjected to

wind load will be sufficient during its expected life with regard to both

serviceability and structural safety. Accordingly, the information on the behavior of

the structure under the wind action is required in order to realize the relation

between the wind environment and the wind action.

Parameter

Location

S′′′′

San′′′′

SanSΩ

anSζζζζ

anSλλλλ

S′′′′

′′′′

Ankara 0.95 0.11 0.60 0.56 -2.36 0.35 0.31 0.30 5.04

Izmir 0.75 0.02 0.67 0.61 -4.10 0.06 0.35 0.05 4.59

Bursa 0.75 0.22 0.77 0.68 -1.75 0.91 0.41 0.75 4.10

Antalya 0.75 0.01 0.52 0.49 -4.73 0.03 0.27 0.03 5.72

Gaziantep 1.25 0.11 0.72 0.65 -2.42 0.42 0.39 0.35 4.33

Samsun 0.75 0.16 0.93 0.79 -2.14 0.77 0.50 0.62 3.54

Malatya 1.35 0.18 0.58 0.54 -1.86 0.56 0.30 0.48 5.19

Erzincan 1.49 0.13 0.59 0.55 -2.19 0.40 0.31 0.34 5.12

Canakkale 0.75 0.11 0.89 0.76 -2.50 0.52 0.48 0.42 3.66

Hakkari 1.84 0.89 0.56 0.52 -0.25 2.68 0.29 2.32 5.36

Göztepe/Istanbul 0.75 0.16 0.72 0.65 -2.04 0.62 0.38 0.52 4.33

Sile/ Istanbul 0.75 0.16 0.81 0.71 -2.09 0.70 0.43 0.57 3.94

Wind loads are derived by using the statistical data based on wind speed, mass

density of air, pressure coefficient, parameters related to wind speed and exposure,

and a gust factor that incorporates the effects of short gusts and the dynamic

response of the structure. The wind load acting on a structure can be determined

from the wind speed by using the standard hydrodynamic relationship, which can be

rewritten for particular structures or surfaces of structures as follows (Melchers,

2002):

2zp V.G.E.c.C W = (5.14)

where;

W: wind load

c: a constant related to mass density of air

Cp: pressure coefficient

Ez: exposure coefficient

G: gust factor

V: wind speed

The pressure factor, Cp, depends on the geometry and shape of the structure. It is the

ratio of the pressure at relevant surface of the structure to the dynamic pressure of

the wind (Simiu and Scalan, 1978). The exposure coefficient, Ez, depends on the

actual topographical conditions (e.g. urban area, enclosed valleys, slopes, hills, open

country and also the presence of constructions near the structure). The gust factor is

associated with the turbulence of the wind and the dynamic interaction between the

structure and wind.

Since the velocity parameter appears with its square in Eq. (5.14), it is a particularly

important parameter in comparison with the other parameters. The overall

uncertainty in wind load is also affected by uncertainties in the estimation of the

pressure coefficient, the exposure factor and the gust factor.

5.5.1 Analysis of Wind Speed

Most of the statistical data available related to wind load are obtained from the

monthly maximum or annual maximum wind speeds; the pressure coefficients and

gust factors are consistent with this maximum wind speeds. The wind speed

changes with latitude, longitude and altitude from the sea level and time (Sahin,

2001). In this study, since it is impractical to perform reliability analysis separately

for each and every location where wind speed data is available, it is decided to

collect this necessary data for twelve different locations in Turkey. Hence, the same

cities considered in the calculation of the snow load, namely, Ankara, Izmir, Bursa,

Göztepe/Istanbul and Sile/Istanbul are selected in order to carry out the wind load

analysis for Turkey. The required data on maximum yearly and maximum daily

wind speeds are taken from the Turkish Meteorological Department (DMI). The

wind speed is measured at 10 meters above the ground level in these locations

(Dündar et al., 2002). These data and the statistics computed are shown in Appendix

D and Appendix E for the locations above.

Type I and Type II extreme value distributions are the most common and

appropriate probability distributions for wind speeds (Simiu and Scalan, 1978 and

Ellingwood et al., 1980). Simiu and Scanlan (1978) indicated that if the wind speed

data are collected in locations where extraordinary wind speeds are very rare, the

use of Type I distribution is more suitable as a probabilistic model. Yücemen and

Gülkan (1989) and Kömürcü (1995) used the Type I distribution for yearly

maximum wind speed, daily maximum wind speed and lifetime maximum wind

speed that were measured in Turkey. Because unusual winds are not seen frequently

in Turkey, Type I distribution can be used to describe the wind speed data. Also the

data analysis with BestFit and Minitab computer programs showed that Type I

distribution fits data satisfactorily. For Lognormal, Normal, Extreme-value (Type

I), Gamma, Weibull, Rayleigh probability distributions, the Chi-Square and

Kolmogorov- Smirnov tests results, which were performed by using computer

programs mentioned above, are given in Appendix D and Appendix E.

In this study, daily maximum wind speed, Vapt, and annual maximum wind speed,

Van, will be used, which are respectively necessary for the calculation of the daily

maximum wind load and the yearly maximum wind load. In addition to these two

parameters, maximum wind speed, V50, and nominal wind speed, V′ , are needed.

V50 is derived from the annual maximum wind speed, Van, and V′ is obtained from

TS 498 (1987). Since the data for the annual maximum wind speed fits the Type I

distribution, maximum wind speed could be described by a Type I distribution, and

the mean value and the basic variability of maximum wind speed are computed

from the mean value and variability of Van by making use of the following

equations. Also, the prediction error due to insufficient sampling, ∆1, is defined by

using these computed values according to Eq. (5.17) (Ellingwood et al., 1980).

+= ln50δπ

anVan50 (5.15)

50anVan50V V/V δ=δ (5.16)

anVan1

δV3.8∆ = (5.17)

where n is the sample size. As n increases, ∆1 decreases.

Dündar et al. (2002) indicated that due to systematic errors and wrong calibration of

devices associated with measurement of wind speed, an uncertainty of 0.05 should

be included. In addition to the uncertainties involved in the recorded data,

conversions including modeling, features of climatic parameters and roughness

parameters of surface also create additional uncertainties. Therefore, an additional

uncertainty of 0.02 is assumed to account for these factors (Ellingwood et. al., 1980;

Kömürcü, 1995).

The mean values and variabilities of Vapt, Van, and V50 for Ankara, Izmir, Bursa,

Göztepe/Istanbul and Sile/Istanbul are presented in Table 5.9. Considering the TS

498 (1997), the nominal wind speeds, V′ , for these locations are also shown in

Table 5.9.

Table 5.9 Mean values and coefficients of variation of wind speeds for different

locations

Parameter

Location

aptVΩΩΩΩ

anV(m/s)

V ′′′′

Ankara 8.50 0.33 20.13 0.24 34.25 0.135 0.045 0.15 36

Izmir 12.45 0.29 26.19 0.14 36.58 0.093 0.036 0.11 36

Bursa 6.53 0.44 23.92 0.21 38.51 0.124 0.043 0.14 36

Antalya 10.23 0.47 26.62 0.21 42.83 0.124 0.042 0.14 36

Gaziantep 5.49 0.44 17.53 0.25 30.63 0.139 0.043 0.16 36

Samsun 8.06 0.53 23.11 0.24 39.23 0.135 0.040 0.15 36

Malatya 6.52 0.54 15.09 0.46 36.26 0.191 0.041 0.20 36

Erzincan 6.65 0.44 19.07 0.29 35.94 0.154 0.046 0.17 36

Canakkale 11.14 0.41 28.99 0.18 44.02 0.112 0.038 0.13 36

Hakkari 7.07 0.54 20.19 0.22 33.12 0.128 0.045 0.15 36

Göztepe/Istanbul 6.95 0.53 19.67 0.30 37.67 0.157 0.046 0.17 36

Sile/ Istanbul 8.72 0.46 25.21 0.29 46.74 0.151 0.043 0.17 36

5.5.2 Maximum, Yearly Maximum and Daily Maximum Wind Loads

As it is stated before, if the wind speed data are collected in locations where

extraordinary wind speeds are very rare, the use of Type I distribution is more

suitable as the probabilistic model; besides the data analysis with BestFit and

Minitab computer programs showed that Type I distribution fits the data

satisfactorily (Appendix D, Table D.2 and Appendix E, Table E.13). Accordingly,

Type I distribution is adopted as the probabilistic model for the wind speed data. On

the other hand, the wind load may not have the same distribution of the wind speed.

Ellingwood et al. (1980) used Monte Carlo techniques assuming that Cp, Ez and G

were described by normal distributions. As a result, it was found out that wind load,

W, could be described by a Type I distribution over the range of the distribution

above its 90th percentile. The parameters of the Type I largest extreme value

distribution can be calculated through the following relationships (Melchers, 2002):

2= (5.18)

γµu −= (5.19)

where, γ =0.577 is the Euler’s constant.

Kömürcü (1995) proposed the mean values of the parameters Cp, Ez and G to be

0.80, 1.61 and 0.45, respectively. Ellingwood et al. (1980) quantified the

variabilities of these parameters as 0.12, 0.11 and 0.16. These variability values are

suitable for use in the code calibration related to wind load (Melchers, 2002).

Ghiocel and Lungu (1975) proposed the constant c to be equal to 0.0625, and

Ellingwood et al. (1980) quantified the variability of this parameter as 0.05. These

values will also be used in this study for all locations considered. The mean and

total variability of the maximum wind load can be computed from the following

equations by utilizing FOSM method:

2zp V.G.E.Cc. W = (5.20)

cW 2Ω+Ω+Ω+Ω+Ω=Ω (5.21)

The statistics related to the yearly maximum wind load, Wan, and daily maximum

wind load, Wapt, can be calculated in a similar way. The mean values and total

uncertainties of the maximum, yearly maximum and daily maximum wind loads for

relevant locations are presented in Table 5.10. In addition, mean to nominal wind

load ratios are shown in Table 5.12. Type I distribution parameters for wind loads

mentioned above are also presented in Table 5.12 for different locations.

Table 5.10 Mean values and the total uncertainties of wind loads for different

locations

Parameter

Location

(kN/m2)

W (kN/m2)

W′′′′

(kN/m2)

aptWΩ

Ankara 0.056 0.147 0.425 0.96 0.52 0.41 0.32

Izmir 0.015 0.248 0.485 0.96 0.47 0.31 0.28

Bursa 0.038 0.207 0.537 0.96 0.67 0.38 0.31

Antalya 0.011 0.257 0.665 0.96 0.71 0.38 0.31

Gaziantep 0.011 0.111 0.34 0.96 0.66 0.42 0.33

Samsun 0.024 0.193 0.558 0.96 0.79 0.41 0.32

Malatya 0.015 0.082 0.476 0.96 0.80 0.69 0.37

Erzincan 0.016 0.132 0.468 0.96 0.67 0.47 0.34

Canakkale 0.045 0.304 0.702 0.96 0.63 0.35 0.30

Hakkari 0.018 0.148 0.397 0.96 0.80 0.39 0.32

Göztepe/Istanbul 0.017 0.14 0.514 0.96 0.40 0.48 0.34

Sile/ Istanbul 0.028 0.23 0.791 0.96 0.70 0.47 0.34

Table 5.11 Mean to nominal wind load ratios and associated total uncertainties for

different locations

Parameter

Location

aptW / W ′′′′

(kN/m2)

aptWΩ anW / W ′′′′

(kN/m2) anWΩ W / W ′′′′

(kN/m2) WΩ

Ankara 0.058 0.52 0.153 0.41 0.443 0.32

Izmir 0.016 0.47 0.258 0.31 0.505 0.28

Bursa 0.040 0.67 0.216 0.38 0.559 0.31

Antalya 0.011 0.71 0.268 0.38 0.693 0.31

Gaziantep 0.011 0.66 0.116 0.42 0.354 0.33

Samsun 0.025 0.79 0.201 0.41 0.581 0.32

Malatya 0.016 0.80 0.085 0.69 0.496 0.37

Erzincan 0.017 0.67 0.138 0.47 0.488 0.34

Canakkale 0.047 0.63 0.317 0.35 0.731 0.30

Hakkari 0.019 0.80 0.154 0.39 0.414 0.32

Sile/ Istanbul 0.029 0.70 0.240 0.47 0.824 0.34

Table 5.12 Type I distribution parameters of mean to nominal wind load ratios for

different locations

aptW / W ′′′′ anW / W ′′′′ W / W ′′′′

Parameter

Location α µ α µ α µ

Ankara 0.044 42.53 0.125 20.44 0.379 9.05

Izmir 0.013 170.55 0.222 15.03 0.441 9.07

Bursa 0.028 47.85 0.179 15.63 0.481 7.401

Antalya 0.007 164.21 0.222 12.59 0.596 5.97

Gaziantep 0.007 176.66 0.094 25.33 0.301 10.98

Samsun 0.016 64.94 0.164 15.56 0.497 5.89

Malatya 0.010 100.20 0.059 21.86 0.413 5.99

Erzincan 0.012 112.63 0.109 19.77 0.413 7.73

Canakkale 0.034 43.32 0.267 11.56 0.632 5.84

Hakkari 0.012 84.38 0.127 21.35 0.354 9.68

Sile/ Istanbul 0.020 63.18 0.189 11.37 0.698 4.58

5.6 EARTHQUAKE LOAD

The properties of the ground motion at the site and the magnitude and location of

the next earthquake in a seismic source zone are inherently random. Inadequacy of

analytical models in evaluating nonlinear structural behavior leads to additional

uncertainties. On the other hand, the capacity of a structure cannot be determined

with reasonable accuracy due to various factors, such as material properties,

workmanship, and climatic nature. Naturally, seismic load, structural response and

structural capacity are all random and involve uncertainties, and a reliability-based

design criterion is required to include all these aspects in earthquake-resistant

design (Hwang and Hsu, 1993). Reliability analysis of structures under the

influence of earthquakes involves the identification of limit states associated with

the structural performance requirements, analysis of overall structural system

response and its components in addition to determination of the seismic hazard.

In this study, advanced computational methods for probabilistic analysis of

structural response to earthquakes are not addressed with all its specifics. A detailed

study of earthquake loading is beyond the scope of this study. However, regarding

the local conditions and data, probabilistic methods are used to determine the load

and resistance factors by taking the uncertainties into account, supported by the

results of studies which have been performed in other countries.

The peak ground acceleration is usually compatible with seismic specifications.

Accordingly, it is used as the seismic hazard parameter in this study. In other words,

the seismic hazard is described in terms of the peak ground acceleration, A. The

probability distribution of peak ground acceleration can be described by the Type II

extreme value distribution (Ellingwood, 1994). In a suitable manner, the cumulative

distribution function of A can be obtained from the following relationship:

k(a/v)A e(a)F

−−= a≥0 (5.22)

where:

v : the characteristic extreme value,

k : the shape parameter of the distribution.

Regarding the 100, 225, 475 and 1000 years return periods, peak ground

accelerations for Ankara, Izmir, Bursa, Antalya, Gaziantep, Samsun, Malatya,

Erzincan, Canakale, Hakkari, Göztepe/Istanbul Sile/Istanbul are obtained from the

study conducted by Gülkan et al. (1993) for the development of seismic zones map

of Turkey.

Table 5.13 Geographical coordinates and seismic zones of selected locations, and

corresponding peak ground acceleration values for different return periods

Peak ground acceleration, A (in g)

Location

Longitude (North) (in degrees)

Latitude (East) (in degrees)

Seismic Zone 100

years return period

225 years return period

Ankara 32.853 39.929 4 0.13 0.16 0.19 0.21

Izmir 27.145 38.433 1 0.36 0.43 0.51 0.59

Bursa 29.075 40.196 1 0.35 0.42 0.50 0.58

Antalya 30.709 36.893 2 0.30 0.37 0.44 0.52

Gaziantep 37.389 37.069 3 0.14 0.17 0.20 0.24

Samsun 36.331 41.293 2 0.19 0.24 0.31 0.36

Malatya 38.309 38.355 1 0.29 0.35 0.41 0.48

Erzincan 39.504 39.740 1 0.40 0.49 0.59 0.70

Canakkale 26.414 40.155 1 0.40 0.48 0.57 0.66

Hakkari 43.751 37.568 1 0.38 0.47 0.56 0.65

Istanbul/Göztepe 29.082 40.980 1 0.29 0.35 0.42 0.50

Istanbul/Sile 29.628 41.175 2 0.21 0.25 0.32 0.38

The peak ground accelerations in these locations are set equal to the values shown

in Table 5.13 for different return periods. By using the acceleration values for 225

and 475 years return periods, the parameters of Type II distribution can be

computed. The probability that the peak ground acceleration will not be exceeded

over a period of 50 years is 0.8 and 0.9 for the return periods of 225 and 475 years,

respectively. It is to be noted that the economic life of a structure is mostly assumed

to be 50 years in codes in different countries. For the purpose of determining the

parameters of the Type II distribution, v and k, for each location, Eq. (5.22) is

solved for 225 years and 475 years return period, simultaneously. The calculated v

and k values for the locations mentioned above are given in Table 5.14.

Table 5.14 Parameters of Type II distribution for peak ground acceleration for

different locations

Location

Parameter Ank

v 0.13 0.32 0.30 0.26 0.12 0.15 0.26 0.34 0.37 0.33 0.35 0.24

k 4.37 4.98 4.30 4.33 4.63 3.36 4.74 4.04 5.06 4.28 3.04 4.11

The values of the means and coefficients of variation of peak ground acceleration

corresponding to Ankara, Izmir, Bursa, Antalya, Gaziantep, Samsun, Malatya,

Erzincan, Canakkale, Hakkari, Göztepe/Istanbul and Sile/Istanbul can be found by

substituting the computed v and k values into Eqs. (5.23) and (5.24), respectively.

The computed values of δA indicate only the basic variability (aleatory uncertainty)

in peak ground acceleration. In addition, modeling error, which is quite high due to

various uncertainties associated with the earthquake process, should be taken into

consideration.

1-1vΓA (5.23)

= (5.24)

where, Γ(.) is the gamma function.

In this study, the modeling error, ∆A, will be taken as 0.9 in view of the studies of

Ellingwood et al. (1980) and Kömürcü (1995) who have reported this uncertainty to

be equal to 0.9. Consequently, total variability, ΩA, is calculated using the basic

variability, δA and the modeling error, ∆A. Results are shown in Table 5.15.

Table 5.15 Mean value and total variability of peak ground acceleration for

different locations

Location

Parameter An

A 0.15 0.37 0.36 0.32 0.15 0.20 0.30 0.41 0.43 0.40 0.48 0.29

δA 0.38 0.32 0.38 0.38 0.35 0.55 0.34 0.42 0.31 0.39 0.66 0.41

∆A 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90

ΩA 0.98 0.95 0.98 0.98 0.97 1.06 0.96 0.99 0.95 0.98 1.12 0.99

5.6.1 Determination of Total Equivalent Lateral Earthquake Load

Building codes specify the seismic load with regards to the maximum shear force at

the base of the building. In other words, the seismic analysis of buildings can be

performed in accordance with the equivalent lateral force procedure. The formal

seismic code TEC-1998 (Specification for Structures to be Built in Disaster Areas)

is used in determining the nominal earthquake loads for Turkey. It is hard to say

which code gives the best estimate of the “true” value of the lateral base shear force

for buildings in Turkey, considering the mean value of earthquake load. TEC-2006

and IBC 2003 (International Building Code) seem to reflect the most up-to-date

version of the equivalent lateral force procedure in terms of the estimation of the

nominal earthquake load and the mean earthquake load for this study, respectively.

However, in IBC- 2003, the earthquake spectral acceleration at short periods (Ss)

and at 1-second period (S1) are taken from the maps which were not mapped for

Turkey. If the base shear is taken into consideration, UBC-1994 is compatible with

TEC-2006 in terms of design variables, such as response modification factor, site

coefficient for soil characteristics. On the other hand, Yüksel (1997) pointed out

that the analysis and design of reinforced concrete buildings and its calculation

principles in UBC-1994 and TEC-1996 (the draft of TEC-1998) are almost the

same. TEC-1996 is the basis of TEC-2006 and the calculation procedure of base

shear in TEC-2006 has not been changed since 1996. Therefore, for the

computation of nominal earthquake loads, TEC-2006 can be also taken into

consideration. In the following sections, brief information associated with these

codes, i.e. UBC-1994 and TEC-2006 is presented.

5.6.1.1 UBC-1994

In UBC-1994, the total design base shear, V, in a given direction is determined

from the following equations:

C I ZV

= (5.25)

S 25.1C

3/2<= (5.26)

075.0R

≥ (5.27)

where:

Z: seismic zone factor

I: importance factor

W: total building weight

C: numerical coefficient

Rw: response modification factor

S: site coefficient of soil properties

T: fundamental period of vibration of the building for the direction considered

Seismic zone factor, Z, is the ratio of the design ground acceleration to the

acceleration of gravity, g (9.81 m/s2). Zone 4 in UBC-1994 is the most critical one,

whereas Zone 1 in TEC-2006 is the most critical one; that is, Zone 4 in UBC-1994

corresponds to Zone 1 in TEC-2006. The values of the seismic zone factor, Z in

UBC-1994 are given in Table 5.16 for different seismic zones.

Table 5.16 Seismic zone factor in UBC-1994

ZONE 1 2A 2B 3 4

Z 0.075 0.15 0.20 0.30 0.40

The ductility of the structural system, the types of member and material which are

normally ignored in linear elastic calculations is quantified by the response

reduction factor, RW in connection with the energy dissipation capacity of the

structure. The response modification factor in UBC-1994 is given in Table 5.17.

The first natural vibration period of the building can be calculated by the following

expression that gives an approximate value:

Nt1H CT = (5.28)

Ct value equals to 0.0731 in UBC-1994 for reinforced concrete moment resisting

frames and eccentrically braced frames.

Table 5.17 Response modification factor (RW) for reinforced concrete buildings in

UBC-1994

Basic structural system

Lateral force- resisting- system description RW

Bearing wall system

Reinforced concrete shear walls 6

Building frame system

Reinforced concrete shear walls 8

Moment resisting frame

system

Special moment-resisting frames(SMRF)

Intermediate moment-resisting frames (IMRF)

Ordinary moment-resisting frames (OMRF)

Dual system Dual system with SMRF capable of resisting at

least 25%of prescribed seismic forces 12

Dual system Dual system with IMRF capable of resisting at

least 25% of prescribed seismic forces 8

5.6.1.2 TEC-2006

The general principle of earthquake resistant design in TEC-2006 is to avoid any

damage in the structural and non-structural elements of buildings for low intensity

earthquakes, to limit the repairable damage levels in structural and non-structural

elements for medium intensity earthquakes, and to avoid the partial or overall

collapse of buildings for high intensity earthquakes in order to prevent the loss of

In TEC-2006, the total design base shear, Vt, is determined by using the following

equation for a given direction:

IW0.10AW)(TR

≥= (5.29)

where:

W :total building weight,

A(T1) : spectral acceleration coefficient,

Ra(T1) : seismic load reduction factor,

T1 :fundamental period of vibration of the building for translation motion in the

direction considered,

A0 :effective ground acceleration coefficient,

I :importance factor.

Total building weight is determined from the following equation:

wW (5.30)

In the above equation, wi is the individual storey weight.

The spectral acceleration coefficient corresponding to 5% damping is given by the

following equation:

IS(T)AA(T)0

= (5.31)

Effective ground acceleration coefficient, A0, can be defined as the ratio of the

design ground acceleration to the acceleration due to gravity, g (9.81 m/s2). The

effective ground acceleration coefficients specified for different seismic zones in

TEC-2006 are shown in Table 5.18.

Table 5.18 Effective ground acceleration coefficients (A0) in TEC-2006

Seismic Zone A0

1 0.40

2 0.30

3 0.20

4 0.10

In TEC-2006, there is no equation in order to calculate the first natural period,

except for two limitations as the highest and lowest level. In TEC-1998 and UBC

1994, the first natural vibration period of a building can be calculated from the

following approximate expression:

Nt1H CT = (5.32)

Ct value equals to 0.07 in TEC-1998 for buildings whose structural system is

composed of only reinforced concrete frames or structural steel eccentric braced

frames. Approximately, the same calculation procedure is given in both UBC-1994

and TEC-1998 for the value of Ct of buildings where seismic loads are fully resisted

by reinforced concrete structural walls.

The spectrum coefficient S(T), which appears in Eq. (5.31) is determined from the

following equations depending on the building’s natural period, T, and the local

site classes. Spectrum characteristic periods (TA, TB) in TEC-2006 are given in

Table 5.19.

1.5T/T1S(T) += (0≤T≤TA) (5.33 a)

5.2S(T) = (TA≤T≤TB) (5.33.b)

B/T)(T2.5S(T) += (T>TB) (5.33.c)

where:

T: fundamental period of vibration of the building in the direction considered

TA, TB : spectrum characteristic periods which depend on the local soil class given

Table 5.19 Spectrum characteristic periods (TA, TB) in TEC-2006

Local site class TA(second) TB (second)

Z1 0.10 0.30

Z2 0.15 0.40

Z3 0.15 0.60

Z4 0.20 0.90

These local site classes are classified according to the thickness of the soil topmost

layer and the soil groups, such as massive volcanic rocks, soft deep alluvial layers

with high water table, and so on.

In order to account for the specific nonlinear behavior of the structural system,

seismic load reduction factor, Ra(T), which corresponds to response modification

factor, RW, in UBC-1994 is used. Regarding the various structural systems and

natural vibration periods, seismic load reduction factors are determined from the

following equations in terms of structural behavior factor, R, which is given in

Table 5.20 according to TEC-2006.

Ra(T)=1.5+(R-1.5)T/TA (0≤T≤TA) (5.34.a)

Ra(T)=R (T>TA) (4.34.b)

Table 5.20 Structural system behavior factor (R) in TEC-2006 for cast-in-situ

reinforced concrete buildings

Lateral force- resisting- system description

System of nominal ductility level

System of high ductility level

Buildings in which earthquake loads are fully resisted by frames

Buildings in which earthquake loads are fully resisted by coupled structural walls

Buildings in which earthquake loads are fully resisted by solid structural walls

Buildings in which earthquake loads are jointly resisted by frames and solid and/or coupled structural walls

Here, in order to determine the mean to nominal ratios of earthquake loads, E/E ′ ,

different cases are taken into consideration with respect to importance factor,

seismic zone and seismic load reduction factor, Ra(T), (this term is given as

response modification factor, RW, in UBC-1994). It is to be noted that, in these

cases, the mean value of earthquake load, E , is computed from UBC-1994 and the

nominal value, E′ , from TEC-2006 by using a code developed in MathCAD 12.

5.6.1.3 Case 1

Considering UBC-1994, importance factor, I, is taken as 1.0 for buildings which are

residential and office buildings, hotels, industrial structures, etc., and the response

modification factor, RW, is assumed to be 8 suitable for buildings in which seismic

loads are resisted by reinforced concrete shear walls and its basic structural system

is building frame system.

As for TEC-2006, the importance factor, I, is taken as 1.0 corresponding to

buildings in which small numbers of people live (houses, hotels, employment

buildings, restaurants, and industrial buildings) and seismic load reduction factor,

Ra(T), is assumed to be 7 in connection with buildings in which earthquake loads

are resisted by frames and solid and/or coupled structural walls.

In the light of above descriptions and values, the mean to nominal ratios of

earthquake load in terms of different local site classes and building heights are

computed by using a code written in MathCAD 12, and the results are summarized

in Tables 5.21 and 5.22.

Table 5.21 Mean to nominal ratios of earthquake load in terms of different local site

classes and building heights (RW=8, Ra(T)=7)

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

Building height (HN) is equal to 8 m, and local site class is Z1

E/E ′ 1.27 0.85 0.83 0.98 0.67 0.69 0.68 0.98 0.95 0.93 0.70 0.71

E/E ′ 1.01 0.68 0.66 0.71 0.53 0.55 0.54 0.78 0.76 0.74 0.56 0.57

E/E ′ 0.87 0.58 0.57 0.67 0.46 0.47 0.47 0.68 0.65 0.64 0.48 0.49

E/E ′ 0.77 0.51 0.50 0.59 0.40 0.42 0.41 0.60 0.57 0.56 0.42 0.43

E/E ′ 1.83 1.23 1.20 1.41 0.97 1.00 0.99 1.42 1.37 1.35 1.01 1.03

E/E ′ 1.15 0.77 0.76 0.89 0.61 0.63 0.62 0.89 0.86 0.85 0.64 0.65

E/E ′ 1.00 0.67 0.66 0.77 0.53 0.54 0.54 0.78 0.75 0.74 0.55 0.56

E/E ′ 0.89 0.60 0.58 0.68 0.47 0.48 0.48 0.69 0.67 0.65 0.49 0.50

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

E/E ′ 1.83 1.23 1.20 1.41 0.97 1.00 0.99 1.42 1.37 1.35 1.01 1.03

E/E ′ 1.16 0.78 0.76 0.90 0.61 0.63 0.65 0.90 0.87 0.86 0.64 0.65

E/E ′ 1.04 0.70 0.68 0.80 0.55 0.57 0.56 0.81 0.78 0.77 0.57 0.58

E/E ′ 1.83 1.23 1.20 1.41 0.97 1.00 0.99 1.42 1.37 1.35 1.01 1.03

E/E ′ 1.79 1.20 1.18 1.38 0.94 0.97 0.96 1.39 1.34 1.32 0.99 1.00

5.6.1.4 Case 2

Considering UBC-1994, the importance factor, I, is taken as 1.0 for buildings which

are residential and office buildings, hotels, industrial structures, etc., and the

response modification factor, RW, is assumed to be 6 corresponding to buildings in

which seismic loads are resisted by reinforced concrete shear walls and its basic

structural system is bearing wall system.

Regarding TEC-2006, importance factor, I, is used as 1.0 corresponding to

buildings in which small number of people live (houses, hotels, employment

buildings, restaurants, industrial buildings) and seismic load reduction factor, Ra(T),

is assumed to be 6 corresponding to buildings in which earthquake loads are fully

resisted by solid structural walls

In view of above descriptions and values obtained from UBC-1994 and TEC-2006,

which are used for the calculation of the mean earthquake load, E , and the nominal

earthquake load, E′ , respectively. The mean to nominal ratios of earthquake load

with corresponding to different local site classes and building heights are computed

and summarized in Tables 5.23 and 5.24.

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

E/E ′ 1.45 0.97 0.95 1.12 0.76 0.79 0.78 1.12 1.08 1.07 0.80 0.81

E/E ′ 1.15 0.77 0.76 0.89 0.61 0.63 0.62 0.90 0.87 0.85 0.64 0.65

E/E ′ 0.99 0.67 0.65 0.77 0.52 0.54 0.54 0.77 0.75 0.73 0.55 0.56

E/E ′ 0.88 0.59 0.58 0.68 0.46 0.48 0.47 0.68 0.66 0.65 0.40 0.49

E/E ′ 2.09 1.40 1.38 1.61 1.10 1.14 1.13 1.62 1.57 1.54 1.16 1.17

E/E ′ 1.32 0.88 0.87 1.02 0.69 0.72 0.71 1.02 0.97 0.97 0.73 0.74

E/E ′ 1.14 0.77 0.75 0.88 0.60 0.62 0.62 0.89 0.86 0.84 0.63 0.64

E/E ′ 1.01 0.68 0.67 0.78 0.53 0.55 0.55 0.79 0.76 0.75 0.56 0.57

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

E/E ′ 2.09 1.40 1.38 1.61 1.10 1.14 1.13 1.62 1.57 1.54 1.16 1.17

E/E ′ 1.33 0.89 0.87 1.02 0.70 0.72 0.72 1.03 0.99 0.98 0.73 0.74

E/E ′ 1.09 0.80 0.78 0.92 0.63 0.65 0.64 0.92 0.89 0.88 0.66 0.67

E/E ′ 2.09 1.40 1.38 1.61 1.10 1.14 1.13 1.62 1.57 1.54 1.16 1.17

E/E ′ 2.04 1.37 1.34 1.58 1.07 1.11 1.10 1.59 1.53 1.50 1.13 1.15

5.6.1.5 Case 3

Considering the UBC-1994, the importance factor I is taken as 1.0 for buildings

which are residential and office buildings, hotels, industrial structures, etc., and the

response modification factor, RW, is assumed to be 6 suitable for buildings in which

seismic loads are resisted by reinforced concrete shear walls and its basic structural

system is bearing wall system.

In TEC-2006, however, the importance factor I is used as 1.0 corresponds to

buildings in which small number of people live (houses, hotels, employment

buildings, restaurants, industrial buildings) and the seismic load reduction factor,

Ra(T), is assumed to be 4 for systems with normal ductility level in connection with

buildings in which earthquake loads are fully resisted by solid structural walls

In the light of above descriptions based on UBC-1994 and TEC-2006, the mean to

nominal ratios of earthquake load according to different local site classes and

building heights are obtained, and results are presented in Tables 5.25 and 5.26.

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

E/E ′ 0.96 0.65 0.63 0.74 0.51 0.52 0.52 0.75 0.72 0.71 0.53 0.54

E/E ′ 0.77 0.52 0.51 0.59 0.40 0.42 0.41 0.60 0.58 0.57 0.42 0.43

E/E ′ 0.66 0.44 0.44 0.51 0.35 0.36 0.36 0.51 0.50 0.49 0.37 0.37

E/E ′ 0.58 0.39 0.38 0.45 0.31 0.32 0.31 0.45 0.44 0.43 0.32 0.33

E/E ′ 1.39 0.94 0.92 1.08 0.73 0.76 0.75 1.08 1.05 1.03 0.77 0.78

E/E ′ 0.88 0.59 0.58 0.68 0.46 0.48 0.47 0.68 0.66 0.65 0.48 0.49

E/E ′ 0.76 0.51 0.50 0.59 0.40 0.41 0.41 0.59 0.57 0.56 0.42 0.43

E/E ′ 0.68 0.45 0.44 0.52 0.36 0.37 0.36 0.52 0.51 0.50 0.37 0.38

Location

Parameter An

A 0.19 0.51 0.50 0.44 0.20 0.31 0.41 0.59 0.57 0.56 0.42 0.32

A0 0.10 0.40 0.40 0.30 0.20 0.30 0.40 0.40 0.40 0.40 0.40 0.30

E/E ′ 1.39 0.94 0.92 1.08 0.73 0.76 0.75 1.08 1.05 1.03 0.77 0.78

E/E ′ 0.88 0.59 0.58 0.68 0.47 0.48 0.48 0.69 0.66 0.65 0.49 0.50

E/E ′ 0.79 0.53 0.52 0.61 0.42 0.43 0.43 0.61 0.59 0.58 0.44 0.44

E/E ′ 1.39 0.94 0.92 1.08 0.73 0.76 0.75 1.08 1.05 1.03 0.77 0.78

E/E ′ 1.36 0.91 0.90 1.05 0.72 0.74 0.73 1.06 1.02 1.00 0.75 0.76

The average values of mean to nominal ratios of the earthquake load displayed in

Table 5.21 to Table 5.26 are summarized in Table 5.27.

Table 5.27 The average mean to nominal ratios of earthquake load obtained from

UBC 1994 and TEC-2006 for different locations

Location

Situation An

Ra(T)=7 1.37 0.92 0.90 1.05 0.72 0.75 0.74 1.06 1.03 1.01 0.76 0.77

Ra(T)=6 1.56 1.05 1.03 1.21 0.82 0.85 0.85 1.21 1.17 1.15 0.86 0.88

Ra(T)=4 1.04 0.70 0.69 0.81 0.55 0.57 0.56 0.81 0.78 0.77 0.58 0.58

Average 1.32 0.89 0.87 1.02 0.70 0.72 0.72 1.03 0.99 0.98 0.73 0.74

On the other hand, assuming that TEC-2006 gives the best estimate of the “true”

value of lateral base shear force for buildings in Turkey, this code can also be used

to compute “true” value of the earthquake load. However, since the nominal

earthquake load is also computed based on TEC-2006, the ratio of E/E ′ will be

equal to A/A0. The resulting mean to nominal ratios of earthquake load are shown in

Table 5.28.

Table 5.28 Mean to nominal ratios of earthquake load for different locations where

both values are computed based on TEC-2006

Location

Parameter An

E/E ′ 1.90 1.28 1.25 1.47 1.00 1.03 1.03 1.48 1.43 1.40 1.05 1.07

In his study, Ellingwood (1994) stated that the uncertainty in earthquake load is

dominated by the uncertainty involved in the seismic hazard analysis; the c.o.v. in A

is typically around 0.80 or more while the c.o.v. due to other structural response

parameters is 0.30 or less. Kömürcü and Yücemen (1996) assumed that the basic

variability due to other factors different than those involved in the estimation of A

in the earthquake load is equal to 0.6. In the light of these studies, we can take the

c.o.v. to be 0.45 as the average of the two values given above for the modeling error

associated with the seismic load in terms of maximum shear forces at the base of

buildings.

It is assumed that mean to nominal ratio of earthquake load exhibits a Type II

extreme value distribution like the peak ground acceleration. The results of the

average mean to nominal ratio of earthquake load and total variability are shown in

Table 5.29 together with the parameters of Type II extreme value distribution. It is

to be noted that in this table, the mean to nominal ratio of earthquake load is the

average value obtained from the mean to nominal ratios given in Tables 5.27 and

Table 5.29 Statistical parameters of the mean to nominal ratio for earthquake load

Location

Parameter An

A 0.15 0.37 0.36 0.32 015 020 0.30 041 0.43 0.40 0.48 0.29

ΩA 0.98 0.95 0.98 0.98 0.97 1.06 0.96 0.99 0.95 0.98 1.12 0.99

E/E ′ 1.61 1.08 1.06 1.24 0.85 0.88 0.87 1.25 1.21 1.19 0.89 0.91

∆ 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45

E/E ′Ω 1.08 1.05 1.08 1.08 1.07 1.15 1.06 1.09 1.05 1.08 1.21 1.09

v 1.10 0.74 0.73 0.85 0.58 0.59 0.54 0.86 0.83 0.82 0.60 0.62

k 2.46 2.49 2.46 2.46 2.47 2.42 2.48 2.46 2.49 2.46 2.38 2.46

CHAPTER 6

ASSESSMENT OF THE SAFETY LEVELS INHERENT IN THE CURRENT DESIGN PRACTICE

6.1 INTRODUCTION

In developing, a probability based load and resistance criterion for reinforced

concrete beam, column and shear wall design in flexure and shear as well as column

design in combined action of flexure and axial load, it is first necessary to evaluate

the current level of safety inherent in the design practice in Turkey and the relevant

“Turkish Codes”. Here, the term of “Turkish Codes” stands for a group of codes

including “Requirements for Design and Construction of Reinforced Concrete

Structures” (i.e. TS 500 (2000)), “Design Loads for Buildings” (i.e. TS 498 (1997))

and “Specification for Structures to be Built in Disaster Areas (1998)”. The required

information and data which will be used in the assessment of the levels of safety

inherent in the Turkish Codes are given in the previous chapters of this dissertation.

Probability based load and resistance design traditionally employs resistances which

are multiplied by resistance factors and loads or load effects which are multiplied

by load factors in a set of safety checking equations (Ellingwood et al., 1980). In its

most general form, probability based load and resistance design criterion can be

represented as follows (Israel et al., 1987):

Factored resistance ≥ Effects of factored load (6.1)

In the above equation, resistance factors are generally smaller than one while load

factors are greater than one. While developing a probability based load and

resistance criterion, these factors should be determined in such a way that the

probability of an unfavorable combination of resistance and load variables is

acceptably small for all likely combinations of the design variables which are

involved in the safety checking equation (Ellingwood and Galambos, 1982).

6.2 LOAD COMBINATION

Different types of loads act on a structure during its lifetime, and most of these

loads, such as wind, snow and earthquake exhibit a large degree of variation from

one location to another, with both time and their randomness in nature. In a load

combination case, if a structural member is subjected to only one time-varying load

together with dead load, it is essential to make use of the lifetime maximum load for

the time-varying load. On the other hand, when more than one time-varying load act

on a structure, it is not suitable to consider their lifetime maximum all together; in

this respect, the load combination problem becomes rather complex. In such a case,

the total maximum load effects of these time-varying loads are not the sum of their

maximums since the simultaneous occurrence of the maximum load effects of these

time-varying loads are rarely observed. For example, there is a very low chance of a

strong earthquake load taking place along with an extreme high live load.

Consequently, a structural component should rationally be designed for a total load

which is less than the sum of the time-varying loads at their maximum (Galambos et

al., 1982).

Three methods are generally used in load combination problems, namely Ferry-

Borges Model, Wen’s Load Coincide Method and Turkstra’s rule (Aktas et al.,

2001). Since Turkstra’s rule has been widely used in code calibration processes in

most of today’s codes due to its practicality in application, this method is adopted in

this study. Another reason for the selection of this load combination rule is that it is

consisted with the observations which failures frequently occur resulting from only

one load reaching its maximum value.

6.2.1 Turkstra’s Rule

As the probability of simultaneous occurrence of time-varying loads at their

maximum simultaneously is so small, this rule assumes that the maximum of

combined loads will occur when one of the loads is at its maximum while the rest

are at their arbitrary point-in-time values. If the total load effect U(t) is assumed as

given in Eq. (6.2), then a group of sub-combinations is achieved as given in Eq.

(6.3), and the maximum value obtained from these groups is maximum of the

combined loads.

U(t)= X1(t)+X2(t)+…+Xn(t) (6.2)

max U=

maxn321

n3max21

n32max1

X...XXX

where Xi represents the arbitrary point-in-time load and Ximax stands for the

maximum value of ith load.

If the combination of dead, live and snow loads are considered, dead load can be

assumed to be time independent owing to the fact that variation in dead load

throughout the lifetime of a structure is significantly low in comparison with live

and snow loads. Hence, the combined effect of dead load, live load and snow load

would be the maximum of dead load plus the maximum combination of maximum

live load with arbitrary point-in-time value of snow load or maximum snow load

with arbitrary point-in-time value of live load, which can be represented as follows:

U(t)= D+L(t)+…+S(t)

max U=

maxapt

aptmax

SLmaxD

6.2.2 Safety Criterion

The safety criterion for a reinforced concrete structural element can be written as

follows:

φR ≥ γDD + γYQ + ∑γJjaptQ (6.5)

where:

γ : load factor

D : dead load

Q : principle variable load

japtQ : arbitrary point-in-time values of the other variable loads.

The expression on the right hand side of the inequality consists of nominal loads

multiplied by load factors, and is consistent with Turkstra’s rule for load

combination (Kömürcü and Yücemen, 1996). As it is indicated before, R is the

nominal capacity, and φ is the resistance factor. One expects that the capacity R and

the different loads considered in this study to be correlated to a certain extent since

the basic variables related to dimensions appear both in the resistance and the load

effect equations. This is observed especially between the dead load, D, and the

capacity, R. However, since the variabilities in the dimensions are quite small (see

Section 3.3) compared to the other basic variables, the contribution of the

correlation to the total uncertainty will be of negligible magnitude. Accordingly, the

possible correlations between capacity and different load effects are not considered.

The fundamental formulation related to the load combinations in TS 500 (2000) is

given by Eq. (6.6), and safety criterion given in Eq. (6.5) is based on this formula

(Ersoy and Özcebe, 2004).

α+γ+γ= ∑

≠ jijojiQ

dQQDUEffects Load Factored (6.6)

where:

Qi : characteristics value of principle variable load

Qj : characteristics value of other less important variable load

αoj : ratio of arbitrary point-in-time value of the ith load to its nominal value.

In view of the above equations, only dead, live, wind, snow and earthquake loads

will be taken into consideration in this study. Furthermore, instead of all possible

combinations, only five load combinations, which are also considered in TS 500,

will be analyzed. These combinations are as follows:

a) LDULD

′γ+′γ=

b) SDULD

′γ+′γ=

c) WLDUWaptaptLD

′γ+′γ+′γ=

d) aptaptWtLD

WLDU ′γ+′γ+′γ=

e) ELDUEaptaptLD

′γ+′γ+′γ=

6.2.3 Load Statistics

As stated before, it is necessary to deal with the effects of loads rather than the

loads themselves. In Chapter 5, structural load effects resulting from dead, live,

wind, snow and earthquake loads are evaluated. The data published in literature and

the local data collected in Turkey constitute the main sources of the information

used in the evaluation of the load statistics. For calibration purposes, the ratios of

mean to nominal load values are determined. The nominal values of loads are

obtained from TS 498 (1997) and Specification for Structures to be Built in Disaster

Areas (1998)

Although dead and live loads acting on a structure are independent of the

geographical location of the structure, environmental loads, such as snow, wind and

earthquake loads are highly dependent. Therefore, in order to compute the

environmental loads, some representative cities (see Section 5.1), namely Ankara,

Izmir, Antalya, Bursa, Gaziantep, Samsun, Malatya, Erzincan, Canakkale, Hakkari,

Göztepe/Istanbul and Sile/Istanbul are considered. The overall load effects of snow,

wind and earthquake loads for Turkey include the mean values of arbitrary point-in-

time and maximum lifetime loads in these locations.

On the other hand, it is impractical to compute the values of the safety level

inherent in the Turkish Codes for each location separately. For this reason,

considering each environmental load individually, the average mean to nominal

load ratio and total uncertainty for the corresponding load for Turkey are

determined from the twelve locations mentioned above. Furthermore, for a specific

load, it is necessary to compare these average values computed for the whole

Turkey with the highest of the 12 pairs (mean to nominal ratio and total uncertainty

for each location). It should be noted that the location having the highest mean to

nominal ratio and total uncertainty will be selected as the critical location.

According to relevant standards, these critical locations are taken as Bursa,

Canakkale and Ankara for snow, wind and earthquake loads, respectively. In fact,

for the snow load, the highest mean to nominal ratio among these 12 locations is

observed for Hakkari with respect to the present standard (i.e. TS 498 (1997)).

However, the mean to nominal maximum snow load ratio computed for Hakkari

( 68.2SS =′ ) is not in accordance with the ratios of maximum snow loads proposed

in the foreign load standards. Furthermore, the nominal snow load values in TS 498

(1997) are expected to be revised in the near future by the authorities, especially in

locations where snowfall is excessive. Accordingly, since Bursa has the second

highest mean to nominal ratio among the above-mentioned 12 locations, based on

the Turkish Standards, this location is taken as the critical one for snow load.

The statistical parameters of dead, live, snow, wind and earthquake loads for critical

locations and for the whole Turkey, which were assessed in Chapter 5, are

summarized in Table 6.1. Note that the values computed for Turkey are the

averages of these twelve locations. In Table 6.1, APT stands for arbitrary point-in-

Table 6.1 Statistics of dead, live, wind and earthquake loads

Type of Load

Mean to Nominal Ratio

Total Variability

Ankara Bursa Canak-

kale Turkey Ankara Bursa

Canak- kale

Turkey

Dead Load (D)

1.05 1.05 1.05 1.05 0.10 0.10 0.10 0.10

Live Load (L)

1.00 1.00 1.00 1.00 0.27 0.27 0.27 0.27

APT Live Load (Lapt)

0.28 0.28 0.28 0.28 0.70 0.70 0.70 0.70

Wind Load W

0.44 0.55 0.73 0.55 0.32 0.31 0.30 0.32

APT Wind Load Wapt

0.15 0.22 0.32 0.19 0.41 0.38 0.35 0.43

Snow Load S

0.35 0.91 0.52 0.58 0.31 0.41 0.48 0.39

Earthquake Load E

1.61 1.06 1.21 1.09 1.08 1.08 1.05 1.09

6.3 RESISTANCE STATISTICS

The published data in literature and the local data collected in Turkey constitute the

main sources of information in evaluating the resistance statistics. For calibration

purposes, the ratios of mean to nominal values are determined. The nominal values

of resistance parameters are obtained from TS 500 (2000), TS EN 206-1 (2002) and

TS 708 (1996). In this study, C14, C16, C18, C20, C25 and C30 concrete classes,

which are given in TS 500 (2000), are taken into consideration. The nominal

average value of concrete (i.e. weighted average concrete class) and in-situ average

value (i.e. real weighted average compressive strength) are determined from the

statistical analysis of 28 day compressive strength data for Turkey. BCIII(a)

reinforcing steel bars with diameters of 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 and 32

mm are examined. The average yield strength of BCIII(a) reinforcing steel bars

used in reliability analysis include above diameters. In addition, the dimensional

characteristics of reinforced concrete members are also taken into account. The

mean to nominal ratios of beam, column and shear wall dimensions like width,

depth and effective depth and total variabilities in these dimensions are used to

obtain the resistance statistics.

In Chapter 3, the mean to nominal ratios and the total variabilities of basic

resistance variables, such as compressive strength of concrete, yield strength of

reinforcing steel bars and dimensions of three types of reinforced concrete elements,

beams columns and shear walls are quantified. In Chapter 4, using these values, the

mean to nominal ratios and the total uncertainties of resistances for different failure

modes of these structural members are computed within the framework of reliability

analysis. In this chapter, probability based resistance criterion for the design of

reinforced concrete beams, columns and shear walls in the flexure and shear failure

modes as well as the design of column in the combined action of flexure and axial

load failure mode will be examined within the scope of the information provided in

previous chapters. The resistance statistics for different failure modes of structural

members, which are determined in Chapter 4, are given in Table 6.2.

Table 6.2 Resistance statistics for different reinforced concrete members in different

failure modes

Structural member

Failure mode RR

′′′′ Ω

Flexure 1.24 0.13 Beam

Shear 1.24 0.17

Combined action

1.24 0.14 Column

Shear 1.24 0.17

Flexure 1.24 0.13 Shear wall

Shear 1.24 0.14

When the mean to nominal ratios of the capacities of a reinforced concrete member

are computed by using the mean to nominal ratios of all basic variables, it is

observed that while the computed values may vary for different cases, their average

values are equal to approximately 1.24 (see Tables 4.6 to 4.9). In fact, this is not an

unexpected result considering that the mean to nominal ratios of the capacities are

governed by two “primary” basic variables, namely, compresive strength of

concrete and yield strength of reinforcing steel bars, whose mean to nominal ratios

are very close to each other, respectively 1.24 and 1.25, which are significantly

greater than that of the other parameters, such as the member dimensions for which

this ratio is 1.0. On the other hand, since the coefficients of variation of these

“primary” variables, 0.18 for concrete compressive strength and 0.09 for yield

strength of reinforcing steel bars, are much different compared to their mean to

nominal ratios; such a consistency could not be achieved in the coefficients of

varition for the capacities of structural members in different failure modes; which

are observed to range from 0.13 to 0.17.

6.4 COMPUTATION OF RELIABILITY INDEXES

Utilizing the statistical information presented in the previous chapters of this

dissertation, one can compute reliability index, β, which provides a basis for the

reliability based design criteria. Reliability indexes give guidance for the

determination of the target reliabilities to be used in the establishment of load and

resistance factor design criteria. However, since they include the shortcomings of

existing standards, strict reliance on these computed values is not recommended by

researchers. In this section, the β values corresponding to the safety level inherent

in the current Turkish design practice and the Turkish Codes will be computed for

the following failure mode and structural member combinations:

- reinforced concrete beams in the flexural failure mode,

- reinforced concrete beams in the shear failure mode,

- reinforced concrete columns in the combined action of flexure and axial

load failure mode,

- reinforced concrete columns in the shear failure mode,

- reinforced concrete shear walls in the flexural failure mode,

- reinforced concrete shear walls in the shear failure mode.

The weights for the relative frequency of live, wind, snow and earthquake loads in

proportion to dead load, which are given by Kömürcü and Yücemen (1996)

according to the conditions specific to Turkey, are presented in Table 6.3. These

values also agree with the values proposed by Ellingwood et al. (1980), with minor

differences. The most likely value of reliability index, β, can be found by computing

the value of β for each design situation, which is defined by a set of nominal load

and resistance variables in proportion to dead load, and then by taking its

expectation over the relative frequency distribution given in Table 6.3.

Table 6.3 Relative frequency distribution of the ratio of a given load to dead load

(from Kömürcü and Yücemen, 1996)

D/Y ′′′′′′′′

Y (Load Type)

0.25 0.50 1.00 2.00 3.00

Live Load 0.10 0.45 0.35 0.10 0.00

Wind Load 0.40 0.30 0.20 0.10 0.00

Snow Load 0.00 0.40 0.30 0.20 0.10

Earthquake Load 0.00 0.25 0.25 0.25 0.25

6.4.1 Reliability Indexes for Reinforced Concrete Beams in the Flexural Failure Mode

6.4.1.1 Gravity Loads

In this study, the load combination alternatives involving gravity loads are taken as

the sum of dead load and maximum live load (D+L), and dead load and maximum

snow load on roofs (D+S). In TS 500 (2000), the following load combination is

considered:

L6.1D4.1U ′+′= (6.8)

For the snow load on the roofs, by replacing the live load, L′, with snow load, S',

Eq. (6.8) can be rewritten as follows:

S6.1D4.1U ′+′= (6.9)

Based on the load combination format in TS 500 (2000) and the loads in TS 498

(1997), the reliability indexes, β, for the flexural failure mode of reinforced concrete

beams subjected to D+L combination are given in Table 6.4. In this table, each

design situation, which is defined by a set of nominal load and resistance variables

consists of three main design variables: D/R ′′ , D/D ′′ and D/L ′′ . In computing

D/R ′′ values, the safety criterion (R= 1.4D+1.6L) specified in TS 500 (2000) is

used. In the computations of β values, the relative frequency distribution of D/L ′′

is taken from Table 6.3.

Table 6.4 Reliability indexes and design situations for the flexural failure mode of

reinforced concrete beams subjected to D+L combination

′ β

Expected value of reliability index

1.8 1 0.25 2.98

2.2 1 0.50 2.99

3.0 1 1.00 2.84

4.6 1 2.00 2.64

As it can be observed from Table 6.4, the reliability index changes within a range of

2.64 and 2.99 depending on the design situations, i.e. the D/L ′′ ratios. For this load

combination, the expected value of the reliability index is equal to 2.90. Ellingwood

et al. (1980) obtained a range from 2.6 to 3.2 for the corresponding β with an

expected value of 2.9 based on the design practice in the USA (ACI Code 1977,

1983, 1989). Likewise, Yücemen and El-Etoom (1986) reported that the β values

for this load combination change within a range of 2.6 and 3.09 with an expected

value of 2.7 based on the design practice in Jordan (Arabic Code 1977 was used). In

a similar study, Kömürcü (1995) reported a range of 2.30 and 2.40 for the β values

with an expected value of 2.38 with respect to TS 500 (1984). The value computed

here, 2.90, is consistent with the values reported in these studies.

Snow load is an environmental load which changes from one location to another.

For this reason, reliability index, β, is calculated mainly for three different critical

locations, namely, Ankara, Bursa and Canakkale (in Table 6.5, the reliability index

values corresponding to Hakkari are given for the comparison of the values

obtained from these three locations). Besides, while computing the average snow

load reliability indexes for the whole Turkey, Izmir and Antalya are not taken into

consideration since there is no snowfall in Izmir and Antalya. Here, it is important

to note that the nominal snow load values in TS 498 (1997) will be revised in the

near future by the authorities, especially in locations where snowfall is excessive

(personal communication by TSE Standard Preparation Group, 2006). Therefore,

the reliability indexes pertaining to Hakkari are not used in the determination of the

load and resistance partial factors (in Table 6.5, the reliability index values

corresponding to Hakkari are given for the comparison of the values obtained from

three locations). Based on the load combination format given in TS 500 (2000) and

the loads in TS 498 (1997), the reliability indexes for the flexural failure mode of

reinforced concrete beams subjected to dead load and snow load combination are

given in Table 6.5.

reinforced concrete beams subjected to D+S combination

Reliability indexes

2.20 1.00 0.50 4.07 2.76 3.28 1.27 3.39

3.00 1.00 1.00 4.08 2.50 3.07 0.68 3.16

4.60 1.00 2.00 3.95 2.32 2.93 0.24 3.01

6.20 1.00 3.00 3.90 2.25 2.88 0.05 2.96

Expected value of reliability indexes

4.03 2.54 3.11 0.76 3.20

As shown in Table 6.5, depending on the design situations, the reliability indexes

are found to range from 3.90 to 4.08; 2.25 to 2.76; 2.88 to 3.28 and 0.05 to 1.27 for

Ankara, Bursa, Canakkale and Hakkari, respectively. Accordingly, for these four

locations, the most likely reliability index values become 4.03, 2.54, 3.11 and 0.76,

respectively. For the whole Turkey, it is observed that the reliability index varies

between 2.96 and 3.39 with a most likely value of 3.20.

From Tables 6.4 and 6.5, it can be seen that while the value of D/L ′′ or D/S ′′

increases, the value of reliability index decreases. The relatively higher value of β

corresponding to small ratios of D/L ′′ or D/S ′′ is because the dead load is the

dominant component. It should be noted that dead load has smaller variability and

higher mean to nominal ratio compared to live and snow loads. For these reason, β

decreases with the increasing values of D/L ′′ or D/S ′′ . In Appendix F, the

variations of β values for load combinations considered in this study are displayed

in a graphical form.

6.4.1.2 Gravity and Wind Loads

The load combination alternatives involving gravity and wind loads will be dead

load plus maximum live load plus arbitrary point-in-time wind load (D+L+Wapt),

and dead load plus arbitrary point-in-time live load plus maximum wind load

(D+Lapt+W). In TS 500 (2000), the corresponding load combination is :

W3.1L3.1D0.1U ′+′+′= (6.10)

Based on the load combination format in TS 500 (2000) and the nominal loads in

TS 498 (1997), the reliability indexes, β, for flexural failure mode of reinforced

concrete beams subjected to D+L+Wapt and D+Lapt+W combinations are given in

Table 6.6 and Table 6.7, respectively.

reinforced concrete beams subjected to D+Lapt+W combination

Reliability indexes

1.98 1.00 0.50 0.25 3.36 3.25 3.18 3.29

2.30 1.00 0.50 0.50 3.63 3.43 3.24 3.48

2.95 1.00 0.50 1.00 3.97 3.60 3.17 3.64

4.25 1.00 0.50 2.00 4.05 3.54 2.96 3.55

2.62 1.00 1.00 0.25 3.27 3.47 3.20 3.24

2.95 1.00 1.00 0.50 3.48 3.67 3.34 3.43

3.60 1.00 1.00 1.00 3.81 3.91 3.54 3.72

4.90 1.00 1.00 2.00 4.34 3.87 3.34 3.90

Expected value of reliability indexes 3.59 3.51 3.24 3.45

As shown in Table 6.6, depending on the design situations, the reliability indexes, β,

for the first load combination, i.e., for D+L+Wapt range from 3.27 to 4.34; 3.25 to

3.91; 2.96 to 3.54, with expected values of 3.59, 3.51 and 3.24 for Ankara, Bursa

and Canakkale, respectively. For the whole Turkey, this range is 3.24 to 3.90 with a

most likely value of 3.45.

reinforced concrete beams subjected to D+L+Wapt combination

Reliability indexes

1.98 1.00 0.50 0.25 2.42 2.38 2.32 2.40

2.30 1.00 0.50 0.50 3.01 2.94 2.81 2.97

2.95 1.00 0.50 1.00 3.85 3.72 3.50 3.78

4.25 1.00 0.50 2.00 4.77 4.55 4.12 4.65

2.62 1.00 1.00 0.25 2.32 2.21 2.17 2.22

2.95 1.00 1.00 0.50 2.66 2.62 2.55 2.64

3.60 1.00 1.00 1.00 3.34 3.26 3.12 3.29

4.90 1.00 1.00 2.00 4.26 4.12 3.86 4.18

From Table 6.7, it can be seen that the reliability indexes, β, for D+L+Wapt

combination, range from 2.32 to 4.77; 2.21 to 4.55 and 2.17 to 4.12 and expected

values are 2.99, 2.90 and 2.78 for Ankara, Bursa and Canakkale, respectively. For

the whole Turkey, reliability index changes within a range of 2.22 and 4.65 with a

6.4.1.3 Gravity and Earthquake Loads

The load combination alternative involving gravity loads and earthquake load will

be D+Lapt+E, which is the most critical load combination in terms of three design

variables: D, L (S or W) and E. According to TS 500 (2000), this load combination

is as follows:

E0.1L0.1D0.1U ′+′+′= (6.11)

While the live load to be used in load combinations is taken from TS 498 (1997) as

stated before, the design earthquake load is obtained from the calculation methods

proposed in Specification for Structures to be Built in Disaster Areas (1998). The

average mean to nominal ratios and total uncertainties associated with earthquake

loads in twelve locations mentioned before are used in the determination of

reliability index for Turkey. In addition, Ankara, Bursa and Canakkale are

considered as critical locations. Based on the load combination format given in TS

500 (2000) and the loads specified in TS 498 (1997) and Specification for

Structures to be Built in Disaster Areas (1998), the reliability indexes for flexural

failure mode of reinforced concrete beams subjected to D+Lapt+E combination are

computed and are given in Table 6.8.

As shown in Table 6.8, the reliability index inherent in Turkish design practice

varies in the range of 0.27 and 1.55; 0.91 and 1.96; 0.76 and 1.88 with a

corresponding most likely values: 0.76, 1.31 and 1.19 for Ankara, Bursa and

Canakkale, respectively for the flexural failure mode of beams. For the whole

Turkey, it is observed that the reliability index varies between 0.93 and 1.98 with a

most likely value of 1.33. From Table 6.8, the variation of β values with L'/D' and

E'/D' ratios can be seen; as observed there is a tendency for the values of reliability

index to decrease, as the values of L'/D' and E'/D' increase. The corresponding plots

are given in Appendix F.

reinforced concrete beams subjected to D+Lapt+E combination

Reliability indexes

2.00 1.00 0.50 0.50 1.13 1.60 1.50 1.62

2.50 1.00 0.50 1.00 0.72 1.26 1.14 1.28

3.50 1.00 0.50 2.00 0.40 1.01 0.87 1.03

4.50 1.00 0.50 3.00 0.27 0.91 0.76 0.93

2.50 1.00 1.00 0.50 1.55 1.96 1.88 1.98

3.00 1.00 1.00 1.00 1.06 1.55 1.44 1.56

4.00 1.00 1.00 2.00 0.65 1.21 1.09 1.23

5.00 1.00 1.00 3.00 0.46 1.06 0.93 1.09

6.4.2 Reliability Indexes for Reinforced Concrete Beams in the Shear Failure Mode

As stated before, the load combination alternative involving gravity loads is the sum

of dead load and maximum live load (D+L), and dead load and maximum snow

load on roofs (D+S). According to TS 500 (2000), these load combinations are as

follows:

L6.1D4.1U ′+′= (6.12)

S6.1D4.1U ′+′= (6.13)

Based on the load combination format in TS 500 (2000) and loads in TS 498

(1997), the reliability indexes, β, for the shear failure mode of reinforced concrete

beams subjected to dead load plus live load combination are given in Table 6.9. In

this table, each design situation, which is defined by a set of nominal load and

resistance variables consists of three main design variables: D/R ′′ , D/D ′′ and

D/L ′′ . In computing D/R ′′ values, the safety criterion (R= 1.4D+1.6L) specified

in TS 500 (2000) is used. In the computations of β values, the relative frequency

distribution of D/L ′′ is taken from Table 6.3.

reinforced concrete beams subjected to D+L combination

′ β

1.8 1 0.25 2.36

2.2 1 0.50 2.42

3.0 1 1.00 2.42 Des

4.6 1 2.00 2.35

As it can be observed in Table 6.9, the reliability index changes within a narrow

range of 2.36 and 2.42 depending on the design situations, i.e. D/L ′′ ratios. For

this load combination, the most likely reliability index value is equal to 2.41.

Based on the load combination format in TS 500 (2000) and loads in TS 498

(1997), the reliability indexes, β, for the shear failure mode of reinforced concrete

beams subjected to dead load and snow load combination are given in Table 6.10.

reinforced concrete beams subjected to D+S combination

Reliability indexes

2.20 1.00 0.50 3.18 2.51 2.98 1.05 2.95

3.00 1.00 1.00 3.63 2.35 2.91 0.57 3.05

4.60 1.00 2.00 3.82 2.20 2.79 0.19 2.94

6.20 1.00 3.00 3.79 2.14 2.75 0.03 2.89

3.50 2.36 2.90 0.63 2.97

As shown in Table 6.10, depending on the design situations, the reliability indexes

are found to range from 3.18 to 3.82; 2.14 to 2.51; 2.75 to 2.98 and 0.03 to 1.05 for

Ankara, Bursa, Canakkale and Hakkari, respectively. Accordingly, for these four

locations, the most likely reliability index values are 3.50, 2.36, 2.90 and 0.63,

respectively. For the whole Turkey, it is observed that the reliability index varies

between 2.89 and 3.05 with a most likely value of 2.97.

From Tables 6.9 and 6.10, it can be seen that while the value of D/L ′′ or D/S ′′

increases, the value of reliability index decreases. As it is stated before the

relatively higher value of β corresponding to small ratios of D/L ′′ or D/S ′′ is

because the dead load which has smaller variability and higher mean to nominal

ratio in comparison with live load and snow load is the dominant component. For

these reason, β, decreases with the increase of the values of D/L ′′ or D/S ′′ . The

related figures are given Appendix F.

Here, the load combination alternatives involving gravity loads and wind loads will

be “D+L+Wapt” and “D+Lapt+W”. In TS 500 (2000), the following load

combination is provided:

W3.1L3.1D0.1U ′+′+′= (6.14)

Based on the load combination format in TS 500 (2000) and snow loads in TS 498

(1997), the values of the reliability index for the shear failure mode of reinforced

concrete beams subjected to D+Lapt+W and D+L+Wapt are given in Table 6.11 and

6.12, respectively

reinforced concrete beams subjected to D+Lapt+W combination

Reliability indexes

1.98 1.00 0.50 0.25 2.68 2.62 2.52 2.63

2.30 1.00 0.50 0.50 2.87 2.76 2.57 2.77

2.95 1.00 0.50 1.00 3.15 2.94 2.63 2.96

4.25 1.00 0.50 2.00 3.38 3.06 2.60 3.08

2.62 1.00 1.00 0.25 3.03 2.99 2.94 3.00

2.95 1.00 1.00 0.50 3.20 3.13 3.01 3.14

3.60 1.00 1.00 1.00 3.43 3.27 3.03 3.29

4.90 1.00 1.00 2.00 3.60 3.32 2.91 3.34

As shown in Table 6.11, depending on the design situations, the reliability indexes,

β, range from 2.68 to 3.60; 2.62 to 3.32; 2.52 to 3.03, and expected values are 3.04,

2.93 and 2.75 for Ankara, Bursa and Canakkale, respectively. For the whole

Turkey, it is observed that the reliability index varies between 2.63 and 3.34 with a

reinforced concrete beams subjected to D+L+Wapt combination

Reliability indexes

1.98 1.00 0.50 0.25 1.97 1.94 1.89 1.95

2.30 1.00 0.50 0.50 2.42 2.37 2.27 2.39

2.95 1.00 0.50 1.00 3.06 2.96 2.79 3.00

4.25 1.00 0.50 2.00 3.74 3.60 3.33 3.66

2.62 1.00 1.00 0.25 1.91 1.89 1.85 1.90

2.95 1.00 1.00 0.50 2.27 2.22 2.16 2.24

3.60 1.00 1.00 1.00 2.80 2.73 2.61 2.76

4.90 1.00 1.00 2.00 3.48 3.36 3.15 3.41

In Table 6.11, for D+Lapt+W combination, β increases as 'D/'W increases up to

'D/'W =1 and after this ratio β values do not change significantly. In Table 6.12, for

D+L+Wapt combination, β values decrease while 'D/'W and D/L ′′ increase. In

Appendix F, β values for D+Lapt+W and D+L+Wapt load combinations are displayed

in a graphical form.

Here, the load combination alternative involving gravity loads and earthquake loads

will be D+Lapt+E, which is the most critical load combination in view of three load

variables: D, L (S or W) and E. According to TS 500 (2000), this load combination

is as follows:

E0.1L0.1D0.1U ′+′+′= (6.15)

While the live load to be used in load combinations is taken from TS 498 (1997) as

stated before, the design earthquake load is obtained utilizing the calculation

methods proposed in “Specification for Structures to be Built in Disaster Areas

(1998)”. The average mean to nominal ratios and total uncertainties associated with

earthquake load in these 12 locations mentioned before are used in the

determination of reliability index for Turkey. Additionally, Ankara, Bursa and

Canakkale are considered as critical locations.

The reliability indexes and design situations for the shear failure mode of reinforced

concrete beams subjected to D+Lapt+E combination are given in Table 6.13. In this

table, each design situation, which is defined by a set of nominal load and resistance

variables consists of four main design variables: D/R ′′ , D/D ′′ , D/L ′′ and D/E ′′ .

In computing D/R ′′ values, the safety criterion (R= 1.0D+1.0L+1.0W) specified in

TS 500 (2000) is used. In the computations of β values, the relative frequency

distribution of D/L ′′ is taken from Table 6.3.

From Table 6.13, the reliability index inherent in Turkish design practice varies

between 0.26 and 1.49; 0.93 and 1.93; 0.74 and 1.82 with the corresponding most

likely values: 0.73, 1.30 and 1.15 for Ankara, Bursa and Canakkale in connection

with the shear failure mode of beams. For Turkey, reliability index ranges from 0.91

to 1.92 with an expected value of 1.29.

reinforced concrete beams subjected to D+Lapt+E combination

Reliability indexes

2.00 1.00 0.50 0.50 1.07 1.56 1.43 1.55

2.50 1.00 0.50 1.00 0.69 1.26 1.10 1.24

3.50 1.00 0.50 2.00 0.39 1.02 0.85 1.01

4.50 1.00 0.50 3.00 0.26 0.93 0.74 0.91

2.50 1.00 1.00 0.50 1.49 1.93 1.82 1.92

3.00 1.00 1.00 1.00 1.02 1.54 1.40 1.53

4.00 1.00 1.00 2.00 0.63 1.22 1.06 1.20

5.00 1.00 1.00 3.00 0.45 1.08 0.91 1.06

6.4.3 Reliability Indexes for Reinforced Concrete Columns in the Combined Action of Flexure and Axial Load Failure Mode

Based on the load combination format in TS 500 (2000) and loads specified in TS

498 (1997), the reliability indexes, β, for reinforced concrete columns in combined

action of flexure and axial load subjected to D+L and D+S load combinations are

given in Tables 6.14 and 6.15, respectively.

Table 6.14 Reliability indexes and design situations for reinforced concrete columns

in the combined action of flexure and axial load subjected to D+L

′ β

1.8 1 0.25 2.80

2.2 1 0.50 2.84

3.0 1 1.00 2.74

4.6 1 2.00 2.58

in the combined action of flexure and axial load subjected to D+S

Reliability indexes

2.20 1.00 0.50 3.81 2.67 3.12 1.17 3.35

3.00 1.00 1.00 4.01 2.42 2.96 0.63 3.14

4.60 1.00 2.00 3.89 2.25 2.83 0.21 2.99

6.20 1.00 3.00 3.84 2.18 2.78 0.03 2.94

3.89 2.46 2.98 0.67 3.17

As shown in Table 6.15, the reliability indexes range from 3.81 to 4.01; 2.18 to

2.67; 2.78 to 3.12 and 0.03 to 1.17 for Ankara, Bursa, Canakkale and Hakkari,

respectively. Accordingly, for these four locations, the most likely reliability index

values are 3.89, 2.46, 2.98 and 0.67, respectively. For the whole Turkey, it is

observed that the reliability index varies between 2.94 and 3.35 with a most likely

value of 3.17.

The reliability indexes and design situations for the flexural failure mode of

reinforced concrete beams subjected to D+Lapt+W combination and D+L+Wapt are

given in Table 6.16 and Table 6.17, respectively. As it can be shown in Table 6.16,

depending on the design situations, the reliability index, β, changes within a range

of 3.12 and 4.11; 3.03 and 3.73; 2.92 and 3.42, and expected values are 3.50, 3.38

and 3.13 for Ankara, Bursa and Canakkale, respectively. For the whole Turkey, the

reliability index varies between 3.04 and 3.76 with an expected value of 3.36.

in the combined action of flexure and axial load (for D+Lapt+W)

Reliability indexes

1.98 1.00 0.50 0.25 3.12 3.03 2.92 3.04

2.30 1.00 0.50 0.50 3.39 3.24 3.02 3.25

2.95 1.00 0.50 1.00 3.71 3.43 3.02 3.45

4.25 1.00 0.50 2.00 3.87 3.43 2.86 3.46

2.62 1.00 1.00 0.25 3.40 3.44 3.29 3.36

2.95 1.00 1.00 0.50 3.62 3.53 3.39 3.54

3.60 1.00 1.00 1.00 3.92 3.73 3.42 3.75

4.90 1.00 1.00 2.00 4.11 3.73 3.21 3.76

in the combined action of flexure and axial load (for D+L+Wapt)

Reliability indexes

1.98 1.00 0.50 0.25 2.28 3.26 2.20 2.28

2.30 1.00 0.50 0.50 2.81 2.78 2.66 2.81

2.95 1.00 0.50 1.00 3.56 3.51 3.30 3.56

4.25 1.00 0.50 2.00 4.36 4.28 3.91 4.36

2.62 1.00 1.00 0.25 2.14 2.13 2.09 2.14

2.95 1.00 1.00 0.50 2.54 2.52 2.45 2.54

3.60 1.00 1.00 1.00 3.16 3.13 2.99 3.16

4.90 1.00 1.00 2.00 3.98 3.92 3.67 3.98

For reinforced concrete columns in the combined action of flexure and axial load,

subjected to D+Lapt+E load combination, the reliability index inherent in the

Turkish design practice varies between 0.27 and 1.53; 0.94 and 1.98; 0.76 and 1.86

with the corresponding most likely values: 0.76, 1.33 and 1.18 for Ankara, Bursa

and Canakkale, respectively. Reliability index changes within a range of 0.92 and

1.97 with a most likely value of 1.32 for the whole Turkey. The design situations

and corresponding reliability index values belonging to these locations are

summarized in Table 6.18. In this table, each design situation, which is defined by a

set of nominal load and resistance variables consists of four main design variables:

D/R ′′ , D/D ′′ , D/L ′′ and D/E ′′ . In computing D/R ′′ values, the safety criterion

(R= 1.0D+1.0L+1.0E) specified in TS 500 (2000) is used. In the computations of β

values, the relative frequency distribution of D/L ′′ is taken from Table 6.3.

in the combined action of flexure and axial load (for D+Lapt+E)

Reliability indexes

2.00 1.00 0.50 0.50 1.12 1.62 1.49 1.60

2.50 1.00 0.50 1.00 0.71 1.29 1.13 1.27

3.50 1.00 0.50 2.00 0.40 1.05 0.87 1.03

4.50 1.00 0.50 3.00 0.27 0.94 0.76 0.92

2.50 1.00 1.00 0.50 1.53 1.98 1.86 1.97

3.00 1.00 1.00 1.00 1.05 1.57 1.43 1.56

4.00 1.00 1.00 2.00 0.65 1.24 1.08 1.23

5.00 1.00 1.00 3.00 0.46 1.10 0.92 1.08

6.4.4 Reliability Indexes for Reinforced Concrete Columns in the Shear Failure Mode

The mean to nominal ratio and the total uncertainty of the shear failure mode of

columns are the same as those computed for the shear failure mode of beams.

Furthermore, the load statistics shown in Table 6.1 will be used for all failure modes

and all structural members. As a result, the reliability indexes to be computed for

the shear failure mode of columns will be the same as those found for the shear

failure mode of beams. Accordingly, the reliability indexes reported in Section 6.4.2

are exactly the same in this section. However, for the sake of completeness, the

results are duplicated in a summary form in Table 6.19.

Table 6.19 Reliability indexes for reinforced concrete columns in the shear failure

Ankara Bursa Canakale Turkey Locations Load combinations

D+L 2.36-2.42 2.41

D+S 3.18-3.82 3.50 2.14-2.51 2.36 2.75-2.98 2.90 2.89-3.05 2.97

D+Lapt+W 2.68-3.60 3.04 2.62-3.32 2.93 2.52-3.03 2.75 2.03-3.34 2.94

D+L+Wapt 1.91-3.74 2.44 1.89-3.60 2.38 1.85-3.33 2.28 1.90-3.66 2.40

D+Lapt+E 0.26-1.49 0.73 0.93-1.93 1.30 0.74-1.82 1.15 0.91-1.92 1.29

6.4.5 Reliability Indexes for Reinforced Concrete Shear Walls in the Flexural Failure Mode

The mean to nominal ratio and the total uncertainty of shear walls in the flexural

failure mode are the same as those computed for the flexural failure mode of beams.

Furthermore, the load statistics shown in Table 6.1 will be used for all failure modes

and all structural members. For these reasons, the reliability indexes to be computed

for the flexural failure mode of shear walls will be the same as those found for the

flexural failure mode of beams. Accordingly, the reliability indexes reported in

Section 6.4.1 are exactly the same in this section, too. A summary of results of

reliability indexes is given in Table 6.20.

Table 6.20 Reliability indexes of reinforced concrete shear walls in the flexural

failure mode

Ankara Bursa Canakale Turkey Location Load combination

D+L 2.64-2.99 2.90

D+S 3.90-4.08 4.03 2.25-2.76 2.54 2.88-3.28 3.11 2.96-3.99 3.20

D+Lapt+W 3.27-4.34 3.59 3.25-3.91 3.51 2.96-3.54 3.24 3.24-3.90 3.45

D+L+Wapt 2.52-4.77 2.99 2.21-4.55 2.90 2.17-4.12 2.78 2.22-4.05 2.73

D+Lapt+E 0.27-1.55 0.76 0.91-1.96 1.31 0.76-1.88 1.19 0.93-1.98 1.33

6.4.6 Reliability Indexes for Reinforced Concrete Shear Walls in the Shear Failure Mode

The values to be computed in this section are the same as those reported in Section

6.4.3. In other words, the reliability indexes computed for reinforced concrete

columns in combined action and flexure are also the same for the reinforced

concrete shear walls failing in the shear failure mode. However, for the sake of

completeness, the previous results are repeated in a summary form in Table 6.21.

Table 6.21 Reliability indexes of reinforced concrete shear walls in the shear failure

Ankara Bursa Canakale Turkey Locations Load combinations

D+L 2.58-2.84 2.78

D+S 3.81-4.01 3.89 2.18-2.67 2.46 2.78-3.12 2.98 2.94-3.35 3.17

D+Lapt+W 3.12-4.11 3.50 3.03-3.73 3.38 2.52-3.42 3.13 3.04-3.76 3.36

D+L+Wapt 2.14-4.36 2.79 2.13-4.28 2.76 2.09-3.91 2.64 2.14-4.36 2.79

D+Lapt+E 0.27-1.53 0.76 0.94-1.98 1.33 0.76-1.86 1.18 0.92-1.97 1.32

6.4.7 Assessment of Target Reliability Indexes

In general, basic requirements for the safety of a structure can be expressed in terms

of either the accepted minimum reliability index or accepted maximum failure

probability. From a reliability based safety assessment point of view, the acceptable

risk level can be quantified by specifying the value of the reliability index known as

target reliability index, βT.

After the determination of the safety levels inherent in the existing standards that

have resulted in acceptable performance earlier, the optimum value of target

reliability index can be assessed based on two factors: cost of safety and

consequences of failure (Kömürcü and Yücemen, 1996; Melchers, 2002 and Nowak

and Szerszen 2003b). Ellingwood et al. (1980), Kömürcü (1995), and Nowak and

Szerszen (2003b) first calculated the safety levels and then proposed a set of target

reliability indexes for both different failure modes of structural members and

different load combinations. These safety levels and selected target reliabilities are

summarized in Table 6.22. In the following paragraphs, considering also these

earlier studies, the target reliability indexes for the studied failure modes of

reinforced concrete beams, columns and shear walls will be determined consistent

with the safety level inherent in the current standards.

Table 6.22 Reliability indexes corresponding to the current design practice and the

target reliability indexes for different load combinations and different structural

members according to different studies

Failure mode

Reference Load

Combination currentββββ β T

LD ′+′ 2.62-3.58 3.0

SD ′+′ 3.33/3.08 3.0

WLD apt′+′+′ 2.74/2.50/3.90/3.24/2.90 2.5

aptWLD ′+′+′ 2.98/3.34/4.55/2.78/3.76 2.5

Ellingwood et al. (1980)

ELD ′+′+′ 1.75

LD ′+′ 2.38 2.7

SD ′+′ 2.97/2.96/2.30 2.7

WLD apt′+′+′ 3.19/3.17/2.93 2.5

aptWLD ′+′+′ 3.17/3.14/3.16 2.5

Kömürcü(1995)

ELD ′+′+′ 0.98/1.22/1.04 1.75

Nowak and Szerszen (2003b)

LD ′+′ 3.83 3.5

LD ′+′ 1.99-2.45 3.0

SD ′+′ 3.0

WLD apt′+′+′ 2.5

aptWLD ′+′+′ 1.97/2.32/2.38 2.5

Ellingwood et al.

(1980)

ELD ′+′+′ 1.75

Nowak and Szerszen (2003b) LD ′+′ 3.78 3.5

LD ′+′ 2.98-3.49 3.0

SD ′+′ 3.0

WLD apt′+′+′ 2.5

aptWLD ′+′+′ 2.74/2.96 2.5

Ellingwood et al. (1980)

ELD ′+′+′ 1.75

Nowak and Szerszen (2003b) LD ′+′ 4.68 4.0

As listed in Table 6.22, when the flexural failure mode of a beam is taken into

consideration, Ellingwood et al. (1980) proposed the target reliability index to be

3.0 for gravity loads, 2.5 for gravity loads combined with wind load and 1.75 for

gravity loads combined with earthquake load. For the same load combinations,

Kömürcü (1985) selected the target reliability index as 2.7, 2.5, 1.75. In another

study, Nowak and Szerszen (2003b) proposed this index to be 3.5 for gravity loads.

While the reliability indexes which are computed in this study based on Turkish

Codes are higher than those reported by Ellingwood et al. (1980) and Kömürcü

(1995), especially for the D+L+W combination, one can see that they are smaller

than the values computed by Nowak and Szerszen (2003b). However, it should also

be noted that the study of Nowak and Szerszen (2003b) was conducted only for the

D+L combination (1.2D+1.6L). On the other hand, the coefficient of variations of

the variables used in the study of Nowak and Szerszen (2003b) are usually small in

comparison with those used in this study. For example, the c.o.v.’s of concrete

compressive strength and maximum live load are equal to 0.10 and 0.18,

respectively, while these values are taken as 0.18 and 0.27, respectively in this

study.

Considering the studies mentioned above (Table 6.22) and the safety levels inherent

in the Turkish current design practice, a set of target reliabilities are selected as

given in Table 6.23 for beams in the flexural failure mode.

Table 6.23 Current and the target reliability indexes for different load combinations

considering beams in the flexural failure mode

Reliability Indexes Values

Load Combination (According to TS 500)

Location β ββββ β T

LD ′+′ 6.14.1 Turkey 2.64-2.99 2.90 3.0

Ankara 3.90-4.07 4.03

Bursa 2.25-2.76 2.54

Canakkale 2.88-3.28 3.11 SD ′+′ 6.14.1

Turkey 2.96-3.39 3.20 3.0

Ankara 3.27-4.34 3.59

Bursa 3.25-3.91 3.51

Canakkale 3.17-3.54 3.24 W3.1L3.1D0.1 apt

′+′+′

Turkey 3.24-3.90 3.45 3.0

Ankara 2.32-4.26 2.99

Bursa 2.21-4.55 2.90

Canakkale 2.17-4.12 2.78

aptW3.1L3.1D0.1 ′+′+′

Turkey 2.22-4.65 2.93 2.7

Ankara 0.27-1.55 0.76

Bursa 0.91-1.96 1.31

Canakkale 0.76-1.88 1.19

E0.1L0.1D0.1 apt′+′+′

Turkey 0.93-1.98 1.33 1.75

As far as the shear failure mode is considered for beams, Ellingwood et al. (1980)

proposed the target reliability index to be 3.0 for D+L and D+S combination, 2.5 for

D+L+W combination and 1.75 for D+L+E combination whereas Nowak and

Szerszen (2003b) proposed the target reliability index to be 3.5 for D+L

combination. The target reliabilities selected by considering these studies and the

safety levels inherent in the Turkish design practice are tabulated in Table 6.24

considering beams in the shear failure mode

Reliability Index Values

LD ′+′ 6.14.1 Turkey 2.36-2.42 2.41 3.0

Ankara 3.18-3.82 3.50

Bursa 2.14-2.51 2.36

Canakkale 2.75-2.98 2.90 SD ′+′ 6.14.1

Turkey 2.89-3.05 2.97 3.0

Ankara 2.68-3.60 3.04

Bursa 2.62-3.32 2.93

′+′+′

Turkey 2.63-3.34 2.94 3.0

Ankara 1.91-3.74 2.44

Bursa 1.89-3.60 2.38

Canakkale 1.85-3.33 2.28

aptW3.1L3.1D0.1 ′+′+′

Turkey 1.90-3.66 2.40 2.7

Ankara 0.26-1.49 0.73

Bursa 0.93-1.93 1.30

Canakkale 0.74-1.82 1.15

E0.1L0.1D0.1 apt′+′+′

Turkey 0.91-1.92 1.29 1.75

For reinforced concrete columns, the target reliability values proposed by

Ellingwood et al. (1980) are the same with those proposed for the flexural and shear

failure modes of beams. Nowak and Szerszen (2003b) proposed the target

reliability index as 4.0 for D+L combination. Failure of one column in a critical

region can lead to the subsequent collapse of the adjoining floors yielding to total

collapse of the entire structure. Accordingly, the target reliabilities to be used for

columns should be higher than those selected for beams. Taking the studies

mentioned above and the safety levels inherent in the Turkish design practice into

account, the proposed target reliabilities are listed in Table 6.25.

considering columns in the combined action failure mode

Location

β ββββ β T

LD ′+′ 6.14.1 Turkey 2.58-2.84 2.78 3.2

Ankara 3.81-4.01 3.89

Bursa 2.18-2.67 2.46

Canakkale 2.78-3.12 2.98 SD ′+′ 6.14.1

Turkey 2.94-3.35 3.17 3.2

Ankara 3.12-4.11 3.50

Bursa 3.03-3.73 3.38

′+′+′

Turkey 3.04-3.76 3.36 3.2

Ankara 2.14-4.36 2.79

Bursa 2.13-4.28 2.76

Canakkale 2.09-3.91 2.64

aptW3.1L3.1D0.1 ′+′+′

Turkey 2.14-4.36 2.79 3.0

Ankara 0.27-1.53 0.76

Bursa 0.94-1.98 1.33

Canakkale 0.76-1.86 1.18

E0.1L0.1D0.1 apt′+′+′

Turkey 0.92-1.97 1.32 1.75

Structural column failure is of main concern with respect to not only economic but

also human losses. Hence, great care should be given during the design of a column

with a higher reserve strength compared to beams and other horizontal structural

elements, especially since failure provides little visual warning (Nawy, 2005).

Accordingly, the target reliabilities to be used for columns should be higher than

those selected for beams and other horizontal structural elements. Considering the

safety levels inherent in the Turkish design practice, the selected target reliabilities

are listed in Table 6.26

considering columns in the shear failure mode

LD ′+′ 6.14.1 Turkey 2.36-2.42 2.41 3.0

Ankara 3.18-3.82 3.50

Bursa 2.14-2.51 2.36

Canakkale 2.75-2.98 2.90 SD ′+′ 6.14.1

Turkey 2.89-3.05 2.97 3.2

Ankara 2.68-3.60 3.04

Bursa 2.62-3.32 2.93

′+′+′

Turkey 2.63-3.34 2.94 3.2

Ankara 1.91-3.74 2.44

Bursa 1.89-3.60 2.38

Canakkale 1.85-3.33 2.28

aptW3.1L3.1D0.1 ′+′+′

Turkey 1.90-3.66 2.40 3.0

Ankara 0.26-1.49 0.73

Bursa 0.93-1.93 1.30

Canakkale 0.74-1.82 1.15

E0.1L0.1D0.1 apt′+′+′

Turkey 0.91-1.92 1.29 1.75

As it is already mentioned, shear walls behave like fixed supported beams, and the

design of shear walls can be carried out in the same way as beams (Park and Paulay,

1975; Celep and Kumbasar, 2005). On the other hand, the values of safety levels in

shear walls (Table 6.26 and 6.27) are higher than those computed for beams (Table

6.22 and Table 6.23). In view of these considerations, the target reliabilities are

selected considering the existing safety levels in the Turkish design practice and the

selected target reliabilities are listed in Tables 6.27 and 6.28.

considering shear walls in the flexural failure mode

LD ′+′ 6.14.1 Turkey 2.64-2.99 2.90 3.0

Ankara 3.90-4.07 4.03

Bursa 2.25-2.76 2.54

Canakkale 2.88-3.28 3.11 SD ′+′ 6.14.1

Turkey 2.96-3.39 3.20 3.2

Ankara 3.27-4.34 3.59

Bursa 3.25-3.91 3.51

′+′+′

Turkey 3.24-3.90 3.45 3.2

Ankara 2.32-4.26 2.99

Bursa 2.21-4.55 2.90

Canakkale 2.17-4.12 2.78

aptW3.1L3.1D0.1 ′+′+′

Turkey 2.22-4.65 2.93 2.7

Ankara 0.27-1.55 0.76

Bursa 0.91-1.96 1.31

Canakkale 0.76-1.88 1.19

E0.1L0.1D0.1 apt′+′+′

Turkey 0.93-1.98 1.33 1.75

considering shear walls in the shear failure mode

Location

β ββββ β T

LD ′+′ 6.14.1 Turkey 2.58-2.84 2.78 3.2

Ankara 3.81-4.01 3.89

Bursa 2.18-2.67 2.46

Canakkale 2.78-3.12 2.98 SD ′+′ 6.14.1

Turkey 2.94-3.35 3.17 3.2

Ankara 3.12-4.11 3.50

Bursa 3.03-3.73 3.38

′+′+′

Turkey 3.04-3.76 3.36 3.2

Ankara 2.14-4.36 2.79

Bursa 2.13-4.28 2.76

Canakkale 2.09-3.91 2.64

aptW3.1L3.1D0.1 ′+′+′

Turkey 2.14-4.36 2.79 3.0

Ankara 0.27-1.53 0.76

Bursa 0.94-1.98 1.33

Canakkale 0.76-1.86 1.18

E0.1L0.1D0.1 apt′+′+′

Turkey 0.92-1.97 1.32 1.75

CHAPTER 7

SELECTION OF LOAD AND RESISTANCE FACTORS

7.1 INTRODUCTION

In this chapter, based on the statistical analysis carried out in the previous chapters,

the resistance and load factors for different load combinations will be developed by

using the Advanced First Order Second Moment (AFOSM) method for reinforced

concrete beams, columns and shear walls in the flexure and shear failure modes and

also for columns subjected to the combined action of flexure and axial load.

The required information and data needed for the computations of the resistance and

load factors are presented in the previous chapters of this dissertation. In Chapter 3,

the parameters which influence the capacity of structural members are described in

a detailed way and the various sources of uncertainties are quantified using the local

and international data and information. In Chapter 4, using these values, the mean to

nominal ratios and the total uncertainties of resistances for different failure modes

of three basic types of reinforced concrete structural members, namely beams

columns and shear walls, are computed. In Chapter 5, structural load effects

resulting from dead, live, wind, snow and earthquake loads are evaluated. In

Chapter 6, reliability based resistance criterion for the failure modes of reinforced

concrete structural members are examined within the scope of the previous chapters

and the target reliability indexes are selected. These target reliability indexes will be

used in the AFOSM computations associated with the new load and resistance

factors, which will be proposed at the end of this chapter.

7.2 LOAD AND RESISTANCE FACTORS CORRESPONDING TO THE SELECTED TARGET RELIABILITIES

In this section, the load and resistance factors corresponding to target reliabilities

are determined for different design situations, i.e., the situations for L'/D', S'/D',

W'/D' and E'/D' values according to D+L, D+S, D+Lapt+W, D+L+Wapt and

D+Lapt+E load combinations. In Figures 7.1 to 7.36, the values of the load and

resistance factors computed for different load combinations considered in this study

are plotted for different failure modes of beams, columns and shear walls.

As stated before, snow, wind and earthquake loads for the whole Turkey include the

mean values of loads for some representative locations, namely Ankara, Izmir,

Antalya, Bursa, Gaziantep, Samsun, Malatya, Erzincan, Canakkale, Hakkari,

Göztepe/Istanbul and Sile/Istanbul. The critical locations are taken as Bursa,

Canakkale and Ankara for snow, wind and earthquake loads, respectively.

Correspondingly, the figures are plotted for both each critical location and for the

whole Turkey for each load combination.

These figures show that the resistance factors are rather insensitive to the time-

varying loads in the load combinations, when these loads are small. For all of the

studied failure modes of the structural members, the dead load factor, γD, is

observed to be about 1.1. The reason why these values are the same is due to the

fact that the variability in dead load is small in comparison to the other time-varying

loads. These figures also indicate that the live load factor in D+L+W and D+L+E

load combinations is quite small. This is because the value of Lapt is much less than

the nominal live load, L'. If the different resistance statistics of failure modes of

structural members are considered, load factors do not appear to be sensitive to the

resistance statistics. It should be noted that while the resistance factors depend on

the material and the limit state of interest, the load factors are independent of these

considerations. On the other hand, the different load and resistance factors are

observed for each failure mode of each structural member due to the fact that the

target reliability as well as resistance statistics are different. Besides, the

observations indicate that the load factors for the time-varying loads in the load

combination increases as the proportion of that load to dead load, such as L'/D',

S'/D' and E'/D', increases. The computed load and resistance factors are given in a

graphical form in Sections 7.2.1 to 7.2.6.

7.2.1 Load and Resistance Factors for Reinforced Concrete Beams in the Flexural Failure Mode

Based on the load combination format mentioned in Section 6.2 and the nominal

loads in TS 498 (1997) and “Specification for Structures to be Built in Earthquake

Areas (2006)”, the load and resistance factors for reinforced concrete (RC) beams in

the flexural failure mode are computed considering different load ratios. The

variations are shown in a graphical form in Figures 7.1 to 7.9.

0.25 0.5 1 2

Resistance

factor

Dead load

factor

Live load

factor

Figure 7.1 Variation of the load and resistance factors for RC beams in the flexural

failure mode (Turkey; D+L; βT=3.0)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

failure mode (Bursa; D+S; βT=3.0)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

failure mode (Turkey; D+S; βT =3.0)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

failure mode (Canakkale; D+Lapt+W; βT =3.0)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

failure mode (Turkey; D+Lapt+W; βT =3.0)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

failure mode (Canakkale; D+L+Wapt; βT =2.7)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load

factor(L/D=0.5)

Live load

factor(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

failure mode (Turkey; D+L+Wapt; βT =2.7)

0.5 1 1.5 2 2.5 3

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

failure mode (Ankara; D+Lapt+E; βT =1.75)

0.5 1 1.5 2 2.5 3

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

failure mode (Turkey; D+Lapt+E; βT =1.75)

7.2.2 Load and Resistance Factors for Reinforced Concrete Beams in the Shear Failure Mode

In this section, the load and resistance factors are computed for reinforced concrete

beams in the shear failure mode, on the basis of load combination format mentioned

in Section 6.2 and the nominal loads in TS 498 (1997) and Specification for

Structures to be Built in Earthquake Areas (2006). The corresponding plots are

given in Figures 7.10 to 7.18.

0.25 0.5 1 2

Resistance

factor

Dead load

factor

Live load

factor

Figure 7.10 Variation of the load and resistance factors for RC beams in the shear

failure mode (Turkey; D+L; βT =3.0)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

failure mode (Bursa; D+S; βT =3.0)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

L ive load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.5 1 2 3

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

0.5 1 2 3

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

7.2.3 Load and Resistance Factors for Reinforced Concrete Columns in the Combined Action Failure Mode

Established upon the load combination format mentioned in Section 6.2 and the

nominal loads in TS 498 (1997) and “Specification for Structures to be Built in

Earthquake Areas (2006)”, the load and resistance factors for reinforced concrete

columns in the combined action failure mode are computed. In Figures 7.19 to 7.27,

the values of load and resistance factors computed for different load combinations

considered in the study are plotted.

0.25 0.5 1 2

Resistance

factor

Dead load

factor

Live load

factor

combined action failure mode (Turkey; D+L; βT =3.2)

1.21.4

1.61.8

22.22.4

2.62.8

3.43.6

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

combined action failure mode (Bursa; D+S; βT =3.2)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

combined action failure mode (Turkey; D+S; βT =3.2)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

combined action failure mode (Canakkale; D+Lapt+W; βT =3.2)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

combined action failure mode (Turkey; D+Lapt+W; βT =3.2)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

combined action failure mode (Canakkale; D+L+Wapt; βT =3.0)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

combined action failure mode (Turkey; D+L+Wapt; βT =3.0)

0.5 1 2 3

Load a

tance F

rs Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

combined action failure mode (Ankara; D+Lapt+E; βT =1.75)

0.5 1 2 3

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

combined action failure mode (Turkey; D+Lapt+E; βT =1.75)

7.2.4 Load and Resistance Factors for Reinforced Concrete Columns in the Shear Failure Mode

Based on the load combination format mentioned in Section 6.2 and the nominal

loads in TS 498 (1997) and “Specification for Structures to be Built in Earthquake

Areas (2006)”, the load and resistance factors for reinforced concrete columns in

the shear failure mode are computed. In Figures 7.28 to 7.36, the load and resistance

factors for different load combinations considered in this study are displayed in a

graphical form.

0.25 0.5 1 2

Resistance

factor

Dead load

factor

Live load

factor

Figure 7.28 Variation of the load and resistance factors for RC columns in the shear

failure mode (Turkey; D+L; βT =3.0)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

failure mode (Bursa; D+S; βT =3.2)

0.5 1 2 3

Resistance

factor

Dead load

factor

Snow load

factor

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.25 0.5 1 2

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load

factor(L/D=0.5)

Live load

factor(L/D=1)

Wind load factor

(L/D=0.5)

Wind load factor

(L/D=1)

0.5 1 2 3

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

0.5 1 2 3

Load a

tance F

Resistance factor

(L/D=0.5)

Resistance factor

(L/D=1)

Dead load factor

(L/D=0.5)

Dead load factor

(L/D=1)

Live load factor

(L/D=0.5)

Live load factor

(L/D=1)

Earthquake load

factor (L/D=0.5)

Earthquake load

factor (L/D=1)

7.2.5 Load and Resistance Factors for Reinforced Concrete Shear Walls in the Flexural Failure Mode

It is observed that the load and resistance factors computed for reinforced concrete

shear walls in the flexural failure mode are almost identical to those computed for

beams in the flexural failure mode (Section 7.2.1) For this reason, the graphs for the

load and resistance factors are not replotted in this section; the figures given in

Section 7.2.1 are also applicable for this section.

7.2.6 Load and Resistance Factors for Reinforced Concrete Shear Walls in the Shear Failure Mode

Similar to the previous section, the resistance statistics and target reliabilities for

shear walls in the shear failure mode are observed to be of the same values as those

computed in Section 7.2.3. Hence, the results related to load and resistance factors

to be computed for the shear failure mode of shear walls will be the same as those

found for columns in the combined action failure mode. Accordingly, the figures

drawn for the resistance and load factors displayed in Section 7.2.3 are exactly the

same for this section.

7.3 OPTIMAL LOAD AND RESISTANCE FACTORS

Load and resistance factors depend on the mean, variance and probability

distribution of basic variables involved in the limit state functions as well as type of

the load combinations considered. As observed in Section 7.2, load and resistance

factors corresponding to a specified target reliability show quite a high variability

depending on the ratio of the selected load to the dead load. If a constant set of load

and resistance factors are recommended, the corresponding reliabilities will deviate

from the target reliabilities for most of the design situations. This is due to the fact

that when the magnitudes of the time-varying loads increase, the related load factors

also increase. Nevertheless, it is possible to select one set of load and resistance

factors that minimizes the extent of the deviation from the target reliability when all

likely combinations of a particular load, which is given in Table 6.1, are taken into

consideration.

In fact, as emphasized by Ellingwood et al. (1980), “in general, an optimal set of

load factors can be selected by first defining some function which measures the

“closeness” between the target reliability and the reliability associated with the

proposed load and resistance factors set, and then selecting the load factors so as to

minimize this function”.

By using the load and resistance factors given in Section 7.2, a nominal resistance,

IInR , corresponding to a given set of nominal loads and a target reliability, can be

obtained. In addition, a design equation, which prescribes a set of load factors that

are constant for all load ratios will also result in a nominal resistance, InR . For

example, in the case of D+L+E load combination, if the factored resistance and the

D, L and E loads are linearly related, InR will be equal to:

ϕ′γ+′γ+′γ= /)ELD(R ELDIn (7.1)

Considering these two nominal resistance values, a set of load and resistance factors

can be selected in order to minimize the following difference equation:

IInii pRR),(D ∑ −=γϕ (7.2)

where pi is the relative weight assigned to the ith load situation for the relative

frequencies shown in Table 6.3. Ellingwood et al. (1980) stated that optimal load

and resistance factors are significantly more sensitive to the range of the ratio of

time-varying load to dead load than to the distribution of pi within that range,

implying that any deviation from the actual values of pi does not considerably

influence the values of optimal load and resistance factors.

Here, the optimal load and resistance factors are computed by utilizing a computer

program (MINMUM) in which Fletcher-Powell numerical search method is used

for the minimization procedure. The results corresponding to different failure

modes of beams, columns and shear walls are given in Tables 7.1 through 7.6.

Table 7.1 Optimal load and resistance factors for reinforced concrete beams in the

flexural failure mode

Optimal Load and Resistance Factors Load Combination Location

D+L Turkey 1.11D+1.80L 0.92

Bursa 1.06D+3.38S 1.14 D+S

Turkey 1.07D+2.00S 1.11

Canakkale 1.10D+0.49L+1.23W 0.88 D+Lapt+W

Turkey 1.10D+0.55L+0.89W 0.89

Canakkale 1.10D+1.40L+0.43W 0.90 D+L+Wapt

Turkey 1.10D+1.44L+0.21W 0.89

Ankara 1.02D+0.26L+3.75E 1.19 D+Lapt+E

Turkey 1.03D+0.23L+2.51E 1.19

Table 7.2 Optimal load and resistance factors for reinforced concrete beams in the

shear failure mode

D+L Turkey 1.10D+1.26L 0.65

Bursa 1.06D+3.30S 1.03 D+S

Turkey 1.08D+1.55S 0.87

Turkey 1.10D+0.44L+0.74W 0.68

Turkey 1.09D+1.26L+0.21W 0.67

Turkey 1.06D+0.20L+2.43E 1.12

Table 7.3 Optimal load and resistance factors for reinforced concrete columns in the

combined action failure mode

D+L Turkey 1.10D+1.92L 0.83

Bursa 1.06D+3.85S 1.10 D+S

Turkey 1.07D+2.29S 1.08

Turkey 1.10D+0.56L+0.88W 0.80

Turkey 1.10D+1.46L+0.25W 0.81

Turkey 1.06D+0.28L+2.45E 1.11

Table 7.4 Optimal load and resistance factors for reinforced concrete columns in the

shear failure mode

D+L Turkey 1.10D+1.41L 0.71

Bursa 1.06D+3.65S 1.02 D+S

Turkey 1.07D+0.94S 0.54

Turkey 1.10D+0.44L+0.76W 0.66

Turkey 1.09D+1.23L+0.22W 0.66

Turkey 1.06D+0.20L+2.43E 1.12

Table 7.5 Optimal load and resistance factors for reinforced concrete shear walls in

the flexural failure mode

D+L Turkey 1.11D+1.80L 0.92

Bursa 1.06D+3.94S 1.13 D+S

Turkey 1.07D+2.33S 1.10

Turkey 1.11D+0.54L+0.88W 0.89

Turkey 1.10D+1.44L+0.21W 0.89

Turkey 1.03D+0.23L+2.51E 1.19

Table 7.6 Optimal load and resistance factors for reinforced concrete shear walls in

the shear failure mode

D+L Turkey 1.10D+1.92L 0.83

Bursa 1.06D+3.85S 1.10 D+S

Turkey 1.07D+2.29S 1.08

Turkey 1.10D+0.56L+0.88W 0.80

Turkey 1.10D+1.46L+0.25W 0.81

Turkey 1.06D+0.28L+2.45E 1.11

7.4 MODIFIED OPTIMAL LOAD AND RESISTANCE FACTORS

As shown in Section 7.3, the resistance factors range from 0.65 to 0.92 for D+L and

from 0.65 to 0.90 for D+L+W load combinations. On the other hand, for the D+S

and D+L+E load combinations, these ranges are respectively 0.54 to 1.14 and 1.11

to 1.19. However, a resistance factor greater than 1.0 is not accustomed

(Ellingwood et al, 1980; Kömürcü and Yücemen, 1996). In order to reduce the

resistance factors which are greater than 1.0, the dead load factor is increased to 1.2,

which has been computed approximately to be 1.1 for all load combinations and for

all failure modes (Tables 7.1 to 7.6). It should be noted that in similar studies,

Ellingwood et al. (1980) and Kömürcü (1995) also increased the value of the dead

load factor from the optimal value of 1.1 to 1.2. In this study, to decrease the

resistance factor, the live load factors are also slightly increased and rounded to 0.4

in D+L+E load combination for all failure modes and for all structural members.

Also the resistance factors are set equal to the same value for all load combinations

for each structural member failing in a specific failure mode. The resistance factor

values are selected close to the most frequently observed value for the case under

consideration (i.e. the case corresponding to a certain structural member in a

specified failure mode), and are rounded. After these modifications, a new set of

load and resistance factors are obtained for each failure mode and for each

structural member. These load and resistance factors, which are called as modified

optimal load and resistance factors, are given in Tables 7.7-7.12.

beams in the flexural failure mode

Load and Resistance Factors Load Combination

Location γ φ

D+L Turkey 1.2D+1.74L 0.90

Bursa 1.2D+2.56S 0.90 D+S

Turkey 1.2D+1.44S 0.90

Turkey 1.2D+0.59L+0.91W 0.90

Turkey 1.2D+1.44L+0.22W 0.90

Turkey 1.2D+0.40L+1.37E 0.90

beams in the shear failure mode

Location γ φ

D+L Turkey 1.2D+1.38L 0.70

Bursa 1.2D+2.01S 0.70 D+S

Turkey 1.2D+1.03S 0.70

Turkey 1.2D+0.44L+0.74W 0.70

Turkey 1.2D+1.39L+0.32W 0.70

Turkey 1.2D+0.40L+0.91E 0.70

columns in the combined action failure mode

Location γ φ

D+L Turkey 1.2D+1.80L 0.80

Bursa 1.2D+2.65S 0.80 D+S Turkey 1.2D+1.45S 0.80

Canakkale 1.2D+0.49L+1.18W 0.80 D+Lapt+W Turkey 1.2D+0.56L+0.87W 0.80

Canakkale 1.2D+1.38L+0.42W 0.80 D+L+Wapt Turkey 1.2D+1.40L+0.24W 0.80

Ankara 1.2D+0.40L+2.10E 0.80 D+Lapt+E Turkey 1.2D+0.40L+1.27E 0.80

columns in the shear failure mode

Location γ φ

D+L Turkey 1.2D+1.39L 0.70

shear walls in the flexural failure mode

Location γ φ

D+L Turkey 1.2D+1.74L 0.90

shear walls in the shear failure mode

Location γ φ

D+L Turkey 1.2D+1.80L 0.80

For the beam flexure, Ellingwood et al. (1980), El-Etoom (1985) and Kömürcü and

Yücemen (1996) also suggested a different set of load and resistance factors. Their

results are given in Tables 7.13 and 7.14.

Table 7.13 Load and resistance factors in USA and Jordan for beams in the flexural

failure mode

Load Combination Country Load and Resistance Factors

USA 1.2D+1.6L 0.81 D+L (or D+S)

Jordan 1.2D+1.7L 0.77

1.2D+0.5L+1.3W 0.84 USA

1.2D+1.6L+0.1W -

1.2D+0.4L+1.6W 0.78 D+L+W

Jordan 1.2D+1.7L 0.72

USA 1.2D+0.2L+1.5E 0.82 D+L+E

Jordan 1.2D+0.4L+2.0E 0.80

Table 7.14 Load and resistance factors recommended by Kömürcü and Yücemen

(1996) for beams in the flexural failure mode

Load Combination Location Load and Resistance

Factors

D+L Turkey 1.3D+1.67L 0.90

Erzincan 1.3D+1.80S 0.90 D+S

Turkey 1.3D+1.20S 0.90

Erzincan 1.3D+0.49L+0.96W 0.90 D+L+W

Turkey 1.3D+0.5L+0.8W 0.90

Ankara 1.3D+0.30L+2.21E 0.90 D+L+E

Turkey 1.3D+0.30L+2.10E 0.90

In order to come up with a single set of load factors applicable to all members and

failure modes, the load factors given in Tables 7.7 to 7.12 are averaged. The

resulting load factors are tabulated in Table 7.15. It is to be noted that these load

factors should be used together with the appropriate resistance factors, which will

be computed in Section 7.5 for rounded load factors.

Table 7.15 Average load factors for all structural members in different failure

Load Combination

Location Average Load Factors

D+L Turkey 1.2D+1.64L

Bursa 1.2D+2.52S D+S Turkey 1.2D+1.38S

Canakkale 1.2D+0.53L+1.15W D+Lapt+W Turkey 1.2D+0.57L+0.89W

Canakkale 1.2D+1.34L+0.38W D+L+Wapt Turkey 1.2D+1.37L+0.23W

Ankara 1.2D+0.40L+2.05E D+Lapt+E Turkey 1.2D+0.40L+1.18E

In TS 500 (2000), material safety factors are used but there is no resistance factor;

that is, the resistance factor, φ, is equal to 1.0. Furthermore, the specified load

factors have to be used for all structural members and failure modes. Here, a set of

load factors are developed just for the sake of establishing a parallelism with the

provisions in TS 500 (2000), based on the load factors modified for achieving a

resistance factor, φ=1.0. The resulting load factors, which will be used for all

members and for all failure modes, are given in Table 7.16. However, the reliability

index values corresponding to these load factors will vary according to different

structural members and failure modes. To examine the extent of this variability, the

reliability index values corresponding to this case are computed and shown in Table

7.16. Although the table is constituted only for beams in the flexural and shear

failure modes, and columns in the combined action failure mode, they also represent

the reliability index values for the other failure modes. The reliability index values

computed for columns in the shear failure mode are identical to those of beams.

Similarly, the reliability indexes pertaining to the flexural and the shear failure

mode of shear walls are the same as those for the flexural failure mode of beams

and the combined action failure mode of columns, respectively.

Table 7.16 Load and resistance factors and corresponding reliability index values

for different structural members and failure modes for φ=1.0

Load Factors Beams in the

flexural failure mode

Beams in the shear failure mode

Columns in the combined action

failure mode

β ββββ β ββββ β ββββ

1.3D+1.9L 2.93-3.09 3.07 2.32-2.67 2.54 2.78-2.98 2.94

1.3D+1.6S 2.92-3.27 3.12 2.60-2.98 2.88 2.91-3.23 3.09

1.3D+0.80L+1.0W 3.02-3.28 3.18 2.54-2.80 2.65 2.98-3.16 3.06

1.3D+1.6L+0.4W 2.77-3.10 2.93 2.33-2.62 2.41 2.67-3.07 2.79

1.3D+0.6L+1.6E 1.51-2.12 1.78 1.51-2.00 1.68 1.50-2.11 1.74

As observed in Table 7.16, for example, for D+L load combination, while the

reliability index value for beams in the flexural failure mode is observed to be about

3.07 (βT=3.0), this value is 2.54 (βT=3.0) and 2.94 (βT=3.2) for beams in the shear

failure mode and for columns in the combined action, respectively. In other words,

for the same resistance factor, φ=1, the reliability indexes deviate significantly from

the selected target reliability index value, βT, according to the type of structural

member and failure mode. This shows the deficiency of TSE 500 (2000).

Accordingly, different resistance factors should be used for different failure modes

and different structural member types if the same load factors are used.

7.5 RECOMMENDED LOAD AND RESISTANCE FACTORS

In order to simplify the works of structural engineers, it is desirable to propose only

one set of load factors. For this purpose, the average load factors computed for

Turkey (see Table 7.15) are slightly rounded towards larger values and are

presented in Table 7.17. These are the final load factors that are recommended to be

used in design practice for all structural members in different failure modes.

Consistent with these proposed load factors, new resistance factors are computed

for each structural member failing in a specific failure mode, based on the target

reliability indexes given in Section 6.4.7. The reliability index values corresponding

to the recommended load and resistance factors are computed in order to compare

them with the selected target reliabilities. The results are tabulated in Tables 7.18-

Table 7.17 Recommended load factors for all structural members in different failure

modes for Turkey

Load Combination

Recommended Load Factors

D+L 1.2D+1.7L D+S 1.2D+1.4S

D+Lapt+W 1.2D+0.6L+0.9W D+L+Wapt 1.2D+1.4L+0.3W D+Lapt+E 1.2D+0.40L+1.3E

reliability index values for beams in the flexural failure mode

Reliability index values Load Combination

Resistance Factor

Recommended Load Factors ΒT β β

D+L 1.2D+1.7L 3.0 3.0-3.14 3.10

D+S 1.2D+1.4S 3.0 2.89-3.28 3.04

D+Lapt+W 0.90 1.2D+0.6L+0.9W 3.0 2.92-3.25 3.11

D+L+Wapt 1.2D+1.4L+0.3W 2.7 2.70-2.95 2.84

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.39-1.98 1.62

reliability index values for beams in the shear failure mode

Resistance Factor

D+L 1.2D+1.7L 3.0 2.83-3.06 3.00

D+S 1.2D+1.4S 3.0 3.08-3.25 3.19

D+Lapt+W 0.78 1.2D+0.6L+0.9W 3.0 3.04-3.25 3.12

D+L+Wapt 1.2D+1.4L+0.3W 2.7 2.77-2.93 2.82

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.57-2.18 1.90

reliability index values for columns in the combined action failure mode

Resistance Factor

D+L 1.2D+1.7L 3.2 3.15-3.27 3.24

D+S 1.2D+1.4S 3.2 3.02-3.44 3.26

D+Lapt+W 0.83 1.2D+0.6L+0.9W 3.2 3.16-3.43 3.30

D+L+Wapt 1.2D+1.4L+0.3W 3.0 2.91-3.20 3.03

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.50-2.11 1.74

reliability index values for columns in the shear failure mode

Resistance Factor

D+L 1.2D+1.7L 3.0 2.96-3.15 3.10

D+S 1.2D+1.4S 3.2 3.12-3.33 3.28

D+Lapt+W 0.75 1.2D+0.6L+0.9W 3.2 3.06-3.27 3.14

D+L+Wapt 1.2D+1.4L+0.3W 3.0 2.90-3.03 2.93

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.63-2.25 1.87

reliability index values for shear walls in the flexural failure mode

Resistance Factor

D+L 1.2D+1.7L 3.0 3.08-3.23 3.19

D+S 1.2D+1.4S 3.2 2.94-3.34 3.16

D+Lapt+W 0.88 1.2D+0.6L+0.9W 3.2 3.06-3.37 3.23

D+L+Wapt 1.2D+1.4L+0.3W 2.7 2.79-3.14 2.93

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.42-2.02 1.65

reliability index values for shear walls in the shear failure mode

Resistance Factor

D+L 1.2D+1.7L 3.2 3.15-3.27 3.24

D+S 1.2D+1.4S 3.2 3.02-3.44 3.26

D+Lapt+W 0.83 1.2D+0.6L+0.9W 3.2 3.16-3.43 3.30

D+L+Wapt 1.2D+1.4L+0.3W 3.0 2.91-3.20 3.03

D+Lapt+E 1.2D+0.4L+1.3E 1.75 1.50-2.11 1.74

As observed in Tables 7.18 to 7.23, the resulting mean reliability index values are

very close to the selected target reliability indexes, and in the majority of cases

these reliability index values are slightly greater than the target reliability values;

accordingly this creates a safer condition and it does not necessitate further

consideration. In Appendix G, the safety levels (in terms of reliability index) related

to the recommended load and resistance factors are plotted as functions of L'/D',

S'/D', W'/D' and E'/D' for the load combinations considered. It is to be noted that the

reliability index values computed for the combined action failure mode of columns

are identical to those of the shear failure mode of shear walls owing to the same

target reliability indexes and resistance statistics. Therefore, the graphs are not

plotted for the shear failure mode of shear walls. In these figures, the target

reliability indexes are also marked so that the deviations of reliability indexes from

target reliabilities, which is known to depend highly on the load and resistance

statistics and on the ratio of given loads to dead load, can also be evaluated.

CHAPTER 8

SUMMARY AND CONCLUSIONS

This thesis work is carried out to establish a reliability based design criterion for

different reinforced concrete structural members under different failure modes

considering the local conditions and the design practice in Turkey. The probabilistic

method of analysis utilized is the Advanced First Order Second Moment (AFOSM)

procedure. Factored resistance and factored loads form the basis for the limit state

function under consideration. The load combination model used is Turkstra’s rule.

Various sources of uncertainties associated with the load and resistance parameters

are analyzed and quantified based on the data available in Turkey. The published

data in the international literature are used to supplement the data compiled within

the framework of this study whenever local data are insufficient. In addition, related

results reported by other researchers are examined for the comparison of the results

found in this study.

The reliability indexes corresponding to the current design practice in Turkey for

reinforced concrete beam, column and shear wall design in flexure and shear as well

as column design in combined action of flexure and axial load subjected to different

load combinations are computed. Considering these values and those reported from

other studies, target reliabilities are selected for different failure modes of structural

members under different load combinations. Finally, a new set of load and

resistance factors corresponding to selected target reliabilities and levels of

uncertainties are proposed. The computer program A58LF (Ellingwood et al., 1980)

is utilized for the reliability calculations. A58LF computes the reliability index

values for a given design situation established by a set of nominal load and

resistance values (analysis problem) and computes the needed resistance and load

factors for a prescribed a set of nominal loads (design problem). The optimal load

and resistance factors are obtained by utilizing a code written in Fortran 77

(MINMUM). In addition to the programs mentioned above, the resistance statistics

of reinforced concrete members in different failure modes are obtained by using

five different codes, which are developed in MathCAD 12 for this study.

The main conclusions and recommendations derived from this study are listed

below:

1- Based on the evaluation of the 28 day concrete compressive strength test results

of approximately 11000 specimens collected in Turkey, the mean value of cubic

compressive strength is found as 29.87 N/mm2, and c.o.v is computed as 0.105. If

the cubic compressive strength of concrete data is converted to the standard cylinder

strength value, then cf and δfc are found to be 24.87 N/mm2 and 0.105, respectively.

It should be noted that the values of c.o.v. (i.e. δfc) are obtained for each

construction site individually in this study. The mean to nominal concrete

compressive strength ratio is computed as 1.25. In other words, the “true”

compressive strength obtained from the field data (i.e. in-situ data) is 25% higher

than the nominal compressive strength specified in the relevant standards. The

uncertainty analysis showed that the total uncertainty for concrete compressive

strength equals to 0.18 if the prediction uncertainties (epistemic uncertainties) are

combined with the basic variability (aleatory uncertainty). When these results are

compared with the ones obtained in the earlier years, it can be concluded that the

quality of concrete has been improved over the years from the compressive strength

and basic variability points of view.

2- The statistical parameters of yield strength, ultimate strength and elongation of

reinforcing steel bars are obtained from the production reports of the seven steel and

iron plants. In addition, the data based on the civil engineering materials

laboratories of Istanbul Technical University, Middle East Technical University and

Selcuk University are investigated. After conducting a set of statistical analyses on

the collected data, the mean yield strength is computed to be 501.37 N/mm2 as the

weighted average value, obtained from the data supplied by iron and steel plants

and university laboratories. The basic variability in yield strength is found to range

from 0.02 to 0.07 with a weighted average value of 0.038 for individual bar sizes

based on the data obtained from the iron and steel plants. In this study, the mean to

nominal ratio of yield strength of reinforcing steel bars and total uncertainty in them

are calculated as 1.24 and 0.09, respectively.

3- Depending on the analysis of local data obtained from different construction

sites, the average basic variabilities in the various dimensions, such as width, depth,

effective depth for beams, columns and shear walls range from 0.03 to 0.07. The

total variabilities in these dimensions change between 0.038 and 0.074. For all

dimensions, the mean to nominal ratios are observed to be about 1.00.

4- The mean to nominal ratios and the total uncertainties of resistances in different

failure modes for different reinforced structural members are computed by using the

compressive strength of concrete, the yield strength of reinforcing steel bars and the

dimensions of structural members within the framework of the reliability model.

While the mean to nominal ratio (the ratio of “true” mean value to nominal value

specified in relevant standards) is found as 1.24 for all failure modes and for all

reinforced concrete structural members considered in this study, the total

uncertainties vary within a range of 0.13 and 0.17 depending on the failure mode

and the member type.

5- Loads considered in this study are dead, live, snow, wind, and earthquake. Due to

lack of local data, the statistical parameters of dead and live loads are calculated

based on the information assessed from the foreign literature. This can be accepted

as a reasonable assumption owing to the fact that the characteristics of dead and live

loads are believed not to change noticeably from one country to another. It is

assumed that the mean to nominal ratio and total variability of dead load are 1.05

and 0.10, respectively, as the approximate average value of the studies reported in

the international literature. As for live load, the mean to nominal ratios are taken as

1.00 and 0.28 for maximum live load and arbitrary point-in-time live load, while

total variabilities are obtained as 0.28 and 0.70, respectively.

6- Although dead and live loads acting on a structure are independent of the

geographical location of the structure; snow, wind and earthquake loads, which can

be termed as environmental loads, are quite dependent. For this reason, in order to

compute the parameters of environmental loads for the whole Turkey, some

representative cities, namely Ankara, Izmir, Antalya, Bursa, Gaziantep, Samsun,

Malatya, Erzincan, Canakkale, Hakkari, Göztepe/Istanbul and Sile/Istanbul are

considered. In order to compute snow, wind and earthquake loads, the mean values

of arbitrary point-in-time and maximum lifetime loads in these locations are

considered separately.

7- Snow depth is the main parameter affecting the snow load. The data on snow

depth are obtained from the records of Turkish Meteorological Department. The

nominal roof snow load, S′ , can be obtained from TS 498 (1997). The mean to

nominal ratios range 0.01 to 0.89 and 0.06 to 2.68 for annual extreme roof snow

load and maximum roof snow load in the geographical locations listed above. As

indicated by these values, the differences between mean and nominal values are

excessive for some of these locations. Therefore, it is recommended that the

nominal snow load values in TS 498 (1997) should be revised. The total

uncertainties in annual extreme roof snow load and maximum roof snow load range

from 0.60 to 0.93 and 0.27 to 0.48, respectively.

8- The daily and annual wind speed data, which are necessary for the wind load

statistics, are obtained from the meteorological stations of Turkish Meteorological

Department located in twelve different cities. For these cities, the mean to nominal

ratios range from 0.09 to 0.32 and from 0.35 to 0.82 for arbitrary point-in-time and

maximum wind loads, and also the total uncertainties in these loads range from 0.60

to 0.93 and from 0.27 to 0.48, respectively. As it is seen from these values, the

nominal wind load values in TS 498 (1997) stay on the safe side for all locations.

9- Earthquake load is assumed to depend mainly on the peak ground acceleration.

For the twelve locations, the outcomes of the seismic hazard analysis conducted by

Gülkan et al. (1993) are used for estimating the statistical parameters of peak

ground accelerations. The mean to nominal ratios change between 0.85 and 1.61 for

earthquake loads, and also the total uncertainties in this load, which is quantified in

terms of coefficient of variation, change within a range of 1.05 and 1.21. It is to be

noted that earthquake load shows the most variation among all of the loads.

10- The current design practice is assumed to depend on TS 500 (2000), TS 498

(1997), and Specifications for the Structures to be Built in Disaster Areas (1998).

By utilizing the AFOSM method, the safety levels inherent in the current design

practice are examined for reinforced concrete beams, columns and shear walls in

the flexural and shear failure modes, and also columns in the combined action

depending on the load and resistance statistics compiled in this study. Considering

the failure modes of reinforced concrete structural members studied, the average

reliability index values for the whole Turkey (i.e. the average of values obtained

from twelve location) range from 2.41 to 2.90 for D+L; from 2.97 to 3.20 for D+S;

from 2.94 to 3.36 for D+Lapt+W; from 2.40 to 2.79 for D+L+Wapt and from 1.29 to

1.32 for D+Lapt+E. The target reliabilities are selected according to these safety

level values, and also by taking into consideration the target reliabilities reported

from the international literature. In this study, the selected target reliabilities vary

within a range of 1.75 and 3.2 depending on the load combination, the failure mode

and the member type.

11- A new set of load and resistance factors corresponding to the selected target

reliabilities are determined for different design situations, i.e. for L'/D', S'/D', W'/D'

and E'/D' values according to D+L, D+S, D+Lapt+W, D+L+Wapt and D+Lapt+E load

combinations. The load and resistance factors show variability based on the ratio of

the selected load to the dead load. It is possible to select one set of optimal load and

resistance factors that minimizes the extent of the deviation from the selected target

reliability. After computing these optimal load and resistance factors for each

failure mode of reinforced concrete structural members considered in this

dissertation, some modifications are made in order to obtain more accustomed

resistance factors (i.e. less than 1.0). These factors which are termed as modified

optimal load and resistance factors are as follows:

E37.1L4.0D2.1

W91.0L59.0D2.1

S44.1D2.1

L74.1D2.1

U and φ= 0.90 for beams in the flexural failure mode

E91.0L4.0D2.1

W74.0L44.0D2.1

S03.1D2.1

L38.1D2.1

U and φ= 0.70 for beams in the shear failure mode

E27.1L4.0D2.1

W87.0L56.0D2.1

S45.1D2.1

L8.1D2.1

U and φ= 0.80 for columns in the combined action

E91.0L4.0D2.1

W8.0L6.0D2.1

S20.1D2.1

L39.1D2.1

U and φ= 0.70 for columns in the shear failure mode

failure mode

E37.1L4.0D2.1

W91.0L54.0D2.1

S69.1D2.1

L74.1D2.1

U and φ= 0.9 for shear walls in the flexural failure mode

E27.1L4.0D2.1

W87.0L6.0D2.1

S45.1D2.1

L8.1D2.1

U and φ= 0.8 for shear walls in the shear failure mode

12- In TS 500 (2000), material safety factors are used but resistance factors are not

considered; in other words, the resistance factor, φ, equals 1.0. Furthermore, the

specified load factors have to be used for all structural members and failure modes.

Therefore, a set of load factors are computed corresponding to φ=1 in order to have

a parallelism with the provisions in TS 500 (2000) as given below:

E6.1L6.0D3.1

W0.1L8.0D3.1

S6.1D3.1

L9.1D3.1

U φ= 1.0 for all failure modes and all structural members

When the reliability index values corresponding to this case are computed, it is seen

that the reliability indexes exhibit high variability according to structural members

and failure modes, and deviate significantly from the selected target reliability index

βT. Therefore, different resistance factors should be used for each failure mode and

each structural member in such a case where the same load factors are used.

13- In order to simplify the works of structural engineers, only one set of load

factors are proposed by averaging the load factors computed for reinforced concrete

structural members failing in different failure modes. However, the use of the same

resistance factors is not rational due to the fact that the related reliability index

values vary according to different failure modes and member types. Therefore, the

following one set of load factors and six different resistance factors are proposed for

each failure mode of the reinforced concrete structural members considered:

E3.1L4.0D2.1

W9.0L6.0D2.1

S4.1D2.1

L7.1D2.1

mode failureshear in the sshear wallfor 83.0

mode failure flexural in the sshear wallfor 88.0

mode failureshear in the columnsfor 75.0

mode failureaction combined in the columnsfor 83.0

mode failureshear in the beamsfor 78.0

mode failure flexural in the beams for 90.0

It is to be noted that these load and resistance factors are to be used in connection

with TS 500 (2000), TS 498 (1997) and Specification for Structures to be Built in

Earthquake Areas (2006).

14- In addition to load combinations consisting of primary loads, different load

combinations including secondary loads, (e.g. temperature and soil load) can be

considered, within the same framework.

15- The statistical data on loads and the probabilistic methodology provided in this

dissertation can be extended to the limit state design of different construction

materials, such as metal structures, engineering masonry and prestressed concrete.

16- The load and resistance factors proposed in this study are open to future

adjustments if new local and relevant international data as well as information

become available.

REFERENCES

American Concrete Institute, Building Code Requirements for Reinforced Concrete,

ACI 318/05, ACI, Detroit, Michigan, USA, 2005.

American Society of Civil Engineers, Minimum Design Loads for Buildings and

Other Structures, ASCE Standard, ASCE/SEI 7-05, USA, 2006.

Aktas, E., Structural Design Code Calibration Using Reliability Based Cost

Optimization, Ph. D. Thesis, The University of Pittsburgh, Pittsburgh, 2001.

Aktas E., Moses, F. and Ghosn, M., Cost and Safety Optimization of Structural

Design Specifications, Reliability Engineering and System Safety 73, pp. 205-212,

Ang, A. H.S and Tang, W.H., Probability Concepts in Engineering Planning and

Design, Volume II, John Wiley and Sons Inc., New York, 1984.

Atimtay, E., Reinforced Concrete Fundamentals, Bizim Büro Basimevi, Ankara,

Turkey, 1998.

Ayaroglu F., Türkiye’de Kar Yagislari, Uzmanlik Tezi, T.C. Basbakanlik Devlet

Meteoroloji Genel Müdürlügü, Ankara, 1991.

Celep, Z. and Kumbasar, N., Betonarme Yapilar, Beta Dagitim, Istanbul, 2005.

Dislitas, S., Ahiska R. and Yanmaz, H., Beton Karakteristik Basinc Dayanimi

Testinin Bilgisayar Kontrollü Yapilmasi, Bilgi Teknolojileri Kongresi, Akademik

Bilisim 2006, Pamukkale Üniversitesi, Denizli, 2006.

Durmaz, M. and Daloglu A., Kar Verilerinin İstatistiksel Analizi ve Dogu

Karedeniz Bölgesinin Zemin Kar Haritasinin Olusturulmasi, İMO Teknik Dergi,

pp 3619-3642, 2005.

Dündar C., Türkiye Rüzgar Atlasi, T.C. Basbakanlik Devlet Meteoroloji Genel

Müdürlügü ve Enerji Tabii Kaynaklar Bakanligi Elektrik İsleri Etüt İdaresi Genel

Müdürlügü, Ankara, 2002.

Ellingwood, B.R., Galambos, T.V., MacGregor, J.G. and Cornell, C.A.,

Development of a Probability Based Load Criterion for American National

Standards A58, NPS Special Publication 577, 1980.

Ellingwood, B. and Galambos, T.V., Probability-Based Criteria for Structural

Design, Structural Safety, No.1, pp. 15-26, 1982.

Ellingwood, B., Ang. A. H. S., Probabilistic Study of Safety Criteria for Design,

Structural Research Series No. 387, Department of Civil Engineering, University of

Illinois, Urbana, 1972.

Ellingwood, B.R., Probability-based codified design for earthquakes, Engineering

Structure, Vol. 16, Number 7, pp. 498-506, 1994.

Ellingwood, B.R., Reliability-based condition assessment and LRFD for existing

structures, Structural Safety, Vol. 18, pp 67-80, 1996.

Ersoy, U. and Özcebe, G., Reinforced Concrete, Evrim Yayinevi, Ankara, 2004.

Faber, M.H., Kübler, O. and Köhler, J. Tutorial for the JCSS code calibration

program CodeCal 03, 2003.

Ferguson, P.M., Breen, E.B. and James, O.J., Reinforced Concrete Fundamentals,

John Wiley & Sons, Inc., Singapore, 1988.

Galambos, T. V., Ellingwood, B., MacGregor, J.G. and Cornell C.A., Probability

Based Load Criteria: Load Factors and Load Combinations, Journal of The

Structural Division, ASCE, Vol 108, No. ST5, pp. 978-997, 1982.

Ghiocel, D. and Lungu, D., Wind, Snow and Temperature Effects on Structures

Based On Probability, Abacus Press, Turbridge Wells, Kent, 1974.

Gülkan, P., Kocyigit A., Yücemen, M.S., Doyuran, V. and Basöz, N., En Son

Verilere Göre Hazirlanan Türkiye Deprem Bölgeleri Haritasi, Rapor No. 93-01,

Deprem Mühendisligi Arastirma Merkezi, ODTÜ, Türkiye, 1993.

Gündüz, A., Beton Mukavemetinin Betonarme Yapilarin Göcme Riski Üzerine

Etkisi, Ülkemizin Kalkinmasinda Mühendisligin Rolü Sempozyumu, Istanbul, 1988

Hasofer, A. and Lind, N.C., Exact and Invariant Second-Moment Code Format,

Journal of Engineering Mechanics Division, ASCE, Vol. 100, No. EM. 1, pp. 111-

121, 1974

Hwang, H.H.M. and Hsu, H.M., Seismic LRFD Criteria for RC Moment-Resisting

Frame Buildings, Journal of Structural Engineering, Vol. 119, Number 2921, pp.

1807-1824, 1993.

International Code Council, International Building Code 2003, USA, 2003.

Israel, B. M., Ellingwood, B. and Corotis, R., Reliability Based Code Formulations

for Reinforced Concrete Buildings, Journal of the Structural Engineering, Vol 113,

No. 10, October, 1987.

Turkish Iron and Steel Producers Association, Iron & Steel Sector in Turkey,

http://www.dcud.org.tr/indextur.htm, last accessed date 2004.

Jeff Quell, P.E, Determining Snow Loads, A Quarterly Information Source from

Benchmark, Inc., Volume 34, 1998.

Kömürcü, A.M., A Probabilistic Assessment of Load and Resistance Factors for

Reinforced Concrete Structures Considering the Design Practice in Turkey, M. Sc.

Thesis, Department of Civil Engineering, METU, Ankara, 1995.

Kömürcü, A.M. and Yücemen, M.S., Load and Resistance Factors for Reinforced

Concrete Beams Considering the Design Practice in Turkey, Concrete Technology

for Developing countries, Fourth International Conference, Eastern Mediterranean

University, Gazi Magusa, North Cyprus, 1996.

Kumar, S., Live Loads in Office Buildings: Point in Time Load Intensity, Building

and Environment, Vol. 37, pp- 79-89, 2002a.

Kumar, S., Live Loads in Office Buildings: Lifetime Maximum Load, Building and

Environment, Vol. 37, pp- 91-99, 2002b.

Melchers R.E., Structural Reliability Analysis and Prediction, John Wiley & Sons,

Inc., Chichester, England, 2002.

Meyer, C., Design of Concrete Structures, Prentice-Hall, Inc., New Jersey, USA,

Minciarelli, F., Gioffre, M., Grigoriu, M. and Simiu, E., Estimates of Extreme Wind

Effects and Wind Load Factors: Influence of Knowledge Uncertainties,

Probabilistic Engineering Mechanics, Vol. 16, pp 331-340, 2001.

Mirza, S. A. and MacGregor, J.G., Variations in Dimensions of Reinforced

Concrete Member, Journal Of The Structural Division, ASCE, Vol. 105, No. ST4,

pp. 921-937, 1979.

Mirza, S.A. and MacGregor, J.G., Variability of Mechanical Properties of

Reinforced Bars, Journal of the Structural Division, ASCE, Vol. 105, No. ST4, pp.

751-766, 1979.

Mirza, S.A., Hatzinikolas, M. and MacGregor, J.G., Statistical Description of the

Strength of Concrete, Journal of the Structural Division, ASCE, Vol. 105, No. ST6,

pp. 1021-1037, 1979.

Mirza, S.A. and MacGregor, J.G., Probabilistic study of strength of Reinforced

concrete members, Can. J. Civ. Engrg., Ottawa 9, pp. 431-438, 1982.

Nawy, E.G., Reinforced Concrete A Fundamental Approach, Pearson Education,

Inc., New Jersey, USA, 2005.

Nilson, A.H., Darwin, D. and Dolan, C.W., Design of Concrete Structures,

McGraw-Hill Companies, Inc. Singapore, 2004.

Nowak, A.S. and Szerszen, M.M., Calibration of Design Code for Buildings (ACI

318): Part 1- Statistical Models for Resistance, ACI Structural Journal, May-June,

pp. 377-382, 2003a.

Nowak, A.S. and Szerszen, M.M., Calibration of Design Code for Buildings (ACI

318): Part 2- Reliability Analysis and Resistance Factors, ACI Structural Journal,

May-June, pp. 383-391, 2003b.

Park R. and Paulay, T., Reinforced Concrete Structures, John Wiley & Sons, Inc.,

Singapore, 1975.

Paulay, T. and Priestley, M.J.N., Seismic Design of Reinforced Concrete and

Masonry Buildings, John Wiley & Sons, Inc., USA, 1992.

Q’ Rourke M.J., Redfield, R. and Bradsky, P.V., Uniform Snow Loads on

Structures, Journal of the Structural Division, ASCE, Vol. 108, No ST12, pp. 2781-

2798, 1982.

O’Rourke, M. and Wrenn, P.D., A Guide to the Use and Understanding of the Snow

Load Provisions of ASCE 7-02, ASCE, 2004.

Özsoy, D., İnsaat Celigi ve Kontrollü Su Sogutma Yöntemi”, http://www.mmo. org.

tr/ mühendis makine/arsiv/2001/martinsaatt.htm, last accessed date, 2007

Joint Committee on Structural Safety, Probabilistic Model Code, 2001.

Rackwitz, R., Optimization- the Basis of Code-Making and Reliability Verification,

Structural Safety, Vol. 22, pp. 27-60, 2000.

Real, M.V., Filho, A.C. and Sergio, R.M., Response Variability in Reinforced

Concrete Structures with Uncertain Geometrical and Material Properties, Nuclear

Engineering and Design, pp. 205-220, 2003.

Rusten, A., Sack, R. L. and Malnav, M., Snow Load Analysis for Structures,

Journal of the Structural Division, ASCE, Vol. 108, No ST1, pp.11-21, 1980.

Schiever, W.R., Estimating Snow Loads, CBD-193, Canadian Building Digest,

1978, http://irc.nrc-cnrc.gc.ca/pubs/cbd/cbd193_e.htm , last accessed date 2005.

Simiu E. and Scalan, R.H., Wind Effects on Structures, 1st ed., John Wiley, New

York, 1978.

Spiegel, L. and Limbrunner, G.F., Reinforced Concrete Design, Pearson Education,

Inc., New Jersey, USA, 2003.

Sahin, A.D., Türkiye Rüzgarlarinin Alan Zaman Modellemesi, Ph. D. Thesis, İTÜ,

Istanbul, 2001.

T.C. Bayindirlik ve İskan Bakanligi, Deprem Surasi-2004. Yapi Malzemeleri

Komisyonu Raporu, Ankara, Temmuz 2004.

T.C. Bayindirlik ve İskân Bakanligi, Afet Bölgelerinde Yapilacak Yapilar Hakkinda

Yönetmelik, Nihai Deprem Yönetmeligi Taslagi, Türkiye, 1996.

Yönetmelik, Türkiye, 1998.

Yönetmelik, Nihai Deprem Yönetmeligi Taslagi, Türkiye, 2006.

Türk Standartlari, Yapi Elemanlarinin Boyutlandirilmasinda Alinacak Yüklerin

Hesap Degerleri (TS 498 ), Türk Standartlari Enstitüsü , Ankara, 1997.

Türk Standartlari, Betonarme Yapilarin Hesap ve Yapim Kurallari (TS 500), Türk

Standartlari Enstitüsü, Ankara, 2000.

Türk Standartlari, Beton- Bölüm 1: Özellik, Performans, İmalat ve Uygunluk (TS

EN 206-1), Türk Standartlari Enstitüsü, Ankara, 2002.

International Conference of Buildings Officials, Uniform Building Code 1994,

Whitter, California, USA., 1994.

Toft-Christensen, P. and Baker, M. J., Structural Reliability Theory and Its

Applications, Springer Verlag, Berlin, 1982.

Topcu, İ.B. and Karakurt, C., Eskisehir’de Kullanilan Yapi Celiklerinin Istatistiksel

Olarak Incelenmesi, Seventh International Congress on Advances in Civil

Engineering, Yildiz Technical University, Istanbul, Turkey, 2006.

Udoeyo, F. F. and Ugbem, P.I, Dimensional Variations in Reinforced Concrete

Members, Journal of the Structural Engineering, December, pp. 1865-1868, 1995.

Vrouwenvelder, A.C.W.M., Developments towards Full Probabilistic Design

codes. Structural Safety. Vol.24, 417-432, 2002.

Yücemen, M.S. and Gülkan, P., Betonarme Yapilar İcin Yük ve Dayanim

Katsayilarinin Belirlenmesi, 10. Teknik Kongre, Cilt 2, İnsaat Mühendisleri Odasi,

s. 637-651, 1989.

Yücemen, M.S. and El-Etoom, A., Reliability Based Load and Resistance Factors

for Reinforced Concrete Beams in Jordan, Proceedings, The Second International

Conference on Concrete Tecnology for Developing Countries, Vol. I, Tripoli,

Libya, pp. 4.1-4.17, 1986.

Yüksel, S.B., A Comparative Study on Seismic Codes, M. Sc. Thesis, Department of

Civil Engineering, METU, Ankara, 1997.

APPENDIX A

STATISTICAL PARAMETERS OF 7 AND 28 DAY COMPRESSIVE

STRENGTH DATA ACCORDING TO CONCRETE CLASS AND REGION

Table A.1.a Statistical parameters of 7 day compressive strength data according to concrete class and region

Concrete Class

Number of samples

(N/mm2)

Mean (N/mm2)

Standard deviation

Corlu Region

C20 577 25 24.01 3.28 0.137

C25 405 30 26.18 4.11 0.157

C30 33 37 30.07 3.67 0.122

Overall 1015 25.07 3.61 0.144

Trabzon Region

C14 6 18 10.18 0.71 0.07

C18 139 22 13.87 2.54 0.183

C20 162 25 17.24 2.84 0.165

Overall 307 15.58 2.66 0.171

Erzurum Region

C14 12 18 12.53 2.07 0.165

C18 6 22 17.24 2.47 0.143

C20 135 25 15.14 0.908 0.06

Overall 153 15.02 1.08 0.072

Samsun Region

C14 6 18 22.02 5.15 0.234

C16 45 20 21.01 3.74 0.178

C18 3 22 17.86 6.97 0.39

C20 231 25 22.84 3.81 0.167

C25 3 30 30.33 0.52 0.017

C30 21 37 36.17 4.56 0.126

Overall 309 23.49 3.95 0.168

Bursa Region

C16 17 20 15.73 1.37 0.087

C18 10 22 19.94 0.89 0.045

C20 272 25 20.15 2.18 0.108

C25 138 30 22.57 2.39 0.106

Overall 437 20.74 2.18 0.105

Table A.1.b Statistical parameters of 7 day compressive strength data according to concrete class and region

Concrete Class

Number of samples

(N/mm2)

Mean (N/mm2)

Ankara Region

C16 9 20 19.47 3.12 0.160

C18 8 22 16.63 4.99 0.30

C20 193 25 23.13 2.94 0.127

C25 175 30 27.43 3.46 0.126

C30 143 37 32.71 3.57 0.109

Overall 528 26.99 3.37 0.125

Izmir Region

C20 603 25 26.82 - -

C25 627 30 28.61 - -

C30 159 37 35.39 - -

Overall 1389 28.60 - -

Gaziantep Region

C16 17 20 17.09 0.87 0.051

C20 181 25 26.34 3.08 0.117

C25 3 30 30.33 4.55 0.15

C30 5 37 37.76 261 0.069

Overall 206 - 25.91 2.88 0.111

Denizli Region

C18 41 22 21.18 3.35 0.158

C20 176 25 24.37 3.99 0.164

C25 31 30 27.26 2.67 0.098

Overall 248 24.20 3.75 0.155

Antalya Region C16 137 20 20.79 2.39 0.115 C18 169 22 19.65 2.69 0.137 C20 345 25 20.92 2.85 0.136 C25 267 30 25.12 2.56 0.102 C30 102 37 28.08 2.13 0.076

Overall 1020 22.51 2.66 0.118

Konya Region

C16 193 20 20.42 3.88 0.190

C18 159 22 21.32 2.96 0.139

C20 216 25 22.53 2.63 0.117

C25 52 30 28.58 3.97 0.139

Overall 620 22.07 3.24 0.147

Table A.2.a Statistical parameters of 28 day compressive strength data according to concrete class and region

Concrete Class

Number of samples

fck (N/mm2)

Mean (N/mm2)

Corlu Region

C20 580 25 31.09 3.52 0.113 9 1.5

C25 392 30 34.04 4.02 0.118 18 4.6

C30 21 37 38.73 2.43 0.063 0 0

Overall 993 32.42 3.69 0.114 27 2.7

Trabzon Region

C14 6 18 17.95 1.87 0.104 0 0

C18 43 22 24.74 2.97 0.12 3 6.9

C20 163 25 25.98 1.64 0.063 2 1.2

Overall 212 25.5 1.94 0.076 5 2.4

Erzurum Region

C14 24 18 17.31 1.64 0.095 0 0

C18 37 22 19.21 1.36 0.071 2 5.4

C20 228 25 25.25 2.20 0.087 27 11.8

Overall 289 23.82 2.07 0.087 29 0.100

Kayseri Region

C18 179 22 24.96 2.21 0.10 3 1.7

C20 123 25 27.24 1.77 0.069 1 0.8

Overall 302 25.89 2.25 0.087 4 0.013

Samsun Region

C14 6 18 29.3 8.06 0.275 0 0

C16 45 20 28.67 5.05 0.176 2 4.4

C18 18 22 29.08 6.28 0.216 1 5.5

C20 229 25 30.51 3.94 0.129 10 4.4

C25 6 30 35.93 1.69 0.047 0 0

C30 20 37 39.04 4.02 0.103 2

Overall 324 30.78 0.140 15 4.6

Bursa Region

C16 17 20 24.04 2.57 0.107 0 0

C18 12 22 30.24 2.72 0.09 2 16.7

C20 235 25 28.33 2.21 0.078 3 1.3

C25 156 30 30.42 3.44 0.113 13 8.3

Overall 420 28.99 2.70 0.093 18 0.043

Table A.2.b Statistical parameters of 28 day compressive strength data according to concrete class and region

Concrete Class

Number of samples

fck (N/mm2)

Mean (N/mm2)

Izmir Region

C20 603 25 33.34 3.29 0.099 - -

C25 627 30 35.92 2.72 0.076 - -

C30 159 37 43.33 3.11 0.072 - -

Overall 1389 - 35.64 3.03 0.085 - -

Gaziantep Region

C16 13 20 28.07 4.01 0.143 0 0

C20 170 22 34.2 3.76 0.11 2 1.2

C25 6 25 38.17 8.24 0.216 0 0

C30 10 30 48.12 4.96 0.103 0 0

Overall 199 34.62 3.98 0.115 2 1.0

Denizli Region

C14 9 18 24.89 5.25 0.211 0 0

C18 44 22 28.54 3.97 0.139 0 0

C20 200 25 30.91 4.27 0.138 2 1.0

C25 40 30 32.18 4.11 0.128 2 5.0

C30 6 37 31.78 1.21 0.038 0 0

Overall 299 30.57 4.19 0.137 4 1.3

Antalya Region

C16 137 20 25.22 2.32 0.092 2 1.5

C18 182 22 25.70 2.80 0.109 2 1.1

C20 353 25 27.79 2.58 0.093 6 1.7

C25 264 30 34.31 3.02 0.088 3 1.4

C30 99 37 39.39 1.69 0.043 2 2.0

Overall 1035 29.85 26.87 0.90 15 0.014

Table A.2.c Statistical parameters of 28 day compressive strength data according to concrete class and region

Concrete Class

Number of samples

fck (N/mm2)

Mean (N/mm2)

Ankara Region

C16 21 20 23.66 3.12 0.132 0 0

C18 16 22 24.13 4.89 0.203 5 3.1

C20 660 25 29.33 3.20 0.109 35 5.3

C25 217 30 33.05 4.00 0.121 9 4.1

C30 227 37 40.41 3.96 0.098 10 4.4

Overall 1141 32.06 3.53 0.11 59 5.2

Konya Region

C16 432 20 25.24 4.04 0.160 9 2.1

C18 390 22 26.44 3.28 0.124 7 1.8

C20 549 25 26.19 3.06 0.117 18 3.3

C25 126 30 33.98 3.77 0.111 6 4.8

C30 12 37 37.32 4.25 0.114 0 0

Overall 1509 26.72 3.5 0.131 40 2.7

Malatya Region

C14 92 18 19.80 2.34 0.115 1 1.1

C16 90 20 22.68 1.86 0.080 0 0

C20 281 25 31.96 4.34 0.135 3 1.1

C25 55 30 34.58 3.11 0.090 2 3.6

C30 12 37 42.63 3.26 0.065 0 0

Overall 530 28.79 0.116 6 1.1

Istanbul Region

C20 1443 25 24.90 6.63 0.263 - -

C25 878 30 28.63 6.40 0.219 - -

C30 304 37 38.40 6.62 0.174 - -

C35 252 45 38.21 6.85 0.18 - -

Overall 2877 --- 28.63 6.58 0.23 - -

APPENDIX B

STATISTICAL PAREMETERS OF BCIII(A) REINFORCING STEEL BARS

USED IN TURKEY

Table B.1. Statistical parameters of BCIII(a) reinforcing steel bars produced by Habas steel plant

Diameter (mm)

Number of samples

Mean value (N/mm2)

10 835 420 546.45 25.65 0.047 12 300 420 511.28 19.21 0.038 16 2174 420 521.42 20.55 0.039 18 30 420 574.83 20.39 0.036 20 1695 420 529.93 19.49 0.037 25 1830 420 531.24 14.24 0.027

32 2329 420 537.75 13.22 0.024 40 406 420 529.18 28.04 0.053

Overall 9619 420 530.01 18.06 0.034

Table B.2. Statistical parameters of BCIII(a) reinforcing steel bars produced by Icdas steel plant

Diameter (mm)

Number of samples

Mean value of yield strength (N/mm2)

Required ultimate strength (N/mm2)

Mean value of ultimate strength (N/mm2)

Required minimum elongation (%)

Mean value of elongation (%)

8 100 420 495 500 603 12 21.2 10 100 420 512 500 617 12 18 12 100 420 508 500 601 12 18.3 14 100 420 507 500 616 12 19.2 16 100 420 531 500 640 12 20 18 100 420 523 500 621 12 19.4 20 100 420 518 500 641 12 18

22 100 420 506 500 597 12 18.6 24 100 420 510 500 625 12 18.7 25 100 420 535 500 624 12 17.2 26 100 420 514 500 608 12 17.3 28 100 420 542 500 638 12 17.5 30 100 420 509 500 621 12 16.6 32 100 420 525 500 642 12 16.5

Overall 1400 420 516.8 500 621 12 18.32

Table B.3. Statistical parameters of BCIII(a) reinforcing steel bars produced by Colakoglu steel plant

a. Yield strength

Diameter (mm)

Number of samples

Required strength (N/mm2)

Mean value (N/mm2)

8 57 420 487.00 31.59 0.065 10 70 420 457.60 14.91 0.033 12 62 420 481.42 24.30 0.050 14 72 420 469.64 20.46 0.044 16 77 420 465.81 19.93 0.043 18 58 420 477.08 20.58 0.043 20 51 420 470.41 23.94 0.051 22 9 420 497.44 18.39 0.040 25 56 420 478.00 30.73 0.064 32 18 420 489.00 23.33 0.047

Overall 530 420 473.63 22.79 0.048

b. Ultimate strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 57 500 682.44 62.24 0.091 10 70 500 703.89 30.63 0.044 12 62 500 582.46 46.38 0.079 14 72 500 575.58 38.15 0.066 16 77 500 581.99 26.74 0.046 18 58 500 613.83 48.83 0.071

20 51 500 608.02 44.76 0.074 22 9 500 638.22 19.08 0.030 25 56 500 598.03 45.84 0.076 32 18 500 618.23 26.84 0.043

Overall 530 500 617.95 40.96 0.065

c. Minimum elongation

Diameter (mm)

Number of samples

Required elongation (%)

Mean value (%)

Standard deviation (%)

8 57 12 17.82 1.89 0.106 10 70 12 18.05 1.72 0.095 12 62 12 20.07 1.57 0.078 14 72 12 18.46 1.91 0.104 16 77 12 20.16 2.01 0.100 18 58 12 19.04 1.91 0.100 20 51 12 18.67 2.34 0.125 22 9 12 23.29 0.75 0.032

25 56 12 20.88 1.21 0.058 32 18 12 20.15 1.42 0.071

Overall 530 12 19.25 1.99 0.094

Table B.4. Statistical parameters of BCIII(a) reinforcing steel bars produced by Egecelik steel plant

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

12 454 420 489.98 23.85 0.049 14 395 420 485.58 25.24 0.052 16 146 420 501.35 34.33 0.068 18 54 420 487.83 14.81 0.039 20 24 420 485.96 28.92 0.059

Overall 1073 420 489.71 25.45 0.052

Diameter (mm)

Number of samples

Mean value (N/mm2)

12 454 500 632.68 33.93 0.053 14 395 500 626.39 37.92 0.061 16 146 500 640.12 44.18 0.069

18 54 500 625.61 24.11 0.039 20 24 500 651.75 29.24 0.045

Overall 1073 500 631.45 36.19 0.057

Diameter (mm)

Number of samples

Mean value (%)

12 454 12 19.00 1.88 0.099 14 395 12 19.26 1.91 0.099

16 146 12 18.84 1.85 0.098 18 54 12 18.69 1.58 0.084 20 24 12 17.38 1.44 0.083

Overall 1073 12 19.02 1.86 0.097

Table B.5. Statistical parameters of BCIII(a) reinforcing steel bars produced by Kroman steel plant

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 166 420 463 19.52 0.042 10 349 420 463 16.42 0.035 12 478 420 462 16.02 0.035 14 350 420 464 16.33 0.035 16 226 420 453 14.54 0.032 18 57 420 452 14.36 0.032 20 40 420 447 9.73 0.022 22 7 420 439 7.86 0.018

Overall 1673 420 460.71 1.07 0.035

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 166 500 667 33.82 0.051 10 349 500 677 27.30 0.040 12 478 500 680 26.24 0.039 14 350 500 681 26.82 0.039 16 226 500 667 24.44 0.037 18 57 500 666 25.02 0.038 20 40 500 668 18.72 0.028 22 7 500 657 21.39 0.033

Overall 1673 500 675.68 26.85 0.040

Diameter (mm)

Number of samples

Mean value (%)

8 166 12 25 3.58 0.141 10 349 12 24 2.52 0.105 12 478 12 24 2.58 0.108 14 350 12 23 2.26 0.097

16 226 12 23 2.13 0.091 18 57 12 23 1.95 0.084 20 40 12 23 2.29 0.102 22 7 12 22 0.88 0.040

Overall 1673 12 23.69 2.50 0.105

Table B.6. Statistical parameters of BCIII(a) reinforcing steel bars produced by Ekiciler steel plant

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 198 420 485.5 24.25 0.050 10 459 420 480.2 21.98 0.046 12 580 420 478.6 25.34 0.053 14 573 420 476.8 17.03 0.036 16 430 420 485.4 24.88 0.051 18 31 420 493.5 36.85 0.075 20 74 420 490.5 25.1 0.051 22 8 420 483.1 20.67 0.043 24 10 420 505.5 26.87 0.053 25 21 420 469.9 24.9 0.053 32 6 420 501 44.79 0.089

Overall 2390 420 480.94 22.71 0.047

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 198 500 595.0 20.63 0.035 10 459 500 587.7 18.16 0.031 12 580 500 593.2 38.42 0.065 14 573 500 585.9 26.07 0.044 16 430 500 593.4 25.88 0.044 18 31 500 617.7 46.20 0.075 20 74 500 611.4 46.38 0.076 22 8 500 589.0 18.91 0.032 24 10 500 613.6 24.10 0.039 25 21 500 600.0 24.06 0.040 32 6 500 604.0 43.00 0.071

Overall 2390 500 563.81 27.95 0.047

Diameter (mm)

Number of samples

Mean value (%)

8 198 12 19.80 1.18 0.059 10 459 12 18.80 1.49 0.079 12 580 12 19.61 1.48 0.075 14 573 12 18.16 1.30 0.072 16 430 12 18.46 1.35 0.073 18 31 12 17.83 2.35 0.132 20 74 12 17.52 2.18 0.124 22 8 12 17.63 0.74 0.042 24 10 12 16.20 4.62 0.285 25 21 12 17.41 0.97 0.056 32 6 12 17.00 1.55 0.091

Overall 2390 12 18.78 1.43 0.076

Table B.7. Statistical parameters of BCIII(a) reinforcing steel bars produced by Yesilyurt steel plant

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 950 420 480 18.5 0.039 10 270 420 465 17 0.037 12 524 420 461 14.4 0.031 14 551 420 458 15.9 0.035 16 311 420 468 15.7 0.034 18 100 420 455 16.9 0.037 20 72 420 462 15.9 0.034 22 58 420 457 24.2 0.053 24 46 420 456 26.9 0.06 26 142 420 444 16.9 0.038

Overall 3024 420 466.4 16.9 0.036

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 950 500 587 21.5 0.037 10 270 500 579 21.3 0.037 12 524 500 580 21.5 0.037 14 551 500 578 20.6 0.036 16 311 500 588 36.9 0.063 18 100 500 581 33.8 0.058

20 72 500 582 28.4 0.049 22 58 500 679 78.1 0.11 24 46 500 731 42.8 0.058 26 142 500 714 36.3 0.051

Overall 3024 500 593.1 25.6 0.043

Diameter (mm)

Number of samples

Mean value (%)

8 950 12 23 1.8 0.078 10 270 12 22.9 1.8 0.079 12 524 12 22.7 1.3 0.057 14 551 12 22.1 1.8 0.081 16 311 12 21.2 2 0.094 18 100 12 20.7 1.9 0.092 20 72 12 21 2 0.095 22 58 12 15.3 3.3 0.22

24 46 12 12.9 1.9 0.147 26 142 12 13.2 1.7 0.129

Overall 3024 12 21.7 1.8 0.081

Table B.8. Statistical parameters of BCIII(a) reinforcing steel bars based on data obtained from the Civil Engineering Materials laboratory of METU (1999)

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 166 420 491.43 6758 0.14 0 0

10 349 420 452.29 9231 0.21 21 42.5

12 478 420 486.69 59.62 0.12 5 10.9

14 350 420 477.18 43.72 0.10 3 8.8

16 226 420 481.19 94.07 0.20 9 22.5

18 57 420 443.93 33.96 0.08 7 11.7

20 40 420 495.20 54.52 0.11 0 0

Overall 1673 420 469.34 63.13 0.14 45 17.1

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 166 500 698.9 46.73 0.07 0 0

10 349 500 631.72 120.36 0.19 9 18.4

12 478 500 700.46 69.41 0.10 0 0

14 350 500 694.76 59.47 0.09 0 0

16 226 500 648.21 92.40 0.14 6 15

18 57 500 700.34 64.07 0.09 0 0

20 40 500 689.33 96.22 0.14 0 0

Overall 1673 500 678.05 80.83 0.12 15 5.7

Diameter (mm)

Number of samples

Mean value (%)

8 166 12 17.89 2.37 0.13 0 0

10 349 12 20.23 4.56 0.22 1 2

12 478 12 17.61 3.83 0.22 4 8.7

14 350 12 19.15 3.18 0.17 0 0

16 226 12 20.66 4.58 0.22 0 0

18 57 12 18.76 2.78 0.15 0 0

20 40 12 17.61 1.77 0.10 1 5.3

Overall 1673 12 19.04 3.52 0.18 6 2.3

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 40 420 444.35 72.03 0.16 13 33

10 58 420 469.26 52.76 0.11 6 10

12 52 420 499.54 57.49 0.12 1 2

14 43 420 463.84 35.00 0.08 1 2

16 49 420 460.36 60.68 0.13 1 2

18 25 420 487.35 60.79 0.12 3 12

20 16 420 444.33 51.18 0.12 6 37

Overall 283 420 469.13 55.64 0.12 31 11

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 40 500 629.93 128.32 0.20 10 25

10 58 500 691.05 85.23 0.12 4 7

12 52 500 721.45 103.53 0.14 0 0

14 43 500 684.71 37.97 0.06 0 0

16 49 500 697.29 102.89 0.14 0 0

18 25 500 695.19 65.77 0.09 0 0

20 16 500 670.85 56.80 0.08 0 0

Overall 283 500 687.34 87.23 0.12 14 5

Diameter (mm)

Number of samples

Mean value (%)

8 40 12 21.09 5.02 0.24 0 0

10 58 12 19.18 4.16 0.22 0 0

12 52 12 16.94 3 0.18 4 8

14 43 12 18.63 1.43 0.08 0 0

16 49 12 19.10 2.76 0.14 3 8

18 25 12 18.45 1.69 0.09 0 0

20 16 12 22.13 3.18 0.14 0 0

Overall 283 12 19.04 3.14 0.16 7 2.5

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 31 420 482.81 23.06 0.05 0 0

10 49 420 478.66 51.02 0.11 4 8.2

12 91 420 504.79 93.30 0.18 10 11

14 42 420 475.17 35.45 0.07 0 0

16 55 420 458.09 73.12 0.16 7 13

18 13 420 444.30 46.97 0.11 3 23.1

20 70 420 505.75 59.51 0.12 0 0

Overall 351 420 486.29 62.65 0.13 24 6.8

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 31 500 718.17 28.82 0.04 0 0

10 49 500 689.69 60.28 0.09 0 0

12 91 500 682.12 94.02 0.14 8 8.8

14 42 500 708.78 38.44 0.05 0 0

16 55 500 671.37 94.78 0.14 7 12.7

18 13 500 711.4 70.73 0.10 0 0

20 70 500 682.02 46.79 0.07 0 0

Overall 351 500 688.94 66.74 0.10 15 4.3

Diameter (mm)

Number of samples

Mean value (%)

8 31 12 19.12 4.05 0.21 2 6.5

10 49 12 17.5 3.81 0.22 2 4.1

12 91 12 16.56 2.7 0.16 3 3.3

14 42 12 18.51 2.01 0.11 0 0

16 55 12 18.76 2.14 0.11 1 1.8

18 13 12 18.01 1.52 0.08 0 0

20 70 12 19.1 2.24 0.12 0 0

Overall 351 12 18.06 2.67 0.15 8 2.2

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 52 420 508.69 51.54 0.10 1 1.9

10 50 420 512.08 59.48 0.12 1 2

12 61 420 513.86 55.78 0.11 0 0

14 37 420 507.23 47.98 0.09 3 8.1

16 67 420 499.05 36.91 0.07 0 0

18 31 420 521.07 31.41 0.06 0 0

20 41 420 527.61 55.09 0.10 0 0

Overall 339 420 511.48 48.78 0.09 5 1.5

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 52 500 674.13 58.19 0.09 1 1.9

10 50 500 677.12 32.13 0.05 0 0

12 61 500 683.05 54.69 0.08 0 0

14 37 500 659.03 48.48 0.07 0 0

16 67 500 657.57 57.57 0.09 0 0

18 31 500 667.58 51.57 0.08 0 0

20 41 500 684.90 53.22 0.08 0 0

Overall 339 500 671.99 51.33 0.08 1 0.3

Diameter (mm)

Number of samples

Mean value (%)

8 52 12 18.31 3.59 0.2 3 5.9

10 50 12 16.24 3.22 0.2 4 8

12 61 12 16.46 2.33 0.14 2 3.3

14 37 12 18.48 2.37 0.13 1 2.7

16 67 12 18.51 1.7 0.09 0 0

18 31 12 17.51 1.4 0.08 0 0

20 41 12 16.83 2.09 0.12 1 2.4

Overall 339 12 17.48 2.42 0.14 11 3.2

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 30 420 479.65 66.88 0.14 4 13

10 54 420 484.72 57.04 0.12 4 7

12 72 420 499.92 60.65 0.12 2 3

14 51 420 458.38 50.88 0.11 6 12

16 75 420 502.38 68.09 0.14 0 0

18 14 420 505.25 74.81 0.15 0 0

20 68 420 491.70 55.28 0.11 3 4

22 14 420 473.79 33.09 0.07 1 7

Overall 378 420 488.77 59.32 0.12 20 5

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 30 500 680.77 99.38 0.15 2 7

10 54 500 694.51 59.23 0.09 0 0

12 72 500 700.79 47.58 0.07 0 0

14 51 500 661.94 89.58 0.14 3 6

16 75 500 702.81 94.89 0.14 0 0

18 14 500 722.88 100.03 0.14 0 0

20 68 500 714.72 87.39 0.12 0 0

22 14 500 655.18 64.33 0.10 0 0

Overall 378 500 695.10 78.13 0.12 5 1

Diameter (mm)

Number of samples

Mean value (%)

8 30 12 18.35 4.84 0.26 3 10

10 54 12 16.87 2.98 0.18 2 4

12 72 12 16.72 3.22 0.19 1 1

14 51 12 18.41 3.69 0.20 1 2

16 75 12 16.77 2.82 0.17 5 7

18 14 12 19.65 2.49 0.13 0 0

20 68 12 19.84 2.32 0.14 3 4

22 14 12 18.76 1.72 0.09 0 0

Overall 378 12 17.85 3.06 0.18 15 4

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 27 420 510.01 58.34 0.11 0 0

10 28 420 495.35 61.81 0.12 4 14

12 53 420 520.58 60.08 0.12 0 0

14 16 420 459.14 20.38 0.05 0 0

16 30 420 493.62 33.18 0.07 0 0

20 39 420 514.09 46.01 0.09 0 0

22 5 420 483.40 78.78 0.16 0 0

Overall 198 420 504.30 50.50 0.10 4 2

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 27 500 695.31 45.88 0.07 0 0

10 28 500 707.47 73.65 0.10 0 0

12 53 500 683.30 50.97 0.07 0 0

14 16 500 663.09 87.21 0.13 0 0

16 30 500 692.94 38.89 0.06 0 0

20 39 500 708.11 60.27 0.09 0 0

22 5 500 690.3 6.61 0.01 0 0

Overall 198 500 693.24 55.29 0.08 0 0

Diameter (mm)

Number of samples

Mean value (%)

8 27 12 14.97 4.12 0.28 6 22

10 28 12 17.23 3.29 0.19 1 4

12 53 12 16.72 2.33 0.14 0 0

14 16 12 19.71 2.93 0.15 0 0

16 30 12 17.86 2.97 0.17 0 0

20 39 12 16.38 1.85 0.11 0 0

22 5 12 16.48 1.04 0.06 0 0

Overall 198 12 16.89 2.72 0.16 7 4

Table B.14. Statistical parameters of BCIII(a) reinforcing steel bars based on data obtained from the Civil Engineering Materials laboratory of ITU (1999)

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 59 420 434.89 85.66 0.17 23 32.2

10 76 420 519.87 84.42 0.16 8 9.2

12 78 420 500.24 85.48 0.17 12 15.4

14 83 420 493.34 71.20 0.14 11 14.5

16 78 420 494.65 70.95 0.14 9 10.3

18 43 420 518.29 76.38 0.15 5 11.6

20 96 420 523.72 74.61 0.14 8 6.3

22 70 420 520.36 52.61 0.10 1 1.4

Overall 583 420 502.07 74.95 0.15 77 12

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 59 500 596.29 99.4 0.17 12 20.3

10 76 500 658.10 80.80 0.12 5 6.6

12 78 500 631.78 88.86 0.14 8 10.3

14 83 500 606.28 78.68 0.13 7 8.4

16 78 500 621.97 67.00 0.11 2 2.6

18 43 500 641.12 59.08 0.09 2 4.7

20 96 500 652.92 68.18 0.10 4 4.2

22 70 500 677.55 59.00 0.09 0 0

Overall 583 500 636.34 75.31 0.12 40 6.9

Diameter (mm)

Number of samples

Mean value (%)

8 59 12 22.86 5.80 0.25 1 1.7

10 76 12 18.50 3.81 0.2 1 1.3

12 78 12 19.47 4.33 0.22 0 0

14 83 12 19.21 3.84 0.2 1 1.2

16 78 12 18.96 3.80 0.2 1 1.3

18 43 12 17.60 3.55 0.2 1 2.3

20 96 12 18.01 2.79 0.15 1 1

22 70 12 17.17 1.75 0.1 0 0

Overall 583 12 18.93 3.65 0.19 6 1

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 82 420 460.12 77.45 0.17 24 29.3

10 78 420 506.26 77.17 0.15 9 11.5

12 79 420 509.34 68.7 0.13 5 6.3

14 77 420 495.13 43.21 0.09 1 1.3

16 76 420 493.43 56.74 0.11 7 9.2

18 63 420 491.90 65.78 0.14 5 7.9

20 78 420 524.03 46.81 0.09 2 2.6

22 61 420 527.2 41.41 0.08 0 0

Overall 594 420 500.18 60.19 0.12 53 8.9

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 82 500 614.25 101.48 0.17 11 13.4

10 78 500 654.68 69.34 0.11 4 5.1

12 79 500 631.53 61.62 0.10 1 1.3

14 77 500 625.71 53.84 0.09 2 2.6

16 76 500 620.65 60.83 0.10 1 1.3

18 63 500 621.09 67.84 0.11 3 4.8

20 78 500 638.34 64.17 0.10 2 2.6

22 61 500 634.72 52.15 0.08 0 0

Overall 594 500 630.15 67.05 0.11 24 4.04

Diameter (mm)

Number of samples

Mean value (%)

8 82 12 22.63 5.35 0.24 2 2.4

10 78 12 18.85 4.55 0.23 0 0

12 79 12 19.91 3.74 0.19 0 0

14 77 12 19.41 1.95 0.10 0 0

16 76 12 18.81 2.75 0.15 0 0

18 63 12 19.11 3.16 0.17 0 0

20 78 12 18.05 2.57 0.14 0 0

22 61 12 18.22 1.85 0.10 0 0

Overall 594 12 19.44 3.3 0.17 2 0.3

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 86 420 488 76.89 0.16 16 18.6

10 85 420 510.06 73.52 0.14 9 10.6

12 96 420 524.26 51.51 0.10 0 0

14 77 420 505.83 57.24 0.11 5 6.5

16 88 420 502.98 74.29 0.15 7 8

18 49 420 508.61 60.42 0.12 2 4.1

20 64 420 554.5 55.58 0.10 0 0

22 56 420 508.93 43.06 0.08 1 1.9

Overall 601 420 512.11 62.70 0.12 40 6.7

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 86 500 631.41 81.29 0.13 5 5.81

10 85 500 649.73 60.68 0.09 2 2.4

12 96 500 640.57 61.40 0.08 0 0

14 77 500 630.73 50.77 0.08 1 1.3

16 88 500 649.54 65.69 0.10 3 3.4

18 49 500 649.41 52.85 0.08 0 0

20 64 500 676.23 53.82 0.08 0 0

22 56 500 647.89 42.08 0.08 0 0

Overall 601 500 645.81 60.11 0.09 11 1.8

Diameter (mm)

Number of samples

Mean value (%)

8 86 12 21.37 5.31 0.25 1 1.2

10 85 12 19.04 4.33 0.23 1 1.2

12 96 12 18.41 2.59 0.14 0 0

14 77 12 19.13 2.33 0.12 0 0

16 88 12 19.07 3.78 0.2 0 0

18 49 12 18.53 2.77 0.15 0 0

20 64 12 16.59 2.87 0.17 0 0

22 56 12 18.32 2.45 0.14 0 0

Overall 601 12 18.92 3.4 0.18 2 0.3

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 42 420 468.71 74.21 0.16 9 21.4

10 87 420 494.74 59.72 0.12 3 3.4

12 81 420 500.93 56.73 0.11 2 2.5

14 80 420 480.64 42.81 0.09 2 2.5

16 80 420 474.41 58.79 0.12 12 15

18 51 420 492.56 41.22 0.08 2 3.9

20 81 420 510.61 36.37 0.07 0 0

22 56 420 492.09 34.05 0.07 0 0

Overall 558 420 490.58 50.16 0.10 30 5.4

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 42 500 614.67 87.73 0.14 6 14.3

10 87 500 689.84 67.52 0.10 0 0

12 81 500 651.32 65.51 0.10 2 2.5

14 80 500 633.56 56.71 0.09 2 2.5

16 80 500 635.71 57.38 0.09 1 1.3

18 51 500 637.9 62.08 0.10 2 3.9

20 81 500 644.25 45.34 0.07 0 0

22 56 500 631.07 51.28 0.08 0 0

Overall 558 500 645.49 60.40 0.09 13 2.3

Diameter (mm)

Number of samples

Mean value (%)

8 42 12 21.26 3.91 0.18 0 0

10 87 12 18.29 2.49 0.14 0 0

12 81 12 19.34 3.14 0.16 0 0

14 80 12 19.85 2.16 0.11 1 1.3

16 80 12 19.76 2.42 0.12 0 0

18 51 12 19.26 2.40 0.12 1 2

20 81 12 18.89 2.89 0.15 1 1.2

22 56 12 18.98 1.81 0.10 0 0

Overall 558 12 19.34 2.62 0.13 3 0.5

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 55 420 461.24 72.18 0.16 15 27.3

10 57 420 515.91 52.44 0.10 0 0

12 60 420 500.65 85.21 0.17 0 0

14 54 420 512.96 51.59 0.10 0 0

16 55 420 494.57 43.86 0.09 0 0

18 31 420 482.87 56.82 0.12 1 3.2

20 54 420 501.39 52.57 0.11 2 3.7

22 26 420 497.16 62.35 0.13 2 7.7

Overall 392 420 496.65 59.93 0.12 20 5.1

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 55 500 640.31 87.86 0.14 6 10.9

10 57 500 688.17 16.85 0.10 0 0

12 60 500 666.57 61.52 0.09 0 0

14 54 500 668.04 59.85 0.09 0 0

16 55 500 667.31 47.38 0.07 0 0

18 31 500 638.10 52.18 0.08 0 0

20 54 500 648.26 54.45 0.08 0 0

22 26 500 629.00 62.63 0.10 0 0

Overall 392 500 659.07 54.87 0.09 6 1.5

Diameter (mm)

Number of samples

Mean value (%)

8 55 12 21.85 4.49 0.21 0 0

10 57 12 18.81 2.39 0.13 0 0

12 60 12 20.08 2.32 0.12 0 0

14 54 12 18.89 2.38 0.13 0 0

16 55 12 19.27 1.88 0.10 0 0

18 31 12 19.93 2.21 0.11 0 0

20 54 12 19.17 2.42 0.13 0 0

22 26 12 20.44 2.47 0.12 0 0

Overall 392 12 19.75 2.6 0.13 0 0

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 29 420 480.21 40.94 0.085 1 3.5

10 57 420 479.52 40.97 0.085 2 3.5

12 50 420 491.24 47.54 0.097 1 2

14 54 420 458.35 41.41 0.09 8 14.8

16 42 420 495.6 49.52 0.10 0 0

18 40 420 467.28 35.56 0.08 6 15

20 47 420 501.21 39.93 0.08 3 6.4

22 35 420 502.38 28.98 0.058 0 0

Overall 354 420 483.66 41.04 0.085 21 5.9

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 29 500 657.96 78.83 0.12 1 3.4

10 57 500 655.18 45.04 0.07 0 0

12 50 500 681.03 65.55 0.096 1 2

14 54 500 644.4 58.95 0.09 0 0

16 42 500 663.59 60.88 0.09 0 0

18 40 500 619.08 44.88 0.07 0 0

20 47 500 629.65 52.32 0.08 3 6.4

22 35 500 631.50 26.93 0.04 0 0

Overall 354 500 648.6 53.86 0.08 5 1.4

Diameter (mm)

Number of samples

Mean value (%)

8 29 12 21.21 2.96 0.14 0 0

10 57 12 20.44 2.25 0.11 0 0

12 50 12 19.10 2.58 0.14 0 0

14 54 12 20.5 2.08 0.10 0 0

16 42 12 18.86 2.30 0.12 0 0

18 40 12 20.13 2.72 0.14 0 0

20 47 12 19.77 2.67 0.14 0 0

22 35 12 19.64 1.52 0.08 0 0

Overall 354 12 19.93 2.37 0.12 0 0

Table B.20. Statistical parameters of BCIII(a) reinforcing steel bars based on data obtained from different materials laboratories in Konya

a. Yield strength

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 68 420 468.27 58.13 0.124 10 14.71

10 47 420 478.42 62.50 0.131 3 6.38

12 64 420 466.31 69.57 0.149 10 15.63

14 72 420 470.00 64.74 0.138 6 8.33

16 45 420 479.86 55.31 0.115 6 13.33

18 23 420 473.52 48.28 0.101 2 8.69

20 14 420 514.14 108.31 0.211 1 7.14

Overall 333 420 473.56 63.43 0.134 38 11.41

Diameter (mm)

Number of samples

Mean value (N/mm2)

8 68 420 693.72 73.96 0.107 1 1.47

10 47 420 710.36 72.75 0.102 2 4.26

12 64 420 677.61 86.35 0.127 3 4.69

14 72 420 701.18 100.44 0.143 3 4.17

16 45 420 691.93 48.21 0.070 0 0

18 23 420 686.61 51.79 0.075 0 0

20 14 420 714.00 113.21 0.158 0 0

Overall 333 420 694.71 78.54 0.113 9 2.7

Diameter (mm)

Number of samples

Mean value (%)

8 68 420 27.26 12.51 0.459 1 1.47

10 47 420 25.24 8.67 0.343 0 0

12 64 420 24.67 7.96 0.323 0 0

14 72 420 23.39 5.86 0.250 0 0

16 45 420 22.17 3.92 0.177 0 0

18 23 420 21.36 3.64 0.170 0 0

20 14 420 22.21 4.64 0.209 0 0

Overall 333 420 24.33 7.55 0.303 1 0.3

APPENDIX C

ANNUAL MAXIMUM SNOW DEPTHS FOR DIFFERENT LOCATIONS

The data given in Table C.1 are obtained from Turkish Meteorological Department

Table C.1.a. Annual maximum snow depths for different locations (cm)

1947 18 * * * * 8 * 13 * * 12 *

1948 20 * * * 5 * * 14 * * 17 *

1949 20 * * * 16 20 * 17 * * 15 *

1950 * * 16 37 15 * * 25 17

1951 7 * * 22 23 24 14 * 5 2

1952 8 * * 8 35 40 7 * 6

1953 25 * * 35 26 10 23 2 * 14 20

1954 19 4 * * 16 30 36 46 5 * 9 28

1955 5 * * 7 * 13 8 5 *

1956 10 * * 11 25 29 25 24 * 18 13

1957 8 * 11 50 29 16 * 13

1958 * * 23 10 15 44 3 *

1959 8 * 2 25 21 33 29 10 * 3 2

1960 11 1 8 8 * 17 11 * 3

1961 15 35 16 49 54 23 97 8 32

1962 7 12 16 24 15 74 7

1963 9 26 4 6 13 7 10 52 15 22

1964 12 14 47 47 26 27 5 136 12 6

1965 15 22 20 5 15 26 3 167 11 18

1966 18 14 3 9 5 57 3

1967 10 22 18 32 37 26 12 204 15 22

1968 12 23 3 50 29 6 87 15 19

1969 12 14 11 5 26 24 3 216 19 16

1970 14 2 3 7 89 3 4

1971 9 8 4 30 20 12 90 7 5

1972 12 20 40 5 17 12 6 190 24

1973 14 11 21 4 25 11 6 89 21 20 1974 7 15 14 31 18 5 * 7 10

Table C.1.b. Annual maximum snow depths for different locations

1975 10 13 30 13 14 19 81 11 1976 24 11 15 36 25 30 2 114 25 8 1977 10 * 22 3 17 16 8 98 20 1978 6 10 14 21 30 98 1979 13 23 24 3 21 25 79 10 4 1980 22 23 15 16 19 17 100 18 13 1981 15 2 10 6 4 38 90 6 15 1982 4 50 9 23 7 11 80 19 6 1983 25 1 45 10 18 12 10 6 123 26 14 1984 4 * 9 2 35 9 51 1985 30 20 12 14 15 55 6 80 25 55 1986 12 1 12 2 9 41 33 10 70 4 14 1987 20 21 1 12 6 13 19 24 139 44 40 1988 3 9 6 15 28 5 160 3 1989 8 2 25 4 61 26 71 5 3 1990 6 8 22 22 14 62 8 1991 14 3 10 12 22 16 25 10 62 12 10 1992 16 41 28 24 48 35 10 260 21 18 1993 16 4 20 8 32 20 10 246 11 6 1994 13 13 4 19 29 30 4 79 17 9 1995 3 9 4 23 31 84 14 1996 10 3 21 4 16 6 7 86 4 7 1997 7 24 10 4 15 8 70 10 13 1998 7 12 4 2 21 16 9 50 4 2 1999 6 34 2 21 9 4 22 2 2000 28 9 26 10 38 14 108 12 19 2001 13 13 15 4 18 8 32 94 40 6 2002 30 23 22 20 33 17 3 71 22 12 2003 8 27 47 5 42 30 7 184 33 34 2004 7 66 12 11 22 17 36 111 32 28 2005 6 18 4 12 6 8 80 23 8

Aver 12.7 2 18.8 1.5 16.0 14.1 24.9 20.7 10.6 105.7 14.6 14.6

Std. 6.86 1.26 13.3 0.71 10.4 12.4 12.6 10.8 9.10 53.37 9.58 11.2

C.o. 0.54 0.63 0.71 0.47 0.66 0.88 0.52 0.51 0.85 0.50 0.66 0.76

Max 30 4 66 2 47 49 61 55 38 260 44 55

Note: In this table, “*” shows that no data that belongs to that year has been obtained.

Table C.2. The Chi-Square (χ2) and Kolmogorov- Smirnov (K-S) tests results for annual snow depths

Annual snow depth

Tests Prob. Dist.

P value

Tests Prob. Dist.

P value

Ankara Erzincan

Lognormal 0.667 0.9996 0.0909 Rayleigh 2.842 0.9439 0.0649

Weibull 4.667 0.7295 0.0765 Normal 4.737 0.7855 0.0736

Ext. value 9.00 0.3426 0.1145 Lognormal 5.053 0.7519 0.0844

Rayleigh 12.00 0.1512 0.1357 Weibull 5.368 0.7196 0.0779

Normal 14.00 0.0815 0.1208

Bursa Canakkale

Lognormal 11.33 0.1247 0.0927 Lognormal 11.14 0.1326 0.0940

Gamma 11.33 0.1247 0.1053 Ext. value 7.791 0.3514 0.1570

Ext. value 7.143 0.4142 0.1258 Rayleigh 15.60 0.029 0.2613

Weibull 10.57 0.1584 0.1204 Hakkari

Rayleigh 15.14 0.0342 0.173 Ext. value 6.909 0.4384 0.1489

Gaziantep Lognormal 10.91 0.1426 0.1418

Ext. value 2.667 0.9535 0.08373 Gamma 13.09 0.0699 0.1588

Weibull 6.00 0.6472 0.07035 Weibull 18.55 0.0097 0.1669

Rayleigh 8.667 0.3712 0.1259 Göztepe

Normal 11.00 0.2017 0.1299 Rayleigh 2.868 0.9424 0.1025

Samsun Ext. value 4.226 0.8326 0.0766

Rayleigh 18.82 0.0088 0.2369 Weibull 6.264 0.6177 0.0741

Normal 34.82 1.2E-4 0.1888 Normal 17.81 0.0227 0.1143

Ext. value 38.38 2.6E-6 0.1992 Sile

Malatya Lognormal 4.095 0.7687 0.1199

Lognormal 11.36 0.1820 0.1124 Ext. value 5.238 0.6309 0.1007

Ext. value 7.962 0.4370 0.1385 Rayleigh 6.742 0.4541 0.1153

Weibull 13.06 0.1099 0.1081 Normal 22.76 0.0019 0.1047

Normal 16.45 0.0363 0.1501

Rayleigh 17.47 0.0256 0.1678

Note 1: At the significance level α=5%, 1-α percentile value of the Chi-Square test, χ.95,5=11.1 for Bursa,

Samsun, Canakkale, Hakkari and Sile; and , χ.95,6=12.6 for Ankara, Gaziantep, Malatya, Erzincan and Göztepe.

Note 2: The critical value of K-S test at the 5% significance level, 05.50D =0.19.

APPENDIX D

ANNUAL MAXIMUM WIND SPEEDS FOR DIFFERENT LOCATIONS

The data given in Table D.1 are obtained from Turkish Meteorological Department

Table D.1.a. Annual maximum wind speeds for different locations (m/sn)

1949 12.9 1950 12.1 12 19.7 1951 11.7 11.4 15.6 19.2 1952 15.2 15 18 18.8 1953 15 8.4 21 1954 15 20.4 22.8 1955 18.7 15.2 27.6 24.6 1956 28.9 21.2 18.6 15.6 23 28 1957 28.9 20.8 20.4 20.1 13 21.1 17.2 1958 31.2 21 19.6 20.7 8.5 23.3 14.5 1959 23.8 21.2 19.2 20.4 12.1 21.6 18.5 1960 22.7 29.3 23 27.3 10.5 21.5 18.5 1961 24.8 28.9 23.8 28.5 20.5 21.5 16 15.2 23.2 13.9 15.6 26.6 1962 25.4 27 24.2 25.5 22.5 25.8 26.8 14.3 28.5 20.7 24 20.2 1963 28.3 27.5 25.2 25.5 19.6 18.3 23.2 15.6 28.2 13.3 17.2 1964 19.1 27.5 28.6 20.7 16.2 20.2 14.9 24.2 29.5 11.7 18.4 1965 29.6 27.4 31.1 30.6 24.1 28.8 17.2 30.4 30.3 30.2 13.3 1966 23 24.8 32.2 35.6 23 24 24.7 28 29 25.3 12.2 9.3 1967 23.2 21.2 28.2 29.5 24.9 25.5 21 27.9 31 22.7 10 14.4 1968 32.1 27.8 30 36.9 31 31.2 21.1 30.9 33.7 30.2 0 1969 24.4 28.8 29.6 38.7 22.1 23.9 25 26.2 34.1 27.4 10 1970 28.5 33.9 29 34.6 22.2 20.2 21.5 39.5 35.4 25 11.1 1971 29.2 32.5 31.2 36 24.4 19.1 18.9 25.8 33.2 26 10 19.4 1972 25.1 31.7 25.6 28.7 23 19.2 6.4 21 28 21 24.5 36 1973 23.2 28.9 29.1 32.4 17.9 27.8 7.8 23 31.8 22.3 27.7 42.4 1974 23.3 30 26 31.2 19.9 27 17.7 19.6 32 24.1 25.5 32.9

1975 17.8 26.8 26 29.8 23.4 30 22.6 22.8 25.9 25.6 27.4

1976 22 26 29.5 28.5 20.2 31.1 5 17.6 32.7 20 23.9 32.9

Table D.1.b. Annual maximum wind speeds for different locations (m/sn)

1977 16.9 27.3 26.7 26.5 17.7 28.2 5.6 16.5 32 21 24 35.2

1978 17.6 25.4 27.7 25.8 18 34.5 10 20.6 31.8 24.2 20 35

1979 16.5 25.9 29.9 25.5 16.7 31.2 21 17.6 34.5 25.2 21 39.5

1980 14.7 27 26 28.6 16.1 29.6 8.7 16.9 35.2 21.6 20.1 34.1

1981 17.7 27.8 30.7 22.4 10.6 34.2 4.8 17.3 28.5 21 21.7 36.3

1982 17 25 29.2 24 13.8 25.7 6.2 16.2 29 18.8 18.9 36.2

1983 17.2 21.5 23.3 22 13.6 27 4.6 15 31.8 16 19.6 27.4

1984 24.1 26.9 18.5 23.8 15.4 24 11.6 14.6 26.7 15.8 15.8 24.7

1985 22.2 24.2 20.6 23.6 16.1 26.9 8 13.8 29.4 17.1 25.8 29.6

1986 19.2 25.3 18.6 27.6 12.3 23.8 5.6 16.9 24 20 24 28.5

1987 18.2 29.1 22.9 22 13.3 23.1 3.8 19 35 20.7 22.7 28

1988 16.7 24.4 21.6 22.3 14.8 24.8 26.8 15.6 26.8 17.9 21.7 28.6

1989 15.8 25 22 19.8 13.7 26.9 3 16.2 32.6 18.6 25.1 28

1990 14.4 20 18.5 22.7 13.7 20 3.4 15 26.6 16.7 25.2 25.4

1991 15.3 22.3 22.7 20.6 13.6 15.2 21.3 17 38.7 13.4 27 28.3

1992 13.5 23.4 21.6 20.3 16.3 19.6 17.5 19.1 33.9 13.5 26.3 25.9

1993 13.5 22.1 19.8 22.1 14.6 23.2 15.2 14.2 31.8 15 21.2 23.3

1994 14.5 19 16 21.1 16.7 22 26.2 16.1 24.2 16.4 20.2 25.8

1995 18.1 26.8 19.1 21.9 13.7 25.2 17 16.5 32.7 20.5 21.5 28.4

1996 17.4 24.3 20.5 28.6 15.1 22.4 15.9 17.1 31.5 19.8 23.8 24

1997 17.7 23.5 17.2 25 15 26.3 19.6 15.7 27.6 18.3 19.2 27.5

1998 16.3 21.8 15.2 43.2 14.1 23.4 19.1 18.9 31 16.3 18.7 22.8

1999 20.2 23.8 21.3 22.6 16.6 27.1 17.4 16.6 36.2 14.5 20.4 26.2

2000 17.7 27.2 18.8 23.1 14.9 24.9 21.4 16.9 34.5 13.6 21.1 24.9

2001 19.4 29.2 22.2 25.5 15.6 20.3 20 20 29.9 18.5 20.5 22.2

2002 19.4 19.6 17.1 27.8 13.7 21.6 20.6 14.8 28 18.3 18.8 17.1

2003 19.3 29.8 23.1 30.8 11.3 22.4 19.5 17.2 28.7 19.5 25.3 23.1

2004 16.8 25.4 17.9 28.4 13.3 24.5 19.8 15.7 28.2 20.6 16.9 17.9

2005 17 23.6 19.2 23.8 13.4 22.4 20 17.9 25.8 20.9 18.6 19.2

Average 20.13 26.19 23.92 26.62 17.53 23.11 15.09 19.07 28.99 20.19 19.67 25.21

Std. dev 4.65 3.33 4.74 5.36 4.28 5.26 6.87 5.50 4.88 4.31 5.86 7.03

C.o.v. 0.23 0.13 0.20 0.20 0.24 0.23 0.46 0.29 0.17 0.21 0.30 0.28

Max. 32.10 33.90 32.20 43.20 31.00 34.50 26.80 39.50 38.70 30.20 27.70 42.40

Table D.2. The Chi-Square (χ2) and Kolmogorov- Smirnov (K-S) tests results for annual wind speeds

Annual wind speed

Tests Prob. Dist.

P value

Tests Prob. Dist.

P value

Ankara Malatya

Ext. value 8.957 0.2558 0.5953 Normal 9.333 0.3150 0.1013

Normal 9.304 0.2315 0.1244 Weibull 9.333 0.3150 0.1074

Rayleigh 10.00 0.1886 0.8595 Rayleigh 13.67 0.0909 0.1541

Weibull 11.74 0.1095 0.4555 Ext. value 17.00 0.0301 0.1587

Lognormal 12.93 0.0871 0.4513 Erzincan

Izmir Lognormal 12.43 0.0871 0.1496

Normal 4.080 0.7705 0.0929 Ext. value 13.48 0.0613 0.1617

Weibull 4.080 0.7705 0.0884 Gamma 12.43 0.0871 0.1641

Ext value 7.600 0.3692 0.1296 Weibull 16.26 0.0228 0.1607

Bursa Rayleigh 23.91 0.0012 0.1999

Ext value 5.478 0.6018 0.0935 Normal 32.96 2.7x10-5 0.2149

Rayleigh 2.696 0.9117 0.0988 Canakkale

Weibull 2.696 0.9117 0.1014 Normal 4.667 0.7925 0.0919

Lognormal 4.087 0.7697 0.1030 Weibull 7.00 0.5366 0.0682

Normal 5.478 0.6018 0.0997 Ext. value 19.33 0.0132 0.1512

Antalya Hakkari

Weibull 3.408 0.8449 0.0727 Lognormal 4.442 0.7277 0.1220

Rayleigh 4.714 0.6948 0.1273 Normal 4.442 0.7277 0.1229

Ext value 6.020 0.5374 0.1010 Rayleigh 8.163 0.3185 0.0853

Gaziantep Göztepe

Ext. value 9.612 0.2116 0.0869 Normal 15.62 0.0288 0.1607

Rayleigh 8.633 0.2801 0.1160 Sile

Normal 10.92 0.1422 0.1484 Weibull 11.65 0.16.77 0.0969

Samsun Normal 14.47 0.0703 0.0990

Normal 9.333 0.3150 0.1074 Gamma 15.18 0.0558 0.0815

Rayleigh 13.67 0.0909 0.1541 Lognormal 15.18 0.0558 0.0808

Ext. value 17.00 0.0301 0.1587

Note 1: At the significance level α=5%, 1-α percentile value of the Chi-Square test, χ.95,5=11.1 for

Ankara, Izmir, Bursa, Antalya, Gaziantep, Erzincan, Hakkari and Göztepe; and , χ.95,6=12.6 for Samsun, Malatya, Sile and Bursa.

APPENDIX E

DAILY WIND SPEEDS OBSERVED IN 2004 IN DIFFERENT LOCATIONS

The data in Tables E.1-E12 are obtained from Turkish Meteorological Department

Table E.1. Daily Maximum Wind Speeds observed during the year 2004 in Ankara

1 6.7 10.8 7.2 6.7 4.6 9.8 10.3 10.3 10.3 7.7 4.4 4.9 2 8.2 6.7 7.2 11.3 8.8 4.6 7.5 11.3 14.4 8.0 8.8 5.2 3 7.2 5.2 6.7 11.3 9.8 9.0 8.8 9.3 9.8 7.0 10.3 4.1 4 10.3 10.3 6.2 5.7 7.2 6.2 12.4 7.2 10.8 10.0 9.3 4.6 5 11.8 5.7 10.8 5.7 10.3 11.8 10.3 7.7 11.6 9.8 7.2 7.7 6 8.8 6.2 9.3 7.2 8.8 13.9 8.8 6.7 11.3 10.8 5.9 5.2 7 8.8 10.3 6.7 10.3 12.9 7.2 10.8 12.4 11.8 9.0 5.4 9.3 8 6.2 13.9 8.2 8.8 6.7 10.8 13.9 10.8 7.2 7.2 6.2 5.9 9 6.2 10.8 7.0 6.2 7.2 13.9 11.8 9.3 11.8 6.2 6.2 6.4 10 9.8 11.3 13.4 5.7 11.6 7.2 8.2 11.8 9.8 6.7 5.7 4.6 11 12.9 7.7 8.8 5.7 11.8 5.2 7.7 10.3 8.2 6.4 4.1 5.4 12 8.8 16.5 7.2 6.7 9.3 4.1 10.3 10.8 6.7 14.4 3.6 4.1 13 5.7 18.5 9.8 6.2 9.0 6.2 10.3 5.4 5.7 11.8 4.1 5.9 14 5.2 10.3 10.8 19.1 11.8 11.8 9.0 7.2 5.7 8.2 5.2 10.8 15 11.8 10.0 6.2 10.8 9.8 10.3 11.3 13.4 5.2 4.6 7.7 7.7 16 13.4 10.3 9.8 14.9 7.7 6.7 11.8 15.2 5.7 7.7 15.5 5.4 17 7.2 7.2 8.2 3.6 11.6 8.8 11.8 9.5 10.3 8.2 9.8 4.1 18 6.7 9.3 10.8 7.7 11.3 11.6 9.3 10.3 8.2 9.0 4.1 8.2 19 6.7 7.2 5.2 5.2 10.3 11.8 10.8 10.3 5.2 8.2 5.7 6.2 20 6.2 7.7 6.2 7.0 5.7 6.2 13.4 8.2 5.7 7.2 14.9 6.4 21 11.8 12.4 9.3 9.8 5.2 11.3 10.8 7.2 5.2 5.2 5.9 7.0 22 19.1 11.6 10.3 8.2 6.2 7.2 9.3 5.2 5.7 5.2 8.2 6.7 23 9.8 4.6 9.8 6.2 7.2 10.3 8.2 8.2 6.2 7.2 6.7 8.2 24 6.7 5.7 12.4 7.7 9.5 6.7 6.7 7.2 7.2 5.7 7.7 6.2 25 12.4 9.8 11.8 4.1 9.5 9.8 13.4 9.3 6.2 4.6 6.4 4.4 26 7.7 9.8 10.0 9.3 11.3 7.7 8.8 6.2 5.2 5.4 11.3 7.7 27 5.2 8.2 11.8 15.5 9.8 12.9 9.3 6.7 4.6 8.8 5.2 8.2 28 5.2 13.1 7.2 10.8 9.8 8.8 8.2 15.5 3.6 5.7 3.6 5.7 29 8.8 10.3 10.8 9.0 11.8 6.2 7.7 7.7 7.7 6.2 4.1 9.8 30 10.3 9.3 6.7 11.8 12.4 9.8 6.2 7.7 2.8 5.7 7.7 31 13.4 6.2 7.2 8.2 7.2 5.2 5.7

Average: 8.50 Std. Dev: 2.83 C.o.v.: 0.33 Count: 366

Table E.2. Daily Maximum Wind Speeds observed during the year 2004 in Izmir

1 10.9 10.9 7.2 10.8 9.4 9.0 12.7 13.6 13.9 13.3 5.8 8.5 2 11.3 8.6 10.0 13.6 8.6 10.2 14.4 14.7 13.2 13.3 6.0 8.7

3 9.6 9.2 10.1 15.8 9.8 9.6 12.7 13.8 12.4 13.3 17.3 11.0 4 8.6 12.0 13.0 19.1 10.9 8.8 11.5 11.1 13.6 15.0 17.4 11.4

5 8.6 9.0 12.6 7.0 16.4 22.5 14.3 11.6 14.6 16.2 9.3 7.0

6 14.6 7.5 11.5 12.7 29.9 10.6 13.7 10.7 14.0 15.0 3.0 8.0 7 13.3 17.0 9.9 15.5 16.5 11.3 15.1 11.3 13.9 10.9 4.4 15.4

8 10.7 14.7 12.6 13.0 10.0 15.3 14.8 12.8 12.8 11.0 15.0 12.5 9 4.9 13.4 22.8 10.0 12.0 12.5 14.7 14.1 13.8 8.0 12.6 7.3

10 15.0 13.2 21.0 10.8 12.8 14.0 12.9 13.8 15.7 8.3 8.3 10.3

11 19.0 12.6 11.3 11.3 13.7 13.8 12.6 14.6 15.3 13.1 9.6 13.5 12 9.8 16.0 11.8 10.4 11.7 10.4 10.1 12.8 13.3 11.2 5.3 11.8

13 9.4 15.0 14.2 19.8 24.7 8.1 12.8 10.6 10.5 11.2 14.0 7.6

14 11.3 11.6 14.8 12.1 12.7 13.4 14.5 10.3 9.6 7.7 20.3 15.3

15 19.8 17.0 10.1 17.5 11.8 12.0 16.5 13.0 11.0 10.6 19.5 16.8

16 15.8 11.2 12.2 15.0 14.8 14.1 15.3 12.8 12.6 12.6 13.6 11.7 17 6.0 15.1 12.0 12.8 9.0 11.8 14.0 11.6 16.1 11.8 12.4 10.0

18 10.6 12.0 13.2 14.2 9.9 16.0 12.5 13.6 13.0 9.0 8.8 17.8

19 10.3 4.6 10.0 8.1 14.9 9.8 11.0 14.2 11.4 10.1 10.2 16.5

20 15.6 11.3 6.2 10.1 12.2 12.6 12.0 14.2 10.0 8.7 18.8 9.2

21 15.1 21.0 11.6 12.2 10.3 10.4 12.7 11.4 9.4 8.1 13.8 13.0

22 23.1 14.4 14.0 12.8 9.6 14.1 14.7 9.8 9.8 11.3 10.3 12.3 23 17.0 12.2 12.3 12.2 10.0 15.0 14.0 13.5 8.6 11.0 8.4 8.5

24 9.3 17.4 16.7 8.7 10.8 14.5 13.0 15.2 14.3 10.0 13.1 10.1

25 12.0 18.7 13.0 7.0 10.5 12.0 13.5 14.4 17.2 6.9 14.8 5.7 26 10.0 21.2 14.1 9.3 15.5 13.2 9.5 7.5 13.3 7.0 13.6 10.1

27 14.3 23.9 22.9 13.8 16.3 13.6 11.4 12.3 10.8 7.0 6.6 13.7 28 18.9 24.2 9.4 9.8 15.0 16.0 10.6 14.3 14.5 7.5 8.2 14.1

29 19.5 9.6 14.8 12.8 11.9 11.0 10.4 13.3 11.0 6.9 12.8 20.7

30 11.3 15.1 7.1 14.2 13.5 12.2 13.0 11.5 5.7 11.0 5.9 31 13.4 13.0 13.1 14.0 13.0 8.7 9.7

Table E.3. Daily Maximum Wind Speeds observed during the year 2004 in Bursa

1 6.4 3.7 5.2 6.6 8.7 5.8 8.6 5 8.3 5.6 2.5 2.8

2 6.5 5 7.5 11.5 4.7 8 7 5.7 7.2 3.3 4.2 3.8

3 3.5 5.8 7.3 8.2 2.2 4.9 5.6 5.9 10.2 4.3 9.1 3.8

4 4.2 7.4 7.8 8.6 3.7 5 9.8 5.7 8.3 4.3 6.2 2.9

5 4.4 3.7 8 4.5 9.5 6 9.4 5.1 8.7 4.6 5.5 4.8

6 5.6 3.9 8.8 7.7 2.1 11.1 9.4 6 11 5.4 2.1 3.8

7 4.7 13 4.5 11.8 2.2 6.2 9.7 6 9.5 3.3 1.6 4.7

8 4.4 12 8.3 12.4 8.4 6.9 9.4 8.9 6.7 6.1 3.4 3.5

9 3.5 11.2 8.7 6.8 5.4 6.5 7.2 6.6 8.4 1.7 2.1 3.7

10 7 7.3 17.4 6.5 7.2 6.9 7.2 6.6 7.7 1.4 2 6.5

11 8.7 7.5 5.6 4.4 7.4 6.3 5.6 6 8 5.2 3.4 4.2

12 4.4 9.1 7.3 6.4 5.5 3.8 6.3 6.4 7.2 6.8 3.6 2.3

13 2.6 8.9 7.9 6.4 7 6 17.9 5.4 4.7 6.5 1.7 2.5

14 6.8 6.2 6.9 12.8 6.8 7.7 5 6.7 4.9 4 6 7

15 10 6.4 3.4 7.2 7.4 9 10.4 8.8 4.7 2.5 14.2 6.1

16 12 4 6.5 6.4 5.7 4.9 8.6 10.5 5 6 3.9 4

17 2.5 5.3 4.7 5.9 6.4 6.3 9.4 5.4 9.1 10.1 5.1 5.6

18 7 4.2 6.9 5.2 6.5 9.5 8.4 5 9.7 8.4 1.1 7

19 5.8 1.5 3.5 4.4 8.5 6.6 9.6 4.2 5.7 4.5 16 6.1

20 8.1 8.4 3.9 3.9 4.7 5.2 10.2 6.6 3.8 6.8 14 3.4

21 15 6.9 10.2 6.6 5.4 5.9 8.8 5 6 5 7.7 6.9

22 15 3.8 9.9 5.4 7 7.4 7.8 6.5 5.1 4 5.8 4.9

23 5 6.9 3.7 5 5.8 5.7 7.7 7.5 4.2 4.3 5.7 3.8

24 4.7 6.4 12 4.6 7.2 6.2 7.7 8 8.3 3.9 6.7 3.4

25 5.9 11.3 13 3.6 7.3 5.7 8.4 8.1 7.8 3 7.6 4.3

26 3 12.2 9.2 10 9.7 6.5 5.6 4 2.4 2.7 6.9 9.4

27 4.5 19 14.2 5.4 8.3 7.6 5.4 5.7 3.5 1.3 4.2 6.3

28 16 8.9 4.7 8.9 8 7.4 8.4 2.9 3 6.8 6.3

29 16.8 11.1 5.5 6.8 6.6 6.1 6.4 4.5 2 6.4 11.7

30 7.7 7.8 3.7 7.8 7.8 6.4 5 3.7 2 3.4 6.7

31 5.3 7.3 8.9 7.2 5.6 2.5 3.8

Table E.4. Daily Maximum Wind Speeds observed during the year 2004 in Antalya

1 7.0 12.9 6.3 8.5 6.6 15.3 8.1 7.3 8.0 5.7 8.2

2 9.5 9.3 4.3 13.7 6.8 9.5 9.2 7.7 7.4 6.8 4.3 5.6

3 6.3 8.0 7.6 16.0 7.3 10.3 7.6 7.8 8.4 12.9 5.4 3.6

4 24.9 9.6 12.2 15.3 8.8 7.0 11.2 9.0 9.8 10.0 7.3 3.6

5 5.0 11.0 17.7 10.2 5.9 9.4 8.8 12.8 6.5 9.0 8.2 6 16.7 11.6 25.0 8.3 6.2 9.1 8.2 10.0 13.1 5.4 9.0

7 20.9 8.0 16.7 9.0 6.2 8.1 12.5 8.2 13.0 8.7 13.9 16.9

8 15.5 6.7 7.2 8.0 8.2 11.5 10.0 8.0 8.5 6.6 9.4 19.4

9 9.8 9.0 9.0 6.0 11.4 11.6 14.1 7.2 8.0 7.6 6.2 6.9

10 8.1 8.7 10.8 7.3 9.2 11.0 12.8 7.2 20.0 6.7 5.6 8.0

11 26.9 22.0 14.0 6.5 11.8 10.9 10.0 13.2 14.6 6.9 6.0 18.3 12 9.6 20.7 8.7 8.2 15.1 7.7 11.6 12.9 11.1 7.1 6.1 11.8

13 6.9 23.4 16.8 6.2 7.6 6.9 9.3 12.7 7.8 7.2 5.4 5.6

14 8.1 21.2 15.8 8.8 7.8 11.6 12.2 9.2 6.4 7.7 4.9 17.7 15 7.6 12.0 15.1 26.0 16.3 9.8 9.2 7.0 7.4 7.6 18.0 20.1

16 13.5 7.2 7.6 25.6 15.0 11.5 20.1 8.4 6.9 9.2 11.1 11.3 17 14.9 6.5 11.4 8.1 9.5 10.0 9.8 8.6 7.0 7.1 17.3 5.9

18 6.3 7.6 14.6 10.2 16.8 17.1 10.8 9.4 8.0 5.0 12.6 18.8

19 5.0 7.6 12.4 8.4 12.0 11.6 8.9 13.5 7.3 5.7 6.9 21.8 20 4.5 5.3 10.0 8.2 10.0 8.2 10.0 10.2 7.0 5.0 9.9 20.3

21 19.5 24.4 7.0 12.5 8.3 7.5 12.2 8.3 5.5 12.6 25.0 5.8 22 32.3 22.1 7.0 8.8 8.7 7.5 14.3 11.4 7.6 7.0 25.9 5.7

23 18.2 6.1 6.3 8.0 6.2 18.6 8.9 11.6 9.4 6.1 17.9 3.5

24 13.8 6.3 12.7 7.9 6.7 14.0 12.9 9.9 8.5 5.4 5.9 9.4 25 23.0 7.0 9.7 7.8 6.3 8.6 9.2 9.2 8.2 5.0 20.7 8.3

26 7.8 5.2 6.2 7.1 6.5 9.4 7.9 9.9 9.2 5.9 23.2 7.4

27 14.6 3.9 4.8 18.0 10.8 10.0 8.2 9.2 7.5 6.6 17.0 3.7

28 7.3 6.9 6.3 8.6 10.7 11.8 7.3 11.5 10.1 5.2 7.5 4.0

29 19.0 5.5 7.9 8.2 9.1 12.0 7.0 8.6 8.5 7.3 4.6 15.0 30 22.5 16.4 9.6 10.2 8.2 8.0 8.0 7.0 6.0 5.0 15.0

31 10.8 10.0 11.0 7.1 8.2 5.3 5.5

Table E.5. Daily Maximum Wind Speeds observed during the year 2004 in Gaziantep

1 3.9 8.6 3.3 8.5 4.0 7.8 8.3 5.8 3.7 6.8 4.2 4.0

2 8.1 6.7 3.8 9.5 13.9 7.3 8.9 5.4 3.3 7.2 2.9 3.4

3 3.6 3.6 6.2 9.4 3.9 4.4 5.6 6.7 2.7 7.8 3.6 2.1

4 4.2 7.9 5.7 9.5 6.5 4.0 8.2 5.1 4.6 3.3 3.4 2.0 5 6.5 3.6 13.8 5.1 6.9 3.7 7.8 4.1 10.6 3.8 4.3 3.2

6 10.0 7.8 7.8 4.3 4.3 6.4 3.8 6.0 8.2 8.7 4.8 3.8

7 11.1 7.2 6.8 5.2 5.0 10.0 3.9 5.0 4.9 4.1 3.5 2.0 8 6.7 4.7 5.0 6.9 5.8 8.0 4.0 4.9 3.8 3.5 3.0 7.4

9 3.5 3.8 3.6 3.5 6.4 8.1 11.8 3.7 6.5 5.0 3.6 3.5 10 6.6 4.5 6.2 5.7 7.8 7.5 7.9 4.0 8.7 3.8 3.5 3.5

11 4.6 6.0 7.0 6.5 8.2 5.5 7.0 6.9 8.9 3.7 3.8 2.7

12 4.6 4.3 4.0 7.0 10.8 5.9 5.7 6.4 11.6 3.6 3.0 3.4 13 5.9 10.6 4.0 3.4 9.8 3.4 5.6 5.5 3.4 3.0 2.7 2.1

14 3.8 11.9 6.3 7.3 6.7 7.4 5.6 3.9 2.0 3.2 2.3 3.0 15 4.2 9.2 9.1 11.0 7.3 8.1 8.1 7.4 2.2 3.2 2.1 4.4

16 4.5 4.9 4.9 13.5 8.1 9.7 6.9 8.8 1.6 3.4 3.4 5.9

17 5.6 4.1 5.6 6.7 5.1 6.8 5.8 3.8 3.6 2.4 5.9 2.3 18 4.5 5.3 6.2 3.2 8.3 5.6 9.2 4.9 4.7 1.9 3.8 5.4

19 3.0 2.0 5.4 8.2 9.0 7.0 8.7 7.8 4.3 4.9 2.2 5.2 20 3.8 3.4 5.3 4.5 8.6 5.8 3.0 8.4 3.3 3.9 2.9 4.3

21 3.2 9.0 4.8 5.8 3.2 7.4 4.7 3.3 5.8 4.5 11.7 1.9

22 13.6 12.0 6.9 6.2 5.0 8.1 8.3 3.6 4.4 3.0 7.7 2.3

23 10.3 7.2 3.5 5.8 4.4 6.6 8.3 4.9 6.2 3.2 8.4 2.5 24 10.0 3.9 8.2 3.8 4.5 6.3 7.0 4.0 3.7 4.1 3.9 8.0

25 8.5 5.0 5.8 4.6 7.0 5.0 4.9 3.3 5.3 5.4 7.1 6.0

26 4.2 3.3 3.4 6.1 5.4 7.8 5.4 6.8 3.6 5.0 5.1 2.9

27 4.4 3.3 2.8 10.8 5.0 6.2 5.1 3.1 3.2 2.1 8.0 1.8

28 3.1 2.2 3.8 5.4 7.2 8.0 4.0 5.0 3.2 3.3 2.0 2.0 29 4.0 3.2 5.1 6.0 6.0 9.5 5.0 6.4 3.6 3.7 2.1 4.0

30 4.0 8.5 5.0 5.1 5.4 9.0 3.2 3.4 3.2 1.4 3.7

31 6.4 3.1 6.8 3.6 3.3 6.0 4.7

Table E.6. Daily Maximum Wind Speeds observed during the year 2004 in Samsun

1 11.2 9.0 7.3 6.5 3.2 4.1 6.2 3.0 4.7 6.7 3.0 7.0

2 7.0 5.2 5.1 11.0 6.5 3.4 7.5 10.5 3.8 6.5 7.0 14.5 3 8.2 8.2 6.8 12.2 4.7 5.0 7.4 8.5 6.6 7.4 6.7 18.2

4 10.7 7.0 9.0 7.8 3.9 3.0 4.0 4.3 8.5 7.1 6.3 16.2 5 13.9 6.2 10.0 6.1 7.9 7.5 4.3 5.8 10.4 7.0 4.8 7.8 6 16.0 16.2 11.6 5.9 6.2 9.0 4.5 3.6 10.1 5.9 5.5 9.8

7 12.0 11.1 6.8 6.3 8.0 5.9 4.3 5.0 8.6 2.1 3.0 15.0 8 12.6 18.8 7.6 4.8 3.8 5.9 7.1 3.9 5.6 4.4 2.4 6.6

9 13.0 9.0 8.0 2.7 5.5 6.3 7.6 3.7 12.8 5.7 5.7 11.2

10 11.8 12.2 14.6 5.8 11.9 7.2 5.0 6.1 10.0 6.1 2.3 7.0 11 10.8 7.8 7.2 4.3 7.8 5.6 5.4 7.3 6.3 14.5 3.3 8.8

12 6.6 12.4 5.0 10.0 7.7 5.7 5.2 8.5 4.0 11.6 3.2 7.3 13 4.6 17.4 8.0 5.9 4.3 2.4 4.8 5.9 5.3 6.3 6.2 10.4

14 11.2 9.8 8.0 7.2 8.9 3.0 14.6 6.4 5.4 5.3 8.8 11.4

15 14.0 20.0 6.1 7.5 17.4 8.5 7.0 11.3 4.2 5.3 11.2 9.2

16 13.0 21.8 4.8 13.6 11.7 4.7 6.1 5.0 3.4 4.4 6.8 5.9 17 7.1 10.3 5.0 6.9 3.8 3.1 7.2 7.5 7.0 9.4 10.6 12.3

18 15.3 5.5 3.3 5.2 7.2 4.6 6.4 9.7 5.8 10.0 7.5 17.4

19 14.5 5.9 6.3 2.5 7.5 9.3 6.6 5.0 4.3 4.7 12.4 20.7

20 17.2 13.1 8.0 4.5 5.2 8.1 5.5 5.4 3.1 8.6 18.6 18.4

21 21.0 14.1 13.2 3.1 7.9 6.0 6.7 5.2 4.4 9.0 8.9 7.0 22 19.3 13.6 9.0 9.0 4.0 4.1 6.4 4.9 5.7 3.8 15.3 4.0

23 26.1 9.2 4.3 9.7 5.9 4.0 8.6 8.5 8.2 7.5 10.0 7.8

24 5.8 16.4 7.6 6.3 4.3 7.7 3.2 7.4 6.3 5.4 21.1 6.0

25 8.9 14.0 11.2 4.2 12.2 6.0 4.6 7.3 4.0 4.6 8.0 5.0

26 5.3 7.7 7.2 6.0 4.0 3.7 6.6 5.2 2.5 5.0 10.2 14.4 27 6.6 21.9 12.7 6.3 8.8 10.5 7.0 9.4 3.1 7.2 14.0 18.2

28 19.2 20.0 14.6 10.0 7.8 8.0 5.7 9.0 3.2 6.2 17.2 11.3 29 19.1 16.8 8.2 3.9 5.3 4.8 4.0 8.2 4.3 2.8 13.7 12.4 30 6.6 7.6 3.9 3.3 13.3 4.6 3.8 8.7 5.4 18.0 9.0

31 7.5 5.6 5.0 5.2 4.9 2.2 2.9

Table E.7 Daily Maximum Wind Speeds observed during the year 2004 in Malatya

1 2.2 2.2 3.8 3.8 6.7 8.7 11.8 3.6 3.3 4.3 2.1 8.0

2 3.0 4.4 2.3 10.0 7.8 9.3 9.4 8.7 5.0 6.4 3.0 4.8

3 4.0 4.3 3.6 12.6 3.1 13.0 4.7 8.8 5.1 8.3 4.3 2.9

4 4.0 2.9 3.2 13.1 8.0 5.8 8.9 6.4 4.1 3.0 6.7 2.0 5 4.8 5.0 18.3 5.8 5.0 4.5 5.7 5.9 9.6 3.2 3.2 3.4

6 4.4 10.6 16.0 4.2 5.0 11.5 5.2 9.8 7.5 3.8 3.1 4.2

7 13.5 11.0 9.0 4.0 4.2 5.9 5.6 5.4 3.0 9.7 3.2 3.0 8 8.6 8.6 6.0 6.9 4.9 10.0 14.5 5.2 8.7 4.6 3.0 2.8

9 3.8 8.6 3.8 4.8 10.1 8.4 15.1 7.7 8.4 4.5 2.5 5.0 10 3.9 10.8 8.4 4.9 8.2 6.3 7.8 4.7 9.9 3.4 2.9 8.4

11 2.3 7.5 9.3 4.0 10.7 8.3 8.2 13.1 8.0 3.3 2.8 2.7

12 1.7 4.0 6.8 3.6 13.3 8.7 9.4 9.7 6.8 6.0 2.8 10.0 13 4.6 12.6 7.1 5.2 11.0 4.2 9.8 4.7 2.9 8.0 2.5 4.2

14 2.9 12.8 9.2 19.8 9.9 9.8 9.0 4.3 3.0 6.0 2.0 9.8 15 2.7 10.0 8.6 10.0 10.0 9.6 11.2 4.0 3.2 3.7 3.9 13.0

16 4.0 3.0 11.2 10.0 7.6 9.8 13.3 5.4 3.1 9.0 3.6 10.8

17 13.6 3.6 8.7 5.1 9.7 9.8 10.0 8.6 7.1 4.1 8.3 5.0 18 4.4 3.0 4.6 9.8 16.0 4.2 10.8 10.3 2.5 2.4 7.4 3.0

19 2.9 4.2 7.1 13.0 16.6 14.6 6.3 9.3 2.9 2.3 2.6 3.0 20 2.5 4.0 4.4 7.7 8.7 9.3 4.3 6.3 3.3 6.1 7.2 2.4

21 2.2 10.4 4.0 8.5 4.4 7.2 9.9 5.6 3.5 10.8 10.5 2.2

22 6.4 11.0 6.2 7.1 5.0 9.6 11.4 4.1 4.5 6.3 16.2 2.3

23 16.1 10.4 8.3 10.8 4.4 8.5 6.2 3.6 8.8 3.0 11.5 2.5 24 10.5 1.8 6.9 2.8 4.3 9.8 4.7 7.0 5.0 2.6 5.2 2.2

25 3.9 1.5 9.3 7.5 11.0 9.8 9.6 6.8 4.4 3.1 8.3 3.2

26 5.0 2.2 4.3 6.1 13.1 8.0 3.8 2.8 3.3 2.6 5.0 3.8

27 2.1 2.9 3.7 13.1 9.1 4.8 8.5 4.4 4.0 3.1 7.8 2.8

28 3.1 3.4 4.4 11.0 6.6 12.6 9.8 7.0 3.7 2.4 5.0 3.0 29 3.7 3.3 8.8 17.0 8.1 10.4 4.7 10.0 4.2 5.2 3.2 3.7

30 2.7 12.4 9.6 9.0 4.7 4.6 3.2 3.4 2.1 3.0 2.7

31 2.8 6.4 12.3 4.9 3.6 3.0

Table E.8. Daily Maximum Wind Speeds observed during the year 2004 in Erzincan

1 2.3 3.7 2.1 4.5 5.6 7.9 9.5 3.8 6.2 8.3 3.5 5.0 2 4.2 3.4 3.6 10.0 3.8 9.0 7.5 6.8 8.7 6.5 3.0 8.1

3 4.1 3.3 2.2 11.0 7.5 12.7 4.2 9.6 8.5 6.3 6.4 2.5

4 5.9 3.0 9.0 12.8 9.7 3.9 8.3 6.7 6.8 6.8 9.0 2.8 5 6.5 3.4 10.2 5.7 7.3 3.2 8.0 5.6 10.0 4.1 3.2 2.8

6 9.1 7.1 9.3 4.1 5.6 9.7 4.3 9.6 9.4 4.8 4.5 4.0 7 9.5 7.2 10.9 4.9 6.7 7.5 5.7 7.7 3.5 6.7 4.9 4.1

8 7.0 7.0 4.0 6.3 9.1 10.0 7.5 8.8 10.0 9.2 3.3 3.1

9 1.1 5.0 3.2 6.0 12.6 7.5 8.3 7.8 8.4 8.0 2.8 2.6

10 3.0 7.1 3.6 4.2 10.9 9.2 15.7 5.9 9.1 5.6 3.0 3.1 11 2.1 7.6 9.7 6.5 9.9 6.0 7.6 14.7 9.8 3.0 2.0 2.7

12 3.0 6.6 7.3 3.9 13.0 6.6 8.5 10.9 10.2 4.2 3.0 10.6

13 4.8 10.8 9.6 8.2 7.9 5.0 8.1 6.4 5.7 5.9 2.3 4.4

14 5.2 8.2 9.5 9.8 11.7 10.1 4.9 3.8 5.1 3.6 2.8 7.8

15 2.5 9.0 10.6 12.1 9.9 9.3 7.8 9.4 6.9 4.9 3.3 9.3 16 9.3 4.1 8.4 12.4 7.5 7.3 8.8 3.8 4.6 4.20 6.7 7.9

17 7.5 3.2 7.2 12.0 8.2 7.5 10.9 6.0 7.9 3.3 7.8 3.7

18 2.0 2.6 4.8 8.5 9.8 6.6 10.3 11.0 5.2 3.6 9.8 3.1

19 3.1 2.0 9.5 10.0 8.2 12.3 11.3 10.0 3.1 4.8 3.1 3.4

20 2.2 3.2 7.3 7.6 9.7 10.9 8.2 8.6 3.3 6.9 9.1 3.9 21 2.2 9.0 3.5 8.9 7.2 6.1 10.0 7.6 5.8 8.2 9.1 3.9

22 13.1 10.0 5.3 7.2 4.3 9.4 9.9 5.5 3.5 4.7 11.9 4.9 23 11.9 10.4 5.6 9.2 9.4 7.1 7.7 7.2 5.3 2.9 9.2 4.0 24 9.6 1.8 7.9 9.9 4.1 7.2 6.2 7.9 3.4 2.9 4.1 3.7

25 5.8 2.2 8.7 11.1 9.1 8.1 6.6 8.8 8.8 2.7 9.9 3.9 26 6.0 2.0 7.6 4.1 9.9 7.4 9.2 6.5 5.7 2.5 9.7 3.1

27 3.5 2.6 3.3 10.2 11.4 7.0 12.5 4.9 2.8 2.8 9.9 3.0

28 3.9 3.7 5.6 11.4 7.6 10.3 6.1 4.2 7.1 3.3 6.4 3.1 29 2.9 3.7 8.8 11.1 6.4 10.1 6.9 7.0 4.0 4.7 3.9 4.0

30 5.0 10.0 6.1 8.2 8.4 5.1 7.2 3.4 6.0 3.1 5.0 31 3.0 12.4 12.3 6.2 10.0 2.8 3.7

Average: 6.65 Std. Dev:2.92 C.o.v.: 0.44 Count:366

Table E.9. Daily Maximum Wind Speeds observed during the year 2004 in Canakkale

1 4.1 5.5 6.7 9.1 10.9 5.4 10.3 10.8 9.9 7.0 3.4 6.1

2 6.8 3.6 11.1 15.0 10.4 4.4 9.6 8.1 12.1 6.1 13.5 12.0

3 9.4 12.9 14.7 13.9 5.4 8.0 9.1 7.5 16.5 10.5 17.5 11.2 4 17.0 11.1 17.8 11.3 5.9 10.4 15.3 4.0 15.3 14.0 21.0 11.7

5 9.5 5.0 15.4 5.5 18.5 7.0 17.2 5.3 16.7 16.5 16.5 9.0 6 11.7 8.8 7.4 12.2 17.8 9.0 17.5 8.1 22.0 18.4 11.5 5.6 7 11.2 10.1 8.2 14.6 15.0 6.7 18.2 8.8 19.4 13.8 5.2 13.9

8 5.8 15.1 3.0 15.0 11.0 11.0 19.0 9.5 10.9 5.7 10.0 6.7 9 4.0 17.0 14.0 10.8 5.0 7.7 13.8 9.1 11.8 4.3 12.0 10.5

10 8.4 9.8 13.9 8.7 6.4 10.2 12.8 11.2 14.0 8.0 3.6 14.3

11 22.9 11.1 8.1 8.5 8.0 10.7 8.9 7.1 14.0 15.2 7.3 12.3 12 11.0 18.8 12.3 8.9 6.0 5.0 7.1 6.6 13.0 17.4 8.1 6.8

13 6.0 14.7 12.1 11.1 7.5 4.5 10.3 6.6 12.0 17.0 4.4 7.9 14 12.4 4.2 14.1 10.7 6.8 17.1 9.7 13.4 14.0 12.9 24.6 12.6

15 18.4 10.7 8.5 10.6 9.2 12.7 13.8 13.7 13.3 4.4 20.5 12.8

16 20.1 7.5 10.9 9.9 11.7 6.7 14.3 13.9 8.6 13.1 15.8 7.1

17 8.2 12.7 7.1 5.0 14.1 13.0 13.3 10.8 16.3 17.6 13.5 10.2 18 13.7 9.4 9.1 4.5 10.6 11.0 16.1 5.7 15.8 13.9 6.3 20.4

19 10.0 5.5 3.9 10.1 6.7 7.6 15.5 5.7 15.2 10.9 19.3 22.8

20 22.3 11.8 7.8 5.6 3.5 8.1 15.2 6.2 12.9 8.0 19.7 8.9

21 20.7 14.2 12.2 11.0 5.0 7.1 17.6 5.2 7.0 9.0 10.1 15.2

22 20.0 5.4 16.8 8.1 10.7 12.4 14.1 11.8 7.5 12.5 11.5 16.3 23 9.4 6.5 13.3 7.5 12.1 16.0 11.4 9.3 8.6 11.2 13.6 9.9

24 4.0 10.4 22.0 5.4 13.4 8.7 10.9 12.4 15.0 5.9 12.1 3.7

25 13.8 17.7 14.9 9.0 11.0 8.1 11.0 11.3 16.3 9.1 12.4 3.8

26 5.6 18.9 15.4 10.2 13.9 8.0 12.1 6.0 11.9 4.9 7.6 15.0

27 15.8 31.0 16.5 13.9 14.3 12.8 12.3 10.1 9.6 8.4 12.7 16.1 28 22.8 14.1 7.3 6.1 15.2 9.4 12.4 10.0 6.7 3.5 8.6 17.1

29 22.9 13.9 11.3 7.0 12.0 8.9 7.5 6.3 7.0 4.4 8.2 23.0 30 14.4 15.3 9.3 11.7 12.3 11.8 7.4 6.3 3.8 9.2 12.6 31 20.2 13.6 7.5 9.0 8.0 3.2 15.0

Table E.10. Daily Maximum Wind Speeds observed during the year 2004 in Hakkari

1 2.5 5.3 3.0 5.4 8.8 11.3 9.2 4.7 7.9 6.7 2.2 1.4

2 2.0 8.3 4.7 11.3 5.2 8.7 8.4 5.7 5.5 6.7 2.1 1.7 3 3.1 2.5 2.2 14.3 9.2 8.1 7.6 9.9 8.3 12.2 8.6 1.4

4 1.4 3.2 4.6 10.2 7.3 8.1 11.2 6.7 6.8 10.3 3.9 1.1 5 8.6 3.1 17.9 5.1 9.8 6.2 9.7 6.1 14.1 7.1 4.0 1.2 6 2.2 5.7 15.3 2.9 8.7 6.9 9.7 5.8 11.3 11.7 4.6 4.6

7 18.1 9.2 10.2 5.9 6.5 9.1 10.0 7.0 11.2 5.5 2.2 3.4 8 15.9 10.0 3.2 5.0 6.8 9.4 12.1 6.1 11.4 20.6 2.0 3.4

9 8.2 8.5 2.8 5.5 10.2 13.3 13.3 4.8 13.1 10.5 2.0 1.4 10 10.0 8.6 5.1 7.1 14.9 10.0 9.8 8.7 11.8 12.2 5.7 7.5 11 1.2 10.3 4.4 6.6 11.5 9.5 8.8 9.3 8.4 6.8 5.1 6.5

12 2.2 8.1 4.9 6.5 12.0 6.2 7.6 10.2 9.4 11.9 3.4 3.3 13 3.9 15.6 7.0 2.8 11.2 9.8 6.9 5.6 7.0 9.1 3.1 1.8

14 6.7 17.1 6.0 3.6 11.4 11.0 7.3 4.1 5.9 10.4 3.0 6.2

15 3.1 4.9 9.2 12.8 14.0 11.0 6.8 3.8 7.8 6.3 3.6 9.9

16 2.8 12.2 6.4 14.1 9.7 18.5 11.4 4.6 8.7 4.0 7.9 3.0

17 3.0 7.5 5.3 7.9 15.9 11.0 5.8 5.4 6.0 4.6 6.9 6.3 18 3.7 1.3 6.5 10.4 11.0 9.9 8.1 8.8 6.5 2.6 8.7 1.5

19 3.6 2.0 6.7 10.0 13.0 5.7 8.3 8.8 7.5 5.0 7.0 1.0

20 2.0 7.3 6.5 6.0 12.8 9.0 8.7 7.5 9.0 4.4 6.8 0.9

21 2.2 8.6 3.9 8.1 6.0 10.2 8.1 7.4 4.0 12.8 9.0 1.4 22 9.0 5.2 4.5 17.1 9.6 8.0 10.0 6.5 6.2 4.9 12.0 1.1

23 14.2 5.6 6.6 13.7 6.9 8.1 8.9 4.4 11.7 5.2 4.8 1.3

24 10.5 1.8 4.7 7.9 10.1 7.4 10.0 6.5 8.5 3.7 5.3 1.0

25 3.2 1.4 4.9 8.7 7.0 10.2 10.0 7.4 3.4 7.5 1.6 6.2

26 1.4 1.6 5.8 4.4 10.6 9.4 8.1 8.8 3.0 4.2 11.2 13.2 27 4.9 1.5 5.0 3.8 14.0 8.8 5.6 4.4 5.1 6.5 7.9 4.9

28 3.9 1.5 4.8 6.5 11.9 6.0 10.4 9.2 8.2 11.1 1.5 1.4 29 3.5 1.5 5.3 2.1 12.5 14.0 9.6 3.8 11.3 4.2 1.4 1.1 30 2.0 16.2 9.2 11.8 5.7 4.0 6.8 3.2 11.5 1.2 1.1

31 2.3 6.6 7.9 7.9 8.7 1.5 1.1

Table E.11. Daily Maximum Wind Speeds observed during the year 2004 in Istanbul/ Göztepe

1 1.7 2.6 3.5 4.6 7.0 2.1 5.0 6.2 7.8 4.1 1.5 2.3

2 2.7 3.6 5.3 10.0 9.8 4.2 7.8 4.9 8.0 5.8 7.6 7.8 3 8.3 8.0 9.1 7.9 2.9 9.8 5.0 5.0 10.4 7.5 10.1 5.7 4 11.0 9.2 9.1 4.8 2.2 8.4 9.0 3.8 10.9 9.9 15.1 4.2

5 9.0 4.1 11.9 2.3 8.0 6.8 14.9 6.3 12.5 15.5 11.2 4.8 6 11.5 3.1 9.2 3.2 2.3 3.1 13.5 7.1 14.7 14.5 5.9 3.9

7 8.7 7.8 2.7 6.1 10.7 5.7 12.7 8.9 13.3 9.6 6.9 8.7

8 4.7 4.0 3.1 7.3 2.7 2.6 10.3 6.9 8.1 5.6 6.2 2.5 9 1.8 9.6 4.0 2.3 2.9 4.4 10.2 6.3 12.3 4.5 3.7 7.1

10 2.5 6.0 11.0 4.7 8.3 5.0 7.8 5.9 11.4 6.4 4.2 7.7 11 11.0 4.2 3.3 1.6 7.5 6.0 4.1 4.8 11.1 8.3 8.4 3.5

12 6.8 13.4 8.5 2.8 4.4 2.6 5.3 4.9 7.7 15.6 5.1 1.9

13 4.4 9.9 7.0 2.3 3.9 3.7 5.8 3.1 6.2 13.4 1.9 3.3

14 3.8 4.9 6.4 11.0 4.0 10.9 5.3 7.2 8.3 12.2 6.0 9.6 15 12.8 15.9 3.7 10.3 10.1 7.0 5.8 9.1 7.0 1.8 9.7 7.1

16 15.9 2.2 4.2 4.2 5.8 2.6 8.2 15.0 5.9 6.3 11.0 2.2

17 1.9 5.5 2.5 1.6 9.9 7.2 8.3 8.0 12.0 8.5 16.4 3.9

18 8.3 3.2 4.9 4.2 10.0 4.4 9.8 4.0 10.7 6.5 6.0 2.6

19 3.5 3.6 2.6 3.9 2.7 4.4 12.3 4.2 8.8 4.0 15.6 3.1 20 11.7 10.1 1.9 4.7 3.6 6.3 10.9 2.7 7.2 5.0 16.9 5.1

21 13.1 9.9 11.4 10.0 3.4 4.3 11.9 2.8 4.8 4.8 7.5 14.0

22 16.8 3.3 8.1 4.0 3.7 3.9 9.7 14.8 4.4 8.8 11.0 14.8

23 5.9 2.1 2.5 2.7 3.6 4.1 6.1 15.0 8.8 7.0 13.8 3.8

24 2.9 2.2 11.8 4.2 12.9 5.1 5.9 9.2 5.0 1.9 14.8 2.7 25 3.0 7.4 12.8 8.0 6.0 4.1 6.3 6.4 10.4 4.6 13.3 2.7

26 9.3 3.3 9.3 11.0 11.4 4.6 8.5 5.4 2.0 5.2 10.0 5.9 27 4.6 14.2 9.4 12.1 9.2 5.5 5.4 6.5 5.0 3.2 9.8 5.0 28 11.8 9.9 10.0 3.3 12.4 5.2 4.0 10.0 8.2 1.7 6.9 5.0

29 13.4 6.8 9.1 3.8 6.5 2.5 9.5 5.0 7.1 6.0 2.0 7.3 30 9.0 8.1 4.7 4.7 6.5 9.9 2.6 5.5 2.1 9.2 8.4

31 13.6 10.5 7.2 11.0 4.4 1.6 7.7

Table E.12. Daily Maximum Wind Speeds observed during the year 2004 in Istanbul/ Sile

1 3.3 8.0 9.7 13.2 4.8 5.7 8.0 6.0 5.5 4.1 5.3 7.0 2 4.4 11.5 6.2 10.8 6.2 6.8 9.2 4.0 6.1 5.6 8.5 10.0

3 8.3 8.0 7.1 8.9 3.5 8.3 5.8 4.5 12.1 7.9 14.3 17.1

4 12.6 7.1 12.0 8.0 9.1 8.0 6.7 4.1 9.0 14.2 14.8 10.4 5 11.0 15.9 14.5 6.8 13.7 9.0 10.2 6.0 13.9 15.1 9.8 9.3

6 11.3 14.7 8.9 10.4 13.4 8.0 9.4 5.9 16.5 16.3 3.0 6.8 7 9.0 14.8 7.4 14.8 14.8 5.0 7.0 8.3 15.0 13.8 3.7 7.5

8 6.4 15.6 11.3 19.5 9.3 5.0 7.2 6.1 9.0 8.7 7.9 5.0

9 6.0 12.9 4.9 10.0 8.9 5.0 7.5 6.0 10.5 7.0 5.2 7.0

10 5.0 8.6 15.9 13.5 9.4 10.8 8.0 4.0 10.7 8.1 5.2 8.0 11 11.9 8.4 10.0 6.0 6.1 7.0 4.1 5.0 8.0 16.6 4.9 7.7

12 5.2 13.2 5.9 13.6 7.2 5.7 10.5 6.0 7.8 19.7 5.0 3.8

13 8.0 16.2 6.1 9.8 13.7 9.4 14.5 5.4 4.4 19.4 7.0 6.7

14 11.3 14.0 6.6 5.6 8.0 7.0 5.4 6.4 5.7 14.4 10.4 7.8

15 17.8 16.6 9.0 13.8 6.9 5.0 6.8 12.0 5.5 4.0 10.8 8.3 16 11.0 6.4 5.0 6.2 5.9 4.5 10.6 21.5 5.4 8.1 9.1 4.6

17 6.0 6.2 6.1 8.5 7.1 5.7 14.6 8.2 8.7 9.5 13.9 7.4

18 12.3 5.0 8.4 4.8 5.3 11.5 8.3 4.4 9.7 6.9 8.9 7.2

19 11.4 5.6 5.5 3.8 5.0 5.5 8.3 6.6 6.5 4.5 12.7 7.5

20 21.0 11.2 10.1 5.0 6.8 5.0 7.0 3.4 5.6 8.2 17.6 5.9 21 14.2 12.0 13.6 5.8 6.4 9.8 7.9 4.3 6.0 9.6 11.2 18.1

22 21.4 10.0 15.4 4.8 6.1 4.0 6.0 10.2 4.4 8.0 16.1 15.0 23 13.7 5.7 8.9 5.0 6.9 5.7 4.4 13.4 7.8 6.1 11.2 7.2 24 3.4 13.4 9.8 5.0 8.7 4.1 5.0 7.7 10.1 3.3 16.8 4.5

25 5.2 16.8 17.2 7.8 9.8 4.3 5.3 5.2 8.0 6.2 15.5 5.9 26 7.7 13.0 15.1 5.6 8.7 5.0 6.7 10.0 7.3 3.9 13.5 6.2

27 5.0 29.1 7.7 6.1 8.0 7.9 6.9 8.4 7.8 4.3 13.9 9.9

28 19.4 14.0 8.7 5.4 9.3 5.3 6.3 10.6 5.0 5.0 9.9 10.0 29 15.4 9.3 8.6 5.1 7.7 5.3 5.3 5.8 7.0 3.8 8.0 11.7

30 10.3 7.3 6.5 5.4 7.9 8.2 6.0 5.0 6.0 10.8 7.1 31 15.5 8.0 8.3 5.7 4.0 4.0 9.0

Table E.13. The Chi-Square (χ2) and Kolmogorov- Smirnov (K-S) tests results for daily maximum wind speeds recorded in the year 2004

Daily wind speed

Tests Prob. Dist.

P value

Tests Prob. Dist.

P value

Ankara Malatya

Weibull 56.36 7.8E-6 0.0655 Weibull 75.12 6.3E-9 0.0820

Ext. value 75.88 4.5E-9 0.0780 Lognormal 86.16 0.00 0.1036

Lognormal 83.25 2.3E-10 0.0736 Ext. value 109.8 0.00 0.1035

Normal 125.8 0.00 0.0999 Rayleigh 93.03 0.00 0.1512

Izmir Normal 170.4 0.00 0.1506

Gamma 31.75 0.0235 0.0648 Erzincan

Lognormal 32.38 0.0198 0.0624 Ext. value 86.85 3.4E-6 0.0878

Normal 37.36 0.0047 0.0783 Rayleigh 58.64 2.0E-10 0.092

Ext. value 50.03 7.5E-5 0.0781 Weibull 58.85 0.00 0.089

Weibull 52.93 2.7E-5 0.0869 Lognormal 83.56 0.00 0.0958

Bursa Normal 120.2 3.13E-7 0.1048

Gamma 25.40 0.1144 0.0397 Canakkale

Ext. value 31.97 0.0222 0.0480 Weibull 14.42 0.7016 0.038

Rayleigh 30.41 0.0337 0.0547 Lognormal 17.84 0.4661 0.038

Normal 43.46 6.7E-4 0.0866 Normal 30.20 0.0356 0.048

Antalya Hakkari

Gamma 41.23 0.0014 0.0914 Weibull 27.29 0.0737 0.05577

Ext. value 70.23 4.1E-3 0.0915 Rayleigh 30.40 0.0337 0.05468

Weibull 77.45 2.4E-9 0.1031 Ext. value 31.13 0.0278 0.06340

Gaziantep Göztepe

Ext. value 51.69 4.2E-5 0.0768 Weibull 22.31 0.2187 0.047

Lognormal 65.60 2.5E-7 0.0850 Rayleigh 29.99 0.0376 0.090

Rayleigh 59.79 2.2E-6 0.0910 Lognormal 33.93 0.0128 0.060

Normal 94.98 0.000 0.1005 Ext. value 35.08 0.0092 0.059

Samsun Sile

Ext. value 30.92 0.0294 0.0637 Ext. value 57.63 4.9E-6 0.0773

Weibull 36.01 0.0070 0.0708 Weibull 61.90 1E-8 0.055

Rayleigh 47.85 1.6E-4 0.133 Rayleigh 76.78 3E-8 0.116

Note 1: At the significance level α=5%, 1-α percentile value of the Chi-Square test, χ.95,16=26.3

APPENDIX F

FIGURES SHOWING THE VARIATION OF RELIABILITY INDEX OBTAINED ACCORDING TO THE TURKISH DESIGN PROVISIONS

0.25 0.5 1 2

bility

Turkey

Figure F.1 Variation of reliability index for D+L combination (RC beams in flexural failure mode)

0.5 1 2 3

bility

Ankara

Çanakkale

Turkey

Figure F.2 Variation of reliability index for D+S combination

(RC beams in flexural failure mode)

0.25 0.5 1 2

Ankara

(L'/D'=0.5)

Çanakkale

(L'/D'=0.5)

Turkey

(L'/D'=0.5)

Ankara

(L'/D'=1)

Çanakkale

(L'/D'=1)

Turkey

(L'/D'=1)

Figure F.3 Variation of reliability index for D+Lapt+W combination (RC beams in flexural failure mode)

0.25 0.5 1 2

bility in

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5)Çanakkale

(L'/D'=0.5Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.4 Variation of reliability index for D+L+Wapt combination (RC beams in flexural failure mode)

0.50 1.00 2.00 3.00

bility

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5)Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.5 Variation of reliability index for D+Lapt+E combination (RC beams in flexural failure mode)

0.25 0.5 1 2

bility

Turkey

Figure F.6 Variation of reliability index for D+L combination (RC beams in shear failure mode)

0.5 1 2 3

bility

Ankara

Çanakkale

Turkey

Figure F.7 Variation of reliability index for D+S combination (RC beams in shear failure mode)

0.25 0.5 1 2

bility

Ankara

(L'/D'=0.5)

Çanakkale

(L'/D'=0.5)

Turkey

(L'/D'=0.5)

Ankara

(L'/D'=1)

Çanakkale

(L'/D'=1)

Turkey

(L'/D'=1)

Figure F.8 Variation of reliability index for D+Lapt+W combination (RC beams in shear failure mode)

0.25 0.5 1 2

bility in

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.9 Variation of reliability index for D+L+Wapt combination (RC beams in shear failure mode)

0.50 1.00 2.00 3.00

bility

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5)Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.10 Variation of reliability index for D+Lapt+E combination (RC beams in shear failure mode)

0.25 0.5 1 2

bility

Turkey

Figure F.11 Variation of reliability index for D+L combination (RC columns in combined action)

0.5 1 2 3

bility

Ankara

Çanakkale

Turkey

Figure F.12 Variation of reliability index for D+S combination (RC columns in combined action failure mode)

0.25 0.5 1 2

Ankara

(L'/D'=0.5)

Çanakkale

(L'/D'=0.5)

Turkey

(L'/D'=0.5)

Ankara

(L'/D'=1)

Çanakkale

(L'/D'=1)

Turkey

(L'/D'=1)

Figure F.13 Variation of reliability index for D+Lapt+W combination (RC columns in combined action failure mode)

0.25 0.5 1 2

liability inde

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.14 Variation of reliability index for D+L+Wapt combination (RC columns in combined action failure mode)

0.50 1.00 2.00 3.00

bility

Ankara

(L'/D'=0.5)Bursa

(L'/D'=0.5)Turkey

(L'/D'=0.5)Ankara

(L'/D'=1)Bursa

(L'/D'=1)Çanakkale

(L'/D'=1)Turkey

(L'/D'=1)

Figure F.15 Variation of reliability index for D+Lapt+E combination (RC columns in combined action failure mode)

APPENDIX G

FIGURES SHOWING THE VARIATION OF SAFETY LEVEL CORRESPONDING TO THE RECOMMENDED LOAD AND

RESISTANCE FACTORS

0.25 0.5 1 2

bility

Safety level

Target reliability

Figure G.1 Variation of safety level for D+L combination (RC beams in flexural failure mode)

0.5 1 2 3

bility

Safety level

Target reliability

Figure G.2 Variation of safety level for D+S combination (RC beams in flexural failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.3 Variation of safety level for D+Lapt+W combination (RC beams in flexural failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.4 Variation of safety level for D+L+Wapt combination (RC beams in flexural failure mode)

0.5 1 2 3

bility

index Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.5 Variation of safety level for D+Lapt+E combination (RC beams in flexural failure mode)

0.25 0.5 1 2

Safety level

Target reliability

Figure G.6 Variation of safety level for D+L combination (RC beams in shear failure mode)

0.5 1 2 3

bility

Safety level

Target

Figure G.7 Variation of safety level for D+S combination (RC beams in shear failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.8 Variation of safety level for D+Lapt+W combination (RC beams in shear failure mode)

0.25 0.5 1 2W'/D'

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.9 Variation of safety level for D+L+Wapt combination (RC beams in shear failure mode)

0.5 1 2 3

bility

index Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.10 Variation of safety level for D+Lapt+E combination (RC beams in shear failure mode)

0.25 0.5 1 2

Safety level

Target reliability

Figure G.11 Variation of safety level for D+L combination (RC columns in combined action failure mode)

0.5 1 2 3

Safety level

Target reliability

Figure G.12 Variation of safety level for D+S combination (RC columns in combined action failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.13 Variation of safety level for D+Lapt+W combination (RC columns in combined action failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.14 Variation of safety level for D+L+Wapt combination (RC columns in combined action failure mode)

0.5 1 2 3

bility

index Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.15 Variation of safety level for D+Lapt+E combination (RC columns in combined action failure mode)

0.5 1 2 3

bility

Safety level

Target reliability

Figure G.16 Variation of safety level for D+L combination (RC columns in shear failure mode)

0.5 1 2 3

Safety level

Target reliability

Figure G.17 Variation of safety level for D+S combination (RC columns in shear failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.18 Variation of safety level for D+Lapt+W combination (RC columns in shear failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.19 Variation of safety level for D+L+Wapt combination (RC columns in shear failure mode)

0.5 1 1.5 2 2.5 3

bility

index Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.20 Variation of safety level for D+Lapt+E combination (RC columns in shear failure mode)

0.25 0.5 1 2

Safety level

Target reliability

Figure G.21 Variation of safety level for D+L combination (RC shear walls in flexural failure mode)

0.5 1 2 3

liabili

Safety level

Target reliability

Figure G.22 Variation of safety level for D+S combination (RC shear walls in flexural failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.23 Variation of safety level for D+Lapt+W combination (RC shear walls in flexural failure mode)

0.25 0.5 1 2

bility

Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.24 Variation of safety level for D+L+Wapt combination (RC shear walls in flexural failure mode)

0.5 1 2 3

bility

index Safety level

(L'/D'=0.5)

Safety level

(L'/D'=1)

Target reliability

Figure G.25 Variation of safety level for D+Lapt+E combination (RC shear walls in flexural failure mode)

CURRICULUM VITAE

PERSONAL INFORMATION Surname, Name: Fırat, Fatih Kürsat Nationality: Turkish (TC) Date and Place of Birth: 14 August 1973, Malatya email: fkfirat@gmail.com.tr EDUCATION

Degree Institution Year of Graduation

PhD METU, Department of Civil Engineering 2001-2007

MS Selcuk University, Department of Civil Engineering

1997-1999

BS Fırat University, Department of Civil Engineering

1990-1995

ACADEMIC EXPERIENCE

Year Place Rank

2000-2007 METU Department of Civil Engineering Research Assistant

1998-2000 Selcuk University, Department of Civil Engineering

Research Assistant

1996-1998 Nigde University, Department of Civil Engineering

Research Assistant

WORK EXPERIENCE

Year Place Rank

1995-1996 Sirkeciogulları Construction Company Civil Engineering 1994-1995 Gücar Construction Company Civil Engineering

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