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PERFORMANCE EVALUATION OF RC STRUCTURES UNDER EARTHQUAKE

LOADING

2009

MUHAMMAD RIZWAN

2005-Ph.D-CIVIL-08

DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF ENGINEERING AND TECHNOLOGY

LAHORE, PAKISTAN

PERFORMANCE EVALUATION OF RC STRUCTURES UNDER EARTHQUAKE LOADING

by

MUHAMMAD RIZWAN

2005-Ph.D-CIVIL-08

INTERNAL EXAMINER

(Prof. Dr. Muhammad Ilyas)

EXTERNAL EXAMINER

(Prof. Dr. Qaiser uz Zaman Khan)

CHAIRMAN DEAN

Civil Engineering Department Faculty of Civil Engineering

Thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Civil Engineering.

DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF ENGINEERING AND TECHNOLOGY

LAHORE, PAKISTAN

2009

ii

ABSTRACT Existing seismic risk in Pakistan, especially in its Northern Areas, emphasis for a detailed

and careful design of RC structures to withstand expected earthquake loads. The seismic

performance of RC multistory structures is a complex process. An accurate assessment of

seismic behavior of RC structures requires an analysis carried out under time history or

parameters of time history of real time recorded earthquakes. In Pakistan, a large data

bank of strong motion recorders exists in analog form, and its use in performance

assessment of structures is very difficult without digitizing it. The response of a

multistory RC building is greatly dependant on performance of its columns especially in

inelastic range, which can be improved by providing sufficient confinement. Post

earthquake surveys revealed that most of the RC buildings collapsed due to insufficient

performance of their columns, which were found deficient in confinement. A limited

work has been carried out in Pakistan to study the performance of RC columns under

axial and lateral loading. Internationally, the efforts are continued to enhance the

performance of RC columns subjected to seismic loads.

The objective of this research has three main parts. The first part is to collect, segregate

and digitize available analog form of earthquake data, which has been recorded in

Pakistan. The second part is to device and test a technique which could enhance strength,

ductility and stiffness of RC columns subjected to seismic loads and result in lesser

residual deformations. The third part is to carry out seismic analysis of a RC multistory

frame, using material behavior studied experimentally, under application of ground

motion data of Pakistan.

A novel digitizing technique is developed in this study that extracts the trace of recorded

acceleration as a whole by saving all points required to draw digitized ground

acceleration. The proposed digitizing approach has been compared with the available

techniques to assess its efficiency.

The confinement technique for RC columns developed in this study utilizes specialized

rings of steel strips applied as transverse reinforcement in hinge zone. Eight large scale

specimens have been cast and tested to study the performance of proposed technique. The

experimental results indicated that proposed confining reinforcement, although with

lesser volumetric ratio, improved the performance of RC columns by enhancing their

shear resistance, ductility, energy dissipation capacity and reducing residual deformations.

iii

The columns confined by proposed technique have been named as Steel Strip Confined

(SSC) columns. The observed column behavior has been modeled in Response-2000 and

DRAIN-3DX.

RC frames are modeled in DRAIN-3DX using material properties calibrated with

experimental data. The frames are analyzed under north-south component of El Centro

ground motion and east-west component of Kashmir earthquake recorded at Abbottabad.

The frames, modeled with properties of SSC columns, showed better performance by

reducing the damage. The analysis indicates that Kashmir earthquake is more damaging

in nature than El Centro ground motion.

iv

To my Beloved Parents, Brothers, Sister, Wife and Daughters. They all stood by me through out these

difficult years

v

ACKNOWLEDGEMENT

All thanks to Almighty Allah, who bestowed upon me enlightenment and courage

to complete this research work. I gratefully acknowledge the valuable advice, sound

guidance and encouragement of my advisor Professor Dr. Muhammad Ilyas, during all

the phases of this research work. I would like to extend my appreciation to Professor Dr.

Muhammad Ashraf, Professor Dr. Zahid Ahmed Saddique and Professor Dr. Afzal Javed.

They, being part of my research committee, helped me to focus on my ideas through their

positive criticism. I would also acknowledge precious guidance of Dr. Muhammad Tariq

Amin Chaudhary, who is presently working in Canada. His timely support, valuable

feedback and expert opinion always helped me to pull through when ever I got stuck. I

am thankful to Professor Dr. Qaiser Uz Zaman Khan of University of Engineering and

Technology, Taxila, Pakistan, Dr. Taiki Saito of Building Research Institute, Japan and

Professor Dr. Muhammad Baluch of King Fahd University of Petroleum and Minerals, Saudi

Arabia for becoming part of my examination committee. Their timely and constructive

comments have helped me to improve on this dissertation. I recognize the support of Dr.

Noor Muhammad Khan and Dr. Asad Ullah Qazi in finalizing this dissertation. I thank

my colleagues Asif Masood, Shaukat Ali, Kafeel Ahmed, Abdul Ghaffar, Adnan Ahmed

Rashidi, Hassan Farooq, Muhammad Ashfaq and M. I. Hassan for their encouragement

and support during the research. I am thankful to Vice Chancellor of University of

Engineering and Technology, Lahore and Professor Dr. Abdul Sattar Shakir, Chairman of

Civil Engineering Department for facilitating research activities. I extend my special

thanks to Muhammad Farooq, Munir Ahmed Lodhi, Khalid Nawaz and Attique-ur-

Rehman for their help and support in completing the work. I am thankful to laboratory

and office staff of civil Engineering Department for their administrative support.

I acknowledge enabling role of Higher Education Commission Islamabad,

Pakistan and appreciate its financial support through “Merit Scholarship for Ph.D Studies

in Science and Technology (200 Scholarships)”. Finally, I owe my deepest gratitude to

my employer Pakistan Army for its support to complete this research work.

Muhammad Rizwan

vi

Contents Abstract ii

Acknowledgement v

Contents vi

1. Introduction 1.1 General 1

1.2 Aim and Objective 2

1.3 Scope of Work 3

1.4 Thesis Overview 3

2. Literature Review

2.1 Introduction 6

2.2 Seismological background of Pakistan – an overview 7

2.3 Digitization of analog form of acclerograms 10

2.3.1 Hand digitization 11

2.3.2 Automatic digitization 11

2.3.3 Problems identified in digitization 13

2.3.3.1 Synchronization of time scale 13

2.3.3.2 Variation in optical density 14

2.3.3.3 Thickening of traces 14

2.3.3.4 Film speed 14

2.3.3.5 Absolute Triggering Time 15

2.3.3.6 Rotational problems 15

2.3.3.7 Noise introduced in strong motion records 15

2.3.4 Elastic response spectrum 16

2.3.5 Elastic design spectrums 16

2.4 Confinement 17

2.4.1 Confinement models 19

2.5 Experimental performance of confined rc columns 20

2.5.1 Spacing and configuration of confining reinforcement 21

vii

2.5.2 Affect of rate of loading 24

2.5.3 Different confining arrangements 25

2.5.3.1 Orthogonal system of steel bolts 25

2.5.3.2 Ferrocement jacket 26

2.5.3.3 Partially stiffened steel jackets 27

2.6 Performance of RC buildings under seismic loads 28

2.6.1 Performance criteria 30

2.6.2 Inelastic response 31

2.6.3 Push over analysis 32

2.6.3.1 Conventional pushover analysis 33

2.6.3.2 Modal push over analysis 33

2.6.4 Incremental dynamic analysis 34

2.6.5 Capabilities and limitations of DRAIN-3DX 35

3. Digitization and Analysis of Seismic Data

3.1 Introduction 36

3.2 Seismological background of the region 36

3.3 Analog form of recorded acceleration 37

3.4 Digitizing approach 39

3.4.1 Steps of algorithm used in proposed technique 46

3.4.2 Digitized data 47

3.4.3 Comparison of results of digitizing approach 51

3.5 Modified digitizing approach 53

3.5.1 Steps of modified digitizing approach 56

3.6 Design spectrums 56

3.7 Limitations 60

4. Performance of Conventional and Steel Strip Confined RC Columns

4.1 Introduction 62

4.2 Description of Specimens 62

viii

4.3 Constituting materials 64

4.4 Construction of specimen 65

4.5 Testing arrangement 70

4.6 Loading history 72

4.7 Instrumentation and data acquisition system 73

4.8 Testing of specimen 75

4.8.1 Group 1 specimen 75

4.8.1.1 CRCS-40 cast with 25 Mpa concrete 75


4.8.1.3 SSC-02 cast with 25 Mpa concrete 79

4.8.1.4 SSC-1.3 cast with 25 Mpa concrete 82

4.8.2 Group 2 specimen 84




4.9 Yield and ultimate points 90

4.9.1 Group 1 columns 91

4.9.1.1 CRCS-40 Cast With 25 Mpa Concrete 91








4.10 Comparison of yielding, peak and ultimate cycles for critical

direction

99



4.11 Lateral load capacity 103


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4.12 Stiffness degradation 105



4.13 Ductility 108



4.14 Residual Displacements 111



4.15 Energy dissipation 114



4.16 Modeling on response 2000 118

4.16.1 Approaches to plot theoretical load displacement curves 118

4.16.1.1 Linear variation approach 119

4.16.1.2 Interpolation approach 121

4.16.2 Comparison of results 122

4.16.2.1 CRCS-60 column cast with 32 Mpa concrete 122



4.17 Modeling on DRAIN-3DX 127

4.17.1 Element selected in modeling of columns 128

4.17.1.1 Material modeling for element 129

4.17.1.2 Material model for connection hinge 129

4.17.2 Calibration of material properties of RC columns 131




4.17.2.4 Comparison of calibrated material properties 137

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5. Performance of RC Building

5.1 Introduction 138

5.2 Description of basic building structure 139

5.3 Ground motion selected 141

5.4 Description of modeling 143

5.5 Nonlinear time history analysis (NTHA) 145

5.6 Damage index used in performance evaluation 145

5.7 Analysis of CRCS-60 under application of El Centro ground motion 146

5.7.1 Story displacement history 146

5.7.2 Max displacement of floors and inter story drifts 147

5.7.3 Sequence of formation of plastic hinges 149

5.7.4 Mode shapes and structural damage 150

5.8 Analysis of CRCS-60 under application of Abbottabad ground

motion

150





5.9 Analysis of crcs-60 under application of abbottabad-scaled ground

motion

155





5.10 Analysis of SSC-02 under application of Abbottabad-scaled ground

motion

160





5.11 Analysis of SSC-1.3 under application of Abbottabad-scaled ground 165

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motion





5.12 Comparison of El Centro, Abbottabad and Abbottabad-scaled

ground motions

171

5.12.1 Ductility factors and energy dissipated 171

5.12.2 Base shear and top roof displacement 175

5.12.3 Moment curvature hysteresis 179

5.13 Summation of comparison of analysis of CRCS-60 frame analyzed

by El Centro, Abbottabad and Abbottabad-scaled ground motion

180

5.14 Comparison of CRCS-60, SSC-02 and SSC-1.3 frames analyzed by

Abbottabad ground motion

180

5.14.1 Ductility factors and energy dissipated 180

5.14.2 Base shear and top roof displacement 185

5.14.3 Moment curvature hyteresis 187

5.15 Summation of comparison of CRCS-60, SSC-02 and SSC-1.3 188

6. Conclusion and Recommendation Conclusions 189 Recommendations 192 7. References 193

CHAPTER 1

INTRODUCTION 1.1 GENERAL

The seismic environment in Pakistan emphasize for a detailed and careful analysis

and design of RC structures to withstand expected earthquake loads. An accurate assessment

of seismic demands imposed on RC structures requires Nonlinear Time History Analysis

(NTHA) carried out under application of real time recorded data of earthquakes. NTHA, in

addition to real time recorded data, involves damage model of materials representing their

behavior during cyclic loads. Thus real time recorded data of earthquakes and material

models are the two basic inputs for NTHA. In Pakistan, the seismic data of earthquakes is

being recorded since 1969 by analog accelerograms. The out put of the analog recorders is in

the form of 70 mm wide film and cannot be used or interpreted directly in NTHA. Also, no

research in Pakistan has been carried out to study the behavior of local materials under cyclic

loads.

In this research seismic data recorded by analog accelerograms was collected. The

analog data was digitized by developing a novel technique. The digitized data have been

used to suggest response and design spectrums, with different damping values, for Tarbela

region. In order to study the performance of local materials under cyclic loads, prototype

specimens of RC columns were constructed in the laboratory and tested. The performance of

RC columns, which is greatly affected by confinement provided in hinge zone, plays a vital

role in overall performance of structures. The confinement provided in a RC column is

influenced by spacing of longitudinal and transverse reinforcement and configuration of the

later. In the research, a new technique has been suggested to confine the RC columns with

steel strips of 2 mm and 1.3 mm thickness. The width of strips was adjusted so as to achieve

a cross sectional area equivalent to that of standard 10 mm diameter stirrups. The confining

hoop of the steel strip has a specially designed seismic hook. The suggested confining

reinforcement was only provided in hinge zone and in the remaining column standard

reinforcement was used. Control specimens, using standard transverse stirrups, were also cast

for comparison. The columns confined by the suggested technique have been named as Steel

CHAPTER 1 INTRODUCTION

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Strip Confined (SSC) columns. The performance of SSC columns have been compared with

conventional columns. Experimentally achieved load-displacement envelops of the columns

were modeled on Response-2000 and DRAIN-3DX. An eight story RC frame was modeled

in DRAIN-3DX using material properties calibrated during modeling. Two RC frames were

modeled with material properties of SSC columns and one with those of conventionally

confined column. For NTHA north-south component of Imperial Valley Earthquake

recorded at El Centro and east-west component of Kashmir earthquake recorded at

Abbottabad was used. The deformation demands of Kashmir and El Centro earthquakes are

compared and performance of SSC and conventional frames is also compared.

The digitizing approach, presented in the study, can be used easily to digitize analog

records of earthquakes recorded at different locations in Pakistan and other parts of the

world. The confining technique suggested in this research work is simple and enhance

performance of RC columns. Therefore, this technique can be developed further so that it can

be used by people involved in design of RC structures which are expected to experience

seismic forces during their service life. The analysis of RC frames under Kashmir earthquake

will help to understand more about the effects of the event. Also, the performance evaluation

carried out will give a guide line to the practicing engineer to quantify damage. This study

will contribute useful information towards improvement of seismic design of multistory RC

building structure.

1.2 AIM AND OBJECTIVES

The main aim of this research is to comprehensively understand the affects of column

confinement on performance of a RC building structure under indigenous earthquake records.

This aim of the research will be accomplished by attaining following objectives:

(i) Propose a technique to improve the confinement of columns and study its affects

experimentally.

(ii) Determine strength, stiffness and ductility of confined columns.

(vi) Collect data of local earthquakes in analog form and develop a simple technique to

digitize it.


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(v) Study experimentally the response of conventionally confined columns and suggest a

confining technique which could enhance performance of RC columns.

(vi) Study capabilities and limitations of different FEM based computer programs and

understand to quantify seismic response of RC building structure.

(vii) Study performance of RC multistory building, modeled with material properties of

columns tested in laboratory, under application of ground acceleration data recorded

in Pakistan.

1.3 SCOPE OF WORK

The scope of the thesis is to study the performance of reinforced concrete building

subjected to time histories of earthquakes recorded in Pakistan and using material properties

determined from cyclic testing of confined columns. The following is a list of scope of

work:

(i) Square columns with 230 x 230 mm cross section will be tested in laboratory.

(ii) The parameters selected to study affects of confinement will include type of confining

steel and compressive strength of concrete.

(iii) The time axis of the digitized time history will not be constant.

(iv) Only one computer program will be selected for analysis, which could calculate

variation in time period of a RC building structure at selected intervals of time history

to which it is subjected.

(v) Only one RC multistory frame will be selected for analysis.

1.4 THESIS OVERVIEW

The thesis has been organized in six chapters.

Chapter 1 gives introduction, aim, objective and scope of the research work.

Chapter 2 reports a review of required literature studied during the research work.

The chapter starts with seismological back ground of Pakistan. It includes different

digitizing techniques and their limitations. The problems which have been identified in


4

digitizing analog records are discussed. The literature reviewed to comprehend affects and

importance of confinement is included. The experimental studies carried out by different

researchers are reviewed to understand the affect of configuration of confinement on

response of columns. Performance of RC building is studied and performance criteria as

presented by different researchers are included. Few inelastic concrete models are reviewed

and different types of analysis procedures are studied. Capabilities and limitations of

DRAIN-3DX are also covered in this chapter.

Chapter 3 presents the digitizing technique proposed in this research. The chapter

gives out the seismological background of Tarbela region where analog recorders were

installed. The problems faced in originally developed technique are identified and modified

technique is also included. The digitized data is shown and compared with analog records.

The comparison is also carried out with available digitizing technique. The digitized data is

used to calculate response spectrums and suggest design spectrums for Tarbela region.

Chapter 4 explains the experimental work carried out in this research. The chapter

starts with the properties of constituting materials. The experimental test setup,

instrumentation and construction process of specimens is covered in the chapter. The

proposed confining technique is explained in detail and testing of the entire specimens is

covered. The resulting hysteresis curves are discussed and observations made during testing

are also included. The performance of proposed and conventional RC columns is compared

in terms of lateral strength, yielding, stiffness degradation, ductility and residual

displacements. The experimental results are modeled on Response-2000 and DRAIN-3DX.

During modeling on DRAIN-3DX, the material properties are calibrated to match the

experimental hysteresis curves.

Chapter 5 discusses the performance evaluation of RC multistory building structure.

The building model is given and detailed analysis of time histories of ground accelerations

selected for NTHA is presented. The story displacement history and peak inter story drift of

all stories is discussed. The hysteretic response of the reinforced concrete building is plotted


5

between roof displacement and base shear histories. The sequence of formation of plastic

hinges is marked on line diagram of building structure at selected instances of time history.

The mode shapes, along with respective time periods, at start and end of time history are

calculated. Initial and final time periods have been used to calculate damage. The

performance of conventionally confined RC frame under El Centro ground motion is

compared with that achieved from Kashmir earthquake. The performance of conventionally

confined RC multistory frame structure is compared with that of RC frames confined with

proposed confinement technique.

Chapter 6 includes the major and specific conclusions obtained from digitizing

technique, experimental work and performance evaluation of RC frame structure. This

chapter also discusses recommendations for future studies.

CHAPTER 2

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LITERATURE REVIEW 2.1 INTRODUCTION This chapter includes the review of literature studied for this research work. The chapter

starts with an overview of different faults located in Pakistan. Few significant Earthquakes

which have occurred are reported here. Categorization of seismic activity of Pakistan is also

discussed.

The importance of digitization has been felt since production of first strong-motion

accelerogram recorded during Long Beach earthquake of 1933. The digitization techniques

started to develop since late 60s. In order to digitize the data collected in this work it was

necessary to understand different available digitizing techniques. The problems faced in

digitizing, which results in errors in the digitized data are discussed. The procedure to

generate elastic response and design spectrums is reviewed.

In order to understand the behavior of RC columns under cyclic loads, affects of confinement

on strength enhancement and ductility were studied. Different analytical models studied to

understand the mechanism of confinement are presented. Affects of rate of loading,

configuration and spacing of transverse reinforcement on response of RC columns is studied.

Different confining techniques proposed by researchers to enhance performance of RC

columns are also included.

The performance criteria of Multistory RC building as defined by FEMA, IBC-2003, UBC-

97 and different researchers were studied and presented here. In order to quantify the

performance of multistory RC building different analysis approaches such as push over

analysis, modal push over analysis, incremental dynamic analysis and time history analysis

were reviewed. Limitations and capabilities of DRAIN-3DX, which has been selected for

analysis of RC multistory frames under application of time history of selected ground motion

and material properties calibrated during experimental work, are also presented.

CHAPTER 2 LITERATURE REVIEW

7

Figure 2.1: Show location of Pakistan at the boundaries of Indo-Australian and Eurasian

Plates (Ilyas and Rizwan, 2004)

Figure 2.2: shows active fault zone in Pakistan (Ilyas et al. 2005)

2.2 SEISMOLOGICAL BACKGROUND OF PAKISTAN – AN OVERVIEW

Northern and Northern-Western regions of Pakistan are located over the boundaries of Indian

and Eurasian Plates as shown in Figure 2.1. India collided into Asia 50 million years ago and

is moving slowly, in north east direction, at a rate of about 3.5 cm/year relative to the Burma

and Eurasian plates. This results in oblique convergence with Burma Plate at Sunda trench

and at the Himalayas with Eurasian plate (US Geological Survey). The major tectonic

activities due to the movement and convergence of Indian plate has shaped the geological

structures as observed in Pakistan today (Rizwan, 2004). The seismic activity observed in the

region is also attributed to movement of the plate.

The zone of deformation that extends from Makran region in southwest to Hazara-Kashmir

synthesis of the Himalayas in northwest was produced by interaction among the Indian,

Indian Plate


8

Arabian, and Eurasian plates. In Makran region, the oceanic portion of the Arabian plate is

sub-ducted beneath continental material to its north (Stoneley, 1974) and (Jacob and

Quittmeyer, 1979). In central and northern Pakistan, a belt of folds and faults has developed

in the zone along which the continental portion of the Indian and Eurasian plates collided.

Documented historical and modern seismic knowledge indicate that this entire zone of

deformation is currently active, although the type and level of activity vary from region to

region. Many surface faults have been mapped in Pakistan (Hunting Survey Cooperation,

1961). The interpretations of “landsat” satellite imagery (Preliminary Determination of

Epicenters) have added to our knowledge of faults and lineations in this region. Although

seismic activity in the region is due to movements along faults, but it is difficult to associate

individual earthquakes with specific mapped faults because of insufficient knowledge of the

depths of most earthquakes and lack of comprehensive field mapping. In some cases these

earthquakes can be related to particular faults. The main faults of Pakistan are marked in

figure 2.2. Seismic activity in Pakistan and its vicinity can be separated into three categories

(Farah and Dejong, 1979).

First category includes earthquakes characterized by faults capable of generating large

earthquakes. Some of the events in this category, such as those associated with Chaman fault,

produced rupture at the surface and can easily be associated with mapped surface faults.

Others, however, such as those in the Northern Kirthar Ranges, did not produce surface

faulting. The combined evidences from seismology and geology are not sufficient to

determine that large events in the Northern Kirthar Ranges were related to faults mapped at

the surface.

Second category contains those events that define relatively narrow and elongated zones of

seismicity. Activity in the Quetta transverse zone, the Suleiman Ranges and the Himalayas

are this type of seismicity. The exact nature of these seismic zones is of great interest with

regard to seismic risk evaluation. Such a zone may be related to a continuous fault capable of

rapture in a large earthquake or, alternatively, to activity on a group of smaller faults with

similar orientation, none of which can produce a large earthquake. But with available data it

is difficult to decide that which of the seismicity is true.


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Third category of seismicity is composed of activity that is characterized by a diffuse nature.

The significance of this type of activity is not well understood at the present time. It may be

caused by movements on faults with a wide distribution, or by sparse activity on a shallow

dipping fault. The occurrence of diffuse activity in a particular region does not mean that

region is safe from large earthquakes. This category is found in coastal regions, south east of

Karachi, and in the southern Kirthar Ranges.

Many earthquakes have been generated due to release of energy along faults which exists in

Pakistan. On 8th October, 2005 at 08:52 local time Kashmir earthquake, with magnitude 7.6

on the Richter scale, struck the Azad Jammu and Kashmir and North-West Frontier Province

of Pakistan. The earthquake has approximately affected an area of 30,000 Km2 (Naeem et al,

2005). The devastation caused by Kashmir earthquake has been administered all over the

world. As per official figures more than 80000 were dead, 200,000 injured and 4 million

families were displaced (Ilyas M. et al. 2006 & 2006a). The epicenter of the earthquake has

been located at 34.44N 73.58E, near Muzaffarabad, approximately 95 Km north of Islamabad.

The earthquake occurred due to a rupture along Kashmir Boundary Thrust (KBT). The KBT,

which is part of Hazara Thrust system, connects to Himalayan Thrust near its north west end

in Kashmir (Mahdi S. K. et al. 2005). The fault falls in second category as explained above.

The KBT is active and there are number of events that have been located in this area in the

past history. In 1669 and 1828 two significant earthquakes occurred in this area (NEIC,

2002). The study of data from year 1972 to 2002 indicated that there are about 38 events,

with magnitude 4 and above, which have been located in the same area (Burg et al, 2005).

The other recognized earthquakes which have been recorded in history include Quetta

earthquake, 1935 (Andrew and Robin, 2002). From November 2002 to March 2003, 72

earthquakes with magnitude ranging from 3.7 to 5.3 on Richter scale were observed in

northern areas. On 14th February 2004 an earthquake measuring 5.7 on the Richter scale

struck Battagram and Mansehra districts located in northern areas of Pakistan (Ilyas M. et al.

2004).


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2.3 DIGITIZATION OF ANALOG FORM OF ACCLEROGRAMS The analog strong motion recorders were developed and installed in early 30s (Hudson, 1979

and Chen and Scathorn, 2002). First record of ground acceleration was obtained in Long

Beach California in 1933 (Boore and Bommer, 2005). The earlier analog recorders yielded

output of ground acceleration in the form of photographic trace or a scratch on wax paper.

Such analog data can only be segregated and stacked based on its PGA, duration, depth and

location but no further analysis is possible without digitizing it. The first digitizing technique

was hand digitizing, which involved physical interpretation of recorded data (Lee and

Trifunac, 1990). In late 60s semiautomatic digitization systems were developed (Lee, 2002).

Up to 1973 hand digitization was most popular. In 1973 the hand digitization was integrated

with computer (Trifunac and Lee, 1973). In late 60s and early 70s, image processing

software and hardware were developed, which brought a revolution in digitization of strong

motion data recorded in analog form.

The development of digital strong motion recorders was started in 70s and were

commercially available in 1980s (Trifunac and Lee, 1979), but even up till 1989 Loma Pieta

Earthquake the majority of the records were in analog form (Lee and Trifunac, 1990). The

advantage in digital recorder is that these can digitize the data internally and output is in

digital form. This equipment was looked at as a complete replacement of old system and it

was thought that by end 80s these new recorders will completely replace the old analog

acceleraograms. But it did not happen due to higher prices of new recorders and

advancement in solid state physics. The chips used in digitized recorders were upgraded

very frequently, therefore, end users were not satisfied about their useful life and did not

replace the old network. The digital recorders later by about late 90s replaced the analog

recorders completely in the developing countries but in under develop countries the analog

recorders are still in use and need of digitizing techniques is still felt by people involved in

handling of analog recorders.


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2.3.1 Hand Digitization The analog record is enlarged by five times (Lee, 2002). The technique used a digitizing

table which had scaled grids marked on it and a cross hair which could be moved with hand.

The enlarged image of the record was fitted on the table. The zero acceleration line of the

record being digitized was aligned with x axis of the digitizing table by physical observation

only. It was also possible to use the original record but enlargement made the process more

reliable. An issue of resolution of enlarge record have been addressed separately (Batlló,

1997). The cross hair was moved manually to lines existing in sequence. The digitizer

attached with the table converted the coordinates of crosshair into numbers, which were

saved on a tape or punched in a card. The data saved in this form was read by specially

written computer program which plotted to the same scale as that of original record being

digitized. The digital plot of the record was compared with original analog form and

variations were noted. The portion of record containing error was again digitized and

compared with original record for errors. The process was continued until final and original

records fairly match each other. In semiautomatic technique data was collected by hand

digitizing technique and later processed on computer.

2.3.2 Automatic Digitization The hand digitization was laborious task which took several days to digitize a single record.

With development in hardware and software in field of image processing Trifunac and Lee

developed an automatic digitization system in 1979, which consisted of four programs

(Trifunac and Lee, 1979). The system was designed to reproduce up to four ten inch long

sections of the analog ground acceleration records in form of 10 inch x 10 inch output. The

output was rolled on a drum of photodensitometer for scanning (Trifunac and Lee, 1979).

The densitometer was controlled by a program “FILM” which was used with NOVA-3 Data

general mini computer. The program FILM was designed to save the scanned data on disk for

further processing by “TRACE” which moved through the scanned traces and found

coordinates of its points. The traces, in the form of coordinates, were read by the program

“TV”. The program displayed the traces graphically on the Tektronix terminal. The

displayed traces could be edited, checked and corrected on the terminal. At the end, the data

of corrected traces was plotted on a plotter and saved by the help of program “SCRIBE”.


12

In late 80s, with development of personnel computers which could be interfaced with desk

top scanners, the digitization was upgraded in 1990 (Lee and Trifunac, 1990) to new system

which worked on PC, with 286, 386 and 486 Intel processors. The newly developed program

consisted of SCAN, FILM, TRACE, TV and SCRIBE and used EGA or VGA display

terminal. The PC was interfaced with a Hewlett-Packard digital scanner and a graphic

memory printer. The densitometer used in previous version (Trifunac, 1976) could also be

used with new version. The difference was only in creation of enlargement which could now

be done on a photocopy machine. A long record could be copied on a single 8.5x11 inch

(A4) paper in three portions placed one over the other. The software could read the images

and join them before digitizing. A long record could alternatively scanned by desktop

scanner, in portions, and while processing joined in the software. The noise in digitized

record depends on its resolution, which is defined as number of points digitized per unit

length of record. The analog recorders working with acceleration transducers have lesser

noise as compared to those using displacement transducers (Trifunac and Udwadia, 1974).

Resolution of a 600 dbi scanner was found to be 236 points per second which means a

sufficient frequency of 118 Hzs is achieved.

The record was scanned by program “SCAN” which could scan on 600 dbi and 300 dbi

depending on resolution of the record. The program “FILM” checked the data and activated a

cross hair which read different coordinates of traces. The program created a reference file

which was updated as the digitizing process progressed. The program “FILM” could identify

zero base line, half second line, beginning of time hacks and fiducials reference point. Lower

and upper limit of acceleration traces was also saved by “FILM” for further use by “TRACE”.

The program “TRACE” worked with raw data file. It traversed through the traces and

located all black pixels, which represent width of the record. The program started by saving

an initial segment of the acceleration trace. It then traversed through the complete record and

saved all segments pointing in y direction. If distance between the segments was within

certain limit, defined empirically, those were said to be connected. Any segment which had

number of points less than those already decided as minimum limit was discarded because

such segment results from scratches and imperfections in the record. The program “TRACE”

could eliminate confusions created due to intersection of segments, scratches and other


13

imperfections. The program could not resolve issues like overlapping of segments, gaps or

two or more segments intersecting at the same point. The program, “TRACE” saved its

output in a file, which contained information of all the segments including their respective x

and y coordinates. The program TV read the data saved by “TRACE” and displayed it on

display adapter for editing. In TV a single trace of acceleration record was generated from

left to right. While editing the user could display all segments and separate those which

indicated some problem. After editing the program “SCRIBE” could write or plot the trace.

In 1995-96 the version of digitization explained above was upgraded to LeAuto. The new

technique was more users friendly and consisted of LeFilm to scan the image record,

LeTrace to read the scanned data, LeTV to edit the data and LeScribe to read the trace

segments and assemble them (Lee, 2002). The sequence of activities in this version was

unchanged. This new version was also used to re-digitize the Rinaldi Strong Motion

Accelerogram of the Northridge Earthquake (Trifunac, 1998). LeAuto has been continuously

upgraded and improved to meet capabilities of the new hardware developed in the field of

image processing (Lee, 2002).

2.3.3 Problems Identified In Digitization The major problems which have been identified while handling and working with analog

form of strong motion records are discussed in the following sections.

2.3.3.1 Synchronization Of Time Scale The strong motion recorders, on triggering, start recording of three components of ground

acceleration simultaneously. If during digitization first point is not digitized properly the

start of three traces of ground acceleration will not be synchronized. Lamp of analog

recorders warm up in about 0.1 sec after triggering. In this way the initial portion of record

has usually lesser resolution as compared to remaining record. The synchronization of time

scale is important for many type of analysis such as inverse analyses of the earthquake source

mechanism. If time scale has unusual delays the inversion will not be numerically stable.

Applications using linear combination of the three components, such as calculation of radial

and transfer component of motion, will have problems of peak amplitudes, if time scale is not

synchronized (Todorovska and Trifunac, 1997). The error will also affect building response


14

under wave propagation. The errors arising due to misalignment of transducers cannot be

corrected if the three traces are not synchronized (Wong and Trifunac, 1977).

2.3.3.2 Variation In Optical Density

The traces of acceleration should have same resolution through out their length but it is not

actually true. The reason for variation in optical density can be due to scratches, dust, dirty

mirror or scratches on the mirror, improper focusing of lenses and variable darkness of

background film. For a properly working analog recorder, with accurate recording speed and

lamp intensity, the traces will be recorded with thin and clear line. However, near peaks

there will be a duplication of the traces and any fluctuation in recording speed causes

thickening of traces at different places. Resolution selected for scanning will also affect

thickness of traces. If the optical density of background tape is not constant it will result in

irregular edges of acceleration trace. If a white spot exists in the trace it will result in

discontinuity of its mean. This problem need to be addressed while selecting a threshold

value for a scanned record.

2.3.3.3 Thickening of Traces

The problem arise near peaks where exposure to light lamp causes thickening of trace due to

overlapping and merging of peak with the segment just below peak. The problem is more

pronounced in vertical acceleration because of higher frequency as compared to horizontal

acceleration. The thickening is more on side which is away from zero acceleration line. To

resolve this problem a threshold level can be selected which reduces the affect of thickened

peaks or by drawing mean of the trace this problem can be compensated.

2.3.3.4 Film Speed

The problems in recording speed of analog recorder may occur due to dust or rust in film

driving mechanism, friction in roll of recording film and fault in speed of driving motors.

The problem in speed causes abrupt changes in records including stalls. Long stalls cannot

be corrected; however, small stalls or missing segment can be regenerated (Lee and Trifunac,

1984) by stretching the time scale back to original length. Higher recording speed, such as

2.5 cm/sec or 2 cm/sec, increases resolution and accuracy of traces.


15

2.3.3.5 Absolute Triggering Time

Initially it was thought that absolute triggering time was not important in recording of strong

ground motions (Hudson, 1970). But its introduction by Dielman (1975) open new ways for

studies in advance wave propagation. In some recorder both time marker, marking 2PPS

scale, are calibrated with running time to capture triggering, so that if one time marker misses

other is still available. But problem arise when both markers stop working simultaneously.

2.3.3.6 Rotational Problems

Any rotation of analog record occurring during scanning can translate in large errors in

digitized data. Specially, while dealing with long records which are to be scanned in portions

the rotational problem can result in misaligned records. Special care is required to cater for

such errors occurring during scanning of records being digitized.

2.3.3.7 Noise Introduced In Strong Motion Records

The noise is inherently present in analog and digital accelerograms produced by strong

motion recorders. The long-period noise, introduced due to deficiency of tracking in

digitizers (Trifunac and Todorovska, 2001) or lateral movements of film during recording

can be removed by using low-cut filter (Trifunac, 1971). Studies have been carried out to

identify noises introduced in digitized records (Shakal and Ragsdale, 1984) and (Skarlatoudis

et al., 2003). In these studies the identified noises depend on combination of type of strong

motion recorder and digitizing process used. The noise from a signal of strong ground motion

can be removed by defining an acceptable range of signal to noise ratio and remove all such

frequencies which fall into unacceptable range. The noises introduced due to limitations of

recorders and digitizing process are the standard noises. These may include noise introduced

at or close to natural period of transducer (Trifunac, 1972), error in base line, connecting

segments of a long record digitized separately and long period noise. The noise due to

transducer characteristics can be minimized by using second order central difference

derivatives. But this method can only be used for a data recorded at higher frequency

(Shyam and Connor 1982) and (Joyner and Boore 1988). The noise introduced by natural of

transducer can also be removed by frequency domain corrections (Converse and Brady,

1992). The noise due to misalignment of base line can be corrected by adjusting small


16

segments in a trace. In addition to the standard noise non standard noises can also be

introduced due to scratches or folding of records (Douglas, 2003). Such noise can be

removed by carefully handling the records.

2.3.4 Elastic Response Spectrum It has been recognized that elastic response spectrum is a good tool to study the nature of an

earthquake. The response spectrums represent behavior of single degree of freedom (SDOF)

structures, with varied time periods, to a strong motion record. For every structure the peak

response is noted and plotted as ordinate of response spectrum at that particular time period,

which is actually the natural period of the SDOF structure under consideration. The

deformation response spectrum is the spectrum of peak displacements of number of SDOF

structures, selected over a range of time periods, to a particular ground motion record. The

solution for peak displacement of SDOF structures can be achieved numerically by any

suitable method. The other form of spectrum which could be derived from deformation

response spectrums is known as pseudo-acceleration response spectrum (Chopra, 2002). The

ordinates of deformation response spectrum can be related to pseudo acceleration spectrum

through 2nA Dω= . Here “A” has acceleration units and can be used to determine maximum

base shear. Similarly, velocity spectrum can also be achieved from deformation spectrums.

The three spectrums can be plotted on separate plots or together on a single four way

logarithmic paper in form of D-V-A spectrum.

2.3.5 Elastic Design Spectrums The elastic response spectrums of number of earthquakes recorded in a particular region are

averaged to give elastic design spectrums. When earthquake data is not available for a region,

for which elastic design spectrums are to be suggested, then data can be selected from a

source of similar seismological background. There are several ways to drive elastic design

spectrums. One approach has been suggested by Housner. The design spectrum obtained by

this approach is known as Housner’s Average Design Spectra (Cheng, 2001). Housner

selected horizontal components of El Centro (18 May 1940), El Centro (30 December 1940),

Olympia (13 April, 1949), Taft (31 July, 1952 and Vernon (10 March, 1933) earthquakes and

plotted their response spectrums for different damping values. He averaged these response

spectrums and carried out their smoothening. Then he carried out PGA scaling of the records


17

and again repeated the procedure. Another approach has been suggested by Newmark

(Cheng, 2001) known as Newmark Elastic Design Spectra. He constructed an elastic design

spectrum for peak acceleration, velocity and displacement values selected as 1.0 g, 48 in/sec

(1.2192 m/sec) and 36 in (0.9144 m) respectively. In this way three regions, sensitive to

acceleration, velocity and displacement, are established in high, intermediate and low

frequency ranges. The spectral ordinates for other damping values are found by multiplying

the peak spectral values with respective amplification factor. If the peak ground acceleration

is less than 1.0 g then the response spectrum of peak acceleration, velocity and displacement

is reduced with respective factor.

2.4 CONFINEMENT

The ductility and flexural strength of RC columns is greatly influenced by strength of

confined concrete and descending branch of stress-strain curve of concrete. The stress-strain

relationship of confined concrete is influenced by the strength of concrete, diameter and yield

strength of the confining reinforcement, volumetric ratio of confining reinforcement to

concrete core, dimensions of the column, and configuration of the longitudinal as well as

lateral confining reinforcement. The strength of concrete in post peak region is required to

allow columns to undergo large number of inelastic deformation reversals under cyclic

loading. The ability of column to sustain inelastic deformation cycles is referred to as

deformability. The performance of RC multistory building structures largely depends on the

deformability of its columns.

In RC columns yielding of reinforcement and crushing of concrete cover causes stress

redistribution at critical sections and plastic hinge is formed (Razvi and Saatcioglu, 1999).

With further decay in moment resistance and increase in curvature a plastic region is formed.

In this region moment resistance has dropped at constant curvature. As the moment

resistance further drops, simultaneously with increase in curvature, the hinge progression

takes places and it becomes localized with a length equal to dimension of column in direction

of loading. This region is known as constant curvature region (Razvi and Saatcioglu, 1999).

Has there been no confinement phenomenon the curvature of column would have continued

to increase within the same constant curvature region. At this stage the lateral expansion of


18

the column triggers the confinement which increases the compressive strength of core

concrete. The increased compressive strength of concrete, along with the strain hardening of

reinforcement, once again increases the column curvature along its length. This results in

new redistribution of stresses and the hinge progression starts towards the elastic zone.

Performance of columns during earthquake depends on drift demands imposed. The drift

demands can be calculated for a given seismic region and performance level expected by the

governing code such as American Concrete Institute (2005), International Conference of

Building Officials (1997) and International Code Council (2003). Up to 1991 drift level

corresponding to peak lateral force resistance was considered as limiting drift level for

performance of RC confined columns (Park R. at al. 1975). However, it is unnecessarily

conservative and it may be suitable to allow 20% decay in strength of columns beyond their

maximum lateral load strength (Razvi and Saatcioglu, 1999) and (Muguruma et al., 1991).

The drift attained by a column up to 20% decay in its lateral force resistance is referred to as

capacity of the column. This capacity is dependant on amount, yield strength, spacing and

arrangement of transverse steel and compressive strength of concrete. An accurate selection

of these parameters would enhance capacity of RC columns both in terms of magnitude and

efficiency. The uniformity in distribution of transverse steel will enhance its efficiency. The

uniformity can be achieved through closely spaced transverse and longitudinal reinforcement

which provides a uniform lateral pressure and efficient confinement. Further it has been

found in research that transverse steel is effective as confinement reinforcement if its spacing

is limited to half of its shorter core dimension (Razvi and Saatcioglu, 1989). Also, a limit of 6

times the bar diameter or 150 mm is necessary for bar buckling (Pauly and Priestly, 1992)

and (International Conference of Building Officials, 1997).

The strength of concrete also plays an important role in confinement. The strength of

concrete and its deformability are inversely proportion. Therefore, higher strength concrete

requires higher lateral pressure (Razvi and Saatcioglu, 1994). The confinement pressure

required for concrete with compressive strength fc′ can be found from c yt cf fρ ′ , where cρ

and ytf are volume and strength of transverse steel respectively. In order to understand the


19

affects of lateral confinement on the behavior of the column number of confinement models

were studied few of which are presented here.

2.4.1 Confinement Models

The ability of the columns to sustain large deformations, without sufficient strength decay,

can be improved by sufficiently confining its concrete core. The previous research

(Saatcioglu, 1991) and performance of columns during past earthquakes indicate that a strong

relation exists between concrete confinement and lateral drift. Number of mathematical

models has been studied to understand affects of confinement on performance of columns.

These include EL-Dash and Ahmad (1994), Park (1982), Sheikh and Uzumeri (1980),

Mander (1988), Saatcioglu and Razvi (1992), Hoshikuma (1994) and Bousalem and Chikh

(2006).

The Sheikh and Uzumeri (1982) model assumes that effectively confined concrete area is

lesser than the actual area of concrete core. The researchers introduced an effectiveness

factor which utilizes the distribution of longitudinal reinforcement and configuration and

spacing of transverse reinforcement. The model of Sheikh and Uzumeri (1982) was modified

by Sheikh and Yeh (1982) in the same year. Park et al. (1982) modified the original model of

Sheikh and Uzumeri (1982) by incorporating the increase in concrete strength and peak strain

due to confinement. Mander et al. (1988) proposed a model based on properties of concrete.

The model gives a fractional equation to determine ascending and falling branch of stress-

strain curve of confined concrete. The configuration of lateral and longitudinal

reinforcement is taken in to account by defining an effective lateral confining stress. This

approach is similar to the one used by Sheikh and Uzumeri (1982). Saatcioglu and Razvi

(1992) presented a model which related the strength and deformability to confinement. The

efficiency of confinement was quantified through a factor *2k and later the factor was

modified to a simpler version (Razvi and Saatcioglu, 1996) and (Razvi and Saatcioglu,1999a).

Hoshikuma. et al. (1994) developed a model for bridge peers using their indigenous

experimental data. The model proposed by Park et al. and Hoshikuma et al. is found

conservative because these do not incorporate affects of configuration of longitudinal and

transverse reinforcement.


20

EL-Dash and Ahmad (1994) proposed a fractional equation in which peak stress and strain

are managed through two enhancement coefficients “A” and “B” separately. The affects of

configuration of confining and longitudinal reinforcement on strength and strain is dealt

separately by means of factors “k1” and “k2” respectively. These factors are known as

efficiency coefficient. The model considers the affect of spacing by means of a factor “m”.

The affect of spacing of longitudinal reinforcement is considered in the model through

volumetric ratio “ seρ ”. Bousalem and Chikh (2006) define the stress, strain curve for

confined concrete by ascending branch, descending branch and a sustaining branch. The

model adopts the equation proposed by Popovics (1973) for ascending branch and Bing at el.

(2001) equation is used to define the sustain branch. Bousalem model presents its own

descending branch. The model includes affects of configuration and spacing through

efficiency factor “Ks” and “Kd”.

The entire models considered above include the affects of configuration and spacing of

longitudinal and transverse reinforcement through efficiency coefficient “k”. The basic

argument used in modeling indicates that stress-strain behavior of confined concrete is

dependant on peak stress, peak strain and deteriorating rate. The predicted peak stress of

confined concrete has been found in good agreement with experimental data for all the

models. The peak stain, however, showed some variation from the experimental data. The

Bousalem model has shown improvements in estimation of peak strain.

2.5 EXPERIMENTAL PERFORMANCE OF CONFINED RC COLUMNS The overall performance of RC building structure is greatly influenced by response,

especially in post peak region, of its columns. For instance failure of a beam element may

result in a localized collapse but even a single column can result in collapse of complete

structure (Ilyas and Rizwan, 2006b). Many experimental studies of behavior of RC column

did not include post peak behavior (Mortazavi et al., 2003) and (Fam and Rizkalla, 2003).

The work carried out to study the affect of configuration of transverse reinforcement on

performance of RC columns, discusses complete behavior of the RC element. Here in the


21

literature review few of the experimental studies, including those conducted on high strength

concrete, of interest are discussed.

2.5.1 Spacing And Configuration Of Confining Reinforcement

Němeček et al (2005) cast thirty prototype specimens with square cross section of 150 mm x

150 mm and 1150 mm length. In the study four longitudinal reinforcing bars of 12 mm

diameter were provided at corners. Transverse reinforcement comprised of 6 mm diameter

bars was provided at 50 mm, 100 mm and 150 mm center to center distance in the middle

half of the column. The two quarters at ends had smaller spacing between transverse steel in

order to avoid failure in that zone. The three type of reinforcement were cast with concrete

of 30.0 ± 1.6 and 67.2 ± 3.4 Mpa strength. In this way, in total there were six types of

columns which were tested. The columns were subjected to axial load applied at 15 mm

eccentricity. The experimental results showed that all columns damaged from their mid

heights. The damage in columns with coarser arrangement at transverse steel was localized

as compared to denser arrangement. The study show that by increasing transverse

reinforcement there will be improvement in energy dissipation of the column but it will not

be directly proportional to the amount of transverse reinforcement being increased.

(a) (b)

(c)

Figure 2.3: Layout of tie configuration used by Mo and Wang (2000) Mo and Wang (2000), studied the affects of configuration of transverse reinforcement on

performance of RC columns by testing nine prototype columns under cyclic lateral and

constant axial loads. Type 3 configuration (Sheikh and Khoury, 1997) was provided in three


22

different ways in a column section of 400 mm x 400 mm. The longitudinal reinforcement

was provided as 12 bars of 20 mm diameter. The transverse reinforcement was furnished by

6.35 mm bars. In standard pattern, given in figure 2.3(a), a hoop was provided to include four

corner bars and four ties were used to engage the remaining eight bars. In second pattern,

shown in figure 2.3(b), three hoops were provided so that a larger hoop support four corners

bars and two smaller hoops included the middle longitudinal bars. The third pattern,

proposed in the study, consisted of four smaller ties. In the proposed pattern, shown in figure

2.3(c), ties supported the longitudinal bars at corners. In order to achieve same volumetric

ratios the three pattern of configuration were provided at 50 mm, 52 mm and 54 mm center to

center. It was found that for axial load of 15% and 20% the proposed technique showed

some improvement but for remaining specimen standard reinforcement governed. The failure

pattern observed during testing was almost similar for all column specimens.

(a) (b) (c) (d)

Figure 2.4: Layout of tie configuration used by Cusson and Paultre (1994)

Influence of spacing of ties on confinement had been an issue under study since late 70s. In

late 70s it was thought that circular cross section is more efficient in confinement as

compared to square section (Sheikh and Uzumeri, 1980 and Vallenas et al., 1977). Twenty

four large scale specimens were tested in 1980 (Sheikh and Uzumeri, 1980) to study the

affect of different parameters such as volume and quality of confined concrete, quantity and

spacing of longitudinal and transverse steel and configuration of later. It was concluded that

a dense cage of longitudinal and transverse steel will provide more affective confinement to

the core concrete. The numerical models as explained earlier have been suggested for

quantifying confinement of normal strength concrete. In early 90s the emphasis of studies on

confinement shifted towards high strength concrete (Bajerkeli, Itakura and Yagenji and

Nagashima et al., 1992). Later, study of Sheikh S. A. (Sheikh and Uzumeri, 1980) was


23

repeated using high strength concrete by Cusson and Paultre (1994). In the study seventy

large scale specimens, dimension greater than 200mm, were cast. The four cross section cast

with 60, 80, 100 and 120 Mpa concrete are shown in figure 2.4. The configuration shown in

figure 2.4(a) and 2.4(c) were cast with 100 Mpa concrete only. The specimens were tested in

concentric loads and load-displacement curves were plotted. On ascending branch of load

displacement curve the strain in transverse steel is 50%. At this time strain and cover is

intact. AT end of ascending branch the specimens touched their first peak of load. At this

stage cover shows separation and axial load drops by 10% to 15% and strain in transverse

steel starts to increase. This increases strength of concrete core. Again the load displacement

curve sets off on to an ascending branch. Now, if the column is well confined stress in

transverse steel will reach yielding value. The second ascending branch will end at second

peak which will be lower than first peak if confinement provided by transverse reinforcement

is lesser and vice versa. When yield stress is reached in transverse stirrup the axial load starts

falling and sudden decrease is observed at rupture. It has been observed in study that higher

concrete compressive strength and denser transverse reinforcement resulted in higher second

peak or directly indicated higher confinement.

In 1997 high strength circular and square concrete columns were tested under lateral cyclic

loads (Baingo and Saatcioglu, 1997) and (Lipien and Saatcioglu, 1997). Later (Saatcioglu

and Baingo, 1999) studied affects of concrete strength and cover, ratio and yield strength of

transverse reinforcement, level of axial force and configuration of transverse reinforcement

were studied in circular columns. The test specimens were 250 mm in diameter and 1365 mm

in height. The columns were cast with 65 Mpa and 90 Mpa concrete strength. Eight bars of

16 mm diameter with yield strength of 419 Mpa were provided as longitudinal steel.

Different volumetric ratio of transverse reinforcement varied from 1.59% to 3.67%. The

spacing of transverse reinforcement was kept as 50 mm in all specimens less one where it

was 100 mm. In order to study the affect of yield strength of transverse steel three different

yield strengths i.e. 420, 580 and 1000 Mpa were used. A concrete cover of 10 mm was

provided in all columns except for one column which had no cover. The test was performed

under lateral cyclic load and three varying level of constant axial load applied as 22%, 30%

and 43% of column capacity. The behavior of all columns was nearly similar up to yield


24

displacement observed at about 1% drift level. The deformation in all columns started as

flexure cracking appeared near the base perpendicular to the direction of loading. Near

yielding cracks started to fan out to the side faces of the columns parallel to the direction of

loading. After yielding flexure and shear stresses increased the cracks and spalling occurred.

The strength degradation in post peak region was influenced by level of axial load, strength

of concrete and yield strength, spacing and configuration of transverse reinforcement. It has

been found that higher yield strength of transverse steel gave greater deformability. The

performance of column was also improved by decreasing the spacing of transverse steel.

In above study it has been recognized that spacing and configuration of transverse

reinforcement influence the over all performance of a RC column to a great extent. The

other important parameter that can affect the performance of RC column subjected to cyclic

loading, either lateral or axial, is rate of loading.

2.5.2 Affect Of Rate Of Loading

The post peak behavior of RC columns is influenced by rate of loading. Many experimental

studies have been carried out under a constant axial and cyclic or monotonic lateral load

(Stevens et al. 1991 and Kowalsky et al., 1995). In actual situation RC columns of building

structures may be subjected to varying axial load due to vertical component of ground

acceleration. The variable axial load along with lateral base shear will affect strength,

stiffness, ductility and energy dissipation of the RC columns. The affect of axial load has

been studied experimentally in detail (Benzoni et al., 1996 and Asad and Yan, 2004) and it

has been found that both magnitude and pattern of axial load greatly influence seismic

behavior of RC columns. Later in 2005 eight large-scale and eight small scale specimens

were tested in Kyoto University by Bechtoula (2005). The specimens were subjected to

variable axial loads along with quasi static unidirectional and bi-directional displacement-

controlled horizontal loads. It has been observed in the study that axial load has lesser

influence when a structure is subjected to unidirectional lateral load. In columns subjected to

biaxial lateral loads damage is much more pronounced with variation of axial loads. For

example, under 30% axial load the strength loss in a RC column subjected to unidirectional

bending is 3% and under biaxial bending it has been observed up to 25% at same drift levels.


25

This study has summarized that there is a changeover zone between 30% and 60% axial load,

in which behavior of column changes from tensile and compressive strain to only

compressive strain under lateral loads. If a column during application of lateral loads is

subjected to only compressive strains then its response will be brittle. Therefore, it has been

suggested that 60% and higher axial loads must be dealt with caution. The variation in axial

load influenced post peak behavior more than peak response.

Figure 2.5: Representation of confinement provided by steel bolts, Cheong and Perry (1993)

2.5.3 Different Confining Arrangements

Many confinement techniques have been developed to enhance performance of RC elements

by improving their concrete strength in post peak region. Some techniques of interest are

explained in the following sections.

2.5.3.1 Orthogonal System Of Steel Bolts

Cheong and Perry (1993) proposed a technique to confine core of rectangular columns by

passing steel bolts, housed in ducts, orthogonally through the concrete and tightening their

nuts on column surface. A steel mesh may be placed all around the concrete core. It can be

observed in view AA shown in figure 2.5 that three bolts were placed in either direction. The

layers of bolts were provided at a distance of 46 mm center to center. In total eight columns

were cast in two groups of four columns each. The bolts of one group were grouted with

cement while in other these were only tightened. The columns were subjected to monotonic

and cyclic axial loads applied at low rates. The backbones or envelops of cyclic loading were

compared with those achieved from monotonic loads. The results were also compared with

available results of monotonic curves of conventionally reinforced and plain concrete


26

columns. Sinha et al. (1964) was the first one to use the concept of backbone or envelop

curves. Later Karsan I. D. et al (1969), Perry S. H. et al (1991) and Spooner D. C. et al (1985)

showed that backbone or envelop curves and monotonic load displacement curves are related

and equivalence exists. It was observed during the test that washers, attached to the bolts,

restricted expansion of concrete and transfer confining pressure to the core concrete. The

columns confined with proposed technique showed more energy dissipation and absorption

capacity.

2.5.3.2 Ferrocement Jacket

Ferrocement is being used in construction since last 50 years, Naaman (2000). The technique

was developed to retrofit shear deficient RC columns. The application is similar to wrapping

of FRP, around RC columns to improve their performance. Takiguchi and Abdullah (2001)

and Abdullah and Takiguchi (2003) used the Ferrocement jacket for shear strengthening of

RC columns for first time in laboratory. Ferrocement is a composite material available in

form of thin walls and has in plane isotropic properties in both principle directions. The

orthotropic properties, major strength in one principal direction, can be developed by using

steel wire mesh, shown in figure 2.6. ACI Committee 549 (1993) has commented that

strength and stiffness of ferrocement jacket is higher in long diagonal direction of mesh.

Kazemi M. T. et al (2003) studied the affects of ferrocement jackets by testing six short

columns in laboratory. Each specimen was 1200 mm long cast in two different section

dimensions. The central length of 400 mm was kept as 200 mm x 200 mm and a cross

section of 150 mm x 150 mm was set for 400 mm length on its either side. The dimensions

are shown in figure 2.7(a) and loading arrangement is shown in figure 2.7(b). The central

portion was used as support and 400 mm length on side was tested as short column. The 150

mm x 150 mm cross section was strengthened by 25 mm thick ferrocement jacket, as shown

in figure 2.7(c). The columns were reinforced by four longitudinal bars of 16 mm diameter

with 500 Mpa yield strength. The transverse reinforcement was in the form of 6 mm diameter

bars with 300 Mpa yield strength. Affects of thickness of wire mesh were also studied by

using 3 mm and 0.8 mm thick wire mesh. It was found that specimens with 0.8 mm thick

wire mesh achieved its nominal strength, as defined by code, but did not perform well at


27

higher displacement levels. The jacket containing 3 mm thick wire mesh performed well and

20% degradation was achieved at larger displacement and load levels.

Figure 2.6: Wire mesh used in ferrocement jacket, Kazemi . and Morshed (2005)

Figure 2.7: Layout used in testing of ferrocement jackets by Kazemi . and Morshed (2005) (a) dimensions of short columns (b) boundary conditions and load application (c) detail of

strengthening

2.5.3.3 Partially Stiffened Steel Jackets

Figure 2.8: Confinement of CFT using stiffened steel jackets proposed by Xiao Y. et al. (2003) (a) steel plate stiffener (b) angle iron stiffener (c) square pipe stiffener (Mao. and

Xiao, 2006)

The technique was developed by Xiao and Wu (2003) to retrofit existing shear deficient

columns. The basic motivation of the authors was concept of Concrete Filled Tube (CFT)

columns. The concept of CFT in its early ages was studied by Sakino and Ishibashi (1985).

(a) (b) (c)

(a) (b)

(c)


28

It has been found that response of CFT deteriorate rapidly under axial loads due to weaker

out of plane strength and stiffness of steel tube (Tomii et al., 1987). In the study four

columns were cast as CFT columns and three specimens were retrofitted in hinge zone using

proposed technique. Three type of stiffeners used in proposed technique included 3.175 mm

thick plate, 31.8 x 31.8 x 6.4 mm angle iron and 31.8 x 31.8 x 6.4 mm square pipe. The plate

was used as plate stiffener covering the complete hinge zone and three stiffener beams were

formed by angle iron and square pipe. The three methods are presented in figure 2.8(a), 2.8(b)

and 2.8(c). This technique was later developed and presented as Confined Concrete Filled

Tube column, Xiao et al. (2005). All the three methods used in proposed technique enhanced

performance of shear deficient columns and drift levels of more than 8% were achieved.

However, the steel plate stiffener was found brittle as compared to angle iron and square pipe

stiffeners.

2.6 PERFORMANCE OF RC BUILDINGS UNDER SEISMIC LOADS

Up to 1960s the emphasis was laid on strength of RC structures rather than their performance.

The seismic design of structures according to provisions of codes is under way since last

about 80 years. In early days, up to approximately 1975, it was thought that strength and

performance of a RC structure is interrelated. In late 60s and early 70s people involved in

design process realized importance of inelastic response of RC structures exposed to large

seismic events. Main concern of researchers, at that time, was to quantify inelastic

deformations of RC structures and their elements. The capacity design principles developed

by Park and Pauly (1975) are considered as basis of performance based approach in

earthquake engineering. It has been realized that distribution of strength in a structure is

more important than just increasing its strength to resist an input ground motion. It has been

found that a building structure designed by elastic design principals when subjected to severe

ground shaking undergoes unevenly distributed inelastic damage due to which the response

of the structure suffers (Leelataviwat, 1999).

Performance based approach requires that response of a structure should match the demands

to which it is subjected. The demands are referred to as structural requirements and response

level is said to be performance expectations. When these two are equated we can quantify


29

hazard and evaluate different losses which will occur if a desired performance level is not

achieved. Performance of a building structure includes both structural and non structural

damages and is quantified in terms of a limit state known as damage state or performance

limit state. Level of demand and response is defined for every limit state. A performance

limit state is said to be achieved when defined level of demand and response is matched.

Different codes define discrete limit states out of many expected damage states to be

experienced by the building structure when subjected to an anticipated level of ground

shaking. FEMA 273 (1997) and FEMA 440 (2005) defines four performance limit states for

building structure namely operational (OP), immediate occupancy (IO), life safety (LS), and

collapse prevention (CP). In OP limit state building structure suffers minimum or no damage

to both its non-structural and structural component. The structure performing at OP limit

state can be put back to function immediately after the event is over. Any minor damage to

structural or non-structural components can be repaired during operation. The damage can

be in electric or water supplies or other utilities. In IO minor damage occur in non-structural

components and no or minor damage is found in structural component. The structure can be

occupied immediately after earthquake. There can be problems of lift operation (due to

disruption of electric power or minor damage to lift operation system), telecommunication

and water supply etc. The damages which have occurred in the structure can be repaired after

occupying. In LS limit state major damage occur to both structural and non structural

components. There is no threat to life safety but structure could not be occupied without

major and properly planed repairs. In some cases it may be found that the repair of the

structure is uneconomical as compared to its expected operational value. In CP limit state the

structure suffers sever damage and is in the state of impending partial or total collapse. The

structure considerably poses threat on the life safety and cannot be repaired for reuse. The

main difference in LS and CP limit states is the level of damage to lateral force resistant

system. In terms of performance parameters OP and IO states require that structure should

undergo no or minor inelastic deformation. The designers emphasize more on reducing

inelastic deformations and ensure that structure responds in elastic range during its exposure

to design earthquake. In LS and CP the emphases is on controlling the deformations such as


30

roof displacements and inter story drifts and keeping them with in prescribed limits (Collins

et al., 1998).

2.6.1 Performance Criteria

Performance criteria have been defined by different methods and codes. FEMA 273 and 440

uses global roof drift levels of 0.7%, 2.5% and 5% for defining IO, LS and CP limit states for

RC multistory building structure. The drift levels below 0.7% can be referred to as OP limit

states. Same performance parameters are also defined in FEMA 356. Section 1617.3 of IBC

specifies that deflections and drift limits shall be governed by section 9.5.2.8 of ASCE 7

(ASCE, 2002), which limits roof drift of structures, with more than four stories, up to 2.5%.

Different researchers have given various damage indictors to quantify performance. These

performance indicators revolve around basic criteria defined by FEMA and IBC codes. Park

et al (1987) gave a damage index which is commonly known as Park and Ang model. The

damage is mathematically presented in equation 2.1. If the damage index DIPA < 0.4 then

structure is in repairable damage state and if DIPA ≥ 0.4 & ≤ 1 the structure will be in beyond

repairable damage state. The value of DIPA ≥ 1 will indicate total collapse.

m hPA

u y y u

EDIF

µ βµ δ µ

= + (2.1)

In equation 2.21:

µm = maximum ductility demand imposed by the ground motion

µu = Ultimate ductility capacity under monotonic load

Eh = Hysteretic energy dissipated

Fy = Yield strength of structure

δy = Deformation capacity at yield

β = a constant (dimensionless)

DIPA = Damage index proposed by Park and Ang.

Another approach to quantify performance is capacity spectrum approach. The capacity

spectrum approach was first developed by Freeman et al. (1975) and Freeman(1978). The

method uses base shear versus roof displacement plot or push over curve. The push over


31

curve is converted to capacity spectrum by dividing base shear with effective modal mass

and roof displacements are transformed into spectral displacements by treating them with

modal participation vector. The demand spectrum, which is basically response spectrum for

OBE, is converted to A-D format by using angular frequencies which relate spectral

displacements with spectral accelerations. Both curves are superimposed and point at which

these cut each other is identified as displacement demand. The displacement demand can be

converted to roof displacement, which can be compared with the performance criteria to

declare limit state for the building structure. The capacity spectrum method initially used

only first mode shape and assumed a fixed distribution of lateral force. Paret et al. (1996) and

Bracci et al. (1997) suggested use of higher modes for development of capacity spectrum.

Later Chopra and Goel (1999) replaced elastic design spectrum with constant-ductility

spectrum for determining demand curve. Few analysis soft wares, like IDARC2D (Sadjadi et

al., 2007), can calculate the damage indices while analyzing a building structure. Dipasquale

et al. (1987) quantified performance of a building structure through a global index using

variation in its natural time period. The index has been explained in chapter 5 in detail and

used for damage evaluation of eight story RC building.

2.6.2 Inelastic Response Inelastic response is intended in seismic design of RC structures. The inelastic behavior not

only induces economy but also achieve safety through a ductile response. Since early 70s

considerable endeavor has been made in developing the technique to design and quantify the

inelastic response in structures subjected to cyclic loading. Many models, based on

experimental studies, have been proposed to predict the inelastic response of RC building

structures. These models include those based on simple bilinear relationship and complex

fiber models utilizing hysteretic laws. First simple inelastic model has been presented by

Clough et al. (1965). Experimental observations soon exposed that Clough et al. model did

not account for cyclic deformation and cannot give accurate estimates of rotational ductility

demand. Experiments also revealed that inelastic deformation is concentrated at ends of a

beam element. Giberson (1974) proposed a model which assumed an inelastic spring at each

end of the beam element. The model consisted of single component and all properties of

hysteretic behavior could be assigned to the spring. The model assumed that all plasticity in


32

beam element could be represented by deformations of the two springs attached at ends of

the element.

Takeda et al. (1970) presented a model which consisted of tri-linear behavior. The different

parameters required to define hysteretic behavior such as unloading and reloading were

defined based on experimental data of tests of RC subassemblies carried out in a seismic

simulator in Japan. Otani (1974) presented a new approach of modeling inelasticity. He

divided a beam element in to elastic and an inelastic element. Both the elements are assumed

to act parallel to each other. The fixed end rotations are represented through an inelastic

rotational spring attached at ends of the elements. This is the first model which recognizes

the importance of fixed end rotations (Filippou et al., 1992).

The models up to 1979 only accounted for lumped plasticity. Soleimani (1979) proposed

first model which deal with spread of plasticity as a function of loading history. The spread

is considered from face of beam column joint in to the member up to a length depending on

loading history. The fixed end rotations at beam column interface are model with zero length

hinges. Banon et al. (1981) modified Takeda model to propose a moment-rotation relation

for beam elements. Pinching affect due to bond deterioration and shear was catered by

employing a nonlinear rotational spring at the ends of beam element. The pinching affect is

also modeled by Ozcebe and Saatcioglu (1989) which could simulate the stiffness

degradation observed during experiments through empirical expressions catering for affects

of axial load on hysteretic behavior.

2.6.3 Pushover Analysis After shifting to performance based approach in seismic design of structures a need was felt

to develop analysis procedures (Krawinkler and Seneviratna, 1998). The much popular

procedures include linear static, non-linear static (push over analysis), linear dynamic, and

nonlinear dynamic analysis procedures (FEMA-273, 1997). Every method has few inherent

shortcomings and cannot be used as a total solution. The linear static or linear dynamic

methods are insufficient because most of the structures are supposed to deform in the

inelastic range when subjected to earthquake ground motion. The nonlinear dynamic

analysis is computationally complex and need state of the art equipment and expertise to


33

achieve the solution. The pushover analysis procedures are getting popular because of their

simplicity and ability to estimate deformation demands of a structural system with an

acceptable accuracy. The two most popular types of push over analysis are explained below.

2.6.3.1 Conventional Pushover Analysis The static pushover procedure was firstly presented by Saiidi and Sozen (1981), and was

later used in many seismic analysis studies. In conventional push over analysis the building is

pushed through by a first mode shape forcing function so that control node, which is

normally the roof of a building structure, reaches a target displacement. Alternatively the

structure can be pushed up to a level of base shear which is expected to be achieved during a

design earthquake. The gravity loads are considered as constant during the procedure. The

target displacements are selected as desired performance levels to be achieved during a

design earthquake (Bruneau et al., 1998). The first mode shape is generally considered

critical in MDOF structures. Due to this consideration pushover analysis is restricted to low

and medium rise buildings. The element forces and system deformations are observed

continuously as the model is displaced laterally. The procedure can determine the collapse

mechanism and point out the sequence of yielding and failure of components. The ductility

and strength demands at the target displacement or target base shear are used to ensure the

acceptance of the structural design. The capacity spectrum is basic output of pushover

analysis and describes overall performance of a building. FEMA 273 also includes this

method and recommends its use for analysis of new and old structures. The procedure is

now acceptable and considered as an easy solution which could give estimate of deformation

demands with reasonable accuracy.

2.6.3.2 Modal Push Over Analysis In late 90s the limitation of conventional push over analysis to only consider first mode shape

forcing function was subjected to research (Krawinkler and Seneviratna, 1998). Most of

researchers, (Bracci et al., 1997); (Gupta and Kunnath, 2000) and (Chopra and Goel, 2002),

suggested using an adaptive forcing function which could account for higher modes by

catering for time-variant distribution of inertial forces. The procedure suggested by Chopra

and Goel (2002), known as Modal Pushover Analysis (MPA) procedure is most popular

method among all suggested.


34

The procedure carries out conventional pushover analysis procedure while using a forcing

function of selected significant mode shapes. However, first two or three modal force

distributions are considered sufficient to account for higher modes. The response of all

pushover analyses is combined using any combination rule such as square-root-of-sum-of-

squares (SRSS) rule. The MPA method is corresponding to typical response spectrum

analysis of an elastic structural system. It is assumed, for an inelastic system, that modal

response can be uncoupled such that conventional pushover analysis is still applicable for

each mode. The assumption produces small errors which are acceptable for practical

applications (Chopra and Goel, 2002). The procedure was later improved to account for P-∆

affects in each mode (Goel and Chopra, 2004). Later MPA procedure was simplified and

named as Modified Modal Pushover Analysis procedure (MMPA) (Chopra et al., 2004). In

MMPA computation of the response contributions of higher vibration modes are done by

considering the building to be linearly elastic.

2.6.4 Incremental Dynamic Analysis Performance-Based approach in earthquake engineering requires estimation of percentage of

exceeding of structural demands (e.g., peak inter storey drift ratio θmax) or a certain limit-

state capacity (e.g., global dynamic instability). Vamvatsikos and Cornell (2002) proposed a

new method that meets the requirements of performance based earthquake engineering. The

procedure is called as Incremental Dynamic Analysis (IDA), which involves performing

nonlinear dynamic analyses of the structural model under a suite of selected ground motion

records, each scaled to several intensity levels designed to force the structure all the way

from elasticity to final global dynamic instability (Vamvatsikos D. et al. 2002). The

structural response is presented by IDA curves plotted between Damage Measure (DM) and

Intensity Measure (IM). DM can be peak roof drift or inter story drift. IM is ground motion

intensity for example, peak ground acceleration or 5%-damped first-mode spectral

acceleration Sa (T1; 5%). The IDA curves summarize the distribution of demand DM for

given intensity IM. The probability of exceedance of a limit-state, such as Immediate

Occupancy or Collapse Prevention (FEMA-350, 2000a) can be defined on each IDA curve.

The output of IDA can be easily superimposed with conventional hazard curves to calculate

annual rates of exceeding of a certain limit-state capacity or a certain demand.


35

2.6.5 Capabilities And Limitations Of DRAIN-3DX DRAIN-3DX (Prakash et al., 1994) uses an incore equation solver and is suitable only for

relatively small structures. The structure is modeled as a 3D assemblage of nonlinear

elements connected at nodes. The program considers all the six degree of freedoms at each

node until restraints are defined. The structural mass is lumped at the nodes, and matrix is

diagonal. When a node is slaved to master node, its masses are transformed to equivalent

masses at the master node, and hence the mass matrix will always be diagonal. DRAIN-3DX

considers both stiffness and mass proportional damping. The complex elements can also be

modeled through compound node. With all theses modeling capabilities DRAIN-3DX can

carryout following analysis:-

(a) Linear and non linear static analysis.

(b) At the end of dynamic analysis restore to static equilibrium.

(c) Calculate mode shape or period in the initial state or any later state.

(d) Response spectrum analysis.

(e) Pushover analysis.

(f) Non Linear dynamic analysis under ground displacement history.

(g) Non linear dynamic analysis under ground acceleration history.

(h) Non linear dynamic analysis under dynamic force.

(i) Non linear dynamic analysis for nodal velocities.

Seven non linear elements are presented in element guide of DRAIN-3DX (Powell and

Campbell, 1994). The elements are capable of modeling pullout behavior of reinforced

concrete element by defining a hinge at its ends. Anderson and Townsend (1977) studied the

effect of reinforcing bar slippage in the joint by inserting a small hinge element of predefined

length between the rigid joint element and the flexible beam element. It was found that

degradation of stiffness of RC elements due to bar slippage considerably affects dynamic

response of the structure. DRAIN-3DX is capable of keeping track of bond degradation

during the analysis. The biggest drawback of DRAIN-3DX is non availability of a Graphic

User Interface, therefore, modeling is difficult and time consuming.

CHAPTER 3

36

DIGITIZATION AND ANALYSIS OF SEISMIC DATA 3.1 INTRODUCTION

In Pakistan, the instruments to record ground acceleration were first installed in June 1969 at

Tarbela to observe seismic behavior of the site of first hydropower project of the country. In

August 1972, 10 months prior to first impounding of Tarbela Dam, a seismic network of

thirteen stations was setup at Tarbela (Mahdi et al., 2005). The accelerogram used at that

time were typical analog type. A large body of ground acceleration data, including Kashmir

earthquake, is available in analog form but its use for research purposes requires colossal

efforts.

After Kashmir earthquake a need was felt to digitize the recorded data. In this chapter an

approach to convert analog ground motion records into digital form is explained. The chapter

starts with seismological background of Tarbela region and explains analog form of seismic

data. The digitizing technique is explained with the help of a portion of a analog

acclerogram recorded at Tarbela. Analog records are digitized and resulting data is compared

with available techniques. The problems encountered in developed technique are removed in

modified digitizing approach also included in this chapter. The pseudo acceleration response

spectrums generated from digitized data are discussed and design spectrum suggested for

Tarbela region is also presented. The digitizing approach is simple and easy to implement

and digitized data will be available for seismic response analysis of structures and studied of

seismic risk analysis of the region.

3.2 SEISMOLOGICAL BACKGROUND OF THE REGION Tarbela region is located in the lower-Himalayas, a part of famous collisional plate boundary

between north-south converging Indian and Eurasian plates. The region is seismically active

due to presence of faults and large water reservoir of capacity 13.7 km3. In 1983 to 1984 a

seismotectonic study of the region was carried out (Harza Engineering Company

International, 1983 & 1984) based on data of 4000 earthquakes, with magnitude between 0.5

and 5.8 on Richter scale, recorded from April 1974 till 31 January 1984. In the report

CHAPTER 3 DIGITIZATION AND ANALYSIS OF SEISMIC DATA

37

Darband and Panjal fault have been identified within 20 Km radius of Tarbela Dam site. Both

the faults display strike-slip nature.

In addition to the faults, the Reservoir Induced Seismicity is an additional source of

generating earthquakes. Mahdi et al., (2005) has studied the reservoir induced seismicity of

Tarbela site and concluded that reservoir has modulated the seismicity of Tarbela zone with

in a radius and depth of 20 Km. The Harza Engineering Company International (1984) in

their work estimated the risk of exceedance of seismic acceleration, given in table 3.1, at

Tarbela site due to the combined affect of Darband and Panjal fault along with varying levels

of reservoir. The report (Harza Engineering Company International, 1984) concluded that

though presence of the water reservoir has a great influence on siesmicity of the region but

still Darband fault, by virtue of its proximity to Tarbela, contribute more to the probabilities

of exceedance for all water levels and Panjal fault dominated during water levels above 455

m. According to report of National Engineering Services Pakistan (Pvt) Limited (1995) the

Darband fault is capable of producing magnitude 6.5 earthquake in immediate vicinity of

Dam site, while Panjal fault is considered capable of producing a magnitude 7.5 earthquake

at a distance of about 12 Km from the Dam site.

Table 3.1 Risk of exceedance of seismic acceleration at Tarbela site, combined sources

Acceleration at site (g)

Annual Probability (combined)

Return Period (years)

Probability of exceedance in 100 years (%)

0.15 0.310303 3.2 100 0.2 0.0877 11.4 100

0.25 0.027316 36.6 93.5 0.3 0.009562 105 61.6

0.35 0.003993 250 32.9 0.4 0.001881 532 17.1

0.45 0.000903 1108 8.6 0.5 0.000431 2320 4.2

3.3 ANALOG FORM OF RECORDED ACCELERATION

Typical output of analog accelerograms is in the form of 70 mm film negative as shown in

figure 3.1. The basic idea behind such data is that human eye is a good interpreter and can

recognize distribution of peaks easily. It cannot quantify but it can certainly give an idea of

relative difference in peaks occurring in a component of a record. The PGA reported by


38

analog accelerograms of earthquakes and study of associated damage give information of

nature of earthquake. Information like velocity, displacement and frequency content cannot

be extracted from such records with out digitizing.

The accelerograms are triggered with more rapidly arriving longitudinal P-waves, thus

allowing for recording of complete sequence of the shear waves. The time on the film is

recorded as two-pulse-per-second (2PPS) by an internal time marker, which has been

calibrated to an accuracy of 0.2% so that non-uniformities in the recording speed can be

corrected (Hudson, 1979). After every half second the time marker marks the small dash as

Figure 3.1: Typical form of analog accelerogram recorded at Tarbela on 20 Feb, 1996

Figure 3.2: Trace of east-west and vertical component of ground acceleration recorded at

Tarbela in 1972. shown in figure 3.1. Thus two consecutive long dashes, as marked in figure 3.1, are equal to

one second. Three components of acceleration i.e. longitudinal, vertical and transverse are


39

recorded separately on a single film. The three components of acceleration, separated by

straight lines, are marked in figure 3.1. The acceleration record presented in figure 3.1 was

recorded on 20 February 1996 at Tarbela. The dynamic transducers of each instrument have

their own calibration, known as sensitivity, in terms of g. The sensitivity is measured in terms

of mm and traces of ground acceleration are drawn in accordance with respective sensitivity.

The sensitivities of the components of the record (figure 3.1) are given in table 3.2. The other

record which is presented in figure 3.2 was recorded in 1972 to observe the seismic behavior

of the project site prior to first impounding. The earthquake was recorded by SMAC B-2

strong motion recorder which recorded the acceleration on wax paper. In order to preserve,

these records were photographically converted to metallic sheet. Further the records were

converted into a film negative which was then converted to paper. The sensitivity of the

record is 80 mm/g. In the analog records, such as shown in figure 3.1, problems like

thickening of traces near peaks, break in recording of component, missing time marker, break

in time recording and darkening of record due to improper developing can occur. These

problems need special attention during digitization.

Table 3.2 Sensitivity of analog accelerogram recorded at Tarbela on 20 Feb 1996. S/No Component Sensitivity

1 Longitudinal 19.4 mm/g 2 Vertical 19.3 mm/g 3 Transverse 18.9 mm/g

3.4 DIGITIZING APPROACH

The film record is scanned by a 600 dpi optical resolution scanner and the record is saved as

a grayscale image. In most of the digitizing approaches use of binary images is not

recommended because these require extensive effort for correct digitization. Due to only two

colors it has problems of contrast and it is difficult to maintain accuracy near peaks

(Todorovska and Trifunac, 1997). When image is converted to binary image there is also a

risk of loss of information but this aspect can be looked after by using a suitable thresholding

level. A comprehensive review of the sixteen ground motion records selected for digitization

revealed that in most of the cases the noise can be minimized by converting the records to

binary images at some appropriate threshold level. In order to ensure that no information is


40

lost during the threshholding it was decided to compare the binary image, converted at

selected threshold level, with the original in an image editor. If there is some noticeable

dissimilarity, due to some noise, the original image is again converted to binary image at a

new threshold level after manual treatment. The decision to work with binary images was

done because these reduces or eliminates problems arising due to optical density and

thickening of traces near peaks (Trifunac et al., 1999).

Figure 3.3. Accelerogram recorded at Tarbela on 20 Feb, 1996 after applying thresholding T=0.5.

Figure 3.4. Accelerogram recorded at Tarbela on 20 Feb, 1996 after thresholding at 0.5 and

removing the remaining noise manually.

Figure 3.5. Accelerogram recorded at Tarbela on 8th August 1996.

Figure 9 (a)


41

(a) (b) (c)

Figure 3.6. Portion of the record of ground acceleration recorded at Tarbela on 8th August 1996: (a) original analog record (b) binary image of the record at threshold level of 0.45 (c) binary image of the record at threshold level of 0.45, after manually removing noise in the

vicinity of the longitudinal trace.

The record of figure 3.1 was converted to binary image at threshold level of T=0.5, where 0 ≤

T ≤ 1 (0=black pixel and 1 = white pixel). Therefore, all pixels with T≤0.5 were converted to

white and other to black. The record of figure 3.1 after applying threshold T=0.5 is shown in

figure 3.3. The remaining black pixels, other then the acceleration traces and time scale, are

referred to as noise in back ground of the record. In the proposed technique only two end

points of one sec or 2PPS time scale are preserved and rest of the time scale is removed

manually along with the noise of the back ground (Rizwan et al., 2007). Generation of the

time scale will be explained later in this chapter. The noise can either be removed in original

image or in the binary image. In the later case the acceleration traces of three components of

earthquakes should be clear. In case of any affects of thresholding or errors, which may

occur during recording or developing of recorded film, the record can be adjusted

interactively. For example, in figure 3.3 there is a break at the start of each component of

acceleration trace and the bottom time marker has missed to mark the time scale. Both these

problems were treated interactively in an image editor and the final image is shown in figure

3.4. It can be observed in figure 3.4 that separating lines between the components are

removed manually along the remaining noise. The end points of one sec time scale (figure

3.4) have been shifted below the transverse component and enclosed in small squares for

clarification. The time scale can also be adjusted at top but in present study it has been kept

at bottom.


42

There can be a situation when the acceleration trace exists within the noise left after

threshholding. Such noise, near the vicinity of the trace, is removed manually and the

selected threshold level is applied again to remove the rest of the noise. This is explained in

figure 3.6 with the help of a portion of the accelerogram recorded at Tarbela on 8th August

1996 shown in figure 3.5. The image shown in 3.6(a) is converted to binary at threshold

T=0.45, where 0 ≤ T ≤ 1, and the resulting image is shown in figure 3.6(b). All pixels with T

≤ 0.45 would be converted to white and other to black. The selected threshold level could not

clear the noise completely and a portion of the trace is entwined in the left over noise. The

affected portion of the longitudinal trace is freed from the noise manually in the original

image and it is again converted to binary image at same threshold level. In the resulting

image shown in figure 3.6(c) the rest of the noise in the background of the longitudinal trace

can be removed. While clearing noise near acceleration trace it should be compared with

original record so that no information is lost in thresolding.

Figure 3.7. Portion of the record of ground acceleration recorded on 20 February, 1996 in Tarbela to highlight the summation of rows of pixel in the binary image of the records.

In order to explain the technique and clarify different terms used in it a portion of the

transverse component of 20 Feb 1996 record will be used. The selected portion is marked in

figure 3.4 and shown in figure 3.8(a). The final image of figure 3.4 is read as input record by

the algorithm. In binary images, as a standard practice, zero value is assigned to black pixels

(0-black(0)) and one to white pixels (1-white(255)). However, inversely value one can be

assigned to black and zero to every white pixel. Each row of the image is read by the

algorithm and summed.

Sum = 0Sum > 0

Sum > 0Sum = 0


43

(a) (b) (c)

(d) (e)

(f) Figure 3.8. Portion of the record of ground acceleration recorded on 20 February, 1996 in Tarbela: (a) the binary image (b) all points marked at a constant interval of 1/49 sec (c) indication of points where center line is changing slope (d) maximal and minimal points marked (e) plateau are marked to indicate duplication of the acceleration (f) points are

marked after removing duplication of acceleration

This is highlighted in figure 3.7 in which horizontal lines are drawn to indicate the rows of

the pixels. The lines are just marked to explain the technique and do not represent the actual

width of rows of pixels on the image. In figure 3.7 sum of rows, which contain only white

pixels is zero and those which also contain black along with white pixels is greater than zero.

In this way sum of every such row which constitute the acceleration trace will be greater than

zero. The location and continuity of rows, with sum greater than zero, is checked to group all

Local Maxima

Local Minima


44

the connected pixels. As a result, three components of the acceleration are separated.

Normally flat-bed scanners are 300 mm in length and any record with length greater than 300

mm cannot be scanned completely at one time. Such record is scanned in portions and after

separating the three components of acceleration the record is concatenated. Preferably, before

scanning, a thin line can be drawn along the width of the record to exactly identify the

boundaries of the portions in an image editor. The end and start of every portion of the record

to be concatenated is examined in the image editor to ascertain that no information has been

lost while scanning the record in portions. The length of one second can be marked only on

first portion of the record being concatenated. The length of each portion of long record is

measured in terms of pixels and time scale is adjusted as running time.

Each separated component is converted to a single pixel thick line by taking mean of

thickness of the trace. The line (figure 3.8(b)) at the center represents the single pixel line

that has been drawn by taking mean of the trace thickness all along its length. The end points

of one second time scale are picked up and the algorithm calculate its length in terms of

pixels. The horizontal scale (time) of rest of the record is adjusted according to the pixel

value of one sec scale. The pixel value of 1g is calculated from the sensitivity (table 3.2) of

the record. Number of pixels in one mm is calculated from width of the image. From

sensitivity of each component of the record number of pixel in 1g and value of one pixel in

terms of “g” is calculated. For example, one second of time scale of the image shown in

figure 3.4 is equal to 49 pixels and 1 g, calculated from the sensitivity of the longitudinal

component, is equal to 113 pixels. The vertical scale for longitudinal component of this

record will be used as one pixel equal to 1/113 g. Similarly, vertical scale of the other two

components of the record shown in figure 3.4 can be adjusted using their respective

sensitivities. The algorithm reads the center line of each component of recorded acceleration

from left to right and saves the first point, where slope of center line of the trace is changing,

as start of ground motion or 0 sec on the time scale. This allows synchronization of the three

components of the record. After saving the initial points, the algorithm traverses rest of the

trace and saves every point where the trace is changing slope. In figure 3.8(c) all such points

where slope of the center is changing have been marked. From the saved data the algorithm

extracts maximal and minimal points, which are the peaks of the curve in positive and


45

negative range of acceleration respectively. The local maximal and minimal points, located in

between the peak points, are also extracted along with the maximal and minimal points. The

peak points are located where previously positive slope changes to negative and vice versa.

The local maximal and minimal points are located on positive or negative slope i.e the slope

previously positive is still positive after the local maxima point and inverse is true for local

minima. In figure 3.8(d) maximal and minimal points, including local maxima and minima,

are marked. For clarification the maximal points are enclosed in circles and minimal points in

squares. The local maxima and minima points are also highlighted in the figure. The

maximal and minimal points could also be extracted directly from the traces. However, in

this approach these points are extracted after locating points where slope of the trace is

changing because it allows synchronization of the time scale and ensures that none of the

peak point is missed.

The mean of the trace thickness may result in some plateaus located in the center line of the

trace. The plateaus occur because of thickening of traces due to problems in developing.

These plateaus can be located at peak points or at local maxima or minima points. In figure

3.8(e) plateaus of peak points are marked with circles and those occurring at local maximal

and minimal points are marked with squares. Only two corner points of the plateaus are

saved while extracting maximal and minimal points. It can be observed in figure 3.8(e) that

the two corners of the plateau give same value of the acceleration at consecutive time

interval. This duplication of acceleration is removed by saving one point out of the two

corner points of the plateau. The final points saved for drawing digitized curve are marked in

figure 3.8(f). The location of these final points is calculated in terms of pixel for both

vertical and horizontal scale. The vertical pixel value of each point is multiplied with the

vertical scale set in terms of pixel to get acceleration value and pixel value of 1 sec or 2PPS

scale is used to determine the corresponding time value.

A long side of the record is aligned with the longitudinal axis of the scanner to achieve its

perfectly horizontal image, however, some error may occur in aligning the record. The traces

and time scale in the image, achieved from scanning of a misaligned record, will not be

exactly horizontal. The rotation may be minute but still it affects the resultant digitized data

(Trifunac et al., 1999). The algorithm removes any affects of rotation by intelligently fitting


46

straight line between start and end points. In figure 3.8(b) the points marked on the center

line of the trace are at equal interval along time axis. These points are at a time interval of

1/49 sec, where “49” is the pixel value of 1 sec time scale as calculated for the record of

figure 3.4 from which figure 3.8 has been extracted. The reader can appreciate from figure

3.8(b) that there are many points that are neither maximum nor minimum along the trace and

are just located on the slope of the trace. Such points does not furnish any useful

information, therefore, the algorithm discard such points and save only maximal and minimal

points as are marked in figure 3.8(f). The corresponding time scale of these points may not be

constant, therefore, time for every acceleration value is saved along with its corresponding

time to plot digitized acceleration curves.

3.4.1 Steps Of Algorithm used in Proposed Technique

• Scan the recorded film and save in its original grayscale format.

• Convert the image into binary by thresholding.

• Remove the noise, left over after thresholding, manually.

• Locate the curves by checking the continuity of the pixels.

• Reduce the thickness of the trace to single pixel by taking its mean.

• Concatenate the record (if required).

• Eliminate the rotational error, occurring due to misalignment of the image during

scanning, by fitting straight line.

• Locate all points where slope of the center line of each trace is changing.

• Extract maxima and minima points (including local maxima and minima) from the

points located in above step.

• Represent acceleration and time scale in pixel value.

• Remove local maximal and minimal points.

• Remove any duplication of time histories at consecutive time instances.

• From the data of the points saved and the representation of the acceleration and time

scales, plot the digitized time histories.


47

3.4.2 Digitized Data

The absolute PGA values of selected components of some of the digitized earthquakes along

with their date of occurrence are compared with values of original analog records in table

3.3. The digitized time history of east-west component of earthquake recorded in 1972,

transverse component of 20 February 1996 earthquake and Kashmir earthquake are presented

in figures 3.9 to 3.10. The pseudo-acceleration response spectrums of these digitized

components are plotted in figure 3.11 to 3.12.

Table 3.3 Comparison of PGA values of digitized time histories versus analog records

S/No Date of Occurrence

Digitized Absolute PGA (g)

Analog PGA (g)

Component

1. 1972 0.23 0.23 East-West 2. 20 May 1992 0.0609 0.058 Longitudinal 3. 20 Feb 1996 0.155 0.15 Transverse 4. 08 August 1996 0.091743 0.0886 -do- 5. 08 Nov 1999 0.05357 0.054 -do- 6. 25 Feb 2001 0.05454 0.052 -do- 7. 3 Mar 2002 0.0619 0.06 Longitudinal 8. 8 October 2005 0.11039 0.11 Transverse* * Main shock of Kashmir earthquake recorded at Tarbela 62 Km South-

West of the epicenter.

(a) (b) Figure 3.9. Digitized time histories of Tarbela (a) east-west component of earthquake recorded in 1972 (b) transverse component of earthquake recorded on 20 Feb 1996

The resultant of the Kashmir earthquake calculated from the analog record of the main shock

is 0.136 g occurring at 26.6 sec and same has been achieved from digitized time history at

same time incident. According to the record the resultant of 1972 earthquake is 0.25 g and

that calculated from digitized data is 0.2353 g. The time scale, for comparison, was marked

as zero at the same point on the analog scale which has been identified as start of the ground

-0.30-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.25

0.00 5.00 10.00 15.00 20.00

Time (Secs)

Acc

eler

atio

n (g

)

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00Acc

eler

atio

n (g

)

Time (Secs)


48

motion in the digitized record and no difference in the two scales has been found. The

Response spectra for Tarbela dominates in short period range i.e below 1 sec.

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.00 20.00 40.00 60.00 80.00 100.00 120.00A

ccel

erat

ion

(g)

Time (Secs)

Figure 3.10. Digitized time history of transverse component of Kashmir earthquake recorded at Tarbela on 8th October, 2005.

(a) (b)

Figure 3.11. Acceleration response spectrum derived from digitized time history of earthquakes recorded at Tarbela (a) earthquake of 1972 (b) transverse component of

earthquake of 20 Feb 1996.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.5 1 1.5 2 2.5

A =

max

(u(t

)) x

ω

n2

Time Period (Secs) Figure 3.12. Acceleration response spectrum derived from digitized time history of

transverse component of Kashmir earthquake recorded at Tarbela on 8th October, 2005.

00.10.20.30.40.50.60.70.80.9

1

0 0.5 1 1.5 2

A =

max

(u(t

)) x

ω

n2

Time Period (Secs)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2

A =

max

(u(t)

) x

ω n

2

Time Period (Secs)


49

Figure 3.13. Portion of the analog record of ground acceleration of 1972 earthquake

Figure 3.14. Curve extracted by algorithm from portion of the analog record of ground

acceleration of 1972 earthquake

Figure 3.15. Center line of the curve, extracted by algorithm from portion of the analog record of ground acceleration of 1972 earthquake, is marked

Zoom 1

Zoom 1


50

Figure 3.16. Slope variation of center line of the curve, extracted by algorithm from portion

of the analog record of ground acceleration of 1972 earthquake, is marked

Figure 3.17. Maximal and minimal points of the center line of the curve, extracted by

algorithm from portion of record of ground acceleration of 1972 earthquake, are marked

Figure 3.18. Final points, after removing duplication of the acceleration values from maximal

and minimal points extracted from portion record of 1972 earthquake, are marked.

Zoom 2

Zoom 3

Zoom 3

Zoom 2

Zoom 4

Zoom 4


51

3.4.3 Comparison Of Results Of Digitizing Approach

To compare the results of the proposed algorithm it is applied on a portion of east-west

component of the earthquake recorded in 1972 (figure 3.2). Different steps of digitizinf

technique are explained in figures 3.13 to 3.18. It can be observed from figure 3.18 that

sufficient information is stored for plotting digitized ground acceleration. The technique,

through out its application, extract data from center line of the trace. Final points, used in

plotting digitized time history, are also located on the center line of the analog trace. In figure

3.14 to 3.18 zoom of initial part of a portion of the record is also given for comparison.

The second comparison is carried out with accelerogram of Northridge aftershock recorded

on 20 March, 1994 at Sylmar Converter Station. This portion is beginning of the record and

has been taken from work of Trifunac et al (1999). The originally scanned image is shown in

figure 3.19(a), however, for comparison only the vertical component was selected. There

was no data of the original analog record available, therefore, the parameters i.e sensitivity of

the vertical component and the time scale were regenerated from the acceleration and time

scales shown in figure 3.19(a). The sensitivity of the component has been worked out to be

114 mm equal to 1g and two points of 0.1 sec time scale were preserved. The reader can

appreciate from figure 3.19(b) that the record has been processed in its original form and

during editing phase only the comparison carried out by Trifunac et al. (1999) in their work

has been removed from back ground of the traces. The points where slope of the center line is

changeing have been marked, along with the line itself, in figure 3.19(b). It can be seen in

figure 3.19(a) that the thickness of the vertical component is changing continuously and

irregularly at the beginning of the trace. Therefore, the slope of the center, which is the mean

of the line thickness, is also changing continuously (figure 3.19(b)). The first point where the

slope change has occurred has been saved as initialization of the component at time zero.

Though the problem can be easily resolved during editing of the original record or it can be

removed from the digitized data but here it is presented in its original form for comparison.

The digitized trace is given in figure 3.20. The seven points marked on the digitized trace are

compared in table 3.4 with values of same points calculated manually from the original

image of the record. The manual calculation of the original image were done by first drawing


52

mean line of the trace and then measuring acceleration values in mm, which were converted

in terms of g by applying sensitivity value given above.

(a) (b)

Figure 3.19: Beginning of the accelerogram of the 20 March, 1994, Northridge aftershock at Sylmar Converter Station, Valve Group 7 (Trifunac et al 1999): (a) Originally scanned image

from the reference and (b) Processed vertical component of the record.

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.1 0.2 0.3 0.4 0.5 0.6

Acc

eler

atio

n (g

)

Time (Secs) Figure 3.20: Digital out put of the vertical component of beginning of the accelerogram of

the 20 March, 1994, Northridge aftershock at Sylmar Converter Station, Valve Gp 7 Trifunac et al (1999).

1

2

3

4

5

6

7


53

Table 3.4 Comparison of acceleration values of beginning of the accelerogram of the 20 March, 1994, Northridge aftershock at Sylmar Converter Station, at points marked in figure 3.14.

Points Analog (g) Digitized (g) 1 0.035 0.037037 2 -0.0438 -0.04152 3 0.0526 0.05499 4 -0.04175 -0.0404 5 0.05965 0.0606 6 -0.06228 -0.06397 7 0.05438 0.053872

Figure 3.21. Portion of analog record of Kashmir earthquake recorded at Tarbela Pakistan on 8th October 2005

3.5 MODIFIED DIGITIZING APPROACH

Close observation of data, digitized by previously developed technique (Rizwan et al., 2007),

revealed some problems in records whose length was more than effective length of scanner.

The long records were scanned in pieces and concatenated during digitizing. The rotational

affects were removed by fitting straight line but at concatenating points misalignments of

some records were found. A thorough inspection of originally scanned long records revealed

that rotational error may be very complex. For every piece of long record, scanned

separately, the rotational error is varying. Therefore misalignment will result and problem is

further aggravated when concatenated acceleration traces are converted to single pixel thin

line because mean lines of two portions of a record, which are already misaligned may not

join at all. Rotational affects of a long record, which is constituted by number of misaligned

portion of images scanned separately, cannot be removed by merely fitting straight line. The

Longitudinal

Vertical

TransverseTime


54

modified approach (Rizwan et al., 2008) uses distance between the time scale and

acceleration trace to locate zero acceleration line. The rotational problems are eliminated by

using orientation or alignment of time scale.

In the modified digitizing technique, time scale is identified by preserving three points at

same location where the scale actually exists on analog record. Two points are preserved at

ends of one sec or 2PPS time scale and a third point is preserved between the end points. In

this way actual orientation of time scale can be preserved. Rest of the time scale is removed

manually along with noise. The accelerogram shown in figure 3.21 is the record of Kashmir

earthquake recorded at Tarbela. The sensitivity of the record is given in table 3.5. The record

is converted to binary image at thresholding value of 0.42. Three points of the time scale of

the record of figure 3.21 are closed in squares for clarity in figure 3.22.

Figure 3.22 - Appearance of Fig. 16 after thresholding at 0.42 and manually removing noise

Table 3.5 Sensitivity of analog accelerogram recorded at Tarbela on 08 October 2005 S/No Component Sensitivity

1 Longitudinal 19.6 mm/g 2 Vertical 20.0 mm/g 3 Transverse 19.4 mm/g

Like previous approach the final image of figure 3.22 is read as input. Three components of

acceleration are separated and converted to a thin line of single pixel thickness. Two end

points, out of the three points of time scale preserved in the image editor and shown in figure

3.22, are used to generate a line along the time scale of the record. This line is known as time

scale line. The middle point out of the three points of time scale can exists close to first or

last point. The distance between middle and first or last point is equal to 1 sec and is used to


55

calculate 1 sec in terms of pixel distance. In the record of figure 3.22, 1 sec = 67 pixels. The

straight line at start of each component of every record, which is marked by recorder between

triggering and actual recording of earthquake acceleration, represent the location of zero

acceleration line. The perpendicular distance between time scale line and zero acceleration

line is noted for all components and preserved. The time scale and zero acceleration line have

same orientation as that of the scanned record. Therefore, even if there is any rotation in the

alignment of the record, zero acceleration and time scale lines of each component of the

record will remain parallel. The zero acceleration line serves as a reference for calculating

acceleration values measured perpendicularly to the line. In this way, affects of rotation are

removed. The zero acceleration line for each component is an offset to time scale line drawn

at a distance, which has been preserved for each component. Time scale line is generated for

every piece of record to be concatenated. The distance of zero acceleration line from time

scale line, in any subsequent piece of record to be concatenated, is calculated in proportion of

difference in widths of first and every subsequent scanned piece of the record. In subsequent

pieces, to be concatenated, zero acceleration lines are offsets to respective time scale lines

drawn at the calculated distance. The use of orientation of time scale line to draw zero

acceleration line removes rotational affects for both long and short length records. The results

of modified digitizing technique are compared with previous approach in figure 3.23, where

longitudinal component of Kashmir earthquake recorded at Tarbela on 8 October 2005 is

presented after digitizing by old and modified technique. The reader can fairly appreciate the

efficiency of the modified approach.

-0.1

-0.05

0

0.05

0.1

0 20 40 60 80 100 120 140 160

Time (Sec)

Acc

eler

atio

n (g

)

-0.1

-0.05

0

0.05

0.1

0 20 40 60 80 100 120 140 160

Time (Secs)

Acc

eler

atio

n (g

)

(a) (b)

Figure 3.23: Digitized time history of longitudinal component of Kashmir earthquake (a) original digitizing approach (b) modified digitizing approach


56

3.5.1 Steps Of Modified Digitizing Approach

The algorithm used for modified digitizing approach is listed below. The steps of original

digitizing approach, explained above, which have been used in modified approach are also

included so that reader can view the difference between the two algorithms.

• Scan the recorded film and save in its original grayscale format.

• Convert the image into binary by thresholding.

• Manually remove the left over noise after thresholding.

• Locate the curves by checking the continuity of the pixels.

• Reduce thickness of the trace to single pixel by taking its mean.

• Generate time scale line for each portion of record and zero acceleration line for each

component.

• Measure distance between time scale and zero acceleration line.

• Concatenate the record (if required).

• Locate all the points where slope of center line of each trace is changing.

• Extract the maxima and minima points (including local maxima and minima) from the

points highlighted in the previous step.

• Represent the acceleration and time scale in pixel value. The pixel value of acceleration

is measured perpendicularly from zero acceleration line.

• Remove any duplication of time histories at consecutive time instances.

• From data of points and representation of the acceleration and time scales, plot the

digitized time histories.

3.6 DESIGN SPECTRUMS

Two elastic design spectrums are derived for different level of PGA scaling carried out based

on risk analysis studies of the region (Harza Engineering Company International, 1984) and

review of available data of earthquakes. Professor H. Bolton Seed (National Engineering

Services Pakistan (Pvt) Limited,1995) recommended an accelerogram of Pacoima Dam

record modified to a PGA of 0.65 g to represent ground acceleration of expected earthquake

at Darband fault. Although, table 3.1 indicates a PGA value of 0.5 g with a probability of


57

exceedance of 4.2% but due to recommendation of Professor Bolton Seed one design

spectrum has been derived by carrying out PGA scaling up to 0.65 g. A close review of table

3.1 indicates that from all aspects, i.e probability of exceedance, return period and

acceleration at site, the PGA value of 0.25 g appears to be most appropriate, therefore, other

level of PGA scaling has been selected as 0.25 g. The PGA value of 0.25 g is also the

maximum resultant ground acceleration so far recorded at Tarbela. The selected earthquakes

for deriving the design spectrums are listed in table 3.6. The scaling of all components is

also listed for both levels of PGA. Some of the digitized time histories of earthquakes with

considerable PGA value are given in figure 3.24 to 3.28.

Table 3.6 PGA scaling factors of selected earthquakes to drive design spectrums Longitudinal Transverse

Date of Occurrence PGA 0.65 Scaling 0.25 Scaling PGA 0.65

Scaling 0.25

Scaling 17 April 72 0.134 4.85 1.86 0.23 2.82 1.08 20 May 92 0.05652 11.5 4.42 0.0491 13.24 5.09

9 August 93 0.0174 37.35 14.36 0.02678 24.27 9.33 4 September 93 0.02174 29.9 11.5 0.03125 20.8 8

18 September 93 0.026 25 9.61 0.02139 30.3 11.7 18 October 95 0.01293 50.27 19.33 0.0219 29.68 11.41 20 February 96 0.04867 13.35 5.13 0.154 4.22 1.62

8 August 96 0.02155 30.16 11.6 0.03508 18.53 7.12 8 November 99 0.03478 18.7 7.18 0.0491 13.23 5.1 25 February 01 0.03982 16.32 6.27 0.04545 14.3 5.5

3 March 02 0.05752 11.3 4.34 0.03636 17.87 6.87 8 October 05 0.07742 8.4 3.23 0.126 5.1 1.98

-0.15-0.1

-0.050

0.050.1

0.15

0 5 10 15 20

Time (Secs)

Acc

eler

atio

n (g

)

-0.25-0.15-0.050.050.150.25

0 5 10 15

Time (Secs)

Acc

eler

atio

n (g

)

(a) (b) Figure 3.24: Digitized ground acceleration recorded at Tarbela on 17 April 72 (a) north-south

component (b) east-west component


58

-0.08

-0.04

0

0.04

0.08

0 5 10 15

Time (Secs)

Acc

eler

atio

n (g

)

-0.06-0.04-0.02

00.020.040.06

0 5 10 15

Time (Secs)

Acc

eler

atio

n (g

)

(a) (b) Figure 3.25: Digitized ground acceleration recorded at Tarbela on 20 May 92 (a) longitudinal

component (b) transverse component

-0.1

-0.05

0

0.05

0 2 4 6 8 10 12 14 16

Time (Secs)Acc

eler

atio

n (g

)

-0.1

0

0.1

0.2

0 5 10 15

Time (Secs)Acc

eler

atio

n (g

)(a) (b)

Figure 3.26: Digitized ground acceleration recorded at Tarbela on 20 February 92 (a) longitudinal component (b) transverse component

-0.1

-0.05

0

0.05

0.1

0 10 20 30 40 50 60

Time (Secs)Acc

eler

atio

n (g

)

-0.04

-0.02

0

0.02

0.04

0 10 20 30 40 50 60

Time (Sec)

Acc

eler

atio

n (g

)

(a) (b)

Figure 3.27: Digitized ground acceleration recorded at Tarbela on 3 March 02 (a) longitudinal component (b) transverse component

-0.1

-0.05

0

0.05

0.1

0 20 40 60 80 100 120 140 160

Time (Secs)

Acc

eler

atio

n (g

)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 20 40 60 80 100 120 140 160

Time (Secs)

Acc

eler

atio

n (g

)

(a) (b) Figure 3.28: Digitized ground acceleration recorded at Tarbela on 8 October 05 (a)

longitudinal component (b) transverse component

The elastic design spectrum in the present study is generated using Housner’s approach

Cheng (2001). In this approach elastic spectrums of selected earthquakes are generated,

normalized, averaged and smoothened to give elastic design spectrums. The design


59

spectrums given in figure 3.29 and 3.30 are similar in shape and only differ in amplitudes of

respective spectral ordinates. The time histories of longitudinal and transverse components of

twelve selected earthquakes are scaled to PGA value of 0.65g and 0.25g. For each level of

scaling twenty four response spectrums are derived. The resultant response spectrums are

averaged and smoothened to produce two design spectrums. The design spectrums indicate

that peak response occur at Tn = 0.5 secs for damping ξ = 0.0%. The curves get flattened and

smoothened with increase in damping and peak responses occur between Tn = 0.5 & 0.6 secs

for higher damping values. However, the maximum effective range for the design spectrum

occurs in short and intermediate time period range (0.2≤ Tn≤ 0.8 secs) for all percentages of

damping. A 20% increase in damping i.e 0 to 2%, decreases the response by approximately

48%. While an increase of 300% in damping from 10 to 40% caused a decrease of only 36%

in values of spectral ordinates. After approximately a time period of 0.6 secs the design

spectrum, for all ranges of damping, descends with mild slope with increase in damping

percentage.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time Period (Secs)

ξ = 0.0

ξ = 0.02

ξ = 0.05

ξ = 0.1

ξ = 0.4

Acc

eler

atio

n (A

= D

*

ω n2 )

Figure 3.29: Elastic design spectrum (ξ = 0, 2, 5, 10 and 40%) derived, after PGA scaling to

0.65 g, from record of twelve selected earthquakes listed in table 3.3 The mean response spectrum, irrespective of the type of soil, location and magnitude, is

plotted in figure 3.31. The frequency content of the earthquakes recorded at Tarbela site

exists in short (0.2 < Tn ≤ 0.5 secs) and intermediate (0.5 < Tn ≤ 0.8 secs) time period range.

However, for longer period (3 < Tn < 5 secs) range the amplifications are less. Therefore, the

data indicates that the strong ground motions that occurred at Tarbela, since 1972 have high

frequency content. The amplification of systems with 5% damping is approximately double


60

in the range of 2 and 5 CPS and after that it has an almost smooth descend, as shown in

figure 3.32. Amplification has been found higher for damping values lower than 5%.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time Period (Secs)

ξ = 0.0

ξ = 0.02

ξ = 0.05

ξ = 0.1

ξ = 0.4

Acc

eler

atio

n (A

= D

*

ω n2 )

Figure 3.30: Elastic design spectrum (ξ = 0, 2, 5, 10 and 40%) derived, after PGA scaling to

0.25 g, from record of twelve selected earthquakes listed in table 3.3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time Period (Secs)

ξ = 0.0

ξ = 0.02

ξ = 0.05

ξ = 0.1

ξ = 0.4

Acc

eler

atio

n (A

= D

*

ω n2 )

Figure 3.31: Elastic mean response spectrum (ξ = 0, 2, 5, 10 and 40%) derived from 24

components of twelve selected earthquakes recorded at Tabela, Pakistan.

3.7 LIMITATIONS

• The thickness near peaks increases towards inner side of the acceleration traces,

therefore, the mean of the thickness will result in lower acceleration values. This

problem can be reduced by selecting points from the outer edges of the trace instead of


61

the mean line, however, this procedure will result in higher values thus a balance is

required to be maintained.

• If noise of back ground is higher and involve more of manual clearing it will be time

consuming.

• Start of analog image require careful editing because a continuous and irregular change

in thickness of the beginning of trace will result in change of slope of the center line,

which will result in a false start of time scale.

• There can be a possibility that two ground motions are recorded on one tape. In such

situation it will be difficult to identify zero acceleration line at start of second and

subsequent records. This situation may result in false start of time scale. However, a

zero acceleration line of even two pixels can serve the purpose. Such records must be

dealt with caution.

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Frequency (CPS)

ξ = 0.0

ξ = 0.02

ξ = 0.05

ξ = 0.1

ξ = 0.4

Am

plifi

catio

n

Figure 3.32: Spectrum of amplification (ξ = 0, 2, 5, 10 and 40%) derived from 24

components of twelve selected earthquakes recorded at Tabela, Pakista

CHAPTER 4

62

PERFORMANCE OF CONVENTIONAL AND STEEL STRIP CONFINED RC COLUMNS

4.1 INTRODUCTION The response of column elements in their inelastic range is greatly affected by strength of

concrete in post peak region of stress-strain curve. The region is influenced by confinement,

provided in the form of transverse reinforcement. In this chapter a new technique has been

suggested in which the transverse reinforcement, in hinge zone, is provided in form of steel

strips of 2 mm and 1.3 mm thickness. The dimensions of steel strips are adjusted to provide

a cross sectional area equivalent to that of standard 10 mm diameter reinforcement. The

chapter starts with description of specimens and properties of constituting materials. The

construction of column specimens, including details of suggested transverse reinforcement

and specimens is given. The test setup has been presented graphically and equipment used in

testing is listed and explained. Behavior of specimens during testing is discussed and data

recorded is analyzed. In analysis lateral strength, stiffness, ductility, residual displacement

and energy dissipation of columns confined by proposed technique is compared with that of

standard columns. The experimental results give an insight of the affects of confinement on

behavior of columns. The study highlights the improvements in performance of columns due

to suggested transverse reinforcements.

4.2 DESCRIPTION OF SPECIMENS In this section nomenclatures and groups, assigned to columns are explained. The

nomenclature explained here will be used throughout chapter 4 and 5. In total eight large size

specimens were cast for testing in laboratory. To observe the affects of compressive strength

of constituting concrete, the specimens were cast in two groups of 25 Mpa (Group 1) and 32

Mpa (Group 2) concrete strength. The proposed reinforcement is provided in the form of

steel strips of 1.3 mm and 2 mm thickness in hinge zone only. The transverse reinforcement

outside the hinge zone consisted of standard seismic stirrups. The width of strip is calculated

so as to ensure a cross sectional area equivalent to that of standard 10 mm diameter steel

CHAPTER 4 PERFORMANCE OF CONVENTIONAL AND STEEL STRIP CONFINED RC COLUMNS

63

stirrup. The response of columns confined by proposed technique was compared with

columns containing standard 10 mm diameter stirrups of 275 Mpa and 415 Mpa strength

through out their length. The columns containing proposed transverse reinforcement in their

hinge zone have been named as Steel Strip Confined (SSC) columns. For Identification the

standard columns are named as Conventionally Reinforced Concrete Stirrup (CRCS)

columns. In each group two columns were SSC and other two were CRCS. Further

identification of SSC and CRCS is given in table 4.1. In the table 1.3 and 02 attached to SSC

refers to thickness of transverse stirrups and 40 and 60 used as suffix with CRCS identifies

yield strength of stirrup. The nomenclature of columns, in their respective groups, along

with type of transverse reinforcement and strength of concrete are listed in table 4.2. In

group 2 columns CRCS-40 is not included because the specimen was used in adjusting the

test setup.

Table 4.1: Nomenclatures of columns S/No Type of Transverse steel Nomenclature

1 Standard #3 bar of 275 Mpa CRCS-40 2 Standard #3 bar of 415 Mpa CRCS-60 3 2mm strip of 275 Mpa SSC-02 4 1.3 mm strip of 275 Mpa SSC-1.3

Table 4.2: Properties of columns Group Type of column Nomenclature Remarks

Type I CRCS-40 Standard 10 mm bars of 275 Mpa yield strength are used as transverse reinforcement and cast with 25 Mpa concrete

Type II CRCS-60 Standard 10 mm bars of 415 Mpa yield strength are used as transverse reinforcement and cast with 25 Mpa concrete

Type III SSC-02 Proposed 2 mm thick strip of 275 Mpa yield strength are used as transverse reinforcement and cast with 25 Mpa concrete

1

Type IV SSC-1.3 Proposed 1.3 mm thick strip of 275 Mpa yield strength are used as transverse reinforcement and cast with 25 Mpa concrete

Type V CRCS-60 Standard 10 mm bars of 415 Mpa yield strength are used as transverse reinforcement and cast with 32 Mpa concrete

Type VI SSC-02 Proposed 2 mm thick strip of 275 Mpa yield strength are used as transverse reinforcement and cast with 32 Mpa concrete

2

Type VII SSC-1.3 Proposed 1.3 mm thick strip of 275 Mpa yield strength are used as transverse reinforcement and cast with 25 Mpa concrete


64

4.3 CONSTITUTING MATERIALS The fine aggregates considered for concrete mix included Chenab and Lawrancepur sand and

later was selected on the basis of bulk density, specific gravity and finess modulus. The

Lawrancepur sand is well graded and relatively coarser than majority of other sands found in

Pakistan. Among coarse aggregates Sargodha crush was found better than Margella and

Sakhi Sarwar crush due to its higher bulk density and lower value of water absorption and

crushing. The crushing value of Sargodha crush is 44% and 51% lesser than Margella and

Sakhi Sarwar crush. The 80% value of coarse aggregate consisted of 10 mm and 5 mm,

where as 20% crush was 20 mm in size. This is the gradation of crush which is normally

used in Pakistan for concreting RC elements. Ordinary Portland cement was used in

concreting.

(a) (b) Figure 4.1: Graphical representation of fc' of concrete used in casting specimens (a) Group

1 columns (b) Group 2 columns Table 4.3: Cylinder strength of concrete used in casting of columns determined at 28 days

Group 1 Group 2 Type Type I

CRCS-40 Type II

CRCS-60 Type III SSC-02

Type IV SSC-1.3

Type V CRCS-60

Type VI SSC-02

Type VII SSC-1.3

fc' 25.3188 25.2115 25.587 24.6885 32.641 32.1044 31.8899 The selected materials were mixed in 1:2:4 and 1:1.36:2.72 ratios to attain concrete mix of 25

Mpa and 32 Mpa strength respectively with w/c ratio of 0.54. The compressive strength of

concrete for different columns determined at 28 days is given in table 4.3. The stress-strain

relation of 25 Mpa and 32 Mpa concrete used in casting of group 1 and group 2 respectively,


65

is shown in figure 4.1(a) and 4.1(b). Among concrete of group 1, shown in figure 4.1(a), the

concrete for CRCS-40 has indicated comparatively smaller post peak branch. The initial

slope of CRCS-40 and CRCS-60 is alike and higher then the other two. The post peak

behavior of CRCS-60, SSC-02 and SSC-1.3 is almost similar to each other. The SSC-02

curve, shown in figure 4.1(b), has least initial slope but its peak stress is dominating.

Table 4.4: Stress-strain relationship of different steels used in specimens at Yield Stress at Max Stress at Ultimate Stress

S/No Steel (Mpa) fy (kN)

εy (mm/mm)

fmax (kN)

ε fu εu

1 13 mm (415) 416.25 0.0024 614.22 0.2367 610.34 0.316 2 10 mm (415) 454 0.00271 706.65 0.16 696.74 0.17 3 10 mm (275) 302.16 0.00124 448.38 0.194 442.3 0.19 4 2 mm Strip (275) 259.88 0.0012 374.4 0.16 356.53 0.1919 5 1.3 mm Strip (275) 245.4 0.0011 388.6 0.22 323 0.22

The properties of reinforcing steel used in the specimens are listed in table 4.4. The steel

strips were tested as longitudinal flat rectangular tension test specimen, as specified by

ASTM standard A370. The 10 mm 275 Mpa steel has indicated more yield and ultimate

strengths as compared to 2 mm and 1.3 mm thick steel strip specimens. However, 2 mm and

1.3 mm steel strips have shown 27% and 32% elongation respectively as compared to 16%

elongation of 10 mm diameter 275 Mpa steel. The 415 Mpa steel of transverse stirrup was

found brittle as compared to 275 Mpa steel.

4.4 CONSTRUCTION OF SPECIMEN The layout of reinforcement provided in the column and the shear block is given in figure

4.2(b) and actual reinforcement cage is shown in figure 4.2(c). The specimens were prepared

in a specially designed form work, which resulted in monolithic base and column. Four

plastic pipes were placed in base in order to house anchoring bolts, as shown schematically in

figure 4.2(a). The cage of the column, shown in figure 4.2(b) and 4.2(c), has total 26

transverse stirrups. The first ring was fixed at 50 mm from the face of shear block. First nine

seismic stirrups, from face of the shear block, were in hinge zone and spaced at 57 mm centre

to centre. The spacing of stirrups out side the hinge zone is at 76 mm centre to centre. The

first nine stirrups were replaced with rings of proposed steel strip in SSC columns.


66

(a) (b) (c) Figure 4.2: Detail of test specimen (a) line diagram (a) Layout of control column with 10

mm stirrups in hinge zone drawn to scale (c) actual cage of the column CRCS-40 The steel strips were cut out of sheets of A36 steel. The cross sectional area of steel strip was

calculated in order to provide an area equivalent to that of standard transverse stirrup of 10

mm diameter. Thus the width of 2 mm and 1.3 mm strips was kept as 35.5 mm and 54.6 mm.

The weight of individual rings of steel strip and standard stirrup was also same. The proposed

confining reinforcement is prepared by bisecting ends of steel strip up to 6db (International

Code Council, 2003), where db is diameter of longitudinal steel, and bending a leg of one end

inwards and other outwards. The legs of other end of the strip are bent in opposite directions

as compared to the fingers of first end. In figure 4.3(a) an end of a 2 mm thick steel strip is

being cut with steel cutter. In figure 4.3(b) both ends of seismic hoop of proposed technique

are shown. It can be seen that bottom finger of one end in bent inwardly where as at other

100 mm

148.12 KN

P

1734mm


67

end it is bent outwardly. Similar approach was used for upper finger of the proposed seismic

ring in the same figure. The fingers at the ends of the steel strips are criss crossed and a

seismic hook is formed in one corner of the ring. In figure 4.4(a) a completed ring of

proposed confinement is shown. The proposed ring of steel strips can be seen fitted in

reinforcement cage in figure 4.4(b).

At the point of application of load there are chances that some localized crushing of concrete

or cracks may occur. These localized deformations are attributed to application of point load

and can unnecessarily contribute to over all response of the column. In order to avoid any

such situation a frame was made with steel angles (25 mm x 25 mm x 3mm) connected to

each other by means of steel strips (255mm x 9mm x 3mm), and placed in top portion of RC

columns at the time of casting. The resulted arrangement is shown in figure 4.5(a) and in

figure 4.5(b) the arrangement is being placed in top portion of column. The SSC-02 frame

has six proposed seismic ring of 2 mm thick steel strips in hinge zone, as shown in figure

4.6(a). The SSC-1.3 column has five rings of 1.3 mm thick strip in hinge zone. The cage of

column is shown in figure 4.6(b). As the transverse rings in proposed technique are provided

at clearing spacing of 57 mm, therefore, their number has reduced from nine to six and five

in SSC-02 and SSC-1.3 respectively. In this way volume of transverse reinforcement is

11.53% and 15.38% lesser in SSC columns as compared to CRCS columns. The wires seen

in figure 4.6(a) and 4.6(b) are attached to strain gages installed on reinforcement.

Surface of steel bars was prepared for attaching strain gages at selected locations, before

fixing the reinforcement cages. In figure 4.7(a) a strain gauge has been shown attached on

the longitudinal steel. The ribs of deformed steel were removed in the areas selected for

strain gauges. Similarly, surface of 10 mm stirrup was prepared for application of strain gage.

The surface of transverse reinforcement, including proposed ring, was also prepared before

fixing it in the cage. A transverse ring of 1.3 mm thick strip used in SSC-1.3 column has

been shown in figure 4.7(b). After removing form work the specimen were wrapped in wet

jute bags, which were covered with polythene sheets to prevent the moisture from escaping

from the concrete. Two cylinders of concrete of 150 mm diameter and 300 mm height were

cast and cured in similar environments for every specimen. It was done to check the strength

gain by the concrete, in actual conditions, on day of testing of the specimen.


68

(a) (b) Figure 4.3: Forming of transverse ring of steel strip of SSC column (a) cutting of ends of

steel strips from centre (b) bending of figures of steel strip rings in criss cross manner

(a) (b) Figure 4.4: Transverse ring of steel strip used in SSC column (a) Strip formed in to ring (b)

Strip ring fixed in SSC column

(a) (b) Figure 4.5: Arrangement to transfer load to the specimen without localized failure

(a) shear frame to be fixed at the top of column (b) Shear frame placed in the specimen


69

(a) (b) Figure 4.6: Proposed confining rings placed in hinge zone (a) Reinforcement cage of SSC-02

specimen indicating six rings of 2 mm thick strip (b) Reinforcement cage of SSC-1.3 specimen indicating five rings of 1.3 mm thick strip

(a) (b) Figure 4.7: Application of steel strain gage on reinforcement bars (a) on longitudinal steel (b)

on transverse steel of SSC column


70

Figure 4.8: General layout of the setup used in testing of RC column specimens

4.5 TESTING ARRANGEMENT

Test assembly for static cyclic loading was designed and fabricated as shown in figure 4.8.

The shear block was anchored on the strong floor by means of four anchor bolts and steel

plates. The columns were tested as cantilever element subjected to static cyclic lateral loads.

In order to achieve cantilever behavior, the axial load was applied through a bridge bearing

assembly as shown in figure 4.9. The bridge bearing consisted of two 38 mm thick steel

plates and a 25 mm diameter roller pin sandwiched between them. The square plates were

230 x 230 mm in dimensions. The bottom plate was simply placed over specimen and the

top plate was kept in position by means of four 19 mm diameter balance rods. The assembly

ensured transfer of axial load without restraining any degree of freedom at top node.

Fixed axial load of 0.1Agfc' was applied by means of manual jack and was monitored during

application of cyclic load. However, a variation of 7% to 10% has been observed during

testing. The cyclic lateral load was applied through double action manual hydraulic jacks.

The load was measured by means of load cells fixed against the columns. All the jacks were

E D

A

C B

G F

H

I

JK L

M

N O

P

DE


71

Table 4.5: Detail of experimental setup shown in figure 4.8 and 4.9 Alphabet Instruments and Their Location

A Hydraulic jack for application of axial load B Steel packing for adjusting the axial load jack C Bridge roller assembly

D* Reference steel plate fixed on the column to push LVDTs E* LVDTs to record the displacements F* Reversible hydraulic jack to apply the lateral load G* Bolt and plate assembly to hold the jacks in position for lateral load H* Steel spacer to increase the length of plunger of the jacks I* Steel stiffener to increase lateral strength of shear frames J Column specimen

K* Steel girder of shear frame for application of lateral loads L* Steel girders of shear frame for application of axial loads M* Dimic points to measure surface strain of concrete N* Bolts to hold down the anchor the column specimen O* Steel plates to create a reaction UDL to hold down shear block P Shear block of the column specimen

Q* Separate reference frames to hold LVDTs R* Sleeve to hold LVDT to record first 50 mm of displacement S* Sleeve to hold LVDT to record displacement after 50 mm T* Arrangement allow the complete LVDT to be pushed back under push from the column U* Fixed support holding the sleeve of LVDT recording after 50 mm displacement V* Complete stand to install LVDTs in series W* Reference steel plate to push LVDT under application of lateral load X Head beam to take reaction of axial load jack Y Pair of balancing rods holding the bridge roller assembly in position Z* Load cell to measure the lateral load AA LVDTs to measure displacement in hinge zone

* Similarly, it was also used on other side to cater for both directions of loading

Figure 4.9: Layout of instrumentation used in testing of RC column specimens

X

YZ

AA AA

AA

R

S

T

U W

V

Q


72

fixed against steel shear frames through specially designed assemblies, for developing

required reaction during application of loads. The axial load was applied through a separate

arrangement of shear frames placed perpendicular to lateral load system. The head beam

restraining the axial load jack, placed perpendicular to shear frames of lateral loads, offered

lesser resistant as compared to an in plane head beam. The detachable spacers increased

plunger length of jacks and yet kept room for column displacement. The LVDTs used to

measure displacement of the top node were fixed on a separate reference frame. The

maximum available length of the LVDTs was 50 mm, therefore, these were used in series. A

specially designed stand, as shown in 4.8(b), which held the LVDTs in sleeves served the

purpose. In each stand two LVDTs were fixed in a way that first LVDT, fixed on a

moveable assembly of stand, was touching the reference plate and the second LVDT, fixed in

a static holder, was placed 50 mm away from reference plate. When the plunger of the first

LVDT was fully pressed the holding sleeve touched the reference plate and plunger came to

rest in side the sleeve. At the same time second LVDT touched the reference plate which

started pushing back its plunger with application of load. When plunger of second LVDT

was pushed the moveable part of the stand was also pushed back along with stationery

LVDT. LVDTs were also fixed at hinge and shear depths, as shown in figure 4.9. The setup

has been numbered with alphabets in figure 4.8 and 4.9 and its detail is given in table 4.5.

Figure 4.10: Loading cycles applied in testing of specimens

4.6 LOADING HISTORY

All specimens were tested under displacement control cyclic loads. Maximum possible

displacement that could be achieved, through two 50 mm LVDTs used in series, was 95 mm


73

or 5.5% drift level. Therefore, after attaining the maximum possible displacement the final

cycle was repeated until 20% degradation was achieved in lateral load. The cycles applied in

terms of drift levels and mm are highlighted in table 4.6. All loading cycles except for 0.25%

drift level were repeated at least for two times. The test was carried out at 0.004167 Hrzs.

Figure 4.11: Line diagram of test setup indicating instrumentation installed to record response of column specimen

4.7 INSTRUMENTATION AND DATA ACQUISITION SYSTEM

The displacements were measured by means of LVDTs installed at 1734 mm, 1515 mm and

169 mm from shear block. The location represented full, hinge and shear depth of the

specimen. For full depth node two 50 mm LVDTs were installed in series as shown in figure

4.9. The LVDTs were connected on Strain Smart 5000 data acquisition system of Vishay

Negative Positive

910

2345

67

8

13

1112

1415 1


74

origin. In addition to these LVDTs three to four steel strain gages, type EA-13-240LZ-120,

of Vishay Micro-Measurements were installed to measure strain variation of two longitudinal

and one transverse reinforcement bar. The steel strain gages were installed at middle of

plastic hinge region. The strain variation of balance rods of bridge roller assembly was also

monitored by applying strain gages. Later, force acting on the balance rods was calculated

and subtracted from lateral load applied. In total seventeen to nineteen channels of the

scanner were used for collecting data of a column specimen. The axial load was monitored

by hydraulic pressure cell. The lateral load was recorded by load cells attached with Strain

Smart 5000. The instrumentation is shown in line diagram given in figure 4.11. The

instruments used in testing are numbered in figure 4.11 and their detail is given in table 4.7.

Table 4.6: Detail of cycles applied during testing of column specimen Cycle Drift Level (%) Displacement (mm) Cycle Drift Level (%) Displacement (mm)

1 0.25 4.3 14 3.5 60.69 2 0.5 8.67 15 3.5 60.69 3 0.5 8.67 16 4 69.36 4 1 17.34 17 4 69.36 5 1 17.34 18 4.5 78.03 6 1.5 26.01 19 4.5 78.03 7 1.5 26.01 20 5 86.7 8 2 34.68 21 5 86.7 9 2 34.68 22 5.2 90.168

10 2.5 43.35 23 5.2 90.168 11 2.5 43.35 24 5.5 95.37 12 3 52.02 25 5.5 95.37 13 3 52.02

*5.5% drift is repeated till 20% degradation is achieved Table 4.7: Detail of instrumentation as marked on line diagram of figure 4.11 Serial Instruments and Their Location

1 Axial load jack 2 Lateral load jack for negative direction of loading 3 Lateral load jack for positive direction of loading 4 LVDT at top for lateral displacement caused by positive loading jack, two were used in series 5 LVDT at top for lateral displacement caused by negative loading jack, two were used in series 6 LVDT at hinge depth to measure positive displacement 7 LVDT at hinge depth to measure negative displacement 8 LVDT at shear depth measuring displacements in both directions of loading 9 Pair of steel strain gages measuring strain of balancing rods for negative direction

10 Pair of steel strain gages measuring strain of balancing rods for positive direction 11 Steel strain gage measuring strain of longitudinal steel bar 12 Steel strain gage measuring strain of longitudinal steel bar 13 Steel strain gage measuring strain of transverse steel bar 14 Load cell measuring lateral load in negative direction 15 Load cell measuring lateral load in positive direction


75

4.8 TESTING OF SPECIMEN In this section execution of actual tests conducted in the laboratory are explained. Total eight

specimens were cast in the laboratory. As the testing arrangement was fabricated locally its

test trial was obvious. CRCS-40, cast with 32 Mpa concrete, was placed as first column in

the testing arrangement and problems identified in the testing arrangement were rectified.

The results of first column were discarded because of frequent halts during testing and data

recording. Here in this section testing of remaining seven columns is presented in respective

groups listed in table 4.2. Only data of LVDTs located at top of the columns will be

presented and analyzed in this report. The hysteresis curves along with backbone curves are

discussed in this section. The backbone curve is smoothened and compared with actual

backbone curve of the respective column. In the following sections the appearance of cracks,

during testing, is indicated in terms of depth measured from face of shear block of the

column specimen. The entire columns were tested under a constant axial load of 0.1 g cA f ′ .

Group 1 Specimen

The columns of the group have been cast with 25 Mpa concrete. The pattern of deformation

observed in SSC columns was different from conventional columns. The testing of columns

of group 1 will be explained in following sections.

4.8.1.1 CRCS-40 Cast With 25 Mpa Concrete The column consisted of standard stirrups of 275 Mpa yield strength. Total 29 cycles were

applied to the column in order to achieve 20% strength degradation. The First crack, in

positive direction of loading, was observed in the column at 220 mm from the face of the

shear block. At that moment a lateral displacement of 5.5 mm was achieved at a load of

13.01 kN. The second and third crack appeared at 420 and 540 mm depths respectively.

These cracks appeared just after the first crack at 6.1 mm displacement and 13.73 KN load.

The fourth crack was observed at 400 mm depth in 4th cycle at 12.5 mm displacement and

21.5 kN load. Up till fourth crack all cracks on positive face were completely closing on

unloading. In 7th cycle a new crack appeared at 70 mm depth at a lateral displacement and

load of 20.54 mm and 26.75 kN, respectively. After the fifth crack the deformations were

permanent and cracks were not completely closing on unloading.


76

(a) (b) Figure 4.12: Final damage observed in CRCS-40 cast with 25 Mpa concrete (a) positive

loading face (b) negative loading face

(a) (b) Figure 4.13: Side view of final damage observed in CRCS-40 cast with 25 Mpa concrete (a)

north view (b) south view The negative face showed the first three cracks nearly at same load and displacement. These

cracks appeared at distances of 240 mm, 380 mm and 490 mm from column base. The fourth

crack on negative face appeared in 7th cycle at a depth of 35 mm. It is same cycle in which

residual displacement was observed in positive direction. After fourth crack the majority of

deformation, in negative direction, occurred up to 140 mm from the face of shear block. For

instance fifth, sixth and seventh cracks appeared at 100 mm, 140 mm and 57 mm depth. In

6th cycle a crack appeared at base of the column at lateral displacement of 64.79 mm in

negative direction. The crack widened as the test progressed.

The peak load of the column has been found as 29.89 kN occurring in the positive direction

at 40.22 mm displacement. On positive side, above a depth of 100 mm, the width of cracks


77

was very less. The spalling of concrete also occurred with in 100 mm depth. The extent of

deformation on negative side was higher and spalling was noted up to a depth of about 220

mm. The final damage observed in positive and negative direction is shown in figure 4.12(a)

and 4.12(b) respectively. The view of other two faces of the column is shown in figure

4.13(a) and 4.13(b). The width of thick cracks has been measured as 2 mm. In figure 4.13(a)

a thick crack can be observed at base of the column, which indicates that at higher drift levels

deformation can occur even near the face of the support.

(a) (b) Figure 4.14: Load-displacement curves of CRCS-40 cast with 25 Mpa concrete

(a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves The hysteresis curve of cyclic test of column, along with the backbone curve, is shown in

figure 4.14(a). The backbone curve has been smoothened by load vector and both curves are

overlapped in figure 4.14(b). The hysteresis indicates a steady response and lesser lateral

strength in negative direction. Reduced slope of hysteresis, in initial portion of higher cycles,

is due to closing of already opened cracks in the previous direction. In figure 4.14(a) it can

be seen that as drift level is increased residual displacements are also increased accordingly.

The decrease in residual displacements in last six cycles is due to repetition of 5.5% drift

level until 20% degradation of strength.

4.8.1.2 CRCS-60 Cast With 25 Mpa Concrete The column consisted of 415 Mpa standard transverse stirrups through out its length. The

20% degradation was achieved in 27 cycles. The deformation in the column started in 2nd

cycle at 7.3 mm lateral displacement achieved at 13.87 kN load with a hair line crack

appearing at 232 mm depth. Three cracks appeared in 4th cycle at 310 mm, 490 mm and 592


78

mm from face of shear block. These cracks appeared at a lateral displacement of 17.25 mm

occurring at a lateral load of 18.633 kN. The cracks on positive side were closing completely

up to 7th cycle. During 8th cycle at 1.7% drift or 29.47 mm lateral displacement a crack

appeared at 64 mm depth. The crack appeared and widened in the same cycle. The damage

observed on positive face of the column is shown in figure 4.15(a).

(a) (b) Figure 4.15: Final damage observed in CRCS-60 column cast with 25 Mpa concrete (a)

positive loading face (b) Negative loading face On the negative face first crack appeared at 186 mm depth in the 2nd cycle at a lateral

displacement and load of 5.75 mm and 9.5 kN respectively. In 3rd cycle at 6.8 mm lateral

displacement and 12.67 kN load second crack appeared at 384 mm from the face of shear

block. In the 4th cycle third and fourth crack appeared at 278 mm and 433 mm depths

respectively. At appearance of these cracks the lateral displacement was 17.22 mm achieved

at a lateral load of 21.88 kN. In 8th cycle two cracks appeared at 67 mm and 95 mm from

face of shear block. These cracks were visible at a lateral displacement of 31.22 mm. It was

observed that crack, which appeared at the depth of 64 mm in positive direction of same

cycle, propagated to negative face. The shift in equilibrium at end of the 8th cycle was

expected due to this crack. Both the cracks, appearing at 67 mm and 95 mm, widen as the

test progressed. The damage observed in negative loading direction is given in figure 4.15(b).

The peak load achieved was 31.4863 kN occurring in the 12th cycle at 2.98% drift level. The

spalling of cover for both directions started at 4.5% drift level. Side view of the damage

occurring in the hinge zone is shown in figure 4.16(a) and 4.16(b). In figure 4.16(b) it can be

observed that the cover has separated from core but it is not crushed. The hysteresis response


79

of the column is plotted in figure 4.17(a). The backbone curve of the hysteresis, overlapped

with smoothened curve, has been marked in figure 4.17(b). The hysteresis loops indicate that

lateral strength of the column in negative direction is lesser then that observed in positive

direction. The residual displacements are prominent after 11th cycle. In the last cycles the

residual displacement has decreased due to repetition of 5.5% drift level.

(a) (b) Figure 4.16: Side view of final damage observed in CRCS-60 column cast with 25 Mpa

concrete (a) north view from positive side (b) north view from negative side


(a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves

4.8.1.3 SSC-02 Cast With 25 Mpa Concrete The column consisted of six confining rings of 2 mm thick steel strip of A36 steel in hinge

zone. The remaining height of column contained standard stirrups of 275 Mpa strength. First

crack in the column appeared at a depth of 80 mm on its negative face at a lateral

displacement and load of 8.5 mm and 13.2 kN respectively measured in 2nd cycle. The


80

second crack on this face appeared in 4th cycle at 190 mm from face of its shear block. At

this moment lateral displacement and load was 15.71 mm and 18.65 kN, respectively. The

third crack appeared at 285 mm depth in 6th cycle at lateral displacement of 19.01 mm

occurring at a lateral load of 20.15 kN. In the same cycle fourth crack appeared at a distance

of 365 mm from the face of shear block. More cracks appeared during 8th cycle at 476 mm

and 626 mm depth. These crack showed up at lateral displacements of 27.1 mm and 31 mm

occurring at 21.2 kN and 23.8 kN respectively. The damage observed in the column on the

negative side is shown in figure 4.18(b). In 14th cycle at a lateral displacement of 59 mm the

first crack started to widen. The surface started to show spalling in 16th cycle at a lateral

displacement of 66 mm and spalling was aggravated in 18th cycle at a lateral displacement of

76 mm.

(a) (b) Figure 4.18: Final damage observed in SSC-02 column cast with 25 Mpa concrete

(a) positive loading face (b) Negative loading face The first two cracks on positive face were observed in the 3rd cycle at a lateral displacement

of 6.9 mm and lateral load of 9.44 kN. The cracks appeared at 90 mm and 249 mm depths.

In 4th cycle at a lateral displacement of 17.2 mm and load of 19.14 kN third and fourth crack

appeared at 357 mm and 439 mm depths respectively. The fifth crack was seen in 5th cycle at

a distance of 555 mm depth and lateral displacement and load of 17.3 mm and 21.31 kN

respectively. The sixth, seventh and eighth crack appeared at 629 mm, 724 mm and 805 mm

distance from the face of the shear block. These cracks were noted in 8th cycle at a lateral

displacement and load of 32.3 mm and 27.8 kN respectively. The cracks above 249 mm

depth almost closed completely on removal of the lateral load. The spalling of the positive


81

face started in eighteenth cycle at a lateral displacement of 73 mm. In figure 4.19(a), the

damage is seen from positive direction and figure 4.19(b) shows it from negative direction.

The deformation started within a depth of 100 mm and remaining length of column was

intact due to greater confinement. Later the deformation expanded with in the hinge zone to

accommodate larger drift levels.

(a) (b) Figure 4.19: Side view of final damage observed in SSC-02 column cast with 25 Mpa


(a) (b)

Figure 4.20: Load-displacement curves of SSC-02 cast with 25 Mpa concrete (a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves

The peak load of 30.89 kN occurred in the 14th cycle, in positive direction, at a drift of

3.34%. The load displacement hysteresis is plotted in figure 4.20(a). The backbone curve of

the hysteresis is also marked in the figure. The backbone curve is smoothened by the load

vector and superimposed with original curve in figure 4.20(b). The higher level confinement


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provided by proposed technique resulted in similar strength and degradation in both positive

and negative loading direction. The column degraded to 80% of its maximum lateral strength

in 31 cycles. The smoothened backbone curve shown in figure 4.20(b) is also nearly

identical in both directions. The residual displacements have similar distribution for positive

and negative direction.

4.8.1.4 SSC-1.3 Cast With 25 Mpa Concrete The nine rings in hinge zone of CRCS-40 column were replaced with five rings of 1.3 mm

thick strip to achieve reinforcement cage of SSC-1.3 column. First two cracks appeared at

190 mm and 320 mm depth on positive face in the 2nd cycle at 7.1 mm lateral displacement

and 16.07 kN load. In the 4th cycle at a lateral displacement of 14.62 mm and load of 21.34

kN four more cracks appeared on the positive face of the column. These cracks were located

at 85 mm, 420 mm, 659 mm and 494 mm respectively. Three more cracks were visible in

the 6th cycle of the test. At this moment the scanner read the lateral displacement and load as

25.4 mm and 23.56 kN respectively. The seventh and eighth crack appeared at 583 mm and

535 mm depth. The 9th crack appeared near base of the column at a distance of 20 mm from

face of the shear block. Deformation occurring in positive direction of loading is shown in

figure 4.21(a).

(a) (b) Figure 4.21: Final damage observed in SSC-1.3 column cast with 25 Mpa concrete

(a) positive loading face (b) Negative loading face The cracking on the negative face also started in the 2nd cycle. Three cracks occurred at

lateral displacement and load of 6.4 mm and 12.83 kN respectively at depths of 240 mm, 408

mm and 57 mm. At a lateral displacement of 16.9 mm and load of 18.04 kN three more


83

cracks appeared at a distance of 591 mm, 107 mm and 751 mm from face of shear block of

the specimen. In 6th cycle, at a lateral displacement and load of 23.4 mm and 20.6 kN

respectively, two more cracks were visible on the negative face at 947 mm and 326 mm

depth. In 9th cycle at a lateral displacement of 32.8 mm and load of 22.3 kN a crack was

visible near the base at a depth of 39 mm. The damage observed on the negative face is

shown in figure 4.21(b). In SSC-1.3 column the pattern of deformation was similar to that of

standard transverse stirrup. However, the deformation was well distributed with in hinge

zone due to increased confinement.

(a) (b) Figure 4.22: Load-displacement curves of SSC-1.3 cast with 25 Mpa concrete

(a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves

(a) (b) Figure 4.23: Side view of final damage observed in SSC-1.3 column cast with 25 Mpa


The peak load of the column was noted as 31.826 kN, in the positive direction, occurring at a

lateral drift of 2.92%. The load displacement hysteresis curve of the column along with


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backbone curve is plotted in figure 4.22(a). In figure 4.22(b) the smoothened and actual

backbone curves have been superimposed. The crack near base of the column on its positive

face started to widen in the 11th cycle at a lateral displacement of 40 mm. Bottom crack on

negative face widened in 17th cycle at a lateral displacement of 65 mm. The spalling of the

surface concrete was triggered in 13th cycle on the negative face at a lateral displacement of

52 mm. The spalling was aggravated in 20th cycle at a lateral displacement of 83.5 mm. The

column strength was degraded by 20% in 25 cycles. The side view of the damage observed in

the hinge zone is shown from positive and negative loading direction in figure 4.23(a) and

4.23(b). The hyteresis curve indicates that residual displacements achieved at end of middle

cycles were nearly similar in both loading directions. In last eight cycles, due to ingress of

inelasticity, a difference in the response of two loading directions is evident.

4.8.2 Group 2 Specimen The columns of this group were cast with 32 Mpa concrete. The group include only one

control column containing standard 10 mm diameter stirrups of 415 Mpa strength. Like

group 1 columns, again a balanced response has been observed for SSC columns of this

group. Observations made during testing are explained below.

4.8.2.1 CRCS-60 Cast With 32 Mpa Concrete The column contained 415 Mpa steel stirrups throughout its length. The loading cycles

applied during testing did not include the half loading cycles, after 1% drift level, as

mentioned in table 4.11. However, the results were found comparable with other columns.

The first crack on the positive face appeared at a depth of 220 mm and a lateral displacement

and load of 8.2 mm and 10.32 kN respectively. The second and third crack on positive face

appeared in 4th cycle at lateral displacement of 17 mm and load of 17.34 kN. These cracks

were located at a depth of 160 mm and 90 mm. Three more cracks appeared in 6th cycle at a

lateral displacement and load of 22.54 mm and 21.6 kN respectively. Distance of these

cracks, measured from face of shear block along length of the column, has been measured as

270 mm, 380 mm and 490 mm. In the same cycle at lateral displacement of 31.2 mm and

load of 24.2 kN another crack appeared at a depth of 630 mm. In the 8th cycle at lateral

displacement of 39 mm and load of 29.8 kN a crack appeared at a depth of 790 mm. The

damage observed in the column in its hinge zone is shown in figure 4.24(a).


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(a) (b) Figure 4.24: Final damage observed in CRCS-60 column cast with 32 Mpa concrete

(a) positive loading face (b) Negative loading face


(a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves On negative side of the columns first two cracks appeared at a depth of 240 mm and 160 mm

at a lateral displacement and load of 7.3 mm and 9.4 kN respectively. Three cracks were

further introduced on the negative face during 4th cycle at lateral displacement and load of

15.4 mm and 11.2 kN respectively. The distance of the cracks from shear block was 270

mm, 340 mm and 440 mm. In 6th cycle, at a lateral displacement of 32.9 mm and load of

18.2 kN, three more cracks appeared at 560 mm, 640 mm and 880 mm depths. In 10th cycle

at a lateral displacement of 60.7 mm and load of 19.5 kN a crack appeared at 50 mm depth.

The peak load was noted as 34.09 kN occurring at 2.85% drift level. The spalling was

initiated at lateral displacement of 65 mm and aggravated at 72 mm. The required 20%

degradation in strength was achieved in 15 cycles. The hysteresis curve of response of the


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column is given in figure 4.25(a). The backbone curve is overlapped with smoothened curve

in figure 4.25(b). Lateral resistance of the column is quite deficient in negative direction. It

can be seen in figure 4.25(a) that residual displacements are also higher in negative direction.

In last six cycles variation in residual displacements is very less. The north and south

elevation of the damage is shown in figure 4.26(a) and 4.26(b) respectively.

(a) (b) Figure 4.26: Side view of final damage observed in CRCS-60 column cast with 32 Mpa

concrete (a) north view (b) south view

4.8.2.2 SSC-02 Cast With 32 Mpa Concrete The column only differ in strength of concrete (32 Mpa), used in its casting, as compared to

SSC-02 column cast with 25 Mpa concrete. First crack in positive direction appeared in 2nd

cycle at a depth of 80 mm. The lateral displacement and load was noted as 6.55 mm and 6.72

kN respectively. The second and third crack was noticed in the 4th cycle at a depth of 210

mm and 402 mm respectively and a lateral displacement of 16.64 mm and load of 15.54 kN.

Two more cracks appeared during 6th cycle at a lateral displacement of 22 mm and load of

18.88 kN. The depth of the cracks was measured as 490 mm and 130 mm in the sequence of

their occurrence. The damage observed on the face is shown in figure 4.27(a).

On the negative face first crack occurred in 4th cycle at a depth of 157 mm and lateral

displacement and load of 8.57 mm and 13.24 kN respectively. Two cracks were visible at

lateral displacement and load of 16.62 mm and 19.32 kN. These cracks were noted at a

distance of 265 mm and 460 mm from face of shear block of the specimen. Fourth crack was

seen in 5th cycle at lateral displacement and load of 17.1 mm and 19.42 kN respectively. In

6th cycle a crack appeared near base of the column. The crack occurred at a depth of 94 mm


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and lateral displacement of 24 mm and load of 24.56 kN. Two cracks were observed at a

distance of 510 mm and 940 mm from face of shear block of the specimen. These cracks

appeared at a lateral displacement of 30 mm and a load of 26.116 kN in 8th cycle. The

damage observed on the negative face is shown in figure 4.27(b). The deformation in the

column appeared near the base of face of the shear block and then extended outwardly due to

confinement.

(a) (b)

Figure 4.27: Final damage observed in SSC-02 column cast with 32 Mpa concrete (a) positive loading face (b) Negative loading face

(a) (b)

Figure 4.28: Load-displacement curves of SSC-02 cast with 32 Mpa concrete (a) Backbone marked on hyteresis curves (b) Actual and smoothened backbone curves The peak lateral load of 32.62 kN was achieved at 2.94% lateral drift. After 8th cycle the

cracks started to widen and grow towards sides. The required level of degradation was

achieved in 26 cycles. The load displacement hysteresis plotted from cyclic load test is

shown in figure 4.28(a). The backbone curve was smoothened and is superimposed with


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original curve in figure 4.28(b). The residual displacements achieved at end of middle cycles

are nearly alike in both loading direction. The higher confinement provided by transverse

rings of the columns resulted in approximately equal response in both loading directions.

The side elevation of the damage is given in figure 4.29, in which concrete crushing and

growing of cracks towards sides is seen.

Figure 4.29: Side elevation of damage in SSC-02 column cast with 32 Mpa concrete 4.8.2.3 SSC-1.3 Cast With 32 Mpa Concrete The configuration of lateral reinforcement of column discussed in section 4.8.1.4 has been

cast with 32 Mpa concrete. The cracking on positive face started in 4th cycle when at a lateral

displacement of 6.1 mm and load of 6.5 kN a crack appeared at 28 mm depth. Two more

cracks were visible in the 4th cycle at a depth of 178 mm and 313 mm. The cracks appeared

at lateral displacement and load of 8.3 mm and 13.84 kN respectively. In the same cycle

another crack appeared at a lateral displacement of 12.64 mm and load of 20.6 kN. The crack

was visible at a depth of 411 mm. In 6th cycle two more cracks were visible at a depth of 535

mm and 892 mm and lateral displacement and load of 21.7 mm and 24.63 kN, respectively.

Damage observed on positive face of specimen is shown in figure 4.30(a).

On negative face first crack was visible at a depth of 76 mm and lateral displacement and

load of 6.13 mm and 9.92 kN. Second and third crack appeared in 4th cycle at a lateral

displacement and load of 10.8 mm and 15.84 kN respectively. These cracks were seen at 244

mm and 345 mm depths. In the same cycle another crack came into view at a depth of 530

mm and a lateral displacement and load of 15.7 mm and 19.08 kN. In 6th cycle at a lateral

displacement and load of 26.04 mm and 23.7 kN respectively three more cracks appeared at


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depths of 620 mm, 771 mm and 485 mm in the sequence of their occurrence. In 9th cycle a

crack appeared at the junction of column specimen and shear block. At this moment the

scanner measured the lateral displacement and load as 24 mm and 23.2 kN respectively.

Damage observed on negative face of the column is shown in figure in 4.30(b).

(a) (b) Figure 4.30: Final damage observed in SSC-1.3 column cast with 32 Mpa concrete

(a) positive loading face (b) Negative loading face

(a) (b) Figure 4.31: Load-displacement curves of SSC-1.3 cast with 32 Mpa concrete

(a) Backbone marked on hysteresis curves (b) Actual and smoothened backbone curves The peak load of the specimen was noted as 33.96 kN in positive direction occurring at 2.5%

drift level in tenth loading cycle. The cracks started to grow to sides at 3% drift level. The

crushing of concrete cover started at 3.5% drift level. The spalling started to occur in

eighteenth cycle at 4.5% drift level. The column strength in the positive direction was

degraded by 20% in 21 cycles. The load displacement hysteresis of the column is shown in

figure 4.31(a). The backbone curve is smoothened by load vector and is overlapped with


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original curve in figure 4.31(b). The hysteresis curve is deficient in negative direction but its

performance is much more balanced as compared to CRCS-60 column, which is due to

higher level of confinement provided by 1.3 mm strips. Distribution of residual

displacements is not similar in both directions. In figure 4.32(a) and 4.32(b) the side

elevation is shown from positive and negative directions respectively. The side elevation is

showing deep ingress of cracks along with crushing of concrete cover.

(a) (b) Figure 4.32: Side view of final damage observed in SSC-1.3 column cast with 32 Mpa

concrete (a) north view from positive side (b) north view from negative side 4.9 YIELD AND ULTIMATE POINTS There are many methods, found in the literature, to define the yield and the ultimate points on

the load displacement curves of shear walls, beams and columns. In the present study, the

concept of equivalent elastic-perfectly plastic system proposed by Muguruma et al., (1991)

has been used for identification of the yield point. The graphical representation of the model

is given in figure 4.33. The method has been selected because of its ease and accuracy with

which it can be applied on experimental data, achieved in the form of load displacement

curves, of the specimens. The max drift ratio which could be attained was 5.5% due to non

availability of longer LVDTs. Therefore, 5.5% drift level was repeated until 20%

degradation was achieved. In all such cases where 5.5% drift level was repeated to achieve

desired level of degradation, the ultimate displacement is calculated by fitting straight line in

last portion of load displacement curve. The fitted lines are extended to achieve ultimate

displacement corresponding to the recorded 20% degraded load. This level of strength


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degradation is in accordance with work of Muguruma et al., (1991) and Saatcioglu (1989,

1991a), who has found that ultimate displacement of RC columns is corresponding to 20%

reduction in its strength. The equations, along with “R” factor, used in achieving the ultimate

displacements are also given. The direction of loading, in which a column has indicated

lower shear strength, is identified as critical.

Figure 4.33: Graphical representation of equivalent elastic perfectly-plastic system proposed by Muguruma et al., (1991)

4.9.1 Group 1 Columns The yield points, as defined by the secant stiffness, are marked on the backbone curves. The

columns in this group include all specimens cast with concrete of fc′ = 25 Mpa.

4.9.1.1 CRCS-40 Cast With 25 Mpa Concrete The ultimate displacement in the positive and negative direction is determined from equation

4.1 and 4.2 respectively. The values of yield point, peak load and ultimate displacement are

given in table 4.8. The backbone curves of load displacement hysteresis for positive and

negative direction of loading are given in figures 4.34(a) and 4.34(b) respectively. The yield

and peak load of positive direction is 14.35% and 14.04% higher than negative direction. The

yielding has been located at same drift level in both directions because in positive direction

peak load is higher achieved at lower displacement and vice versa has happened in negative

loading direction. This phenomenon has equalized the areas in such a manner which resulted

in same yield drift level. Table 4.8 shows that longitudinal reinforcement has reached its

yield strain at point of yielding. The strain in transverse steel is very less because the

confining pressure developed due to resistance of confining steel was not so high which

could cause the transverse steel to yield. The ductility of negative direction is 6.22% higher


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than positive loading direction. However, while looking at yield and peak lateral strengths,

negative direction of loading has been considered as critical direction of loading.

(a) (b)

Figure 4.34: Yield, peak load and ultimate displacement marked on load-displacement curves of CRCS-40 cast with 25 Mpa concrete (a) Positive loading direction (b) Negative loading

direction. y = -2.9644x + 41.675, R2 = 1 (4.1) y = -1.6894x + 32.589, R2 = 1 (4.2)

Table 4.8: Parameters of backbone curves of CRSCS-40 cast with 25 Mpa concrete Positive Direction Negative Direction Strains Reinforcement Parameter Drift Load Drift Load Main Shear

Yield point 1.3 25.85692 1.3 22.14582 0.002168 0.0001217 Peak load 2.324187 29.89817 3.777958 25.74764 0.003028 0.0000764 Ultimate

displacement 6.072284 23.67432 6.483876 21.63514 Off scale 0.000631

Ductility 4.670988 4.987597 4.9.1.2 CRCS-60 Cast With 25 Mpa Concrete The ultimate displacement, at 20% degraded strength, in positive direction was achieved at

5.428% drift level. Where as, in negative direction it was achieved by extending the curve

given by equation 4.3. The values of yield point, peak load and ultimate displacement are

given in table 4.9. The positive and negative loading directions are given in figure 4.35(a)

and 4.35(b). The yield load of positive direction is 12.31% higher than negative direction.

The yielding in positive direction occurred at 1.27% lesser drift level than that at which it

was achieved in negative direction. The strain in longitudinal steel, given in table 4.9, is

indicating yielding at yield and peak load levels. The gauge was off scale at ultimate load.

The strain in transverse steel are, however, quite low than the yield strain, which indicates


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that a low level of confining pressure has been resisted by the stirrup. The peak load in

positive direction is 15.05% higher than negative loading direction of the column. The

ductility of negative direction is 12.6% higher than that of positive loading direction. The

backbone curve of negative loading direction has indicated more ductility but lower lateral

resistance. Therefore, negative direction has been considered as critical for this column.

(a) (b)


direction. y = -3.3115x + 42.234, R2 = 1 (4.3) Table 4.9: Parameters of backbone curves of CRSCS-60 cast with 25 Mpa concrete

Positive Direction Negative Direction Strains Reinforcement Parameter Drift Load Drift Load Main Shear


displacement 5.42828 24.81052 6.291922 21.3983 Off scale 0.0004

Ductility 3.502117 4.007594

4.9.1.3 SSC-02 Cast With 25 Mpa Concrete The column has shown nearly a balanced response for both direction of loading. The ultimate

displacement corresponding to desired degradation level was achieved by extrapolating

equation 4.4 and 4.5 for positive and negative direction respectively. The values of yield

point, peak load and ultimate displacement are given in table 4.10. The load displacement

backbone curves of positive and negative direction are presented in figure 4.36(a) and

4.36(b) respectively. The yield of negative direction is only 1.4% higher, occurring at 1.28%

higher drift, than positive direction. In table 4.10 it can be seen that longitudinal steel starts

yielding at yield point and its strain is much higher at ultimate displacement. At ultimate


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displacement the strain in proposed transverse confinement has also reached yield strain,

which is a direct indicator of higher level of confinement provided by proposed transverse

ring of 2 mm thick steel strip. In negative direction of loading the peak load is 3.7% higher

than positive direction. The ductility of positive direction is 7.2% higher than negative

loading direction. The backbone curve of positive loading direction has been considered as

critical due to its lower lateral strength.

(a) (b)

Figure 4.36: Yield, peak load and ultimate displacement marked on load-displacement curves of SSC-02 cast with 25 Mpa concrete (a) Positive loading direction (b) Negative loading

direction. Table 4.10: Parameters of backbone curves of SSC-02 cast with 25 Mpa concrete



displacement 6.008496 23.80338 5.658001 25.65887 0.008562 0.0020507

Ductility 3.901621 3.626924 y = -5.3224x + 55.783, R2 = 1 (4.4) y = -6.8049x + 64.161, R2 = 1 (4.5)

4.9.1.4 SSC-1.3 Cast With 25 Mpa Concrete The shear capacity in the positive loading direction was reduced to 80% at 5.415% drift

level. The column in negative loading direction did not degraded up to 5.5% drift level and

therefore the ultimate displacement is determined by extrapolating line represented by

equation 4.6. The values of yield point, peak load and ultimate displacement are given in

table 4.11. The backbone curves are given in figure 4.37(a) and 4.37(b) for positive and

negative loading directions respectively. The yield load in positive direction is 21.5% higher,


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occurring at 3.7% higher displacement, than that of negative loading direction. The strains in

steel reinforcement are given in table 4.11. The yield strain in longitudinal steel was reached

at yield point. The strains in longitudinal steel at ultimate displacement were noted as 70.33%

higher than those recorded at yield point. At ultimate displacement strain in proposed

transverse confining ring of 1.3 mm thick strip reached its yield strain because at higher

deformations the proposed transverse reinforcement is offering higher confinement. The

peak load in positive loading direction is 20.6% higher than that of negative direction. The

ductility calculated from backbone curve of negative loading direction is 21.4% higher than

that worked out for positive direction. The negative loading direction has lesser lateral

resistance as compared to positive direction and is therefore considered critical.

(a) (b)

Figure 4.37: Yield, peak load and ultimate displacement marked on load-displacement curves of SSC-1.3 cast with 25 Mpa concrete (a) Positive loading direction (b) Negative loading

direction.

Table 4.11: Parameters of backbone curves of SSC-1.3 cast with 25 Mpa concrete Positive Direction Negative Direction Strains Reinforcement Parameter Drift Load Drift Load Main Shear

Yield point 1.35 27.34 1.3 21.46 0.00254 0.000144 Peak load 2.92 31.826 2.44 25.27 0.002895 0.00026

Ultimate displacement 5.415 24.954 6.89 20.22 0.008562 0.00333 Ductility 4.011 5.3

y = -2.0436x + 34.289, R2 = 1, (4.6) 4.9.2 Group 2 Columns The axial load was higher due to corresponding 32 Mpa compressive strength of concrete.

The contribution of concrete to overall performance of columns, subjected to cyclic loads, is


96

more under greater axial loads (International Code Council, 2003). As compared with

columns of group 1 the flexure strength decay for group 2 was more rapid. This response is

very much according to the previous studies (Muguruma et al., 1991) and (Saatcioglu and

Ozcebe, 1989). The yield point, peak load and ultimate displacement are marked on the

backbone curves. The backbone curves are plotted in first quadrant for comparison.

0

5

10

15

20

25

0 1 2 3 4 5 6

Drift Ratio (%)L

oad

(KN

)

CRCS-60

Ultimate Point

Peak Point

Yield Point

(a) (b)


direction. Table 4.12: Parameters of backbone curves of CRCS-60 cast with 32 Mpa concrete


Yield point 1.645 30.47 1.86 19.084 0.002208 0.000405 Peak load 2.85 34.09 3.9 22.03 0.00443 Off scale

Ultimate displacement 4.94 27.08 5.58 17.62 0.004822 Off scale Ductility 3.0 3.0

4.9.2.1 CRCS-60 Cast With 32 Mpa Concrete This column was the second column tested during the experimental work. The drift levels

selected at that time did not include 1.5%, 2.5%, 3.5% and 4.5% drift levels, mentioned in

table 4.6. The greater shear capacity in positive direction is presumed to be a direct influence

of the lesser number of cycles applied up to 20% degradation. The overall behavior of the

column was, however, found to be brittle. The 20% degraded shear strength in positive

direction was achieved at 4.94% drift level. The line given by equation 4.7 was extrapolated

to locate the ultimate displacement, for negative loading direction, corresponding to 20%

degraded strength. The values of yield point, peak load and ultimate displacement are given


97

in table 4.12. In figure 4.38(a) and 4.38(b) backbone curves of positive and negative loading

directions are given respectively. The yield displacement in positive loading direction is

11.56% lesser with 37.36% higher load than that of negative direction. The steel strains,

given in table 4.12, indicate that longitudinal steel yielded at yield point. At ultimate

displacement the strain in longitudinal steel was 54.2% higher than its value at yield. The

strain in transverse steel did not indicate yielding up to yield and later the strain gauge was

off scale. The peak load recorded in positive loading direction was 35.37% higher then that

documented for negative direction. Same ductility has been calculated for both loading

directions. The negative loading direction is considered critical due to its lesser lateral

resistance.

y = -4.6446x + 43.539, R2 = 1 (4.7)

4.9.2.2 SSC-02 Cast With 32 Mpa Concrete

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6

Drift Ratio (%)

Loa

d (K

N)

SSC-02

Ultimate Point

Peak Point

Yield Point

(a) (b)

Figure 4.39: Yield, peak load and ultimate displacement marked on load-displacement curves of SSC-02 cast with 32 Mpa concrete (a) Positive loading direction (b) Negative loading

direction.

Table 4.13: Parameters of backbone curves of SSC-02 cast with 32 Mpa concrete Positive Direction Negative Direction Strains Reinforcement Parameter Drift Load Drift Load Main Shear

Yield point 2.08 29.12 1.425 26.24654 0.00352 0.00022 Peak load 2.94 32.63 2.458403 30.41234 Off scale 0.00021

Ultimate displacement 5.71 26.05 5.43004 23.55503 Off scale 0.00217 Ductility 2.75 3.810555

y = -2.5172x + 40.431, R2 = 1 (4.8)


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The positive loading direction of the column had an initial, relatively, gentle slope. Due to

which the yield displacement for the positive direction was 31.5% higher than negative

direction. The ultimate displacement, corresponding to 80% shear capacity, in positive

direction was calculated form equation 4.8. But the response in this direction was relatively

less ductile due to higher level of yield displacement. The ultimate displacement for negative

direction, at required degradation level, was achieved at 5.43% drift level. The values of

yield point, peak load and ultimate displacement are given in table 4.13. The points are

graphically presented for positive and negative loading directions in figure 4.39(a) and

4.39(b) respectively. The yield load in positive direction was 9.9% higher than that noted for

negative direction of loading. The steel strain shown in table 4.13 indicates that longitudinal

steel reached yield strain at yield point. The strain gauge was off scale after yielding. The 2

mm thick transverse confinement also yielded at ultimate displacement. The peak load

recorded in positive loading direction was 6.6% higher than negative direction. Ductility

calculated for negative loading direction is 27.63% higher than its value worked out for

positive direction. The negative loading direction is considered critical due to lesser lateral

resistance.

(a) (b)

Figure 4.40: Yield, peak load and ultimate displacement marked on load-displacement curves of SSC-1.3 cast with 32 Mpa concrete (a) Positive loading direction (b) Negative loading

direction.

4.9.2.3 SSC-1.3 Cast With 32 Mpa Concrete The column reached its required level of degraded strength at relatively lower drift levels. A

loss in drift capacity was observed as compared to SSC-1.3 cast with 25 Mpa concrete. The

ultimate drift level, at the selected degradation level, was 4.87% and 4.85% for positive and


99

negative directions respectively. The values of yield point, peak load and ultimate

displacement are given in table 4.14. The backbone curves for positive and negative loading

direction are shown in figure 4.40(a) and 4.40(b) respectively. The yield displacement for

negative direction was 14.4% higher, recorded at 14.11% lesser load, than positive direction.

The steel strains given in table 4.14 indicate that longitudinal steel reached its yield strain at

yield point. The strain in transverse ring of 1.3 mm thick steel strip did not yield up to peak

load. The strain gauge was off scale near ultimate displacement. At ultimate displacement

the strain in longitudinal steel was 71.12% higher than its value at yield. The peak load

noted for positive loading direction was 15.72% higher than its value in negative direction.

Ductility calculated for positive loading direction is 15.05% higher than that of negative

direction. The negative direction is considered critical due to lesser lateral resistance.

Table 4.14: Parameters of backbone curves of SSC-1.3 cast with 32 Mpa concrete Positive Direction Negative Direction Strains Reinforcement Parameter Drift Load Drift Load Main Shear

Yield point 1.31 29.33 1.53 25.19 0.00198 0.000207 Peak load 2.38 33.96 3.33 28.62 0.00265 0.001565

Ultimate displacement 4.87 26.31 4.8531 22.89 0.00686 Off scale Ductility 3.734 3.172

4.10 COMPARISON OF YIELDING, PEAK AND ULTIMATE CYCLES FOR

CRITICAL DIRECTION The load-displacement hysteresis loops at yield point, peak load and ultimate displacement

stages can characterize hysteretic response of RC columns. The area enclosed by hysteresis

loop increases as the drift level is increased. Individual column’s yield point, peak load and

ultimate displacement loops for critical loading direction, determined in preceding section, is

superimposed for comparison in following section.

4.10.1 Group 1 Columns The yield, peak load and ultimate hysteresis loops of columns in group 1 are overlapped in

figure 4.41(a), 4.41(b) and 4.42 respectively. The energy dissipated, calculated as area

enclosed by these loops, is given in table 4.15 and compared in tables 4.16 to 4.18. In tables

4.16 to 4.18 negative sign, indicates a decrease and vice versa. In figure 4.41(a) it can be

observed that hysteresis curve of CRCS-60 at yield is thinner then the curves of remaining


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(a) (b) Figure 4.41: Loading cycles of group 1 columns cast with 25 Mpa concrete overlapped

(a) yield loading cycle (b) peak load cycle

Figure 4.42: Ultimate displacement cycles of group 1 columns cast with 25 Mpa concrete three columns. In table 4.17 the yield cycle of SSC-02 and SSC-1.3 is showing an increase

of 12.765% and 8.71% respectively as compared to CRCS-60 column. In table 4.18 the area

of yielding loop of CRCS-60 is 6.85% lesser than that of CRCS-40. The table 4.16 shows

that area of all loops, except for peak load cycle, has increased in case of SSC-02 and SSC-

1.3 columns as compared to CRCS-40 column. In figure 4.41(b), table 4.16 and 4.18 the area

of peak load cycle of CRCS-40 is found to be largest as compared to other columns. In table

4.17 it can be observed that both SSC-02 and SSC-1.3 has dominated the CRCS-60 column

but energy dissipated in hysteresis loop of peak load cycle of SSC-1.3 is found deficient. In

table 4.18, the energy of all the three loops of CRCS-60 is lesser than that of CRCS-40 and

likewise SSC-02 has dominated SSC-1.3 column. The hysteresis loop of ultimate

displacement cycle of SSC-02 has higher slope in loading and reloading direction. It is

because the core of the column is subjected to higher confinement as compared to remaining


101

columns. From table 4.16 through 4.18 it is found that peak load hysteresis of SSC-1.3

exhibited the minimum energy as compared to other three columns. The SSC-02 column has

dominated all the columns at selected three stages except for only peak load cycle in which

CRCS-40 has indicated greater energy.

Table 4.15: Energy dissipated in yield, peak and ultimate loading cycles of group 1 Group Column Energy in yield

cycle (KN-m) Energy in peak load

cycle (KN-m) Energy in ultimate

displacement cycle (KN-m) CRCS-40 0.238 2.015 3.33 CRCS-60 0.2217 1.236 3.2539 SSC-02 0.25 1.521 3.6 1

SSC-1.3 0.241 1.0919 3.4 Table 4.16: Yield, peak and ultimate cycles of SSC-02 & 1.3 compared with CRCS-40

Group Energy in Values of CRCS-40 (KN-m)

Gain / loss SSC-02 (%)

Gain / loss SSC-1.3 (%)

yield cycle 0.238 5.04 1.26 peak load cycle 2.015 -24.52 -45.81 1

ultimate displacement cycle 3.33 8.11 2.1 Table 4.17: Yield, peak and ultimate cycles of SSC-02 & 1.3 compared with CRCS-60




yield cycle 0.2217 12.765 8.71 peak load cycle 1.236 23.05 -11.66 1

ultimate displacement cycle 3.2539 10.63 4.5 Table 4.18: Yield, peak and ultimate cycles of CRCS and SSC columns Group

Energy in Gain / loss CRCS-60 versus CRCS-40 (%)

Gain / loss SSC-1.3 versus SSC-

02 (%) yield cycle -6.85 -3.6

peak load cycle -38.66 -28.212 1 ultimate displacement cycle -2.3 -5.5

4.10.2 Group 2 Columns The hysteresis loops at yielding, peak load and ultimate displacement stages are overlapped

in figures 4.43(a), 4.43(b) and 4.44 respectively. The values of energy calculated as area

enclosed by these loops is given in table 4.19 and compared in table 4.20 and 4.21. It can be

observed from the tables that CRCS-60 has greater energy dissipated in its yielding and peak

load cycles than other columns. The energy dissipated in ultimate displacement cycle of

CRCS-60 column was 9.812% lesser and 4.645% greater than SSC-02 and SSC-1.3 columns

respectively. It can be appreciated from table 4.21 that SSC-1.3 dissipated more energy in the


102

peak load cycle. However, at yielding and peak load stages SSC-02 has dissipated more

energy. Initially at yielding and peak load stages CRCS-60 has greater energy in the

hysteresis loops but SSC-02 dominated at ultimate displacement stage. The peak load

hysteresis of SSC-02 is thin and hence its energy is lesser than other two columns. CRCS-60

has been subjected to lesser cycles and yet SSC-02 has dominated at ultimate displacement

stage, therefore, it can be said that SSC-02 column has shown good performance.

(a) (b) Figure 4.43: Loading cycles of group 2 columns overlapped (a) yield loading cycle

(b) ultimate loading cycle

Figure 4.44: Ultimate loading cycle of group 2 columns overlapped Table 4.19: Energy dissipated in yield, peak and ultimate loading cycles of group 2

Group Column Energy in yield cycle (KN-m)

Energy in peak load cycle (KN-m)

Energy in ultimate displacement cycle (KN-m)

CRCS-60 0.5156 1.886 3.251 SSC-02 0.3752 1.2 3.5764 2 SSC-1.3 0.257 1.664 3.1


103

Table 20: Yield, peak and ultimate cycles of SSC-02 & 1.3 compared with CRCS-60




yield cycle 0.5156 -27.23 -50.15 peak load cycle 1.886 -36.37 -11.771 2 ultimate displacement

cycle 3.251 9.812 -4.645

Table 21: Yield, peak and ultimate cycles of SSC-02 versus SSC-1.3 Group

Energy in Gain / loss SSC-1.3 versus SSC-02 (%)

yield cycle -31.5 peak load cycle 38.66 2

ultimate displacement cycle -13.32 4.11 LATERAL LOAD CAPACITY The lateral load capacity of the columns is discussed in respective groups. The backbone

curves drawn in section 4.9.1 and 4.9.2 above have been superimposed in the following

sections. The maximum lateral load resisted by a column is its shear strength. In order to

simplify this comparison only critical directions have been superimposed in first quadrant.

4.11.1 Group 1 Columns The backbone curves of critical directions of group 1 columns cast with 25 Mpa concrete are

drawn in figure 4.45. The peak lateral load resisted by the columns is also marked. It can be

observed that up to 15 kN all the columns exhibited similar behavior. Initially, the slope of

curve of CRCS-60 is lesser than other columns but later it recovered and gave a higher peak

load as compared to CRCS-40 and SSC-1.3 column. The peak values achieved by different

columns of group 1 are compared in table 4.22. The gain/loss, mentioned in table 4.22,

indicates an increase if a value is positive and vice versa. It can be observed in figure 4.45

and table 4.22 that CRCS-40 and SSC-1.3 has indicated nearly equivalent lateral load

resistance. The SSC-02 column has indicated largest lateral strength in the group. Its lateral

load is 20%, 15.51% and 18.22% greater than CRCS-40, CRCS-60 and SSC-1.3 columns.

The lateral load of SSC-1.3 column is 1.86% and 5.533% lesser than CRCS-40 and CRCS-60

column. According to lateral force resisted by the columns of group-1 it has been found that

SSC-02 column showed better performance in the post yield region due to higher

confinement provided by the proposed transverse reinforcement.


104

Figure 4.45: Peak load marked on backbone curves of critical direction of group-1 columns

Table 4.22: Comparison of peak loads achieved by columns of group-1 Group Column Peak load

(KN) Gain / loss versus

CRCS-40 (%) Gain / loss versus


SSC-02 (%) CRCS-40 25.75 - - - CRCS-60 26.75 3.88 - - SSC-02 30.9 20 15.51 - 1

SSC-1.3 25.27 -1.86 -5.533 -18.22

Figure 4.46: Peak load marked on backbone curves of critical direction of group-2 columns

4.11.2 Group 2 Columns The peak lateral load resisted by the columns of group 2 is compared in figure 4.46. SSC-02

column has dominated the response for all drift levels. After 3% drift level there is sudden

drop in backbone curve of SSC-02 column and after a drift level of 3.8% it has recovered.

The peak load of SSC-02 has occurred at a drift level lower than other two columns. Up to 15

kN SSC-1.3 and SSC-02 had followed nearly a similar path. Table 4.23 shows that lateral

force resistance of SSC-02 and SSC-1.3 was 38.05% and 29.914% greater than that of

CRCS-60 column. The lateral resistance of SSC-1.3 column was 5.7% deficient as compared


105

to SSC-02 column. Both SSC columns exhibited greater peak load because their cores were

subjected to higher confining pressure exerted by the proposed transverse reinforcement. In

group 2 shear resistance of SSC-02 column was found highest.

Table 4.23: Comparison of peak loads achieved by columns of group-2 Group Column Peak load

(KN) Gain / loss versus


CRCS-02 (%) CRCS-60 22.03 - - SSC-02 30.412 38.05 - 2 SSC-1.3 28.62 29.914 -5.7

4.12 STIFFNESS DEGRADATION The stiffness of specimens is calculated as secant stiffness at yielding, peak load and ultimate

displacement. The three stiffness are called as initial, peak and ultimate denoted as Ko, Kp

and Ku. The yielding, peak load and ultimate displacement points are given in section 4.9.

(a) (b) Figure 4.47: Stiffness Ko, Kp and Ku of group 1 column (a) CRCS-40 (b) CRCS-60

(a) (b)

Figure 4.48: Stiffness Ko, Kp and Ku of group 1 column (a) SSC-02 (b) SSC-1.3

4.12.1 Group 1 Columns The stiffness of CRCS-40 column shown in figure 4.47(a) has higher slope of initial stiffness

as compared to its value in case of CRCS-60 column given in figure 4.47(b). The peak and


106

ultimate stiffness are higher in case of CRCS-60 column. The value of the stiffness is given

in table 4.24. The secant stiffness of SSC-02 and SSC-1.3 is drawn on respective backbone

curves in figure 4.48(a) and 4.48(b). The peak load of SSC-02 is located at a higher drift

level; therefore, it has lesser slope as compared to SSC-1.3 columns. The slopes of Ko and Ku

are higher in case of SSC-02 column.

Table 4.24: Values of stiffness Ko, Kp and Ku of group 1 column Group Column Ko

(KN/m) Kp

(KN/m) Ku

(KN/m) CRCS-40 982.425 393.035 192.43 CRCS-60 855.723 447.96 196.13 SSC-02 1016.47 533.016 228.47 1

SSC-1.3 952.105 596.523 169.305 Table 4.25: Stiffness Ko, Kp and Ku of SSC-02 and SSC-1.3 compared with CRCS-40 column of group 1

Group Parameter Values of CRCS-40 (KN/m)

Gain / loss SSC-02

(%)

Gain / loss SSC-1.3

(%) Ko 982.425 3.46 -3.086 Kp 393.035 35.615 51.774 1 Ku 192.43 18.72 -12.02

Table 4.26: Stiffness Ko, Kp and Ku of SSC-02 and SSC-1.3 compared with CRCS-60 column of group 1




Ko 855.723 18.785 11.26 Kp 447.96 18.99 33.2 1 Ku 196.13 16.5 -13.67

Table 4.27: Ko, Kp and Ku of CRCS-60 versus CRCS-40 and SSC-02 versus SSC-1.3 column of group 1

Group Parameter Gain / loss CRCS-60

versus CRCS-40 (%) Gain / loss SSC-1.3 versus SSC-02 (%)

Ko -12.9 -6.33 Kp 13.97 11.91 1 Ku 1.92 -25.9

The stiffness levels are compared in table 4.25 to 4.27. In the tables negative and positive

signs represent increase and decrease respectively. The stiffness of SSC-02 column, given in

table 4.25, has totally dominated the standard CRCS-40 column. The initial and ultimate

stiffness of SSC-1.3 is 3.086% and 12.02% respectively lesser than that of CRCS-40 column.


107

The initial, peak and ultimate stiffness of SSC-02 column is again found to be greater than

standard CRCS-60 column in table 4.26. The ultimate stiffness of SSC-1.3 is 13.67%

deficient as compared to that of CRCS-60 column. The CRCS-60 column has 12.9% lesser

initial stiffness but its peak and ultimate stiffness is higher than CRCS-40 column given in

table 4.77. The initial and ultimate stiffness of SSC-1.3 column is 6.33% and 25.9% lesser

than that of SSC-02 column. The peak stiffness of SSC-1.3 has been found higher than all

the columns. The Ku of SSC-1.3 is lesser because the column has achieved higher ultimate

displacement at lower value of load. The SSC-1.3 column achieved higher level of peak

stiffness due to greater width of its transverse rings. Based on the comparison of initial, peak

and ultimate stiffness the performance of SSC-02 column has been found better than

remaining columns.

(a) (b) Figure 4.49: Stiffness Ko, Kp and Ku of group 2 column (a) CRCS-60 (b) SSC-02

4.12.2 Group 2 Columns The stiffness of CRCS-60 and SSC-02 columns is given in figure 4.49(a) and 4.49(b)

respectively. The stiffness of SSC-1.3 column is marked on its backbone curve in figure 4.50.

The value of initial, peak and ultimate stiffness of group 2 columns is given in table 4.28. It

can be observed in table 4.29 that SSC-02 has initial, peak and ultimate stiffness 79.515%,

118.91% and 37.4% higher than that of CRCS-60 column. Similarly, the stiffness of SSC-

1.3 is 60.45%, 52.1% and 49.7% higher than CRCS-60 column. The initial and peak stiffness

of SSC-1.3 is lesser than that of SSC-02column but its ultimate stiffness is higher, as given in

table 4.30. The comparison of stiffness of group 2 columns indicates that SSC columns have

dominated CRCS column because of higher confinement provided by steel strips. Stiffness of


108

SSC-02 column was greater than remaining two columns and only its ultimate stiffness was

lesser than SSC-1.3 column. Among group 2 columns SSC-02 has shown good performance.

Figure 4.50: Stiffness Ko, Kp and Ku of SSC-1.3 column of group 2

Table 4.28: Values of stiffness Ko, Kp and Ku of group 2 column Group Column Ko

(KN/m) Kp

(KN/m) Ku

(KN/m) CRCS-60 591.705 325.904 182.077 SSC-02 1062.204 713.424 250.17 2 SSC-1.3 949.412 495.62 272.55

Table 4.29: Stiffness Ko, Kp and Ku of SSC-02 and SSC-1.3 compared with CRCS-60 column of group 2




Ko 591.705 79.515 60.45 Kp 325.904 118.91 52.1 2 Ku 182.077 37.4 49.7

Table 4.30: Ko, Kp and Ku of SSC-02 versus SSC-1.3 column of group 2

Group Parameter Gain / loss SSC-1.3

versus SSC-02 (%) Ko -10.62 Kp -30.53 2 Ku 8.94

4.13 DUCTILITY Ductility is the property of a structure due to which it can deform beyond its peak strength

without collapse. The ductile behavior of RC structures is greatly influenced by

confinement. Mathematically, it is the ratio of prescribed displacement beyond yield to the

displacement at yield. Hence, the ductility can be, in general terms, determined from

equation 4.9 and 4.10.


109

* pd

y

µ∆

=∆

(4.9)

ud

y

µ ∆=∆

(4.10)

Where, *dµ and dµ are displacement ductility at prescribed and ultimate displacement

respectively. y∆ , p∆ and u∆ are yield, prescribed and ultimate displacements respectively.

Figure 4.51: Yield and ultimate displacement marked on backbone curves of group 1

columns

4.13.1 Group 1 Columns The yield and ultimate displacements are marked on the backbone curves of group 1 columns

in figure 4.51. The ductility calculated for different columns is compared in table 4.31.

Negative sign, under parameter gain/loss, represents decrease and vice versa. The

comparison with CRCS-40 column indicates that its ductility is 19.52% and 21.7% higher

than that of CRCS-60 and SSC-02 columns respectively. SSC-1.3 column has its ductility

6.425% higher than ductility of CRCS-40 column. The ductility of CRCS-60 column is

2.7% higher and 32.24% lesser than that of SSC-02 and SSC-1.3 columns respectively. The

ductility of SSC-02 column is deficient by 35.9% as compared to SSC-1.3 column. The

initial slope of backbone curve of SSC-02 column was similar to that of other three columns

but after achieving a lateral load of 15 kN the curve exhibited a higher slope and the column

achieved its yield point at higher displacement. It is because SSC-02 degraded at a lower rate

due to the confinement provided by 2 mm thick strips. The response of SSC-02 column has

been found brittle due to higher yield displacement. The SSC-1.3 column, due to lesser


110

thickness of strip, could not maintain the higher slope of backbone curve and yielded at lesser

load as compared to SSC-02 column. The ductility of SSC-02 column is comparable with

standard CRCS-60 column but it has been found lesser than CRCS-40 column. The SSC-1.3

column achieved largest ultimate displacement and, therefore, its ductility has been found

highest as compared to remaining columns.

Table 4.31: Ductility of group 1 columns and its comparison Group Column

dµ (m/m)

Gain / loss versus CRCS-40 (%)


Gain / loss versus SSC-02 (%)

CRCS-40 4.98 - - - CRCS-60 4.008 -19.52 - - SSC-02 3.9 -21.7 -2.7 - 1

SSC-1.3 5.3 6.425 32.24 35.9

Figure 4.52: Yield and ultimate displacement marked on backbone curves of group 2 columns

4.13.2 Group 2 Columns The ductility of group 2 columns is calculated by equation 4.10 using yield and ultimate

displacements marked in figure 4.52. Table 4.32 indicates that ductility of CRCS-60 is 27%

and 6.67% lesser than that of SSC-02 and SSC-1.3 columns. The axial load, applied as

0.1Agfc′, has increased due to higher strength of concrete used in casting of group 2 column.

The increased axial load has decreased the ductility of conventionally reinforced concrete

column. Also the CRCS-60 column of this group has degraded rapidly in negative loading

direction. The ductility of SSC-1.3 column is 16.01% lesser as compared to SSC-02 column

because thinner strip could not achieve higher ultimate displacement under increased axial

load. The backbone curve of SSC-02 column shows a recovery in post peak region which

indicate the role of higher level of confinement. The comparison of ductility calculated for


111

columns of group 2 shows that performance of SC-02 column has been superior to CRCS-60

and SSC-1.3 columns cast with 32 Mpa concrete.

Table 4.32: Ductility of group 2 columns and its comparison Group Column

dµ (m/m)



CRCS-60 3.0 - - SSC-02 3.81 27 - 2 SSC-1.3 3.2 6.67 -16.01

4.14 RESIDUAL DISPALCEMENTS When RC column suffers inelastic damage due to earthquake loading it acquires a new

equilibrium position due to residual displacements introduced in it during the event. The

column, which has good seismic detailing, develops sufficient confining pressure on its core.

Such column will have greater capability to recover and come back to its original position.

In the following section the residual displacements are presented and compared as bar charts

for each group of columns.

Figure 4.53: Residual displacements of group 1 columns Table 4.33: Values of residual displacements of columns of group 1 given as percentage drift

Group Column At yield point (Drift (%))

At Peak load (Drift (%))

At ultimate displacement (Drift (%))

CRCS-40 0.1443 1.97 3.43 CRCS-60 0.16 1.23 3.6 SSC-02 0.0066 1.13 3.1 1

SSC-1.3 0.19 1.26 3.64


112

Table 4.34: Residual displacements of SSC-02 and SSC-1.3 as compared with CRCS-40 of group 1

Group Occurrence Values of CRCS-40 (Drift (%))



At yield point 0.1443 -95.43 31.67 At peak load 1.97 -42.64 -36.04 1 At ultimate displacement 3.43 -9.621 6.122

Table 4.35: Residual displacements of SSC-02 and SSC-1.3 as compared with CRCS-60 of group 1




At yield point 0.16 -95.875 18.75 At peak load 1.23 -8.13 2.44 1 At ultimate displacement 3.6 -3.89 1.11

Table 36: Comparison of residual displacements of CRCS-60 versus CRSC-40 and SSC-1.3 versus SSC-02 column of group 1

Group Occurrence Gain / loss CRCS-60 versus CRCS-40 (%)

Gain / loss SSC-1.3 versus SSC-02 (%)

At yield point 10.88 27 times At peak load -37.56 11.5 1 At ultimate displacement 4.95 17.42

4.14.1 Group 1 Columns The equilibrium shift noted at end of each loading cycle, applied on columns of group 1, is

plotted as bar chart in figure 4.53. The value of equilibrium shift after yield point, peak load

and ultimate displacement are given in table 4.33. In table 4.34 equilibrium shift of SSC-02

column is 95.43%, 42.64% and 9.621% lesser than those noted for CRCS-40 column. SSC-

1.3 has shown a decrease of 36.04% in equilibrium shift at peak load stage. However,

residual drifts of the column were more after yield and ultimate loading stage. In table 4.35

equilibrium shift of SSC-02, after yield, peak load and ultimate displacement cycle was

95.875%, 8.13% and 3.89% respectively lesser than for CRSC-60 column. In table 4.36 the

equilibrium shift of CRCS-60 column at yield point and ultimate displacement is 10.88% and

4.95% greater than that of CRCS-40 column. According to table 4.36, SSC-1.3 column

showed greater equilibrium shift than SSC-02 column. According to the comparison of


113

equilibrium shift SSC-02 had shown lesser residual displacements than other columns of

group 1.

Figure 4.54: Residual displacements of group 2 columns Table 4.37: Values of residual displacements of columns of group 2 given as percentage drift Group Column At yield point

(Drift (%)) At peak load (Drift (%))

At ultimate displacement (Drift (%))

CRCS-60 0.52045 2.38 3.98 SSC-02 0.2016 1.25 3.76 2 SSC-1.3 0.19 1.5035 2.97

Table 4.38: Residual displacements of SSC-02 and SSC-1.3 as compared to CRCS-60 of group 2




At yield point 0.52045 -61.26 -63.5 At peak load 2.38 -47.48 -36.83 2 At ultimate displacement 3.98 -36.83 -25.4

Table 4.39: Comparison of residual dispalcements of SSC-1.3 versus SSC-02 column of group 2

Group Occurrence Gain / loss SSC-1.3 versus SSC-02 (%)

At yield point -5.754 At peak load 20.28 2

At ultimate displacement -21.01 4.14.2 Group 2 Columns In figure 4.54 equilibrium shift of group 2 columns observed at end of each loading cycle is

presented in the form of bar chart. Only those cycles has been compared which were applied

to CRCS-60 column of this group. The residual displacements resulting after yield, peak load


114

and ultimate displacement cycle are given in table 4.37 in terms of percentage drift level.

Table 4.38 indicates that SSC-02 column has 61.26%, 47.48% and 36.83% lesser equilibrium

shift at yield, peak load and ultimate displacement respectively as compared to those noted

for CRCS-60 column. Similarly, SSC-1.3 also resulted in lesser displacements as compared

to CRCS-60 column. In table 4.39 equilibrium shift of SSC-1.3 column is 5.754% and

21.01% lesser as compared to that of SSC-02 column. However, equilibrium shift at peak

load noted for SSC-02 was 20.28% lesser than the value of SSC-1.3 column. The

comparison indicates that both SSC columns had lesser equilibrium shift as compared to

conventionally reinforced concrete columns.

(a) (b) Figure 4.55: Different energies defined on load displacement hysteresis (a) total energy,

damage energy and damp energy (b) strain energy 4.15 ENERGY DISSIPATION

The energy dissipated by any structural component subjected to cyclic loading can be

measured from load displacement hysteresis of their response. Total energy dissipated in a

cycle is defined as the area enclosed by the hysteresis cycle. Total energy is sum of damage

and damp energy. The total, damage and damp energy are marked on the hysteresis loop

shown in figure 4.55(a). The strain energy dissipated in a cycle is shown in figure 4.55(b).

The energy dissipated by columns is discussed in the following section.

4.15.1 Group 1 Columns SSC-02 has dissipated maximum total and strain energy among columns of group 1, shown

in figure 4.56(a) and 4.56(b) respectively. The energy dissipated in the form of damping and

damage, given in figure 4.57(a) and 4.57(b), has also been found highest in SSC-02 column.

Total Energy

Strain Energy


115

It is observed that up to 10th cycle, difference in energy dissipated by the columns of group 1

is less. It is because main portion of energy has been dissipated in inelastic range of column

specimen. The total energy dissipated is given in table 4.40. The SSC-02 column has

dissipated 19.12% and 19.37% more total and strain energy than CRCS-40 column, given in

table 4.41. However, SSC-1.3 column has been found deficient in energy dissipation by

31.77% and 27.93% respectively than CRCS-40 column. The total and strain energy of SSC-

02 column is 58.9% and 63.47% higher than CRCS-60 column as given in table 4.42. The

energy dissipated by SSC-1.3 column has been found lesser than CRCS-60 column. The

energy dissipated by CRCS-60 has been compared with CRCS-40 column in table 4.43. In

the same table energy dissipated by SSC-02 has been compared with SSC-1.3 column. It can

be noted that CRCS-60 has dissipated lesser energy as compared to CRCS-40 column.

Similarly, SSC-1.3 column has dissipated lesser energy as compared to SSC-02 column.

According to comparison of energies SSC-02 has dissipated maximum energy which is a

good indicator of performance.

(a) (b) Figure 4.56: Energy dissipated by columns of group 1 (a) total energy (b) strain energy

(a) (b) Figure 4.57: Energy dissipated by columns of group 1 as (a) damping (b) damage


116

Table 4.40: Energy dissipated by columns of group 1 columns Energy dissipated CRCS-40

(KN/m) CRCS-60 (KN/m)

SSC-02 (KN/m)

SSC-1.3 (KN/m)

Total energy 49.865 37.444 59.4016 34.022 Damping energy 25.7 19.14 31.865 18.94 Damage energy 24.2 18.31 27.537 15.07 Strain energy 21.5 15.7 25.665 15.065

Table 4.41: Comparison of energy dissipated by SSC-02 and SSC-1.3 compared with CRCS-40 of group 1 columns

Energy dissipated Value of CRCS-40 (KN/m)



Total energy 49.865 19.12484 -31.7718 Damping energy 25.7 23.98833 -26.3035 Damage energy 24.2 13.78926 -37.7273 Strain energy 21.5 19.37209 -29.9302

Table 4.42: Comparison of energy dissipated by SSC-02 and SSC-1.3 compared with CRCS-60 of group 1 columns





Table 4.43: Dissipated energy of CRCS-60 versus CRCS-40 and SSC-1.3 and SSC-02 of group 1 columns

Energy dissipated

Gain / loss CRCS-60 versus CRCS-40 (%)

Gain / loss SSC-1.3 versus SSC-02 (%)

Total energy -24.9093 -42.7254 Damping energy -25.5253 -40.5617 Damage energy -24.3388 -45.2736 Strain energy -26.9767 -41.3014

4.15.2 Group 2 Columns

The energy dissipated by columns of group 2 is presented graphically in figure 4.58 and 4.59.

All graphs are plotted only for drift levels which have been applied to CRCS-60. The total

energy curve of SSC-1.3, shown in figure 4.58(a), has higher slope as compared remaining

columns but the curve terminates earlier. The damping energy presented in figure 4.59(a) is

same up to seventh cycle for all columns of group 2. After seventh cycle SSC-02 dominates.

The strain energy curves of SSC-1.3 and SSC-02 columns followed nearly similar path up to

13th cycle as shown in figure 4.58(b). The values of energy dissipated by columns of group 2


117

are presented in table 4.44. The total and strain energy of SSC-02 is 57.837% and 75.54%

higher than CRCS-60 column as given in table 4.45. SSC-1.3 exhibited 27.24% and 24.5%

lesser total and strain energy dissipation than CRCS-60 column. SSC-02 dissipated higher

energy than SSC-1.3 column, as given in table 4.46. The SSC-02 column has dissipated

highest energy and hence indicated better performance.

(a) (b) Figure 4.58: Energy dissipated by columns of group 2 (a) energy calculated as area under

backbone curve (b) energy dissipated

(a) (b) Figure 4.59: Energy dissipated by columns of group 2 as (a) damping (b) damage

Table 4.44: Energy dissipated by columns of group 2 Energy dissipated CRCS-60

(KN/m) SSC-02 (KN/m)

SSC-1.3 (KN/m)

Total energy 19.325 30.502 14.06 Damping energy 10.305 17.17 7.92 Damage energy 9.02 13.332 6.14 Strain energy 7.713 13.54 5.823


118

Table 4.45: Comparison of energy dissipated by SSC-02 and SSC-1.3 with CRCS-60 of group 2





Table 4.46: Dissipated energy of SSC-1.3 and SSC-02 of group 2 Energy dissipated Gain / loss SSC-1.3 versus SSC-02 (%)

Total energy -53.9047 Damping energy -53.873 Damage energy -53.9454 Strain energy -56.9941

4.16 MODELING ON RESPONSE 2000

The load-displacement curve of RC elements, subjected to shear, axial force and bending

moment, can be estimated using response 2000 (Bentz and Collins, 2009). It is windows

based program with a well developed GUI. The analysis of Response-2000 is based on

engineering beam theory, assuming that rate of flexural stresses across a section defines shear

stresses and plane section remains plane. The variation of stresses and strains is related using

Modified Compression Field Theory (Bentz, 2001). The program generates a load-

displacement response by using its member response function. The curves generated by

member response function were found deficient in estimating ultimate displacement for the

columns tested in the laboratory. Therefore, two other approaches have been suggested here

in this research and presented in the following sections.

4.16.1 Approaches To Plot Theoretical Load Displacement Curves The push-over curve of a column as shown in figure 4.60 can be calculated by integrating

curvature and shear strain distribution along its height. The displacement “∆” under

application of a load vector “P” is contributed by flexure and shear strain. Consider the

column of figure 4.60, contribution of flexure to the deflection at point “B”, with respect to

the tangent drawn to elastic curve at point “A”, is equal to the first moment of the area

between point “A” and “B” of the curvature diagram taken about point “B”. The moment-

area of curvature diagram over height of the column can be numerically integrated by

dividing the entire column into strips. The shear contribution to the total deflection at point


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“B” is the sum of product of shear strain and height of strips considered. Mathematically the

procedure can be represented by equation 4.11. The required curvature iφ and shear

strain iγ can be determined using Response-2000.

Figure 4.60: Graphical representation of flexure and shear components of deflection under a

lateral load vector “P” and axial load “N”

[ ]1

n

i i i i ii

d x dφ γ=

∆ = +∑ (4.11)

In the present study, the curvature and shear strain achieved from Response-2000 have been

used in two different ways to determine the displacement of column components. The two

procedures have been named as linear variation and interpolation. These procedures have

been compared with the experimental results and member response of Response-2000.

4.16.1.1 Linear Variation Approach The moment-curvature and shear-shear strain plots given by Response-2000 caters for full

inelasticity. The shear dominant section is located at 0.9d from the shear block supporting

the column, where as, maximum moment is considered at the face of the shear block (Bentz

and Collins, 2009). The critical section can be determined by carrying out analysis at shear

and moment dominant sections and comparing their peak loads. In this approach analysis on

response-2000 is carried out for critical section only. The curvature and strains for remaining

strips are found linearly. It is assumed that deformations in an element are concentrated at

critical section. The deformations at other section can be estimated by linearly varying

deformation of critical section along length of the element. The procedure is listed below.

a. Analyze shear and moment dominant sections and determine their peak loads.

b. Declare the section failing at lower load as critical.

N


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c. The moment vector of moment-curvature relationship of Response-2000 is converted

to load vector by dividing it by the moment arm.

d. Divide the column in to “n” number of strips.

e. Three vectors i.e force “Pn”, curvature “Φn” and shear strain “Γn” achieved from

analysis of critical section on Response-2000 are used to determine the load-displacement

curve for the column. The curvature niφ and shear strain niγ , in figure 4.61, are the ith

element of curvature vector “Φn” and shear strain vector “Γn” respectively.

f. The curvature of jth element, shown in figure 4.61, can be determined

from ( )j ni n jx xφ φ= . The curvature jφ is assumed to be constant for entire height of strip.

d. The flexure contribution of jth strip to deflection under Pni (ith element of load vector

Pn) is given as j ix dφ .

g. The shear strain niγ is constant through out the height of the column, therefore,

j niγ γ= . Thus the shear contribution of jth strip is nidγ .

h. The total contribution of jth strip to the deflection under load Pni is given by

j ix dφ + nidγ .

i. Similarly, determine contribution of remaining strips to the deflection under load Pni.

j. Change the value of niφ and niγ for next value of Pni and determine the complete load

deflection curve.

k. In cases where shear section is critical the values of niφ are determined by linearly

extending curvatures of critical section to the base. The shear strain niγ is constant.

Figure 4.61: Graphical representation of linear variation approach


121

4.16.1.2 Interpolation Approach In this approach the curvature and shear strain for each strip are found by interpolation, at

each load step. The analysis for moment-curvature and shear-shear strain is carried out on

Response-2000. The procedure is explained below.

Figure 4.62: Graphical representation of interpolation approach.

a. Find a critical section as done in linear variation approach.

b. The force vector “Pc” is achieved from analysis of critical section. If moment

section is critical convert the moments to force by dividing it by respective moment arm

given as input in Response-2000.

c. Divide the column into “n” strips.

d. For each strip carryout the analysis on Response-2000 i.e if you have “n” strips of

thickness “d”, there will be “n” analysis.

e. For each element of “Pci” of force vector “PC” find the corresponding curvature and

shear strain, by interpolation, in the moment-curvature and shear-shear strain relationship of

each strip given by Response-2000.

f. Mathematically the displacement “∆i” for load “Pci” is given by equation 4.12 below.

In the equation 1,cni cji c iandφ φ φ are the curvatures for nth, jth and 1st element corresponding to

force vector Pci and xn, xj and x1 are respective moment arms of strips. Similarly,

1,cni cji c iandγ γ γ are shear strains for nth , jth and 1st element corresponding to force Pci.

Graphically the approach is presented in figure 4.62.

g. For each value of Pci in the force vector Pc find the corresponding curvature and

shear strain from analysis output of Response-2000 carried out for each strip.


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1 1 1...... ......i cni n cni cji j cji c i c idx d dx d dx dφ γ φ γ φ γ∆ = + + + + + (4.12) 4.16.2 Comparison Of Results The two approaches are applied on CRCS-60 cast with 32 Mpa concrete, CRCS-60 and

CRCS-40 cast with 25 Mpa concrete. The analytical curves do not capture strain penetration

and pinching in the negative direction accurately. Therefore, for comparison mean curve of

positive and negative backbone curves of experimental load-displacement hysteresis are

used. The approaches are also compared with member response of Response-2000. The

linear variation approach has shown satisfactory results for estimating the ultimate

displacement of the experimental backbone curve. The results of interpolation approach were

almost identical with member response of Response-2000 program.

Figure 4.63: Mean curve of CRCS-60 column cast with 32 Mpa concrete drawn by plotting backbone curves of positive and negative direction in first quadrant

4.16.2.1 CRCS-60 Column Cast With 32 Mpa Concrete The backbone curves of load-displacement hysteresis for positive and negative direction are

plotted in first quadrant in figure 4.63 and the mean curve is drawn. The load displacement

curve generated for CRCS-60 column by linear variation approach is overlapped with

experimental mean curve in figure 4.64(a). The theoretical curve has over estimated load

displacement response which is obvious because it is difficult to capture strain penetration

accurately. The estimated peak load is 10% higher than that of mean curve. The linear

variation approach has estimated ultimate displacement quite accurately. The member

response of Response-2000 is overlapped with the mean curve in figure 4.64(b). The lateral

force of Response-2000 curve is 10% higher but it has estimated 66% lesser ultimate

displacement. In figure 4.65(a) load displacement curve plotted by linear variation approach


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is overlapped with member response curve of Response-2000. The response curve has higher

initial slope but its estimate of peak lateral force is same as that of linear variation approach.

The member response of Response-2000 and interpolation approach has been plotted

together in figure 4.65(b). Both curves has followed almost same path but interpolation

(a) (b) Figure 4.64: Theoretical and experimental load displacement curves of CRCS-60 cast with 32 Mpa concrete (a) experimental and linear variation curves overlapped (b) experimental

curve and member response of response 2000 overlapped

(a) (b) Figure 4.65: Theoretical load displacement curves of CRCS-60 cast with 32 Mpa concrete

(a) linear variation and member response of response 2000 overlapped (b) member response of response 2000 and interpolation overlapped

approach has estimated 27% larger ultimate displacement than member response of

Response-2000. In figure 4.66 linear variation and interpolation approach has been

superimposed. The estimate of peak lateral force is again same but ultimate displacement of

linear variation approach is 57% higher than interpolation approach. Similar, level of lateral

force has been estimated by all approaches. However, only linear variation approach

estimated the ultimate displacement accurately.


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Figure 4.66: Theoretical load displacement curves of CRCS-60 cast with 32 Mpa concrete,

linear variation and interpolation overlapped

4.16.2.2 CRCS-60 Column Cast With 25 Mpa Concrete The backbone curves drawn on hysteresis in negative and positive direction are plotted in

first quadrant for taking its mean in figure 4.67. The mean curve of CRCS-60 column has

Figure 4.67: Mean curve of CRCS-60 column cast with 25 Mpa concrete drawn by plotting

backbone curves of positive and negative direction in first quadrant been compared with linear variation and member response of Response-2000 in figure

4.68(a) and 4.68(b) respectively. Both the curves have estimated peak lateral force

accurately. The estimate of ultimate displacement is 17% and 69% lesser than mean

experimental curve. The linear variation and interpolation approaches are compared with

member response of Response-2000 in figure 4.69(a) and 4.69(b) respectively. The estimate

of peak lateral force is same in the three approaches. The ultimate displacement given by

linear variation and interpolation is 66% and 13% higher than that achieved from Response-

2000. The two suggested approaches are compared in figure 4.70. The ultimate displacement

of linear variation curve is 69.24% higher than interpolation curve. It is noted that estimated

ultimate displacement by linear variation approach is quite accurate.


125

(a) (b) Figure 4.68: Theoretical and experimental load displacement curves of CRCS-60 cast with 25 Mpa concrete (a) experimental and linear variation curves overlapped (b) experimental

curve and member response of response 2000 overlapped




linear variation and interpolation overlapped


126

Figure 4.71: Mean curve of CRCS-40 column cast with 25 Mpa concrete drawn by plotting backbone curves of positive and negative direction in first quadrant

Figure 4.72: Theoretical and experimental load displacement curves of CRCS-40 cast with 25 Mpa concrete (a) experimental and linear variation curves overlapped (b) experimental

curve and member response of response 2000 overlapped 4.16.2.3 CRCS-40 column cast with 25 Mpa concrete The backbone curves, in negative and positive direction, of CRCS-40 column cast with 25

Mpa concrete have been plotted in first quadrant and their mean is drawn in figure 4.71. The

peak lateral load estimated by all approaches, for CRCS-40 column, is approximately equal

and closely matches the value of peak load of mean experimental curve. The ultimate

displacement estimated by linear variation approach is 20.21% lesser than mean experimental

curve, shown in figure 4.72(a). The Response-2000 curve has under estimated ultimate

displacement by 72% plotted in figure 4.72(b). The linear variation and interpolation

approach has been compared with Response-2000 curve in figure 4.73(a) and 73(b). The

estimate of ultimate displacement of interpolation and linear variation approach is 12.6% and

64.7% higher than the value given by Response curve. The linear variation and interpolation

approach has been compared with each other in figure 4.74. The ultimate displacement of

linear variation curve is 69.4% higher than interpolation curve. Comparison carried out here


127

dictates that estimate of linear variation approach has been more realistic due to its accuracy

in calculation of ultimate displacement.




linear variation and interpolation overlapped 4.17 MODELING ON DRAIN-3DX The estimation of response of RC elements under cyclic loads is a complex phenomenon

involving strain penetration, distribution of strain across crack, contribution of flexure and

shear to lateral displacement and contribution of reinforcement slip to lateral displacement

etc. In order to estimate response of a RC element, with reasonable accuracy, DRAIN-3DX

was selected to model the observed response of SSC and conventionally reinforced concrete

columns. DRAIN-3DX is a finite element based program which contains a cyclic shear

element. The program has a element library combined with a accessible source code. The

program does not have a graphic user interface and the user has to input the data in form of a

large general format file.


128

4.17.1 Element Selected In Modeling Of Columns The element manual (Powell and Campbell, 1994) of DRAIN-3DX explains seven elements.

The manual includes an element 15 which is used to model flexural behavior. The element is

also known as flexure element and it is assumed to be elastic in shear and torsion (Powell and

Campbell, 1994) and (Prakash et al., 1994). The element can model a concrete or steel beam

and column. It can model even a single cross section of concrete or steel beam and column.

The element can also be used to model beams and columns of a large RC or steel structure.

The local axis of the element is defined and complete element to be modeled is divided into

number of segments. Along length of the segment, behavior is monitored only at central

cross section. The cross sectional properties and behavior can vary from segment to segment

but not with in the segment. The segment is also known as deformable region and caters for

spread of inelasticity over the cross section and along length of the member through

distributed plasticity. The cross section is divided into number of fibers. A reinforced

concrete section has its concrete and steel fibers defined separately. The cross sectional area

and location of each fiber is defined in terms of coordinates measured from local axis of the

element. The element caters for interaction of axial load and bending moment. Element 15

is graphically presented in figure 4.75.

Figure 4.75: Graphical presentation of element 15 (Powell and Campbell, 1994)

The total response of an element is accumulation of responses of fibers calculated at their

centers, therefore, higher number of fibers will result in greater accuracy. In figure 4.75, rigid

end zones have been marked which are used to simulate joints. Zero length connection

hinges can also be introduced, with or without rigid zone, to calibrate pull out properties and

cater for deformation. By increasing length of hinge or dividing it into parts does not


129

increase accuracy of estimating distribution of curvature along ends of elements (Isakovic

and Fischinger, 1998). In present modeling, hinge has been used and rigid zone discarded.

4.17.1.1 Material Modeling For Element The steel and concrete model used in element type 15 of DRAIN-3DX is shown in figure

4.76(a) and 4.76(b) respectively. In post peak behavior the concrete model assume strength

degradation and steel model assumes kinematic strain hardening. The concrete model in its

post peak includes intermediate and full degradation in unloading stiffness, defined by

unloading factor. It has been shown that only full degradation option is affective (Isakovic

and Fischinger, 1998). Both the models are defined by five stress-strain points of envelops

shown in figures 4.76(a) and (b). The concrete model includes two points to cater for tensile

strength of concrete. The steel model uses same properties in tension and compression.

(a) (b) Figure 4.76: Stress-strain model (a) steel (b) concrete (Powell and Campbell, 1994)

4.17.1.2 Material model for connection hinge

Figure 4.77: Basic properties of pullout fiber (Powell and Campbell, 1994)

Element type 15 of DRAIN-3DX caters for deformations like distribution of rotation over

ends, opening of concrete fibers and reinforcement slippage at ends by employing a zero

length connection hinge. In the connection hinge steel and concrete fibers, as explained in


130

element properties, are replaced by pullout and gap fibers. The pullout fibers model the

reinforcement slippage and gap fibers take into account opening of gaps in concrete fibers.

The properties of pullout fiber are given in the form of a trilinear curve which has similar

degradation properties in positive and negative loading directions as shown in figure 4.77.

The trilinear curve can be calibrated to match the required behavior. The parameters cater for

repeated cyclic loading/unloading and also take into account the affects of strength

degradation, stiffness and pinching behavior in unloading branch of each cycle.

The trilinear curve is decomposed in to two bilinear curves and one elastic curve as shown in

figure 4.78(a). The elastic curve acts parallel to the bilinear curves. The degradation of

bilinear curve is defined by the stiffness degradation factor (SDF) as shown in figure 4.78(b).

The factor SDF can be assigned a value of degradation between zero and one which causes

the bilinear curve to degrade at a slope existing between two extremes.

(a) (b) Figure 4.78: Degradation parameters for connection hinge (a) decomposition of basic

trilinear curve (b) stiffness degradation factor applied to elastic-plastic components (Powell and Campbell, 1994)

(a) (b) Figure 4.79: Parameters defining strength loss of decomposed components (a) Strength loss in each component depends on strength degradation factor (STDF or SCDF) and the ratio of accumulated plastic displacement to saturated displacement (ST or SC) (b) Pinch factor (PF),

pinch strength factor (PSF and plateau factor (PPF) (Powell and Campbell, 1994)


131

The strength loss in a component is defined by strength degradation factor STDF or SCDF.

The factor has only two possible inputs i.e zero and one, indicating no and full degradation. It

means that STDF or SCDF only put on the degradation and does not quantify it. The rate of

degradation is defined through a ratio of accumulated plastic displacement and saturated

displacement denoted by ST or SC as shown in figure 4.79(a). The ratio ST represents

tensile plastic slip and causes compressive strength degradation and affects of SC are vice

versa. The pinching is modeled through three parameters PF, PSF and PPF as shown in

figure 4.79(b). The factor PF determines strength of the fiber which under goes pinching.

The strength occurring at pinching is known as pinch strength and is determined by PSF. The

length of the plateau, which occurs after pinching, is defined by pinching plateau factor PPF.

If PPF is kept equal to one it means that plateau will extend until it meets last unloading

curve. There is no broad experimental data which could guide about value of factor PPF. In

modeling value of PPF has been considered equal to unity. The gap fiber properties are

given in figure 4.80. The factor SC1 and SC2 are defined in terms of compressive stress and

corresponding displacement occurring in concrete gap fibers due to opening of cracks. Factor

FU defines unloading branch of curve. In present study FU has been kept as 0.5.

Figure 4.80: Gap fiber properties of concrete fibers (Powell and Campbell, 1994)

4.17.2 Calibration Of Material Properties Of RC Columns Three columns of group 2 were selected for analytical modeling. The selected columns

included CRCS-60, SSC-02 and SSC-1.3 columns cast with 32 Mpa concrete. The basic

column element, modeled by element type 15, has been divided into three segments of

different lengths. Before carrying out actual calibration accuracy of DRAIN-3DX was

checked by calculating moment curvature of CRSC-60 column by section analysis using

interaction equation and comparing it by moment curvature of critical section plotted by


132

carrying out push over analysis of same column on DRAIN-3DX. Both the curves are

superimposed in figure 4.81. The curve of DRAIN-3DX has higher initial slope, which is

expected from a finite element based analysis. The comparison of two curves indicates

reasonable accuracy of DRAIN-3DX. The calibration of experimental results of columns is

explained in following section. In sections 4.10 to 4.14 only backbone curves of critical

loading direction were compared. It has been noted in section 4.8 that some columns

exhibited balanced behavior in both loading direction while some other were found deficient

in one direction. In order to cater for this aspect and reduce the affects of limitations of test

setup, it was decided to take mean of the backbone curves of both loading directions. In

calibration the properties of material models, used in generating analytical hysteresis of

columns, have been adjusted to match the mean experimental curves.

Figure 4.81: Moment curvature plotted by section analysis and DRAIN-3DX

4.17.2.1 CRSC-60 Column Cast With 32 Mpa Concrete The mean curve of the column has been presented in figure 4.76. The hysteresis curve

generated in DRAIN-3DX along with backbone curve is shown in figure 4.82. The

experimental mean backbone curve of load displacement hysteresis is also marked in figure

4.82. Analytical curve closely matches the mean curve. In figure 4.83(a) complete

calibrated curve of steel model is shown and in figure 4.83(b) the curve has been plotted up

to start of strain hardening in order to view the initial slope. The high stress and strain value

in the last branch of steel model have been kept to simulate strain hardening. The calibrated

concrete model is shown in figure 4.84. The properties of pullout and gap fibers, used in

calibration, are given in table 4.47 and 4.48. In table dimensionless degradation factors are

also mentioned.


133

Figure 4.82: Hysteresis of CRCS-60 column cast with 32 Mpa concrete generated on DRAIN-3DX and compared with its mean experimental envelop

(a) (b) Figure 4.83: Calibrated model for reinforcement for CRCS-60 column cast with 32 Mpa (a)

complete model including strain hardening (b) up to start of strain hardening

Figure 4.84: Calibrated model for concrete for CRCS-60 cast with 32 Mpa

Table 4.47: Pullout fibers calibrated for hysteresis of CRCS-60 cast with 32 Mpa

Stiffness Modulus

K1

Stiffness Modulus

K2

Stiffness Modulus

K3

Stress S1T

Stress S2T

Stress SC1 Stress Overshoot

Basic Properties (kN/m2) 190000000 1 0.5 400000 580000 400000 580000 0.01

Degradation 0.48 0.9 0.9 0.004 0.004 1 0.2 0.5

Table 4.48: Gap fibers calibrated for CRCS-60 cast with 32 Mpa concrete Stress SC1

(kN/m2) Stress SC2

(kN/m2) Modulus K1

(kN/m2) Modulus K2

(kN/m2) Modulus K3

(kN/m2) Unloading Overshoot

30000 32000 1.01E+15 1.01E+14 1E+13 0.5 1


134

Figure 4.85: Mean curve of SSC-02 column cast with 32 Mpa concrete Figure 4.86: Hysteresis of SSC-02 column cast with 32 Mpa concrete generated on DRAIN-

3DX and compared with its mean experimental envelop

(a) (b) Figure 4.87: Calibrated model for reinforcement for SSC-02 column cast with 32 Mpa (a)


Figure 4.88: Calibrated model for concrete for SSC-02 cast with 32 Mpa

4.17.2.2 SSC-02 Cast With 32 Mpa Concrete The mean curve of SSC-02 column is plotted in figure 4.85 by taking mean of backbone

curves of positive and negative loading directions. The hysteresis of SSC-02 generated in


135

DRAIN-3DX is shown in figure 4.86 and experimental mean curve is superimposed. The

calibrated hysteresis is found in good agreement with the experimental mean curve. The

steel properties finalized in calibration are plotted in figure 4.87(a). The high value of stress

and strain at ultimate has been selected to cater for strain hardening. In order to view initial

slope of steel curves it has been plotted up to start of strain hardening in figure 4.87(b). The

calibrated concrete model is shown in figure 4.88. The properties of pullout and gap fibers

found in calibration are given in table 4.49 and 4.50 respectively.

Table 4.49: Pullout fibers calibrated for hysteresis of SSC-02 cast with 32 Mpa

Stiffness Modulus

K1

Stiffness Modulus

K2

Stiffness Modulus

K3

Stress S1T

Stress S2T



Degradation 0.75 0.5 0.5 0.004 0.004 1 0.25 0.5 Table 4.50: Gap fibers calibrated for SSC-02 cast with 32 Mpa concrete Stress SC1

(kN/m2) Stress SC2

(kN/m2) Modulus K1

(kN/m2) Modulus K2

(kN/m2) Modulus K3


30000 34000 1.02E+15 1.01E+14 1E+13 0.5 1

Figure 4.89: Mean curve of SSC-1.3 column cast with 32 Mpa concrete

Figure 4.90: Hysteresis of SSC-1.3 column cast with 32 Mpa concrete generated on DRAIN-

3DX and compared with its mean experimental envelop


136

(a) (b) Figure 4.91: Calibrated model for reinforcement for SSC-1.3 column cast with 32 Mpa (a)


4.17.2.3 SSC-1.3 Cast With 32 Mpa Concrete The backbone curves of positive and negative direction are drawn in first quadrant in order to

take their mean, plotted in figure 4.89. The hysteresis of SSC-1.3 generated in DRAIN-3DX

is shown in figure 4.90 and mean experimental backbone curve is superimposed. The

calibrated hysteresis is found in good agreement with the experimental mean curve. The

calibrated curve of steel is shown in figure 4.91(a). The strain hardening is modeled by

selecting a high value of ultimate stress and strain. The reinforcement curve has been plotted

up to start of strain hardening in figure 4.91(b), in order to view its initial slopes. The

concrete model finalized in calibration is shown in figure 4.92. The properties of pullout and

gap fibers confirmed in calibration are given in table 4.51 and 4.52 respectively.

Figure 4.92: Calibrated model for concrete for SSC-1.3 cast with 32 Mpa

Table 4.51: Pullout fibers calibrated for hysteresis of SSC-1.3 cast with 32 Mpa

Stiffness Modulus

K1

Stiffness Modulus

K2

Stiffness Modulus

K3

Stress S1T

Stress S2T



Degradation 0.8 0.59 0.55 0.004 0.004 1 0.2 0.5


137

Table 4.52: Gap fibers calibrated for SSC-1.3 cast with 32 Mpa concrete Stress SC1

(kN/m2) Stress SC2

(kN/m2) Modulus K1

(kN/m2) Modulus K2

(kN/m2) Modulus K3


30000 33000 1.02E+15 1.01E+14 1E+13 0.5 1

(a) (b)

Figure 4.93: Calibrated material model (a) concrete model (b) initial slope of steel model

4.17.2.4 Comparison Of Material Properties The calibrated concrete model and initial slope of calibrated steel model of all columns is

plotted in figure 4.93(a) and 4.93(b) respectively. It is observed that initial slope of steel

model of CRCS-60 is 28.42% higher than SSC-02 and 38.04% lower than SSC-1.3 columns.

The initial slope of concrete model of both the SSC columns is same but CRCS-60 column is

lacking by about 14%. The second slope of concrete model is equal for all columns but in

steel model SSC-02 still lacks CRCS-60 by 38%. The steel model of SSC-1.3 is, however,

4% higher than CRCS-60 column. In third slope steel model of all columns is same but

concrete model of SSC-1.3 is 5% higher than SSC-02 and CRCS-60 column. In the fourth

slope SSC-02 starts dominating CRCS-60 column. The concrete and steel model of SSC-02

is 20% and 14.5% higher than CRCS-60 column respectively. The final slope of steel model

of SSC-02 column is also 5% higher than CRCS-60 column. The properties of material

models calibrated here in this section will be used in modeling of RC multistory frame in

next chapter. It is expected that the time period of the frame which will be modeled with

material properties of SSC-1.3 will lesser because of higher initial slope of its steel model.

The SSC-02 frame have least initial slope of its steel model, therefore, the frame which will

be modeled with its properties will have highest time period. After initial branch both the

material models of SSC-02 column show equal or greater slope as compared to CRCS-60

column, which indicate that the former will improve the performance of the RC frame.

CHAPTER 5

138

PERFORMANCE OF RC FRAMES 5.1 INTRODUCTION In the previous chapters the ground motions recorded within Pakistan has been digitized and

behavior of RC columns confined with different confining arrangements studied. The main

purpose of seismic resistant structure is to save precious lives and allow only repairable

damage. Structural engineers in Pakistan, before Kashmir earthquake, considered most of its

regions in moderate seismic zones. A review of the losses, which occurred in Pakistan before

Kashmir earthquake (Ilyas and Rizwan, 2004) and (Ilyas et al., 2005) reveals that northern

regions of the country were always seismically active. However, these earthquakes were not

large enough to change the mind set until Kashmir earthquake. The damages which occurred

in Kashmir earthquake (Ilyas and Rizwan, 2006 and 2006a) were totally unexpected for the

structural engineers working in the country. In addition to irreparable life losses the economy

of the country also suffered a major set back. The performance objectives, code provisions

considered in designing and quality of construction all was questionable. A need has been

felt to study the performance of structures under earthquakes recorded in Pakistan.

In this chapter performance of an eight storey RC frame has been evaluated under application

of east-west component of Kashmir earthquake recorded at Abbottabad. The performance

parameters achieved from application of Kashmir earthquake are compared with those

resulted from application of north-south component of Imperial Valley earthquake, 1940,

recorded at El Centro. The third time history used in the study is scaled Kashmir earthquake.

The Kashmir earthquake recorded at Abbottabad has been scaled to study the hypothesis that

damage in the city from the earthquake would have been many folds if the PGA of the

ground acceleration was equal to PGA of El Centro ground motion. The affect of confining

technique of Steel Strip Confined columns, presented in previous chapter, is studied by

analyzing three eight storey RC frames respectively modeled with material properties of

CRCS-60, SSC-02 and SSC-1.3 columns calibrated in section 4.17.2. The analysis of the

frames will indicate the affect of type of column, used in modeling, on overall performance

CHAPTER 5 PERFORMANCE OF RC FRAMES

139

of the frame. The RC frames are analyzed in DRAIN-3DX (Prakash et al., 1994), which can

describe the hysteretic behavior of beam and column hinges under cyclic loading. In this

study the damage is quantified through final softening (Ghobarah and Biddah, 1999) and max

roof drift (Yanglin, 2003), (Federal Emergency Management Agency, 1997) and (Federal

Emergency Management Agency, 2005).

The response parameters studied and presented here includes storey displacement history,

inter storey drift, max storey displacement achieved, base shear versus roof displacement

hysteresis, total energy dissipated and energy dissipated by RC elements at each level. The

analysis of response parameters indicate that damage due to Kashmir earthquake increases

four folds in a structures with time period falling in intermediate range. The best

performance has been achieved for RC building modeled with SSC-02 columns. The result

of this research will acquaint engineers, involved in design process, with response of

structures under earthquake loading.

5.2 DESCRIPTION OF BASIC BUILDING STRUCTURE The basic RC building frame selected for performance evaluation has been selected from

literature (Sashi et al., 2004). However, in order to induce considerable damage, the cross

sectional properties of columns have been reduced by 30% and that of beam by 40%. The

plan of the building is shown in figure 5.1. The building has five and three bays of 9.1 m

width in north-south and east-west direction respectively. The building consists of typical RC

frames. The uniformly distributed roof and floor loads are 7.55 kN/m2 and 8.9 kN/m2

respectively. These unit loads does not include self weight of different components which is

added separately. For performance evaluation an exterior frame in east west direction is

selected and modeled in DRAIN-3DX. The elevation of eight storey frame is shown in

figure 5.2(a). First storey of the frame is 4.3 m and remaining stories are 3.66 m in height.

The typical frame consists of three bays of 9.1 m width. The column grids, stories and beam

levels are identified in figure 5.2(b). The cross sectional sizes of column and beam elements

are given in table 5.1 and 5.2. The sizes of columns and beams are given according to stories

and levels shown in figure 5.2(b). It can be observed in table 5.1 and 5.2 that reinforcement


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ratio is also varied in cross sections of same sizes to achieve required strength at different

stories and levels.

Figure 5.1: Plan view of the eight storey RC frame Table 5.1: Detail of columns of eight storey RC frame. All dimensions are in cm

Exterior Column Interior Column Storey Size Steel Group Size Steel Group 1 85 x 85 18 # 10 1 94 x 77 16 # 10 5 2 85 x 85 18 # 8 2 94 x 77 16 # 9 6 3 85 x 85 18 # 8 2 94 x 77 16 # 9 6 4 81 x 81 18 # 8 3 90 x 73 16 # 9 7 5 81 x 81 18 # 8 3 90 x 73 16 # 9 7 6 77 x 77 16 # 8 4 90 x 73 14 # 9 8 7 77 x 77 16 # 8 4 81 x 64 12 # 8 9 8 77 x 77 16 # 8 4 81 x 64 12 # 8 9

`


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(a) (b) Figure 5.2: RC multistorey frame (a) Elevation (b) identification of column grids,

level and stories

Table 5.2: Detail of beams of eight storey RC frame. All dimensions are in cm All beams Level Size Top Steel Bottom Steel Group

2 87 x 51.5 4 # 10 4 # 9 10 3 87 x 51.5 4 # 10 4 # 9 10 4 83 x 51.5 4 # 10 4 # 9 11 5 83 x 51.5 4 # 10 4 # 9 11 6 75 x 51.5 4 # 10 4 # 8 12 7 71 x 47.5 4 # 9 4 # 7 13 8 67 x 48 4 # 9 4 # 6 14 9 67 x 48 4 # 9 4 # 6 14

5.3 GROUND MOTION SELECTED In this study real time recorded data of Kashmir earthquake has been used in analysis. The

7.9 magnitude earthquake occurred on 8th October, 2005 with its epicenter near Balakot,

Pakistan (Ilyas et al., 2005). The earthquake is recognized as one of the largest events in the

world’s history. The nearest recording station to the epicenter of the earthquake was

Abbottabad, which is located at a distance of about 40 KM. The PGA of ground acceleration

of Kashmir earthquake, at Abbottabad, was 0.2517 g recorded in its east-west component.

The total time of the ground motion recorded was of 152.9 secs, out of which effective

portion lies between 20 and 80 secs of the record, as shown in figure 5.3(a). Therefore, the


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time history used in the analysis is a portion, from 22 to 78 secs, of east west component of

Kashmir earthquake, recorded at Abbottabad. The selected record is shown in figure 5.3(b).

In this chapter the time history will be known as Abbottabad ground motion. The other

record selected for analysis is north south component of Imperial Valley earthquake recorded

at El Centro, given in figure 5.4(b) and will be referred as El Centro ground motion. Third

ground motion was obtained by carrying out scaling of Abbottabad ground motion with a

factor of 1.2674 in order to achieve a PGA equivalent to that of El Centro ground motion.

This record is shown in figure 5.4(a) and is named as Abbottabad-scaled ground motion.

(a) (b) Figure 5.3: East west component of Kashmir earthquake recorded at Abbottabad. (a)

Complete time history (b) selected portion for analysis

(a) (b) Figure 5.4: Time histories used in the analysis (a) Abbottabad-scaled ground motion (b) El

Centro (ground motion)


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Figure 5.5: Pseudo-acceleration 5% damped response spectrum (a) Abbottabad and El Centro

ground motions (b) Abbottabad-scaled and El Centro ground motion The response spectrum of El Centro ground motion is overlapped with response spectrum of

Abbottabad and Abbottabad-scaled, ground motion in figure 5.5(a) and 5.5(b) respectively.

The response of El Centro is higher than Abbottabad-scaled ground motion up to time period

of 0.325 Sec and afterwards later dominates. The response of both the ground motion is

equal in lower time period range i.e up to 0.03 secs. The response of El Centro ground

motion dominates Abbottabad ground motion up to a time period of 0.385 secs at which

response of both ground motions become equal. In between time period of 0.385 and 0.479

secs response of El Centro again dominates. After 0.479 secs response of Abbottabad ground

motion is higher as compared to El Centro.

5.4 DESCRIPTION OF MODELING The RC frame presented in figure 5.2(a) and 5.2(b) with cross sectional properties given in

tables 5.1 and 5.2 is modeled as CRCS-60, SSC-02 and SSC-1.3 frames by using the material

properties of respective column achieved by calibration carried out in section 4.17.2. The

analysis of the RC frame under consideration can be carried out on number of FEM based

computer programs. In present study DRAIN-3DX was selected for analysis. Element 15,

calibrated in chapter 4, has been used in each frame. In columns the element is used by only

changing the cross sectional properties. While in beams the hinge at ends has been replaced

by rigid end zone to simulate joints (Kiriakidies, 2008). The column and beam elements are

divided into 9 and 5 groups respectively. In figure 5.6 these groups are shown along with

number of elements in the group. In figure 5.6 GP and ELE stands for group and element

respectively. It can be appreciated from table 5.1 and 5.2 that all elements with similar


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properties have been kept in same group in figure 5.6. The elements in this chapter will be

identified from their number and group shown in figure 5.6.

Figure 5.6: Presentation of modeling of structural elements into groups

The ratio proportion of segments in which the elements are divided is kept same through out

the structure. Ends of the elements are kept as separate segment with 10 percent of length of

the member. This would allow better simulation of rotations along the member length

(Isakovic and Fischinger ,1998). The hinges, provided at the ends of the column elements,

are not divided into segments because it will not have much affect on the performance of the

structure (Isakovic and Fischinger ,1998). The cross sections of all elements are divided into

six rectangular concrete fibers and each reinforcement bar is considered as a single fiber.

Although denser grid of fibers will improve the accuracy of results but at the same time it

will be computationally rigorous. The output required from each analysis includes mode

shape before application of time history, mode shape after application of earthquake, storey

displacement history, storey acceleration history and moment curvature history of each

element. Size of an .OUT file containing all these outputs will become so large that it will not

be able to handle easily. Therefore, analysis of every RC frame was run for eight times and

each time different output was written in .OUT file. In this way analysis of one structure


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under application of single time history was performed in 4.5 to 5 hours. By increasing

number of concrete fibers this time would have increased accordingly. Thus six fibers for

concrete were considered optimum for analysis of the RC frames.

The concrete strength used in the beams is 20% lesser then that of columns. It is according

to general practice being followed in Pakistan, where mostly designers consider a lower

strength concrete in beams as compared to that utilized in columns. The length of rigid zone

at ends of the beam elements is kept equal to half the depth of adjacent connection. The RC

building structure has been considered as series of planner frames linked at floor levels. For

each floor only one degree of freedom, represented by master node, has been retained. The

mass of every floor is assigned to its respective master node. The viscous damping matrix,

corresponding to 5% damping, is setup as stiffness and mass proportional Rayleigh damping.

Soil-structure interaction is ignored during modeling.

5.5 NONLINEAR TIME HISTORY ANALYSIS (NTHA) The nonlinear time history analysis (NTHA), carried out on DRAIN-3DX, can examine the

performance of structural elements. The program simulates the load-deformation response of

RC frames and their elements modeled by employing material properties calibrated in

previous chapter. DRAIN-3DX does not have a post processor, therefore, in this study it was

prepared in MATLAB. The processor has been designed to read the output file (.OUT) and

segregate, store and plot the data for each element separately. In the following sections

results of analysis and their comparison is given.

5.6 DAMAGE INDEX USED IN PERFORMANCE EVALUATION The damage index used in performance evaluation is a function of initial and final time

period, measured at start and end of the ground motion, of the structure. The index is simple

because time period can be measured easily. The fundamental time period of a structure

changes with its tangent stiffness and directly quantifies damage which has occurred in the

structure during the earthquake (DiPasquale and Cakmak , 1987). The index represented by

di is given in equation 5.1 below. The index indicates “no damage” and “collapse” at value

0.0 and 1.0 respectively. At value of di = 0.7, a structure can be considered at verge of


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collapse (Ghobarah and Biddah, 1999) and (Rodriguez and Cakmak, 1990). After value of

0.7 few more hinges are formed and the structure oscillates with rotations increasing at

already developed hinges. The increase in rotation further reduces tangent stiffness which in

turn reduces time period of the structure and collapse is reached at di = 1.0. In equation 5.1

Tstart and Tend represent the initial and final time periods respectively. 2

1 starti

end

TdT

⎛ ⎞= − ⎜ ⎟

⎝ ⎠ (5.1)

5.7 ANALYSIS OF CRCS-60 UNDER APPLICATION OF EL CENTRO GROUND

MOTION The material properties used for this structure were achieved through calibration, carried out

in section 4.17.2.1, of analytical hysteretic behavior of CRCS-60 column with that observed

during experimentation. The frame is known as CRCS-60 frame. The El Centro ground

motion used in the analysis is shown in figure 5.4(b).

5.7.1 Storey Displacement History

The displacement history of all floors is overlapped in figure 5.7(a). Total time of El Centro

ground motion, used in analysis, is about 40 secs but response of the structure has been

measured up to 45 secs. The behavior of the structure after 40 secs is due to vibrations which

are present in the structure after the in put ground motion ends. A close observation indicates

that the floor displacement did not follow first mode shape from 5 to 6 and 10 to 11 Secs.

From 5 to 6 Secs, figure 5.7(c), displacement response of sixth and eighth floor is showing

variation from first mode shape. In figure 5.7(d) displacement history of all floors is

overlapped from 10 secs to 11 secs. It can be observed that first four floors are clearly

following the path of first mode but response of upper floors is different. The floor responses

are modified due to yielding, therefore, first mode does not dominate at these time instances.

The stretch in which peak roof displacement occurred has been plotted in figure 5.7(b). It

can be seen that sixth storey is almost following the displacement pattern of first storey. This

behavior of sixth storey justify the peak inter storey drift occurring at seventh storey. The

peak roof displacement achieved is 0.100456 m which corresponds to 0.3% drift level.


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Although, yielding is reported at elements ends but drift level of 0.3% suggest that the frame

building is in elastic range (Federal Emergency Management Agency, 2005).

Figure 5.7: Floor displacement history of CRCS-60 from NTHA using El Centro ground motion (a) complete time history of all floors overlapped (b) from 2 to 7 Secs (c) from 5 to 6

Secs (d) from 10 to 11 Secs 5.7.2 Max Displacement Of Floors And Inter Storey Drifts The peak value of displacements occurring at each floor both in positive and negative

direction are given in figure 5.8(a). The values of these displacements, in meters, are given in

table 5.3. The negative side has indicated more displacements because PGA of the event is

laying in that direction. Generally, the peak displacement response in the negative direction

can be represented by inverted triangle. In positive direction response showed linearity up to

fourth storey but thereafter the slope decreased. This variation in trend of peak displacement

is due to change in relative stiffnesses of stories due to yielding. The roof displacement

history is plotted versus base shear history in figure 5.9. The max base shear achieved is

6890.028 kN occurring at a roof drift of 0.25%, which indicates an elastic response (Federal

Emergency Management Agency, 2005).

(a) (b)

(c) (d)


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Peak inter storey drift of the structure, measured in meters, is shown in figure 5.8(b) and its

values are given in table 5.3. It can be appreciated that inter storey drift in both directions are

almost identical. The variation is more in fourth, fifth and sixth storey. It is in accordance

with response of structure from 2 to 7 secs of applied time history.

(a) (b) Figure 5.8: Peak response of CRCS-60 from NTHA using El Centro ground motion (a)

displacement response (b) inter storey drift response

Figure 5.9: Hyteresis response of base shear versus roof displacement of CRCS-60 from NTHA using El Centro ground motion


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Table 5.3: Peak displacement and drift response of floors of CRCS-60 from NTHA using El Centro ground motion

Peak Displacement Response Peak Drift Response Storey Positive peaks (m) Negative peaks (m) Positive Drift (m) Negative Drift (m) 1 0.003926 -0.0093 0.011752 -0.01276 2 0.009182 -0.02006 0.012658 -0.01351 3 0.015558 -0.0323 0.013365 -0.01328 4 0.023325 -0.04696 0.013041 -0.01513 5 0.0364 -0.06213 0.014189 -0.01532 6 0.05616 -0.07758 0.019761 -0.01747 7 0.075786 -0.09177 0.019995 -0.02082 8 0.087495 -0.10046 0.011969 -0.01207

Figure 5.10: Sequence of formation of plastic hinges (a) at 1.93 Secs (b) at 1.95 Secs (c)

at 1.97 Secs (d) at 2.86 Secs

5.7.3 Sequence Of Formation Of Plastic Hinges

The sequences in which beam ends moments have exceeded nominal moment capacity are

shown in figures 5.10(a) to 5.10(d). First hinge is located at level 3 at 1.93 Secs, shown in

figure 5.10(a). Major damage, in beams, occurred at 1.97 Secs at which hinges appeared in

beams of all levels except for roof. The deformations further increased at 2.86 Secs with few

more hinges appearing in beams. However, no hinge has been observed in the columns and

(a) (b)

(c) (d)


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two beams of roof of the frame. No hinge was observed after 2.86 Secs and further

deformation was accommodated in already existing hinges.

5.7.4 Mode Shapes And Structural Damage

The mode shapes after application of the El Centro ground motion are given in figure 5.11.

First mode is dominating with 84.7% of total mass of the structure contributing to it. The

time period of various modes before and after application of El Centro ground motion is

given in table 5.4. The variation in modes 2 to 6 is higher than remaining modes. The index

di calculated from equation for fundamental time period is 0.462.

Figure 5.11: Mode shapes of CRCS-60 at end of El Centro ground motion

Table 5.4: Time period of mode shapes of CRCS-60 before and after application of El Centro ground motion

Time period Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Before 0.94758 0.35267 0.18453 0.11552 0.079944 0.059215 0.044264 0.035098After 1.2921 0.47272 0.27442 0.18846 0.14322 0.11531 0.096156 0.085008

5.8 ANALYSIS OF CRCS-60 UNDER APPLICATION OF ABBOTTABAD GROUND MOTION

The CRCS-60 frame, modeled with material properties of CRCS-60 column, is now being

analyzed under application of Abbottabad ground motion, shown in figure 5.3(b), which is a

portion of east-west component of Kashmir earthquake recorded at Abbottabad and shown in

figure 5.3(a).


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Figure 5.12: Floor displacement history of CRCS-60 from NTHA using Abbottabad ground motion (a) complete time history of all floors overlapped (b) from 10 to 20 Secs (c) from 17

to 18 Secs (d) from 45 to 47 Secs 5.8.1 Storey Displacement History

Displacement history of all stories of CRCS-60 frame resulting from application of

Abbottabad ground motion is given in figure 5.12(a). The total time of Abbottabad ground

motion is 56 Secs, however, in order to study the post event behavior of the structure its

response is measured up to 60 Secs. The floor displacements suggest that mostly first mode

shape has dominated the response. As yielding occurred the response was modified due to

change in storey stiffnesses. The region where peak displacement has occurred is shown in

figure 5.12(b). The time instances where first mode shape did not dominate include 4 to 5,

17 to 18, 21 to 21.5, 26.5 to 27 and 45.5 to 47 Secs. Two selected locations i.e 17 to 18 Secs

and 45.5 to 47 Secs has been shown separately in figure 5.12(c) and 5.12(d). The response of

fourth to eighth storey jumbled up during these time instances. The peak roof drift of

0.7353% (0.22 m), which is greater than 0.7%, suggest that repairable damage has occurred

in the structure (Federal Emergency Management Agency, 2005 and DiPasquale and

Cakmak, 1987). The overall displacement response of all floors has increased as compared

to that estimated for El Centro ground motion. Also, deviation of response from first mode

(a) (b)

(c) (d)


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shape has been observed relatively more as compared to El Centro ground motion. This

difference is due to comparatively greater change in lateral stiffness of the structure due to

yielding.

5.8.2 Max Displacement Of Floors And Inter Storey Drifts The peak values of displacement response occurring during the Abbottabad ground motion

are graphically presented in figure 5.13(a) and given in tabular form in table 5.5. The peak

roof displacement is in positive direction. The peak responses of the floors are

approximately linear in both directions. The base shear-roof displacement hysteresis is

plotted in figure 5.14. The max base shear achieved is 4760 KN resulting in 0.22% of roof

drift, which represents elastic response (Federal Emergency Management Agency, 2005).

The peak inter storey drifts of the structure are given in figure 5.13(b) and their values are

shown in table 5.5. The roof drift is lesser than lower stories in both directions. The

maximum inter storey drift has been observed from storey 2 to 4. The maximum of peak inter

storey drift demand of 0.986% has been estimated in positive direction for third storey. The

higher level of inter storey drift demands estimated for lower floors, indicates that Kashmir

earthquake resulted in higher loads applied at lower levels.

(a) (b)

Figure 5.13: Peak floor response of CRCS-60 from NTHA using Abbottabad ground motion (a) displacement response (b) inter storey drift response


153

Table 5.5: Peak displacement and drift response of floors of CRCS-60 from NTHA using Abbottabad ground motion


Figure 5.14: Hyteresis response of base shear versus roof displacement of CRCS-60 from NTHA using Abbottabad ground motion

5.8.3 Sequence Of Formation Of Plastic Hinges The sequence in which deformation have been noted in CRCS-60 frame under application of

Abbottabad ground motion is given in figures 5.15(a) to 5.15(h). First hinge appeared in

beam of 7th storey at 5.84 secs followed by second hinge occurring at level 2 at 7.04 secs.

The formation of first hinge at 8th level indicates that initially the dynamic force was more in

upper stories and later it shifted to lower. It can be seen in figure 5.15(c) and 5.15(d) that

major beam deformation has occurred at 7.09 and 7.10 secs. Finally, at 9.55 secs hinges

appeared in all beams of the frame. At 9.57 secs first hinge in columns appeared in interior

column of 1st storey as shown in figure 5.15(f). Another hinge appeared at base of other

interior column of 1st storey along with two hinges occurring in interior columns of 7th storey


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at 9.62 secs, as shown in figure 5.15(g). At 10.41 secs final shape of damage in the structure

appeared, given in figure 5.15(h), with two new hinges appearing in interior columns of 4th

storey and one hinge in interior column of 2nd storey. The NTHA of the structure under

Abbottabad ground motion show that the earthquake was much more damaging as compared

to El Centro ground motion.

Figure 5.15: Sequence of formation of plastic hinges (a) at 5.84 Secs (b) at 7.04 Secs (c) at 7.09 Secs (d) at 7.10 Secs (e) at 9.55 Secs (f) at 9.57 Secs (g) at 9.62 Secs (h) at 10.41 Secs

(a) (b) (c)

(d) (e) (f)

(g) (h)


155

Figure 5.16: Mode shapes of CRCS-60 at end of Abbottabad ground motion 5.8.4 Mode Shapes And Structural Damage The mode shape of the structure, as it stands after Abbottabad ground motion is shown in

figure 5.16 and time period of the modes are given in table 5.6. The comparison of mode

shapes of the frame drawn after El Centro ground motion, shown in figure 5.11, with those

resulting from Abbottabad ground motion indicates that amplitudes in case of later have

increased. Especially, the difference is more for third and higher modes. Time period of the

first mode shape of the structure, after application of Abbottabad ground motion, is 1.3828

secs. The damage index di calculated for dominating first mode shape is 0.53.

Table 5.6: Time periods of mode shapes of CRCS-60 before and after of Abbottabad ground motion


5.9 ANALYSIS OF CRCS-60 UNDER APPLICATION OF ABBOTTABAD-

SCALED GROUND MOTION The third ground motion which has been used for analysis is the Abottababd-scaled ground

motion. The PGA of time history of Abbottabad has been scaled to El Centro ground

motion. For purpose of comparison Abbottabad-scaled ground motion has been applied to

CRCS-60 frame. The ground motion is given in figure 5.4(a).


156

5.9.1 Storey Displacement History The storey displacement history of all floors resulting from NTHA of CRCS-60 under

Abbottabad-scaled ground motion is given in figure 5.17(a). The region of peak roof

displacement has been enlarged in figure 5.17(b). The peak roof drift level has increased

from 0.7353% (0.22 m) for Abbottabad to 0.956% (0.2862 m) for Abbottabad-scaled ground

motion. The performance level is still IO but damage in the structure has increased. The

structure did not follow the first mode shape at almost same locations where NTHA under

Abbottabad ground motion has shown. But the displacement response of all floors is

enhanced and different from that resulting from Abbottabad ground motion. If we compare

figure 5.12(c) and 5.12(d) with 5.17(c) and 5.17(d) respectively we will find that in later

deviation of response of floor displacements from first mode shape path is also more as

compared to Abbottabad ground motion. Increased amplitudes of floor displacements with

same performance level suggest that damage has only increased to some extent.

Figure 5.17: Floor displacement of CRCS-60 from NTHA using Abbottabad-scaled ground motion (a) complete time history of all floors overlapped (b) from 10 to 20 Secs (c) from 17

to 18 Secs (d) from 45 to 47 Secs

(a) (b)

(c) (d)


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(a) (b) Figure 5.18: Peak response of floors of CRCS-60 from NTHA using Abbottabad-scaled

ground motion (a) displacement response (b) inter storey drift response Table 5.7: Peak floor response of CRCS-60 from NTHA using Abbottabad-scaled ground motion


5.9.2 Max Displacement Of Floors And Inter Storey Drifts The peak displacement response of all floors of the structure for Abbottabad-scaled ground

motion has been plotted in figure 5.18(a). The peak roof displacement of 0.286177 m

occurred in positive direction. The values of peak displacement achieved for each floor are

given in table 5.7. The base shear-roof displacement hysteretic response is given in figure

5.19. The structure under goes a drift of 0.9368%, which indicates a repairable damage

(Federal Emergency Management Agency, 2005), at a maximum base shear of 5855 kN.

The maximum floor drift demand has been estimated for second to fourth floor. The peak


158

floor drift 1.242% has been calculated for third floor in negative direction. The estimated

peak floor drift demands are plotted in figure 5.18(b) and tabulated in table 5.7.

Figure 5.19: Hyteresis response of base shear versus roof displacement of CRCS-60 from NTHA using Abbottabad-scaled ground motion


First four hinges are formed in beams of 6th and 7th storey at 3.4 secs of the applied time

history. The sequence in which deformation has occurred in the frame is shown in figures

5.20(a) to 5.20(i). The deformation increases in upper floors at 5.82 secs and another hinge is

formed in beams of 6th storey. At 5.85 secs four new hinges are formed in beams located at

7th and 8th level as shown in figure 5.20(c). It means that by scaling the Abbottabad ground

motion initially more force is concentrated towards upper floors of the structure. The

damage shifted towards lower stories and hinges appeared in 2nd and 3rd level at 7.04 secs.

At 7.09 secs the structure undergoes a large deformation and hinges appears in its all floors

except for roof. A hinge in interior column of first storey, along with a hinge in a beam of

roof becomes visible at 7.14 secs as shown in figure 5.20(f). At 7.17 secs a hinge is formed at

base of other interior column of first storey. At 9.78 secs hinges appeared in all beams of

roof and all interior columns except for those located at 3rd and 8th storey. The shape of final

damage is shown in figure 5.20(i). Two hinges appeared in interior columns of 3rd storey and

one in interior column of 8th storey at 10.48 secs. No new hinges were formed after 10.48

secs and deformation accumulated on already formed hinges.


159

Figure 5.20: Sequence of formation of plastic hinges in CRCS-60 frame under application of Abottabad-scaled ground motion (a) at 3.4 Secs (b) at 5.82 Secs (c) at 5.85 Secs (d) at 7.04

Secs (e) at 7.09 Secs (f) at 7.14 Secs (g) at 7.17 Secs (h) at 9.78 Secs (i) at 10.48 Secs 5.9.4 Mode Shapes And Structural Damage The mode shape of the structure at end of the Abbottabad-scaled ground motion is shown in

figure 5.21. Figures 5.16 and 5.21 indicate that modal coordinates have further increased by

scaling Abbottabad ground motion. The time period of modes before and after application of

Abbottabad-scaled ground motion are given in table 5.8. The mass contributed in the first

mode by the structure after application of Abbottabad-scaled ground motion is 84.16%,

which is same as was contributed in this mode after Abbottabad ground motion. The time

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)


160

period of the first mode is 1.4443 Secs which gives the index di, calculated from equation 1

for fundamental time period, as 0.57.

Figure 5.21: Mode shapes of CRCS-60 at end of Abbottabad-scaled ground motion Table 5.8: Time period of mode shapes of CRCS-60 before and after application of Abbottabad-scaled ground motion


5.10 ANALYSIS OF SSC-02 UNDER APPLICATION OF ABBOTTABAD-SCALED

GROUND MOTION The fourth frame considered in this work has been assigned the material properties which

were achieved during calibration of SSC-02 column in section 4.17.2.2 of Chapter 4. This

frame has been named as SSC-02 frame. For comparison the frame has been analyzed under

Abbottabad-scaled ground motion.


The storey displacement history of SSC-02, as given by NTHA under Abbottababd-scaled

ground motion, has been overlapped in figure 5.22(a). The region of peak roof displacement

has been enlarged in figure 5.22(b). The peak roof drift of the structure has reduced from

0.956% (0.2862 m) to 0.891% (0.2667 m). The reduction in the roof drift of SSC-02 frame is

due to the confinement provided by the strips used. The response of the structure from 17


161

secs to 18 secs as shown in figure 5.22(c) is almost similar to that achieved for CRCS-60

frame, as shown in figure 5.17(c). The only difference is in response of first and eighth

storey. Figure 5.22(d) indicates that response of the structure from 45.75 to 46.5 Secs is

following the first mode shape. After 46.5 Secs the response of second, third and fourth

storey jumbles up. However, in figure 5.17(d), it can be seen that response of CRCS-60

frame did not follow first mode shape path for longer time, which indicate more deformation.

Figure 5.22: Floor displacement of SSC-02 from NTHA using Abbottabad-scaled ground motion (a) complete time history of all floors overlapped (b) from 10 to 20 Secs (c) from 17

to 18 Secs (d) from 45 to 47 Secs 5.10.2 Max Displacement Of Floors And Inter Storey Drifts

The peak displacement response of all floors of SSC-02 frame, estimated by NTHA under

application of Abbottabad-scaled ground motion, has been plotted in figure 5.23. The peak

roof displacement of 0.266733 m occurred in positive direction. The peak displacement

response for each floor is given in table 5.9. The base shear-roof displacement hysteretic

response is given in figure 5.24. A maximum base shear of 6009 kN was experienced by the

frame at a drift level of 0.86%, which is about 8.5% lesser than that achieved for CRCS-60

(a) (b)

(c) (d)


162

frame under Abbottabad-scaled ground motion. The maximum drift demands for SSC-02

frame are shown in figure 5.23(b) and their values in meters are given in table 5.9. It can be

observed that peak drift has occurred at first storey, in negative direction, with a peak drift

level of 1.18%. The plot of positive direction is similar to that of CRCS-60 frame for

Abbottabad-scaled ground motion. However, the drift of first four stories has been found

greater due to higher force acting on these stories.

(a) (b) Figure 5.23: Peak response of floors of SSC-02 from NTHA using Abbottabad-scaled

ground motion (a) displacement response (b) peak drift response

Figure 5.24: Hyteresis response of base shear versus roof displacement of SSc-02 from NTHA using Abbottabad-scaled ground motion


163

Table 5.9: Peak floor displacements of SSC-02 from NTHA using Abbottabad-scaled ground motion


5.10.3 Sequence Of Formation Of Plastic Hinges The deformation in SSC-02, under Abbottabad-scaled ground motion, are shown in sequence

of their occurrence in figures 5.25(a) 5.25(i). The deformation started at 3.38 secs in 7th

storey as shown in figure 5.25(a). At 5.82 secs another hinge appeared in 7th and three hinges

in beams of 6th storey. The deformations continue to increase in upper stories and at 5.84 secs

three more hinges appeared in beams located at 7th level. Major deformation in 1st and 2nd

stories is seen at 5.05 secs with hinges forming in all beams of these stories. The deformation

further extends towards upper stories and beams of 3rd and 4th storey show hinge formation at

7.09 secs. All beam ends, except for roof, indicate hinges at 7.12 secs. At the same instance

first two column hinges appeared in 1st storey columns. The frame at this occasion is shown

in figure 5.25(f). The damage sequence of SSC-02 indicates that initially drift demands were

more in upper stories and later it shifted to lower stories.

At 7.71 secs as shown figure 5.25(g) hinges formed in interior columns of 7th storey. At the

same instant three hinges also appeared in beams of roof. At 7.71 secs the damage in

structure has again shifted towards upper stories. Damage in middle stories appeared at 9.68

secs when hinges formed in interior column of 4th, 5th and 6th storey. At 9.68 secs hinges

formed at ends of remaining beams of roof. The final shape of deformed structure at 10.47

secs is shown in figure 5.25(j). After 10.47 secs the deformation was only increased at

already formed hinges and no new hinge was formed. The distribution of damage in the

structure was almost similar as in CRCS-60 frame analyzed with Abbottabad-scaled ground

motion. The difference in sequence of occurrence of individual hinges is because of different

stress redistribution in SSC-02 frame, which is due to affects of confinement.


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Figure 5.25: Sequence of formation of plastic hinges in SSC-02 frame under application of

Abbottabad-scaled ground motion (a) at 3.38 secs (b) at 5.82 secs (c) at 5.84 secs (d) at 7.05 secs (e) at 7.09 secs (f) at 7.12 secs (g) at 7.71 secs (h) at 9.68 secs (i) at 10.47 secs

5.10.4 Mode Shapes And Structural Damage The mode shapes of SSC-02 at end of Abbottabad-scaled ground motion is shown in figure

5.26 and its natural time period before and after application of Abbottabad-scaled ground

motion is given in table 5.10. The contribution of mass in the first mode has reduced from

84.7% for CRCS-60 frame to 74.4% for SSC-02 frame. The time period of first mode of

SSC-02 frame is higher than that of CRCS-60 frame due to affect of material properties used

in former. It has been explained in section 4.17.2.4. The time period of SSC-02 frame at end

of the ground motion is 1.4064 Secs, which is lesser than time period of CRCS-60 presented

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)


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in table 5.8. It means that reduction in stiffness, due to deformation introduced by application

of Abbottabad-scaled ground motion, is lesser in case of SSC-02 frame because its material

model has higher stiffness after initial branch, as explained in section 4.17.2.4. Due to

increased stiffness in later branches the SSC-02 frame performed well and has a damage

index di 0.47. The index indicates that damage in the structure is 17.5% lesser then CRCS-60

frame.

Figure 5.26: Mode shapes of SSC-02 frame at end of Abbottabad-scaled ground motion

Table 5.10: Time period of mode shapes of SSC-02 before and after application of Abbottabad-scaled ground motion


5.11 ANALYSIS OF SSC-1.3 UNDER APPLICATION OF ABBOTTABAD-SCALED

GROUND MOTION SSC-1.3 is fifth frame analyzed in this research work. Material properties used in modeling

the structure in DRAIN-3DX have been calibrated in section 4.17.2.3 of Chapter 4.

Following its parental column, the frame has been named as SSC-1.3. The structure has been

analyzed by Abbottabad-scaled ground motion.


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Figure 5.27: Floor displacement of SSC-1.3 from NTHA using Abbottabad-scaled ground

motion (a) complete time history of all floors overlapped (b) from 10 to 20 Secs (c) from 17 to 18 Secs (d) from 45 to 47 Secs

Displacement history of all floors of SSC-1.3 frame has been overlapped in figure 5.27(a).

The region of peak roof displacement has been enlarged in figure 5.27(b). The peak roof

drift of the frame is 0.83% (0.248 m). The estimated drift is 13.4% and 7.04% lesser then its

comparative frames i.e CRCS-60 and SSC-02 respectively analyzed under Abbottabad-scaled

ground motion. The confinement, represented through material model, resulted in reduction

of roof drift. Unlike CRCS-60 and SSC-02 frames, this frame has almost followed first shape

during 17 to 18 Secs of applied time history. Only seventh and eighth storey has crissed

crossed over small length as shown in figure 5.27(c). From 46.5 to 47 secs the structure has

two distinct behaviors i.e if lower three floors are following the first mode shape path the

upper five are criss crossing and vice versa. The amplitudes of floor displacements have been

found minimum when compared with CRCS-60 and SSC-02 frames. This performance of

SSC-1.3 is due to affect of confinement provided through material model.

(a) (b)

(c) (d)


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(a) (b) Figure 5.28: Peak response of floors of SSC-1.3 from NTHA using Abbottabad-scaled

ground motion (d) displacement response (b) peak drift response

Table 5.11: Peak floor displacements of SSC-1.3 from NTHA using Abbottabad-scaled ground motion


5.11.2 Max Displacement Of Floors And Inter Storey Drifts The peak displacement response of floors of SSC-1.3 frame has been plotted in figure 5.28(a)

and its values are given in table 5.11. The peak roof displacement of 0.2483 has been

calculated for SSC-1.3 frame. The displacement is about 7% lesser than that achieved for

SSC-02 frame. The peak displacement of this frame at lower stories is greater than the other

two frames. However, for fourth to eighth floors the peak displacement is found to be lesser

than the two competitors. The base shear-roof displacement hysteretic response is given in

figure 5.29. A maximum base shear of 6200 kN was experienced by the frame at a drift level

of 0.033%. The maximum drift demands estimated for SSC-1.3 frame are shown in figure


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5.28(b) and listed in table 5.11. A maximum peak drift level of 1.137% has occurred at first

storey of SSC-1.3 frame in negative direction. This frame has also indicated greater drift

levels at lower stories which mean that lower stories have experienced greater force.

Figure 5.29: Hyteresis response of base shear versus roof displacement of SSC-1.3 from NTHA using Abbottabad-scaled ground motion


The deformation in SSC-1.3 frame has started at 2.6 secs, which is bit earlier as compared to

CRCS-60 and SSC-02 frame. First hinge in the frame was formed in beams of 7th storey as

shown in figure 5.30(a). The sequence in which deformation has been registered in SSC-1.3

frame is given in figures 5.30(a) to 5.30(i). The deformations continued and more hinges

appeared at 3.4 and 5.77 secs in beams of 3rd, 5th, 6th and 7th level. At 6.27 secs hinges

appeared in all beams except for 1st and 8th storey. This is the main difference between

performance of CRCS-60 and SSC-02, where the deformation after appearing in top floors

shifted to the lower floors. But in SSC-1.3 frame the deformation has spread from upper

stories towards lower stories. At 7.02 secs hinges were seen in beams of 1st storey of the

structure, as shown in figure 5.30(e). Abbottabad-scaled ground motion, like previous cases,

initially concentrated more force at upper floors. The spread of deformation was due to

redistribution of stresses in the structure as the yielding progress. The redistribution of

stresses in SSC-1.3 frame is different because of higher initial slope of steel model.


169

Figure 5.30: Sequence of formation of plastic hinges in SSC-1.3 frame under application of Abbottabad-scaled ground motion (a) at 2.6 Secs (b) at 3.4 Secs (c) at 5.77 Secs (d) at 6.27

Secs (e) at 7.02 Secs (f) at 7.14 Secs (g) at 9.59 Secs (h) at 9.67 Secs (i) at 10.4 Secs

First two column hinges were formed at 7.14 Secs in interior columns of first storey. At the

same instant two hinges were also formed in the roof. The structure at 7.14 Secs is shown in

figure 5.30(f). At 9.59 Secs, figure 5.30(g), three more hinges were formed at roof level and a

hinge each was formed in exterior column of first storey and interior column of seventh

storey. In figure 5.30(h) SSC-1.3 frame at 9.67 Secs is shown. At this time instant the

structure developed a hinge in other exterior column of first storey and a hinge each in

interior column of second and fourth storey. The final shape of the deformed structure was

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)


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achieved at 10.4 Secs of time history, shown in figure 5.30(j). The deformation after this

time was accommodated at already formed hinges. The spread of deformation, as the

earthquake progress, was different than CRCS-60 and SSC-02 frames because material

model of SSC-1.3 frame had greater stiffness as explained in section 4.17.2.4.

Figure 5.31: Mode shapes of SSC-1.3 frame (a) before application of Abbottabad-scaled ground motion (a) at end of Abbottabad-scaled ground motion

Table 5.12: Time period of mode shapes of SSC-1.3 before and after application of Abbottabad-scaled ground motion


5.11.4 Mode Shapes And Structural Damage The mode shape of SSC-1.3 frame is given in figure 5.31 and time periods of mode shapes

before and after application of Kashmir earthquake are given in table 5.12. The time period

of fundamental mode of SSC-1.3 frame has reduced to 0.7798 Secs due to higher initial

stiffness of calibrated steel model given in section 4.17.2.3 and explained in section 4.17.2.4.

The time period of the frame is in maximum amplification range as indicated by response

spectrum analysis of Abbottabad-scaled ground motion in section 5.3 and shown in figure 5.5

Comparatively, SSC-1.3 frame has been subjected to maximum base shear, as presented in

section 5.11.2, due to its dynamic properties.


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The damage index di, for SSC-1.3 frame, has been calculated as 0.555. The above discussion,

suggests that even though SSC-1.3 has higher stiffness in material models, presented in

section 4.17.2.3, the damage in structure has increased by 18%, as compared with SSC-02

frame, due to its dynamic properties.

5.12 COMPARISON OF EL CENTRO, ABBOTTABAD AND ABBOTTABAD-

SCALED GROUND MOTIONS Performance of the CRCS-60 frame subjected to El Centro, Abbottabad and Abbottabad-

scaled ground motion will be discussed in the following section. The CRCS-60 has been

designed to satisfy performance requirements for El Centro ground motion. Therefore,

ductility demand determined for other ground motions is higher than acceptable range.

(a) (b) (c) Figure 5.32: Ductility factors calculated for CRCS-60 at beam ends (a) for El Centro ground

motion (b) Abbottabad ground motion (c) Abbottabad-scaled ground motion 5.12.1 Ductility Factors And Energy Dissipated The demands for all beams are less then 4 for El Centro ground motion, as given in figure

5.32(a). The ductility demands are increased by about 1.15 to 2.5 times for CRCS-60 frame

analyzed by Abbottabad ground motion, as shown in figure 5.32(b). The maximum ductility

demand, for El Centro, has been estimated for level 7 whereas in Abbottabad ground motion

it is at second floor. The trend of distribution of ductility demands indicates that generally

the factors are decrease with increasing number of storey. But there is a sudden increase in

factors at level 7 and 3 for El Centro and Abbottabad ground motion respectively. As

mentioned earlier the Abbottabad-scaled ground motion is 1.2674 times the acceleration


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values of Abbottabad ground motion. The ductility factors achieved for Abbottabad-scaled

ground motion are about 1.5 times greater then Abbottabad ground motion. The estimated

factors for Abbottabad-scaled ground motion are given in figure 5.32(c). The estimates for

Abbottabad-scaled ground motion are approximately 2 to 4 times greater than those

calculated for El Centro ground motion. Beams of storey six are critical for El Centro ground

motion, where as storey two is critical for Abbottabad and Abbottabad-scaled ground motion.

It means that certainly El Centro and Abbottabad ground motions have different frequency

content. The scaling factor did not change the frequency contents of the time history because

still beams of second storey are critical under application of Abbottabad-scaled ground

motion.

(a) (b) Figure 5.33: Ductility factors calculated for CRCS-60 at column ends (a) Abbottabad ground

motion (b) Abbottabad-scaled

The columns of CRCS-60 did not indicate any hinge under El Centro ground motion.

However, some yielding has been found in columns under Abbottabad ground motion, as

shown in figure 5.33(a). The number of column hinges increased with application of

Abbottabad-scaled ground motion as shown in figure 5.33(b). An increase of 80% has been

found in interior column of first floor. The damage in upper stories is nominal and at places

the columns have just yielded. Even though El Centro has greater PGA value, which is

capable of generating greater base shear, but larger range of frequency content of Abbottabad

ground motion made it more lethal for the structure. The Abbottabad-scaled ground motion,

due to its scaling, gave larger values of ductility factors.


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(a) (b) Figure 5.34: Energy dissipated at each floor of eight storey frame (a) energy dissipated as

moment-curvature hyteresis in beams (b) energy dissipated as moment-curvature hysteresis in columns

Figure 5.35: Total energy dissipated at each floor of eight storey frames The total energy dissipated by the frames has been calculated as area enclosed by moment

curvature hysteresis at ends of all elements of the structure. The energy dissipated at ends of

beams is presented in figure 5.34(a) and that dissipated at column ends is given in figure

5.34(b). It can be seen that maximum energy in beams has been dissipated at level 3 or


174

beams of second storey. The columns have dissipated maximum energy in first storey. The

values of energy dissipated by beam and column hysteresis at each level are given in table

5.13. The maximum variation of energy dissipated in beams, from level 3 to 7, is 25%, 68%

and 73% for El Centro, Abbottabad and Abbottabad-scaled ground motion. The total energy

dissipated at each storey is the summation of energy dissipated by beams and columns at that

storey. The total energy has been plotted in figure 5.35 and its values are given in table 5.14.

It can be observed that maximum energy has been dissipated by frame subjected to

Abbottabad-scaled ground motion. The frame subjected to Abbottabad ground motion

dissipated 77% and 87% more energy in beams and columns respectively as compared to that

resulting from El Centro ground motion. The PGA of El Centro is greater than Abbottabad

ground motion but the dynamic properties of the frame are such that it has been subjected to

greater displacements in case of later. Therefore, a greater kinetic energy was induced in the

frame analyzed by Abbottabad ground motion. The frame analyzed by Abbottabad-scaled

ground motion has dissipated 89% and 51% greater energy in beam hysteresis as compared

with frame analyzed with El Centro and Abbottabad ground motion respectively. The

energy dissipated as column hysteresis due Abbottabad-scaled ground motion is 94% and

58.62% greater than that dissipated due to El Centro and Abbottabad ground motion

respectively. The frame has dissipated more energy through beam deformation for all the

ground motions. The damage index di, in frame subjected to El Centro ground motion,

increased by 14% and 23.37% when subjected to Abbottabad and Abbottabad-scaled ground

motion. The damage index of frame analyzed by Abbottabad-scaled ground motion is 7%

greater than that achieved from Abbottabad ground motion.

The ductility factors and energy dissipated, presented above, suggests that Abbottabad-scaled

ground motion is more damaging as compared to other two ground motions. The frame

analyzed with Abbottabad scaled ground motion also gave the largest damage index. The

above discussion implies that the general hypothesis, which is accepted by many engineers

involved in designing, that Kashmir earthquake did not cause much damage in Abbottabad,

because of its lesser PGA, may not be true. The study of results of Abbottabad-scaled ground

motion indicate that Kashmir earthquake did not cause large scale damage in Abbottabad


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because most of the structures in the region have dynamic properties which do not fall in

peak amplification range of the earthquake.

Table 5.13: Energy dissipated as moment-curvature hysteresis at element ends Beam Ends Column Ends Level

/storey

CRCS-60 El Centro

CRCS-60 Abbottabad

CRCS-60 Abbottabad-

scaled

CRCS-60 El Centro

CRCS-60 Abbottabad

CRCS-60 Abbottabad-

scaled 2/1 50.17492 292.8865 623.5336 11.92 118.35 293.5 3/2 63.36581 379.2852 825.3613 1.625 15.26 36.26 4/3 59.80447 323.876 683.9456 1.408 12.36 23.022 5/4 53.00687 225.8216 460.6579 1.61 14.16 33.153 6/5 55.84151 173.8734 346.5663 1.027 3.32 7.36 7/6 47.48814 120.684 221.1364 1.73 4.45 11.334 8/7 15.38572 32.92032 58.48849 2.31 5.72 14.858 9/8 1.430434 2.390292 4.212718 0.741 1.48 3.68

Table 5.14: Total energy dissipated at each floor level as moment-curvature hysteresis Storey CRCS-60

El Centro CRCS-60

Abbottabad CRCS-60 Abbottabad-

scaled 1 62.1 411.236 917 2 65 394.54 861.62 3 61.21 336.24 706.96 4 54.62 239.98 493.81 5 56.87 177.19 353.93 6 49.22 125.14 232.47 7 17.7 38.64 73.346 8 2.17 3.87 7.89

5.12.2 Base Shear And Top Roof Displacement

The base shear, acting in positive direction, resulting from El Centro ground motion is 1.56%

greater than that found from Abbottabad ground motion, shown in figure 5.36(a). However,

the corresponding displacement in this direction is 70% lesser as compared to the later. It is

shown in figure 5.36(b). The base shear calculated due to El Centro earthquake for negative

loading direction is 31% more than that acting due to Abbottabad ground motion but the

estimate of corresponding displacement for later is 200% greater than former. The base-

shear and corresponding displacement resulting from Abbottabad-scaled ground motion, in

positive direction, dominates completely the estimates for El Centro and Abbottabad ground

motion, as shown in figure 5.35(a). The base shear acting on CRCS-60 frame, in negative

direction, due to El Centro ground motion is 15% greater then that found from Abbottabad-


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scaled ground motion. On the other hand, the corresponding displacements estimated for later

are 300% more then the former. This can be seen in figure 5.35(b).

(a) (b) Figure 5.36: Backbone curves drawn on base shear-roof displacement hysteresis of CRCS-60 frame analyzed with El Centro, Abbottabad and Abbottabad-scaled ground motion (a)

backbone curve in positive direction of loading (b) backbone curve in negative direction of loading

The roof displacement history in case of three ground motion has been overlapped in figure

5.37. The peak roof displacements are compared in figure 5.38(a) and 5.38(b) for both

positive and negative directions, respectively. Roof displacement history of the frame under

El Centro ground motion dominates the response up to 6.4 Secs. Up till this time the peak of

roof displacement response estimated for El Centro ground motion has passed. The peak of

roof displacement history under Abbottabad and Abbottabad-scaled ground motion occurs at

10.57 Secs. The peak roof displacements estimated for positive and negative direction under

Abbottabad ground motion are 159% and 79% greater than those achieved for El Centro

ground. At fourth storey, the peak displacements for Abbottabad ground motion are 400%

and 125% higher, in positive and negative directions respectively, than those estimated for El

Centro ground motion. The displacement response of Abbottabad-scaled ground motion has

dominated completely. The analysis indicate that by scaling Abbottabad ground motion, with

a factor 1.2674, the displacements increases by 26% and 45% in positive and negative

directions respectively.


177

Figure 5.37: Roof displacement history of CRCS-60 analyzed with El Centro, Abbottabad and Abbottabad-scaled ground motion overlapped

Figure 5.38: Peak floor displacement of CRCS-60 frame (a) in negative direction (b) in positive direction

The inter storey drifts are given in figure 5.39(a) and 5.39(b) for positive and negative

direction respectively. As seen in peak displacement charts, the inter storey drifts for El

Centro ground motion is higher in upper stories with its peak value at sixth and seventh

storey. The peak for Abbottabad and Abbottabad-scaled occurred at third storey. The peak

(a) (b)


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drift for El Centro, at seventh storey, is 81% lesser than the peak drift for Abbottabad ground

motion, at third storey, in positive direction. The negative peak inter storey drift under El

Centro is 48% lesser than that resulting from Abbottabad ground motion. The scaling of

Abbottabad ground motion increased the peak inter storey drift by approximately 25%. The

drift of third and seventh storey of the frame in positive direction, under application of El

Centro ground motion, is 26% and 170% respectively lesser than the drift achieved from

Abbottabad ground motion. The displacements of these stories in negative direction are 7%

and 130% greater than estimates of El Centro ground motion.

Figure 5.39: Peak inter storey drift of CRCS-60 frame (a) in negative direction (b) in positive direction

The CRCS-60 frame subjected to El Centro earthquake experienced maximum base shear but

its performance parameters like roof displacement history, peak storey displacement and

peak inter storey drifts were lesser as compared to Abbottabad ground motion. The maximum

values of these parameters have been found for Abbottabad-scaled ground motion. In figure

5.37 it is seen that main grunt of roof displacements estimated for El Centro ground motion

ends at about 5 secs of the time history. In case of Abbottabad and Abbottabad-scaled ground

motion the major roof displacements are occurring from about 7 to 30 secs. The displacement

(a) (b)


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achieved even at 25 and 30 Secs of Abbottabad ground motion are almost equal to peak

displacement of El Centro ground motion. The increased floor displacements even with

lesser force, due to comparatively lesser PGA, indicate the vast destruction power of

Kashmir earthquake. It is also evident from figure 5.37 that Abbottabad ground motion was

destructive over longer duration as compared to El Centro ground motion. The Abbottabad-

scaled ground motion has resulted in max values of peak floor displacements and inter-storey

drifts and can be recognized as most damaging out of the three ground motions. The damage

in structure has increased in order to dissipate greater amount of energy resulting from

scaling of Abbottabad ground motion.

(a) (b) Figure 5.40: Moment-curvature hysteresis for CRCS-60 overlapped for Abbottabad and

Abbottabad-scaled ground motion (a) element 1 of group 5 (b) element 2 of group 5 5.12.3 Moment Curvature Hysteresis The columns of CRCS-60 frame, analyzed with El Centro ground motion, did not indicate

any yielding. The yielding in columns induced by Abbottabad and Abbottabad-scaled

ground motion has been discussed earlier in section 5.12.1. The moment curvature hysteresis

resulting from Abbottabad and Abbottabad-scaled ground motion for element 1 and 2 of

group 5 has been overlapped in figure 5.40(a) and 5.40(b) respectively. The elements and

groups of structure are identified in figure 5.6. The scaling of Abbottabad ground motion has

increased the curvature demands of the column elements. The curvature of element 1, shown

in figure 5.40(a), in positive and negative direction has increased by 84% and 70% for an

increase in moment of 5% and 3% respectively. The curvature of element 2 as shown in


180

figure 5.40(b) has increased in positive directions only and its negative direction has shown

pinching because in this direction most of the deformation has been accommodated in beams.

5.13 SUMMATION OF COMPARISON OF ANALYSIS OF CRCS-60 FRAME

ANALYZED BY EL CENTRO, ABBOTTABAD AND ABBOTTABAD-SCALED GROUND MOTION

The damage capacity of Imperial Valley, May 1940 and Kashmir, October 2005 earthquakes

have been compared in above sections. These earthquakes have been presented here in the

study as El Centro and Abbottabad ground motion. The RC frame has dynamic properties

falling in maximum amplification range of Abbottabad ground motion. The base shear

experienced in El Centro ground motion is 31% higher than that experienced in Abbottabad

ground motion. However, the displacement demands resulting from Abbottabad ground

motion are 200% higher than those estimated for El Centro ground motion. The frequency

content and duration of Abbottabad ground motion make it more lethal as compared to El

Centro ground motion. The energy dissipated by frame in Abbottabad ground motion is

approximately 58% higher than El Centro ground motion. The Abbottabad ground motion

also resulted in 14% greater damage index. To study the affects of increased PGA of the

Abbottabad ground motion it was scaled by 1.2674. Scaling increased the energy dissipation

of the frame by 25% and damage by about 7%.

5.14 COMPARISON OF CRCS-60, SSC-02 AND SSC-1.3 FRAMES ANALYZED BY

ABBOTTABAD GROUND MOTION

In order to study the affects of confining reinforcement, which was proposed in previous

chapter, the performance of the frames modeled with properties of CRCS-60, SSC-02 and

SSC-1.3 columns will be compared in following sections.

5.14.1 Ductility Factors And Energy Dissipated

The maximum ductility demand of CRCS-60 and SSC-02, presented in figure 5.41(a) and

5.41(b), occurred at second and first storey respectively. The ductility factors of SSC-02

reduced as the number of storey increases. The difference between ductility factors of

CRCS-60 and SSC-02 frames also decreases in upper stories. The maximum ductility factor

in beams of SSC-1.3 frame, as shown in figure 5.41(c), is observed at first storey. The beam


181

ductility factors of the frame decreased up to fourth storey but again a increase occurred at

fifth storey.

(a) (b) (c) Figure 5.41: Ductility factors calculated for beams of RC frames analyzed by Abbottabad

scaled ground motion (a) CRCS-60 frame (b) SSC-02 frame (c) SSC-1.3 frame

Figure 5.42(a), 5.42(b) and 5.42(c) articulate the ductility factors for columns of CRCS-60,

SSC-02 and SSC-1.3 frame respectively. Yielding has occurred in most of the interior

columns of frames. The yielding in exterior columns has been restricted in first storey only.

In all the three frames maximum yielding has occurred in first storey columns. The ductility

of columns of first storey of SSC-02 and SSC-1.3 is 19.54% and 15.85% greater than CRCS-

60 column. SSC-02 has shown decrease in ductility demand in fourth, sixth and seventh

storey. The columns of first storey of SSC-1.3 have shown decrease of 10.69% in ductility

demand as compared to SSC-02. No hinge has been observed in columns of fifth storey of

SSC-1.3 frame, however, an increase is observed in ductility of beams of same storey. This

is due to affect of change of stiffness between fifth and sixth storey in combination with

calibrated material properties. Largely, the yielding in SSC-1.3 frame is approximately 34%

lesser then that observed in SSC-02 frame. CRCS-60 frames have indicated 15% lesser

yielding as compared with SSC-1.3 frame.

The basic properties of the eight storey frame have been adjusted for El Centro ground

motion. The increased ductility factors observed in figure 5.41 and 5.42 are due to

Abbottabad-scaled ground motion to which the structures are subjected. As discussed earlier


182

in section 5.4 the concrete model for beams has been reduced by 20%. Therefore, for SSC-

02 and SSC-1.3 frame, due to higher concrete and steel model used for columns, sufficient

deformation has already occurred in beams before start of yielding in columns. In SSC-02

frame the initial steel stiffness is comparatively low due to which yielding of its columns

started earlier as compared to CRCS-60 and SSC-1.3 frames. For comparison yielding in

every beam and column element has been summed up and is given in table 5.15. The yielding

of SSC-02 frame is 8.7% and 7.25% lesser than that occurred in CRCS-60 and SSC-1.3

frames respectively. Although SSC frames have shown higher ductility in beams of lower

stories but in general, ductility demand, in SSC-02 frame is lesser than CRCS-60 frame.

(a) (b) (c) Figure 5.42: Ductility factors calculated for columns of RC frames analyzed by Abbottabad

scaled ground motion (a) CRCS-60 frame (b) SSC-02 frame (c) SSC-1.3 frame Table 5.15: Total yielding in beams and columns of RC frames under Abbottabad-scaled ground motion

Element CRCS-60 SSC-02 SSC-1.3 Beam 335.77 294 325.402

Column 28.87 38.69 33.3 Total 364.64 332.69 358.7

The energy dissipated in RC frames is given in figure 5.43 and 5.44. The beams at level 3

have dissipated maximum energy for CRCS-60 and SSC-02 frames. Beams of SSC-02 frame,

as shown in figure 5.43(a), has dissipated least energy at each level except for first storey.

The beam energy at each floor of the frames is listed in table 5.16. The energy dispersed by

columns of the frames is plotted in figure 5.43(b) and tabulated in table 5.16. At first storey

columns of SSC-02 frames has dissipated maximum energy and for remaining stories SSC-


183

1.3 frame has lead the other two. Maximum energy has been dissipated by SSC-1.3 frame

and minimum by SSC-02 frame. The total energy, shown in figure 5.44, dissipated by SSC-

02 frame is 3% and 20% lesser than that of CRCS-60 and SSC-1.3 frames. The values of

total energy for each floor are given in table 5.17. The energy dissipated in beams of frames

has been 88.4%, 85.1% and 86.86% of the total energy in case of CRSC-60, SSC-02 and

SSC-1.3 frames respectively. Correspondingly, columns have contributed 11.6%, 14.9% and

13.13% energy to the total energy. Similar to ductility factors, the energy dissipated by

beams of SSC-02 frame is lesser and that dissipated by its columns is greater as compared to

other two frames. According to damage index di maximum damage has occurred in CRCS-60

frame, which has been found 21% and 2% more than that observed in SSC-02 and SSC-1.3

frames respectively. The SSC frames have reduced the damage index because of the affect

of increased confinement included in their material models.

(a) (b) Figure 5.43: Energy dissipated at each floor of eight storey RC frame (a) energy dissipated

as moment-curvature hyteresis in beams (b) energy dissipated as moment-curvature hysteresis in columns


184

Figure 5.44: Total energy dissipated at each floor of eight storey frames Table 5.16: Energy dissipated as moment-curvature hysteresis at element ends

Beam Ends Column Ends Level/store

y CRCS-60 SSC-02 SSC-1.3 CRCS-60 SSC-02 SSC-1.3

2/1 623.5336 767.5082 1024.896 293.5 422.95 379.62 3/2 825.3613 783.3428 1011.36 36.26 25.1 46.32 4/3 683.9456 588.3759 719.6227 23.022 19.88 46.64 5/4 460.6579 379.7625 466.0061 33.153 26.44 55.4 6/5 346.5663 271.6001 330.749 7.36 6.42 9.97 7/6 221.1364 169.4127 208.1086 11.334 9.12 13.86 8/7 58.48849 32.75232 57.69204 14.86 12.2 20.58 9/8 4.212718 1.300195 4.989549 3.68 2.63 5.67

Table 5.17: Total energy dissipated at each floor level as moment-curvature hysteresis

Storey CRCS-60 SSC-02 SSC-1.3 1 917 1190.46 1404.52 2 861.62 808.44 1057.7 3 706.96 608.26 766.3 4 493.8 406.2 521.4 5 353.9 278.02 340.72 6 232.5 178.54 222 7 73.34 45 78.3 8 7.9 3.93 10.66


185

(a) (b) Figure 5.45: Backbone curves drawn on base shear-roof displacement hysteresis of CRCS-60 frame analyzed with El Centro, Abbottabad and Abbottabad-scaled ground motion (a)

backbone curve in positive direction of loading (b) backbone curve in negative direction of loading

Figure 5.46: Roof displacement history of CRCS-60 analyzed with El Centro, Abbottabad and Abbottabad-scaled ground motion overlapped 5.14.2 Base Shear And Top Roof Displacement

The backbone curves plotted on base shear-roof displacement hysteresis, in figures 5.45(a)

and 5.45(b) for positive and negative loading directions respectively. The maximum base

shear in both directions has been achieved in SSC-1.3 frames. In positive direction it is 5%

and 8% and in negative direction it is 3% and 5% greater than the base shear achieved in

CRCS-60 and SSC-02 frames respectively. The peak base shear has almost occurred at same

displacement levels. Maximum difference of 7% has been observed between peak base shear

displacements of SSC-1.3 and CRCS-60 frames.


186

(a) (b) Figure 5.47: Peak floor displacement of CRCS-60 frame (a) in negative direction (b) in

positive direction The roof displacement history of the three frames has been overlapped in figure 5.46. The

peak values of displacement of each floor are given in figures 5.47(a) and 5.47(b) for

negative and positive directions respectively. The peak inter storey drift achieved from

NTHA of the frames is given in figures 5.48(a) and 5.48(b). The peak roof displacement, for

all the frames, has been noted at 10.55 secs as shown in figure 5.46. Maximum roof

displacement of 0.2862 m occurred in CRCS-60 frame. Up to third storey the peak

displacements of SSC-1.3 dominates by about 6%, in both directions of loading, and there

after its floor displacements are lesser than those of CRCS-60 and SSC-02. The inter storey

drift of first storey of SSC-02 frame in negative direction is 4% and 34% greater than that of

SSC-1.3 and CRCS-60 frames respectively. The difference reduces to 0% and 6% at second

storey for SSC-1.3 and CRCS-60 frames. In positive direction first storey of SSC-1.3 has

experienced 15% more drift than CRCS-60 and SSC-02 frames. The difference reduces to

0% and 7.5% for CRCS-60 and SSC-02 frame respectively at second storey. The drift of

third to eighth storey of CRCS-60 frame in negative direction is 28% and 20% higher than

those of SSC-1.3 and SSC-02 frames. On positive side the drift of CRCS-60 is 20% and

7.5% higher than SSC-1.3 and SSC-02 frames respectively. The SSC frames are subjected to


187

higher base shear but due to their larger confinement the deformations are lesser than CRCS-

60 frame.

(a) (b) Figure 5.48: Peak inter storey drift of CRCS-60 frame (a) in negative direction (b) in

positive direction

While resisting the maximum base shear the SSC-1.3 frame has under gone minimum roof

displacements. The displacements in positive direction are 6.9% and 12.3% and in negative

direction 8.2% and 15% lesser than the roof displacements estimated for SSC-02 and CRCS-

60 frames respectively. The SSC-02 frame experienced approximately equal force as

compared to CRSC-60 frame but still it showed lesser roof displacements and inter storey

drifts. The increased drift and displacement levels at lower storey are due to the fact that

more deformation has been observed in these stories for SSC-02 and SSC-1.3 frames. The

pattern of deformation has varied due to material models employed.

5.14.3 Moment Curvature Hysteresis

The moment curvature of the two interior column elements in the first storey of the frames is

shown in figure 5.49(a) and figure 5.49(b). The maximum curvature has been found in SSC-

02 frame. This is as expected because, as commented earlier, deformations in columns of

this frame started earlier than other two. The moment curvature hysteresis of element 1 of

group 5, as identified in figure 5.6, of all the three frames have been over lapped in figure

5.49(a). In positive direction SSC-02 frame achieved max curvature at a moment of 4088

kN-m. On negative side CRCS-60 frame is dominating at 3854 kN-m and 0.00871 radians.


188

The peak moment of SSC-1.3 on positive side is 12% and 20% lesser than CRCS-60 and

SSC-02 frames. Correspondingly, the curvature of SSC-1.3 is 3.5 and 4.3 times lesser than

the other columns. The moment-curvature of element 2 of group 5 (figure 5.8) is given in

figure 4.49 (b). The moment-curvature of SSC-02 is dominating in both loading directions.

SSC-02 and SSC-1.3 has achieved same moment in positive direction but the curvature of

later is 34% lesser than the former. The pinching is visible on negative side in hysteresis of

all the columns. The pinching has occurred because in negative loading direction more

energy has been dissipated in beams.

(a) (b) Figure 5.49: Moment-curvature hysteresis of CRCS-60, SSC-02 and SSC-1.3 for

Abbottabad-scaled ground motion (a) element 1 of group 5 (b) element 2 of group 5 5.15 SUMMATION OF COMPARISON OF CRCS-60, SSC-02 AND SSC-1.3

The SSC-1.3 frame has been subjected to maximum base shear due to its dynamic properties.

This is also obvious from energy dissipated by the frame which is of the order of up to 20%

greater than SSC-02 and CRCS-60 frame. The peak roof displacement achieved by SSC-1.3

frame during NTHA is approximately 15% lesser than the other two. The damage index is

15% greater than that of SSC-02 frame. The index of CRCS-60 is only 2.6% lesser than

index of SSC-1.3 frame. The NTHA of SSC frames indicate that their performance is better

due to the affect of confinement which has been included through material properties. The

drifts of SSC-1.3 are minimal among the three frames although the frame has been subjected

to largest base shear, due to its dynamic properties. The SSC-02 frame has been assigned to a

level of base shear equal to that of CRCS-60 frame, yet it also has lesser roof displacements,

inter storey drifts and damage index. Therefore, the performance SSC-02 frame is also better

than CRCS-60 frame.

CHAPTER 6

189

CONCLUSIONS AND RECOMMENDATIONS

6.1 CONCLUSIONS The major conclusions drawn from the study are enlisted below:- a. The digitizing approach presented in the study is novel and resolve concatenating and

rotation problems with more reliability. The digitized data will be useful for studying

the nature of earthquakes and carrying out risk analysis studies of Northern region of

Pakistan. The proposed technique will also be useful in other developing countries

where analog recorders are still in use. The proposed technique can be further

developed and improved to minimize its limitations and transforming it to a more

user-friendly environment.

b. The response spectrums of ground motions recorded in Pakistan, since 1972,

indicates that amplification of these earthquakes exists in short and intermediate time

period range. The peak spectral ordinates of design spectrums, derived in this study,

also exist in short and intermediate time period range. It means that earthquakes of

Pakistan are more damaging for structures with time periods falling in this range. It is

concluded and emphasized that in Pakistan only those response and design spectrums

should be used in analysis and design which have been developed based on local

seismic data. The seismic parameters in national building code should also be set

based on indigenous earthquake data.

c. The Steel Strip Confined (SSC) columns due to greater effect of confinement showed

a balanced behavior in both loading directions. It means that higher confinement also

reduced the pinching effect which is mainly responsible for increasing the

deterioration of negative loading direction.

d. The pattern of deformation of SSC was different than conventional columns. In

SSC columns the deformation started within 100 mm from face of shear block of the

column and then it extended away from the shear block. The deformations were also

found well distributed within hinge zone. In conventional columns no regular pattern

CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS

190

of deformation was found. The SSC columns in over all performance took more

cycles to achieve the required level of strength degradation. Energy dissipation,

lateral strength, stiffness and residual displacements indicate that performance of

SSC-02 columns is better then remaining columns. Higher ductility and lower lateral

strength of SSC-1.3 than SSC-02 columns suggest that width and thickness of

confining strips need to be optimized. Overall performance of both SSC columns has

been found higher than conventional columns.

e. The use of extrapolation of end segment of backbone curves helped in locating the

ultimate displacement. In this way, the effects of limitation of 100 mm in application

of lateral displacement were reduced. The yield drift levels located by equivalent

elastic-perfectly plastic procedure were found approximately equal to the drift levels

identified during testing. This means that the method is quite promising.

f. The use of mean experimental curves catered for any short fall which may be present

in experimental setup. Mostly, hysteresis plotted by analytical procedure has similar

properties in both positive and negative direction. The use of mean of backbone curve

of positive and negative directions has accommodated limitation of analytical

procedures. This procedure has also accounted for balanced behavior of SSC columns

in both loading directions.

g. Estimate of ultimate displacement of load-displacement curves by response-2000 has

been much conservative. The estimation of load-displacement curves of RC columns

by interpolation approach approximately matches member response option of

response-2000. The load-displacement curves estimated by linear variation approach

were found closest to the mean experimental curves.

h. The calibration of hysteresis curves on DRAIN-3DX has resulted in close match with

mean experimental curves. The calibrated material properties are in form of simple

stress-strain curves which could be used with analysis of any multi storey RC

building structure.

i. The experimental work and its modeling carried out in this study give an insight of

cyclic behavior of RC columns. The importance of confinement highlighted in this

study will guide engineers to take into account its benefits during designing. The


191

enhancement of performance by using steel strips has opened new path of research

and will give guide line to improve response of RC columns by using proposed

confinement.

j. Area of core concrete, which is wasted in arching action, does not take part in

generating confining force. The proposed confining technique, due to greater width

of transverse reinforcement, results in reduction of ineffective area.

k. The yielding of proposed transverse reinforcement during cyclic loading gives a clear

indication that it has provided higher confinement as compared to standard stirrups.

l. The longer duration, higher frequency content and consistent peak nature of Kashmir

earthquake makes it more lethal as compared to El Centro ground motion.

m. The maximum amplification from Abbottabad ground motion has been noted in

intermediate time period range. Most of the structures in Abbottabad were saved

during event of Kashmir earthquake because their natural period was lower than 0.33

secs.

n. Keeping in view the level of force, inter story drifts, roof displacements and damage

index it has been found that SSC-1.3 frame gave the best performance. The CRCS-60

and SSC-02 frames were subjected to approximately same level of force, yet SSC-02

frame resulted in lower damage index. Therefore, it is concluded that performance of

SSC-02 frame was also better than CRCS-60 frame.


192

6.2 RECOMMENDATIONS

a. The analog data should be grouped according to the type of recording site and

location of epicenter. Detail analysis of digitized time histories should be carried out

to determine cut off frequencies for the earthquakes.

b. The analog form of earthquake data available with metrological department should

also be digitized in order to increase the data bank of real time recorded time histories.

c. The data of indigenous earthquakes available in Pakistan should be used to suggest

response and design spectrums for different seismic zones of the country.

d. The reduction in ductility of SSC-02, as compared to SSC-1.3 column, requires that

more experiments should be carried out to optimize the width and thickness of

proposed confining ring.

e. It is recommended that analytical model of proposed confining reinforcement should

be established. The proposed SSC columns should be tested under cyclic axial loads

in order to determine parameters required for modeling.

f. Further experimental studies of SSC columns are recommended under variable axial

loads and biaxial bending. Studies should also be carried out with more varying

concrete strength.

g. The RC frame should be analyzed by further scaling the time history of Kashmir

earthquake in order to study the effects of other PGA values on performance of

structures.

h. More analysis of RC frames with different number of stories and story heights should

be carried out to study the effects of Kashmir earthquake on structures with different

natural time period.

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