computational strategy for rehabilitation of reinforced …
TRANSCRIPT
i
COMPUTATIONAL STRATEGY FOR REHABILITATION OF
REINFORCED CONCRETE FRAMED STRUCTURE USING FIBRE
REINFORCED POLYMER CONFINEMENT OF COLUMNS
by
SEYEDMOHSEN SEYEDASAEI
Thesis submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Universiti Sains Malaysia
January 2014
ACKNOWLEDGMENTS
ii
Acknowledgement
First and foremost, all praise to the Great GOD for His blessings and merciful
that enabled me to learn.
I would like to express my deepest appreciation to my supervisor, Dr. Lau Tze
Liang for his constructive inspiration and invaluable guidance. I really was honoured
to have the opportunity to work under his supervision. I also would like to extend my
sincere gratitude to my co-supervisor, Dr. Norazura Muhamad Bunnori for her
advice and concern throughout my study.
Last but not least, I am grateful to my family specially my parents, Mr.
Seyedghasem Asaei, and Mrs. Marzieh Berimani, who are always my source of
inspiration. They encouraged me to learn and supported me throughout my life and I
would like to dedicate this thesis to my family.
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TABLE OF CONTENTS Page
ACKNOWLEDGMENTS ii
TABLE OF CONTENTS iii
LIST OF FIGURES vi
LIST OF TABLES x
LIST OF ABBREVIATIONS xi
LIST OF SYMBOLS xiv
ABSTRAK xviii
ABSTRACT xix
CHAPTER 1 – INTRODUCTION
1.1 Background 1
1.2 Problem Statement 11
1.3 Objectives 14
1.4 Scope of Study 14
1.5 Structure of Thesis 15
CHAPTER 2 - LITERATURE REVIEW
2.1 Introduction 17
2.2 Seismic Rehabilitation Procedure 17
2.3 Numerical Modelling of FRP-Confined RC Column 22
2.4 Retrofit Scheme and Local-Global Consequence 31
2.5 Systematic Methods for Seismic Rehabilitation 32
2.6 Summary 36
CHAPTER 3 - THEROTECAL FRAMEWORK
3.1 Introduction 39
3.2 Characteristics of FRP-confined Columns 39
3.3 Nonlinear Method of RC Frame Evaluation 47
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3.4 Linear Method of RC Frame Evaluation 52
3.5 Theoretical Calculation of Displacement of RC Frames 59
CHAPTER 4 – METHODOLOGY
4.1 Introduction 62
4.2 Local and Global Response of Retrofitted Structure Using FRP-confined Columns 64
4.3 Systematic Method Based on Nonlinear Method of Structural Assessment 82
4.4 Systematic Method Based on Linear Method of Structural Assessment 90
CHAPTER 5 - RESULTS AND DISCUSSION
5.1 Verification of SAP2000 Results 95
5.1.1 Analysis of Ductility Parameters of FRP-confined RC Section 95
5.1.2 Verification of Software Analysis Result for FRP-confined columns 98
5.1.3 Summary Verification of Analysis Results using SAP2000 110
5.2 Expected Sequence of Events after Retrofit Using FRP on Columns 110
5.3 Systematic Method for Rehabilitation of RC Structures Using FRP-Confined Columns Based On Nonlinear Manner of Assessment 120
5.4 Result Verification
131
5.5 Systematic Method for Rehabilitation of RC Structures Using FRP-Confined Columns Based On Linear Manner of Assessment 136
5.6 Summary and Comparison of Proposed Methods 142
CHAPTER 6 - CONCLUSION AND RECOMMENDATIONS
6.1 Conclusion 144
6.2 Recommendation 145
v
REFERENCES 147
LIST OF PUBLICATIONS 157
APPENDICES 158
Appendix A: Calculation of stress strain relationship and moment curvature of FRP confined section 158
Appendix B: VBA program for calculation number of required FRP layers 164
Appendix C: Calculation of PMM interaction surface for FRP confined column according to Lawrence. C. Bank method (Bank, 2006) 168
Appendix D: Calculation of lateral force due to earthquake for case study 171
Appendix E: Results of case studies in detail 172
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LIST OF FIGURES Page
Figure 1.1: Failure of RC columns due to earthquake (Canfield and Sabrina, 2010) 1
Figure 1.2: Assessment of structures (ATC-40) 3
Figure 1.3: Defining performance level based on displacement capacity (ATC-40) 4
Figure 1.4: Performacnce point determination (ATC-40, 1996) 5
Figure 1.5: Effect of local behaviour of structural member on global response of RC frame (Kam et al., 2011) 7
Figure 1.6: Local and global response of structure 8
Figure 2.1: Initial and secant stiffness (Sullivan et al., 2003) 19
Figure 2.2: The process of rehabilitation according to ATC-40 (1996) 20
Figure 2.3: Rehabilitation process flowchart (FEMA356, 2000) 21
Figure 2.4: Modeling the axial force on confined column using FRP wrapping in finite element (Koksal et al., 2009) 23
Figure 2.5: Modelling and result of Parvin and Jamwal (2006) for confined column 24
Figure 2.6: Modelling columns under axial eccentrically load and compare to analytical 26
Figure 2.7: Results of Wang et al. (2010) work on strengthened RC columns 27
Figure 2.8: The comparison of experiments and SAP2000 and SeismoStruc software result (Savoia et al., 2010) 28
Figure 2.9: Comparison of software analysis with experiments of wrapped and unwrapped RC frames (Sha'lan, 2009) 29
Figure 2.10: The overall PBD design process (Liang, 2004) 33
Figure 2.11: Zou et al. (2007) study for optimizing the FRP confining the columns 35
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Figure 3.1: Stress-Strain curve of confined concrete proposed by Lam and Teng (2003a and 2003b) 41
Figure 3.2: MC diagram calculation (Yuan et al., 2008) 43
Figure 3.3: Simplified interaction diagram (Rocca et al., 2009) 44
Figure 3.4: PMM interaction diagram and correspondant strain of concrete in various points (Bank, 2006) 45
Figure 3.5: Demand spectrum before and after pulling over using reduction factors and (ATC-40) 49
Figure 3.6: Bilinear form of capacity in ADRS format, and , and are representation of shear force and displacement of structure respectively in yield and ultimate condition (ATC-40) 51
Figure 3.7: Performance point (ATC-40, 1996) 52
Figure 3.8: General structure response against the cumulative lateral force (Mahmoudi and Zaree, 2010) 54
Figure 3.9: Nonlinear behaviour of structure under cumulative lateral force (Izadinia et al., 2012) 55
Figure 3.10: Fluxural rotation of rigid frames at every single storey (Smith and Coull, 1991) 59
Figure 3.11: MC diagram and calculating moment inertia 60
Figure 3.12: Determination of total displacement of RC frame against lateral force 61
Figure 4.1: Research methodology 63
Figure 4.2: Verification of analysis result for FRP-confined columns 65
Figure 4.3: Experimental model and load-deformation result for Endeshaw et al. (2008)
67
Figure 4.4: Experimental model and load-deformation result for Xiao and Ma (1997) 69
Figure 4.5: Reinforcement details of tested column samples in circular and rectangular form (Haroun and Elsanadedy, 2005) 71
Figure 4.6: Backbone curve of hysteresis loops (Haroun and Elsanadedy, 2005) 71
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Figure 4.7: Construction of backbone curve based on ATC-40 and FEMA356 74
Figure 4.8: Bilinear form of capacity curve 74
Figure 4.9: Load deformation hysteresis of samples 75
Figure 4.10: Procedure for investigation and verification of global response of retrofitted structure 79
Figure 4.11: Case studies 80
Figure 4.12: Proposed systematic method based on nonlinear method of assessment 83
Figure 4.13: The formulation of post-yield envelope of capacity curve and range of T 85
Figure 4.14: Dependence of RC column displacement capacity to curvature of RC column section 86
Figure 4.15 Assigned RC section to 3 storey level case study 88
Figure 4.16: Systematic method based on linear analysis method 92
Figure 4.17: Calculating required R factor in more detail 94
Figure 5.1: Comparison of ultimate moment and ultimate curvature based on Yuan et al. (2008), theoretical solution and SAP2000 analysis result 96
Figure 5.2: Comparison of PMM interaction 97
Figure 5.3: Reinforcement area and stress-strain of concrete of RC section 98
Figure 5.4: Comparison of capacity curves from experimental and analysis results for rectangular section 99
Figure 5.5: Comparison of capacity curves from experimental and analysis results for circular section 103
Figure 5.6: The global response of original and retrofitted RC frame: Case study of three-storey RC frame 112
Figure 5.7: The global response of original and retrofitted RC frame: Case study of four-storey RC frame 113
Figure 5.8: The global response of original and retrofitted RC frame: Case 114
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study of four-storey RC frame
Figure 5.9: The global response of original and retrofitted RC frame: Case study of four-storey RC frame 115
Figure 5.10: The global response of original and retrofitted RC frame: Case study of four-storey RC frame 116
Figure 5.11: MC diagram of RC member in confined and unconfined form. Note: (The numbers after FRP denotes strain and stress respectively after retrofitting of columns) 118
Figure 5.12: Extracting the factor G.A using pushover curve 119
Figure 5.13: Three storey RC frame and analysis result 121
Figure 5.14: Stress strain relation and MC diagram of column A4 and D4 before and after retrofit 123
Figure 5.15: The case study of Zou et al. (2007) and capacity curve in ADRS format 131
Figure 5.16: The result of 3 storey RC frame same to case stdy of study by 133
Figure 5.17: The stress ratio of RC columns of RC frame before retrofit 137
Figure 5.18: The material and time consumption corresponding to linear and nonlinear methods of assessment 143
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LIST OF TABLES Page
Table 2.1: Design procedures for structure assessment through Displacement Based Design Methods (Sullivan et al., 2003) 18
Table 2.2: Research studies of confined concrete and modeling in various software 30
Table 2.3: The local and global effect of retrofit interventions 31
Table 3.1: Values of parameters a and b based on post stiffness slope of structure 57
Table 4.1: Summary of the selected specimens and calculated ultimate stress and strain based on considering ACI440 (2002) recommendation and not considering ACI440 recommendation for rupture strain 72
Table 4.2: Effective stiffness value according to FEMA 356 (2000) 78
Table 4.3: Material properties of RC frame structural members as case study 82
Table 5.1: Values of ultimate moment and curvature 96
Table 5.2: Comparison of yield and ultimate force-displacement between SAP2000 analysis result and results of selected columns 108
Table 5.3: Initial stiffness of FRP-confined RC columns based on experiments and result of analysis and comparison of result 109
Table 5.4: Results of retrofitted three storey RC frame in the first iteration 122
Table 5.5: Results of retrofitted for four storey RC frame 127
Table 5.6: Summary of results for case studies 129
Table 5.7: The retrofitted columns and thickness of FRP 135
Table 5.8: Comparison of time and material consumption between present study and Zou et al. (2007) study 135
Table 5.9: Lateral force distribution along the height of RC frame 136
Table 5.10: Summary of application of proposed systematic method on case studies of RC frames 141
xi
LIST OF ABBREVIATIONS
ADRS Acceleration Displacement Response Spectrum
ATC Applied Technology Council
CFFT Concrete Filled Fiber-reinforced- polymers Tube
CFRP Carbon Fiber Reinforced Polymer
CSM Capacity Spectrum Method
DBD Displacement Based Design
DCB Deformation –Calculation Based
DDSB Direct Deformation Specification Based
DL Damage Limit
DOF Degree of Freedom
FEM Finite Element Modelling
FEMA Federal Emergency Management Agency
FI Force Index
FRP Fiber Reinforced Polymer
GFRP Glass Fiber Reinforced Polymer
HSC High Strength Concrete
IDSB Iterative Deformation –Specification Based
JBDPA Japan Building Disaster Presentation Association
LS Life Safety
M Moment
MC Moment-Curvature
MDF Multi Degree of Freedom
M-N Moment- Axial force
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MRF Moment Resisting Frame
NSAP Nonlinear Static Analysis Procedure
NSP Nonlinear Static Procedures
PBD Performance Based Displacement
PI Performance Index
PMM Axial force along with moments in two axes of X and Y
RC Reinforced Concrete
SD Severe Damage
SDF Single Degree of Freedom
UBC Uniform Building Code
VS Fluid Viscous Dampers
RC Reinforced Concrete
FRP Fiber Reinforced Polymer
JBDPA Japan Building Disaster Presentation Association
ATC Applied Technology Council
FEMA Federal Emergency Management Agency
PBD Performance Based Displacement
FEM Finite Element Modelling Method
DBD Displacement Based Design
NSP Nonlinear Static Procedures
SDF Single Degree of Freedom
CSM Capacity Spectrum Method
NSAP Nonlinear Static Analysis Procedure
DCB Deformation –Calculation Based
xiii
IDSB Iterative Deformation –Specification Based
DDSB Direct Deformation Specification Based
GFRP Glass Fiber Reinforced Polymer
CFFT Concrete Filled Fiber-reinforced- polymers Tube
HSC High Strength Concrete
CFRP Carbon Fiber Reinforced Polymer
MC Moment-Curvature
MRF Moment Resisting Frame
ADRS Acceleration Displacement Response Spectrum
PI Performance Index
FI Force Index
M-N Moment- Axial force
LS Life Safety
DL Damage Limit
SD Severe Damage
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LIST OF SYMBOLS
Ac Cross-sectional area of concrete in column = Ag (1 )
Ae Effectively confined area
Ag Total cross-sectional area
As Area of tensile steel reinforcement
A‟s Area of compression steel reinforcement
Asi Cross-sectional area of „„ith” layer of longitudinal steel reinforcement
Spectral acceleration of performance point
Yield spectral acceleration of bilinear representation of spectral capacity
a Depth of compression block in RC section
b Short side dimension of a non-circular cross-section
Concrete compression force
Steel compression force
Sum of columns stiffness in given storey of building
and Elastic response spectrum coefficients based on seismic sites
Spectral displacement of performance point
Yield spectral acceleration of bilinear representation of spectral capacity
Displacement of top of buildings structure due to lateral push over force
dsi Distance from position of „„ith” layer of longitudinal steel reinforcement to geometric centroid of the cross-section
D Diameter of circular cross-section or diameter of equivalent circular column for non-circular cross-section column for non-circular cross-sections = √
d Distance from top of the section to centroid of last tensile steel
e Eccentricity of axial load
Minimum eccentricity of axial load
Slope of linear portion of confined stress–strain curve
Initial modulus of elasticity of concrete
Ef Tensile modulus of elasticity of FRP
Characteristic concrete compressive strength determined from
standard cylinder
xv
Maximum compressive strength of confined concrete
Ultimate tensile strength of FRP
Design ultimate tensile strength of FRP
Confinement pressure due to FRP jacket
Stress in „„ith” layer of longitudinal steel reinforcement
Yield strength of longitudinal steel reinforcement
Nominal yield strength for lateral force –deformation
G Sum of girders stiffness in given storey
G.A Shear force necessary to cause unit inclination of shear resistance structure
H Height of column
h Long side dimension of a non-circular cross-section
Maximum bending moment
Mn Nominal bending moment capacity
Ultimate moment of RC section
of RC section
n Number of FRP plies composing the jacket
Pa Constantly applied axial load
Pmax Maximum applied axial load
Pn Nominal axial load capacity of a RC column
Q Lateral shear force due to seismic force
Spectral acceleration of capacity curve
Spectral displacement of capacity curve
and Seismic response spectrum reduction factors based on damping ratio
r Corner radius of non-circular cross-sections
FRP nominal ply thickness
Steel tensile force
X The neutral axis distance from top of the RC section
⁄ Mass assigned to level i
Mean stress factor for confined RC section using FRP
Equivalent viscous damping associated with full hysteresis loop area
The effective equivalent viscous damping using for spectral viscous damping reduction factor
xvi
Linear gradiant coefficient correlated to second part of bilinear shape of spectral capacity
Required additional displacement of column in order to reach
imperative criterions of safe quality
Existing displacement of column due to lateral push over force
The angle in ith step of pushover curve
Factor relating the uniform compressive stress of the equivalent rectangular block in the compression zone to the compressive strength
Factor relating depth of equivalent rectangular compressive stress block to neutral axis depth
Axial compressive strain corresponding to
Ultimate axial compressive strain of confined concrete
Ultimate axial compressive strain of unconfined concrete = 0.003 mm/mm
FRP effective strain (strain level reached at failure)
Ultimate tensile strain of the FRP
Strain corresponding to the yield strength of steel reinforcement
Rupture tensile strain of the FRP
Transition strain in stress–strain curve of FRP-confined concrete. It corresponds to point of change between initial parabola and straight line
Strength reduction factor
FRP Effective strain (strain level reached at failure)
Rupture tensile Strain of the FRP
Yield curvature of RC section
Ultimate curvature of RC section
Plastic curvature ( )
Angle of inclination based on Stafford theory
Amplitude of mode 1 at level i
Buildings frequency ⁄
Efficiency factor for FRP strain proposed to account for the difference between the actual rupture strain observed in FRP confined specimens, and the FRP material rupture strain determined from tensile coupon testing
Ratio of the area of longitudinal steel reinforcement to the cross-sectional area of a compression member
xvii
Efficiency factor for FRP reinforcement in the determination of
(based on the geometry of the cross-section)
Efficiency factor for FRP reinforcement in the determination of (based on the geometry of the cross-section)
Additional FRP strength reduction factor
Yield curvature of RC section
Ultimate curvature of RC section
Target curvature of collapsed column to reach the desired displacement
Z Seismic zone factor mentioned from Table 16-I of the UBC
L Column length
I Importance factor from Table 16-K of UBC code
Constantly applied axial load
Rw Response modification factor (R) from Table 16-N or 16-P of the UBC
W Total weight of the structure in seismic form.
V The lateral force due to given earthquake, the base shear of structure
C Earthquake force coefficient multiplying to building weight (W)
A B Design spectral acceleration, is known as the ratio of gravitational acceleration corresponding to fundamental period of structure T and also soil type
R Response modification factor, for specific structural system from UBC and 2800 buildings code
Ductility base reduction factor
Maximum displacement against the lateral force
Yield displacement
Predominant period of ground motion
T Natural period of structure
Amplification factor
xviii
STRATEGI PENGIRAAN UNTUK PEMULIHAN STRUKTUR
KERANGKA KONKRIT BERTETULANG MENGGUNAKAN TIANG
TERKURUNG POLIMER BERTETULANG GENTIAN
Abstrak
Pemulihan seismik untuk struktur konkrit bertetulang (RC) menggunakan Polimer
Bertetulang Gentian (FRP) untuk tiang terkurung telah digunakan dengan meluas.
Walau bagaimanapun, tindak balas global struktur yang dipulihkan dengan
menggunakan Rekabentuk Berpandukan Pesongan tidak dikaji sepenuhnya.
Tambahan pula, pengurangan dalam penggunaan bahan dan masa analisis perlu
ditimbangkan. Oleh itu, kajian ini dijalankan untuk menyiasat tindak balas
keseluruhan struktur RC yang dipasang tiang terkurung FRP apabila analisis tidak
lelulus digunakan untuk menilai struktur. Keputusan analisis untuk tiang terkurung
FRP disahkan terlebih dahulu dengan menggunakan keputusan lapan belas
eksperimen. Ini diikuti oleh kajian tindak balas global struktur yang terdiri daripada
tiga ke tujuh tingkat. Tindak balas global struktur kerangka yang dipulihkan dengan
tiang terkurung FRP didapati sama tanpa perubahan kekukuhan di sampul pasca-alah
dalam lengkung “pushover” konvensional dan ADRS. Tindak balas kerangka konkrit
bertetulang yang dipulihkan disahkan terlebih dahulu dengan penyelesaian analitik.
Satu prosedur yang sistematik kemudiannya dicadangkan untuk pemulihan seismic
struktur berkerangka RC menggunakan tiang terkurung FRP berdasarkan kaedah
sistem penilaian lelurus dan tidak lelurus. Kaedah tidak lelurus menunjukkan
penggunaan bahan yang kurang daripada kaedah lelurus. Akan tetapi, masa
pengiraan bertambah dengan ketara. Keputusan kajian ini menunjukkan prosedur
sistematik pemulihan untuk kerangka konkrit bertetulang dengan FRP yang
dicadangkan mampu mencapai objektif pencapaian dengan penggunaan bahan dan
masa analisis yang kurang.
xix
COMPUTATIONAL STRATEGY FOR REHABILITATION OF
REINFORCED CONCRETE FRAMED STRUCTURE USING FIBRE
REINFORCED POLYMER CONFINEMENT OF COLUMNS
ABSTRACT
Fibre Reinforced Polymer (FRP) has been widely used for retrofitting of
reinforced concrete (RC) columns. However, the global response of retrofitted RC
framed structure based on Displacement Based Design (DBD) method is not clearly
known. In addition, reducing consumption of material and analysis time should be
taken into account. Thus, this study is aimed to determine the global response of
retrofitted structure using FRP-confined columns when nonlinear analysis is used to
assess the structure. The analysis results for FRP-confined RC columns were first
verified using eighteen experimental results found in literature. The analysis was
then proceeded to the whole RC frame consisting of three to seven storey levels. The
global response of retrofitted RC frame using FRP-confined columns has been found
to be identical in post-yield envelope at pushover curve in conventional and ADRS
formats without changing in initial stiffness. Response of retrofitted RC frame was
firstly verified using analytical solution. A systematic procedure was then developed
for seismic rehabilitation of RC frame based on both linear and nonlinear methods of
assessment. Four case studies were used to demonstrate the applicability of proposed
systematic procedures for linear and nonlinear methods of assessment. It was found
that retrofitting using nonlinear method give less material consumption as compared
to linear method. However, the computational time increases substantially. Results
of the current study have demonstrated that the proposed systematic rehabilitation
procedure for RC framed structure using FRP is capable to reach its performance
objective using less material as well as computational time.
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1 A CHAPTER 1 – INTRODUCTION
INTRODUCTION
1.1 Background
Recent studies have shown that reinforced concrete (RC) buildings without
adequate reinforcement are inherently brittle during earthquakes (Pampanin et al.,
2002; Hart, 2005; Galasso et al., 2010; Pampanin et al., 2011). The inadequate
resistance of building against earthquake and gravity loads may result in failure of
RC columns and consequently the collapse of buildings and loss of human life. RC
failure may occur because of shortage of stiffness or displacement capacity of RC
columns against combination of earthquake and gravity loads. Figure 1.1 shows the
inadequacy of transverse steel reinforcement at beam column joints subjected to
simultaneous axial and lateral force resulting in loss of capacity of the RC column.
Figure 1.1: Failure of RC columns due to earthquake (Canfield and Sabrina, 2010)
2
Low displacement capacity of the RC column at the local aspect results in the
formation of undesirable soft-stories and greatly affects the overall structural
performance. To avoid such tragedy, structures must be assessed for their ability to
withstand against seismic loads. Structural assessment is divided into two
subdivision: force control and displacement control. Conventionally, seismic
assessment and rehabilitation of existing structures have been carried out by using
the force-based approach. In this method, a combination of gravity and lateral force
due to earthquake is applied to the structures and consequent forces in members are
estimated. In the last decade displacement-based methods have emerged as a
favoured alternative because displacement-based parameters can quantify structural
and non-structural damage better than force-based parameters (Priestley, 1997;
Sullivan et al., 2004; Oğuz, 2005; Faella et al., 2008). Although the stress ratio of
structural members is defined as a criterion in force control codes, displacement is
the main criterion used in displacement-based design (DBD) codes for assessing
building structures.
The current procedure of assessment based on displacement based-design
(DBD) codes such as ATC-40 is shown in Figure 1.2. As shown in Figure 1.2, the
capacity curve can provide insight to engineers to make them aware about the
condition of the structure in terms of its elastic and inelastic parts by comparing the
parts with the demand of the earthquake curve.
Capacity of structure is plotted with earthquake demand to determine visually
the structure ability in elastic and inelastic segment. Structure capacity is defined as
the displacement of structure, corresponding to lateral force plotted in the pushover
curve. Seismic demand is the maximum identified damage caused by seismic force.
3
Thus, performance thus is defined based on the displacement of a structure against
lateral force due to earthquake. The overall goal of performance-based design (PBD)
methods is to develop structures that can satisfy the desired performance objectives
and consequently achieve the desired life-safe quality.
Figure 1.2: Assessment of structures (ATC-40)
Engineers and designers have to develop their skills to evaluate the
performance of buildings by using recent methods of assessment, such as PBD. The
Performance Based Design (PBD) method has become the most common method for
evaluating RC frames using nonlinear analysis on the basis of displacement-based
design (DBD) (ATC40, 1996; Sullivan et al., 2003). The rationale behind
displacement-based methods is that; contrary to force-based methods, DBD does not
consider earthquake force as a set of lateral force in the seismic design. Displacement
of structure against lateral force is used as criterion for evaluating and assessing safe
quality of structures (Priestley, 1997).
In PBD methods, the acceptable performance is calculated by measuring the
level of structural and non-structural damage levels. Damage is expressed in terms of
Bilinear form of capacity
Capacity (V versus ∆)
Inelastic Elastic
Demand Reduced Based on Inelastic Capacity of Building
Earthquake Displacement
Earthquake Force
𝑑𝑝 𝑆𝑑
𝑆𝑎
4
inelastic deformation limit of RC frame that is called post-yield behaviour of the RC
frame in pushover analysis. The analysis procedure concerning post-yield behaviour
of structures is more complex compared with that of traditionally used in the force-
based design process for evaluating performance of structure against earthquake
(FEMA440, 2004; Oğuz, 2005).
Currently, seismic assessment based on performance based design (PBD)
consists of collecting the as-built information and analysing the structure to obtain
the current situation of structure. The DBD method is known as the most recent tool
for assessing structural performance against earthquake (Sullivan et al., 2003;
Sullivan et al., 2004; Kim and Choi, 2006). The performance of structures according
to ATC-40 (1996) for structural level is defined in six groups, namely, immediate
occupancy, damage control, life safety, limited safety, structural stability and the not
considered that as shown in Figure 1.3. They are defined based on displacement of
structure.
Figure 1.3: Defining performance level based on displacement capacity (ATC-40)
To assess the resistance of a structure against earthquake, many performance
objectives are introduced to analytically predict the performance of structure against
Not considered
5
the combination of earthquake and gravity loads. For example, stress ratio of
columns is the performance objective in code such as uniform building code (UBC)
which is used to assesses structures on the basis of linear analysis methods. The
column stress ratio (CSR) is defined as the ratio between stress on the top of the
column caused by axial and moment forces to the average applied embankment
stress at the level of the top of the column. The axial and moment are caused by the
combination of gravity and earthquake loads. It is the factor that specifies the desired
seismic performance of the RC frame. Performance objective determines the ideal
seismic performance of RC frame. Seismic performance is described by designating
the maximum permitted damage status (performance level) for a particular seismic
hazard (earthquake ground motion).
On the other hand, displacement capacity of a structure up to having
performance point is one of the performance objectives according to ATC-40 that
follows nonlinear method of analysis. The procedure of defining performance point
is shown in Figure 1.4 where the performance point is known as intersection of
earthquake demand to capacity in spectral form.
Figure 1.4: Performacnce point determination (ATC-40, 1996)
Spectral earthquake demand
Reducing the earthquake demand
Bilinear form of capacity curve
6
Demand is produced based on characteristics of earthquake in spectral form
and is reduced corresponding to ductility of structure. For reducing the demand
earthquake, capacity curve as shown in Figure 1.4 is bilinearized and damping ratio
for reducing the demand based on characteristics of bilinear form of capacity is
calculated.
Structures that do not comply with the design codes criterions (i.e., having
performance objectives) should be retrofitted so that the deficiency of weak
structural members with insufficient force or displacement capacity can be rectified.
The performance objective has to be determined according to the building owner‟s
decisions for safe quality classifications and performance level. After the owner
selects the performance level, the engineer will develop a sufficient plan to reach the
desired performance objective.
Building deficiencies may be caused by changes in the occupancy of the
building, occurrence of earthquakes, errors of contractors and designers, and
alterations in geotechnical resistance. These deficiencies lower the strength and
ductility of the structure, thus placing the life of building occupants at risk. To avoid
tragedies, various types of rehabilitation methods have been proposed during the last
two decades (Thermou and Elnashai, 2006). Engineers and researchers have to
determine the optimum solution in terms of time, cost, and structural integrity in
selecting appropriate rehabilitation techniques. The decision making process for RC
frame retrofitting depends on the experience of engineers and designers. Not only the
local behaviour of retrofitted members should be known, the impact of response of
local retrofitted member on global response of RC frame also has to be recognized
before making decisions. This is because both local and global responses such as
displacement or internal forces are used to assess the structures. When evaluating
7
structures, engineers and researchers should not only consider the local response of
retrofitted structure but also the global response of structures. For example, brittle
mechanism of column can be developed from local (captive or short columns) to
global level (soft-storey) (Kam et al., 2011). As can be seen in Figure 1.5, local
deficiency of RC column may result in global collapse of RC frame.
Figure 1.5: Effect of local behaviour of structural member on global response of RC
frame (Kam et al., 2011)
8
In Figure 1.6 (a), displacement of a column is local displacement and the
displacement of the entire structure is known as global displacement. Local response
of frame as shown in Figure 1.6 (b) refers to response of material, section, type of
structural member and connection between members. Global response of structure is
the response of the RC frame such as displacement or drift of frame against applied
force due to lateral and gravity loads.
a) Local and global displacement
b) Hierarchical relationship between local and global structural response
(Elnashai and Di Sarno, 2008)
Figure 1.6: Local and global response of structure
Gravity load Lateral Load
h
Global displacement
Local displacement Local
displacement
9
Local response of members in structure affects global response of structure.
For example by increasing displacement capacity through changing material or
section of structural member, displacement capacity of frame is consequently
increased.
In the current PBD evaluation processes, the analytical models of structure
through a full range of global and local displacements must represent complete
characteristics of RC frame behaviour, including mass distribution, strength, stiffness
and deformability. The consequences of elastic and inelastic response should be
considered at both local and global levels to ensure the safety of structures (ATC40,
1996; FEMA356, 2000).
Enhancing the global capacity of the retrofitted structure up to the expected
levels of stiffness and ductility can be conducted through the increment of local
capacity of structural members. The stiffness and ductility of the structure are the
functions of the structural member stiffness and ductility and any changes in stiffness
of structural member such as size increment, will change the stiffness of entire
structure. The stiffness of the whole structure is obtained by dividing lateral force to
its corresponding displacement. The calculation process of structure stiffness
involves complex computation. The ductility increment of the local RC member
during retrofitting will change the entire ductile behaviour of the structure. Thus, the
retrofitting approach for seismic enhancement should focus on the required capacity
of structure against the seismic-induced displacement demand. The increment of
ductility of the structural member should consider the global flexibility of the
structure. In addition, the lateral force resisting system of the existing structure
should be taken into consideration. As a result, the displacement of the retrofitted
10
structure ranges within the limits of the displacement capacity of the existing
structure.
Many types of rehabilitation, such as using shear walls, steel braces, steel
jacketing and concrete jacketing are available for increasing stiffness of structure.
Other types of retrofitting, such as using FRP jacketing of columns, viscous dampers,
and isolators, are adopted to increase the displacement capacity of members and
structure. Generally, after selecting the type of retrofit for overcoming deficiency of
structural members and consequently the entire structure, the amount of material and
size of additional retrofit elements must satisfy performance objectives in codes. The
conventional method of rehabilitation does not take into account of the optimum
amount of material needed by the structural member in RC frames. The method
relies on the experience, creativity, capability, and intuition of decision makers and
designers. In the absence of any systematic method, the conventional method adopts
trial-and-error approach for rehabilitating elements of frames to select the size and
location of retrofit element. This approach may cause ineffectiveness in terms of
material usage for rehabilitation. For example, using FRP for columns in order to
overcome the problem of lack of ductility of structures and reach desired
performance objective. In this case, to achieve desired performance objective that
contained specified ductility of structure based on codes, emplacement of FRP-
confined columns and amount of material in the absence of any systematic method
must be selected by using trial-and-error approach. To solve this problem, various
studies have proposed the use of the systematic methods for eliminating problems
arising from conventional approach of rehabilitation for selecting the location and
amount of material of retrofit elements. Previous studies have systemically selected
the stiffness characteristics of nonlinear fluid viscous damper (VS) (Martinez-
11
Rodrigo and Romero, 2003), amount of FRP and emplacement at weak joints at RC
beam and columns joint (Pampanin et al., 2007) and geometric characteristics and
stiffness of haunches at RC beam and columns joints (Pampanin and Christopoulos,
2003). These systematic methods aimed to select amount, location and characteristics
of retrofit elements to maximize the performance of structural components while
minimize the consumption of computational time and materials.
FRP is one of the popular materials for structural rehabilitation. The
advantages of FRP are the light weight, ease of application on RC columns, and
noncorrosiveness. However this material is costly. Although the advantage of this
material for enhancing shear and deformation of RC columns is proven (El-Sokkary
and Galal, 2009), nevertheless global response of structure retrofitted by FRP-
confined columns is not known in DBD methods of RC frame assessment. An ideal
retrofit strategy for RC structures not only protect the column, by identifying
damaged columns and applying FRP on weak columns, but also further upgrade the
RC frame to exhibit the desired behaviour according to performance objectives
specified in codes.
1.2 Problem Statement
The performance of structure is affected because of changes in the occupancy
of the building, occurrence of earthquakes, errors of contractors and designers, and
alterations in geotechnical resistance. For assessing performance of RC frames, every
code has introduced specified range of performance objectives that must be satisfied
to ensure safe quality. The values for performance objectives are obtained by
analysing RC frame. Performance objectives include the specified range of both local
12
and global response of RC frame against seismic and gravity forces. Buildings with
shortage of specified values of performance objective must be retrofitted.
For retrofitting RC frame, the first stage is the selection of the appropriate
retrofit strategy. Thus the best decision must be made concerning cost and weakness
of structure. For selecting the most rational retrofit strategy, decision makers and
designer teams must be clearly aware about impact of retrofit strategy on given
performance objectives. Otherwise, retrofit plan may lead to inappropriate response
of structure and undesired performance objectives.
Although FRP studies have reported elimination of shear failure of retrofitted
RC column (Thermou and Elnashai, 2006), the global response of RC retrofitted
frame has not been studied based on PBD methods of assessment. Although,
confining RC columns by FRP has impact on local response of structural member as
increment of ductility of RC member without considerable effect on stiffness
(Balsamo et al., 2005; Zou et al., 2007; El-Sokkary and Galal, 2009), global response
of RC frame is still not known in PBD method of RC frame assessment. Therefore
impact of using FRP-confined columns on global response of RC frame when
assessed based on PBD method of assessment is not known. Thus, for researcher and
practical engineer, effect of FRP on specified global performance objectives
specified in ATC-40 is unknown. ATC-40 is the code using displacement for
assessing performance of RC frame (PBD) and displacement is obtained using
nonlinear method of analysis that is inherently complex and time-consuming (ATC-
40, 1996; FEMA440, 2004; Oğuz, 2005).
13
Although having adequate information about the effect of FRP-confining
columns on performance objectives aids designers to appropriately make decision
but, emplacement and amount of material to achieve ideal performance objectives
according to ATC-40 and UBC-97, is conventionally determined following
conventional trial-and-error approach since there are no systematic methods. Apart
from structural response of retrofitted structure using FRP-confined columns,
systematic method to rehabilitate structures using the optimum material and analysis
time to achieve the required performance objectives according to ATC-40 and UBC-
97 is still not available. Although Zou et al. (2007) has optimized FRP consumption
for RC frame using complex mathematical procedure, the method is based on
performance objectives specified in Chinese code. Emplacement of FRP-confined
columns has not been considered and FRP must be applied to all columns of RC
frame which is costing. Owner of buildings will not accept demolishing all non-
structural elements of building such as infill walls and HVAC that will cost more
than reconstruction of the building. Meanwhile moment-curvature (MC) diagram of
FRP-confined columns that determines displacement capacity of column in study by
Zou et al. (2007) had not been verified. Global response of RC frame after
retrofitting is not reliable, without verification of local response of RC frame.
The analysis process according to ATC-40 and UBC-97 codes usually needs a
linear and nonlinear static analysis of structure that are considerably time-consuming.
Therefore, developing a systematic procedure for selecting the amount of material
and location of FRP-confined columns is needed to reduce computational efforts and
to make seismic assessment more reliable.
14
1.3 Objectives
The objectives of this study are as follows:
i) To study the local and global structural response of RC frames after
retrofitting with FRP-confined columns
ii) To propose a systematic procedure for selecting the proper location of
FRP-confined columns and number of FRP layers for RC column on the basis
of linear and nonlinear methods of structural assessment
iii) To assess the performance of the proposed systematic methods in terms of
time and material consumption.
1.4 Scope of Study
This study focuses on the seismic rehabilitation of rigid RC-framed with FRP-
confined columns. Pushover nonlinear static analysis is adopted to evaluate the
safety level of RC frames. Structural assessment is carried out based on nonlinear
and linear methods (ATC-40 and UBC97). To verify the analysis results for FRP-
confined columns, 18 experimental results are compared with the analysis results
from SAP2000 modeling.
The case studies consisted of 3D frames for investigating the global response
of retrofitted structures and 2D frame for evaluating the proposed systematic
methods. 3, 4, 5, 6 and 7 stories RC frames were analysed in pushover analysis. The
cross sections of structural members in the case studies were limited to rectangular.
15
SAP2000 was used to analyse the behaviour of RC frames. In this study, the
confined concrete material properties are defined according to Lam and Teng (2003a
and 2003b). ACI440 is used to define the behaviour of confined concrete to limit the
rupture strain of FRP. Thus, columns of RC frames were modeled with and without
consideration to ACI440 limitation for rupture strain. RC frames were simulated with
assumption that hinges are formed at both ends of columns and beams.
The variables used in this study to reach performance objectives were the
number of FRP layers and emplacement of FRP-confined columns. Performance
point is denoted as the performance objective according to ATC-40, whereas CSR is
denoted as the performance objective based on UBC97.
1.5 Structure of Thesis
This thesis is divided into six chapters.
Chapter 1 introduces the research background, problem statement, objectives
of research and scope of work. Chapter 2 reviews the background of seismic
rehabilitation. Experimental and numerical researches on FRP-confined columns
were then reviewed. Rehabilitation methods and consequent local and global
response of structure using various retrofit elements is then described. It is followed
by review on systematic methods of rehabilitation using FRP.
Chapter 3 presents the theoretical background and basic formulations for
behaviour of FRP-confined columns. The processes of assessment of RC frames
based on linear and nonlinear methods are described and all formulations that are
16
used in this study are presented. The formulations used for determining displacement
of RC rigid frame against lateral force are also mentioned.
Chapter 4 describes the research methodology used in this study. The
procedure of modelling FRP-confined columns to compare to experiments from
previous studies is explained. Then systematic methods based on linear and nonlinear
methods of assessment of RC frames are described and illustrated in terms of flow
chart and scheme of algorithm.
Chapter 5 presents the result of analysis and discussion. The analysis results
for FRP-confined columns are verified using 18 experiment columns that had been
studied before. The results of comparison of analysis and experimental results are
presented. Whole retrofitted structures are modelled and global response of
retrofitted RC frame is shown and discussed. The global response of retrofitted RC
frame is verified using theoretical solution. The applicability of proposed systematic
method based on nonlinear and linear methods of assessment are evaluated using
four case studies. Advantages of proposed systematic method are then highlighted by
comparing to other similar study on optimization of FRP consumption for retrofitting
RC frames.
Finally the conclusion and recommendation for future research work are
presented in Chapter 6.
17
2 CHAPTER 2 - LITERATURE REVIEW
LITERATURE REVIEW
2.1 Introduction
This chapter is divided into four sections. The general procedure of seismic
rehabilitation and analysis methods is first presented. The effect of retrofit on the
local and global response of RC frame by using FRP is described. Subsequently,
reviews on related past studies on FRP-confined columns are presented, and the
systematic method to achieve cost-effective solution in seismic rehabilitation is
depicted.
2.2 Seismic Rehabilitation Procedure
Many recent codes, such as SEAOC (1999), ATC-40 (1996), FEMA 356
(2000), FEMA 440 (2002), and FEMA P695 (2009), that define the performance of
structures on the basis of displacement are used to evaluate structures. Some of
aforementioned code such as ATC-40 (1996), FEMA 440 (2002) employ the
capacity spectrum method (CSM) in first and second stiffness approaches to analyse
and assess the performance of RC frames. In the CSM proposed by Freeman (1998),
the capacity in spectral form has to be linearized to obtain the required parameters,
such as performance point and reduction factor.
The role of analysis methods in obtaining accurate displacement of the RC
frame against force has attracted much attention. Table 2.1 lists the research studies
on the calculation of the displacement of structures against forces. In Table 2.1, the
18
horizontal row shows the displacement method used in the design process, whereas
the vertical column shows the analysis method. ATC-40 is generally in the category
of the methods of Freeman (Freeman, 1998), Paret et al. (1996), and Chopra and
Goel (2001) that are based on CSM. However, other methods have also adopted the
secant stiffness for structure assessment and analysis (Gulkan and Sozen, 1974;
Priestley, 1993). The base method of guidelines, such as ATC-40, involves the
calculation of maximum displacement expected from a given structure. DBD
methods which are based on initial stiffness determine the displacement of structures
by using elastic stiffness of structure and approximate the relation between elastic
and inelastic responses.
Table 2.1: Design procedures for structure assessment through Displacement Based Design Methods (Sullivan et al., 2003) Deformation –
Calculation Based (DCB)
Iterative Deformation –
Specification Based (IDSB)
Direct Deformation Specification Based
(DDSB)
Response Spectra: Initial Stiffness Based
Moehele (1992) FEMA (2000) UBC (1997)
Panagiotakos and Fardis (1999)
Albanesi et al. (2000) Fajfar (2000)
Browning (Browning, 2001)
SEAOC (1999) Aschheim and Black
(2000) Chopra and Goel
(2001)
Response Spectra: Secant Stiffness Based
Freeman (1978) Paret et al. (1996)
Chopra and Goel (1999) ATC-40 (1996)
Gulkan and Sozen (1974)
Kowalsky et al.(1995)
SEAOC (1999) Priestly and
Kowalsky (1998) Direct Integration: Time Historey Analysis Based
Koppas and Manafpour (2001) N/A N/A
Figure 2.1 illustrates the meaning of initial and secant stiffness. The dynamic
information of structures can be obtained from the elastic behaviour of structure in
the initial stiffness method by approximating the elastic and inelastic responses of the
structure.
19
Figure 2.1: Initial and secant stiffness (Sullivan et al., 2003)
The flowcharts of retrofitting process based on ATC-40 and FEMA 356 are
shown in Figure 2.2 and Figure 2.3, respectively. A retrofit plan is first assumed in
this process. The resulting capacity and demand spectrum is developed, and the
performance point is determined. If the results are in the acceptable performance
objective range, then the design is adequate. If not, the design must be revised by
changing the placement and sizes of retrofit elements. The process is subsequently
repeated, or an alternative strategy is employed (ATC40, 1996). Thus, to achieve the
desired performance level and performance objectives of a structure, a formulation of
rational retrofit plan must be considered.
To reach this aim, the design team must be aware about the effect of any
possible retrofit strategy on performance objectives. Otherwise, the highlighted
stages in Figure 2.2 and Figure 2.3 must be performed by a conventional trial-and-
error approach. The formulation of retrofit strategies requires experienced decision
makers. Without any clear information on the effect of possible retrofit strategies on
performance objectives, developing any plan for retrofitting may lead to undesired
values. If the designer does not know the exact local and global response of the
structure after rehabilitation by using possible retrofit strategies, the developed plan
20
may not be able to overcome the structure deficiency.
To achieve the desired performance objectives, the placement and
determination of sizes of retrofit element and material consumption must be initially
decided after selecting the retrofit element. The selection of placement and sizes of
retrofit element must be revised or altered if the desired performance objective is not
achieved (ATC-40).
Figure 2.2: The process of rehabilitation according to ATC-40 (1996)
• Jurisdictional Requirements •Architectural Changes •Voluntary Upgrade
1- Initiate the process
•Structural Engineer •Architect 2-Select Qualified Professionals
•Structural Stability or Limited Safety or life Safety, Damage Control
3- Establish Performance Objectives
•Review Drawings •Visual Inspection •Prelininary Calculations
4- Review Building Conditions
•Simplified Procedures • Inelastic Capacity Methods •Complex Analyses
5- Formulate a Strategy
•Building Official •PeerReview 6- Begin the Approval Process
•Site Analysis •N Material Properties •Construction Details
7- Conduct Detailed Investigations
•Modeling Rules •Force and Displacement 8- Characterize Seismic Capacity
•Seismic Hazard • Interdependence with Capacity •Target Displacement
9- Determine Seismic Demand
•Global Response Limits •Component Acceptability •Conceptual Approval
10- Verify Performance
•Similarity to New Construction •Plan Check •A Formof Construction Contract
11- Prepare Construction Documents
•Submittals, Tests, and Inspections •Verification of Existing Conditions • . Construction Observation by Designer
12- Monitor Construction Quality
Prior Seismic Evaluation
Interest in reducing seismic risk
21
Figure 2.3: Rehabilitation process flowchart (FEMA356, 2000)
Prior Seismic Evaluation
Interest in reducing seismic risk
1- Review Initial Considerations as follow and collecting the information: • Structural characteristics • Site seismic hazards • Results from prior seismic evaluations • Occupancy • Historic status • Economic considerations (Section C1.2.6.2) • Societal issues Obtain As-Built Information • Local jurisdictional requirements
Select Rehabilitation Objective • Target Building Performance level • Seismic Hazard
Is the building is able to comply with guidelines criterions and resist again given earthquake force?
Buildings Structure strength is sufficient to resist a ga in s t e a r th q u a k e an d g ra v i t y fo r c es
Yes No
Select Rehabilitation Method∗
Other Choices • Reduce occupancy • Demolish
5A Perform Rehabilitation Design • Determine and design rehabilitation measures to meet applicable ATC-40 requirements
6.1A Redesign Unacceptable Rehabilitation • Return to 4A to reconsider rehabilitation Objective or to 5A to revise corrective measures
6.2A Prepare Construction Documents of Acceptable Rehabilitation • Develop construction Documents • Begin rehabilitation • Exercise quality control
No Yes
Perform Rehabilitation Design • Develop mathematical model • Perform force and deformation response evaluation • Size elements, components, and connections
6.2B Prepare Construction Documents of Acceptable Rehabilitation • Develop construction documents • Begin rehabilitation • Exercise quality control
No Yes
4B Systematic Rehabilitation • Consider deficiencies • Select rehabilitation strategy • Select analysis procedure • Consider general requirements
4A Simplified Rehabilitation • Identify building model type • Consider deficiencies • Select full or partial rehabilitation (Note: Simplified Rehabilitation shall be used for Limited Objectives only.)
• Review for economic acceptability∗
Verify Rehabilitation Design • Apply component acceptance criteria • Review for conformance with ATC − 40 requirements∗
6A Verify Rehabilitation Design • Reevaluate building to assure that rehabilitation measures remove all deficiencies without creating new ones • Review for economic acceptability
2- Create the model according to collected information and analyze and compare the results to relevant guidelines criterions
6.1B Redesign •Unacceptable Rehabilitation • Return to 4B to revise analysis and design or to 2 to reconsider Rehabilitation Objective
Prior Seismic Evaluation
Interest in reducing seismic risk
1- Review Initial Considerations as follow and collecting the information: • Structural characteristics • Site seismic hazards • Results from prior seismic evaluations • Occupancy • Historic status • Economic considerations (Section C1.2.6.2) • Societal issues Obtain As-Built Information • Local jurisdictional requirements
Select Rehabilitation Objective • Target Building Performance level • Seismic Hazard
Is the building able to comply with guidelines criterions and resist again given earthquake force?
Buildings Structure strength is sufficient to resist a ga in s t e a r th q u a k e an d g ra v i t y fo r c es
3- Selecting rehabilitation method
Other Choices • Reduce occupancy • Demolish
5A Perform Rehabilitation Design • Determine and design rehabilitation measures to meet applicable ATC-40 requirements
6.1A Redesign Unacceptable Rehabilitation • Return to 4A to reconsider rehabilitation Objective or to 5A to revise corrective measures
6.2A Prepare Construction Documents of Acceptable Rehabilitation • Develop construction Documents • Begin rehabilitation • Exercise quality control
No Yes
Perform Rehabilitation Design • Develop mathematical model • Perform force and deformation response evaluation • Size elements, components, and connections
6.2B Prepare Construction Documents of Acceptable Rehabilitation • Develop construction documents • Begin rehabilitation • Exercise quality control
No Yes
4B Systematic Rehabilitation • Consider deficiencies • Select rehabilitation strategy • Select analysis procedure • Consider general requirements
4A Simplified Rehabilitation • Identify building model type • Consider deficiencies • Select full or partial rehabilitation (Note: Simplified Rehabilitation shall be used for Limited Objectives only.)
• Review for economic acceptability⬚
Verify Rehabilitation Design • Apply component acceptance criteria • Review for conformance with code requirements⬚
6A Verify Rehabilitation Design • Reevaluate building to assure that rehabilitation measures remove all deficiencies without creating new ones • Review for economic acceptability
2- Create the model according to collected information and analyse and compare the results to relevant guidelines criterions
6.1B Redesign •Unacceptable Rehabilitation • Return to 4B to revise analysis and design or to 2 to reconsider Rehabilitation Objective
4-
22
In order to achieve desired performance objectives, placement and
determination of sizes of retrofit element and material consumption must be initially
decided in first step after selecting retrofit element. The selection of location and
sizes of retrofit element must be revised or altered if desired performance objective is
not achieved.
2.3 Numerical Modelling of FRP-Confined RC Column
Predicting the behaviour of FRP-confined columns against the lateral and
gravity loads has attracted the attention of researchers. Researchers not only
attempted to predict the behaviour of FRP-confined columns by using various
experiments but also modeled FRP-confined columns numerically to analytically
estimate column responses against forces. Koksal et al. (2009) studied the axial force
modeling of the FRP-confined column by using the cohesion parameter of Drucker–
Prager criterion in terms of cylindrical compressive strength to predict the
compressive performance of concrete under high confinement pressures. Koksal et
al. (2009) also modeled 42 small- and large-scale column specimens tested by eight
different researchers. Analysis results have achieved adequate accuracy for axial
stress-strain relation of FRP-confined RC column. Figure 2.4 shows the finite
element model of the column.
Figure 2.4 shows that eight- and four-point elements were used for solid
elements of concrete and FRP. The top surface of the element is modeled in a rigid
form. An eight-node concrete in 3D form and isoperimetric (isotropic) material was
defined for concrete, and the elements were modeled in LUSAS software.
23
The axial behaviour of confined concrete was simulated by using LSDYNA
finite element software (Wu et al., 2009). The result was validated by comparing the
analysis and experiment results (Wu et al., 2009).
Confined concrete specimens were modeled by using ANSYS. The ANSYS
software can automatically generate the mesh for various geometric shapes and
material properties. Results show that the response of this software is sufficient
considering some coefficients, such as the dilatancy angle of FRP-confined concrete,
are proposed to be zero (Mirmiran et al., 2000). The dilatancy angle (Ψ) is a measure
of contractive or dilative nature of the volumetric response due to shearing. Montoya
et al. (2004) introduced and employed a specific program to predict the behaviour of
confined concrete axial stress and strain. New constitutive models for confined
concrete that focus on the analysis of axisymmetric solids were formulated and used.
Results have been found to be acceptable following the proposed modeling process
Figure 2.4: Modelling the axial force on confined column using FRP wrapping in
finite element (Koksal et al., 2009)
24
of Montoya et al. (2004). Parvin and Jamwal (2006) attempted to determine the
behaviour of confined concrete section by using MSCMarc™ 2001 (MSC, 2001)
software, as shown in Figure 2.5.
a) Model of MSCMarc 2001 b) Analysis result
Figure 2.5: Modelling and result of Parvin and Jamwal (2006) for confined column
Parvin and Jamwal (2006) investigated the angle of FRP wrap on a confined
section. FRP laminates in 0° show the highest axial stress-carrying capacity of
confined concrete. However, given that the best angle to reach the highest axial stress
is 0° for FRP laminates, ±15° has shown to be the best angle to achieve the highest
strain.
Shahawy et al. (2000) studied another ANSYS finite element model of
uniaxial concrete specimen. A total of 45 carbon-wrapped concrete specimen of two
types of normal- and high-strength concrete with different number of FRP plies have
been verified. The models contained the concrete originally developed for concrete-
filled glass FRP tubes. Numerical computation of confined concrete following non-
associate Drucker–Prager procedure has been conducted. The accuracy of the model