seismic performance evaluation of different …
TRANSCRIPT
SEISMIC PERFORMANCE EVALUATION OF DIFFERENT
RETROFITTING SCHEMES USING PUSHOVER ANALYSIS.
SK. MD. GOLAM RABBI
MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
DHAKA-1000, BANGLADESH
MAY, 2019
SEISMIC PERFORMANCE EVALUATION OF DIFFERENT
RETROFITTING SCHEMES USING PUSHOVER ANALYSIS.
by
SK. MD. GOLAM RABBI
A thesis submitted to the Department of Civil Engineering of Bangladesh University of
Engineering and Technology,Dhaka in partial fulfillment of the requirements for
the degree of
MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
DHAKA-1000, BANGLADESH
MAY, 2019
iv
ACKNOWLEDGEMENT
Thanks to Almighty Allah for HIS Gracious, unlimited Kindness and with the
Blessings of whom the good deeds are fulfilled.
The author wishes to express his deepest gratitude to Dr. RupakMutsuddy,Assistant
professor,Department of Civil Engineering,BUET, Dhaka for his continuous guidance,
invaluable suggestions and affectionate encouragement at every stage of this study.
The author wishes to express his profound gratitude to Engr. Khandakar Md. Wahid
Sadique, Executive Engineer,North Dhaka (RAJUK) Division&Urban Resilience
Project (RAJUK), for his continuous support and allowing the use of different facilities
in connection with RAJUK to complete the thesis work.
A very special debt of deep gratitude is offered to the author’s parents, wife,and brother
for their continuous encouragement and cooperation during this study.
v
ABSTRACT
The traditional approach to seismic design is a force-based design where there is no measure of the deformation capability of a member or of a building. According to Bangladesh national building code,2006the buildings are designed with equivalent static force method, response spectrum method and time history analysis. However, the actual performance of a structure can hardly be found by these methods. Structural failures in recent earthquake have exposed the weakness of current design procedures and leads to the development of Performance Based Earthquake Engineering (PBEE).
As a relatively new development, Pushover-based seismic evaluation and design methods offered a great opportunity to engineers. Applied Technology Council (ATC-40),1996 and Federal Emergency Management Agency-(FEMA),2000proposed a simplified nonlinear static analysis (Pushover Analysis) procedure for PBEE which provides a better understanding about the actual behavior of the structures during earthquake. There are established numerical tools like ETABS v 9.7.4 developed by Computers and Structures Inc..1995which can perform the pushover analysis.
The present study investigates and compares the seismic performance of two existing buildings as per as built structural drawings by pushover analysis. Among the two buildings one is airregular shaped government office buildingand another one is a regular shapedgovernment residential building which are located at different locationsof Dhaka city.The buildings are of6 storied and constructed 20 years ago. Different infill conditions (i.e. bare frame, full infilled and soft ground storey)along with different earthquake conditions(i.e. serviceability earthquake, design basis earthquake and maximum earthquake) were considered during analysis. For different conditions mainly a structure is analyzed with the help of capacity curve, capacity spectrum,deflection,drift and seismic performance level. Effect of infill is modelled using equivalent strut width theory.
It is found that performance of full infilled frame condition is better than that of bare frame condition. Capacity curve of the both structures meets the demand curve at lower displacement value. Lateral drift ratios are less than that of bare frame structure. Investigation of building with soft storey condition shows that it contains seismic deficiencies and need some remedial measures or retrofitting.
The performances of the structures with different remedialmeasures (i.e. insertion of shear wall,buttresswall,column jacketing) have been studied both individually and combindly. Among the considered retrofitting measures "insertion of shear wall" shows better performance over "column jacketing and buttress wall" in terms of lateral inelastic drift ratio and number of hinges formed.
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SEISMIC PERFORMANCE EVALUATION OF DIFFERENT
RETROFITTING SCHEMES USING PUSHOVER ANALYSIS.
TABLE OF CONTENTS
Page No
Certificate of approval ii
Declaration iii
Acknowledgement iv
Abstract v
Table of Contents vi
List of Tables xiii
List of Figures xvii
List of Symbols xxiv
Chapter 1 Introduction
1.1 General 1
1.2 Back Ground And Present State of the Problem 2
1.3 Objective and Scope of the Study 3
1.4 Outline of the Methodology 4
1.5 Layout of the Thesis 5
Chapter 2 Literature Review
2.1 Introduction 6
2.2 Earthquake Ground Motion 6
2.3 Ground Motion And Building Frequencies 7
2.4 Response Spectra 8
2.5 Analysis of Structure Due To Earthquake Forces 9
2.5.1 Equation of Motion: Earthquake Excitation 9
2.5.2 Code Specified Equivalent Static Load Method 10
2.5.3 Response Spectrum Analysis 11
2.6 Earthquake Loading In The Light of BNBC 14
2.6.1 Equivalent Static Load Method 14
2.6.2 Calculation of Base Shear 14
2.6.3 Zone Coefficient, Z 15
2.6.4 Structure Importance Coefficient, I 15
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Page No
2.6.5 Seismic Dead Load, W 15
2.6.6 Response Modification Factor, R 15
2.6.7 Numeric Coefficient, C 16
2.7 Response Spectrum Method 17
2.8 Time History Analysis 18
2.9 Limitation of BNBC 2006 18
2.9.1 The Zoning Map 18
2.9.2 Structure Period 18
2.9.3 Base Shear Distribution 18
2.10 Seismic Strengthening 19
2.11 Retrofit Strategies 19
2.11.1 Technical Strategis 20
2.11.2 Management Strategies 27
2.12 Past Research on Seismic Performance Evaluation
of different Retrofitting Schemes Using Non-Linear Analysis 28
Chapter 3 Concept of Performance Based Design
3.1 General 33
3.2 Seismic Analysis Methods 33
3.3 Methods to Perform Simplified Non Linear Analysis 34
3.3.1 Capacity Curve of a Structure 35
3.3.2 Demand Curve of a Structure 35
3.3.3 Performance Point of a Structure 36
3.4 Non Linear Static (Push Over) Analysis 36
3.4.1 Capacity Spectrum Method 39
3.4.2 Displacement Coefficient Method 39
3.5 Seismic Performance Evaluation 39
3.6 Nonlinear Static Procedure for Capacity Evaluation of Structures 40
3.7 Structural Performance Levels and Ranges 41
3.7.1 Immediate occupancy structural performance level (S-1) 42
3.7.2 Damage control structural performance range (S-2) 43
3.7.3 Life safety structural performance level (S-3) 43
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Page No
3.7.4 Limited safety structural performance range (S-4) 44
3.7.5 Collapse prevention structural performance level (S-5) 44
3.8 Target Building Performance Levels 44
3.9 Response Limits 45
3.9.1 Global building acceptability limits 45
3.9.1.1 Gravity Load 45
3.9.1.2 Lateral Load 45
3.9.2 Element and component acceptability limits 46
3.9.2.1 Primary and secondary elements and components 46
3.9.2.2 Deformation of force controlled action 46
3.9.2.3 Deformation Controlled and Force Controlled
Behaviour 46
3.10 Acceptability Limit 48
3.11 Seismic Demand 49
3.11.1 The Serviceability Earthquake(SE) 50
3.11.2 The design earthquake (DE) 50
3.11.3 The maximum earthquake (ME) 50
3.12 Development of Elastic Site Response Spectra 50
3.12.1 Seismic Zone 51
3.12.2 Seismic Source Type 51
3.12.3 Near Source Factor 51
3.12.4 Seismic Coefficients 51
3.13 Element Hinge Property 51
3.13.1 Concrete Axial Hinge 52
3.13.2 Concrete moment hinge and concrete P-M-M hinge 52
3.13.3 Concrete Shear Hinge 53
3.14 Concrete Frame Acceptability Limits 54
3.15 Hinge Properties for Modeling 54
3.16 Assumption for Pushover Analysis 55
Chapter 4 Effect of Masonry Infill in RC Buildings
4.1 Introduction 56
4.2 Computational Modeling of Infill Panel 59
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Page No
4.2.1 Equivalent strut method 59
4.2.2 Equivalent strut width 60
4.2.3 Eccentricity of equivalent strut 62
4.3 Perforated Panels 63
4.4 Partially Infilled Frames 64
4.5 Existing Infill Damage 64
4.6 Properties to be Determined 65
4.7 Calculation of Equivalent Strut Width 65
Chapter 5 Seismic Performance Evaluation of Two 06 (Six) Storey
RC Buildings
5.1 General 66
5.2 Structural Characteristic Features of Building 1 66
5.3 Performance Evaluation of The Building 1 67
5.4 Calculation and Selection of Seismic Coefficient For Building 1 74
5.5 Performance Evaluation of Bare Frame Condition of Building 1 69
5.5.1 Hinge formation Status of Bare Condition of Building 1 72
5.5.2 Lateral Drift Ratio for Bare Frame Condition of Building 1 73
5.6 Performance Evaluation of Full Infilled Condition of Building 1 74
5.6.1 Hinge formation Status of Full Infilled Condition of
Building1 77
5.6.2 Lateral Drift Ratio for Full Infilled Condition of Building 1 78
5.7 Performance Evaluation of Soft Storey Condition of Building 1 79
5.7.1 Hinge formation Status for Soft Storey Condition of
Building 1 82
5.7.2 Lateral Drift Ratio for Soft Storey Condition Of Building 1 82
5.8 Comparison of The Performance Evaluation of The Building 1
Considered for Analysis 83
5.8.1 Comparison Of Hinge Formation And Base Shear of
Building 1 83
5.9 Structural Characteristic Features of Building 2 84
5.10 Performance Evaluation of The Building 2 85
5.11 Calculation and Selection of Seismic Coefficient for Building 2 85
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Page No
5.12 Performance Evaluation of Bare Frame Condition of Building 2 86
5.12.1 Hinge formation Status of Bare Condition of Building 2 89
5.12.2 Lateral Drift Ratio for Bare Frame Condition of Building 2 90
5.13 Performance Evaluation of Full Infilled Condition of Building 2 91
5.13.1 Hinge formation Status of Full Infilled Condition of
Building 2 94
5.13.2 Lateral Drift Ratio for Full Infilled Condition of
Building 2 95
5.14 Comparison of The Performance Evaluation of The Building 2
Considered for Analysis 95
5.14.1 Comparison of Hinge Formation And Base Shear of Building 2 96
5.15 Summary 96
Chapter 6 Performance Evaluation of Retrofitted Structures
6.1 Remedial Measures For Retrofitting Of The Structure 1 98
6.1.1 Structural Retrofitting of The Building 1 Using Column
Jacketing And Providing Additional Buttress Wall 98
6.1.1.1 Performance Evaluation of The Retrofitted Building 1
retrofitted with Column Jacketing And Buttress Wall 99
6.1.1.2 Hinge Formation status of The Retrofitted Building 1
retrofitted with Column Jacketing And Buttress Wall 101
6.1.1.3 Lateral Drift Ratio of The Retrofitted Building 1
retrofitted with Column Jacketing And Buttress Wall 102
6.1.2 Structural Retrofitting Of The Building 1 Using Insertion
of Additional Shear Wall 102
6.1.2.1 Performance Evaluation of The Retrofitted Building 1 retrofitted With additional Shear wall 103
6.1.2.2 Hinge Formation status of the Retrofitted Structure 1
retrofitted With additional Shear wall 106
6.1.2.3 Lateral Drift Ratio of The Retrofitted Building 1
retrofitted With additional Shear wall 107
6.2 Comparison of The Performance Evaluation of The
Retrofitted Structure with Unretrofitted Building (Building 1) 107
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Page No
6.2.1 Comparison of Hinge Formation of The Retrofitted
Building with Unretrofitted Building (Building 1) 108
6.2.2 Comparison of Lateral Drift Ratios of The Retrofitted
Building with Unretrofitted Building (Building 1) 109
6.3 Remedial Measures For Retrofitting of The Building 2 110
6.3.1 Structural Retrofitting of The Building 2 Using
Column Jacketing 110
6.3.1.1 Performance Evaluation of The Retrofitted Building
2 retrofitted with Column Jacketing 111
6.3.1.2 Hinge Formation status of The Retrofitted Building
2 retrofitted with Column Jacketing 113
6.3.1.3 Lateral Drift Ratio of The Retrofitted Building 2
retrofitted with Column Jacketing 114
6.3.2 Structural Retrofitting of The Building 2 retrofitted
with Column Jacketing and Buttress Wall 114
6.3.2.1 Performance Evaluation of The Retrofitted Building
2 retrofitted with Column Jacketing and Buttress Wall 115
6.3.2.2 Hinge Formation status of the Retrofitted Building
2 retrofitted with Column Jacketing and Buttress Wall 118
6.3.2.3 Lateral Drift Ratio of The Retrofitted Building 2
retrofitted with Column Jacketing and Buttress Wall 119
6.3.3 Structural Retrofitting of The Building 2 retrofitted with
Column Jacketing and Shear Wall 119
6.3.3.1 Performance Evaluation of The Retrofitted Building
2 retrofitted with Column Jacketing and Shear Wall 120
6.3.3.2 Hinge Formation status of the Retrofitted Building
2 retrofitted with Column Jacketing and Shear Wall 122
6.3.3.3 Lateral Drift Ratio of The Retrofitted Building 2
retrofitted with Column Jacketing and Shear Wall 123
6.4 Comparison of The Performance Evaluation of The Retrofitted
Building with Unretrofitted Building (Building 2) 124
6.4.1 Comparison of Hinge Formation of The Retrofitted
Building with Unretrofitted Building(Building 2) 125
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6.4.2 Comparison of Lateral Drift Ratios of The Retrofitted
Building with Unretrofitted Building (Building 2) 126
Chapter 7 Conclusions And Recommendations
7.1 General 127
7.2 Findings of The Study 127
7.3 Recommendations for Future Studies 129
References 130-132
Appendix 133-155
xiii
LIST OF TABLES
Table No. Page No.
Effect of Masonry Infill in RC Buildings
4.1 In-Plane Damage Reduction Factor 65
Seismic Performance Evaluation of Two 6 (Six) Storey
RC Buildings
5.1 Different Parameter’s Values for Different Earthquake Conditions
for Bare Frame Condition of Building 1 72
5.2 Hinge Formation Status for Different Earthquake Conditions for
Bare Frame Condition of Building 1 72
5.3 Deformation Limits For Various Performance Level(ATC-40) 73
5.4 Drift Ratio In X Direction for Bare Frame Condition of
Building 1 74
5.5 Different Parameter’s Values for Different Earthquake Conditions
for Full Infilled Condition of Building 1 77
5.6 Hinge Formation Status for Different Earthquake Conditions
for Full Infilled Condition of Building 1 77
5.7 Drift Ratio in X Direction for Full Infilled Condition of
Building 1 78
5.8 Different Parameter’s Values for Different Earthquake Conditions
for Soft Storey Condition of Building 1 81
5.9 Hinge Formation Status For Different Earthquake Conditions
for Soft Storey Condition Of Building 1 82
5.10 Drift Ratio In X Direction For Soft Storey Condition 0f
Building 1 83
5.11 Comparison of Different Parameter’s Values for Different
Earthquake Conditions for Bare Frame,Full In Filled, Soft Storey
Condition of Building 1 83
5.12 Comparison of Hinge Formation and Base Shear for Design
Earthquake Criteria For Bare Frame,Full In Filled, Soft
Storey Condition of Building 1 84
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Table No. Page No.
5.13 Comparison of Hinge Formation and Base Shear for Maximum
Earthquake Criteria for Bare Frame, Full In Filled, Soft Storey
Condition of Building 1 84
5.14 Different Parameter’s Values for Different Earthquake Conditions
for Bare Frame Condition of Building 2 89
5.15 Hinge Formation Status for Different Earthquake Criteria for Bare
Frame Condition of Building 2 89
5.16 Drift Ratio In Y Direction For Bare Frame Condition of
Building 2 90
5.17 Different Parameter’s Values for Different Earthquake Conditions
for Full Infilled Condition Of Building 2 93
5.18 Hinge Formation Status for Different Earthquake Criteria
for Full Infilled Condition of Building 2 94
5.19 Drift Ratio In Y Direction for Full Infilled Condition of Building 2 95
5.20 Comparison of Different Parameter’s Values for Different
Earthquake Conditions for Bare Frame,Full In Filled, Soft Storey
Condition of Building 2 95
5.21 Comparison of Hinge Formation and Base Shear for Serviceability
Earthquake Criteria for Bare Frame,Full In Filled, Soft
Storey Condition of Building 2 96
5.22 Comparison of Hinge Formation and Base Shear for Design
Earthquake Criteria for Bare Frame,Full In Filled, Soft
Storey Condition of Building 2 96
Performance Evaluation Of Retrofitted Buildings
6.1 Different Parameter’s Values for Different Earthquake Conditions for
the Retrofitted Building 1 Retrofitted With Buttress Wall and
Column Jacketing 101
6.2 Hinge Formation Status for Different Earthquake Conditions
for the Retrofitted Building 1 Retrofitted With Buttress Wall and
Column Jacketing 101
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Table No. Page No.
6.3 Drift Ratio In X Direction for the Retrofitted Building 1
Retrofitted With Buttress Wall and Column Jacketing 102
6.4 Different Parameter’s Values for Different Earthquake Conditions
for the Retrofitted Building 1 Retrofitted With Additional
Shear Wall 105
6.5 Hinge Formation Status for Different Earthquake Conditions
for the Retrofitted Building 1 Retrofitted With Additional
Shear Wall 106
6.6 Drift Ratio in X Direction for the Retrofitted Building 1
Retrofitted with Additional Shear Wall 107
6.7 Comparison of Different Parameter’s Values for Different
Earthquake Conditions for Unretrofitted and Retrofitted Structure
(Building 1) 107
6.8 Comparison of Base Shear and Hinge Formation at Performance
Point for X Direction At Design Earthquake Condition For
the Unretrofitted and Retrofitted Building (Building 1) 108
6.9 Comparison Of Base Shear and Hinge Formation at Performance
Point For X Direction At Maximum Earthquake Condition For
The Unretrofitted and Retrofitted Building (Building 1) 108
6.10 Deformation Limits for Various Performance Level (ATC-40) 109
6.11 Comparison of Performance Between Unretrofitted and
Retrofitted Building In Terms of Lateral Drift (Building 1) 109
6.12 Different Parameter’s Values for Different Earthquake Conditions
for Retrofitted Building 2 Retrofitted With Column Jacketing 113
6.13 Hinge Formation Status for Different Earthquake Conditions
for Retrofitted Building 2 Retrofitted With Column Jacketing 113
6.14 Drift Ratio In Y Direction for the Retrofitted Building 2
Retrofitted With Column Jacketing 114
6.15 Different Parameter’s Values for Different Earthquake
Conditions for the Retrofitted Building 2 Retrofitted With
Buttress Wall and Column Jacketing 117
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Table No. Page No.
6.16 Hinge Formation Status for Different Earthquake Conditions
for the Retrofitted Building 2 Retrofitted With Buttress Wall
and Column Jacketing 118
6.17 Drift Ratio In Y Direction for The Retrofitted Building 2
Retrofitted With Buttress Wall and Column Jacketing 119
6.18 Different Parameter’s Values for Different Earthquake Conditions
for the Retrofitted Building 2 Retrofitted With Shear Wall and
Column Jacketing 122
6.19 Hinge Formation Status for Different Earthquake Conditions
for the Retrofitted Building 2 Retrofitted With Shear Wall and
Column Jacketing 122
6.20 Drift Ratio In Y Direction for the Retrofitted Building 2
Retrofitted With Shear Wall and Column Jacketing 123
6.21 Comparison of Different Parameter’s Values for Different
Earthquake Conditions for Unretrofitted and Retrofitted
Building (Building 2) 124
6.22 Comparison of Base Shear and Hinge Formation at Performance
Point for X Direction At Design Earthquake Condition for
the Unretrofitted and Retrofitted Building (Building 2) 125
6.23 Comparison of Base Shear and Hinge Formation at Performance
Point for X Direction At Maximum Earthquake Condition for
the Unretrofitted and Retrofitted Building (Building 2) 125
6.24 Deformation Limits for Various Performance Level (ATC-40) 126
6.25 Comparison of Performance Between Unretrofitted and
Retrofitted Building in Terms of Lateral Drift (Building 2) 126
xvii
LIST OF FIGURES
Figure No. Page No
Literature Review
2.1 Fault Movement During Earthquake 6
2.2 Response Spectra 8
2.3 Idealized One Storey System Subjected to Ground Acceleration 9
2.4 Fundamental Mode of A Shear Type Structure 11
2.5 Distribution of Lateral Forces In multistory Building 11
2.6 Response of Different Fundamental Period 12
2.7 Equivalent Static Force 13
2.8 Normalized Response Spectra of BNBC 1993 17
2.9 RC Shear Walls to Resist Lateral Earthquake Loads 21
2.10 RC Shear Walls Layout System 21
2.11 Braced Steel Frames 21
2.12 Application of buttresses for retrofitting 22
2.13 Detailing requirement for moment resisting frame 22
2.14 Beam and column jacketing for an existing RCC strcture 23
2.15 A conceptual detailing of gap for isolating infill wall from column 24
2.16 Base Isolation system 26
2.17 Various types of mechanical damper 26
Concept of Performance Based Design
3.1 Typical Capacity Curve 37
3.2 Component Force Versus Deformation Curves
(FEMA-356, 2000) 47
3.3 Force-Deformation Action And Acceptance Criteria 48
3.4 Concrete Axial Hinge Property 52
3.5 Concrete Moment And P-M-M Hinge Property 53
3.6 Concrete Shear Hinge Property 53
3.7 Generalized Load-Deformation Relations For Components 54
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Figure No. Page No
Effect of Masonry Infill in RC Building
4.1 Change In Lateral Load Transfer Mechanism Due To
Masonry Infill 57
4.2 Analogous Braced Frame 57
4.3 Modes of Infill Failure 58
4.4 Modes of Frame Failure 59
4.5 Specimen Deformation Shape 60
4.6 Strut Geometry of a Infill Wall 61
4.7 Placement of Strut 63
4.8 Perforated Panel 64
4.9 Types of Infill Damage 64
Seismic Evaluation of Two 6(Six) Storey RC Buildings
5.1 Typical Load-Deformation Acceptance Criteria 68
5.2 Typical Plan and 3d view of the Building 1 69
5.3 Base Shear vs Displacement Curve in X Direction for
Bare Frame Condition of Building 1 at Maximum EQ 70
5.4 Base Shear vs Displacement Curve in Y Direction for
Bare Frame Condition of Building 1 at Maximum EQ 70
5.5 Capacity Spectrum Curve In X Direction for Bare Frame
Condition of Building 1 at Maximum EQ 71
5.6 Capacity Spectrum Curve in Y Direction for Bare Frame
Condition of Building 1 at Maximum EQ 71
5.7 Hinge State of Bare Frame Condition of Building 1 at the
Performance Point In X-Direction at Maximum EQ 73
5.8 Base Shear vs Displacement Curve in X Direction for
Full Infilled Condition at Maximum EQ for Building 1 75
5.9 Base Shear vs Displacement Curve in Y Direction for
Full Infilled Condition at Maximum EQ for Building 1 75
5.10 Capacity Spectrum Curve in X Direction for
Full Infilled Condition at Maximum EQ for Building 1 76
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Figure No. Page No
5.11 Capacity Spectrum Curve in Y Direction for
Full Infilled Condition at Maximum EQ for Building 1 76
5.12 Hinge State of Full Infilled Condition of Structure 1 at
The Performance Point In X-Direction at Maximum EQ 78
5.13 Base Shear vs Displacement Curve in X Direction for
Soft Storey Condition at Maximum EQ for Building 1. 79
5.14 Base Shear vs Displacement Curve in Y Direction for
Soft Storey Condition at Maximum EQ for Building 1 80
5.15 Capacity Spectrum Curve in X Direction for
Soft Storey Condition at Maximum EQ for Building 1 80
5.16 Capacity Spectrum Curve in Y Direction for
Soft Storey Condition at Maximum EQ for Building 1 81
5.17 Hinge State of Soft Storey Condition of Building 1 at
the Performance Point In X-Direction at Maximum EQ 82
5.18 Typical Plan and 3d view of the Building 2 86
5.19 Base Shear vs Displacement Curve in X Direction for
Bare Frame Condition of Building 2 at Maximum EQ 87
5.20 Base Shear vs Displacement Curve in Y Direction for
Bare Frame Condition of Building 2 at Maximum EQ 87
5.21 Capacity Spectrum Curve In X Direction for Bare Frame
Condition of Building 2 at Maximum EQ 88
5.22 Capacity Spectrum Curve In Y Direction for Bare Frame
Condition of Building 2 at Maximum EQ 88
5.23 Hinge State Of Bare Frame Condition Of Building 2 at The
Performance Point In Y-Direction at Maximum EQ 90
5.24 Base Shear vs Displacement Curve in X Direction for
Full Infilled Condition at Maximum EQ for Building 2 91
5.25 Base Shear vs Displacement Curve in Y Direction for
Full Infilled Condition at Maximum EQ for Building 2 92
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Figure No. Page No.
5.26 Capacity Spectrum Curve in X Direction for
Full Infilled Condition at Maximum EQ for Building 2 92
5.27 Capacity Spectrum Curve in Y Direction for
Full Infilled Condition at Maximum EQ for Building 2 93
5.28 Hinge State of Full Infilled Condition Of Building 2 at
the Performance Point In Y-Direction at Maximum EQ 94
Performance Evaluation of The Retrofitted Buildings
6.1 Plan View of the Retrofitted Building 1 Retrofitted By
Column Jacketing and Providing Buttress Wall 98
6.2 Base Shear vs Displacement Curve in X Direction for
Retrofitted Building 1 (with buttress wall and column jacketing)
at Maximum EQ 99
6.3 Base Shear vs Displacement Curve in Y Direction for
Retrofitted Building 1 (with buttress wall and column jacketing)
at Maximum EQ 99
6.4 Capacity Spectrum Curve in X Direction for Retrofitted Building
1 (with buttress wall and column jacketing) at Maximum EQ 100
6.5 Capacity Spectrum Curve in Y Direction for Retrofitted Building
1 (with buttress wall and column jacketing) at Maximum EQ 100
6.6 Hinge State of The Retrofitted Building 1 Retrofitted with
buttress wall and column jacketing at the Performance Point in
X Direction at Maximum EQ 102
6.7 Plan View of The Retrofitted Building 1 Retrofitted by
Providing Additional Shear Wall 103
6.8 Base Shear vs Displacement Curve in X Direction For
Retrofitted Building 1 (with additional Shear Wall) at
Maximum EQ 103
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Figure No. Page No.
6.9 Base Shear vs Displacement Curve in Y Direction For
Retrofitted Building 1 (with additional Shear Wall) at
Maximum EQ 104
6.10 Capacity Spectrum Curve in X Direction for
Retrofitted Building 1 (with additional Shear Wall) at
Maximum EQ 104
6.11 Capacity Spectrum Curve in Y Direction for
Retrofitted Building 1 (with additional Shear Wall) at
Maximum EQ 105
6.12 Hinge State of the Retrofitted Building 1 Retrofitted with
Additional Shear Wall at the Performance Point in
X Direction at Maximum EQ 106
6.13 Plan View of The Retrofitted Building 2 Retrofitted by
Column Jacketing 110
6.14 Base Shear vs Displacement Curve in X Direction for
Retrofitted Building 2 (with column jacketing) at
Maximum EQ 111
6.15 Base Shear vs Displacement Curve in Y Direction for
Retrofitted Building 2 (with column jacketing) at
Maximum EQ 111
6.16 Capacity Spectrum Curve in X Direction for
Retrofitted Building 2(with column jacketing) at
Maximum EQ 112
6.17 Capacity Spectrum Curve in Y Direction for
Retrofitted Building 2 (with column jacketing) at
Maximum EQ 112
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Figure No. Page No.
6.18 Hinge State of The Retrofitted Building 2 Retrofitted with
column jacketing at the Performance Point in
Y Direction at Maximum EQ 114
6.19 Plan View of The Retrofitted Building 2 Retrofitted by
Column Jacketing and Buttress Wall 115
6.20 Base Shear vs Displacement Curve in X Direction for
Retrofitted Building 2 (with buttress wall and column jacketing)
at Maximum EQ 115
6.21 Base Shear vs Displacement Curve in Y Direction for
Retrofitted Building 2 (with buttress wall and column jacketing)
at Maximum EQ 116
6.22 Capacity Spectrum Curve in X Direction for
Retrofitted Building 2 (with buttress wall and column jacketing)
at Maximum EQ 116
6.23 Capacity Spectrum Curve in Y Direction for
Retrofitted Building 2 (with buttress wall and column jacketing)
at Maximum EQ 117
6.24 Hinge State of The Retrofitted Building 2 Retrofitted with
buttress wall and column jacketing at the Performance Point
in Y Direction at Maximum EQ 118
6.25 Plan View of The Retrofitted Building 2 Retrofitted by
Column Jacketing and Shear Wall 119
6.26 Base Shear vs Displacement Curve in X Direction For
Retrofitted Building 2 (with Shear wall and column jacketing)
at Maximum EQ 120
6.27 Base Shear vs Displacement Curve in Y Direction For
Retrofitted Building 2 (with Shear wall and column jacketing)
at Maximum EQ 120
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Figure No. Page No.
6.28 Capacity Spectrum Curve in X Direction for
Retrofitted Building 2 (with Shear wall and column jacketing)
at Maximum EQ 121
6.29 Capacity Spectrum Curve in Y Direction For
Retrofitted Building 2 (with Shear wall and column jacketing)
at Maximum EQ 121
6.30 Hinge State of The Retrofitted Building 2 Retrofitted with
buttress wall and column jacketing at the Performance Point in
Y Direction at Maximum EQ 123
xxiv
List of Symbols ϋ = Total displacement at time instant t ϋg(t) = Total displacement at time instant t due to ground motion ωn = Natural frequency at Nth mode Ζ = Critical damping Peff(t) = Effective earthquake force at time instant t ω’ = Radial frequency of the effective first mode A = Acceleration due to gravity A(t) = Pseudo acceleration A's = Compression Steel area Ag = Gross concrete area As = Tensile Steel area bw = Width of beam stem c = Damping coefficient C = Conforming transverse reinforcement CA = Seismic coefficient for accelaration Ct = Numerical coefficient Cv = Seismic coefficient for velocity d = Lateral displacement ∆y = Yield displacement f'c = 28 days cylinder strength of concrete fD = Force due to damping FEMA = Federal Emergency Management Agency EQ = Earthquake fi = Force due inertia Fn = Lateral force at level n fs = Inertia force fs(t) = Force at time instant t Ft = Concentrated force on rooftop for accommodating higher mode Fx = Lateral force at level x fy = Yield strength of steel Fy = Ultimate strength of steel g = Acceleration due to gravity hn = Height at level n hx = Height at level x R = Response modification factor I = Second moment of Inertia K = Stiffness of a system M = Mass of a system M3 = Moment about major axis Mb(t) = Moment at base at time instant t NA = Near source coefficient for seismic source Nv = Near source coefficient for seismic source P = Axial force P(t) = Force at time instant t PC = Axial force contributed by concrete PF1 = Modal participation factor for the first mode Pi = Total gravity load at level i Py = Axial force up to yield Q = Lateral load Qv = Lateral load up to yield level R = Response modification factor
xxv
RSA = Response Spectrum Analysis Sa = Spectral acceleration Sai = Spectral acceleration at time instant i Sd = Spectral displacement Sdi = Spectral displacement at time instant i T = Time period T' = Effective time period TA = Coefficient TS = Coefficient u = Displacement u(t) = Displacement at time instant t ug = Displacement due to ground acceleration ut = Total displacement V = Base shear Vb(t) = Shear force at base at time instant t Vi = Total calculated shear force at level i W = Seismic dead weight Z = Zone coefficient u΄ = Velocity ∆T = Time increment Φ1,Roof = Roof level amplitude for the first mode α1 = Modal mass coefficient for the first mode ɸi1 = Amplitude of mode 1 at level I 𝞺 = Steel ratio 𝞺' = Compression steel ratio 𝞺bal = Balanced steel ratio E = Earthquake hazard level h = Height of building hm/t = Slenderness ratio I = Structural Importance factor a = Equivalent strut width Beff = Effective damping ratio Teff = Effective time SRA = Spectral reduction factor SRV = Spectral reduction factor T = Period ZEN = Shaking Intensity SE = Serviceability earthquake DE = Design earthquake ME = Maximum earthquake S = Site coefficient V = Base shear D = Displacement
1
CHAPTER 1
INTRODUCTION
1.1 General
The effects of an earthquake on a building are primarily determined by the time
histories of the three ground motion parameters ground acceleration, velocity and
displacement with their specific frequency contents.
The ground motion parameters and other characteristic values at a location due to an
earthquake of a given magnitude may vary strongly. They depend on numerous factors,
such as the distance, direction, depth and mechanism of the fault zone in the earth's
crust (epicenter), as well as, in particular, the local soil characteristics (layer thickness,
shear wave velocity). In comparison with rock, softer soils are particularly prone to
substantial local amplification of the seismic waves. As for the response of a building
to the ground motion, it depends on important structural characteristics (Eigen
frequency, type of building, ductility etc).
The response of a building during earthquake is a complicated issue. Till now, no
mathematical tool is available to predict the behavior of a building during earthquake
accurately. Basically this is because of the unpredictable nature of earthquake
excitation that might occur at a specific time and site and then resulting complicated
response of a building itself.
Civil engineers all around the world are, by tradition, trained for linear analysis.
Consequently, seismic evaluation or design process, which essentially involves a
nonlinear behavior, is linearized. As relatively new development, pushover-based
seismic evaluation and design methods offered a great opportunity to engineers such
that they are now able to directly calculate the nonlinear seismic demand and evaluate
its consequences on the building, which might be considered as a breakthrough in
earthquake engineering. As a matter of fact, pushover-based methods, which were long
treated only as capacity estimation tools, created a great deal of enthusiasm in
engineering community when they were reintroduced in the last decade for the purpose
2
of estimating seismic deformation demands in the development of performance-based
seismic evaluation and design (ATC 1996, FEMA 356). Now a days, due to
advancement of computer technology, different tools are being developed to capture
and predict the response of a building due to specified earthquake excitation.
1.2 Background And Present State Of The Problem
For a long time earthquake risk was considered unavoidable. It was accepted that
buildings would be damaged as a result of an earthquake's ground shaking. Preventive
measures for earthquake were therefore mostly limited to disaster management
preparedness. Although measures related to construction methods had already been
proposed at the beginning of the 20th century, it is only during the few decades that
improved and intensified research has revealed how to effectively reduce the
vulnerability of buildings to earthquakes.
The traditional approach to seismic design of a building is a force-based design. The
design lateral forces on the building are determined using the response spectrum. The
building is subsequently analyzed to determine the member forces. The members are
designed to withstand those forces. In this approach, there is no measure of the
deformation capability of a member or of a building. At best, an elastic drift is
computed under the design forces and checked against an elastic drift limit.
Alternatively, an inelastic drift is estimated from the calculated elastic drift by
multiplying the later by a factor and checking the inelastic drift against an inelastic drift
limit. Various analysis methods, both elastic (linear) and inelastic (nonlinear), are
available for the analysis of the existing concrete buildings. Applied Technology
Council-40 (ATC-40), 1996 and Federal Emergency Management Agency (FEMA),
2000 proposed a simplified nonlinear static analysis (pushover analysis) procedure
which is not yet used extensively in Bangladesh. The central focus of the simplified
nonlinear procedure is the generation of the "pushover" or capacity curve. This
represents the lateral displacement as a function of the force applied to the building.
There are established numerical tools like Etabs developed by Computers and
Buildings Inc., 1995 which can perform the pushover analysis.
In seismic design, it is not significant to make a building or a member strong. It must
also have sufficient ductility to dissipate or absorb energy imparted to the building by
3
an earthquake. The ductility and integrity of the building may be induced through
proper configuration and detailing as prescribed in different codes and standards like
Bangladesh National Building Code (BNBQ, 2006 or more recent American Concrete
Institute (ACI)-318, 2014. So the conceptual design and the detailing of the structural
elements (walls, columns, slab) and the non-structural elements (partition walls,
facades) plays a central role in determining the structural behavior and vulnerability of
buildings during an earthquake. Errors and defects in the conceptual design cannot be
compensated in order to achieve a good earthquake resistance without incurring
significant additional costs.
The seismic risk is equal to the product of the hazard (intensity) probability of
occurrence of the event, local soil characteristics, the exposed value and the
vulnerability of the building stock. The current building stock is constantly enlarged by
the addition of new buildings, many with significant or even excessive earthquake
vulnerability in Bangladesh. Many govt. buildings were built around the country before
publication of the Bangladesh National Building Code (BNBC),2006. So a lack of
proper seismic detailing were present during construction of those buildings. In many
cases lateral loads were not considered during design phase of those building. A lot of
govt. officials are currently using these buildings for official activities. These under
designed govt. official buildings are posing a great earthquake risk for the users.All
such type of buildings cannot be demolished overnight as govt. official works will be
hampered, rather they can be retrofitted. The present study is aimed to determine
deficiencies focusing seismic conceptual design requirements of these buildings and
also to identify the present situation of the so far constructed buildings in govt. sector.
After identifying the seismic deficiencies (if any), remedial/retrofitting measures should
be investigated.
1.3 Objectives and Scope of The Study
The primary focus of the present study is structural performance estimation of building
designed as per BNBC 2006.The vital part of seismic performance evaluation of
building and other buildings is estimating damage with respect to multiple performance
objectives. For seismically active areas like Bangladesh, the proper evaluation of
seismic performance is essential for safety and evaluating risk of the infrabuilding.
4
With a view of evaluating the performance of building designed as per BNBC, the
objectives of the thesis can be summarized as follows
i. To evaluate the adequacy and seismic performance of conventionally designed
typical bare frame, fully in-filled, soft ground storey condition of buildings
with the help of capacity curve obtained from push over analysis under
earthquake loading.
ii. To identify the deficiencies in the seismic performance of the building and to
see whether any performance improvement is required or not after the pushover
analysis.
iii. To study and compare the effect of infill on the frame for different infill
conditions such as fully in-filled, soft ground storey condition on the
performance of the building with respect to conventionally designed typical
bare frame model.
iv. To investigate the performance of the existing R.C. buildings after inclusion of
various retrofitting schemes such as insertion of shear wall, wing
wall/buttresses, column jacketing etc.
This study will give an insight about the performance of a low rise building (6 storied
and 20 years old) under seismic loading with various configurations (i.e. bare frame
condition, soft storey condition, frame building with masonry infill at different
levels).Based on their performance evaluation effective retrofitting schemes along
with their cost involvement can be proposed.
1.4 Outline of the Methodlogy
Reinforced concrete moment resisting frame with open ground storey and un-reinforced
brick infill walls in the upper stories is modeled using available finite element software
package for this study. Nonlinear static pushover analysis has been performed. The
infill wall is modeled as shell element and equivalent strut width (Mainstone 1971)
theory is used. The modeling procedure, acceptance criteria and analysis procedures for
pushover analysis is developed as per ATC-40, 1996 and FEMA-356 guidelines. The
analysis and design is carried out for the given dead, live, wind and earthquake loads as
specified in the Bangladesh National Building Code, BNBC 2006.
5
After observing the performance evaluation of existing buildings some of the available
retrofitting schemes such as insertion of shear wall, wing wall/Buttresses, column
jacketing is applied in the finite element model of those buildings. Performance after
addition of retrofitting schemes is observed.
1.5 Layout of The Thesis
The general background, objectives of the study and methodology of the work are
presented in Chapter 1 to give basic idea of the work being done under the research. In
Chapter 2, response of a building during an earthquake is being described along with
basic analysis procedures for earthquake loads detailed seismic load provisions in
BNBC 2006, its contents and limitations and different retrofitting methods are
described. Concept of seismic performance evaluation of building, on-linear analysis,
push-over analysis and the basic tool for developing capacity curve are detailed in
Chapter 3. Effect of masonry infill in rcc building and procedure of computational
modelling of infill panel is described in Chapter 4. Basic modeling and analysis
parameters along with evaluation of seismic deficiencies of the case study building is
presented in chapter 5. In chapter 6 performance evaluation of the retrofitted building is
done Conclusion derived from the present studies and recommendations for future
work are presented in chapter 7.
6
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
The dynamic response of the building to earthquake ground motion is the most
important cause of earthquake-induced damage to buildings. Failure of the ground and
soil beneath buildings is also a major cause of damage. However, contrary to popular
belief, buildings are rarely, if ever, damaged because of fault displacement beneath a
building.
Fig. 2.1 Fault Movement During Earthquake
Most earthquakes result from rapid movement along the plane of faults within the
earth's crust. (Fig. 2.1) This sudden movement of the fault releases a great deal of
energy, which then travels through the earth in the form of seismic waves. The seismic
waves travel for great distances before finally losing most of their energy.
At some time after their generation, these seismic waves reach the earth's surface, and
set it in motion, which we refer to as earthquake ground motion. When this earthquake
ground motion occurs beneath a building and when it is strong enough, it sets the
building in motion, starting with the building's foundation, and transfers the motion
throughout the rest of the building in a very complex way. These motions in turn
induce forces which can produce damage.
2.2 Earthquake Ground Motion
Real earthquake ground motion at a particular building site is more complicated than
the simple wave form of motion. Here it's useful to compare the surface of the ground
7
under an earthquake to the surface of a small body of water, like a pond. One can set
the surface of a pond in motion—by throwing stones into it, let's say. The first few
stones create a series of circular waves, which soon begin to collide with one another.
After a while, the collisions, which termed as interference pattern begin to predominate
over the pattern of circular waves. Soon, the entire surface of the water is covered by
ripples, and one can no longer make out the original wave forms. During an earthquake,
the ground vibrates in a similar complex manner, as waves of different frequencies and
amplitude interact with one another.
The complexity of earthquake ground motion is due to three factors 1) The seismic
waves generated at the time of earthquake fault movement were not all of a uniform
character; 2) As these waves pass through the earth on their way from the fault to the
building site, they are modified by the soil and rock media through which they pass; 3)
Once the seismic waves reach the building site they undergo further modifications,
which are dependent upon the characteristics of the ground and soil beneath the
building. These three factors are referred to as
• Source effects
• Path effects
• Local site effects
2.3 Ground Motion and Building Frequencies
The characteristics of earthquake ground motions which have the greatest importance
for buildings are the duration, amplitude (of displacement, velocity and acceleration)
and frequency of the ground motion.
Surface ground motion at the building site, then, is actually a complex superposition of
vibrations of different frequencies. At any given site, some frequencies usually
predominate. The distribution of frequencies in a ground motion is referred to as its
frequency content.
The response of the building to ground motion is as complex as the ground motion
itself, yet typically quite different. It also begins to vibrate in a complex manner, and
because it is now a vibrator)' system, it also possesses frequency content. However, the
building's vibrations tend to center around one particular frequency, which is known as
its natural or fundamental frequency. In general, the shorter a building is, the higher its
natural frequency. The taller the building is, the lower its natural frequency.
8
When the frequency contents of the ground motion are centered around the building's
natural frequency, the building and the ground motion are said to be in resonance with
one another. Resonance tends to increase or amplify the building's response. Because of
this, buildings suffer the greatest damage from ground motion at a frequency close or
equal to their own natural frequency.
2.4 Response Spectra
Different buildings can respond in widely differing manners to the same earthquake
ground motion. Conversely, any given building will act differently during different
earthquakes, which gives rise to the need of concisely representing the building's range
of responses to ground motion of different frequency contents. Such a representation is
known as a response spectrum. A response spectrum is a kind of graph which plots the
maximum response values of acceleration, velocity and displacement against period
and frequency. Response spectra are very important "tools" in earthquake engineering.
Fig. 2.2 Response Spectra
Figure 2.2 shows a highly simplified version of a response spectrum. Even though
highly simplified, it does show how building response characteristics vary with
building frequency and period as building period lengthens, accelerations decrease
and displacement increases. On the other hand, buildings with shorter periods (but
higher natural frequencies), undergo higher accelerations but smaller displacements.
9
In the subsequent chapters, it will be described in more detail, the amount of
acceleration which a building undergoes during an earthquake is a critical factor in
determining how much damage it will suffer. The spectra described in figure 2.2
provides some indication of how accelerations are related to frequency characteristics
which shows one way in which response spectra can be useful, since identifying the
resonant frequencies at which a building will undergo peak accelerations is one very
important step in designing the building to resist earthquakes.
2.5 Analysis of Buildings Due to Earth Quake Forces
2.5.1 Equation of motion Earthquake excitation
In earthquake-prone regions, the principal problem of structural dynamics that concern
the structural engineers is the behavior of buildings subjected to earthquake-induced
motion at the base of the building. If the displacement of the ground is denoted by ug
the total displacement of the mass by ut, and the relative displacement between the
mass and ground by u then at each instant of time t these displacements are related by
ut(t)=u(t)+ug(t)........................(2.1)
Both u, and ug refer to the same inertial frame of reference and their positive directions
coincide.
Fig. 2.3 Idealized one-storey system subjected to ground acceleration.
Equation of motion for the idealized one-storey system of Fig. 2.3 subjected to
earthquake excitation can be written as
fi+fo+fs=0............................................(2.2)
Only the relative motion u between the mass and the base due to structural deformation
produces elastic and damping forces. Thus for a linear system linear elastic force,
10
fs=ku, damping force, fd=cu΄and inertia force f1 is related to the acceleration ϋ' of the
mass by f, = mϋ, Substituting these values to Equation 2.2,
mϋ + cu΄ + ku = -mϋg(t).......................(2.3)
This is the equation of motion governing the relative displacement or deformation u(t)
of the linear building of Fig. 2.3 subjected to a ground acceleration ϋ'g(t).
Dividing equation. 2.3 bym gives
ϋ + 2ζωnu΄+ ωn²u =mϋg(t)....................(2.4)
Where ωn is the natural circular frequency =√k/m
ζis the critical damping coefficient =c/2mωn
This is the basic equation of motion for a single degree of freedom system.
2.5.2 Code specified equivalent static load method
Equation 2.4 is identical to the idealized one-storied frame same as figure 2.3 subjected
to external dynamic force, P(t) which is
mϋ + cu΄ + ku = P(t).............................(2.5)
Comparing Eqs. 2.3 and 2.4 it is seen that the equation of motion for the building
subjected to two separate excitations - ground acceleration ϋg(t)and external force -
mϋg(t) are one and the same. Thus the relative displacement or deformation u(t) of the
building due to ground acceleration ϋg(t)will be identical to the displacement u(t) of the
building if its base werestationary and if it were subjected to an external force =-mϋg(t).
Thus the ground motion can therefore be replaced by the effective earthquake force
Peff(t)=-mϋg(t) .............................(2.6)
In this method the dynamic earthquake effect is represented by equivalent static load at
different levels. Earthquake load is a dynamic load. Due to earthquake load, a building
vibrates in different mode shapes and the load on the building, its intensities and
direction are dependent on the mode shapes.
For example, the figure 2.4 below shows first three fundamental modes of a shear type
building.
11
Fig. 2.4 Fundamental Mode of a shear type building
From the figure it is seen that different mode shape of the building cause different load
intensities and direction to the building. If only the 1stmode is considered and assumed
linear mode shape then the building experiences a triangular shaped lateral load.
Equivalent Static Load method is simple approximation of first mode of vibration with
the mode shape considered as linear. So, for a building of homogeneous mass, the
lateral forces are likely to be as figure 2.5
Fig. 2.5 Distribution of lateral forces in multistorey building.
However, for building with higher time period (flexible ones), the effect of higher
modes become important. This is accounted by considering an extra concentrated force
Ft at the top of building. For regular shaped and not very tall buildings the equivalent
static method gives an approximate estimation of seismic force demand on the building.
2.5.3 Response spectrum analysis
The seismic force generated in buildings varies according to their dynamic properties even though they stand on the same ground and are subjected to the same seismic motion.
12
The response spectrum is schematically depicted in the figure 2.6. Three types of
single-degree-of-freedom systems with the same damping constants h1 but different
natural periods [figure 2.6(b)] are subjected in the same manner to the earthquake
motion shown in the figure 2.6(a). However, each point mass shows a different
response according to the relation between properties of earthquake motion and its
natural period under the single-degree-of-freedom system.
Mass having a comparatively shorter natural period T1 vibrates rapidly while mass
having a longer natural period T3 vibrates slowly. This situation is illustrated in the
figure 2.6(c). The bold line plot in the figure 2.6(d) shows the maximum response value
for a given time interval and the natural period. If the vibration characteristics
continuously varied for the systems corresponding to extremely rigid buildings with a
very short natural period to flexible buildings having long natural periods, then plot the
maximum response values, a response spectrum for damping constant h1 is obtained.
So, knowing the period of the building, peak spectral acceleration of the building can
be estimated.
Fig. 2.6 Response of different fundamental period.
Response spectrum analysis (RSA) is a procedure for computing the statistical
maximum response of a building to a base excitation (or earthquake). Each of the
vibration modes that are considered may be assumed to respond independently as a
single-degree-of-freedom system. Various design codes specify response spectra which
determine the base acceleration applied to each mode according to its period. Having
determined the response of each vibration mode to the excitation, it is necessary' to
obtain the response of the building by combining the effects of each vibration mode.
Because the maximum response of each mode will not necessarily occur at the same
13
instant, the statistical maximum response, where damping is zero, is taken as the square
root of the sum of the squares of the individual response.
It is clear from equation 2.4 that for a given ϋg(t), the deformation response u(t) of the
system depends only on the natural frequency ωnor natural period Tnof the system and
its damping ratios,ζ.Thus any two systems having the same values of Tn and ζwill have
the same deformation response u(t) even though one system may massive than the other
and one may be stiffer than the other.
Fig. 2.7 Equivalent static force.
Once the deformation response history u(t) has been evaluated by dynamic analysis of
the building, the internal forces can be determined by static analysis of the building at
each time instant. Preferred approach in earthquake engineering is based on the concept
of the equivalent static force fs. fs at any time instant t, may be defined as
fs(t)=ku(t)…………………............(2.12) wherek is the lateral stiffness of the frame. Expressing k in terms of mass gives fs(t)=mωn²u(t)=mA(t)……………..(2.13) where A(t)=ωn²u(t) The equivalent static force is m times A(t), the pseudo-acceleration. The pseudo-
acceleration response A(t) of a system can readily be computed from the deformation
response u(t).
For the one-storey frame as shown the figure 2.7, the internal forces like the shears and
moments in the columns an beams or stress at any location can be determined at a
selected instant of the time by static analysis of the building subjected to the equivalent
static lateral forces fs(t) at the same time instant. Thus a static analysis of the building
14
would be necessary at each time instant when the responses are desired. In particular,
the base shear Vb(t) and the base over-turning moment Mb(t) are
Vb (t) = fs, (t) and Mb(t) = hfs(t) where h is the height of the mass above the base.
Putting the value of fs(t), one may get, Vb(t) = mA(t) and Mb(t) = hVb (t).
2.6 Earthquake Loading in the Light of BNBC
Bangladesh National Building Code was published in 2006 by Housing and Building
Research Institute. Like other building codes BNBC has different provisions for
calculation of earthquake load and analysis procedures for buildings subjected to
earthquake.
The BNBC, divides the country into three region of different possible earthquake
ground acceleration ranging from 0.075g to 0.25g. The Code also defines a simple
method to represent earthquake induced inertia forces by Equivalent Static Force for
static analysis. For dynamic analysis two methods are defined, namely
i. Response Spectrum Analysis and
ii. Time History Analysis.
2.6.1 Equivalent Static Load Method
In this method the dynamic earthquake effect is represented by an equivalent static load
at different levels proportion to mass at that level. Earthquake load is a dynamic load.
Due to earthquake load, a building vibrates in different mode shapes and load on the
building and its intensities and direction is dependent on the mode shapes. Equivalent
Static load method is an assumption of linear mode shape for the first mode of the
building. It is basically calculation of base shear from an earthquake load and its
comparison with the base shear capacity of the building.
2.6.2 Calculation of base shear
Total design base share, denoted by V, in a given direction is determined from the
following relation ………….……..(3.1)
The terms in the right hand side of the 3.1 may be explained as below
15
2.6.3 Zone coefficient, Z
This is the coefficient that represents the earthquake severity of the regions. Bangladesh
is divided into three zones of different earthquake severity. These are presented in table
A-13 in Appendix A.
The values of this coefficient is considered to represent the effective peak ground
acceleration (associated with an earthquake that has a 10% probability of being
exceeded in 50 years) expressed as a fraction of the acceleration due to gravity.
2.6.4 Structure importance coefficient, I
This is the coefficient that accounts the importance of building for post earthquake
activities. This coefficient is introduced from the experience of the previous
earthquakes when destruction of hospital and other important installation which has an
important role in post earthquake disaster management results in additional
'encumbrance. Now, some buildings like hospital, fire station, police station etc. are
designed giving more importance so that possibilities of these buildings to survive in
earthquake increase.
The earthquake lateral force is multiplied by some factor called Building Importance
Coefficient and are designed for a higher level of force so that the possibility of these
building being undamaged during an earthquake remains higher.
2.6.5 Seismic dead load, W
This is the seismic weight of the building that participates in earthquake response of the
building. This includes the self-weight of the building, other permanent dead load and
the part of the live load as prescribed by the Code defined in BNBC.
2.6.6 Response modification factor, R
Earthquake force is reduced by dividing this factor. This factor accounts the building's
ability to undergo inelastic deformation during earthquake. This factor depends on
building type, its damping properties and ductility. R is a measure ofthe capacity of the
structural system to absorb energy in the inelastic range through ductility and
redundancy. It is based primarily on the performance of similar systems in past
earthquakes. Different values of R are listed in BNBC/93.
16
2.6.7 Numeric coefficient, C
This is the coefficient that accounts for fundamental period of the building and soil
property of the building site.
C is calculated as C
where S is the Site coefficient depending on the characteristics of the soil at the site as
described in the Table 6.2.25 and T is the fundamental period of the building.
Fundamental period the building is calculated by some empirical formula as
T=Cthn3/4....................................................(3.3)
Where, hn = Total height of the building above the base.
Ct = a coefficient that depends on the building type and given in the code.
As it was discussed in the previous chapter, due to earthquake the building is subjected
to acceleration. This acceleration produces inertia force in the building. Applying
Newton's second law of motion, inertia force can be estimated by equation---
F = ma............................................................(3.4) Where m is the mass of the building
a is the ground acceleration.
Replacing the mass 'm' by one can get,
where, Z = ground acceleration in g.
This is the total force acting on the building.
Thus total base shear, V= WZ
Building deflects due to lateral force and this deflection absorbs some energy. How
much energy it absorbs, depend on the structural system, its damping properties etc. So,
the depending on the factors, the total force is reduced by dividing it by some factor, R
17
which is called the Response Modification factor. Value of R depends on the structural
system and is given in BNBC/93.
Further, the base shear is multiplied by a coefficient C called the Elastic Response
coefficient that account the fundamental period of the building and the soil property
under the building.
Thus with these coefficient, the equation of base shear becomes,
This base shear is distributed along the building height in a linear fashion mainly to
represent the first mode of deformation considering the first mode is linear.
2.7 Response Spectrum Method
BNBC recommends that response spectrum to be used in dynamic analysis shall be i. Site Specific Design Spectra A site specific response spectra shall be developed base
on the geologic, tectonic, seismologic, and soil characteristics associated with the
specific site.
ii. Normalized Response Spectra In absence of a site-specific response spectrum, the
normalized response spectra shall be used.
The response spectrum curves in the code are prepared for three different soil types and
5% of the critical damping. The ordinate represent the spectral acceleration and the
abscissa represents the natural period. Three soil types are defined in BNBC.
BNBC defines three normalized curves to be used in dynamic analysis performed using
Response Spectrum Analysis Method. The curve is shown below. In analysis
parameter, this curve to be modified as per specific site condition.
Fig. 2.8 Normalized Response Spectra of BNBC 2006.
18
BNBC does not provide any guideline for construction of Site Specific response
spectra.
2.8 Time History Analysis
Ground motion time history developed for the specific site shall be representative of
actual earthquake motions for an earthquake. Until recently, Bangladesh did not have
strong motion data recording centre. Few instruments for strong motion data recording
have been instrumented in Jamuna multi-purpose bridge and in Dhaka University.
2.9 Limitations of BNBC 2006 Though the code is comprehensive, few more details, in presentation even, could
enhance the acceptability of the code.
2.9.1 The zoning map
The code divides the country into three zones of different zoning coefficients with
marking only the districts. A detailed map as supplement would have been better for
the professionals to work with.
2.9.2 Structure period
Code defines 'Equivalent Static Load Method'- an alternate method to calculate
earthquake forces for regular buildings. In Equivalent Static Load Method, building
period is calculated as a function of building height. As a result, constant Base Shear in
all direction of the building is produced. Practically, building period is a function of
structural mass and stiffness. Unless the building is perfectly symmetric in both axes,
considerable change in building period may be found in other direction resulting
different base shear acting in that direction.
2.9.3 Base Shear Distribution
Unless the storey mass varies, the base shear distribution along the height of the
building is linear. Practically none of the fundamental mode shapes are linear. Many
codes, like current Uniform Building Code (UBC/2005), Indian Code (IS) etc.
recognizes non-linear distribution of base shear matching the 1st Fundamental mode
shape.
19
2.10 Seismic Strengthening
Retrofitting is technical interventions in structural system of a building that improve the
resistance to earthquake by optimizing the strength, ductility and earthquake loads.
Strength of the building is generated from the structural dimensions, materials, shape,
and number of structural elements, etc. Ductility of the building is generated from good
detailing, materials used, degree of seismic resistant, etc. Earthquake load is generated
from the site seismicity, mass of the buildings, important of buildings, degree of
seismic resistant, etc.
A retrofit strategy is a basic approach adopted to improve the probable seismic
performance of the building or otherwise reduce the existing risk to an acceptable level.
Both technical strategies and management strategies can be employed to obtain seismic
risk reduction. Technical strategies include such approaches as increasing building
strength, correcting critical deficiencies, altering stiffness, and reducing demand.
Management strategies include such approaches as change of occupancy, incremental
improvement and phased construction.
Engineers sometimes confuse systems and strategies. Strategies relate to modification
or control of the basic parameters that affect a building's earthquake performance.
These include the building's stiffness, strength, deformation capacity, and ability to
dissipate energy, as well as the strength and character of ground motion transmitted to
the building and the occupant and contents exposure within the building. Seismic risk
reduction strategies include such approaches as increasing strength, increasing stiffness,
increasing deformability, increasing damping, reducing occupancy exposure, and
modifying the character of the ground motion transmitted to the building. Strategies can
also include combinations of these approaches. Retrofit systems are specific methods
used to implement the strategy such as. For example, the addition of shear walls or
braced frames to increase stiffness and strength, the use of confinement jackets to
enhance deformability.
2.11 Retrofit Strategies
A wide range of technical and management strategies are available for reducing the
seismic risk inherent in an existing building. Technical strategies are approaches to
modifying the basic demand and response parameters of (Jhe building for the Design
Earthquake. These strategies include system completion, system strengthening, system
stiffening, and enhancing deformation capacity, enhancing energy dissipation capacity,
20
and reducing building demand.
2.11.1 Technical Strategies
As a building responds to earthquake ground motion, it experiences lateral
displacements and, in rum, deformations of its individual elements. At low levels of
response, the element deformations will be within their elastic (linear) range and no
damage will occur. At higher levels of response, element deformations will exceed their
linear elastic capacities and the building will experience damage. In order to provide
reliable seismic performance, a building must have a complete lateral force resisting
system, capable of limiting earthquake-induced lateral displacements to levels at which
the damage sustained by the building’s elements will be within acceptable levels for die
intended performance objective. The basic factors that affect the lateral force resisting
system’s ability to do this include the building’s mass, stiffness, damping, and
configuration; the deformation capacity of its elements; and die strength and character
of the ground motion it must resist.
Technical strategies can be grouped in the following categories
a) Building System Strengthening and stiffening
b) Enhancing Deformation capacity
c) Reducing Earthquake Demand
d) By Energy dissipation capacity
e) Controlling Lateral drift.
(a) Building system strengthening and stiffening
System strengthening and stiffening are the most common seismic performance
improvement strategies adopted for buildings with inadequate lateral force resisting
systems. The two are closely related but different. The effect of strengthening a
building is to increase the amount of total lateral force required to initiate damage
events within the building, if this strengthening is done without stiffening, then the
effect is to permit the building to achieve larger lateral displacements without damage.
System Strengthening and stiffening can be done by the following ways
Shear Walls: The introduction of shear walls into an existing concrete building is one
of the most commonly employed approaches to seismic upgrading. It is an extremely
effective method of increasing both building strength and stiffness. A shear wall system
21
is often economical and tends to be readily compatible with most existing concrete
buildings.
Fig. 2.9 RC Shear walls to resist lateral earthquake loads.
Fig. 2.10 RC shear wall layout a) unsymmetrical location not desirable b)symmetric layout desirable. Braced Frames: Braced steel frames are another common method of enhancing an
existing building's stiffness and strength. Typically, braced frames provide lower levels
of stiffness and strength than do shear walls, but they add far less mass to the building
than do shear walls, can be constructed with less disruption of the building, result in
less loss of light, and have a smaller effect on traffic patterns within the building.
Fig. 2.11 Braced steel frames.
22
Buttresses: Buttresses are braced frames or shear walls installed perpendicular to
an exterior wall of the building to provide supplemental stiffness and strength. This
system is often a convenient one to use when a building must remain occupied
during construction,, as most of the construction work can be performed on the
building exterior, minimizing the inconvenience to building occupants. Sometimes
a building addition intended to provide additional floor space can be used to
buttress the original building for added seismic resistance.
Fig. 2.12 Application of buttresses for retrofitting. Moment Resisting Frames: Moment-resisting frames can be an effective system to
add strength to a building without substantially increasing the building’s stiffness.
Moment frames have the advantage of being relatively open and therefore can be
installed with relatively minimal impact on floor space.
Fig. 2.13 Detailing requirement for moment resisting frame.
23
(b) Enhancing deformation capacity
Improvement in building seismic performance through enhancement of the ability of
individual elements within the building to resist deformations induced by the building
response is a relatively new method of seismic upgrading for concrete buildings. Some
of the methods for enhancing deformation capacity are discussed below
Adding Confinement The deformation capacity of nonductile concrete columns can be
enhanced through provision of exterior confinement jacketing. Jacketing may consist of
continuous steel plates encasing the existing element, reinforced concrete annuluses,
and fiber-reinforced plastic fabrics.
Confinement jacketing can improve the deformation capacity of concrete elements in
much the same way that closely spaced hoops in ductile concrete elements do. To be
effective, the jacketing material must resist the bursting pressure exerted by the existing
concrete element (under the influence of compressive stresses,) in a rigid manner.
Circular or oval jackets can provide the necessary confinement in an efficient manner
through the development of hoop stresses. Rectangular jackets tend to be less effective
and require cross ties in order to develop the required stiffness.
Fig. 2.14 Beam and column jacketing for an existing RCC strcture.
24
Local stiffness reductions: Local reductions in stiffness can be an effective way to
prevent undesirable damage modes as well as to minimize damage to a few scattered
elements that are not essential to die building’s overall performance. Many older
concrete buildings are subject to short-column failures at perimeter walls, resulting
from the presence of deep spandrels. These effects can often be reduced by introducing
joints between the face of the column and adjacent architectural elements, such as
spandrel panels or infill that create the condition. Some buildings may have one or
more walls that are present for architectural rather than structural reasons. These walls
may be quite stiff and either attract more lateral force than they can resist or introduce
torsional response or discontinuous load paths into the building. Local demolition of
these elements, or modification of them to reduce their stiffness, can result in a cost-
effective performance improvement for the building.
Fig. 2.15 A conceptual detailing of gap for isolating infill wall from column.
25
(c) Reducing earthquake demands
Rather than modifying the capacity' of the building to withstand earthquake-induced
forces and deformations, this strategy involves modification of the response of the
building such that the demand forces and deformations are reduced. In effect, the
demand spectrum for the building, rather than the capacity spectrum, is modified.
Methods for achieving this strategy include reductions in the building’s mass and the
installation of systems for base isolation and/or energy dissipation. The installation of
these special protective systems within a building typically entails a significantly
larger investment than do more-conventional approaches. However, these special
systems do have the added benefit of providing for reduced demands on building
contents. Consequently, these approaches are often appropriate for buildings housing
critical occupancies with sensitive equipment or a need to attain rapid post earthquake
functionality. They may also be attractive for the retrofitting of historic buildings
because they may make it possible to retrofit the building to be retrofitted without
extensive invasive construction within the historic spaces.
Base Isolation: This approach requires the insertion of compliant bearings within a
single level of the building’s vertical load carrying system, typically near its base. The
bearings are designed to have relatively low stiffness, extensive lateral deformation
capacity and may also have superior energy dissipation characteristics. Installation of
an isolation system results in a substantial increase in the building’s fundamental
response period and, potentially, its effective damping. Since the isolation bearings
have much greater lateral compliance than does the building itself, lateral deformation
demands produced by the earthquake tend to concentrate in tile bearings themselves.
Together these effects result in greatly reduced lateral demands on the portion of the
building located above the isolation bearings.
Base isolation may be most effective as a retrofit system when applied in buildings
for which there are enhanced performance objectives. The significant reduction in
displacement response and accelerations that occur within the superbuilding of an
isolated building results in much better performance of equipment, systems, and other
nonstructural elements than is attainable with most other retrofit systems.
26
Fig. 2.16 Base Isolation system.
(d) Energy Dissipation Systems: Energy dissipation systems directly increase the
ability of the building to dampen earthquake response in a benign manner, through
either viscous or hysteretic damping. This approach requires die installation of energy
dissipation units (EDUs) within the lateral force resisting system. The EDUs dissipate
energy and in the process reduce the displacement demands on the building. The
installation of EDUs often requires the installation of vertical braced frames to serve as
a mounting platform for the units and therefore, typically results in a simultaneous
increase in system stiffness. Energy dissipation systems typically have a greater cost
than conventional systems for stiffening and strengthening a building but have the
potential to provide enhanced performance.
Fig. 2.17 Various types of mechanical damper.
27
Mass Reduction: The performance of some buildings can be greatly improved by
reducing the building mass. Building mass reductions reduce the building’s natural
period, the amount of inertial force that develops during its response and the total
displacement demand on the building. Mass can be reduced by removing heavy
nonstructural elements, such as cladding, water tanks and storage. In the extreme,
mass reduction can be attained by removing one or more building stories.
2.11.2 Management Strategies
Management strategies are programmatic in nature and are typically controlled by the
building owner rather than the design team. Management strategies tend to be of two
types strategies that affect the acceptability of the building’s probable performance and
strategies that regulate the way in which a technical strategy is implemented. They
include such approaches as occupancy change, demolition, temporary retrofit, phased
retrofit, retrofit while occupied, retrofit while vacant, exterior retrofit, and interior
retrofit. (a) Occupancy Change
Some buildings with inadequate performance capability for the current occupancy
may be an acceptable seismic risk if assigned other occupancies. The best risk
reduction approach for such buildings may simply be to alter the use of the building.
For example, a building capable of meeting the Substantial Life Safety performance
level, but not the Immediate Occupancy level would not be an acceptable risk for an
acute care facility at a hospital. It might be very adequate, however, for use as a day
care center or for medical offices. An appropriate strategy for such a situation may
be to use the existing building for one of these latter occupancies and construct a
new acute care facility. The desirability of this approach would obviously depend on
a number of factors, including a need for the building in the alternative use, the
availability of funding to construct a replacement facility, and the availability of
land.
28
2.12 Past Research On Seismic Performance Evaluation of Different
Retrofitting Schemes Using Non-Linear Analysis
Many studies have been conducted on seismic performance evaluation of different retrofitting schemes. The study (Huang et al. 2008) conducted a performance based evaluation and retrofit of
an existing hospital building in California, U.S. A nonlinear static pushover analysis as
described in FEMA 356, was used to evaluate the seismic performance of the existing
building. A seismic retrofit based on the pushover analysis was proposed and the
results showed that the life-safety target performance of the upgraded building was
achieved. In addition, the performance based retrofit scheme was compared to different
seismic retrofit scheme based on a prescriptive code design approach. The comparison
showed that the performance based approach lead to a better understanding of the
nonlinear behavior of the building during severe earthquakes and provided a more
efficient and cost effective strengthening solution for this building.
Another study (Gupta et al. 2015) highlighted the importance of adding shear wall in
increasing the lateral load carrying capacity of the building as well as the ductility. It’s
observed that the building before adding shear wall was not designed as earthquake
resistant. But after adding shear wall, significant improvement is seen in seismic
performance of the building. The columns which were failing before addition of shear
wall became safe after addition of shear wall. Also, the problem of soft story present
was solved. It’s suggested that as addition of shear wall imposes very less disturbance
to the existing building so it is still very viable option in improving the earthquake
resistance of the existing buildings.
Bilgin (2015) (Bilgin 2015) assessed the seismic performance evaluation of a typical
school building in accordance with the rules of Turkish Earthquake Code-2007. The
performance analysis was carried out by using nonlinear static analysis. The analytical
solutions showed that the intended performance level had not been satisfied for this
building and decided to retrofit the structural system. To strengthen the structural
system, shear walls were added in both directions. In order to find the economical
solution for the new strengthening system, nonlinear analyses are repeated with
29
different number of shear wall options. It’s observed that addition of shear walls
increases lateral load capacity and decreases displacement demands significantly.
Another study (Varum et al. 2013) highlighted the effectiveness of reinforced concrete
(RC) column jacketing for improving the seismic performance of existing RC building
buildings. Four three storey buildings with different structural configuration and
detailing were selected for seismic assessment and retrofitting purpose. The response of
buildings (original and retrofitted) was evaluated in terms of capacity curve and inter-
storey drift. The case studies also included the effect of P-delta effects and bi-axial
response of columns. The nature of the capacity curve represented the strong impact of
the P-delta effect, leading to a reduction of the global lateral stiffness and reducing the
strength of the building. Finally, a seismic safety assessment was performed based on
the drift limit proposed by FEMA-356. The assessment of original building buildings
indicated that they may exhibit inadequate seismic performance. However, RC column
jacketing highly improved seismic performance of all the buildings and mitigated
maximum drift demand within the drift limit proposed by FEMA-356.
The study (Akshara 2015) highlighted the need for performance based seismic
engineering in contrast to force-based design approaches. Four building performance
levels namely operational, immediate occupancy, life safety and collapse prevention
were studied in detail using FEMA 356 by conducting pushover analysis for an existing
five storied residential building. It’s observed that in performance based design, multi-
level seismic hazards were considered with an emphasis on the transparency of
performance objectives, thus ensuring better performance and minimum life-cycle cost.
Kumar et al. (2007) (Kumar et al. 2007) studied the usefulness of RC jacketing
technique to strengthen lightly reinforced beam-column joints experimentally. A full-
scale lightly reinforced concrete beam-column sub-assembly was strengthened by
casting an RC jacket outside the column and the joint, and the improvement brought
over by the retrofitting technique in the cyclic response of the specimen was verified
experimentally When subjected to cyclic lateral loading, The original specimen was
vulnerable to joint shear failure. On the other hand, the retrofitted specimen failed after
the formation of a plastic hinge in the beam, and the joint was no longer the weakest
component of the sub-assembly. It’s observed that Apart from the increase in the
30
capacity and deformability, the shear deformation of the joint panel reduced
significantly after retrofitting indicating that the RC jacketing method is effective in
strengthening non-seismic RC frames with inadequately reinforced joints.
Another study (Abd-Elhamed and Mahmoud 2017) investigated performance of a
residential 12-storey RC framed building, through pushover analysis, designed in
accordance with the Egyptian code following the (ATC 40) procedures using the well-
known software package ETABS. It’s observed that the plastic hinges started to occur
in beam ends and then the formation of these hinges started at columns of lower levels
before they extend to the upper level columns showing a strong column-weak beam
configuration. The analysis considered two levels of shakings. One of the chosen levels
fits the seismicity of Cairo zone and the other level is of higher magnitude. It has been
found from the analysis using level of shaking of intensity level that fits Cairo zone, the
demand curve intersects the capacity curve near the elastic zone. Consequently the
formed plastic hinges are always away from critical levels of performance and ensure
that the building behaves like the strong column-weak beam mechanism which
indicates that proposed model for nonlinear static analysis has produced satisfactory
behavior, better seismic performance and capability to sustain seismic loads fit code
requirements. However, exposing the framed building to seismic load exceeds twice the
one recommended by design code showed that the demand curve intersected the
capacity curve in the inelastic zone leading to formation of plastic hinges in the
dangerous level. Accordingly, the building behaves poorly and needs to be
strengthened to avoid severe damage or even collapse.
Leslie (2013) (Leslie 2013) explained the Pushover analysis in a simple way. He
mentioned that although elastic analysis gives a good indication of elastic capacity of
buildings and shows where yielding might first occur, it cannot account for
redistribution of forces during the progressive yielding that follows and predict its
failure mechanisms, or detect possibility and location of any premature failure. A non-
linear static analysis can predict these more accurately since it considers the inelastic
behavior of the building. It can help identify critical members likely to reach critical
states during an earthquake for which attention should be given during design and
detailing. Pushover analysis is a non-linear analysis procedure to estimate the strength
capacity of a building beyond its elastic limit (meaning Limit State) up to its ultimate
31
strength in the post-elastic range. In the process, the method also predicts potential
weak areas in the building, by keeping track of the sequence of damages of each and
every member in the building (generally known as ‘hinges’).He also pointed out some
of the major limitations of the PA such as the procedure basically takes into account
only the fundamental mode shape assuming it to be the predominant response and does
not consider effects of higher modes.
Giannopoulos (2009) (Giannopoulos 2009) investigated a typical five storey non-
ductile RC frame building which has been designed following past seismic regulations
in Greece has been analyzed using a nonlinear static (pushover) analysis. Few critical
sections are selected and the rotational ductility supply at various limit states as
predicted by FEMA 356 and Annex A of EC8 Part 3 (Eorocode 8) is calculated. The
two predictions are compared with each other and with results from the finite element
software analysis. The comparison demonstrates that there are differences in the results
produced by the two approaches and the results obtained from analysis provided useful
information for further development of Euro code 8.
The study (Inel and Ozmen 2006) pointed out the importance of user-defined nonlinear
hinge properties over default-hinge properties during pushover analysis. He mentioned
that studied the possible differences in the results of pushover analysis due to default
and user-defined nonlinear component properties. Four- and seven-story buildings are
considered to represent low- and medium- rise buildings for this study. Plastic hinge
length and transverse reinforcement spacing are assumed to be effective parameters in
the user-defined hinge properties. Observations showed that plastic hinge length and
transverse reinforcement spacing had no influence on the base shear capacity, while
these parameters had considerable effects on the displacement capacity of the frames.
Comparisons pointed out that an increase in the amount of transverse reinforcement
improves the displacement capacity. Although the capacity curve for the default-hinge
model is reasonable for modern code compliant buildings, it may not be suitable for
others. He concluded that the user-defined hinge model is better than the default-hinge
model in reflecting nonlinear behavior compatible with the element properties.
Lodi et al. (2011) (Lodi et al. 2011) discussed and illustrated the procedures to analyze
infill building with an example in ETABS, building analysis and design software by
32
Computers and Buildings, Inc. of a 2-D nonlinear static “pushover” analysis of a six
storey RC building with URM infill walls, based on guidelines and modeling
procedures given in the ATC-40 and FEMA-356 documents.
The study (Borkar and Pitale 2017) described the importance of performance based
analysis for soft storey building An existing open ground storey building with G+5
storey had been considered. Infill walls were modelled using procedure given in
FEMA. Non-linear static pushover analysis was done and studied effects of infill on
dynamic characteristics, yield patterns, seismic performance using finite element
software SAP 2000.It’s observed that the RC frame with open ground storey exhibited
very poor lateral strength stiffness and energy dissipation capacity due to formation of
shear hinges in ground storey columns under lateral load resulting uncontrolled
excessive deformation in the ground storey and need some retrofitting measures.
Hassaballa et al. (2014) (Hassaballa et al. 2014) mentioned the importance of
reinforced concreteshear walls in attaining the desired performance level of existing
hospital buildings in Sudan.
Another study (Naim and B. K Singh 2018) described the effectiveness of RC
Jacketing for seismic retrofitting of Buildings. In this case study, a G+3 storey RC
Building was considered for seismic analysis to calculate the additional seismic
strength of structural members like beams and columns. Based on this analysis
retrofitting measure RC Jacketing are suggested.
33
CHAPTER 3
CONCEPT OF PERFORMANCE BASED DESIGN
3.1 General
The primary objective of earthquake resistant design is to prevent building collapse
during earthquakes thus minimizing the risk of death or injury to people in or around
those buildings. The dynamic response of the building to earthquake ground motion is
the most important cause of earthquake-induced damage to building. The dynamic
nature of the response makes earthquake loadings markedly different from other
building loads. Through the careful selection of appropriate, well distributed lateral
load resisting systems, and by ensuring the building is reasonably regular in both plan
and elevation, the influence of many second order effects, such as torsional effects, can
be minimized and significant simplification can be made to model the dynamic
building response.
The traditional approach to seismic design of a building is a force-based design. The
design lateral forces on the building are determined using the response spectrum. In this
approach, there is no measure of the deformation capability of a member or of the
building. The performance based analysis is based on quantifying the deformations of
the members and the building as a whole, under the lateral forces of an earthquake of a
certain level of seismic hazard. The deformations or strains are better quantities to
assess damage than stress or forces. Since the deformations are expected to go beyond
the elastic values, a performance based analysis requires a nonlinear lateral load versus
deformation analysis. The performance based analysis give the analyst more choices of
'performance' of the building as compared to the limit states of collapse and
serviceability in a design based on limit state method.
3.2 Seismic Analysis Methods
There are different methods of seismic analysis which provide different degrees of
accuracy. The analysis process can be categorized on the basis of three factors the type
of the externally applied loads, the behavior of building/or structural materials and the
type of structural model selected. Based on the type of external action and behavior of
building, the analysis can be further classified as linear static analysis, linear dynamic
34
analysis, nonlinear static analysis, or non-linear dynamic analysis. Linear static analysis
or equivalent static analysis can only be used for regular building with limited height.
Linear dynamic analysis can be performed in two ways either by mode superposition
method or response spectrum method and elastic time history method. This analysis
will produce the effect of the higher modes of vibration and the actual distribution of
forces in the elastic range in a better way. They represent an improvement over linear
static analysis. The significant difference between linear static and dynamic analysis is
the level of force and their distribution along the height of the building. Non-linear
static analysis, which forms the basis of performance based design, is an improvement
over the linear static or dynamic analysis in the sense that it allows the inelastic
behavior of the building. The method still assumes a set of static incremental lateral
load over the height of building. The method is relatively simple to be implemented,
and provides information on the strength, deformation and ductility of the building and
the distribution of demands. These permits to identify critical members likely to reach
limit states during the earthquake, for which attention should be given during the
design and detailing process. But this method contains many limited assumptions,
which neglect the variation of loading patterns, the influence of higher modes, and the
effect of resonance. This method, under the name of push over analysis has acquired a
great deal of popularity now a days and in spite of these deficiencies this method
provides reasonable estimation of the global deformation capacity, especially for
buildings which primarily respond according to the first mode. A non-linear dynamic
analysis or inelastic time history analysis is the only method to describe the actual
behavior of the building during an earthquake. The method is based on the direct
numerical integration of the motion differential equations by considering the elasto-
plastic deformation of the building element. This method captures the effect of
amplification due to resonance, the variation of displacements at diverse levels of a
frame, an increase of motion duration and a tendency of regularization of movements
result as far as the level increases from bottom to top.
3.3 Methods to Perform Simplified Non Linear Analysis
Various analysis methods, both elastic (linear) and inelastic (nonlinear), are available
for the analysis of concrete buildings. Elastic analysis methods available include code
static lateral force procedures, code dynamic lateral force procedures and elastic
procedures using demand capacity ratios.
35
The most basic inelastic analysis method is the complete nonlinear time historey
analysis, which at this time is considered overly complex and impractical for general
use. Available simplified nonlinear method (ATC-40, 1996) [2] referred to as nonlinear
static analysis procedures, include the capacity spectrum method (CSM) that uses the
intersection of capacity (push over) curve and a reduced response spectrum to estimate
maximum displacement. Simplified nonlinear static analysis procedure using pushover
methods, such as the capacity spectrum method and the displacement co-efficient
method requires determination of three primary elements capacity, demand
(displacement) and performance. Each of these elements is briefly discussed below.
3.3.1 Capacity curve of a structure
The overall capacity of a building depends on the strength and deformation capacities
of the individual components of the building. In order to determine capacities beyond
the elastic limits, some form of nonlinear analysis such as the push over procedure, is
required. This procedure uses a series of sequential elastic analyses, superimposed to
approximate a force-displacement capacity diagram of the overall building. As the
loading progresses, the mathematical model of the building is modified to account for
reduced resistance of yielding components through insertion of plastic hinges. A lateral
force distribution is again applied until the additional components yield. This process is
continued until the building becomes unstable or until a predetermined limit is reached.
The push over capacity curve approximates how building behaves after exceeding their
elastic limit. Details of the procedure how a capacity curve is developed are presented
in section 3.4.
3.3.2 Demand curve of a structure
Ground motion during an earthquake produce complex horizontal displacement
patterns in buildings that may vary with time. Tracking this motion at every time-step
to determine structural design requirements is judged impractical. Traditional linear
analysis methods use lateral forces to represent a design condition. For nonlinear
methods it is easier and more direct to use a set of lateral displacements as a design
condition. For a given building and ground motion, the displacement demand is an
estimate of the maximum expected response of the building during the ground motion.
The displacement demand is established by use of the conventional response spectra-
36
by converting, it into Spectral Acceleration vs. Spectral Displacement format (Sec
3.4.1).
3.3.3 Performance point of a structure.
Once a capacity curve and demand displacement is defined, a performance check can
be done. A performance check verifies that structural and nonstructural components arc
not damaged beyond the acceptable limits of the performance objective for the forces
and displacement imposed by the displacement demand. Details of the procedure how
performance is ascertained are presented in section 3.4.1
3.4 Non Linear Static (Push Over) Analysis
As a building responds to earthquake ground motion, it experiences lateral
displacements and, in turn, imparts deformations to its individual elements. At low
levels of response, the element deformations will be within their elastic (linear) range
and no damage will occur. At higher levels of response, element deformations will
exceed their linear elastic capacities and the building will experience damage. In order
to provide reliable seismic performance, a building must have a complete lateral force
resisting system, capable of limiting earthquake-induced lateral displacements to levels
at which the damage sustained by the building's elements will be within acceptable
levels for the intended performance objective. The basic factors that affect the lateral
force resisting system's ability to do this include the building's mass, stiffness, damping
and configuration; the deformation capacity of its elements; and the strength and
character of the ground motion it must resist.
The nonlinear pushover analysis requires development of the capacity curve. The
capacity curve is derived from a nonlinear analysis for the building. In the process of
performing this incremental nonlinear static analysis, a capacity curve is developed for
the building. This capacity curve is simply the plot of the total lateral seismic demand
"V," on the building, at various increment of loading, against the lateral deflection of
the building at the roof level, under that applied lateral force. If a building had infinite
linear capacity, this capacity curve would be a straight line with a slope equal to the
global stiffness of the building. Since real building do not have the infinite linear
capacities, the capacity curve typically consists of a series of straight line segments
with decreasing slope, representing the progressive degradation in structural stiffness
that occurs as the building is subjected to increased lateral displacement, yielding and
37
damage. The slope of a straight line drawn from the origin of the plot for this curve to a
point on the curve at any lateral displacement, "d" represent the secant or "effective"
stiffness of the building when pushed laterally to that displacement. A typical capacity
curve of a hypothetical building is shown in Fig.3.1
Fig. 3.1 Typical Capacity Curve (ATC-40,1996)
In Fig.3.1, the discreet points indicated by the symbol "*" represent the occurrence of
important events in the lateral response historey of the building. Such an event may be
the initiation of yield in a particulars structural element or a particular type of damage,
such as spalling of cover concrete on a column or shear failure of a spandrel element.
Each point is determined by a different analysis sequence. Then by evaluating the
cumulative effects of damage sustained at each of the individual events, and the overall
behavior of the building's increasing lateral displacement, it is possible to determine
and indicate on the capacity curve those total structural lateral displacements that
represent limits on the various structural performance levels, as has been done in
Fig.3.1. The Immediate Occupancy (IO), the Life Safety level (LS) and the Structural
Stability level (SS) are three performance levels, indicated in Fig. 3.1 and described in
section 3.7.
The process of defining lateral deformation points on the capacity curve at which
specific structural performance levels may be said to have occurred requires the
exercise of considerable judgment on the part of the engineer. Each of the several
structural performance levels and global performance levels (FEMA 356) are defined in
Section 3.7. The global system response limits as well as acceptance criteria for the
38
individual structural elements that make up typical buildings are described in section
3.8 to 3.9. These acceptance criteria generally consist of limiting values of element
deformation parameters, such as the plastic chord rotation of a beam or shear angle of a
wall. These limiting values have been selected as reasonable approximate estimates of
the average deformations at which certain types of element behavior such as cracking,
yielding, spalling, or crushing, may be expected to occur. As the incremental static
nonlinear analyses are performed, the engineer must monitor the cumulative
deformations of all important structural elements and evaluate them against the
acceptance criteria set before.
The point on the capacity curve at which the first element exceeds the permissible
deformation level for a structural performance level does not necessarily represent that
the building as a whole reaches that structural performance level. Most buildings
contain many elements and have considerable redundancy. Consequently, the onset of
unacceptable damage to a small percentage of these elements may not represent an
unacceptable condition with regard to the overall performance of the building. When
determining the points along the capacity curve for the building at which the various
structural performance level may said to be reached, the engineer must view the
performance of a building as whole and consider the importance of damage predicted
for the various elements on the overall behavior of the building.
The methodology described by ATC-40,1996 incorporates the concept of "Primary"
and "Secondary" elements to assist the engineers in making these judgments. Primary
elements are those that are required as part of the lateral force resisting system for the
building. All the other elements are designated as secondary elements. For a given
performance level, secondary elements are generally permitted to sustain more damage
than primary elements since degradation of secondary elements does not have a
significant effect on the lateral load resisting capability of the building. If in the
development of the capacity curve it is determined that a few element fail to meet the
acceptance criteria for a given performance level at an increment of lateral loading and
displacement, the engineer has the ability to designate these nonconforming elements as
secondary, enabling the use of more liberal acceptance criteria for these few elements.
Care is exercised not to designate an excessive number of elements that are effective in
resisting lateral force as secondary (ATC-40, 1996).
39
3.4.1 Capacity Spectrum Method
The capacity spectrum method, a nonlinear static procedure, provides a graphical
representation of the global force-displacement capacity curve of the building (i.e.
pushover curve) and compares it to the response spectra representations of the
earthquake demand. This method is a very useful tool in the evaluation and retrofit
design of existing concrete buildings. The graphical representation provides a clear
picture of how a building responds to earthquake ground motion, and, as illustrated
below, it provides an immediate and clear picture of how various retrofit strategies,
such as adding stiffness or strength, will affect the building's response to earthquake
demands.
The capacity spectrum curve for the building is obtained by transforming the capacity
curve from lateral force (V) vs. lateral displacement (d) coordinates to spectral
acceleration (Sa) vs. spectral displacement (Sa) coordinates using the modal shape
vectors, participation factors and modal masses obtained from a modal analysis of the
building. In order to compare the Building's capacity to the earthquake demand, it is
required to plot the response spectrum and the capacity spectrum on the same plot. The
conventional response spectrum plotted in spectral acceleration vs. period coordinate
has to be changed in to spectral acceleration vs. spectral displacement coordinate. This
form of response spectrum is known asacceleration displacement response spectrum
(ADRS). The details of the procedure for conversion of conventional response spectra
to ADRS and capacity curve to capacity spectrum are provided in Appendix-A.
3.4.2 Displacement Coefficient Method
Another procedure for calculating demand displacement is Displacement Coefficient
Method which provides a direct numerical process for calculating the displacement
demand. Details of displacement Coefficient Method is available in ATC-40, 1996.
Performance analysis of the buildings under this thesis was made using Capacity
Spectrum Method.
3.5 Seismic Performance Evaluation
The essence of virtually all seismic evaluations procedures is a comparison between
some measures of the "demand" that earthquake place on building to a measure of the
40
"capacity" of the building to resist the induced effects. Traditional design procedures
characterize demand and capacity as forces. Base shear (total horizontal force at the
lowest level of the building) is the normal parameter that is used for this purpose. The
base shear demand that would be generated by a given earthquake, or intensity of
ground motion is calculated, and compares this to the base shear capacity of the
building. If the building were subjected to a force equal to its base shear capacity some
deformation and yielding might occur in some structural elements, but the building
would not collapse or reach an otherwise undesirable overall level of damage. If the
demand generated by the earthquake is less than the capacity then the design is deemed
acceptable.
The first formal seismic design procedures recognized that the earthquake accelerations
would generate forces proportional to the weight of the building. Over the years,
empirical knowledge about the actual behavior of real buildings in earthquakes and
theoretical understanding of structural dynamics advanced. The basic procedure was
modified to reflect the fact that the demand generated by the earthquake accelerations
was also a function of the stiffness of the building.The inherently better behavior of
some buildings over others have also been begun to be recognized. Consequently, the
reduced seismic demand has been assumed for some building based on the
characteristics of the basic structural material and system. The motivation to reduce
seismic demand for design came because it could not be rationalized theoretically how
buildings resisted the forces generated by earthquakes. This was partially the result of
the fundamental assumption that buildings resisted loads linearly without yielding or
permanent structural deformation.
3.6 Nonlinear Static Procedure for Capacity Evaluation of Structures
Instead of comparing forces, nonlinear static procedures use displacements to compare
seismic demand to the capacity of a building. This approach included consideration of
the ductility of the building on an element by element basis. The inelastic capacity of a
building is then a measure of its ability to dissipate earthquake energy. The current
trend in seismic analysis is toward these simplified inelastic procedures.
The recommended central methodology is on the formulation of inelastic capacity
curve for the building. This curve is a plot of the horizontal movement of a building as
it is pushed to one side. Initially the plot is a straight line as the building moves
linearly. As the parts of the building yield the plot begins to curve as the building
41
softens. This curve is generated by building a model of the entire building from
nonlinear representations of all of its elements and components. Most often this is
accomplished with a computer and structural analysis software. The specific forces and
displacement characteristics are specified for each piece of the building resisting the
earthquake demand. These pieces are assembled geometrically to represent the
complete lateral load resisting system. The resulting model is subjected to increasing
increment of load in a pattern determined by its dynamic properties. The corresponding
displacements define the inelastic capacity curve of the building. The generation of the
capacity curve defines the capacity of the building uniquely and independently of any
specific seismic demand. In this sense it replaces the base shear capacity of
conventional procedures. When an earthquake displaces the building laterally, its
response is represented by a point on this curve. A point on the curve defines a specific
damage state of the building, since the deformation of its entire components can be
related to the global displacement of the building.
The capacity of a particular building and the demand imposed upon it by a given
earthquake motion are not independent. One source of this mutual dependence is
evident from the capacity curve itself. As the demand increases the building eventually
yields and, as its stiffness decreases, its period lengthens. Since the seismic
accelerations depend on period, demand also changes as the building yields. Another
source of mutual dependence between capacity and demand is effective damping. As
building yields in response to seismic demand, it dissipates energy with hysteretic
damping. Building that have large, stable hysteretic loops during cyclic yielding
dissipate more energy than those with pinched loops caused by degradation of strength
and stiffness. Since the energy that is dissipated need not be stored in the building, the
damping has the effect of diminishing displacement demand.
3.7 Structural Performance Levels and Ranges
The performance of a building under any particular event is dependent on a wide range
of parameters. These parameters are defined (ATC-40, 1996; FEMA 356, 2000)
qualitatively in terms of the safety afforded by the building to the occupants during and
after the event; the cost and feasibility of restoring the building to pre-earthquake
condition; the length of time the building is removed from service to effect repairs; and
economic, architectural, or historic impacts on the larger community. These
42
performance characteristics are directly related to the extent of damage that would be
sustained by the building.
The Federal Emergency Management Agency in its report 'Prestandard and
Commentary for the Seismic Rehabilitation of Buildings, (FEMA-356, 2000) defines
the structural performance level of a building to be selected from four discrete
structural performance levels and two intermediate structural performance ranges. The
discrete Structural Performance Levels are
• Immediate Occupancy (S-1)
• Life Safety (S-3)
• Collapse Prevention (S-5), and • Not Considered (S-6).
The intermediate Structural Performance Ranges are the
• Damage Control Range (S-2) and the
• Limited Safety Range (S-4)
The definition of these performance ranges are given by FEMA (FEMA-356, 2000).
Acceptance criteria for performance within the Damage Control Structural Performance
Range may be obtained by interpolating the acceptance criteria provided for the
Immediate Occupancy and Life Safety Structural Performance Levels. Acceptance
criteria for performance within the Limited Safety Structural Performance Range may
be obtained by interpolating the acceptance criteria provided for the Life Safety and
Collapse Prevention Structural Performance Levels. The performance levels and
ranges, as per FEMA (FEMA-356, 2000), are described in the sections that follow.
3.7.1 Immediate occupancy structural performance level (S-1) Structural Performance Level S-1, Immediate Occupancy, may be defined as the post-
earthquake damage state of a building that remains safe to occupy, essentially retains
the pre-earthquake design strength and stiffness of the building, and is in compliance
with the acceptance criteria specified in this standard for this Structural Performance
Levels defined at Tables B1-B3 in FEMA-356, 2000 (Appendix-B).
Structural Performance Level S-1, Immediate Occupancy, means the post-earthquake
damage state in which only very limited structural damage has occurred.
43
The basic vertical and lateral-force-resisting systems of the building retain nearly all of
their pre-earthquake strength and stiffness. The risk of life-threatening injury as a result
of structural damage is very low, and although some minor structural repairs may be
appropriate, these would generally not be required prior to re-occupancy.
3.7.2 Damage control structural performance range (S-2)
Structural Performance Range S-2, Damage Control, may be defined as the continuous
range of damage states between the Life Safety Structural Performance Level (S-3) and
the Immediate Occupancy Structural Performance Level (S-l) defined at Tables B1-B3
in FEMA-356, 2000 (Appendix-B).
Design for the Damage Control Structural Performance Range may be desirable to
minimize repair time and operation interruption, as a partial means of protecting
valuable equipment and contents, or to preserve important historic features when the
cost of design for immediate occupancy is excessive.
3.7.3 Life safety structural performance level (S-3) Structural Performance Level S-3, Life Safety, shall be defined as the post-earthquake
damage state that includes damage to structural components but retains a margin
against onset of partial or total collapse in compliance with the acceptance criteria
specified in FEMA for this Structural Performance Level defined at tables B1-B3 in
FEMA-356, 2000 (Appendix-B).
Structural Performance Level S-3, Life Safety, means the post-earthquake damage state
in which significant damage to the building has occurred, but some margin against
either partial or total structural collapse remains. Some structural elements and
components are severely damaged, but this has not resulted in large falling debris
hazards, either within or outside the building. Injuries may occur during the earthquake;
however, the overall risk of life-threatening injury as a result of structural damage is
expected to be low. It should be possible to repair the building; however, for economic
reasons this may not be practical. While the damaged building is not an imminent
collapse risk, it would be prudent to implement structural repairs or install temporary
bracing prior to re-occupancy.
44
3.7.4 Limited safety structural performance range (S-4) Structural Performance Range S-4, Limited Safety, may be defined as the continuous
range of damage states between the Life Safety Structural Performance Level (S-3) and
the Collapse Prevention Structural Performance Level (S-5) defined at tables B1-B3 in
FEMA-356, 2000 (Appendix-B).
3.7.5 Collapse prevention structural performance level (S-5) Structural Performance Level S-5, Collapse Prevention, may be defined as the post-
earthquake damage state that includes damage to structural components such that the
building continues to support gravity loads but retains no margin against collapse in
compliance with the acceptance criteria specified in FEMA for this Structural
Performance Level defined at tables B1-B3 in FEMA-356, 2000 (Appendix-B).
Structural Performance Level S-5, Collapse Prevention, means the post-earthquake
damage state in which the building is on the verge of partial or total collapse.
Substantial damage to the building has occurred, potentially including significant
degradation in the stiffness and strength of the lateral-force resisting system, large
permanent lateral deformation of the building, and to a more limited extent degradation
in vertical-load-carrying capacity. However, all significant components of the gravity
load resisting system must continue to carry their gravity load demands. Significant risk
of injury due to falling hazards from structural debris may exist. The building may not
be technically practical to repair and is not safe for re-occupancy, as aftershock activity
could induce collapse.
3.8 Target Building Performance Levels
Building performance is a combination of the both structural and nonstructural
components. Tables B1-B3(Appendix-B) in FEMA-356, 2000 describe the
approximate limiting levels of structural damage that may be expected of buildings
evaluated to the levels defined for a target seismic demand. These tables represent the
physical states of mathematical calculation of different performance levels.
45
3.9 Response Limits
To determine whether a building meets a specified performance objective, response
quantities from a nonlinear analysis are compared with limits given for appropriate
performance levels (ATC-40, 1996 and FEMA-356, 2000). The response limits fall into
two categories (i) Global Building Acceptability Limits and (ii) Element and
Component Acceptability Limits. These are described next.
3.9.1 Global building acceptability limits
These response limits include requirements for the vertical load capacity, lateral load
resistance, and lateral drift. Table B4 (Appendix-B) gives the limiting values as per
ATC-40 for different performance levels. These are described below.
3.9.1.1 Gravity Load
The gravity load capacity of the building building must remain intact for acceptable
performance at any level. Where an element or component loses capacity to support
gravity loads, the building must be capable of redistributing its load to other elements
or components of the existing system.
3.9.1.2 Lateral Load
Some component types are subjected to degrading over multiple load cycles. If a
significant number of components degrade, the overall lateral force resistance of the
building may be affected. The lateral load resistance of the building system, including
resistance to the effects of gravity loads acting through lateral displacements, should
not degrade by more than 20 percent of the maximum resistance of the building for the
extreme case.
Two effects can lead to loss of lateral load resistance with increasing displacement. The
first is gravity loads acting through lateral displacements, known as the P-∆ effect. The
P-∆ effect is most prominent for flexible buildings with little redundancy and low
lateral load strength relative to the building's weight. The second effect is degradation
in resistance of individual components of the building under the action of reversed
deformation cycles. When lateral load resistance of the building degrades with
46
increasing displacement, there is a tendency for displacements to accumulate in one
direction. This tendency is especially important for long-duration events.
Table B4 in ATC-40,1996(Appendix-B) gives the deformation drift limits for different
performance level. Maximum total drift is defined as the inter-storey drift at the
performance point displacement. Maximum inelastic drift is defined as the portion of
the maximum total drift beyond the effective yield point. For Structural Stability, the
maximum total drift in storey i at the performance point should not exceed the quantity
0.33 where Vi is the total calculated shear force in storey i and Pi is the total gravity
load (i.e. dead plus likely live load) at storey i(ATC-40, 1996).
3.9.2 Element and component acceptability limits
It can be divided in two categories.
3.9.2.1 Primary and secondary elements and components
Each element and component is classified as primary or secondary depending on its
significance to the lateral load resisting system at or near the performance point.
Elements and components that provide a significant portion of the building's strength or
lateral stiffness at the performance point are considered primary. Other elements and
components may be considered secondary (ATC-40, 1996).
3.9.2.2 Deformation of force controlled action
All structural actions may be classified (FEMA-356, 2000) as either deformation
controlled or force-controlled using the component force versus deformation curves
shown in Fig. 3.2. The Type 1 curve depicted in Fig. 3.2 is representative of ductile
behavior where there is an elastic range (point 0 to point 1 on the curve) followed by a
plastic range (points 1 to 3) with non-negligible residual strength and ability to support
gravity loads at point 3. The plastic range includes a strain hardening or softening range
(points 1 to 2) and a strength-degraded range (points 2 to 3). Primary component
actions exhibiting this behavior shall be classified as deformation-controlled if the
strain-hardening or strain-softening range is such that e > 2g; otherwise, they shall be
classified as force controlled. Secondary component actions exhibiting Type 1 behavior
shall be classified as deformation-controlled for any e/g ratio. The Type 2 curve
depicted in Fig. 3.2 is representative of ductile behavior where there is an elastic range
47
(point 0 to point 1 on the curve) and a plastic range (points 1 to 2) followed by loss of
strength and loss of ability to support gravity loads beyond point 2. Primary and
secondary component actions exhibiting this type of behavior shall be classified as
deformation-controlled if the plastic range is such that e > 2g; otherwise, they shall be
classified as force controlled. The Type 3 curve depicted in Fig. 3.2 is representative of
a brittle or non-ductile behavior where there is an elastic range (point 0 to point 1 on
the curve) followed by loss of strength and loss of ability to support gravity loads
beyond point 1. Primary and secondary component actions displaying Type 3 behavior
shall be classified as force-controlled (FEMA-356, 2000).
Fig. 3.2 Component force versus deformation curves (FFMA-356, 2000).
3.9.2.3 Deformation Controlled and Force Controlled Behaviour
Acceptance criteria (FEMA-356, 2000) for primary components that exhibit Type 1
behavior are typically within the elastic or plastic ranges between points 0 and 2,
depending on the performance level. Acceptance criteria for secondary elements that
exhibit Type 1 behavior can be within any of the performance ranges. Acceptance
criteria for primary and secondary components exhibiting Type 2 behavior will be
within the elastic or plastic ranges, depending on the performance level. Acceptance
criteria for primary and secondary components exhibiting Type 3 behavior will always
be within the elastic range. Table B5 in Appendix-B provides some examples of
possible deformation- and force-controlled actions in common framing systems.
48
3.10 Acceptability Limit
A given component may have a combination of both force- and deformation-controlled
actions. Each element must be checked to determine whether its individual components
satisfy acceptability requirements under performance point forces and deformations.
Together with the global requirements, acceptability limits for individual components
are the main criteria for assessing the calculated building response.
Fig. 3.3 Force-deformation action and acceptance criteria. (ATC-40, 1996)
The fig. 3.3 (ATC-40, 1996) shows a generalized load - deformation relation
appropriate for most concrete components. The relation is described by linear response
from A (unloaded component) to an effective yield point B, linear response at reduced
stiffness from B to C, sudden deduction in lateral load resistance to response at reduced
resistance to E, and final loss of resistance thereafter. The following main points relate
to the depicted load-deformation relation
• Point A corresponds to the unloaded condition. The analysis must recognize that
gravity loads may induce initial forces and deformations that should be
accounted for in the model. Therefore, lateral loading may commence at a point
other than the origin of the load- deformation relation.
• Point B has resistance equal to the nominal yield strength. The slope from B to C,
ignoring the effects of gravity loads acting through lateral displacements, is usually
taken as between 5% and 10% of the initial slope. This strain hardening, which is
observed for most reinforced concrete component, may have an important effect
on the redistribution of internal forces among adjacent components.
49
• The abscissa at C corresponding to the deformation at which significant strength
degradation begins.
• The drop in resistance from C to D represents initial failure of the component.
• The residual resistance from D to E may be non-zero in some cases and may be
effectively zero in others. Where specific information is not available, the residual
resistance usually may be assumed to be equal to 20% of the nominal strength.
• Point E is a point defining the maximum deformation capacity. Deformation beyond
that limit is not permitted because gravity load can no longer be sustained.
Tables B6-B12 in Appendix-B give the acceptance criteria for Nonlinear Procedures
for the individual components (ATC-40, 1996) used in prepare acceptance model of
individual structural elements of a building that is to be evaluated for finding seismic
performance under this thesis.
3.11 Seismic Demand
Earthquake is an uncertain phenomenon. It is not possible to predict the time and what
intensity of earthquake that may hit in some specific regions. For example, large
devastating earthquake that hit in the region was the Great Indian Earthquake in 12
June, 1897. Recent devastating earthquakes around the sub-continent leads to the
assessment that Bangladesh is very vulnerable to earthquake. It is possible to design a
building that will withstand such a major devastating earthquake but this huge
investment is not always feasible economically for such an uncertain event.
Thus the earthquake design philosophy adopted in building codes accepts that
• Under minor but frequent shaking, the main members of the building that carry
vertical and horizontal forces should not be damaged; however building parts that do
not carry load may sustain repairable damage.
• Under moderate but occasional shaking, the main members may sustain repairable
damage, while the other parts of the building may be damaged such that they may
even have to be replaced after the earthquake.
• Under strong but rare shaking, the main members may sustain severe (even
irreparable) damage, but the building should not collapse.
Severity of earthquakes as classified in ATC-40, 1996 is defined below.
50
3.11.1 The serviceability earthquake (SE) The Serviceability Earthquake (SE) is defined probabilistically as the level of ground
shaking that has a 50 percent chance of being exceeded in 50-year period. This level of
earthquake ground shaking is typically about 0.5 times of the level of ground shaking
of the Design Earthquake. The SE has a mean return period of approximately 75 years.
Damage in the non structural elements is expected during Serviceability Earthquake.
3.11.2 The design earthquake (DE)
The Design Earthquake (DE) is defined probabilistically as the level of ground shaking
that has a 10 percent chance of being exceeded in a 50-year period. The DE represents
an infrequent level of ground shaking that can occur during the life of the building. The
DE has a mean return period of approximately 500 years. Minor repairable damage in
the primary lateral load carrying system is expected during Design Earthquake. For
secondary elements, the damage may be such that they require replacement.
3.11.3 The maximum earthquake (ME)
The Maximum Earthquake (ME) is defined deterministically as the maximum level of
earthquake ground shaking which may ever be expected at the building site within the
known geologic frame work. In probabilistic terms, the ME has a return period of about
1,000 years. During Maximum Earthquake, buildings will be damaged beyond
repairable limit but will not collapse.
3.12 Development of Elastic Site Response Spectra
Elastic response spectra for a site are based on estimate of Seismic Coefficient, CA
which represents the effective peak acceleration (EPA) of the ground and Cv which
represents 5 percent-damped response of a 1-second system. These coefficients for a
particular zone are dependent on the seismicity of the area, the proximity of the site to
active seismic sources, and site soil profile characteristics.
51
3.12.1 Seismic zone
Bangladesh is divided into three seismic zones as per BNBC. Table B13 in
BNBC,2006(Appendix-B) shows the values of zone coefficients of Bangladesh.
3.12.2 Seismic Source Type
As per ATC-40 (1996), three types of seismic source may be defined as shown in Table B14 in ATC-40,1996(Appendix-B)
3.12.3 Near Source Factor
Currently data pertaining to the active faults close to Dhaka city is not available. It is
not possible to estimate the seismic source distance from a specific site being
considered in this thesis. But for the analysis of the buildings considered in this thesis,
it may be safely assumed that all the sources are located at distance more than 15 km
and the Table B15 in ATC-40,1996 (Appendix-B) may be used to neglect the Near-
Source effects for the present study.
3.12.4 Seismic Coefficients
For each earthquake hazard level, the building is assigned a seismic coefficient CAin
accordance Table B16 in ATC-40,1996 (Appendix-B) and a seismic coefficient Cv in
accordance with Table B17 in ATC-40,1996 (Appendix-B). Seismic coefficient CA
represents the effective peak acceleration (EPA) of the ground. A factor of about 2.5
times CA represents the average value of peak response of a 5 percent-damped short-
period system in the acceleration domain. The seismic coefficient Cv represents 5
percent-damped response of a 1-second system. Cv divided by period (T) defines
acceleration response in the velocity domain. These coefficients are dependent on soil
profile type and the product of earthquake zoning coefficient-Z, severity of earthquake-
E and near source factor-N (ZEN). The soil profile types are classified in Table B18 in
ATC-40,1996(Appendix-B).
3.13 Element Hinge Property
It is known that reinforced concrete does not respond elastically to load level about half
the ultimate value. When an element is stressed beyond its elastic limit, due to inelastic
deformation of the materials, the element will continue to deform disproportionate to its
52
load, this process is called formation of plastic hinge. Hinge properties of RC members
under different loading conditions are likely to be different. These are discussed in the
next sections.
3.13.1 Concrete Axial Hinge
Concrete axial hinge is formed when the axial load carrying capacity of a section
exceeds its elastic limit. The elastic limit for axial capacity is different for tension and
compression. The limits are explained in Fig. 3.4
Fig. 3.4 Concrete axial hinge property.
Axial hinge features used in analysis • Py =Asfy
• Pc =0.85Ac
• Slope between points B and C is taken as 1 0% total strain hardening for steel
• Hinge length assumption for Ay is based on the full length
• Point B, C, D and E based on recommendation of Federal Emergency
Management Agency
• [Prestandard and Commentary for the Seismic Rehabilitation of Buildings]
Table 5.8, Braces in Tension.
• Point B' =PC
• Point E' taken as 9∆y.
•
3.13.2 Concrete moment hinge and concrete P-M-M hinge
Concrete moment hinge is formed when the flexural moment carrying capacity of a
section exceeds its elastic limit. The limits of flexural moment capacity and bi-axial
moment with axial load are explained in Fig 3.5
53
Fig. 3.5 Concrete moment and P-M-M hinge property.
P-M-M hinge Features used in analysis • Slope between points B and C is taken as 10% total strain hardening for steel
• ɵy= 0, since it is not needed
• Points C, D and E based on the recommendation of Advance Technology
Council(ATC-40, 1996)(see table 6.3).
• My based on reinforcement provided.
• P-M-M curve is for major axis moment and is taken to be the same as the
Moment curve in conjunction with the definition of Axial-Moment interaction
curves.
3.13.3 Concrete Shear Hinge
Concrete shear hinge is formed when the shear carrying capacity of a section exceeds
its elastic limit. The elastic limit for shear carrying capacity for coupling beams
controlled by flexure and controlled by shear is explained in Fig. 3.6 (ATC-40,1996).
Fig. 3.6 Concrete shear hinge property.
54
Shear hinge features used in analysis
• Slope between points B and C is taken as 10% total strain hardening for steel
• Vy = 2AS (fc ΄) + fyAsvd
Points C, D and E based on the recommendation of Advance Technology Council
(ATC-40, 1996).
3.14 Concrete Frame Acceptability Limits
To determine the performance of a building, response quantities from a nonlinear static
analysis are compared with limits for appropriate performance levels. Fig. 3.7
illustrates a generalized load-deformation relation applied in the structural components
under the present study. Curve Type I in the Fig. 3.7 has been used when the
deformation is a flexural plastic hinge. Curve type II in the Fig. 3.7 has been used when
the deformation is inter-storey drift, shear angle, sliding shear displacement, or beam-
column joint rotation.
Fig. 3.7 Generalized load-deformation relations for components
Tables 9-6, 9-7 and 9-12 in ATC-40 define the modeling parameters for beam and
column in terms of plastic angles within the yielding plastic hinge.
3.15 Hinge Properties for Modeling
Depending upon the longitudinal reinforcement, transverse reinforcement etc. different
hinge properties may be modeled based on the modeling parameter defined through
Tables 9-6, 9-7 and 9-12 in ATC-40. Different points A, B, C, etc. are defined in Fig.
3.3 of this Chapter. For the purpose of the thesis, the ETABS's built-in default hinge
properties of concrete have been assumed. These built-in default hinge properties are
generally based on Tables 9.6,9.7 and 9.12 in ATC-40.
55
3.16 Assumption for Pushover Analysis
The following assumptions relate to the pushover analysis of the building
• Moment (M2-M3) hinges are considered at the ends of beam members and
moment and axial. (P-M-M) is considered at the ends of column members.
Here 2 and 3 specify the axis or directions of the loads. For column members
axis 2 is perpendicular to the line object. The projection of the positive local 2
axis onto the global X-axis is in the same direction as the positive global X-axis.
Axis 3 is perpendicular to the line object. The direction of the positive local 3
axis is determined from applyingthe right-hand rule using the directions of the 1
and 2 axes where 1 is alongthe line object. For beam members, axis 2 is
perpendicular to the line object. The positive local 2 axis points in the same
direction as the global Z-axis, upward. Axis 3 is perpendicular to the line object
and is horizontal. The direction of the positive local 3 axis is determined from
applying the right-hand rule using the directions of the 1 and 2 axes where 1 is
along the line object (ETABS manual).
• Push-over analysis has been done using load pattern of equivalent static load
calculated as per provision of BNBC, 2006.
• Gravity load has been considered as the previous pushover cases for each
analysis.
• Unload entire building is selected for distribution of loads when local hinges
fail. When a hinge reaches a negative-sloped portion of the stress-strain curve,
the program continues to try to increase the applied load. If this results in
increased strain (decreased stress) the analysis proceeds. If the strain tries to
reverse, the program instead reverses the load on the whole building until the
hinge is fully unloaded to the next segment on the stress-strain curve. At this
point the program reverts to increasing the load on the building. Other parts of
the building may now pick up the load that was removed from the unloading
hinge.
• Geometric non-linearity (P-∆ effect) is considered with full dead load and 50%
live load.
• Horizontal displacement of topmost corner node has been selected for performance monitoring of the roof displacement.
56
CHAPTER 4
EFFECTS OF MASONRY INFILL IN RC BUILDINGS
4.1 Introduction
Masonry infill (MI) elements are used extensively as infill wall panels in reinforced
concrete and steel frame buildings. Masonry infill fulfill architectural and other
functional requirements, such as forming a significant portion of building envelop,
partitioning, temperature and sound barriers, while also providing adequate
compartmentalization against fire hazard. Lack of knowledge on its performance under
seismic loading has discouraged engineers from relying on the interaction of infill with
the enclosing structural system. Therefore, it has become a common practice to ignore
the participation of infill in resisting lateral loads. Research has shown the beneficial
effects of the interaction between masonry infill and structural elements for seismic
performance of existing frame buildings. Researchers have concluded that proper use of
infill in frames could result in significant increases in the strength and stiffness of
buildings subjected to seismic excitations (Klingner and Bertero 1978),(Mehrabi et al.
1996),(Bertero and Brokken 1983). However, the locations of infill in a building must
be carefully selected to avoid or minimize torsional effects as well as soft storey effect.
Architectural restrictions have to be considered when assigning these locations.
Masonry infill walls confined by reinforced concrete (RC) frames on all four sides play
a vital role in resisting the lateral seismic loads on buildings. The behavior of masonry
infilled frames has been extensively studied (Stafford Smith and Coull 1991);(Murty
and Jain 2000);(Moghaddam and Dowling 1987) in attempts to develop a rational
approach for design of such frames. It has been shown experimentally that MI walls
have a very high initial lateral stiffness and low deformability (Moghaddam and
Dowling 1987). Thus introduction of MI in RC frames changes the lateral-load transfer
mechanism of the building from predominant frame action to predominant truss action
(Murty and Jain 2000), as shown in Fig. 4.1, which is responsible for reduction in
bending moments and increase in axial forces in the frame members.
57
Fig. 4.1 Change in lateral load transfer mechanism due to masonry infill
(Murty and Jain 2000)
The high in-plane rigidity of the masonry wall significantly stiffens the otherwise
relatively flexible frame. The result is, therefore, a relatively stiff and tough bracing
system. The wall braces the frame partly by its in plane shear resistance (Fig. 4.2) and
partly by its behavior as a diagonal bracing strut.
Fig. 4.2 Analogous braced frame
The frame of Fig. 4.3 shows such mode of behavior. When the frame is subjected to
horizontal loading, it deforms with double-curvature bending of the columns and
beams. The translation of the upper part of the column in each storey and the shortening
of the leading diagonal of the frame cause the column to lean against the wall as well as
58
to compress the wall along its diagonal. It is roughly analogous to a diagonally braced
frame, shown in fig 4.3.The potential modes of failure, of the wall arise as results of its
interaction with the frame are given below
1. Tension failure of the tension column due to overturning moments.
2. Flexure or shear failure of the columns.
3. Compression failure of the diagonal strut.
4. Diagonal tension cracking of the panel and
5. Sliding shear failure of the masonry along horizontal mortar beds the above failure
modes are shown in Fig. 4.4 and 4.5.
The "perpendicular" tensile stresses are caused by the divergence of the compressive
stress trajectories on opposite sides of the leading diagonal as they approach the middle
region of the infill. The diagonal cracking is initiated at and spreads from the middle of
the infill, where the tensile stresses are a maximum, tending to stop near the
compression corners, where the tension is suppressed.
Fig. 4.3 Modes of infill failure
59
Fig. 4.4 Modes of frame failure
The nature of the forces in the frame can be understood by referring to the analogous
braced frame shown in Fig. 4.3 The windward column or the column facing earthquake
load first, is in tension and the leeward column or the other side of the building facing
earthquake load last, is in compression. Since the infill bears on the frame not as a
concentrated force exactly at the corners, but over short lengths of the beam and
column adjacent to each compression comer, the frame members are subjected also to
transverse shear and a small amount of bending. Consequently, the frame members or
their connections are liable to fail by axial force or shear, and especially by tension at
the base of the windward column.
4.2 Computational Modeling Of Infill Panel
Modeling of RC buildings as well as infill panels are based mainly on finite element
methods and sophisticated material models. The modeling of infill panel with
reinforced concrete frame can be broadly categorized into two approaches a) equivalent
diagonal strut approach and b) continuum approach. Here in this study equivalent strut
method will be used for simplicity. The method is discussed below.
4.2.1 Equivalent strut method
Strength predictions of in filled frames are a complex, statically indeterminate
problem. The strength of a composite in filled frame system is not only the
summation of the infill properties plus those of the frame. Great efforts have
beeninvested, both analytically and experimentally, to better understand and estimate
60
the composite behavior of masonry in filled frames, (Polyakov 1960)(work back to
the early 1950s),(Stafford Smith and Carter 1969), (Klingner and Bertero 1978), , to
mention just a few, formed the basis for understanding and predicting in filled frame
in-plane behavior. Their experimental testing of in filledframes under lateral loads
resulted in specimen deformation shapes similar to the one illustrated in Fig 4.5.
Fig. 4.5 Specimen deformation shape
During testing of the specimens, diagonal cracks developed in the center of the panel,
gaps formed between the frame and the infill in the non-loaded diagonal corners of the
specimens, while full contact was observed in the two loaded diagonal corners. This
behavior, initially observed by Polyakov, lead to the simplification in filled frame analysis
by replacing the masonry infill with an equivalent compressive masonry strut as shown in
Fig. 4.5. The equivalent masonry strut of width, a, with same net thickness and
mechanical properties (such as the modulus of elasticity, Em) as the infill itself, is assumed
to be pinned at both ends to the confining frame.
4.2.2 Equivalent strut width
The evaluation of the equivalent width, a, varies from one reference to the other.The
most simplistic approaches by (Paulay and Priestley 1992) and (Mehrabi et al. 1996)
have assumed constant values for strut width, a, between 12.5 to 25 percent of the
diagonal dimension of the infill, with no regard for any infill or frame
properties.(Stafford Smith and Carter 1969), (Mainstone 1971), and others, derived
complex expressions to estimate the equivalent strut width, a, that consider parameters like
the length of contact between the column/beam and infill, as well the relative
61
stiffness of the infill to the frame.Expressions used in this chapter have been adopted
from (Mainstone 1971) and Stafford-Smith and Carter (1969) for their consistently
accurate predictions of in filled frame in-plane behavior when compared with
experimental results (Mainstone 1971);Stafford-Smith and Carter (1969) and (Klingner
and Bertero 1978).The masonry infill panel will be represented by an equivalent
diagonal strut of width, a, and net thickness, t, as shown in Fig 4.6.
Fig. 4.6 Strut Geometry of a infill wall
The equivalent strut width, a, depends on the relative flexural stiffness of the infill to
that of the columns of the confining frame. The relative infill-to-frame stiffness shall be
evaluated using Eq.4.1 Stafford-Smith and Carter (1969)
λ1H =H( ) ¼
Where, t is the thickness of the masonry wall.
Using this expression,(Mainstone 1971) considers the relative infill-to-frame
flexibility in the evaluation or the equivalent strut width of the panel as shown in
Eq.4.2
a, Strut width =0.175 x D x(λ1H)-0.4
If there are openings present, existing infill damage, and/or FRP overlay, however, the
equivalent strut which must be modified using
amod =a(R1)i (R2)I ζi
.…..........……...(4.1)
…………………...(4.2)
…………………................(4.3)
62
Where,
(R1)i = reduction factor for in-plane evaluation due to presence of openings (Eq. 4.3)
(R2)i = reduction factor for in-plane evaluation due to existing infill damage
ζi = Strength increase factor due to presence of FRP overlay.
Although the expression for equivalent strut width given by Equation 4.3 was
derived to present the elastic stiffness of an infill panel, this document will extend its
use to determine the ultimate capacity infilled buildings. The strut will be assigned
strength parameters consistent with the properties of the infill it represents. A
nonlinear static procedure commonly referred to as a pushover analysis, will be used
to determine the capacity of the infilled building.
4.2.3 Eccentricity of equivalent strut
The equivalent masonry strut is to be connected to the frame members as depicted in
Fig 4.7 , where the bold double-sided arrow represents the location of the strut in the
structural model. The infill forces are assumed to be mainly resisted by the columns,
and the struts are placed accordingly. The strut should be pin connected to the
column at a distance lcolumn from the face of the beam. This distance is defined in Eq. 4.4
and 6.5 and is calculated using the strut width, a, without any reduction factors.
lcolumn =( )
tan (ɵcolumn)=( )
Using this convention, the strut force is applied directly to the column at the edge of
its equivalent strut width, a. Fig 4.7 illustrates this concept.
…….....…………….......(4.4)
.....……….…….......(4.5)
63
Fig. 4.7 Placement of strut
4.3 Perforated Panels
In the case of a perforated masonry panel, the equivalent strut is assumed to act in the
same manner as for the fully in filled frame. Therefore, the eccentric strut should be
placed at a distance lcolumn from the face of the beam as shown in the Fig 4.8. The
equivalent strut width, a, shall be multiplied, however, by a reduction factor to
account for the loss in strength due to the opening. The reduction factor, (R1)iis
calculated using Eq.4.6
(R1)i = - +1
Where
Aopen= Area of the opening (in2)
Apanel= = Area of infill panel (in2) =lxhm
Note If the area of the opening (A open) is greater than or equal to 60 percent of the
infill panel (Apanel) then the effect of the infill should be neglected.
.....…………….....(4.6)
64
Fig. 4.8 Perforated panel
4.4 Partially Infilled Frames
In the case of a partially infilled frame, the reduced column length, lcolumn is equal to the
unbraced opening length for the windward column, while lcolumn for the leeward column is
defined as usual. The strut width should be calculated from Eq.4.2, using the reduced
infill height for hm, in Eq.4.1. Furthermore, the only reduction that should be taken into
account is (R2)i; which accounts for existing infill damage.
4.5 Existing Infill Damage
Masonry infill panel behavior deteriorates as the elastic limit is exceeded. For this reason,
it is important to determine whether the masonry in the panel has exceeded the elastic
limit and, if so, by how much. The extent of existing infill damage can be determined by
visual inspection of the infill. Existing panel damage (or cracking) must be classified as
either no damage, moderate damage, or severe damage presented in Fig 4.9. If in
doubt as to the magnitude of existing panel damage assume severe damage for a safer
(conservative) estimate. A reduction factor for existing panel damage (R2)i, must be
obtained from Table 4.1. Note that, if the slenderness ratio (hm/t) of the panel is greater
than 21, (R2)i, is not defined and repair is required. For panels with no existing panel
damage, the reduction factor (R2)i; must be taken as 1.0.
Fig. 4.9 Types of in-fill damage
Moderate Damage(Crack width <1/8 in) Severe Damage(Crack width >1/8 in)
65
Table 4.1 In-plane damage reduction factor
(R2)i, for Type of Damage
hm/t Moderate Severe
<21 0.7 0.4
>21 Requires repair.
4.6 Properties to be Determined
The infill masonry panel will be represented as strut member. The equivalent strut
width shall be determined according to Coull and Smith described earlier. For the
modeling of infill the following properties must be determined.
Modulus of elasticity of concrete Ec value for column and beam materials.
Sectional properties (i.e. Depth, Width, Moment of Inertia, centroid) of the
column and beam.
Equivalent width of the masonry infill strut "a"
fm, compressive strength of the masonry assemble units.
Em modulus of elasticity of the masonry unit.
4.7 Calculation of Equivalent Strut Width
Detail sample calculation of equivalent strut width and eccentricity is given in the
appendix C.
66
CHAPTER 5
SEISMIC PERFORMANCE EVALUATION OF TWO 06 (SIX) STOREY RC
BUILDINGS
5.1 General
For the performance evaluation purposes Dhaka is selected as the site and seismic
demand for Dhaka has been estimated as per guideline of ATC-40.Structural
performances of an existing 6(Six) storey building of medium-rise building of height
around 60 feet have been ivestigated.This height range has been selected because of the
fact that buildings with this height range are very common in Dhaka city. The
performances of the buildings as evaluated through pushover analysis have been
presented through capacity curves and capacity spectrums described in the sections that
follow.
5.2 Structural Characteristic Features of Building 1
Building 1 considered in this study is located at Mohakhali.
For basic design and evaluation of the buildings the following loading conditions have
been considered. Self-weight of the building has been assumed as per geometric
dimension of the structural elements with the unit weight of the concrete has been taken
as 150 lb/ft3. Other loading due to partition wall, floor finish, cladding loading etc are
considered as per available drawing of the selected building. Code specified floor finish
30 lb/ft2 has been considered on the floors and live load considered as 40 lb/ft2
irrespective of different use/inhabitable area. Seismic load has been considered as per
UBC 1994 loading and base shear has been compared with BNBC 2006. Equivalent
Static Load method has been used with response modification factor, R = 8. No live
load has been considered in calculating Seismic Dead Load. Other coefficients used in
seismic load calculation are Z =0.15, I = 1.0, S = 1.5. Earthquake load at any level
equally distributed among all the nodes in that level.
The material properties and relevant features are as follows
The building was designed with load combination defined in the ETABS 9.7.4 with
• Cylinder strength of concrete, f”c = 3000 psi (as per drawing)
• Yield strength of steel fy= 60000 psi (as per drawing)
67
Sections of the columns and beams as per drawing have been chosen.
• Column sizes are 10"x20",10"x24",10"x32",10"x36"
• Beam sizes are 10"x20.5"
• Grade Beam sizes are 12"x18"
• Slab Thickness is 5.5"
• Shear Wall Thickness is 6"
• All supports are considered as fixed support.
The following assumptions are considered for the pushover analysis of the building
• Moment (M3) hinges are considered at the ends of beam members and P-M-M
hinges are considered at the ends of the column members. All hinges are according
to as per ATC 40 document.
• Pushover analysis has been done using load pattern Equivalent Static Load of
BNBC 2006. Load intensities have been normalized with the base shear.
Geometric non-linearity (P-∆ effect) of the building was considered with full dead
loads and 50% of the live load.
• In each case, the horizontal displacement of the right top most node of the building
has been selected for performance monitoring of roof displacement.
• The general-purpose finite element program ETABS-9.7.4. has been used as the
tool for modeling the buildings and study its behavior in terms of capacity and
performance. Non-linear Static Pushover analysis has also been done using the same
program.
5.3 Performance Evaluation of The Building 1
The buildingis modeled and analyzed using Etabs-9.7.4. After analyzing the buildings,
hinges defined in ATC-40,1996 have been assigned to the respective members and
pushover analyses have been performed to develop capacity curves for each of the
buildings. The capacity curves such as base shear - displacement and capacity
spectrums can be obtained after push over analysis. Accordingly performance points of
the buildings for the estimated seismic demand have been determined from the curve.
Resulting outputs for building presented next. Hinge states near the performance point
have been shown in color code. Different performance levels are determined as per
68
ATC-40 documents. A general graphical representation of the performance point is
given in Figure below
Fig 5.1 Typical Load-Deformation Acceptance Criteria
5.4 Calculation and Selection of Seismic Coefficient as Per ATC-40,1996 for
Building 1 Location of the site = Dhaka City (Mohakhali)
Zone Factor, Z = 0.15
Type of Soil Profile =Sd (Footing foundation,Table 4-3,ATC-40,1996.
600<Vs<1200, 15<N<50
1000<Su<2000, where,Vs=Shear wave velocity
N=Standard Penetration Test
Su=Undrained Shear Strength of soil)
Near source Factor ; N = 1.0 (>15 Km,Table 4-5,ATC-40)
For Serviceability Earthquake, E = 0.50
For Design Earthquake, E= 1.00
For Maximum Earthquake, E= 1.25
Shaking Intensity , ZEN= 0.15 x 0.5 x 1 = 0.075 (When E = 0.5)
ZEN= 0.15 x 1 x 1 = 0.15 (When E = 1.0)
ZEN= 0.15 x 1.25 x 1 = 0.1875 (When E = 1.25)
69
Summary of CAandCv (Table 4-7,4-8,ATC-40)Done by interpolation.
Type of Building E = 0.5 E = 1.0 E = 1.25 CA Cv CA Cv CA Cv
6 Storied Building 0.19 0.18 0.22 0.32 0.265 0.38
5.5 Performance Evaluation of Bare Frame Condition of Building 1
Building is a six-storied building. Detailed configuration is given in the following
figure. Well-defined capacity curves have been found in two orthogonal directions
which are shown in the following Figures.Capacity of the building in the X-direction is
slightly more because structural capacity of the members in X-direction is slightly more
than that in the Y-direction.
Fig 5.2 Typical Plan and 3d view of the Building 1.
70
The Capacity curves have been converted into capacity spectrums as per pushover
analysis using ETABS-9.7.4, which are shown in following Figures below.
Fig 5.3 Base shear vs Displacement curve in X Direction for bare frame condition of building 1 at maximum EQ .
Fig 5.4 Base shear vs Displacement curve in Y Direction for bare frame condition of building 1 at maximum EQ .
71
Fig 5.5 Capacity spectrum curve in X Direction for bare frame condition of building 1 at maximum EQ.
Fig 5.6 Capacity spectrum curve in Y Direction for for condition of building 1 at Maximum EQ.
72
For Bare frame condition of building 1 and for three Earthquake conditions (i.e.
Serviceability Earthquake, Design earthquake, Maximum Earthquake) different values
of base shear, displacement, Spectral acceleration, Effective Time period, Effective
Damping values at Performance point for X direction are summarized as follows
Table 5.1 Different parameter’s values for different earthquake conditions for a bare frame condition of building 1. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E = 1.00
Maximum EQ, E = 1.25
CA =0.19, Cv=0.18
CA =0.22, Cv =0.32
CA =0.265, Cv=0.38
6 Storied Building
(Bare Frame)
(V,D)= (397.89,2.26) (528.77,4.146) (555.69,4.974)
(Sa,Sd)= (0.091,2.027) (0.126,3.836) (0.135,4.653)
Teff, Beff, (1.485,0.124) (1.758,0.169) (1.875,0.190)
From the above table it is clear that with the increase of magnitude of earthquake base
shear, displacement, Time period, Effective Damping values of the bare frame building
increases. It means with the increase of magnitude of earthquake,building has to deform
higher than the previous EQ conditions to meet the performance point. As a result
elements are stressed beyond their elastic limits.
5.5.1 Hinge formation status of bare frame condition of building 1
At performance point hinge formation for different types of earthquake for X direction
has been shown in the figure below
Table 5.2 Hinge formation status for different earthquake criteria for bare frame condition of building 1.
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ
452 132 62 26 0 0 0 0 672
Design EQ 441 135 63 32 0 1 0 0 672
Maximum EQ 423 147 55 41 0 2 4 0 672
73
Fig 5.7 Hinge state of bare frame condition of building 1 at the performance point in X-direction at maximum EQ In the above figures Hinge states of bare frame Building at the performance in X-
direction represents the hinge states of the building. It may be seen that beam hinges
formed are in beams and no hinge formed in column. That means the building is strong
column-weak beam system.
5.5.2 Lateral Drift ratio for bare frame condition of building 1
According to ATC-40,1996 deformation limits for various performance level are as follows
Table 5.3 Deformation limits for various performance level (ATC-40, 1996) Performance Level Inter storey Drift Limit Immediate
Occupancy Damage Control
Life Safety Structural Stability
Maximum total drift Δ/H *
0.01 0.01-0.02 0.02 0.33*(Vi/Pi)
Maximum inelastic drift, Δin/H *
0.005 0.005-0.015 No limit No limit
* Δ= Storey displacement, Δin = Inelastic storey displacement and H= Storey height,Vi=Total calculated shear force in storey I and Pi =Total gravity load
74
Performance of bare frame condition of building 1 as calculated has been presented in the
following Table.
Table 5.4 Drift ratio in X direction for bare frame condition of building 1
At Performance Point X-Direction
Maximum elastic total drift ratio Maximum inelastic drift ratio 0.0037 Immediate Occupancy 0.026 Structural stability
It has been found that at performance point, the maximum total drift ratio ( deflection
by corresponding storey height) is 0.0037 in the X-direction and that of maximum
inelastic drift ratio (inelastic deflection by height) is 0.026 in X-direction. As per the
acceptance limit given in ATC-40,1996 the global performance of the building meets
Immediate Occupancy (IO) performance level in elastic range and structural stability in
inelastic range.
5.6 Performance Evaluation of Full InFilled condition of building 1
The performance of a bare frame building can be improved significantly by placing in-
filled masonry panels. The masonry walls provide additional lateral stiffness to the
building,which contributes to the stability of the building against earthquake.
The in fill walls used in the buildings for partitions and other purposes can be
represented in many ways. Here in this study equivalent strut method proposed by
Stafford-Smith and Carter (1969), Mainstone (1971) has been used for simplicity.
Modelling parameters for the equivalent struts are given below
Equivalent strut width = 23.06 inch
Thickness of strut = 5 inch
Ecentricity from face of beam (bottom =66.61 inch, top=28.39 inch)
Building is a six-storied building. Detailed configuration is given in the figure
above.Capacity of the building in the X-direction is slightly more because structural
capacity of the members in X-direction is slightly more than that in the Y-direction.The
Capacity curves have been converted into capacity spectrums as per pushover analysis
using ETABS 9.7.4, which are shown in following Figures below.
75
Fig 5.8 Base shear vs Displacement curve in X Direction for full infilled condition at Maximum EQ for Building 1.
Fig 5.9 Base shear vs Displacement curve in Y Direction for full infilled condition at Maximum EQ for Building 1.
76
Fig 5.10 Capacity Spectrum curve in X Direction for ful infilled condition at Maximum EQ Condition for Building 1.
Fig 5.11 Capacity Spectrum curve in Y Direction for ful infilled condition at Maximum EQ for Building 1.
77
For full infilled condition for building 1 and for three Earthquake conditions (i.e.
Serviceability Earthquake,Designearthquake,Maximum Earthquake) different values of
base shear,displacement,Spectralacceleration,Effective Time period, Effective
Damping values at Performance point for X direction are summarised as follows
Table 5.5 Different parameter’s values at different earthquake conditions for full in- filled condition of building 1. Type of Building
Parameters Serviceability Earthquake, E = 0.5
Design Earthquake, E = 1.0
Maximum EQ, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Full In filled condition)
(V,D)= (477.77,2.32) (651.302,4.157) (710.463,5.004)
(Sa,Sd)= (0.101,2.044) (0.142,3.770) (0.157,4.575)
Teff, Beff, (1.429,0.107) (1.64,0.145) (1.725,0.158)
From the above table it is clear that with the increase of magnitude of earthquake base
shear, displacement, Time period, Effective Damping values of the bare frame building
increases.It means with the increase of magnitude of earthquake , building has to
deform higher than the previous EQ conditions to meet the performance point.As a
result elements are stressed beyond their elastic limits.
5.6.1 Hinge Formation status for full infilled condition of building 1
At performance point hinge formation for different types of earthquake for X direction
has been shown in the figure below
Table 5.6 Hinge formation at different earthquake conditions for full infilled condition
of building 1.
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability
EQ
799 129 30 14 0 0 0 0 972
Design EQ 744 135 63 28 0 2 0 0 972
Maximum EQ 727 147 55 37 0 0 6 0 972
78
Fig 5.12 Hinge state of full infilled condition of building 1 at the performance point in X- Direction at Maximum EQ. In the above figures Hinge states of bare frame Building at the performance in X-
direction represents the hinge states of the building It may be seen that beam hinges
formed are in beams and no hinge formed in column. That means the building is strong
column-weak beam system.
5.6.2 Lateral drift ratio for full infilled condition of building 1
Performance of full infilled frame building as calculated has been presented in the following Table.
Table 5.7 Drift ratio in X direction for a full in-filled condition of building 1
At Performance Point X-Direction
Maximum total drift rati0 Maximum inelastic drift ratio
0.0036 Immediate Occupancy 0.025 Structural stability
It has been found that at performance point, the maximum total drift ratio (total
deflection by total height) is 0.0036 in the X-direction and that of maximum inelastic
drift ratio (inelastic deflection by total height) is 0.025 in X-direction. As per the
79
acceptance limit given in ATC-40,1996 the global performance of the building meets
Immediate Occupancy (IO) performance level in elastic range and structural stability in
inelastic range.
5.7 Performance Evaluation of Soft Storey Condition of Building 1
Building is a six-storied building. Detailed configuration is given in the figure above.
Formation of a soft storey is caused by the difference in storey stiffness with the upper
stories.The stiffness difference in between stories is mainly caused by having bare
ground floor while the upper floor have in filled masonry panel. This is most common
case in residential building and could be fatal in earthquake.A regular 6 storey building
which has all the storey height same was designed first and then to use the ground floor
as a car parking, its partition walls were removed,which has become a soft storey.
Loading condition, material property and salient features of the building are same as the
full- infilled condition of building described as before.
Detailed configuration is given in the figure above.Capacity of the building in the X-
direction is slightly more because structural capacity of the members in X-direction is
slightly more than that in the Y-direction.
The Capacity curves have been converted into capacity spectrums as per pushover
analysis using Etabs-v-9.7.4, which are shown in following Figures below.
Fig 5.13 Base shear vs Displacement curve in X Direction for soft storey condition at Maximum EQ for Building 1.
80
Fig 5.14 Base shear vs Displacement curve in Y Direction for soft storey condition at Maximum EQ for Building 1.
Fig 5.15 Capacity Spectrum curve in X Direction for soft storey condition at Maximum EQ for Building 1.
81
Fig 5.16 Capacity Spectrum curve in Y Direction for soft storey condition at Maximum EQ for Building 1. For soft storey condition of building 1 and for three Earthquake conditions (i.e.
Serviceability Earthquake,Designearthquake,Maximum Earthquake) different values of
base shear,displacement,Spectralacceleration,Effective Time period, Effective
Damping values at Performance point for X direction are summarized as follows.
Table 5.8 Different parameter’s values at different earthquake criteria for soft storey condition of building 1. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Full In filled condition)
(V,D)= (446.13,2.322) (612.697,4.22) No performance
point found (Sa,Sd)= (0.095,2.072) (0.135,3.878)
Teff, Beff, (1.477,0.114) (1.710,0.151)
From the above table it is clear that with the increase of magnitude of earthquake base
shear, displacement, Time period, Effective Damping values of the bare frame building
increases.It means with the increase of magnitude of earthquake , building has to
deform higher than the previous EQ conditions to meet the performance point.It is seen
82
that at ME EQ condition no performance point is found at X direction.This means the
building fails before meeting the demand.This means the building needs remedial
measures to suit the E=1.25 for “ME”.
5.7.1 Hinge formation status of soft storey condition of building 1
At performance point hinge formation for different types of earthquake for X direction has been shown in the figure below
Table 5.9 Hinge formation status at different earthquake conditions for soft storey condition of building 1. A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ 749 131 32 10 0 0 0 0 922
Design EQ 683 144 64 30 0 1 0 0 922
Maximum EQ No performance point found.All hinges are in the elastic range.
Fig 5.17 Hinge state of soft storey condition of building 1 at the performance point in X-Direction @ Maximum EQ. 5.7.2 Lateral Drift ratio for soft condition of building 1
Performance of soft storey frame building as calculated has been presented in the following Table.
83
Table 5.10 Drift ratio in X direction for soft storey condition of building 1
X-Direction Maximum total drift rati0 Maximum inelastic drift ratio
0.0038 Immediate Occupancy
0.026 Structural stability
5.8 Comparison of The Performance Evaluation of The Building 1 Considered
For Analysis
Comparison of the performance evaluation of the building 1 is shown in the table below. Table 5.11 Comparison of Different parameter’s values at different earthquake conditions for bare frame, full in-filled frame building, soft storey condition of building 1. Type of Building
Parameters
Serviceability Earthquake, E = 0.5
Design Earthquake, E =1.00
Maximum Earthquake, E=1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Bare Frame)
(V,D)= (397.89,2.26) (528.77,4.146) (555.69,4.974) (Sa,Sd)= (0.091,2.027) (0.126,3.836) (0.135,4.653) Teff, Beff, (1.485,0.124) (1.758,0.169) (1.875,0.190)
6 Storied Building
(Full in filled condition)
(V,D)= (477.77,2.32) (651.302,4.157) (710.463,5.004) (Sa,Sd)= (0.101,2.044) (0.142,3.770) (0.157,4.575) Teff, Beff, (1.429,0.107) (1.64,0.145) (1.725,0.158)
6 Storied Building
(Soft storey condition)
(V,D)= (446.13,2.322) (612.697,4.22) No performance
point found. (Sa,Sd)= (0.095,2.072) (0.135,3.878)
Teff, Beff, (1.477,0.114) (1.710,0.151)
5.8.1 Comparison of hinge formation and base shear of building 1
Base shear at performance point and number of hinges developed up to Performance Point for X direction at Design EQ
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Table 5.12 Comparison of Hinge formation and base shear at design earthquake condition for bare frame, full infilled,soft storey condition of building 1
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Bare Frame 529 441 135 63 32 0 1 0 0 672
Full In-filled Frame
651 744 135 63 28 0 2 0 0 972
Soft Storey Frame 613 683 144 64 30 0 1 0 0 922
Base shear at performance point and number of hinges developed up to Performance Point for X direction Maximum EQ
Table 5.13 Comparison of Hinge formation and base shear at maximum earthquake condition for bare frame, full infilled, soft storey condition of building 1
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Bare Frame 556 423 147 55 41 0 2 4 0 672
Full In-filled Frame
710 147 55 37 0 0 6 0 972 727
Soft Storey Frame No performance point found.
5.9 Structural Characteristic Features of Building 2
Building 1 considered in this study is located at Mirpur.
For basic design and evaluation of the buildings the following loading conditions have
been considered.Self-weight of the building has been assumed as per geometric
dimension of the structural elements with the unit weight of the concrete has been taken
as 150 lb/ft3. Other loading due to partition wall, floor finish, cladding loading etc are
considered as per available drawing of the selected building. Code specified floor finish
30 lb/ft2 has been considered on the floors and live load considered as 40 lb/ft2
irrespective of different use/inhabitable area. Seismic load has been considered as per
UBC 1994 loading and base shear has been compared with BNBC 2006. Equivalent
Static Load method has been used with response modification factor, R = 8. No live
load has been considered in calculating Seismic Dead Load. Other coefficients used in
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seismic load calculation are Z =0.15, I = 1.0, S = 1.5. Earthquake load at any level
equally distributed among all the nodes in that level.
The material properties and relevant features are as follows.
The building was designed with load combination defined in the ETABS 9.7.4 with
• Cylinder strength of concrete, f”c = 3000 psi (as per drawing)
• Yield strength of steel fy= 60000 psi (as per drawing)
Sections of the columns and beams as per drawing have been chosen.
• Column sizes are 12"x15",
• Beam sizes are 10"x15"
• Grade Beam sizes are 12"x15"
• Slab Thickness is 5.0"
• All supports are considered as fixed support.
The assumptions for the pushover analysis are discussed above.
5.10 Performance Evaluation of The Building 2
The building is modeled and analyzed using Etabs-9.7.4. After analyzing the buildings,
hinges defined in ATC-40 have been assigned to the respective members and pushover
analyses have been performed to develop capacity curves for each of the buildings. The
capacity curves such as base shear - displacement and capacity spectrums can be
obtained after push over analysis. Accordingly performance points of the buildings for
the estimated seismic demand have been determined from the curve. Resulting outputs
for building presented next. Hinge states near the performance point have been shown
in color code. Different performance levels are determined as per ATC-40 documents.
5.11 Calculation and Selection of Seismic Coefficient as Per ATC-40,1996 for
building 2 Location of the site = Dhaka City (Mirpur)
Zone Factor, Z = 0.15
Type of Soil Profile =Sd (Footing foundation,Table 4-3,ATC-40,1996
600<Vs<1200, 15<N<50
1000<Su<2000, where,Vs=Shear wave velocity
N=Standard Penetration Test
Su=Undrained Shear Strength of soil)
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Near source Factor ; N = 1.0 (>15 Km,Table 4-5,ATC-40)
For Serviceability Earthquake, E = 0.50
For Design Earthquake, E= 1.00
For Maximum Earthquake, E= 1.25
Shaking Intensity , ZEN= 0.15 x 0.5 x 1 = 0.075 (When E = 0.5)
ZEN= 0.15 x 1 x 1 = 0.15 (When E = 1.0)
ZEN= 0.15 x 1.25 x 1 = 0.1875 (When E = 1.25)
Summary of CA and Cv (Table 4-7,4-8,ATC-40)Done by interpolation.
Type of Building E = 0.5 E = 1.0 E = 1.25 CA Cv CA Cv CA Cv
6 Storied Building 0.19 0.18 0.22 0.32 0.265 0.38
5.12 Performance Evaluation Of Bare Frame Condition of Building 2
Building is a six-storied building. Detailed configuration is given in the following
figure. Well-defined capacity curves have been found in two orthogonal directions
which are shown in the following Figures.Capacity of the building in the X-direction is
slightly more because structural capacity of the members in X-direction is slightly more
than that in the Y-direction.
Fig 5.18 Typical Plan and 3d view of the Building 2.
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The Capacity curves have been converted into capacity spectrums as per pushover
analysis using ETABS-9.7.4, which are shown in following Figures below.
`Fig 5.19 Base shear vs Displacement curve in X Direction for bare frame condition of building 2 at maximum EQ.
Fig 5.20 Base shear vs Displacement curve in Y Direction for bare frame condition of building 2 at maximum EQ.
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Fig 5.21 Capacity spectrum curve in X Direction for bare frame condition of building 2 at maximum EQ.
Fig 5.22 Capacity spectrum curve in Y Direction for bare frame condition of building 2 at Maximum EQ.
89
For Bare frame condition of building 2 and for three Earthquake conditions (i.e.
Serviceability Earthquake, Design earthquake, Maximum Earthquake) different values
of base shear, displacement, Spectral acceleration, Effective Time period, Effective
Damping values at Performance point for Y direction are summarized as follows
Table 5.14 Different parameter’s values for different earthquake conditions for bare frame condition of building 2. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E = 1.00
Maximum EQ, E = 1.25
CA =0.19, Cv=0.18
CA =0.22, Cv =0.32
CA =0.265, Cv=0.38
6 Storied Building
(Bare Frame)
(V,D)= (383.736,1.710) (507.69,3.058) No Performance
point found. (Sa,Sd)= (0.145,1.358) (0.193,2.469)
Teff, Beff, (0.959,0.114) (1.133,0.169)
From the above table it is clear that with the increase of magnitude of earthquake base
shear, displacement, Time period, Effective Damping values of the bare frame building
increases.It means with the increase of magnitude of earthquake, building has to deform
higher than the previous EQ conditions to meet the performance point.As a result
elements are stressed beyond their elastic limits. It is seen that no performance point
has been found for Y direction at maximum earthquake condition.
5.12.1 Hinge formation status of bare frame condition of building 2
At performance point hinge formation for different types of earthquake for Y direction
has been shown in the figure below
Table 5.15 Hinge formation status at different earthquake criteria for bare frame condition of building 2.
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ 859 168 7 0 0 0 0 0 1034
Design EQ 831 68 129 4 0 1 0 1 1034
Maximum EQ No performance point found.All hinges are in the elastic range.
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Fig 5.23 Hinge state of Bare frame condition of Building 2 in Y-Direction at maximum EQ In the above figures Hinge states at the bare frame condition of Building 2 are seen. It
is found that beam hinges formed are in beams and hinges are also formed in column.
That means the building is strong beam weak column system.It means that the building
fails at maximum earthquake condition before reaching the performance point. 5.12.2 Lateral Drift ratio for bare frame condition of building 2
Performance of bare frame building as calculated has been presented in the following
Table.
Table 5.16 Drift ratio in Y direction for bare frame condition of building 2
Y-Direction Maximum total drift rati0 Maximum inelastic drift ratio
0.0012 Immediate Occupancy 0.01 Damage Control It has been found that at performance point, the maximum total drift ratio ( deflection
by corresponding storey height) is 0.0012 in the Y-direction and that of maximum
inelastic drift ratio (inelastic deflection by height) is 0.01 in Y-direction. As per the
acceptance limit given in ATC-40,1996 the global performance of the building meets
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Immediate Occupancy (IO) performance level in elastic range and damage control in
inelastic range.
5.13 Performance Evaluation of Full In-Filled condition of building 2
The performance of a bare frame building can be improved significantly by placing in-
filled masonry panels. The masonry walls provide additional lateral stiffness to the
building,which contributes to the stability of the building against earthquake.
The in fill walls used in the buildings for partitions and other purposes can be
represented in many ways. Here in this study equivalent strut method proposed by
Stafford-Smith and Carter (1969), Mainstone (1971) has been used for simplicity.
Modelling parameters for the equivalent struts are given below
Equivalent strut width = 13.5 inch
Thickness of strut = 5 inch
Ecentricity from face of beam (bottom =83.24 inch, top=16.76 inch)
Building is a six-storied building. Detailed configuration is given in the figure
above.Capacity of the building in the X-direction is slightly more because structural
capacity of the members in X-direction is slightly more than that in the Y-direction.The
Capacity curves have been converted into capacity spectrums as per pushover analysis
using ETABS 9.7.4, which are shown in following Figures below.
Fig 5.24 Base shear vs Displacement curve in X Direction for full infilled condition at Maximum EQ criteria for building 2.
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Fig 5.25 Base shear vs Displacement curve in Y Direction for ful infilled condition at Maximum EQ criteria for building 2.
Fig 5.26 Capacity Spectrum curve in X Direction for full-infilled condition at Maximum EQ criteria for building 2.
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Fig 5.27 Capacity Spectrum curve in Y Direction for full infilled condition at Maximum EQ criteria for building 2. For full infilled condition of building 2 and at three Earthquake conditions (i.e.
Serviceability Earthquake,Designearthquake,Maximum Earthquake) different values of
base shear,displacement,Spectralacceleration,Effective Time period, Effective
Damping values at Performance point for Y direction are summarized as follows.
Table 5.17 Different parameter’s values at different earthquake criteria for full in-filled condition of building 2. Type of Building
Parameters Serviceability Earthquake, E = 0.5
Design Earthquake, E = 1.0
Maximum EQ, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
No Performance point found. 6 Storied
Building (Full In filled
condition)
(V,D)= (432.33,1.776) (588.357,3.203)
(Sa,Sd)= (0.152,1.408) (0.208,2.574)
Teff, Beff, (0.948,0.095) (1.101,0.139) From the above table it is clear that with the increase of magnitude of earthquake base
shear, displacement, Time period, Effective Damping values of the bare frame building
increases.It means with the increase of magnitude of earthquake , building has to
deform higher than the previous EQ conditions to meet the performance point.As a
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result elements are stressed beyond their elastic limits. It is seen that no performance
point has been found for Y direction at maximum earthquake condition.
5.13.1 Hinge Formation status for full infilled condition of building 2
At performance point hinge formation for different types of earthquake for X direction
has been shown in the figure below
Table 5.18 Hinge formation at different earthquake criteria for full infilled condition of
Building 2.
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ
799 129 30 14 0 0 0 0 972
Design EQ 744 135 63 28 0 2 0 0 972
Maximum EQ No performance point found.All hinges are in the elastic range.
Fig 5.28 Hinge state of full in filled condition of building 2 at the performance point in Y- Direction at Maximum EQ. In the above figures hinge states at the bare frame condition of building 2 are seen. It is
found that beam hinges formed are in beams and hinges are also formed in column.
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That means the building is strong beam –weak column system.It means that the
building fails at maximum earthquake condition before reaching the performance point. 5.13.2 Lateral drift ratio for full infilled condition of building 2
Performance of bare frame building as calculated has been presented in the following
Table.
Table 5.19 Drift ratio in Y direction for full infilled condition of building 2
Y-Direction Maximum total drift rati0 Maximum inelastic drift ratio
0.0011 Immediate Occupancy 0.0070 Damage Control It has been found that at performance point, the maximum total drift ratio ( deflection
by corresponding storey height) is 0.0011 in the Y-direction and that of maximum
inelastic drift ratio (inelastic deflection by height) is 0.0070 in Y-direction. As per the
acceptance limit given in ATC-40,1996 the global performance of the building meets
Immediate Occupancy (IO) performance level in elastic range and damage control in
inelastic range.
5.14 Comparison of the performance evaluation of the building 2 considered for
Analysis
Table 5.20 Different parameter’s values for different earthquake conditions for bare frame, full in-filled condition condition of building 2.
Type of Building
Parameters
Serviceability Earthquake, E = 0.5
Design Earthquake, E =1.00
Maximum Earthquake, E=1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265,Cv =0.38
6 Storied Building
(Bare Frame)
(V,D)= (383.736,1.710) (507.69,3.058) No Performance
point found. (Sa,Sd)= (0.145,1.358) (0.193,2.469) Teff, Beff, (0.959,0.114) (1.133,0.169)
6 Storied Building (Full in filled
condition)
(V,D)= (432.33,1.776) (588.357,3.203) No Performance
point found. (Sa,Sd)= (0.152,1.408) (0.208,2.574) Teff, Beff, (0.948,0.095) (1.101,0.139)
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5.14.1 Comparison of hinge formation and base shear of building 2
Base shear at performance point and number of hinges developed up to Performance Point for Y direction at Serviceability EQ
Table 5.21 Comparison of Hinge formation and base shear for serviceability earthquake condition for a bare frame,full in-filled condition of building 2
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Bare Frame 384 859 168 7 0 0 0 0 0 1034
Full In-filled Frame
508 831 68 129 4 0 1 0 1 1034
Base shear at performance point and number of hinges developed up to Performance Point for Y direction at Design EQ
Table 5.22 Comparison of Hinge formation and base shear for design earthquake condition for a bare frame,full in-filled condition of building 2
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO I0-LS LS-CP CP-C C-D D-E >E Total
Bare Frame 433 830 65 133 5 0 1 0 0 1034
Full In-filled 588 830 65 133 4 0 1 0 1 1034
5.15 Summary
Two types of building has been analyzed in this chapter. Building 1 is an irregular building and building 2 is a regular building.
From the above tables it is clear that for building 1 the base shear developed at
performance point is lower for bare frame building than that of full in-filled frame and
soft storey frame because of less mass in stories due to absence of infill.For building 2
the findings are same, except the fact that no soft story condition has been analyzed.
Building’s natural period(T) is less than that of bare frame which means masonry infill
contributes for stiffness of the building.
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Performance of full in-filled condition is better than that of bare frame condition.
Capacity curve of building meets the demand curve at lower displacement value.
Lateral drift ratios are less than that of bare frame condition.Deformation of different
storey is less than that of bare frame and each storey deforms uniformly.Performance
point of the building stands within immediate occupancy level.
For building 1 Capacity curve of soft storey frame just reaches the demand curve but
considerable deformation of the building beyond its elastic limit occurs. At maximum
EQ condition no performance point found which means building need remedial
measure to suit the maximum EQ condition.For building 2 at maximum earthquake
condition no performance point found both for bare frame and full infilled condition.So
building 2 needs remedial measure to suit the maximum EQ condition.
For building 1 performance point of the building exceeds life safety performance level.
It is also observed that hinges formed for soft storey building is more and some of them
reach damage state. Also the building fails before developing base shear demand.
So considering the above mentioned tables and comparing the performance condition
of the building at variable EQ condition and varaiable in-fill condition we can set a
specific performance objective at a specific EQ condition.
Let say,for maximum EQ condition performace criteria collapse prevention, and for
design EQ condition Life safety criteria is set both for building 1 and building 2.
Now some retrofitting scheme/remedial measures to gain the above mentioned
performance criteria will be investigated in the following chapter.
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CHAPTER 6
PERFORMANCE EVALUATION OF RETROFITTED BUILDINGS
6.1 Remedial Measures for Retrofitting of the Building 1
Structural retrofitting of the building 1 using different retrofitting methods are investigated below. 6.1.1 Structural retrofitting of the building 1 using column jacketing and
providing additional buttress wall
Building is a 6-storied building with ground floor open for parking. It is found from
capacity spectrum curves it is not fit for maximum earthquake i.e. for "ME" at E=1.25.
Whole building collapses before meeting the performance point.Considering maximum
earthquake the structural members need to be retrofitted. However, to do the retrofit
works some trials have been given using additional buttress wall in four corners at Grid
intersection point-1A,5A,A1F,3/B1. Moreover, some columns such as 10x20
inch,10x24 inch, 10x32 inch, 10x36 inch at different points needed to increase in sizes
by jacketing with re-bar in the X directions. These modifications are shown in Figure
8.1 below which is modified plan of the building.
Fig 6.1 Plan view of the retrofitted building retrofitted by column jacketing and providing buttress wall.
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6.1.1.1 Performance evaluation of retrofitted building 1 retrofitted with column
jacketing and buttress wall.
The revised well defined capacity curves have been found based on the retrofit building
in two orthogonal directions, which are shown in the following Figures 8.2 and 8.3.
Capacity of the building in the X-direction is slightly more because structural capacity
of the members in X-direction is slightly more than that in the Y-direction.
Fig 6.2 Base shear vs Displacement curve in X Direction for retrofitted Building 1(with buttress wall and column jacketing at Maximum EQ Condition.
Fig 6.3 Base shear vs Displacement curve in Y Direction for retrofitted building 1 (with buttress wall and column jacketing at Maximum EQ Condition.
100
The revised capacity curves have been converted into capacity spectrums as per
pushover analysis using ETABS 9.7.4 based on the retrofit proposed in the above fig. It
is also found that the capacity curves now in both directions shows performance point
at E=1.25 for 'ME' which did not intersect the 5% elastic demand curve before
retrofitting.
Fig 6.4 Capacity Spectrum curve in X Direction for retrofitted building 1(with buttress wall and column jacketing at Maximum EQ Condition.
Fig 6.5 Capacity Spectrum curve in Y Direction for retrofitted building 1(with buttress wall and column jacketing at Maximum EQ Condition.
101
For the retrofitted building 1(with buttress wall and column jacketing) and for three
Earthquake conditions (i.e. Serviceability Earthquake,Designearthquake,Maximum
Earthquake) different values of base shear,displacement,Spectralacceleration,Effective
Time period, Effective Damping values at Performance point for X direction are
summarised as follows
Table 6.1 Different parameter’s values for different earthquake conditions for the retrofitted building 1 retrofitted with buttress wall and column jacketing. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Retrofitted with buttress wall and
column jacketing)
(V,D)= (554.473,2.144) (781.294,3.868) (875.287,4.694)
(Sa,Sd)= (0.123,1.793) (0.179,3.275) (0.205,3.997)
Teff, Beff, (1.216,0.096) (1.362,0.127) (1.412,0.131)
6.1.1.2 Hinge formation status of the retrofitted building 1 retrofitted with
buttress wall and column jacketing
At performance point hinge formation for different types of earthquake for X direction has been shown in the figure below
Table 6.2 Hinge formation for different earthquake conditions for the retrofitted building 1 retrofitted with buttress wall and column jacketing. A-B B-IO IO-
LS LS-CP
CP-C C-D D-E >E Total
Serviceability
EQ
773 143 30 8 0 0 0 0 954
Design EQ 704 157 63 30 0 0 0 0 954
Maximum EQ 699 155 64 35 1 0 0 0 954
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Fig 6.6 Hinge state of retrofitted building 1 with buttress wall and column jacketing at the performance point in X-Direction at Maximum EQ.
6.1.1.3 Lateral drift ratio of the retrofitted building 1 retrofitted with
buttress wall and column jacketing
Lateral drift ratio of the retrofitted building 1 retrofitted with buttress wall and column jacketing is shown in the table below
Table 6.3 Drift ratio in X direction for retrofitted building 1retrofitted with buttress wall and column jacketing
At Performance Point X-Direction (Retrofitted building with buttress wall and column jacketing) Maximum total drift rati0 Maximum inelastic drift ratio
0.0027 Immediate Occupancy 0.019 Life Safety
6.1.2 Structural retrofitting of the building 1 using insertion of additional shear
wall
Building is a 6-storied building with ground floor open for parking. It is found from
capacity spectrum curves it is not fit for maximum earthquake i.e. for "ME" at E=1.25.
Whole building collapses before meeting the performance point.Considering maximum
earthquake the structural members need to be retrofitted. However, to do the retrofit
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works some trials have been given using additional shear wall in four corners along
Grid line-1,2,A1,4,5,F. Shear walls are provided in such a way that ground floor
parking is not hampered.These modifications are shown in Figure 8.7 below which is
modified plan of the building.
Fig 6.7 Plan view of the retrofitted building 1 retrofitted by providing additional shear wall.
6.1.2.1 Performance evaluation of retrofitted building 1 retrofitted with
additional shear wall
The revised well defined capacity curves have been found based on the retrofit building
in two orthogonal directions, which are shown in the following Figures 8.8and 8.9.
Capacity of the building in the X-direction is slightly more because structural capacity
of the members in X-direction is slightly more than that in the Y-direction.
Fig 6.8 Base shear vs Displacement curve in X Direction for retrofitted building 1 (with additional shear wall ) at Maximum EQ Condition.
104
Fig 6.9 Base shear vs Displacement curve in Y Direction for retrofitted building 1(with additional shear wall ) at Maximum EQ Condition. The revised capacity curves have been converted into capacity spectrums as per
pushover analysis using ETABS 9.7.4 based on the retrofit proposed in the above fig. It
is also found that the capacity curves now in both directions shows performance point
at E=1.25 for 'ME' which did not intersect the 5% elastic demand curve before
retrofitting.
Fig 6.10 Capacity Spectrum curve in X Direction for retrofitted building 1 (with additional shear wall ) at Maximum EQ Condition.
105
Fig 6.11 Capacity Spectrum curve in Y Direction for retrofitted building 1(with additional shear wall ) at Maximum EQ Condition. For the retrofitted building 1(with additional shear wall) and for three Earthquake
conditions (i.e. Serviceability Earthquake,Designearthquake,Maximum Earthquake)
different values of base shear,displacement,spectralacceleration, effective time period,
effective Damping values at Performance point for X direction are summarised as
follows
Table 6.4 Different parameter’s values for different earthquake conditions for retrofitted building 1 retrofitted with additional shear wall. Type of Building
Parameters Serviceability Earthquake, E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19,Cv =0.18
CA =0.22, Cv =0.32
CA =0.265,Cv =0.38
6 Storied Building
(Retrofitted with
additional shear wall)
(V,D)= (637.882,1.568) (928.715,2.787) (1036.919,3.33)
(Sa,Sd)= (0.181,1.257) (0.274,2.275) (0.311,2.737)
Teff, Beff (0.823,0.087) (0.914,0.114) (0.949,0.123)
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6.1.2.2 Hinge formation status of the retrofitted building 1 retrofitted with
additional shear wall
At performance point hinge formation for different types of earthquake for X direction has been shown in the figure below
Table 6.5 Hinge formation status at different earthquake conditions for the retrofitted building 1 retrofitted with additional shear wall. A-B B-IO IO-
LS LS-CP CP-
C C-D D-E >E Total
Serviceability EQ 694 126 40 20 0 0 0 0 880
Design EQ 680 135 42 23 0 0 0 0 880
Maximum EQ 666 144 46 22 2 0 0 0 880
Fig 6.12 Hinge state of retrofitted building 1 retrofitted with additional shear wall at the performance point in X-Direction at Maximum EQ.
107
6.1.2.3 Lateral Drift ratio of building 1 retrofitted with additional shear wall
Lateral drift ratio of building 1 retrofitted with additional shear wall is shown in the table below Table 6.6 Drift ratio in X direction for retrofitted building 1 retrofitted with the additional shear wall.
At Performance Point X-Direction (Retrofitted buildingwith additional shear wall )
Maximum total drift rati0 Maximum inelastic drift ratio 0.0023 Immediate Occupancy 0.016 Life Safety
6.2 Comparison of the performance evaluation of the retrofitted building with
unretrofitted building( for building 1)
Comparison of the performance evaluation of the retrofitted building with unretrofitted building( for building 1) is shown in the table below.
Table 6.7 Comparison of Different parameter’s values for different earthquake conditions for unretrofitted and retrofitted building. Type of Building
Parameters Serviceability Earthquake, E = 0.5
Serviceability Earthquake,E = 0.5
E = 1.25
CA =0.19,Cv =0.18
CA =0.22, Cv =0.32
CA =0.265,Cv =0.38
6 Storied Building
(Soft storey condition)
(V,D)= (446.13,2.322) (612.697,4.22) No performance
point found. (Sa,Sd)= (0.095,2.072) (0.135,3.878)
Teff, Beff, (1.477,0.114) (1.710,0.151) 6 Storied Building (Building
retrofitted with buttress wall and
column jacketing)
(V,D)= (554.473,2.144) (781.294,3.868) (875.287,4.694)
(Sa,Sd)= (0.123,1.793) (0.179,3.275) (0.205,3.997) Teff, Beff, (1.216,0.096) (1.362,0.127) (1.412,0.131)
6 Storied Building (Building
retrofitted with shear wall)
(V,D)= (637.88,1.568) (928.715,2.787) (1036.919,3.33)
(Sa,Sd)= (0.181,1.257) (0.274,2.275) (0.311,2.737)
Teff, Beff, (0.823,0.087) (0.914,0.114) (0.949,0.123)
From the table it is evident that, performance point is achived at lower displacement
values for rerofited building than the unretrofitted soft storey building.
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6.2.1 Comparison of hinge formation status of the retrofitted building with
unretrofitted building( for building 1)
At performance point hinge formation for different types of earthquake for X direction has been shown in the table below.
Table 6.8 Comparison of Base shear and Hinge formation at performance point and number of hinges developed up to performance point for X direction for Design EQ.
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Soft Storey Frame 613 683 144 64 30 0 1 0 0 922
Retrofitted Building (with buttress wall
and column jacketing)
781 704 157 63 30 0 0 0 0 954
Retrofitted Building (with shear wall)
929 680 135 42 23 0 0 0 0 880
Table 6.9 Comparison of Base shear and Hinge formation at performance point and number of hinges developed up to performance point for X direction for Maximum EQ.
In-fill Condition of Frame
Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Soft Storey Frame No performance point found.Building totally collapses before reaching the performance point.
Retrofitted Building (with buttress wall
and column jacketing)
875 699 155 64 35 1 0 0 0 954
Retrofitted Building (with shear wall)
1037 666 144 46 22 2 0 0 0 880
From the above table it is evident that hinges formed in the retrofitted building for
design EQ condition do not cross the life safety range,and for maximum EQ it does not
cross the collapse prevention range.
109
6.2.2 Comparison of lateral drift ratios of the retrofitted building with unretrofitted
Building ( for building 1)
According to ATC-40,1996 deformation limits for various performance level are as follows
Table 6.10 Deformation limits for various performance level (ATC-40, 1996) Performance Level Inter storey Drift Limit Immediate
Occupancy Damage Control Life Safety Structural
Stability Maximum total drift Δ/H *
0.01 0.01-0.02 0.02 0.33*(Vi/Pi)
Maximum inelastic drift, Δin/H *
0.005 0.005-0.015 No limit No limit
* Δ= Storey displacement, Δin = Inelastic storey displacement and H= Storey height,Vi=Total calculated shear force in storey I and Pi=Total gravity load
Table 6.11 Comparison of Performance between unretrofitted and retrofitted building in terms of lateral drift (for building 1)
At Performance Point X-Direction(Soft storey)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0038 Immediate Occupancy 0.025 Structural Stability
At Performance Point X-Direction(Retrofitted Building with buttress wall and column jacketing)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0027 Immediate Occupancy 0.019 Life Safety At Performance Point
X-Direction(Retrofitted Building with shear wall)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0028 Immediate Occupancy 0.016 Life Safety From the above table it is evident that lateral drift ratios for design EQ condition do
not cross the life safety range,and for maximum EQ it does not cross the collapse
prevention range.
So our expected performance objective is achieved through retrofitting.
110
6.3 Remedial Measures for retrofitting of the Building 2
Results of the performance evaluation from the finite element models with different retrofitting methods are discussed below .
6.3.1 Structural retrofitting of the building 2 using column jacketing
Building is a 6-storied regular shaped building. It is found from capacity spectrum
curves it is not fit for maximum earthquake i.e. for "ME" at E=1.25. Whole building
collapses before meeting the performance point.Considering maximum earthquake the
structural members need to be retrofitted. However, to do the retrofit works some trials
have been given using column jacketing method at Grid intersection point-
B2,B4,C2,C4,F2,F3,G2,G3. Initially the column sizes were 12x15 inch. As
defeciencies were found in Y direction some colums needed to increase in sizes by
jacketing with re-bar in the Y directions. Finally the column sizes were 12x22 inch.
These modifications are shown in Figure 6.13 below which is modified plan of the
building.
Fig 6.13 Plan view of the retrofitted building 2 retrofitted by column jacketing.
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6.3.1.1 Performance evaluation of retrofitted building 2 retrofitted with column
jacketing
The revised well defined capacity curves have been found based on the retrofit building
in two orthogonal directions, which are shown in the following Figures 6.14 and 6.15.
Capacity of the building in the X-direction is slightly more because structural capacity
of the members in X-direction is slightly more than that in the Y-direction.
Fig 6.14 Base shear vs Displacement curve in X Direction for retrofitted building 2 (with column jacketing) at Maximum EQ Condition.
Fig 6.15 Base shear vs Displacement curve in Y Direction for retrofitted Building 2(with column jacketing) at Maximum EQ Condition.
112
The revised capacity curves have been converted into capacity spectrums as per
pushover analysis using ETABS 9.7.4 based on the retrofit proposed in the above fig. It
is also found that the capacity curves now in both directions shows performance point
at E=1.25 for 'ME' which did not intersect the 5% elastic demand curve before
retrofitting.
Fig 6.16 Capacity Spectrum curve in X Direction for retrofitted building 2 (with column Jacketing) at Maximum EQ Condition.
Fig 6.17 Capacity Spectrum curve in Y Direction for retrofitted building 2 (with column jacketing) at Maximum EQ Condition.
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For the retrofitted building 2(with column jacketing) and for three Earthquake
conditions (i.e. Serviceability Earthquake, Design earthquake, Maximum Earthquake)
different values of base shear, displacement, Spectral acceleration, Effective Time
period, Effective Damping values at Performance point for Y direction are summarized
as follows
Table 6.12 Different parameter’s values for different earthquake conditions for the retrofitted building 2 retrofitted with column jacketing. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Retrofitted with column
jacketing)
(V,D)= (451.721,1.660) (613.284,3.035) (686.315,3.656)
(Sa,Sd)= (0.162,1.309) (0.220,2.414) (0.246,2.914)
Teff, Beff, (0.887,0.096) (1.031,0.138) (1.096,0.157)
6.3.1.2 Hinge formation status of the retrofitted structure 2 retrofitted with
column jacketing
At performance point hinge formation for different types of earthquake for Y direction has been shown in the figure below
Table 6.13 Hinge formation for different earthquake conditions for the retrofitted building 2 retrofitted with column jacketing. A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ 1262 86 138 5 1 0 0 0 1492
Design EQ 1262 86 138 6 2 0 0 0 1492
Maximum EQ 1262 86 136 6 1 1 0 0 1492
114
Fig 6.18 Hinge state of retrofitted building 2 retrofitted with column jacketing at the performance point in Y-Direction at Maximum EQ. 6.3.1.3 Lateral drift ratio of the retrofitted building 2 retrofitted with column
Jacketing
Lateral drift ratio of the retrofitted building 2 retrofitted with column jacketing is shown in the table below. Table 6.14 Drift ratio in Y direction for retrofitted building with column jacketing
At Performance Point Y-Direction (Building retrofitted with column jacketing)
Maximum total drift rati0 Maximum inelastic drift ratio 0.0010 Immediate Occupancy 0.0068 Damage Control
6.3.2 Structural retrofitting of the building 2 using column jacketing and buttress
wall
Building is a 6-storied regular shaped building. It is found from capacity spectrum
curves it is not fit for maximum earthquake i.e. for "ME" at E=1.25. Whole building
collapses before meeting the performance point.Considering maximum earthquake the
structural members need to be retrofitted. However, to do the retrofit works another
option such as column jacketing with buttress wall will be trialed this time as only
column jacketing method did not give satisfactory performance result.Additional
buttress wall in four corners at grid intersections point-A6,A1,H1,H5 along with
retrofitted columns at grid intersection point-B2,B4,C2,C4,F2,F3,G2,G3 are placed.
115
Initially the column sizes were 12x15 inch. As defeciencies were found in Y direction
some colums needed to increase in sizes by jacketing with re-bar in the Y directions.
Finally the column sizes were 12x20 inch. The thickness of the buttress wall is 8 inch
and it is placed upto 2nd floor.These modifications are shown in Figure 6.19 below.
Fig 6.19 Plan view of the retrofitted building 2 retrofitted by column jacketing and buttress wall. 6.3.2.1 Performance evaluation of retrofitted building 2 retrofitted with column
jacketing and buttress wall
The revised well defined capacity curves have been found based on the retrofit building
in two orthogonal directions, which are shown in the following Figures 6.14 and 6.15.
Capacity of the building in the X-direction is slightly more because structural capacity
of the members in X-direction is slightly more than that in the Y-direction.
Fig 6.20 Base shear vs Displacement curve in X Direction for retrofitted Building 2 (with column jacketing and buttress wall) at Maximum EQ Condition.
116
Fig 6.21 Base shear vs Displacement curve in Y Direction for retrofitted Building 2 (with column jacketing and buttress wall) at Maximum EQ Condition. The revised capacity curves have been converted into capacity spectrums as per
pushover analysis using ETABS 9.7.4 based on the retrofit proposed in the above fig. It
is also found that the capacity curves now in both directions shows performance point
at E=1.25 for 'ME' which did not intersect the 5% elastic demand curve before
retrofitting.
Fig 6.22 Capacity Spectrum curve in X Direction for retrofitted building 2 (with column Jacketing and buttress wall) at Maximum EQ Condition.
117
Fig 6.23 Capacity Spectrum curve in Y Direction for retrofitted building 2 (with column jacketing and buttress wall) at Maximum EQ Condition. For the retrofitted building 2 (with column jacketing) and for three Earthquake
conditions (i.e. Serviceability Earthquake,Designearthquake,Maximum Earthquake)
different values of base shear,displacement,Spectralacceleration,Effective Time period,
Effective Damping values at Performance point for Y direction are summarised as
follows
Table 6.15 Different parameter’s values for different earthquake conditions for the retrofitted building 2 retrofitted with column jacketing and buttress wall. Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Retrofitted with column jacketing and buttress wall)
(V,D)= (480.08,1.584) (652.91,2.89) (730.497,3.477)
(Sa,Sd)= (0.176,1.239) (0.241,2.275) (0.270,2.740)
Teff, Beff, (0.827,0.092) (0.953,0.131) (1.010,0.148)
118
6.3.2.2 Hinge formation status of the retrofitted structure 2 retrofitted with
Buttress wall and column jacketing
At performance point hinge formation for different types of earthquake for Y direction has been shown in the figure below
Table 6.16 Hinge formation for different earthquake conditions for the retrofitted building 2 retrofitted with column jacketing and buttress wall.
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability EQ 1250 140 102 0 0 0 0 0 1492
Design EQ 1250 119 120 3 0 0 0 0 1492
Maximum EQ 1250 119 119 4 1 0 0 0 1492
Fig 6.24 Hinge state of retrofitted building 2 retrofitted with column jacketing and buttress wall at the performance point in Y-Direction at Maximum EQ.
119
6.3.2.3 Lateral drift ratio of the retrofitted building retrofitted with column
jacketing and buttress wall
Lateral drift ratio of the retrofitted building retrofitted with column jacketing and buttress wall is shown in the table below. Table 6.17 Drift ratio in Y direction for retrofitted building 2 retrofitted with column jacketing and buttress wall.
At Performance Point Y-Direction (Building retrofitted with column jacketing and buttress wall)
Maximum total drift rati0 Maximum inelastic drift ratio 0.0009 Immediate Occupancy 0.0068 Damage Control
6.3.3 Structural retrofitting of the building 2 using column jacketing and shear
wall
Building is a 6-storied regular shaped building. It is found from capacity spectrum
curves it is not fit for maximum earthquake i.e. for "ME" at E=1.25. Whole building
collapses before meeting the performance point.Considering maximum earthquake the
structural members need to be retrofitted. However, to do the retrofit works another
option such as column jacketing with additional shear wall will be trialed this time as
only column jacketing method did not give satisfactory performance result.Additional
shear wall along grid lines-AandH along with retrofitted columns at grid intersection
point-B2,B4,C2,C4,F2,F3,G2,G3 are placed. Initially the column sizes were 12x15
inch. As defeciencies were found in Y direction some colums needed to increase in
sizes by jacketing with re-bar in the Y directions. Finally the column sizes were 12x20
inch. The thickness of the shear wall is 10 inch and it is placed upto 3rd floor.These
modifications are shown in Figure 6.25 below.
Fig 6.25 Plan view of the retrofitted building 2 retrofitted by column jacketing and shear wall.
120
6.3.3.1 Performance evaluation of retrofitted building 2 retrofitted with column
jacketing and buttress wall
The revised well defined capacity curves have been found based on the retrofit building
in two orthogonal directions, which are shown in the following Figures 6.20 and 6.21.
Capacity of the building in the X-direction is slightly more because structural capacity
of the members in X-direction is slightly more than that in the Y-direction.
Fig 6.26 Base shear vs Displacement curve in X Direction for retrofitted Building 2(with column jacketing and shear wall) at Maximum EQ Condition.
Fig 6.27 Base shear vs Displacement curve in Y Direction for retrofitted Building 2 (with column jacketing and shear wall) at Maximum EQ Condition.
121
The revised capacity curves have been converted into capacity spectrums as per
pushover analysis using ETABS 9.7.4 based on the retrofit proposed in the above fig. It
is also found that the capacity curves now in both directions shows performance point
at E=1.25 for 'ME' which did not intersect the 5% elastic demand curve before
retrofitting.
Fig 6.28 Capacity Spectrum curve in X Direction for retrofitted building 2 (with column Jacketing and shear wall) at Maximum EQ Condition.
Fig 6.29 Capacity Spectrum curve in Y Direction for retrofitted building 2 (with column jacketing and buttress wall) at Maximum EQ Condition.
122
For the retrofitted building 2 (with column jacketing and shear wall) and for three
Earthquake conditions (i.e. Serviceability Earthquake,Designearthquake,Maximum
Earthquake) different values of base shear,displacement,Spectralacceleration,Effective
Time period, Effective Damping values at Performance point for Y direction are
summarised as follows
Table 6.18 Different parameter’s values for different earthquake conditions for the retrofitted building 2 retrofitted with column jacketing and shear wall . Type of Building
Parameters Serviceability Earthquake,E = 0.5
Design Earthquake, E =1.0
Maximum Earthquake, E = 1.25
CA =0.19, Cv =0.18
CA =0.22, Cv =0.32
CA =0.265, Cv =0.38
6 Storied Building
(Retrofitted with column jacketing and buttress wall)
(V,D)= (677.234,1.322) (1062.763,2.339) (1256.007,2.848)
(Sa,Sd)= (0.275,0.960) (0.434,1.678) (0.513,2.037)
Teff, Beff, (0.564,0.057) (0.599,0.069) (0.617,0.075)
6.3.3.2 Hinge formation status of the retrofitted building 2 retrofitted with shear
wall and column jacketing
At performance point hinge formation for different types of earthquake for Y direction has been shown in the figure below.
Table 6.19 Hinge formation status of the retrofitted building 2 retrofitted with shear wall and column jacketing
A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Serviceability
EQ
1150 177 83 10 0 0 0 0 1420
Design EQ 1116 125 157 22 0 0 0 0 1420
Maximum EQ 1116 125 157 21 1 0 0 0 1420
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Fig 6.30 Hinge state of retrofitted building 2 retrofitted with column jacketing and shear wall at the performance point in Y-Direction at Maximum EQ. 6.3.3.3 Lateral drift ratio of the retrofitted building 2 retrofitted with column
jacketing and shear wall
Lateral drift ratio of the retrofitted building 2 retrofitted with column jacketing and shear wall is shown in the following table Table 6.20 Drift ratio in Y direction for retrofitted building 2 with column jacketing and shear wall
At Performance Point Y-Direction (Building retrofitted with column jacketing and buttress wall) Maximum total drift rati0 Maximum inelastic drift ratio
0.0005 Immediate Occupancy
0.0060 Damage Control
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6.4 Comparison of the performance evaluation of the retrofitted building with
unretrofitted building(for building 2)
Comparison of the performance evaluation of the retrofitted building with unretrofitted building is shown in the table below. Table 6.21 Comparison of different parameter’s values for different earthquake conditions for unretrofitted and retrofitted building 2.
Type of Building
Parameters Serviceability Earthquake, E = 0.5
Serviceability Earthquake,E = 0.5
E = 1.25
CA =0.19,Cv =0.18
CA =0.22, Cv =0.32
CA =0.265,Cv =0.38
6 Storied Building (Without
Retrofitting)
(V,D)= (432.33,1.776) (588.357,3.203) No performance
point found. (Sa,Sd)= (0.152,1.408) (0.208,2.574)
Teff, Beff, (0.948,0.095) (1.101,0.139)
6 Storied Building (Building
retrofitted with column
jacketing)
(V,D)= (451.721,1.660) (613.284,3.035) (686.315,3.656)
(Sa,Sd)= (0.162,1.309) (0.220,2.414) (0.246,2.914)
Teff, Beff, (0.887,0.096) (1.031,0.138) (1.096,0.157)
6 Storied Building (Building
retrofitted with buttress wall and
column jacketing)
(V,D)= (480.08,1.584) (652.91,2.89) (730.497,3.477)
(Sa,Sd)= (0.176,1.239) (0.241,2.275) (0.270,2.740)
Teff, Beff, (0.827,0.092) (0.953,0.131) (1.010,0.148)
6 Storied Building (Building
retrofitted with shear wall and
column jacketing)
(V,D)= (677.234,1.322) (1062.763,2.339) (1256.007,2.848)
(Sa,Sd)= (0.275,0.960) (0.434,1.678) (0.513,2.037)
Teff, Beff, (0.564,0.057) (0.599,0.069) (0.617,0.075)
From the table it is evident that, performance point is achived at lower displacement
values for retrofitted building which was not found for unretrofitted building.
125
6.4.1 Comparison of hinge formation status of the retrofitted building with
unretrofitted building (for building 2)
At performance point hinge formation for different types of earthquake for X direction
has been shown in the table below
Table 6.22 Comparison of Base shear and hinge formation at performance point and number of hinges developed up to performance point for Y direction for Design EQ
Type of Building Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO 10-LS LS-CP CP-C C-D D-E >E Total
Unretrofitted Building
588 830 65 133 4 0 1 0 1 1034
Retrofitted Building
(with column
jacketing)
613 1262 86 138 6 2 0 0 0 1492
Retrofitted Building
(with buttress wall
and column
jacketing)
653 1250 119 120 3 0 0 0 0 1492
Retrofitted Building
(with shear wall
and column
jacketing)
1068 1116 125 157 22 0 0 0 0 1420
Table 6.23 Comparison of Base shear and hinge formation at performance point and number of hinges developed up to performance point for Y direction for Maximum EQ
Type of Building Base Shear inKN
Status of Hinge Formation at different Performance Stages
A-B B-IO I0-LS LS-CP CP-C C-D D-E >E Total
Unretrofitted Building
No performance point found. Building totally collapses before reaching the performance point.
Retrofitted Building (with column
jacketing)
686 1262 86 136 6 1 1 0 0 1492
Retrofitted Building (with buttress wall
and column jacketing)
730 1250 119 119 4 1 0 0 0 1492
Retrofitted Building (with shear wall and column jacketing)
1263 1116 125 157 21 1 0 0 0 1420
126
From the above table it is evident that hinges formed in the retrofitted building for
design EQ condition do not cross the life safety range,and for maximum EQ it does not
cross the collapse prevention range.
6.4.2 Comparison of lateral drift ratios of the retrofitted building with unretrofitted
Building
According to ATC-40,1996 deformation limits for various performance level are as follows Table 6.24 Deformation limits for various performance level (ATC-40, 1996) Performance Level Inter storey Drift Limit Immediate
Occupancy Damage Control Life Safety Structural
Stability Maximum total drift Δ/H * 0.01 0.01-0.02 0.02 0.33*(Vi/Pi)
Maximum inelastic drift, Δin/H *
0.005 0.005-0.015 No limit No limit
* Δ= Storey displacement, Δin = Inelastic storey displacement and H= Storey height,Vi=Total calculated shear force in storey I and Pi=Total gravity load
Table 6.25 Comparison of Performance between unretrofitted and retrofitted building 2 in terms of lateral drift.
Y-Direction (Unretrofitted Building)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0011 Immediate Occupancy 0.0070 Damage Control Y-Direction(Retrofitted Building with column jacketing)
Maximum total drift rati0 Maximum inelastic drift ratio 0.0010 Immediate Occupancy 0.0068 Damage Control
Y-Direction(Retrofitted Building with buttress wall and column jacketing)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0009 Immediate Occupancy 0.0065 Damage Control Y-Direction(Retrofitted Building with shear wall and column jacketing)
Maximum total drift rati0 Maximum inelastic drift ratio
0.0005 Immediate Occupancy 0.0060 Damage Control From the above table it is evident that lateral drift ratios for design EQ condition do
not cross the life safety range,and for maximum EQ it does not cross the collapse
prevention range.
So our expected performance objective is achieved also for building 2 through retrofitting.
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CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 General
For understanding the performance of building under different seismic conditions
pushover analysis has now been considered as an effective tool which is a vast
nonlinear analysis method. There are some desired levels of seismic performance when
the building is subjected to specific levels of seismic ground motion. Acceptable
performance is measured by the level of structural and/or nonstructural damage
expected from the earthquake excitation.
The main goal of the study was to evaluate the adequacy and seismic performance of
conventionally designed typical bare frame, fully in-filled, soft ground storey condition
of buildings with the help of pushover curve (capacity curve) under earthquake
loading. Another goal of the study was to identify the deficiencies in the seismic
performance of the building and to see whether any performance improvement is
required or not after the pushover analysis, by using a finite element software. Two
types of building were analyzed in this thesis. Building 1 is an irregular shaped office
building and building 2 is a regular shaped residential building.Bare,in-filled frame and
soft storey condition of the buildings were considered and their seismic performance
was evaluated in a detailed way. Two specific performance criteria were selected (i.e.
Life safety, collapse prevention) for two specific earthquake condition(i.e. Design
Earthquake, Maximum earthquake).In order to gain those performance objectives some
retrofitting measures were applied and the performance of the particular building was
evaluated and was found satisfactory.
7.2 Findings of The Study
Within the scope of this study the main conclusions can be summarized as follows
(i) For building 1 Base shear developed at performance point is 20% lower for
bare frame condition than that of full in-filled frame condition and 12.1% lower
than soft storey frame condition because of less mass in stories due to absence
of infill. For building 2 base shear developed at performance point is 12.7%
lower for bare frame condition than that of full in-filled frame condition.
128
(ii) For both the buildings (1 and 2) natural period (T) is less than that of bare frame
which means masonry infill contributes for stiffness of the building.
(iii) Seismic performance of full in-filled frame condition is better than that of bare
frame condition. Capacity curve of both the buildings meets the demand curve at
lower displacement value. Lateral drift ratios are 4 % less than that of bare frame
condition of building 1.Performance point of the building stands within immediate
occupancy level.For realistic modelling, infill has been considered and better
performance is found than bare frame.
(iv) The addition to infill in the upper stories leaving the ground floor open makes soft
storey case which can be fatal for earthquake. The seismic performance of
buildings having soft ground stories are very poor during earthquake shaking. In
most of the cases building collapses due to failure of ground storey columns before
reaching performance point. As open ground storey is unavoidable considering the
functional requirement, alternative measures need to be adopted for this specific
situation for reduction of vulnerability and achieve acceptable performances. The
performances can be improved through improved systems which would improve
stiffness of the ground floor and reduce the otherwise excessive ductility demand
of the soft storey.
(v) For the three types of buildings considered (bare, full in-filled, soft ground
storey),roof displacement is highest for bare frame and ground floor displacement
is highest for soft storey.
(vi) Top and bottom corners of the column are most vulnerable point since strut action
of infill imposes a concentrated load at these joints. So special detailing
considerations should be adopted.
(vii) The performance evaluation of the case study buildings (soft storey condition for
building 1 and full infilled condition for building 2) indicate that it does not show
any performance point at Maximum Earthquake (ME), that means it totally
collapses and at Design Earthquake (DE) condition, hinges formed crosses the
collapse prevention level. So, the building is retrofitted with some available
retrofitting schemes such as column jacketing with buttress wall and insertion of
shear wall.Evaluating the performance after retrofitting it is found that the
specified building satisfies the "Life safety" performance criteria for the Design
Earthquake (DE) and ''Collapse prevention (CP)" criteria for Maximum Earthquake
(ME).
129
(viii) Among the considered retrofitting measures "insertion of shear wall" shows better
performance over "column jacketing with buttress wall" in terms of lateral inelastic
drift ratio and number of hinges formed for building 1. For building 2 retrofitting
measure “shear wall with column jacketing” shows better performance over
"column jacketing with buttress wall" and "column jacketing” in terms of lateral
inelastic drift ratio and no of hinges formed. But "insertion of shear wall" creates
some problems too such as restricted parking facilities in the ground floor.
7.3 Recommendations for Future Studies
Considering the limitations, the following recommendations for further study can be
made from the present study
(i) The thesis concentrated its study mainly on a medium rise building.
Performance study on high rise buildings can be studied further.
(ii) The effect of type of foundation and soil on earthquake response of a building
can be investigated.
(iii) Verification of the proposed remedial measures can be done by a properly
conducted shake table test of scale models.
(iv) This thesis is concentrated only on the reinforced concrete building. Further
analysis can be done on steel building.
(v) Connection detailing between the old structural member and strengthened
retrofitted structural members can be investigated.
130
References
American Concrete Institute-318 (2005), Building Code Requirements for Structural Concrete, USA. Applied Technology Council (1996), California Seismic Safety Commission, Seismic Evaluation and Retrofit of Concrete Buildings-Report No. SSC 96-01 (ATC-40), California, USA. Bangladesh National Building Code (BNBC 2006), Housing and Building Research Institute, Bangladesh Standard and Testing Institution , Dhaka, Bangladesh. Computers and Buildings, Inc.(1995), Integrated Design and Analysis software for Building System-ETABS (Linear and Nonlinear, Static and Dynamic ). Berkeley, California, USA. Federal Emergency Management Agency (2000), Pre-standard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356), Washington, D.C., USA.
International Building Code-2000 (IBC-2000), International Code Council Inc., USA.
Abd-Elhamed, A., and Mahmoud, S. (2017). “Nonlinear static analysis of reinforced concrete framed buildings-A case study on Cairo earthquake.” Journal of Engineering Research, 4(4). Akshara, S. P. (2015). “Performance based seismic evaluation of multi-storeyed reinforced concrete buildings using pushover analysis.” 02(03), 6. Bertero, V., and Brokken, S. (1983). “Infills in seismic resistant building.” Journal of Structural Engineering, 109(6), 1337–1361. Bilgin, H. (2015). “Seismic performance evaluation of an existing school building in Turkey.” CHALLENGE, 1(4), 161–167. Borkar, S. S., and Pitale, N. H. (2017). “Seismic Evaluation and Retrofitting of Open Ground Storey.” International Journal of Science Technology & Engineering, 3(10), 10. Giannopoulos, P. I. (2009). “Seismic Assessment of RC Building according to FEMA 356 and Eurocode 8.” 16th Conference on Concrete, TEE, ETEK, 21–23. Gupta, N., Dhiman, P., and Gupta, A. K. (2015). “Case Study: Retrofitting of an Existing Residential Building by Using Shear Wall.” 2(7), 5.
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APPENDIX A
Conversion to ADRS Spectra
(i) Response Spectrum Conversion
Capacity Spectrum method requires plotting the capacity curve in spectral acceleration
and spectral displacement domain. This representation of spectral quantities is known
as Acceleration- Displacement-Response-Spectra in brief ADRS, which was introduced
by Mahaney et al., (1993). Spectral quantities like spectral acceleration, spectral
displacement and spectral velocity is related to each other to a specific structural period
T. Building code usually provide response spectrum in spectral acceleration vs. period
format which is the conventional format.
Each point on the curve defined in the Fig. A.1 is related to spectral displacement by
mathematical relation, Sd = 1
4𝜋2Sa T2.Converting with this relation response
spectrum in ADRS format may be obtained.
Fig. A1 Response spectrum in traditional format ( Sa vs. T)
Fig. A2 Response spectrum in ADRS format ( Sa vs. Sa)
134
Any line from the origin of the ADRS format represent a constant period T, which is
related to spectral acceleration and spectral displacement by the mathematical relation,
T=2π√𝑆𝑎
𝑆𝑑
(ii) Capacity Spectrum Conversion
Capacity spectrum is a simple representation of capacity curve in ADRS domain. A
capacity curve is the representation of Base Shear to Roof displacement. In order to
develop the capacity spectrum from a capacity curve it is necessary to do a point by
point conversion to first mode spectral coordinates.
Fig. A3 A typical capacity curve
Any point corresponding values of base shear, V, and roof deflection, A, may be converted to the corresponding point of spectral acceleration, Sai, and spectral
displacement, Sdion the capacity spectrum using relation,
Modal participation factor, PFi is calculated using equation,
Modal mass coefficient for the first mode, α1, is calculated using equation,
135
Where: PF1 = Modal participation factor for the first natural mode. α1 = Modal mass coefficient for the first natural mode Φ1,Roof =Roof level amplitude of the first mode. Wi/g = Mass assigned to level i
φi,1 = Amplitude of mode 1 at level i N = Level N, the level which is the uppermost in the main portion of the structure V = Base shear W = Building dead weight plus likely live loads ∆Roof= Roof displacement Sa= Spectral acceleration Sd = Spectral displacement
Fig. A4 Capacity Spectrum
Fig. A.4 shows a typical capacity spectrum converted from capacity curve of Fig. C.3
of a hypothetical structure. It is seen in the capacity spectrum that up to some
displacement corresponding to point A, the period is constant T1. That is the structure is
behaving elastically. As the structure deflects more to point B, it goes to inelastic
deformation and its period lengthens to T2
When the capacity curve is plotted in Sa vs. Sd coordinates, radial lines drawn from the
origin of the plot through the curve at various spectral displacements have a slope (ω΄),
where, ω΄is the radial frequency of the effective (or secant) first-mode response of the
structure if pushed by an earthquake to that spectral displacement.
Using the relationship T΄=2𝜋
ω΄, it is possible to calculate, for each of these radial lines,
the effective period of the structure if it is pushed to a given spectral displacements.
Fig. A.5 is a capacity spectrum plot obtained from the capacity curve of a hypothetical
structure shown in Fig. 3.1 and plotted with the effective modal periods shown.
136
Fig. A5 Typical capacity spectrum of a hypothetical structure.
The particular structure represented by this plot would have an elastic period of
approximately 1/2second. As it is pushed progressively further by stronger ground
motion, this period lengthens. The building represented in Fig. 3.1 and Fig. A.5 would
experience collapse before having its stiffness degraded enough to produce an effective
period of 2 seconds.
The capacity of a particular building and the demand imposed upon it by a given
earthquake motion are not independent. One source of this mutual dependence is
evident from the capacity curve itself. As the demand increases, the structure eventually
yields and, as its stiffness decreases, its period lengthens. Conversion of the capacity
curve to spectral ordinates (ADRS) makes this concept easier to visualize. Since the
seismic accelerations depend on period, demand also changes as the structure yields.
Another source of mutual dependence between capacity and demand is effective
damping. As a building yield in response to seismic demand it dissipates energy with
hysteretic damping. Buildings that have large, stable hysteresis loops during cyclic
yielding dissipate more energy than those with pinched loops caused by degradation of
strength and stiffness. Since the energy that is dissipated need not be stored in the
structure, the effective damping diminishes displacement demand.
a) Performance Point
The capacity spectrum method initially characterizes seismic demand using an elastic
response spectrum. This spectrum is plotted in spectral ordinates (ADRS) format
showing the spectral acceleration as a function of spectral displacement. This format
allows the demand spectrum to be "overlaid" on the capacity spectrum for the building.
The intersection of the demand and capacity spectra, if located in the linear range of the
capacity, would define the actual displacement for the structure; however this is not
137
normally the case as most analyses include some inelastic nonlinear behavior. To find
the point where demand and capacity are equal, a point on the capacity spectrum need
to be selected as an initial estimate. Using the spectral acceleration and displacement
defined by this point, reduction factors may be calculated to apply to the 5% elastic
spectrum to account for the hysteretic energy dissipation, or effective damping,
associated with the specific point. If the reduced demand spectrum intersects the
capacity spectrum at or near the initial assumed point, then it is the solution for the
unique point where capacity equals demand. If the intersection is not reasonably close
to the initial point, then a new point somewhere between may be assumed and repeat
the process until
Fig. A6 Determination of performance point
a solution is reached. This is the performance point where the capacity of the structure
matches the demand or the specific earthquake.
Once the performance point has been determined, the acceptability of a rehabilitation
design to meet the project performance objectives can be judged by evaluating where the
performance points falls on the capacity curve. For the structure and earthquake
represented by the overlay indicated in Fig. A.6, the performance point occurs within the
central portion of the damage control performance range as shown in Fig. A.5, indicating
that for this earthquake this structure would have less damage than permitted for the Life
Safety level and more than would be permitted for the Immediate Occupancy level. With is
information, the performance objective and/or the effectiveness of the particular
rehabilitation strategy to achieve the project performance objectives can be judged.
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APPENDIX B
Table B-l Damage control and building performance levels (FEMA-356, 2000)
Target Building Performance Levels
Collapse Life Safety Immediate Operational
Prevention level Level Occupancy level Level
Overall Severe Moderate Light Very Light Damage General Little residual Some residual No permanent drift. No permanent
stiffness and strength and Structure drift. strength, but stiffness left in all substantially retains Structure load-bearing stories. Gravity- original strength substantially columns load- bearing and stiffness. retains original and walls elements function. Minor cracking of strength and function. Large No out-of-plane facades, partitions, stiffness. Minor permanent drifts. failure of walls or and ceilings as well cracking of Some exits tipping of parapets. as structural facades, blocked. In fills Some permanent elements. Elevators partitions, and and drift. Damage to can be restarted. ceilings as well unbraced partitions. Building Fire protection as structural parapets failed or may be beyond operable. elements. at incipient economical repair All systems failure. Building important to is near collapse. normal operation are functional.
Nonstructural Extensive Falling hazards Equipment and Negligible components damage mitigated but contents are damage occurs.
many generally secure, Power and architectural, but may not operate other utilities mechanical and due to mechanical as available, electrical systems failure or lack of possibly from are damaged. utilities. standby sources.
Comparison Significantly Somewhat more Less damage and Much less with more damage damage and lower risk. damage and
performance and greater slightly higher lower risk. intended for risk. risk.
buildings designed under
theNEHRP '' Provisions, for
the Design Earthquake
139
Table B-2 Structural performance levels and damagel,2,3 -Vertical Elements (FEMA-356, 2000)
Elements Structural Performance Levels
Type Collapse Prevention S-5 Life Safety S-3 Immediate Occupancy S-l
Primary Extensive cracking and hinge formation in ductile elements. Limited cracking and/or splice failure in some nqn-ductile columns. Severe damage in short columns.
Extensive damage to beams. Spalling of cover and shear cracking (<l/8" width) for ductile columns. Minor spalling in non-ductile columns. Joint cracks < 1/8" wide.
Minor hairline cracking. Limited yielding possible at a few locations. No crushing (strains below 0.003).
Secondary Extensive spalling in columns (limited shortening) and beams. Severe joint damage. Some reinforcing buckled.
Extensive cracking and hinge formation in ductile elements. Limited cracking and/or splice failure in some non ductile columns. Severe damage in short columns.
Minor spalling in non-ductile columns and beams. Flexural cracking in beams and columns. Shear cracking in joint width.
Drift 4% transient or permanent
2% transient; 1% permanent
1% transient; Negligible permanent
Steel Moment Frames
Primary Extensive distortion of beams and column panels. Many fractures at moment connections, but shear connections remain intact.
Hinges form. Local buckling of some beam elements. Severe joint distortion; isolated moment connection fractures, but shear connections remain intact. A few elements may experience partial fracture.
Minor or local yielding at a few places. No fractures. Minor buckling or observable permanent distortion of members.
Secondary Same as primary. Extensive distortion of beams and column panels. Many fractures at moment connections, but shear connections remain intact
Same as primary
Drift 5% transient or permanent
2.5% transient; 1% permanent
0.7% transient; negligible permanent
140
Table B-2 Structural performance levels and damagel,2,3 -Vertical Elements (FEMA-356, 2000) (Continued)
Elements
Structural Performance Levels
Type
Collapse Prevention
S-5 Life Safety S-3
Immediate
Occupancy S-l
Braced Steel Frames
Primary Extensive yielding and buckling of braces. Many
braces and their connections may fail.
Many braces yield or buckle but do not totally fail. Many
connections may fail
Minor yielding or buckling of
braces.
Secondary Same as primary. Same as primary. Same as primary.
Drift 2% transient or perjnanent 1.5% transient; 0.5% permanent 0.5% transient; negligible permanent
Concrete Walls Primary Major flexural and shear cracks and voids. Sliding at joints. Extensive crushing
and buckling of reinforcement. Failure
around openings. Severe boundary element damage. Coupling beams shattered and virtually disintegrated.
Some boundary element stress, including limited buckling of
reinforcement. Some sliding at joints. Damage around openings.
Some crushing and flexural cracking. Coupling beams: extensive shear and flexural cracks; some crushing, but
concrete generally remains in place.
Minor hairline cracking of
walls, <1/16" wide. Coupling
beams experience
cracking < 1/8" width.
Secondary Panels shattered and virtually disintegrated.
Major flexural and shear cracks. Sliding at joints. Extensive crushing, Failure around
openings. Severe boundary element damage. Coupling
beams shattered and virtually disintegrated.
Minor hairline cracking of walls. Some evidence of sliding at
construction joints. Coupling
beams experience cracks <l/8
width. Minor spalling
Urranfcrced Masonry Infill
Walls
Primary Extensive cracking and crushing; portions of face
course shed.
Extensive cracking and some crushing but wall remains in
place. No falling units. Extensive crushing and spalling of veneers
at corners of openings.
Minor (<l/8"width) cracking of
masonry infills and veneers.
Minor spalling in veneers at a few corner openings.
Secondary Extensive crushing and shattering; some walls
dislodge.
Same as primary Same as primary
Drift 0.6% transient or permanent
0.5% transient; 0.3% permanent'
0.1% transient; negligible permanent
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Table B-2 Structural performance levels and damagel,2,3-Vertical Elements (FEMA-356, 2000) (Continued)
Elements
Structural Performance Levels
Type
Collapse
Prevention S-5 Life Safety S-3
Immediate
Occupancy S-l Un-reinforced Masonry (Non infill) Walls
Primary Extensive cracking; face course and veneer may peel off. Noticeable in plane and out-of-plane offsets.
Extensive cracking. Noticeable in-plane offsets of masonry and minor out-of-plane offsets.
Minor (<I/8" width) cracking of veneers. Minor spalling in veneers at a few corner openings. No observable out-of-plane offsets.
Secondary Nonbearing panels dislodge.
Same as primary Same as primary
Drift 1% transient or permanent
0.6% transient; 0.6% permanent
0.3% transient; 0.3% permanent
Reinforced Masonry Walls
Primary Crushing; extensive cracking. Damage around openings and at corners. Some fallen units.
Extensive cracking (<l/4") distributed throughout wall. Some isolated crushing.
Minor(< 1/8" width) cracking. No out-of-plane offsets.
Secondary Panels shattered and virtually disintegrated.
Crushing; extensive cracking. Damage around openings and at corners; some fallen units.
Sameas primary
Drift 1.5% transient or permanent
0.6% transient; 0.6% permanent
0.2% transient; 0.2% permanent
Wood Stud Walls
Primary Connections loose. Nails partially withdrawn. Some splitting of members and panels. Veneers dislodged.
Moderate loosening of connections and minor splitting of members.
Distributed minor hairline cracking of gypsum and plaster veneers.
Secondary Sheathing sheared off. Let-in braces fractured and buckled. Framing split and fractured.
Connections loose. Nails partially withdrawn. Some splitting of members and panels.
Same as primary.
Drift 3% transient or permanent
2 % transient; 1 % permanent
1% transient; 0.25% permanent
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Table B-2 Structural performance levels and damagel,2,3-Vertical Elements (FEMA-356, 2000) (Continued)
Elements
Structural Performance Levels
Type
Collapse
Prevention
S-5 Life Safety S-3
Immediate
Occupancy S-l
Precast Concrete Connections
Primary Some connection failure but no
elements disclosed
Local crushing and spalling at connections, but no gross failure of
connections.
Minor working at connections; cracks
<1/16" width at connections.
Secondary Same as primary Some connection failures but no elements
dislodged.
Minor crushing and spalling at connections.
Foundations General Major settlement and tilting
Total settlements <6" and differential
settlements <1'2" in 30ft.
Minor settlement and negligible tilting.
1. Damage states indicated in this table are provided to allow an understanding of the severity of damage that may be sustained by various structural elements when present in structures meeting the definitions of the Structural Performance Levels. These damage states are not intended for use in post-earthquake evaluation of damage or for judging the safety of, or required level of repair to, a structure following an earthquake. 2. Drift values, differential settlements, crack widths, and similar quantities indicated in these tables arc not intended to be used as acceptance criteria for evaluating the acceptability of a rehabilitation design in accordance with the analysis procedures provided in this standard; rather, they are indicative of the range of drift that typical structures containing the indicated structural elements may undergo when responding within the various Structural Performance Levels. Drift control of a rehabilitated structure may often be governed by the requirements to protect nonstructural components. Acceptable levels of foundation settlement or movement are highly dependent on the construction of the superstructure. The values indicated are intended to be qualitative descriptions of the approximate behavior of structures meeting the indicated levels. 3. For limiting damage to frame elements of in filled frames, refer to the rows for concrete or steel frames.
143
Table B-3 Structural performance levels and damage1,2 - Horizontal elements (FEMA-356, 2000) Elements Structural Performance Levels
Collapse Prevention
S-5 Life Safety S-3
Immediate
Occupancy S-l
Metal Deck Diaphragms Large distortion with bucking of some units and tearing of many welds and seam attachments.
Some -localized failure of welded connections of deck to framing and between panels. Minor local bucking of deck.
Connections between deck units and framing intact. Minor distortions.
Wood Diaphragms Large permanent distortion with partial withdrawal of nails and extensive splitting of elements.
Some splitting at connections. Loosening of sheathing. Observable withdrawal of fasteners. Splitting and sheathing.
No observable loosening or withdrawal of fasteners. No splitting of sheathing or framing.
Concrete Diaphragms Extensive crushing and observable offset across many cracks.
Extensive cracking (<l/4"width). Local crushing and spalling.
Distributed hairline cracking. Some minor cracks of larger size (<l/8" width)
Precast Diaphragms Connections between units fail. Units shift relative to each other. Crushing and spalling at joints.
Extensive cracking (<l/4" width). Local crushing and spalling.
Some minor cracking along joints.
1. Damage states indicated in this table are provided to allow an understanding of the seventy of damage that may be sustained by various structural elements when present in structures meeting the definitions of the Structural Performance Levels. These damage states are not intended for use in post-earthquake evaluation of damage or for judging the safety of, or required level of repair to, a structure following an earthquake. 2. Drift values, differential settlements, crack widths, and similar quantities indicated in these tables are not intended to be used as acceptance criteria for evaluating the acceptability of a rehabilitation design in accordance with the analysis procedures provided in this standard; rather, they are indicative of the range of drift that typical structures containing the indicated structural elements may undergo when responding within the various Structural Performance Levels. Drifts control of a rehabilitated structure may often be governed by the requirements to protect nonstructural components. Acceptable levels of foundation settlement or movement are highly dependent on the construction of the superstructure. The values indicated are intended to be qualitative descriptions of the approximate behavior of structures meeting the indicated levels. Table B-4 Deformation Limits (ATC-40, 1996) Performance Level
Inter- story Drift Limit Immediate Occupancy
Damage Control
Life Safety Structural Stability
Maximum total drift 0.01 0.01 -0.02 0.02 0.33𝑉𝑖
𝑃𝑖
Maximum inelastic drift 0.005 0.005-0.015 No limit No limit
144
Table B-5 Examples of Possible Deformation-Controlled and Force-Controlled Actions(FEMA-356, 2000)
Component Deformation-
Controlled Action Force-Controlled Action
Moment Frames Beam Columns Moment (M) M Shear (V) Axial load (P), V Joints - V1 Shear Walls M, V P Braced Frames Braces P — Beams — P Columns — P Shear Link V P, M
Connections P, V, M3 P, V, M
Diaphragms M,V2 P, V, M
1. Shear may be a deformation-controlled action in steel moment frame connection 2. If the diaphragm carries lateral loads from vertical seismic resisting elements above the
diaphragm level, then M and V shall be considered force-controlled actions. 3. Axial, shear, and moment may be deformation-controlled actions for certain steel and wood
connections. Table B-6 Numerical Acceptance Criteria for Plastic Hinge Rotations in Reinforced Concrete Beams, in radians (ATC-40, 1996) Performance Level3
Primary Secondary Component Type IO LS SS LS SS 1. Beams Controlled by Flexure1
𝜌 − 𝜌′
𝜌𝑏𝑎𝑙
Transverse Reinforcement2 𝑉4
𝑏𝑤𝑑 √𝑓′𝑐
≤0.0 C ≤3 0.005 0.020 0.025 0.020 0.050 ≤0.0 C ≥6 0.005 0.010 0.020 0.020 0.040 ≥0.5 C ≤3 0.005 0.010 0.020 0.020 0.030 ≥0.5 C ≥6 0.005 0.005 0.015 0.015 0.020 ≤0.0 NC ≤3 0.005 0.010 0.020 0.020 0.030 ≤0.0 NC ≥6 0.000 0.005 0.010 0.010 0.015 ≥0.5 NC ≤3 0.005 0.010 0.010 0.010 0.015 ≥0.5 NC ≥6 0.000 0.005 0.005 0.005 0.010 2. Beams controlled by shear1 Stirrup spacing ≤ d/2 0.0 0.0 0.0 0.010 0.02 Stirrup spacing > d/2 0.0 0.0 0.0 0.005 0.01 3. Beams controlled by inadequate development or splicing along the span1 Stirrup spacing ≤d/2 0.0 0.0 0.0 0.010 0.02 Stirrup spacing > d/2 0.0 0.0 0.0 0.005 0.01 4. Beams controlled by inadequate embedment into beam-column joint1 0.0 0.01 0.015 0.02 0.03
145
1. When more than one of the conditions 1.2.3 and 4 occur for a given component, use the minimum appropriate numerical value from the table. 2. Under the heading "transverse reinforcement." 'C' and 'NC' are abbreviations for conforming and non-conforming details, respectively. A component is conforming if within the flexural plastic region: (1) closed stirrup are spaced at <d/3 and 2) for components of moderate and high ductility demand the strength provided by the stirrup (Vs) is at least three-fourths of the design shear. Otherwise,component is considered non-conforming. 3. Linear interpolation between values listed in the table is permitted.
IO = Immediate Occupancy LS = Life Safety SS = Structural Stability. 4. V = Design Shear Table B-7 Numerical Acceptance Criteria for Plastic Hinge Rotations in Reinforced ' Concrete Columns, in radians (ATC-40, 1996) Performance Level4
Primary Secondary Component Type IO LS SS LS SS 1. Columns Controlled by Flexure1
𝑃5
𝐴𝑔𝑓′𝑐
Transverse Reinforcement2
𝑉4
𝑏𝑤𝑑 √𝑓′𝑐
≤0.1 C ≤3 0.005 0.010 0.020 0.015 0.030 ≤0.1 C ≥6 0.005 0.010 0.015 0.010 0.025 ≥0.4 C ≤3 0.000 0.005 0.015 0.010 0.025 ≥0.4 C ≥6 0.000 0.005 0.010 0.010 0.015 ≤0.1 NC ≤3 0.005 0.005 0.010 0.005 0.015 ≤0.1 NC ≥6 0.005 0.005 0.005 0.005 0.005 ≥0.4 NC ≤3 0.000 0.000 0.005 0.000 0.005 ≥0.4 NC ≥6 0.000 0.000 0.000 0.000 0.000 2. Columns controlled by shear1"3 Hoop Spacing
≤ d/2 Or
𝑃5
𝐴𝑔𝑓′𝑐
0.000 0.000 0.000 0.01 0.015
Other cases 0.000 0.000 0.000 0.00 0.000 3. Columns controlled by inadequate development or splicing along the clear height1"3 Hoop spacing <d/2 0.0 0.0 0.0 0.01 0.02 Hoop spacing >d/2 0.0 0.0 0.0 0.005 0.01 4. Columns with axial loads exceeding 0.70 '** Conforming reinforcement over
the entire length 0.0 0.0 0.005 0.005 0.01
All other cases 0.0 0.0 0.0 0.0 0.0
1. When more than one of the conditions 1.2.3 and 4 occur for a given component, use the minimum appropriate numerical value from the table. See Chapter 9 for symbol definitions.
2. Under the heading "transverse reinforcement." "C' and 'NC' are abbreviations for conforming and non-conforming details, respectively. A component is conforming if within the flexural plastic hinge region: (1) closed hoops are spaced at <d/3 and 2) for components of moderate and high ductility demand the strength provided by the stirrup (Vs) is at least three-fourths of the design shear. Otherwise, the component is considered non-conforming
146
3. To qualify. (1) hoops must not be lap spliced in the cover concrete, and (2) hoops must have hooks embedded in the core or must have other details to ensure that hoops will be adequately anchored following spalling of cover concrete.
4. Linear interpolation between values listed in the table is permitted. IO = Immediate Occupancy, LS = Life Safety, SS = Structural Stability
5. P = Design axial load 6. V = Design shear force Table B-8 Numerical Acceptance Criteria for Chord Rotations for Reinforced Concrete Coupling Beams. (ATC-40, 1996) _ Performance Level
Primary Secondary
Component Type IO LS SS LS SS 1. Coupling beams controlled by flexure Longitudinal reinforcement and transverse reinforcement1
𝑉2
𝑏𝑤𝑑 √𝑓′𝑐
Conventional longitudinal reinforcement with conforming transverse reinforcement
≤3 0.006 0.015 0.025 0.025 0.040
Conventional longitudinal reinforcement with conforming transverse reinforcement
≤6 0.005 0.010 0.015 0.015 0.030
Conventional longitudinal reinforcement with non-conforming transverse
≤3 0.006 0.012 0.020 0.020 0.035
reinforcement Conventional longitudinal ≥6 0.005 0.008 0.010 0.010 0.025 Performance Level3
Primary Secondary
Component Type IO LS SS LS SS reinforcement with non-conforming transverse reinforcement
Diagonal reinforcement N/A 0.006 0.018 0.030 0.030 0.050 2. Coupling beams controlled by shear Longitudinal reinforcement and transverse reinforcement1
𝑉2
𝑏𝑤𝑑 √𝑓′𝑐
Conventional longitudinal reinforcement with conforming transverse reinforcement
≤3 0.006 0.012 0.015 0.015 0.024
Conventional longitudinal reinforcement with conforming transverse reinforcement
≥6 0.004 0.008 0.010 0.010 0.016
Conventional longitudinal reinforcement with non-conforming transverse reinforcement
≤3 0.006 0.008 0.010 0.010 0.020
Conventional longitudinal reinforcement with non-conforming transverse reinforcement
≥6 0.004 0.006 0.007 0.007 0.012
147
1. Conventional longitudinal steel consists of top and bottom steel parallel to the longitudinal axis of the beam. The requirements for conforming transverse reinforcement are: (1) closed stirrups are to be provided over the entire length of the beam at spacing not exceeding d/3: and (2) the strength provided by the stirrups (Vs) should be at least three-fourths of the design shear. 2. V = the design shear force on the coupling beam in pounds, bw = the web width of the beam, d = the effective depth of the beam and fc' = concrete compressive strength in psi. 3. Linear interpolation between values listed in the table is permitted. IO = Immediate occupancy LS = Life Safety SS = Structural Stability Table B-9 Numerical Acceptance Criteria for Reinforced Concrete Column Axial Hinge[FEMA-356, 2000] Plastic Deformation1
Primary Secondan Component Type IO LS SS LS SS 1. Braces in Tension (except EBF braces)
7∆T 9∆T 11 ∆T 11∆T 13 ∆T
∆T is the axial deformation at expected tensile yielding load. Table B-10 Numerical Acceptance Criteria for Total Shear Angle in Reinforced Concrete Beam-Columns Joints, in radians (ATC-40, 1996.) Performance Level4
Primary6 Secondary
Component Type IO LS ss LS ss 1. Interior joints
𝑃2
𝐴𝑔𝑓′𝑐
Transverse Reinforcement1
𝑉3
𝑉𝑛
≤0.1 C ≤1.2 0.0 0.0 0.0 0.020 0.030 ≤0.1 C ≥1.5 0.0 0.0 0.0 0.015 0.020 ≥0.4 C ≤1.2 0.0 0.0 0.0 0.015 0.025 ≥0.4 C ≥1.5 0.0 0.0 0.0 0.015 0.020 ≤0.1 NC ≤1.2 0.0 0.0 0.0 0.015 0.020 ≤0.1 NC ≥1.5 0.0 0.0 0.0 0.010 0.015 ≥0.4 NC ≤1.2 0.0 0.0 0.0 0.010 0.015 ≥0.4 NC ≥1.5 0.0 0.0 0.0 0.010 0.015 2. Other joints
𝑃2
𝐴𝑔𝑓′𝑐
Transverse Reinforcement1
𝑉3
𝑉𝑛
≤0.1 C ≤1.2 0.0 0.0 0.0 0.015 0.020 ≤0.1 C ≥1.5 0.0 0.0 0.0 0.010 0.015
148
≥0.4 C ≤1.2 0.0 0.0 0.0 0.015 0.020 ≥0.4 C ≥1.5 0.0 0.0 0.0 0.010 0.015 ≤0.1 NC ≤1.2 0.0 0.0 0.0 0.005 0.010 ≤0.1 NC ≥1.5 0.0 0.0 0.0 0.005 0.010 ≥0.4 NC ≤1.2 0.0 0.0 0.0 0.000 0.000 ≥0.4 NC ≥1.5 0.0 0.0 o.o . 0.000 0.000 1. Under the heading "transverse reinforcement." 'C' and :NC' are abbreviations for conforming
and non-conforming details, respectively. A joint is conforming if closed hoops are spaced at <hu/3 within the joint. Otherwise, the component is considered non-conforming. Also, to qualify as conforming details under condition 2, (1) closed hoops must not be lap spliced in the cover concrete, and (2) hoops must have hooks embedded in the core or must have other details to ensure that hoops will be adequately
anchored following spalling of cover concrete.
2. The ratio 𝑃2
𝐴𝑔𝑓′𝑐 is the ratio of the design axial force on the column above the joint to the
product Of the gross cross-sectional and lateral forces. 3. The ratio V/Vn is the ratio of the design shear force to the shear strength for the joint. 4. Linear interpolation between values listed in the table is permitted. IO = Immediate Occupancy LS = Life Safety SS = Structural Stability. 5. No inelastic deformation is permitted since joint yielding is not allowed in a conforming building. Table B-11 Numerical Acceptance Criteria for Total Shear Angle in Reinforced Concrete Beam-Columns Joints, in radians (ATC-40, 1996) Performance Level4
Primary Secondary Component Type IO LS SS LS SS 1. Slabs controlled by flexure and slab column connections'
𝑉𝑔2
𝑉𝑛𝑜
Continuity Reinforcement3
≤0.2 Yes 0.01 0.015 0.02 0.030 0.05 ≥0.4 Yes 0.00 0.000 0.00 0.030 0.04 ≤0.2 No 0.01 0.015 0.02 0.015 0.02 ≥0.4 No 0.00 0.000 0.00 0.000 0.00 2. Slabs controlled by inadequate development or splicing along the span1 0.00 0.00 0.000 0.01 0.02 3. Slabs controlled by inadequate embedment into slab-column joint1 0.01 0.01 0.015 0.02 0.03
1. When more than one of the conditions 1,2,3 and 4 occur tor a given component, use the minimum appropriate numerical value Irom the table
2. Vg = the gravity shear acting on the slab critical section as defined by AC1 318. Vo= the direct punching shear strength as defined by ACl 318.
149
3. Under the heading "Continuity reinforcement" assume 'Yes' where at least one of the main bottom bars in each direction is effectively Continuous through the column cage. Where tile slab is post- tensioned. assume "Yes" where at least one of the post-tensioning tendons in each direction passes through tile column cage. Otherwise, assume "No."
5. Linear interpolation between values listed in the table is permitted. IO = Immediate Occupancy
LS = Life Safety SS = Structural Stability Table B-12 Numerical Acceptance Criteria for Plastic Hinge Rotations in Reinforced Concrete Walls and Wall Segments Controlled by Flexure, in radians (ATC-40, 1996).
1. A,=the cross-sectional area of longitudinal reinforcement in tension. As ' = the cross-sectional area of longitudinal reinforcement in compression, f, = yield stress of longitudinal reinforcement ,P= axial force acting on the wall considering design load combinations. tu = wall web thickness, lw = wall length, and fc’:concrete compressive strength. 2. V = the design shear force acting on the wall, and other variables are as defined above. 3. The term "C" indicates the boimdary reinforcement effectively satisfies requirements of.ACI 318. The term "NC" indicates the boundary requirements do not satisfy requirements of ACl 318. 4. Linear interpolation between values listed in the table is permitted. 5. IO = Immediate Occupancy 6. LS = Life Salety 7. SS = Structural Stability. Table B-13 Seismic zone factor Z (BNBC, 1993) Zone 1 2 3
Z 0.075 0.15 0.25
Performance Level4
Primary6 Secondary
Component Type IO LS SS LS SS 1. Walls and wall segments controlled by flexure
(𝐴𝑠
− 𝐴𝑠′)𝑓𝑦
+ 𝑃′
𝑡𝑤𝑙𝑤𝑓′𝑐
𝑉2
𝑡𝑤𝑙𝑤 √𝑓′𝑐
Boundary Element
≤0.1 ≤3 C 0.005 0.010 0.015 0.015 0.020 ≤0.1 ≥6 C 0.004 0.008 0.010 0.010 0.015 ≥0.25 ≤3 C 0.003 0.006 0.009 0.009 0.012 ≥0.25 ≥6 C 0.001 0.003 0.005 0.005 0.010 ≤0.1 ≤3 NC 0.002 0.004 0.008 0.008 0.015 ≤0.1 ≥6 NC 0.002 0.004 0.006 0.006 0.010 ≥0.25 ≤3 NC 0.001 0.002 0.003 0.003 0.005 ≥0.25 ≥6 NC 0.001 0.001 0.002 0.002 0.004
150
Table B-14 Seismic source type as per ATC-40, 1996 Seismic Source Definition
Seismic Seismic Source Description Maximum Slip Rate, SR
Source Moment (mm/yr) Type Magnitude, M A Faults that are capable to produce M >7.0 SR >5.0
large magnitude events and which have a high rate of seismic activity B All faults other than types A and C Not applicable Not applicable
C Faults that are not capable to produce
M<6.5 SR<2.0
large magnitude events and which have a high rate of seismic activity
Table B-15 Seismic source factor (ATC-40, 1996) Seismic Source Type
Closed Distance to Known Seismic Source
<2km 5km 10km >15km
NA Nv NA Nv NA Nv NA Nv
A 1.5 2.0 1.2 1.6 1.0 1.2 1.0 1.0
B 1.3 1.6 1.0 1.2 1.0 1.0 1.0 1.0
C 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.The near-source factor may be used on the linear interpolation of values for distance other than those shown in the table. 2. The closest distance of the seismic source shall be taken as the minimum distance between the site and the area described by the vertical projection of source on the surface (i.e., surface projection of fault plane). The surface projection need not include portions of the source a depths of 1 Okm or greater. The largest value of the near-source factor considering all sources shall be used for design.
151
Table B-16 Seismic coefficient CA(ATC-40,1996) Soil Profile Type
Shaking Intensity, ZEN1'2
=0.075 =0.15 -0.20 =0.30 SB 0.08 0.15 0.20 0.30 Sc 0.09 0.18 0.24 0.33 SD 0.12 0.22 0.28 0.36 SE 0.19 0.30 0.34 0.36 SF Site-specific geo-technical investigation required to
determine CA 1. The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0. for the Design Earthquake, and 1.25 for the Maximum Earthquake. 2. Seismic coefficient CA should be determined by linear interpolation for values of the product ZEN other than those shown in the table. Table B-17 Seismic coefficient Cv (ATC-40, 1996) Soil Profile Type
Shaking Intensity, ZEN1'2
=0.075 =0.15 =0.20 =0.30 SB 0.08 0.15 0.20 0.30 Sc 0.13 0.25 0.32 0.45 So 0.18 0.32 0.40 0.54 SE 0.26 0.50 0.64 0.84 SF Site-specific geo-technical investigation required to
determine Cv
1.The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0 for the Design Earthquake, and 1.25 for the Maximum Earthquake.
2. Seismic coefficient Cv should be determined by linear interpolation for values of the product ZEN other than those shown in the table.
152
Table B-18 Soil profile types (ATC-40, 1996) Average Soil Properties for Top 100 ft of Soil Profile
Soil Soil Profile Share Wave Standard Undrained Shear
Profile Name/ Velocity, Vs (ft/sec) Penetration Test, Strength, Su Type Generic N or Ncn for (psf) Description cohesion less soil layers (blow/ft) SA Hard Rock Vs>5,000 Not Applicable
SB Rock 2,500 < Vs< 5,000 Not Applicable SC Very Dense 1,200 <VS< 2,500 N>50 N>50 Soil and Rock SD Stiff Soil 600 <VS< 1,200 15 < N < 50 1,000<SU Profile < 2,000 SE Soft Soil Vs< 600 N<50 Su< 1,000 Profile SF Soil Require Site-Specific Evaluation
Soil profile SA is not applicable to site in Dhaka. For the purpose of the analysis of the structures considered in this thesis soil type SD has been considered.
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APPENDIX C
Calculation of equivalent Strut width for structure 1:
EConcrete,EC=3000 ksi EMorter,Em=1200 ksi Thickness of Infill, t = 5 in. CL Distance between Column, L=15 ft. Floor to Floor Height, H=10 ft
Beam dimension 10inx20.5in Column dimension 10inx20in ɵ = tan-1(H
L) = tan-1( 10
20.83) =0.447 rad
Icol=(bh3
12)==(10x203
12)=6666.67 in4
l=L -2*(column dimension
2)=(20.83x12)-2*(20/2)=229.96 in
hm=H -2*(beam dimension
2)=(10x12)-2*(20.5/2)=99.5 in
λ1H =H(𝐸𝑚tsin2ɵ
4𝐸𝑐Icol ℎ𝑚) ¼ =(10x12)(
1200 𝑥 5 𝑥 sin (2x.447)
4 𝑥 3000 𝑥 6666.67 𝑥 99.5) ¼
λ1H = 120 x 0.0276 =3.32 in D=√229.962 + 99.52 =250.56 in a, Strut width =0.175 x D x(λ1H)-0.4
=0.175 x 250.56 x (3.32) -0.4 =27.13 inch Taking effect of Perforated Panels
(R1)i =0.6𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙 - 1.6
𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙 +1
154
Where: Aopen= Area of the opening (in2)
Apanel= = Area of infill panel (in2) =lxhm
Note: If the area of the opening (A open) is greater than or equal to 60 percent of the infill panel (Apanel) then the effect of the infill should be neglected.
Aopen=5 ft x 4.5ft x12x12 =3240 in2
Apanel=l x hm =229.96 x 99.5=22881.02 in2
( 𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙)= ( 3240
22881.02)=0.1416
(R1)i=0.6 x 0.1416 –(1.6 x 0.1416)+1=0.8584=0.86 Modified strut width for perforated panel = 0.86 x 27.13 in =23.05 inch.
tan (ɵcolumn)=(ℎ𝑚−
a
cos (ɵcolumn))
𝑙)
For, ɵcolumn = 0.45 radian
tan (0.45)=(99.5−
27.13
cos (0.45))
229.96)
= 0.30 Assuming ɵcolumn = 0.30 radian lcolumn =( a
cos (ɵcolumn)= ( 27.13
cos (0.3))
= 28.39 inch ≅ 29 inch Calculation of equivalent Strut width for structure 2:
EConcrete,EC=3000 ksi EMorter,Em=1200 ksi Thickness of Infill, t = 5 in. CL Distance between Column, L=12.83 ft. Floor to Floor Height, H=10 ft
155
Beam dimension 10 x15 in Column dimension 12 x15 in ɵ = tan-1(H
L) = tan-1( 10
12.83) =0.662 rad
Icol=(bh3
12)==(12x153
12)=3375 in4
l=L -2*(column dimension
2)=(12.83x12)-2*(15/2)=138.96 in
hm=H -2*(beam dimension
2)=(10x12)-2*(15/2)=105 in
λ1H =H(𝐸𝑚tsin2ɵ
4𝐸𝑐Icol ℎ𝑚) ¼ =(10x12)(
1200 𝑥 5 𝑥 sin (2x0.662)
4 𝑥 3000 𝑥 3375 𝑥 105) ¼
λ1H = 120 x 0.0342 =4.10 in D=√138.962 + 1052 =174.17 in a, Strut width =0.175 x D x(λ1H)-0.4
=0.175 x 174.17 x (4.10) -0.4 =17.334 inch. Taking effect of Perforated Panels
(R1)i =0.6𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙 - 1.6
𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙 +1
Where:
Aopen= Area of the opening (in2)
Apanel= = Area of infill panel (in2) =lxhm
Note: If the area of the opening (A open) is greater than or equal to 60 percent of the infill panel (Apanel) then the effect of the infill should be neglected.
Aopen=5 ft x 4.5ft x12x12 =3240 in2
Apanel=l x hm =138.96 x 105=14590.8 in2
( 𝐴𝑜𝑝𝑒𝑛
𝐴𝑝𝑎𝑛𝑒𝑙)= ( 3240
14590.8)=0.2221
(R1)i=0.6 x 0.2221 –(1.6 x 0.2221)+1=0.77779=0.78 Modified strut width for perforated panel = 0.78 x 17.334 in =13.521 inch.
tan (ɵcolumn)=(ℎ𝑚−
a
cos (ɵcolumn))
𝑙)
For, ɵcolumn = 0.662 radian
tan (0.662)=(105−
13.52
cos (0.662))
138.96)
= 0.632 Assuming ɵcolumn = 0.632 radian lcolumn =( a
cos (ɵcolumn)= ( 13.52
cos (0.632))
= 16.756 inch ≅ 17 inc