Retrofit of Soft Storey Buildings Using Gapped … of Soft Storey Buildings Using Gapped Inclined...

Retrofit of Soft Storey Buildings Using Gapped Inclined Brace Systems

by

Hossein Agha Beigi

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Civil Engineering

Under Joint Educational Placement with IUSS Pavia and

University of Toronto

© Copyright by Hossien Agha Beigi (2014)

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Retrofit of Soft Storey Buildings Using Gapped Inclined Brace Systems

Hossein Agha Beigi

Doctor of Philosophy

Department of Civil Engineering

Under Joint Educational Placement with IUSS Pavia and

University of Toronto

2014

Abstract

Although a soft storey mechanism is generally undesirable for the seismic response of building structures, it

could provide potential benefits due to the isolating effect it produces. This thesis proposes a retrofit strategy

for buildings that are expected to develop soft storey mechanisms, taking advantage of the positive aspects of

the soft storey response while mitigating the negative ones.

After a review of traditional considerations that are made for soft storey structures, the work starts by

comparing the behaviour of an RC frame building with two infill configurations; in the first configuration, it

is assumed that masonry infills are distributed over all storeys uniformly, while in the next step and in order to

consider soft storey effects, it is assumed that masonry infills are not present at the ground storey. Results of

incremental dynamic analyses indicate that structures with uniform infill are less likely to collapse. However, if

the displacement demands at the first level of soft storeys could be sustained, their overall performance

would be significantly improved.

Following this initial study, a gapped inclined brace (GIB) system is proposed with the aim of significantly

reducing the likelihood of collapse whilst ensuring that the seismic damage concentrates at this single

level, protecting the rest of the structure located above. The GIB system achieves these aims by reducing P-

Delta effects at the first floor of soft storey buildings without significantly increasing their lateral resistance.

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The mechanics of the proposed system are defined and a systematic design procedure is explained and

illustrated. The theoretical relations that are derived for GIB systems are verified through numerical analyses.

Results of cyclic static and incremental dynamic analyses demonstrate that the overall seismic performance of

soft storey buildings retrofitted using a GIB system is greatly improved, indicating that the GIB system

produces an efficient and intelligent soft storey mechanism at the first level of such buildings, which provides

several advantages over conventional approaches. The last part of the thesis discusses various uncertainties

that remain about the potential of GIB systems, including the best likely connection details for GIB systems,

which should be investigated as part of future research.

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ACKNOWLEDGEMENTS

First, I would like to express my deepest gratitude to all my supervisors:

• Professor Tim Sullivan, for his invaluable advising in all the time of my research and writing of this

thesis. Without his supervision and constant help, this dissertation would not have been possible.

• Professor Constantin Christopoulos, for his gracious support, excellent guidance and insightful

comments through my thesis. Working under his supervision was a unique instructive experience for

me.

• Professor Gian Michele Calvi, for his support, guidance and encouragement during my research

period. He is definitely one of my respected professors.

I was fortunate to work with such expert supervisors having experiences from different continents. You

kindly shared your wisdom with me and greatly helped me to having a worldwide perspective to problem

solving. Thank you all.

I am grateful to Professor Nigel Priestley for providing his elegant guidance in the beginning of my thesis. His

comments were very helpful to form the general idea of my thesis.

I gratefully acknowledge Professor Guido Magenes and Mr. Mario Galli for providing background data and

analytical models of the case study structure.

In addition to my advisors, I would like to thank the UME School Board in Pavia and the Graduate Student's

Union at the University of Toronto for providing me the opportunity of taking the advantage of the Joint

Placement Program at these two universities.

I would like to thank the financial support offered by the ROSE programme at the UME School, IUSS Pavia

as well as the Italian national 2010-2013 RELUIS project. I would like to thank Professor Christopoulos who

provided me additional funding from the University of Toronto.

I especially thank my mom and dad as well as my brothers Ehsan and Soroosh for all their love over the

years. Without their constant support and encouragement, I would have never given myself the chance to

continue my education.

As an international student, I had the privilege of interacting with wonderful people from different parts of

the world. I want to express my gratitude to all my friends who created one of my best memorable times with

them: Mostafa Masoudi, Fereidon Atarodi, Sevgi Ozcebe, Sujith Mangalathu, David Ruggiero, Paolo Calvi,

Paola Costanza, Fei Tong.

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Thanks to my class mates Abbas Mirfattah, Guney Ozcebe and Jetson Ronald for their warm messages in the

last days of our theses submission. I would like to also thank all my officemates in GB-403C to provide a

friendly atmosphere during my study at the University of Toronto.

Special thanks to my friend Mohsen Kohrangi, who did an unforgettable job to deliver the hard copy of my

thesis to IUSS Pavia.

Finally, I would like to thank the quite patient and unwavering love of my wife Marjan Haji Heshmati. She

was the only one who was continuously beside me during the last four years of my PhD study. You dedicated

your best part of your lifetime to me. This thesis is dedicated to you.

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TABLE OF CONTENTS

ACKNOWLEDGEMENTS ........................................................................................................................................................ iv

TABLE OF CONTENTS ............................................................................................................................................................ vi

LIST OF FIGURES ....................................................................................................................................................................... ix

LIST OF TABLES ........................................................................................................................................................................ xv

LIST OF SYMBOLS.................................................................................................................................................................... xvi

LIST OF ACRONYMS ............................................................................................................................................................... xxi

LIST OF ACRONYM IN CASE STUDIES ......................................................................................................................... xxii

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

1.1 MOTIVATION: ....................................................................................................................................................................... 1

1.2 BACKGROUND ...................................................................................................................................................................... 1

1.3 LITERATURE OVERVIEW ..................................................................................................................................................... 3

1.3.1 Modern Architecture and Soft Storeys ................................................................................................................ 3

1.3.2 Earthquake Engineering and Soft Storeys .......................................................................................................... 4

1.4 OBJECTIVE AND SCOPE OF THE THESIS ........................................................................................................................... 4

1.5 ORGANIZATION OF THESIS................................................................................................................................................ 5

2. CLASSIFICATION OF SOFT STOREY BUILDINGS ................................................................................................... 5

2.1 INTRODUCTION .................................................................................................................................................................... 6

2.2 DISCONTINUOUS STRUCTURAL WALLS OR INFILLS ....................................................................................................... 6

2.3 STRONG BEAM – WEAK COLUMN IN FRAME TYPE ....................................................................................................... 8

2.4 DISCONTINUOUS LOAD PATHS ......................................................................................................................................... 9

2.5 STRUCTURAL WALLS WITH LARGE OPENINGS AT THE BASE .................................................................................... 11

2.6 SUMMARY AND CONCLUSION .......................................................................................................................................... 12

3. ASSESSMENT CASE STUDIES .......................................................................................................................................... 13

3.1 INTRODUCTION .................................................................................................................................................................. 13

3.2 DESCRIPTION OF THE CASE STUDY ................................................................................................................................ 13

3.3 MODELLING APPROACH ................................................................................................................................................... 16

3.3.1 Modelling of beams and columns ....................................................................................................................... 16

3.3.2 Modelling of masonry infills: ............................................................................................................................... 20

3.3.3 Modelling of joint elements: ................................................................................................................................ 22

3.4 GROUND MOTION USED FOR TIME HISTORY ANALYSIS........................................................................................... 24

3.5 ANALYTICAL RESULTS ....................................................................................................................................................... 25

3.5.1 Variant 1: Uniform Distribution of Infills (FI) ................................................................................................ 26

3.5.2 Variant 2: Partial Distribution of Infills- Soft First Storey (SS)..................................................................... 30

3.5.3 IDA response comparison of variants ............................................................................................................... 35


4. FACTORS AFFECTING SOFT STOREY RESPONSE ................................................................................................ 41

4.1 INTRODUCTION .................................................................................................................................................................. 41

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4.2 EFFECT OF P-DELTA ......................................................................................................................................................... 41

4.2.1 Introduction ............................................................................................................................................................ 41

4.2.2 Effect of P-Delta on hysteretic response .......................................................................................................... 43

4.2.3 Design procedure for P-Delta effects ................................................................................................................ 44

4.2.4 Code recommendations ........................................................................................................................................ 44

4.2.5 Numerical results ................................................................................................................................................... 45

4.2.6 Effect of Increased P-Delta Effects ................................................................................................................... 46

4.3 EFFECT OF POST YIELD STIFFNESS ................................................................................................................................ 48

4.4 EFFECT OF DURATION OF GROUND MOTION ............................................................................................................... 49

4.4.1 Selection of records ............................................................................................................................................... 49

4.4.2 Match records to the design spectra and cornet period 2sec ......................................................................... 50

4.5 KEY CHARACTERISTICS AFFFECTING COLUMN HYSTERETIC BEHAVIOUR ............................................................. 52

4.5.1 Description of RC Column Categories .............................................................................................................. 52

4.5.2 Description of numerical modelling ................................................................................................................... 54

4.5.3 Verification of numerical modelling with an experimental result ................................................................. 55

4.5.4 Numerical results ................................................................................................................................................... 57

4.5.5 Comparison of cyclic analysis with the section analysis ................................................................................. 64

4.5.6 Effect of column characteristics on the demand to capacity ratio ............................................................... 67

4.6 DISCUSSION OF RESULTS ................................................................................................................................................... 69


5. GAPPED INCLINED BRACE SYSTEM TO RETROFIT SOFT STOREY BUILDINGS ................................. 73

5.1 INTRODUCTION .................................................................................................................................................................. 73

5.1 EFFECTIVE AXIAL FORCE TO COUNTERACT P-DELTA EFFECTS .............................................................................. 75

5.2 EFFECT OF AXIAL LOADS ON THE DEFORMATION CAPACITY OF RC COLUMNS ................................................... 77

5.3 effP FOR RC COLUMNS ...................................................................................................................................................... 77

5.3.1 Verification with fibre analysis ............................................................................................................................ 78

5.3.2 Effect of effP on a column response ................................................................................................................. 79

5.4 PROPOSAL OF A GAPPED INCLINED BRACE TO ACHIEVE THE effP ........................................................................ 80

5.5 MECHANICS OF THE GIB SYSTEM .................................................................................................................................. 81

5.5.1 Initial position of the GIB ................................................................................................................................... 81

5.5.2 Gap distance ........................................................................................................................................................... 83

5.5.3 Design of the inclined brace ................................................................................................................................ 84

5.5.4 Design Summary .................................................................................................................................................... 85

5.6 DESIGN EXAMPLE AND NUMERICAL VERIFICATION ................................................................................................. 86

5.7 PARAMETRIC STUDY .......................................................................................................................................................... 88

5.8 NUMERICAL CYCLIC RESPONSE OF A SOFT STOREY FRAME RETROFITTED WITH THE GIB SYSTEM ............... 89


6. SEISMIC RESPONSE OF BUILDINGS USING GIB SYSTEM AND DESIGN RECOMMENDATIONS ......................................................................................................................................... 94

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6.1 INTRODUCTION .................................................................................................................................................................. 94

6.2 SOFT STOREY CONCEPT FOR MULTI STOREY BUILDINGS ......................................................................................... 94

6.3 DESIGN CONSIDERATION OF SOFT STOREY BUILDINGS USING THE GIB SYSTEM ............................................. 94

6.4 NUMERICAL INVESTIGATION .......................................................................................................................................... 97

6.5 GIB- 1 VARIANT ................................................................................................................................................................. 98

6.5.1 Numerical Modelling........................................................................................................................................... 100

6.5.2 Verification with Nonlinear Fiber Element modelling ................................................................................. 100

6.5.3 Comparison of variants using fiber analysis ................................................................................................... 105

6.5.4 Results from Nonlinear Time History Analyses ............................................................................................ 106

6.6 COMPARISON OF VARIANTS AT FLOOR LEVEL ............................................................................................................ 110

6.7 COMPARISON OF IDA RESULTS .................................................................................................................................... 112

6.7.1 IDA results............................................................................................................................................................ 112

6.8 EFFECT OF GAP DISTANCE ............................................................................................................................................ 113

6.9 EFFECT OF GIB LOCATIONS: GIB-2 VARIANT AND GIB-3 VARIANT .................................................................... 114

6.9.1 Seismic performance of GIB scenarios ........................................................................................................... 116

6.10 COLLAPSE POTENTIAL OF CASE STUDY VARIANTS ................................................................................................. 117

6.11 SUMMARY AND CONCLUSION ....................................................................................................................................... 117

7. FUTURE STUDIES REGARDING THE UNCERTAINTIES OF THE GIB SYSTEM .................................... 119

7.1 INTRODUCTION ................................................................................................................................................................ 119

7.2 CONSTRUCTABILITY ........................................................................................................................................................ 119

7.3 STRESS CONCENTRATION AT THE CONNECTION ...................................................................................................... 121

7.3.1 Connection of GIB to beam:............................................................................................................................. 121

7.3.2 Connection of GIB to column .......................................................................................................................... 122

7.3.3 Improved Connection of GIB to column ....................................................................................................... 124

7.4 EFFECT OF SUPPLEMENTAL DAMPING ON RESPONSE OF GIB-3 VARIANT ....................................................... 124

7.5 SUMMARY AND CONCLUSION ........................................................................................................................................ 126

8. CONCLUSIONS .................................................................................................................................................................... 128

8.1 CHAPTER 1 AND 2 ............................................................................................................................................................ 128

8.2 CHAPTER 3 ......................................................................................................................................................................... 128

8.3 CHAPTER 4 ......................................................................................................................................................................... 129

8.4 CHAPTER 5 ......................................................................................................................................................................... 129

8.5 CHAPTER 6 ......................................................................................................................................................................... 129

8.6 CHAPTER 7 ......................................................................................................................................................................... 130

REFERENCES ............................................................................................................................................................................ 131

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LIST OF FIGURES

Figure 1.1.Different pattern of damage a) beam side sway, b) column side sway in soft first storey ............................... 2

Figure 1.2.Villa Savoye, the early construction of the open ground storey buildings, picture from

the art of the architect [Filler 2009] ....................................................................................................................... 3

Figure 1.3.Bauhaus Dessau, the open ground storey buildings[Poling 1977] ....................................................................... 4

Figure 2.1.Common residential building with disconnection of stiff elements in the first level ....................................... 7

Figure 2.2.Typical damage due to infill discontinuity, a)Managua, 1972 [NISEE 1972] ,

b)Izmit 1999 [NISEE 1999] ................................................................................................................................... 7

Figure 2.3. Common existing Strong beam – weak column frames ....................................................................................... 8

Figure 2.4. Damage to soft storey behaviour a: Strong beam- weak column in 2010 Haiti

Earthquake ,[NISEE 2010b] b: poor joint connection in the first floor in 1999

Turkey earthquake, [NISEE 2010b], c: lack of confining at thejoint in 1994

Northridge earthquake [Blakeborough 1994] ...................................................................................................... 9

Figure 2.5.Discontinuous load path causes soft storey mechanism ...................................................................................... 10

Figure 2.6.Typical damage due to wall discontinuity a) Olive View hospital, 1971 San Fernando

earthquake [NISEE 2010a] b) Imperial Country Service building, 1979

Imperial Valley earthquake [NISEE 1979] ........................................................................................................ 10

Figure 2.7. Structural wall with opening in the first and typical floors ................................................................................. 11

Figure 2.8. a) Masonry building with large opening at base, Loma Prieta, 1989 b) detail damage to the pier .............. 11

Figure 3.1. Six-storey concrete frame: a) bare frame, b) full infill uniform distribution (FI), c)

Partial infill disconnected in the first floor or Soft storey (SS) ...................................................................... 14

Figure 3.2. Geometric and mechanical properties of beams and columns, from Galli [2006] ....................................... 15

Figure 3.3. Takeda hysteretic rule, Emori unloading [Otani 1974] ....................................................................................... 17

Figure 3.4. Mechanical properties defined for columns a) Moment-Curvature, b) axial load–moment interaction .... 18

Figure 3.5. Shear capacity of columns at the first floor .......................................................................................................... 19

Figure 3.6. Hysteretic cycles of Masonry struts, [Carr 2004] .................................................................................................. 22

Figure 3.7. Modelling of beam column joint [Trowland 2003] .............................................................................................. 22

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Figure 3.8. Monotonic and cyclic behaviour of shear hinge joint model, [Pampanin et al. 2002] .................................. 23

Figure 3.9. Pampanin Hysteretic rule used in Ruaumoko, [Carr 2004] ................................................................................ 24

Figure 3.10. Acceleration and displacement Response Spectra for the selected records sets ......................................... 26

Figure 3.11. Peak floor acceleration profile obtained from the nonlinear time-history

analysis for different hazard levels, full infill (FI) variant ................................................................................ 27

Figure 3.12. Inter storey drift profile obtained from nonlinear time-history analysis for

different hazard levels, full infill (FI) variant .................................................................................................... 28

Figure 3.13. Inter storey residual drift profile obtained from nonlinear time-history analysis

for different hazard levels, full infill (FI) variant ............................................................................................. 29

Figure 3.14. Peak response of interests obtained from incremental dynamic analysis,

full infill (FI) variant ............................................................................................................................................... 30

Figure 3.15. Peak floor acceleration profile obtained from nonlinear time-history analysis

for different hazard levels, Soft storey (SS) variant .......................................................................................... 31

Figure 3.16. Inter storey drift profile obtained from nonlinear time-history analysis for

different hazard levels, soft storey (SS) variant ................................................................................................. 32

Figure 3.17. Residual storey drift profile obtained from nonlinear time-history analysis for

different hazard levels, soft storey (SS) variant ................................................................................................. 33

Figure 3.18. Peak response of interests obtained from incremental dynamic analysis,

soft storey (SS) variant ........................................................................................................................................... 34

Figure 3.19. Displacement damage index (DDI) for beams and columns obtained from

nonlinear time-history analysis for different hazard levels, soft storey (SS) variant ................................... 35

Figure 3.20. Comparison of the peak inter storey drift ratio (PRD) obtained

from IDA for two variants of FI and SS ........................................................................................................... 36

Figure 3.21. Comparison of the residual inter storey drift ratio (RRD) obtained from IDA

for two variants of full infill (FI) and partial infill (SS) ................................................................................... 37

Figure 3.22. Comparison of the average inter storey drift ratio obtained from IDA for

two variants of full and partial infill .................................................................................................................... 37

Figure 3.23. Comparison of the peak floor acceleration (PFA) obtained from IDA for

two variants of full and partial infill .................................................................................................................... 38

Figure 3.24. Mean acceleration spectra for a period between 0.3 and 2.1 sec .................................................................... 38

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Figure 3.25. Comparison of the beams and columns DDI for the two FI and SS variants ............................................. 39

Figure 4.1. P-∆ Effects on design moments ............................................................................................................................ 42

Figure 4.2. P-∆ Effects on force and response characteristics: a) general load deformation relationship;

b) bilinear positive curve ....................................................................................................................................... 42

Figure 4.3. Comparison of IDA response with and without P-∆ effects: a) peak drift ratio, b) residual drift ratio .. 46

Figure 4.4. Dummy column modelling for considering effect of axial load........................................................................ 47

Figure 4.5. Comparison of responses obtained from incremental NTHA when the total gravity load is doubled ..... 47

Figure 4.6. Effect of post yield ratio of responses .................................................................................................................. 48

Figure 4.7. Acceleration and displacement Response Spectra for the selected records sets:

matched to the displacement spectrum soil C, Td=8.sec ............................................................................... 51

Figure 4.8. Acceleration and displacement response spectra match to displacement spectra for

soil A with corner period of 2sec soil type A: a) Short duration records b) Long duration records ....... 51

Figure 4.9. Comparison responses for short and long duration records ............................................................................ 52

Figure 4.10. Different configuration of steel reinforcement and column size of the RC concrete columns ............... 54

Figure 4.11. Geometrical characteristics of the specimen and history of cyclic loading .................................................. 56

Figure 4.12. Comparison between numerical and experimental results of cyclic behaviour of RC column ................ 57

Figure 4.13. Effect of longitudinal reinforcement ratio on column hysteretic response (Moment-chord rotation)

Variant I, D=0.4, σ� = 0.3 confinement factor: 1.2, cantilever length =3m ............................................. 58

Figure 4.14. Effect of column dimension on hysteretic response (Moment-Chord rotation)

Variant II, ρ=0.015, σ� = 0.3 confinement factor: 1.2, cantilever length =3m ........................................ 60

Figure 4.15. Effect of axial force ratio (σ�)on column hysteretic response (Moment-Chord rotation),

Variant III: Column dimension: 40x40cm, ρ=0.015, confinement factor: 1.2, cantilever length =3m .. 61

Figure 4.16. Effect of confinement factor on column hysteretic response (Moment-Chord rotation)

Variant IV: Column dimension: 40x40cm, ρ=0.015 σ� = 0.3 , cantilever length =3m......................... 62

Figure 4.17. Comparison of key characteristics on the cyclic behaviour of RC columns ................................................ 63

Figure 4.18. Effect of key characteristics on the hysteretic response of RC columns ..................................................... 63

Figure 4.19. Section stress – strain distribution in reinforcement concrete column ........................................................ 65

Figure 4.20. Comparison of key characteristics on column response based on section analysis ................................... 66

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Figure 4.21. Comparison of key characteristics on Demand-Capacity Ratio (DCR) ....................................................... 68

Figure 4.22. Possible means of de-coupling gravidity loads from lateral loads in a soft storey building ...................... 71

Figure 5.1. Proposed mitigation strategies, a) roller system b) gapped inclined braced (GIB) system ........................ 74

Figure 5.2. Single-Degree-of-freedom system subject to axial load and lateral displacement......................................... 75

Figure 5.3 a) Influence of the P-Delta effect and the effP on the force-displacement response

b) Effective axial force ( effP ) ............................................................................................................................... 76

Figure 5.4.a Numerical analysis of a 0.40m×0.40m RC column: 1.5%ρ = , 1.15CF = , axial load ratio

range 0: 0.05 to 0.5 in increments of 0.05 a) Axial load ratio versus lateral drift capacity ratio,

( effP in normalized form), b) Lateral resistance versus lateral drift capacity ratio, referred to

as degraded capacity curve ................................................................................................................................... 78

Figure 5.5. Gapped-Inclined Brace (GIB) system to the existing column a) Initial condition

b) Closing gap condition c) Ultimate condition ................................................................................................ 80

Figure 5.6. Mechanics of the GIB system a) Initial position, b) elastic behaviour of the column before gap is

closed c) post yield condition ............................................................................................................................... 81

Figure 5.7. Effect of the GIB on the lateral resistance and the displacement capacity of RC columns ....................... 82

Figure 5.8. Axial force in the column and the inclined brace ............................................................................................... 87

Figure 5.9. Total behaviour of the proposed method in comparison to the existing column only ............................... 87

Figure 5.10. Effect of the GIB system on response of 0.40x0.40m RC columns with different height H .................. 88

Figure 5.11. Effect of the GIB system on response of 0.40x0.40m RC columns with different

height initial axial load ratio ................................................................................................................................. 89

Figure 5.12. Effect of the GIB system on response of 0.40x0.40m RC columns with different

height initial confinement actor CF .................................................................................................................... 89

Figure 5.13. Single one storey RC frame retrofitted using GIB and subjected to quasi-static loading ......................... 90

Figure 5.14. Axial force history of the right and left gap elements, b) Moment –

Curvature response of the existing column ....................................................................................................... 91

Figure 5.15. Moment – Curvature response of the existing column ................................................................................... 92

Figure 5.16. Hysteretic response of the hybrid system in comparison to the existing frame........................................... 92

Figure 6.1. Case study building configuration (details in chapter 3) .................................................................................... 97

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Figure 6.2. Position of the GIB system in the soft storey building bases on three configurations:

a) GIB 1 variant, b) GIB 2 variant, c) GIB 3 variant ...................................................................................... 99

Figure 6.3. Modelling of GIB system in Ruaumoko for time history analysis ................................................................. 100

Figure 6.4. Modelling masonry infills in Ruaumoko, a) infill panel element configuration

b) shear spring modelling .................................................................................................................................... 102

Figure 6.5. Comparison of the pushover curves obtained from the lumped plasticity and the fibre

element modelling of the existing soft storey frame ...................................................................................... 103

Figure 6.6. modelling of GIB system in Seismo-Struct for push over analysis ............................................................... 103

Figure 6.7. Axial forces in the first storey columns and the GIB of the GIB-1 variant: comparison

between fibre models and lumped plasticity models, see Figure 6.2........................................................... 104

Figure 6.8. Push over curve capacity of the GIB-1 variant from nonlinear fibre element (SeismoStruct)

modelling and lumped plasticity modelling(Ruaumoko) ............................................................................... 105

Figure 6.9. Push over curve capacity for the six-storey frame buildings a) Full infill, b) Partial infill,

c) GIB-1 variant ................................................................................................................................................... 106

Figure 6.10. Damage limit state pattern in the six-storey frame a) Full infill, b) Partial infill, c GIB-1 variant,

(Dr : Roof drift(%) ; Vb: Base shear (kN)) ........................................................................................................ 107

Figure 6.11. Global seismic response in GIB-1 variant obtained from NTHA for three earthquakes:

a) Global hysteresis, b) Inter-storey drift, c)Floor acceleration ................................................................... 108

Figure 6.12. Element hysteretic responses in GIB-1 variant: a) Moment-curvature of exterior Beams

and columns, b) Moment-curvature of interior Beams and columns c) Axial GIBs hysteresis ............. 109

Figure 6.13. Axial force on the columns and the GIBs of the first storey, GIB-1 variant ............................................. 110

Figure 6.14. Response parameters at storey levels ................................................................................................................. 111

Figure 6.15. IDA responses ....................................................................................................................................................... 112

Figure 6.16. Effect of gap distance on the seismic response of the GIB-1 variant ......................................................... 114

Figure 6.17. Locations of GIBs ................................................................................................................................................ 115

Figure 6.18. Seismic parameters for different GIB scenarios a) DDI, b) Peak floor acceleration ................................ 116

Figure 6.19. Seismic parameters for different GIB scenarios a) DDI, b) Peak floor acceleration ................................ 117

Figure 7.1. Hysteretic response of the hybrid system using different behaviour of the inclined column.................... 120

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Figure 7.2. A proposed connection for the GIB system using the offset ........................................................................ 121

Figure 7.3. a)Possibility of Shear failure at the beam and the GIB connection, b) possible retrofit strategy ............ 122

Figure 7.4. Connection of the GIB system to the column only: a) connection detail,

b) actions in the gusset plate, c) actions in the bolts ...................................................................................... 123

Figure 7.5. Alternative connection proposal of GIB to column using gusset plate........................................................ 124

Figure 7.6. Adding viscose dampers to the GIB-3 variant in the numerical modelling (DGIB-3 variant) ................. 125

Figure 7.7. Effect of adding dampers on the response of the GIB-3 variant ................................................................... 126

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LIST OF TABLES

Table 3.1. Masonry mechanical properties ................................................................................................................................ 19

Table 3.2. Parameters of the equivalent diagonal strut model [Bertoldi 1993] ................................................................... 20

Table 3.3. Masonry mechanical properties ................................................................................................................................ 21

Table 3.4. Failure modes in masonry infill panels [Bertoldi 1993] ........................................................................................ 21

Table 3.5. Record Set used for nonlinear time history analysis ............................................................................................. 25

Table 3.6. Summary of response parameters obtained for three variants of case 1 with full infill,

partial infill and bare frame ................................................................................................................................... 35

Table 4.1. Long duration record sets .......................................................................................................................................... 50

Table 4.2. Characteristics of different column studied, with a cantilever length of 3m .................................................... 53

Table 6.1. Column configurations at the open ground level ................................................................................................. 98

Table 6.2. GIB configurations associated to each column type for GIB-1 ........................................................................ 99

Table 6.3. GIB configurations for different scenarios ......................................................................................................... 115

Table 7.1. Shear force in beams at the first floor of the GIB-1 building .......................................................................... 122

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LIST OF SYMBOLS

α Takeda parameter

Ac Column cross section

Ag Gross section area of RC column

αP∆ Second order amplification factor

Asi Total are of longitudinal reinforcement at layer i in section analysis

Ast Total area of longitudinal reinforcement

b Width of RC column section

β Takeda parameter, Strength reduction factor

βP∆ Second order parameter

bw Equivalent height of infill strut

CF Confinement factor

∆ displacement

db beam depth in joint modelling

∆ci Displacement capacity at level i

DCR Demand-capacity ratio

∆d Demand displacement

∆d Equivalent target displacement of building

∆f Lateral displacement of first floor

∆gap Gap distance inside GIB system

∆GIB Distance between the base of GIB system and the bace of RC column

∆Lc Axial elongation of RC column

dm Ultimate displacement

∆u Roof lateral displacement at ultimate state

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dw Diagonal length of infill panel

dy Yield displacement

∆y Yield drift displacement

ε Axial strain of the GIB system, non dimensional mass properties

Ec Elastic modulus of concrete

Gc Shear modulus of concrete

εc Extreme concrete fibre compression strain

εcu Ultimate concrete strain

ED Energy dissipated per cycle at target displacement

Es Young'g modulus of steel

εsn Reinforcement strain at maximum distance from the neutral axis

Ew Elastic modulus of masonry infill

εy Yield axial strain of GIB system

Fy Yield force in Takeda hysteretic rule

F0 Lateral force at yield without P-Delta effects

f'c Compressive strength of concrete

fc(x) Force in concrete in section x

f'cc Confined concrete compressive strength

Fi Lateral force at level i

Fp Lateral force at yield with P-Delta effects

Fw Horizontal projection of ultimate load of masonry infill

f'w Compressive resistance of material of masonry infill

fws Shear resistance of masonry infill under diagonal compression

fwu Sliding resistance of mortar joints of masonry infill

Fyh Yield strength of transverse reinforcement in RC column

fys Rebar yield strength

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γ non dimensional frequency properties

H Inter-storey height

Hc Column cantilever height

Hi Height of building at storey i

hw Height of infill panel

Ip Moment of inertial of column section

ϕ curvature in section analysis

ϕy Yield curvature

K0 First order initial stiffness

K1 Parameter of the equivalent diagonal strut model

K2 Parameter of the equivalent diagonal strut model

Kc Axial stiffness of RC column

Keff Effective stiffness

Ker Equivalent stiffness of the storeys above the first floor

Kf First floor stiffness

kp Second order initial stiffness

Ku Unloading stiffness

λ Parameter of the equivalent diagonal strut model

L half of joint panel height in joint modelling

Lb0 Length of GIB system at closing gap

LGIB Initial length of GIB system

Lp Plastic hinge length of RC column

M Bending moment at the base of cantilever

M Mass

µ ductility

Mi Moment at level i

xix

µm Limit of ductility for P-Delta effects

ng Number of values in geometric mean

P Gravity load

P0 Axial load on RC columns in parametric study

Pb Axial force in GIB system

Pu Axial load on column at the ultimate sate

θ Panel inclination respect to horizontal

θ Inter-storey drift ratio

θGIB Initial angle of GIB system

θi Drift Capacity at level i

θP∆ Stability index

θy Yield lateral drift ratio of

ρ Reinforcement ratio

R Ratio of upper floor storeys stiffness to that of first floor

r , r0 First order post yield stiffness ratio

Rd Spectral displacement reduction factor

rp Second order post yield stiffness ratio

ρsx Geometrical ratio of confining reinforcement in horizontal direction

ρsy Geometrical ratio of confining reinforcement in vertical direction

ρv Geometrical ratio of confining reinforcement

σ0 Initial axial load ratio

σdes Inclined brace design stress

σv Vertical compression stress on masonry infill due to gravity loads

σw Equivalent strength of masonry infill

τ Ratio of total vertical load (dead load plus reduced live load) to dead load

xx

Teff Effective Period

tw Thickness of infill panel

VBc Base shear capacity of first floor

VBd Demand base shear

Vu,col Lateral strength of RC column at ultimate state

Vy,col Lateral strength of RC column at yield

ωer Natural frequency of storeys above the first floor

ωf Natural frequency of first floor

ξeq Equivalent damping ratio

xg Geometric mean value of response

xxi

LIST OF ACRONYMS

FMPM first mode participation mass in the elastic range

GIB Gapped Inclined Brace

IDA Incremental Dynamic Analysis

PDR Peak Inter-Storey Drift Ratio

PFA Peak Floor Acceleration

PRDR Peak Inter-Storey Residual Drift Ratio

DBE Design basis Earthquake

FE Frequent Earthquake

MCE Maximum Credible Earthquake

xxii

LIST OF ACRONYM IN CASE STUDIES

Variant Acronym Description

1 FI-NPD Full Infill No P-Delta

2 SS-NPD Soft Storey No P-Delta

3 BF-NPD Bare Frame No P-Delta

4 FI Full Infill with P-Delta

5 SS Soft Storey with P-Delta

6 BF Bare Frame with P-Delta

7 SS-DPD Similar to SS when P-Delta effects are doubled

8 SS-R-0.05 Similar to SS with Post yield stiffness ratio R=0.025




12 GIB-I SS retrofitted Using GIB system- Configuration I

13 GIB-II SS retrofitted Using GIB system- Configuration II

14 GIB-III SS retrofitted Using GIB system- Configuration III

15 DGIB-25 Similar to GIB-III with Supplemental damping C=25 kN.s/m




1

1.INTRODUCTION

1.1 MOTIVATION:

Over the past few centuries, the number of buildings constructed in urban areas have increased saliently. The

urban zoning regulations in many countries encourage engineers and architects to consider modern

architectural configurations in their designs. Open ground storey buildings (also known as soft storey, pilotis

or soft, weak or open front, SWOF) are one of the most common types of such configurations. For example,

an extensive study by the Applied Technology Council [ATC-52-3 2009] indicated that in San Francisco, 2800

out of 4600 residential wood frame buildings had significant openings at the ground level. Having parking,

retail areas, storefront windows, shopping areas, and lobbies at the first floor of multi storey buildings are the

architectural and social advantages of such buildings. Similar statistics have been reported for other

communities, which indicate the prevalence of such buildings.

On the other hand, earthquake surveys have shown that soft storey buildings are some of the most vulnerable

structures, and their behaviour has been recognized as one of the most undesirable mechanisms by the

structural and earthquake engineering community [Chopra et al. 1973; Rutenberg et al. 1982; Arnold 1984].

Almost two thirds of the 46,000 units that were uninhabitable after the Northridge earthquake and a high

percentage of the death toll were attributed to such buildings [Comerio 1995]. Because of the similarity in

housing stocks, a similar percentage could also be expected for other megacities in the world following a

major earthquake.

Since earthquakes have been recorded, over 8.5 million deaths and almost $2.1 trillion damages have been

reported all around the world [Daniell et al. 2011]. Recently, global fatalities from earthquakes has been

estimated as 100,000 per year [Bilham 2004; USGS 2013]. Considering the high contribution of soft storey

buildings in the loss of life and money, it could be estimated that such buildings were responsible for a few

million fatalities and several billions of dollars of losses.

1.2 BACKGROUND

Beside the architectural advantages, the potential structural benefits of soft storey buildings had also been

studied by well-known researchers as early as the 1930s [Martel 1929; Green 1935; Jacobsen 1938; Chopra et

al. 1973; Arnold 1984].This proposal relied on mitigating the total inertial forces using the soft link concept at

the first floor (Figure 1.1). A number of buildings were designed based on this idea by some engineers and

experts. The six-storey cast-in-place Olive View hospital was a good example of implementing such designs

in the 1970s. However, the building suffered significant damage and it was decided to demolish and rebuilt it

[Mahin et al. 1976a].

INTRODUCTION 2

Figure 1.1.Different pattern of damage a) beam side sway, b) column side sway in soft first storey

Similar poor performances of such buildings in past earthquakes led to the development of design procedures

that do not allow column side-sway mechanisms, and a series of steps were taken to prevent engineers from

designing such structures [Park and Paulay 1975; Naeim 1989; Esteva 1992; Vukazich et al. 2006]. It has also

been recognized that second order effects increase the residual and the maximum displacement demands

beyond those obtained from the first order analysis, and during severe ground motion excitation structures

may reach a state of dynamic instability at a rapid rate[Jennings and Husid 1968; Bernal 1987; MacRae 1994;

Christopoulos et al. 2003; Adam and Jager 2011]. Most of these studies emphasized the fact that the

displacement demands of the first storey vertical elements reach their ultimate capacity and will cause a

sudden failure due to extra gravity loads in a certain performance level. Others concluded that forming soft

storey mechanisms is very dangerous since the lateral response is characterized by a large rotation and

ductility demand concentrated at the extreme sections of the columns of the ground floor, while the

superstructure behaves like a quasi-rigid body [Mezzi 2004].

Even though recent codes address this problem by prescribing an increase in the strength and stiffness of the

columns of existing structures[FEMA 2000; ATC 2007a] to reduce the probability of collapse, such

requirements do not necessarily reduce the expected total damage because strengthening the first floor could

increase seismic forces that are transferred to the storeys located above. In addition, traditional retrofitting

approaches, such as added RC walls or inclined steel braces, present several limitations to the architectural

functionality of structures. Although increasing the confinement in reinforcement concrete columns achieves

this improvement, it may not necessarily prevent the collapse due to significant gravity loads. Other solutions

for mitigating soft storeys that have been proposed by researchers and engineers [Boardman et al. 1983; Chen

and Constantinou 1990; J 1995; Todorovska 1999; Iqbal 2006] might require advanced technologies and

devices, which are not likely to be cost effective in many countries.

INTRODUCTION 3

1.3 LITERATURE OVERVIEW

As mentioned in the previous sections, a series of problems associated with soft storey buildings have ruled

them out in seismic regions. Thus, it is difficult to find much material in the recent literature that implements

the soft storey concept as a reliable tool for retrofitting. To achieve the goal of this thesis, any relevant

literature review is directed inside each chapter separately. However, the following two subsections review

current considerations for soft storey buildings from two different perspectives.

1.3.1 Modern Architecture and Soft Storeys

The first appearance of modern soft storey buildings dates back to 1914, where the famous architect Le

Corbusier developed the term "Dom-ino system" for economic housing [Glassman 2001]. This model, which

was proposed by a pioneer of modern architecture, proposed five points, in which one main point was that

that upper storey slabs should be supported by an open floor plan consisting of perimeter slender columns,

known as pilotis (Floating concept).

Figure 1.2 shows an example of an early open ground storey construction. This concept was followed by

another architect in 1925, Walter Gropius, who proposed Bauhaus buildings, an open ground storey building

using a number of windows on the façade. Figure 1.3 shows a model of a school designed using this idea,

where the building has both horizontal and vertical irregularity. The Bauhaus had a major impact on art and

architecture trends in Western Europe and the North America[Poling 1977].

The two aforementioned concepts became the principal of the modern architecture in the 20th and the 21th

centuries, and spread out quickly all around the world. The open ground floors are nowadays used for socio-

economical purposes including parking, garage space or stores.

The current urban zoning regulations of many countries encourage owners to use soft storey configurations

because the area enclosed by a soft storey is rewarded to them. This area is neither computable as part of the

maximum allowable built area, nor for tax, but is computable for selling purposes [Guevara-Perez 2010].

Figure 1.2. Villa Savoye, the early construction of the open ground storey buildings, picture from the art of the architect

[Filler 2009]

INTRODUCTION 4

Figure 1.3. Bauhaus Dessau, the open ground storey buildings[Poling 1977]

1.3.2 Earthquake Engineering and Soft Storeys

In terms of earthquake engineering, the viewpoint on soft storey buildings is extremely different to that of the

architectural viewpoint. The general recognition is to say that a soft-storey building is one in which

deformations are expected to be concentrated in a single “soft” storey [Bertero 1984]. Based on the current

code definition [FEMA310 1998; UBC 2009], buildings are classified as having a "soft storey" if that level is

less than 70% as stiff as the floor immediately above it, or less than 80% as stiff as the average stiffness of the

three floors above it.

Such buildings are categorised as vulnerable structures to collapse in moderate to severe earthquakes in a

phenomenon known as a soft storey collapse. The weak storey is relatively less resistant than surrounding

floors to lateral earthquake motion, so a disproportionate amount of the building's overall side-to-side drift is

focused on that floor. Subject to such large deformations, the floor becomes a weak point that may suffer

structural damage or complete failure, which could increase the possibility of the collapse of the entire

building. The behaviour of such buildings in recent earthquakes is reviewed in more detail in chapter 2.

1.4 OBJECTIVE AND SCOPE OF THE THESIS

With previous efforts in mind, the main objective of this research is to find a retrofitting strategy for soft

storey buildings that takes advantages of such buildings while mitigating the negative aspects.

Some other potential advantages of soft storey buildings are:

• Limited direct losses: The vast majority of the first floor application are parking or stores. This areas are

less valuable compared to the more expensive part of the building, including residential or office sections.

Thus, by accumulating damage in this "cheap floor", the total repair cost could be minimized.

INTRODUCTION 5

• Indirect loss: The down time could be minimised because only one floor could go out of service, while

the rest of the building could be even at the immediate occupancy performance level. This benefit is

likely to require that some other form of access be provided to upper floors.

• Retrofit cost: Only one floor is required to be retrofitted, which is likely to save cost and time.

1.5 ORGANIZATION OF THESIS

Chapter 2 starts with a brief literature review on the response of buildings with soft storey configurations to

past earthquakes. The common types of such buildings are classified and their seismic responses are

qualitatively reviewed. This chapter indicates that buildings in which masonry infills are disconnected in the

first level are one of the most common types of soft storey building. This conclusion led to the choice of the

building that is extensively studied in Chapter 3.

The seismic vulnerability of a six-storey RC frame building typical of construction practice from the 1970’s is

examined in Chapter 3, initially considering two different infill configurations; the first considers full masonry

infill and the second considers an open ground storey with full masonry infill on all floors except for the first

floor. The seismic response of the two configurations is compared using incremental nonlinear time history

analyses.

To provide insight into the factors affecting the vulnerability of soft storey structures, chapter 4 investigates

the impact of some key characteristics on the soft storey response. The impact of P-Delta effects, the post-yield

stiffness ratio and the ground motion duration on the seismic behaviour of such structures is studied. Then, the

effect of some key characteristics on the cyclic behaviour of columns is numerically investigated. The results

presented in this chapter lead to the definition of a new retrofit approach for soft storey buildings.

Chapter 5 proposes the Gapped-Inclined Brace (GIB) system for retrofitting the seismic response of soft

storey structures that, in addition to reducing the likelihood of collapse at the first level of soft storey

buildings, concentrates seismic damage at this single level, while protecting the rest of the structure located

above. The mechanics of the proposed system are first defined. Theoretical relations and numerical models

are derived to verify the response. The cyclic behaviour of a single degree of freedom RC frame retrofitted

using the GIB system is numerically investigated.

Chapter 6 investigates the dynamic characteristics of MDOF buildings that are retrofitted using the GIB at

the ground floor. This chapter presents a case study of the soft storey building that is retrofitted using the

GIB system. To investigate the effectiveness of alternate retrofit configurations, different scenarios of the

GIB systems is explored.

Chapter 7 highlights uncertainties regarding the performance of the GIB system on the soft storey response,

and recommends future studies to further develop this concept.

6

2.CLASSIFICATION OF SOFT STOREY BUILDINGS

2.1 INTRODUCTION

This chapter presents a brief literature review of the seismic behaviour of buildings using soft storey

configurations in past earthquakes. The common types of such buildings are classified and their seismic

responses are qualitatively reviewed. The result of this chapter lead to the selection of a sample structure that

will be analytically studied in the next chapter.

Soft storey buildings have been classified in four categories [Arnold 1984]: tall first storey, discontinuous

infills, discontinuous shear walls and discourteous load path. A similar classification but with a slightly

broader range is reviewed in this chapter:

• Discontinuous structural walls or infills

• Strong beam - weak column in frame type

• Discontinuous load path

• Walls in large openings at the base

In the following sections, all types of aforementioned structures are discussed.

2.2 DISCONTINUOUS STRUCTURAL WALLS OR INFILLS

These types of structures are often observed in commercial and residential buildings. In such configurations,

masonry partitions or structural walls are disconnected in the first stories due to operational reasons. Vertical

loads are usually transferred by transfer beams and carried by columns to form the lateral load path. In

commercial buildings, this discontinuity is more likely due to the presence of large store-front windows for

business purposes.

Discontinuous infills are the most common type of existing soft storey buildings. In residential buildings, they

are usually present because of large open areas such as parking or garages, which create a first floor that has

fewer walls, and thus, is much softer than the levels above. A comprehensive study on the multifamily

dwelling MFD buildings in Santa Clara County [Selvaduray et al. 2003; Vukazich et al. 2006] indicated that 36

percent of the existing buildings encompassed this architectural configuration, known as the "tuck under

parking". Another study in Berkeley [Bonowitz 2005; MacQuarrie 2005] showed that only 15% of soft storey

buildings had residential use in the ground floor; most of them had non-residential use such as parking or

garage. Figure 2.1 shows a typical multi-storey structural frame in which masonry infills are disconnected at

the first bottom storey. Such buildings are often referred to partial infill frames.

CLASSIFICATION OF SOFT STOREY BUILDINGS 7

Figure 2.1. Common residential building with disconnection of stiff elements in the first level

Figure 2.2 shows typical damages to buildings with this type of soft storey configuration during past

earthquakes. On the left side of the figure, there is a two storey RC commercial building "Casa Micasa S.A.",

which suffered significant lateral displacement at the ground floor level during the 1972 Managua Earthquake.

This storey was completely open (except for glass partitions all around), while the upper storey had walls and

partitions that significantly increased the lateral stiffness of this second storey relative to the first. The flexural

plastic hinges formed at the top and bottom of the first storey columns [Bertero 1997]. In the right hand of

this figure, a six-storey residential reinforced concrete building that was damaged in the Izmit, Turkey

earthquake in 1999 is shown. The significant density of masonry infills in the upper storeys omitted in the

first two stories. These floors were completely collapsed, while even windows in the upper stories remained

intact.

a) b)

Figure 2.2. Typical damage due to infill discontinuity, a)Managua, 1972 [NISEE 1972] , b)Izmit 1999 [NISEE 1999]


Arnold [1984] stated that if pre-cast cladding systems or lightweight partitions are used in the storeys above

the ground level, the problem might be less significant. Because their in-plane stiffness is not considerable,

especially when their connection to the main structure is poor or they are applied separately.

2.3 STRONG BEAM – WEAK COLUMN IN FRAME TYPE

When a span length of a frame is long, without careful application of capacity design rules, there is a

possibility to have gravity bending moments and shear forces in beams that are much greater than those in

their supporting columns. This situation may lead the engineer to choose beams that are stronger than

columns. As a result, plastic hinges are more likely formed at the two ends of the columns instead of beams

(Figure 2.3). Such a mechanism depends on some important factors including the storey number, the joint

strength, the lap splice effect and the column size reduction.

Figure 2.3. Common existing Strong beam – weak column frames

Figure 2.4.a shows a partial storey collapse of an RC residential building after the 2010 Haiti earthquake.

Collapse shows the large, heavy, concrete slabs and beams supported by very lightly reinforced and under-

sized concrete columns. The column dimension comparison to the deck depth is considerably low, which

causes flexural plastic hinges to form at the top two ends of this floor. The adjacent building probably

prevented further collapse and loss of life [Fierro and Perry 2010; NISEE 2010b]. Another example of this

type of damage is shown in part b; poor connections in the moment frame beam-column joint caused heavy

damage to the corner column and subsequently failure of the first floor of this building [Sharma et al. 2011].

Figure 2.4.c shows a heavy damage to the Kaiser Permanente health institution during the Northridge

earthquake. A partial collapse occurred through a pancaking of a weak second storey, which was possible due

to the weak column-strong beam mechanism that were intensified by lack of confining reinforcement at the

joint [Blakeborough 1994].

Stong Beam

Wea

k C

olu

mn

possible Plastic

hinge location


(a) (b)

(c)

Figure 2.4. Damage to soft storey behaviour a: Strong beam- weak column in 2010 Haiti Earthquake ,[NISEE 2010b] b:

poor joint connection in the first floor in 1999 Turkey earthquake, [NISEE 2010b], c: lack of confining at the

joint in 1994 Northridge earthquake [Blakeborough 1994]

2.4 DISCONTINUOUS LOAD PATHS

Discontinuous load paths are to some extent similar to the first group, in which shear walls or braces are

disconnected at the top of the first level (Figure 2.5). The use of large entrances including lobbies or business

shops are the common reasons of such configurations. Figure 2.5.a shows a situation that the shear force at

the second storey is transferred through the first floor diaphragm to other resisting elements below. If the

diaphragm cannot transfer all shear forces from the stiffer span to the adjacent one, it could cause a soft

storey mechanism at the first floor. The concern is that the wall or braced frame may have more shear

capacity than considered in the design. These capacities impose overturning forces that could overwhelm the

columns. While the strut or connecting diaphragm may be adequate to transfer the shear forces to adjacent

elements, the columns which support vertical loads are the most critical [FEMA310].


(a) (b)

Figure 2.5. Discontinuous load path causes soft storey mechanism

Discontinuous load paths can also occur due to the omission of structural walls in some part of the structural

system (Figure 2.5b). Olive View Hospital is a well-known example of a discontinuous structural wall as

shown in Figure 2.6.a. This lateral load resisting structural system did not extend through the first and ground

floors of the structure, so that the slabs and columns of these lower two stories behaved more like a flexible,

moment resisting space frame.

(a) (b)

Figure 2.6. Typical damage due to wall discontinuity a) Olive View hospital, 1971 San Fernando earthquake [NISEE 2010a]

b) Imperial Country Service building, 1979 Imperial Valley earthquake [NISEE 1979]

Event though the building was designed for lateral forces higher than code requirements, the building had

been badly damaged (75 cm residual deformation at the ground floor) during the 1971 San Fernando

earthquake and subsequently had to be demolished. An analytical study by Mahin et al. [1976b] confirmed that

the brittle shear failure at the ground floor columns and the near field characteristic of the ground motion

were the two main reasons for such a significant damage. They suggested that if the shear walls were

continued to the foundation, better seismic performance could be expected.

The other example of this type of structure is the Imperial County Services (ICS) building, which is shown in

Figure 2.6.b. This six-storey reinforced concrete structures has a continuous shear wall at the east end of the

building, resulting in a severe discontinuity in east-west direction and a practically completely open first

Incomplete load

path

critical colums


storey. During the Imperial Valley earthquake in 1979, corner columns of the building were subjected to

significant bending, shear and axial forces, which led to the failure of the corner column as well as the first

storey columns at the end of the building [Pauschke et al. 1981]. This building was one of the first buildings

that was extensively instrumented and damaged by a moderate near field earthquake [Bertero 1997].

2.5 STRUCTURAL WALLS WITH LARGE OPENINGS AT THE BASE

This type of soft storey building is the less common. This is often found in masonry buildings, where

perforated structural walls are used at the first floor due to entrances or some other architectural

requirements, as shown in Figure 2.7.

Figure 2.7. Structural wall with opening in the first and typical floors

An example of such a structures is the three-storey shop in Santa Cruz that was damaged in the Loma

Prieta earthquake in 1989. Figure 2.8.a. shows the external view of this masonry building. The major damage

to this building is shown in Figure 2.8.b where the masonry pier were severely cracked. The normal forces at

the bottom of the pier causes such a compressive failure [EFFIT 1993]. This kind of failure mode is also

known as toe crushing fracture.

(a) (b)

Figure 2.8. a) Masonry building with large opening at base, Loma Prieta, 1989 b) detail damage to the pier


2.6 SUMMARY AND CONCLUSION

In summary, various kinds of soft storey buildings exhibit different behaviour to seismic ground motion.

Discontinuous infills in the ground floors cause a high reduction in stiffness at the first floor, which results in

forming plastic hinges at the top and the bottom of the vertical elements at this floor. Discontinuous

structural walls at the first floor are likely to suffer shear failures at this floor because shear strength is

reduced significantly in comparison to the adjacent upper floors. This phenomenon is to some extent

different to the strong beam-weak column in a frame type building. In such structures, flexural hinges are

more likely formed in the two ends of the first storey column instead of the beams. The reason is that the

flexural capacity of vertical columns is less than that of horizontal beams.

Among the aforementioned soft storey mechanisms, the first category is more common and could be more

applicable for this research purpose. Because discontinuous infills in the first floors are very likely to cause a

soft-storey at the ground level. In addition, they are likely to be characterised by reasonable displacement

capacity with flexural response of the hinging columns. This argument will be demonstrated analytically in the

next chapter through comparison of the results observed for different case study structures.

13

3.ASSESSMENT CASE STUDIES

3.1 INTRODUCTION

This chapter explores the analytical seismic response of a series of case study buildings. The seismic

vulnerability of a six-storey RC frame building is examined considering two different infill configurations. In

the first scenario, it is assumed that masonry infills are distributed over all storeys uniformly (referred to as

full infill), while in the next step and to consider soft storey effects, it is assumed that masonry infills are

omitted at the ground storey (referred to as partial infill or soft storey). The frame is representative of typical

buildings designed before the 1970s without following any capacity design rules for seismic protection.

With this in mind, Section 3.2 briefly introduces the case study configurations. The modelling approach and

analytical tools along with discussion on uncertainties on the joint modelling and masonry walls are discussed

in Section 3.3. Section 3.4 briefly describes selected ground motions used for nonlinear time history analyses.

Section 3.5 presents the analytical results obtained using nonlinear incremental dynamic analyses. The seismic

responses of the two frame buildings are also compared in this section, and then, potential advantages of a

partial infill case over the full infill case is studied. Section 3.2 briefly discusses and draws conclusions on the

results obtained in this chapter.

3.2 DESCRIPTION OF THE CASE STUDY

The six-storey three bay concrete frame structure shown in Figure 3.1 is studied in this work for two different

distributions of masonry infills. In the first scenario, it is assumed that masonry infills are distributed over all

storeys uniformly, while in the next step and for consideration of soft storey effects, it is assumed that

masonry infills are omitted at the ground storey. The first variant is called a full infill (FI) variant, while the

latter is called a partial infill variant, but can also be referred to as an open ground storey, or soft storey (SS) in

this report. The frame configurations are taken from Galli [2006]. These frames are representative of typical

buildings designed in Italy (and arguably elsewhere) during the 1950s to the 1970s. Accordingly, structural

elements were designed only for gravity loads without following any capacity design rules for seismic

protection.

The structure is part of a building formed by a series of parallel frames at a distance of 4.5 m between centrelines of columns. The first floor height is 2.75 m, while other floors have the same height of 3m such that all storeys have the same clear height. The frame consists of two equal exterior bays of 4.5 m length and one interior span with a length of 2 m. The frame is therefore symmetric about the vertical axis.

Figure 3.2 shows section configurations and reinforcement detailing of beams and columns in a typical bay of

the frame taken from Galli [2006].

The geometrical and material properties is summarized as follows:

ASSESSMENT CASE STUDIES 14

• Beam dimensions are assumed equal for all floors with 50 cm depth by 30 cm width, while, column

dimensions reduce up the frame height and were obtained from axial compression force requirements

only.

• All reinforcing bars are smooth round bars with hooked ends for anchorage.

• The amount of steel reinforcement for beams and columns were determined by Galli [2006] based on

Italian code provisions and the design handbook in effect before 1970 (Figure 3.2).

• Gravity design loads for beams are taken as 60 kN/m on the floor slabs and 50 kN/m at the roof level.

• Characteristic yielding strength of the bars and the concrete compressive strength are defined as 380 MPa

and 20 MPa respectively.

• Compressive strengths of masonry parallel and perpendicular to the holes are respectively 3.84 MPa and

2.7 MPa

(a)

(b) (c)

Figure 3.1. Six-storey concrete frame: a) bare frame, b) full infill uniform distribution (FI), c) Partial infill disconnected in

the first floor or Soft storey (SS)

C2 C3 C3 C2

C1 C2 C2 C1

C1 C2 C2 C1

C1 C1 C1 C1

C1 C1 C1 C1

C1 C1 C1 C1

C-I C-II C-III C-IV


Figure 3.2. Geometric and mechanical properties of beams and columns, from Galli [2006]

Section A-A Section B-B

Column C1 Column C2 Column C3


3.3 MODELLING APPROACH

In order to permit the development of the various possible failure mechanisms in the model, care should be

taken in the modelling approach. For the case of RC frames, in addition to allowing beam hinging, it is

important to adequately capture the effects of axial load-moment interaction in columns, masonry infill

failure, and joint failure. The following sections discuss the methodology that is used for the modelling of

components of the case study RC frame.

3.3.1 Modelling of beams and columns

Several approaches are available in the literature to model the nonlinear behaviour of structural elements,

which are differentiated depending on the distribution of the plasticity through the member cross sections

and along its length. For simulating the inelastic response of beam-columns, two general idealized models can

be found in the literature; distributed plasticity and concentrated plasticity. The former approach is

subcategorized to three methodologies as finite length hinge zone, fibre section or finite element, while the

latter could be found in the form of the lumped plastic hinge or the nonlinear spring hinge [Deierlein et al.

2010]. Among them, the fibre element and the lumped plastic hinge are the most common approaches that

are used for modelling of structural elements.

The fibre element model allows representation of details of the geometry and material properties of members

and enables the description of the history of stresses and strains at fibres along the length or across the

section dimensions. The sectional stress-strain is obtained through the integration of the nonlinear uniaxial

material response of the individual fibres, in which the section area of the element is subdivided into finite

regions referred to fibers. The number of fibres depends on the type of the section, the target of the analysis

and the level of accuracy that one wants to achieve. However, to achieve a high level of accuracy, a high

level of knowledge of mechanical and geometrical properties of the structural elements is required. As a

results of high level of uncertainties in a real building, this may lead into a significant error. In addition, it is an

expensive approach due to high computational demands.

The lumped plasticity model concentrates inelastic deformations at the two ends of the member. Beams and

columns are modelled using the Giberson one-component model [Sharpe, 1974]. The stiffness of the hinge is

characterised using the appropriate moment-curvature hysteretic rule over a predefined plastic hinge length.

Such elements have a relatively condensed numerically efficient formulation, and thus, it is the simplest

approach for frame structures. To take into account the effect of axial load variation on the capacity of the

column elements, the M-N interaction diagram is defined. Furthermore, strength degradation curves, which

are a function of the number of cycles or ductility demand, can be associated to the chosen hysteretic rule to

consider the increasing loss of strength in elements that experience in-elastic deformations.


To select the analysis tool, it is essential to understand the assumptions and the expected behaviour of the

model type. The focus of this section is to compare the global seismic response of the two RC frames with

different infill configuration, rather than calculate the exact seismic capacities. While distributed plasticity

formulations can precisely predict variations of the stress and strain through the section and along the

member, the phenomenological concentrated hinge model may capture more effectively the relevant feature

with the same level of approximation. As such, the lumped plasticity model is used for all numerical analyses.

The inelastic dynamic analysis program Ruaumoko [Carr 2004] was used for the numerical analyses. A two-

dimensional non-linear Giberson beam element (refer Carr, 2006) was used for modelling the beams and

columns in Ruaumoko. This Program contains several types of moment-curvature hysteretic rules for

definition of plastic hinges in the elements and joints. Among them, the Takeda hysteretic rule [Otani 1974]

was selected. In this model, the unloading and reloading stiffness reduces as a function of ductility

(Figure 3.3).

Figure 3.3. Takeda hysteretic rule, Emori unloading [Otani 1974]

The Emori and Schonbrich [1978] model was used in order to obtain the unloading stiffness. Due to the fact

that the structure is designed for gravity loads only, the hysteretic shape should be defined so that relatively

low levels of energy dissipation occur, assuming relatively high axial load ratios (which lead to relatively

pinched hysteretic response), low effective confinement and possible effects of bar slip. For this reason the

parameters � and � of the Takeda model [Carr 2004] were chosen to be 0.5 and 0.0 respectively, instead of

larger factors that are traditionally recommended [see Priestley et al. 2007]for new RC frames. Future research

could investigate the impact of using alternative hysteretic models on the global response of the structure. The numerical program CUMBIA [Montejo 2007] was used to define the initial and the post-yield stiffness of

beam and column elements . This program contains a set of Matlab codes to perform monotonic moment

curvature analyses. Figure 3.4.a shows the moment -curvature of columns of the first and the second floor.

Displacement

FFy

dy

dm

Ku

rK0

rK0

dp

β.dp

K0

Force

� = � �� ∝


The default values proposed by the program were used to obtain these curves. The unconfined strain of

concrete and the ultimate steel strain were determined as 0.005 and 0.1, respectively.

(a)

(b)

Figure 3.4. Mechanical properties defined for columns a) Moment-Curvature, b) axial load–moment interaction

To take into account the effect of axial load variations due to the lateral loading on the column strength, the axial load-moment interaction diagrams were also determined. Figure 3.4.b shows the axial load-moment interaction of the three types of the columns (see

Figure 3.2).

Shear Capacity:

The shear strength of columns was calculated using the program CUMBIA [Montejo 2007]. This model,

which is based on the revised UCSD shear model, calculates the shear capacity of members as sum of three

separate components: steel, concrete and the axial load [Kowalsky 2000].

Figure 3.5 shows the shear capacity versus the lateral drift ratio of the columns at the first floor. The shear

surface line corresponds to the assessment of the shear strength of existing structures (rather than design new

structures). The double bending condition was assumed to calculate the shear capacity and the lateral

resistance of columns. This assumption, however, could be conservative because column ends can rotate due

to the flexibility of the structure. For both columns, the minimum shear capacity Vmin (occurs at the

0 0.05 0.1 0.15 0.2 0.250

50

100

150

Curvature (1/m)

Mo

mn

et(

kN

)

(b)

1st floor-middle

1st floor-side

2nd floor-middle

2nd floor-side

0 50 100 150 200-1000

0

1000

2000

3000

Momnet (kN.m)

P(k

N)

Column C1

Column C2

Column C3


maximum drift ratio) is higher than the maximum lateral resistance obtained from the moment curvature

analysis. This implies that shear failure does not occur at columns of the first floor.

Lateral drift ratio (%) Lateral drift ratio (%)

(Middle columns) (Side columns)

Figure 3.5. Shear capacity of columns at the first floor

Table 3.1shows the minimum and the maximum shear capacity (Vmin and Vmax in Figure 3.5) of all beams

and columns of the building. The maximum lateral resistance of columns that are obtained from the moment

curvature analysis (Fmax) is also shown in this table. The table indicates that the shear capacity of all beams

and columns is higher than their lateral resistance. Thus, shear failure would not be critical in the responses of

this case study frame.

Table 3.1. Masonry mechanical properties

Element Floor Column Fmax (kN) Vmin (kN) Vmax (kN) Shear Check

Column 1 Middle 91 123 193 ok

Side 58 92 144 ok


Side 41 73 107 ok


Side 38 66 107 ok


Side 35 64 105 ok


Side 31 62 102 ok


Side 27 58 99 ok

Beam All Middle 114 207 207 ok

Side 59 212 212 ok

0

50

100

150

200

250

0 1 2 3 4 5

Force (kN)

Laterar resistance

Shear Capcity

Vma

Vmin

0

50

100

150

200

0 1 2 3 4 5

Force (kN)

x 0.0275

Lateral resistance

Shear capacity

Vmin

Vmax


3.3.2 Modelling of masonry infills:

A widely used approach was adopted for the modelling of masonry infills, which is based on the use of axial

springs acting as equivalent compression diagonal struts. To this end, two diagonal compressive struts

connecting centre to centre of the panel zone were modelled as an axial spring. Despite the fact that local

effects of the frame-panel interaction are ignored with this model, it was assumed that this will not have a

significant effect on the results of this study, since global behaviour of frames with different mechanisms is

the majority of interest to be explored. Nevertheless, future research could check this assumption.

The stiffness of the equivalent diagonal strut was evaluated according to modified Stafford [1969] model

proposed by Bertoldi [1993], where the height of the equivalent strut section, b� is calculated as

Equation 3.1:

�� = �λℎ + � , λ = � �!�sin (2')4 *+,ℎ�

- ( 3.1 )

where �� is the diagonal length of the panel, E� and E/ are elastic modulus of masonry and concrete, h�and

t� are height and thickness of the panel, I3 moment inertia of the column cross section and θ the panel

inclination respect to the horizontal. Parameters of K� and K� are described in Table 3.2 as a function of λh. Table 3.2. Parameters of the equivalent diagonal strut model [Bertoldi 1993]

λh <3.14 3.14<λh<7.85 λh >7.85

K1 1.3 0.707 0.47

K2 -0.178 0.01 0.04

The properties of the equivalent diagonal struts used in the model were defined to be representative of a

masonry type similar to the one used for the pseudo-dynamic tests performed at the Structural Laboratory of

the University of L'Aquila[Colangelo 1999]. Compressive strength for (246 × 118 × 79) horizontal hollow

brick in the direction parallel and perpendicular to the holes is respectively, 16.36 MPa and 2.19 MPa. The

mechanical properties of the masonry walls are given in Table 3.3. The compressive strength and the elastic

modulus of the masonry are obtained in two directions of parallel (horizontal) and perpendicular (vertical) to

the brick holes.

Four modes of failures were considered in order to evaluate strength of masonry infills [Bertoldi 1993]:

compression at the centre of the panel, compression of corners, sliding shear failures, and diagonal tension

(induced by shear). The equivalent strength σ� for the all mentioned mechanisms was evaluated according to

Table 3.4. In this table, parameters f�=, f�>and f�? are respectively, sliding resistance of mortar joints, shear


resistance under diagonal compression and compression resistance of the material. The parameter σ@ is the

vertical compression stress due to gravity loads.

Table 3.3. Masonry mechanical properties

Properties of Masonry (Mpa) Mean

Horizontal Compressive strength 3.84

Elastic modulus 2586

Vertical Compressive strength 2.7

Elastic modulus 11.95

Shear modulus 1389

Shear strength 0.57

Sliding resistance of mortar 0.3

Poisson coefficient 0.2

Table 3.4. Failure modes in masonry infill panels [Bertoldi 1993]

Failure mechanism Ultimate strength (AB)

sliding shear (1.2sin ' + 0.45c�E ')F�G + 0.3 H��

diagonal tension 0.6 f�> + 0.3 σ@b�d�

compression at centre of panel 1.16f�′ tan θK� + K�λh

compression of corners 1.12f�? Sin θ cos θK�(λh)M�.�� + K�(λh)M�.NN

The horizontal projection of ultimate load corresponding to each failure mechanism was obtained so that the

ultimate stress is considered constant on the cross section of the masonry strut, and calculated as

Equation 3.2

O� = �!��cos' ( 3.2 )

The cyclic behaviour of the infill panel was modelled adopting the hysteretic rule proposed by Crisafulli

[1997]. This model takes into account the non-linear response of masonry in compression, including contact

effects in the cracked material (pinching) and small cycle hysteresis. Based on this model, stiffness

degradation due to shortening of the contact length between the frame and panel is also considered, as shown

in Figure 3.6.


Figure 3.6. Hysteretic cycles of Masonry struts, [Carr 2004]

It should be noted that this model incorporates only the most frequent of modes of failure, which could

predict the exact behaviour of the structure. In addition, the dispersion of mechanical properties of masonry

with respect to the mean values increases uncertainty of the infills characteristics and affects the global

response of the structure.

3.3.3 Modelling of joint elements:

The beam-column joints were modelled with a couple of rotational and axial springs based on a modified

simple model proposed by Trowland [2003]. A prior model of this type, proposed by Pampanin et al. [2002],

consists of a nonlinear rotational spring that permits to model the relative rotation between beams and

columns. In the modified model (Figure 3.7), the spring is split in two elements that are interposed between

the beam’s connection node and the upper and lower column nodes respectively. The upper and the lower

column ends are slaved in lateral translation and rotational. The advantage of the modified model is that

effect of axial load on the joint resistance is also included, when structure is subjected to cyclic lateral loading.

To this end, the axial load-moment interaction surface was introduces to the joint springs. This interaction

allows to consider the variation of the cracking moment in the positive and the negative direction.

Figure 3.7. Modelling of beam column joint [Trowland 2003]

γE

Axial Strain

Ax

ial

Str

ess

Linear elastic

frame element

Rigid end blocks

Potential flexural

plastic hinges

Zero length

axial spring Rotational

spring


The moment-rotation relationship of the rotational spring was obtained based on experimental tests

implemented by Pampanin et al. [2002]. A relation between the shear deformation and the principal tensile

stress was found and transformed into the moment-rotation relationship. It was assumed that the shear

deformation of the joint panel is equal to the rotation of the spring. The moment was calculated from the

principal of tensile stress evaluated based on the Mohr theory. According to the test results [Pampanin et al.

2002], the principal tensile stress at first cracking was defined as P. QRST? and P. QURST? for exterior and

interior joints, respectively (Figure 3.8). Hardening behaviour for post-cracked area was assumed for interior

joints up to P. VQRST?, while elasto-plastic behaviour model was adopted for exterior joints.

The spring elements used were identical and they both had half of the joint strength and stiffness. The elastic

axial and rotational stiffness of the joint spring was calculated from:

W = *X*Y , Z = [* \ 0.9�]^^ − 0.9�]` X* ( 3.3 )

where ab and cb are concrete elastic and shear modulus, dT is the column cross section area, e , fg and h

are inter-storey height, beam depth and half of joint panel height, respectively.

Figure 3.8. Monotonic and cyclic behaviour of shear hinge joint model, [Pampanin et al. 2002]


Figure 3.9. Pampanin Hysteretic rule used in Ruaumoko, [Carr 2004]

The cyclic behaviour of the joint rotational spring was defined using a hysteretic rule available in Ruaumoko

program and specifically proposed to describe the characteristics of the joint response. In particular, the

adopted hysteretic loop is able to describe the typical "pinching" effect due to the slippage of plain round

reinforcing bars through the joint panel zone and to the opening and closing of diagonal shear cracks in the

joint region. As it can be seen in Figure 3.9, the hysteretic rule needs the definition of some parameters

governing the unloading and reloading phases of the cycle.

3.4 GROUND MOTION USED FOR TIME HISTORY ANALYSIS

Time history analyses were carried out using ten recorded horizontal accelerograms selected as part of the

DISTEEL project [Maley et al. 2013]. The record set consisted of 10 records that were scaled to be

compatible with Eurocode 8 spectrum [CEN 2004] for soil type C and a corner period Td = 8s. Figure 3.10

shows the acceleration and displacement response spectra of the selected records. The records show a good

fit with the EC8 design displacement spectrum (shown for a peak ground acceleration (PGA) on rock of

0.4g) but they drop below the design acceleration spectrum in the low period range (T< 1s). This variation is

evident from the COV of 0.553 for the short period range. In comparison, the COV for the medium and

long period ranges are 0.262 and 0.182 respectively. Table 3.5 lists all earthquake records used in the time

rK0

Kα2

Ks2

Kα1

Ks1

Ks1

K0

rKo

Ks2

dpβ.dp

Kα2

Kα1∆F

∆F

F

∆

Parameter T1 T2 L1 C2 �E1 1.2 1.3 1.3 1.2 ij 1.5 1.3 1.4 1.3 ��1 -0.1 -0.1 -0.1 -0.1 ��2 0.9 0.8 0.8 0.95 ∆O 30 30 20 30 � -0.2 -0.3 -0.1 0

l� = m/olG�

l� = m/olG�

p� = m/olp� p� = m/olp�

p� = m/olp�


history analysis and includes the event magnitude (M), scaling factor and scaled PGA required to obtain

compatibility with the EC8 spectrum constructed at a PGA of 0.4g.

Table 3.5. Record Set used for nonlinear time history analysis

No. Earthquake M Distance

(km)

Scaling

Factor

Scaled

PGA (g)

EQ 01 Chi-Chi, Taiwan 7.62 36 2.1 0.14

EQ 02 Kocaeli 7.51 127 7.9 0.70

EQ 03 Landers 7.28 157 4 0.21

EQ 04 Hector 7.13 92 2.9 0.29

EQ 05 St Elias, Alaska 7.54 80 1.5 0.24

EQ 06 Loma Prieta* 6.93 28 1.8 0.45

EQ 07 Northridge-01 6.69 52 5.8 0.32

EQ 08 Superstition Hills-02 6.54 13 2.3 0.49

EQ 09 Imperial Valley-06 6.53 22 5.1 0.71

EQ 10 Chi-Chi, Taiwan-03 6.2 40 5.6 0.38

In order to run Incremental Dynamic Analyses (IDA) nine different hazard levels are used for the set of

records with the following peak ground accelerations for each intensity level: 0.05g, 0.10g, 0.15g, 0.20g, 0.25g,

0.30g, 0.35g, 0.40g, and 0.60g. As such, 90 non-linear time-history (NLTH) analyses were run for each

building.

3.5 ANALYTICAL RESULTS

Response parameters of interest such as the peak inter storey drift ratio , the peak floor acceleration and the

residual inter storey drift ratio are plotted versus the intensity of the ground motions. In order to estimate the

mean response of all ground motions, the geometric mean value (defined as per [Shome 1999]) using

Equation 3.4 is adopted. The geometric mean is a logical estimation of the median especially if the data are

sampled from lognormal distribution [Benjamin and Cornell 1970].

xr = exp[∑ ln xxyxz�{| ] ( 3.4 )

where x~ geometric means value and n is is the number of observations. The response of each variant is

described in the following sections.


Figure 3.10. Acceleration and displacement Response Spectra for the selected records sets

3.5.1 Variant 1: Uniform Distribution of Infills (FI)

The natural first period of the full infill case is 0.328 sec, which represents to some extent a stiff structure.

Results of nonlinear time history analysis are presented in the following graphs. Figure 3.11 to Figure 3.14

present response parameters of interest, which include maximum storey drift, residual drift storey, and

maximum floor acceleration at each intensity (hazard) level. The dashed lines represent the responses from

each individual earthquake, while the solid thick line provides the geometric mean values calculated from

Equation 3.4.

The peak floor accelerations over the building height are presented in Figure 3.11. At the range of low

intensity levels (PGA less than 0.2g), the plot indicates a linear distribution of the acceleration over the height.

However, when the intensity increases, the distribution is changed. For the range of high intensity levels,

more than 0.35g, the acceleration is almost uniform through the building height. This is likely because the soft

storey mechanism is formed, as explained in the next paragraph.

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8A

cce

lera

tio

n (

g)

Period (s)

Earthquakes

Design

Mean

0

50

100

150

200

0 2 4 6 8

Dis

pla

cem

en

t (c

m)

Period (s)

Earthquakes

Design

Mean


Figure 3.11. Peak floor acceleration profile obtained from the nonlinear time-history analysis for different hazard levels, full

infill (FI) variant

Figure 3.12 shows the peak drift ratio over the height of the frame structure for intensity levels from 0.05g to

0.6g. When the intensity levels are less than 0.05g and 0.1g, the peak drift ratio over the height of the

structure decreases almost uniformly. Tis pattern of the drift ratio indicates that the soft storey mechanism is

not formed at these low intensity levels. However, when the intensity increases to 0.15g, the peak drift ratio at

the second floor is larger than that of the first floor, which implies the presence of soft storey mechanism at

the send floor. When the intensity level increases, the increase of the drift ratio at the second floor is much

more than that at other storeys. This increase is another indication of forming soft storey mechanism at the

second floor.

The formation of soft storey at the second floor is likely because infills are crashed at higher intensity level,

which produces a significant reduction of stiffness at this level. Consequently, and since the lateral resistance

of columns at this floor is less than the shear storey demand, and that gravity columns are designed weaker

that beam elements, plastic hinges are formed at the columns of the second floor.

0 0.2 0.41

2

3

4

5

6PGA=0.05g

0 0.5 11

2

3

4

5

6PGA=0.10g

0 0.5 11

2

3

4

5

6PGA=0.15g

0 0.5 11

2

3

4

5

6PGA=0.20g

sto

rey

0 0.5 1 1.51

2

3

4

5

6PGA=0.25g

0 0.5 1 1.51

2

3

4

5

6PGA=0.30g

0 0.5 1 1.51

2

3

4

5

6PGA=0.35g

0 0.5 1 1.51

2

3

4

5

6PGA=0.40g

Peak floor acceleration (g)

0 0.5 1 1.51

2

3

4

5

6PGA=0.60g

Mean value Individual Earthquake


Figure 3.12. Inter storey drift profile obtained from nonlinear time-history analysis for different hazard levels, full infill (FI)

variant

The peak drift ratio at the second floor compared to that of the other floors increases more rapidly when the

intensity increases. For example, the peak drift ratio of the third floor at the intensity levels of 0.3g and 0.6g

are 0.5% and 1.0%, which is almost doubled. However, it is quadrupled at the second floor, in which the peak

drift ratio is increased from 0.8% at the intensity level 0.3g to almost 3.2% at the intensity level 0.6g. This

rapid increase could be attributed to the presence of the soft storey mechanism that is formed at the second

floor.

Forming soft storey mechanism at upper storeys can be a possible response of these types of structures

because columns were designed for gravity loads only, and thus section depths are reduced in the upper

stories. Sullivan and Calvi [2011] proposed the sway-demand index, SDi for prediction of the column sway

behaviour, according to Equation 3.4:

SDx = ��,��,��],��],� ( 3.5 )

0 0.05 0.10

2

4

6PGA=0.05g

0 0.2 0.40

2

4

6PGA=0.10g

0 0.2 0.40

2

4

6PGA=0.15g

0 0.5 10

2

4

6PGA=0.20g

sto

rey

0 1 20

2

4

6PGA=0.25g

0 1 2 30

2

4

6PGA=0.30g

0 2 40

2

4

6PGA=0.35g

0 2 4 60

2

4

6PGA=0.40g

Peak drift ratio(%)

0 5 100

2

4

6PGA=0.60g



where Vx.� and Vx,� are the storey shear demand and resistance at level i, respectively, V�,� is the base shear

demand, and V�,� is the shear resistance at the base of the structure. The higher sway demand index

represents the higher possibility of occurrence of the column sway mechanism.

Figure 3.13 shows the residual inter storey drift ratio obtained from the IDA. The time history analyses were

run 100 seconds more than the actual records in order to have a better estimation of residual displacement.

Residual displacement for the intensity level 0.60g is to some extent considerable and remained as 0.45%,

while for other levels it is less than 0.2%. Similar to the case of inter storey drifts, residual drifts are also

dominant in the second floor where the soft storey has occurred.

Figure 3.13. Inter storey residual drift profile obtained from nonlinear time-history analysis for different hazard levels, full

infill (FI) variant

Figure 3.14 shows the maximum response of interest obtained from the IDA. The thin dashed lines show the

responses obtained from individual time history analysis records. The thick dashed and the thick solid line

represents the mean and the geometric mean of the responses, respectively. As shown in Figure 3.14.a, the

mean and the geometric mean of the peak drift ratio are close to each other which indicates a monolithic

increase with the intensity level. However, the slope increases as the intensity level increases.

0 2 4

x 10-3

0

2

4

6PGA=0.05g

0 2 4 6

x 10-3

0

2

4

6PGA=0.10g

0 0.005 0.010

2

4

6PGA=0.15g

0 0.01 0.02 0.030

2

4

6PGA=0.20g

sto

rey

0 0.1 0.20

2

4

6PGA=0.25g

0 0.5 10

2

4

6PGA=0.30g

0 0.5 10

2

4

6PGA=0.35g

0 0.5 10

2

4

6PGA=0.40g

Residual drift ratio (%)

0 0.5 10

2

4

6PGA=0.60g



This trend is to somehow different for residual drift ratio (Figure 3.14.b), which is almost zero for the

intensity levels below 0.2g, and then, it increases rapidly. The classic mean value calculates the average of all

individual responses better than the geometric mean value. That is likely due to the presence of zero residual

drift ratio (or very low values) that are obtained from some ground motions. That could create misleading

values in the logarithmic calculations. Thus, the geometric mean value could not be an appropriate tool to

represent the residual drift ratio, if values are very low.

Figure 3.14. Peak response of interests obtained from incremental dynamic analysis, full infill (FI) variant

Figure 3.14.c presents the IDA curve for the peak floor acceleration, which is increased almost linearly up to

the intensity level of 0.35g. After this level, the slope is decreased as the intensity increases, which could be

due to forming plastic hinges at the second floor. Figure 3.14.d shows the comparison of the peak drift ratio

and the residual drift ratio. Despite the fact that the peak drift ratio at the highest intensity level reaches

almost 3.5%, the peak residual displacement are very low (0.5%). The presence of infills at all floors could be

the reason that the residual displacements are not significant.

3.5.2 Variant 2: Partial Distribution of Infills- Soft First Storey (SS)

In the second case study, the aforementioned frame analysed for a condition that the masonry infills on all

floors are removed at the first floor. Figure 3.15 presents the peak floor acceleration obtained from individual

ground motions as well as the mean values.

0.050.10.150.20.250.30.350.4 0.60

2

4

6

8

Pea

k d

rift r

atio %

PGA(g)

(a)

0.050.10.150.20.250.30.350.4 0.60

0.2

0.4

0.6

0.8

1

Resid

ua

l dri

ft r

atio

%

PGA(g)

(b)

0.050.10.150.20.250.30.350.4 0.60

0.5

1

1.5

Pe

ak flo

or a

cce

lera

tio

n(g

)

PGA(g)

(c)

Mean Geomteric Mean Individual Earthquake

0.050.10.150.20.250.30.350.4 0.60

1

2

3

4

PGA(g)

Pea

k a

nd r

esid

ual d

rift

(d)

Mean Interstory Drift

Mean Interstory Residual Drift


The plots show almost uniform distribution of the acceleration response over the height of the building. This

distribution is almost the same over all the intensity levels, which indicates that the soft storey is likely formed

at even the low intensity levels. However, the shape of the peak floor acceleration is changed slightly when

the intensity level is increased. This could because the nonlinear response changes the governing mechanism

at higher intensity levels.

Figure 3.15. Peak floor acceleration profile obtained from nonlinear time-history analysis for different hazard levels, Soft

storey (SS) variant

Figure 3.16 shows the peak drift ratio of the SS variant. The plots indicate that at the intensity level 0.4g

(DBE) the drift ratio at the first floor is very large, e.g. 3.9%. However, the upper stories are isolated and

remained without considerable amount of drift, i.e. less than 0.5%. Furthermore, the soft storey mechanism

at the first floor is formed at even a very low level of intensity. At the intensity level 0.2g, the drift ratio at this

first floor is almost five time than that of the upper floors (compare 0.2g to 0.05g).

In contrast with the FI variant, as the intensity level increases, the drift ratio at the first floor of the SS variant

is not changed significantly compared to that of the other storeys. Thus, it could be concluded that the

relative stiffness of the first floor to that of the other floors remains constant or is changed slightly. This

0 0.1 0.21

2

3

4

5

6PGA=0.05g

0 0.2 0.41

2

3

4

5

6PGA=0.10g

0 0.5 11

2

3

4

5

6PGA=0.15g

0 0.5 11

2

3

4

5

6PGA=0.20g

sto

rey

0 0.5 11

2

3

4

5

6PGA=0.25g

0 0.5 11

2

3

4

5

6PGA=0.30g

0 0.5 11

2

3

4

5

6PGA=0.35g

0 0.5 11

2

3

4

5

6PGA=0.40g

Peak floor acceleration (g)

0 0.5 11

2

3

4

5

6PGA=0.60g



could be due to the absence of the infills in the first floor. On the other hand, and similar to the FI variant,

the drift ratio at the second floor has an increasing trend as the intensity increased. This increase can be again

due to failure of masonry infills at this level.

Figure 3.16. Inter storey drift profile obtained from nonlinear time-history analysis for different hazard levels, soft storey

(SS) variant

Figure 3.17 shows the residual drift ratio of the SS variant at all level of intensities. The pattern of the residual

drift ratio at all intensity levels are similar to what observed for the peak drift ratio. The figure indicates that

the residual deformations are also concentrated at the first floor, while other floors remain without or with

very low values. At the level of intensity 0.4g, the residual drift ratio at the first floor is almost 0.5%.

However, the residual drift at storeys above the first floor is almost zero. Similarly, at the intensity level of

0.10 g, the residual drift ratio at the first floor is almost 0.01%, which is much more than that of storeys

above this floor.

Again, as the intensity level increases, the residual drift ratio at the first floor increases more rapidly than that

of the storeys above the first floor. It can be seen that the residual drift ratio at upper storeys are almost zero

or very low at all levels of intensity.

0 0.2 0.40

2

4

6PGA=0.05g

0 0.5 10

2

4

6PGA=0.10g

0 1 20

2

4

6PGA=0.15g

0 1 2 30

2

4

6PGA=0.20g

sto

rey

0 2 40

2

4

6PGA=0.25g

0 2 4 60

2

4

6PGA=0.30g

0 2 4 60

2

4

6PGA=0.35g

0 5 100

2

4

6PGA=0.40g

Peak drift ratio(%)

0 5 100

2

4

6PGA=0.60g



As a result, the reduction of the residual deformations at storeys above the first floor is another advantage of

forming soft storey at the first floor. However, one should note that the residual drift at the first floor must

be controlled and remain in an acceptable range. Otherwise, the building could not be in a suitable

performance after the earthquake.

Figure 3.17. Residual storey drift profile obtained from nonlinear time-history analysis for different hazard levels, soft storey

(SS) variant

Similar to the FI variant, peak responses from different hazard levels are plotted for the SS variant.

Figure 3.18 shows the IDA curves corresponding to the peak drift ratio, the residual drift ratio and the peak

floor acceleration. In contrast to the FI variant, the mean and the geometric mean values shown in this figure

are closer to each other. As the intensity level increases, the peak floor acceleration increases almost

constantly, whereas the residual displacement has some fluctuations.

In order to find the pattern of the damage and to compare the seismic demand to the capacity of structural

elements, a displacement damage index DDI defined as the following equation is calculated for structural

elements.

��+ = �� ( 3.6)

0 2 4

x 10-3

0

2

4

6PGA=0.05g

0 0.02 0.040

2

4

6PGA=0.10g

0 0.2 0.40

2

4

6PGA=0.15g

0 0.2 0.40

2

4

6PGA=0.20g

sto

rey

0 0.2 0.40

2

4

6PGA=0.25g

0 0.5 10

2

4

6PGA=0.30g

0 0.5 10

2

4

6PGA=0.35g

0 0.5 1 1.50

2

4

6PGA=0.40g

Residual drift ratio (%)

0 0.5 1 1.50

2

4

6PGA=0.60g

Figure A.4.2. Residual drift ratio, Variant: SS-NPD



where �� is the maximum curvature demand attained during the seismic loading and �G is the ultimate

curvature capacity of the section obtained from the section analysis presented in 3.3.1. A value of DDI larger

than unity indicates that an element reaches its ultimate capacity.

Figure 3.18. Peak response of interests obtained from incremental dynamic analysis, soft storey (SS) variant

Figure 3.19 shows the maximum DDI obtained for beams and columns of each storey of the SS variant. First,

the DDI for all columns are higher than that of the beams in all storeys (especially at the first floor), and the

difference increases as the intensity increases. This significant difference could be because beams are stronger

than columns, and thus, plastic hinges are formed only in columns, as discussed before.

Second, the DDI for columns at the first floor is significantly higher than that of the floors above the first

floor. The DDI for columns at the first floor is almost unity at the intensity level 0.30g, which indicates that

these columns reach their ultimate capacity at this intensity level. This ultimate limit state corresponds to the

core crushing of the corner column (CI) and the middle column (CII) at the first floor, which is shown in the

IDA curve in Figure 3.18.a. As a results, the possibility of collapse of columns at the first floor and

consequently the soft storey frame increases after this intensity level. As it was explained in Section 3.3.1, no

shear failure in beams and columns was expected to occur.

0.050.10.150.20.250.30.350.4 0.60

2

4

6

8

10

Pe

ak d

rift r

atio

%

PGA(g)

(a)

0.050.10.150.20.250.30.350.4 0.60

0.5

1

1.5

Re

sid

ua

l dri

ft ra

tio%

PGA(g)

(b)

0.050.10.150.20.250.30.350.4 0.60

0.2

0.4

0.6

0.8

1

Pe

ak flo

or

acce

lera

tion

(g)

PGA(g)

(c)

Mean Geomteric Mean Individual Earthquake

0.050.10.150.20.250.30.350.4 0.60

1

2

3

4

5

6

PGA(g)

Pea

k a

nd

re

sid

ua

l d

rift r

aio

(%

)

(d)

Peak drift ratio

Residual drift ratio

Core crashof CI

Core crashof CII


Figure 3.19. Displacement damage index (DDI) for beams and columns obtained from nonlinear time-history analysis for

different hazard levels, soft storey (SS) variant

3.5.3 IDA response comparison of variants

This section presents the comparison of dynamic responses of each variant. Table 3.6 illustrates response

parameters obtained for the two aforementioned variants in addition to the bare frame (Frame with no infills

in all floors). The acronyms T, FMPM, PDR, PRDR and PFA are, respectively, elastic period, first mode

participation mass in the elastic range, peak inter-storey drift ratio, peak residual drift ratio, and peak floor

acceleration at the level of intensity at which the PGA is 0.40g.

Table 3.6. Summary of response parameters obtained for three variants of case 1 with full infill, partial infill and bare frame

Variant Description T FMPM PDR PRDR PFA

Sec % % % g

Var. 1 Full Infill 0.32 78 3.05 0.42 1.01

Var. 2 Soft Storey 0.78 100 5.9 0.5 0.75

Var. 3 Bare Frame 1.94 78 - - -

Table 3.6 indicates the effect of infill on linear and nonlinear responses when infills are eliminated at the first

floor or through the whole structure. The elastic period is changed significantly from 0.32 sec with full infill

to 0.78 sec with partial infill, which represents a reduction in stiffness of around six times(R0.78/0.32 =5.95). The first mode participates 78% in the full infill case, while for the open ground storey case, the

0 0.02 0.04 0.060

2

4

6PGA=0.05g

0 0.1 0.20

2

4

6PGA=0.10g

0 0.2 0.40

2

4

6PGA=0.15g

0 0.5 10

2

4

6PGA=0.20g

sto

rey

0 0.5 10

2

4

6PGA=0.25g

0 0.5 10

2

4

6PGA=0.30g

0 0.5 1 1.50

2

4

6PGA=0.35g

0 1 20

2

4

6PGA=0.40g

DDI for Columns DDI fo Beams

0 1 2 30

2

4

6PGA=0.60g


dynamic response is fully governed by the first mode (FMPM = 100%). As such, the rigid body movement of

the building is dominant in the dynamic behaviour of the open ground storey frame, and thus, the effect of

higher modes could be negligible in such buildings.

Nonlinear response values in Table 3.5 change less than elastic values; peak and residual drift ratios increases

by factors of 1.9 (5.9/3.05) and 1.2 (0.5/0.42), respectively. The reason could be that masonry infill in the

second floor of the full infill case is damaged at higher intensity levels and causes a reduction of stiffness in

this floor. The full soft storey mechanism for the partial infill case occurs at the intensity level of 0.20g, where

all plastic hinges are formed in the first floor columns. A soft storey mechanism also forms for the full infill

case at 0.30g, when plastic hinges form in the second storey columns, after the masonry infill has lost its

resistance. The mechanism for the bare frame occurs at a low intensity level of 0.15g in the third and fourth

floors. However, due to the very high displacement demands on the bare frame variant at higher intensity

levels, the comparable peak response parameters could not be obtained.

Figure 3.20 shows the maximum of peak inter-storey drift ratio obtained from the nonlinear incremental

dynamic analysis (IDA) for the FI and SS variants. The maximum of peak inter-storey drift in the FI variant,

the maximum of peak inter-storey drift in the SS variant, and the maximum of peak inter-storey drift above

the first floors of the SS variant (referred as to isolated floors) are plotted separately. The maximum of peak

inter-storey drift in the SS variant occurs at the open ground floor, and thus, is indicated as the first floor in

this figure. It can be seen that the inter-storey drift of the isolated floors is reduced significantly. As the

intensity level increases, the level of isolation is increased. The maximum drift ratio at the first floor of the SS

variant at the intensity level of 0.6g is double of what it is for the FI variant, while the average drift in the

upper floors are less than 0.3%.

Figure 3.20. Comparison of the peak inter storey drift ratio (PRD) obtained from IDA for two variants of FI and SS

Figure 3.21 shows the comparison of the residual inter storey-drift for the two variants FI and SS. The

reduction of the residual drift at the isolated floors at this intensity level is even more considerable, where it is

reduced from 0.50% at the first level to 0.04%. The peak residual inter-storey drift for the FI variant is

around 0.47%, which is considerably larger than the values obtained for the upper floors of the partial infill

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.60

1

2

3

4

5

6

Pe

ak d

rift r

atio

(%)

PGA(g)

Variant 1, Full Infill

Variant 2, Partial Infill, first floor

Variant 2, Partial Infill, isolated floors


case. Furthermore, the peak and residual storey drift at the isolated floors are not increased considerably by

the increments of the intensity level.

Another parameter of interest is the average of the peak drifts over the total height of the building, which is

defined as the “average inter-storey drift”, shown in Figure 3.22. This parameter can be a good index for

estimation of the total distribution of damage in the building. By comparing the mean drift for the two

variants of full and partial infill, one can see that average drift of the partial infill (SS) variant is larger than

what for the full infill (FI) variant. However, the difference between the averages is considerably less than the

difference between peak values (that was previously shown in Figure 3.20). The reason is that the first storey

isolates the floors above itself, and consequently, the total drift distribution in the building is reduced. The

results of this figure provide motivation to carry out damage analysis and investigate loss estimates for the

two variants as a part of the future research.

Figure 3.21. Comparison of the residual inter storey drift ratio (RRD) obtained from IDA for two variants of full infill (FI)

and partial infill (SS)

Figure 3.22. Comparison of the average inter storey drift ratio obtained from IDA for two variants of full and partial infill

Figure 3.23 compares the maximum of peak floor accelerations over the height of both FI and SS variants.

Overall, the acceleration of the SS variant is less than that of the FI variant over a wide range of level of

intensities. As the intensity increases, the difference between floor accelerations increases. However, at lower

intensity levels, the peak floor accelerations of both variants are close to each other. This is explained by

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.60

0.1

0.2

0.3

0.4

0.5

Resid

ua

l d

rift r

atio

(%)

PGA(g)


Variant 2, Partial Infill, first floor

Variant 2, Partial Infill,isolated floors

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.60

0.5

1

1.5

2

Ave

rag

e In

ters

tore

y D

rift %

PGA(g)


Variant 2, Partial Infill


examining the acceleration response spectra that are shown in Figure 3.24. The elastic period of the full and

partial infill frames is 0.78 and 0.32 sec respectively. It can be seen that both these periods correspond to the

short period spectral plateau.

For high intensity levels, the period elongation of the SS variant is higher than that of the FI variant, which

results in lower acceleration demands for the whole structure. The maximum floor acceleration for the

seismic intensity corresponding to a PGA of 0.6 g is 1.03g for the full infill case, which is around 40% more

than the soft storey case, which is 0.74g.

Figure 3.23 could represent a potential financial advantage of the SS variant over the FI variant. The reduction

in peak floor accelerations in the soft storey frame could have a significant effect on the damage sustained by

non-structural components and building contents. This could highly reduce direct losses after a given

earthquake, as the value of non-structural elements usually comprises a significant percentage of a building

value.

Figure 3.23. Comparison of the peak floor acceleration (PFA) obtained from IDA for two variants of full and partial infill

Figure 3.24. Mean acceleration spectra for a period between 0.3 and 2.1 sec

Figure 3.25 compares the maximum of the DDI value of beams and columns of the two variants FI and SS.

For both variants and over all intensity levels, the DDI for all beams are less than unity, which indicates that

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.60

0.2

0.4

0.6

0.8

1

1.2

1.4

Pe

ak flo

or

acce

lera

tio

n (

g)

PGA(g)


Variant 2, Partial Infill

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.3 0.6 0.9 1.2 1.5 1.8 2.1

Acc

ele

rati

on

(g

)

Period (s)


no ultimate failure occurs in beams of the two variants. Although, beams at the first level of the SS variant are

much damaged than those in the FI variant, they are less damaged at the storeys above the first floor.

Figure 3.25. Comparison of the beams and columns DDI for the two FI and SS variants

For the FI variant, the DDI is more than unity only at the intensity level 0.6g, whereas for the SS variant, this

was occurred earlier at the intensity level 0.30g. At the intensity level 0.4g, the DDI of columns at the second

floor of the SS variant is significantly reduced (less than 0.1), while for the FI variant, this value is more than

0.6. The DDI of columns at all the isolated floors are less than that of the FI variant. One possible conclusion

could be that if the displacement capacity of the columns at the first floor of the SS variant is increased, the

total seismic damage and consequently the potential total repair cost of the building could be less than what is

expected in FI variant. Chapter 5 of this thesis proposes a strategy to achieve this goal. However, to better

understand the effect of potentially critical parameters, some key characteristics on the seismic response of

soft storey buildings are first explored in the next chapter.


A six-storey reinforced concrete frame building was analysed for two scenarios of partial and full masonry

infill, with soft-storey response developing at the ground storey for the partial infill case. The potential

advantages of buildings with open ground storeys were discussed. The modal analysis showed that the higher

mode effects are less important in the global dynamic responses of the partial infill case.

0 1 20

2

4

6PGA=0.2g

Sto

rey

0 0.5 10

2

4

6PGA=0.2g

Sto

rey

0 0.05 0.10

2

4

6

Sto

rey

0 2 40

2

4

6PGA=0.40g

Maximum Drift ratio(%)

0 1 20

2

4

6PGA=0.40g

DDI for columns

0 0.1 0.20

2

4

6

DDI for beams

0 5 100

2

4

6PGA=0.60g

0 2 40

2

4

6PGA=0.60g

0 0.2 0.40

2

4

6

FI-NPD SS-NPD


From an assessment perspective, the implications of the incremental non-linear time history analysis results

are that despite the large displacement demand at the soft storey level, the rest of the building is isolated

significantly. The peak floor accelerations in partial infill case are less than the full infill case, which can

reduce damage to non-structural elements. In addition, the peak and the residual inter storey drift at storeys

above the open ground floor was highly decreased. The average drift indicated that the total damage is

considerably reduced at the building level compared to the first storey level. Thus, one could say that the soft

storey mechanism could provide a tool for controlling the damage over the total building height, which could

affect the total repair cost. However, the potential of collapse of the soft storey variant is increased as the

intensity level is increased, reflecting the observations made in past earthquakes. The next chapter will study

the key parameters on the response of soft storey buildings.

41

4.FACTORS AFFECTING SOFT STOREY RESPONSE

4.1 INTRODUCTION

The effect of different structural characteristics on the seismic response of structures with soft storey

mechanisms is examined in this chapter. The objective is to explore the influence of potentially critical

parameters such as P-Delta effects, gravity loads, column post-yield ratio and ground motion duration on the

performance and vulnerability of structures with soft storey mechanisms.

The case studies assessed in the previous chapter are taken again as benchmark buildings and incremental

non-linear time history analyses are repeated varying some key parameters. In section 4.2, variants are

analyzed with and without inclusion of P-Delta effects, and responses are compared for a range of intensity

level. The influence of increasing axial load is also explored in this section. Section 4.3 repeats the numerical

analyses using a range of post-yield stiffness ratio for first storey columns to investigate the significance of

this parameter on the response of soft storey buildings. Section 4.4 explores the effect of ground motion

durations on the soft storey response. In section 4.5, the influence of some parameters such as longitudinal

bar ratio, dimension, axial load, and confinement factor on the hysteretic behaviour of reinforcement

concrete columns is investigated. This is attained by some cyclic analyses on columns with different

characteristics. The results obtained in this chapter will be helpful in development of an appropriate solution

to improve the response of soft storey buildings. Following a discussion of the results obtained in all sections,

section 4.6 proposes a potential retrofit strategy for soft storey buildings, which will then be then examined in

detail in the net chapter.

4.2 EFFECT OF P-DELTA

4.2.1 Introduction

The movement of the structural mass to a deformed position generates a second order-overturning moment,

which is generally termed a P-Delta Effect. Due to this effect, the overturning moment due gravity loads adds

to those results from lateral inertia forces. The next effect of this action is typically to increase the

displacement beyond those obtained from first order analysis. While P-Delta is usually negligible in the elastic

range of deformation, it may become significant for inelastic structural behaviour [Bernal 1987; Priestley et al.

2007]. The effect can also be intensified in case of large lateral inter-storey displacements, which is common

in soft or weak storeys. For such conditions, the displacements tend to be amplified in a single direction, and

during the impact of strong motion earthquakes, the building may reach a state of dynamic instability at a

rapid rate. Fundamental investigations of P-Delta induced collapse of inelastic SDOF systems subjected to

severe earthquakes have been presented by many researchers [Jennings and Husid 1968; Bernal 1987; MacRae

FACTORS AFFECTING SOFT STOREY RESPONSE 42

1994; Bernal 1998]. The description of the influence of P-Delta action on system behaviour is shown in

Figure 4.1 . In this figure, a single mass supported with a cantilever height H is subjected by a downward

gravity load ��and an equivalent lateral force O�. At a lateral displacement ∆ and under the combined lateral

and vertical loading, the base moment is developed from the two components. Thus, the lateral resistance O�

shown in Figure 4.2.a is calculated:

O� = � − ��.∆^ = O� − ��.∆^ = O�(1 − ��.∆O�^ ) ( 4.1 )

Figure 4.1. P-∆∆∆∆ Effects on design moments

(a) (b)

Figure 4.2. P-∆∆∆∆ Effects on force and response characteristics: a) general load deformation relationship; b) bilinear positive

curve

The term ��.∆/O�^ is a dimensionless parameter traditionally called the stability coefficient ' , used to

characterize second order effects. For a single storey structure it is defined as the reduction in the lateral

stiffness due to P-Delta effects. Neglecting local p- � effects and restricting deformations to amplitudes, the

stability coefficient were obtained as[Bernal 1987]:

H

P0

∆∆∆∆

P0

M=FH+P0 ∆

F

P-∆ FH

F 0

Without P∆

K0

r0 K0

F p

K p

F

∆

∆y ∆ u

1

Without P ∆

r0

1-θ

1

µµ m

rp Kp r0-θ

With P∆

F/F0

With P∆


'�∆ = �.∆O�^ = � �^ ( 4.2 )

where � is the first order initial lateral stiffness, and P is the total vertical load. Therefore, the reduced lateral

force capacity and stiffness shown in Figure 4.2.a was determined as

O� = O�(1 − '�∆) � = O�∆� = �(1 − '�∆) ( 4.3 )

The amount that the post-yield stiffness ratio is decreased as a function of the stability coefficient was found

as:

�� = �� − '�∆1 − '�∆ ( 4.4 )

Figure 4.2.b shows the influence of P-Delta effects on the normalized bilinear force displacement curve. For

an elasto-plastic system (r0 =0), the second order curve is defined by the first order results and '. The post

yield stiffness of a single-degree-of-freedom SDOF systems considering P-Delta effect KPP is calculated as

[Bernal 1987]

� = �� = �� − '�∆1 − '�∆ �(1 − '�∆) = �� − '�∆ ( 4.5 )

The limit of ductility o� was found as:

o� − 1 = 1 − '�∆�� − '�∆ = 1�, → o� = 1 + 1�, ( 4.6 )

4.2.2 Effect of P-Delta on hysteretic response

The significance of P-Delta effects depends on the shape of the hysteretic response. If the earthquake record

is long enough, reduction of post-yield stiffness instability will eventually occur, which causes collapse.

[Priestley et al. 2007] This phenomenon more likely happens if an elasto-plastic curve is adopted for defining

hysteretic characteristics. The reason has been explained because unloading lines has a tendency to shift to the

right hand of the graph, which after several cycles, strength will be lost. Furthermore, considering P-Delta

effects can increase residual displacements. On the other hand, if Takeda hysteretic rule is considered, this

effect can be less important due to gradual reduction of residual displacement. [Priestley et al. 2007]


4.2.3 Design procedure for P-Delta effects

There are several design procedures and recommendations proposed by researchers when P-Delta effects are

considered. Among them a displacement amplification factor �,∆, the ratio between displacement spectra

with and without P-Delta effects, proposed by Bernal [1987] is outlined here. Based on this work, behaviour

of displacement amplification factors for linear and nonlinear SDOF systems were investigated. Bernal found

that the inelastic amplification was only weakly dependent on the period for a range of initial period from

zero to two seconds. In the course of his parametric study, the following expression for �,∆, which is only a

function of stability coefficient and the design ductility, was proposed as:

�,∆ = 1 + �,∆',∆1 − ',∆ ( 4.7 )

where �,∆ = 1.87(o − 1)for mean amplification and �,∆ = 2.69(o − 1) for mean+1 standard deviation

amplification. He also offered a limiting ductility o�, which should be considered for design:

o� = 0.4',∆ ( 4.8 )

This ductility limit was obtained based on the concept of ultimate stability under the permanently deformed

state of the structure following the earthquake and assuming that the post-earthquake permanent deformation

is the maximum value compatible with the response ductility.

In addition to the above consideration, a practical range of values for stability ratio was determined as follows

[Bernal 1998]:

',∆ = � �^ = �� ^ = �� ^ = �'� ( 4.9 )

where � is the ratio of the total vertical load (dead load plus reduced live load) to the dead load, � is the inter-

storey drift ratio, and C is the code seismic coefficient.

4.2.4 Code recommendations

Most building design codes do not appear to give adequate guidance or advice on methods of counting for

and reducing P-Delta effects [Paulay and Priestley 1992]. In some instances [FEMA 1997]displacement

amplification factors are provided thus forcing implicit allowance for the modified response, rather than

explicit account for P-Delta behaviour. In the newer version [FEMA 356, 2000] all seismic forces and

displacements obtained from linear analysis approach are increased by the factor 1/(1 − ') when stability

coefficient of the first mode is more than 0.1. However, this limit could be inadequate unless the response is

elastic[Bernal 1987].


In most of the recent codes, the structure is considered as unstable when stability coefficient is more than a

limit. FEMA 356 considers this limit as 0.33, while based on Eurocode 8 [CEN 2004] this upper limit is

recommended as 0.3. In the recent New Zealand seismic design code provisions, considerations that are more

comprehensive have been provided. NBCC requires that the structure be stiffened if the stability coefficient

exceeds 0.4.

In the International Building Code [IBC 1998] and the National Earthquake Hazard Reduction Program

(NEHRP) 1997 provisions [BSSC 1997], the upper limit for the stability coefficient is given using the

following expression:

θ�� = 0.5�� ( 4.10 )

where � is the ratio of storey shear strength to the minimum storey design strength and �� is the deflection

amplification factor.

The upper limit of the stability coefficient recommended by these codes are essentially on the basis of the

Bernal [1987] study (summarised in the previous section) to guard against the potential for instability after

severe earthquakes. For a structure exhibiting an elastic-perfectly plastic hysteretic behaviour, the value of

0.40 ensures that structures are statically stable under factored gravity loads and post-earthquake permanent

displacements.

In addition to FEMA 356 condition, an analytical account of P-Delta effects under the ultimate limit state is

required for structures with period greater than 0.4 seconds or structures taller than 15m with period of 0.6

seconds. Based on this code, amplification is applied as a modifier to P-Delta moments such that the design

base moment becomes:

��? = ��^� + �. �. Δ��

� = � − 1o. ' ( 4.11 )

where � is the amplification of strength ��? /��, and o is the ductility demand.

4.2.5 Numerical results

This section presents numerical analyses of the two six-storey frame variants when P-Delta effects are

included in the nonlinear dynamic time history analysis.

Figure 4.3 compares the structural responses with and without P-Delta effects. For the full infill variant,

considering P-Delta effects does not have influence on the responses at intensity levels less than 0.4.


However, after this intensity level, both peak drift ratio and residual drift ratio amplifies in a rapid rate. This

amplification could be due to the failure of masonry infills at the second floor and forming soft storey

mechanism at this intensity level.

For the soft storey variant, the impact of P-Delta effects is significant in a broader range of intensity level.

The P-Delta amplification on the peak drift ratio can be seen after intensity level 0.25. The difference

between the system response with and without P-Delta effects is not significant at low levels of intensity, and

this is probably a reflection of the low stability indices for this structure. As the intensity increases, this

difference increases. The drift ratios for the SS variant at the hazard level 0.6g is less than 6.0%, while when

P-Delta are considered, this value exceeds 8.5%.

( a) ( b)

Figure 4.3. Comparison of IDA response with and without P-∆∆∆∆ effects: a) peak drift ratio, b) residual drift ratio

The effect of P-Delta on the residual drift is much more sensitive to the increasing level of intensity. It can be

seen that the residual drift at a PGA of 0.6g is less than 1% without P-Delta effects, while P-Delta effects

amplify this value by a factor of approximately 5.

4.2.6 Effect of Increased P-Delta Effects

The effect of increased P-Delta loads on the SS variant response is investigated in this section. This could be

expected for buildings with lateral load resisting frames in external bays and gravity frames internally, where

diaphragms are rigid and can transfer lateral loads from the middle spans to external ones. In this case,

vertical loads due to P-Delta effects are increased, while gravity loads on the columns are not changed. The

increasing of the P-Delta loads in critical conditions could easily be two times, where the P-Delta tributary

area in the external resisting frames is doubled.

Assuming this scenario, the nonlinear IDA was repeated when P-Delta loads are doubled. In order to

consider the effect of increasing the axial load related to P-Delta effects without changing the gravity load on

the case study column elements, dummy columns were added to the structure and extra vertical loads are

assigned to them (Figure 4.4).

0.050.10.150.20.250.30.350.4 0.60

2

4

6

8

10

Pe

ak d

rift r

atio

(%)

PGA(g)

0.050.10.150.20.250.30.350.4 0.60

1

2

3

4

5

6

Re

sid

ua

l d

rift r

atio

(%)

PGA(g)PGA(g)

FI-NPD SS-NPD FI SS


Figure 4.4. Dummy column modelling for considering effect of axial load

It should be noted that care is required in order to ensure that dummy columns do not add any stiffness to

the structure. For this reason, dummy columns are transversally slaved to a structural element at each level,

while other degrees of freedom (including end rotations) were released.

Results obtained for the SS variant where the total gravity load related to P-Delta effects is doubled (i.e. two

times the P-Delta coefficients, SS-DPD) are shown in Figure 4.5. In this case, the structure was unstable for

certain accelerograms at intensities greater than PGA=0.3g, with 90% of records causing dynamic instability

at a PGA=0.4g, and thus, the drift response is shown only up to an intensity level of 0.4g.

Figure 4.5. Comparison of responses obtained from incremental NTHA when the total gravity load is doubled

The results of this section indicate that vertical loads can have a significant effect on the response. The

incremental nonlinear time history analysis shows that for the case where the gravity load related to P-Delta

effects is doubled, the peak storey drifts at moderate levels of intensity and higher are more than two times

those for the case without P-Delta effects, and thus the potential collapse of the soft storey frame is

significantly increased. However, the increasing P-Delta effect on soft storey behaviour at low intensity levels

is not significant. As a result, it can be concluded that the importance of gravity load on the response of soft

storey buildings is highly affected by the intensity level, and the effect is increased as the intensity level is

Dummy

Column

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

5

10

15

20

Pea

k d

rift ra

tio

(%)

PGA(g)

SS-NPD

SS

SS-DPD


increased. Thus, the influence of gravity loads should be considered carefully in vulnerability assessments and

in the selection of retrofitting strategies.

4.3 EFFECT OF POST YIELD STIFFNESS

In this section, the effect of the post-yield stiffness ratio on the response trend lines is explored. The post

yield moment-curvature stiffness (r in Figure 3.3) were initially considered as r=0.01 percent of the initial

stiffness, which were obtained from the moment curvature analysis (Section 3.3.1). To this end, the nonlinear

analyses of the SS variant considering P-Delta effects repeated with a range of r-ratios: 0.025, 0.05 and 0.10.

Figure 4.6 represents comparison of responses using different r ratios and at different level of intensities.

Figure 4.6. Effect of post yield ratio of responses

The time history results indicate that the post yield ratio can affect responses particularly for some intensity

ranges. In a range of low and medium intensity levels, residual displacements at the first level are significantly

reduced by increasing r ratio. At the intensity level 0.40g, the residual drift ratio at the first floor is dropped

from 2.5 to 0.5 percent. However, the residual displacement at the second floor increases as r ratio increases,

and it is significant for r=0.10. Because the maximum floor resistance and consequently the tangent stiffness

at the first floor increase, which result in increase in seismic demands to upper storeys.

At the intensity level 0.6 g, when r increases from 0.01 to 0.1, the peak drift ratio at the first floor decreases

from 8.0% to almost 5.0%. The residual displacement at the first floor is also significantly reduced from 8.0%

to almost 1.0%. On the other hand, the peak drift ratio at the second floor increases significantly from almost

zero (for r=0.01) to more than 6.0% (for r=0.10). Such a large drift ratio at the second floor indicates that the

columns at this floor reaches their ultimate capacity, and consequently could increase the likelihood of

collapse of the building.

0 1 20

5

10PGA=0.2g

Sto

rey

0 0.2 0.40

5

10

Sto

rey

0 50

5

10PGA=0.40g


0 2 40

5

10

Residual drift ratio(%)

0 5 100

5

10PGA=0.60g

0 10 200

5

10

SS SS-R-0.025 SS-R-0.05 SS-R-0.10


As a conclusion, the potential advantage of increasing post yield drift ratio of columsn at the first level of soft

storey buildings could be reducing both peak and residual displacements at this single level. However, the

disadvantage is that they can increase seismic demands at the storeys above this floor. This strategy might not

be the best solution for retrofitting soft storey buildings because structural elements at the upper storeys

might be required to be strengthened, which could increase the retrofit cost.

4.4 EFFECT OF DURATION OF GROUND MOTION

The influence of strong-ground motion duration is the focus of this section. The importance of this effect is

due to the fact that the strong duration is closely related to the number of inelastic cycles that structural

elements suffer during earthquake excitation.

There are a number of studies related to effects of the strong-motion duration on the seismic response of

building structures. However, the findings regarding these effects are contradictory. Some studies report

significant effects, while other studies report minimal or no effects.

Hancock and Bommer [2006] observed that this controversy begins with response parameter used for the

quantification of the effects of strong-motion duration, and the definition of duration of strong ground

shaking of acceleration time histories recorded from earthquake events that adequately represent the time

interval when the energy content of the earthquake ground shaking produces significant damage to the

excited structure. Ruiz-Garcia [2010] concluded that strong motion duration does not have a significant

influence on the amplitude of peak residual drift demands in multi-degree-of-freedom MDOF systems, but

he pointed out that records having long strong-motion duration tend to increase residual drift demands in the

upper stories of long-period generic frames.

The following subsections investigate the effect of the strong-motion duration on the response of the

reinforced concrete frames with soft first storey (SS variant).

4.4.1 Selection of records

There are several definitions in the literature for determining the effective time duration of accelograms.

Among them, the most widely used measure of strong ground motion duration for earthquake engineering

purposes corresponds to the time interval over which 5% to 95% of the Arias intensity is transferred in the

acceleration time-history [Trifunac and Brady 1975]. The merit of this definition is that the use of Arias

Intensity has strong correlation with observed earthquake damages in short period structures as well as

structures on soils susceptible to liquefaction, but a limitation is that it does not explicitly take into account

differences in ground motion frequency-content as well as the source geophysical features [Bommer and

Martinez-Pereira 1999].


Based on the aforementioned definition, the records with relatively long duration were selected as tabulated in

Table 4.1. The motions originate from strong with a magnitude Mw of 8.0 to 9.0. The effective durations teff

are between 50 to 100 sec, which is (in average) 35% of the total motion duration t.

Table 4.1. Long duration record sets

It should be noted that the records were compatible with Eurocode 8 spectrum [CEN 2004] for soil type C

and a corner period Td = 8s. Acceleration and displacement response spectra for these set of records are

shown in Figure 4.7.a. It can be seen that the records does not show a good fit to the both acceleration and

displacement spectra especially for the period range between 0 to 4.0 sec. The corner period for these records

is almost 2.0 sec rather than 8.0 sec. In addition , as it can be seen from Table 4.1, for some records, the

scaling factor is significantly high, which could increase the inaccuracy of the analysis.

As a result, it was decided to match the records to the displacement design spectra with corner period Td=2.0

sec. To make a better comparison, new records set were also adopted for the short duration ground motions

that were matched to the same design spectrum, i.e. Td=2.0 sec, as it is discussed in the next section.

4.4.2 Match records to the design spectra and cornet period 2sec

A new record set of short duration is shown in Figure 4.8.a, which are matched to the displacement design

spectra with corner period 2 sec. These records were again chosen from DISTEEL project. Since the

available data (for short period ground motions) were based on soil type A, both short and long duration

ground motions were matched to this type of soil. Figure 4.8.b shows the acceleration and the displacement

spectra for the long duration records. Both record types were matched to the mentioned spectra with a

concentration of period range between 0.8 sec to 4.0 sec, which is the range of the elastic period to the

nonlinear period. It can be seen that both record sets, are well compatible to the design spectra, which means

that the comparison could be fare.

Earthquake Year Station Mw Dist. PGA t teff Scaling Factor

# Name

Name

km g sec sec Td=4sec Td=2sec

1 Chile, EW 2010 Colegio S.Pedro 8.8 30 0.70 180 50 5.2 1.0

2 Chile, NS 2010 Colegio S.Pedro 8.8 30 0.93 180 51 9.6 2.2

3 Sumatra, EW 2007 Sikuai Island 8.4 392 0.04 129 47 15.6 6.9

4 Sumatra, NS 2007 Sikuai Island 8.4 392 0.04 129 45 18.3 6.8

5 Chile,EW 1985 Llolleo 8 42 0.71 116 36 3.4 0.8

6 Chile,NS 1985 Llolleo 8 42 0.71 116 36 3.4 0.8

7 Japan,EW 2011 IWT008 9 123 0.33 300 79 6.7 2.3

8 Japan,NS 2011 IWT008 9 123 0.25 300 69 10.7 4.2

9 Japan,EW 2011 MYG011 9 170 0.68 300 105 2.9 1.0

10 Japan,NS 2011 MYG011 9 170 0.92 300 104 2.7 1.8

11 Mexico,EW 1985 Zihuatanejo 8.3 133 0.17 180 38 1.7 0.3

12 Mexico,NS 1985 Zihuatanejo 8.3 133 0.11 180 72 1.7 0.5


Figure 4.7. Acceleration and displacement Response Spectra for the selected records sets: matched to the displacement

spectrum soil C, Td=8.sec

(a)

(b)

Figure 4.8. Acceleration and displacement response spectra match to displacement spectra for soil A with corner period of

2sec soil type A: a) Short duration records b) Long duration records

Figure 4.9 shows the comparison of incremental dynamic analysis results obtained for both variants with long

and short durations based on new record sets. The peak storey drift is almost the same for both variants. This

is also true for the residual displacement for low to moderate level of intensity. However, the considerable

difference is appeared for high level of intensity, PGA =0.6. The long duration motion imposes higher

residual displacement compared to the short deformation. The reason would be due to the hysteretic

deterioration, which is caused by the P-Delta effects at the first level of the SS variant (See Section 4.2.2). As

it will be shown later, the strategy proposed in Chapter 5 could be an effective solution to reduce the residual

displacements if ground motions with long duration are likely to be occurred.

0

0.5

1

1.5

2

2.5

3

0.5 1.5 2.5 3.5 4.5

Acc

eler

atio

n (

g)

Period (s)

Design

Mean

0

20

40

60

80

100

120

140

0 2 4 6 8

Dis

pla

cem

ent

(cm

)

Period (s)

Design

Mean

0

0.5

1

1.5

2

2.5

3

0.5 1.5 2.5 3.5 4.5

Acc

eler

atio

n (

g)

Period (s)

0

5

10

15

20

25

30

35

40

0 1 2 3 4

Dis

pla

cem

ent

(cm

)

Period (s)

Design

Mean

0

0.5

1

1.5

2

2.5

3

0.5 1.5 2.5 3.5 4.5

Acc

eler

atio

n (

g)

Period (s)

Design

Mean

0

5

10

15

20

25

30

35

40

0 1 2 3 4

Dis

pla

cem

ent

(cm

)

Period (s)

Design

Mean


Figure 4.9. Comparison responses for short and long duration records

4.5 KEY CHARACTERISTICS AFFECTING COLUMN HYSTERETIC BEHAVIOUR

Another aspect to consider in this study is the impact of different column response characteristics on a frame

capacity. In order to identify the likely hysteretic shape and deformation capacity of RC columns,

deformation limits was attained by some cyclic analyses on columns of different section depth, different axial

load ratio and different longitudinal reinforcement content, as it is described in the following sections.

4.5.1 Description of RC Column Categories

Cyclic analyses were carried out for the columns shown in Table 4.2, considering different section depths,

different axial load ratios and different reinforcement ratios in order to identify the likely strength and

deformation capacity of the columns. Parameters γ, ρ and CF are axial force ratio, longitudinal reinforcement

ratio, and confinement factor, respectively, defined as:

σ� = ��X|F*? , ρ = Xp�X| , CF = F*?F**? � = � − 1o. ' ( 4.12 )

where �� is the axial load, Xp� is the total area of the longitudinal reinforcement, X| is the gross section area;

F*? and F**?are respectively the unconfined and confined concrete compressive strength. For this study,

wherever one parameter is changed, other parameters remain constant. The reference values of the variables

include a column dimension, D, of 40x40 cm, a longitudinal reinforcement ratio of 0.015, an axial load ratio

of 0.30 and a confinement factor of 1.2. Figure 4.10 shows the geometric dimensions and reinforcement

configurations of RC columns.

0.050.10.150.20.250.30.350.4 0.60

1

2

3

4

5

Mean P

eak S

tore

y D

rift (%

)

PGA(g)

0.050.10.150.20.250.30.350.4 0.60

1

2

3

4

5

6

7

8

Mean P

eak R

esid

ual S

tore

y D

rift (%

)

PGA(g)

SS (Soil A-Corner period=2sec) SS Long Duration


Table 4.2. Characteristics of different column studied, with a cantilever length of 3m

Var. Case Depth Width ¡ σ� CF

m m

Var

iant I

1 0.4 0.4 0.0025 0.3 1.2

2 0.4 0.4 0.005 0.3 1.2

3 0.4 0.4 0.01 0.3 1.2

4 0.4 0.4 0.015 0.3 1.2

5 0.4 0.4 0.02 0.3 1.2

6 0.4 0.4 0.03 0.3 1.2

7 0.4 0.4 0.035 0.3 1.2

8 0.4 0.4 0.04 0.3 1.2

Var

iant II

1 0.25 0.25 0.015 0.3 1.2

2 0.3 0.3 0.015 0.3 1.2

3 0.35 0.35 0.015 0.3 1.2

4 0.40 0.40 0.015 0.3 1.2

5 0.50 0.50 0.015 0.3 1.2

Var

iant II

I

1 0.4 0.4 0.015 -0.05 1.2

2 0.4 0.4 0.015 0 1.2

3 0.4 0.4 0.015 0.05 1.2

4 0.4 0.4 0.015 0.1 1.2

5 0.4 0.4 0.015 0.2 1.2

6 0.4 0.4 0.015 0.3 1.2

7 0.4 0.4 0.015 0.4 1.2

8 0.4 0.4 0.015 0.5 1.2

Var

iant IV

1 0.4 0.4 0.015 0.3 1

2 0.4 0.4 0.015 0.3 1.05

3 0.4 0.4 0.015 0.3 1.1

4 0.4 0.4 0.015 0.3 1.2

5 0.4 0.4 0.015 0.3 1.4

6 0.4 0.4 0.015 0.3 1.6

7 0.4 0.4 0.015 0.3 1.8

8 0.4 0.4 0.015 0.3 2


Figure 4.10. Different configuration of steel reinforcement and column size of the RC concrete columns

4.5.2 Description of numerical modelling

Numerical models were developed and analyzed in Seismo-Struct [SeismoSoft 2004] for all geometrical and

loading characteristics. All 3.00m high piers were modelled by three force-based elements along the column

height, the bottom one having 0.50m.

Five integration sections per element were used, each one containing 200 integration points. In order to

account for the cyclic degradation of steel strength depicted by the experimental results without changing the

steel model, a negative value of the parameter a3 was considered. The steel Young’s modulus was taken equal

to 200 GPa. The hardening and cyclic behaviour parameters were calibrated in order to better reproduce past

experimental results (see next section): b = 0.015, R0 = 20, a1 = 18.5, a2 = 0.15, a3 = -0.025 and a4 =15.

The model of Filippou et al. [1983] was applied for the longitudinal reinforcement. The steel Young’s

modulus was taken equal to 200 GPa. The iterative procedure developed by Taucer et al. [1991] and Spacone

et al. [1996] was adopted for the force-based element. Additionally, a co-rotational formulation was used to

account for geometrical nonlinear effects.

The force or flexibility-based formulation was used for defining the nonlinear fibre element. Force-based

elements satisfy exactly the equilibrium conditions by using an exact description for the stress resultants’ field

throughout the frame element length. On the other hand, in displacement based elements an approximation

is made for the displacement field throughout the frame element length, from which strains, stresses and


stress resultants are computed. The fact that this displaced shape is only approximate is responsible for most

of the problems that these elements present when inelastic behavior is expected [Correia et al. 2008]. The

main disadvantage of this approach is the need of a three-level iterative procedure: structure, element and

cross-section. However, recent work has shown that this iterative procedure can be transformed in a two

level or even a single level iterative procedure, without loss of accuracy [Neuenhofer and Filippou 1997].

4.5.3 Verification of numerical modelling with an experimental result

Before running all configurations described in section 4.5.1, and in order to obtain a better understanding of

the numerical modelling of fibre elements in Seismo-Struct, a validation of one specimen was carried out

through the comparison of numerical response estimates with experimental results from the Kawashima

Laboratory of the Tokyo Institute of Technology. There are several experimental results of the cyclic

behaviour of reinforced concrete specimens available at the website of the Kawashima Laboratory

(http://seismic.cv.titech.ac.jp).

The experimental specimen used for this study was identified with the number TP-011. The general

geometrical characteristics and reinforcement detailing are presented in Figure 4.11 as well as the history of

imposed lateral displacements. It should be noted that footing sliding and rotation are taken into account for

such displacements. The vertical load is constant and equal to 160 kN downward. The cylinder strength of

concrete and the yield strength of the longitudinal reinforcement are 20.6 MPa and 367 MPa respectively.

The numerical model developed for this specimen was made based on the consideration mentioned in

section 4.5.2. The 1.45m height pier was modelled by two finite elements, the bottom one having 0.45m.

Three integration sections per element was used (Gauss quadrature), each one containing around 150

integration points. In order to better reproduce the experimental results, hardening and cyclic behaviour

parameters were considered as b = 0.015, R0 = 20, a1 = 18.5, a2 = 0.15, a3 = -0.025 and a4 =15.

Figure 4.12 depicts the numerical results obtained from fibre modelling with the experimental data. From this

comparison, one can see that the numerical modelling shows a good prediction to what experimental results

presented. However, there is a slightly difference: at high level of lateral displacement, the lateral force that is

generated in the numerical model is less than of that were captured from experimental tests. This difference

could be due to assumptions that are made in the fibre element modelling, which could be a prat of

uncertainties. One of these uncertainties could be that the nonlinear behaviour of the material (concrete or

steel) is not accurate during the analysis. The other reason could be that the base of the column was

considered as fixed end in the numerical modelling. However, a some extent of rotation could be expected in

the experimental modelling. Thus, the lateral resistance of the RC column obtained from the experimental

test could be less that of the numerical analysis.


Figure 4.11. Geometrical characteristics of the specimen and history of cyclic loading

-100

-50

0

50

100

0 1 2 3 4 5 6 7 8 9 10 11 12

Displacement (m

m)

Cycle


Figure 4.12. Comparison between numerical and experimental results of cyclic behaviour of RC column

4.5.4 Numerical results

Cyclic loading was implemented by displacement control, where the top end of the each column was

displaced by a certain amount. The history of imposed lateral displacement is the same indicated in

Figure 4.11. Loading was continued until columns reached a certain limit state, or analysis is interrupted. The

performance criteria defined for analysis was obtained for each fibre. Based on that, the yield strain of steel

was defined as ¢£ = 0.002 , spalling of concrete cover was set as -0.005, and steel rupture was determined as

0.1. The ultimate concrete strain, core crushing limit state, was given by Equation 4.13 with a multiplication

factor of 1.5, which is a modification from the original expression. This is because experimental studies have

shown consistently conservative results of 50% [Kowalsky 2000].

ϵ/ = ε/= = 1.5 \0.004 + 1.4¡HO£¦¢pGF**? ` , ¡H = ρ>§ + ρ>¨ ( 4.13 )

where ρ>§ and ρ>¨are respectively the geometrical ratio of confining reinforcement in the X and Y directions.

O£¦ is yield strength of transverse reinforcement, and F**? is the compression strength of the confinement

concrete proposed by Mander et al. [1988]. For confinement factor of 1.2, this value was obtained as 0.019.

For variant IV, in which the condiment factors vary, this limit state is various for each configuration. It

should be noted that analysis was interrupted when either core crushing or steel rupture was reached.

Figure 4.13 to Figure 4.16 show the cyclic response of all variants that are shown in terms of moment

capacity versus chord- rotation.

-150

-100

-50

0

50

100

150

-5 -3.75 -2.5 -1.25 0 1.25 2.5 3.75 5

La

tera

l Fo

rce

(k

N)

Lateral Displacement(mm)

Experimental

Numerical


Figure 4.13 indicates that the longitudinal reinforcement ratio has a direct effect on the hysteretic response of

RC columns. Increasing the longitudinal reinforcement ratio increases the area of hysteretic shapes

constantly. This indicates that the energy absorbed is growing because both the moment and the rotational

capacity are increased.

Figure 4.13. Effect of longitudinal reinforcement ratio on column hysteretic response (Moment-chord rotation) Variant I,

©=0.4, AP = P. ª confinement factor: 1.2, cantilever length =3m

The yield moment increases from180 kN.m (for case ρ = 0.25% )to 400 kN.m (for case= 4.0%). The

growth of the moment capacity is because that the stress in the tensile reinforcement area increases without

-600

-400

-200

0

200

400

600

-0.05 -0.03 -0.01 0.01 0.03 0.05

r=0.25%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=1.0%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=2.0%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=3.5%

-600

-400

-200

0

200

400

600

-0.05 -0.03 -0.01 0.01 0.03 0.05

r=0.50%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=1.5%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=3.0%

-600

-400

-200

0

200

400

600

-0.04 -0.02 0 0.02 0.04

r=4.0%

Chord rotation

Resisting M

oment (kN.m

)


considerable changes in the coupling arm, which consequently multiplies the resisting moment. Furthermore,

increasing the reinforcement in the concrete column improves the ductility and consequently the rotational

capacity, which increases from 0.02 to 0.035. In addition, the hysteretic shape is changed, and the column

behaviour is close to the hysteretic behaviour of steel material. On the other hand, when low longitudinal

ratio is used, pinching effects are more significant. One other conclusion is that the post yield stiffness is also

amplified as the reinforcement is increased, which improves the total moment-rotation response. This could

be due to the effect of the hysteretic shape of the steel material.

Figure 4.14 shows the hysteretic response of RC columns using different dimensions. The dimension has a

significant effect on the moment capacity. If the diameter of the column is doubled, the moment capacity

increases 8 times, i.e. starting from 62kN.m to almost 500KN.m. The increase could be accounted for the

second order increase of coupling arm and the first order increase of the column depth. However, no

variation can be seen in drift capacity. The discussion on this behaviour is presented in the next section,

where results are compared in one graph.

-60

-40

-20

0

20

40

60

-0.05 -0.03 -0.01 0.01 0.03 0.05

Hc = 0.25 x 0.25

-300

-200

-100

0

100

200

300

-0.05 -0.03 -0.01 0.01 0.03 0.05

Hc = 0.25 x 0.25

-150

-100

-50

0

50

100

150

-0.05 -0.03 -0.01 0.01 0.03 0.05

Hc = 0.25 x 0.25

-200

-150

-100

-50

0

50

100

150

200

-0.05 -0.03 -0.01 0.01 0.03 0.05

Hc = 0.25 x 0.25

-800

-600

-400

-200

0

200

400

600

800

-0.05 -0.03 -0.01 0.01 0.03 0.05

Hc = 0.25 x 0.25

Resisting M

oment (kN.m

)

Chord rotation


Figure 4.14. Effect of column dimension on hysteretic response (Moment-Chord rotation) Variant II, ¬=0.015, AP = P. ª confinement factor: 1.2, cantilever length =3m

The axial load has a detrimental effect on the cyclic response of the RC column, as shown in Figure 4.15. As

the axial load increases, the number of cycle applied is rapidly decreased, and thus, the RC columns reaches

the failure limit states quicker than the lower axial load. Moreover, the hysteretic shape of the response is

slightly changed. For the negative axial load (tension condition), the hysteretic response of the RC column is

almost close to the hysteretic response of the steel reinforcement, which is because of the elimination of the

role of concrete due to tension. In contrast, the pinching effect appears as the axial load increases, which

could be due to the concrete behaviour. The effect of the axial load has a direct influence on the strength

capacity, which increases from 200 kN.m to 500 kN.m, while there is a fluctuation on the drift capacity, as is

discussed later.

Figure 4.16 shows the effect of the confinement on the cyclic response of the RC Columns. As expected,

increasing the confinement ratio improves the drift capacity without significant changes in the strength

capacity. The RC column with low confinement fails more quickly after only a few cycles at a chord rotation

of 0.01. However, for high levels of confinement, columns sustain a several cycles up to the drift capacity of

0.1. This behaviours are because confinement of RC section prevents bar buckling; this help prevent brittle

fracture of the concrete column, and thus, increases the ductility.

Figure 4.17 Compares the hysteretic responses of columns with deferent reinforcement ratio, column

dimension, axial load, and confinement factor. In this figure, three groups from each variant are plotted

together in order to distinguish the effect of each parameter on the cyclic response. The effect of the

longitudinal bar ratio on the moment and the displacement capacity is considerable. However, the column

dimension affects the moment resistance more than the displacement capacity. Increasing the axial load tends

to increase the moment resistance, which moves the neutral axis to the tension part because the normal

compressive stress increases. On the other hand, adding compressive vertical load on the column reduces the

drift capacity, which could be due to the buckling of rebar reinforcements. As expected, the confinement

factor increases the ductility and the displacement capacity, significantly. Increasing the confinement slightly

increases the lateral moment resistance.

The effect of each parameter on the column performance is shown in Figure 4.18. The influence of the

aforementioned characteristics on the lateral strength and the drift capacity of the columns are plotted inside

one same figure.

Generally, the effect of the longitudinal reinforcement and the column dimension on the lateral resistance is

more prominent in comparison to the other effects. As shown in Figure 4.18.a, increasing the reinforcement


Chord rotation

ratio increases the lateral resistance and the drift capacity with an almost constant trend line. However, the

drift capacity rises more quickly in a low range of bar ratio. On the other hand, and as shown in Figure 4.18.b,

increasing column dimension not only has a slight effect on the displacement response, but also reduces the

drift capacity of the column.

Figure 4.15. Effect of axial force ratio (AP)on column hysteretic response (Moment-Chord rotation), Variant III: Column

dimension: 40x40cm, ¬=0.015, confinement factor: 1.2, cantilever length =3m

-400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Axial load ratio = 0.05

-400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15


-400

-300

-200

-100

0

100

200

300

400

-0.1 -0.05 0 0.05 0.1

Axial load ratio = -0.05

-400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15


-400

-300

-200

-100

0

100

200

300

400

-0.06 -0.04 -0.02 0 0.02 0.04 0.06


-400

-300

-200

-100

0

100

200

300

400

-0.04 -0.02 0 0.02 0.04


-400

-300

-200

-100

0

100

200

300

400

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Axial load ratio =0.1

-400

-300

-200

-100

0

100

200

300

400

-0.02 -0.01 0 0.01 0.02

Axial load ratio =0.05

Resisting M

oment (kN.m

)


Chord rotation

Figure 4.16. Effect of confinement factor on column hysteretic response (Moment-Chord rotation) Variant IV: Column

dimension: 40x40cm, ¬=0.015 AP = P. ª , cantilever length =3m

-400

-300

-200

-100

0

100

200

300

400

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

CF = 1

-400

-300

-200

-100

0

100

200

300

400

-0.02 -0.01 0 0.01 0.02

CF = 1.05

-400

-300

-200

-100

0

100

200

300

400

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

CF = 1.1

-400

-300

-200

-100

0

100

200

300

400

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

CF = 1.2

-400

-300

-200

-100

0

100

200

300

400

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

CF = 1.4

-400

-300

-200

-100

0

100

200

300

400

-0.1 -0.05 0 0.05 0.1

CF = 1.6

-400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

CF =1.8

-400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

CF = 2

Resisting M

oment (kN.m

)


Figure 4.17. Comparison of key characteristics on the cyclic behaviour of RC columns

(a) ( b)

(c) ( d)

Figure 4.18. Effect of key characteristics on the hysteretic response of RC columns

Figure 4.18.c shows the effect of the axial load on the drift capacity and the lateral resistance of the RC

column. By increasing the axial load, the moment capacity of the column increases a certain amount and then

reduces. This is attributed to the classic axial load-bending moment interaction, whereby the most resistance

-600

-400

-200

0

200

400

600

-0.06 -0.04 -0.02 0 0.02 0.04

Mo

mn

et (k

N.m

)

Chord rotation

Varient 1

ρ=4.0%ρ=1.5%ρ=0.5% -800

-600

-400

-200

0

200

400

600

800

-0.04 -0.02 0 0.02 0.04

Mo

mn

et (k

N.m

)

Chord rotation

Varient 2

Hc=0.5x0.5

Hc=0.35x0.35

-400

-300

-200

-100

0

100

200

300

400

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Mo

mn

et (k

N.m

)

Chord rotation

Varient 3

σ0 = −0.05σ0 = −0.5σ0=−0.20 -400

-300

-200

-100

0

100

200

300

400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Mo

mn

et (k

N.m

)

Chord rotation

Varient 4

CF = 1.2CF = 2

CF = 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0

20

40

60

80

100

120

140

160

180

200

0.000 0.020 0.040 0.060

Sto

rey

dri

ft c

ap

aci

ty (%

)

La

tera

l Res

ista

nce

(k

N)

Longitudinal reinforcement ratio

Lateral reistance

Drift capacity0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0

20

40

60

80

100

120

140

160

180

200

0.20 0.40 0.60

Sto

rey

dri

ft c

ap

aci

ty (%

)

La

tera

l Res

ista

nce

(kN

)

Column Dimension (m)

Lateral reistance

Drift capacity

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0

20

40

60

80

100

120

-0.1 0.2 0.4 0.6

Sto

rey

dri

ft c

ap

aci

ty (%

)

late

ral r

esis

tan

ce(k

N)

Axial load ratio

Lateral reistance

Drift capacity

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0

20

40

60

80

100

120

140

1.00 1.50 2.00

Sto

rey

dri

ft c

ap

aci

ty (%

)

late

ral r

esis

tan

ce (

kN

)

Confinemnet Factor

Lateral reistance

Drift capacity


is achieved when deformation limits for the concrete and the reinforcement are obtained at the same time, i.e.

balance condition.

The results shown in Figure 4.18.d indicate that confinement has a significant influence on the drift capacity

up to a certain level, but doesn’t affect the strength significantly. This also agrees with traditional structural

mechanics considerations (see, for example, Paulay and Priestley [1992]). Some further discussion of the trend

lines and their implications for retrofit is provided at the end of this chapter.

4.5.5 Comparison of cyclic analysis with the section analysis

In this section, all variants are investigated again with section analysis and the results are compared to those

obtained based on fibre modelling from static time historey analysis. To this end, a detailed moment-

curvature analysis is conducted for all variants described in the previous section, and the effect of each

characteristic is investigated on the response.

Two concrete material models were used in the analysis; unconfined concrete for the cover and confined

concrete for the core of the section where lateral reinforcement surrounds the concrete. The same model of

Mander et al. [1988] was used as the constitutive relation for concrete in compression. For what concerns the

constitutive relations for reinforcement steel, the model of King et al. [1986] is adopted.

In deriving the expressions of the moments and curvatures for the confinement concrete section, the

following classical assumptions were made:

• The strain profile is linear at all stages of loading up to failure.

• The stress-strain relationship is taken as a stress block, and the idealised stress-strain relation for the

tension and compression steel is used

• The tensile strength of concrete is neglected.

• The steel is perfectly bonded.

• Axial force is applied in the section centroid.

For obtaining the complete moment–curvature relationship for any cross-section, discrete values of concrete

strains (εc) were selected such that an even distribution of points on the plot were obtained, both before and

after the maximum. The procedure used to obtained moment-curvature is in accordance with the following

steps:

i) After dividing the section in to number of slices, the area of cover, core, and reinforcing steel in each

layer is determined.

ii) The strain of the extreme fibre (εc in


iii) Figure 4.19) is assumed with the lowest value. In this study, the values of εc are selected in the range of

0.0001 to the failure strain, 0.01. The neutral axis is also assumed initially as the half of the effective

depth.

iv) Concrete and steel force in each layer is calculated based on stress-strain relationship of each material.

v) Axial force equilibrium on the section is controlled in accordance to 4.14:

N = ® F*(�)��¯ + ° Fp�Xp� =±�

® *¢(�)�(²)�¯ + ° p¢(�)�Xp�±�

( 4.14 )

Figure 4.19. Section stress – strain distribution in reinforcement concrete column

where F*(�)and Fp�(�) are the force concrete and steel, b is the width of the section, Xp� is the total are of the longitudinal reinforcement at layer i, distance yi from the centroid axis, as shown in

Figure 4.19. Variables * and p ³�´ the secant slope of the nonlinear stress-strain relationship of concrete

and steel respectively. It should be noted that the neutral axis is modified by trial and error until the above

axial equilibrium is satisfied.

vi) For the final value of the neutral axis depth, moment and corresponding curvature is thus calculated as:

M = ® *¢(�)�(²)¯. �¯ + ° p¢(�)�¯�Xp�±�

� = ¶*· = ¢p±� − ·

( 4.15 )

where ¶*and ¢p± are the extreme fibre compression strain, and the strain at the level of the reinforcing bars at

maximum distance from the neutral axis.

vii) The strain at the extreme compression fibre is increased until the ultimate compression strain is reached.

Based on the method described above, a detailed moment-curvature analysis was carried out for each variant.

To this end, a numerical program, CUMBIA, [Montejo 2007] was used. This program includes all

aforementioned steps, where moment curvature curve is obtained based on several iterations. All material

F* Fp�

Fp� Fp�

¢*

¢p

·

� ¯

�


properties and geometrical configurations were defined similar to what was modelled with fibre time history

analysis.

The lateral resistance and drift capacity of the single bending column was evaluated based on the following

relation:

Fx = Mx∆/x ( 4.16 )

∆x= ∆¨ + ∆3= φ¨¹H + L>3¼�3 + ¹φ= − φ3¼L3H , θx = ∆cxH ( 4.17 )

where Mx, Fx , ∆/x andθxare moment, lateral resistance, displacement capacity and drift capacity at each level

of the moment-curvature analysis. H is the cantilever length of the column and is considered as 3.0 m.

Figure 4.20 shows the results comparison of all key characteristics for each variant. With a comparison to

what described in Figure 4.18 obtained from static time history fibre-based analysis, one can see that the

results are to somehow similar to the section analysis. Based on this figure, increase of bar ratio causes growth

in lateral resistance and drift capacity.

Figure 4.20. Comparison of key characteristics on column response based on section analysis

Effect of column dimension is the same as what obtained in the previous section, whereby the increasing the

dimension causes reduction in drift capacity and improvement in strength capacity. The trend of drift capacity

due to increasing axial load is almost negative while increases the strength capacity which is almost close to

fibre results. The difference is that for a low level of axial load slope obtained from section fibre analysis is

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

100

200

long. bar ratio

Effect of longitudinal reinforcement

Lat

eral

res

ista

nce

(kN

)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

5

10

Dri

ft C

apac

ity

(%

)

200 250 300 350 400 450 5000

100

200

Column dimension

Effect of Column dimension

Lat

eral

res

ista

nce

(kN

)

200 250 300 350 400 450 5000

5

10

Dri

ft C

apac

ity

(%

)

-0.1 0 0.1 0.2 0.3 0.4 0.50

60

120

Axial ratio

Effect of Axial load

Lat

eral

res

ista

nce

(kN

)

-0.1 0 0.1 0.2 0.3 0.4 0.50

5

10

Dri

ft C

apac

ity

(%

)

1 1.2 1.4 1.6 1.8 260

80

100

Confinement ratio

Effect of Confinement

Lat

eral

res

ista

nce

(kN

)

1 1.2 1.4 1.6 1.8 20

5

10

Dri

ft C

apac

ity

(%

)


positive, while in section analysis is almost flat. Effect of confinement ratio is also close for both analyses,

where increasing confinement improves drift capacity without significant effect on lateral resistance.

4.5.6 Effect of column characteristics on the demand to capacity ratio

In this section, the displacement demand-capacity ratio DDCR of reinforcement concrete columns is

obtained, and the effect of each key characteristic is investigated on this ratio.

The effective stiffness of the cantilever column, ½¾¾ , is the lateral resistance divided by displacement

capacity. Thus, the effective period ¿½¾¾will be calculated as Equation 4.17 :

½¾¾ = Y³!´�³À �´EjE!³{·´�jEÁÀ³·´�´{! �³Á³·j!� = O∆* , ¿½¾¾ = 2Â� MKÃÄÄ ( 4.18 )

where M is the mass of the single degree freedom of the column.

The demand displacement of the system for the determined effective period, ∆� , is obtained from the

inelastic displacement spectra. The spectral displacement reduction factor is determined from the following

relationship:

Å� = � 0.070.02 + Æ½Ç ( 4.19 )

where Æ½Çis the equivalent damping estimated by the following relation [Priestley et al. 2007]:

Æ½Ç = 0.05 + 0.444 o − 1oÂ ( 4.20 )

where o is the system ductility obtained from the ratio of displacement capacity by the yield displacement ∆£.

The value of 0.444 is adopted because the Takeda thin model coule better represent columns under high axial

loads. The yield displacement for a cantilever column with a single fixed condition is calculated as:

μ = ∆*'£^* , '¨ = ∅£Y3 ( 4.21 )

where ∅£ is the yield curvature of the column section. For a rectangular RC column section is estimated by

the following relation. ^* is the column cantilever height.

∅£ = 2.1 ¢£� ( 4.22 )

Demand displacement can be now determined from the reduced spectral displacement as: Δ� = Å�Ê�.


where Ê�is the spectral displacement for a given intensity and period using Equation 4.18.

Finally, the displacement demand-capacity ratio is calculated as:

DDCR = Displacement DemandDisplacement Capacity = ΔÎΔ/ ( 4.23 )

To determine the effect of column characteristics on DDCR, the design displacement spectrum were

assumed to be identical to what in Figure 3.10. Furthermore, it was assumed that the dynamic weight

associated to each system corresponds to the ultimate axial capacity force, i.e.

M = σ�f/?X*Ï ( 4.24 )

where g is the gravity acceleration. For variants using negative and zero axial load ratio (variant III, case 1 and

2), a minimum axial load ratio of 0.05 were considered.

Figure 4.21 shows the effect of each key characteristic on obtained DDCR. Increase in longitudinal

reinforcement and dimension reduces the DDCR value, because the displacement demand increases for both

cases. However, increasing confinement factor does not have significantly effect on the DDCR value. The

reason could be that as the confinement factor increases, both the displacement demand and the

displacement capacity increases almost at a same rate. When axial load is reduced, the DDCR is reduced.

Figure 4.21. Comparison of key characteristics on Demand-Capacity Ratio (DCR)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 0.01 0.02 0.03 0.04 0.05

DD

CR

Longitudinal reinforcement ratio

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-0.05 0.05 0.15 0.25 0.35 0.45 0.55

DD

CR

Axial load ratio

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.20 0.30 0.40 0.50

DD

CR

Dimension (m)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00 1.25 1.50 1.75 2.00

DD

CR

Confinement factor


4.6 DISCUSSION OF RESULTS

This work began by comparing the behaviour of two RC frame buildings in Chapter 3 (variant 1 and variant 2

of Figure 3.1) that differed only by the fact that one had masonry infill from the first floor upwards whereas

the other had masonry infill over its full height. Results of incremental dynamic analyses tend to indicate that

the full masonry infill case could sustain much larger ground motion intensities when considering the collapse

limit state. This might encourage structural engineers faced with the task of retrofitting the partial infill

building to consider adding infills to the ground storey to render the structure similar to variant 1.

While this option may help in reducing the probability of collapse, it would not necessarily reduce the damage

and losses expected in the building for low to moderate earthquake intensities. This is partly because the floor

accelerations for the infill case are likely to be higher than in the partial infill case but in addition, it is well

known that damage to infill masonry occurs at much lower levels of drift than traditional RC frame

structures, with masonry infills requiring repair at drifts as low as 0.3% [Hak et al. 2012]. In addition, the open

ground storey scenario would have a lower probability of reaching a partial-collapse limit state associated with

masonry failure out-of-plane.

In addition to the points made above, it is recognised that the decision to retrofit a structure or not should be

made within a risk assessment framework in which the probability of different levels of seismic intensity is

considered along with the probable losses for each intensity level. With this in mind, it was decided that the

effect of different structural characteristics on the seismic vulnerability of RC frame structures with soft

storey mechanisms should be examined in more detail. As such, sections 4.2, 4.3 and 4.4 have, respectively,

examined the influence of P-delta effects, post yield stiffness ratio and the ground motion duration on the

drift and acceleration demands of the open-ground-storey structure, whereas Section 5 examined how

column dimensions, reinforcement contents and axial loads could affect deformation capacity.

The results of Section 4.2 have shown that P-delta effects will tend to increase the probability of collapse

significantly, increasing peak and residual drifts significantly, particularly at high intensities. This intuitive

observation is not yet well recognised by code assessment methods and therefore improvements to code

assessment procedures should be an area for future research. Furthermore, it suggests that soft-storey

structures could benefit from de-coupling of the gravity system from the lateral load resisting system. This

point will be discussed further in later paragraphs.

The results of Section 4.3 have instead shown that while an increased value of post-yield stiffness ratio does

help reduce both peak and residual drifts, the overall impact does not appear to be large. As such, while the

provision of some post-yield stiffness is important, it should not necessarily be a critical factor in retrofit

efforts for soft-storey structures.


The results of Section 4.3 have shown that the long duration ground motions imposed higher residual

displacement on soft storey frame compared to that of the short duration. The effect on floor acceleration is

not noticeable for the two variants. However, as Priestley et al. [2007] demonstrated, reduction of P-Delta

effects could considerably improve the hysteretic response, because it increases the global post yield stiffness

ratio.

The results of Section 4.5 permit a number of points to be made regarding RC columns that are relevant for

retrofit design. Firstly, note that the drift capacity of RC columns will tend to increase in proportion to the

confinement provided. This supports the increasing use of jacketing and FRP wrapping solutions in the

retrofit of structures. Secondly, and perhaps most interestingly, note that columns with high axial load ratios

are likely to possess considerably less deformation capacity than those low to moderate axial load ratio. It was

demonstrated in Figure 4.18 that by reducing the axial load ratio on a column from 0.4 (typical of existing RC

buildings in many countries) to 0.1, the deformation capacity of the column could increase by a factor of four,

from 2.0% to 8.0%. This again suggests that retrofit solutions that manage to reduce the axial loads on

columns could greatly reduce the vulnerability of the soft-storey structures.

The above discussion has argued that if the gravity load system could be de-coupled from the lateral load

resisting system this could help reduce the likely deformation demands, which tend to be amplified by P-delta

effects. In addition, it was demonstrated that if the axial load ratios on column sections could be reduced

their deformation capacities could be significantly increased. One potentially effective and innovative means

of retrofitting a structure with an open-ground storey could therefore be to introduce a series of gravity

columns at the ground level, as shown in Figure 4.22, that slide with the first storey. By doing this, P-delta

effects would be minimised. In addition, by jacking the gravity column system into position, the axial loads on

existing columns could also be reduced, thus greatly increasing their deformation capacity, without

significantly affecting their lateral strength and potential for energy dissipation. To this end, a portion of

exiting vertical forces could be unloaded using some new gravity bearing elements. This unloading could be

carried out by lifting up the building, to ensure that the axial forces are transferred to the new gravity-bearing

elements.


Figure 4.22. Possible means of de-coupling gravidity loads from lateral loads in a soft storey building


The effect of some key characteristics on the behaviour of soft first storey buildings was explored. The case

studies assessed in the previous chapter were taken as the benchmark building and incremental non-linear

time history analyses were repeated varying some key parameters.

The analysis results indicated that P-Delta effects can considerably affect the vulnerability of partial infill RC

frames, although the effect depends on the intensity level. The influence of P-Delta effects is increased as the

intensity level is increased. Moreover, it was shown that high gravity loads related to P-Delta effects could be

very significant for moderate and high intensity levels, and greatly increases the potential collapse of soft

storey buildings. Although increasing the post-yield stiffness ratio of the first floor columns could be helpful

to reduce both peak and residual deformations at this level, it increases the seismic demand at storeys above

New gravity columns introduced to

slide with the overlying the structure

Connectionelement


this floor. This option might increase the retrofit cost of soft storey buildings. It was also demonstrated that,

at high intensity levels, long duration ground motions could increase the residual drift at the first floor of soft

storey buildings significantly.

The results of static cyclic analyses of RC columns with different geometrical and mechanical properties were

used to highlight the influence of some characteristics such as bar ratio, section dimensions, axial load ratio

and confinement factor on the lateral resistance and drift capacity of RC columns. The trends observed are

considered to be helpful in assessing the potential vulnerability of RC frame structures in which soft-storeys

are expected to develop at the ground floor.

The implications of the analysis findings were discussed in relation to potential retrofit schemes. A novel

retrofit scheme was proposed in which sliding gravity columns were introduced to reduce the impact of P-

Delta effects on displacement demands and to increase the deformation capacity of existing columns. That

the detailed design and development of this type proposed system is not presented hers as it is out of the

scope of this thesis. The next chapter will briefly discuss the limitation of this proposed retrofitting strategy.

As such, an alternative solution (gapped inclined brace GIB system) is proposed that reduces the drawbacks

of this proposal, while takes the positive aspects.

73

5.GAPPED INCLINED BRACE SYSTEM TO RETROFIT SOFT STOREY

BUILDINGS

5.1 INTRODUCTION

The results of the Chapter 4 suggested a potential retrofit strategy for open ground storey buildings in which

a portion of the existing vertical forces carried by the columns is transferred to new added gravity bearing

elements that slide with the first storey. This solution (Figure 5.1.a), however requires significant effort and

cost to lift the structure to ensure that the axial forces are transferred to the new gravity-bearing elements.

Moreover, because the lifting may not applied to all gravity elements simultaneously, it may also cause

unsymmetrical settlement to the existing columns, and foundation during the building lifetime. In addition,

the residual drift might not be reduced significantly when using such a retrofit strategy.

The results of the Chapter 4 suggested a potential retrofit strategy for open ground storey buildings in which

a portion of the existing vertical forces carried by the columns is transferred to new added gravity bearing

elements that slide with the first storey. This solution (Figure 5.1.a), however requires significant effort and

cost to lift the structure to ensure that the axial forces are transferred to the new gravity-bearing elements.

Moreover, because the lifting is not applied to all gravity elements simultaneously, it may also cause

unsymmetrical settlement to the existing columns, and foundation during the building lifetime. In addition,

the residual drift might not be reduced significantly when using such a retrofit strategy.

Alternatively, this chapter proposes the gapped-inclined brace (GIB), which consists of an elastic inclined

brace with a carefully selected gap element (Figure 5.1.b), to enhance the displacement capacity of the soft

floor while not increasing its lateral resistance. This is achieved by a mechanism that props and lifts the

structure during the earthquake, in effect using the input seismic energy to achieve an axial unloading of the

existing columns as the structure sways laterally. The GIB is installed at the ground level without inducing any

force on the existing elements. During the lateral motion of the building, the lateral movement of the

existing columns induces an axial shortening of the GIB, as illustrated in Figure 5.1.b. The gap inside the GIB

closes once the first floor displacement exceeds a critical value. This critical displacement is set by considering

either P-Delta effects or column deformation limits at the first floor. As the retrofit strategy is designed to

avoid adding significant lateral resistance to the structure, the building remains subject to low accelerations on

the floors above the soft storey when the lateral movement is controlled.

GAPPED INCLINED BRACE SYSTEM TO RETROFIT SOFT STOREY BUILDINGS 74

(a) (b)

Figure 5.1. Proposed mitigation strategies, a) roller system b) gapped inclined braced (GIB) system

Once the gap is closed, the GIB activates, and begins to share the vertical and the lateral load with the

existing columns. As the lateral displacement increases, the axial load on the first storey columns is carefully

reduced by the GIB so that, first, it counteracts the P-Delta effect, and second, it increases the lateral

deformation capacity of the first storey columns. At each level of lateral displacement, the axial load on the

columns that meets these two requirements is referred to as the effective axial force effP .

The advantage of this approach with respect to traditional brace retrofit solutions is that the retrofit strategy

does not shift the weakest point in the structure elsewhere (which would necessitate retrofitting measures in

the new location of the “weakest-link”) and is not very intrusive. Its advantage in comparison to installing

rollers, as suggested in Chapter 4, is that there is no need to uplift the building, which obviously represents

significant time and cost advantages.

To develop this retrofit scheme, in Section 5.1, the effective axial load effP to counteract P-Delta effects is

first derived. In Section 5.2, the effP for RC columns is obtained, and consequently, the details of the

proposed system are then defined such that it achieves the desired effP in Section 5.4. Section 5.5 describes the

mechanics of the hybrid system (RC column and Gapped-Inclined Brace, GIB) and derives the equations that

govern the response. In Section 5.6 a systematic design procedure are then explained and illustrated, and the

theoretical relations that are derived are verified through nonlinear pushover analyses. In Section 5.7 a

Initial condition Initial condition

Ultimate condition Initial condition

Residual condition Residual condition


parametric study on the key characteristics of the GIB system design is explored. Finally, the analytical cyclic

response of a single bay frame using the proposed approach is presented in Section 5.8, and its behaviour is

compared to the existing as-built frame.

5.1 EFFECTIVE AXIAL FORCE TO COUNTERACT P-DELTA EFFECTS

In order to identify an ideal effective axial force, the SDOF system shown in Figure 5.2 is considered. The

system has a cantilever height of H , and is subjected to an initial vertical load 0P . Bernal [1987] showed that

as the lateral displacement ∆ increases, the lateral resistance of this cantilever is reduced according to the

following relationship (see Section 4.2):

p 0F F PH

∆= − ( 5.1 )

Figure 5.2. Single-Degree-of-freedom system subject to axial load and lateral displacement

where, pF and F are respectively, the lateral resistance of the cantilever with and without the P-Delta effect.

The response of a simplified elasto-plastic system with and without the P-Delta effect, are illustrated in

Figure 5.3.a (the dark solid line and the dark dashed line, respectively). The reduction of the lateral resistance

at a lateral displacement ∆ is:

0pF F P

H

∆− = ( 5.2 )

The critical lateral displacement at which the P-Delta effect becomes significant is defined as cr∆ . This critical

displacement is a design choice and affects the properties of the GIB system. For nonlinear systems, this

critical displacement is likely corresponds to the yield displacement because P-delta effects are usually only

significant in the inelastic range. However, this amplification should also be important in the elastic range if

the stability index (�Ð∆ÑÒÓÔ ) is significant. A first step towards developing the proposed retrofit strategy is to

GAPPED INCLINED BRACE SYSTEM TO RETROFIT SOFT STOREY BUILDINGS

define effP such that it counteracts the P

reduction of the second roder lateral resistance (

This results in:

eff 0P ,

Since P-Delta effects are assumed to be insignificant

Assuming that cr y∆ = ∆ , to identify the desired

inelastic range, the axial load effP

point (Figure 5.3.b); then, the axial load should be reduced following

that when the P-Delta effect is counteracted in this manner, the initial lateral response of the system dra

with the dark dashed line in Figure

same figure.

Figure 5.3 a) Influence of the P-Delta effect and the

GAPPED INCLINED BRACE SYSTEM TO RETROFIT SOFT STOREY BUILDINGS

such that it counteracts the P-Delta effect for displacements greater than cr∆

lateral resistance ( effPH

∆) is maintained at a value as close as possible

eff 0P ,cr

crP

H H

∆∆= ∆ > ∆ ( 5.

assumed to be insignificant for displacements smaller than cr∆

eff 0

eff 0

P ,

P ,

cr

cr

cr

P

P

= ∆ ≤ ∆ ∆

= ∆ > ∆ ∆

( 5.

, to identify the desired effP that would counteract the P-Delta effect within the

eff should be equal to the initial axial load 0P until the system reaches the yield

.b); then, the axial load should be reduced following eff 0P ,y

P∆

= ∆ > ∆∆

Delta effect is counteracted in this manner, the initial lateral response of the system dra

Figure 5.3.a is altered to a response that is illustrated by the light solid line in the

Delta effect and the effP on the force-displacement response b) Effective axial force (

76

cr∆ . This requires that the

) is maintained at a value as close as possible to 0

crPH

∆.

.3 )

cr∆ , effP is given by

.4 )

Delta effect within the

until the system reaches the yield

y= ∆ > ∆ . Figure 5.3.a shows

Delta effect is counteracted in this manner, the initial lateral response of the system drawn

illustrated by the light solid line in the

displacement response b) Effective axial force ( effP )


5.2 EFFECT OF AXIAL LOADS ON THE DEFORMATION CAPACITY OF RC COLUMNS

Irrespectively of P-Delta effects, axial loads can have a negative effect on the deformation capacity of RC

columns [Paulay and Priestley 1992; Fardis and Biskinis 2003; Lam et al. 2003]. As such, the ideal effective

axial load should also consider column sectional resistance.

To achieve the desired effP , the response of a typical 0.40 0.40× m RC column with 3.0 m cantilever height,

longitudinal reinforcement ratio of 0.01 and confinement factor of 1.15 is determined through moment

curvature analyses for various axial load ratios ( '

0 gσ P /A f c= σ = ÕÖ×Ä′/) ranging from 0.01 to 0.5 in increments

of 0.02. The compressive strength of the concrete 'f c and the rebar yield strength fys are assumed 20 MPa,

and 370 MPa, respectively. The Mander model [Mander et al. 1988] is used to evaluate constitutive relations

for the confined and the unconfined concrete in compression. For what concerns the constitutive relations

for reinforcement steel, the model proposed by King et al. [1986] is adopted. The strain at maximum stress

for unconfined concrete is assumed 0.002, while the ultimate concrete strain is governed by the core crushing

limit state proposed by Kowalsky [2000], and the ultimate tensile strain of the reinforcement is assumed as

12%. The lateral displacement of the cantilever was estimated using the simplified lumped plasticity approach

using Equation 5.5 as the sum of the elastic and plastic deformations.

2( )( )

3

y sp

u y p

H LL H

ϕϕ ϕ

+∆ = + − ( 5.5 )

where yϕ and uϕ are the yield and ultimate curvature, respectively; H is the cantilever height of the RC

columns; spL and p

L are strength penetration length and the plastic hinge length, and were estimated from

equations proposed by Priestley et al. [2007]. The lateral resistance of the RC column was calculated by

dividing the moment resistance obtained from the section analyses by the cantilever height.

The dotted line in Figure 5.4.a indicates the variation in the maximum lateral drift capacity ratio versus the

axial load ratio. The lateral drift capacity decreases almost linearly when the axial load ratio increases. An

increase in the axial load ratio from 0.1 to 0.5 leads to a reduction in the drift capacity from 9.0% to almost

4.0%. However, P-Delta effects were not considered in calculating the relationship between the axial load and

the drift capacity ratio of the RC column.

5.3 effP FOR RC COLUMNS

To consider the influence of P-Delta effects, the lateral resistance was reduced based on Equation 5.1. The

analysis stopped when the lateral resistance reduced to 70% of the yield resistance. This value corresponds to

a stability coefficient of 0.3, which is recommended by many current seismic codes [FEMA 1997; ATC

2007a] as an upper bound limit.


The dashed line in Figure 5.4.a indicates the variation in the maximum lateral drift capacity versus the axial

load ratio resulting from analyses in which P-delta effects were considered. The lateral drift capacity decreases

significantly for high axial load ratios, especially those in the range of 0.2 to 0.5. A reduction in the axial load

ratio from 0.5 to 0.05 leads to an increase in the drift capacity from 2.0% to almost 8.0%.

The dashed line in Figure 5.4.a describes the effect of the axial load as well as P-Delta effects on the

deformation capacity of the RC column. However, it has another meaning: If the axial load on existing

columns is reduced following in a manner similar to this curve, the deformation capacity of the column

increases during the lateral loading history. The dashed line in Figure 5.4.a is referred to as PÃÄÄ for RC

columns (shown in normalized form).

(a)

(b)

Figure 5.4.a Numerical analysis of a 0.40m×0.40m RC column: 1.5%ρ = , 1.15CF = , axial load ratio range ÙP: 0.05 to 0.5 in increments of 0.05 a) Axial load ratio versus lateral drift capacity ratio, ( effP in normalized form), b) Lateral

resistance versus lateral drift capacity ratio, referred to as degraded capacity curve

5.3.1 Verification with fibre analysis

The results obtained from section analysis were verified with those obtained from a nonlinear fibre element

analysis. A fibre-element program “SeismoStruct“ [SeismoSoft 2004] was used for numerical analysis. The

limit states were set similar to those considered in the section analysis approach. For the range of the low

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

Ax

ial

load

rat

io

Section analysis without P-Delta

Section Analysis with P-Delta

Fiber model with P-Delta

Pu

P0

θuLateral drift ratio (%)

Peff

(Fiber model)

Peff

(Section analysis)

0 1 2 3 4 5 6 7 80

20

40

60

80

100

Lat

eral

res

ista

nce

(kN

)

Degraded capacity curve from fiber model

Envelope of section analyses

Section analysis of individual case

Fy,col

(P0=1600kN)

σ0=0.5

Lateral drift ratio (%)

Fu,col

Reducing axial load ratio from 0.5 to 0.05


axial load, the response was controlled by shear failure or the steel fracture within the section. However, in

the case of this reinforced concrete column, shear failure did not govern, and the fracture of the steel

reinforcement (at an axial strain equal to 12%) controlled the ultimate limit state. The analysis incorporated

large displacements as well as P-Delta effects.

The solid line in Figure 5.4.a shows the relation between the axial load and the deformation capacity of the

RC column as obtained from the nonlinear fibre element analysis. Similarly, this curve describes PÃÄÄ (the

solid line) for the RC column. The figure shows that PÃÄÄthat is obtained from the nonlinear fibre analysis is

close to what was plotted from the section analysis (compare the solid line and the dashed line in Figure 5.4.a).

The results were obtained from a monotonic loading. Bar slip and tension shift effects were neglected due to

the hypothesis of plane-sections remaining plane. As such, it is expected that the drift capacity ratio during

cyclic response (especially in the low axial load ratio range) would be smaller than what is obtained using

monotonic loading [Priestley et al. 2007]. However, the general relationship between the drift capacity and the

axial load ratio would still be expected to remain very similar, as has been observed in the available

experimental databases [Kawashima Laboratory ; NIST 1997; Elwood 2002]

5.3.2 Effect of effP on a column response

The RC column studied in the previous section was subjected to a lateral displacement, and during the

analysis, the axial load was removed gradually. The initial axial load 0 1600P kN= ( 0 0.5σ = ) was kept constant

until the lateral drift ratio of almost 1.5%, and then was reduced to 320uP kN= ( 0.1uσ = ) at the end of the

analysis. The reduction of the axial load followed the effP that is shown in Figure 5.4.a. The dashed line in

Figure 5.4.b, which is referred to the degraded-capacity curve, shows the pushover curve obtained from the

nonlinear fibre analysis under the effP . The lateral resistance of the column is degraded from the lateral yield

resistance , 80y col

NF k= to the lateral ultimate resistance , 60colu

NF k= . This is because the axial load is reduced

during the analysis. In contrast to the case where the axial load is constant and equal to 0P during the whole

analysis, the deformation capacity of the column under effP is considerably improved. For the case where a

constant axial load 0P is applied, when its strength drops to 75% of its maximum strength, the lateral drift

capacity ratio is about 1.5%. Whereas, for the effP case, the drift capacity is approximately 8.0%, which is

almost five times greater than that of the existing column.

Due to the good agreement between the sectional analysis results (considering P-Delta effects) and the fibre

modelling results in Figure 5.4.a, the DC curve could also be defined by plotting the envelope of all lateral

resistance-drift capacity curves obtained from individual sectional analyses (with constant axial loads, shown

by the dotted lines). This envelop is shown by the solid line in Figure 5.4.b. This simplifies the approach, as


there is no requirement to run several pushover analyses with fibre modelling. The degraded-capacity curves

obtained from both approaches are close to each other. However, results are slightly different in the high

axial load range (low deformation capacity). The lateral resistance from the section analysis starts to reduce at

a drift ratio of 1.2%, while this value is 1.0% based on fibre modelling. The difference could be due to

assumptions considered in each approach, which is a source of uncertainty. However, the overall match can

be considered acceptable as they have similar behaviour in the lower axial load ranges, which are being

targeted because of the higher deformation capacity they given the columns.

5.4 PROPOSAL OF A GAPPED INCLINED BRACE TO ACHIEVE THE effP

To achieve the desired effP within a retrofit strategy, a Gapped-Inclined Brace (GIB), composed of an inclined

brace fitted with a carefully selected gap, could be installed at the ground level without inducing any force to

the exiting elements, as shown in Figure 5.5.a The lateral movement of the existing column results in an

elastic rotation of the GIB system. The gap is required to limit the increase of the lateral strength of the

system caused by the GIB. When the gap is closed, the GIB activates, and shares the vertical and lateral load

with the existing column. The lateral resistance provided by the GIB compensates for the lateral strength

degradation of the columns that occurs due to the reduction of their axial load.

(a) (b) (c)

Figure 5.5. Gapped-Inclined Brace (GIB) system to the existing column a) Initial condition b) Closing gap condition c)

Ultimate condition

Figure 5.5.c illustrates the deformed state of the hybrid system when the ultimate displacement is reached.

However, it is conservative if the ultimate displacement demand of the whole system is reached before the

GIB reaches the vertical position. Mechanics of the GIB system

Lb

Gap Gap is closedGap isopenned

P P P

Lb0

Inclined

brace


5.5 MECHANICS OF THE GIB SYSTEM

As the next step within the retrofit strategy of soft storey buildings, the GIB should be carefully designed so

that the desired effP is achieved as the floor sways laterally. The properties of the GIB are defined based on

three major parameters: The initial angle of the GIB , GIBθ , the gap distance GIB∆ , and the mechanical

properties of the inclined brace. These parameters are obtained based on a free-end column condition to

simplify the problem and to illustrate the purposes of the proposed strategy. However, the equations that are

derived can be directly extended to fixed-end column conditions, which is a better representation of columns

at the ground level. In this derivation, the column is assumed to behave as a cantilever before the gap is

closed (Figure 5.6.a), and its lateral deformation can be easily calculated. As a simplification, it is assumed that

once the gap is closed, the plastic hinge is formed at the end of the column, while the rest of the column

rotates without any plastic flexural deformation, as shown in Figure 5.6.b and Figure 5.6.c.

Figure 5.6. Mechanics of the GIB system a) Initial position, b) elastic behaviour of the column before gap is closed c) post

yield condition

5.5.1 Initial position of the GIB

The distance between the existing column and GIB , GIB∆ (or more precisely, the brace angle) can control the

total lateral resistance of the system. The lateral resistance of the GIB should ideally compensate for the

∆GIB

Hc

∆cr − ∆y

∆u ∆r

∆v

∆vy− 0

LGIB=Lb0+∆gap

∆gap

Lb0

Lb

LcθGIB

θ y

(a) (b) (c)

∆GIB ∆GIB

~

B C

A

B CC B

A

A

θ u

θ r

~

Not to scale

F

P0

F F

θGIB-θ y θ r=θGIB-θ uθGIB

PGIB=(P0-Pucosθ u)/cosθ r

P0 P0

PG

IB =0

PG

IB =0 P

u

Pc=

P0

Pc=

P0

A A A


lateral strength degradation of the column, which decreases from the yield strength ,y

V col to the ultimate

strength ,uV col .

, ,GIB r y col u colP Fs n ) Fi (θ = − ( 5.6.a )

where rθ is the angle of the GIB with respect to the vertical axis at the ultimate state (Figure 5.6.c). The

vertical component of the GIB axial force GIB rcos( )P θ is the difference between the initial axial force of the

column 0 P and its vertical component at the ultimate states GIB r 0 u ucos( ) sP P - P coθ θ= (Figure 5.7):

GIB r 0 u ucos( ) sP P - P coθ θ= ( 5.6.b )

Figure 5.7. Effect of the GIB on the lateral resistance and the displacement capacity of RC columns

where uθ is the ultimate lateral drift capacity of the column. Dividing Equation 5.6.a by Equation 5.6.b and

assuming that 0 u u 0 ucosP - P P - Pθ ≈ , and r GIB uθ θ θ= − , the initial angle of the GIBθ , shown in Figure 5.6, is

given by

y,col u,col-1

GIB u

0 u

F - Ftan +

P - P,θ θ= ( 5.7 )

The distance between the base of the GIB and the column centreline GIB∆ (node B to node C in Figure 5.6) is

y,col u,col-1

GIB u

0 u

F - Ftan +

P - P,θ θ= ( 5.8 )

Lat

eral

res

ista

nce

Lateral drift ratio

GIB

Fu,col

Fy,col

θgc

Column

Lateral resistance of

the GIB: FGIB=PGIB sinθr

θcr (controlled by the gap)

θGIB

Lateral degradation of

the RC column: Fy,col - Fu,col

θu

GIB compansates for the

degradation: FGIB=Fy,col-Fu,col

θr=θGIB-θu


Figure 5.7 also demonstrates the effect of the GIB on the lateral resistance and the deformation capacity of

RC columns. The lateral force could also be controlled by varying the gap distance as it controls the effP in the

GIB, which is explained in the next paragraphs.

5.5.2 Gap distance

The role of the gap element is important as it controls the point at which the lateral resistance of the existing

column starts to decrease. If the gap distance is more than required, the delay in the unloading of the existing

column may cause the overloading of the column, and also increase the residual displacement. However, if

the gap is too small, the lateral resistance of the system starts to increase before than the lateral resistance of

the column starts to decrease. This increases the total lateral resistance of the first floor, which would

consequently increase the seismic demands that are transferred to the upper storeys. However, a small gap

distance could change the column mechanism from being mainly flexure/shear with some axial force, to

being mainly axial, which might be an effective solution in cases where columns are critical in shear but this

aspect is not examined here.

As a result of this retrofit strategy, the lateral drift ratio corresponding to a closed gap gcθ can be obtained

from the two following conditions:

a) gcθ controls the lateral resistance at the ultimate state. In this case uθ in Figure 5.7 should occur when the

lateral resistance of the GIB is maximized, i.e., ) / 2(r GIB gc

θ θ θ= − , Thus, since r GIB uθ θ θ= − , the lateral drift

ratio once the gap is closed gcθ is given by

2gc u GIB

θ θ θ= − ( 5.9 )

b) gcθ controls the critical lateral drift ratio of existing columns. In this case, gc cr

θ θ= . In many cases, this

condition governs, and could conservatively be considered as the yield drift ratio of the existing column yθ , at

which the lateral resistance starts to degrade (Figure 5.7).

The gap distance gap∆ is the difference between the initial length of the GIB, GIBL , and the length of the GIB

when the gap is closed 0bL ,i.e. 0gap GIB bL L∆ = − :

( ) ( )cos cos

c vyc

gap

GIB GIB gc

HH

θ θ θ∆ =

−

+−

∆ ( 5.10 )

where vy ∆ is the vertical displacement of the column at yield, which could be assumed negligible even though

this assumption is not likely to be very accurate for exterior columns.


5.5.3 Design of the inclined brace

From geometrical compatibility, the deformation of the inclined brace could be obtained from the difference

between its initial length and the length during the loading history

( )( )

( )( )0

cos

coscos

xc

b b b c C

GIB xGIB y

HL L L H L

θ

θ θθ θ∆ = − −= + ∆

−− ( 5.11 )

where c L∆ is the axial elongation of the existing column and could be considerable as the compressive force

of the column at the ultimate state is significantly reduced. Neglecting the concrete tension stiffness in the

plastic hinge region, the axial elongation of the column is obtained from the axial stiffness of the

reinforcement only in the plastic hinge area pK and the axial stiffness of the concrete in the rest of the

column elK .This assumption could only be appropriate for external columns, which are subjected to tension.

However, the accuracy could be reduced for middle columns and is a part of uncertainty. Considering this

assumption in mind, the axial elongation of RC columns in the GIB system could be estimated as:

0 , u

c c

c

P PL H

K

−∆ = ,

el p

C

el p

K KK

K K

×=

+, s s

p

p

E AK

L=

0.5

c C

el

c p

E AK

H L=

− ( 5.12 )

where uP is the axial force of the column obtained from the effP curve; iscK the axial stiffness of the

column. s cE and E are the modulus of elasticity of steel and concrete; st cA and A represent the reinforcement

area and the column cross section area, respectively. For low axial load ratio, the cracked area of the RC

column could lead to a better estimation. pL is the plastic hinge length, and could be estimated from

recommended equations [Priestley et al. 2007]. For typical columns with rebar ratio 0.01, s cE / E 10= and

plastic hinge length of 0.15 times the total column height (range is usually between 0.1 to 0.2), the column

axial deformation obtained from Equations 5.11 and 5.12 could be estimated as

0

. .

u

c c

c c

P PL H

E Aα

−∆ ≅ ( 5.13 )

where α is obtained as 0.4. For a fixed-end column, considering that the plastic hinges form at the two ends

of the column, α is estimated as 0.25. A parametric study is recommended as a part of the future research to

better estimate the effect of axial elongation of RC columns on the design parameters of the GIB system.

The axial force in the GIB is obtained from the equilibrium condition in the vertical axis

( )0

cos

u

b

GIB x

P PP

θ θ

−=

− ( 5.14 )


where, P0 and cP are the initial axial load and the unloading axial force on the existing column. Pc varies

during the drift history and has a direct relation to the drift ratio , xθ . Thus, by dividing the axial force of the

inclined brace (Equation 5.14) by its axial deformation (Equation 5.11), the axial stiffness of the inclined

brace can be determined. The brace axial deformation is also required to ensure that the brace comes into

contact at that the drift corresponding to the column yield and reaches the design resistance at column

ultimate drift. Thus, the sectional area of the inclined brace should satisfy the following equation

, b

b des y

des y

PA fσ

σ= =

ε

ε

( 5.15 )

where desσ is the inclined brace design stress; yε and ε are the yield axial strain and axial strain of the inclined

brace respectively.

5.5.4 Design Summary

The proposed design procedure for the GIB is summarized in to the five following steps:

1. Plot the degraded-capacity curve by plotting the envelope of force- displacement capacity curves for

the existing ground storey columns using a range of potential axial loads (Similar to Figure 5.4.b). This

curve determines ,,y,col u,col cr

F F θ and uθ .

2. Plot effP by plotting the axial load versus the lateral drift capacity (similar to Figure 5.4.a)

3. Calculated the gap distance using ∆rÚ3 using Equation 5.9 and 5.10. Note that gc crθ θ< .

4. Calculate the required axial stiffness of the inclined brace by dividing Equation 5.14 by Equation 5.11.

Check the design stress using Equation 5.15, and finally, check its buckling resistance.

• Alternative equations based on work method

The lateral strength of the column alone decreases due to P-delta effects. However, as a goal of the retrofit

strategy, the properties the GIB should be found so that the lateral strength of the whole system remain

constant (equal as the yield resistance) during the loading. Thus, the external work due to lateral force F and

the gravity load P0 is obtained as:

( 5.16 )

Where, ¯ is the lateral displacement, ∆£ and V¨ are respectively, the lateral displacement and lateral resistance

of the whole system at yield. Where, ∆Y* is the axial deformation of the existing column and can be

determined from the following equation:

Wex x( )1

2Vy ∆ y Vy x ∆ y−( )⋅+ P0 ∆ v x( )⋅+


The internal work is calculated due to the axial deformations of the column and the GIB in addition to the

flexural deformation of the existing column. Using lumped plasticity simplification, and assuming that the

column has an elastics-perfectly plastic behaviour, the internal work can be determined:

( 5.17 )

Where, '�, '£ and My are, respectively, the lateral rotation, and the yield rotation and the yield moment of the

existing column. ∆Y] is the axial deformation of the inclined brace, and �] is the axial force in the inclined

brace is estimated from equilibrium.

Thus, the axial deformation of the inclined brace can be obtained from the principle of the equal work

resulting from internal and external forces:

∆Y] = 0.5(�� + �)∆Y* − ��∆H − ��'£�(o − 0.5) *̂0.5�] ( 5.18 )

5.6 DESIGN EXAMPLE AND NUMERICAL VERIFICATION

The proposed design approach was applied to the RC concrete column that was studied previously; the

column was subjected to an initial axial load ratio of 0.5 such that the total axial load was 1600kN (column

dimension of 0.4 0.4× m, and a concrete compressive strength of 20MPa). As a first step towards defining the

properties of the GIB, the degraded-capacity curve of the column is determined according to the procedure

given earlier (Figure 5.4b). This curve indicated that the ultimate axial load is 320uP kN= ( 0.1)uσ = , which

corresponds to an ultimate lateral drift ratio of around 5.5%uθ = . At this drift ratio the lateral strength

degradation due to second order effects of the RC column is 15 kN (reduced from , 78y col

F kN= to

, 63u col

F kN= ). Thus, using Equation 5.7, the GIB should be located 201 mm from the centre of the column (

6.7%GIBθ = ).

The critical drift capacity crθ at which the lateral resistance starts to degrade is 1.2%, corresponding to a

stability coefficient of ,/ 1600 / 78 0.012 0.24P cr y col

P F Hθ ∆ = ∆ × = × = , which is less than the code limit of 0.3.

The drift ratio when the gap is closed is calculated as 4.3%cg

θ = , which is larger than crθ . Thus, using cg crθ θ=

,the gap distance and the axial deformation of the inclined brace is calculated as 2.7 mm and 5.8 mm using

Equations 5.10 and 5.11, respectively.

Win x( )1

2My θy⋅ My θ x( ) θy−( )⋅+

0.5Pb x( ) ∆L b x( )⋅+ 0.5 P0 P x( )+( ) ∆L c x( )⋅−


Using Equation 5.12, the axial elongation of the column is calculated to be 3.1 mm, which is close to what

was estimated from Equation 5.13, i.e., 2.8mm. When the column axial load ratio is reduced to 0.1, the axial

load of the inclined brace is 1320 kN (Equation 17). The design stress is then 424 MPa, which is more than

the yield strength of the brace. Thus, the brace is designed based on the yield stress, and the sectional area of

the inclined brace obtained from Equation 5.15 is 3710 mm2. Finally, a steel square hollow section (HSS

127 127 13× × CSA grade H) was used as the inclined brace. The factored buckling resistance of this member

was 1400 kN, which is greater than the demand force (1320kN).

Numerical models were developed using the nonlinear fibre-based software SeismoStruct (2008). The inclined

brace was modeled using fibre elements with the characteristics described above. To incorporate the gap

distance of the GIB into the modelling, a gap element was introduced in the axial direction of the inclined

brace, while its deformation in the other directions was restrained.

Figure 5.8.a compares the axial force in the column with that of the GIB. Although the brace exhibits a linear

elastic response, the force deflection curve is nonlinear because of the geometry of the system. The column

axial force starts to decrease at a lateral drift ratio of around 1.2%, and is 320 kN at the ultimate state (a lateral

drift ratio of 5.5%). The inclined brace axial force, at this ultimate state, is around 1300 kN which is close to

what was intended.

a) b)

Figure 5.8. a) Axial force in the column and the inclined brace, b) Total behaviour of the proposed method in comparison

to the existing column only

Figure 5.8.b compares the total response of the hybrid system to that of the existing cantilever column. The

drift capacity of the whole system increased significantly, from 1.6% to 5.5%, while the lateral strength did

not increase significantly (less than 5.0 %). The lateral resistance of the column degraded by around 20% at

the ultimate state, an amount comparable to the additional lateral resistance provided by the GIB, as was

intended.

0

300

600

900

1200

1500

1800

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Ax

ial

forc

e (k

N)

Lateral drift ratio (%)

Column

GIBPeff

(Figure 4a)

0.0

0.1

0.3

0.4

0.5

0.6

0.8

0.9

1.0

1.1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

No

rmal

ized

lat

eral

res

ista

nce

(F/F

y)

lateral drift ratio (%)

GIB

RC column

GIB system (RC column+GIB)

Un-retrofitted

RC column


5.7 PARAMETRIC STUDY

Figure 5.9 to Figure 5.11 illustrate the design parameters of the GIB system that are obtained following the same

procedure for various column configurations, considering different height, different initial axial load ratio and

different confinement conditions. Wherever one parameter is changed, other parameters are kept constant.

The reference values of the variables include a column dimension of 0.40 0.40m× , a longitudinal

reinforcement ratio of sρ = 0.015, an axial load ratio of 0σ =0.30, and a confinement factor of CF = 1.15.

Figure 5.9 indicate that as the column height increases, the both required gap∆ and GIB∆ increase, and

obviously, a stronger brace is required to avoid buckling.

Figure 5.9. Effect of the GIB system on response of 0.40x0.40m RC columns with different height H

It should be note that the initial axial load has the greatest effect on the inclined brace sizing; the brace

section thickness increases from 4.8 mm to 13 mm, due to the increase of axial load (Figure 5.10). The GIB∆ is

also increased, which requires larger gap distance. As the axial load increases the effect of the GIB system is

more obvious, which implies that the GIB system is more useful for columns with higher axial loads.

The confinement has a stronger influence on the gap distance as shown in Figure 5.11. When the confinement

increases, the drift at which the degradation takes place ( mθ ) increases due to the improvement of the column

post-yield stiffness. Moreover, the maximum drift capacity of the hybrid system increases. Thus, by

combination of the proposed GIB system and the confinement, the displacement capacity of the system can

be greatly improved. As will be discussed in the following section, the suggested detail connection of the GIB

system could improve the confinement condition at the top of the column.

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=2.5 m, CF=1.15, σ0=0.3

0

20

40

60

80

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.5 m, CF=1.15, σ0=0.3

∆GIB = 244 mm, ∆gap = 3.6mm

HSS 127 x 127 x 4.8

∆GIB = 215 mm, ∆gap = 2.8mm

HSS 127 x 127 x 4.8

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=4.0 m F=1.15,σ0=0.3

∆GIB = 255 mm, ∆gap = 3.9mm

HSS 127 x 127 x 6.40

10

20

30

40

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=5.0 m, CF=1.15, σ0=0.3

∆GIB = 277 mm, ∆gap = 5.5mm

HSS 127 x 127 x 8.0


Figure 5.10. Effect of the GIB system on response of 0.40x0.40m RC columns with different height initial axial load ratio

Figure 5.11. Effect of the GIB system on response of 0.40x0.40m RC columns with different height initial confinement

actor CF

5.8 NUMERICAL CYCLIC RESPONSE OF A SOFT STOREY FRAME RETROFITTED WITH THE GIB

SYSTEM

The cyclic response of a single-bay open ground storey frame retrofitted by the proposed approach and

subjected to quasi-static loading is presented. The length of the span and the frame height are set to 5.0 m

and 3.0 m, respectively (Figure 5.12). The RC concrete column is similar to the one used in the example

presented earlier. The beam has a height of 500 mm and width of 300 mm, and has a longitudinal

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σσσσ0=0.2 , CF=1.15

∆GIB = 268mm, ∆gap = 3.6mm

HSS 127 x 127 x 4.80

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σσσσ0=0.3, CF=1.15

∆GIB = 230mm, ∆gap = 3.2mm

HSS 127 x 127 x 4.8

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σσσσ0=0.4, CF=1.15

∆GIB = 207mm, ∆gap = 2.8mm

HSS 127 x 127 x 8.00

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σσσσ0=0.5, CF=1.15

∆GIB = 201 mm, ∆gap = 2.7mm

HSS 127 x 127 x 13

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σ0=0.3, CF=1.4

∆GIB = 218 mm, ∆gap = 3.6mm

HSS 127 x 127 x 4.80

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σ0=0.3, CF=1.1

∆GIB = 234 mm, ∆gap = 3.2mm

HSS 127 x 127 x 4.8

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σ0=0.3, CF=1.7

∆GIB = 217 mm, ∆gap = 4.1mm

HSS 127 x 127 x 4.80

20

40

60

80

100

0.0 2.0 4.0 6.0 8.0

Lat

eral

res

ista

nce

(k

N)

Drift ratio (%)

H=3.0 m, σ0=0.3, CF=2.0

∆GIB = 214 mm, ∆gap = 4.6mm

HSS 127 x 127 x 6.4


reinforcement ratio of 0.008, distributed symmetrically at the top and bottom of this section. By doing so,

plastic hinges are formed at the top and bottom of the column, and a column sway mechanism governs.

Thus, the fixed-end column condition is considered for the determination of the GIB system properties.

Figure 5.12. Single one storey RC frame retrofitted using GIB and subjected to quasi-static loading

The effP and the DC curves are obtained using a procedure similar to what was described in the previous

section, but assuming fixed-end conditions at the top and bottom of the columns. The column lateral force at

the initial axial load ratio of 0.5 is 170 kN. The maximum lateral drift capacity occurs at a lateral drift ratio of

6.5%, which corresponds to a lateral force of 100 kN. The distance between the GIB and the centerline of

the existing columns is obtained as GIB∆ =260 mm (see Figure 5.6), which is larger than the cantilever case, 201

mm. Due to the flexibility of the beams, however, a smaller distance than 260 mm could result in a better

response. For external GIBs, larger GIB∆ could also be used due to the increase of axial force imposed during

the lateral loading, but does not have a notable affect on the total response. Considering GIB∆ =240 mm, GIBs

occupy less than 15% of the frame span, which does not impact the architectural functionality considerably.

The axial deformation of the column is estimated as being 4.6 mm from Equation 5.11, and the gap distance

is calculated as 1.3 mm. The same brace section that was used in the previous section, i.e. HSS 127 127 13× ×

is also used in this design. The GIB is located on both sides of the existing column to allow for cyclic

reversed loading. The axial load is carried through bearing in the closed gap elements, and no additional force

is transferred to the system when the gaps are opened.

Since the inclined brace is linear elastic, its axial deformation at the end of a loading cycle is zero. As a result,

the GIB system pushes the frame towards its initial at rest position and thus the total residual inter storey

deformation is significantly reduced. One could estimate that the maximum residual deformation corresponds

to the point where the closed gap starts to re-open.

P0

P 0

H=3.00 m

5.00 m


A fibre-element model is defined using Seismo-Struct. The model of Filippou et al. (1983) is applied for the

hysteretic of the longitudinal reinforcement in the program Seismo-Struct. The 3.0m high pier is modelled by

four finite elements, the bottom one having 0.45m. Three integration sections per element are used (Gauss

quadrature), each one containing around 300 integration points. The Young’s modulus of steel was taken as

200 GPa. The iterative procedure developed by Taucer et al. (1991) and Spacone et al. (1996) is adopted for

the force-based element. Additionally, a co-rotational formulation was used to account for geometrical

nonlinear effects. The hardening and cyclic behaviour parameters were calibrated using the guidelines

recommended within Seismostruct to match experimental results: b = 0.015, R0 = 20, a1 = 18.5, a2 = 0.15,

a3 = -0.01 and a4 =15. A negative value is used for parameter a3 to account for the cyclic degradation of the

steel strength observed in the experimental results without changing the steel model.

The inclined braces are modelled using nonlinear fibre elements located on both sides of the RC columns.

The gaps are defined so that they can be activated in compression only without any resistance in tension. Due

to the cyclic behaviour of the columns, the designed values could be modified through a few more iterations

in order to achieve a better response. Since the frame is symmetrical, the designed elements are similar for

both columns. However, for non-symmetrical frames there could be more difficulties to adjust the activation

points. One option would be to treat each column as a separate sub-system, setting the GIB properties as a

function of the axial load and lateral deformation capacity of each individual column.

Positive and negative values in Figure 5.13 represent compressive forces in the right side and the left side gap

element of a column, respectively. The compressive forces in the gap elements increases gradually as the

lateral deformation is increased. The force in the gap element is equal to the force in the inclined brace, as

they are modeled in series. When the force in one gap increases, the force in the other gap is zero, which

means that it is opening. When the column returns to its initial position, the forces in both gaps become zero.

However, the figure shows an initial delay between the loading of the brace on one side versus the other. This

could be due to observed axial stress in the column at zero deformation. The axial force in the inclined brace

increases linearly up to about 1500 kN, which results in a reduction of the axial force ratio in the RC column

from 0.5 to 0.063, which is close to 0.1, the value at the design level ( x∆ =100mm).

Figure 5.13. Axial force history of the right and left gap elements, b) Moment – Curvature response of the existing column

-1800-1200

-6000

60012001800

0 200 400

Fo

rce

(kN

)

Step

Right gap element

Left gap element


The hysteretic moment-curvature response at the bottom of the RC column in Figure 5.14.a shows that the

column has a good dissipation capacity, despite the confinement is relatively low. The gradual degradation of

the moment capacity is because the axial force in the column is reduced as the deformation increases.

Figure 5.14.b shows the total hysteretic response of the entire system (the frame and the GIB system) and

compares to the response of the existing frame. The hysteretic response of the system exhibits a self-centring

response with good energy dissipation capacity, which can significantly reduce demand parameters in the

floors above the ground level. The ultimate drift capacity of the system is increased considerably without any

notable increase in resistance. Moreover, the residual displacements greatly reduce to around 1.0% that could

be considered acceptable for most existing buildings for the life-safety performance level.

a) b)

Figure 5.14. a) Moment – Curvature response of the existing column, b) Hysteretic response of the hybrid system in

comparison to the existing frame


This chapter proposes an approach for enchasing the seismic response of buildings with open ground storey.

A Gapped-Inclined Brace (GIB) system is introduced to existing columns of the ground level to reduce the

impact of P-Delta effects, minimize residual displacements and increase the deformation capacity of existing

columns without a significant increase in the lateral resistance of the system. The potential advantage of this

approach could be that damage to the structural and nonstructural elements are concentrated at the ground

storey, which could reduce the direct and indirect losses in other floors. In addition, this methodology

minimizes the possible impacts to architectural functionality imposed by traditional seismic retrofitting

approaches.

The mechanics of the proposed system was illustrated, and a brace sizing procedure was proposed. The

results from pushover analyses of RC columns with different configurations verified various mathematical

relations developed for the purpose of sizing the braces. It was concluded that increasing confinement in

addition to the proposed approach could greatly improve the deformation capacity of RC columns. Nonlinear

-300

-200

-100

0

100

200

300

-0.50 -0.30 -0.10 0.10 0.30 0.50

Mo

mn

et (

kN

.m)

Curvature (1/m)

-400

-300

-200

-100

0

100

200

300

400

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Bas

e S

hea

r (k

N)

Drift (%)

Existing Frame

Hybrid system


quasi-static cyclic analysis of a single span RC frame indicated that the proposed strategy could significantly

improve the hysteretic response of a soft storey frame in terms of energy dissipation capacity and residual

deformation.

The proposed strategy could also be applicable to other types of structures including steel structures, and

bridge piles under high vertical loads. It is, however, recommended that dynamic analyses of case studies be

carried out along with experimental validations to further develop the proposed system and demonstrate its

applicability for the seismic upgrade of such structures.

94

6.SEISMIC RESPONSE OF BUILDINGS USING GIB SYSTEM AND

DESIGN RECOMMENDATIONS

6.1 INTRODUCTION

This chapter presents the seismic responses of the retrofitted soft storey building (using GIB system) that was

studied in Chapter 3. Key aspects related to the numerical modelling of the retrofitted building and the results

from the nonlinear time-history analyses are presented in Section 6.2 to Section 6.5. In Section 6.6 and

Section 6.7, the response of the soft storey building retrofitted using the GIB system is compared with the

existing soft storey building, and the building in which masonry infills are distributed uniformly over the

building height. To investigate the effectiveness of alternate retrofit configurations, different scenarios of GIB

systems is explored in Section 6.8 and 6.9.

6.2 SOFT STOREY CONCEPT FOR MULTI STOREY BUILDINGS

The soft storey concept to reduce the seismic response of buildings by making the first floor to be flexible

dates backs as early as 1920s [Martel 1929]. His study on a four storey building showed that if the stiffness of

the first-story columns are one tenth of that of the floors above it, the response is similar to the one-story

bent. Moreover, he pointed out that the flexible first story could reduce the floor accelerations above the

first storey if the period of the earthquake is less than the free period of the building. This concept

followed by a few researchers [Green 1935; Jacobsen 1938].

In the late of 1960, Fintel and Khan [1969] took first steps to reduce seismic forces using the weak storey

energy dissipated concept. Their proposal was that the first floor should yield at a specific value that cannot

transmit a greater force to the super structure above itself. Chopra et al. [1973] argued that the complexity of

the dynamic earthquake behaviour of multi-storey buildings could invalidate these results. Their parametric

study on an eight storey building concluded that the displacement capacity of the first storey should be very

large. In addition, the yield force and the post yield ratio were required to be very low in order to protect the

super structure effectively.

It should be noted that because the post yield stiffness ratio of the GIB system (existing structural system +

GIB)at the first level is almost zero, it could provide such an effective protection to the super structure.

However, it is recommended to develop a robust methodology to design GIB system for multi-storey

buildings which ensure that storeys above the first floor is protected for desired seismic demands.

6.3 DESIGN CONSIDERATION OF SOFT STOREY BUILDINGS USING THE GIB SYSTEM

Prior to developing a retrofit design solution using a GIB system, it is recommended that the structure first

be assessed using the displacement-based assessment approach of Priestley et al. [2007]. This assessment will

SEISMIC RESPONSE OF BUILDINGS USING GIB SYSTEM AND DESIGN RECOMMENDATIONS 95

indicate whether a soft-storey mechanism is likely to occur and what intensity the collapse (or other relevant)

limit state will occur. Subsequently, if the results of such an assessment suggest that the GIB system might be

an effective retrofit option, the retrofit guideline of soft storey buildings using GIB is recommended based on

the following steps:

Step 1: Check if the soft storey mechanism is governed. The first step in the design will require evaluation of

strength and deformation characteristics of the existing columns at the ground storey. This assessment should

also aim to establish the maximum allowable strength of the first floor elements that would ensure (via

capacity design principles) that the response of the existing structure above the first level (upper storeys)

remains elastic or within desired limits. In other words, the upper storeys should remain with little or no

damage which implies that their inter storey deformations and floor accelerations should be limited. This

assessment could be carried out using an adaptive pushover analysis. For frame buildings, Priestley et al.

[2007] proposes an approximate indication by calculating a sway potential index Sx

Sx = ∑ (M�Û + M�Ü)Ý∑ (M/Ú + M/�)Ý ( 6.1 )

where �]Þ and �]ß are the beam expected flexural strengths at the left and right of the joint, respectively,

and �]Þ and �]ß are the expected column flexural strengths above and below the joint. The value of Sx larger than unity indicates a columns sway mechanism at level i.

Sullivan and Calvi [2011] proposed a similar sway-demand index SDi for prediction of the column sway

behaviour, according to the following equation

SDx = Vx,�Vx,�V�,�V�,� ( 6.2 )

where Vx.� and Vx,� are the storey shear demand and resistance at level i, respectively, V�,� is the base shear

demand, and V�,� is the shear resistance at the base of the structure. The higher sway demand index

represents the higher possibility of occurrence of the column sway mechanism.

Step 2: Identify the increased displacement capacity that can be achieved by implementing GIB devices, and

compute the effective period of the equivalent SDOF system [Priestley et al. 2007]at the new ultimate

displacement capacity.

Step 3: Define an appropriate deformation profile. Considering that the upper stories are assumed not to

deform beyond their yield limit, i.e. ∆½ß= ∆£½ß, the total plastic deformation of the entire structure must be

accommodated at the first storey. The displacement profile at the yield, the plastic and the ultimate state for a


2DOF system is shown in Figure 6.1. �½ß , and ∆½ß represents the equivalent mass and the lateral

displacement at the storeys above the first floor.

For an existing building, ∆¨ÃÜ is known. Assuming that the total displacement of the building at a given

hazard level is known (for example by limiting the roof displacement), the first floor displacement is

∆¾= ∆G − ∆£½ß ( 6.3 )

(a) (b) (c)

Figure 6.1. Displacement profile for soft storey frames, a) yield b) plastic, c) Ultimate displacement profile

It could be possible that the deform shape of the structure at the ultimate state is similar to that of the plastic

deformation. This implies that at the ultimate limit state, there is no lateral deformation at the storeys above

the first floor, i.e. ∆¾= ∆G, which simplifies the approach. The displacement ductility capacity o is

calculated as ∆G/∆£¾.

Step 4: Determine the base shear capacity and the effective stiffness. The base shear capacity Và/ is

calculated as

Và/ = °¹�áâ,] + �áã,�¼��z�

/ ¾̂ ( 6.4 )

where �áâ,] and �áã,� are the column moment capacities at the column base and at the beam

centreline at the first level. The equivalent stiffness including P-Delta effects are then given by

KÃ = ��*∆G − � (� − ∑ �äå�)¾̂ ( 6.5 )


where � is the weight of the whole building and �äå� is the maximum vertical load in the GIB

system associated to each column. For RC structures, C is taken as 0.5 [Priestley et al. 2007].

Step 5: By estimating the likely combined hysteretic response and ductility demand of the equivalent SDOF

system, a value of the equivalent viscous damping for the system could then be computed using expressions

for a flag-shaped hysteretic model (refer Priestley et al. 2007 and [Ceballos and Sullivan 2011]). Subsequently,

the likely intensity that would cause the retrofitted structure to exceed the ultimate limit state can be

evaluated, again using the displacement-based assessment procedure of Priestley et al. [2012]. If this new

intensity level is acceptable, then the details of the retrofit solution can be finalized. If not, one could consider

the use of supplemental dampers to further reduce the likelihood of collapse, or an alternative retrofit strategy

could be developed.

6.4 NUMERICAL INVESTIGATION

This section involves a case study analysis of an existing soft storey building retrofitted by the GIB system.

The building example that was used for this study consists of the six-storey reinforcement concrete frame

that was studied in Chapter 3 (

Figure 6.2). Accordingly, this frame configuration is taken from Galli [2006], which is a representative of

typical buildings have been designed during 1950 and 1970. As outlined in Galli [2006], the structural

elements were designed just for gravity loads without any specific considerations for seismic loading. The

four columns at the ground level consist of two internals ones, and two externals ones.

Figure 6.2. Case study building configuration (details in chapter 3)

C2 C3 C3 C2

C1 C2 C2 C1

C1 C2 C2 C1

C1 C1 C1 C1

C1 C1 C1 C1

C1 C1 C1 C1

C-I C-II C-III C-IV


The structure is part of a frame system building formed by a series of parallel frames at a distance of 4.5 m

between the centrelines of the columns. The first floor height is 2.75 m, while the other floors have the same

height of 3 m. The frame consists of two 4.5m long identical exterior bays and one interior 2 m bay. Thus,

the frame is symmetric about the vertical axis.

Table 6.1 lists the column details at the first level. Parameters ρ>CFand σ� represent the longitudinal

reinforcement ratio, the confinement factor and the axial load ratio, respectively.

Table 6.1. Column configurations at the open ground level

Column

Type

Dimension Height �] CF

M m %

C1 250 2750 1.29 1.12

C2 300 2750 0.89 1.08

C3 350 2750 0.83 1.07

To determine the most effective use of the system, different implementation configurations of the GIB are

studied, as shown in Figure 6.3:

i) Configuration 1 (Figure 6.3.a): the properties of the GIB system are defined without considering the

changes in the axial load during the ground motion history. This configuration is referred to as GIB-1

variant.

ii) Configuration 2 (Figure 6.3.b): the increase and decrease in the column axial loads due to lateral loads is

considered. As such, GIBs that are at the exterior side of the exterior columns are designed for stronger

actions, while GIBs that are at the interior side of the exterior columns are eliminated, because their

actions are not significant. This configuration is referred to as GIB-2 variant.

iii) Configuration 3 (Figure 6.3.c): The number of GIBs in the interior columns are also decreased. As such,

GIBs that are at the interior side of the interior columns are eliminated. The aim is to reduce the cost

and to increase the architectural functionality. This configuration is referred to as GIB-3 variant.

The response of the retrofitted building is compared with the existing soft storey building, and the building in

which masonry infills are distributed uniformly over the building height (full infill). Finally, the effect of

supplemental damping on the response of the GIB-3 variatn will be explored numerically.

6.5 GIB- 1 VARIANT

As a first step, the GIB system associated with each column is designed based on the aforementioned

procedure which neglects the axial loads while the effect of the varying axial load will be further discussed

later. This configuration is shown in Figure 6.3 , which is referred as GIB1 Variant. As such, the GIBs that

corresponds to the exterior columns, i.e., GIB-1L, GIB-1R, GIB-4L, GIB-4R, are designed for the same


action, and are referred to type GIB-Ex. Similarly, the GIBs that corresponds to the interior columns, i.e.,

GIB-2L, GIB-2R, GIB-3L, GIB-3R, are designed for the same action, which are referred to type GIB-In.

Figure 6.3. Position of the GIB system in the soft storey building bases on three configurations: a) GIB 1 variant, b) GIB 2

variant, c) GIB 3 variant

Table 6.2 illustrates the design parameters for the two types of GIBs. The gap distance ∆rÚ3 and the ∆æçà of

the both types are close to each other, while the inclined brace thickness t that corresponds to the internal

column GIB-In is almost two times of that the external one GIB-Ex, because they need to design for larger

effP .

Table 6.2. GIB configurations associated to each column type for GIB-1

Column

Type

σ� ∆äå� ∆|�, �] X] ! Mm mm kN mm2 mm

C2 0.19 269 3.65 170154 598 1.19

C3 0.22 266 3.33 305262 1075 2.15

C-I C-II C-III C-IV

GIB

-3L G

IB-3

R

GIB

-2L

GIB

-2R

GIB

-1L

GIB

-1R

GIB

-4L

GIB

-4R

GIB

-3L G

IB-3

R

GIB

-2L

GIB

-2R

GIB

-1L

GIB

-4R

C-I C-II C-III C-IV

GIB

-3R

GIB

-2L

GIB

-1L

GIB

-4R

C-I C-II C-III C-IV

(a)

(b)

(c)


6.5.1 Numerical Modelling

The inelastic dynamic analysis program RUAUMOKO [Carr 2004] was used for the nonlinear time-history

analyses. A two-dimensional non-linear Giberson beam element (refer Carr, 2006) is used for modelling the

beams and columns. The Takeda hysteretic rule [Otani 1974] is selected, where unloading and reloading

stiffness reduces as a function of ductility (Figure 6.4).

The Emori and Schonbrich [1978] model is used to obtain the unloading stiffness. To take into account the

effect of axial load variation on the capacity of the column elements, an M-N interaction diagram is defined.

Masonry infills are modelled based on the equivalent compression diagonal struts. The spring model

proposed by Trowland (2003) is used to consider the beam-column joint behaviour. More detailed

information on the modelling is provided in Chapter 3.

Figure 6.4. Modelling of GIB system in Ruaumoko for time history analysis

The GIBs were modelled using contact elements on both sides of the RC columns. The bilinear slackness

hysteretic rule (Figure 6.4) is used to model the gap distance. The parameter � is defined as unit because the

brace must be linear elastic. The contact element does not activate in during static loading, and is only

activated in the time history analysis. A large value for ∆|�, in tension is considered, which enables the GIB

to activate under compression only without any resistance in tension

6.5.2 Verification with Nonlinear Fiber Element modelling

To verify the lumped plasticity model used in the RUAUMOKO model, a static nonlinear analysis was first

carried out using a fiber modeling in the Seismo-Struct (2008) software. The Filippou et al. (1983) model was

used to model the hysteresis of the longitudinal reinforcement. All columns at the first level are modelled

using four finite elements along the length2.75m, the bottom one being 0.50m long. Three integration

y

z x

F

F y+

F y −

∆

Hysteretic behaviour of the GIB

in the axial direction usingcontact element

Release for rotation about z

kb=Eb A b /Lb

rkb

kb kb

∆ gap+

∆gap−

kb

rk b Existing RC column using

lumped plasticity model beamcolumn element

GIBGIB


sections per element are used (Gauss quadrature), each one containing around 250 integration points. The

Young’s modulus of steel was taken as 200 GPa.

The Mander model [Mander et al. 1988] was used to evaluate the constitutive relations for the confined and

the unconfined concrete under compression. To incorporate the constitutive relations for reinforcement steel,

the model proposed by King et al. [1986] was adopted.

The strain at maximum stress for unconfined concrete was assumed to be 0.002. The ultimate concrete strain

was governed by the core crushing limit state proposed by Kowalsky [2000], and the ultimate tensile strain of

the reinforcement was assumed to be 12%.

The iterative procedure developed by Taucer et al. (1991) and Spacone et al. (1996) is adopted for the force-

based element. Additionally, a co-rotational formulation was used to account for geometrical nonlinear

effects. The hardening and cyclic behaviour parameters were calibrated using the guidelines recommended

within Seismostruct to match experimental results: b = 0.015, R0 = 20, a1 = 18.5, a2 = 0.15, a3 = -0.01 and

a4 =15. A negative value is used for parameter a3 to account for the cyclic degradation of the steel strength

observed in the experimental results without changing the steel model.

The four-node masonry panel element, which is initially developed by programmed by Crisafulli [1997], is

used in SeismoStruct for modelling the nonlinear response of infill panels (Figure 6.5). Each panel is

represented by six strut members; each diagonal direction features two parallel struts to carry axial loads

across two opposite diagonal corners and a third one to carry the shear from the top to the bottom of the

panel. This latter strut only acts across the diagonal that is on compression, hence its "activation" depends on

the deformation of the panel.

To consider the actual points of contact between the frame and the infill panel, four internal nodes are

employed. These four nodes corresponds for the width and height of the columns and beams, respectivel. In

addition, four dummy nodes are introduced to consider the contact length between the frame and the infill

panel. The properties of the masonry infill and the related assumptions are found in Chpater3.

It should be noted that this model incorporates only the most frequent of modes of failure, which could

predict the exact behaviour of the structure. In addition, all dispersion of mechanical properties of masonry

could increase uncertainty of infills characteristics and affects the global response of the structure.


Figure 6.5. Modelling masonry infills in Ruaumoko, a) infill panel element configuration b) shear spring modelling

Beam column joint elements were modelled using the same approach that is described in Chapter 3. As such,

springs are inserted at beam-column locations using the approach proposed by Trowland (2003). The

adaptive pushover analysis was used for all variants. Thus, the distribution of the lateral forces is changes

thought the nonlinear analysis. In this case, the soft storey behavior could be predicted regardless of the

predefined load or displacement pattern.

To check the validity of fiber element model in Seismo-Struct, the response of the soft storey building was

first compared to what was obtained using lumped plasticity model in Ruaumoko. The dotted and the dashed

line in Figure 6.6 shows the pushover curves of the existing soft storey frame that are obtained from the

lumped plasticity and the fiber element models respectively.

The figure shows the response for both the cases with and without P-Delta considerations and indicates a

good agreement between the different approaches. The figure also shows the ultimate concrete strain that is

governed by the core crushing limit state [Kowalsky 2000] at each column. The right-middle column (C-III)

reaches this limit state at a drift ratio of around 1.7%, while this value for right-side column (CIV) is 2.1%.

The inclined braces were then modelled into Seismo-Struct using fibre elements positioned in series with the

nonlinear gap elements, as shown in Figure 6.7.

Activates in compression

Dectivates in tension


Figure 6.6. Comparison of the pushover curves obtained from the lumped plasticity and the fibre element modelling of the

existing soft storey frame

Figure 6.7. modelling of GIB system in Seismo-Struct for push over analysis

6.5.2.1 Consideration of Column elongation

As discussed in Chapter 5, the axial load on the exiting columns at the first level of the soft storey building is

reduced due to the presence of the GIB system. The force imposed by the GIB system could cause axial

elongation of existing columns at the first floor, which could be significant depending on the initial axial load,

location of the columns (exterior or interior) and the seismic demand parameters. To take into account the

axial deformation of the first storey columns in the lumped plasticity model, the axial stiffness of the columns

needed to be modified. Assuming zero stiffness for concrete in tension, Chapter 5 recommended a reduction

factor of 0.25 to 0.4 to the axial stiffness of RC columns at this single level.

Figure 6.8 presents the axial force in columns and GIBs at the first storey as a function of the lateral drift.

The results were obtained from the pushover analysis. The solid line shows results obtained from the fiber

element modelling, while the dashed line indicates the results that were obtained using the lumped plasticity

0

50

100

150

200

250

300

350

0.0 1.0 2.0 3.0 4.0B

ase

Sh

ear

(kN

)

First Storey Drift (%)

Fiber element

Lumpled Plasticity

With P-∆

Without P-∆

Core crushing of C-IV

Core crushing of C-III


modelling when the full column axial stiffness is considered. These results show the significant differences in

the column axial loads, especially for column CI, because this column is under tension due to the lateral

overturning moment.

Figure 6.8. Axial forces in the first storey columns and the GIB of the GIB-1 variant: comparison between fibre models and

lumped plasticity models, see Figure 6.3

The dotted line in Figure 6.8 shows results obtained using a reduced axial stiffness and indicates a better

agreement to those obtained from the fiber element analysis. If the column axial stiffness is not reduced, the

-600

-500

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0

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orc

e (k

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Axia

l F

orc

e (k

N)

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l F

orc

e (k

N)

GIB-1L GIB

Left Column ,C-I Middle Columns, C

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I Middle Columns, C-III Right Colum

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3L GIB-4L

III Right Column, C-IV

Fiber element

Lumped -with elongation

Lumped-without elongation


GIB axial forces are not likely to be accurate. The same is observed for the axial loads in the GIB. The axial

force in the GIB1-L increases up to 500 kN, while in the fiber element, this value is almost half, i.e. 250 kN.

However, for column C-III and C-IV, the difference is less significant, because these columns do not go into

tension during the push over analysis.

Figure 6.9 shows the pushover curve of the GIB1 variant that is obtained using the both lumped plasticity

and fibre modelling approaches. The figure indicates that the two approaches provide a good agreement. In

addition, the GIB system improves the lateral response significantly. The drift capacity ratio is almost tripled,

which increases from 1.7.0% (see Figure 6.6) to 6.0%.

Figure 6.9. Push over curve capacity of the GIB-1 variant from nonlinear fibre element (SeismoStruct)modelling and

lumped plasticity modelling(Ruaumoko)

6.5.3 Comparison of variants using fiber analysis

For gaining insight into the effect of the GIB system on the lateral capacity of the soft storey frame,

Figure 6.10 shows the comparison of the push over curve of the six-storey frame obtained from the fiber

element analysis and using three different scenarios: soft storey variant, GIB-1variant, and full infill frame

variant. The full infill variant has masonry infill distributed over the height uniformly as were illustrated in

Chapter 3. The plot indicates the lateral resistance versus the lateral roof drift ratio. The pushover analysis

was run until either concrete at the core of each beam column is crushed, or the steel is ruptured. Although

adding infills in the first level of the soft storey increases the lateral resistance significantly, its resistance is

reduced rapidly because of the brittle behaviour of masonry infills. Moreover, the lateral drift capacity is not

increased significantly (from 0.50% to 0.70%), because the core of the right column at the second floor (C-IV

second floor) is crushed at the lateral roof drift ratio of almost 0.70%. In the meantime, the lateral drift ratio

of the second floor reaches almost 1.5%. This is close to the out of plain failure of infills that are

perpendicular to this frame. On the other hand, the lateral roof drift capacity ratio is more than 1.2% for the

GIB-1 variant, which is almost two times of the full infill variant.

0

50

100

150

200

250

300

350

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Lat

eral

res

ista

nce

(k

N)


Fiber element

Lumped plasticity


Figure 6.10. Push over curve capacity for the six-storey frame buildings a) Full infill, b) Partial infill, c) GIB-1 variant

Figure 6.11 depicts the material limit states pattern in the beam and the column elements of the three

variants. These damage states are obtained at the ultimate drift capacity of each variant, which was shown in

Figure 6.10. The limit states are illustrated at the bottom of this figure, which are separated by different

colors. The damage pattern for the full infill case is much more evenly distributed. Plastic hinges are mainly

formed in the second. Concrete core strain at the columns of the second floors exceeds its ultimate capacity,

i.e. 2.0%, and in the third and the fourth floors, some elements yield.

For the partial infill case, all damage is concentrated in the first floor only. Plastic hinges form in all columns

at the first level at the lateral roof drift ratio of 0.50%, which corresponds to the lateral first storey drift ratio

of 1.7% that were previously shown in Figure 6.6 . As discussed, at this drift ratio, columns CIII and CIV

reached the core crushing limit states.

However, when the building is retrofitted using the GIB system (GIB-1 variant), the roof drift capacity

increases to 1.2%, while all damages are still accumulated at the first level of the soft storey building. Before

this drift ratio, none of the beams and columns of the first floor reach their ultimate limit states before, which

is core crush of concrete, rebar buckling or steel rupture. The first floor displacement and the roof

displacement at this level are 0.21m and 0.17m, respectively, which denotes that the drift ratio at the floors

above the first floor is very low, and all are in the elastic range. The figure denotes that at this roof drift ratio,

neither cover spalls or nor steels yields in beams and columns in all the storeys above the first floor.

6.5.4 Results from Nonlinear Time History Analyses

Time history analyses are also carried out using ten recorded horizontal accelerograms selected as part of the

DISTEEL project [Maley et al. 2013]. The record set consists of 10 records that are scaled to be compatible

with Eurocode 8 spectrum [CEN 2004] for soil type C and a corner period Td = 8s.

0

200

400

600

800

1000

1200

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Lat

eral

res

ista

nce

(kN

)

Roof Drift (%)

Full infill variantSoft storey varinatGIB-1 variant

First floor: core crushing of C-IV

First floorSteel

rupture of C-ISecon floor: Core crushing of C-IV

+ potential out of plain failure of infills

in prependicular frames


(a) (b) (c)

Roof

Drift (%) 0.67% 0.39% 1.2%

Base

Shear

(kN)

1050 280 280

Figure 6.11. Damage limit state pattern in the six-storey frame a) Full infill, b) Partial infill, c GIB-1 variant, (Dr : Roof

drift(%) ; Vb: Base shear (kN))

Figure 6.12.a shows the global hysteretic response parameters of the retrofitted structure obtained from three

ground motions (Landers, Loma Prieta and Northridge). The dotted line is the total lateral resistance of the

structure, which indicates all the ground motions produce approximately a flat hysteretic curve without

negative slope. However, the total lateral resistance is almost close to that of the existing columns at the first

level, shown by the grey line. Thus, the GIBs do not induce a significant resistance to the existing soft storey

building, as intended. This can be seen in the part (b); the gray line compares the first inter storey drift ratio to

that of the floors located above, shown with the dark line.

Despite the discrepancy between the variability responses obtained from each ground motion, all results

indicate a significant reduction of the maximum and residual displacements at the upper storeys. However,

the residual displacement of the first soft storey highly depends on the characteristics of the ground motions.

This value due to the second earthquake is almost half than that of the first and the third ones, while its peak


ground acceleration is almost one half (the dotted line in Figure 6.12.b). One possible solution to reduce the

residual displacements is to decrease the displacement demand at the first floor, which could be achieved

using larger initial GIB angle or by decreasing the gap distance. However, this would increase the lateral

resistance and consequently the forces that would be transferred to the upper storeys.

(a) (b) (c)

Figure 6.12. Global seismic response in GIB-1 variant obtained from NTHA for three earthquakes: a) Global hysteresis, b)

Inter-storey drift, c)Floor acceleration

Part a and b in Figure 6.13 present the hysteretic response of beams and columns at the first floor of the

retrofitted soft storey building, which are located in the exterior (C-I) and the interior (C-II) sides of the

frame (see Figure 6.3).

The results indicate that all beam elements at the first level (either interior or exterior) exhibit almost linear

responses. However, the exterior beams show a low level of nonlinearity, which are negligible compared to

columns. Thus, no significant damage was found in the beam elements of the soft storey building. The

degraded capacity (DC) curve can also be seen in the column hysteresis; the moment resistance of these

columns is reduced due to PÃÄÄthat is induced by the GIBs. The level of the reduction is increased as the

curvature increases, which is higher for the interior columns because the interior GIBs (GIB-In) are designed

for higher axial loads. The hysteretic axial load-axial deformation curve in Figure 6.13.c also verify that the

-0.1 0 0.1-400

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400

Re

sis

tan

ce

(kN

)

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Drift (

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AC

C(g

)

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Roof displacement(m)

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AC

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Time

First floor acceleration

Ground acceleration

Column resistance

Toral resistance

First floor drift (%)

Upper floors drift (%)

Landers

Loma Prieta

Northridge


axial load in interior GIBs (GIB-In, the dark line) is larger than that of the exterior ones (GIB-Ex, the gray

line). In addition, the stiffness of GIB-In is larger than that of GIB-Ex. The gap distance for both the interior

and exterior GIBs is almost the same, and is 3.65 mm.

(a) (b) (c)

Figure 6.13. Element hysteretic responses in GIB-1 variant: a) Moment-curvature of exterior Beams and columns, b)

Moment-curvature of interior Beams and columns c) Axial GIBs hysteresis

Figure 6.14 shows the time history of the axial loads of the first storey elements (Columns and GIBs) at

different sides of the frame under the three earthquakes at the design (DBD) level. The axial force of the

middle columns decreases from 500 kN to almost 190 kN, which result in a maximum axial load of 310kN in

the GIB-In, which is less than for the GIB-Ex. For the columns at the right side of the building, the

maximum axial compressive load is even increased from 350 kN to almost 600 kN. On the other hand, the

column in the left side goes to tension (maximum axial force 210 kN). The tension in these columns could

decrease their lateral displacement capacity. Thus, using the GIB-1R and GIB-4L could have even negative

effects on the lateral capacity of columns at the first floor. As a result, if these GIBs are eliminated, and

instead, GIB-1L and GIB-4R are designed for stronger actions, the seismic response of the retrofitted

building could be improved. Section 6.9 will investigate this scenario.

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Mo

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Beam and Column (Exterior)

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Axia

l fo

rce

(kN

)

GIB Elongation (m)Column Beam Exterior Interior

Landers

Loma Prieta

Northridge


(a) (b) (c)

Figure 6.14. Axial force on the columns and the GIBs of the first storey, GIB-1 variant

6.6 COMPARISON OF VARIANTS AT FLOOR LEVEL

Figure 6.15 presents a comparison of the peak response parameters of interest including the peak inter storey

drift, the peak acceleration and residual drift for the three variants of full infill (FI), soft storey (SS) and GIB-

1. The geometric mean value was used to estimate the mean response for all ground motions. The three

intensity levels of 0.2g, 0.4g, and 0.6g could correspond to the FE, DBE and the MCE hazard levels.

The damage assessment of all variants are presented in Section 6.7. At the intensity level 0.20g, the maximum

drift ratio at the first level of the existing soft storey frame shown by the dashed line is 1.8%, which is almost

close to its ultimate drift capacity (1.7%, see Figure 6.6). This drift ratio is around six times that of the full

infill case (0.29%), shown by the solid line. However, the drift ratio at the second and the third floors is

significantly reduced to 0.24% and 0.14%, respectively, while the corresponding values for full infill case

being 0.39 and 0.23. The GIB-1 variants have almost the same effects, and do not change the drift demand at

the storeys above the first floor. In addition, the average of the floor accelerations of the soft storey variant

and the GIB-1 variant are almost 0.35g that is less than that of the full infill frame that is 0.50g. This would be

another advantage as it could reduce the total damage to the non-structural elements through the entire

building.

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l lo

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)

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Time0 50 100

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Time

Column GIB(L) GIB(R)

Landers

Loma Prieta

Northridge


Figure 6.15. Response parameters at storey levels

At the design level (PGA=0.4g), the drift demand at the first level of the existing soft storey building is more

than 4% which is more than the ultimate capacity of the first storey columns, i.e. 1.7%. Thus, the numerical

results could no longer be valid for this variant. However, the drift demands at the first level of the GIB-1 is

less than the ultimate limit states (Figure 6.6) of the retrofitted columns at this level (compare 4.1% to almost

6.0%). The second floor of the full infill case has a drift demand of 1.75% at the design level, which is close

to its ultimate drift capacity. This value for the GIB-1 variant is 0.38%. The reduction of the average drift in

the storeys above the first floor at DBE level (PGA=0.4) is more than the FE level, which indicates that the

damage to structural components of the GIB-1 variant at the DBE level are expected to be less than for the

full infill case for higher intensity levels. This could be an advantage of using this approach in areas of high

seismic risk. Floor acceleration is also decreased from 0.75g to 0.6g. However, the residual drift at the first

floor of the DBD level is 1.25%.

At the intensity level corresponding to a PGA of 0.6g, the drift demand at the second floor of the full infill

case is more than 13%, which significantly exceeds the drift capacity of columns at this floor. The drift ratio

at the first level of the GIB-1 building is almost 8%, which is more than the lateral drift capacity of the

retrofitted columns at this level. However, if the drift capacity of the columns at the first storey increases to

8.0%, the responses at the upper storeys is significantly reduced compared to the full infill case. However, it

would not be a good solution because the residual displacement is almost 6.0%, which is too large. Using a

larger GIB angle could decrease the maximum and the residual drifts at the first level, though it could

0 0.5 1 1.50

2

4

6PGA=0.2g

Sto

rey

0 0.1 0.20

2

4

6

Sto

rey

0.2 0.4 0.6 0.80

2

4

6

Sto

rey

0 2 40

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6PGA=0.40g


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2

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6


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6PGA=0.60g

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6

0.4 0.6 0.8 10

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FI SS GIB-1


increase the demand at the upper storeys as well. An alternative solution could be to use supplemental

dampers at the first level of the GIB-1 variant. This solution could also reduce the acceleration response,

although the peak first floor accelerations (shown by the gray line) are very close to the PGA values. This

potential benefit of adding damping to the GIB system is explored parametrically in the next section.

6.7 COMPARISON OF IDA RESULTS

To explore the seismic behaviour of each variant in different intensity levels, this section compares the

demand parameters as well as the damage analysis obtained from the incremental dynamic analysis.

6.7.1 IDA results

Figure 6.16 compares IDA responses of the three aforementioned variants (FI, SS and GIB-1) along with the

ratio of the maximum curvature demand to the ultimate curvature capacity of beams and columns, known as

deformation damage index DDI.

Figure 6.16. IDA responses

Figure 6.16.a indicates that using GIB does not reduce the peak inter-storey drift ratio of SS variant before

intensity level 0.35g. This level is the onset of amplifying the lateral displacement at the first level SS variant

due to P-Delta effects. For intensity levels more than 0.35g, the peak drift ratio of SS variant increases rapidly,

while for the GIB-1 variants, this ratio increases gradually. This implies that GIBs could reduce P-Delta

effects at the first level of soft storey buildings efficiently, which results in the reduction of the likelihood of

collapse at this level. For the FI variant, the amplification of the peak drift ratio occurs at the intensity level

0.4. Even though adding infills at the first level of the soft storey buildings could delay in the likelihood of

collapse at this level, but it is not as effective as using GIB.

0.050.10.150.20.250.30.350.4 0.60

5

10

Pe

ak in

ters

tore

y d

rift (

%)

PGA(g)0.050.10.150.20.250.30.350.4 0.6

0

2

4

6

Re

sid

ua

l in

ters

tore

y d

rift (

%)

PGA(g)

0.050.10.150.20.250.30.350.4 0.60

0.5

1

1.5

Pe

ak flo

or

acce

lera

tion

(g

)

PGA(g)0.050.10.150.20.250.30.350.4 0.6

0

2

4

6

Pe

ak D

DI

PGA(g)

FI SS GIB-1

(a) (b)

(c) (d)


Figure 6.16.b. compares peak floor accelerations of all five variants. The advantage of GIB-1 variant over the

FI variant is obvious for a wide range of intensity levels, especially for higher values. At PGA 0.35g, the peak

floor acceleration of the FI variant is almost 30% more than that of GIB variants. However, the difference

increases as the intensity level increases, and is almost 50% at the intensity level 0.6g. This reduction could

reduce the total damage to the non-structural elements, and, consequently the whole building, significantly.

The capacity check of all variants over all intensity levels are compared using the deformation damage index

DDI, as shown in Figure 6.16.c. Over the whole range of intensity levels, DDI of the SS variant is more than

that of the FI variant, which indicates that the former is more vulnerable than the latter. However, the GIB-1

variant could be much reliable than these two variants. For intensity levels more than 0.2g, DDI of the GIB-1

variant is less than that of the FI variant. At the intensity level 0.3g, the curvature demand of columns at the

first level of SS variant reaches their ultimate curvature capacity. For the FI variant, this value occurs later at

intensity level 0.4. However, GIB could shift this ultimate state to much higher value, i.e. almost 0.55g.

The effect of GIB on the reduction of the residual deformation of SS variant is shown in Figure 6.16.d.

Although GIB does not reduce its residual displacement at low and moderate level of intensities, its effect is

significant at the high intensity level. At intensity levels below than 0.4g, adding infills could reduce the

residual displacement much more than using GIB. Using GIBs with smaller gap distances could reduce the

residual displacement at the first floor of the GIB-1 variant, as it is discussed in the next section.

6.8 EFFECT OF GAP DISTANCE

In order to explore the effect of gap distance on the residual deformation of soft storey building, the

numerical analyses of the variant GIB-1 were repeated using a range of gap distances:

• GIB-G-0.5, Similar to GIB I, gap distance is halved

• GIB-G-2, Similar to GIB I, gap distance is doubled

• GIB-G-0, Similar to GIB I, gap distance is zero

As shown in Figure 6.17, at all intensity levels, decreasing the gap distance reduces the maximum inter storey

drift ratio very slightly. However, this effect is significant on the residual displacement.

If zero gap distance is selected, the lateral residual displacement at the first level of the GIB-I variant is

significantly reduced from 1.3% to less than 0.2%. However, it has a negative effect; the floor accelerations

are increased. At the low intensity level, the floor acceleration at most of the floors of the GIB-G-0 variant is

even higher than that of the FI variant, which indicates that using zero gaps is not an appropriate solution if

the intensity of the earthquake is low. At the intensity 0.4g, the floor acceleration at GIB-G-0 variant is less

than that of FI variant, but is still higher than that of the GIB-I variant.


Figure 6.17. Effect of gap distance on the seismic response of the GIB-1 variant

If the gap distance is doubled, the residual drift ratio at the first floor is slightly increased from 1.4% to 1.5%.

However, the advantage is that the floor acceleration is reduced at all storeys above the ground floor. Another

advantage of increasing of the gap distance could be the constructability of the gap inside the GIB. On the

other hand, if the gap is halved, the floor acceleration could be increased, but the benefit is that the residual

drift ratio at the first floor is reduced from 1.4% to 1.0%. The peak lateral drift ratio is not changed

significantly.

As a result, increasing the gap distance could have both beneficial and detrimental effect on the seismic

response of the GIB variants. The decision could depend on the performance of the building. If residual

displacement is important, a GIB system without gap distance has the most appropriate effect, whereas, if the

floor acceleration is the key parameter, it is recommended that the gap distance is not reduced.

6.9 EFFECT OF GIB LOCATIONS: GIB-2 VARIANT AND GIB-3 VARIANT

In all GIB design procedure, which was presented in section 6.5, the effect of the lateral load on the axial

forces of the existing columns was neglected. This assumption is not accurate for exterior columns, especially

if the number of stories is high, because of the effect of the overturning moment on the column axial forces.

The previous results from the pushover analysis (Figure 6.8) indicated that the axial load in the exterior

columns fluctuate before the gap is closed. Thus, the GIBs at one side of the building should be designed for

0 0.5 1 1.50

2

4

6PGA=0.2g

Sto

rey

0 0.2 0.40

2

4

6

Sto

rey

0.2 0.4 0.60

2

4

6

Sto

rey

0 2 40

2

4

6PGA=0.40g


0 1 20

2

4

6


0.4 0.6 0.80

2

4

6


0 5 100

2

4

6PGA=0.60g

0 1 20

2

4

6

0.4 0.6 0.8 10

2

4

6

GIB-3 GIB-1-No Gap GIB-1-Half Gap GIB-1-Double Gap


greater forces, than the opposite. This is the second design scenario that is shown in Figure 6.18.b, i.e. GIB-2

variant The design parameters are shown in Table 6.3.b. For GIB-1L and GIB-4R, the design axial load are

increased 55%, while for GIB-1R and GIB-4L, the design axial load is decreased almost 60% and are very low

(almost zero). As a result, these GIBs could be eliminated to reduce the cost of the retrofit as their effects is

negligible. Similarly, the design axial load on GIB-2L and GIB-3R are increased 20%, and the design axial

load on GIB-2R and GIB-2L is decreased 20%.

Figure 6.18. Locations of GIBs

The third scenario (GIB-3) is that the GIB-2R and GIB-3L are eliminated, which is shown in Figure 6.18.c.

Due to the overturning moment only, the axial load on column II and III at the first floor (in one direction)

are decreased 20%. However, this reduction could not be adequate to increase the deformation capacity of

these columns. As a result, this option could not improve the seismic behaviour of soft storey buildings

significantly, but might be beneficial as it reduces the retrofit cost and increases the architectural functionality.

One solution could be to decrease the lateral displacement demand at the first floor (e.g. increasing GIB

angles). This strategy, however, could increase the seismic demand at the storeys upper the first floor.

C-I C-II C-III C-IV

GIB

-3L G

IB-3

R

GIB

-2L

GIB

-2R

GIB

-1L

GIB

-1R

GIB

-4L

GIB

-4R

GIB

-3L G

IB-3

R

GIB

-2L

GIB

-2R

GIB

-1L

GIB

-4R

C-I C-II C-III C-IV

GIB

-3R

GIB

-2L

GIB

-1L

GIB

-4R

C-I C-II C-III C-IV

Table 6.3. GIB configurations for different scenarios

(a-GIB-1)

Column Type

∆GIB ∆Gap Kb

mm mm kN/m

GIB-1L 269 3.65 43315

GIB-1R 269 3.65 43315

GIB-2L 266 3.33 78180

GIB-2R 266 3.33 78180

(b-GIB-2)

Column Type

∆GIB ∆Gap Kb

mm mm kN/m

GIB-1L 225 2.98 92675

GIB-1R - - -

GIB-2L 250 3.00 106170

GIB-2R 292 3.60 49696

(c-GIB-3)

Column Type

∆GIB ∆Gap Kb

mm mm kN/m

GIB-1L 225 2.98 92675

GIB-1R - - -

GIB-2L 250 3.00 106170

GIB-2R - - -


Alternatively, the deformation capacity of these columns could be improved using confinement. To achieve

this goal, a GIB- column connection detail is proposed in Chapter 8.

6.9.1 Seismic performance of GIB scenarios

Figure 6.19 shows two demand parameters obtained from incremental dynamic analyses. Overall, all the GIB

variants (dotted lines indicated by circle, square and star for GIB-1, GIB-2 and GIB-3, respectively) have

almost a similar effect on the lateral drift ratio of the soft storey building (Figure 6.19.b). Thus, eliminating four

GIBs from the first floor does not have a significant effect on the seismic demand parameters. However, as it

was mentioned before, one would expect that the drift capacity of GIB-3 variant is not improved

significantly, which is explained in the next paragraph.

Figure 6.19.a shows the ratio of the maximum curvature demand to the ultimate curvature capacity

(deformation damage index DDI) of all beams and columns in all GIB variants. Because all these variants

have soft storey configuration, the maximum DDIs occur at columns of the first floor. DDI of both GIB-I

and GIB-2 variants are very close to each other. Because their displacement demands are almost the same

over the whole range of the intensity level (Figure 6.19.b), the drift capacity of these two variants are also

close to each other. However, the DDI of GIB-2 variant is slightly less than that of GIB-1, which indicates a

potential advantage of the eliminating GIBs at the interior face of exterior columns.

Figure 6.19. Seismic parameters for different GIB scenarios a) DDI, b) Peak floor acceleration

On the other hand, the seismic behaviour of the GIB-3 variant is less improved; its DDI is more than the

other two variants over the whole intensity levels, and the difference increases as the intensity increases. At

the intensity level more than 0.4g, DDI of columns II and III exceeds unity, which indicates that these

columns reach their ultimate capacity. For GIB-1 and GIB-2 variants, this value occurs at the intensity level

almost 0.55g.

0.050.10.150.20.250.30.350.4 0.60

2

4

6

8

Pe

ak in

ters

tore

y d

rift (

%)

PGA(g)

0.050.10.150.20.250.30.350.4 0.60

0.5

1

1.5

2

Pe

ak D

DI

PGA(g)

GIB-1 GIB-2 GIB-3


6.10 COLLAPSE POTENTIAL OF CASE STUDY VARIANTS

In order to perform a meaningful assessment of the seismic performance of different scenarios, this section

explores the effect of retrofit scenarios on the reducing the potential of collapse of the soft storey variant. As

such, collapse fragility functions associated to each variant is determined and compared to each other.

To develop collapse fragility curves, the methodology described in ATC-58 [ATC 2007b] was used. As such,

results from the incremental dynamic analysis was used. The intensity at which 50% of the analyses predict

collapse is taken as the median collapse intensity. Using the median value and the dispersion due to record-to-

record variability, the collapse fragility functions are obtained following a lognormal distribution. In this

methodology, collapse is defined as either: sidesway failure, characterized by loss of lateral stiffness and

development of P-Delta instability, or Loss of vertical load carrying capacity of gravity framing members due

to earthquake-induced building drifts.

Figure 6.20 compares the collapse fragility curves for the four variants soft storey SS, full infill FI, GIB-2 and

GIB-3. For a wide range of intensity levels, the probability of collapse of the FI variant is less than the SS

variant. However, when the soft storey is retrofitted using GIB-2 configuration, this probability is reduced

significantly.

Figure 6.20. Collapse fragility curves for different variants

It should be noted that a large number of ground motions (order of 20 records) have been recommended to

obtain reliable estimates of the collapse fragility [ATC 2007b]. Since only 10 ground motions were used in

IDA analyses, these results could be arguable. However, for the purpose of comparison (not absolute

values), it is expected that these results could be acceptable.


The case study soft storey frame that were studied in Chapter 3 was retrofitted using the GIB system and

different scenarios of GIB location. It was found that the GIBs that are inside the face of the exterior

columns would not have significant effect on improving the response of the first floor of soft storey

0 0.2 0.4 0.6 0.8 10

0.5

1

Pro

ba

bili

ty o

f co

llap

se

PGA(g)

FI

SS

GIB-1

GIB-3


buildings. As a results, these GIBs could be eliminated, which in addition to improve the seismic response of

the soft storey buildings are beneficial due to the architectural and economical aspects.

The last scenario studied was to explore the response of the GIB building if the GIBs that are inside the face

of the interior columns are eliminated in addition to those of the exterior ones. The architectural and the

economic advantage of this solution could be more than the second scenario; however, this strategy could

reduce the displacement capacity of interior columns, and consequently, could increase the possibility of

collapse of the first floor. As such, the displacement capacity of these columns should be increased using

supplemental retrofitting measures including FRP wrapping or steel jacketing. The next chapter proposes a

connection detail between GIBs and existing columns that achieves this goal. In addition, uncertainties

regarding the performance of the GIB system will be discussed in the next chapter.

119

7.FUTURE STUDIES REGARDING THE UNCERTAINTIES OF THE

GIB SYSTEM

7.1 INTRODUCTION

The results of Chapter 5 and Chapter 6 indicated that the presence of the GIB system improves the response

of soft storey buildings significantly. Although, the static and the dynamic behaviour of the GIB system is

obtained based on the theoretical solutions and numerical analyses only, it is expected that its real response

could be similar to the predication. However, a number of questions could be still raised because the GIB

system (or systems with behaviour similar to this) has not been constructed in practice or tested in structural

laboratories. In this chapter, uncertainties regarding the performance of GIB system on the soft storey

response is studied, and future studies to further develop this concept is recommended.

7.2 CONSTRUCTABILITY

One of the major limitations is the constructability of the GIB due to the small distance between the column

and the GIB. For the case study example that was presented in Chapter 5, the offset distance was 50 mm

from the face of the column. Such small offsets could make the brace installation very difficult, or impossible.

Although one solution would be to select a larger distance between the column and the GIB, this would

result in an additional lateral resistance to the system. To deal with this issue, a nonlinear elastic behaviour

could be prescribed for the inclined brace itself. This could be achieved using post tensioning of the inclined

brace, SCED brace [Christopoulos et al. 2008] or using a nonlinear elastic material (such as rubber) in

combination with the inclined brace.

The detailed properties and the related design procedure of such GIB system are not explained here. The

axial-deformation relationship of the inclined brace was obtained from an iteration procedure, and the

relationship was introduced to the numerical modelling. It is, however, recommended that the design

procedure and governing equations of nonlinear GIB be obtained to further develop the proposed system.

The nonlinear elastic behaviour of the inclined brace was modelled using a Ramberg Osgood curve in

SeismoStruct. It was observed that if a nonlinear elastic behaviour is considered for the inclined brace, the

distance between the column and the GIB could be increased to 320 mm. The dotted line in Figure 7.1shows

the hysteretic response of the total system using nonlinear elastic inclined brace, which is close to what is

provided with the linear elastic brace.

Another scenario was studied in which the inclined brace is allowed to yield. This option can be implemented

by using elements such as buckling resistance braces [Sabellia et al. 2003]. The Ramberg Osgood curve with

inelastic behaviour is again defined based on an iteration procedure. In this case, a similar response is

achieved if GIB∆ is adopted as 270 mm, as shown in Figure 7.1 by a dashed line. Although the lateral resistance

FUTURE STUDIES REGARDING THE UNCERTAINTIES OF THE GIB SYSTEM 120

is close to the previous case, the residual displacement is greater, due to the plastic deformation of the

inclined brace.

Figure 7.1. Hysteretic response of the hybrid system using different behaviour of the inclined column

Alternatively, to deal with constructability issues, offsetting both the bottom and the top of the brace could

be a better solution, schematically shown in Figure 7.2. Such a connection may need to resist moments due to

the eccentricity, but is beneficial because it increases construction tolerance. This connection could require

local steel jacketing at the top of the column to connect steel GIBs to the concrete columns. As a result, even

if GIBs are not located at both sides of columns, the confinement of the concrete at the top of the RC

column could be increased. This solution could be beneficial if configuration GIB-3 (Figure 6.3) is used at the

first floor because GIBs are located only at one face of columns and thus activates in only one direction. The

proposed connection could increase the displacement capacity of columns in the opposite direction.

This proposal recognizes that in addition to the gap, the critical characteristic for the GIB is the brace angle,

rather than the offset distance itself. The proposed connection is only shown for one side of the column, but

would be applicable for the other side as well symmetrically. Care should be taken to prevent the beam shear

failure at the location where the beam and the GIB are connected. However, the detailed design of the

connections is not presented as it is not the focus of this thesis.

Considering the offset distance of 250 mm, and assuming that the confinement factor increases to 1.6, the

distance between the GIB and the face of the RC column increases to 200 mm ( 450GIB∆ = mm), which

provides enough space for the installation of the GIB. The gap distance could increases to 2.50gap

∆ = mm (the

previous one was 1.3mm). However, using a gap distance larger than 2.50 mm could also increase the ultimate

displacement capacity of the total system but would increase the residual displacement. The solid line in

Figure 7.1 indicates that, using the proposed connection, the deformation capacity of the system increases

compared to that of the aforementioned approaches, but does not increase the lateral resistance and the

-400

-300

-200

-100

0

100

200

300

400

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Bas

e S

hea

r (k

N)

Drift (%)

Linear elastic using offset

Nonlinear inelastic

Nonlinear elastic

∆GIB=450 mm

∆GIB=270 mm

∆GIB=320 mm


residual displacement. Moreover, this solution improves the post yield stiffness compared to the similar

option without offset (see Section 5.8).

Figure 7.2. A proposed connection for the GIB system using the offset

7.3 STRESS CONCENTRATION AT THE CONNECTION

As shown in Section 7.2, the connection of the GIB system to the existing structure seems to be simple

without requiring advanced technologies. However, care should be taken for some locations

where stress might be concentrated. These locations could be either at the connection between the GIB and

the existing column or at the connection between the GIB and its adjacent beam. In the following

subsections, three possible connections are proposed. For each proposal, a connection strategy is

recommended.

7.3.1 Connection of GIB to beam:

Since the angle GIBθ is not large and it is reduced as the force in the GIB increases (almost vertical), the sheer

force in the column could not be significant. However, as it is shown in Figure 7.3.a, the shear force that is

transferred to the beam could be critical, and is increased as the lateral displacement increases. The maximum

beam shear force beamV occurs at the ultimate state and is given by

cos beam b r bV P Pθ= � ( 7.1 )

The shear strength of the first floor beam should be larger than the shear beamV .

Existing RC column

∆ GIB

θGIB

Offset

Axial gap in sliding brace

Rigid connection to thecolumn and the beam

GIB


(a) (b)

Figure 7.3. a)Possibility of Shear failure at the beam and the GIB connection, b) possible retrofit strategy

For configuration GIB-1, the maximum shear force in beams at the first floor obtained from the time history

analysis at the intensity level 0.6g and 0.4g is shown in Table 7.1. The shear force in the exterior face of side

beams, (Corresponding to GIB-1R and GIB-4L) in less than the shear capacity at all intensity levels.

However, at their interior sides (corresponding to GIB-2L and GIB-3R), the shear force exceeds the shear

capacity of beams at both intensity levels. For the middle beam, the shear force exceeds only at the intensity

level 0.6g.

As such, the shear strength of the beam at the location shown in Figure 7.3.b should be increased using

retrofit approaches, such as jacketing, or increase the section area of the beam. However, strengthening of

existing RC beams could not be easy and could require significant effort, which might not be cost effective.

Table 7.1. Shear force in beams at the first floor of the GIB-1 building

Beam properties PGA=0.4g PGA=0.6g

Name type face Shear

Strength(kN)

Shear

Force (KN) Check

Shear

Force(kN) Check

B-S-L Side left 220 130 ok 210 ok

B-S-R Side right 220 290 Not ok 380 Not ok

B-M Middle both 220 210 Not ok 320 Not ok

7.3.2 Connection of GIB to column

Another solution could be that the GIB is connected to the column without any connection to the beam. In

this case, the gusset plate should be located with an offset to the face of the beam, as shown in Figure 7.4.a.

In such case, the axial force in the GIB should be transferred by the gusset plate and the bolts. Thus, these

two components should be designed for the required actions.

Pbsinθr

θr

Pbcosθr

P b

Vbeam =Pb cosθr

Beam Beam

Shear in beam

Vbeam

Vcolumn

Increase the shear

strength of the beam


Figure 7.4. Connection of the GIB system to the column only: a) connection detail, b) actions in the gusset plate, c)

actions in the bolts

The gusset plate should be designed for the bending moment at the connection between the GIB and the

column, as shown in Figure 7.4.b. The design moment of the gusset plate gussetM is:

cos gusset b r offset

M P θ= ∆ ( 7.2 )

The bolts should be designed for the normal stress that is caused by the gussetM . Figure 7.4.c shows the

compression and the tension force in the bolts assuming that two bolts in one row is used. The shear strength

of the connection bolts should be designed for the shear force as shown in Figure 7.4.c.

cos b r

bolt

PV

n

θ= ( 7.3 )

where n is the number of bolts used for the connection of the column and the GIB. It should be noted that

both the gusset plate and the bolts should be also checked for the bearing resistance. However, the

disadvantage of this connection proposal is that the axial load on the column section immediately above the

connection could not be reduced.

Pbsin θr

Beam

θr

Pbcosθr

Pb

No connection

to beam

Pbcosθr

n

Pbcosθr

Mgusset

M gusset

lbolt

lbolt

Section C-CPb

∆off

Mgusset =Pbcosθr ∆off

Pbcosθr

C C

Connection plate

(a)

(b) (c)


7.3.3 Improved Connection of GIB to column

To improve the disadvantage regarding the previous connection, one possibility could be to strengthen the

flexural capacity of the column at the connection by considering the plate and bolts in the beam like a gusset

flange at the end of the column, as shown in Figure 7.5. Using this connection, the column could be

retrofitted to form a plastic hinge immediately below the connection location, instead of just below the beam

face. The advantage of this proposal is that that the column axial load is reduced at the critical section.

However, the disadvantage is that the confinement of the critical column section would not be increased.

Another alternative might be to transfer the axial forces to the base of column at second floor by cutting

through floor and connecting to the corners. However, this solution could not be cost effective depending on

flooring system.

As a summary, with some additional reflection to the all connection proposed in this section, one might be

able to identify a practical connection detail. An efficient and cost-effective connection strategy is

recommended to be explored as a part of the future development to the GIB system.

Figure 7.5. Alternative connection proposal of GIB to column using gusset plate

7.4 EFFECT OF SUPPLEMENTAL DAMPING ON RESPONSE OF GIB-3 VARIANT

A parametric study was carried out to explore the effect of added dampers on the response of the GIB-3

variant system that were studied in Chapter 6. Since the purpose of this section is to see the effect of the

adding damping on the seismic response of soft storey buildings, the added damper was modelled using a

B B

HSS

ABeam

Gusset

plate

Connection

plateRC

Column

D

D

Section D-D

HSS

Slotted end connection to HSS


simple horizontal configuration as shown in Figure 7.6. However, other configurations can also be studied in

future. Figure 7.7 presents the peak responses, where viscous dampers using damping coefficients of C= 25,

50, 150 and 250 kN.Sec/m are added at the first level, and are referred as DGIB-3-25, DGIB-3-50, DGIB-3-

150, DGIB-3-250, respectively.

The results of Figure 7.7 indicate that viscous dampers could reduce both the peak and the residual

displacements, depending on the damping characteristics, and the intensity levels, but the effect on the

acceleration could be negative.

At the lowest intensity level, corresponding to a PGA of 0.20g, adding damping directly reduces the peak and

the residual drifts as well as the peak floor accelerations . The peak and residual drift ratio at the first level of

the GIB-3 variant is 1.25% and 0.17%, respectively, shown by the dotted line. Adding dampers using C=25,

50, 150 and 250 kN. Sec/m decreases the peak drift ratio to 1.21%, 1.15%, 0.9%, and 0.82%, and residual

drift ratio to 0.12%, 0.09%, 0.06% and 0.02%, respectively. The peak floor acceleration in the middle height

of the building (storey between 2 and 4) is decreased from 0.42g to almost 0.37g.

GIB

-3R

GIB

-2L

GIB

-1L

C-I C-II C-III C-IV

GIB

-3R

ViscoseDamper

Figure 7.6. Adding viscose dampers to the GIB-3 variant in the numerical modelling (DGIB-3 variant)

Using supplemental dampers at the intensity level 0.40g has almost the same effect on the peak and the

residual drifts, while it has a negative effect on the floor accelerations. Using dampers C=250 kN.Sec/m

reduces the peak drift ratio and the residual drift ratio at the first level of the GIB-3 variant from 3.6% to

2.0%, and 1.35% to 0.55%, respectively. However, the peak acceleration at the middle height of the building

(storey No. 4) increases from 0.65g to 0.75g. This is probably because the dampers increase the resistance of

the first storey, which results in higher forces at this level, and consequently higher accelerations to the upper

storeys.

At the high intensity level corresponding to a PGA of 0.60g, the dampers have a similar effect as they did for

the 0.40g intensity level, except for the damper using C=250 kN.Sec/mm. Using a damper with C=250 has

almost similar effect to the full infill variant. The peak drift ratio at the second floor significantly increases to


40%. Because it increases the resistance of the first floor, which increases the demand parameters at the

second floor.

The peak drift ratio at the first level of the building is reduced from 5.5% to 3.2%, but the drift ratio at the

second level amplifies to almost 15%, which infers a likely collapse of the building. At this level, the response

is to somehow similar to that of the full infill case shown in Figure 6.15. Because the first floor resistance

increases significantly, which increases the forces that are transferred to the storey immediately above it.

Thus, care should be taken to carefully assess the implications of using supplemental dampers at the first level

of the soft storey buildings. The value of the damping coefficient must be limited to control the additional

resistance at this level. However, using nonlinear viscous dampers could also be beneficial, as it would limit

the forces that are transferred to the existing structure. The potential advantage of such systems is

recommended to be investigated as a part of future research.

Figure 7.7. Effect of adding dampers on the response of the GIB-3 variant


Uncertainties regarding the response of the GIB system were discussed, and some possibilities for future

research were identified.

The effect of using brace properties was explored on the cyclic behaviour of a SDOF system. It was found

that if the inclined brace has a nonlinear elastic behaviour, the initial angle of the GIB can be increased which

0 0.5 1 1.50

2

4

6PGA=0.2g

Sto

rey

0 0.1 0.20

2

4

6

Sto

rey

0.2 0.3 0.4 0.50

2

4

6

Sto

rey

0 2 40

2

4

6PGA=0.40g


0 0.5 1 1.50

2

4

6


0 0.5 10

2

4

6


0 5 10 150

2

4

6PGA=0.60g

0 2 4 60

2

4

6

0.4 0.6 0.8 10

2

4

6

GIB-3 DGIB-25 DGIB-50 DGIB-150 DGIB-250


could improve the construction of the GIB. The increase in angle, however, did not affect the total response.

Alternatively, it was suggested that both the bottom and the top of the brace are offset. This solution can

increases the construction tolerance of the connection in addition to increase the column confinement.

Some possible types of connections of the GIB system to exiting columns were proposed and illustrated. In

the first proposal, the GIB system is connected to both the beam and the column. The connection requires

that the beam is checked for shear and possible strengthening. The second proposal was that the GIB system

is connected to the column only. In this case, the gusset plate and the connectors should be strong enough to

ensure that the vertical forces are transferred to the GIB system.

The effect of supplemental viscous damping on the seismic response of the soft storey building was

investigated through a parametric study. It was found that adding damping could reduce both the ultimate

and the residual deformations. However, at high intensity levels, dampers could have negative effects on the

response; using viscous damping with high damping coefficient could increase the lateral resistance of the

first floor.

128

8.CONCLUSIONS

Although each chapter outlined related results and conclusions separately, the main conclusion of this work is

to, however, raise the question that has not been asked for a few decades: Can buildings with soft storey

configurations perform well in earthquakes? The real behaviour of such buildings in the past earthquakes

might give a negative answer to this question. However, the results of this thesis provided an insight that

intelligent and efficient soft storey structures could have an acceptable seismic performance. The gapped

inclined brace GIB system was one solution that this work proposed to retrofit soft storey buildings. This

strategy in addition to take their architectural and structural advantages, it mitigated the collapse possibility in

strong ground motions.

The following sections of this chapter provide an overview of the previous chapters and integrate their results

to show how this work has responded to the objectives that were outlined in Chapter 1.

8.1 CHAPTER 1 AND 2

This work began with a brief literature review on the performance of buildings with soft storey

configurations. Their potential advantages of such buildings in the architectural and the structural point of

view were discussed. Various types of buildings with such configurations were categorised in Chapter 2.

Typical problems associated with such buildings and their failure mechanisms in the past earthquakes were

summarised.

Chapter 1 and 2 showed that among the available buildings with soft storey configuration, buildings that

masonry infills are disconnected in the first floor are the most common type. In addition, earthquake surveys

have shown that discontinuous infills in the first floors are very likely to cause a soft-storey mechanism at the

ground level.

8.2 CHAPTER 3

Thus, Chapter 3 started the numerical case study assessment on a six-storey reinforced concrete frame

building for two scenarios of full masonry infill and partial and with soft-storey response developing at the

ground storey for the partial infill case. Incremental nonlinear time history analyses were used to compare the

seismic response of the two scenarios. Potential advantages of each scenario in different hazard level were

discussed.

The incremental non-linear time history analysis results in Chapter 3 illustrated that peak floor accelerations

in partial infill case are less than the full infill case, which can reduce damage to non-structural elements. In

addition, the peak and residual inter storey drift at storeys above the open ground floor was highly reduced.

CONCLUSIONS 129

However, the potential of collapse of the partial infill case was increased as the intensity level is increased,

reflecting the observations made in past earthquakes.

8.3 CHAPTER 4

The effect of some key characteristics including P-Delta effects and post yield stiffness on the behaviour of

soft first storey buildings was explored in Chapter 4. The results of static cyclic analyses of RC columns with

different geometrical and mechanical properties were used to highlight the influence of some characteristics

such as bar ratio, section dimensions, axial load ratio and confinement factor on the lateral resistance and drift

capacity of RC columns. The implications of the analysis findings were discussed in relation to potential

retrofit schemes.

The analysis results on Chapter 4 indicated that if the gravity load system could be de-coupled from the lateral

load resisting system, this could help reduce the likely deformation demands, which tend to be amplified by

P-delta effects. In addition, it was demonstrated that if the axial load on column sections could be reduced,

their deformation capacities could be significantly increased. Thus, a potentially effective and innovative

means of retrofitting a structure with an open-ground storey were proposed by introducing a series of gravity

columns at the ground level that slide with the first storey. By doing this, P-delta effects were minimised, and

the deformation capacity of the first storey columns were increased, without significantly affecting their lateral

strength and potential for energy dissipation.

8.4 CHAPTER 5

The limitation of this proposed retrofitting strategy were discussed in the beginning of Chapter 5, and then

gapped inclined brace GIB system were alternatively proposed that could reduce the drawbacks of the sliding

gravity columns proposal, while takes the positive aspects. The mechanics of the proposed system was

illustrated, and a brace sizing procedure was proposed.

The results from pushover analyses of RC columns with different configurations verified various

mathematical relations developed for the purpose of sizing the braces. It was concluded that increasing

confinement in addition to the proposed approach could also improve the deformation capacity of RC

columns. Nonlinear quasi-static cyclic analysis of a single span RC frame indicated that the proposed strategy

could significantly improve the hysteretic response of a soft storey frame in terms of energy dissipation

capacity and residual deformation.

8.5 CHAPTER 6

The dynamic characteristics of MDOF buildings that were retrofitted using the GIB system at the ground

floor were investigated in Chapter 6. Design considerations based incorporating the soft storey mechanisms

CONCLUSIONS 130

were briefly presented in this chapter. Subsequently, the buildings that were studied in chapter 3 retrofitted

using the GIB system, and the numerical results were compared using different scenarios of GIB locations.

The numerical analysis of the retrofitted soft storey building indicated that the GIBs that are inside the

exterior columns don't have significant effect of the improving the response. As results, these GIBs could be

eliminated at the ground floor of soft storey buildings, which are beneficial due to the architectural and

economical aspects.

8.6 CHAPTER 7

Chapter 7 discussed uncertainties regarding the response of the GIB system and described recommend issues

to be investigated in future research. Some aspects including construction issues and connection

considerations were briefly discussed. The effect of supplemental vicious damping in addition to the GIB

system was initially investigated to further develop the concept as a part of future studies.

This chapter concluded that if the inclined brace has a nonlinear elastic behaviour, the initial angle of the GIB

can be increased which could improve the construction of the GIB. Alternatively, it was suggested that both

the bottom and the top of the brace are offset to increase the construction tolerance in addition to increase

the column confinement.

It was also found that adding damping could reduce both the ultimate and the residual deformations.

However, at high intensity levels, dampers could have negative effects on the response, because their effect of

the lateral resistance is higher than reducing accelerations.

It is, however, recommended that dynamic analyses of more case studies be carried out along with

experimental validations to further develop the proposed system and demonstrate its applicability for the

seismic upgrade of soft storey structures.

131

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