a study of pounding between adjacent...

A STUDY OF POUNDING BETWEEN

ADJACENT STRUCTURES

MS by Research Thesis

submitted by

Chenna Rajaram

(200814001)

in partial fulfillment of the requirements for the degree

of

MASTER OF SCIENCE (BY RESEARCH)

in

Computer Aided Structural Engineering

under the guidance of

Dr. Ramancharla Pradeep Kumar

Earthquake Engineering Research Centre,

International Institute of Information Technology, Hyderabad-500 032

April 2011

CERTIFICATE

It is certified that the work contained in this thesis, titled ”A study of Pounding be-

tween Adjacent Structures” by Mr. Chenna Rajaram, has been carried out under my

supervision and is not submitted elsewhere for a degree.

Advisor: Dr.Ramancharla Pradeep Kumar

Associate Professor

Earthquake Engineering Research Centre

International Institute of Information Technology

Hyderabad-500 032

INDIA

Dedicated to my mother Bharathi and father Rajagopal who have worked hard throughout

my education and gave me the opportunity to do research.

Acknowledgements

I would like to express my sincere gratitude to my thesis supervisor Associate Prof. Dr.

Pradeep Kumar Ramancharla, for the continuous support of my research, for his patience,

motivation, enthusiasm, and immense knowledge. His guidance helped me alot in all the time of

research and writing of this thesis. I would like to thank to him for teaching me various courses

and Jeevan Vidya, which will be very useful for everyone.

I would also like to thanks Prof. M. Venkateswarlu for teaching me Mathematical Foun-

dations of Solid Mechanics and Theory of Elasticity and Assistant Prof. Dr. Neelima

Satyam for her support. My sincere thanks goes to Prof. B.Venkat Reddy for his encour-

agement to do research.

I would like to express sincere thanks to all my colleagues (CASE), EERC members (Admin

Staff, Project Staff, Research Staff and office boy) and M.Tech Students which contributes di-

rectly and indirectly in various ways for my research.

I would like to express sincere thanks to Prof. Wijeyewikrema (Tokyo Institute of

Technology, JAPAN), Prof. Maekawa (Univ. of Tokyo, JAPAN), Prof. Jankowski

(Gdansk Univ. of Technology, POLAND), Prof. Anagnostopoulos (Univ. of Patras,

GREECE) and Prof. Kun Ye (Huazhong Univ. of science and Technology, CHINA)

for sending their journal papers which are very useful for my literature review. Special thanks

to NICEE (National Information Centre of Earthquake Engineering)for sending the

codes which are very useful for my study.

Finally, I would like to dedicate this work to my mother Chenna Bharathi and father

Chenna Rajagopal, whose continuous love and support guided me. Without their encourage-

ment and understanding it would have been impossible for me to finish this work. My special

thanks goes to my brother Chenna Sai Krishna for their loving support.

Chenna Rajaram

Earthquake Engineering Research Centre

IIIT-H, Hyderabad

INDIA

Abstract

Pounding between adjacent structures is commonly observed phenomenon during major

earthquakes which may cause both architectural and structural damages. To satisfy the func-

tional requirements, the adjacent buildings are constructed with equal and unequal heights,

which may cause great damage to structures during earthquakes. To mitigate the amount of

damage from pounding, the most simplest and effective way is to provide minimum separation

distance. Generally most of the existing buildings in seismically moderate regions are built

without codal provisions. Past earthquakes have shown an evidence that the buildings are more

vulnerable to pounding. Building codes provide a set of guidelines for the practice of structural

engineering and play an important role of transferring technology from research to practice.

In numerical modeling, different combination of structures are considered for doing the anal-

ysis using Applied Element Method (AEM). The separation distance between the structures is

provided according to various codes from different countries and are subjected to ten different

ground motions. Some codal provisions failed to satisfy the requirements. The shortcomings in

codal provisions are identified and provided with proper suggestions to them.

To study the behavior of structures due to structural pounding, linear and nonlinear analysis

are done for different structures subjected to ground motion. The analysis considers equal and

unequal height of structures. The behavior of adjacent structures is similar as linear till failure

of first spring or first collision. The displacement responses for flexible structures are less com-

pared to stiff structures when structures vibrate at dominant period and also the responses for

flexible structures are more when structures vibrate at non-dominant period. Also we estimate

the amount of damage for structures in terms of stiffness degradation. For unequal height of

structures, the interaction is between slab and column. During this interaction, shear causes

more damage to the column which leads to collapse of structure.

To study the torsional effects due to pounding, buildings with different setbacks and unequal

storey levels are analyzed using SAP 2000. The effect of collision is more when structures are

kept at extreme levels of setback. When the structures are kept at different elevation levels

(setback=0), the pounding response changes significantly as the height of structure decreases.

At mid height of structure, the collision force is more compared to other height levels because

of shear amplification.

List of Publications

1. Chenna Rajaram and Ramancharla Pradeep Kumar: ”Three Dimensional Pounding

Analysis between Two Structures”, Journal of Structural Engineering SERC-Chennai,

Vol.**, No.** (Under Review).

2. Chenna Rajaram and Ramancharla Pradeep Kumar: ”Pounding Analysis of Adjacent

Structures with Equal and Unequal Heights”, Earthquake Spectra, Vol.**, No.** (Under

Review).

3. Chenna Rajaram and Ramancharla Pradeep Kumar., ”Linear and Nonlinear Numerical

Analysis of Pounding Between Adjacent Buildings”, 8th International conference on Earth-

quake Resistant Engineering Structures, Chianciano Terme, Italy (Abstract accepted).

4. Chenna Rajaram and Ramancharla Pradeep Kumar., ”Numerical Modeling of Pound-

ing Between Adjacent Buildings: Some Corrections to Codal Provisions”, Earthquake

Engineering and Engineering Vibrations, Vol.**, No.** (submitted).

5. Chenna Rajaram and Ramancharla Pradeep Kumar., ”Comparison of codal provisions

on pounding between adjacent buildings”, International Journal of Earth science and

Engineering (IJEE), Vol**, No**, (Under Review).

6. Chenna Rajaram, Bodige Narender, Neelima Satyam and Ramancharla Pradeep Ku-

mar., ”Preliminary Seismic Hazard Map of Peninsular India”, Proc. 14th Symposium on

Earthquake Engineering, IIT Roorkee 2010, pp 497-491.

7. Chenna Rajaram and Ramancharla Pradeep Kumar., ”Comparison of codal provisions

on pounding between adjacent buildings: Some Corrections to Codal Provisions”, Indian

Concrete Journal (ICJ), Vol**, No**, (Under Review).

iii

Contents

List of Publications iii

1 Introduction and Literature Review 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Causes of pounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Worldwide observations . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.2 Indian observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 Analytical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.2 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.3 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Summary of contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.1 Mitigation measures . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.2 Impact models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.3 Codal provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.6 Objective of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.7 Organization of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Numerical Modeling of Pounding 22

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Selection of buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Building geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Selection of ground motions . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.1 Characteristics of ground motions . . . . . . . . . . . . . . . . . . . 24

2.4 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.2 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.3 Element size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4.4 Material model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4.5 Collision model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.4.6 Failure criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

iv

CONTENTS

2.4.7 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.5 Linear pounding analysis of structures . . . . . . . . . . . . . . . . . . . . 38

2.5.1 Structures with equal heights . . . . . . . . . . . . . . . . . . . . . 38

2.5.2 Structures with unequal heights . . . . . . . . . . . . . . . . . . . . 45

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3 Pounding Analysis With Equal Heights 56

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.2 Non-linear analysis of pounding . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 Damage analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3.1 Damage model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3.2 Damage calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3.3 Proposed damage scale . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4 Pounding Analysis With Un-equal Heights 69

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2 Pounding analysis for structures with un-equal heights . . . . . . . . . . . 69

4.2.1 Single-single storey structural pounding . . . . . . . . . . . . . . . . 69

4.2.2 Single-two storey structural pounding . . . . . . . . . . . . . . . . . 74

4.2.3 Two-two storey structural pounding . . . . . . . . . . . . . . . . . . 77

4.2.4 Two-three storey structural pounding . . . . . . . . . . . . . . . . . 82

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5 3D Analysis of Pounding 88

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.2 Modeling of structures in 3D . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.2.1 Geometry and material details . . . . . . . . . . . . . . . . . . . . . 88

5.2.2 Gap element model . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.3 Non-linear analysis of pounding . . . . . . . . . . . . . . . . . . . . 91

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 Conclusions 104

6.1 General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A Comparision of codal provisions on pounding 106

A.1 Review on codal provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

A.2 Minimum separation between buildings . . . . . . . . . . . . . . . . . . . . 107

A.3 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

B Calculation of separation distance from codes 115

B.1 Calculation of separation distance from codes . . . . . . . . . . . . . . . . 115

v

CONTENTS

Bibliography 122

vi

List of Figures

1.1 Representation of different places where pounding occurs . . . . . . . . . . 2

1.2 Pounding damage of Olive View hospital. (a) View of Olive View hospital

(b)Permanent tilting of a stairway tower during San Fernando earthquake,

1971 (Courtesy: EERC, University of California, Berkeley). . . . . . . . . . 3

1.3 Pounding damage due to insufficient separation distance during 1999 Chi-

Chi earthquake, Taiwan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Pounding damage due to unequal slab levels during 2007 Niigata Chuetsu-

Oki Japan earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Significant pounding was observed Santa Clara River Bridge during Northridge

earthquake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Pounding damage at the intersection of approach to main jetty at Diglipur

harbor during Diglipur Earthquake . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Linear Spring Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.8 Kelvin Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1 Geometry of single storey structure . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Geometry of two storey structure . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Geometry of three storey structure . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Geometry of five storey structure . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Reinforcement details of single and two storey structures . . . . . . . . . . 26

2.6 Reinforcement details of three and five storey structures . . . . . . . . . . 26

2.7 Athens ground motion record and its fourier spectrum amplitude (a) Ground

motion record (b) Fourier amplitude spectrum . . . . . . . . . . . . . . . 27

2.8 Athens(tran) ground motion record and its fourier spectrum amplitude (a)

Ground motion record (b) Fourier amplitude spectrum . . . . . . . . . . . 27

2.9 Ionian ground motion record and its fourier spectrum amplitude (a) Ground


2.10 Kalamata ground motion record and its fourier spectrum amplitude (a)


2.11 Umbro ground motion record and its fourier spectrum amplitude (a) Ground


2.12 Elcentro ground motion record and its fourier spectrum amplitude (a)


vii

LIST OF FIGURES

2.13 Olympia ground motion record and its fourier spectrum amplitude(a) Ground


2.14 Parkfield ground motion record and its fourier spectrum amplitude(a) Ground


2.15 Northridge ground motion record and its fourier spectrum amplitude(a)


2.16 Lomaprieta ground motion record and its fourier spectrum amplitude(a)


2.17 Element components for formulating stiffness matrix (SOURCE: Kimuro

Meguro and Hatem, 2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.18 Quarter portion of stiffness matrix . . . . . . . . . . . . . . . . . . . . . . 32

2.19 Uttarkasi ground motion record and its fourier spectrum amplitude(a)


2.20 Material models for concrete and steel (a) Tension and compression con-

crete Maekawa model (b) Bi-linear stress strain relation model for steel

reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.21 Arrangement of collision springs . . . . . . . . . . . . . . . . . . . . . . . . 35

2.22 (a) Principal Stress determination and (b) Redistribution of spring forces

at element edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.23 Linear pounding response of two single storey structures separated by 2

mm subjected to Northridge ground motion (@ slab level 3.0 m) . . . . . . 40

2.24 Pounding force between two single storey structures separated by 2 mm

subjected to Northridge ground motion (@ slab level 3.0 m) . . . . . . . . 40

2.25 Linear pounding response of single-two storey structures separated by 2


2.26 Pounding force between single-two storey structures separated by 2 mm


2.27 Linear pounding response of two-two storey structures separated by 2 mm


2.28 Pounding force between two-two storey structures separated by 2 mm sub-

jected to Northridge ground motion (@ slab level 3.0 m) . . . . . . . . . . 43

2.29 Linear pounding response of two-three storey structures separated by 2 mm


2.30 Pounding force between two-three storey structures separated by 2 mm


2.31 Geometry details of structure-B @2.75 m slab levels in the single storey

structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46


structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46


structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

viii

LIST OF FIGURES

2.34 Geometry details of structure-B @2.75 m slab levels in the two storey struc-

ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.35 Geometry details of structure-B @3.25 m slab levels in the two storey struc-

ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.36 Geometry details of structure-B @3.5 m slab levels in the two storey structure 48

2.37 Geometry details of structure-B @2.75 m slab levels in the three storey

structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51


mm subjected to Northridge ground motion (@ slab level 2.75 m) . . . . . 52











3.1 Pounding nonlinear response of two single storey structures separated by

2 mm subjected to Northridge ground motion (@ slab level 3.0 m) . . . . . 57



3.3 Pounding nonlinear response of single-two storey structures separated by




3.5 Pounding nonlinear response of two-two storey structures separated by 2




3.7 Pounding nonlinear response of two-three storey structures separated by 2




3.9 Load vs displacement curve for structure having a period of 0.127 sec . . . 66


ix

LIST OF FIGURES





2 mm subjected to Northridge ground motion (@ slab level 2.75 m) . . . . 70





































x

LIST OF FIGURES











5.1 Geometry details of structures . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2 Gap-joint element from SAP 2000 . . . . . . . . . . . . . . . . . . . . . . . 90

5.3 Link element internal forces and moments at the joints . . . . . . . . . . . 90

5.4 Response of structures in x-direction at location Ct with setback of 1.5 m . 92

5.5 Pounding force between structures with setback of 1.5 m . . . . . . . . . . 92

5.6 Response of structures in y-direction at location Ct with setback of 1.5 m . 93

5.7 Response of structures in x-direction at location Cb with setback of 1.5 m . 93

5.8 Response of structures in y-direction at location Cb with setback of 1.5 m . 94




5.12 Response of structures in x-direction at location Cb with setback of 3.0 m . 96




5.16 Response of structures in x-direction at location Ct with height of 2.25 m . 99

5.17 Pounding force between structures with height of 2.25 m . . . . . . . . . . 99

5.18 Response of structures in x-direction at location Cb with height of 2.25 m . 100

5.19 Pounding force between structures with height of 2.25 m . . . . . . . . . . 100

5.20 Response of structures in x-direction at location Ct with height of 1.5 m . . 101

5.21 Pounding force between structures with height of 1.5 m . . . . . . . . . . . 102

5.22 Response of structures in x-direction at location Cb with height of 1.5 m . 102

5.23 Pounding force between structures with height of 1.5 m . . . . . . . . . . . 103

A.1 Idealized model of SDOF system . . . . . . . . . . . . . . . . . . . . . . . 107

A.2 Minimum space provided between two structures having different dynamic

properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

xi

List of Tables

1.1 List of codal provisions on pounding . . . . . . . . . . . . . . . . . . . . . 20

2.1 Details of ground motions . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2 Fundamental period of the structures . . . . . . . . . . . . . . . . . . . . . 39

2.3 Maximum displacement response of structures, pounding forces and num-

ber of collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.4 Fundamental period of the structures at different slab levels . . . . . . . . 49

2.5 Maximum displacement response of structures, pounding forces and num-

ber of collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Maximum nonlinear displacement response of structures, pounding forces

and number of collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Stiffness degradation for different structures during pounding . . . . . . . . 65

4.1 Maximum nonlinear displacement response of structures, pounding forces

and number of collisions for structures with unequal heights . . . . . . . . 87

A.1 Details of codal provisions on pounding . . . . . . . . . . . . . . . . . . . . 107

A.2 Details about mass, stiffness and spacing provided between two structures . 108

A.3 Lomaprieta ground motion record having amplitude of 0.22 g, duration

9.58 sec and predominant time period 0.41-1.61 sec . . . . . . . . . . . . . 110

A.4 Elcentro ground motion (S00E) record having amplitude of 0.348 g, dura-

tion 24.44 sec and predominant time period ranges from 0.45-0.87 sec . . . 111

A.5 Parkfield ground motion record having amplitude of 0.430 g, duration 6.76

sec and predominant time period 0.3-1.20 sec . . . . . . . . . . . . . . . . . 112

A.6 Petrolia ground motion record having amplitude of 0.662 g, duration 48.74

sec and predominant time period 0.50-0.83 sec . . . . . . . . . . . . . . . . 112

A.7 Northridge ground motion record having amplitude of 0.883 g, duration

8.94 sec and predominant time period ranges from 0.2-2.2 sec . . . . . . . . 113

B.1 Separation distances from codes . . . . . . . . . . . . . . . . . . . . . . . . 118

B.2 Status on separation distance from codes for single-single storey structures

in group-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

B.3 Status on separation distance from codes for single-two storey structures

in group-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

xii

LIST OF TABLES

B.4 Status on separation distance from codes for two-two storey structures in

group-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

B.5 Status on separation distance from codes for three-three storey structures

in group-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

xiii

Chapter 1

Introduction and Literature Review

1.1 Introduction

Structures are built very close to each other in metropolitan areas where the cost of land

is very high. Due to closeness of the structures, they collide with each other when sub-

jected to earthquake or any vibration. This collision of buildings or different parts of the

building during any vibration is called pounding which may cause either architectural and

structural damage or collapse of the whole structure. This may happen not only in build-

ings but also in bridges and towers which are constructed close to each other. Although

some modern codes have included seismic separation requirement for adjacent structures,

large areas of cities in seismically active regions were built before such requirements were

introduced. Many investigations have been carried out on pounding damage caused by

previous earthquakes.

1.2 Causes of pounding

Structural pounding damage in structures can arise from the following: (1) Adjacent

buildings with the same heights and the same floor levels (fig 1.1a). (2) Adjacent build-

ings with the same floor levels but with different heights (fig 1.1b). (3) Adjacent structures

with different total height and with different floor levels (fig 1.1c). (4) Structures are situ-

ated in a row (fig 1.1d). (5) Adjacent units of the same buildings which are connected by

one or more bridges or through expansion joints. (6) Structures having different dynamic

characteristics, which are separated by a distance small enough so that pounding can

occur. (7) Pounding occurred at the unsupported part (e.g., mid-height) of column or

wall resulting in severe pounding damage. (8) The majority of buildings were constructed

according to the earlier code that was vague on separation distance. (9) Possible settle-

ment and rocking of the structures located on soft soils lead to large lateral deflections

which results in pounding. (10) Buildings having irregular lateral load resisting systems

in plan rotate during an earthquake, and due to the torsional rotations, pounding occurs

near the building periphery against the adjacent buildings (fig 1.1e).

1

CHAPTER 1. INTRODUCTION AND LITERATURE REVIEW

Figure 1.1: Representation of different places where pounding occurs

1.3 Case studies

During past earthquakes, structural pounding was noticed in buildings and bridges. Some

of the cases observed on pounding are listed below:

1.3.1 Worldwide observations

In the Alaska earthquake of 1964, the tower of Anchorage westward hotel was damaged

by pounding with an adjoining three storey ballroom portion of the hotel (Pantelides

et al., 1998). In Sanfernando earthquake (Jankowski et al., 2009) of 1971, the second

storey of the Olive View hospital struck the outside stairway; in addition, the first floor

of the hospital was hit against a neighboring warehouse. The pounding of the main

building against the stair way tower during the earthquake evoked considerable damage

at the contact points and caused permanent tilting of the tower (fig 1.2). During Mexico

City earthquake (Aguilar et al., 1989) on 19th September 1985, more than 20% of the 114

affected structures were damaged because of pounding. Among them more than 10% were

due to failure of concrete frames and 3% were due to failure of concrete walls and frames.

During Loma Prieta earthquake (Kasai et al., 1997) in 1989, significant pounding was

observed at sites over 90 km from the epicenter. Many old buildings constructed prior to

1930 suffered. The typical floor mass of the five-storey building is about eight times that

of the ten-storey building. Pounding was located at the 6th level in the ten-storey building

and at the roof level in the five-storey building because of less separation distance of 1.0

to 1.5 inches was present. The ten storey building suffered structural pounding damage

result large diagonal shear cracks in the masonry piers. In 1999, the chi-chi earthquake

(Lin et al., 2002) in central Taiwan, structural pounding were also observed during the

2


earthquake. Having constructed at different times, the old and the new classrooms could

be different in height, weight or stiffness. Thus, the two structures may possess different

fundamental vibration periods. In Taiwan, a large number of old school buildings had

been constructed and later expanded. The old and new classrooms may not have vibrate

in-phase during the Taiwan earthquake (Chung et al., 2007). The class rooms may have

pounded with each other because of lack of sufficient space between them (fig 1.3). During

2007 Niigata Chuetsu-Oki Japan Earthquake (Global risk Miyamoto, 2007) one type of

observed damage in school buildings was the pounding of buildings against adjacent units.

This type of damage occurred when adjacent structures had floor slabs located at different

elevations and insufficient separation distance between them (fig 1.4). Pounding damages

were also observed in recent massive Wenchuan earthquake on May 12, 2008.

(a) (b)

Figure 1.2: Pounding damage of Olive View hospital. (a) View of Olive View hospital(b)Permanent tilting of a stairway tower during San Fernando earthquake, 1971 (Courtesy:EERC, University of California, Berkeley).

The 4-in wide seismic joint used to separate both structures was not sufficient to

accommodate the actual relative displacements that were developed during the ground

motion. In 1994 Northridge earthquake (Pantelides et al., 1998) at the interstate 5 and

state road 14 interchange, which was located approximately 12 km from the epicenter,

significant pounding damage was observed at expansion hinges of the Santa Clara River

Bridge (fig 1.5). Poundings between adjacent decks or between a deck and an abutment

occurred in 1995 Hyogo-ken Nanbu earthquake (Kawashima et al., 2000). Pounding bring

damage at not only expansion joints and contact faces of decks but also other elastomeric

bearings and column.

1.3.2 Indian observations

The observations on pounding from the Indian earthquakes are as follows:

The powerful 2001 Bhuj earthquake (Jain et al., 2001) has been the most damaging

earthquake in the last five decades in India. Reinforced concrete buildings suffered the

3


Figure 1.3: Pounding damage due to insufficient separation distance during 1999 Chi-Chiearthquake, Taiwan

Figure 1.4: Pounding damage due to unequal slab levels during 2007 Niigata Chuetsu-OkiJapan earthquake

heaviest damage during the earthquake because of poor design and construction practices.

Pounding of adjacent structures was evident at Ayodhya apartments in Ahmedabad with

significant damages. The Sikkim earthquake (Kaushik et al., 2006) on 14th February 2006

of 5.3 magnitude caused damage to a nine storey masonry infill RC frame hostel building

at Sikkim Manipal Institute of Medical Sciences (SMIMS) Tadong, Gangtok which caused

severe damages in walls and columns. Pounding damages were observed between two long

wings in the building and corridors connecting the wings.

4


(a) (b)

Figure 1.5: Significant pounding was observed Santa Clara River Bridge during Northridgeearthquake.

The only road link between Kutch and Saurashtra areas is the road bridge at Sura-

jbadi, which was damaged. Pre-stressed concrete girder bridge spans sustained substantial

damage like pounding of the deck slab, horizontal movement of girder, and damage at

the bottom of girders(Mistry et al., 2001). In Diglipur(Rai et al., 2003) harbor pounding

damage was observed at the intersection of the approach segment and the main berthing

structure (fig 1.6). During Sumatra earthquake (Rai et al., 2005) of 26th December 2004,

pounding damage at junctions was noticed at the same top ends of piles of the approach

jetty, which were covered up.

Figure 1.6: Pounding damage at the intersection of approach to main jetty at Diglipurharbor during Diglipur Earthquake

From above observations, it is concluded that major pounding damages are caused

due to insufficient separation distance. Hence, there is a need to do research on sepa-

5


ration distance between adjacent structures and pounding behavior of structures during

earthquakes.

1.4 Literature review

Impact between adjacent structures during an earthquake is a phenomenon that has at-

tracted considerable research interest in the recent past. Pounding is a non-linear problem

due to its impact. Most of the numerical studies utilize single-degree-of-freedom (SDOF)

and multi-degree-of-freedom (MDOF) systems in order to simplify the problem and con-

centrate on the non-linear aspects.

The studies presented for literature review are categorized as:

X Analytical studies

X Experimental studies

X Numerical studies

1.4.1 Analytical studies

Lin (1997) analyzed the uncertainty of the separation distance required to avoid seismic

pounding of two adjacent buildings. The analytical procedures were based on random

vibrations. The results indicated that the theoretical results agree well with simulated

results. A larger separation distance is required for both adjacent buildings having a

longer fundamental period.

Lin (2002) investigated the pounding probability of buildings designed according to

1997 Taiwan building code (TBC) to gain an insight into the validity of the pounding

related provisions. A total of 36 cases of adjacent buildings A and B are considered.

The conditional probabilities of adjacent buildings separated by minimum code-specified

separation distance under earthquakes with different peak ground acceleration (PGA)

are investigated under 1000 artificial earthquakes. From the results it was revealed, the

building separation specified by TBC is approximately 1.6 times that specified by Uni-

form building code (UBC) for the same building and soil properties. The probability of

exceeding the design basis ground motion specified in UBC-94 during 50 year period is

10%.

Garcia (2004) proposed a new method to calculate critical separation distances be-

tween adjacent nonlinear hysteretic structures. A pair of single degree of freedom (SDOF)

systems was considered and the mean peak displacement responses were obtained through

numerical simulations (nonlinear time history analysis). He examined the correlation co-

6


efficient ρ, which was obtained for calculating the separation distance proposed by Filia-

trault, Penzien, Kasai and Valles. Results were expressed in terms of the ratio minimum

separation to peak relative displacement response. Results showed that the proposed

method provides consistently conservative estimates of critical separation distances, the

degree of conservatism being slight in most cases. When compared to other existing

methods, the proposed approach exhibited a number of convenient advantages. The main

disadvantage was the fact that the proposed values of ρ are available only in charts.

Ye et al., (2008) reexamined the derivation of the formula for damping constant ζ in

Hertz damp contact model. They found that the derivation is based on the following

assumptions: (1) The energy dissipated during impact is small compared with maximum

absorbed elastic energy. (2) The penetration velocities during the compression and resti-

tution are equal. In order to remedy the Hertz damp model valid for pounding analysis in

structural engineering, the corrected expression for the damping constant ζ should be de-

rived again. Through numerical analysis, the correctness of formula and its corresponding

theoretical derivation has been verified. More reliable results of pounding simulation in

structural engineering can be provided by using the Hertz damp model with the corrected

formula for damping constant.

It is observed from the past analytical studies on pounding, that they assure the

dynamic response of a building can be well simulated by using lumped mass structural

system and the excitation can be considered as a non-stationary Gaussian random pro-

cess with zero mean. Torsional effects on structural responses are ignored. It is also

assumed that floor elevations are same for all buildings so that pounding occurs only at

those elevations where the masses are lumped. It has been observed that the adjacent

buildings may be constructed with different materials and exhibit different hysteretic be-

havior(Jankowski, 2009). To better simulate the actual pounding probability of adjacent

buildings with different materials, the use of different hysteretic loops for each building

will be necessary.

1.4.2 Experimental studies

Papadrakakis et al., (1995) performed shaking table experiments on pounding between

two-storey reinforced concrete buildings with zero gap separation, subject to sinusoidal

excitation. The test structures were designed to remain elastic under an excitation with an

acceleration design spectrum of 1.0 g. A shaking table test was conducted with a ramped

sinusoidal displacement signal having a peak displacement of 0.13 cm and at resonance

with the fundamental frequency(f) of the flexible structure (f=4.1 Hz). Both pounding

and no-pounding cases were studied. The results indicated that pounding amplified the

displacement responses of the stiffer structure and reduced the responses of the flexi-

ble structure. Increase in accelerations peaks up to six was recorded during impact but

they take place within a very short-time duration. Comparison of the experimental results

7


with analytical predictions using the Lagrange multiplier method showed good agreement.

Chau et al., (2003) performed shake table tests on pounding between two steel tow-

ers subject to both harmonic and El-Centro ground motions. The natural frequency,

damping, the stand-off distance between the towers and the forcing frequency were varied

during the experiment. Under sinusoidal excitations, impacts were either periodic (one

impact within each excitation cycle or within every other excitation cycle) or chaotic.

Chaotic motions dominated when there was a large difference in the natural frequencies

of the two towers. It was observed that pounding amplified the response of the stiffer

structure and reduced the flexible tower response. The maximum relative impact velocity

was found to occur at an excitation frequency between the natural frequencies of the two

towers. The experimental findings were then compared with results from an analytical

model where impact was modeled using the Hertz contact law [Chau and Wei, 2000].

The region of excitation frequency within which impact occurred was well predicted by

the analytical model. The estimated relative impact velocity and the maximum stand-off

distance to prevent pounding agreed qualitatively with the experiments.

1.4.3 Numerical studies

The numerical studies can be categorized into SDOF and MDOF cases,

Studies on SDOF structures

Anagnostopoulos (1988) studied the case of several adjacent buildings in a row subjected

to pounding. Pounding is simulated using linear visco-elastic impact elements that are

introduced between the masses and act only when the masses are in contact. Elastic and

inelastic systems have been examined using a set of five real earthquake motions and a

wide variation of the problem parameters. Results are given in terms of displacement

amplifications for exterior and interior structures. The results indicate that the displace-

ment of exterior structures may be considerably amplified, while interior structures may

experience amplification or deamplification, depending on the ratio of structural periods.

A gap size equal to square root of sum of squares(SRSS) of the design peak displacements

of the adjacent structures could be sufficient to avoid pounding. The results show that

the effects of pounding diminish as the gap increases. Larger differences in the masses of

two adjacent structures make the effect of pounding more pronounced for the structure

with the smaller mass. Other parameters, like the stiffness of the contact element, play

a minor role in the response. Impact generated accelerations which can cause damage to

the contents of the building but have a little effect on the displacement response of the

colliding masses.

Davis (1992) has used a SDOF oscillator interacting with either a stationary or moving

neighboring barrier. Impact forces are described by non-linear Hertz law of contact and

results are given in the form of impact velocity spectra for harmonic excitation. These

8


spectra are characterized by a strong peak near a period equal to one half the natural

period of a similar non-impacting oscillator. In effect, the impact oscillator has a natural

period equal to roughly half the value it would have had if the neighboring structure had

not been present.

Athanassiadou et al., (1994) studied the seismic response of adjacent series of struc-

tures with similar and different dynamic characteristics subjected to five different seismic

excitations. The inelastic load displacement relation for the structures followed Clough

hysteresis model. From the results it was concluded that the effect of pounding from

adjacent buildings on the seismic behavior of a structure is more pronounced for the end

structures in a row. The effect of pounding is smaller when the adjacent structures have

similar dynamic characteristics with equal heights. In case of adjacent structures with

different natural periods, the most affected by pounding are rigid ones, irrespective of

their relative position in the row. The most adverse case is when the rigid structures are

placed at the end of the row. It was found that the seismic response of adjacent buildings is

not considerably affected by their strength, coefficient of restitution and relative mass size.

Pantelides et al., (1998) considered poundings between a damped SDOF structure

with either elastic and inelastic structural behavior and a rigid barrier. The pounding

phenomenon is modeled as a Hertz impact force. Artificial as well as actual earthquake

excitations were used in numerical evaluations of the seismic response. The response of

the inelastic structural system is compared to that of an elastic structure. The inelastic

structure has considerably smaller accelerations as compared to the elastic structure and

the maximum displacement of the inelastic structure is larger than that of the elastic

structure. Moreover, the maximum pounding force and number of pounding occurrences

are considerably less in the inelastic case as compared to the elastic case. The inelastic

behavior of structures under pounding is less conservative than the elastic behavior as-

sumption. This could be one of the explanations of why in general buildings experiencing

pounding have shown satisfactory response in past earthquakes.

Muthukumar et al., (2004) examined the effectiveness of various analytical impact

models for two closely spaced SDOF adjacent structures. Only elastic responses are con-

sidered in the analysis. A suite of twenty seven ground motion records from thirteen

different earthquakes was selected in parametric study. The records are chosen such that

the ground motion period ratio (T2/Tg = flexible system period over the ground motion

characteristic period) is less than one. To examine the effects of energy loss during impact,

two values of the coefficient of restitution(e) are chosen, e = 1.0 (no energy loss) and e =

0.6 (some energy loss). The contact force-based models predict higher accelerations due to

pounding. The acceleration responses from the stereo-mechanical model are much smaller

than those from the contact models. The displacement amplifications get closer to unity,

as the system gets more in-phase. Neglecting energy loss during impact overestimates the

stiff system displacement, when subjected to high levels of PGA. Pounding models that

9


account for energy loss during impact are best suited to simulate pounding. The Hertz-

damp model appears to be an effective contact based approach, as it can model energy loss.

Jankowski (2006) proposed the idea of impact force response spectrum for two adja-

cent structures, which shows the plot of the peak value of pounding force as a function of

the natural structural vibration periods. The structures had modeled as SDOF systems

and pounding had simulated by a nonlinear visco elastic model. The structural natural

periods T1, T2 had ranged from 0.05s to 3s with an increment of 0.05s under different

ground motion records. The results are shown as pounding force spectra. In a pound-

ing force spectra, where the pounding force is becomes equal to zero region concerns the

cases when the natural vibration periods are very small for both structures. When the

damping ratios of two structures are different, pounding force for the cases of identical

natural vibration periods is not always equal to zero. It is indicated that peak impact

force values depends on the consideration of which of the structures is elastic and which

is the inelastic one. The results indicated that impact force response spectra might serve

as a very helpful tool for the design purposes of closely spaced adjacent structures.

It is observed from the past analytical studies on pounding of SDOF structures, the

local effects such as damage of a column being pounded by a slab of adjacent building

was not considered whereas, the effects of pounding on the overall structural response was

concerned. It is assumed that all systems are subjected to same input ground motion i.e.

the effects of phase difference due to travelling waves are not considered. It is assumed

that the various seismic waves which compose the complex motion represented by an

accelerogram propagate with the same average velocity.

Studies on MDOF structures

Westermo (1989) examined the dynamic implications of connecting closely neighboring

structures for the purpose of eliminating pounding. The structures were assumed and

modeled as linear, MDOF systems where the mass is concentrated at each floor and the

stiffness is provided by walls and columns and subjected to harmonic and earthquake exci-

tation. Coupling reduces the potential for pounding by maintaining a separation distance

between the structures. The contact is likely to occur at a single point (due to predom-

inant first mode vibration), a single connection may be sufficient. However, at higher

modes multiple connection points are necessary. The linkage not only reduces the relative

overlap deflection of the structures at large amplitudes but also increase the base shear on

the stiffer of the two structures at excitation frequencies below the fundamental frequency.

Maison et al., (1990) presented a formulation and solution of the multiple degree of

freedom equations of motion. The studied building undergoes pounding at a single floor

level with a rigid adjacent building. A single linear spring represents the local flexibility

of the buildings at their locations of contact. They found that even at the relatively large

separation (90% of the sum of maximum displacements obtained without pounding) the

10


increases in drifts and shears are significant. In situations where pounding may potentially

occur, neglecting its possible effects leads to unconservative building design/evaluation.

The story drifts, shears, and overturning moments in the stories above the pounding ele-

vation will be underestimated (pounding occurred at 8th level in a 15 story structure).

Anagnostopoulos et al., (1992) extended their studies on a series of SDOF systems to

MDOF. They investigated the linear as well as the non-linear response of several adjacent

buildings in a row under conditions of pounding. They idealized the buildings as lumped

mass, shear beam type and MDOF systems with bilinear force-deformation characteris-

tics. Furthermore, the structural models include foundation compliance by means of a

linear spring for translational and rotational motions. The constants for the foundation

springs were determined. Collisions were simulated by visco-elastic impact elements (a

Kelvin solid) and five real earthquake motions were used. The coefficient restitution used

to simulate real collision in structural engineering varies in the range of 0.5-0.75. If there

are large differences in the masses of the colliding buildings then pounding can cause

high overstresses in the building with the smaller mass. Greater consequences for the tall

building can be expected if the lower building were more massive and stronger. The effects

of pounding are reduced as the separation distance increases, even if the code (Uniform

Building Code and Euro No. 8) specified gap proved inadequate in some future strong

shaking.

Rahman et al., (2000) investigated the influence of soil flexibility on the dynamic

response of structures subjected to pounding. The 12 and 6-storey reinforced concrete

moment-resisting frames were subjected to ground motion and the time-history response

of this system (linear soil behavior and nonlinear structural response) was evaluated by

means of the structural analysis software RUAUMOKO. The soil flexibility was modeled

as discrete elements and the parameters were chosen from previous investigators. The

results indicated that the effect of foundation compliance is to increase of the natural

periods of both structures from the fixed base condition. Consideration of the flexibility

of the soil mass between the structures, even for the large separation distance, shows a

slight difference from the compliant foundation case.

Raheem et al., (2006) developed a methodology for the formulation of adjacent build-

ing pounding problems based on classical impact theory through parametric study to

identify the most important parameters. The steel moment resisting frame building of 8

storey and 13 storey was modeled as 3D finite element model and nonlinear time history

analyses were performed. Nine ground motion records [Muthu kumar 2004] are taken and

grouped into three levels depending on PGA. For the purpose of evaluating the effect of

torsion, a torsional unbalanced model is defined where the centre of mass lies at a distance

’e’ from centre of rigidity. Impact energy dissipation is also introduced. Bilinear truss

contact model is used for the analysis. It was found that pounding in severe load condi-

tion could result in high acceleration pulses in the form of short duration spikes which in

11


turn cause greater damage. Pounding response is increased in the flexible building and

reduced in stiff building at dominant frequency. The amplification in building response

is a function of TA, TB, (TA/TB) and dominant frequency of input ground motion. An

increase in the damping energy absorption capacity of pounding element results in the

reduction of the acceleration spikes, impact force and building global response. It is clear

that an energy dissipation system installed at potential pounding level could be an effec-

tive tool to reduce the effect of impact.

Polycarpou et al., (2008) investigated the influence of the impacts on the overall struc-

tural response, seismically isolated buildings in series with adjacent structures numerically.

A four storey seismically isolated building and neighboring two fixed supported buildings

were subjected to six strong motions. A linear visco elastic impact model with plastic de-

formations is employed for pounding simulation. A series of dynamic analyses conducted

in order to investigate the responses for isolated building adjacent to other fixed sup-

ported buildings, compared to the case of the seismically isolated building standing alone

surrounded only by the moat wall. It was found that the presence of a fixed-supported

building in close proximity with the seismically isolated building may cause unexpected

impact phenomena at upper floors due to the deformation of the buildings in series. Also,

the number of stories of the adjacent fixed-supported buildings seems to play a significant

role to the severity of the impact.

Goltabar et al., (2008) studied the impact between adjacent structures of different

heights using gap joint element and nonlinear time history analyses during earthquakes

and their effective parameters. In this case 10 and 13 storey structures were chosen,

the connection modeling was done using gap joint element. The two structures were sub-

jected under three accelerographs. The analysis was done using SAP 2000 software. From

the analysis, maximum responses (lateral displacements and storey shears) in the shorter

building decreased throughout the whole building except for the impact point. Maximum

responses in the taller buildings increased throughout the building. One of the ways to

decrease impact effects is considering a proper distance between two structures. As a

result the responses will be similar to non-impact case. By hardening the building also

we can reduce the impact effects.

Tande et al., (2009) investigated the optimal seismic response of two adjacent struc-

tures through passive energy dissipation devices in order to minimize the pounding effect.

Two twenty storey buildings having same floor elevation with dampers connecting two

neighboring floors were used. The damping ratio for both the buildings is taken as 5%.

Time history analysis is carried out using Elcentro ground motion 1940 earthquake data

to find out the maximum top floor displacements for three cases. The first case is that of

unconnected structures, second is when the two buildings are connected at all floor levels

and third case is at optimal locations. The damper stiffness coefficient is chosen such that

the addition of dampers doesn’t change the modal frequencies of the individual buildings.

12


The value of 5.0x104 N/m is selected as optimal stiffness for the dampers. When the

value of stiffness is increased to 1.0x109 N/m, the relative displacement between the ad-

jacent buildings becomes nearly zero, implying that both buildings are rigidly connected.

The maximum top floor displacement is lowest when the damper damping coefficient is

1.0x104 Ns/m. Beyond this value there is no significance reduction in the displacements of

both the buildings. If a very high of damping coefficient is chosen, the structure becomes

over-damped and hence becomes stiff. Optimal damper damping coefficient is in between

5.0x105 and 3.0x106 Ns/m. The natural frequencies for both the buildings should not

change after the insertion of external damping devices. As the damping coefficient of

visco-elastic damper is increased, there is no significant decrease of response beyond cer-

tain value. Hence this value is selected as optimal damper damping coefficient. It is not

necessary to connect the two adjacent buildings by dampers at all floor levels. Dampers

at appropriate locations can significantly reduce the earthquake response of the combined

system.

Mahmoud et al., (2009) studied and compared the maximum elastic with inelastic re-

sponses under three ground motions. Two adjacent four storey buildings are considered in

which the building parameters are assumed to be same for all floor levels. The buildings

are modeled as MDOF systems and the nonlinear visco-elastic model is used to simu-

late impact force during collisions. The peak responses are considerably reduced for all

ground motions for different values of separation distances. For both elastic and inelastic

systems, the peak responses are of the flexible building increase up to a certain value of

the gap distance and with further increase in gap a decrease trend can be observed. The

responses of the elastic systems are significantly different comparing to the responses of

inelastic one. Especially, the flexible building easily enters into the yielding range as a

result of pounding. The maximum impact forces and the number of impacts are larger in

the elastic case. The normalized errors increase with the increase of levels of PGA of the

earthquake records.

It is observed from the past numerical studies on pounding of MDOF structures, are

modeled as linear systems using link and beam elements and considered MDOF systems

where the mass is concentrated at each floor level and the stiffness is provided by walls

and columns. The building of interest dynamically vibrates and laterally collides with

an adjacent rigid building. This implies that the building of interest is very flexible and

possesses low mass relative to the adjacent building. The pounding occurs at a single

floor level in the building of interest and the floor diaphragms are rigid in plane. A single

linear spring represents the local flexibility of the buildings at their locations of contact.

It is assumed that floor elevations are the same for all buildings so that pounding can

occur only at these elevations where the masses are lumped. Local damage effects due

to pounding are not addressed. All the systems are subjected to same base acceleration

and so any effects due to spatial variations of the ground motion or due to soil structure

interactions are neglected. The material damping of the soil was not accounted for in the

13


soil structure interaction models and only radiation damping was present.

1.5 Summary of contribution

1.5.1 Mitigation measures

In the past, large metropolitan areas (eg.Mexico) were affected by major earthquakes

which induced severe pounding damage. To minimize the effects of pounding, mitigation

techniques are used and some of them are listed below.

Mitigation techniques are used to minimize the damages from pounding as follows:

1. In link element technique, forces in links can be same order of magnitude of base

shear. This link may sometimes totally alter the distribution of the forces.

2. Bumper damper elements are link elements that are activated when gap is closed.

Such elements reduce energy transfer during pounding and the high frequency pulses.

The damper will yield a smaller value for the coefficient of restitution. These bumper

elements have already been incorporated in the Greek code and in Euro code-08 for

earthquake resistant design.

3. Supplemental energy devices can be used in the structures for pounding mitigation

depending on the additional damping supplied.

4. The use of shear walls that are constructed at right angles to the divided line between

two buildings in contact, so that they can be used as bumper elements in the case

of pounding.

5. Provide sufficient minimum distance between adjacent structures.

6. Provide sufficient seated length between the decks or provide shock absorbing devices

between the decks and bearings under the extremities of the decks in bridges.

7. Buildings having simple regular geometry, uniformly distributed mass and stiffness

in plan as well as in elevation, suffer very less damage than buildings with irregular

configurations.

From the above reasons, it is widely accepted that pounding is an undesirable phe-

nomenon that should be prevented or mitigated. Several impact models are available to

understand the pounding behavior of structures.

1.5.2 Impact models

The collisions between adjacent buildings are simulated by means of contact elements

that are activated when the bodies come in contact and deactivated if they are separated.

A brief summary with advantages and disadvantages of the various modeling techniques

are presented below.

14


Coefficient of restitution model

Stereo-mechanical model

The stereo-mechanical theory of impact is the classical formulation to the problem of

impacting bodies. The stereo-mechanical approach assumes instantaneous impact and

uses momentum balance and the coefficient of restitution to modify velocities of the

colliding bodies after impact. The original theory considered the impacting bodies as

rigid; later a correction factor to account for energy losses was introduced. The theory

concentrates on determining the final velocities of two impacting bodies depending on their

initial velocities and a coefficient of restitution to account for plasticity during impact. The

final velocities of the bodies are determined from equation 1.1 to 1.2. The disadvantage

of the method is that it is no longer valid if the impact duration is large enough so

that significant changes occur in the configuration of the system. This implies that the

duration of impact is neglected. Traditionally the value of the coefficient of restitution was

assumed to depend only on the material properties. The stereo-mechanical model is not

a force-based model. Hence, there is no impact force and consequently, no amplification

in the acceleration response.

v′1 = v1 − (1 + e)m2(v1 − v2)m1 +m2

(1.1)

v′2 = v2 + (1 + e)m1(v1 − v2)m1 +m2

(1.2)

Where v′1 and v′2 are final velocities, v1, v2 are initial velocities of the colliding bodies,

e is co.efficient of restitution, m1, m2 are the mass of bodies.

Contact force based models

Linear spring element model

The simplest contact element consists of a linear elastic element (fig 1.7). The spring

Figure 1.7: Linear Spring Model

is assumed to have restoring force characteristics such that only when the relative dis-

tance between the masses becomes smaller than the initial distance, the spring contracts

15


and generates forces which enable us to consider the phenomenon of pounding. This col-

lision spring is assumed to be the axial stiffness of the floors and the beams in each storey.

The force in the contact element can be expressed according to equation 1.3:

Fc =

kl(u1 − u2 − δ), (u1 − u2 − δ) ≥ 0

0, (u1 − u2 − δ) < 0(1.3)

Where u1 and u2 are the displacements of the impacting bodies, kl is the spring con-

stant of the element and δ is the separation distance between the structures.

However, energy loss during impact cannot be modeled. Whenever two mechanical

systems collide there is an exchange of momentum and also energy is dissipated in the

high stress region of contact.

Kelvin-Voight element model

The Kelvin-Voight element is represented by a linear spring in parallel with a damper (fig

1.8). This model has been widely used in some studies [Anagnostopoulos 1988, Jankowski

Figure 1.8: Kelvin Model

2004]. This impact model is capable of modeling energy dissipation during impact and

the impact force is represented by equation 1.4.

Fc =

kk(u1 − u2 − δ) + ck(u1 − u2), (u1 − u2 − δ) ≥ 0

0, (u1 − u2 − δ) < 0(1.4)

Where u1, u2 and its derivatives are the displacements and velocities of the impacting

bodies, kk is the spring constant of the element and δ is the separation distance between

the structures. The damping coefficient ck can be related to the coefficient of restitution

(e), by equating the energy losses during impact.

ck = 2ζ

√kk

m1m2

m1 +m2

; ζ = − lne√π2 + (lne)2

(1.5)

Where m1 and m2 are the mass of colliding bodies and ζ is the damping co.efficient.

16


Modified Kelvin element model

The disadvantage of the Kelvin model is that its viscous component is active with the same

damping coefficient during the whole time of collision. The damping forces causes negative

impact forces that pull the colliding bodies together, during the unloading phase, instead

of pushing them apart. Ye et al., (2009) reexamined and modified the Kelvin model

and theoretical derivation has been verified with numerical experiment. The corrected

damping ratio value can be expressed as:

ζk =3kk(1 + e)

2e(v1 − v2)(1.6)

Hertz contact model

In pounding, one would expect the contact area between neighboring structures to in-

crease as the contact force grows, leading to a non-linear stiffness. In order to model

highly non-linear pounding more-realistically, Hertz impact model has been adopted by

various authors [Davis 1992, Jing 1990, Chau and Wei, 2001, Chau et al., 2003]. This

model uses the Hertz contact law: a non-linear spring in an impact oscillator. The main

restriction of their works is that only pounding of a SDOF oscillator on a stationary bar-

rier or on a barrier moving with ’locked-to-ground-motion’ is considered.

The force in the contact element can be expressed as:

Fc =

kh(u1 − u2 − δ)32 , (u1 − u2 − δ) ≥ 0

0, (u1 − u2 − δ) < 0(1.7)

The coefficient kh depends on material properties and geometry of colliding bodies.

The Hertz contact law, is incapable of taking into account dissipation during impact

phenomenon. The value of the Hertz exponent, 3/2, may be different for real pounding,

but Davis [1992] has shown that the exact value may be altered without radically changing

the oscillator response.

Hertz-damp contact model

An improved version of the Hertz model, called Hertz-damp model, has been considered

by Muthukumar and DesRoches [2004] whereby a non-linear damper is used in addition

with the Hertz spring. The force in the contact element can be expressed as:

Fc =

kh(u1 − u2 − δ)32 + ch(u1 − u2), (u1 − u2 − δ) ≥ 0

0, (u1 − u2 − δ) < 0(1.8)

Where ch is the damping coefficient, (u1 − u2 − δ) is the relative penetration and

derivative of (u1 − u2) is the penetration velocity. A nonlinear damping coefficient (ch)

is proposed so that the hysteresis loop matches the expected loop due to a compressive

17


load that is applied to and removed from a body within its elastic range at a slow rate.

The damping co.efficient can be expressed as,

ch = ζ(u1 − u2 − δ)n (1.9)

Where ζ is damping constant.

Equating the energy loss during stereo-mechanical impact to the energy dissipated by

the damper, the value of ζ can be related to the spring constant, kh, the coefficient of

restitution (e), and the relative velocity of the bodies at the instant of impact, (v1 − v2),as shown below.

ζ =3kh(1− e2)4(v1 − v2)

(1.10)

Hence, the force during contact can be expressed as:

Fc =

kh(u1 − u2 − δ)32 + [1 + 3(1−e2)

4(v1−v2)(u1 − u2)], (u1 − u2 − δ) ≥ 0

0, (u1 − u2 − δ) < 0(1.11)

The Hertz model with nonlinear damper shall be referred to as the Hertz-damp model.

1.5.3 Codal provisions

Most of the world regulations for seismic design do not take into account this phenomenon

and some of the ones which do, do not provide specific rules that must be followed (Paz,

1994). Among the exceptions are the codes of Argentina, Australia, Canada, France,

India, Indonesia, Mexico, Taiwan and USA which specify a minimum gap size between

adjacent buildings.

In some cases gap depends only on the maximum displacements of the each building.

The rule to determine the size is nevertheless variable, being in some cases the simple sum

of the displacements of each building (eg. Canada and Israel) and in other cases a small

value that may be either a percentage of previous one or a quadratic combination of the

maximum displacements (eg. France). In other cases the gap size is made dependent on

the building height (eg.Taiwan), in some cases a combination of two rules is implemented

and in others there is a even a minimum gap size which varies between 2.5 cm (eg. Ar-

gentina) and 1.5 cm (eg.Taiwan). In some cases these values depend on the type of soil

and seismic action.

However most of the studies assume only two dimensional behaviors i.e. only transla-

tional pounding is considered. But actually torsional pounding tends to be more common

than uni-directional pounding during real ground motions. This problem is particularly

18


common in many cities located in seismically active regions. The list of various country

codal provisions on pounding is shown in table 1.1 (Source: IAEE):

1.6 Objective of the study

Structural pounding is a complex phenomenon which involves local damage to structures

during earthquakes. It is necessary to quantify the amount of damage due to structural

pounding. In numerical modeling, the research on structural pounding has not been

upgraded till quantification of damage and damage scale. The main objective of this

research is to study pounding of structures using applied element method (AEM).

1.7 Organization of thesis

The body of this thesis is organised in six chapters. Chapter(2) deals about modeling of

structures which are subjected to pounding. Also, linear pounding behavior of structures

with equal and un-equal heights are discussed.

Chapter(3) discusses about nonlinear pounding behavior of different structures with

equal heights subjected to ground motion. Furthermore, a damage scale has proposed for

all structures to categorize the level of damage due to pounding.

Chapter(4) discusses the nonlinear pounding behavior of different structures with un-

equal heights. Different un-equal heights are considered in this analysis and the level of

damage for all structures are estimated from the above damage scale.

Chapter(5) extends the analysis to 3D. This chapter introduces nonlinear torsional

pounding between structures and structures are placed in staggered manner.

Finally, the general conclusions and future direction of research are introduced in

chapter(6).

19


Table 1.1: List of codal provisions on pounding

Country Provision on pounding

Australia

Structures over 15 m shall be separated from adjacent structures or set-back from building boundary by a distance sufficient to avoid damagingcontact. This clause is deemed to be satisfied if the primary seismicforce-resisting elements are structural walls that extend to the base, orthe setback from a boundary is more than 1% of the structure height.[clause 5.4.5]

CanadaAdjacent structures shall be separated by the sum of their individuallateral deflections obtained from an elastic analysis. [clause 4.1.9.2(6)]

Egypt

• Each building separated from its neighbor shall have a minimum clearspace from the property boundary, other than adjoining a public space,either by 2.0 times the computed deflections or 0.002 times its heightwhichever is larger, and in many cases, not less than 2.5 cms. • Parts ofthe same building or buildings on the same site which are not designed toact as an integral unit shall be separated from each other by a distanceof at least 2.0 times the sum of the individual computed deflections or0.004 times its height whichever is larger, and in many cases, not lessthan 5.0 cms. [clause 2.7.2]

EthiopiaTo prevent collision of buildings in an earthquake, adjacent structuresshall either be separated by twice the sum of their individual deflectionsobtained from an elastic analysis. [clause 7.7]

Greece

For buildings which are in contact with each other but there is no possi-bility for any columns to be rammed, the width of the respective joint,in the absence of more accurate analysis may be determined on the basisof the total number of storeys in contact above the ground as follows: •4 cm up to and including 3 storeys in contact • 8 cm from 4-8 storeysin contact • 10 cm for more than 8 storeys in contact. For undergroundfloors a seismic joint is not obligatory. [clause 4.1.7.2]

India

R times the sum of the calculated storey displacements as perclause7.11.1. When floors levels of two similar adjacent units or build-ings are at the same elevation levels, factor R in this requirement maybe replaced by R/2.[clause7.11.10.]

Mexico

When using the simplified seismic analysis method the separation dis-tance shall be neither smaller than 5 cm nor smaller than the height ofthe level over the ground multiplied by 0.007, 0.009 or 0.012 dependingon the site in zones I, II or III respectively. [article 211]

Nepal

• Above ground level, each building of greater than three storeys shallhave a separation from the boundary, except adjacent to a designed streetor public way, of not less than the design lateral deflection or 0.002 hi or25 mm whichever is greater. • Parts of buildings or buildings on the samesite which are not designed to act as an integral unit shall be separatedfrom each other by a distance of not less than the sum of the designlateral deflections or 0.004 hi or 50 mm whichever is greater. [clause 9.2]

20


Peru

• The minimum distance shall not be less than 2/3 of the sum of themaximum displacements of the adjacent blocks, nor shall it be less than:S=3+0.004(h-500) (h and S are in cms) S>3 cm. • The building shall beset back from adjacent property lines of empty plots that can built on orfrom existing buildings, by distances no less than 2/3 of the maximumdisplacement nor less than S/2. [article 15.2]

Serbia

• The minimum width of the aseismic joint shall be 3.0 cm. It shall beincreased by 1.0 cm for every increase of 3.0 meters of height above 5.0mts. • In the case of buildings higher than 15 m, as well as in the case offlexible structures of lesser height such as unbraced frames, it shall notbe less than the sum of the maximum deflections of adjacent parts of thebuilding, nor shall it be less than the above. [article 47]

Taiwan

Pounding may be presumed not to occur wherever buildings are separatedby a distance greater than or equal to 0.6x1.4fyRa times the displacementcaused by the determined seismic base shear. [clause 2.5.4] *The factor0.6 is used because of low probability that two adjacent buildings willmove in the opposite directions and reach the maximum displacementsimultaneously.

21

Chapter 2

Numerical Modeling of Pounding

2.1 Introduction

The main focus of this chapter is to study the linear pounding behavior of structures with

equal and un-equal heights. Also discuss on separation distance from different country

seismic codes for different structures subjected to different ground motions. Furthermore,

provide suggestions for the codes which are underestimated on separation distance.

2.2 Selection of buildings

2.2.1 Building geometry

The analysis considers single storey, two storey, three storey and five storey structures

and the details of the structures are shown in fig 2.1 to 2.4.

Figure 2.1: Geometry of single storey structure

The single storey structure has a total height of 3.12 m including the thickness of slab.

The dimension of column is 0.24 m x 0.24 m. For two storey structure the total height is

22

CHAPTER 2. NUMERICAL MODELING OF POUNDING

Figure 2.2: Geometry of two storey structure

6.24 m and the thickness of slab is 0.12 m. The total height of three storey structure is

9.36 m having a column size of 0.3 m x 0.3 m. The total height of five storey structure

is 15.6 m having a column size of 0.3 m x 0.3 m. All the above mentioned structures are

designed as per IS-456:2000 and minimum reinforcement is provided. The reinforcement

details for single and two storey structures are shown in fig 2.5 and for three and five storey

structures are shown in fig 2.6. For all the structures the slab thickness is considered as

0.12 m. The foundation reinforcement details are not considered and assumed as fixed at

ground surface level.

2.2.2 Material properties

The grade of concrete, grade of steel for reinforcement and poission’s ratio are same for

all the structures. The details of material properties for the structures (ref 2.2.1) are as

follows:

Grade of concrete : M25

Grade of steel for reinforcement : Fe415

Poission’s ratio : 0.2

For the pounding analysis minimum two structures are considered namely structure-A

and B. It is assumed that the live load acting on the structure-A is 2 kN/m2 and for

structure-B is 5 kN/m2. The above mentioned live load is applied for the structures

hereafter.

23


Figure 2.3: Geometry of three storey structure

2.3 Selection of ground motions

Ten moderate ground motions are choosen for the analysis whose peak ground acceleration

(PGA) ranging from 0.25-0.55 g. The PGAs and duration of ground motions ranges from

low to high and the frequency content ranges from resonating to non-resonating conditions.

The details of the ground motions are listed in table 2.1 and the ground motion records

and its fourier amplitude spectrums are shown in fig 2.7 to 2.16. The characteristics of

corresponding ground motions are described in next sub-section.

2.3.1 Characteristics of ground motions

For engineering purposes, (1) amplitude (2) frequency and (3) duration of the motion are

the important characteristics (Kramer, 1996).

Horizontal accelerations have commonly been used to describe the ground motions.

The peak horizontal acceleration for a given component of motion is simply the largest

24


Figure 2.4: Geometry of five storey structure

25


Figure 2.5: Reinforcement details of single and two storey structures

Figure 2.6: Reinforcement details of three and five storey structures

Table 2.1: Details of ground motions

S.No Earthquake Date Station CompAmplitude(g)

Duration(sec)

Frequency(Hz)

1 Athens 1999 Kallithea N46 0.265 4.1 1.5-4.52 Athens 1999 Sepolia Garage Tran 0.31 4.44 2.0-6.03 Ionian 1973 Lefkada-Ote NS 0.525 6.9 0.85-2.44 Kalamata 1986 Kalamata N355 0.297 5.27 0.7-1.75 Umbro 1997 Nocera Umbra NS 0.47 9.35 6.2-7.26 Elcentro Imperial Valley S00E 0.348 29 1.15-2.27 Olympia Washington N86E 0.28 20.82 1.12-4.668 Parkfield Parkfield N85E 0.43 6.55 0.8-3.39 Northridge 1994 New Hall LA Up 0.548 12.44 2.2-5.310 Lomaprieta 1989 Lomaprieta 2700 0.276 9.78 0.65-1.72

(absolute) value of horizontal acceleration obtained from the accelerogram of that com-

ponent. The largest dynamic forces induced in certain types of structures (very stiff) are

closely relate to the peak horizontal accelerations (Kramer, 1996).

Earthquakes produce complicated loading with components of motion that span a

broad range of frequencies. The frequency content describes how the amplitude of ground

26


(a) (b)

Figure 2.7: Athens ground motion record and its fourier spectrum amplitude (a) Groundmotion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.8: Athens(tran) ground motion record and its fourier spectrum amplitude (a)Ground motion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.9: Ionian ground motion record and its fourier spectrum amplitude (a) Groundmotion record (b) Fourier amplitude spectrum

27


(a) (b)

Figure 2.10: Kalamata ground motion record and its fourier spectrum amplitude (a)Ground motion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.11: Umbro ground motion record and its fourier spectrum amplitude (a) Groundmotion record (b) Fourier amplitude spectrum

motion is distributed among different frequencies. The frequency content of an earth-

quake motion will strongly influence the motion of structure. The broad band width

of the Fourier amplitude spectrum is the range of frequencies over which some level of

Fourier amplitude is exceeded. Generally band width is measured at a level of 1√2

times

of maximum Fourier amplitude.

The fourier transform of an accelerogram x(t) is given by,

X(ω) =1

2π

∫ ∞−∞

x(t)e−iωtdt (2.1)

Where, x(t) is the acceleration record and ω is frequency.

The duration of strong ground motion can have a strong influence on earthquake dam-

28


(a) (b)

Figure 2.12: Elcentro ground motion record and its fourier spectrum amplitude (a)Ground motion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.13: Olympia ground motion record and its fourier spectrum amplitude(a) Groundmotion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.14: Parkfield ground motion record and its fourier spectrum amplitude(a)Ground motion record (b) Fourier amplitude spectrum

29


(a) (b)

Figure 2.15: Northridge ground motion record and its fourier spectrum amplitude(a)Ground motion record (b) Fourier amplitude spectrum

(a) (b)

Figure 2.16: Lomaprieta ground motion record and its fourier spectrum amplitude(a)Ground motion record (b) Fourier amplitude spectrum

age. It is related to the time required for accumulation of strain energy by rupture along

the fault.

There are different procedures for calculating the duration of ground motion,

Brackted Duration: It is the time between the first and last exceedances of a threshold

acceleration (usually 0.05 g)

Trifunac and Brady Duration: It is the time interval between the points at which 5%

and 95% of the total energy has been recorded.

In our analysis brackted duration is used for calculating the duration of ground motion.

30


2.4 Numerical method

2.4.1 Introduction

The numerical techniques can be categorize in two ways. The first case assumes that the

material as continnum like finite element method (FEM). In this method, elements are

connected by nodes where the degrees of freedom are defined. The displacement, stresses

and strains inside the element are related to the nodal displacements. The analysis can

be done in elastic and nonlinear materials, small and large deformations except collapse

behavior. At failure, the location of cracks should be defined before analysis which is not

possible in collapse analysis.

The other catogory assumes that the material as discrete model like rigid body spring

model (RBSM), extended distinct element method (EDEM) and applied element method

(AEM) (Hatem, 1998). The RBSM performs only in small deformation range. EDEM

overcomes all the difficulties in FEM, but the accuracy is less than FEM in small defor-

mation range. Till now there is no method among all the available numerical techniques,

in which the behaviour of the structure from zero loading to total complete collapse can

be calculated with high accuracy. The modeling of AEM and formulation are as follows.

Applied element method is a discrete method in which the elements are connected by

pair of normal and shear springs which are distributed around the element edges. These

springs represents the stresses and deformations of the studied element. The elements

motion is rigid body motion and the internal deformations are taken by springs only. It

is advisable to increase the number of elements than connecting springs for improving

the accuracy. The general stiffness matrix components corresponding to each degree of

freedom are determined by assuming unit displacement and the forces are at the centroid

of each element. The element stiffness matrix size is 6x6. The stiffness matrix components

diagram is shown in fig 2.17. The first quarter portion of the stiffness matrix is shown

in fig 2.18. However the global stiffness matrix is generated by summing up all the local

stiffness matrices for each element.

2.4.2 Mathematical formulation

In order to begin any physical system, it is necessary to formulate it in a mathematical

form. The general dynamic equation for a structure is given in equation 2.2

Mu+ Cu+Ku = ∆f(t)−Mug (2.2)

Where [M ] is mass matrix; [C] is damping matrix; [K] is nonlinear stiffness matrix;

∆f(t) is incremental applied load vector ∆U and its derivatives are the incremental dis-

placement, velocity and acceleration vectors respectively. The above equation is solved

numerically using Newmark’s beta method.

31


Figure 2.17: Element components for formulating stiffness matrix (SOURCE: KimuroMeguro and Hatem, 2001)

Figure 2.18: Quarter portion of stiffness matrix

For mass matrix the elemental mass and mass moment of inertia are assumed lumped

at the element centroid so that it will act as continuous system. The elemental mass

matrix in case of square shaped elements is given in equation 2.3M1

M2

M3

=

D2tρ

D2tρ

D4tρ/6.0

(2.3)

Where D is the element size; t is element thickness and ρ is the density of material.

From the above equation it is noticed that [M1] and [M2] are the element masses and

[M3] is the mass moment of inertia about centroid of the element. The mass matrix is a

diagonal matrix. The response of the structure is very near to the continuous/distributed

mass system if the element size becomes small. If the damping is present, the response of

the structure will get reduced. The damping matrix is calculated from the first mode as

follows:

32


C = 2ζMωn (2.4)

Where ζ is damping ratio and ωn is the first natural frequency of the structure. For

finding out the dynamic properties such as natural frequencies of a structure requires

eigen values. The general equation for free vibration without damping is:

Mu+Ku = 0 (2.5)

For a non trival solution, the determinant of the above matrix must be equal to zero.

The solution of determinant of matrix gives the natural frequencies of the structure.

2.4.3 Element size

In numerical modeling, element size of the structure is important. Using large element

size decreases the displacement of the structure and finally leads to the larger failure load

than actual failure load. For any kind of numerical analysis three important requirements

(convergence, stability and accuracy) are necessary.

1. Convergence - As the time step decreases, the numerical solution should close to the

exact/theoretical solution.

2. Stability - The numerical solution should be stable in the presence of numerical

round off errors.

3. Accuracy - The numerical procedure should provide results that are close to the

exact solution.

The details of the structures are taken from fig 2.1 to 2.4 for fixing the element size

and the structures are subjected to uttarkasi ground motion having PGA of 0.252 g shown

in fig 2.19.

The displacement response of the structure is calculated using Newmarks beta method.

Initially the response is calculated with an element size of 0.24 m. As the size of the

element decreases, the response level will get saturate. This means the response will be

same with decreasing the element size further. The same analysis is done for two storey,

three storey and five storey structures. Finally, the element size is fixed at 0.06 m for all

the structures.

2.4.4 Material model

The material model used in this analysis is Maekawa compression model (Tagel-Din

Hatem, 1998). In this model, the tangent modulus is calculated according to the strain at

the spring location. After peak stresses, spring stiffness is assumed as a minimum value

to avoid having a singular matrix. The difference between spring stress and stress cor-

responding to strain at the spring location are redistributed in each increment in reverse

33


(a) (b)

Figure 2.19: Uttarkasi ground motion record and its fourier spectrum amplitude(a)Ground motion record (b) Fourier amplitude spectrum

direction. For concrete springs are subjected to tension, spring stiffness is assumed as the

initial stiffness till it reaches crack point. After cracking, stiffness of the springs subjected

to tension are assumed to be zero. For reinforcement, bi-linear stress strain relationship

is assumed. After yield of reinforcement, steel spring stiffness is assumed as 0.01 of initial

stiffness. After reaching 10% of strain, it is assumed that the reinforcement bar is cut.

The force carried by the reinforcement bar is redistributed force to the corresponding

elements in reverse direction. For cracking criteria (Hatem, 1998), principal stress based

on failure criteria is adopted. The models for concrete, both in compression and tension

and the reinforcement bi-linear model are shown in fig 2.20 (a) and (b).

(a) (b)

Figure 2.20: Material models for concrete and steel (a) Tension and compression concreteMaekawa model (b) Bi-linear stress strain relation model for steel reinforcement

2.4.5 Collision model

Collision springs are added between the collide elements to represent the material behav-

ior during contact. As the collision check of irregularly shaped elements is more difficult

34


Figure 2.21: Arrangement of collision springs

and time consuming, the element shape during collision is assumed as circle. This as-

sumption is acceptable even in case of relatively large elements because the sharp corners

of elements are broken due to stress concentration during collision and edge of elements

become round shape. The arrangement of collision springs are as shown in fig 2.21

The normal spring stiffness is calculated as follows:

kn =Edt

D(2.6)

Where, ’E’ is minimum Young’s modulus of the material, ’t’ is the element thickness,

’D’ is the distance between element centroids and ’d’ is the contact distance which is

assumed as 0.1 times of the element size. The shear spring stiffness is assumed as 0.01

times of normal spring stiffness. The normal contact spring is not allowed to fail, instead

of that compression failure of the distributed springs connecting to the elements allowed

to fail. Here the objective of the collision spring is to transmit the stress wave to other

elements. The tensile force in the normal spring indicates that elements tend to separate

each other. Then, the residual tension is redistributed in the next increment.

Procedure for finding out the response of colliding structures is as follows:

The displacement response of the structure is calculated using Newmarks β technique.

Using geometric coordinate technique, contact between elements is checked and its neigh-

bour elements instead of all elements. If collision occurs, the following steps to be followed:

STEP 1: The time increment should be reduced to follow the material behavior prop-

erly during collision. This value depends on many factors like relative velocity between

elements before collision and force transmitted during collision. After separation of ele-

35


ments the time increment is increased. Shorter time increment should be used because of

excessive overlapping between elements if time increment value is relatively large which

leads to numerical errors.

STEP 2: The collision of normal and shear springs is added between two elements.

The normal spring direction passes through the elements centroid, while shear spring di-

rection is tangent to the assumed entire circles. These springs exist if the elements are in

contact and removed after separation. When elements separate, residual tension is redis-

tributed by applying the forces in reverse direction. Set collision spring stiffness equal to

zero if separation occurs.

STEP 3: Finally the stiffness values are added in the global stiffness matrix.

STEP 4: Determine the resultant spring forces including forces from springs at location

of each element centroid. The geometrical residuals are calculated as,

Fg = F (t)−Mu− Cu− Fm (2.7)

Determine the new stiffness matrix for the new configuration.

STEP 5: Calculate the incremental displacement, velocity and acceleration for each

element in the next increment.

Based on the calculated displacement from collision, collision force is calculated as

follows:

The collision force is kn times to the relative displacement response at the contact

point.

2.4.6 Failure criteria

To determine the principal stresses at each spring location, the following technique is

used in this analysis. The shear and normal stress components (τ and σ1) at point A

are determined from the normal and shear springs attached at the contact point location

shown in figure 2.22 (a) & (b).

The secondary stress σ2 from normal stresses and at point B and C can be calculated

by using the equation given below:

σ2 =x

aσB +

a− xa

σC (2.8)

The principal tension is calculated as:

σP =σ1 + σ2

2+

√(σ1 − σ2

2)2 + τ 2 (2.9)

36


(a) (b)

Figure 2.22: (a) Principal Stress determination and (b) Redistribution of spring forces atelement edges

The value of principal stress (σP ) is compared with the tension resistance of the studied

material. When σP exceeds the critical value of tension resistance, the normal and shear

spring forces are redistributed in the next increment by applying the normal and shear

spring forces in the reverse direction. These redistributed forces are transferred to the

element center as a force and moment, and then these redistributed forces are applied to

the structure in the next increment.

When the element is subjected to shear, the crack propagation is mainly on shear

stress value. To represent the occurance of cracks, two techniques can be used. Among

these techniques, the one which we adopt is as follows:

It is assuming that failure inside the element is represented by failure of attached

springs (Hatem et al., 2000). If the spring gets failed, then the force in the spring is redis-

tributed. During this process, springs near the crack portion tend to fail easily. However,

the main disadvantage of this technique is that the crack width can not be calculated

accurately.

In each increment, stresses and strains are calculated for reinforcement and concrete

springs. In case of springs subjected to tension, the failure criterion is checked (refer

failure criteria).

2.4.7 Limitations

1. When the collision takes place, virtual collision springs are developed between the

collided elements. But virtual dampers were not provided in this model to describe

37


the collision behavior. These virtual collision springs and dampers together will

describe the collision behavior in numerical model.

2. Buckling of reinforcement was not included in this method.

2.5 Linear pounding analysis of structures

A study has been conducted in order to investigate the minimum separation distance

and structural pounding behavior between two adjacent structures using linear analysis.

Study on minimum separation distance is discussed in appendix-B. To study the linear

pounding behavior, structures with equal heights separated by 2 mm under Northridge

ground motion are considered in this analysis. The material and geometrical details of

the structures which are considered in this analysis are mentioned in previous section.

The behavior of structures at different slab levels are discussed in subsequent sections.

2.5.1 Structures with equal heights

Pounding doesn’t happen for the structures having same dynamic properties, even though

the separation distance is zero. When the response between two adjacent structures is

in same direction, those vibrations are called inphase vibrations and when they are in

opposite direction called as out-of-phase vibrations. Inphase or out-of-phase or both vi-

brations can occur during collision of structures. It depends on the dynamic properties

and velocities of the structures. It is difficult to find out whether the structures have

undergone inphase or out-of-phase during earthquake. During collision, there is sudden

change in velocity (vertical drop) in phase potrait diagrams and also have a great impact

on the structures.

A large amount of force is generated when two adjacent structures collide. This col-

lision/pounding force is dependent on many parameters like velocity of the structures,

stiffness provided between two structures and separation distance between them. Dur-

ing compression phase of collision, the force is getting increased from zero force and for

restitution phase, the force reduces to zero. The procedure for calculating the collision

response and force are described in earlier sections.

As inertia is main important criteria for accelerations, higher amplification pulses are

observed in acceleration when two structures collide. These amplification pulses cause

great damage to the structures. These pulses occur at the places where collision takes

place and will have short duration.

The present study is carried out in four cases: (1) single-single storey, (2) single-two

storey, (3) two-two storey and (4) two-three storey structural pounding. For the above

cases, the damping ratio is taken as 5%. The fundamental natural periods of the structure-

38


A and B are listed in table 2.2 given below:

Table 2.2: Fundamental period of the structures

Fundamental period (sec)Case Structure-A Structure-Bsingle-single 0.127 0.155single-two 0.127 0.304two-two 0.253 0.304two-three 0.253 0.334

Case-I: Structures with equal slab levels

(a) Single-single storey structural pounding

The analysis is carried out for the structures with equal slab levels. The time history

of pounding displacement responses and corresponding forces for the single-single storey

structures are shown in figure 2.23 to 2.24. Since the dynamic properties of the structures

are different, collision takes place between them. In practical situation, pounding between

adjacent buildings may also occur when the structures have same dynamic properties due

to time lag which depends mainly on the propagation of seismic waves. This effect is not

considered in this study. Structural pounding is mainly dependent on the input ground

motion and displacement response of the structures. From the analysis, the maximum

displacement response for structure-A and B are 0.0064 and 0.0083 m respectively. Since

flexible structure vibrates far from the dominant period of ground motion, the response

of flexible structure is more compared to stiffer structure. The response of structures

doesn’t change with their positions till they reach initial collision. It means if structure-A

is replaced by structure-B and vice versa, the responses will not change till first collision.

After first collision, the responses are catastrophic. But in case of nonlinear, the responses

are same till first collision starts or failure of spring, whichever comes first. The calculated

maximum collision force between them is 40.11x103 kN and the number of collisions are

30. At initial stage of collision, the collision force is less and its value is 15.44x103 kN. This

initial collision force may become maximum depending on response of both structures.

(b) Single-two storey structural pounding

Since structure-B is flexible, the displacement responses are higher than in single-single

storey structural pounding. The time history of pounding displacement responses and

corresponding forces for the single-two storey structures are shown in figure 2.25 to 2.26.

The maximum displacement response for structure-A and B are 0.0114 and 0.0112 m

respectively. When any one of the structures or both vibrate near to the dominant period

of the input ground motion, the response of flexible structure amplifies the response

39


Figure 2.23: Linear pounding response of two single storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

Figure 2.24: Pounding force between two single storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

40


of stiffer structure. If both structures vibrate far from dominant period, the response

of flexible structure will be more than stiffer one. From the analysis, structure-B is

vibrating near to dominant period of input ground motion, resulting high initial impact

force between the structures. Because of reduction in period ratio, the first collision force

increases to 18x103 kN. It means, as the period ratio approaches to zero, the first impact

force will be high. The maximum collision force between two structures is 58.76x103 kN.

The maximum pounding force between them is more than the force for single-single storey

structural pounding, because of flexibility and less separation distance.

Figure 2.25: Linear pounding response of single-two storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

(c) Two-two storey structural pounding

The fundamental period of the structure-A is changed to 0.253 sec. The time history of

pounding displacement responses and corresponding forces for the two-two storey struc-

tures are shown in figure 2.27 to 2.28. As both structures vibrate in the dominant fre-

quency of ground motion, the responses of structure are high. The maximum displacement

response for structure-A and B are 0.0330 and 0.0250 m respectively. The period ratio

of structure-A to B is 0.83. Here, the period ratio is increased due to change in storey

level of structure-A and fundamental period. As period ratio of structures increases, the

first collision force decreases to 15x103 kN. In case-I(a)&(b), the period ratio is decreased

from (a) to (b) due to structure-A. Because of decrease in period ratio, the first colli-

sion force increases. The maximum collision force between them is 147.30x103 kN. Since

41


Figure 2.26: Pounding force between single-two storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

both structures vibrate at the dominant frequency of ground motion, the displacement

responses are higher than in case-I(a)&(b). Here the response of structure-A is more than

structure-B. Because flexible structure amplifies the response of stiffer one.

(d) Two-three storey structural pounding

The fundamental period of the structure-B is changed to 0.334 sec. The time history

of pounding displacement responses and corresponding forces for the two-three storey

structures are shown in figure 2.29 to 2.30. The response of both structures are higher

than the response in case-I(a), (b) and (c). Because they vibrate at dominant frequency.


respectively. The response in the stiffer structure is more than the response in flexible

structure, because both structures vibrate in the dominant frequency. The period ratio of

the structures decreased to 0.75. Because of decrease in the period ratio, the first collision

force increased to 22x103 kN. The maximum collision force between them is 147.30x103

kN. In case of nonlinear, this maximum pounding force will be much higher than linear

case pounding which will be discuss in subsequent chapters. The maximum displacement

responses for structure-A and B, initial and maximum collision forces and number of

collisions are listed in table-2.3.

42


Figure 2.27: Linear pounding response of two-two storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

Figure 2.28: Pounding force between two-two storey structures separated by 2 mm sub-jected to Northridge ground motion (@ slab level 3.0 m)

43


Figure 2.29: Linear pounding response of two-three storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

Figure 2.30: Pounding force between two-three storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

44


Table 2.3: Maximum displacement response of structures, pounding forces and numberof collisions

Displacement response (m) Pounding force (MN) No. of collisionsCase Structure-A Structure-B First Maximumsingle-single 0.0064 0.0083 15.44 40.11 30single-two 0.0114 0.0112 18.00 58.76 44two-two 0.0330 0.0250 15.00 147.30 48two-three 0.0450 0.0200 22.00 175.1 30

Discussion on structures with equal slab levels

In this study, the analysis considered four different structures subjected to Northridge

ground motion. From the analysis, the response of stiffer structure is more than flexi-

ble structure, when structures vibrate at dominant frequency. Also, response of flexible

structure is more, when they vibrate at non-dominant frequency. As the period ratio

of structures increases, the first collision force decreases. But same collision force and

responses will not occur if position of structures are exchanged. It means, in case of ad-

jacent structures with different natural periods, the most affected are the rigid structures

irrespective of their position due to pounding. After first collision force, the response of

structures are catastrophic. The effect of pounding is less when the adjacent structures

having almost similar dynamic properties. Also, the larger the difference in the periods

of adjacent structures, the effect of pounding will be more. For the design of structures

against lateral loads, maximum pounding force is needed. In general, the adjacent struc-

tures are not at the same level. So it is necessary to understand the behavior of adjacent

structures at unequal levels.

2.5.2 Structures with unequal heights

Pounding of adjacent structures with unequal heights is the most critical case between ad-

jacent buildings and also a common problem in practice. To understand the pounding be-

havior of adjacent structures at unequal levels we consider four different structures(single-

single, single-two, two-two and two-three) with different slab levels(2.75 m, 3.25 m and 3.5

m) subjected to Northridge ground motion and the separation distance provided between

them is 2 mm.

The material properties and reinforcement details are same as mentioned earlier. The

geometry details of structure-B for all cases are as shown in fig 2.31 to 2.39. Also the

fundamental periods of structures are tabulated in table 2.4.

45


Figure 2.31: Geometry details of structure-B @2.75 m slab levels in the single storeystructure


Case-II: Structures with unequal slab levels


XAt 2.75 m slab level

In this analysis, the total height of the structure-B is 2.88 m. The time history of pounding

displacement responses and corresponding forces for the single-single storey structures at

2.75 m slab level are shown in figure 2.40 to 2.41. The maximum pounding displacement

response for structure-A and B are 0.0040 and 0.0070 m respectively. From the analysis,

the response of flexible structure is more compared to stiff structure because, structure-

46



Figure 2.34: Geometry details of structure-B @2.75 m slab levels in the two storey struc-ture

B vibrates at non-dominant period of ground motion. The first and maximum collision

force between them are 15x103 kN and 16.33x103 kN respectively. Here the slab level of

structure-B is located just below to the slab level of structure-A. The maximum displace-

ment responses for structure A and B are less compared with structures at equal slab

level because of reduction in the period of structure-B. Now the analysis move towards

to the slab level at 3.25 m.

47


Figure 2.35: Geometry details of structure-B @3.25 m slab levels in the two storey struc-ture

Figure 2.36: Geometry details of structure-B @3.5 m slab levels in the two storey structure

Single-single storey structural pounding at 3.25 m slab level

Here the slab level of structure-B is located just above to the slab level of structure-A.

The time history of pounding displacement responses and corresponding forces for the

48


Figure 2.37: Geometry details of structure-B @2.75 m slab levels in the three storeystructure

Table 2.4: Fundamental period of the structures at different slab levels

Fundamental period (sec)Structure-A Structure-B

Case @ 3.0 m @ 2.75 m @ 3.25 m @ 3.50 msingle-single 0.127 0.143 0.181 0.200single-two 0.127 0.273 0.342 0.360two-two 0.253 0.273 0.342 0.360two-three 0.253 0.380 0.413 0.430

single-single storey structures at 3.25 m slab level are shown in figure 2.42 to 2.43. Since

the structure is vibrating predominantly in the first mode, the response of the structure-B

is less at 3.0 m level. The maximum displacement response for structure-A and B are

0.0063 and 0.0061 m respectively. The maximum collision force between them is 29.34x103

kN. As structure-B is flexible than structure placed at 2.75 m level, the collision force is

slightly higher. Now the analysis move towards to the slab level at 3.50 m.

49


Figure 2.38: Geometry details of structure-B @3.25 m slab levels in the three storeystructure

Single-single storey structural pounding at 3.50 m slab level

In this analysis, the height of the structure-B changes keeping the height of structure-A

constant. The time history of pounding displacement responses and corresponding forces

for the single-single storey structures at 3.25 m slab level are shown in figure 2.44 to 2.45.


respectively. The maximum collision force between them is 16.33x103 kN. Here the slab

level of structure-B is located just below to the slab level of structure-A. The maximum

displacement responses for structure A and B are less compared with structures at equal

slab level because of reduction in the period of structure-B. The summary of all the cases

is tabulated in table 2.5.

In case of unequal slab levels, local damage occurs to the exterior column of the taller

structure due to shorter structure.

2.6 Summary

In this analysis, structures with equal storey heights are considered which are separated

from Australia, Canada, Egypt, Ethiopia, Greece, India, Mexico, Nepal, Peru, Serbia and

50


Figure 2.39: Geometry details of structure-B @3.5 m slab levels in the three storey struc-ture

Taiwan country codal provisions on separation distance. These structures are subjected

to ground motions (Ref. table 2.1) having PGA ranges from 0.25-0.54 g. Using AEM,

parametric study (Ref. Appendix-B) has been conducted on separation distances. These

separation distances are modified with factors if the provided separation distance from

codes are not sufficient for the structures.

To study the linear pounding behavior, equal and unequal heights are considered under

Northridge ground motion. From the analysis results, the displacement response of stiff

structure is more than flexible structure, when they vibrate at dominant frequency. Also,

the displacement response of flexible structure is more, when they vibrate at non-dominant

frequency.

51




52




53




54


Table 2.5: Maximum displacement response of structures, pounding forces and numberof collisions

Displacement response (m) Pounding force (MN) No. of collisionsCase Structure-A Structure-B First Maximumsingle-single@ 2.75 m 0.0040 0.0070 15.00 16.33 6@ 3.25 m 0.0063 0.0061 25.00 29.34 32@ 3.50 m 0.0082 0.0086 19.20 54.85 40single-two@ 2.75 m 0.0140 0.0100 16.64 48.00 38@ 3.25 m 0.0115 0.0118 18.22 64.20 40@ 3.50 m 0.0108 0.0139 18.20 73.30 48two-two@ 2.75 m 0.0286 0.0285 22.60 27.56 34@ 3.25 m 0.0292 0.0299 16.20 57.30 42@ 3.50 m 0.0350 0.0360 18.10 33.51 40two-three@ 2.75 m 0.0440 0.0450 23.40 48.80 34@ 3.25 m 0.0420 0.0440 25.20 234.0 36@ 3.50 m 0.0440 0.0446 25.70 44.40 48

55

Chapter 3

Pounding Analysis With Equal

Heights

3.1 Introduction

The analysis for providing minimum separation distance without pounding was discussed

in Appendix-B. To study the structural pounding behavior of adjacent structures, different

structures with equal roof levels are considered in this chapter. Also explained about

damage analysis during pounding.

3.2 Non-linear analysis of pounding

In order to achieve a safe economical seismic structural design during seismic events,

nonlinear analysis is essential. To investigate the structural pounding behavior using

nonlinear analysis, a study has been conducted on the structures with equal heights

separated by 2 mm under Northridge ground motion. The material and geometrical

details of the structures which are considered in this analysis are mentioned in chapter-2.

Also discussed about the material model and failure criteria of the material in the previous

chapter. The analysis is carried out for structures(single-single, single-two, two-two and

two-three) with equal heights.

Case-I: Structures with equal slab levels


In order to achieve a safe structural pounding during earthquakes, a correct seismic anal-

ysis should take into account by means of nonlinear time history analysis. The nonlinear

behavior of structures will be same as linear, till failure of first spring in the structures.

This failure of spring occurred, when the principle stress of spring exceeds the tensile

resistance value. Also the forces in normal and shear spring are redistributed in next

increment by applying the forces in opposite direction. The stiffness of the structure will

reduce when the spring has failed. Because of reduction in stiffness, the frequency of

56

CHAPTER 3. POUNDING ANALYSIS WITH EQUAL HEIGHTS

structure will come down and structure vibrates with lesser frequency than fundamental

frequency of structure. The pounding displacement responses and corresponding forces

for structure-A & B are shown in figure 3.1 to 3.2. From the result, structure-B is vibrat-

ing with lesser frequency compared to structure-A. Also, pounding increases the response

of flexible structure(structure-B) because, both structures vibrate in non-dominant fre-

quency.

Here, the first spring has failed at the column base(3.71 m, 0.06 m) of second structure.

The first collision occurred after failure of spring. Since the first collision occurred after

failure of springs, the first collision force is not equal to the force obtained from linear

analysis. The magnitude of collision forces and accelerations are less compared to linear

analysis. The maximum displacement responses for structure-A and B are 0.092 m and

0.098 m respectively. These responses are 5-10 times more than the responses obtained

from linear analysis. The first and maximum collision forces are 14.57x103 and 23.22x103

kN respectively.

Figure 3.1: Pounding nonlinear response of two single storey structures separated by 2mm subjected to Northridge ground motion (@ slab level 3.0 m)

(b) Single-two storey structural pounding

A two storey structure with period 0.304 sec is considered in this analysis. The nonlinear

responses for structure-A and B are similar as linear analysis till first collision. The

pounding displacement responses and corresponding forces for structure-A & B are shown

57



in figure 3.3 to 3.4 respectively. During this process, the first spring has failed at beam

location(3.72 m, 3.11 m) of structure-B and the force generated between them is 18x103

kN which is equal to the first collision force in linear analysis. Because of failure of springs,

both structures vibrate at lesser frequency than fundamental frequency of structures and

structure-B frequency is lesser than structure-A frequency. The maximum displacement

responses for structure-A and B are 0.126 and 0.127 m respectively. The response of

structures are more than the responses from case-I(a), because of increase in flexibility

of structure-B. Also structure-B is responding at dominant frequency. The nonlinear

responses for both structures are nearly 10 times more than the responses obtained from

linear analysis. The maximum collision force between them is 35x103 kN, also number

of occurances of collisions are less than linear case. From figure 3.4, the duration of last

collision is around 2 sec. It is because of more intact time for both structures.

(c) Two-two storey structural pounding

Two two storey structures having period of 0.253 sec and 0.304 sec are considered in this

analysis. The pounding displacement responses and corresponding forces for structure-A

& B are shown in figure 3.5 to 3.6 respectively. The maximum displacement responses for

structure-A and B are 0.20 and 0.19 m. Since both structures are vibrating at dominant

frequency, the response for flexible structure is lesser than stiff structure. Whereas, in

the above two cases(I(a) & (b)) the response of flexible structure was more compared to

58


Figure 3.3: Pounding nonlinear response of single-two storey structures separated by 2mm subjected to Northridge ground motion (@ slab level 3.0 m)

Figure 3.4: Pounding force between single-two storey structures separated by 2 mm sub-jected to Northridge ground motion (@ slab level 3.0 m)

59


stiff structure because, they vibrate at non-dominant frequency. Also, the response for

both structures are similar till first failure or collision. The first collision force generated

between them is same as the force in linear case and its magnitude is 15x103 kN. During

initial collision, failure of spring occurred at beam location(0.24 m, 3.10 m) of structure-A.

Because of this failure, both structures vibrate at lesser frequencies. But the maximum

collision force depends on displacement and velocity of the structure. Since the separation

distance and input ground motion are same for all the cases, the maximum collision forces

are increased as the flexibility of the structures increases. The maximum collision force

between them is 73.12x103 kN and also the number of collisions are less than linear case.

Figure 3.5: Pounding nonlinear response of two-two storey structures separated by 2 mmsubjected to Northridge ground motion (@ slab level 3.0 m)

(d) Two-three storey structural pounding

A two storey structure with period 0.304 sec is considered in this analysis. The pounding

displacement responses and corresponding forces for structure-A & B are shown in figure

3.7 to 3.8 respectively. The maximum displacement responses for structure-A and B are

0.246 and 0.210 m respectively. Since the structures are vibrating at dominant period,

the response of flexible structure is lesser than stiff structure. During collision between

two structures, the first spring has failed at beam location(6.78 m, 3.11 m) of structure-

A. This is because of reduction in stiffness of structure. The maximum collision force

is much higher than case-I(a), (b) and (c) due to less separation distance, more flexible

structures and high velocities of structures during motion. The damage will also be higher

60



for structures than the damage for case-I(a), (b) and (c) structures which will be discussed

in damage analysis. The maximum collision force between them is 267.5x103 kN and also

the number of collisions are less than linear case. The brief overview of structures which

are discussed above are summarized and tabulated below:

Table 3.1: Maximum nonlinear displacement response of structures, pounding forces andnumber of collisions

Displacement response (m) Pounding force (MN) No. of collisionsCase Structure-1 Structure-2 First Maximumsingle-single 0.0926 0.0979 14.57 23.22 2single-two 0.1260 0.1271 18.00 35.00 8two-two 0.2000 0.1900 15.00 73.12 16two-three 0.2460 0.2100 22.00 267.5 8

Discussion

This analysis considered four different cases with different structures to study the pound-

ing behavior. This behavior is similar as linear till failure of either first spring or first

collision. The responses for flexible structures are less compared to stiff structures when

structures vibrate at dominant period and also the responses for flexible structures are

61


Figure 3.7: Pounding nonlinear response of two-three storey structures separated by 2mm subjected to Northridge ground motion (@ slab level 3.0 m)

Figure 3.8: Pounding force between two-three storey structures separated by 2 mm sub-jected to Northridge ground motion (@ slab level 3.0 m)

62


more when structures vibrate at non-dominant period. Almost every structure vibrate at

lesser frequencies because of failure of springs. The maximum pounding forces increases,

as the period of structure increases with the same separation distance. The quantification

of damage will be discussed in next section.

3.3 Damage analysis

From the past earthquakes such as 1991 Uttarkasi earthquake, 1993 Killari earthquake,

1997 Jabalpur earthquake, 1999 Chamoli earthquake, 2001 Bhuj earthquake and 2006

Sikkim earthquake it has been observed that the potential damage for RC structures is

more due strong ground shaking. In order to implement seismic safety for RC structures,

the quantitative analysis of structural damage is necessary. In this section, the quantifi-

cation of damage is proposed interms of stiffness and strength degradation for structures

under Northridge ground motion.

3.3.1 Damage model

In case of concrete structures, damage indices has been developed to provide a way to

quantify numerically the seismic damage sustained by individual elements, storeys or

complete structures. These indices are based on the results of a nonlinear dynamic anal-

ysis during an earthquake or on a comparison of a structure’s physical properties before

and after an earthquake. The brief decription about Park-Ang damage model is as follows:

Under seismic loading, RC structures are generally getting damaged. This damage

of RC structures can be expressed as a linear combination of maximum deformation and

absorbed hysteretic energy. Park et al., (1985) expressed seismic structural damage as

follows:

D =xmxu

+ βEH

Qyxu(3.1)

Where, xm is the maximum displacement that the linear equivalent linear SDOF sys-

tem would be subjected to during the base excitation, xu(=µ xy where µ is the ductility)

is the ultimate displacement of the system under monotonic loading, β represents the

effect of cyclic loading on structural damage, EH represents the total energy dissipation

in the structure during excitaiton and Qy is the yield strength of the structure. Later it

was modified by Kunnath (Ramancharla, 1997) and is as follows:

D =xm − xyxu − xy

+ βEH

Qyxu(3.2)

In the above equation, the first term doesn’t take an account of cumulative damage

whereas the second term does. The advantage of this model is its simplicity. In this

study, eq 3.2 is used for estimating the amount of damage. In 1985 Park et.al proposed

regression equations for strength detoriation parameter β, interms of numerical variables

63


including shear span ratio, axial load, longitudinal and confining reinforcement ratios and

material strengths.

Generally in RC structures, failure occurs at beam-column joints. Hence it is necessary

to find out the global damage of the structure. It is to be obtained as the summation of

local damage. The global damage (Gomez et al., 1990) is estimated as follows:

Dg =

∑ni=1DiEi∑ni=1Ei

(3.3)

Where, Di is the local damage index at ith location, Ei is the energy dissipated at ith

location and n is the number of locations at which the local damage computed.

3.3.2 Damage calculation

Damage index is one of the parameters which describes the state of structures. In this

analysis, global damage of structure is calculated. The ductility (Paulay et al., 1992)

values calculated for the beam and column members in a single storey structure(Ref.

2.2.1) are 1.85 and 1.84 respectively. β is a component which is obtained from test data.

Mathematically, the β value can be found out from the below equation:

β = (−0.447 + 0.73l

d+ 0.24no + 0.314Pt)0.7

ρω (3.4)

Where, ld

is shear span ratio, Pt is longitudinal steel ratio, no is axial stress and ρω is

confinement ratio. Generally β ranges from -0.2 - 2.0. Park et al., (1985) established the

value of β is of the order of 0.05 for reinforced concrete members. In this study the value of

β is taken as 0.05. Yielding of the reinforced concrete is defined as when the extreme fibre

compressive strain in the concrete exceeds 1.5 times the crushing strain. Theoretically,

the yield deformation is the combination of deformation due to flexural component, bond

slippage of the reinforcing bar from anchorage, inelastic and elastic shear deformation.

The yield displacement obtained from the above relation is 0.01 m. The local and global

damage of the single-storey structure(Ref. 2.2.1) are calculated using eq 3.2 and 3.3. The

global damage of the structure is 3.0 under Northridge ground motion. It is dependent on

crack length, width and location of crack such as beam column joint, base of column etc.

The damage values are not same for all the structural members. Depending on location

of crack, the damage value changes. A damage scale has been introduced for estimating

damage interms of stiffness and strength degradation.

3.3.3 Proposed damage scale

In this analysis, a damage scale has been proposed for the structures which are mentioned

earlier. The load-displacement plot has drawn for each structure till collapse. The collapse

of the structure might be stiffness or strength degradation. The actual load-displacement

64


plot is smoothened using smoothing techniques. The damage state of structure can be

found out from smooth curve. Now the whole curve is divided into two categories. (i)

Based on stiffness degradation-the range is from zero to maximum loading and (ii) strength

degradation-the range is from maximum loading to complete failure of structure. From

the displacement response of each structure, the end response is considered. If the end

response is at category-1, the damage of structure will be from stiffness degradation. Oth-

erwise, it will be from strength degradation.

From the figure 3.9, it has been observed that as the applied displacement on structure

increases, the lateral load also increases till the displacement reaches 0.04 m. Continuous

failure of springs are observed up to 0.055 m. It means that damage has taken place in

the structure. Thereafter, readjustment of particles in the structure takes place. Since

the analysis allows failure of the reinforcement also, it occurred in the structure at 0.218

m. Because of failure in the reinforcement at critical locations, the load drastically comes

down with small increment in the displacement. Thereafter, no failure in reinforcement

is observed till 0.23 m. There might be a possibility of more number of reinforcement bar

failures at single increment also. From figure 3.1, the end response of structure-A is 0.075

m. The initial stiffness of structure-A is 1.161x104 kN/m. From figure 3.9, the decrease

in stiffness at 0.075 m is 17.3%. Now the end response of structure-A has come under

category-1. From this analysis, one can able to find out that the structure has under gone

stiffness or strength degradation without much doing the analysis. The same analysis is

carried out for the remaining structures and the load vs displacement curves are shown

in figure 3.10 to 3.13. The stiffness degradation for all structures which are considered in

this analysis are tabulated below:

Table 3.2: Stiffness degradation for different structures during pounding

Stiffness DegradationCase Structure-1 Structure-2single-single 17.3 1.3single-two 2.16 3.5two-two 3.1 2.7two-three 3.4 5.5

3.4 Summary

This study is carried out four(single-single, single-two, two-two and two-three storey)

structures under Northridge ground motion with equal heights. To study the pounding

behavior, nonlinear analysis is conducted on the structures. The behavior of the structures

is similar to linear behavior till failure of either first spring or first collision. Because of

springs failure, structures vibrate at lesser frequency and also reduce the pounding force.

65


Figure 3.9: Load vs displacement curve for structure having a period of 0.127 sec


The damage is proposed interms of stiffness degradation for all the structures.

66




67



68

Chapter 4

Pounding Analysis With Un-equal

Heights

4.1 Introduction

Most of the studies on pounding are with buildings that have equal storey levels. In

general, the slabs of structure hit the columns of other structure which are very common

pounding cases during earthquakes. The case of colliding structures with unequal heights

has not yet been studied effectively. In this chapter, different buildings with unequal

roof levels of different storey heights are considered. The analysis is carried out for the

buildings to study the damage due to pounding.

4.2 Pounding analysis for structures with un-equal

heights

In this case, nonlinear analysis is considered for the structures with unequal heights sepa-

rated by 2 mm subjected to Northridge ground motion. The geometry details of structures

are discussed in chapter-2. For nonlinear analysis the material model and failure criteria

(Hatem, 1998) has already been discussed in chapter-2. The analysis considers fourteen

different structures with different heights subjected to Northridge ground motion.

4.2.1 Single-single storey structural pounding

XAt 2.75 m slab level:

In this analysis, structure-B is kept just below to the slab level of structure-A. The pound-

ing displacement responses and corresponding forces for structure-A & B are shown in

fig 4.1 to 4.2 respectively. From results, the maximum pounding displacement responses

for structure-A and B are 0.084 m and 0.106 m respectively. The maximum response

of flexible structure is more than stiff structure, because both structures vibrate at non-

dominant period of ground motion. From these pounding responses collision force will

69

CHAPTER 4. POUNDING ANALYSIS WITH UN-EQUAL HEIGHTS

generate. From the results of equal slab levels, it is clearly shows that the first collision

forces are more in case of unequal slab levels. After first collision, the behavior is catas-

trophic. In case of unequal storey levels, the shear on the column will be more than the

shear at equal slab levels. This shear force may change at different height levels of the

same structure which depends on the pounding response of the structures. This shear

amplification will cause more damage to the column member. The first collision force

between them is 18x103 kN which occured after failure of first spring. It has failed at the

base(3.71 m, 0.06 m) of structure-B.



In this analysis, structure-B is kept just above to the slab level of structure-A. The

pounding displacement responses and corresponding forces for structure-A & B are shown

in fig 4.3 to 4.4 respectively. From results, the maximum pounding displacement responses

for structure-A & B are 0.103 m and 0.107 m respectively. The maximum pounding

response of flexible structure is more than stiff structure, because both structures vibrate

at non-dominant period of ground motion. The first spring has failed at the base(3.71 m,

0.06 m) of structure-B. The stiffness of the structure gets reduced because of failure of

spring which causes the first collision force between them and its magnitude is 19.30x103

kN. Also this collision force is less than the force obtained from linear analysis. If the

first spring has failed after first collision, the collision force from nonlinear analysis would

70



be same as linear analysis. Because of nonlinearity, both structures vibrate at lesser

frequencies.


In this analysis, the slab level of structure-B is kept at 3.50 m. The pounding displace-

ment responses and corresponding forces for structure-A & B are shown in fig 4.5 to 4.6

respectively. From results, the maximum pounding displacement responses for structure-

A & B are 0.107 m and 0.104 m respectively. The maximum response of stiff structure is

more than flexible structure because structure-B vibrates at dominant period of ground

motion. The first collision force generated between them is 16.20x103 kN. Because of this

force, the response of stiffer structure gets amplified. The collision force is less than the

force obtained from linear analysis. The first spring has failed at the base(3.71 m, 0.06

m) of structure-B. Because of nonlinearity, both structures vibrate at lesser frequencies.

Discussion:

In this analysis, two single storey structures are considered with unequal heights. From

the results, we can conclude that the response of stiff structure is more than flexible

structure at dominant period of ground motion irrespective of equal and unequal levels.

If the structures vibrate at non-dominant period of ground motion then, the response of

flexible structure will be more than stiff structure. In case of equal slab levels, the collision

71




72




73


between slab to slab is a rigid body motion whereas, for unequal levels the interaction

is in between slab to column. During this interaction, shear causes more damage to the

column which leads to collapse of structure.

4.2.2 Single-two storey structural pounding


The same analysis is for single-two storey structures. Now the storey height of structure-

B is kept as 2.75 m which is just below to the slab level of structure-A. The pounding

displacement responses and corresponding forces for structure-A & B are shown in fig

4.7 to 4.8 respectively. From results, the maximum pounding displacement response for

structure-A & B are 0.115 m and 0.102 m respectively. Since structure-B is vibrating at

dominant period of ground motion, the response of stiff structure is more than flexible

structure. Whereas, in the earlier case(single-single) the response of flexible structure

is more because of non-dominant period of ground motion. The initial collision force

generated between them is 16.80x103 kN which is almost similar as linear analysis. This

force occurred during failure of springs and the initial spring has failed at column level(3.72

m, 2.86 m) of structure-B. The maximum collision force between them is 80x103 kN. Due

to reduction in stiffness, structures vibrate at lesser frequencies.


74


Figure 4.8: Pounding force between single-two storey structures separated by 2 mm sub-jected to Northridge ground motion (@ slab level 2.75 m)


The storey height of structure-B is kept at 3.25 m which is just above to the slab level of

structure-A. The pounding displacement responses and corresponding forces for structure-

A & B are shown in fig 4.9 to 4.10 respectively. From results, the maximum pounding

displacement responses for structure-A & B are 0.128 m and 0.132 m respectively. Even

though structure-B is vibrating at dominant period of ground motion, the response of

flexible structure is more compared to stiff structure. But the difference in the responses is

less. In case of structure(single-two) with equal levels, the amplification in stiff structure is

more comapred to flexible structure. The initial collision force between them is 18.20x103

kN which is almost similar to the collision from linear analysis. This force occurred

during failure of springs. The initial spring has failed at the column level(3.72 m, 3.33 m)

of structure-B. Due to reduction in stiffness structures vibrate at lesser frequencies. The

maximum collision force between them is 54.10x103 kN.


The storey height of structure-B is kept at 3.50 m. The pounding displacement responses

and corresponding forces for structure-A & B are shown in fig 4.11 to 4.12 respectively.

From results, the maximum pounding displacement responses for structure-A & B are

0.124 m and 0.123 m respectively. Since structure-B is vibrating at dominant period of

ground motion, response amplification in stiff structure is more. Depending on structural

75




76


properties and response of structures, the initial collision force changes. During failure

of spring at column level(6.72 m, 3.47 m), the first collision force generated between

them is 18.10x103 kN. Because of reduction in stiffness, both structures vibrate at lesser

frequencies. The maximum collision force between them is 19.92x103 kN. The maximum

collision force between them is 54.10x103 kN.


XDiscussion:

In this analysis single-two storey structures are considered with unequal heights. In most

of the cases, flexible structures amplifies the response of stiff structure because of dominant

period of ground motion. The number of occurrances of collisions are also decreased when

compared with linear analysis. This is due to vibration of structures at lesser frequencies.

In case of single-single(Ref. 4.2.1) structural pounding, initial pounding forces are different

than linear analysis. This is because of reduction in stiffness before first collision.

4.2.3 Two-two storey structural pounding


The analysis is carriedout for two-two storey structures with a storey height of 2.75 m.

The pounding displacement responses and corresponding forces for structure-A & B are

77



shown in fig 4.13 to 4.14 respectively. From results, the maximum responses for structure-

A & B are 0.195 m and 0.185 m respectively. Because of non-dominant period of ground

motion, the response of stiff structure gets amplified. The first spring has failed at the

column level(0.24 m, 3.10 m) of structure-A which causes the initial collision force with

magnitude of 15.50x103 kN. The initial collision force from linear analysis is different from

nonlinear analysis. This is due to failure of first spring before collision. The stiffness of

structure gets reduced because of failure of springs resulting structures vibrate at lesser

frequencies.


The storey height of structure-B is kept at 3.25 m which is just above to the slab level of

structure-A. The pounding displacement responses and corresponding forces for structure-

A & B are shown in fig 4.15 to 4.16 respectively. From results, the maximum pounding

displacement responses for structure-A & B are 0.218 m and 0.217 m respectively. Here,

the maximum responses for both structures are same even though they vibrate at domi-

nant period of ground motion. Whereas, in the above two cases(single-single, single-two)

the maximum responses for flexible structure are more. The initial collision force between

them is 15.80x103 kN. This force occurred during failure of springs. The initial spring has

failed at the column level(0.24 m, 3.10 m) of structure-A. Due to reduction in stiffness

structures vibrate at lesser frequencies. The maximum collision force between them is

78


Figure 4.13: Pounding nonlinear response of two-two storey structures separated by 2mm subjected to Northridge ground motion (@ slab level 2.75 m)


79


70x103 kN.



The storey height of structure-B is kept at 3.50 m. The pounding displacement responses

and corresponding forces for structure-A & B are shown in fig 4.17 to 4.18 respectively.

From results, the maximum pounding displacement responses for structure-A & B are

0.216 m and 0.215 m respectively. Here, the maximum responses for both structures

are same even though they vibrate at dominant period of ground motion. Depending on

structural properties and response of structures, the initial collision force changes. During

failure of spring at column level(6.72 m, 3.47 m), the first collision force generated between

them is 17.50x103 kN. Because of reduction in stiffness, both structures vibrate at lesser

frequencies. The maximum collision force between them is 136.80x103 kN.

XDiscussion:

In this analysis, two-two storey structures are considered with unequal heights. From the

results, we can conclude that the response of stiff structure is more than flexible structure

at dominant period of ground motion irrespective of equal and unequal levels. But the

initial collision force changes at different levels. These are dependent on the response of

both structures and are less than from linear analysis. The initial collision occurs during

80




81



failure of springs at 3.25 m and 2.75 m. After initial collision, the response of structures

are catastrophic. Due to this, the maximum collision force would be high value.

4.2.4 Two-three storey structural pounding


The same analysis is carriedout for two-three storey structures. Now the storey height

of structure-B is kept as 2.75 m which is just below to the slab level of structure-A.

The pounding displacement responses and corresponding forces for structure-A & B are

shown in fig 4.19 to 4.20 respectively. From results, the maximum pounding displacement

response for structure-A & B are 0.225 m and 0.190 m respectively. Since structure-B

is vibrating at dominant period of ground motion, the response of stiff structure is more

than flexible structure. Except single-single storey structural pounding, in all other cases,

the response of stiff structures is more compared to flexible structures. This is because

of dominant vibration of ground motion. The initial collision force generated between

them is 25.95x103 kN. This force occurred during failure of springs and the initial spring

has failed at column level(6.78 m, 2.87 m) of structure-B. The maximum collision force

between them is 25.95x103 kN. This means that the maximum force and initial force are

equal. Due to reduction in stiffness, structures vibrate at lesser frequencies.

82




83



In this analysis, structure-B is kept just above to the slab level of structure-A. The pound-

ing displacement responses and corresponding forces for structure-A & B are shown in fig

4.21 to 4.22 respectively. From results, the maximum pounding displacement responses

for structure-A & B are 0.217 m and 0.216 m respectively. The maximum pounding re-

sponse of stiff structure is more than flexible structure, because both structures vibrate

at dominant period of ground motion. The first spring has failed at the base(6.78 m, 3.35

m) of structure-B. The stiffness of the structure gets reduced because of failure of spring

which causes the first collision force between them and its magnitude is 25.40x103 kN. Also

this collision force is less than the force obtained from linear analysis. If the first spring

has failed after first collision, the collision force from nonlinear analysis would be same as

linear analysis. Because of nonlinearity, both structures vibrate at lesser frequencies.



In this analysis, the slab level of structure-B is kept at 3.50 m. The pounding displacement

responses and corresponding forces for structure-A & B are shown in fig 4.23 to 4.24

respectively. From results, the maximum pounding displacement responses for structure-

A & B are 0.223 m and 0.222 m respectively. The maximum response of stiff structure is

more than flexible structure because structure-B vibrates at dominant period of ground

motion. The first collision force generated between them is 25.37x103 kN. Because of this

84



force, the response of stiff structure gets amplified. The collision force is less than the

force obtained from linear analysis. The first spring has failed at the base(6.78 m, 3.59

m) of structure-B. Because of nonlinearity, both structures vibrate at lesser frequencies.

Discussion:

In this analysis, two-three storey structures are considered with unequal heights. From

the results, we can conclude that the response of stiff structure is more than flexible

structure at dominant period of ground motion irrespective of equal and unequal levels.

If the structures vibrate at non-dominant period of ground motion then, the response of

flexible structure will be more than stiff structure. The summary of all cases are tabulated

in table 4.1.

4.3 Summary

The analysis considered for the structures under Northridge ground motion with unequal

heights. The nonlinear pounding responses are higher than linear responses because of re-

duction in stiffness. The pounding forces produced by two adjacent structures are higher

than forces from linear case. The maximum collision forces are different due to catas-

trophic behavior of structures after first collision. This can be clearly seen from table 4.1.

The maximum pounding responses are more for stiffer structures, when they vibrate at

85




86


Table 4.1: Maximum nonlinear displacement response of structures, pounding forces andnumber of collisions for structures with unequal heights

Displacement response (m) Pounding force (MN) No. of collisionsCase Structure-1 Structure-2 First Maximumsingle-single@ 2.75 m 0.084 0.106 18.00 22.83 6@ 3.25 m 0.103 0.107 19.30 58.05 6@ 3.50 m 0.107 0.104 16.20 16.23 14single-two@ 2.75 m 0.115 0.102 16.80 80.00 8@ 3.25 m 0.128 0.132 18.20 54.10 6@ 3.50 m 0.124 0.123 18.10 19.92 10two-two@ 2.75 m 0.195 0.185 15.50 116.30 10@ 3.25 m 0.218 0.217 15.80 70.00 6@ 3.50 m 0.216 0.215 17.50 136.80 16two-three@ 2.75 m 0.225 0.190 25.95 25.95 8@ 3.25 m 0.217 0.216 25.40 26.65 8@ 3.50 m 0.223 0.222 25.37 64.50 6

predominant frequency of ground motion irrespective of equal or unequal slab levels.

87

Chapter 5

3D Analysis of Pounding

5.1 Introduction

Numerical simulation of contact between two adjacent structures under the action of

seismic load involves many complexities. The methods for solving contact problems can

be categorize into mass to mass, node to node and node to surface contact(i.e., arbitrary

contact in 3D). The objective of this chapter is to study the torsional pounding behavior

of adjacent structures subjected to El-centro ground motion.

5.2 Modeling of structures in 3D

5.2.1 Geometry and material details

The analysis considers two single storey structures with symmetric (structure-A) and

asymmetric (structure-B) configuration. Different setback levels (1.5 m, 3.0 m and 6.0

m) and structure at different height levels (at (2/4)th and (3/4)th of column height) are

considered in this study. The modeling of structures has done using SAP 2000 (CSI).

The total height for both structures is 3 m. The thickness of the slab is 0.12 m and the

dimensions for all columns are 0.24 x 0.24 m. The slab dimensions for both structures are

taken as 6 x 6 m. It is assumed that the live load acting on the structure-A is 2 kN/m2.

To study the torsional behavior of structures due to pounding an eccentricity is provided

in both x and y directions for structure-B. The centre of mass (CM) and centre of stiffness

(CS) for structure-B are (2.7 m, 3.3 m) and (3.0 m, 3.0 m) respectively. An additional

load of 4 kN/m2 is provided at top left corner of slab portion for structure-B. The plan

and elevation view of structures are shown in fig 5.1.

The material properties such as grade of concrete, grade of steel reinforcement and

poission’s ratio are same as mentioned in chapter-2. The details of gap element model and

material model used for nonlinearity in SAP 2000 are described in the following sections.

88

CHAPTER 5. 3D ANALYSIS OF POUNDING

Figure 5.1: Geometry details of structures

5.2.2 Gap element model

Gap joint element is an element which connects two adjacent nodes to model the contact.

This is activated when structures come closer and deactivate when they go far away. A

collision force will be generated when they come closer. From figure 5.2, it is shown

that, the gap element will activate if ’open’ is equal to zero. In SAP modeling each

element is assumed to be composed of six separate springs with six deformational degree

89


of freedom (DOF) as shown in fig 5.3. Every DOF may has linear effective stiffness and

damping properties. The mass contributed by the link or support element is lumped

at the joints i & j and half of the mass is assigned to the three translational degrees

of freedom at each of the elements joint. No inertial effects are considered within the

element itself. Generally the effective stiffness value is in a range from 102 to 104 times

more than the stiffness in any connected elements. Larger values of effective stiffness may

leads to numerical difficulties during solution. During nonlinear analysis, the nonlinear

force-deformation relationships are used at all degrees of freedom for which nonlinear

properties were specified. For all other degrees of freedom, the linear effective stiffnesses

are used during a nonlinear analysis. The results for linear analyses are based upon linear

effective stiffness and damping properties. Only the results for nonlinear analysis cases

include the nonlinear behavior. The force-deformation relationship is as follows:

f =

k(d+ open), if(d+ open) < 0

0, otherwise(5.1)

Where, k is spring constant, open is the gap opening which must be positive or zero

and d is the relative deformation across the spring.

Figure 5.2: Gap-joint element from SAP 2000

Figure 5.3: Link element internal forces and moments at the joints

90


5.2.3 Non-linear analysis of pounding

To study torsional pounding between the structures, different setbacks are considered in

this analysis. The separation distance between two adjacent structures as 0.01 m. The

structures which are considered in this analysis are subjected to El-centro ground motion

and gap element is provided between them. The stiffness of gap element is 477.6x103

kN/m (Muthukumar et al., 2004). The fundamental natural periods of structure-A & B

are 0.176 and 0.217 sec respectively which are far from predominant period of the ground

motion.

Case-I: Different setback

(a) At setback of 1.5 m

The analysis is carried out for structures with setback of 1.5 m. The structures have re-

sponses in both x and y directions, though the ground motion is restricted to x-direction.

This is because of un-symmetric mass properties about X & Y axes. The pounding at top

edge of structure-B is referred as location ’Ct’ and the bottom edge of structure-A is re-

ferred as location ’Cb’ (Ref. fig 5.1). The maximum pounding responses at location Ct for

structure-A and B are 0.0351 m and 0.043 m respectively. The pounding responses would

be more if structures vibrate near to the predominant period of ground motion. In this

case, both structures vibrate far from predominant period of ground motion. Resulting

more response in flexible structure compared to stiff structure. During vibration, the re-

sponse of structure-A in y-direction is amplified due to collision between structure-A & B.

The maximum pounding responses for structure-A and B in y-direction are 0.00138 m and

0.0073 m respectively. From results, it has been clearly observed that the responses for

stiffer structure get amplified due to collision between them. Also, structure-B vibrates at

lesser frequency because of reduction in stiffness. The maximum pounding force between

them is 53.16 kN. The displacement responses for structure-A & B in x-y directions and

collision forces are shown from fig 5.4 to 5.6.

Due to unsymmetrical mass property of structure-B, the possible pounding may occur

at Cb also. From the results, the maximum responses of structure-A & B in X and Y

directions are 0.0344 m, 0.033 m, 0.00138 m and 0.0073 m respectively. It is clearly

show that the maximum pounding responses at Ct and Cb are same in Y-direction. The

displacement responses for structure-A & B in x-y directions and collision forces are shown

from fig 5.7 to 5.8.

(b) At setback of 3.0 m

The similar analysis is carried out for structures with setback of 3.0 m. The maximum

pounding responses at location Ct for structure-A and B are 0.0347 m and 0.0432 m

respectively. The response of flexible structure is more compared to flexible structure,

because of non-dominant period of ground motion. In the earlier case, more response

91


Figure 5.4: Response of structures in x-direction at location Ct with setback of 1.5 m

Figure 5.5: Pounding force between structures with setback of 1.5 m

is observed at location Ct than at Cb. This is due to eccentricity in mass distribution

resulting torsion induced in the system. This torsion in structure-B initiates the colli-

92


Figure 5.6: Response of structures in y-direction at location Ct with setback of 1.5 m

Figure 5.7: Response of structures in x-direction at location Cb with setback of 1.5 m

sion to structure-A with a magnitude of 73.7 kN. The maximum pounding responses for

structure-A and B in y-direction are 0.00428 m and 0.0090 m respectively. The collision

93


Figure 5.8: Response of structures in y-direction at location Cb with setback of 1.5 m

force increases as the setback level increases. The displacement responses for structure-A

& B in x-y directions and collision forces are shown from fig 5.9 to 5.11.

The pounding occurred at location Cb also. From the results, the responses at location

Cb are less compared at location Ct because of uneven distribution of mass for structure-

B. The responses are similar at location Ct and Cb in Y-direction (Ref. figure 5.8. For

more details refer figure 5.1). The maximum pounding responses for structure-A and B

in x-direction are 0.0344 m and 0.0376 m respectively. The displacement responses for

structure-A & B in x direction are shown from fig 5.12.

(c) At setback of 6.0 m

The analysis is carried out for structures with setback of 6.0 m. In this analysis, the

possible pounding location is at one place only. From the results, the maximum pounding

responses for structure-A and B are 0.0344 m and 0.0432 m respectively. Because of non-

dominant period of ground motion, response of flexible structure is more compared to

stiff structure. The maximum force generated between them is 169.4 kN. From the obser-

vation of all results, it is clearly shown that the maximum pounding forces are increasing

as the setback level increases. The number of collisions are also same for all the cases.

The displacement responses for structure-A & B in x-y directions and collision forces are

shown from fig 5.13 to 5.15.

94




From results, the response for both structures increases as the setback level increases.

But this increase in response is not significant. But the collision force between them

95



Figure 5.12: Response of structures in x-direction at location Cb with setback of 3.0 m

increase significantly. The number of collision occurrences are same in all the cases. It

can be concluded that the effect of collision is more when structures are kept at extreme

96




levels of setback.

97



Case-II: Different height levels

(a) At (3/4)th height of structure

Pounding analysis is carried out for structures at different elevation levels. From the

analysis, the maximum pounding response of structure-A and B in X-direction are 0.21 m

and 0.120 m respectively. Due to unsymmetrical mass of structure-B, they have responses

in both directions. Because of non-dominant period of ground motion, the response of

flexible structure is more than stiff structure. The responses of structure-A and B in

Y-direction are 0.052 m and 0.025 m respectively. The maximum collision force between

them is 1244 kN. The displacement responses for structure-A & B and collision forces are

shown from fig 5.16 to 5.17.

The maximum pounding response of structure-A and B in X and Y direction are

0.126 m, 0.170 m, 0.016 m and 0.062 m respectively. The maximum pounding force

generated between them is 777 kN. It is clearly show that, the pounding forces are more at

where mass concentration is more. If we change the mass concentration to other location

(top right corner of structure-B), the responses and collision forces will be change. The

displacement responses for structure-A & B and collision forces are shown from fig 5.18

to 5.19.

98


Figure 5.16: Response of structures in x-direction at location Ct with height of 2.25 m

Figure 5.17: Pounding force between structures with height of 2.25 m

(b) At (2/4)th height of structure

The same analysis is carried out for structures at mid height of structure-A. From the

analysis, the maximum pounding response of structure-A and B in X and Y direction are

99


Figure 5.18: Response of structures in x-direction at location Cb with height of 2.25 m


0.20 m, 0.168 m, 0.0053 m and 0.02 m respectively. The response of flexible structure

is more than stiff structure due to non-dominant period of ground motion. The collision

100


force between them is 5350 kN. This force is more than the force when structures are kept

at (3/4)th height. From the results it can conclude that the collision force at mid height

level is more than (3/4)th height level because of more shear amplification. Depending on

the response of structures, this collision force changes at different levels. The displace-

ment responses for structure-A & B and collision forces are shown from fig 5.20 to 5.21.

Figure 5.20: Response of structures in x-direction at location Ct with height of 1.5 m

The maximum pounding response of structure-A and B in X and Y direction are 0.20

m, 0.127 m, 0.005 m and 0.022 m respectively. The maximum pounding force generated

between them is 3493 kN. From results, the maximum pounding force at location Ct is

more than at Cb. This is because of uneven mass distribution resulting torsional effect.

The displacement responses for structure-A & B and collision forces are shown from fig

5.22 to 5.23.

From the results, the pounding response changes significantly as the height of structure

decreases. At (2/4)th height of structure, the collision force is more compared to (3/4)th

height. It can be concluded that as the height of structure increases, the collision force

decreases.

5.3 Summary

This analysis considered different setback levels for a single-single storey structure. The

setback levels were 1.5 m, 3.0 m and 6.0 m. The separation distance between them is 0.01

101



Figure 5.22: Response of structures in x-direction at location Cb with height of 1.5 m

m and they subjected to El-centro ground motion.

102



Setback Levels: From results, the response for both structures increases as the

setback level increases. But this increase in response is not significant. But the collision

force between them increase significantly. The number of collision occurrences are same

in all the cases. It can be concluded that the effect of collision is more when structures

are kept at extreme levels of setback. The response of flexible structure is more than stiff

structure when they vibrate at non-dominant period of ground motion. As the setback

distance increases, the collision force between them also increases.

Height Levels: From the results, the pounding response changes significantly as the

height of structure decreases. At (2/4)th height of structure, the collision force is more

compared to (3/4)th height because of shear amplification. It can be concluded that as

the height of structure increases, the collision force decreases.

103

Chapter 6

Conclusions

6.1 General Conclusions

The analysis considered linear and nonlinear pounding analysis of structures with equal

and unequal heights. The damage of structures are estimated from stiffness degradation.

This analysis was extended to 3D also. The main conclusions for all the cases can be

summarized as follows:

Separation distance from different codal provisions:

The separation distances are modified with modification factor in which it is insufficient.

The separation distance does not only depends on PGA but also depends on several other

factors like displacement and velocity responses, material properties of the structures and

characteristics of ground motion.

Linear and Nonlinear analysis:

From the analysis, the response of stiffer structure is more than flexible structure, when

structures vibrate at dominant frequency. Also, response of flexible structure is more,

when they vibrate at non-dominant frequency. But same collision force and responses will

not occur if position of structures are exchanged. It means, in case of adjacent structures

with different natural periods, the most affected are the rigid structures irrespective of

their position due to pounding.

The behavior of structures is similar as linear, till failure of either first spring or first

collision. Almost every structure vibrate at lesser frequencies because of failure of springs.

The maximum pounding forces increases, as the period of structure increases with the

same separation distance.

3D analysis of pounding:

The effect of collision is more when structures are kept at extreme levels of setback. When

the structures are kept at different elevation levels (setback=0), the pounding response

changes significantly as the height of structure decreases. At mid height of structure, the

collision force is more compared to other height levels because of shear amplification.

104

CHAPTER 6. CONCLUSIONS

6.2 Future Work

There are some suggestions for future research work on numerical modeling of pounding

between adjacent structures.

1. Extension of this work needs to consider the soil and brick parameters.

2. Modeling the structures using expansion joints such as filler or rubber material etc.

3. Damage of structure to be implemented in AEM using crack length and crack width

due to pounding.

4. Relationship between setback and collision force need to be calculated.

5. Effect of separation distance on collision force with constant setback need to be

studied.

105

Appendix A

Comparision of codal provisions on

pounding

A.1 Review on codal provisions

Most of the world regulations for seismic design do not take into account the pounding

phenomenon. Among of the ones who do consider it, do not provide specific rules that

must be followed. A list of codal provisions on pounding is described in chapter 1 (Ref

1.5.3). These codes specify a minimum separation distance between adjacent buildings.

In some cases this depends only on the maximum displacements of the each building (eg.,

Canada and Israel) and in other cases a small value that may be either a percentage of

previous one or a quadratic combination of the maximum displacements (eg., France).

In other cases the separation distance is made dependent on the building height (eg.,

Taiwan).

According to International Building Code (IBC) all the structures shall be separated

from adjoining structures. If the adjacent buildings are on the same property line, the

minimum separation distance simply follows SRSS rule and if they are not located on the

same property line (adjacent buildings separated by property line) simply follows the sum

of maximum displacements of the structures. In 2006 version there is no such type of co-

dal provision on building separation. Uniform Building Code (UBC-1997) also follows the

same codal provisions. According to Federal Emergency Management Agency (FEMA:

273-1997) the potential effects of building pounding whenever the side of the adjacent

structure is located closer to the building by less than 4% of the building height above

grade at the location of potential impacts. ASCE (7-05) states that all portions of the

structure shall be designed and constructed to act as an integral unit in resisting seismic

forces unless separated structurally by a distance sufficient to avoid damaging contact

under total deflection as determined in section 12.8.6. The details of codal provisions are

listed in table below:

From the observation of all codal provisions it is seen that most of the codal provisions

106

APPENDIX A. COMPARISION OF CODAL PROVISIONS ON POUNDING

Table A.1: Details of codal provisions on pounding

S.No CODE FORMULAE

1 IBC 2003δM =

√δ2M1 + δ2M2 ..... (Adjacent Buildings located on the

same property line) [Clause 1620.4.5]

2 UBC 1997δM =

√δ2M1 + δ2M2 ..... (Adjacent Buildings located on the

same property line) [Clause 1633.2.11]

3 FEMA: 273-1997

Data on adjacent structures should be collected to permitinvestigation of the potential effects of building poundingwhenever the side of the adjacent structure is located closerto the building than 4% of the building height above gradeat the location of potential impacts. The value of Si (Si =√

∆2i1 + ∆2

i2) calculated by the equation need not exceed

0.04 times the height of the buildings above grade at thezone of potential impacts. [(Clause 2.7.4), (Clause 2.11.10)]

4 ASCE/SEI 7-05 δx = CdδxeI [Clause 12.12.3]

follow SRSS method only. The minimum separation distance is not only depending on

the response of the structure but also various factors like importance factor, amplification

factor etc.

This case study deals about the collision force of first impact of the structure by using

linear impact models. The response considered is in translational direction only and not

consider in torsional direction.

A.2 Minimum separation between buildings

For studying pounding between adjacent structures numerically, we considered two build-

ings as shown in figure A.1. These buildings were idealized as two equivalent linear single

Figure A.1: Idealized model of SDOF system

107


degree of freedom (SDOF) systems. The two structures have lumped masses m1 = 11400

kg, m2 = 6410 kg, equal stiffnesses k = 45000 kN/m and equal damping ratios ζ. Let

u1(t) and u2(t) are independent responses of structure 1 and structure 2. The governing

differential equation of motion of SDOF system is expressed as follows:

miui(t) + ciui(t) + kiui(t) = −miug(t) (A.1)

Where,’i’denotes the building under consideration. For the purpose of studying the col-

lison between the buildings we considered SE component of El-Centro ground motion(Ref

2.3.1) whose PGA is 0.348 g. Newmark’s approach is used for finding the response of the

structures. In case of pounding collision condition to be checked and the condition is as

follows:

u1(t)− u2(t) ≥ δ (A.2)

If the above condition satisfies then collision occurs. For the purpose of finding the

minimum gap between two buildings, we considered different time periods for structure

2 ie., 0.075, 0.10, 0.125, 0.15, 0.175, 0.20, 0.225 and 0.25 sec. The details are given in the

below table.

Table A.2: Details about mass, stiffness and spacing provided between two structures

S.No Mass(kg) Stiffness(MN/m) Time Period(sec) Space Provided(m)

1 06410 45 0.075 0.009

2 11400 45 0.100 0.000

3 17810 45 0.125 0.006

4 25645 45 0.150 0.010

5 34900 45 0.175 0.013

6 45600 45 0.200 0.016

7 57700 45 0.225 0.017

8 71240 45 0.250 0.018

The peak of relative response of adjacent buildings gives the minimum separation

distance between them. The minimum separation distance between two adjacent struc-

tures is as shown in Figure A.2. From this figure it can be observed that as the time

period of the structure increases, minimum distance is increasing to avoid pounding and

for the two structures with same time period, there is no need to provide any separation

distance because these buildings will vibrate in phase and does not collide at any point

of time. However, this situation is not realistic because it is very difficult to construct

two structures with same natural period. Also, it can be observed from the figure that

the minimum separation distance is getting saturated when time period of building 2 is

increasing say beyond 1sec.

108


Figure A.2: Minimum space provided between two structures having different dynamicproperties

A.3 Case study

For the purpose of studying the impact force by providing minimum separation distance

between buildings, we selected structure 1 with time period 0.1 sec time period and varied

time period of other structure i.e, 0.075, 0.1, 0.15, 0.2 sec. Also for the purpose of doing

time history analysis we selected five earthquake records, viz., Loma-Prieta earthquake,

Elcentro earthquake, Parkfield earthquake, Petrolia earthquake and Northridge earth-

quake. For the purpose of analysis, Kelvin impact model (Ref 1.5.2) is choosen. For the

calculation of impact force between two structures stiffness of the spring, kk is assumed

as 4378x103 kN/m. The co-efficient of restitution, e = 0.6 is assumed and it is defined as

the ratio of the relative velocities of the bodies after collision to the relative velocities of

the bodies before collision.

Lomaprieta earthquake occurred in 1989 having a magnitude of 6.9 and PGA value of

0.22 g. The duration of this ground motion is 9.58 sec according to trifunac and broady

calculation. The predominant frequencies range present in the ground motion is 0.62-2.44

hz (0.41-1.61 sec). In this study structures having time period range from 0.075 sec to

0.2 sec with an interval of 0.025 sec has taken. Structure having time period 0.1 sec is

kept constant and others are varying and the minimum separation distances are calcu-

lated from above codal provisions. As the structures time period increases, the response

of the structure is also increases for a given ground motion and damping. According to

IBC, UBC and FEMA follows SRSS rule. According to ASCE codal provisions the min-

imum separation distance is high compared to others. But ASCE codal provision deals

importance factor also. This importance factor is based on occupancy category. The

predominant time period range (0.41-1.61 sec) is not presented in this case and there is

no impact of the structures. Hence the collision force is zero for all the structures.

109


Table A.3: Lomaprieta ground motion record having amplitude of 0.22 g, duration 9.58sec and predominant time period 0.41-1.61 sec

T1=0.075 secT2=0.075 sec T2=0.1 sec T2=0.15 sec T2=0.2 sec

SNo. Code Gap(m) Force(MN) Gap(m) Force(MN) Gap(m) Force(MN) Gap(m) Force(MN)

1IBC-2003

0.0065 0 0.0082 0 0.016 0 0.03 0

2UBC-1997

0.0065 0 0.0082 0 0.016 0 0.03 0

3FEMA-273

0.0065 0 0.0082 0 0.016 0 0.03 0

4 ASCE 0.022 0 0.029 0 0.052 0 0.09 00.017 0 0.023 0 0.042 0 0.071 00.014 0 0.019 0 0.035 0 0.06 0

Elcentro earthquake occurred in 1940 having a magnitude of 7.1 and PGA value of



hz (0.45-0.87 sec). In this study structures having time period range from 0.075 sec to 0.2

sec with an interval of 0.025 sec has taken. Structure having time period 0.1 sec is kept

constant and others are varying and the minimum separation distances are calculated

from above codal provisions. For the structures having time period 0.1 and 0.075 sec the

amount of impact is 20.58x103 kN by providing the minimum separation distance 0.012

m according to IBC, UBC and FEMA. As the minimum space between the structures

decreases the amount of impact increases, but this impact occurs at the same time even

the separation distance decreases. For the structures having same time period, no need to

provide minimum space between them. Because both structures response is same. For the

structures having time period 0.1 and 0.15 sec, the amount of impact is 26.28x103 kN by

providing the minimum separation distance 0.028 m according to IBC, UBC and FEMA.

For the structures having time period 0.1 and 0.2 sec, the amount of impact is 42.92x103

kN by providing the minimum separation distance 0.056 m according to IBC, UBC and

FEMA. The amount of impact depends on response of the structures at particular time,

minimum space between the structures and velocity of the structures. Even though the

predominant time period range (0.45-0.87 sec) is not presented, there are collisions for the

structures. If the predominant time period range structures are present, the collision will

be more. As the time period of the structures near to the predominant time period range,

the response of the structures are more and the impact, damage are more and finally may

lead to collapse of the structure.

Parkfield earthquake occurred in 1966 having a magnitude of 6.0 and PGA value of

110


Table A.4: Elcentro ground motion (S00E) record having amplitude of 0.348 g, duration24.44 sec and predominant time period ranges from 0.45-0.87 sec



1IBC-2003

0.012 20.58 0.014 0 0.028 26.28 0.056 42.92

2UBC-1997

0.012 20.58 0.014 0 0.028 26.28 0.056 42.92

3FEMA-273

0.012 20.58 0.014 0 0.028 26.28 0.056 42.92

4 ASCE 0.042 0 0.032 0 0.091 0 0.164 00.034 0 0.026 0 0.073 0 0.131 00.028 0 0.022 0 0.066 0 0.110 0



hz (0.30-1.2 sec). In this study structures having time period range from 0.075 sec to

0.2 sec with an interval of 0.025 sec has taken. Structure having time period 0.1 sec is

kept constant and others are varying and the minimum separation distances are calcu-

lated from above codal provisions. For the structures having time period 0.1 and 0.075

sec there is no collision and for the structures having same time period also there is no

collision. For the structures having time period 0.1 and 0.15 sec the amount of impact

is 38.98x103 kN by providing the minimum separation distance 0.03 m according to IBC,

UBC and FEMA. In this case the impact occurs at the same time, when the distance

between two structures reduced. For the structures having time period 0.1 and 0.15 sec

there is collision when the provided minimum space is 0.03 m, but if the structure changed

to 0.15 to 0.2 sec there is no collision according to IBC, UBC and FEMA, because the

provided space is more.

Petrolia earthquake occurred in 1992 having a magnitude of 7.2 and PGA value of




sec with an interval of 0.025 sec has taken. Structure having time period 0.1 sec is kept

constant and others are varying and the minimum separation distances are calculated

from above codal provisions. For all the structures there is no impact as per the codal

provisions. The predominant time period range is far away from the existing time period

structures.

Northridge earthquake occurred in 1994 having a magnitude of 6.70 and PGA value of


111


Table A.5: Parkfield ground motion record having amplitude of 0.430 g, duration 6.76 secand predominant time period 0.3-1.20 sec



1IBC-2003

0.016 0 0.021 0 0.03 38.98 0.091 0

2UBC-1997

0.016 0 0.021 0 0.03 38.98 0.091 0

3FEMA-273

0.016 0 0.021 0 0.03 38.98 0.091 0

4 ASCE 0.05 0 0.075 0 0.1 0 0.26 00.04 0 0.06 0 0.08 0 0.21 00.033 0 0.05 0 0.066 0 0.17 0

Table A.6: Petrolia ground motion record having amplitude of 0.662 g, duration 48.74 secand predominant time period 0.50-0.83 sec



1IBC-2003

0.0317 0 0.0356 0 0.0630 0 0.109 0

2UBC-1997

0.0317 0 0.0356 0 0.0630 0 0.109 0

3FEMA-273

0.0317 0 0.0356 0 0.0630 0 0.109 0

4 ASCE 0.111 0 0.126 0 0.208 0 0.328 00.088 0 0.100 0 0.166 0 0.262 00.074 0 0.084 0 0.138 0 0.218 0



sec with an interval of 0.025 sec has taken. For the structures having time period 0.1

and 0.15 sec has no impact. For the structures 0.1 and 0.2 sec time period the minimum

separation distance is 0.23 m according to IBC, UBC and FEMA. The amount of impact

is 56.5x103 kN.

A.4 Conclusions

From the above observations, the duration of strong motion increases with an increase

of magnitude of ground motion. As the PGA value increases, the minimum separation

112


Table A.7: Northridge ground motion record having amplitude of 0.883 g, duration 8.94sec and predominant time period ranges from 0.2-2.2 sec



1IBC-2003

0.041 0 0.053 0 0.093 0 0.23 56.5

2UBC-1997

0.041 0 0.053 0 0.093 0 0.23 56.5

3FEMA-273

0.041 0 0.053 0 0.093 0 0.23 56.5

4 ASCE 0.134 0 0.190 0 0.307 0 0.670 00.100 0 0.152 0 0.240 0 0.530 00.09 0 0.126 0 0.204 0 0.446 0

between the structures also increases.

• The separation distance between the two structures decreases, the amount of impact

is increases, which is not applicable in all cases. It is only applicable when the impact

time is same. It may also decreases when separation distance decreases, which leads to

less impact time.

• At resonance condition the response of the structure is more and may lead to col-

lapse of the whole structure. In this case even though the predominant time period range

is not present, the impact occurs, but this impact is more when the predominant time

period structures present.

• For Elcentro earthquake, the PGA value and duration are slightly less than Petrolia

earthquake, but the collision is significant. The minimum separation distances are differ-

ent in both cases and less in Elcentro earthquake.

• For Parkfield earthquake, magnitude and duration are less and predominant time

period structures are near to the existing structures. Hence collision happens.

• For Northridge earthquake which are less magnitude and duration than Parkfield,

the collision is more because of resonant frequencies. The amount of impact is not only

depending on response and velocity of the structure but also magnitude and duration of

earthquake.

• For IBC, UBC and FEMA codal provisions pounding happens almost structures

having different dynamic properties when El-Centro ground motion is given to the struc-

113


tures. This happens for moderate earthquakes.

• From the all above observation, the duration of strong motion increases with an

increase of magnitude of ground motion. As the PGA value increases, the minimum sep-

aration distance is also increases between the structures.

114

Appendix B

Calculation of separation distance

from codes

B.1 Calculation of separation distance from codes

A series of separation distances are studied to estimate the minimum separation distance

(MSD) between two adjacent structures which are separated with an interval of 5 mm. A

set of structures (equal heights of single, two, three and five storey structures and unequal

heights of single-two and three-five storey structures) are subjected to series of ground

motions (Ref 2.3.1) to estimate MSD. The distance where collision ceases will give the

MSD between them. The separation distances are also calculated from codes (ref 1.5.3).

The calculations for single storey structures are as follows:

According to Greece, the minimum separation distance should be 4 cm upto three

storey level, 8 cm from four to eight storey level and 10 cm for more than eight storey

levels. According to Mexico, it shall be neither smaller than 5 cm nor smaller than the

height of the level over the ground multiplied by 0.007, 0.009, 0.012 depending on site of

zones I, II and III respectively. For Australia, it has given 1% of structure height. From

Serbia, it shall be 3 cm and increased by 1.0 cm for every increase of 3.0 meters of height

above 5.0 mts. From the above codal provisions, it is not given any specific formulation

for the separation of distance. Some of them gave formulations which are described below:

The separation distances are calculated from codes (ref 1.5.3) for single storey struc-

tures. According to Canada codal provisions, the separation distance is the sum of their

individual lateral deflections obtained from an elastic analysis.

The equivalent lateral seismic force representing elastic response, Ve shall be calculated

in accordance with the following:

Ve = V SIFW (B.1)

115

APPENDIX B. CALCULATION OF SEPARATION DISTANCE FROM CODES

Where ’V’ is zonal velocity ratio, ’S’ is seismic response factors, ’I’ is seismic impor-

tance factor and ’F’ is foundation factor. The time period of the structure is calculated

as Tn=0.075h3/4n (concrete moment resisting frames). For calculations, V is taken as 1.0

and S is based on fundamental period of structure and its value is 3.0. I is taken as 1.0

for all buildings. F is taken as 1.3 for firm soils. W is weight of structure which is 100

kN. From the above calculations, the value of Ve is 390 kN.

The minimum lateral seismic force is given as,

Vl = (Ve/R)U (B.2)

Where R is force modification factor and its value is 2.0 and U is 0.6. Finally the value

of Vl is 117 kN. This load is applied on to the structure to get displacements. Finally the

separation distance is 0.025 m.

According to Egypt codal provisions, it shall be either 2.0 times the computed deflec-

tions or 0.002 times of its height whichever is larger and in many cases not less than 2.5

cms. The total horizontal seismic force is calculated as:

V = ZISMRQW (B.3)

Where, ’I’ is importance factor = 1.0, ’S’ is structural system type factor = 1.0 (for

moment resisting frames), ’M’ is material factor =1.0 (for RC material), ’R’ is risk factor

=1.0 (normal buildings), ’Q’ is construction quality control factor = 1.0 and ’Z’ can be

calculated as Z=ACF, where ’A’ is horizontal acceleration ratio = 0.02 (for zone I and

intensity VI), ’F’ is foundation soil factor = 1.3 (for fine grained soils). The value of C

is calculated from time period of the structure. It can be calculated as, T=0.09H√d

. The

calculated value for C is 1.0. Finally the value of V is 2.6 kN and the separation distance

is 0.012 m. The minimum value should be 0.025 m.

According to Ethiopia codal provisions, it shall be twice the sum of their individual

deflections obtained from an elastic analysis. The total seismic force is given as,

F = αβγ(Gk + ψQk) (B.4)

Where, ’α’ is design bedrock acceleration ratio (α=αoI). For zone II αo is taken as

0.05 and ’I’ is taken as 1.0 for buuildings and structures occupancy. β is elastic design

response factor and its value is β=βoS ≤ 2.5. βo=1.2T 1/2 and T=0.09hn√

d, ’S’ is site condition

factor = 1.0 for gravels. Finally the value of β is 2.5, γ is structural system type factor =

0.5 for RC buildings. Gk is characteristic dead load, Qk is characteristic live load and ψ

is live load incident factor = 0.25 for public buildings. The seismic force is 2.64 kN and

the separation distance is 2 mm.

According to Peru codal provisions, the shear in the base of the structure is calculated

as,

116


V =ZUSC

RP (B.5)

The minimum value for C/R is taken as 0.125. Where U is occupancy factor = 1.0 for

common buildings. Z is zone factor = 0.30 for zone II and S is soil parameters = 1.2 for

intermediate soils. The shear value is 4.5 kN. The other formulation is S=3+0.004(h-500)

or greater than 3 cms. Where h is in cms. It must be greater than above claculations.

Finally the separation distance is 3 cms.

According to Indian codal provision, the design seismic base shear is calculated as,

VB = AhW (B.6)

Where Ah=ZISa

2Rg, Ah is design horizontal seismic coefficient, ’Z’ is zone factor=0.24

for zone IV(assumed), ’I’ is importance factor=1.0 for general buildings, ’R’ is response

reduction factor=3.0 for moment resisting frames and Sa

gis taken for medium soil sites.

The calculated fundamental period without considering brick infill panels is T=0.075h0.75

= 0.17 sec. Where h=height of building in m. From all the calculations, the design seismic

base shear is 1.7 kN and the separation distance is 0.01 m.

According to Taiwan codal provision, the seiamic base shear is calculated as,

V =1

1.4αy(SaDFu

)mW (B.7)

Where αy is defined as the first yield seismic force amplification factor that is depen-

dent on the structure types and design method which will be equal to 1.5 for RC structures

using strength design method. The fundamental period is calculated as T=0.07h3/4n for

RC moment resisting frames and its value is 0.159 sec. The value To is 1.3 sec for zone II

(Source: Design response spectrum for Taipei basin).

SaD =

SDs(0.4 + 3T

To), T ≤ 0.2To

SDs, 0.2To < T ≤ To

SDs(ToT

), To < T ≤ 2.5To

0.4SDs, T > 2.5To

(B.8)

Where SDs is site-adjusted spectral response acceleration parameter, the design spec-

tral response acceleration SaD for a given site can be developed directly from the design

spectral response acceleration at short periods and its value is 0.6 g. The value of SaD is

0.46 g. The reduction factor Fu is given by,

117


Fu =

Ra, T ≥ To√

2Ra − 1 + (Ra −√

2Ra − 1)T−0.6To0.4To

, 0.6To ≤ T ≤ To√

2Ra − 1, 0.2To ≤ T ≤ 0.6To√

2Ra − 1 + (√

2Ra − 1− 1)T−0.2To0.2To

, T ≤ 0.2To

(B.9)

The value of Ra = 1 + R−11.5

=1.33. Finally the value of V is 18.6 kN. The calculated

separation diatance is 1 cm.

The total cases can be categorized into two groups. The first group (group-A) deals

with single-single, single-two and two-two storey structures. Whereas, the second group

(group-B) deals with the remaining structures in the analysis.

Table B.1: Separation distances from codes

Code Single-single Single-two Two-two Three-three Three-five Five-five

Australia 3.0 6.0 6.0 12.0 20.0 20.0Canada 2.5 3.2 3.5 4.7 6.0 6.3Egypt 2.5 2.5 2.5 2.5 3.0 3.0Ethiopia 0.2 0.5 0.7 1.8 2.0 2.7Greece 4.0 4.0 4.0 4.0 8.0 8.0India 1.0 3.2 4.0 6.3 7.4 9.6Mexico 5.0 7.2 7.2 14.4 24.0 24.0Peru 3.0 3.5 3.5 4.6 7.0 7.0Serbia 3.0 4.0 4.0 5.0 7.0 7.0Taiwan 1.0 3.9 5.0 7.4 8.5 9.0

* All units are in cms

In first group, Taiwan, Indian, Egyptian and Ethiopian seismic codes doesn’t satisfy

the minimum separation requirement. As per the Indian and Taiwan codal provisions,

the separation distance for single-single storey structures are 1.0 cm. This separation

distance doesn’t satisfy for earthquakes 2 and 5 (Table B.2), because of underestimation

of separation distance between the structures. As per the Ethiopian codal provision, the

separation distance is 2 mm which is insufficient. From the analysis, 15 mm will be the

minimum separation distance between two single storey structures which has passed from

all the considerable ground motions without collision.

For single-two storey structures, Egyptian and Ethiopian codal provisions doesn’t sat-

isfy the minimum requirement on separation distance. As per Egyptian codal provision,

the separation distance is 2.5 cms for single-two storey structures which has not satisfied

for earthquakes 8 and 9. As per the Ethiopian codal provision, the separation distance

is 5 mm which is insufficient. From the analysis, 30 mm will be the minimum separation

distance between two single storey structures which has passed from all the considerable

118


Table B.2: Status on separation distance from codes for single-single storey structures ingroup-A

Code 1 2 3 4 5 6 7 8 9 10

Australia√ √ √ √ √ √ √ √ √ √

Canada√ √ √ √ √ √ √ √ √ √

Egypt√ √ √ √ √ √ √ √ √ √

Ethiopia x x x x x x x x x xGreece

√ √ √ √ √ √ √ √ √ √

India√

x√ √

x√ √ √ √ √

Mexico√ √ √ √ √ √ √ √ √ √

Peru√ √ √ √ √ √ √ √ √ √

Serbia√ √ √ √ √ √ √ √ √ √

Taiwan√

x√ √

x√ √ √ √ √

* 1-Athens ground motion, 2-Athens(trans) ground motion, 3-Ionian ground motion, 4-Kalamata groundmotion, 5-Umbro ground motion, 6-Elcentro ground motion, 7-Olympia ground motion, 8-Parkfieldground motion, 9-Northridge ground motion and 10-Lomaprieta ground motion√

-satisfies the separation distance from codesx-does not satisfy the separation distance from codes

Table B.3: Status on separation distance from codes for single-two storey structures ingroup-A

Code 1 2 3 4 5 6 7 8 9 10

Australia√ √ √ √ √ √ √ √ √ √

Canada√ √ √ √ √ √ √ √ √ √

Egypt√ √ √ √ √ √ √

x x√


√ √ √ √ √ √ √ √ √ √

India√ √ √ √ √ √ √ √ √ √

Mexico√ √ √ √ √ √ √ √ √ √

Peru√ √ √ √ √ √ √ √ √ √

Serbia√ √ √ √ √ √ √ √ √ √

Taiwan√ √ √ √ √ √ √ √ √ √

ground motions without collision. For two-two storey structures, the separation distance

is 35 mm which has passed from all the ground motions without collision.

It is necessary to change some (Taiwan, Indian, Egyptian and Ethopian) codal pro-

visions from the observation of above structures in group A. The change on separation

distance should be such that, it should pass from all the ground motions in group A. The

modified formulae on separation distance with modification factor are as follows:

Taiwan: The separation distance should be 1.5 times of [0.6x1.4αyRa].

Indian: The separation distance should be 1.5 times of [R times the sum of the

119


Table B.4: Status on separation distance from codes for two-two storey structures ingroup-A

Code 1 2 3 4 5 6 7 8 9 10

Australia√ √ √ √ √ √ √ √ √ √

Canada√ √ √ √ √ √ √ √ √ √

Egypt√

x x x√ √ √

x x√


√ √ √ √ √ √ √ √ √ √

India√ √ √ √ √ √ √ √ √ √

Mexico√ √ √ √ √ √ √ √ √ √

Peru√ √ √ √ √ √ √ √ √ √

Serbia√ √ √ √ √ √ √ √ √ √

Taiwan√ √ √ √ √ √ √ √ √ √

calculated storey displacements].

Egypt: The separation distance should be 0.8% of storey height or not less than 3.5

cms.

Ethiopia: The separation distance should be 8 times of [twice the sum of their indi-

vidual deflections].

Table B.5: Status on separation distance from codes for three-three storey structures ingroup-B

Code 1 2 3 4 5 6 7 8 9 10

Australia√ √ √ √ √ √ √ √ √ √

Canada√

x√

x√ √ √

x x√

Egypt x x x x√

x x x x√


√x√

x√ √ √

x x√

India√ √ √ √ √ √ √

x x√

Mexico√ √ √ √ √ √ √ √ √ √

Peru√

x√

x√ √ √

x x√

Serbia√

x√

x√ √ √

x x√

Taiwan√ √ √ √ √ √ √ √

x√

In second group, all the codal provisions doesn’t satisfy the minimum separation dis-

tance except Australian and Mexican codes. According to Canadian seismic codal provi-

sion, the MSD should be 4.7 cms which doesn’t satisfy when the structures (three-three

storey structures) subjected to earthquakes 2, 4, 8 and 9. From the analysis, the MSD

value should be 8.0 cms which passes from all the ground motions. The complete status

for all the ground motions and codes are listed in table B.5.

120


It is necessary to change the codal provisions from the observation of above structures

in group B. The modified formulae on separation distance are as follows:

Taiwan: The separation distance should be 1.16 times of [0.6x1.4αyRa].

Indian: The separation distance should be 1.35 times of [R times the sum of the

calculated storey displacements].

Egypt: The separation distance should be 0.8% of storey height or not less than 8.0

cms.

Ethiopia: The separation distance should be 5 times of [twice the sum of their indi-

vidual deflections].

Canada: The separation distance should be 1.8 times of [sum of their individual

deflections].

Greece: The separation distance should be 8 cms upto three storeys.

Peru: The separation distance should be S = 7+0.004(h-500)...’h’ is in cms.

Serbia: The separation distance should be increased by 1.7 cms for every in-

crease of 3.0 m height of height above 6.0 mts.

121

Bibliography

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Electronic Journal of Structural Engineering, pp. 66-74, 2006.

[2] Aguilar J, Jurez H, Ortega R and Iglesias J., ”The Mexico Earthquake of September

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