I

REDUCTION OF POUNDING AND LATERAL-TORSIONAL COUPLING

OF R/C FRAMES UNDER SIEMIC LOAD

IBRAHIM AHMED LIBAN

Project Submitted to the School of Graduate Studies, Universiti Putra Malaysia,

in Fulfillment of the Requirements for the Degree of Master of Structural

Engineering and Construction

17th

/ May/2011

II

III

ABSTRACT

This project focuses on the validation of passive control systems that can effectively

reduce seismic responses due to pounding and torsional coupling in adjacent and

asymmetrical RC frame building structures. Due to their attractive characteristics for

seismic response control, passive control systems using viscous dampers are

specifically examined in their application in actual RC buildings.

To verify the applicability of the proposed passive control system to pounding and

torsional coupled response reduction in adjacent and asymmetric building

respectively, numerical studies were conducted using a Finite element code. The

three actual RC frame structures examined here were selected from literature and

model using F.E code.

For pounding mitigation investigation two adjacent buildings with 2 cm gap were

select while the other two models were 3D uni-asymmetrical and bi-asymmetrical

structures which were used in the investigation of lateral-torsional response control.

For the uni-asymmetrical model, eccentricity due to stiffness distribution in the

lateral load resisting members resulted in the uni-asymmetrical model while for the

bi-asymmetrical model the asymmetry was due to the plan layout of frames.

Through the work conducted in this project it was found that viscous dampers are

effective in controlling the structural response in both pounding and lateral-torsional

responses.

IV

ABSTRAK

Objektif utama di dalam projek ini adalah untuk mengesahkan samaada sistem

kawalan pasif dapat mengurangkan secara berkesan gerak balas seismos yang di

sebabkan oleh daya godaman dan kilasan gandingan pada rangka stuktur bangunan

konkrit tetulang yang terletak bersebelahan and asimetrik. Sistem kawalan pasif yang

di kaji di dalam projek ini adalah sistem kawalan yang menggunakan perendam likat

(“viscous damper”).

Untuk pengesahan, kajian berangka dengan menggunakan kaedah unsur terhingga

telah di gunakan. Tiga bangunan sediaada telah di pilih dari literatur dan rangka

stuktur bangunan konkrit tetulang bagi ketiga-tiga bangunan tersebut telah di

modelkan mengikut kod unsur terhingga.

Bagi kajian projek ini, rangka stuktur bangunan konkrit tetulang telah di modelkan

seperti berikut :-

i. Jarak di antara bangunan bersebelahan adalah sebanyak 2 centimeter

ii. Model uni asimetrikal 3 Dimensi

iii. Model dwi asimetrikal 3 Dimensi

Dari keputusan kajian dan analisa, secara keseluruhan dapat disimpulkan bahawa

sistem kawalan pasif yang menggunakan perendam likat (“viscous damper”) didapati

berkesan dalam mengawal tindakbalas struktur di sebabkan oleh daya godaman dan

kilasan gandingan lateral yang di sebabkan oleh gerak balas seismos.

V

I would like to dedicate this work to my mother who has been my back bone in all

my life‟s endeavors, my brother and sisters for always believing in me and my better

half to whom I look forward to sharing my life

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ACKNOWLEDGEMENTS

First of all, I would like to address my gratitude to Prof. Dr. Jamaloddin Noorzaei for

accepting me as a graduate student under his supervision and for keeping giving me

valuable advice and suggestions. I have learned a lot from him, not only on research

itself but also on how to think as a researcher and how to get through difficult

situations. I have always been encouraged by him to complete my degree. Without

his direction, this project would not have been completed.

Also, I would like to express my gratitude to my doctoral lecturers ,Professor.Ir.Dr.

Mohd Saleh b.Jaafar, Ir.Dr. Raizal Saifulnaz b.Muhammad, Dr.Farah Nora Aznieta

bt. Abd Aziz for providing me with valuable advice and comments. This dissertation

has been improved by their advice and comments.

I would also like to express my graduate to Mr. Farzad Hejazi PhD candidate for all

the contributions made. For kindly giving your time during the analysis part of the

project i thank you bro.

I would also like to thank the team of PhD candidates at Itma for their valuable

advises on how to tackle certain problems faced during the writing of this project.

I would also like to thank my fellow comrades at the department for making this

journey through life a blessing, I learned a great deal from you all. You made this

journey worth a while. I thank you for the moments of joy which will definitely

make good stories worth tell to the future Ibrahim junior‟s.

VII

APRROVAL SHEET

I certify that an Examination Committee has met on 17 may 2011 to conduct the final

examination of Ibrahim Ahmed Liban on his Master degree project entitled:

“Reduction of pounding and lateral-torsional coupling of RC frames under seismic

load” in accordance with Universiti Putra Malaysia (Higher Degree) act of 1980 and

Universiti Putra Malaysia (Higher Degree) Regulations 1981. The committee

recommends that the student be awarded the Master of structural and Construction

engineering

Jamaloddin Noorzaei Professor. Madhya Dr. ------------------------------

(Project supervisor) Date

Engineering Faculty ------------------------------

Universiti Putra Malaysia Signature

Member of the Examination Committee were as follows

Mohd. Saleh Jaafar, Professor Ir. Dr.

(Project Examiner) ------------------------------

Deputy Vice-chancellor Date

Universiti Putra Malaysia -----------------------------

Signature

Farah Nora Aznieta bt Abd Aziz Phd

Senior Lecturer ------------------------------

(Project Examiner) Date

Engineering faculty -----------------------------

Universiti Putra Malaysia Signature

VIII

DECLARATION

I declare that this project is my original work except for the quotations and citations

which have been duly acknowledge. I also declare that it has not been previously,

and is not currently, submitted for any other degree at Universiti Putra Malaysia or at

any other institution.

Ibrahim Ahmed Liban

Date: 17th may 2011

IX

Table of Contents ABSTRACT III

ABSTRACT Error! Bookmark not defined.

ACKNOWLEDGEMENTS VI

APRROVAL SHEET VII

DECLARATION VIII

LIST OF TABLES XI

LIST OF FIGURES XII

LIST OF SYMBOLS XIV

CHAPTERS 1

1. INTRODUCTION 1

1.1. General 1

1.2. Type of Analysis Methods 7

1.2.1. Equivalent Statcis Analysis 7

1.2.2. Respnse Spectrum Analysis 7

1.2.3. Linear and Nonlinear Dynamic Analysis 8

1.3. Problem Statement 9

1.4. Objective 11

1.5. Scope and Limitations 11

1.6. Organisation of The Project 12

2. LITERATURE REVIEW 13

2.1. General Introduction 13

2.2. Supplementary Dampers 14

2.3. Types Sypplementary Dampers 17

2.4. Pounding 19

2.4.1. Adjacent Buildings 20

2.4.2. Retrofitting of Adjacent Buildings 27

2.5. Torsional Response of Asymmetrical Structures 29

2.5.1. Torsional Response Control of aAsymmetrical structures 33

2.5.2. Passive Control Using Viscous Dampers 35

2.5.3. Concluding Remarks 40

3. METHODOLOGY 41

3.1. Introduction 41

3.2. Physical Modelling 43

X

3.2.1. Physical Modelling of Frame Element 43

3.2.2. Physical Modelling of Damper 44

3.3. Mechanical Property of Damper 45

3.4. Dynamic F.E Formulation for RC Frame Structure 46

3.5. Constitutive Relationship for Concrete and Steel 48

3.5.1. Stress-Strain Relationship of Concrete 48

3.5.2. Stress-Strain Relationship for Steel 49

3.6. Reinforce Concrete Frame with Earthquake Energy Dissipartion System 50

3.6.1. Frame Element 51

3.6.2. Viscous Damper Element 52

3.7. Computer Program 53

3.8. Worl Layout Chart 53

4. RESULTS AND DISCUSSIONS 56

4.1. Introducton 56

4.2. Structures Analysised 57

4.3. Define Damper Properties 57

4.4. Preforme Static Analsis 57

4.5. Select Earthquake Record 58

4.6. Application of Viscous Dampers 59

4.7. Case 1 Pounding Mitigation of Adjacent Structures 59

4.8. Case 2 Torsional Response Reduction of Uni-Asymetrical Structure 64

4.9. Case 3 Torsional Response Reduction of Bi-Asymmetrical Structure 74

5. CONCLUSION 84

5.1. Introduction 84

5.2. Case 1 Pounding Mitigation of Adjacent Structures 84

5.3. Case 2 Torsional Response Reduction of Uni-Asymetrical Structure 84

5.4. Case 3 Torsional Response Reduction of Bi-Asymmetrical Structure 85

5.5. Response of RC Frame Structure Retofitted with Viscous dampers 86

5.6. Suggestions for Futher Studies 87

6. REFERENCES 89

XI

LIST OF TABLES

TABLE: 4.1. Cross-section and reinforcement of structural members 66

TABLE 4.2 displacements and rotations for varying damper coefficients 76

TABLE: 4.3. Displacement reductions in X, Y and Z for node20 83

XII

LIST OF FIGURES

FIGURE 1.1. Fault types 7

FIGURE 1.2. Japan after 2011 earthquake 8

FIGURE 1.3. Effects of Haiti earthquake 9

FIGURE 1.4 homes in Eastern Sichuan China earthquake 10

FIGURE 1.5 residences in October 8 Pakistan earthquake 11

FIGURE 2.1 damper types 23

FIGURE 3.1 Overall schematic view of the methodology of the study 48

FIGURE 3.2 Physical model of beam-column element 50

FIGURE 3.3 Real Viscous Dampers and 3-D Nonlinear

Damper Element Model Constitutive 50

FIGURE 3.4 fluid viscous damper 52

FIGURE 3.5 Stress-Strain Relation for Concrete 54

FIGURE 3.6 Stress-Strain curves for steel reinforcement 55

FIGURE 3.7 structural members of frame element 57

FIGURE 3.8 damper frame elements with added damper element 58

FIGURE 3.9 Overall schematic view of present study 60

FIGURE 3.9 Overall schematic view of present study 60

FIGURE 4.1 Overall schematic view of present study 60

FIGURE 3.9 Overall schematic view of present study 60

FIGURE 4.1 layout of analysis procedure 62

FIGURE 4.2 model plot for 2D adjacent RC structures 66

FIGURE 4.3 Overall schematic view of present study 60

FIGURE 4.4 pounding in adjacent structures 67

FIGURE 4.5 lateral displacements for building 1 and 2 68

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FIGURE 4.6 axial and shear force reductions 70

FIGURE 4.7 front view and top view 71

FIGURE 4.8 damper distributions in 3 side frame 71

FIGURE 4.9 nodal displacements in x, y and z directions 73

FIGURE 4.10 time history displacements x in z direction 75

FIGURE 4.11 nodal shear force in x, y and z directions 78

FIGURE 4.12 torsion and moments in x, y and z directions respectively 79

FIGURE 4.13 plan bi-asymmetrical 3 story RC frame structure 80

FIGURE 4.14 rotations in X and Z directions 82

FIGURE 4.15 displacement time history responses for node 20 85

FIGURE 4.16 axial and shear force time history response for element one 87

FIGURE 4.17 torsion and moment time history response of element 1 73

XIV

LIST OF SYMBOLS

α end rotation of an elastic member

β combined rotation of an elastic member and an end connection

γj coefficients of the combined objective function

∆ incremental structural response or building roof drift

Δs inter-story drift of story s at performance level i

⎯δi, ⎯∆I allowable inter-story and roof drifts at performance level i,

respectively

δ relative magnitude of a combined stress resultant

ε section factor

ζ inter-story drift ratio or angle

λb dual variable vector

λ Lagrange multiplier or dual variable

µ exponent for determining a lateral load distribution

ξ reduction factor for a section strength due to the combined stress state

ρ mass density of material

σy specified design yield stress

σye expected yield stress

τ step length of line search

υi vibration shape of the ith mode

υ plastic rotation of a 'pseudo semi-rigid connection

1

CHAPTERS

1. INTRODUCTION

1.1. GENERAL

Earthquakes are natural disasters brought about by movement of tectonic plates or

rupture of tectonic plates due to pressure build up beneath them. Tectonic plate

movements occur at fault line where the crest is weakest. As rupture occurs at the

faults, strain energy stored is release which travels out words from the point of

origin. It is this strain energy initial stored in the underlying faults which propagates

as waves and is felt on the ground above.

There are three main types of faults, strike-slip fault, normal fault and thrust fault.

FIGURE1.1 Fault types and their behavior during earthquakes:

Thrust faults, particularly those along convergent plate boundaries are associated

with the most powerful earthquakes, including almost all of those of magnitude 8 or

2

more. Strike-slip faults, particularly continental transforms can produce major

earthquakes up to about magnitude 8. Earthquakes associated with normal faults are

generally less than magnitude 7.

Earthquakes are one of the oldest and most destructive forces known to man and his

built environment. Through century‟s man has come into contact with earthquakes

coming out with heavy and deadly losses both to his built environment and his own

life. Few examples of such destructive forces in recent times are shown in the

following pictures

A 9.0-magnitude earthquake hit near the north-eastern coast of Japan on March 11,

2011, which triggered a destructive tsunami killing at least 11600 people while

16450 were pronounced missing and 170500 displaced. 155000 homes, 2035 roads,

56 bridges and 36 railways were damaged or destroyed by the earthquake and

tsunami.

FIGURE1.2 Japan after March 11, 2011 earthquake

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An earthquake measuring 7.0 magnitude claimed the lives of 222,570 people in Haiti

on Jan. 12, 2010. Worldwide relief efforts were launched to aid the 300,000 injured

and 1.3 million displaced. In terms of property damaged, 97294 houses were

destroyed and 188383 damaged in the Port-au-Prince area and in much of southern

Haiti.

FIGURE1.3 Effects of Haiti Jan. 12, 2010 earthquake

The Great Sichuan Earthquake occurred on May 12, 2008, and measured 8.0

magnitude. The earthquake claimed the life‟s of 69195 people and injured 374177

while 18392 were pronounced missing and presumed dead. The earthquake divested

the built environment destroy an estimated 5.36 million buildings and damaging 21

million buildings. The destructive nature of the earth quake affect some 45.5 million

4

people in 10 provinces and regions, causing at least 15 million people to be

evacuated from their homes and more than 5 million being left homeless.

FIGURE1.4 Destroyed homes in Eastern Sichuan China May 12, 2008earthquake

A 7.6-magnitude earthquake hit near Muzaffarabad, Pakistan on Oct. 8, 2005. The

earthquake was reportedly caused by the rising of a mountain range. The earthquake

killed at least 86000 people killed and injured 69000. The damages were more

extensive in northern Pakistan. The heaviest damage occurred in the Muzaffarabad

area, Kashmir were entire villages were destroyed and at Uri were 80 percent of the

town was destroyed. At least 32335 buildings collapsed in Anantnag, Baramula,

Jammu and Srinagar, Kashmir.

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FIGURE1.5 Collapse residences in October 8 Pakistan earthquake

The above examples are just few of those on recorded, earthquakes claim life‟s, leave

large losses in property damages and destroy the social daily living of communities.

Since then man has been struggling to keep his losses to minimum although there has

not be a complete seismic proof structures but the toll of deaths and properties losses

have been reduced. The last couple of decades have witness men‟s development in

fields of material science, construction methods and earthquake engineering. All that

knowledge gained from previous earth quakes have made it possible for us humans

to measure and predicts earth quake forces composing them into what we presently

call seismic design codes of practice.

6

Exposures to previous earthquakes has lead us to examine the design concept we use

in our construction methods, questions like importance of structure, saving life‟s of

occupants have brought about changes in design criterions for selecting structural

performance during earthquakes. Current seismic design codes are based on either

performance based design method or the capacity based designed method. The

performance based design involves a set of procedures by which a building structure

is designed in a controlled manner such that its behavior is ensured at predefined

performance levels under earthquake loading. The design process is an iterative in

which an initial design is modified repeatedly to meet code- and designer-specified

requirements. While the capacity based designed method is in itself a performance

based method in which the ductility of structural members are predefined to meet

certain code requirements.

Changing structural design criterions and construction methods could only do so

much for structure performance and safety. This opened research gates on how to

enhance the energy dissipation techniques of reinforced concrete structures. Through

this research various methods of energy dissipation systems were developed and

classified into three major groups:

i) Passive energy dissipation systems

ii) Semi-active dissipation systems

iii) Active energy dissipation systems

This field of energy dissipating devices has become another important topic in

structural engineering. During the last three decades, significant efforts have been

made to apply modern control technology to civil structures for enhancing structural

safety against natural hazards. Various types of passive and active control systems

have been developed and experimentally verified. A number of them have been

7

implemented in full scale civil structures. Passive systems are well understood and

widely accepted to reduce the damage and the detrimental effect of this destructive

force on structures.

1.2. TYPE OF ANALYSIS METHODS

1.2.1. EQUILVATENT STATIC ANALYSIS

This approach defines a series of forces acting on a building to represent the effect of

earthquake ground motion, typically defined by a seismic design response spectrum.

It assumes that the building responds in its fundamental mode. For this to be true, the

building must be low-rise and must not twist significantly when the ground moves.

The response is read from a design response spectrum, given the natural frequency of

the building either calculated or defined by the building code.

1.2.2. RESPONSE SPECTRUM ANALYSIS

This approach permits the multiple modes of response of a building to be taken into

account (in the frequency domain). This is required in many building codes for all

except for very simple or very complex structures. The response of a structure can be

defined as combinations of many special shapes in a vibrating string correspond to

the "harmonics". Computer analysis can be used to determine these modes for a

structure. For each mode, a response is read from the design spectrum, based on the

modal frequency and the modal mass, and they are then combined to provide an

estimate of the total response of the structure

The result of a response spectrum analysis using the response spectrum from a

ground motion is typically different from that which would be calculated directly

from a linear dynamic analysis using that ground motion directly, since phase

information is lost in the process of generating the response spectrum.

8

In cases where structures are either too irregular, too tall or of significance to a

community in disaster response, the response spectrum approach is no longer

appropriate, and more complex analysis is often required, such as non-linear static or

dynamic analysis.

1.2.3. LINEAR AND NONLINEAR DYNAMIC ANALYSIS

Static procedures are appropriate when higher mode effects are not significant. This

is generally true for short, regular buildings. Therefore, for tall buildings, buildings

with torsional irregularities, or non-orthogonal systems, a dynamic procedure is

required. In the linear dynamic procedure, the building is modelled as a multi-

degree-of-freedom (MDOF) system with a linear elastic stiffness matrix and an

equivalent viscous damping matrix.

The seismic input is modelled using either modal spectral analysis or time history

analysis but in both cases, the corresponding internal forces and displacements are

determined using linear elastic analysis. The advantage of these linear dynamic

procedures with respect to linear static procedures is that higher modes can be

considered. However, they are based on linear elastic response and hence the

applicability decreases with increasing nonlinear behaviour, which is approximated

by global force reduction factors.

9

In non-linear dynamic analysis, the non-linear properties of the structure are

considered as part of a time domain analysis. This approach is the most rigorous, and

is required by some building codes for buildings of unusual configuration or of

special importance. However, the calculated response can be very sensitive to the

characteristics of the individual ground motion used as seismic input; therefore,

several analyses are required using different ground motion records to achieve a

reliable estimation of the probabilistic distribution of structural response. Since the

properties of the seismic response depend on the intensity, or severity, of the seismic

shaking, a comprehensive assessment calls for numerous nonlinear dynamic analyses

at various levels of intensity to represent different possible earthquake scenarios.

1.3. PROBLEM STATEMENT

When structures are excited by earthquakes they vibrate either in-phase or out of-

phase depending on their dynamic properties. In case two structures of different

dynamic properties vibrate out of phase with each other and the gap between the

structures is not sufficient to accommodate their relative displacements a phenomena

known as pounding occurs. This phenomena has been investigated through a number

of papers for instance Jeng and Tzeng, 2000 showed that pounding leads to both

local and overall structural failure during earthquakes in adjacent buildings. While

other researchers such as Munshi, 1997 investigated the effectiveness of Viscoelastic

dampers on the energy dissipation of RC structures and Chen et al., 2010 carried out

investigations on how viscous damper installed in the outside parameter of RC

structure subjected to 5 different bidirectional earthquakes would reduce the response

of the structure. Another issue associated with structural failure during earth quakes

is lateral-torsional couple of asymmetrical structures. Asymmetrical structures are

10

structures that have eccentricities in mass, stiffness or damping centers; during

earthquakes these structures experience different ductility demands on different load

resisting members. this effect is classified as lateral-torsional couple and has been

investigated in a number of papers Goel, 1998.

The response of structures to earth quake excitation is a complex problem, with a lot

of variables that have to be considered during modeling and analysis‟s phase.

However during the view of literature, most of the literature reviewed on both

adjacent and asymmetrical structures used simplified models which could not give

the actual response of multi-story structures under seismic excitations. Secondly

researchers use 2D frame elements excited in a single direction while actual

buildings are 3D and are excited by three component earthquakes hence again the

true response of actual structures cannot be truly represented.

Another issue that is not addressed well is the inelastic behavior of structures during

earthquakes, along with this is that most of the papers view considered elastic range

for supplementary dampers too. Those that did consider material nonlinearity did not

show any plastic formations within the structures and dampers.

Coming to the area of pounding although it is covered in a great extend, it is more on

equal height build pounding which is at floor level pounding. The more severe

problem which is mid column pounding is not covered. Furthermore soil structure

interaction is not considered in any of the papers viewed.

In case of asymmetrical structures, plan asymmetry is not covered. Most papers on

this topic consider eccentricity in mass, stiffness and damper distributions, hardly

11

addressing discontinuity of structural members or floors as is the case in most

modern structures. Again material and damper nonlinearity are not discussed in

detail.

1.4. OBJECTIVES

Although there is a great deal of work to be done in determining the behavior of

actual RC structures excited by earthquakes, this work here address the following

parameters

i) Effect of pounding on adjacent structures

ii) Effect of lateral-torsional couple on asymmetrical structures

iii) How implementing viscous dampers in structures would reduce their

responses and in the process reducing pounding and lateral-torsional

effect.

1.5. SCOPE AND LIMITATIONS

From the title of the project, the scope of this project is confined to the pounding and

lateral-torsional coupling reduction in RC frame structures using viscous dampers.

Response reduction in RC frame structures is a very wide subject. As with all

studies, there is the problem of finding good and relevant information. The

information in this project is restricted whatever relevant information that was found

to relate to the subject matter.

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1.6. ORANISATION OF THE PROJECT

This project consists of 5 chapters namely General Introduction; Literature Review,

Methodology; Results and Discussion; Conclusion and Recommendation. The first

chapter which is the introduction gives a picture of what the rest of the chapters

consists of. Chapter 2 which is the literature review gathers all information about

what a pounding and lateral torsional coupling reduction in RC frame structures, as

well as its challenges and prospects. Chapter 3 is the project methodology. All

information about the way I intend to carry out my project is in there. For example,

the type of materials used, modelling of structural and analysis are covered there.

Chapter 4 is closely linked to chapter 3. The result of the project after it has been

conducted as specified is found here. Finally, chapter 5 summarizes the project as a

whole and gives future investigation along with recommendations.

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2. LITERATURE REVIEW

2.1. GENERAL INTRODUCTION

Recently, several sizeable earthquakes have caused severe damage in civil structures

all over the world, including Japan (2011), Haiti (2010), Pakistan (2008), Eastern

Sichuan China (2008) and Bhuj, India (2001). To protect civil structures from

significant damage, the response reduction of civil structures under such severe

earthquakes v has become an important topic in structural engineering. During the

last three decades, significant efforts have been made to apply modern control

technology to civil structures for enhancing structural safety against natural hazards.

Various types of passive and active control systems have been developed and

experimentally verified. A number of them have been implemented in full scale civil

/structures. Passive systems are well understood and widely accepted. One passive

system that is of great interest is viscous damper.

Viscous dampers are made up of highly viscous fluid in a cylindrical container with

end piston which compresses the viscous fluid in order to dissipate the imposed

forced on the structure through earthquake excitation. Viscous dampers are capable

of reducing both the displacement and the forces generated by earthquakes. These

dampers are installed in structures through bracing systems and can also be installed

in the outside parameters of structures as diagonal system.

This work examines the affect that installing dampers in RC frame structures would

have on their responses in terms of pounding mitigation in adjacent structures and

lateral-torsional response reduction in asymmetrical structures. In the pounding

mitigation, dampers are place in two adjacent RC frame structures of different

14

heights. The seismic gap between the structures was found to be insufficient to

accommodate the relative displacements of the structures thus resulted in pounding,

where the roof of the shorter structure collided with the corresponding floor of the

taller building. Introducing viscous dampers did reduce the amount of displacement

in both structures thereby avoiding contact between the structures.

Also in this work viscous dampers were used to reduce the lateral-torsional response

of two asymmetrical structures. The first asymmetrical structure and different

distribution of stiffness, with one side of building have stiffer frames while the other

three sides had the same stiffness. For the second model a bi-eccentric system

subjected to 3 component earthquake was examined. In both case the use of viscous

dampers did result in reduction of the torsional force developed within the structure

2.2. SUPPLEMENTERY DAMPERS

Reinforced concrete structures during earthquakes are excited by inertia forces which

impart energy again to the structure. This energy has to be dissipated by the structure

through displacement, floor accelerations and rotations which in most cases results in

structural collapse or damage. For this reason the structures are design with certain

amount of ductility in order to limit the damages (local plastic hinges occur at some

locations).

Other then the formation of localized plastic hinge formations there are no ways for

the energy to be dissipated, until the development of supplemental dampers came

into the picture. These supplementary dampers allow for large energy dissipations

15

while limiting the role of the structure in dissipation the energy. There has been a

vast amount of research around the topic area and still continues to be under the spot

light of many earthquake and structural engineers. The reasons for the ongoing

research is to come up with a structure that is both safe and economical, before the

development of supplemental dampers structures had to have a certain stiffness (

additional sections) in order to reduce structural drift, although this worked but it

made the construction really expansive and hence the development of these non

structural mechanical systems. Secondly because of the ductility demand there was a

placement of how stiff the structure could be made, this was also seen as a secondary

reason as to why supplemental dampers would incorporated into the structure would

be a valuable alternative.

Munshi, 1997 investigated the effect of Viscoelastic dampers on the energy

dissipation of RC structures. The structure was modeled as fiber beam-column

element with structural hinges modeled as „fiber hinges of pullout type”. While using

a two node finite element damper model generated with the aid of “step by step

integration scheme proposed by Koh and Kelly”, he investigate how stiffness

degradation, strength degradation and pinching characteristic of reinforced concrete

hinges would be affected by introducing Viscoelastic dampers as energy dissipaters.

Munshi found that the Viscoelastic dampers did reduce the energy dissipation

requirement on the RC structure, and that the damping ratio of the damper depended

on the period of the structure as well as its ductility demand. Tezcan and Uluca, 2003

using SAP2000n the authors investigated how the Viscoelastic supplemental

dampers would alter the seismic response of RC frame structures and found that an

increase in damper ratios resulted in decrease seismic response of the structures,

16

however this was not true for the case when the structures when subjected to low

frequency earthquakes, this being due to the time period of ground motion and that of

the structure being in phase.

Another energy dissipative technique that has been around for a while is the use of

Tune mass dampers (TMD). An investigation of this type dampers by Pinkaew et al.,

2003 revealed that TMD are effective in reducing the amount of damage the

structures under goes during seismic excitation. Although the investigation uses the

damage index to find the effectiveness of the tune mass dampers rather than peak

structure displacements, it shows that TMD are effective in reducing the structures

damage depending on the characteristics of ground excitation.

Chen et al., 2010 using perform-3D the researchers carried out investigations on 46

viscous dampers installed in the outside parameter of RC structure in the form of K-

bracing. They investigated how these dampers would reduce the structural response

when subjected to 5 different earth quakes with two components considered (X and

Y). In their work the researches carried out comparative studies on different method

of analysis such as static nonlinear, dynamic nonlinear analysis, elastic and inelastic:

their target was to determine the short comings of each analysis procedure analysis.

For instance in the static analysis they considered the push over analysis with three

different loading shape distributions namely a triangular load, uniformly distributed

17

load and model load. They found that the modal load and inverse triangular load did

give almost similar results while that of the uniformly distributed load was always

smaller. Another important agenda in their work was the use of fiber model used to

model the energy dissipation of dampers rather than the plastic hinge formation

mechanism which would not incorporate the damping provided by the supplemental

dampers until plastic hinge formation occurs, where‟s the fiber model employs

damping provided by supplementary damping through crack, yielding and failure.

What they finding showed was that for the three different earthquake levels

(frequent, medium and rare) structures without damper did not meet any of the code

specifications while with dampers the plastic deformation of the structures was

reduced. Hence the viscous dampers installed in the structure did reduce the energy

dissipation demand on the structure there by reducing the structures response under

earthquake excitations.

2.3. TYPES OF SUPPLEMENTARY DAMPERS

18

TYPES OF DAMPERS IMAGE

MASS TUNE DAMPER

Used to counteract the displacing force by isolating in the opposite direction to

the force causing the movement.

BALL BEARING TYPE DAMPER

This type of dampers isolate the structure from base movements, reduce shear

force but do not reduce the lateral displacement of structure

VISCOUS DAMPERS

Viscous dampers are velocity dependent and reduce both base shear force and

inter-story drifts

Figure 2.1 damper types

19

There are a number of ways of retrofitting structures each with its own controlling

parameters Zhu et al., 2001,Lu et al., 2002. The retrofitting technique that is going to

be cover here in this thesis is the use of viscous dampers for retrofitting to increase

the energy dissipation of old and new structures under seismic excitation. Viscous

dampers are velocity dependent and do not require an external power source since

there are passive dampers. Another important factor is that the forced generated by

the dampers is out of phase with force due to seismic excitation and hence no

resonance occurs. Thirdly the force generated by the dampers does not lead to

localized force build up with in the structure.

2.4. POUNDING

Due to lack of land and its heavy price tag most of the high-rise buildings in

metropolitan cities around the world are built rather close to each other. Now in

times of earth quakes these structures oscillate and if the gap between them is not

sufficient enough to accommodate their displacements the structures collide. This

collision of structures in structure engineering is referred to as pounding. Pounding in

these structures is primarily associated with the fact that these structures do not have

the same dynamic properties such as stiffness, mass, damping and time period of

oscillation, there in resulting oscillation that are out of phase. The effect of pounding

on structures has been noted by several researches to be one of the leading factors

associated with structural collapse (V.Jeng and W.L.Tzeng), (Rosenblatt and Meli)

reported that in the Mexico city earth quake of 1985 that out of 330 collapsed

buildings 40% of this were due to pounding effect. Depending on the layout of the

adjacent structures pounding could occur at the floor levels if both adjacent buildings

are of equal height or at mid column height if there is a difference with the floor

heights. (V.Jeng and W.L.Tzeng) gave different forms of pounding namely, mid

20

column pounding, heavier adjacent building pounding, taller adjacent building

pounding, eccentric pounding and end building pounding. There are various dynamic

parameters that affect the pounding response of the buildings. For instance difference

in stiffness, damping and mass properties in the buildings would lead to an out-of-

phase oscillation. Another such important factor to consider is the seismic gap

between the two structures, it is not always possible that adjacent or parallel

buildings will have enough gap to accommodate the lateral displacements of both

structures and at times large gap between the two buildings could involve greater

pounding force due to great accelerations and story drifts that are associated with

structural oscillations (Salam 11th

ICSGE Page22-9).

2.4.1. ADJACENT BUILDINGS

Due to lack of available building land most high rise buildings in metropolitan cities

are built without an adequate seismic separation between them, which in turns leads

to pounding effect during medium- high earth quakes. Pounding between adjacent

structures has been noted my several researches to be one of the major factors

leading to structural collapse and serve damages to both structural and non structural

units in buildings Scholl, 1989 and Kasai and Maison, 1997.

Hong et al., 2003 developed a procedure for determining the gap required to prevent

pounding of two nonlinear SDOF systems using structural reliability methods and

random vibration theory. In their work they modeled the excitation as a white noise

excitation and used the peak response from two sided crossing problem. They then

compared their numerical results with the complete quadratic combination rule and

found that the ratio of the former to the later varied between 0.8 and 1.1. Due to the

21

fact the crossing rate for seismic design of individual structure subjected to seismic

excitation is greater than that used for the evaluation of seismic gab, using the

structural response obtained from a two sided crossing problem is always

conservative. They found that the ratio of seismic gap calculated from a one sided

crossing problem to that of two side crossing problem was between 0.85 and 0.95.

Lin, 1997 gave a theoretical solution for determining the seismic gap required to

prevent pounding of adjacent structures subjected to a non stationary Gaussian

random process. The theoretical solution was based on random vibration and the

structural system considered was a linear multi degree of freedom system depicted as

a lumped mass system. He gave the following expression to compute “mean and the

standard deviation of the separation distance of adjacent buildings to avoid

pounding”:

And the standard deviation as:

Where , T is a time duration, is Euler‟s constant,

equal to 0.5772 and

He found that for structure‟s whose period of vibration is the same or nearly equal

the required separation distance would be small since they would vibrate in phase but

for those with large difference in their period of vibration large seismic gap was

required. Secondly structures that had a long fundamental vibration period would

22

also in turn require larger seismic gap. Another parameter that has to be considered

in future work is that variation in the seismic excitation as it travels from the base of

one structure to the next. Secondly the soil-structure interaction has to be taken into

account.

Lin and Weng, 2001 studied the effect of height and period of vibration on the

pounding probability of adjacent structures subjected to artificial earths generated by

multiplying the response spectra of dense soil and soft rock with a trapezoidal

intensity function. They found that the correlations used in the UBC-97 (ABS and

SRSS) overestimated the separation distance require for no pounding. They proposed

a separation distance for a steel moment resisting framed modeled as a shear type

structure with elastoplastic behavior, the proposed method was base on seismic

hazard analysis for a given peak ground acceleration and conditional pounding

probability. They found that the minimum separation provided by the code varied

with “the combination method used, period ratio of adjacent builds and the individual

periods of the structure” they also concluded in their work that structures that have

periods of vibration close to that of the soil have greater pounding probability so do

structures of the same height with well separated periods of vibration.

Lopez-Garcia and Soong, 2009 preformed a comparative study on four criterions for

seismic separations between adjacent nonlinear hysteretic structures. All four

criterions were base on the double difference combinations rule but differed in the

method of correlating the displacements responses of the adjacent structural systems.

The separation distance proposed by the double difference method is as given below:

23

where S is the separation distance and , are the displacement response of the

adjacent structures ``A'' and ``B'', respectively,

ρ δ δ δ δ

δ δ

δ δ

where , and δ

, δ

are the natural periods and damping ratios, respectively. of

the adjacent structures ``A'' and ``B''.”

The four criterions under investigation were the Filiatrault criterion, Kasai criterion,

Penzien criterion and Valles criterion. Filiatrault criterion uses the correlation

between stationary displacement response processes of nonlinear hysteretic SDOF

systems given in eq(4) with the assumption that the correlation of actual nonlinear

hysteretic system characterized by TA, ξA, RA, αA and TB, ξB, RB, αB is the same as

that of linear system characterized by TA, ξA and TB, ξB,.

For the Kasai criterion assumes that the correlation given by eq (4) holds true for a

nonlinear hysteretic system as long as the correlation between the structural

responses of a nonlinear system can be approximated by a linear system whose

parameters were effective parameters. He gave the following expressions for the

effective parameters:

ξ

ξ

Where is the displacement ductility of the structures and ξ are the effective

time and damping coefficients.

Whereas the Penzien criterion used the same expression but introduces the effective

parameters as given below:

24

Valles calculated the values of ρ empirically through a set of equations.

The errors with all above criterions relates to the fact that they all used the

correlation between a linear systems to depict the correlation between structural

responses of nonlinear hysteretic structures.

Jankowski, 2008 carried out a parametric study on to two equal height 3 dimensional

structures subjected to 3 component El-contra earthquake. The structures were

modeled as inelastic multi-degree-of-freedom lumped mass systems and a non linear

Viscoelastic modeled was used to depict the pounding force during contact of the

two adjacent buildings. Jankowski study how the variation in mass, stiffness, gap and

yield strength would affect the structures response, he found that for the lighter more

flexible building “structural pounding during earthquakes had a significant

influence” on the structures response and even more so in the longitudinal direction

as compared to the transverse and vertical directions. Structural pounding forced in

the lighter more flexible structure lead to it having preeminent deformations as it

enter into the yielding zone, however the heavier more stiffer structure did not

experience the same behaviour patterns as in the lighter building.

Pantelides and Ma, 1998 carried out a parametric study on effect of pounding on the

response of elastic and inelastic structural response of a single degree of freedom

25

system subjected to earthquake. He modeled the pounding force as a Hertz nonlinear

spring in an impact oscillator subjected to harmonic excitation. The equation of

motion was then written as:

Where m is the mass of the structure, c is the coefficient of damping and k is the

structural stiffness. Here the pounding force is give as which is expressed as

follows:

Where (a) is the separation distance between adjacent structures and R “is the impact

stiffness parameter which depends on the material of the two structures that come

together as well as the surface geometry”. The parametric studies considered in their

work were the frequency of the excitation, separation gap, period of structural

vibration and the damping ratio. They found that under the same excitation,

structures with different natural periods of vibration would experience different

magnitudes of pounding. Secondly as they compared the structural response of the

elastic and inelastic case they found that although the overall structural displacement

was larger for the inelastic case the acceleration, velocity and the magnitude of

pounding were lower for the inelastic case. Thirdly the pounding occurrence was

lower for the inelastic case than the elastic case.

Agarwal et al., 2007 investigated how introducing friction bearing base isolation

(Teflon base isolation system) would affect the pounding of adjacent structures

subjected to four different earthquakes. The work showed that although base

isolation might eliminated the chance of base pounding the upper story pounding of

26

structures might still occur depending on structural parameters such as, stiffness,

mass, natural period of vibration and type of seismic excitation consider. They

studied 3 different scenarios, when one of the structures was base isolated, both

structures were based isolated and when both were fixed based structures. For the

case in which one of the two adjacent buildings had a base isolation the overall

deflection of the structure decrease but there was still large lateral displacement and

in case where the gap between the two buildings was equal to the overall structural

drift increase in pounding occurrence increased. While for the case of both structures

being base isolated, the magnitude of the impact force was noted to dependent on

whether the sliding friction coefficient was considered constant or varied with the

velocity. In the latter case the pounding forced was reduced while in the early case

impact force was higher. However for both structures base isolated that are chances

that the structures would move in phase keep the same distance between them.

Komodromos, 2008 carried out parametric investigation on seismic base isolated RC

structure. he model the super structure of the RC build as a shear beam with lumped

mass at the story level while the isolation system considered was modeled as a linear

model with effective damping and stiffness. As for pounding a nonlinear Hertz an

impact model was used by the researcher. The following parameters and their

influence on the pounding effect were studied with the aid of a soft ware generated

by the researcher.

1. Effect of the flexibility of the isolation system

2. Effect of the impact stiffness and damping

3. Effect of the superstructure‟s stiffness

27

The following conclusions were arrived at, the more flexible the isolation system the

greater chances of pounding with the force case being if the fundamental period of

vibration concedes with that of the excitation. An increase in impact stiffness is

associated with decrease in relative displacement at the isolation level while the

maximum floor accelerations and inertia forces increase substantially with the

pounding force, it was also noted that an increase in impact stiffness resulted in an

increase in natural frequency which tends to amplify the seismic loading on the

structure. Lastly it was found that an increase in superstructure flexibility resulted in

an increase in the inter-story deflections.

What the research did not mention in his work is how the above parameters would

affect the structure response when pounding locations varied, for instance if

pounding at the isolation level is prevented this would not mean that the

superstructure would not pounding against fix based neighboring buildings, secondly

researcher does not consider the affect of multi component seismic excitation thirdly

he depicts the structural units to be linear are then considering them nonlinear in

which case u could get better sequence of formations.

2.4.2. RETORFITTING OF ADJACENT BUILDINGS

Lu et al., 2002 the team carried out experimental study on a 5 story and 6 story steel

frames subjected to El centre 1945 earthquake to determine how the installation of

fluid dampers would affect the structural response of the building. They took three

different cases, 1st case was two parallel structures with no connections while the 2

nd

case was done for the structures linked with rigid rods and the final case was that of

the structures linked with fluid dampers. In their study they found that fluid dampers

gave the best results in that they did not alter the fundamental periods of the

28

structures but reduced the structural responses of the building more than the rigid

connections.

Benavent-Climent, 2006 preformed experimental (shake table) study on four 6 story-

3 bay reinforcement concrete moment resisting frames with wide beam-column

connection. Of the four samples made two of them were retrofitted with diagonally

braced new dampers developed by Benavent, this diagonal braced dampers consisted

of “H-shaped members designed to remain elastic when the brace is axially loaded”,

the dampers were design to increase the structural stiffnes by ten fold and reduce the

interstory drift below 0.7%. He then compared the structural responses of an extrior

and interior beam-column retrofitted with braced viscous dampers against their

counter parts with out retrofitting. He conclude that the following findings in his

work:

(i) For same PGA the dampers reduced the interstory drift by “70% and 85% in

the exterior connections, and 60% and 85% in the interior”,with the reduction

increasing with increase in peak ground accelerations.

(ii) Dampers increase the UDEC (ultimate energy disipation capacity) for the

exterior and interior wide beam column connections by 12 and 4 holds

respectivly while the maximum lateral force increased by 4 and 2 respectivly.

(iii)Braced dampers reduced the damage to the RC structure by 75%.

(iv) The braced dampers prevent drastic damages to beam column connections

untill one of the dampers yielded.

Zhu et al., 2001 investigated the optimum response reduction of a primary structure

connected to an auxiliary structure through an interconnecting element. Their work

covers two different areas, the first area being how the configuration of the structures

29

would affect the response of the primary structure. Secondly team than studied how

different control techniques (passive, active and semi-active) would affect the

response reduction of interconnect parallel single degree of freedom systems

subjected to the NS component of the EL centre 1940 earthquake. In terms of

structural configuration they conclude “effectiveness increases as the mass of the A-

structure increases, and the natural frequency of the A-structure is further from that

of the P-structure.” and that a flexible auxiliary structure reduced the absolute

acceleration of primary structure (P-structure) while a rigid auxiliary structure

reduces the relative displacement of P-structure. The team future studied the

effectiveness of passive control, active control and semi active control methods,

finding that the semi-active control technique was more effective in response control

of the structure then the optimum passive control method.

2.5. TORSIONAL RESPONSE OF ASYMMETRICAL STRUCTURES

Through the work of varies researches and case studies conducted on structures

subjected to earthquakes, it was found that symmetrical structures had far lesser

damage then asymmetrical structures of the same strength or even higher. The reason

being that in asymmetrical structure coupling occurs between the lateral response of

the structures and their rotation about the centre of resistance. The torsional aspect of

the response is generated through the eccentricity in the structure resulting from

discontinuity in structural members, differences in stiffness of members and

distribution of mass. As the centre of mass, stiffness and resistance shift further apart

the structure would rotate in the direction of the weak section there by creating a

larger deformation in one section of the building as compared to the other and

ultimately may result in failure of that portion.

30

Thambiratnam and Corderoy, 1994 carried out simple microcomputer procedure

using two different analysis techniques, quasistatic and real time dynamic analysis to

determine the effect of degree of asymmetry and direction of twist on the torsional

response of building. The degree of asymmetry in the building was varied through

the positioning of core walls. The analysis were done on a three dimensional 10 story

rectangular and 15 story L shaped building both with a core wall of stiffness 12

time‟s large then that of all columns combined. Both analysis methods did show that

as the core moves away from the centre of resistance the degree of asymmetry

increase does resulting in large torsional response of the structure, for the quasistatic

method a triangular load applied in y direction was used for modeling the earth

quake. “Both the static and dynamic analyses give results which agree qualitatively

and to some extent quantitatively and indicate that the responses are greatly

influenced by the degree of asymmetry in the building”.

K. G. Stathopoulosi and S. A. Anagnostopoulos 2004 investigated the inelastic

response (torsional) of asymmetrical structures excited by 10 different artificial earth

quakes generated to match the design spectra. They compared the response of 3 and

5 story RC structures to a simplified shear type structure under bi-axial earth quake

excitations. Their primary objective was to show that the responses for simplified

shear type structures used in code provisions do not give a true picture of actual

response of multi-story real RC structures. The beam and column members of the

two RC models were modelled as nonlinear using plastic hinge model. Asymmetry in

both structures was introduced through dimensioning of the frame members taking

into account the mass eccentricities and thus stiffness eccentricities were also

generated. The top story displacements and rotational ductility demands for the

multi-storey structures show that the flexible side frames severed more

31

displacements and ductility demands then the stiffer side frames, this demands were

more server for the beams on the flexible side than the columns due to the fact that

capacity design limits the column stiffness to be always in the elastic range.

Thambiratnam and Corderoy, 1994 studied the effect of varying asymmetry on the

structural response and found that variation in asymmetry affected the shear force,

bending moment and deflection response of the structure. While Mansoori and

Moghadam, 2009 worked on the optimal distribution of dampers so as to control the

degree of asymmetry in the structure, thereby reducing the lateral-torsional response

of the structure.

V.I. Fernandez-Davila1 and E.F. Cruz 2008 preformed Time history response

analysis on 5 story asymmetrical RC frame structures subjected to uni- and bi-

directional earthquake excitations. The models considered took into account

nonlinear behaviour of the structure members with failure occurring at member ends.

Using strong column-weak beam design two different cases where consider a

symmetrical model and an asymmetrical model subject to 20 artificial earthquakes

loads. The aim of the paper was to propose a set of combination rules that could

effectively estimate the response of asymmetrical structures using response spectra

analysis of uni-directional earthquake loading applied in x and y direction separately.

For Time history response analysis a bi-directional earthquake loading was applied

on the 3D asymmetric model and the response of the structure monitored for varying

angle of earthquake incidence and reduction factor. Using SRSS and 100/β ( β =40,

60) combination rules, the results of response spectra analysis using unidirectional

earthquake loading applied on the structure gave results that were comparable to

those obtained through time history response analysis which used a bidirectional

earthquake loading.

32

Erduran, 2008 investigated the capability of current nonlinear static analysis in

capturing the effect of torsional response in asymmetric structures. In his work the

author compared the estimate results of N2 and MPA (modal pushover analysis) with

the “exact values” obtained from response history analysis for two RC frame

structures, one with unidirectional eccentricity introduce through shifting of mass

centre through 1.5m and the other with a bidirectional eccentricity due to plan

asymmetry (moving the mass centre .5m in both horizontal directions).Both

structures were subjected to a set of 30 earthquakes, of which 15 were near fault

earthquakes while the other far fault earthquakes. He also considered two different

versions of first pushover mode for the nonlinear static analysis methods, the tow

methods differed only in point of loading application. On comparing the results of

NS and MPA with response history analysis, the author concludes that with the

following points

(i) “The first mode pushover procedure, where the lateral forces are applied at

the mass centre significantly underestimates the torsional rotations resulting

in an underestimation of the displacement demands on the torsional flexible

side for both uni-directionally eccentric and bi- directionally eccentric

systems. For the uni-directionally eccentric system, the underestimation of

torsional rotations results in conservative displacement demand estimates for

the torsional stiff side."

(ii) When the point of load application is change to the shifted mass centre the

first mode push over analysis method gave torsional response estimates. This

being the modified first mode push over analysis employed in current codes

under section of accidental eccentricity design.

33

(iii)The N2 which incorporates response spectra analysis method in estimate

torsional response of asymmetrical structure did give good results that were

comparable with “exact values generated through response history analysis.

However this was true for the flexible side but for the stiffer side the result

was more conservative due to the assumption in N2, which assumes that the

displacement of stiffer side is the same as that at centre of mass.

Modal pushover analysis method gives more conservative results for 50% in 50 years

and 10% IN 50 year‟s hazard levels, but a comparable result for 2% in 50 years

hazard level.

2.5.1. TORSIONAL CONTROLE OF ASYMMETRICAL STRUCTURE

Yoshida and Dyke, 2005 investigated the response control capacity of shear mode

MR damper placed in two numerical full scale asymmetrical structures. In first case

of study the structure had a rectangular plan with asymmetry being due to the

location of a shear wall in the 9 story building. While the second case considered 8

story l shaped structure. The mechanical model of the MR damper was that of Bouc-

Wen model force produced in the damper being controlled through variation in

applied voltage to produce the equivalent damping force within the system:

And

And the “The functional dependence of the device parameters on the command input

u is modelled as”

34

And

In their work they consider three different control systems namely “passive-on,

clipped-optimal control, and ideal active control” to evaluate performance of the MR

damper. They found that the clipped-optimal control method gave better results than

passive-on while ideal active control method gave pretty much the same results.

Acceleration and inter-story drift reductions for the clipped-optimal control method

where more pronounced from smaller earth quakes.

Shook et al., 2009 carried out experimental and numerical investigation on the affect

of semi-active (magneto rheological) dampers in reducing the torsional response of a

3 story, 9m high asymmetrical structure. The resistance of the MR damper was

controlled by fuzz logic algorithm generated through controlled-elitist genetic

algorithm (GA). Results of numerical evaluation of the FLC showed favorable

performance with respect to 1st, 3

rd and 4

th mode of vibrations 4 while the

performance was less favorable with respect to 2nd

mode of vibration. It was

observed that the FLC is effective in decoupling lateral and torsional responses of the

structure.

García et al., 2007 investigated the torsional response control of asymmetrical

structures using viscous-elastic dampers and found that visco-elastic dampers were

capable of reducing the torsional response of asymmetrical structure by shifting the

empirical centre of build to coincide with the geometric centre of the building.

Optimal damper eccentricity values tended to increase linearly as the stiffness or

mass eccentricities increased, but their values depended on the input and system

parameters such as the torsional-to lateral stiffness ratio, uncoupled period,

35

eccentricity of the base structure, and stiffness and damping characteristics of the VE

dampers.

2.5.2. PASSIVE CONTROL USING VISCOUS DAMPERS

Through various researches on structures under earthquake excitations revealed that

structures which are asymmetrical suffer more damage as compared to those which

are symmetrical in nature. The asymmetry in the structures could be due to

eccentricities in mass, stiffness, strength or even damping properties. In certain case

it is the distribution of resisting frames within the structures which are also

responsible, for instance structures with soft stories were found to undergo lateral-

torsional couple when subjected to seismic loads, since continuity in structural

members cause alterations in the load path these structures have been classified as

asymmetrical structures.

Goel, 1998 is one of those leading researchers who have studied various aspects of

earthquake loading affects on asymmetrical structures, and in this paper the resercher

examines how using supplemental damping systems could alter the structural

response under seismic excitation. In this work the researcher examines the affect of

centre of mass, centre of rigidity, and centre of the geometry on the structural

response under lateral-torsional coupling. The model considered was idealized single

story structure incorporated with fluid viscous dampers. The author concluded with

the following findings:

i) Asymmetrical distribution of dampers lead to reduction of edge deformations

of up to 2 time that of symmetrical distribution

ii) The largest reduction in edge deformations in the flexible side was noted for

when the CSD (centre of stiffness of damping) was as far away as possible

36

from CM (centre of mass), while for the reduction of edge deformations in

stiffer side the CSD was on the same side as CR.

iii) Also largest reductions in edge deformation on the flexible side were noted

for when supplemental dampers were distributed as far away as possible from

the CSD.

iv) Since the normalized supplemental damping eccentricity and supplemental

damping radius of gyration cannot take up simultaneously largest possible

values an optimal reduction can be obtain through using fewer dampers

placed at the outer most edges or my place dampers in the perpendicular

direction.

v) The effects of supplemental damping on edge deformations were more

pronounced for strongly coupled torsional flexible asymmetrical plan

systems.

Goel, 2000 using modal analysis techniques the author investigated the effect of plan

wise distribution of viscous dampers on the apparent modal periods, apparent

damping ratios, mode shape components, modal participation factors and dynamic

amplification factors of asymmetric-plan buildings with supplemental viscous

damping subjected to harmonic ground motion. He found that the plan wise

distribution of dampers affect the dynamic amplification factor more than any other

factor.

Goel and Booker, 2001 investigated the effects of supplemental viscous damping on

the seismic response of one-storey, asymmetric-plan systems responding in the

inelastic range of behavior. Through this investigation the authors found that the

deformation, ductility and hysteresis demand on the flexible side lateral load

resisting members could be reduce through the implementation of viscous dampers in

37

asymmetrical structure. The amount of reduction depending on the plan wise

distribution of these supplemental dampers, for instance when the dampers had an

eccentricity equal but opposite in direction to that of structural eccentricity maximum

reduction in deformation and ductility demands of the flexible load resisting frame

was registered.

Goel, 2005 the author investigated the effect of viscous damper nonlinearity on the

response of one story uni-eccentric linear and non linear asymmetrical structure.

Following points are the conclusions derived by the author

(i) Damper non-linearity leads to reductions 25% in the flexible edge

deformations of short-period systems while for longer period systems the

reduction is 10%.

(ii) Effect of damper nonlinearity was found to have a small variation for base

shear and torque of linear and non linear systems. However the dampers did

reduce the torque effect considerable while the base shear was only slightly

effect.

(iii)For both linear and nonlinear systems, nonlinearity in the damper did reduce

the damping force and increase the damping torque.

(iv) Reduction in damper force was only for system with periods longer then

0.2sec

(v) The effect of plan distribution of dampers is not influenced by damper non

linearity

(vi) Combination of system nonlinearity and damper nonlinearity might be used

to remove the adverse effects.

The objective of this current work was to study how using energy dissipating devices

in old and new structures would alter their dynamic behavior under seismic

38

excitation. We have all witness the devastations cause by earthquakes in one way or

the other. Recent earth quakes in this modern time of material development and

construction advancement have resulted in loss of life‟s tolling hundreds of

thousands and property damage in the billions. Although other factors associated

with earthquakes are also reasonable responsible for the deaths and property

damages, but still this are a second nature out breaks.

Structures under seismic excitation are subjected to a sudden again in energy which

has to be dissipated through inter floor accelerations and displacements. This in turn

causes the structure or parts of the structural units to collapse as they were not design

for such extreme displacements. Although the ductile of the structure does help in

dissipating some portion of the energy absorbed through plastic hinge mechanism.

These plastic hinge formation to an extend are acceptable but when the number of

plastic hinge formations exceed the design limit, the structures gives way and

collapse. There have been various ways that have been investigated in order to

compensate for the large displacement in structures, for example shear walls base

isolation techniques.

Here the method under study is the use of viscous dampers in retrofitting old

structures and new designed structures. The viscous dampers considered in this study

are velocity dependent. The advantages of this type of dampers is that they have

forces that are out of phase with the exciting force and no localized forces are

generated were they are installed secondly since these are passive dampers there is

no requirement of an external power source to control the system.

The use of viscous dampers provides the structure with an alternative route to

dissipate the absorbed energy, hence reducing the amount of plastic hinge formations

within the structural units. There are various dynamic properties that are responsible

39

for the behavior of structures under seismic excitation, due to the vast nature of the

topic few parameters will be covered in this work. The parameters are first categories

according to different areas or factors that arise from structural excitation:

For adjacent buildings one of the most server problems is pounding which results

from lack of proper clearance or seismic gap between the two buildings. Seismic gap

is the distance between the two buildings required to accommodate the displacements

of the two structures, this phenomenon is very apparent in metropolitan cities where

tall structures are constructed with little or no seismic gap. This problem is very

apparent where you have new buildings built close to old existing structures, because

of the difference in their dynamic properties the structures vibrate out of phase

resulting in pounding. Depending on whether the structures are of equal heights or

not the location of pounding will vary so will its severity. For instance structures of

equal height experience floor level pounding which is less severe the mid column

pounding.

In this work the employment of dampers is primarily used to reduce the dynamic

response of structures, such as displacement and shear force but this would in turn

reduce the chance of pounding since the displacements of the structures is reduced.

The second agenda in this work is that of asymmetrical structures under seismic

excitation. Asymmetrical structures are structures that have eccentricity in mass,

stiffness or damper locations due to irregular construction or discontinuity in

structural members. Due to eccentricity of stiffness and mass the structure undergoes

uneven lateral deformation. Due to the uneven lateral deformation demand of the

resisting structures there is a couple of lateral and torsional response of the structure.

For this it was suggested using viscous dampers to compensate for the difference in

stiffness in order to reduce the torsional response of the structure.

40

The key difference between this work and the vast amount of research on the topic is

that:

i) Structure is subjected to 3 dimensional earth quake

ii) Plastic hinge formation in damper and structure members are studied for

iii) 3D, multi- story structures are considered with nonlinear structural elements

and dampers.

2.5.3. CONCLUDING REMARKS

Through the literature reviewed and remarks of researchers the following points were

seen as points that require further research

i) Soil structure interaction

ii) Lateral-torsion coupling pounding

iii) Mid column pounding in soft story structures

iv) Use of more detail and as close as possible to actual structural models

41

3. METHODOLOGY

3.1. INTRODUCTION

Although it is not practical or even possible to have structures that are 100% seismic

resistant structures but these structures can be designed to have ductility response

during earthquakes. The ductility of structures is important in the sense that failure is

not sudden and explosive but rather undergoes large deflections which are indicative

of near structural failure. This is the criterion in which most currently seismic

building codes are based on and structures that follow these codes come out with

better performance under seismic excitations compared to the earlier counterparts.

The study of structures under Seismic excitation has come a long way in the last

couple of decade. Developments in technology made it permissible to measure the

intensity, depth and direction of earthquakes. These technological developments and

vast amount of research on the topic have presented new era in the ways structures

can dissipate energy resulting for seismic excitations.

Due to the vast nature of the topic there are two major areas that are going to be

examined here.

i. Retrofitting of adjacent structures to reduce dynamic response

ii. Retrofitting of asymmetrical structures in order to reduce torsional

response.

In the first case researches such as Jankowski, 2008 studied the effect of the

difference of stiffness and mass on the vibration of two equal height structures. He

found that variations in mass, stiffness and gap size does affect the longitudinal

pounding of the lighter building then it does the heavier building. Furthermore

Pantelides and Ma, 1998 investigated the effect that seismic gap and the inelastic

42

structural behavior will have on the magnitude of the pounding force generated

during pounding. The structure was models as a nonlinear single degree of freedom

with one side pounding. On comparison he found that inelastic structure had lower

peak velocity, acceleration and pounding force then the elastic structure.

FIGURE3. 1. Overall schematic view of the methodology of the study

There are various models that can be used for seismic study, but the model employed

here is that of a reinforced concrete framed with added on viscous dampers.

LITERATURE REVIEW

PHYSICAL MODELING CONSITUTIVE

MODELING

FORMULATION AND EXCUTION OF F.E CODE

APPLICATION ON REINFORCE

CONCRETEC STRUCTURES

STOP

START

43

Nonlinearity was considered in both the reinforced concrete frame and the viscous

dampers allowing for plastic hinge formations within the two materials. This chapter

gives the detail account of the material and structural properties and the modeling

aspects of it.

3.2. PHSICAL MODELLING

Three dimensions, nonlinear analytical model of frame element and the developed

viscous damper element are presented in the following sub sections.

3.2.1. PHYSICAL MODELING OF FRAME ELEMENT

The analytical model for RC frame members used in this investigation was

developed by Thanoon (1993-2004). It consists of three different zones as shown in

figure 3.2, the first zone is the rigid block zone located at each end of the member,

the second zone is the 3D plastic hinge zone at each end assumed to have zero length

and the remaining intermediate part of the member represents the third zone which is

assumed to remain elastic. These zones represent the finite width of the beam-

column joints, the plastic hinge zones give the inelastic properties of the member

while the central part of the member (located between two plastic hinges) is assumed

to reflect the elastic behavior of the member.

In constructing an inelastic element for a reinforced concrete section, the following,

basic assumptions, have been made: (Thanoon 1993-2004)

i) The generalized force-deformation relation of the element follows an elasto-

plastic model, having yield strengths corresponding to the ultimate capacities of

the member.

44

FIGURE3.2 Physical model of beam-column element

3.2.2. PHSICAL MODELING OF DAMPER ELEMENT

The analytical model of damper that is used here is the 3 dimensional nonlinear

damper model proposed by F. Hejazi (2008). The model consists of three zones as

shown in figure 3.2 shown below; each zone translates the different behaviors of the

damper. Rigid zone indicates the structural joint, while the hinge zone gives the

inelastic behavior of the damper (plastic hinge formation within the damper) during

inelastic analysis. The intermediate portion gives the elastic stage of the damper

therefore when the damper is still in functionality with therefore analysis within the

elastic limit.

FIGURE3.3 Real Viscous Dampers and 3-D Nonlinear Damper Element Model

Constitutive (F. Hejazi, 2008)

45

3.3. MECHANICAL PROPERTY OF DAMPER

The dampers employed in this work are viscous dampers with the basic layout o the

damper system show in figure 3.8. It consists of cylinders with silicon fluids being

forced through orifices by a stainless steel rode. The damping forced generated is

developed through the pressure difference at the ends of the piston and can be

adjusted by varying the size of orifice or even the viscous fluid used. The damping

force generated by forcing the viscous fluid through orifice is one that is in phase

with velocity although in certain case the restoring force could result in a damping

force that is rather in face with displacement than velocity.

The force-velocity relation is given by Goel, 2005:

Where

Force

Iceint

Ends of the dampers

Α is a positive exponent that varies from 0 to 2, but for most structural engineering

the upper limit is usually 1. When α =1 the damping force varies linearly with

velocity while if α <1 the damping force varies nonlinearly with the velocity. sgn( )

is the signum function and is usually taken to be 1.

46

Figure3.4 fluid viscous damper

3.4. DYNAMIC F.E FORMULATION FOR R/C FRAME STRUCTURE

The basic equation for structures under earthquake excitations considering the

equilibrium of forces is give as:

(3.9)

Where M is the mass of the structure, C is its inherent damping and K the stiffness of

the structure. is the seismic excitation force. For the structure to dissipate the

energy absorbed during the seismic excitation it would have to undergo large

displacements which could result in plastic hinge mechanism depending on the

ductility of the structure. To overcome such a problem external dampers are

employed in structures such that most of the energy dissipation occurs through them

rather than the structure. In such case the above equation is modified for the external

damper matrix and becomes:

(3.10)

Where is the supplementary damping coefficient?

47

For the dynamic analysis of structures with supplementary dampers the Newmark

predictor-corrector algorithm was used to solve for the defined relation

(F. Hejazi, 2008):

(3.11)

Where q is the internal resisting force and depends on the displacement (x) and the

velocity ( , tttted FF

,

are imposed control force (Viscous damper) and

applied earthquake load vector in time (t+Δt) respectively. Also ttx and ttx

are

displacement and velocity of system in time of t+t and defined as follow

( Hejazi, 2008):

tttttt utuu 2)( (3.12)

tttttt utuu (3.13)

Where ttu and ttu

are obtained from these equations (F. Hejazi, 2008):

ttttt ututuu )21()(5.0 2

( 3.14)

tttt utuu )1( ( 3.15)

Here β and γ are the parameters that control the accuracy and stability of the method.

The quantities ttu and ttu

are the historical values and ttu and ttu

are

corrector values (Hejazi, 2008).

48

3.5. CONSITUTITIVE RELATIONSHIP FOR CONCRETE AND STEEL

3.5.1. STRESS-STRAIN RELATIONSHIP OF CONCRETE

The inelastic behavior of reinforced concrete beam-column element requires the

simulation of the interaction between axial forces and bending moments. In the

present study the effect of interaction between these forces is considered in

developing the yield surface for each element. The yield function employed here is

based on the fourth order polynomial first proposed by Medland and Taylor. The

stress-strain curve is shown in Figure 3.. and the Stress σc in concrete corresponding

to strain is given in equation (3.1).

)(85.0 234

cccccc DCBAf ( 3.1)

Where cf is compressive strength (cylinder) of concrete and A, B, C and D are

constant values and given as:

A = 0.292E+10, B = 0.1583E+08, C = - 0.3229E+06, D = 1.0593E+03

Figure 3.5. Stress-Strain Relation for Concrete (Medland and Taylor (1971))

Strain

Stre

ss

U

p

0.002

f׳c

σc

ɛc

49

3.5.2. STRESS-STRAIN RELATIONSHIP FOR STEEL

The behavior of steel in both compression and tension is a well documented behavior

through great deal of experiments steel was found to show three distinct behaviors

under loading. In the initial loading it showed an elastic behavior in which increase

in load resulted in increase in strain, this help true until the yield point where an

increase in load resulted in an increase in strain but not stress. After this stage steel

For the section a stress-strain relation for steel developed by (Thanoon, 1993) is

employed.

Material properties of steel are well known in static and dynamic loading conditions.

A typical stress-strain curve for high yield steel reinforcing bars loaded in direct

tension is as shown in

Idealization of these curves by suitable linear segments, which closely approximate

the experimental stress-strain curve, would have obvious advantages. The initial

elastic part extends up to the yield stress, followed by strain hardening part extending

up to failure. Further, for dynamic analysis, elasto-plastic approximation to the

stress-strain curve of steel is widely used for its simplicity. In the present study, an

elasto-plastic or strain hardening approximation of the behavior of the stress-strain

relation for steel is adopted as shown in

Figure 3.6.

50

(a) Uniaxial (b) Idealized

Figure 3.6. stress-strain graphs for steel

Accordingly, the stress in steel as, corresponding to strain εb can be expressed as

follows:

Elastic state; sss E ( 3.2)

Elasto-Plastic; )( ysstys Ef

( 3.3)

3.6. REINFORCED CONCRETE FRAME WITH EARTHQUAKE ENERGY

DISSIPATION SYSTEM

The simulation of a reinforced concrete frame structure with added energy

dissipating devices requires an idealization of the structure that exhibits a close

approximation to actual structural behavior under seismic excitation. For this

reinforce concrete structure is idealized as a frame element consisting of beams and

columns. The reason for this idealization is that different structural member exhibit

ɛc

σs

ɛc

σs

fy

51

different behaviors under seismic loading, for instance reinforce concrete structure

with an infill frame would behave differently from a frame structure with a shear

wall under seismic loading. The other structural member considered here is that of a

damper (energy dissipating device), this is the seismic response controller of the

structure and as such a proper selection for the member presentation is required in

order to generate as close as possible the actual control property of the damper.

The structural members considered in this work for modeling the reinforced concrete

structure are:

(i) Frame element

(ii) Viscous damper element

3.6.1. FRAME ELEMENT

Frame elements are models as beams and columns. The mathematical model of the

structural elements is 3 dimensional real space state representations of the structural

units (beams and columns). However since there are two different areas that are

covered here namely retrofitting of adjacent structures and the torsional response

reduction of the asymmetrical structure the layouts of the reinforced buildings varies.

In the case of the adjacent structures a 2 dimensional adjacent buildings with 3

dimensional structural members is used will in the case of asymmetrical reinforce

concrete frame structures a 3 dimensional building structure is considered.

The 3 dimensional structural members modeling give a more actual presentation of

the formation of plastic hinges within the structural members during the inelastic

analysis. Figure 3.7 shows the presentation of structural members (beams and

columns)

52

Figure 37: structural members of frame element

3.6.2. VISCOUS DAMPER ELEMENT

The model for dampers employed in this work is that which was developed by Hejazi

(2008) and shown below.

Figure 38: damper frame elements with added damper element

The model that was proposed for the damper by Hejazi (2008) was a 3 dimensional

nonlinear element that is compatible with the mathematical model initial generated

for the reinforced concrete frame.

Damper element

Beam element

Beam e Beam

element

Beam

element

Column element

53

3.7. COMPUTER PROGRAM

The computer program employed in this work is a finite element program code

which was developed by F. Hejazi (2010). This program analysis reinforced concrete

frame structures equipped with earthquake energy dissipation system in the elastic

and inelastic state. The developed program is capable of performing the following

analyses:

(i) Linear static

(ii) Nonlinear static

(iii)Linear dynamic

(iv) Nonlinear dynamic

The program is couple of giving the following results (F. Hejazi, 2008):

(i) It checks yielding that may occur at the ends of any element.

(ii) It calculates the inelastic forces to be redistributed in the next iteration.

(iii)It calculates the plastic deformations.

(iv) It calculates the stiffness matrix, considering current state of stress resultants

It calculates damper damping force and modifies it in each iteration base on the

optimum control system.

3.8. WORK LAYOUT CHART

Although the affects of earthquake on man built environment is an extensive field of

study, this work here is only limited to two parameters namely that of pounding

between two adjacent structures and torsional response of asymmetrical structures.

Both of these parameters have great catastrophic affects on how a structure

performance during and after earth quakes. For instance pounding between two

adjacent structures of different dynamic properties could lead to floor or mid column

54

pounding, with the latter case being more destructive since the top floor of a shorter

structure pounds against the column of the taller building which in turn leads to

failure of load resisting members in that region. This localized damage if extensive

could cause ultimately the failure of structure.

Since it his apparent that simplified models were not adequate enough to capture the

true structural response of reinforced concrete structures under earthquake loading, it

was seen as fit that a more actual R/C structure models should be used. This work is

a continuation of the work done by (Thanoon 1998) and further extended by (Hejazi

2010). The following chart shows the layout of the work plan for (Hejazi 2010).

Figure 3.9 Overall schematic view of present study (Hejazi 2010).

55

Through literature review three R/C frame models are selected to study pounding

affect in adjacent buildings the lateral-torsional couple in asymmetrical structures.

For the pounding case two adjacent R/C frame buildings were selected for the case

study, a 6 story building adjacent to a 12 story building. The separation distance

between the two buildings is 2 cm which was not sufficient to accommodate

structural displacements. Damper where then applied to reduce the displacement of

the structures (findings will be discussed in the results).

For the asymmetrical structures two 3D buildings where examined one with uni-

eccentricity in stiffness and the other bi-direction eccentricity in the plan of the

building. It was found that using the bi-eccentric model subjected to a 3 dimensional

earthquake excitation did give better structural performance picture of building

response under seismic excitation.

In both all three models use of viscous dampers reduced the structural response under

seismic excitation. Finding will be discussed in the following chapter (results)

.

56

4. RESULTS AND DISCUSSIONS

4.1. INTRODUCTION

In chapter 3 the choice of elements to represent the R/C frame structures equipped

with energy dissipation devices has been covered. Furthermore the material

constitutive modeling and program code were also covered in chapter 3.

The application of the proposed methodology will be cover in this chapter using

three different structural models. Following are the examples that are investigated in

this work:

i) Two adjacent structures separated by a seismic gap of 2cm

ii) A uni-asymmetrical 6 story RC frame structures

iii) A bi-asymmetrical RC structures

The response of the structures with respect to displacement, shear force, moment and

plastic hinge formations are plotted and discussed technically.

Figure 4.1 layout of analysis procedure

Define material, geometry and section

properties of RC frame building

Define damper section and

geometric properties

Apply uniform and concentrated static

load and perform static analysis to gain

member forces

Perform dynamic analysis to determine

dynamic response Earthquake load

57

4.2. DEFINE RC FRAME MODEL PARAMETERS

Through the literature reviewed, actual structural models were selected along with

their actual dimensions. On selecting the desire model the material, section and

geometric properties were then feed into the F.E code.

In this work there are three models that were selected from papers that were viewed,

first model is of two adjacent structures one of 6 stories and the other of 12 stories.

The two structures were separated by a gap of 2 cm. in this model the effect of

placing viscous dampers was investigated. The second and the third models were

both used to investigate how viscous dampers would alter the response of

asymmetrical structures under seismic excitation. Second model was a uni-

asymmetrical 6 story 3D RC structure while the forth model was of a bi-

asymmetrical 3 story RC structure.

4.3. DEFINED DAMPER PARAMETERS

This work investigated the performance of viscous dampers placing in RC structures,

there are two major areas in which the damper performance was investigated, and

first being on pounding mitigation of adjacent structures and the second investigation

was on torsional response reduction in asymmetrical structures. The dampers

considered here are nonlinear and the damping coefficient was varied in order to pick

out the best damping coefficient for the dampers. In the F.E code the damper length

and damping coefficients where both defined.

4.4. PREFROM STATIC ANALYSIS

Static analysis was preformed foremost; this was done so what the member force

could be determined. Before performing the static analysis the model structures were

58

subjected to super imposed dead and live static loads which were imposed at all floor

levels.

4.5. SELECT EARTHQUAKE RECORD

All the investigations carried out in this work were subjected to El centre earthquake

record, for the 2D pounding problem of the adjacent structures were subjected to a 2

component (one horizontal record and one vertical record) El centre earth quake.

While for the torsional problem in asymmetrical structures both models were

subjected to 3 component EL centre earthquake record with T= 53 sacs. On selecting

the earthquake record dynamic analysis was preformed. The layouts of investigation

are as given below.

i. Use actual dimensions of models from literature review.

ii. Apply the static dead and live load to the buildings and carry out static

analysis in order to determine member forces which will be as initial

loadings in dynamic analysis.

iii. Subject the structure to seismic excitation using the earthquake records.

iv. Perform nonlinear seismic analysis for the structure.

v. The seismic response of structures is plotted as displacements (translation

and rotations) and plastic hinges. If these plots are within the code

acceptance then the analysis is terminated. If however the design does not

meet the code requirement, supplemental dampers are installed ( viscous

dampers)

vi. Perform dynamic analysis again with dampers in place, if can the code

provisions are not met change damper properties such as damping

coefficient

59

vii. Steps 2 to 6 are repeated until the design criteria are satisfied in step 4 and

the suitable design is obtained.

Based on the final decision, the properties of suitable viscous damper are

recommended.

4.6. APPLICATION OF VISCOUS DAMPERS

This chapter considers the performance of the proposed control system when applied

to full scale RC buildings. There are three different cases investigated in this chapter,

the first case investigates pounding of two adjacent structures and examines how

implementing the proposed control system reduces the pounding of two structures.

The second and third cases examine the torsional response affect on two

asymmetrical structures. In case 2 a uni-asymmetrical systems is investigated for

torsional response and then retrofitted with viscous dampers first in 3 sides and then

in four sides. The results of 3 side retrofitting and 4 side retrofitting are then

compared. For the third case a bi-asymmetrical system retrofitted with viscous

dampers is excited by a 3 component earth quake.

4.7. CASE 1 POUNDING MITIGATION OF ADJACENT STRUCTURES

In this case two adjacent structures of 6-story and 12-story were investigated for

pounding. The two buildings were separated by a gap of 2 cm which during the

analysis of the two structures under El. Centro earthquake was found to be

inadequate to accommodate the relative displacements of the structures. Viscous

dampers were then introduced in to the two buildings being distributed through the

full height of the short building and the same goes for the tall structure except the

middle bay was not retrofitted. Figure 4.2 shows the layout of two adjacent structures

60

along with the tabulated section properties of member elements and the distribution

of dampers is as shown in figure 4.3:

Fig 4.2 model plot for 2D adjacent RC structures

Table 4.1 cross-section and reinforcement of structural members

SECTION AREA

(CM)

MAIN REINFORCEMENT

BEAM 30*50

TOP 2 NO 6 DIA BOTTOM 6 NO16 DIA

COLUMN 30*50

8 NO 16 DIA

COLUMN 30*80

12 NO 16 DIA

COLUMN 30*140

22 NO 16 DIA

61

Figure 4.3: distribution of dampers (blue colored elements)

The following figures highlight the displacements of the two adjacent structures

without damping (dampers were place in the structures but had zero damping

coefficients). Their relative displacements were found to be greater than the gap

provided between the structures hence resulting in pounding of the structures.

Figure 4.4 pounding in adjacent structures

Now since increasing the gap between the buildings is not possible the damper

damping coefficient was increased until there was no pounding. The following

displacement time history responses are plotted for nodes 21 for the first building and

62

node 7 for the second building. Both nodes are at the same height level and this is the

point of contact between the two buildings during pounding. The shorter building in

this work is denoted as building 1 while the taller is denoted as the building 2.

Without damper With damper Amount of reduction

Max: 3.18E+01 1.02E+00 97.03%

Min: -4.63E+01 -1.30E+00

X direction for building 1

Without damper With damper Amount of reduction

Max: 3.52E+01 2.82E+00 90.4%

-50

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50

Time (Sec)

Dis

pla

ce

me

nt

(mm

)

With out damper

With Damper

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50

Time (Sec)

Dis

pla

ce

me

nt

(mm

)

With out damper

With Damper

63

Min: -3.67E+01 -4.09E+00

X direction for building 2

Figure 4.5 lateral displacements for building 1 and 2

From the above plots of displacement in x direction for building 1 and 2, increasing

the damping coefficient of the dampers from zero to 800KN.sec/m resulted in

displacement reductions of 97.03% and 90.4% respectively. This meant that the

pounding effect which resulted for the large lateral displacement of the two

structures was no longer present since both structures had displacements much less

then 5mm.

Without damper With damper reduction

Max: 2.45E+03 2.19E+03 41%

Min: 1.67E+03 1.73E+03

Axial Force

1500

1600

1700

1800

1900

2000

2100

2200

2300

2400

2500

0 10 20 30 40 50

Time (Sec)

Axia

l F

orc

e (

kN

)

With out damper

With Damper

-40

-30

-20

-10

0

10

20

0 10 20 30 40 50

Time (Sec)

Sh

ear

in Y

dir

ecti

on

(kN

) With out damper

With Damper

64

Without damper With damper reduction

Max: 1.42E+01 -3.68E+00 73%

Min: -3.86E+01 -1.73E+01

Shear Force in Y direction

Without damper With damper reductions

Max: 6.04E+02 7.42E+00 76%

Min: -1.12E+03 -4.10E+02

Moment in Z direction

Figure 4.6 axial and shear force reductions

In terms of stress, viscous dampers did reduce them considerable. The axial force

was reduced by 41% while the shear force and moment were reduced by 73% and

76% respectively. One key area to not is that pounding effect in adjacent structures

increase the shear forces, the above force were plotted for element 31 which is the

first column in the tall structure.

4.8. CASE 2 TORSIONAL RESPONSE REDUCTION OF UNI-ASYMMETRICAL

STRUCTURE

In this case a 6 story RC asymmetrical structure was examined. Asymmetry in the

structure was due to the distribution of stiffness in the lateral resisting frames, with

one side frames having columns of large stiffness as compared to the other three side

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

0 10 20 30 40 50

Time (Sec)

Mo

me

nt

aro

un

d Z

dir

ec

tio

n

(kN

.m)

With out damper

With Damper

65

frames. This distribution of stiffness resulted in asymmetry along the x-axis. Due to

this difference in stiffness distribution it was found that when the structure was

excited with El centre earth quake record the less stiff side experience a large

torsional response as compared to the stiffer side. This larger lateral- torsional couple

leads to large ductility demand on the less stiff side frames(Thambiratnam and

Corderoy, 1994),(García et al., 2007). For this reason dampers were installed in the

model. The dampers were first place in 3 less stiff sides of the model and then

distributed symmetrical throughout the model (all four side frames retrofitted). The

layout of the model along with section properties and damper distributions are shown

in the following figures:

Figure 4.7 model front view and top view

66

Figure 4.8 damper distributions in 3 side frame

Retrofitting the above asymmetrical structure with viscous dampers did reduce the

displacement, shear force and torsion in the structure. On comparing the result of

asymmetrical and symmetrical distributed dampers it was found that symmetrical

distribution resulted in better reductions of all three parameters. Following are

displacement comparison for 3 side and 4s damper distributions for node 18 on the

less stiff side.

Displacement in X direction

-50

-40

-30

-20

-10

0

10

20

30

40

50

C=0

(3S)

C=0

(4S)

C=20

(3S)

C=20

(4S)

C=40

(3S)

C=40

(4S)

Different Damper Damping Coefficient

MA

X &

MIN

Dis

pla

cem

en

t in

X d

irecti

on

(mm

)

67

Displacement in Y direction

Displacement in Z direction

Figure 4.9 nodal displacements in x, y and z directions

As seen from above figures the displacement in both x and z directions were reduce

in both 3 and 4 side damper distributions, with the 4 side distribution have larger

reductions comparatively. However the displacements in the y direction were

increased slightly for 4 side distribution as compared with the 3 side distribution.

Following are the time history responses for node 18. Distributing the dampers

symmetrical in the model resulted in better performance in terms of response

reduction; one reason could be due to the affect of damper distribution which was an

asymmetrical distributed when the dampers were placed in 3 sides only (side with

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

C=0

(3S)

C=0

(4S)

C=20

(3S)

C=20

(4S)

C=40

(3S)

C=40

(4S)

Different Damper Damping Coefficient

MA

X &

MIN

Dis

pla

cem

en

t in

Y d

irecti

on

(mm

)

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

C=0

(3S)

C=0

(4S)

C=20

(3S)

C=20

(4S)

C=40

(3S)

C=40

(4S)

Different Damper Damping Coefficient

MA

X &

MIN

Dis

pla

cem

en

t in

Z d

irecti

on

(mm

)

68

less stiff frames). Although the dampers did reduce the displacements in the x

direction, they did however increase the displacement in y direction.

Without Damper 3S 4S

Amount of reduction

3S 4S

Min -37.8758 -28.2515 -25.4617 25% 34%

Max 36.4405 27.6917 23.6974

Displacement in X direction

Without Damper 3S 4S

Amount of reductions

3S 4S

Min -0.41403 -0.40834 -0.405464 39.84% 50.23%

Max 0.356844 0.669674 0.752697

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50

Time (Sec)

Dis

pla

ce

me

nt

(mm

)

With out damper

3 Side Damper

4 Side Damper

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40 45 50 55

Time (Sec)

Dis

pla

cem

en

t (m

m)

With out damper

3 Side Damper

4 Side Damper

69

Displacement in Y direction

W.O Damper 3S 4S

Amount of reduction

3S 4S

Min -50.7354 -37.9151 -30.8801 23% 36%

Max 38.7954 31.4585 26.8319

Displacement in Z direction

Figure 4.10 time history displacements x in z direction

The displacements in Z direction were found to be reduced on the structure was

retrofitted with viscous dampers. The reductions were found to be 23% and 36% for

3 side 4 side damper distributions respectively. Although the magnitudes of rotations

in all three directions were very small, installing viscous dampers in either 3 sides or

four sides did further reduce the torsional response in y direction while increasing the

rotations in x and z. the following table shows the displacement and rotations for

increased damper damping coefficient.

Displacement

X Y Z

C=0 Max 36.44 0.357 38.8

Min -37.9 -0.41 -50.7

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30 35 40 45 50 55

Time (Sec)

Dis

pla

cem

en

t (m

m)

With out damper

3 Side Damper

4 Side Damper

70

RESULTS FOR DAMPER DISTRIBUTION IN 3 SIDES

C=20 Max 29.39 0.694 35.09

Min -32.9 -0.41 -43.5

AMOUNT OF REDUCTION 16% 43.9% 12%

C=40 Max 27.69 0.67 31.46

Min -28.3 -0.41 -37.9

AMOUNT OF REDUCTION 25% 41% 23%

RESULTS OF DAMPER DISTRIBUTION IN ALL FOUR SIDES

C=20 Max 27.09 0.622 32.09

Min -31 -0.41 -38.9

AMOUNT OF REDUCTION 22% 35% 21%

C=40 Max 23.7 0.753 26.83

Min -25.5 -0.41 -30.9

AMOUNT OF REDUCTION 34% 52% 35%

Table 4.2 displacements and rotations for varying damper coefficients

During the investigation it was found that placing viscous dampers in the modeled

structure the displacement in X and Z directions were reduced. The amount of

reduction depended on the damping coefficient of the damper and the arrangement of

the viscous dampers. For instance when the damping coefficient was kept constant at

20KN.sec/m the 3 side damper distribution reduced the displacement in the X and Z

directions by 16% and 12 % respectively while the 4 side damper distribution reduce

the same displacement components by 22% and 21% respectively. However for both

damper damping coefficient and distribution the Y displacement component was

increased.

71

Both 3 and 4 side damper distributions did in fact reduce the axial, shear and,

torsional forces in the model. Moment response of the modeled structured was also

reduce for both damper distributions considered; however the results are only given

for 4 side damper distributions since the amount of reductions in said parameters

were larger in the considered case of damper distribution. For asymmetrical

structures retrofitting was done to reduce the torsional response of the structure,

which in this case was reduced by 63%.

Without damper 4s damper distribution Reduction

Max: 3.60E+02 3.44E+02 20%

Min: -3.96E+00 5.27E+01

Axial Force

-50

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50

Time (Sec)

Axia

l F

orc

e (

kN

)

With out damper

With Damper

72

Without damper 4s damper distribution Reduction

Max: 1.52E+01 7.33E+00 80.4%

Min: -3.54E+01 -2.60E+01

Shear Force in Y direction

Without damper 4s damper distribution Reduction

Max: 7.32E+01 5.14E+01 35%

Min: -9.31E+01 -5.71E+01

Shear Force in Z direction

Figures 4.11 shear force in x, y and z directions

-40

-30

-20

-10

0

10

20

0 10 20 30 40 50

Time (Sec)

Sh

ear

in Y

dir

ecti

on

(kN

) With out damper

With Damper

-100

-80

-60

-40

-20

0

20

40

60

80

0 10 20 30 40 50

Time (Sec)

Sh

ea

r in

Z d

ire

cti

on

(k

N) With out damper

With Damper

73

Without damper 4s damper distribution Reduction (%)

Max: 1.24E+02 5.00E+01 63%

Min: -1.59E+02 -5.49E+01

Torsion

Without damper Damper in 4 sides Reduction (%)

Max: 6.02E+03 3.94E+03 24%

Min: -5.69E+03 -5.00E+03

Moment in Y direction

-200

-150

-100

-50

0

50

100

150

0 10 20 30 40 50

Time (Sec)

To

rsio

n (

kN

.m)

With out damper

With Damper

-6000

-4000

-2000

0

2000

4000

6000

0 10 20 30 40 50

Time (Sec)

Mo

men

t aro

un

d Y

dir

ecti

on

(kN

.m)

With out damper

With Damper

74

Without damper Damper in 4 sides

Reduction

(%)

Max: 7.83E+02 4.53E+02 37%

Min: -1.16E+03 -7.72E+02

Moment in Z direction

Figure 4.12 torsion and moments in x, y and z directions respectively

Retrofitting the structure with viscous dampers increased both the section plastic

hinges and the total number of plastic hinges formed within the model

4.9. CASE 3 TORSIONAL RESPONSE REDUCTION OF BI-ASYMMETRICAL

STRUCTURE

The most serve case of lateral-torsional couple occurs when a bi-asymmetrical

structure model is excited by 3 component earthquake. For this reason a three-storey

building with plan bi- asymmetrical rectangular cross-section, shown in Figure 4.11

is investigated for torsional response. All the columns in this building are symmetric

with 450 mm x450mm cross-section and have a height of 3.5 m between floor

levels the modeled structure was excited with 3 component EL centre earthquake

with T = 53 secs. In the analysis of the model for zero damping it was found that it

experience large torsional responses when excited. Dampers were than places in the

wide side frames. The displacements and rotations are plotted for nodes 20 were as

the stresses are plotted for element 1.

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

0 10 20 30 40 50

Time (Sec)

Mo

me

nt

aro

un

d Z

dir

ec

tio

n

(kN

.m)

With out damper

With Damper

75

Figure 4.13 plan bi-asymmetrical 3 story RC frame structure

Displacement in X direction

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

C=0

C=25

0

C=50

0

C=75

0

C=10

00

C=12

50

C=15

00

Different Damper Damping Coefficient

MA

X &

MIN

Dis

pla

cem

en

t in

X d

irecti

on

(mm

)

76

Displacement in Z direction

Figure 4.12 displacements in X and Z directions

From the above plots of displacement in two horizontal directions for the bi

asymmetrical model, it was found that retrofitting the model with viscous dampers

did reduce the displacements in both directions considerably. Although not shown

here the y displacements were also reduced though not as significant as the other two

directions. However it is these two directional displacements that are responsible for

the lateral torsional coupling response of the structural modal and hence their

reductions are of importance. The rotational displacements of the structural modal in

all three directions were found to be very small and placement of the dampers did

further reduce those values in to insignificant numbers.

-10

-8

-6

-4

-2

0

2

4

6

8

10

C=0

C=25

0

C=50

0

C=75

0

C=10

00

C=12

50

C=15

00

Different Damper Damping Coefficient

MA

X &

MIN

Dis

pla

cem

en

t in

Z d

irecti

on

(mm

)

77

Rotation in X direction

Rotation in Z direction

Figure 4.14 rotations in X and Z directions

DAMPING

COEFFICIENT

(KN.sec/m)

DISPLACEMENT(mm)

X Y Z

C=0 Max 4.2082 0 8.739

Min -4.7554 -0.2897 -7.6292

C=250 Max 2.2313 0 3.4987

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

C=0

C=25

0

C=50

0

C=75

0

C=10

00

C=12

50

C=15

00

Different Damper Damping Coefficient

MA

X &

MIN

Ro

tati

on

arr

ou

nd

X d

irecti

on

(Rad

)

-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

0.0002

C=0

C=25

0

C=50

0

C=75

0

C=10

00

C=12

50

C=15

00

Different Damper Damping Coefficient

MA

X &

MIN

Ro

tati

on

arr

ou

nd

Z d

irecti

on

(Rad

)

78

Min -3.028 -0.2799 -5.1991

REDUCTIONS 41% 3.4% 47%

C=500 Max 1.5079 0 2.4716

Min -2.2335 -0.2781 -4.4948

REDUCTIONS 58% 4% 57%

C=750 Max 1.2978 0 2.1378

Min -1.803 -0.2766 -3.8206

REDUCTIONS 65% 4.5% 64%

C=1000 Max 1.1561 0 1.8689

Min -1.5538 -0.2751 -3.3068

REDUCTIONS 70% 5% 68%

C=1250 Max 1.0617 0 1.64

Min -1.3963 -0.2739 -2.8722

REDUCTIONS 73% 5% 72%

C=1500 Max 0.9793 0 1.4431

Min -1.2719 -0.2738 -2.5412

REDUCTIONS 75% 5.5% 76%

Table 4.3 displacement reductions in X, Y and Z for node 20

From the above table it is seen that retrofitting of the modeled structure did in fact

reduce the displacement in all directions. Move horizontal displacements (X and Z)

which are the main contributors to the lateral-torsional couple of the structure are

considerable reduced. As the damper damping coefficient was increase the amount of

reduction for displacements increased.

The following graphs are the displacement time history response of node 20. The

dark line indicates the displacement time history responses of the structure when

retrofitted with viscous damper of 1500KN.sec/m were as the broken line represents

zero damping coefficients.

79

Without damper With damper reduction

Max: 4.21E+00 9.79E-01 75%

Min: -4.76E+00 -1.27E+00

Displacement in X direction

Without damper With damper reduction

Max: -5.88E-02 -4.52E-02 1%

Min: -2.90E-01 -2.74E-01

Displacement in Y direction

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 10 20 30 40 50

Time (Sec)

Dis

pla

ce

me

nt

(mm

)

-0.25

-0.23

-0.21

-0.19

-0.17

-0.15

-0.13

-0.11

0 10 20 30 40 50

Time (Sec)

Dis

pla

cem

en

t (m

m)

80

Without damper With damper reduction

Max: 8.74E+00 1.44E+00 76%

Min: -7.63E+00 -2.54E+00

Displacement in Z direction

Figure 4.15 displacement time history responses for node 20

Following graphs are plots of stress for element one, again the result follows the

same pattern as previous results except for the for the x component. In the initial few

seconds of stress time history response of the element 1 in the x-direction viscous

damper were found to have increase the axial force, however for time 3 sec the result

started to decrease considerable until final reduction of 14% was noted for damping

coefficient of 1500KN.sec/m. The largest shear force reduction was found to be 60%

which was in the z direction

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50

Time (Sec)

Dis

pla

cem

en

t (m

m)

81

Without damper With damper reduction

Max: 6.49E+02 6.59E+02 14%

Min: 4.23E+02 4.02E+02

Axial Force

Without

damper With damper

Reduction

Max: -3.46E+01 -4.49E+01 44%

Min: -7.04E+01 -6.49E+01

Shear Force in Y direction

400

450

500

550

600

650

700

0 10 20 30 40 50

Time (Sec)

Axia

l F

orc

e (

kN

)

With out damper

With Damper

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

0 10 20 30 40 50

Time (Sec)

Sh

ear

in Y

dir

ecti

on

(kN

) With out damper

With Damper

82

Without damper With damper reduction

Max: 3.00E+01 1.08E+01 60%

Min: -3.39E+01 -1.48E+01

Shear Force in Z direction

Figure 4.16 axial and shear force time history response for element one

In this work the key investigation was determining how viscous dampers install in

the structure would reduce the torsional response of bi-asymmetrical structure

subjected to a 3 component earthquake. The following graphs are the time history

response for torsion and moments. As was expected install viscous dampers in the

system did reduce the torsional response of the bi-asymmetrical modeled system by a

factor of 85%.

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50

Time (Sec)

Sh

ea

r in

Z d

ire

cti

on

(k

N) With out damper

With Damper

-100

-80

-60

-40

-20

0

20

40

0 10 20 30 40 50

Time (Sec)

To

rsio

n (

kN

.m)

With out damper

With Damper

83

Without damper With damper reduction

Max: 3.94E+01 -7.59E+00 85%

Min: -8.24E+01 -2.59E+01

Torsion

Without

damper With damper

Reduction

Max: 8.40E+02 2.87E+02 63%

Min: -8.51E+02 -3.34E+02

Moment in Y direction

Without damper With damper Reductions

Max: -2.09E+02 -4.36E+02 44%

Min: -9.97E+02 -8.79E+02

Moment in Z direction

Figure 4.17 torsion and moment time history response of element 1

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

0 10 20 30 40 50

Time (Sec)

Mo

men

t aro

un

d Y

dir

ecti

on

(kN

.m)

With out damper

With Damper

-1000

-900

-800

-700

-600

-500

-400

-300

-200

0 10 20 30 40 50

Time (Sec)

Mo

me

nt

aro

un

d Z

dir

ec

tio

n

(kN

.m)

With out damper

With Damper

84

5. CONCLUSION

5.1. INTRODUCTION

The aim of this work was to investigate certain short comings of the previous works

review in the literature. Two key areas are investigated and the results obtained from

the investigation agree with those found in the literature reviews of the same

problems solved using simplified models and analysis methods. The aim of this work

was to get more realistic results that would agree with actual real structure behaviors

under seismic load. Hence three actual structural models were selected and time

history analysis was preformed. This investigation is limited to pounding and

torsional response reductions of RC frame structures using viscous dampers.

5.2. LITERATUREEIVEW

Based on the literature reviewed on seismic performance of adjacent and

asymmetrical structures under seismic excitations for 2D and 3D RC frame structures

the following points following points lead to this work

i. Pounding mitigation of adjacent structures using viscous dampers

ii. Torsional response reduction in asymmetrical structures

5.3. CASE 1 POUNDING MITIGATION OF ADJACENT STRUCTURES

The first case examined two adjacent structures one of 6 stories and the other of 12

stories separated by a gap of 2 cm. when the structures were excited by El centre

earthquake record with T = 53 sec it was found that both structures displaced more

than the gap between them could accommodate. Hence structural pounding occurred

at the roof top of the shorter building and the corresponding floor level of taller

building. The pounding of the structures lead to larger shear forces which lead,

although no localized failure was noted for this specific model and gap, it might be

85

possible for taller structural models. In order to prevent such structural poundings

viscous dampers were installed in the adjacent buildings and time history analysis

was perform for the same earthquake loading.

It was found that by retrofitting the short and tall buildings (referred to as building 1

and 2 respectively) with viscous dampers the displacement in the x direction were

reduce by 90.4% and 97% respectively. Hence limiting the horizontal displace of the

two adjacent buildings within 5mm which is easily accommodated by the provided

gap between the buildings. Due to the difficult of handling large data obtained from

the analysis only a single element shear force could be plotted in this case a column

of the tall building was selected. Viscous dampers used were not only capable of

reducing the displacement of the structures but also reduced the shear forces of the

structures considerable, for the selected column the shear force was reduced by 73%

while the axial force and moment reduced by 41% and 76% respectively.

5.4. CASE 2 TORSIONAL RESPONSE REDUCTIONS OF

UNIASYMMETRICAL STRUCTURES

In this case a 3D 6 story RC frame structure was investigated for torsional response

under seismic excitation. The asymmetry in the structure was due to the stiffness

distribution in the load resisting members. The stiffer sides, being the side whose

columns are highlighted in blue in figure 4.7. Due to the asymmetrical distribution of

stiffness, it was found that there was a large torsional demand on the less stiff side

(columns on the edges opposite to the stiff side). In order to control these effect

viscous dampers were distributed in the structure first in the 3 less stiff sides than

distributed in all four sides. The 3 side and 4 side damper distributions are then

compared to see which produce larger reductions in torsional response of the

structure. The 3 side damper distribution will be referred to as asymmetrical

86

distribution while the 4 side distribution will be referred to as symmetrical

distribution. For the asymmetrical distribution the two horizontal displacements X

and Z were found to be reduced by 25% and 23% respectively for the asymmetrical

distribution while for the symmetrical distribution the reductions were larger and

found to be 34% and 36% respectively. For both asymmetrical and symmetrical

distributions the Y displacement component were reduced by 39.84% and50.23%.

hence symmetrical distribution of dampers did result in better displace response

reductions, this could be due to the fact that the dampers do not enhance the stiffness

of the structure so by distributing them asymmetrical would in turn lead to a second

eccentricity in the structure this time it would be due to damper distribution.

Since symmetrical damper distribution preformed better of displacement reductions

the stress reductions give here would be only for the symmetrical distribution which

were again here then their counterpart.

The axial force of the structure was reduced by 20% while the shear forces in the y

and z axis were reduced by 80.4% and 35% respectively. However the key response

that is being investigated is the torsional response of the structure and it was found

by placing dampers the torsional force was reduced by 63% while the moments in y

and z directions were reduced by 24% and 37% respectively. Hence dampers did

actual reduced the lateral-torsional response of the structures. Although the above

percentages are for damper damping coefficient of 800KN.sec/m the amount of

reductions provide by this elements is really remarkable.

5.5. CASE 3 TORISONAL RESPONSE REDUCTIONS OF BI-ASYMMETRICAL

STRUCRURES

This case investigated the torsional response of a bi-asymmetrical structure subjected

to 3 component earthquakes. This is a more server case as compared to the first in

87

which a uni-asymmetrical real structural model was excited by 3 component El

centre earthquake. The real structure model investigated in this case is of 3 stories

with symmetrical columns of 450mm*45omm cross-sections, the beams are of

350mm*450mm. the floor heights of the structure are uniform and are of 3.5 meters,

the structure is made up to 2 bays in each orthogonal directional the short bay being

of 3.5m while the longer bay is of 6.5m. on exciting the structure with El centre

earthquake record it was found that large torsional response were noted for the longer

bays. The dampers were provided in these bays in order to reduce the displacements

and stress in these bays. The following percentage reductions in displacements are

given for node 20 each is on the most effected side while the stress are for element 1

this are highlighted in figure 4.11.

When the structure was retrofitted with dampers in the above said manner the two

horizontal displacements (X and Z) which were responsible of the torsional affect

were reduced by 75% and 76% respectively while the y component was reduced by

1% only. As for the stresses the axial forces was reduced by 145 while the shear

force in Y and Z were reduced by 44% and 60% respectively. The torsional force

was reduced by 85% while moments in Y and Z directions were reduce by 63% and

44% respectively.

5.6. OVER ALL RESPONSE OF RC FRAME STRUCTURES RETROFITTED

ITH VISCOUS DAMPERS

By retrofitting RC frame structures with viscous dampers in both adjacent and

asymmetrical structures the response of the structures were reduce. For the case of

pounding the adjacent structures were separated by a gap of 2cm which was

insufficient to accommodate the relative displacements of the structures. But by

install viscous dampers in the two adjacent buildings the displacements of the two

88

structures were considerable reduced thereby preventing structural pounding. Second

all the stresses within the structures were also reduce. As for the uni-asymmetrical

and bi-asymmetrical structures, the torsional response which was due to stiffness

distribution in the first case and plan asymmetry for the second was reduced with the

aid of viscous dampers. For the case of asymmetrical structures the amount of

reductions in structural response was found to be dependent on the distribution of

dampers in structures, for this reason it is important to select a proper distribution of

dampers to achieve effective reduction without having to employ large number of

dampers.

5.7. SUGGESTIONS FOR FURTHER STUDIES

For better understanding the actual behavior of real RC frame structures under

seismic excitations we have to look into model system that we used to study them,

simplified models and simplified analysis I not give actual site problems faced with

RC frame structures under earthquake loads.

Secondly parameters such as soil structure interactions are very important problems

that need to be studied, so far in the literature reviewed investigation of soil structure

interactions have not be explored. The behavior of structures under different soil

systems will greatly affect how the structure will respond once excited

Thirdly lateral –torsional couple of adjacent buildings with insufficient seismic gap

could lead to a more server case then just lateral pounding between adjacent

structures. Special since now multi-story structures with eccentricities in stiffness

due to discontinued structural members are visible in all our major cities.

89

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