Msc Dissertation Final

SEISMIC PERFOMANCE OF REINFORCED CONCRETE BUILDINGS WITH FRICTION

DEVICES

Dissertation submitted as part requirement

for the degree of Master of Science in

Structural Engineering

By:

Koray Tugay

Supervisor:

Dr. Mihail Petkovski

The University of Sheffield

Department of Civil and Structural Engineering

September 2010

I

Koray Tugay certifies that all the material contained within this document is his own

work except where it is clearly referenced to others.

___________________

(signature)

II

Abstract

Friction devices offer an effective solution for seismic rehabilitation for structures by

energy dissipating capabilities.

In this study, the effectiveness of friction devices are checked by numerical analysis,

using the commercially available software SAP2000 on a 3 storey reinforced concrete

frame structure by non – linear time history analysis using 4 different ground

motions, namely El – Centro, Kobe, Northridge and the Mexico, 3 of them being

modified to hit the structure as strong as possible in the means of frequency

content.

The monitored results are maximum inter – storey drifts at any time and any floor

level, structural damage, maximum top floor displacements and top floor

displacement time history graphs.

It is shown that, a structure designed with a behaviour factor of 6, retrofitted with

friction devices performed better compared to a structure designed with a behaviour

factor of 3 and the optimum yield force distribution is a characteristic that depends

on the structure, however lies in a range.

III

Acknowledgments

Many thanks to...

...all the lecturers of the University of Sheffield, especially Dr. Mihail Petkovski for

his patience, and the enthusiasm for sharing his knowledge his students.

...all my friend in Sheffield but especially Angelos Angelakis for making this MSc year

what it was. I wish our paths meet somewhere in future again.

...my friends back home but especially Basar Aykut a.k.a. “The Warrior of the Light”

for supporting me on my decision on doing this MSc. You are the lecturer of the

lecturers.

...Luis Eduardo Peternell Altamira for helping someone he has never seen and

probably will never see in the future. I hope I can help you, sometime, somehow.

(and last but not least)

...my family for being there for me for the last 25 years, and supporting me

financially, sacrificing a lot for this MSc year. I know it was not easy for you, and I

know I can never pay you back. All I can wish for is that I can provide your grandchild,

what you have provided to me.

...and my special one Bilge Gurhan. We have so much to share.

IV

Contents

Abstract ...........................................................................................................................II

Acknowledgments ..........................................................................................................III

List of Figures ............................................................................................................... VII

List of Tables .................................................................................................................. IX

Introduction ....................................................................................................................1

Aims & Objectives............................................................................................................2

Literature Review ............................................................................................................3

Structural Control ........................................................................................................3

Passive Structural Control ............................................................................................4

Dry Friction ..................................................................................................................5

Friction Devices ...........................................................................................................6

Current Practice Examples .........................................................................................12

Modelling & Methodology .............................................................................................14

Methodology .............................................................................................................14

Modelling of Structures .............................................................................................15

Modelling of Friction Devices .....................................................................................16

Design of Structures...................................................................................................18

Properties of Structure A .......................................................................................20

Properties of Structure B........................................................................................21

Design of Retrofitted Structure ..................................................................................22

Design of Bracing System ...........................................................................................23

Properties of Structure B – Equipped with Braces ..................................................26

Allocation of Yield Forces ...........................................................................................27

Earthquake Records ...................................................................................................29

V

El Centro Earthquake .............................................................................................29

Loma Earthquake ...................................................................................................30

Northridge Earthquake ..........................................................................................31

Mexico Earthquake ................................................................................................32

Analysis Results .............................................................................................................33

Assessed Parameters .................................................................................................33

Inter – Storey Drifts................................................................................................33

Structural Damage .................................................................................................33

Top Floor Displacements ........................................................................................33

Top Floor Displacement Time History Response Comparison .................................33

El – Centro Results .....................................................................................................34

Maximum Inter Storey Drifts ..................................................................................34




Loma Results .............................................................................................................37





Northridge Results .....................................................................................................40

Mexico Results ...........................................................................................................40





VI

Summary and Evaluation of Results ...........................................................................43

Conclusions and Future Work ........................................................................................45

References.....................................................................................................................47

Appendix A – Design of Structures .................................................................................49

Design of Structure A .................................................................................................49

Design of Structure B .................................................................................................53

Appendix B – Allocation of Yield Forces .........................................................................57

First Storey Strength ..................................................................................................57

Second Storey Strength .............................................................................................58

Third Storey Strength .................................................................................................58

VII

List of Figures

Figure 1 - Passive Control Systems [4] ...............................................................................4

Figure 2 - Force Diagram for Block on Ground [9] ..............................................................5

Figure 3 - Friction Force - Applied Force Relationship [9] ...................................................5

Figure 4 - Friction Damper Details [5] ................................................................................6

Figure 5 - Different Configurations [4} ...............................................................................6

Figure 6 - Typical Rectangular Hysteresis Loops [4} ...........................................................7

Figure 7 - Force - Displacement Hysteresis Loops of Friction Device Under 4

Earthquakes [7] .................................................................................................................8

Figure 8 – Equivalent Brace and Frame Unit and the Force – Displacement Relation [6]....9

Figure 9 – Displacement responses of the protected frame and the bare frame for an

initial displacement.[4]......................................................................................................9

Figure 10 – Effects of Bracing Stiffness on Dissipated Energy Percentage [8] ...................11

Figure 11 – Close – Up View of an Installed Buckling – Restrained Braces [1] ...................11

Figure 12 – Patient Tower – Seattle [1] ...........................................................................12

Figure 13 – Completed Damper Installation [1] ...............................................................13

Figure 14 – Hinge Properties ..........................................................................................15

Figure 15 – Definition of parameters for the Wen plasticity property. [9] .......................16

Figure 16 - Plan view of chosen structure ......................................................................18

Figure 17 - Elevation view of chosen structure ...............................................................19

Figure 18 – Placement of Friction Devices on Structure B ..............................................22

Figure 19 – Effects of Damper Stiffness and Yield Force [9] .............................................24

Figure 20 – Top Floor Displacement with Different Bracings ..........................................25

Figure 21 – Top Floor Displacement with Different Bracings in Detail ............................25

Figure 22 – El Centro Acceleration Time History ............................................................29

Figure 23 – El Centro Power Spectrum ...........................................................................29

Figure 24 – Loma ( Modified ) Acceleration Time History ...............................................30

Figure 25 – Loma ( Modified ) Power Spectrum .............................................................30

Figure 26 – Northridge Acceleration Time History..........................................................31

Figure 27 – Northridge Power Spectrum ........................................................................31

VIII

Figure 28 – Mexico ( Modified ) Acceleration Time History ............................................32

Figure 29 – Mexico ( Modified ) Power Spectrum ..........................................................32

Figure 30 – Peak Inter – Storey Drifts / El – Centro ........................................................34

Figure 31 – Structural Damage / El – Centro ..................................................................35

Figure 32 – Top Floor Displacements / El – Centro .........................................................36

Figure 33 – Top Floor Displacement Response Comparison / El – Centro .......................36

Figure 34 – Peak Inter – Storey Drifts / Loma .................................................................37

Figure 35 – Structural Damage / Loma ...........................................................................38

Figure 36 – Top Floor Displacements / Loma .................................................................39

Figure 37 – Top Floor Displacement Response Comparison / Loma ...............................39

Figure 38 – Peak Inter – Storey Drifts / Mexico ..............................................................40

Figure 39 – Structural Damage / Loma ...........................................................................41

Figure 40 – Top Floor Displacements / Mexico ...............................................................41

Figure 41 – Top Floor Displacement Response Comparison / Mexico .............................42

Figure 42 – Response Spectrum Function / Structure A .................................................50

Figure 43 – Interaction Diagram for Columns Storey 1 – 2 / Structure A ........................52

Figure 44 – Interaction Diagram for Columns Storey 3 / Structure A ..............................52

Figure 45 – Response Spectrum Function / Structure B..................................................54

Figure 46 – Interaction Diagram for Columns Storey 1 – 2 / Structure B.........................56

Figure 47 – Interaction Diagram for Columns Storey 3 / Structure B ..............................56

Figure 48 – First Storey Push over Method ....................................................................57

Figure 49 – Second Storey Push over Method ................................................................58

Figure 50 – Third Storey Push over Method ...................................................................58

IX

List of Tables

Table 1 – Element Sizes / Structure A.............................................................................20

Table 2 – Assigned Hinge Values for Beams / Structure A ..............................................20

Table 3 – Modal Information / Structure A ....................................................................20

Table 4 – Element Sizes / Structure B .............................................................................21

Table 5 – Assigned Hinge Values for Beams / Structure B ..............................................21

Table 6 – Modal Information / Structure B.....................................................................21

Table 7 – Storey Shear Forces – Structure B ...................................................................27

Table 8 – Step Numbers and Allocated Yield Forces .......................................................28

Table 9 – Assumed Frame Element Sizes / Structure A ...................................................49

Table 10 – Beam Moment Values / Structure A .............................................................51

Table 11– Column Moment and Axial Load Values / Structure A ....................................51

Table 12 – Assumed Frame Element Sizes / Structure B .................................................53

Table 13 – Beam Moment Values / Structure B..............................................................55

Table 14 – Column Moment and Axial Load Values / Structure B ...................................55

1

Introduction

In January 12, 2010, an estimated 230.000 of people have lost their lives, in the Haiti

earthquake, which is the 6th earthquake ranked by Loss of Life.

When deadliest natural disasters are investigated, earthquakes take 6 places in the

top 10 of the list, for the past century.

When the economical prospects and survived but injured people are considered,

there is no doubt that, earthquakes are one of the most hazardous of the natural

disasters, and cause big losses in human life and economy.

But actually, earthquakes are not the reason for people to lose their lives. The

structures that are not designed properly are most likely to be the reason for people

to lose their lives and the economical sufferings.

We do not have the technology to prevent earthquakes yet, but with new design

methods and approaches and a better understanding of behaviors of materials,

structures can be built to resist even the most intensive earthquakes.

When an earthquake occurs, certain amount of energy is fed to the structure. If this

energy can be dissipated before being fed to the structure, obviously the structure

will need to resist lower lateral forces.

This study focuses on one of these devices, friction devices, which work with this

logic where the input energy is dissipated with friction forces.

2

Aims & Objectives

This study will focus on Passive Control of the Seismic Response of Reinforced Frame

Buildings, namely Friction Devices, mainly on investigating the retrofitting capability

of the Friction Devices on weak Reinforced Concrete structure, studying the

performance with respect to a properly designed RC structure to Eurocode 8.

2 Reinforced Concrete structures are designed with behavior factors of 3 and 6.

These structures are tested under 4 different recorded earthquake accelerations.

The objective is to find the retrofitting capability of friction devices on the structure

designed with the higher behavior factor, and the outputs are compared with the

structure designed with the behavior factor of 3.

Also, an observation on the optimum slip loads for the retrofitting capability is done.

In addition to these, one of the aims of this study is to give a State of the Art Review

of Friction Devices, which includes an introduction to Passive Control Systems and

Principles of Friction Devices, in order to provide the reader a better understanding

of the study in this paper, and to provide a guide and references for further

researches in these areas.

3

Literature Review

Structural Control

Harsh ground motions, as in earthquakes, induce lateral forces on structures, causing

them to swing with amplitude proportional to the energy fed in. This energy

depends on several properties, including: properties of the structure such as the

mass and the natural frequency and the nature of the earthquake and is never easy

to estimate or to calculate.

This energy can be stored in the structural elements with elastic strain up to a

certain level. However, designing a structure to resist an earthquake only with elastic

deformations would end up with huge sections and would be uneconomical.

Because of these reasons, the latest approach in earthquake resistant design relies

on energy dissipating ability of the structural elements with plastic deformations,

which ends in economical solutions, however leaving permanent damage in the

elements.

The energy that is fed to the structure can also be reduced by various structural

control systems, rather than the structural elements. These systems can be either

“passive” or “active”.

Active control systems have the capability to monitor the input signals, such as

ground motions, and to optimize the properties for the best output in seconds.

On the other hand, passive control systems consist of pre – determined properties

that cannot adjust or optimize themselves for different input values.

The idea is not to increase the capacity of the existing structure, but rather to

decrease the demand in different ways, leaving the structure with a less amount of

energy to deal with, which decreases the risk of a total collapse in most severe

earthquakes or decreases the damage in less severe ground motions.

4

Passive Structural Control

There are several different types of passive control devices that have been under

development since mid – 1970’s with a rapid increase in implementations, especially

in U.S.A and Japan, starting in mid – 1990’s. [1], [2], [3]

Passive control devices that are mentioned can be divided into 3 groups depending

on how they work. Figure 1 demonstrates briefly how base isolation systems, energy

dissipating devices and mass dampers work.

Friction devices belong to energy dissipating devices category and as the name

suggests, use the friction forces to dissipate energy.

Using the inter – storey drifts between adjacent floors, two plates located in the

friction devices convert kinetic energy to heat energy and surface deformations, thus

reducing the energy that is transferred to the structural elements.

Figure 1 - Passive Control Systems [4]

5

Dry Friction

Friction devices that are being used in structural engineering field uses dry – friction

contact areas. Dry friction resists relative lateral motion of two solid surfaces which

are in contact.

Figure 2 illustrates the forces that are important in understanding of dry – friction. As

seen in the figure, Ff, the frictional force, opposes to slide between the bodies. µ, the

friction coefficient, depends on the surfaces that are in contact. N, the normal force,

here depends on the self weight of the block, whereas, as will be illustrated later, in

friction devices can be adjusted by bolts. The frictional force is given by: Ff = µ ×N

When the acting force on the block is less than frictional force, the block will stand

still. As the acting force gets larger than the frictional force, the block will move, and

the frictional force will start doing physical work, i.e. dissipating energy. Figure 3

shows this

relationship.

Figure 2 - Force Diagram for Block on Ground [9]

Figure 3 - Friction Force - Applied Force Relationship [9]

6

Friction Devices

The friction device consists of two steel casing and a sliding piece located between

the casings. The interface between the inner and outer pieces in faced with a high

brake pad material and the normal force is adjusted by pre - stressed bolts. [5]

Figure 4 - Friction Damper Details [5]

Friction devices can be inserted in structure in different configurations.

Figure 5 - Different Configurations [4}

Commonly used configurations can be seen in figure 5.

7

Advantages of friction devices can be summarized as:

• High energy absorbing ability.

• Adjustable friction force through pre-stressing.

• Behaviour not affected by number of cycles, high energy dissipation at every

cycle.

• Unlimited capacity of energy dissipation.

• Can be re - used after the earthquake.

• No fatigue effects.

As mentioned above, friction devices dissipate energy at every cycle, when the

lateral force is higher than the friction force. By definition from principles of dry

friction, friction devices show a rectangular hysteresis loops during excitation. Figure

6 shows a typical idealized loop of a friction hysteresis loop adjusted to a certain

level of friction force.

Figure 6 - Typical Rectangular Hysteresis Loops [4}

8

Nh and Xu [7] has done shake table tests on 3 storey and 12 storey structuresequipped with friction devices, and plotted the actual hysteresis loops under 4different recorded earthquakes and proved that the idealized hysteresis loops can beused accurately for modelling the friction devices. (Figure 7)

Figure 7 - Force - Displacement Hysteresis Loops of Friction Device Under 4Earthquakes [7]

Because the friction devices are connected through bracing systems, properties of

these structures equipped with friction devices also change due to these bracings as

well. An equivalent brace and frame unit and the force – displacement relation of

such system can be represented as in Figure 8.

9

Figure 8 Equivalent Brace and Frame Unit and the Force DisplacementRelation [6]

As can be concluded from Figure 8, due to the added bracing and the friction

devices, the fundamental period of the structure is modified. Depending on the

stiffness of the bracings, the number of friction devices, and the current condition of

the friction device in a given instance (slippage condition – locked condition), natural

period of the structure lies between a range of, all being in the slipping condition or

all of them being in locked condition.

De La Cruz showed the time history of displacement response of a frame equipped

with a friction device and a bare frame and concluded that: “The period of the free

response tends to shorten while there is sliding. After the final sticking, the frame

behaves as a SDOF (braced frame) and period keeps constant.” [4]

Figure 9 Displacement responses of the protected frame and the bare frame for an initialdisplacement.[4]

10

It is obvious that, during a ground motion, the response of the structure will depend

on the stiffness of the braces and the adjusted slippage load.

The main goal with retrofitting structures with friction devices is to dissipate the

energy that is input by the earthquake rather than making the frame structure to act

as a braced frame.

High slippage loads will lock the friction devices, as the lateral force will never be

higher than the adjusted load, and the frame will act as a braced frame.

On the other hand, low slippage loads will dissipate energy; however the dissipated

energy will be very low due to this value, and again will be useless.

These facts conclude that the slippage load must be adjusted to a certain value for

best results. Several studies showed that, this value lies between a range, depending

on the properties of the structure that will be discussed later. When the slippage

load is adjusted for an optimum value, the stiffness of the bracing has almost no

effect on the output, therefore for an economical solution, a bracing system that is

enough to take the loads transferred from friction devices and not to buckle under

compression forces should be chosen.

Mualla and Belev did numerical analysis to show the effect of the stiffness of the

bracing on a structure equipped with Friction Devices and concluded that “A change

in brace stiffness leads to shifting the period of vibration and damping ratio”. [8]

However as can be seen from Figure 10, even when the bracing stiffness (the cross

section area of the bracing) is tripled, the difference in dissipated energy is affected

slightly.

11

Figure 10 Effects of Bracing Stiffness on Dissipated Energy Percentage [8]

As mentioned before, due to energy dissipating being the main goal, and the desire

to choose small sections for economical solutions, buckling issues are treated with

special solutions. Figure 11 shows a close – up view of installed buckling – restrained

braces. [1]

Figure 11 Close Up View of an Installed Buckling Restrained Braces [1]

12

Current Practice Examples

A recent and a good example of this design consisting Friction Devices is the Kaiser

Santa Clara Medical Center, Santa Clara, California. This is a 327 bed hospital with a

gross floor area of 65.960 m2 that was opened in mid 2007. This hospital lies

between 2 major fault lines, namely San Andreas and Hayward, and is in a risk of

very strong near – field earthquake action.

The final design had Friction Devices at each floor in ten bays, in two principle

directions of the structure, with slippage values between 1,115 to 2,450 kN.

Seismic analysis of this design shows for a strong ground motion that is expected to

be in the region, a maximum story drift of 1.5 %.

One example for a recently done seismic retrofitting is the retrofitting of the Patient

Tower in Seattle seen in Figure 12.

Figure 12 Patient Tower Seattle [1]

13

The Patient Tower is a structure consisting of 14 floors that was originally

constructed in 1970. First 2 floors consist of relatively rigid RC podium. The 2 floors

above the podium include RC columns that support the shear walls in the above

floors. Therefore, the 2 floors above the podium are soft stories, a high risk for

earthquakes.

The structure has been retrofitted with friction devices, and in accordance with the

FEMA – 356 standards, now it meets Immediate Occupancy performance level for

the design seismic event, and the drifts in the soft floors were reduced by 1.5.

Used friction devices were cross – brace frames, dissipater located in the middle of

the frame, 24 in quantity with a slippage load of 890 kN as can be seen in Figure 13.

This solution contributed the following advantages:

• Solution resulted in approximately $1 million savings on the foundation work

compared to the conventional concrete shear wall seismic upgrade scheme.

• Simplified the construction process with minimum disturbances to an

occupied hospital facility during construction.

• Aesthetically unique and acceptable.

• Added structural integrity and improved building life safety.

• Helps minimizing post – earthquake structural and non structural damage

and reduce potential down time and repair costs after a seismic event.

Figure 13 Completed Damper Installation [1]

14

Modelling & Methodology

Methodology

All the modelling and analysis is done using commercially available software

SAP2000.

For Modal Analysis Eigen Vectors have been used which is used in Response

Spectrum Analysis. 5% of damping is assumed for the structure.

Non – linear time history analyses are used for comparing the behaviours of the

structures under recorded earthquake ground motions.

Time history analysis are performed using the same software, SAP2000, using the

implicit integration method Hilbet – Hughes – Taylor method, as suggested in

SAP2000 help files, in which the equation of motion at a time step is modified by the

inclusion of a numerical damping parameter which takes a value between 0 and –

1/3.

When is set to zero, the method becomes same with the Newmark implicit scheme

wih = 1/4 and = 1/2.

As takes negative values, it tends to dampen the higher modes of vibration,

improving convergence at the cost of a small loss of accuracy.

Analyses are performed with = 0 for frames without friction devices and -0.05 is

used for structures equipped with friction devices, which experienced convergence

problems with = 0, due to very small mass at the intersection of the link elements,

which ended up in high frequency modes.

For time history analysis, a step size of 0.003 seconds is used. Time history analysis

continues from the combination Dead + 0.24 Live.

15

Modelling of Structures

Used material has a self weight of 25 kN / m3 and Young’s modulus of 30000 N /

mm2.

Rigid floor diaphragm constraints are applied to each level, to take into account the

stiffness of the slab, making all nodes lie at the same horizontal plane.

Joints 1, 5, 9 and 13 are fixed to the base and all other connections are rigid

connections as it would be in a RC structure.

Mass is taken into account automatically by SAP with the sum of self weight of the

elements, acting dead loads and 24% of the acting live loads.

Beam and column elements are assumed to be in the elastic zone, except at defined

hinge locations, all located at 5% of the length of the element from each end.

M3 types of hinges are applied to beams and P – M3 interacting hinges are applied

to columns.

Figure 14 Hinge Properties

Hinges are assumed to resist 10% more of the yield value assigned with a rotation of

0.015 rad. After this point, the moment capacity of the hinge drops to 20% of the

yield value, and after a rotation of 0.025 rad. moment capacity drops to zero.

16

Modelling of Friction Devices

Frame with the dissipater located between the braces and the upper slab is used

through this study.

Friction devices are modelled using link elements. Based on the behaviour of friction

devices, an elastic – perfectly plastic element is used.

The plasticity model that was assigned to the friction device is based on the

hysteretic behaviour proposed by Wen where the non – linear force – deformation

relationship is given in Figure 15. [9]

Figure 15 Definition of parameters for the Wen plasticity property. [9]

Where k is the elastic spring constant, Fy is the yield force, r is the specified ratio of

post – yield stiffness to elastic stiffness k, and z is an internal hysteretic variable.

17

This variable z has a range of -1 < z < 1, with the yield surface represented by |z| = 1.

The initial value of this variable is 0, and it is calculated with the equation (1) where

exp is an exponent greater than or equal to unity.

Equation 1 - Value of z

Large values of this exp increase the sharpness of yielding as shown in Figure 15. The

practical limit for exp is about 20 [10] and used for this study.

Post yield stiffness is assigned as 0, assuming there will be no stiffness at all during

yielding, and an elastic stiffness of 2100000 N / mm2 which corresponds to a very

chunky piece of metal, because the stiffness of the bracing will be assigned to the

bracing members in the model.

Braces, that the friction devices are connected to, assume not to fail under

compression therefore buckling is not considered.

Brace member materials have a stiffness value of 210000 N / mm2 which is a

common value for steel used in practice.

18

Design of Structures

Two 3 storey reinforced concrete frame structures were chosen and designed for the

purpose of this study.

The chosen structures have the same properties with an only exception of one being

designed to Eurocode 8 with a behaviour factor of 3 (Structure A), whereas the

second structure designed with a behaviour factor of 6 (Structure B).

Both frame structures have floor height of 4 meters and 3 spans of 6.5m. Also it is

assumed that the frame repeats itself at every 6.5 meters. Plan and the elevation

view of the chosen structure can be seen in Figure 16 and Figure 17.

Figure 16 - Plan view of chosen structure

19

Figure 17 - Elevation view of chosen structure

Frame and joint labelling is also seen in the elevation view and will be consistent

through this paper.

The designed frame is the frame on that lies on the Axis 2 on plan view, also shown

by red colour.

For design purposes, response spectrum is chosen to be Type 1 (for moderate or

large events), soil type C (dense sand or gravel, or stiff clay), scaled to a peak ground

acceleration of 4 m/s2.

Assumed dead loads are to be self weight of the structural elements plus 0.5 kN/m2

on slabs, and a live load of 2.5 kN/m2. Mass for the purpose of the response

spectrum analysis and time history analysis is taken as 0.24 × Live Loads + 1 × Dead

Loads.

20

Properties of Structure A

As mentioned before, Structure A is designed with a behaviour factor of 3.

Step by step detailed calculations can be found in Appendix A.

Frame Element SizesFirst Floor Second Floor Third Floor

Columns 50 x 50 50 x 50 45 x 45Beams 35 x 50 35 x 50 30 x 45

Table 1 Element Sizes / Structure A

Beam Moment Resistance Values ( kN.m )

First Floor Second Floor Third Floor

Design Positive 420 356.5 122

Design Negative -624.5 -575 -300Table 2 Assigned Hinge Values for Beams / Structure A

As mentioned before, due to the fact that the moment resistance values depend on

the axial load on the columns, P – M3 interacting hinge properties are assigned to

columns. These interaction diagrams can be found in Appendix A.

Modal InformationPeriod (sec) Frequency ( hz ) Modal Participating Mass Modal Mass Sum

0.74 1.35 82.94% 83%0.24 4.17 12.65% 96%

0.12 8.33 4.40% 100%Table 3 Modal Information / Structure A

Structure A, structure properly designed to Eurocode 8, has a fundamental period of

0.74 sec. as seen in Table 3.

21

Properties of Structure B

As mentioned before, Structure A is designed with a behaviour factor of 6.

Step by step detailed calculations can be found in Appendix A.

Assumed Frame Element Sizes First Floor Second Floor Third Floor


Table 4 Element Sizes / Structure B

Beam Moment Resistance Values ( kN.m )First Floor Second Floor Third Floor

Design Positive 97.75 70 46Design Negative -300 -287.5 -172.5

Table 5 Assigned Hinge Values for Beams / Structure B

As mentioned before, due to the fact that the moment resistance values depend on

the axial load on the columns, P – M3 interacting hinge properties are assigned to

columns. These interaction diagrams can be found in Appendix A.

Modal InformationPeriod (sec) Frequency ( hz ) Modal Participating Mass Modal Mass Sum

0.91 1.10 82.77% 83%0.29 3.45 12.70% 96%

0.15 6.67 4.52% 100%Table 6 Modal Information / Structure B

Structure B, structure properly designed to Eurocode 8, has a fundamental period of

0.91 sec. as seen in Table 6.

22

Design of Retrofitted Structure

It is clear that the most important value that has to be considered is the yield value

of the friction device for increasing the capacity of the structure against seismic

loading. However, the bracing system which is connected to the friction device has

to be designed as well.

So it is evident that there are 2 main parameters that have to be decided on, for

every individual friction device.

Which means, in the case of this study, due to the structure that is considered is a 3

floor structure; there will be 6 independent values that have to be decided.

It is obvious that, these parameters will affect the seismic capacity increase of the

frame highly, which also depends on the frames individual characteristics.

Proposed placement of the friction devices can be seen in Figure 18.

Figure 18 Placement of Friction Devices on Structure B

23

Design of Bracing System

The bracing system acts as the structural element that causes the friction device to

use inter – storey drifts between adjacent levels by connecting the mentioned levels

with the friction device in between.

Of course, the bracing members should be able to carry the load transferred from

friction devices to the lower floor.

Besides that, due to the added stiffness with the bracing members, the fundamental

period of the structure changes and shifts to higher frequencies, i.e. the structure as

a whole gets stiffer.

However this is only true when all the friction devices are locked, i.e. when the

structure acts as a braced frame. Once the friction devices start yielding, the

structure then acts as the original frame though with dissipating the energy that is

being fed by seismic motion.

Altamira [9] did numerical analysis on a 3 storey steel frame retrofitted with friction

devices with artificially generated ground motions. He applied the same yield forces

on every floor, and increased this value gradually. For every step, he used different

bracing stiffness values as well. With this study, he showed that the response of the

structure depends mainly on the yield force and the bracing stiffness has almost no

effect.

24

Figure 19 Effects of Damper Stiffness and Yield Force [9]

Sang – Hyun Lee et .al, also showed the effect of the damper stiffness and concluded

that the effects of the damper stiffness is minor, compared to the effects of yield

force on seismic performance. [6]

Petkovski and Waldron also did numerical analysis with friction devices connected

with panels instead of braces and came to the conclusion that: “The response of

structures with different panels (stiff or flexible) is almost identical.” [11]

To verify this information, an initial yield force of 200 kN has been assumed in all the

braces, and 3 different kinds of braces are chosen with cross section areas of 10, 15

and 20 cm2 and implemented in Structure B. Analysis has been run with the first 30

seconds of the recorded ground motion El – Centro. With the 3 different kinds of

braces and same yield forces, time history for top floor displacements are given in

Figure 20 and 21.

25

Figure 20 Top Floor Displacement with Different Bracings

Figure 21 shows the first 10 seconds of the Figure 20 in detail for a better evaluation.

Figure 21 Top Floor Displacement with Different Bracings in Detail

Figure 20 and 21 clearly shows and verifies the statement by the mentioned

references that the response does not depend on the brace stiffness as much and is

almost identical.

Therefore, a bracing member with 20 cm2 has been chosen for this study, with the

capability of resisting an axial load of 1000 kN both in compression and tension,

assuming a strength value of 500 N / mm2. Where in any analysis cases the axial load

-6

-4

-2

0

2

4

6

8

0 5 10 15 20 25 30

Dis

plac

emen

ts (

cm )

Time ( sec )

Top Floor Displacements

B15

B20

B25

-6

-4

-2

0

2

4

6

8

0 2 4 6 8 10

Dis

plac

emen

ts (

cm )

Time ( sec )


B15

B20

B25

26

on any bracing member is above 1000 kN, this will be mentioned and the analysis

will be run with a greater cross sectional area.

This study will not investigate the influence of the bracing member stiffness and will

only focus on the influence of the yield force.

Properties of Structure B Equipped with Braces

As mentioned before, friction devices will change the natural period of the structure

dramatically, adding stiffness due to the bracing members.

Structure B – equipped with the bracing members with a cross section area of 20 cm2

has a natural period of 0.4874 sec. , which is equal to a frequency of 2.05 hz.

This means that the structure will have a natural period of 0.4874 sec when all the

friction devices are locked, or will have the same natural period as if it was a bare

frame, when all the friction devices are activated, which is 0.91 sec.

During a ground motion, depending on the number and the status of the friction

devices, the first natural period will be in this range.

For a better understanding of the capability of the friction devices, ground motions

will be chosen to be effective within this range for this study.

27

Allocation of Yield Forces

As mention before, the allocation of the yield force on the friction devices is the

most important variable for seismic retrofitting of structures.

To date, there are no design guidelines in Eurocode for friction devices. There are

several studies done by various researchers on different approaches on design and

allocation of yield forces.

Petkovski and Waldron has done a research on “Optimum Friction Forces for Passive

Control of the Seismic Response of Multi – Storey Buildings” [11] and proposed a

design methodology for allocation of yield forces.

This study will use this approach and will use 20 different sets of yield forces for each

recorded ground motion.

Petkovski and Waldron proposed a method where first the lateral storey stiffness K

and storey yield force, fy is determined and then the yield forces are assigned to the

friction devices with a constant ratio to these values for each storey.

Petkovski and Waldron defines the storey stiffness as the initial stiffness of the

storey, which will be used as defined by them in this study as well, before the

incidence of any plastic hinges and the storey strength as the storey shear force

where first incidence of plastic hinge.

Storey Shear Forces - Structure B

First Storey Second Storey Third Storey

Storey Shear Force ( kN ) 559.078 517.682 330.095Table 7 Storey Shear Forces Structure B

Design steps can be found in detail in Appendix B.

28

Allocated Yield Forces ( kN )Step fy / fs First Storey Second Storey Third Storey

1 0.1 56 52 332 0.2 112 104 663 0.3 168 155 994 0.4 224 207 1325 0.5 280 259 1656 0.6 335 311 1987 0.7 391 362 2318 0.8 447 414 2649 0.9 503 466 297

10 1 559 518 33011 1.2 671 621 39612 1.4 783 725 46213 1.6 895 828 52814 1.8 1006 932 59415 2 1118 1035 660

Table 8 Step Numbers and Allocated Yield Forces

Table 8 shows the chosen fy to fs ratios where fy stands for the yield force and fs for

the storey shear force.

15 steps are chosen for this study as seen in Table 8. Ratios are kept same for all

levels and allocated yield forces are seen for every storey.

29

Earthquake Records

4 recorded ground motions have been chosen for this study, namely the El – Centro

earthquake, Loma earthquake, Northridge earthquake and the Mexico City

earthquake.

El Centro Earthquake

30 seconds of the El Centro earthquake has been used that has a maximum ground

acceleration value of 0.34 g and is effective for the structures with the fundamental

period 1 – 2 Hz. Figure 22 and 23 shows the details for this ground motion.

Figure 22 El Centro Acceleration Time History

Figure 23 El Centro Power Spectrum

-0,4

-0,2

0

0,2

0,4

0 5 10 15 20 25 30

Acc

eler

atio

n ( g

)

Time ( sec )

El Centro - Acceleration Time History

0

0,02

0,04

0,06

0,08

0,1

0,12

0 0,5 1 1,5 2 2,5

Spec

tral

Am

plit

ude

Frequency ( hz )

El Centro - Power Spectrum

30

Loma Earthquake

Like the El – Centro earthquake, first 30 seconds of the Loma earthquake ground

acceleration time history has been used.

Acceleration values of the Loma earthquake are doubled due to low natural values.

This ground motion has greater spectral amplitude values, mainly effective for the

structures with natural periods between 1 – 1.5 hz, also having a peak around 0.5 hz.

Figure 24 and 25 shows the acceleration time history and power spectrum for Loma

earthquake.

Figure 24 Loma ( Modified ) Acceleration Time History

Figure 25 Loma ( Modified ) Power Spectrum

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0 5 10 15 20 25 30

Acc

eler

atio

n ( g

)

Time ( sec )

Loma ( Modified ) - Acceleration Record

00,05

0,10,15

0,20,25

0,30,35

0 0,5 1 1,5 2 2,5

Spec

tral

Am

plit

ude

Frequency ( hz )

Loma ( Modified ) - Power Spectrum

31

Northridge Earthquake

Northridge earthquake time history has been compressed by a factor of 2 in the

means of seconds. This ended up making a 50 seconds recorded motion a 25

seconds motion.

This modification has been done to shift the effective frequencies to the range which

is between 1 – 2 Hz, mainly around 1.5 Hz.

Northridge has a maximum ground acceleration value of 0.4 g and has the greatest

spectral acceleration among the earthquakes used, making it the most destructive.

Figure 26 Northridge Acceleration Time History

Figure 27 Northridge Power Spectrum

-0,6

-0,4

-0,2

0

0,2

0,4

0 5 10 15 20 25

Acc

eler

atio

n ( g

)

Time ( sec )

Northridge ( Modified ) - Acceleration Time History

00,10,20,30,40,50,60,7

0 0,5 1 1,5 2 2,5

Spec

tral

Am

plit

ude

Frequency ( hz )

Northridge ( Modified ) - Power Spectrum

32

Mexico Earthquake

Like the Northridge earthquake, this time history has been modified, but this time

compressed by a factor of 2.5 to make it effective between 1 – 2 Hz as in the

previous ones.

Figure 28 and 29 shows the acceleration time history and the power spectrum for

Mexico earthquake.

Figure 28 Mexico ( Modified ) Acceleration Time History

Figure 29 Mexico ( Modified ) Power Spectrum

-0,2

-0,1

0

0,1

0,2

0 5 10 15 20 25 30 35 40

Acc

eler

atio

n ( g

)

Time ( sec )

Mexico ( Modified ) - Acceleration Time History

0

0,01

0,02

0,03

0,04

0 0,5 1 1,5 2 2,5 3

Spec

tral

Am

plit

ude

Frequency ( hz )

Mexico ( Modified ) - Power Spectrum

33

Analysis Results

Assessed Parameters

Responses of the structures are investigated in 4 categories.

Inter Storey Drifts

Maximum inter – storey drift figures show the maximum inter – storey drifts in any

storeys at any time in the structure and is compared with the Structure A where

possible. If at any step for Structure B, the structure has collapsed, inter – storey drift

is not shown in the figure.

Structural Damage

Structural damage is shown by the number of plastic hinges formed through the

structure in any structural members, beams or columns.

Hinges are shown in 2 different types. Type 1 is a hinge with a plastic rotation less

than 0.003 rad. representing lower damage. Type 2 is a hinge with a plastic rotation

greater than 0.003 rad. representing higher damage in an element.


Maximum top floor displacements are investigated in this part for every step and

compared with Structure A where possible.

Top Floor Displacement Time History Response Comparison

Structure A top floor displacement time history is compared with the best solution

offered with the friction devices.

34

El Centro Results

Structure A which is designed to Eurocode 8 with a behaviour factor of 3 has

performed well through the El – Centro ground motion record, without collapsing,

forming plastic hinges in the structural elements.

Structure B which is designed to Eurocode 8 with a behaviour factor of 6 collapsed

forming plastic hinges beyond the capability of the members, thus dropping the

moment resistance completely.

Adding friction devices to Structure B made it possible for it to stand under this

earthquake up to step 12. After step 12, structure failed like the bare frame.

Maximum Inter Storey Drifts

Structure A had a maximum inter – storey drift of 4.25 cm. Structure B with the

added friction devices had an inter – storey of 2.54 cm. in step 8 which is the

greatest reduction among all the steps in terms of maximum inter – storey drifts.

Figure 30 Peak Inter Storey Drifts / El Centro

00,5

11,5

22,5

33,5

44,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Inte

r-St

orey

Dri

ft (

cm )

Step

Peak Inter - Storey Drifts

Structure B

Structure A

35

Structural Damage

Structure A formed 15 type 1 plastic hinges and 7 type 2 plastic hinges, a total of 22plastic hinges all through the structure in structural elements.

Figure 31 gives the number of plastic hinges formed through the structure in anystructural member.

From the structural damage perspective, step 8 survives the earthquake with theleast structural damage in the members with the least number (6) of Type 2 plastichinges, which have a plastic rotation above 0.003 rad. and 8 plastic hinges withplastic rotations below 0.003 rad.

Step 1 configuration survived the earthquake, however with a great damage in thestructural members with the greatest Type 2 of plastic hinges.

Step 13 14 and 15 did not make it possible for Structure B to survive under El –Centro earthquake.

Figure 31 Structural Damage / El Centro

4

17 1715 16

149

7 8 8 912

N/A N/A N/A

24

8 78 7

7

9

6 6 66

7

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Num

ber o

f Pla

stic

Hin

ges

Step

Structural Damage

Type 2 Plastic Hinges


36


Figure 32 Top Floor Displacements / El Centro

Maximum reduction in top floor displacement is achieved in Step 11. However this

does not necessarily mean that this is the best solution, as can be seen in inter –

storey drifts and structural damages.


Figure 33 shows the time history of the top floor displacement of Structure A and

Structure B – step 8 in the same figure.

Figure 33 Top Floor Displacement Response Comparison / El Centro

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Dis

plac

emen

t ( c

m )

Step

Maximum Top Floor Displacement

Structure B

Structure A

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30

Dis

plac

emen

t ( c

m )

Time ( sec )

Top Floor Displacement Response Comparison

Structure A

Structure B - Step 8

37

Loma Results

Structure A which is designed to Eurocode 8 with a behaviour factor of 3 collapsed

under this acceleration time history.

Structure B which is designed to Eurocode 8 with a behaviour factor of 6 also

collapsed forming plastic hinges beyond the capability of the members, thus

dropping the moment resistance completely.

Adding friction devices to Structure B made it possible for it to stand under this

earthquake up to step 12. After step 12, structure failed like the bare frame.


As mentioned before Structure A collapsed therefore is not available for comparison

in inter – storey drifts. Structure B with the added friction devices had an inter –

storey of 3.24 cm. in step 12 which is the lowest among all the steps in terms of

maximum inter – storey drifts.

Figure 34 Peak Inter Storey Drifts / Loma

00,5

11,5

22,5

33,5

44,5

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Inte

r-St

orey

Dri

ft (

cm )

Step


Structure B

38

Structural Damage

Structure C formed 15 type 1 plastic hinges and 7 type 2 plastic hinges.

Figure 35 gives the number of plastic hinges formed through the structure in anystructural member.

From the structural damage perspective, step 12 survives the earthquake with theleast structural damage in the members with the least number of Type 2 plastichinges, which have a plastic rotation above 0.003 rad. and 8 plastic hinges withplastic rotations below 0.003 rad.

Step 1 configuration survived the earthquake, however with a great damage in thestructural members with the greatest Type 2 of plastic hinges.

Step 13 14 and 15 did not make it possible for Structure B to survive under El –Centro earthquake.

Figure 35 Structural Damage / Loma

610 9 8 8 7 6

3 3 5 7 8N/A N/A

2016 16 16 14

13 1313 11 9 7 6

N/A0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Num

ber o

f Pla

stic

Hin

ges

Step

Structural Damage



39


Figure 36 Top Floor Displacements / Loma

Maximum reduction in top floor displacement is achieved in Step 12. For the case of

Loma earthquake, this also corresponds to the best seismic performance reduction,

matching with structural damage and inter – storey drifts perspectives.


Figure 37 Top Floor Displacement Response Comparison / Loma

Due to a total collapse in time step 8.20 seconds, Structure A is shown in 0 for the

rest of the duration in Figure 37.

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Dis

plac

emen

t ( c

m )

Step


Structure B

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30

Dis

plac

emen

t ( c

m )

Time ( sec )


Structure B - Step 12Structure A

40

Northridge Results

All of the structures that have been used in this study, Structure A, Structure B bare

frame and Structure B equipped with friction devices, failed and collapsed under this

ground motion record, therefore none of the result categories is applicable.

Mexico Results

Structure A and Structure B – bare frame collapsed under this ground motion.

Adding friction devices made it possible for Structure B to not to collapse as in Loma.


Inter – storey drifts and structural damage results are not applicable for Structure A.

Maximum Inter – storey drifts for Structure B equipped with friction devices are

given in Figure 38 for each step.

Figure 38 Peak Inter Storey Drifts / Mexico

0

0,5

1

1,5

2

2,5

3

3,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Inte

r-St

orey

Dri

ft (

cm )

Step


Structure B

41

Structural Damage

Types and number of plastic hinges in the Structure for each step is given in Figure39.

Figure 39 Structural Damage / Loma

Step 1 and Step 2 did not make it possible for Structure B to stand the Mexico

earthquake. After step 7, structure remained in elastic zone as seen in Figure 39.


Figure 40 Top Floor Displacements / Mexico

Figure 40 shows the maximum top floor displacements for the Mexico earthquake.

As in Structural Damage, these parameters remain same after Step 7 with increasing

steps.

N/A N/A

812

16

20 0 0 0 0 0 0 0 0

12 5

02468

101214161820

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Num

ber o

f Pla

stic

Hin

ges

Step

Structural Damage



0123456789

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Dis

plac

emen

t ( c

m )

Step


Structure B

42


Figure 41 Top Floor Displacement Response Comparison / Mexico

Figure 41 shows the top floor displacement response of Structure A and Structure B

equipped with friction devices – Step 15.

Structure A collapses at sec 23 while Structure B survives the earthquake without

any major displacements in top floor.

-10-8-6-4-202468

10

0 5 10 15 20 25 30 35 40

Dis

plac

emen

t ( c

m )

Time ( sec )


Structure B - Step 15

Structure A

43

Summary and Evaluation of Results

Structure A, Structure B bare frame and Structure B equipped with Friction Devices

have been assessed under 4 different ground motions in this Study.

3 of these ground motions have been modified in terms of amplitude and frequency

content to attack the structure harshly.

Structure A was able to stand only under El – Centro ground motion, which was the

only one used as original. Same structure, Structure A has failed in ground motions

Loma, Northridge and Mexico.

Structure B, which was designed by a behaviour factor of 6 failed in all ground

motions as expected.

Friction devices made it possible for Structure B to show a better seismic

performance for ground motions El – Centro, Loma and Mexico. However, none of

the yield force steps made it possible for Structure B not to collapse under

Northridge earthquake.

In the case of El – Centro, the best seismic performance for Structure B is obtained in

Step 8, in terms of structural damage and inter – storey drifts. This is due to the

optimum possible solution that can be achieved by the friction devices. When the

allocated yield forces were too low, friction devices made more cycles however

dissipating less energy, therefore more energy was induced to the structure. When

the yield forces were higher than this optimum value, the friction devices made less

loops. Even that the yielding force was higher, with less displacements, less induces

energy was dissipated.

After Step 12, the lateral forces in the friction devices were not big enough to

activate them, thus Structure acted as a braced frame only, without dissipating any

energy in Friction devices. This led to a collapse of the structure.

44

When Step 8 for Structure B is compared with Structure A, a reduction ratio of 35% is

observed in peak inter – storey drifts. When structural damage is observed for the

same situations, a reduction of 50% is seen.

Loma results are similar to the El – Centro results; however a comparison with

Structure A is not possible, as in Northridge and Mexico.

This time the best seismic performance is achieved in Step 12 which is different from

the previous mentioned case, El – Centro, however after Step 13 the same output is

seen.

This verifies the information that there is an optimum solution for a Structure,

however this optimum solution is not an exact value for the structure itself, but lies

in a range depending on the earthquake.

Northridge was the most destructive ground motion among the ones that have been

used in this study with the maximum peak ground acceleration value and maximum

peak spectral acceleration values.

There are no outputs available for this ground motion due to a failure in all

numerical analysis.

Output values for Mexico earthquake shows a different perspective of the Friction

Devices. As can be seen from the relevant figures, this time the structure failed in

steps 1 and 2, however was always able to stand with increasing allocated yield

forces.

As in previous examples, with higher yield forces structure acted as a braced

structure only, and the friction devices did not dissipate any energy. But in this

situation, natural frequency of the structure was shifted, where the ground motion is

not effective. It can be seen in Figure 41 that, the braced structure vanished the

resonance effects just by frequency shifting, therefore making it possible for

Structure B to stand. When the yield forces are low, devices are always activated, the

structure is in the danger zone frequency, and the dissipated energy is not enough

for structure to stand.

45

Conclusions and Future Work

This study has presented the basic procedure of designing a frame structure to

Eurocode 8 with 2 different behaviour factors, 3 and 6 respectively and then the

seismic behaviour improvement of the structure designed with the behaviour factor

of 6 with friction devices.

Of course, a behaviour factor of 6 is neither reasonable nor allowed in Eurocode for

any type of structure. This corresponds to a great energy dissipation expectation in

structural members without failing.

Confirming this statement, this structure has failed under all earthquake records.

Structure that is designed with a behaviour factor of 3 could stand only 1 of the

ground motions used out of 4 records. This is mainly due to the fact that the

earthquakes are modified in terms of dominant frequencies and especially adjusted

to be destructive for this structure.

Structure B, retrofitted with friction devices made it possible for this Structure to

stand 3 of the records that have been used.

Due to the fact that Structure A was only able to survive the El – Centro earthquake,

a comparison was available only for this.

Structure B, improved with the optimum solution showed a better seismic

performance than Structure A, lasting with less structural damage.

Also friction devices made it possible for Structure B to stand the earthquakes that

Structure A was not able to.

46

This study also confirms the conclusions previous studies have came to that the most

important parameter is to determine the yield force.

For low values of yield forces, differences in the stiffness of the braces have almost

no effect. As the yield forces get larger, the stiffness of the braces gains relevance,

however, this is mainly due to the fact that friction devices are in locked mode thus

the structure will act more like a braced frame, where the stiffness will have a high

influence. This means that the dissipated energy will be low which means the aim is

not reached.

Friction devices, by nature need non – linear analysis and there are many

combinations possible for allocation of yield forces on the devices.

For every step, a time consuming non – linear time history analysis has to be done to

see the performance of the structure.

Also, it cannot be said that there is only one best optimum yield forces allocation

depending on a structure, but this allocation of yield forces depend on the

earthquake as well. Altamira (2009) also mentioned this fact in his study and

confirmed.

However, a trend is seen in all the studies that have been done in the past on friction

devices that this optimum value lies between in a range.

This fact is also confirmed and observed in this study, that below or above this range,

although being in the activated state friction devices either dissipate very low energy

due to the low yield forces, or get locked and do not dissipate energy at all leaving

the Structure as a braced – frame only.

The study is done with a 3 storey structure. A more detailed study should be done

with different storey levels and different structural properties to see how different

parameters affect the difference between performance levels of structures designed

with low behaviour factors and high behaviour factors but retrofitted with friction

devices.

47

References

1. M.D. Symans et. al, Energy Dissipation Systems for Seismic Applications: Current

Practice and Recent Developments, Journal of Structural Engineering, 01/2008, p3-21

2. G.W. Housner et. al, Structural Control: Past, Present, And Future, Journal of

Engineering Mechanics,09/1997,p897-971

3. Aiken I., Passive Energy Dissipation Hardware And Applications, Proceedings, Los

Angeles County And Seaosc Symposium On Passive Energy Dissipation Systems For

New And Existing Buildings, Los Angeles, 06/1996.

4. De la Crus S.T., Contribution to the assessment of the Efficiency of Friction

Dissipators for Seismic Protection of Buildings, Universitat Politecnica de Catalunya,

06/2003

5. Tehranizadeh M., Design and Construction of a Friction Damper Applying Brake

Lining Pads, Amir Kabir University of Technology, Lecture Notes, 2008.

6. Lee S.H. et al., Allocation and slip load of friction dampers for a seismically excited

building structure based on storey shear force distribution, Engineering Structures,

06/2007, p930-940

7. Nh C. Et .al., Seismic response control of a building complex utilizing passive

friction damper: Experimental investigation, Earthquake Engineering And Structural

Dynamics, 02/2006, p657-677

8. Mualla I.H., Belev B., Performance of steel frames with a new friction damper

device under earthquake excitation, Engineering Structures, 2002, p365-371

9. Altamira L., Seismic Interstory Drift Demands in Steel Friction Damped Braced

Buildings, Msc Thesis, Texas A&M University, 2009

10. CSI, CSI analysis reference manual for SAP2000, ETABS and SAFE, Software

Manual, Computers and Structures Inc, Berkeley, CA, 2007.

48

11. Petkovski M., Waldron P., Optimum friction forces for passive control of the

seismic response of multi storey buildings, Conference Paper

49

Appendix A Design of Structures

Design of Structure A



Table 9 Assumed Frame Element Sizes / Structure A

For purpose of design, preliminary selection of element sizes is as shown in table

above. Slabs are assumed to have a thickness of 0.20 meters.

Self weight and mass of the beam elements are modified by 0.6 since is already

taken into account when the slab weight and mass is added to the frames as dead

loads.

Applied additional dead loads on beams

Self weight of slabs: 2 x [ 0.20 × 3.25 x 25 ] = 32.5 kN / m

Assumed additional dead loads: 2 x [ 0.50 × 3.25 ] = 3.25 kN / m

Applied additional dead loads on joints

Self weight of the beams (Floors 1/2):2 x [ 3.25 x (0.5 – 0.2) x 0.35 x 25 ] = 17.0625 kN

Self weight of the beams (Floor 3 ):2 x [ 3.25 x (0.45 – 0.2) x 0.30 x 25 ] = 12.1875 kN

Dead load transferred from the beams to the joints:

Internal Joints: 6.5 x 35.75 / 2 116.1875 kN

External Joints: 6.5 x 35.75 / 4 = 58.09375 kN

50

Applied live loads on beams

Live load transferred from slabs: 2 x [ 2.50 x 3.25 ] = 16.25 kN / m

Applied live loads on joints

Internal Joints: 6.5 x 16.25 / 2 = 52.8125 kN


Mass Source: 0.24 × Live Loads + 1 × Dead Loads

Response Spectrum Analysis

Response Spectrum to Eurocode 8 with Design Ground acceleration 0.4g, Spectrum

Type:1, Ground Type: C, Behaviour Factor: 3 and Damping Ratio: 0.05

Figure 42 Response Spectrum Function / Structure A

00,05

0,10,15

0,20,25

0,30,35

0,40,45

0 1 2 3 4 5 6 7 8 9 10

Acc

eler

atio

n ( g

)

Period ( sec )

Response Spectrum Function

51

Response Spectrum Analysis Results

Beam Results

Elements have been designed under combination Dead + 0.24 Live + Response

Spectrum

Beam Moment Values ( kN.m )First Floor Second Floor Third Floor

Action Positive 365 310 106Design Positive 420 356.5 122Action Negative - 543 - 500 - 257Design Negative - 624.5 - 575 - 300

Table 10 Beam Moment Values / Structure A

Design moment values are assumed to be 15% more of the action values. Exact

longitudinal reinforcement areas are not calculated.

Column Results

Column Moment and Axial Load Values ( kN.m / kN )Internal Columns External Columns

Max Moment Min Axial Max Moment Minimum AxialFirst Floor 648 903 593 220

Second Floor 490 593 337 148Third Floor 320 285 184 92

Table 11 Column Moment and Axial Load Values / Structure A

Because of the fact that moment resistance values depend greatly on the axial force

acting on the columns, columns are designed properly with reinforcements.

Assumed concrete grade is C30 and rebar grade is S460.

Provided steel area in columns for the columns are: 5 32 on each side with a clear

distance of 40 mm. The interaction diagram for this section is shown below.

(Negative values compression, positive values tension, interaction diagrams are

symmetrical.)

52

Figure 43 Interaction Diagram for Columns Storey 1 2 / Structure A

Figure 44 Interaction Diagram for Columns Storey 3 / Structure A

Red plus signs correspond to calculated values seen in the table. All the values are

within the range of the limits for both column sections.

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

4000

0 100 200 300 400 500 600 700 800 900 1000

Axi

al L

oad

( kN

)

Moment ( kN.m )

Interaction Diagram for Columns Storey 1 - 2

-10000

-8000

-6000

-4000

-2000

0

2000

4000

0 100 200 300 400 500 600 700 800

Axi

al L

oad

( kN

)

Moment ( kN.m )

Interaction Diagram for Columns Floor 3

53

Design of Structure B



Table 12 Assumed Frame Element Sizes / Structure B

For purpose of design, preliminary selection of element sizes is as shown in table

above. Slabs are assumed to have a thickness of 0.20 meters.

Self weight and mass of the beam elements are modified by 0.6 since is already

taken into account when the slab weight and mass is added to the frames as dead

loads.

Applied additional dead loads on beams

Self weight of slabs: 2 x [ 0.20 × 3.25 x 25 ] = 32.5 kN / m

Assumed additional dead loads: 2 x [ 0.50 × 3.25 ] = 3.25 kN / m

Applied additional dead loads on joints

Self weight of the beams (Floors 1/2):2 x [ 3.25 x (0.45 – 0.2) x 0.30 x 25 ] = 12.1875

kN

Self weight of the beams (Floor 3 ):2 x [ 3.25 x (0.40 – 0.2) x 0.30 x 25 ] = 9.75 kN

Dead load transferred from the beams to the joints:



54

Applied live loads on beams

Live load transferred from slabs: 2 x [ 2.50 x 3.25 ] = 16.25 kN / m

Applied live loads on joints



Mass Source: 0.24 × Live Loads + 1 × Dead Loads

Response Spectrum Analysis

Response Spectrum to Eurocode 8 with Design Ground acceleration 0.4g, Spectrum

Type:1, Ground Type: C, Behaviour Factor: 3 and Damping Ratio: 0.05

Figure 45 Response Spectrum Function / Structure B

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 1 2 3 4 5 6 7 8 9 10

Acc

eler

atio

n ( g

)

Period ( sec )

Response Spectrum Function

55

Response Spectrum Analysis Results

Beam Results

Elements have been designed under combination Dead + 0.24 Live + Response

Spectrum

Beam Moment Values ( kN.m )First Floor Second Floor Third Floor

Action Positive 85 60 40Design Positive 97.75 70 46Action Negative -260 -250 -150Design Negative -300 -287.5 -172.5

Table 13 Beam Moment Values / Structure B

Design moment values are assumed to be 15% more of the action values. Exact

longitudinal reinforcement areas are not calculated.

Column Results

Column Moment and Axial Load Values ( kN.m / kN )Internal Columns External Columns

Max Moment Min Axial Max Moment Minimum AxialFirst Floor 252 903 243 361

Second Floor 190 593 150 242Third Floor 132 288 150 165

Table 14 Column Moment and Axial Load Values / Structure B

Because of the fact that moment resistance values depend greatly on the axial force

acting on the columns, columns are designed properly with reinforcements.

Assumed concrete grade is C30 and rebar grade is S460.

Provided steel area in columns for the columns are: 4 25 on each side with a clear

distance of 40 mm. The interaction diagram for this section is shown below.

(Negative values compression, positive values tension, interaction diagrams are

symmetrical.)

56

Figure 46 Interaction Diagram for Columns Storey 1 2 / Structure B

Figure 47 Interaction Diagram for Columns Storey 3 / Structure B

Red plus signs correspond to calculated values seen in the table. All the values are

within the range of the limits for both column sections.

-10000

-8000

-6000

-4000

-2000

0

2000

0 50 100 150 200 250 300 350 400 450 500

Axi

al L

oad

( kN

)

Moment ( kN.m )

Interaction Diagram for Columns Floor 1 2

-10000

-8000

-6000

-4000

-2000

0

2000

4000

0 100 200 300 400 500

Axi

al L

oad

( kN

)

Moment ( kN.m )

Interaction Diagram for Columns Floor 3

57

Appendix B Allocation of Yield Forces

A series of non – linear static analysis has been done as suggested by Petkovski and

Waldron [11] to find each storey strength.

Unit lateral force is applied at every storey, restraining all the nodes in the below

storey. This unit load is increased step by step and the displacement – force graph is

monitored.

Storey strength is defined as the lateral force where the stiffness of the storey

changes, i.e. when first plastic hinge forms in the storey.

First Storey Strength

Restraints: Joints 1, 5,9,13. Load Applied: Joint 2 Monitored Displacement: Joint 14.

Figure 48 First Storey Push over Method

0

200

400

600

800

0 0,5 1 1,5 2 2,5

Stor

ey S

hear

( kN

)

Monitored Displacement ( cm )

First Storey Strength

58

Second Storey Strength

Restraints: Joints: 2, 6, 10, 14, Load Applied: Joint: 3, Monitored Displacement: Joint

15.

Figure 49 Second Storey Push over Method

Third Storey Strength

Restraints: Joints 3, 7,11,15, Load Applied: Joint 4, Monitored Displacement: Joint 16.

Figure 50 Third Storey Push over Method

0100200300400500600700

0 0,5 1 1,5 2 2,5

Stor

ey S

hear

( kN

)


Second Storey Strength

0

100

200

300

400

500

0 0,5 1 1,5 2 2,5

Sto

rey

Shea

r ( k

N )


Third Storey Strength

Msc Dissertation Final

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