base isolation on structures with soft storey

8/12/2019 Base isolation on structures with soft storey

1/77

I

CIVE5708M

Individual Research Project Dissertation

Submitted in partial fulfillment of the requirements for the degree of

MEng inCivil & Structural Engineering

May 2013

School of Civil Engineering

Faculty of Engineering

Investigation of the structural response of 4-Storey partially

infilled seismically isolated and fixed base structures

by

Demetris Demetriou

200444926


2/77

II

ABSTRACT

The subject of the present research is to study the effects on the performance of seismically

isolated structures as opposed to typical fixed base ones. Seismic base isolation is an

earthquake resistant design method that is based on decreasing the seismic demand instead of

increasing the seismic capacity. This method allows alteration of the dynamic characteristics of

a structure and in combination with minor strengthening changes, less vulnerability to

earthquake loads can be achieved. In this project, three structural models for the cases of bare,

fully infilled and partially infilled frames have been considered in order to quantify the

contribution of masonry infills to the stiffness and ultimately the response of the structure prior to

the installation of seismic isolators. The results obtained from the capacity curves for the three

different cases, yield a 60 - 70% increase to the load carrying capacity of the structure due to

the contribution of masonry infills, making infills a factor that has large effects on the behavior of

frames under earthquake loading and by neglecting their contribution severe discrepancies

between the actual and calculated response can occur. A comparison between the structural

response of the partially isolated and partially fixed base structures (which simulate typical

buildings in Greece which their ground floor use is restricted to parking space and stores) was

also performed. The hinge formation, interstorey drifts and floor accelerations being direct

metrics of the structural performance have been investigated. All models have been analyzed

with earthquake characteristics under the guidelines of Eurocode 8 (EC8) and with the use of

SAP 2000, a nonlinear finite element program. The results indicate that under the use of lead-

rubber isolators, the maximum displacements of stories have been increased in comparison

with an ordinary fixed-base model. On the other hand, although maximum displacements

increased, interstorey drift ratios have reduced indicating that isolated structures minimise

cumulative deformation demands (damages). In addition to this, in base isolated structures a

decrease in plastic hinge formation zones was witnessed. Finally floor accelerations are

significantly reduced in the case of the isolated structures therefore damaging to sensitive

internal equipment as well as to primary structural elements such as diaphragms, chords,

collectors is reduced. With regards to the results that are mainly based on typical earthquake

characteristics, it could be concluded that seismic isolation using lead rubber bearings is a

useful method which can be applied in short partially infilled structures, therefore the use of

seismic isolation can not only be restricted to special purpose high rise structures.

Keywords: Pushover Analysis, non linear response, static method, dynamic time history,

seismic performance evaluation, seismic isolation, base isolation, earthquake resistance.


3/77

III

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation and gratitude to my supervisor Dr.Nikolao Nikita

for his support, for believing in me and for providing me with invaluable advice throughout the

duration of this project. I am also thankful to him for his patient and constructive reviews on my

dissertation.

I would also like to express my deepest appreciation to my parents, Chrysostomos and

Valentina, and my sister Anna the most precious people in my life, for their confidence in me

and for their support, love and understanding. I owe very much to them. This dissertation is fully

dedicated to them.

Finally I would like to express my sincerest thanks to all my friends and especially my girlfriend

Liana for their encouragement, belief in me and for their good spirit.


4/77

IV

To

Valentina, Crysostomos, Anna, Liana


5/77

V

Contents

CHAPTER 1

1. Introduction: ............................................................................................................................................. 1

1.1 Purpose of seismic isolation .................................................................................................................... 2

1.2 Principle of seismic isolation: .................................................................................................................. 2

1.2.1 Interstory drift and floor acceleration. ............................................................................................ 4

1.2.2 Ground conditions and technical limitations ................................................................................... 6

1.2.2.1 Ground conditions .................................................................................................................... 6

1.2.2.2 Limitations; ............................................................................................................................... 6

1.2.3 Summary of the tasks of an isolation system .................................................................................. 9

1.2.4 Main consequences of Base isolation .............................................................................................. 9

1.2.5 Summary of the main advantages of seismic isolation ................................................................... 9

1.3 Development of base isolation ............................................................................................................. 10

1.3.1 Recent applications ........................................................................................................................ 10

1.4 Performance of seismic isolated structures.......................................................................................... 11

1.4.1 Experimental demonstration; ........................................................................................................ 14

2. Analysis Method...................................................................................................................................... 16

2.1 Background of pushover analysis ......................................................................................................... 18

2.1.1 Dynamics of pushover analysis ...................................................................................................... 18

2.1.2 Capacity curves .............................................................................................................................. 20

2.1.3 Lateral load patterns ...................................................................................................................... 21

2.2 Capacity spectrum method, CSM.......................................................................................................... 23

2.2.1 Description of the method ............................................................................................................. 23

2.2.2 Capacity curve conversion into capacity spectrum ....................................................................... 24

2.2.3 Elastic response spectrum conversion into accelerationdisplacement spectrum ..................... 25

3.1 Introduction .......................................................................................................................................... 27

3.2 Structure ............................................................................................................................................... 27

3.3 Effects of masonry infills ....................................................................................................................... 28

3.3.1 Simulation of infill contribution ..................................................................................................... 28

3.4 Plastic Hinges ........................................................................................................................................ 30

3.4.1 Plastic hinge length ........................................................................................................................ 30


6/77

VI

3.4.2 Localizing plastic hinges ................................................................................................................. 30

3.4.3 Types of plastic hinge ..................................................................................................................... 31

3.4 Design spectrum ................................................................................................................................... 31

3.5 Lateral Loading Patterns ....................................................................................................................... 31

3.5.1 Inverted triangular load pattern .................................................................................................... 31

3.5.2 Modal pattern ................................................................................................................................ 32

3.5.3 Uniform Load distribution .............................................................................................................. 33

3.6 Results ................................................................................................................................................... 33

3.6.2 Observations: ................................................................................................................................. 36

3.7 Capacity spectrum check ...................................................................................................................... 36

3.7.1 Comparison of bare and partially infilled frame; ........................................................................... 40

4. Introduction ............................................................................................................................................ 42

4.1 Selection of base isolation device ......................................................................................................... 42

4.1.1 Sliding isolation systems ................................................................................................................ 42

4.1.2 Elastomeric isolation systems ........................................................................................................ 43

4.1.2.1 Lead rubber bearings (LRB) ..................................................................................................... 43

4.1.2.2 High damping rubber bearings (HDRB) ................................................................................... 44

4.1.2.3 Hybrid type: Lead high damping rubber bearing (LHDRB) ...................................................... 44

4.2 Modeling of LRB .................................................................................................................................... 45

4.2.1 Selection of LRB ............................................................................................................................. 46

4.2.2 Design parameters for the chosen type of LRB : ........................................................................... 48

4.3 Analysis ................................................................................................................................................. 48

4.3.1 Hinge formation ............................................................................................................................. 48

4.3.2 Interstorey drifts and joint displacements ..................................................................................... 50

4.3.3 Floor accelerations ......................................................................................................................... 52

4.4 Pushover as an alternative method of analysis .................................................................................... 53

5. Summary ................................................................................................................................................. 55

5.1 Conclusions ........................................................................................................................................... 56

References: ................................................................................................................................................. 57


7/77

VII

LIST OF FIGURES

Figure 1 a) Acceleration response spectrum b) Displacement response spectrum 2

Figure 2) dynamic behavior of base isolated frame..4

Figure 3) idealised force-displacement behavior of isolators..4

Figure 4 a) Moment-Rotation curve of hinge b) performance levels..5

Figure 5) Different design spectra for soil classes A-E.7

Figure 6.)Structural response of isolated and fixed base structures founded on soils....7

Figure 7. a) Peffects on columns b) induced bending moments and Pcontribution.7

Figure 8 )Top eqn) Seismic force ratio in ULS, Bottom eqn) Seismic force ratio DLS..11

Figure 9) Interstorey drifts of fixed base and isolated base system by time history analysis ...13

Figure 10).Roof level acceleration of fixed base and isolated base system by time history

analysis..13

Figure 11) Conceptual diagram for transformation of MDOF to SDOF system..18

Figure 12 a) Capacity curve for MDOF structure, b) Bilinear idealization

for equivalent SDOF20

Figure 13 a) FAP (b)SSAP procedures for determination of incremental

applied load pattern at different steps....22

Figure 14 ) Bilinear approximation of the capacity curve...24

Figure 15) Conversion of capacity curve to capacity spectrum24

Figure 16 a) Elastic response spectrum b) demand response spectrum....25


8/77

VIII

Figure 17) Performance point obtained using the displacement rule..26

Figure 18) Performance point obtained through calculation of viscous damping

in the system.....26

Figure 19 a) Structural frame of RC building b) cross- sectional details of beam members,

c) cross-sectional details of column members 27

Figure 20)Concept of equivalent strut method and important parameters .29

Figure 21)From left to right cases of bare, infilled and partially infilled frames .29

Figure 22.a) inverted triangular load pattern b) uniform load pattern based on

, c)

Kunnaths modal pattern..33

Figure 23) Capacity curves obtained for the case of bare frame for the

three lateral load patterns34

Figure 24)Capacity curves obtained for the case of fully infilled frame for the

three lateral load patterns34

Figure 25) Capacity curves obtained for the case of partially infilled frame for thethree lateral load patterns35

Figure 26) Capacity curves showing the contribution of masonry infills

for the most conservative load pattern (modal)35

Figure 27) CSM method, graphical estimation of the performance point of

the partially infilled frame ...37

Figure 28 a) Capacity curve of partially infilled frame. Deformed shapeof partially infilled frame on b) step 9, c) step 10 of analysis, d) performance levels

corresponding to those presented in 1.2.1 ..38

Figure 29 ) CSM method, graphical estimation of the performance point

of the bare frame 39


9/77

IX

Figure 30 a)Capacity curve of bare frame b) Deformed shape of bare frame on step 5 of

analysis, c) performance levels corresponding to those presented in 1.2.1 40

Figure 31)Mixed sideway mechanism ..41

Figure 32 a) Elastomeric bearing b) Lead rubber bearing (LRB)..44

Figure 33 )Mechanical behavior of LRB ..45

Figure 34) a (on the left) and b (on the right) showing the hysteresisloop obtained from idealised bilinear behavior of LRB and typical hysteresis loops

obtained from dynamic tests at increasing shear strain amplitude ..45

Figure 35) Linearised and bilinear relationship of viscoelastic models in terms of force vs

displacements..46

Figure 36)Moment Vs plastic rotation of formed plastic hinges in the isolated structure 49

Figure37)Moment Vs plastic rotation of formed plastic hinges in the isolated structure ..49

Figure 38) Comparison between story displacements of isolated and fixed base structure

in relation to the ground ..51

Figure 39) Comparison of floor accelerations between of isolated and fixed base structure ..52

Figure 40)Interstory drifts obtained for fixed base and isolated structure using linear

and non linear procedures..54

Figure 41 )Comparison of basal shear between the fixed base and isolated structure

using non linear analysis54


10/77

X

NOMECLATURE

ag Design ground acceleration

I. Structural importance factor

agR Reference peak ground acceleration

Ti1 First vibration mode of the isolated structure

Ti2 Second vibration mode of the isolated structure

T Natural period of structure

K Structural stiffness

Ko Initial stiffness of the isolation system

Keff Effective stiffness of the isolation system

Teff Effective period of the isolation system

[M] Mass matrix of MDOF system

[C] Damping matrix of MDOF system

{F} Storey force vector

SDOF Single degree of freedom

MDOF Multi degree of freedom

{} Mode shape factor

ESDOF Equivalent single degree of freedom

Vt Top displacement

Vb Base shear

Uy Yield displacement

Vy Yield strength

Teq Initial period of ESDOF

Strain hardening ration

Wi Weight of ithstorey

j Element mode shape vector corresponding to I storey for mode j

hi Storey height

n Total number of stories

LL Factored or unfactored live loading

S Soil factor

a Global strength ratio

Sd Spectral displacement


11/77

XI

Sa Spectral acceleration

TD Corner period according to EC8

R Seismic force ratio

Sa,fb Spectral acceleration of fixed base

Sa,is Spectral acceleration isolated Effective mass ratio

q Behavior factor

n Reduction factor of spectral ordinate

DLD Damage limitation state

Tf Period of fixed base structure

Tis Period of isolated structure

d Ductility demand

Damping ratioNHA Nonlinear history analysis

NSA Nonlinear static analysis

CSM Capacity spectrum method

ICSM Improved capacity spectrum method

DSM Displacement coefficient method

MPA Modal pushover analysis

PF Participation factor

am Modal mass coefficienteq Equivalent viscous damping

u: Target displacement

Lp Length of plastic hinge

h Height of section

h Length of member

an modification factor

Tbf Period of bare frame

Tfi Period of fully infilled frameTpi Period of partially infilled frame

Ei The modules of elasticity of the infill material

Ef The modules of elasticity of the frame material

Ic The moment of inertia of column

t The thickness of infill


12/77

1

CHAPTER 1 - Introduction

1. Introduction:

Over the years, traditional design concepts that prevailed worldwide for the construction of

earthquake resisting structures were based on ductility (i.e. plastic deformation allowances)

design concepts [Megget , 2006]. Following late major earthquake events including the

earthquake of Northridge in 1994 and Kobe in 1995, the performance of the intended ductile

structures was proved to be unsatisfactory and far below expectation, with extensive large-scale

damages on many modern nominally earthquake-proof buildings, subsequently this raised the

cost for rehabilitating to non sensible levels. The urge to enhance structural safety and further

resilience, led to the development of more reliable and effective techniques based on structural

performance control concepts. One of the most promising of these techniques is seismic

isolation which can apply to new structures as well as for retrofitting existing ones complying or

not with modern design standards .Both of these applications became of great importance

throughout the world following sever late earthquakes. Consequently, seismic isolation is no

longer limited to those buildings at the top end of the importance spectrum level [Mayes, 2012].

Although early seismic isolation proposals go back 100 years [Chopra, 1995], seismic isolation

and particularly base isolation is a relatively new and attractive technology. The idea of base

isolation of a structure is based on the incorporation of flexible isolators which aim the creation

of a low stiffness zone usually at the base of a building, in order to shift the systems

fundamental period outside the range of periods that are dangerous for earthquake resonance

[Champis et al, 2012]. On the contrary, traditional ways of seismically reinforcing a structure,

which focus on increasing the lateral stiffness of the system, may result into an increase in the

acceleration induced forces, a factor that makes past conventional strategies based on

structural strengthening often very invasive and expensive. [Cardone et al, 2012].

Due to the cost associated with installation of seismic isolation systems in small buildings and

due to the clich concept of not seismically isolating residential buildings, a limited number of

studies have been previously undertaken [Cardone, 2006]. Particularly, the lack of informationassociated with practical details and issues such as pounding allowances [Komodromos et al,

2007], or service provisions e.g. cabling and piping, turn the design of such system to a novel

task. Furthermore, the absence of analytical studies on seismically isolated structures

constructed with the ground floor comprising a soft storey in which the absence of masonry

infills at the ground level gives high flexibility but large relatively increase in stiffness in the rest


13/77

2

of the structure ,which in turn is a factor affecting its structural performance, leads to the need of

quantification of the response of such buildings in terms of floor accelerations, peak deflections,

storey and interstorey drifts as well as bending moments at critical locations (hinge formation).

In addition to this, advances in materials and technology in combination with the design tools

available, have not revised the feasibility of provision of such solutions in the present. Althoughthe cost associated with the commissioning of such systems, is thought to be prohibitive,

studies suggest that the difference between the cost of a building designed with a fixed base

and the same building designed with base isolation is very low [Clemente & Buffarini, 2010].

1.1 Purpose of seismic isolation

The purpose of seismic isolation is to enable a structure through proper initial design to survive

the potentially catastrophic impact of an earthquake and maintain structural integrity while at the

same time minimise the damages to both structural and nonstructural components.

1.2 Principle of seismic isolation:

The principle of seismic isolation can be illustrated using the acceleration and displacement

response spectra shown in figure 1. A notional perfectly rigid building (with stiffness

approaching infinity) would have zero natural period, upon ground movement, the acceleration

in the structure is equal to the ground acceleration and the relative displacement between the

ground and the structure is ideally zero. On the contrary a building that is perfectly flexible (with

stiffness equal to zero) would have infinite natural period, therefore the acceleration induced bythe ground movement in the structure would be zero and the relative displacement between the

ground and structure would be equal to the ground

displacement. Real structures are neither perfectly rigid

nor perfectly flexible.

An ordinary low-rising RC structure has stiffness and short

period which leads to high acceleration and low

displacement response (point A on figure 1 a,b).By

extending the natural period of a structure but keeping the

damping at the same level, it can be observed that the

acceleration response reduces greatly and the

displacement response increases accordingly (point B on

figure 1). If the structural damping in the same structure is

Figure 1 a) Acceleration response spectrum

b) Displacement response spectrum [Zhanget al, 2010]


14/77

3

increased, the acceleration response reduces and the displacement response is controlled

(point C on figure 1) [Zhang et al, 2010] .

In order to achieve the aforementioned reduction of acceleration response and consequently

reduction of inertial forces on the members of the system which as it will be discussed in the

following subsection can have catastrophic effects on both structural and nonstructural

members, a discontinuity is created along the height of the structure and the isolation system is

introduced. If the discontinuity is created at the base of the building, the technique is known as

base isolation [Dolce et al, 2007].The isolation system often consists of bearings incorporated

between the structure and the foundation. These bearings are very stiff in the vertical direction

so as to carry the vertical load but very flexible in the horizontal direction allowing the structure

to move during severe ground motion. The low horizontal stiffness of the system allows the

structure to decouple from the horizontal elements of ground motion resulting to a fundamental

frequency of the system significantly lower than both its fixed-base frequency and the

predominant frequencies of ground motion [Kelly et al, 1999]. Typically, earthquake

accelerations have dominant periods 0.1 1 seconds with maximum severity between 0.2 -0.6

seconds. Consequently, buildings with fundamental periods in these ranges tend to resonate.

[EC8, ATC-40, etc]. Concisely, at the presence of isolators, the building moves slower in

comparison to the seismic waves transmitted to the ground, therefore the possibility of

resonance which can lead to high displacements and ultimately collapse of the structure is

reduced.

The dynamic behavior of seismically isolated structures can be visualized in figure 2. Assuming

a single storey fixed base structure, a single mode of vibration exists and for the isolated

structure two modes exist (i.e. the isolated structure can be idealized as a two-storey structure

with the ground floor being very flexible, hence two modes of vibration exist) .The two vibration

modes of the isolated structure are named isolation and structural modes withnatural periods

Ti1andTi2respectively as shown in figure 2. The period of the isolated structure at the isolation

level, due to the low stiffness of the system is larger than the natural period both of the

superstructure of the isolated and the fixed based structures. Therefore, as indicated by themode shape of the isolation mode also in figure 2, most of the deformation occurs in the

isolation level rather than the superstructure. With reference to the horizontal direction, isolators

should present a ForceDisplacement curve with high stiffness at small displacements and low

stiffness for larger displacements. For example, for small loading such as wind or low intensity

earthquakes the structure should have high horizontal stiffness and short period. As the load


15/77

4

increases the stiffness should drop and the period should lengthen. The isolator behavior can

be idealized assuming a bilinear skeleton curve as shown in figure 3 [Vulcano, 1998].

1.2.1 Interstory drift and floor acceleration.

The main dilemma faced by engineers when designing structures in earthquake prone regions

is to manage interstory drifts and floor accelerations [Kelly et al, 1999]. Failing to minimise the

effects of interstorey drifts will result in damages on nonstructural components which fail to

accommodate differential movement at their boundaries and to equipment that interconnects

stories such as interior wall partitions, exterior glazing systems, precast concrete cladding,

stairs, elevators etc. Failing to minimise floor accelerations will induce inertial forces which mustbe resisted by either anchoring the components to the structure or by overturning resistance in

the free standing elements. This can be damaging to sensitive internal equipment as well as for

primary structural elements such as diaphragms, chords, collectors etc. [Morgan, 2007] .The

importance of these two demand parameters for performance based earthquake engineering is

given by Taghavi and Miranda [2003].

Performance based design is based on the selection and assessment of performance

objectives or criteria for which the desired performance level is achieved. Objectives can be

associated with the prevention of structural and nonstructural damage or both and can be

expressed in terms of casualties, economic costs, out of service time etc. In general,

performance levels describe limiting damage conditions which are considered acceptable for a

given building subjected to a given ground motion. The limiting condition is described in terms of

structural-nonstructural damage, risk to the life safety of the buildings occupants due to the

aforementioned damage, and the serviceability of the building after the earthquake event. FEMA

Figure 2) dynamic behavior of base

isolated frame [FEMA 356]

Figure 3) idealised force-displacement

behavior of isolators [Vulcano, 1998]


16/77

5

356 [2000] presents both structural and nonstructural performance levels and ranges for which

design procedures and acceptance criteria corresponding to the desired performance level to be

achieved.

The performance levels are divided into four categories:

- Operational: Related solely to the buildings functionality. Any structural and non

structural damages require minor repairs.

- Immediate occupancy: Most widely used criterion for important structures. Integrity of the

structure is ensured and any spaces and systems are expected to remain usable.

- Life Safety: Any structural or nonstructural damages to the structure will ensure that the

threat to life safety is minimised.

- Structural Stability: The structure will be heavily damaged, however the vertical load

carrying capacity of the system is ensured and collapse is prevented.

Quantification of the limiting damage conditions of a building subjected to a given ground motion

is performed by considering the moment rotation curve of each element/hinge. Figure 4 shows

the moment rotation curve of a typical element (in terms of Moment/Shear force versus

Rotation/Shear force). Increasing moment results into a proportional increase in the rotation of

the hinge. The different phases (and progressive yielding) B-E that an element/hinge undergoes

are plotted. Points B and C correspond to the yield strength and ultimate strength of the element

respectively. Point D corresponds to the residual strength of the element. Point E corresponds

to the maximum deformation capacity of the member. All performance levels lie on the line BC

(Since beyond point C failure takes place) corresponding to the four categories described

above.

Figure 4 a) Moment-Rotation curve of hinge b) performance levels[FEMA 356]


17/77

6

Consequently, in order to reduce interstorey drift stiffening of the structure is required. On the

other hand, stiffening the structure results to a shift of its natural frequency to higher values with

consequent effects the amplification of floor acceleration. It has been observed that base

isolation is the only practical way of reducing simultaneously interstory drift and floor

accelerations through provision of necessary flexibility and concentrating the displacements atthe isolation level [Sharma & Jangid, 2009]. These displacements can be then controlled

through provision of damping on the isolation bearings with the use of either the inherent

properties of high damping rubber or by addition of a lead core (chapter 4 4.1)

1.2.2 Ground conditions and technical limitations

1.2.2.1 Ground conditions ;The influence of local ground conditions on the seismic actions are

taken into account through the selection of appropriate design spectrum (figure 5) and a soil

factor (S) for each of the ground types (A E) as described by the stratigraphic profiles andparameters shown in appendix A figure A5 [EN 1998-1:2004]. Depending on the consequences

of collapse for human life, public safety and civil protection during or after an earthquake event,

the buildings are classified in four importance classes which are characterized by different

importance factors .The importance classes are presented in appendix A figure A4. Each

component of the seismic action is defined in terms of elastic spectrum for the appropriate

ground conditions and design ground acceleration. The design ground acceleration is calculated

by ag= I.agRwhere agR is the reference peak ground acceleration for ground type A and i the

importance factor as defined in section 2.1(4) of EN 1998-1:2004 (EC8).

1.2.2.2 Limitations; In order to achieve the desired reduction of acceleration induced forces and

guarantee the elastic response of the structure, fundamental periods as large as 5-6 seconds

maybe needed. For instance, existing buildings designed for gravity loads or in accordance to

the old seismic codes can exhibit global strength ratio ( = max. base shear / Weight of

structure) ranging from 2% -3%. Considering the response spectrum provided by EC8 for

ground acceleration ag = 0.35g (high seismicity regions), soil type B (S = 1.2) and importance

class II (i= 1.2), the fundamental period required to guarantee elastic behavior should not beless than 5.6 seconds. [Cardone et al, 2012]. With reference to figure 1b, these high

fundamental periods will result in large horizontal displacements which might not be compatible

with the displacement capacity of existing isolation devices. In addition to this, studies have

shown that the derivation of maximum displacements from the relationship S d =Sa / 2 for

periods greater than TD (corner period as presented in EC8) underestimate the horizontal


18/77

7

displacements [Faccioli et al, 2004] aggravating the problem. For these reasons, the isolation

systems aim to control the high displacement response of the structure with additional damping

which as it will be discussed later in the project can be achieved from the incorporation of high

damping materials such as lead or natural high damping rubber.

Another technical limitation to the use of seismic isolation is the effect that soft soils have on the

isolated structures response. Although soft soils in some cases have been observed to provide

a cushioning effect by absorbing seismic waves before they reach the surface [Chau & Lo ;

Lee et al, 2001], soft soils tend to produce ground motion at higher periods resulting into an

amplification of the structures having high periods. Consequently an isolation system with high

fundamental period would not be suitable for these conditions. An example of soft soil with

fundamental natural frequencies circa 2 seconds is the soil in Mexico City [Lee et al, 2001].The

effects of soil condition on an isolated structure are shown in figure 6. If seismic isolation is the

preferred option for a structure constructed on soft soils, it needs to be ensured that selection of

appropriate effective period Teffand consequently effective stiffness Kefffor the isolation system

through several iterations is performed.

Most analyses of multi-storey structures subjected to

earthquake excitation, ignore the effects of the combination ofgravitational forces and lateral displacement. The effects of

these actions are often referred as second order or P-Delta

effects. The reason behind overlooking P-Delta effects, can be

explained by the fact that low rising RC structures (i.e. low

natural period) subjected to earthquake motion, the P-Delta

Figure 5) Different design spectra for

soil classes A-E [ATC-40]Figure 6) Structural response of isolated and fixed

base structures founded on soils [FEMA 356]

Figure 7 a) Peffects on columns b) indu

bending moments and Pcontributio


19/77

8

effects are insignificant. As the structures become taller the P-Delta effects amplify due to the

corresponding increase of lateral displacement. Traditionally, reduction of the influences of P-

Delta effects was performed by controlling lateral displacement through maximum achievable

ductility on beams, columns and joints. On the other hand, In the case of seismic isolation, the

problem amplifies more due to larger lateral displacement (as discussed in 1.2 and shown infigure 1b) which can exceed 400mm ,consequently increasing the bending moments on the

structural components as well as overturning of the structure generating tensile stresses on the

bearings of the isolation system. Balendra and Koh [2006] through a study undertaken on a five-

storey base isolated RC frame building, observed that ignoring P-Delta effects can lead to

considerable errors in the estimation of seismic response [Balendra&Koh,2006]. The effects of

P-Delta effects can be visualized in figures 7 a and b. Controlling the displacement of the

isolation system and consequently reducing the P-Delta effects is discussed further later in this

project.

Through the introduction of flexibility at the isolation level of a nominally stiff building, floor

accelerations and interstorey drifts can be reduced significantly [Sharma and Jangid, 2009,

Komodromos et al, 2007 among others]. On the other hand high flexibility results in large

deformations (figure 1b). Another potential limitation and practical constraint to the application of

seismic isolation is the width of the seismic gap which in turn can be restricted by the availability

of clearance around the isolated structure and therefore being unable to accommodate the

aforementioned large deformations. If the deformation of the structure is unable to be

accommodated by the seismic gap the phenomenon of pounding occurs. Generally pounding

refers to the impact of the structure with either adjacent structures (this phenomenon occurs

mostly in fixed base structures where the maximum displacements occur at the top) or at

isolation level between the isolated structure and the surrounding moat wall (due to the

concentration of deformations at the isolation level). Tsai [1997] simulated pounding between

two adjacent structures at the isolation noting that the structures developed floor accelerations

up to 70 times higher than the peak ground acceleration (PGA) of the El Centro earthquake

[Tsai,1997]. Matsagar and Jangid [2003] also examined the effect of pounding on seismically

isolated structures and concluded that the response of the structures having flexible

superstructure, increased number of stories or relatively stiff adjacent structures increases

[Matsagar & Jangid , 2003]. This concludes that attention to detail, consideration of various

design parameters as well as understanding of the surrounding environment should be taken

into account when considering the option of seismic isolation.


20/77

9

1.2.3 Summary of the tasks of an isolation system

To sum up, seismic isolation is highly dependent on many factors such as the mass and

stiffness of the system (which in turn will affect its natural period, making the choice of isolation

system effective or not. i.e. structures with high mass can achieve the targeted increased period

of the system easier, which in turn makes seismic isolation more efficient), the earthquake

characteristics as well as the soil underlying the foundations of the structure (since the shape of

the response spectrum is dependent on the earthquake characteristics and the soil type, figures

5 & 6). In addition to this, seismic gaps aiming to accommodate the large lateral displacements

of bearings should be adequately provided in order to eliminate the possibility of pounding with

adjacent structures or moat walls. Having also in mind all the other limitations discussed in the

previous subsections, the selection of a seismic isolation system should be made on the basis

of:

Transmission of vertical loads to foundations

Provision of horizontal resistance to minor horizontal actions (wind etc.) [ 1.2 ]

Assure high flexibility under seismic actions

Dissipate an adequate amount of energy through damping

Recentre the structure after an earthquake.

1.2.4 Main consequences of Base isolation

Increase fundamental period of a structure, hence reduction of the design forces. Concentration of inelastic deformations into the bearings

Dissipation of seismic energy into the isolators through the hysteretic damping in its

components. Consequently reducing the shear force and maximum displacement

demands.

1.2.5 Summary of the main advantages of seismic isolation

Reduction of inertia forces and consequently elimination of structural damage under

strong ground motion Reduction of interstory drifts and consequently minimization of nonstructural damage

Protection of the building contents (services etc.)

Reduction to the vibration felt by people and consequently the amount of panic

generated during an earthquake.


21/77

10

1.3 Development of base isolation

The need to uncouple the building from the damaging actions of an earthquake led to the

invention of various mechanisms of base isolation such as rollers, balls, cables, rocking

columns and sand. The apparent problems with the development of the first mechanisms of

base isolation such as inadequate performance under wind loading (University of Tokyo

constructed on balls) and problems of bouncing and rocking during earthquake action

(Pestalozzi school of Skopje constructed on rubber bearings of similar horizontal and vertical

rigidities) [Kelly et al, 1999], led to the development of more sophisticated systems. Such

isolation systems incorporate multilayer elastomeric bearings. These devices are made by

vulcanization bonding of rubber sheets to thin steel reinforcing plates. The natural evolution of

rubber bearings became the lead-plug bearings, where a plug of lead is added in a central hole

of each bearing to add damping to the isolation system. The introduction of elastomeric

bearings allowed the concept of seismic isolation to become a practical reality within the last

years. Earthquake prone regions around the world including the United States, Japan, New

Zealand and Italy adopt these techniques of seismic isolation for protecting important structures

against strong earthquake motion.

1.3.1 Recent applications

The evolution of technology, the advances in materials and tools available for the design of

seismic isolation systems along with the provision of dedicated codes and rules for designing

structures to resist ground motion, convinced engineers to adopt this relatively new earthquake

resistance approach.

Although seismic isolation is deemed to be an attractive and beneficial alternative, the range of

application of seismic isolation depends to a big extend to the additional restrictive cost

associated with the implementation of these systems. A study conducted by Clemente and

Buffarini [2010] on different types of fixed-based and isolated RC buildings yielded that in

general, the difference between the cost of a building designed with a fixed base and the same

building designed with base isolation is very low. However, important differences in cost derivefrom the fact that every institution makes different application rules for seismic isolation. For

example in China base isolation allows for the construction of cheaper structures with result, the

dramatic increase of seismic isolation applications. On the contrary, in USA the overall cost of

seismic isolation is large and the applications are restricted to buildings at the top end of the

importance spectrum level.


22/77

11

1.4 Performance of seismic isolated structures

The application of seismic isolation prior to major earthquake events, gave concrete evidence of

satisfactory response of isolated structures in comparison with adjacent conventionally designed

buildings that have experienced the same ground motion .Despite the evidence of favorable

performance, the need to quantify the actual response and predict the exact performance of

seismic isolated structures has been a subject of various studies over the last years.

Fardis et al [2004] compared design seismic stresses on fixed base and isolated buildings in

two extreme soil conditions (type A and D as described in EC8). The comparison is

demonstrated using the spectral acceleration ratio between a fixed base structure and the

spectral acceleration of a similar seismic isolated structure (i.e. seismic force ratio R = S a,fb(Tf) /

Sa,is (Teff) ) for both ultimate limit and damage limit states. The equations used for the

comparison are shown in figure 8 .Typical values of effective mass ratio , behavior factor q,

and reduction factor of the spectral ordinate are taken as prescribed for the equivalent linear

static analysis. [Fardis et al, 2004]

From the above equations it can be observed that seismic isolation is more beneficial for the

damage limit state DLS because RDLS / RULS = 4 (i.e. the acceleration induced forces for the

fixed base structure in the DLS are four times greater than the forces in ULS). It is also

observed that the seismic force ratio on the ULS varies between 0.63 (for Tf = 1 s and Teff= 2 s)

to 3.00 for (Tf< 0.4 s and Teff=3 s) for soil type A and 0.54 to 1.5 for soil type D which implies

that seismic isolation is more favorable as the higher its effective period (hence greater seismic

ratio, consequently greater reduction to seismic forces). On the DLS the strength ratio is ranging

from 2.52 to 12.00 and 2.16 to 6.00 for soil type A and D respectively emphasizing the

importance of seismic isolation to limitation nonstructural of damages [Fardis et al, 2004].

Figure 8) Top eqn) Seismic force ratio in ULS, Bottom eqn) Seismic force ratio DLS [Fardis et al, 2004]


23/77

12

Most recent, Cardone et al [2012] simulated the structural behavior and earthquake

performance of four typical RC framed buildings constructed in Italy before 1975. The selected

buildings were designed only to carry gravity loads with a structural configuration typical of

many buildings in Italy and Europe of that time. The simulation was performed using 72 models

of superstructure differing in number of storeys (2, 4, 6 and 8 storeys) and 3 different types ofisolation systems. The analysis carried out for the comparison of the fixed-base and isolated

structures were nonlinear static analysis and nonlinear response time history analysis for the

fixed base and isolated structures respectively. An example of the nature of the findings is

presented in Appendix A figures A1 and A2. The diagrams present different strategies of

seismically reinforcing a four storey RC frame building subjected to an earthquake design

intensity of 0.5g which corresponds to a high intensity Mediterranean earthquake.. Force

displacement graphs were plotted for both fixed-base and isolated structure, presenting the

different behavior of the system for different values of strength ratio , ductility demand d= Um/Uy and stiffness of the isolation system. The results yield a significant increase in the base

displacement for the first and less stiff isolation system (T is = 5.84 s) which is designed to

prevent yielding in the structure, the second and stiffer isolation system (Tis= 3.12 s) which is

designed to minimise base displacement with d = 2 in the superstructure has identical

maximum displacement with the conventionally earthquake reinforced structure. A summary of

the most important findings of the study as given by Cardone et al [2012] are presented below:

1) The inelastic behavior of isolated structures is different from that of same fixed-basestructures because of the ability of a fixed-base structure to dissipate energy upon the

occurrence of damages to the system, resulting to a shift of the natural period and consequently

limiting the force demand. On the other hand, for an isolated structure the energy dissipation

capacity is dominated by the isolation system (i.e. plastic deformation of the superstructure does

not affect the maximum response) due to reduction of inelastic cycles experienced.

2) The design of the isolation system is governed from the lateral stiffness and ductility capacity

in the weak direction of the structure.

3) Attention should be paid when selecting values for global ductility demand for the

superstructure.


24/77

13

4) Strength reductions can be accepted due to the contribution of masonry infills to the lateral

resistance of the structure.

5) Given a deficit of strength the ductility demand increases while decreasing the number of

storeys of the building, regardless the type of isolation system.

Another recent comparative study of fixed base and base isolated three-storey RC building was

undertaken by Thakare & Jaiswal [2011].The building had plan dimensions of 12.00 m x 8.00

and an assumed global damping ratio in the superstructure of 5 %, the isolated building was

designed using lead rubber bearings (LRB) which similarly with other elastomer based isolation

systems have identical bilinear behavior (figure 3).The building was analyzed using the

structural analysis software SAP 2000 for both response spectrum and time history analysis.

The findings of the study are presented in summary below;

1) Response spectrum analysis yielded a reduction of 15 % of the interstorey drift and 65 % in

base shear as well as moments and forces in beams and columns between the fixed base and

isolated structures. The exact results are presented in Appendix A figure A3.

2) Time history analysis yielded a reduction of acceleration due to the isolation of 84 % and a

reduction of interstorey displacement of 68 %].The results are presented in figures 9 & 10 as

extracted from the study [Thakare & Jaiswal, 2011].

Figure 9. Interstorey drifts of fixed base and

isolated base system by time history analysis

[Thakare & Jaiswal, 2011]

*NBI =Non-base isolated | BI = Base isolated

Figure 10.Roof level acceleration of fixed base and

isolated base system by time history analysis

[Thakare & Jaiswal, 2011]


25/77

14

1.4.1 Experimental demonstration;

Extensive shake table testing of seismic isolated structures has been conducted over the past

years. The validation of performance helped further the development of suitable isolation

devices for large scale structures and the evolution of seismic isolation practice across the

world. Examples of devices tested in shake tables include lightly damped elastomeric bearings,

elastomeric bearings with steel dampers , lead-rubber bearings etc. (most were developed and

tested in University of California Earthquake Engineering Research Centre).It is worth

mentioning the fact that the tests were subjected to five story RC frame structures to allow the

development of higher mode response hence allowed the effectiveness of various

implementation approaches for seismic isolation to be assessed. Most of the research reports

observed the ability of high levels of damping to control base displacements. However

increased floor acceleration and low period response was observed [Warn & Ryan. 2012].

The ultimate capacity of isolated structure was also examined using shake table testing. Clark et

al [1997] in their study replicated the behavior of a three storey RC framed building under large

earthquakes. The selected isolating system comprised high damping rubber which stiffens at

large displacements allowing the earthquake demand to shift to the superstructure which led to

the development of the typical ductile degradation modes expected under large earthquakes.

The experiment showed that the bearings withstood high tensile stresses due to overturning

[Clark et al, 1997], concluding that design strategies can be adopted to ensure that the isolation

system is not the weak link.

Griffith et al [1988] using shake table tests, examined the performance of a seismically isolated

nine storey RC slender frame structure, under extreme loading conditions such as the possibility

of uplift due to horizontal loading. The study found that an occurrence of uplift produced a

temporary and localized instability in one or more bearing hysteresis loop which was then

balanced by other bearings, therefore the local instability of the bearing did not result in a global

instability of the system [Griffith et al, 1988]. This led to the incorporation of restraining

mechanisms to prevent overturning. Such mechanisms were studied and reviewed by Roussis

[2009].

In Japan, major companies dominating the industry continue to invest on new technologies,

including base isolation. Despite the utilization of shake table testing by some companies

(Mitsubishi, Kajima etc.), the concept of demonstration building as an alternative form of testing


26/77

15

and demonstration was adopted. These buildings were subjected to free and forced vibrations

and in some cases they experienced simulated earthquake motion [Kelly, 1988]. The use of this

practice helped further the development of seismic isolation and particularly the development of

high damping rubber bearings which inherently provides sufficient damping in order to control

basal displacements, making the need of supplementary damping redundant.

The results obtained from shake table testing are of great importance since they validate the

performance of several isolation systems (such as elastomeric bearings, lead rubber bearings,

friction pendulum, etc which claim the majority of market share around the world) and also the

effect on the structural system which is allowed to remain elastic under large earthquake

motion. It can be also suggested, that through sufficient detailing of the isolation system,

seismic isolated buildings can survive earthquakes larger than anticipated in design, provided

that factors which will have considerable effects on the superstructure (i.e. increasing thedemand requirements) such as uplift, rupture of bearings under tension and shear, buckling or

large displacement hardening are considered in design through provision of appropriate ductile

response[ Warn & Ryan, 2012 ].


27/77

16

CHAPTER 2 - Analysis

2. Analysis Method

Several methodologies can be used in the design of structures under seismic actions. Non

linear time history analysis (NHA) is a dynamic method of analysis that represents the actual

response of the structure through integration of the equations of motion of multi degree of

freedom systems MDOF in the time domain using iterations. Although nonlinear time history

analysis is globally accepted as the most accurate and reliable method for the prediction of

force and cumulative deformation demands (damages) in every element of the structural

system, it is also a method that requires costly computational resources such as availability of

ground motion records, modeling capabilities of load-deformation characteristics of the soil-foundation structure system and efficient tools for the implementation of a solution within the

time and financial constraints [Krawinkler & Seneviratna, 1998].The aforementioned arguments

make time history analysis a time consuming and expensive method for daily design purposes.

Concisely, the analysis of structures experiencing seismic actions can be divided in linear

procedures and non-linear procedures. Linear or elastic procedures predict the capacity of

structures as well as identifying the location where the first yielding occurs, however such

methods fail to predict failure mechanisms and redistribution of forces during yielding, making

these procedures inaccurate in relation to non linear procedures. Non linear or inelastic

methods of analysis account for features such as inelastic deformations and dynamic

characteristics of the structure to be taken into account. Non-linear procedures besides the NHA

include the non-linear static procedure (or commonly known as pushover analysis) which was

developed to satisfy the needs for faster, more practical, yet reliable structural assessment or

design of structures subjected to earthquake loading. Its conceptual and computational

simplicity make this method one of the most preferred methods for seismic performance

evaluation of structures.

In pushover analysis, the structure experiences an incremental application of lateral loading in

accordance to a predefined pattern. As the structure is pushed, the deformation allows weak

links (hinges) and failure modes in the structural system to be identified. The structure will

deform until enough hinges have developed to form a collapse mechanism or until a certain

hinge exceeds its plastic deformation limit. Consequently, a carefully performed pushover


28/77

17

analysis will provide an insight into structural aspects that control performance during

earthquake action. In this study, both the existing and reformed (isolated) structures are

examined using this non linear static analysis (NSA). The applicability of the method as an

alternative mean for the design and assessment of isolated structures is also examined.

Limitations: The NSA is nowadays considered as a valid alternative to NHA. Nevertheless, it is

important to realize the limitations and potentialities of the method. The procedure involves

several simplifications and approximations (as it will be discussed in the following sections),

therefore the nature of the analysis cannot represent dynamic phenomena in great accuracy.

Elaborating on this aspect, pushover being a static analysis cannot incorporate various features

exhibited in RC frames during dynamic or cyclic loading (e.g. cyclic degradation, straining rate)

[Pankaj & Ermiao, 2005]. The consequence of overlooking such phenomena is a great deviation

on the predicted and actual response due to modification of modal characteristics and shifting ofnatural period of the structure.

It has been also observed that pushover analysis does not provide good predictions in terms of

storey drifts for tall buildings (more than 5 stories) in which higher modes are excited during

earthquakes. Krawinkler and Seneviratna [1998] through their study investigating structures

from 2 to 40 stories highlighted that pushover analysis is a useful and accurate tool when it

comes to calculation of roof/top displacements and maximum interstorey drift. On the other

hand, they observed a large discrepancy in storey drift predictions between pushover and

dynamic analysis confirming that for higher mode effects pushover analysis should not be the

preferred option.

Another limitation of pushover analysis is the inability to simulate torsional deformation in

structures. Even though modern code guidelines encourage the treatment of inelastic torsional

response of buildings they fail to provide clear guidance on how to do so. The need to tackle

this limitation and make NSA as reliable as NHA led to the development of methods that would

enable modeling of torsional response of buildings using 3D pushover analysis, these methods

although being good in terms of minimizing the discrepancies between the two non linear

approaches, their conceptual complexity and computational demands makes them not

applicable and impractical for every day design purposes. Such methods have been studied and

proposed by Kappos and Penelis among others.


29/77

18

2.1 Background of pushover analysis

Nonlinear static analysis is based on the assumption that a structure can be represented as a

single degree of freedom (SDOF) system; consequently the earthquake response of the

structure is controlled only by one mode which is also assumed to have constant shape (mode

shape vector {} as presented below) throughout the time history. The assumptions can be

considered simplistic and incorrect, however many studies undertaken ,show that these

assumptions lead to good predictions of maximum seismic response of multi degree of freedom

(MDOF) structures with their response being dominated by a single mode [Krawinkler &

Seneviratna, 1998; Lawson, 1994, Fajifar et al, 1996, Antoniou 2002, among others]. The

concept of equivalent SDOF system (ESDOF) is shown in figure 11.

2.1.1 Dynamics of pushover analysis

Earthquake induced motion on MDOF system can be derived from its governing differential

equation of motion:

, Where; {eq.1}[M] = Mass matrix

[C] = Damping matrix

[F] = Storey force vector

Figure 11. Conceptual diagram for transformation

of MDOF to SDOF system [Themelis, 2008]


30/77

19

{1} = Influence vector characterizing the displacements of the masses when a unit ground

displacement is statically applied, and g is the ground acceleration history.

Assuming a single shape vector {} and a defining relative displacement vector U for the MDOF

system as U = {} Utwith Ut being the roof/top displacement. The differential equation of the

MDOF transforms to:

{eq.2}If the reference displacement U*of the SDOF is defined by:

{eq.3}

Multiplying eq.2 with {} T and substituting for Ut the differential equation of the equivalent

SDOF system becomes:

M**+ C**+F*= - M* g {eq.4}

{eq.5}

[Krawinkler & Seneviratna , 1998].

Using the above equations, a non linear static analysis (pushover) of a MDOF structure can be

carried out, allowing the determination of the force-deformation (also known as capacity curve)

characteristics of the equivalent SDOF structure. The capacity curve which is plotted in terms of

base shear Vb and top displacement Ut (Figure 12a), provides valuable information of the

earthquake response of the structure due to the information provided on the post-elastic

behavior of the structure. Idealisation of the curve in a bilinear form is allowed for simplicity(Figure 12b). The effective elastic stiffness and hardening/softening stiffness are defined as Ke=

Vy/Uyand Ks = e respectively. Transforming Utand F of the MDOF using eq.3 and eq.5 can

provide the properties of the equivalent SDOF system (Figure 12b).


31/77

20

Regarding the above, the initial period of Teqof the equivalent SDOF system is calculated by:

With: (Figure 12b)

*Strain hardening ratio, , for both SDOF and MDOF structure is taken the same.

Maximum displacement of SDOF system can be found using elastic or inelastic spectra or time-

history analysis. The corresponding displacement of MDOF system can be estimated from

equation 3 (eq. 3) as follows:

It can be observed that the roof/top displacement is dependent on the choice of the modeshape vector which as mention previously is assumed to remain constant. Studiesundertaken on pushover analysis demonstrate that accurate predictions of displacements can

be obtained from the first mode shape, provided that the response of the structure is dominated

by its fundamental mode [Krawinkler & Seneviratna, 1998; Lawson, 1994, Fajifar et al, 1996,

Antoniou 2002, among others].

2.1.2 Capacity curves

Reinhorn [1997] observed that the capacity curves can be approximated using a set of bilinear

curves according to the following relationship:

= yield strength= displacement at yield point

Figure 12 a) Capacity curve for MDOF structure, b) Bilinear idealization

for equivalent SDOF[Themelis, 2008]


32/77

21

= post yield stiffening ratio Ks/ Ke (with reference to figure 12a) = step function which for

1 equals to 1.

Through simplification the above equation can be expressed in the following format:

=

Although the approximation of capacity curves using this approach seems quite trivial, it can be

deemed as an approach which serves well for everyday design purposes.

2.1.3 Lateral load patterns

In order to simulate the distribution of inertia forces which are produced in a system subjected to

earthquake excitation, patterns of increasing lateral loading are needed to be applied to the

mass points of the system. The incremental application of lateral loading, allows the monitoring

of the progressive yielding behavior of the structure (through force- deformation relationships),

consequently allowing other parameters such as stiffness and change in natural period to be

identified. Krawinkler & Seneviratna [1998] consider the selection of load pattern to be more

critical than the accurate calculation of displacement for performance evaluation

(1.2.1).Limitations to the use of pushover analysis such as torsional effects and calculation of

storey drifts in tall structures are affected from the choice of lateral loading pattern [Krawinkler &

Seneviratna , 1998]. For that reason, EC8 and FEMA 356 state that at least two lateral loadpatterns should be utilized in order to envelope the responses. This allows variations in global

and local demands to be predicted through the formation of upper and lower bounds of inertia

force distributions. Examples of possible load patterns that can be used for pushover analyses

are presented below:

Load pattern based on the mode shape distribution based on the fundamental or other

modes of interest.

*(EC8 presents the relationship in terms of mass m i)Where ;

= weight of istorey = ith element of mode shape vector corresponding to the Istorey for mode j.


33/77

22

Load pattern based on the inverted triangular distribution.(identical to FEMA 2000 load

distribution)

= Storey height= total number of stories= base shear given by: : :acceleration ordinate from designspectrum . : Fundamental period and : total weight of structure.

Uniform Load distribution based on;

( = the weight of each storey, however other pattern of gravitational loadingcan be used for example , where = factored or unfactored live loading)

Other methods of deriving the lateral load pattern exist including Kunnathss load distrib ution,

two-phase load pattern by Jingjiang et al. and many other load distributions. Figure 13 shows

some lateral load patterns that can be adopted depending on the vertical and shear loading.

Figure 13 a) FAP (b)SSAP procedures for determination of incremental applied load

pattern at different steps. [Shakeri et al, 2010].


34/77

23

2.2 Capacity spectrum method, CSM

Pushover analysis methods can be divided into three categories; Conventional, adaptive and

energy-based pushover. In this project a conventional pushover analysis method is utilized and

in particular the capacity spectrum method (CSM) which was first presented by Freeman et al

[1975] in order to quantify structural response. Other conventional pushover analysis methods

include: Improved capacity spectrum method (ICSM), N2 method, displacement coefficient

method (DCM) and modal pushover analysis (MPA).

2.2.1 Description of the method

The capacity spectrum method (CSM) is a nonlinear static analysis method which aims to

quantify structural response through the comparison of force-displacement curve and an

earthquake response spectrum in a graphical shape [Freeman, 1998].Transformation of both

force-displacement curve and earthquake response spectra into acceleration-displacement is

necessary. Because of this transformation the system is required to be reduced to a single

degree of freedom SDOF system (2.1.1) .Using trial and error, the estimation of the

performance point describing the displacement of a building due to a specific seismic loading is

carried out. The procedure is presented in detail in the following sections.

As discussed earlier in 2.1, one of the most important outcomes of pushover analysis is the

force - displacement curve (i.e. Base shear roof/top displacement) also known as capacity

curve. In order to obtain this relationship, a nonlinear static analysis is carried out provided avertical distribution of the lateral load is applied to the structure based on the fundamental mode

or other load patterns as explained earlier in 2.1.3.

A bilinear representation of the capacity curve is performed as shown in figure 14. Global yield

points ( , ) and final displacement points ( , ) are defined. The yield force ,represents the ultimate strength of the idealized system which is equal to the base shear force

at the formation of the plastic mechanism. The initial stiffness of the system should be

determined such as the areas under the idealized force deformation curves (A1and A2) are

approximately equal so as to ensure similar energy is associated with each curve. Using the

equations: ; With: (Figure 12b) derived previously the properties ofthe equivalent SDOF system are defined. This allows the utilization of elastic response

spectrum for SDOF systems [EC8, FEMA etc.] for the determination of the target displacement.


35/77

24

2.2.2 Capacity curve conversion into capacity spectrum

In order to obtain results in terms of earthquake response of the system, the capacity curve

needs to be converted into capacity spectrum using the equations [ATC-40, 1996]: and where;: Mass of the total building: modal amplitude at storey i for mode j.:participation factor calculated by : modal mass coefficient calculated by :

:

Figure 15, presents typical capacity curve and capacity spectrum graphs in terms of base shear

versus roof displacement and spectral acceleration versus spectral displacements respectively.

Figure 14 Bilinear approximation of the capacity curve [Themelis 2008,EN 1994-1 2004]

Figure 15. Conversion of capacity curve to capacity spectrum

[Psycharis, presentation]


36/77

25

2.2.3 Elastic response spectrum conversion into accelerationdisplacement spectrum

Provided that capacity curve is converted to capacity spectrum using the equations mentioned

in the previous sub section, it is required that the design spectrum (or elastic response spectrum

shown in figure 16a) is plotted in terms of acceleration and displacement, the product of the

conversion is also known as the demand spectrum (figure 16 b) [Mahaney et al,1993].

The capacity spectrum and the elastic demand spectrum (for effective damping or inelastic

spectrum) are then plotted together in acceleration displacement format as shown in figure

17.This allows the initial estimation of the performance point (in terms of acceleration apiand

displacement dpi) which in turn enables the estimation of peak structural response for a given

earthquake, based on the concept of displacement based design (DBD) where the real

deformation of each structural element is examined [Psycharis, presentation].

The performance point can be estimated using two methods. The first estimates the

performance point by extending the linear part of the capacity spectrum until it intersects the

demand spectrum. A vertical line is then drawn from the intersection back to the capacity

spectrum. The intersection point of the vertical line and the capacity spectrum indicates the

performance point (api and dpi). This empirical rule is known as the equal displacement rule.

Figure 17 demonstrates the application of this method. Alternatively, the performance point is

obtained through computing the amount of (viscous) damping in the system through the

relationship eq = + 5% [ATC-40, 1996] for which the demand spectrum needs to be

calculated, the intersection of the capacity spectrum and the resulting demand spectrum

indicates the new performance point, consequently the force and displacement of the structure

for that earthquake Figure 18. The method is known as the CSM method [ATC-40, 1996]. The

reader is referred to ATC-40 for more information regarding the calculation of viscous damping.

Figure 16. a) Elastic response spectrum b) demand response spectrum.

[Mahaney et al,1993]


37/77

26

After calculating the performance point, the target displacement of MDOF system can be

obtained using the expression: ui= PF1uSd(PF participation factor, Sd Spectral displacement of

SDOF as shown in 2.2.2). This allows the verification of strength in structural components and

storey drifts for the target displacement.

The concept behind capacity spectrum method (CSM) comes down to the simple notion of;

Given that the capacity curve is extended through the envelope of the demand curve, the

structure can survive the earthquake. [Paret et al, 1996].

Figure 17. Performance point obtained using the

displacement rule

[Mahaney et al,1993]

Figure 18. Performance point obtained through calculation

of viscous damping in the system (CSM method)

[Psycharis,presentation]


38/77

27

CHAPTER 3

Pushover analysis of RC frame structure

3.1 Introduction

Necessary work preceding seismic retrofitting is the evaluation of the existing structure and

identification of any deficiencies. This section of the project examines the earthquake response

of a typical low rise RC frame structure in Greece. Three individual analyses were carried out in

order to quantify and compare the response of the structure for the case of bare frame where

the masonry infill effect is not considered, fully infilled frame where the masonry infill effect is

considered in every storey and partially infilled where only the ground floor has no infills,

simulating a typical structure in Greece which its ground floor use is restricted to parking space

and stores. The three cases can be seen in figure 21. The main goal is to obtain the capacity

curves of the RC frame for the three cases described in order to quantify the contribution of

masonry infills and later check the partially infilled frame (in other words a typical structure in

Greece) for compliance with seismic design demands using the capacity spectrum method. The

pushover analysis is carried out using the finite element software package SAP 2000.

3.2 Structure

The frame of the structure studied in this project is shown in figure 19 a. This particular low rise

RC frame structure has been also studied by Pankaj & Ermiao [2005]. The 4-storey structure

consists of reinforced concrete elements designed to Eurocode 2 for the different combinations

of static loading including wind, dead and variable and a response spectrum in accordance to

Eurocode 8. The cross sections of the designed members are shown in figure 19 b and c. The

total mass of the structure is 97 000 kg (including live loads) with a global damping ratio of 5%

being assumed (typical damping ratio for RC structure) [Pankaj & Ermiao ,2005].

Figure 19. a) Structural frame of RC building b) cross-

sectional details of beam members, c) cross-sectional

details of column members [Pankaj & Ermiao, 2005]


39/77

28

3.3 Effects of masonry infills

Despite the fact that masonry infills are normally being considered as nonstructural members

and their stiffness contribution to the system being ignored in practice, under lateral loading

such as earthquake acceleration induced forces, their interaction with the frame results to an

increase in the systems stiffness, with consequent effect the increase of the systems natural

frequency which in turn leads to higher accelerations as discussed earlier in 1.2.

In order to compensate the effects of infills on the structure, countries across the world adopted

the design practice of physically separating the infills from the RC frame adequately through

appropriately designed joints, so as the interaction between the two under lateral loading which

leads to deformation is minimised, as a result the bare RC frame carries the entire lateral

loading. On the other hand, existing structures around the world (including Greece) were

designed with the masonry infills being built integral with the RC frame whilst being consideredas nonstructural elements, therefore their contribution to the systems earthquake response was

not taken into account. Rathi & Pajgade [2012] through their comparison between a four storey

RC bare frame structure and an identical infilled RC structure indicate that masonry infill panels

have a large effect on the behavior of frames under earthquake loading. In addition to this, it

was observed that the deflection of the bare frame is significantly larger than the infilled one.

The above arguments make the assumption of ignoring the contribution of infills to the structural

system an oversimplified approach which can lead to big discrepancies between the expected

and observed actual response of the structure.

3.3.1 Simulation of infill contribution

In order to describe the nonlinear behavior of masonry infill the equivalent strut method, which

was originally proposed from Polyakov [1966] and developed further by many researches

including Mainstone [1971], Smith & Carter [1969] among others is used in this project

[Schneph et al, 2007]. In this method, the infills are replaced by an equivalent diagonal strut

bracing the frame. The width W of the equivalent diagonal strut is computed using the formulashown below which is widely used in literature [Rathi & Pajgade, 2012].


40/77

29

Where:

= Stiffness reduction factor Ei = the modules of elasticity of the infill material

Ef= the modules of elasticity of the frame material

Ic= the moment of inertia of column

t = the thickness of infill

H =the centre line height of frames

h = the height of infill

L =the centre line width of frames

l = the width of infill

D = the diagonal length of infill panel

= the slope of infill diagonal to the horizontal.

3.3.2 Calculation of equivalent strut width;

L= 5000 mm

l = 4600 mm

H =3000 mm

h = 2700 mm

D =5682 mm = 0.0009t = 250 mm = 670 mmIc = 213,333.33 cm4

Ei = 2 Gpa

Ef = 25 Gpa

=28.4

Figure 21.From left to right cases of bare, infilled and

partially infilled frames

Figure 20.Concept of equivalent strut method and

important parameters [Rathi & Pajgade, 2012]


41/77

30

3.4 Plastic Hinges

Modeling the behavior of different structural components is one of the most important steps for

the implementation of pushover analysis. The inelastic flexure of beams and columns can be

modeled using concentrated (for cases where yielding occurs at the ends of members) or

distributed hinge models (for cases where yielding occurs along the members) [Inel & Ozmen ,

2006]. Concentrated and distributed hinge models are defined by the length of the plastic zone.

Ideally a concentrated plastic hinge model represents all its plastic flexural deformation by a

zero-length point hinge and a distributed hinge model by a series of hinges along the expected

plastic zone of the member.

The nonlinear behavior of the structural components is quantified by strength and deformation

capacities. In order to quantify the ultimate deformation capacity of different components, the

ultimate curvature and plastic hinge length needs to be determined.

3.4.1 Plastic hinge length

The ultimate deformation capacity of an element depends on the ultimate curvature and plastic

hinge length [Inel & Ozmen , 2006] .Identifying the correct length of plastic hinge has been a

subject of study for many years and many expressions have been established since in order to

achieve that. Simple expressions such as Lp = 0.5 h (In which Lp is the length of the plastic

hinge and h the height of the section) proposed by Park and Paulay [1975] exist. Other more

complex and accurate approaches involving bilinear approximations of the moment curvaturerelation, have been proposed by Priestley et al. [1982]. This expression incorporates the length

of the member hand the diameter of the reinforcement bars dhin the form of: Lp= 0.08 h+ 6

dh. However in practical use, default properties provided by FEMA-356 and ATC-40 are

preferred due to convenience and simplicity.

3.4.2 Localizing plastic hinges

In RC structures plastic hinges are commonly known to take place in the extremities of the

elements (edges of beams and columns where cracking takes place). Nonlinear deformations

due to the inelastic behavior of the materials take place at locations where bending moments

are more intense. Using the software SAP 2000 the distance between the concentrated hinge

and the extremity of the element is taken half the length of the hinge [Computers & Structures,

2005].


42/77

31

3.4.3 Types of plastic hinge

The interaction between the axial force and the bending moments (P-My-Mz) needs to be taken

into account for all the columns composing the frame. In the case of beams, their behavior is

simulated with exclusive contribution of the bending moments (MyMz) and by neglecting the

axial force. Finally the behavior of the strut calculated so as to simulate the contribution of the

wall infills is described considering only axial force (P), due to the idealisation that struts only

perform in compression.

3.4 Design spectrum

The seismic design of the structure was performed under the guidelines of Eurocode 8

(EC8).The selection of design spectrum was performed for the corresponding peak ground

acceleration 0.35 g, subsoil class B, 5% critical damping and amplification factor of 2.5.

The behavior f

base isolation on structures with soft storey

Documents