KAntoniou MSc Thesis

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Seismic fragility of RC frame and wall-frame

dual buildings designed to EN- Eurocodes

A Dissertation Submitted in Partial Fulfilment of the Requirements

for the Master Degree in

Earthquake Engineering &/or Engineering Seismology

By

Kyriakos Antoniou

Supervisor(s): Prof. Michael N. Fardis

February, 2013

University of Patras


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The dissertation entitled Seismic fragility of RC frame and wall-frame dual buildingsdesigned to EN-Eurocodes by Kyriakos Antoniou, has been approved in partial fulfilment ofthe requirements for the Master Degree in Earthquake Engineering

Professor M. N. Fardis ________________


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Abstract

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ABSTRACT

Fragility curves are constructed for structural members of regular reinforced concrete frame

and wall-frame buildings designed according to Eurocode 2 and Eurocode 8. Prototype plan-

and height- wise very regular buildings are studied with parameters including the height of the

building, the level of Eurocode 8 design (in terms of design peak ground acceleration and

ductility class) and for dual systems the percentage of seismic base shear taken by the walls.

Member fragility curves are constructed based on the results of nonlinear static (pushover)

analysis (SPO) and incremental dynamic analysis (IDA) using 14 spectrum-compatible semi-artificial accelerograms. Analysis is performed using three-dimensional structural models of

the full buildings. These results are compared to fragility curves obtained from previous

studies for a simplified analysis method using the lateral force method (LFM).

The fragility curves are addressed on two member limit states; yielding and the ultimate

deformation in bending or shear. The peak chord rotation and peak shear force demands at

member ends are taken as damage measures; the peak ground acceleration (PGA) is used as

seismic intensity measure. The probability of exceedance of each limit state is computed from

the probability distributions of the damage measures (conditional on intensity measure) and of

the corresponding capacities.

The alternative methods yield results that are in good agreement for beams and columns in

both frame and dual buildings and for the flexural behavior of walls. Results from the

simplified procedure using the LFM shows that Medium Ductility Class walls are likely to

fail in shear even before their design PGA. The dynamic analysis confirms to a certain extend

the inelastic amplification of shear forces due to higher mode effects and shows that the

relevant rules of Eurocode 8 are on the conservative side.

Keywords: Concrete buildings; Concrete walls; Eurocode 8; Fragility curves; Seismic Design


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Acknowledgements

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ACKNOWLEDGEMENTS

I would like to sincerely thank my supervisor Professor M. N. Fardis for his guidance and the

time dedicated and G. Tsionis for his continuous support for the project.


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Index

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TABLE OF CONTENTS

ABSTRACT ............................................................................................................................................ 1

ACKNOWLEDGEMENTS ..................................................................................................................... 2

TABLE OF CONTENTS......................................................................................................................... 3

LIST OF FIGURES ................................................................................................................................. 6

LIST OF TABLES ................................................................................................................................. 12

LIST OF SYMBOLS ............................................................................................................................. 14

1. INTRODUCTION ........................................................................................................................ 20

2. DEFINITIONS AND BACKGROUND ....................................................................................... 22

2.1. Building codes ..........................................................................................................22

2.2. Performance-based requirements ..............................................................................22

2.3. Intensity Measure ......................................................................................................23

2.4. Damage measures .....................................................................................................25

2.5. Seismic Vulnerability Assessment Methodologies ...................................................26

2.5.1. Empirical Fragility Curves ................................................................................26

2.5.2. Expert Opinion method .....................................................................................27

2.5.3. Analytical Fragility Curves ...............................................................................28

2.5.4. Hybrid methods .................................................................................................30

2.6. Seismic safety assessment of RC buildings designed to EC8...................................30

3. DESCRIPTION OF BUILDINGS ................................................................................................ 32

3.1. Typology of buildings ...............................................................................................32


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Index

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3.2. Geometry of buildings ..............................................................................................32

3.3. Materials ...................................................................................................................34

4.

DESIGN OF BUILDINGS ........................................................................................................... 35

4.1. Actions on structure and assumptions.......................................................................35

4.2. Behaviour factors and local ductility ........................................................................36

4.3. Design procedure ......................................................................................................37

4.3.1. Sizing of beams and columns in frame systems ...............................................37

4.3.2. Sizing of beams, columns and walls in wall-frame (dual) systems ..................38

4.4. Dimensioning of Beams ............................................................................................39

4.5. Dimensioning of Columns ........................................................................................40

4.6. Dimensioning of Walls .............................................................................................42

5. ANALYSIS METHODS AND MODELLING ASSUMPTIONS ................................................ 46

5.1. Nonlinear Static Pushover Analysis ......................................................................46

5.2. Incremental Dynamic Analysis .................................................................................47

5.3. Structural modelling for IDA and SPO .....................................................................51

5.4. Linear Static Analysis - Lateral Force Method.....................................................53

6. ASSESMENT OF BUILDINGS ................................................................................................... 57

6.1. Limit State of Damage Limitation (DL) ...................................................................57

6.2. Limit State of Near Collapse (NC) ...........................................................................60

6.3. Estimation of damage measure demands ..................................................................63

7. METHODOLOGY OF FRAGILITY ANALYSIS ....................................................................... 64

7.1. Damage Measures .....................................................................................................64

7.2. Exclusion of unrealistic results for IDA ...................................................................65

7.3. Determination of variability ......................................................................................65

7.4. Construction of fragility curves ................................................................................69

8. RESULTS AND DISCUSSION ................................................................................................... 71

8.1. Modal analysis results ...............................................................................................72

8.2. Median PGAs at attainment of the damage state for the three methods ...................74

8.3. Fragility curve results for wall-frame dual systems ..................................................76

8.4. Fragility curve results for frame systems ..................................................................91

8.5. Comparison between analysis methods ....................................................................96

8.6. Fragility results of walls in the ultimate state .........................................................111


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Index

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9. SUMMARY AND CONCLUSIONS ......................................................................................... 116

REFERENCES .................................................................................................................................... 119

APPENDIX A ....................................................................................................................................... A1

APPENDIX B ....................................................................................................................................... B1

APPENDIX C ....................................................................................................................................... C1


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Index

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LIST OF FIGURES

FIGURE 2.1DEFINITION OF CHORD ROTATION [ADAPTED FROM FARDIS,2009] ................................... 26

FIGURE 2.2FLOWCHART TO DESCRIBE THE COMPONENTS OF THE CALCULATION OF ANALYTICAL

VULNERABILITY CURVE [ADAPTED FROM DUMOVA-JOVANOSKA (2004)] ................................... 29

FIGURE 3.1PLAN OF WALL-FRAME (DUAL)BUILDINGS [PAPAILIA,2011] ............................................ 33

FIGURE 3.2GEOMETRY OF FRAME BUILDINGS [PAPAILIA,2011] .......................................................... 33

FIGURE 3.3STRUCTURAL 3DMODEL TAKEN FROM ANSRUOP FOR FIVESTOREY DUAL SYSTEM...... 34

FIGURE 4.1CAPACITY DESIGN VALUES OF SHEAR FORCES ON BEAMS [CEN,2004] .............................. 40

FIGURE 4.2CAPACITY DESIGN SHEAR FORCE IN COLUMNS [CEN2004] ............................................... 42

FIGURE 4.3:DESIGN ENVELOPE FOR BENDING MOMENTS IN THE SLENDER WALLS (LEFT:WALL

SYSTEMS ;RIGHT:DUAL SYSTEMS )[CEN2004] .......................................................................... 43

FIGURE 4.4DESIGN ENVELOPE OF THE SHEAR FORCES IN THE WALLS OF A DUAL SYSTEM [CEN2004]

....................................................................................................................................................... 44

FIGURE 5.1PSEUDO-ACCELERATION SPECTRA FOR THE SEMI-ARTIFICIAL INPUT MOTIONS COMPARED

TO THE SMOOTH TARGET SPECTRUM (SHOWN WITH THICK BLACK LINE) ..................................... 49

FIGURE 5.2TIME-HISTORIES OF ACCELEROGRAMS USED IN THE ANALYSIS.......................................... 50

FIGURE 5.3TAKEDA MODEL MODIFIED BY LITTON AND OTANI............................................................ 51

FIGURE 5.4STRUCTURAL MODEL FOR A FIVESTOREY DUAL BUILDING TAKEN FROM ANSRUOP..... 53

FIGURE 5.5STRUCTURAL MODEL FOR AN EIGHTSTOREY DUAL BUILDING TAKEN FROM ANSRUOP53

FIGURE 7.1EXCLUSION OF UNREALISTIC RESULTS IN IDA(DAMAGE INDICES ABOVE CONTINUOUS

LINE ARE NEGLECTED) .................................................................................................................. 65

FIGURE 7.2COEFFICIENT OF VARIATION (COV)OF DM-DEMANDS FOR FIVE-STOREY FRAME BUILDING

DESIGNED TO DCMAND PGA=0.20G.......................................................................................... 67


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FIGURE 7.3COEFFICIENT OF VARIATION (COV)OF DM-DEMANDS FOR FIVE-STOREY FRAME-

EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G.................................................... 68

FIGURE 8.1FRAGILITY CURVES FOR FIVE-STOREY WALL-EQUIVALENT BUILDING DESIGNED TO

PGA=0.20G AND DCMANALYZED USING IDAMETHOD............................................................ 77

FIGURE 8.2FRAGILITY CURVES OF WALLS FOR EIGHT-STOREY FRAME-EQUIVALENT (LEFT)AND WALL-

EQUIVALENT BUILDING (RIGHT)DESIGNED TO PGA=0.20G AND DCMANALYZED USING IDA

METHOD......................................................................................................................................... 78

FIGURE 8.3FRAGILITY CURVES OF WALLS FOR EIGHT-STOREY FRAME-EQUIVALENT (LEFT)AND WALL-

EQUIVALENT BUILDING (RIGHT)DESIGNED TO PGA=0.25G AND DCMANALYZED USING IDA

METHOD......................................................................................................................................... 78

FIGURE 8.4FRAGILITY CURVES OF WALLS FOR FIVE-STOREY FRAME-EQUIVALENT BUILDING DESIGNEDTO PGA=0.20G AND DCM(LEFT)AND WALL BUILDING DESIGNED TO DCHAND PGA=0.25G

(RIGHT)ANALYZED USING IDAMETHOD...................................................................................... 78

FIGURE 8.5FRAGILITY CURVES OF WALLS FOR FIVE-STOREY FRAME-EQUIVALENT (LEFT)AND WALL-

EQUIVALENT (RIGHT)BUILDINGS DESIGNED TO DCHAND PGA=0.25G ANALYZED USING IDA

METHOD......................................................................................................................................... 79

FIGURE 8.6BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE OF A FIVE-STOREY

FRAME-EQUIVALENT (LEFT), WALL-EQUIVALENT (MIDDLE)AND WALL SYSTEM (RIGHT)

BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA ...................................... 80

FIGURE 8.7COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE OF A FIVE-STOREY



FIGURE 8.8BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE OF A EIGHT-STOREY



FIGURE 8.9COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE OF A EIGHT-

STOREY FRAME-EQUIVALENT (LEFT), WALL-EQUIVALENT (MIDDLE)AND WALL SYSTEM (RIGHT)


FIGURE 8.10FRAGILITY CURVES FOR MOST CRITICAL MEMBERS OF FIVESTOREY FRAME-EQUIVALENT

BUILDING DESIGNED TO PGA=0.25G AND DCMANALYZED USING IDAMETHOD...................... 83

FIGURE 8.11FRAGILITY CURVES FOR MOST CRITICAL MEMBERS OF FIVESTOREY WALL-EQUIVALENT

BUILDING DESIGNED TO PGA=0.25G AND DCMANALYZED USING IDAMETHOD...................... 84

FIGURE 8.12FRAGILITY CURVES FOR MOST CRITICAL MEMBERS OF FIVESTOREY WALL BUILDING

DESIGNED TO PGA=0.25G AND DCMANALYZED USING IDAMETHOD...................................... 85


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FIGURE 8.13MEMBER FRAGILITY CURVES OF FRAME-EQUIVALENT DUAL SYSTEMS DESIGNED TO

PGA=0.25G AND DCMFOR:(TOP)FIVESTOREY;(BOTTOM)EIGHT-STOREY USING IDA

METHOD......................................................................................................................................... 86

FIGURE 8.14MEMBER FRAGILITY CURVES FOR WALL SYSTEMS DESIGNED TO PGA=0.25G AND DCM

CURVES OF:(TOP)FIVESTOREY;(BOTTOM)EIGHT-STOREY USING IDAMETHOD...................... 87

FIGURE 8.15MEMBER FRAGILITY CURVES FOR A FIVE-STOREY FRAME-EQUIVALENT (FE),WALL-

EQUIVALENT (WE),WALL DUAL (WS)SYSTEM DESIGNED TO PGA=0.20G AND DCMUSING SPO

METHOD FOR MOST CRITICAL STOREY MEMBERS. ........................................................................ 88

FIGURE 8.16FRAGILITY CURVES OF EIGHTSTOREY FRAME-EQUIVALENT BUILDING DESIGNED TO DC

MAND:(TOP) PGA=0.20G;(BOTTOM)PGA=0.25G ANALYZED USING IDAMETHOD................. 89

FIGURE 8.17MEMBER FRAGILITY CURVES FOR A EIGHT-STOREY WALL-EQUIVALENT SYSTEMDESIGNED TO DCMAND FOR PGA=0.20G AND PGA=0.25G USING IDAMETHOD FOR MOST

CRITICAL STOREY MEMBERS. ........................................................................................................ 90

FIGURE 8.18MEMBER FRAGILITY CURVES FOR A FIVE-STOREY FRAME SYSTEM DESIGNED DCMAND

TO PGA=0.20G AND PGA=0.25G USING IDAMETHOD FOR MOST CRITICAL STOREY MEMBERS. 91

FIGURE 8.19MEMBER FRAGILITY CURVES FOR A FIVE-STOREY FRAME SYSTEM DESIGNED PGA=0.25G

AND TO DCMAND DCHUSING IDAMETHOD FOR MOST CRITICAL STOREY MEMBERS. ............ 92

FIGURE 8.20FRAGILITY CURVES OF FIVE-STOREY BUILDINGS DESIGNED TO PGA=0.25G AND DCM

ANALYZED USING IDAMETHOD:(TOP)FRAME BUILDINGS;(BOTTOM)FRAME-EQUIVALENT

BUILDINGS..................................................................................................................................... 93


ANALYZED USING IDAMETHOD:(TOP)FRAME BUILDINGS;(BOTTOM)WALL-EQUIVALENT

BUILDINGS..................................................................................................................................... 94


ANALYZED USING IDAMETHOD:(TOP)FRAME BUILDINGS;(BOTTOM)WALL BUILDINGS............ 95

FIGURE 8.23BEAM FRAGILITY CURVES IN YIELDING STATE FOR FIVE-STOREY FRAME-EQUIVALENT

BUILDING DESIGNED TO DCMAND PGA=0.20G (LEFT)AND WALL-EQUIVALENT BUILDING

DESIGNED TO DCHAND PGA=0.25G (RIGHT). ............................................................................. 96

FIGURE 8.24BEAM FRAGILITY CURVES IN YIELDING STATE FOR EIGHT-STOREY FRAME-EQUIVALENT

BUILDING DESIGNED TO DCMAND PGA=0.20G (LEFT)AND WALL-EQUIVALENT BUILDING

DESIGNED TO DCMAND PGA=0.25G (RIGHT). ............................................................................ 97

FIGURE 8.25BEAM FRAGILITY CURVES IN YIELDING STATE FOR FIVE-STOREY FRAME BUILDING

DESIGNED TO PGA=0.25G AND DCM(LEFT)AND DCH(RIGHT). ............................................... 97


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FIGURE 8.38WALL FRAGILITY CURVES IN ULTIMATE STATE IN FLEXURE FOR FIVE-STOREY FRAME-

EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G (LEFT)AND WALL-EQUIVALENT

BUILDING DESIGNED TO DCHAND PGA=0.25G (RIGHT). .......................................................... 103

FIGURE 8.39WALL FRAGILITY CURVES IN ULTIMATE STATE IN FLEXURE FOR FIVE-STOREY WALL

BUILDING DESIGNED TO DCMAND PGA=0.25G (LEFT)AND EIGHT-STOREY WALL BUILDING

DESIGNED TO DCMAND PGA=0.20G (RIGHT). .......................................................................... 103

FIGURE 8.40BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR FIVE-STOREY

FRAME-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA

(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .................................................................................. 104


WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .................................................................................. 104


WALL BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA(LEFT),SPO

(MIDDLE)AND LFM(RIGHT). ....................................................................................................... 105

FIGURE 8.43BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR EIGHT-STOREY

FRAME-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA


FIGURE 8.44BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR EIGHT -STOREY

WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA


FIGURE 8.45BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR EIGHT -STOREY

WALL BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA(LEFT),SPO


FIGURE 8.46BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR FIVE -STOREY

FRAME BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA(LEFT),SPO


FIGURE 8.47COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR FIVE-

STOREY FRAME-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH

IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .......................................................................... 108


STOREY WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH



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STOREY WALL BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA(LEFT),

SPO(MIDDLE)AND LFM(RIGHT). .............................................................................................. 109

FIGURE 8.50COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR EIGHT-

STOREY FRAME-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH


FIGURE 8.51COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR EIGHT -

STOREY WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH


FIGURE 8.52COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR EIGHT -

STOREY WALL BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .............................................................................................. 110

FIGURE 8.53COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR FIVE -

STOREY FRAME BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA(LEFT),

SPO(MIDDLE)AND LFM(RIGHT). .............................................................................................. 111

FIGURE 8.54FRAGILITY CURVES OF WALLS FOR THE ULTIMATE DAMAGE STATE IN SHEAR OF A FIVE-

STOREY WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.20G. ......................... 114

FIGURE 8.55FRAGILITY CURVES OF WALLS FOR THE ULTIMATE DAMAGE STATE IN SHEAR OF A FIVE-

STOREY WALL BUILDING DESIGNED TO DCMAND PGA=0.20G. ............................................... 114

FIGURE 8.56FRAGILITY CURVES OF WALLS FOR THE ULTIMATE DAMAGE STATE IN SHEAR OF A EIGHT-

STOREY WALL BUILDING DESIGNED TO DCMAND PGA=0.20G. ............................................... 115


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LIST OF TABLES

TABLE 3.1:MATERIAL FACTORS AND VALUES...................................................................................... 34

TABLE 4.1BASIC VALUES OF THE BEHAVIOUR FACTOR,QO................................................................... 36

TABLE 4.2BASIC FACTORED VALUES OF THE BEHAVIOR FACTOR,QO................................................... 37

TABLE 4.3DEPTHS OF BEAMS (HB)AND COLUMNS (HC)FOR FIVE-STOREY FRAME BUILDINGS [ADAPTED

FROM PAPAILIA,2011] .................................................................................................................. 38

TABLE 4.4DEPTHS OF BEAMS (HB)AND COLUMNS (HC)AND WALL LENGTHS (LW)FOR WALL-FRAME

DUAL BUILDINGS [ADAPTED FROM PAPAILIA,2011] .................................................................... 39

TABLE 5.1:ACCELEROGRAM RECORDS USED IN THE ANALYSIS............................................................ 48

TABLE 7.1VALUES OF COEFFICIENT OF VARIATION FOR DM-CAPACITY VALUES................................ 70

TABLE 7.2VALUES OF COEFFICIENT OF VARIATION FOR DM-DEMAND VALUES.................................. 70

TABLE 8.1MODAL PERIODS AND PARTICIPATING MASSES FOR FRAME SYSTEMS................................. 72

TABLE 8.2MODAL PERIODS AND PARTICIPATING MASSES FOR FRAME-EQUIVALENT DUAL SYSTEMS. 72

TABLE 8.3MODAL PERIODS AND PARTICIPATING MASSES FOR WALL-EQUIVALENT DUAL SYSTEMS... 73

TABLE 8.4MODAL PERIODS AND PARTICIPATING MASSES FOR WALL DUAL SYSTEMS......................... 73

TABLE 8.5MEDIAN PGA(G)AT ATTAINMENT OF THE DAMAGE STATE IN 5-STOREY FRAME SYSTEMS74

TABLE 8.6MEDIAN PGA(G)AT ATTAINMENT OF THE DAMAGE STATE IN 5-STOREY FRAME-

EQUIVALENT SYSTEMS.................................................................................................................. 74

TABLE 8.7MEDIAN PGA(G)AT ATTAINMENT OF THE DAMAGE STATE IN 5-STOREY WALL-

EQUIVALENT DUAL SYSTEMS........................................................................................................ 75

TABLE 8.8MEDIAN PGA(G)AT ATTAINMENT OF THE DAMAGE STATE IN 5-STOREY WALL SYSTEMS. 75

TABLE 8.9MEDIAN PGA(G)AT ATTAINMENT OF THE DAMAGE STATE IN 8-STOREY FRAME-

EQUIVALENT DUAL SYSTEMS........................................................................................................ 75


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Index

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LIST OF SYMBOLS

Ac cross section area

Ecd design value of the modulus of elasticity of concrete

Ecm secant modulus of elasticity of concrete

(EI)b,i effective rigidity of the beams in storey i

(EI)c,i effective rigidity of the columns in storey i

Fb total lateral seismic shear (base shear)

Fi seismic horizontal force in storey i

FV,Ed total vertical load

G permanent (dead) load

Hcl clear height of a column

Hi transverse storey forces which represent the effect of the inclination i

Hst storey height

Ic the moment of inertia of concrete cross section

Is the second moment of area of reinforcement, about the centre of area of the

concrete

Iw second moment of area (uncracked concrete section) of shear wall

Kc factor for effects of cracking, creep etc.Ks factor for contribution of reinforcement

Lb bay length

Lcl,i beam clear span in storey i

Ls shear span of a member

MEb seismic bending moment at beam ends

MEc seismic bending moment at column ends

MEdo bending moment at the base of a wall, as obtained from the elastic analysis for

the design seismic action


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Index

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Mel elastic seismic moment at the end of the element

MRd,b,i- design value of negative beam moment resistance at end

MRd,b,j+ design value of positive beam moment resistance at end

MRdo flexural capacity at the base section of a wall

My yield moment

N axial force

NEd design value of the applied axial force

PGA Peak ground acceleration

PGV Peak ground velocity

Q imposed (live) load

Qd load for the persistent and transient design situation

QEq Combination of actions for seismic design situationsS soil factor according to EC8

Sa Spectral acceleration

Sa,ds spectral acceleration necessary to cause the certain damage state to occur

SD Spectral displacement

Sd(T) Design spectrum

Se(T) elastic response spectrum

T vibration period of a single-degree-of-freedom system

T1 fundamental period of vibration of a building

Tc corner period at the upper limit of the constant acceleration region of the

elastic spectrum

Teff effective period of vibration

VCD,c capacity-design shear of the columns

VEc seismic shear force at column ends

Vg+q,o shear force at end regions of interior beams due to quasi-permanent gravity

loads

VN contribution of the element axial load to its shear resistance

Vo shear force due to gravity loadsVR,c shear force at diagonal cracking of a member

VR,cycl shear resistance under cyclic loading

VR0 shear capacity before plastic hinging

VRs the contribution of transverse reinforcement to shear resistance

VS shear demand before plastic hinging

Vtot,base total base shear of the building

Vwall,base the fraction of the building total base shear taken by the walls

X random variable


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Index

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al tension shift

a effectiveness factor for confinement by transverse reinforcement

1 is the value by which the horizontal seismic design action is multiplied in

order to first reach the flexural resistance in any member in the structure,while all other design actions remain constant

acy zero-one variable for the type of loading

aem ratio of elastic moduli (steel-to-concrete)

g design ground acceleration on type A ground according to EC8

ah reduction factor for height

am reduction factor for number of members

asl zero-one variable accounting for the slippage of longitudinal bars from the

anchorage zone beyond the end section

av zero-one variable

b width of compression zone

bi the centreline spacing of longitudinal bars (indexed by i) laterally restrained

by a stirrup corner or a cross-tie along the perimeter of the cross-section

bo width of confined core of a column or in the boundary element of a wall

bwo wall web thickness

cv coefficient of variation

d effective depth of a section

d1 distance of the center of the compression reinforcement from the extremecompression fibres

dbL mean tension bar diameter

fbc normalised compressive strength of the masonry units

fcd design value of concrete compressive strength

fck characteristic value of concrete compressive strength

fcm mean value of concrete compressive strength

fmc specified compressive strength of the mortar

fyd design value of steel yield strength

fyk characteristic value of steel yield strength

fyL yield stress of the longitudinal bars

fym mean value of steel yield strength

fyw yield stress of transverse steel

h depth of a cross section

hb beam depth

hc column depth

ho depth of confined core of a column or in the boundary element of a wall


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Index

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hw wall height

ig radius of gyration of the uncracked concrete section

k1; k2 relative flexibilities or rotational restrains at member ends 1 and 2

l clear height of compression member between end restrains

l0 effective length of a member

lw wall length

m mean of the non-logarithmized variables of a lognormal distribution

maxVi,d,b capacity design shear at the end regions of interior beams

meff effective mass of a building

mi mass of floor i

n relative normal force for the design value of the applied axial force

nst number of storeysnflx number of flexible frames per one stiff

q behaviour factor

qo basic values of the behaviour factor

s standard deviation of the non-logarithmized variables of a lognormal

distribution

xy neutral axis depth at flexural yielding

z length of the internal lever arm of a member

zi the height of the mass, , above the level of application of the seismic action

(foundation or top of a rigid basement)

i interstorey drift from mid-height of the storey i to the mid-height i+1 of theframe

rotation of restraining member for bending moment M

MRd,b sum of beam design flexural capacities

MRd,c sum of column design flexural capacities

u the value by which the horizontal seismic design action is multiplied in orderto form plastic hinges in a number of sections sufficient for the development

of overall structural instability, while all other design actions remain constant

the normalised composite log-normal standard deviation

D lower bound factor for the horizontal design spectrum

R dispersion of the capacity (in terms of standard deviation)

S dispersion of the demand (in terms of standard deviation)

Sp dispersion of the spectral value (in terms of standard deviation)

c partial factor for concrete

g partial factor for permanent action

q partial factor for variable action


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Index

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Rd factor accounting for steel strain hardening

s partial factor for steel

i the displacement of floor from an elastic analysis of the structure for the set of

lateral forces capacity design magnification factor

RV uncertainty factor for shear capacity

sV,el demand uncertainty factor for shear failure (prior to the formation of a plastichinge)

s uncertainty factor of the chord rotation demand

u capacity uncertainty factor

y uncertainty factor for the yielding chord rotation

damping correction factor with a reference of for 5% viscous damping

member chord rotation

s mean chord rotation demand

u ultimate chord rotation

um the expected chord rotation capacity

y chord rotation at yielding

ym the expected chord rotation value at yielding

1 factor which depends on concrete strength class

2 factor which depends on axial force and slenderness

slenderness ratio

normal distribution mean

pl

ratio of the plastic part of the rotation demand at the end of the member to the

value at yielding

curvature ductility factor

axial load ratio, positive for compression

reduction factor for unfavourable permanent actions

y neutral axis depth at yielding

geometric reinforcement ratio1 ratio of the tension reinforcement

2 ratio of the compression reinforcement

d steel ratio of diagonal reinforcement in each diagonal direction

s ratio of transverse steel parallel to the loading direction

w the transverse reinforcement ratio

ratio of web reinforcement

normal distribution standard deviation

0 basic value of the inclination taking account for the geometric imperfections


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Index

19

eff effective creep ratio of concrete

i inclination taking account for the geometric imperfections

y yield curvature

2 factor for quasi-permanent value of a variable action factor for combination value of a variable action

1 mechanical reinforcement ratio of tension and web longitudinalreinforcement

2 mechanical reinforcement ratio of compression longitudinal reinforcement


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Introduction

21

Dispersions used for the construction of fragility curves from IDA take into account explicitly

model uncertainties for the estimation of the damage measure demands taken from the

analysis. Estimates for the dispersions of the damage measure demands for the SPO method

are taken from previous studies. Both methods use estimates for the damage measure

capacities based on previous studies.

The results of a simplified method using the lateral force method (LFM) taken from Papailia

[2011] is compared against the results from SPO and IDA. The LFM is performed by using

simplified models under the assumption that all beam ends in a storey have the same elastic

seismic moments and inelastic chord rotation demands. Vertical elements are considered to

have negligible bending moments due to gravity loads and the axial force variation due to

seismic action is neglected in interior columns. The shear force demands taken from the LFM

are amplified to take into account higher mode effects.

Discussion will focus on the differences between geometric and design parameters of thebuildings and the differences between the alternative analysis methods. The walls of buildings

designed according to Eurocode 8 for Medium Ductility Class is an important point of the

discussion since according to the results using the lateral force method they fail in shear

before their design PGA.


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Chapter 2: Definitions and Background

22

2.DEFINITIONS AND BACKGROUNDA brief introduction for various definitions and a review of previous studies is found in this

Chapter.

2.1. Building codesThe analysis, design and assessment of the buildings were performed in accordance to the

European Standards; Eurocode 2 [CEN, 2004a], Eurocode 8 - Part 1 [CEN, 2004b] and Part 3

[CEN, 2005]. Eurocode 2 and Eurocode 8 Part 1 were published by the EuropeanCommittee for Standardization (CEN) in December of 2004. Eurocode 2 is for the design of

concrete structures and Eurocode 8 Part 1 is for the seismic design of new buildings.Eurocode 8 Part 3 was published by CEN in June 2005 for the seismic retrofit andassessment of structures. Since March 2010 all CEN member countries use the EN-

Eurocodes.

2.2. Performance-based requirementsPerformance-based earthquake engineering allows for design to meet more than one

performance level thus replacing the traditional design against collapse. The performance

level is the condition of the facility or structure after a seismic event. The seismic event is

identified by the annual probability of exceedence known as the seismic hazard level.

In EN-Eurocodes the performance levels are associated to the Limit States of the structure.

The Ultimate Limit State concerns the safety of people and the Serviceability Limit State

concerns the comfort of its occupants and the function and use of the structure. According to

Eurocode 8Part 1 [CEN, 2004] the following two Limit States (or performance levels) areconsidered:

1. No-(local)- collapse: It is considered as the Ultimate Limit State. This limit stateprotects life against rare seismic events by preventing the collapse of structural

members. The seismic action associated with this limit state is the design seismicaction having 10% probability of being exceeded in 50 years (mean return period of475 years).

2. Damage Limitation. It is considered as the Serviceability Limit State, where thestructural or non structural damage is limited under frequent seismic events. The

structure is expected not to have any permanent deformations and should retain its


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strength and stiffness. The seismic action associated with this limit state is the

damage limitation seismic action with 10% probability of being exceeded in 10years (mean return period of 95 years).

Eurocode 8 Part 3 [CEN, 2005] for the assessment and retrofitting of structures has fullyadopted the performance-based approach for three performance levels:

1. Damage Limitation (DL), structural elements are not significantly yielded and retaintheir strength and stiffness and the structure has negligible permanent drifts and no

repairs are required. It is recommended that the performance objective should be

reached for a 20% probability of exceedence in 50 years (return period of 225 years).

2. Significant Damage (SD), which corresponds to the no-(local)-collapse accordingto EC8-Part 1, where the structure is significantly damaged but retains some residual

lateral strength and stiffness and its vertical load bearing capacity. Non-structural

components are damaged and moderate drifts are present. The structure will be able tosurvive aftershocks of moderate intensity. It is recommended that the performance

objective should be reached for a 10% probability of exceedence in 50 years (return

period of 475 years).

3. Near Collapse (NC), the structure is heavily damaged with large permanent driftsand little residual lateral strength or stiffness is retained although the vertical elements

are still able to retain vertical loads. The structure would most probably not be able to

survive another earthquake. It is recommended that the performance objective should

be reached for a 2% probability of exceedence in 50 years (return period of 2475

years).

This study is addressed on two limit states; the yielding and the ultimate. The yielding

corresponds to the Damage Limitation limit state and the ultimate corresponds to the NearCollapse limit state as defined by Eurocode 8 Part 3 [CEN, 2005].

2.3. Intensity MeasureAn Intensity Measure (IM) is the ground motion parameter that is being used in order to relate

the ground motion to the damage of the building. The selected parameter should be able to

correlate the ground motion to the damage of the buildings. Intensity measures can be divided

into instrumental IM and non-instrumental IM.

For non-instrumental IM, macroseismic data are used in computing the empirical

vulnerability of structures. Macroseismic data is expressed in different macroseismic intensity

scales, which identify the effects of ground motion, and is taken from observation of damage

due to earthquake ground motion and its effects on the earths surface, people and structures.Macroseismic intensity scale is a qualitative scale expressed in terms of Roman numerals

representing different intensity levels. An advantage of this type of intensity measure is that it

is directly related to the vulnerability of the buildings and there is no requirement to take

instrumental measurements. The gathered data depends on the area where it is collected and

how far away this area is from the epicenter.


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The most important IMs for non-instrumental seismicity are the MSK: Medvedev-Sponheur-

Karnik Intensity scale [Medvedev and Sponheuer, 1969], the MMI: Modified Mercalli

Intensity Scale [Wood and Neumann, 1931], the European Macroseismic Sclae (EMS98)

[Grnthal, 1998] and the MCS: MercalliCancaniSieberg [Sieberg, 1923]. The MCS wasproposed as the development of the Mercalli scale and includes twelve degrees from I

Instrumental to XII Cataclysmic. MMI scale is composed of twelve degrees. MSK goesfrom I No perceptible to XII Very catastrophic.

Previous studies made use of the non-instrumental intensity measures using the empirical

vulnerability procedures to produce post-earthquake damage statistics [Calvi et al., 2006].

Such studies include Braga et al. [1982] where the damage probability matrices have been

developed based on damage data obtained from the Irpinia 1980 earthquake. The buildings

were separated in three classes and the matrices were based on the MSK scale for each class.

Di Pasquale et al. [2005] updated Bragas study andchanged the MSK scale to the MCS scalebecause the Italian seismic catalogue is based on this intensity measure. Dolce et. al. [2003]have adapted the damage probability matrices with an additional vulnerability class using the

EMS98 scale, which takes into account the buildings constructed after 1980. Singhal and

Kiremidjian [1996] developed fragility curves and damage probability matrices using the

Modified Mercalli Intensity.

In instrumental intensity measures, instruments are used in order to record the ground motion

and then recorded accelerograms are processed to get the appropriate measurement. The

instrumental intensity measures include the Peak ground Velocity (PGV), the Peak Ground

Acceleration (PGA), the Peak Ground Displacement (PGD), the Spectral Acceleration at the

first mode of vibration Sa(T1,5%) and the spectral displacement Sd. PGV correlates well withthe earthquake magnitude and gives useful information on the ground-motion frequency

content and strong-motion duration which influence the seismic demands of the structure

[Akkar and zen, 2006]. The Spectral Acceleration at the first mode of vibration Sa(T1) isoften used since it is well suited for structures that are sensitive to the strength of the

frequency content near its first mode frequency [Vamvatsikos and Cornell, 2002].

These instrumental intensity measures were used in reference studies such as Kircil and Polat

[2006] where elastic pseudo-spectral acceleration was considered as an intensity measure in

developing fragility curves for RC frame buildings. Akkar et al. [2005] constructed fragility

functions for RC buildings using PGV as the IM since maximum inelastic displacements arebetter correlated with PGV than with PGA and PGV has a good correlation with MMI for

large amplitude earthquakes. Borzi et al. [2006] used PGA as the intensity measure for the

vulnerability analysis of RC buildings. PGA was used since it is consistent with the parameter

used in seismic hazard maps in the current codes.

More complicated IMs have been introduced such as the vector-valued IMs by Baker [2005]

which consists of two parameters; the spectral acceleration and epsilon. Epsilon is found to be

able to predict the structural response. It is defined as the difference between spectral

acceleration of a record and the mean of the ground motion prediction equation at a given


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period. Neglecting the effect of epsilon gives conservative estimates on the response of the

structure.

The ground motion IM that is being used in this study is the Peak Ground Acceleration

(PGA). The reason for this choice is due to the simplicity of its use and due to the fact that theresults can be easily compared against the design acceleration of the structures.

2.4. Damage measuresDamage measure (DM) is a scalar quantity that can be deducted from the analysis and

characterizes the response of the structural model due to seismic loading. Selecting a suitable

DM depends on the application and the structure.

The damage measures for members that are used in reference studies include:

The peak chord rotation demand at member end The peak shear force demand The local Park and Ang Damage Index [1985]. The node rotations Displacement ductility,

The Park and Ang Damage index takes into account the damage due to maximum

deformation and the damage due to repeated cycles of inelastic deformation. The

displacement ductility is associated with the inelastic response and is defined as the ratio of

the maximum displacement to the yield displacement.

Common damage measures selected for the assessment of buildings as a whole include:

The residual deformation The global Park and Ang Damage Index [1985] Maximum base shear The peak roof drift Interstorey drift ratio The peak interstorey drift angle , = (1 ) Peak floor accelerations

The peak interstorey drift angle is used for structural damage of buildings and relates well to

joint rotations. The peak floor accelerations are used for damage to non-structural components

in multi-storey buildings. [Vamvatsikos and Cornell, 2002]. The Interstorey drift ratio is the

ratio of the maximum storey displacement over the storey height. It gives significant

information on the structural and non-structural damage.

Examples of reference studies that used the DMs above include Singhal and Kiremidjian

[1996], where the global damage index based on Park and Ang [1985], in order to develop

fragility curves and damage probability matrices for RC frame structures. zer and Erberik[2008] developed fragility curves for the damage measure of the maximum interstorey drift


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ratio and a softening index (SI) which was originally proposed by DiPasquale and Cakmak

[1987]. SI takes a value according to the stiffness change due to inelastic action. In another

reference study, Borzi et al. [2006] based the building limit conditions on displacements

which are well correlated with building damage.

For the purposes of this study the damage measures used are the peak chord rotations at a

member end and the peak shear force demands. The chord rotation at a member end is defined

as the angle between the tangent to the member section there and the chord connecting the

two members ends as shown in Figure 2.1. When plastic hinge forms in the member end, the

chord rotation is equal to the plastic hinge rotation.

Figure 2.1 Definition of chord rotation [adapted from Fardis, 2009]

2.5. Seismic Vulnerability Assessment MethodologiesDifferent methodologies for the seismic vulnerability assessment of buildings are used

according to the data available and the uncertainties considered. These methods include the

empirical, expert opinion, analytical and hybrid methods.

2.5.1. Empiri cal F ragili ty CurvesEmpirical methods for the vulnerability assessment of buildings are based on the damage

observed after a seismic event. The two main types of empirical methods are the damage

probability matrices (DPM) and the continuous vulnerability functions. DPM is a form of

conditional probability of obtaining a damage level due to the IM. The continuous

vulnerability functions illustrate the probability of exceeding a given damage state as a

function of the seismic IM. The advantages of using empirical fragilities are that the observed

damage from the earthquakes is the most realistic way to model fragility and takes into

account many uncertainties such as soil-structure-interaction and variability of the structural


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capacity. The disadvantages are that the empirical vulnerability functions require that the

survey forms are not incomplete and the way post-processing is done with the data should not

be deficient. These curves need to be derived for buildings in the same region and should

account for damage subjected after a specific earthquake event. Often undamaged buildings

are not recorded so when deriving the vulnerability analysis it is difficult to assess the total

number of buildings in the analysis [SYNER-G, 2012]. Empirical vulnerability cannot model

the evaluation of retrofit options and do not cover all building types and values of IM. [Calvi

et al. 2006].

Sabetta et al. [1998] developed vulnerability curves from post earthquake damage surveys and

estimated ground motion. The damage surveys of nearly 50000 buildings after earthquake

events in Italy together with estimates of strong ground motion parameters from attenuation

relationships was used for the development of fragility curves. The binomial distribution of

the damage was plotted as a function of PGA, Arias Intensity and Effective Peak Acceleration

for three structural classes and six damage levels according to the MSK macroseismic scale.Effective Peak Acceleration is defined as the mean response spectral acceleration divided by a

factor of 2.5.

Sarabandi et. al. [2004] developed empirical fragility functions from recent earthquakes with

data taken from the Northridge, California earthquake in 1994 and the Chi-Chi earthquake in

1999 in Taiwan. Buildings situated near the strong motion recording stations were used in the

assessment and were divided into two groups according to their distance from the recording

station. Empirical fragility curves are produced for steel moment frames, concrete frames,

concrete shear walls, wood frame and unreinforced masonry buildings.

Rota et al. [2006] developed typological fragility curves from post-earthquake survey data on

the damage observed on the buildings after Italian earthquakes from the past three decades.

150,000 survey building records have been post processed to define the empirical damage

probability matrices for different building typologies. Typological fragility curves have been

obtained using advanced nonlinear regression methods. Typological risk maps were then

developed for both single damage state and for average loss parameters after combining the

hazard definitions, fragility curves and inventory data.

2.5.2. Expert Opinion methodExert opinion method is a method to construct fragility curves based on the judgment andinformation taken by experts. The probability of damage for different building typologies

covering a range of ground motion intensities are taken from the opinion of experts. The

advantage of the method is that it is not affected by the quantity and quality of the structural

damage data and statistics. The main disadvantage is that the method is restricted on the

knowledge and experience of the experts consulted. The study of Kostov et a. [2007]

produced damage probability matrices for buildings in Sofia according to the EMS-98. The

damage probability matrices were then converted in vulnerability curves.


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2.5.3. Analytical Fragili ty CurvesThis method features a more detailed vulnerability assessment with direct physical meaning.

The analytical fragility curves are computed by constructing appropriate structural models

which express the probability of damage computed under increasing seismic intensity. Figure

2.2 summarizes the basic procedures that are being followed in order to calculate the

analytical vulnerability curves or damage probability matrices. The advantage of this method

is that it provides results that are very close to reality. One of the main disadvantages of

analytical vulnerability curves is that they are computationally demanding and time

consuming. Also the capability of modelling the structure significantly affects the reliability

of the results.

Eurocode 8 - Part 3 [CEN, 2005] provides guidelines for the assessment of existing buildings

which may be used to develop analytical fragility curves. The methods of analysis include the

lateral force analysis, the modal response spectrum analysis, the nonlinear static pushover

analysis, the nonlinear time-history dynamic analysis. The nonlinear static method applies

forces to the model which includes the nonlinear properties of the elements. The nonlinear

dynamic analysis although time consuming gives results that are closer to reality. Also it

allows the influence of the variability of the accelerogram to be taken into account. These

methods are performed in order to compute the seismic action effects.

In order to choose the type of analysis to be performed and the appropriate confidence factor

values EC8 - Part 3 defines three knowledge levels:

KL1: Limited Knowledge KL2: Normal Knowledge KL3: Full Knowledge

The factors that determine the knowledge levels are the geometrical properties of the

structural system and non structural elements, the details (regarding the reinforcement in

reinforced concrete members, the connections between steel members, the floor diaphragm

connection to lateral resisting structure etc.) and the mechanical properties of the constituent

materials used.

For the purpose of this study analytical fragility curves have been developed using nonlinear

time-history dynamic analysis and nonlinear static (pushover) analysis. The buildingsassessed belong to the Full knowledge level (KL3) of Eurocode 8 Part3 since allgeometrical properties, details and mechanical properties of the materials are known.


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Figure 2.2 Flowchart to describe the components of the calculation of analytical vulnerability curve

[adapted from Dumova-Jovanoska (2004)]

Existing studies for the computation of seismic fragility curves for RC buildings that are

based on the analytical method include the following.

Singhal and Kiremidjian [1996] developed fragility curves and damage probability matrices

using Monte Carlo simulation for low-rise, mid-rise and high-rise RC frames using Park and

Ang (1985) damage index to identify different degrees of damage. The analysis was based on

nonlinear dynamic analysis where the ground motion is characterized by spectral acceleration.

For the computation of damage probability matrices the modified Mercalli intensity was used

as the ground motion parameter.

B. Borzi et. al. [2006] use analytical methods where the nonlinear behavior of a random

population of RC buildings was defined with simplified pushover and displacement based

procedures. The vulnerability curves were generated by comparing the displacement

capacities by the pushover analysis with the displacement demands obtained from response

spectrum of each building in the random population. The vulnerability curves were

formulated using the conditional probability of exceeding a certain damage limit state in terms

of the IM.

Dumova et.al [2000] evaluated the vulnerability curves/ damage probability matrices using

analytical methods for frame-wall RC buildings designed according to the Macedonian design


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code. Two sets of buildings were analyzed; six storey frame buildings and sixteen storey

frame-wall buildings. Nonlinear time-history analysis was performed for a set of synthetic

time histories and the response of the structure to the earthquake excitation was defined

according to modified Park and Ang (1985) damage model using five damage states to

express the condition of damage. The probability of occurrence of damage was assumed to be

normal probabilistic distribution.

Masi [2003] employed analytical methods for the seismic vulnerability assessment of existing

RC frame buildings (bare, regularly infilled and pilotis) designed only to gravity loads for

buildings representative of the Italian building block of the past 30 years designed according

to the building codes at the period of their construction. The analysis was performed using

nonlinear time-history analysis using artificial and natural accelerograms. The vulnerability

was characterized through the use of European Macroseismic Scale.

Kiril and Polat [2006] evaluated the behavior of mid-rise RC frame buildings usinganalytical methods. The building stock represented buildings of 3, 5 and 7 storeys that were

designed according to the (1975) Turkish seismic code. In this study only yielding and

collapse damage levels are considered and they were determined analytically under the effect

of twelve artificial accelerograms using incremental dynamic analysis. The yielding and

collapse capacities are evaluated by statistical methods to develop fragility curves in terms of

elastic pseudo-spectral acceleration. Lognormal distribution is assumed for the construction of

the fragility curves.

2.5.4. Hybrid methodsHybrid damage probability matrices and vulnerability functions combine damage observed

after earthquakes with damage obtained from analytical methods. This method is

advantageous when there is lack of observational data. Also post-earthquake damage data can

be used to calibrate the analytical model. Observational data can reduce the computational

effort that would normally be required to perform complete analytical analysis.

Kappos et. al. [1998] developed the damage probability matrices using a hybrid procedure

where data from past earthquakes was combined with results of nonlinear dynamic analysis

for typical Greek buildings designed for the 1959 codes. The results of the dynamic analysis

were used in order to obtain a global damage index and correlated with loss in terms of cost of

repair. Observational damage from the 1978 Thessaloniki earthquake was combined with theanalytical damage results.

2.6. Seismic safety assessment of RC buildings designed to EC8The efficacy of Eurocode 8 and design provisions and the expected performance has been

evaluated in the past. The following studies were performed for the seismic safety assessment

of RC buildings.

Panagiotakos and Fardis [2004] evaluated the performance of RC buildings designed

according to Eurocode 8 using nonlinear analysis. RC frames of 4, 8 and 12 storeys were


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designed for a PGA of 0.2g or 0.4g and to the three ductility classes. The limit states are

considered as in EC8 for the life-safety (475 years) and the damage limitation (95 years) and

are evaluated through nonlinear seismic response analysis. It was found that the design to

Ductility Class High (DC H) or Medium (DC M) is more cost effective than DC Low even in

moderate seismicity and more cost effective than the 2000 Greek national codes. It was also

found that the large differences in material quantities and detailing of the alternative designs

do not translate into large differences in performance.

Rivera and Petrini [2011] investigate the efficacy of the Eurocode 8 force-based design

provisions for RC frames. This study evaluates whether the RC buildings that are designed

according to the EC8 provisions have the expected performance. Four, eight and sixteen

storey RC frame buildings were designed and analyzed using the EC8 response spectrum

analysis. Nonlinear time-history analysis was performed to determine the seismic response of

the structures and validate the EC8 forced base designs. The results indicate that the design of

flexural members in medium-to-long period structures is not significantly influenced by thechoice of effective member stiffness. However the interstorey drift demands calculated are

significantly affected. Design storey forces and interstorey drift demands found using the

codes force base procedure varied substantially from the results of the nonlinear time-historyanalysis. From the results it was concluded that EC8 may yield life-safe designs. Also the

seismic performance of RC frame buildings of the same type and ductility class can be highly

non-uniform.

Rutenberg and Nsieri [2005] evaluated the seismic shear demand in ductile cantilever wall

systems. Two aspects were considered; (1) Single walls or a system of equal-length walls and

(2) resisting system consisting of walls of different length. The results of the parametricstudies showed that DC M and DC H walls designed to EC8 provisions are in need of revision

since for DC M walls the inelastic amplification which takes into account the higher mode

effects as required in EC8 is under-conservative whereas the amplification used for DC H

walls according to the detailed procedure per Keintzel [1990] overestimates the shear demand

in walls for most cases..


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Chapter 3: Description of Buildings

32

3.DESCRIPTION OF BUILDINGSFor the scope of this study pure frame and wall-frame (dual) reinforced concrete buildings

were analyzed and assessed. Two analysis methods were performed: nonlinear static and

nonlinear dynamic analysis of the structures comprising different design and geometric

parameters. The parameters, methods and assumptions made when modelling the structures

are explained and discussed in this section.

3.1. Typology of buildingsThe design and detailing of the frame and the wall-frame (dual) buildings correspond to

certain design parameters including:

Number of storeys: 5 and 8 storeys Seismic Design level per EC8 for Ductility class

o Medium Ductility Class (DC M)o High Ductility Class (DC H)

Seismic Design level per EC8 for design PGAo 0.20go 0.25g

For wall-frame dual buildings, the fraction of the seismic base shears taken by the walls: Frame-equivalent dual system 0.35Vtot,base Vwall,base 0.50Vtot,base Wall-equivalent dual system 0.50Vtot,base Vwall,base 0.65Vtot,base Wall system Vwall,base 0.65Vtot,base

3.2.

Geometry of buildingsThe buildings are regular in plan and in elevation having storey height of H st=3.0m, where all

storeys are of the same height. The buildings consist of five bays along the two horizontal

directions of bay length Lb=5.0m with the same bay length throughout the plan.

The buildings consist of square columns, beams of width 0.3m and slab thickness of 150mm.

The size of columns is constant throughout all storeys and the size of beams is constant

throughout each storey. The perimeter beams and exterior columns have half the elastic

rigidity of interior ones and corner columns have one quarter of elastic rigidity of interior

ones.


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In wall-framed dual systems two walls on each direction are placed as shown in Figure 3.1

and Figure 3.3 sharing the same displacements with the frame. The geometry of the frame

building is illustrated in Figure 3.2 for a five- and eight-storey building. The beam and

column depths and wall lengths for wall-frame buildings are shown in Table 4.4 and the beam

and column depths for frame buildings are shown in Table 4.3.

Figure 3.1 Plan of wall-frame (dual) buildings [Papailia, 2011]

Figure 3.2 Geometry of frame buildings [Papailia, 2011]


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Figure 3.3 Structural 3D model taken from ANSRuop for fivestorey dual system

3.3. MaterialsThe material strengths and partial factors are taken according to Annex C of Eurocode 2

[CEN,2004a]. The structural materials consist of concrete of class C25/30, having a nominal

strength of 25MPa and Tempocore steel of grade S500 (Class C). The following table

provides the material properties for steel and concrete and their partial factors.

Table 3.1: Material factors and values

Partial factors

Partial factor for Concrete c 1.5

Partial factor for Steel s 1.15

ConcreteC25/30

Concrete compressive strength fck 25 MPa

Design compressive strength fcd=ccfck/ c 16.67MPa

Mean concrete compressive strength fcm=fck+8MPa 33MPa

Mean axial tensile concrete strength fctm 2.56 MPa

Secant modulus of elastic of concrete Ecm 30470 MPa

Design value of modulus of elasticity Ecd=Ecm/ cE 25392 MPa

Concrete Cover cnom 30mm

SteelS500

Characteristic yield strength of reinforcement fyk 500MPa

Design yield strength of reinforcement fyd= fyk/s 434.78MPa

Mean yield strength of reinforcement fym=1.15 fyk 575 MPa

Design value of modulus of elasticity of steel Es 200000 MPa

For the seismic vulnerability assessment the mean values for material strengths are being used

(fym=575MPa for reinforcing steel and fcm=33MPa for concrete).


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Chapter 4: Design of Buildings

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4.DESIGN OF BUILDINGS4.1. Actions on structure and assumptionsThe actions considered in the analysis correspond to the seismic design situation and the

persistent and transient design situation according to EN1990.

The combination of vertical actions for the seismic design situation is:

QEQ = G + 2Q ( 4.1)

Where,

2 quasi-permanent value of a variable action factor (=0.3)

G permanent load (=7 kN/m2)

Q imposed load (=2 kN/m2)

The combination for the persistent and transient design situation according to EN1990 is

given by :

Qd=max(gG+ gQ ; gG+ ogQ) ( 4.2)

where:

is thereduction factor for unfavourable permanent actions (=0.85)

0 is thefactor for combination value of a variable action (=0.7)

g is the partial factor for permanent action (=1.35)

q is the partial factor for variable action (=1.5)

The permanent load acting on the structure is 7kN/m2, which includes the weight of the slab,

finishing, partitions and facades and the weight of the beams, columns and walls. The

occupancy loads (live loads) amount to 2kN/m2.


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The design of the building was taken from Papailia [2011] where the lateral force method isused to proceed with the design according to EC8 [CEN,2004b]. In order to compute the base

shear force, as required by the lateral force method, the design spectrum and the fundamental

period is used. The design spectrum is computed by the use of the behaviour factor q obtained

as explained in the section below and the fundamental period of the structure is obtained by

the Rayleigh quotient.

In concrete buildings the stiffness of the load bearing elements are evaluated by taking into

account the effects of cracking. The cracking effect corresponds to the yielding initiation of

the reinforcement. In Eurocode 8 [CEN, 2004], this simplification can be taken into account

by assuming that the flexural and shear stiffness properties are one half of the initial

uncracked stiffness of the element.

4.2. Behaviour factors and local ductilityIn force-based design according to EC8 [CEN,2004b], the use of the behaviour factor

accounts for a simplification in design where the forces found by elastic analysis are reduced.

The values of the basic behaviour factor for buildings designed to DC M and DC H are given

in Table 4.1 for frame systems, wall-frame systems and uncoupled wall systems. Uncoupled

wall systems are defined as wall systems which are linked by a connecting medium which is

not effective in flexure.

Table 4.1 Basic values of the behaviour factor, qo

DC M DC H

Frame system, wall-frame system 3.0 u/1 4.5 u/1

Uncoupled Wall system 3.0 4.0 u/1

Where,

1 the value by which the horizontal seismic design action is multiplied to reach theflexural resistance in any member in the structure while other design actions remain constant.

u the value by which the horizontal seismic design action is multiplied to form plastichinges in a number of sections sufficient for the development of structural instability, while

all other design actions remain constant.

The ratio of u/1 for frame or frame-equivalent dual system may be taken equal to 1.3, forwall-equivalent systems equal to 1.2 and for wall system with two uncoupled walls per

horizontal direction equal to 1.0. Thus the basic values of the behaviour factor, qo, are:


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Table 4.2 Basic factored values of the behavior factor, qo

Frameequivalent / Frame systems Wall-equivalent Wall systems

DC M 3.9 3.6 3.0

DC H 5.85 5.4 4.0

4.3. Design procedureThis section describes the procedure that was followed for the sizing of beams, columns and

walls.

4.3.1. Sizing of beams and columns in frame systemsThe sizing of beams and columns in frame systems was performed according to Eurocode 8

[CEN,2004b] and Eurocode 2 [CEN,2004a]. The sizing of the beams and the columns was

taken from Papailia [2011]. The procedure to size the member is described in this section.

Eurocode 2 [CEN,2004a] gives a simplified criterion for the slenderness ratio of isolated

columns:

= loig

lim = 20 A B Cn ( 4.3)Where,

ig is the radius of gyration of the uncracked concrete section

l0 is the effective length

n Is the normalised axial force taken as n=Ned/ Acfcdand Ned is the design value of the

applied axial force.

The default values for A, B and C are A=0.7, B=1.1 and C=0.7.

The effective length is given by:

= . 1 + 1 0 1

2

1+ 2 ; 1 + 1

1+ 1 1 + 2

1+ 2 ( 4.4)Where,

ki is the column rotational stiffness at the end node i relative to the total restraining

stiffness of the members framing in the plane of bending.

= , = ,

4 , +4 , ( 4.5)


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Where,

Lcl is the clear length of a beam framing into node i

, is the cracked flexural rigidity, taking into account creep , = + ( )20 2 1+ ( 4.6)Esand Isare the elastic modulus and the moment of inertia of the sections reinforcement with

respect to the centroid of the section. Ic is the moment of inertia of the uncracked gross

concrete section and K2is :

2 =

170

=1

170

0.20 ( 4.7)

The effective length of the column and the size of the section are both unknown at the

beginning, thus iterations are performed after dimensioning of the top beam reinforcement at

the supports.

In pure frame systems the depths of the columns and beams are chosen iteratively as the

minimum values meeting the requirements of Eurocode 2 [CEN,2004a] and Eurocode 8

[CEN,2004b]. This takes into account the above implementation for the slenderness limit to

meet the negligible second order effects and the 0.5% storey drift limit per EC8 under the

damage limitation seismic action, where the 50% of the design seismic action is taken.

In the following table the sizes of the beams and columns are presented for different design

parameters (ductility class and design PGA)

Table 4.3 Depths of beams (hb) and columns (hc) for five-storey frame buildings [adapted from Papailia,

2011]

Design

PGA DC

hb(m) hc (m)

0.20g M/H 0.40 0.55

0.25g M/H 0.45 0.55

4.3.2. Sizing of beams, columns and wal ls in wall -f rame (dual ) systemsIn dual (wall-frame) buildings the lateral force procedure according to EC8 [CEN,2004b] was

performed and iterated until certain criteria were met. The sizing of the members is taken

from Papailia [2011]. The depths of columns (hc) and beams (hb) and the length of the walls

(lw) were chosen iteratively to meet the following requirements according to EC8

[CEN,2004b]:


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Meet the storey drift ratio of 0.5% according to Eurocode 8 [CEN, 2004b]. To cover the three cases for the requirements of the wall to total base shear fraction

following the different behavior factors and design rules per EC8:

o Frame-equivalent dual system 0.35Vtot,base Vwall,base 0.50Vtot,baseo Wall-equivalent dual system 0.50Vtot,base Vwall,base 0.65Vtot,baseo Wall system Vwall,base 0.65Vtot,base

In the following table the sizes of the beams and columns and the length of the walls are

presented for different design parameters (wall base shear fraction, ductility class and design

PGA)

Table 4.4 Depths of beams (hb) and columns (hc) and wall lengths (lw) for wall-frame dual buildings

[adapted from Papailia, 2011]

Design DC 5 storeys 8 storeys

PGA hb(m) hc (m) lw(m) Vwall,b(%) hb(m) hc (m) lw(m) Vwall,b(%)

0.20g M/Ha 0.40 0.40 1.5 37 0.45 0.45 2.0/- 42/-

2.0 53 3.0/3.0b 63/73

2.5 65 4.0/- 76/-

0.25g M/Ha 0.45 0.45 2.0 44 0.50 0.45 2.0/- 40/-

2.5 57 3.0/- 61/-

3.5/3.5b 73/81 4.0/5.5

b 74/90

aWhen DC M and DC H have different fraction of base shear and wall length, this is distinguished

with a slash, where the left hand side is the DC M and the right hand side the DC H.

bWall width is 0.5m. In all other cases wall width is 0.25m.

4.4. Dimensioning of BeamsThe longitudinal reinforcement for ULS in bending in beams is designed for the persistent-

and-transient and the seismic design situations using the lateral force method. The

reinforcement in the effective beam flange was taken to be 500mm2.

For the seismic design situation, the dimensioning of the end regions of the beams is done inaccordance to the capacity design rules computed using the design base shears at the member

ends, according to EC8 [CEN,2004b]. The beam design shear forces were determined under

the transverse load through the seismic design situation and the end moments, M i,d, which

correspond to the formation of plastic hinges.

The end moments Mi,d depend on the moment resistances of the columns it is connected to

and the moment resistance of the beams itself. It can be found using:

,

=

,

min(1,

) ( 4.8)


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40

Where,

Rd factor accounting for steel strain hardening, equal to 1.0 of DC M and 1.2 for DC H.

MRb,i design value of the beam moment resistance at end i

MRc sum of the column design moment of resistance.

MRb sum of the beam design moment of resistance, framing to the point.

Thus the capacity design shear at the member ends corresponds to:

, = 1, +2, + + ,0 ( 4.9)Where,

VEd,i capacity design shear at the member ends.

+ ,0 Shear force at the end regions due to the transverse quasi-permanent loadsunder the design seismic situation.

Figure 4.1Capacity design values of shear forces on beams [CEN, 2004]

4.5. Dimensioning of ColumnsThe vertical reinforcement of the columns for the ULS in bending was designed for the axial

load taken from the actions of the seismic design situation. The detailing rules according to

Eurocode 8 [CEN, 2004] are taken into account for each seismic design level.

The dimensioning for the end regions of the columns is computed in accordance to the

capacity design rule through the design shear forces. The design shear forces are based on the

element equilibrium under the end moments Mi,d which correspond to the formation of plastic

hinges as shown in Figure 4.2. The end moments are computed by taking into account the

moment resistances of the beams to which it is connected and the moment resistances of the

column itself.


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The end moments Mi,d are determined through:

, = , min(1, ) ( 4.10)Where,

Rd factor accounting for steel strain hardening and the confinement of the concrete of thecompression zone of the section, equal to 1.1.

MRc,i design value of the column moment resistance at end i

MRc sum of the column design moment of resistance.

MRb sum of the beam design moment of resistance, framing to the point.

Thus the capacity design shear at the member ends corresponds to:

, = 1, +2, ( 4.11)Where,

VEd,i capacity design shear at the end regions.

clear height of column.


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Figure 4.2 Capacity design shear force in columns [CEN 2004]

4.6. Dimensioning of WallsThe design shear force and moments for the walls are according to the capacity design

principles and their calculation is explained below according to EC8 [CEN,2004b]. The

values for the axial force are computed from the analysis of the structure in the seismic design

situation using the lateral force method.

The design bending moment diagram along the height of slender walls should be given by anenvelope of the bending moment diagram from analysis, with a tension drift, as shown in

Figure 4.3. Slender walls are defined as walls having a height to length ratio greater than 2.0.

The envelope is assumed to be linear since there are no discontinuities over the height of the

building. It takes into account potential development of moments due to higher mode inelastic

response after the formation of plastic hinge at the bottom of the wall, thus the region above

this critical height is designed to remain elastic.


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KEY:

a moment diagram from analysis

b design envelope

a1 tension drift

Figure 4.3: Design envelope for bending moments in the slender walls (left: wall systems ; right: dual

systems ) [CEN 2004]

The design envelope of shear forces, as shown in Figure 4.4, takes into account the

uncertainties of higher modes. The flexural capacity at the base of the wall M Rdexceeds the

seismic design bending moment derived from the analysis, MEd. Thus the design shear found

for the analysis, , is magnified by the magnification factor i.e. the ratio of MRd/MEd. Themagnification factor depends on the ductility class of the structure. The design base shear isthus computed by:VEd= ( 4.12)

Where,

For walls in DC M buildings the magnification factor,is taken as 1.5 For walls in DC H buildings the magnification factor,is taken as:

= . . 2 + 0.1 ( ) (1)2 ( 4.13 )Where,

Rd overstrength factor taken as 1.2

Se(T1) ordinate of the elastic response spectrum at fundamental period

Se(TC) ordinate of the elastic response spectrum at corner period


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KEY:

a shear diagram from analysis

b magnified shear diagram

c design envelope

A Vwall,base

B Vwall,topVwall,base/2

Figure 4.4 Design envelope of the shear forces in the walls of a dual system [CEN 2004]

At the critical regions of the wall the curvature ductility factor is required in order tocalculate the confining reinforcement within boundary elements. The curvature ductility

factor is now the product of the basic behaviour factor qofound in Section 4.2 and the ratio of

the design bending moment from the analysis MEd, to the design flexural resistance MRd. This

confining reinforcement should extend vertically up to a height h crof the critical region and

horizontally along the length lcof the boundary element.

The length of this boundary element is the measure from extreme compression fibre to thepoint where spalling occurs in concrete due to large compressive strains. As a minimum the

boundary region should be taken as being larger than 0.15.lw or 1.5.bw. The wall critical

region height, hcr, is estimated using the following relationship:

hcr=max lw, hw 6 2lwHclfor : nst62 Hclfor : nst7

( 4.14)


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Where,

nst the number of storeys

hw the wall height

Hcl is the clear storey height. The base is defined as the level of the foundation or the top

of the basement storey.

lw is the length of the cross section of the wall

Above the height of the critical region, hcr, the rules of EN1992 apply for the dimensioning of

vertical and horizontal reinforcement.


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Chapter 5: Structural modelling and analysis methods

46

5.ANALYSIS METHODS AND MODELLING ASSUMPTIONSFor the construction of the fragility curves different analysis methods were performed each

following different modelling assumptions. For the purpose of this study two methods were

performed; the nonlinear static pushover analysis and the nonlinear dynamic analysis. The

results from these methods were then compared against a simplified method following the

lateral force analysis method by Papailia [2011]. The following section explains the procedure

and assumptions for the analysis methods and structural models.

5.1. Nonlinear Static PushoverAnalysisStatic pushover(SPO) analysis is performed for the evaluation of the buildings according toEurocode 8Part 1 [CEN,2004b]. SPO is performed using the structural model assumptionsdetermined in Chapter 5.3 and using the computational software of ANSRuop.

SPO is essentially an extension of the lateral force method of static analysis, but in thenonlinear regime. This method simulates the inertial forces due to a horizontal component of

the seismic action. These lateral forces Fiincrease throughout the analysis and are applied in

small steps on the mass miin proportion to the pattern of horizontal displacements, i. Themagnitude of the lateral loads is controlled by and magnified in each step.

= i (5.1)According to EC8 [CEN,2004b], pushover analysis can be performed using the modal

pattern which simulates the inertial forces of the first mode shape in the elastic regime. Since

the buildings in the current study meet the conditions of the linear static analysis an invertedtriangular lateral load pattern is applied. In this method the horizontal displacements iaresuch that i = zi, where ziis the height of th

KAntoniou MSc Thesis

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