Transcript
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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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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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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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9. SUMMARY AND CONCLUSIONS ......................................................................................... 116
REFERENCES .................................................................................................................................... 119
APPENDIX A ....................................................................................................................................... A1
APPENDIX B ....................................................................................................................................... B1
APPENDIX C ....................................................................................................................................... C1
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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
FRAME-EQUIVALENT (LEFT), WALL-EQUIVALENT (MIDDLE)AND WALL SYSTEM (RIGHT)
BUILDING DESIGNED TO DCMAND PGA=0.20G ANALYZED WITH IDA ...................................... 80
FIGURE 8.8BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE OF A EIGHT-STOREY
FRAME-EQUIVALENT (LEFT), WALL-EQUIVALENT (MIDDLE)AND WALL SYSTEM (RIGHT)
BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA ...................................... 81
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)
BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA ...................................... 81
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
FIGURE 8.21FRAGILITY CURVES OF FIVE-STOREY BUILDINGS DESIGNED TO PGA=0.25G AND DCM
ANALYZED USING IDAMETHOD:(TOP)FRAME BUILDINGS;(BOTTOM)WALL-EQUIVALENT
BUILDINGS..................................................................................................................................... 94
FIGURE 8.22FRAGILITY CURVES OF FIVE-STOREY BUILDINGS DESIGNED TO PGA=0.25G AND DCM
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
FIGURE 8.41BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR FIVE-STOREY
WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .................................................................................. 104
FIGURE 8.42BEAM FRAGILITY CURVES FOR A)YIELDING AND B)ULTIMATE STATE FOR FIVE-STOREY
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
(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .................................................................................. 105
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
(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .................................................................................. 106
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
(MIDDLE)AND LFM(RIGHT). ....................................................................................................... 106
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
(MIDDLE)AND LFM(RIGHT). ....................................................................................................... 107
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
FIGURE 8.48COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR FIVE-
STOREY WALL-EQUIVALENT BUILDING DESIGNED TO DCMAND PGA=0.25G ANALYZED WITH
IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .......................................................................... 108
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FIGURE 8.49COLUMN FRAGILITY CURVES FOR C)YIELDING AND D)ULTIMATE STATE FOR FIVE-
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
IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .......................................................................... 109
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
IDA(LEFT),SPO(MIDDLE)AND LFM(RIGHT). .......................................................................... 110
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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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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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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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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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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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
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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
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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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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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Chapter 2: Definitions and Background
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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
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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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Chapter 4: Design of Buildings
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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
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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
top related