Modelling and AnalysisModelling and Analysis - Eurocodeseurocodes.jrc.ec.europa.eu/doc/WS_335/S3_EC8-Lisbon_P FAJFAR.pdf · EUROCODE 8 Background and Applications Dissemination of

EUROCODE 8Background and Applications

Dissemination of information for training – Lisbon 10-11 February 211

Dissemination of information for training – Lisbon, 10-11 February 2011

Modelling and AnalysisModelling and Analysis (Chapter 4 of EC8-1)

Peter FajfarUniversity of Ljubljana

M j K liMaja KreslinUniversity of Ljubljana

AccelerogramsDissemination of information for training – Lisbon 10-11 February 2011 2

Hysteretic behaviourDissemination of information for training – Lisbon 10-11 February 2011 3

STEEL REINFORCED CONCRETE

MASONRY PRESTRESSED CONCRETE

“Philosophy” of seismic designDissemination of information for training – Lisbon 10-11 February 2011 4

PERFORMANCE STATE

frequent operational safe near collapse

PERFORMANCE STATE

qR=95 years41% in 50 years

AK

E

design R=475 years10% i 50TH

QU

A

10% in 50 years

EART

max.considered

Performance statesDissemination of information for training – Lisbon 10-11 February 2011 5

Dissemination of information for training – Lisbon 10-11 February 2011 6

Everything should be made as simple as possible but not simpleras possible, but not simpler

Albert Einstein

ScopeDissemination of information for training – Lisbon 10-11 February 2011 7

EC8-1, Chapter 4, Overview and comments 4.2 Characteristics of earthquake resistant buildings4.2 Characteristics of earthquake resistant buildings 4.3 Structural analysis 4.4 Safety verificationsy

Test building Modellingg Analysis

Code designed versus old buildings g g

Basic principles of conceptual designDissemination of information for training – Lisbon 10-11 February 2011 8

Structural simplicityp y Uniformity, symmetry and redundancy Bi-directional resistance and stiffness Bi-directional resistance and stiffness Torsional resistance and stiffness

Diaphragmatic behaviour at storey level Diaphragmatic behaviour at storey level Adequate foundation

L’Aquila 2009Dissemination of information for training – Lisbon 10-11 February 2011 9



Kobe 1995 Izmit 1999Dissemination of information for training – Lisbon 10-11 February 2011 12

Kobe 1995Dissemination of information for training – Lisbon 10-11 February 2011 13

Chile 2010Dissemination of information for training – Lisbon 10-11 February 2011 14



Montenegro 1979Dissemination of information for training – Lisbon 10-11 February 2011 17




Primary seismic membersDissemination of information for training – Lisbon 10-11 February 2011 21

Members considered as part of the structural system that resists the seismic action, modelled in y ,the analysis for the seismic design situation and fully designed and detailed for earthquake resistance in accordance with the rules of EN 1998

Secondary seismic membersDissemination of information for training – Lisbon 10-11 February 2011 22

Members which are not considered as part of the seismic action resisting system and whose g ystrength and stiffness against seismic actions is neglected

Structural (ir)regularityDissemination of information for training – Lisbon 10-11 February 2011 23

RegularityDissemination of information for training – Lisbon 10-11 February 2011 24

Regularity in plan Symmetry Compact plan configuration Adequate in-plan stiffness of the floors

Small in plan slenderness Small in-plan slenderness Adequate torsional stiffness

Regularity in elevation No interruption of lateral load resisting systems in

ele ationelevation No abrupt changes of stiffness, mass and overstrength Limitations of setbacksLimitations of setbacks

Torsional flexibilityDissemination of information for training – Lisbon 10-11 February 2011 25

T T and/or T TT Tx and/or T Ty

rx ls and/or ry ls

Torsionally stiff Torsionally flexible

Importance classesDissemination of information for training – Lisbon 10-11 February 2011 26

Permanent loads “G” self weight of the structure + 2 kN/m2self weight of the structure 2 kN/m

Variable – live loads “Q”I = 0.8

office building (category B) 2 kN/m2I = 1.0

I = 1.2 Vertical loads (G, Q) were distributed to the

elements with regard to their effective area

I

= 1 4I = 1.4

Importance factorDissemination of information for training – Lisbon 10-11 February 2011 27

Importance factor Return period T (years)0.8 2301.0 4751.2 7801.3 10001 4 12 01.4 1250

(based on data for Slovenia)

Combination of loads (EC0)Dissemination of information for training – Lisbon 10-11 February 2011 28

k,j E,d 2,i ,1 i 1G "+" P "+" A "+" k i

jQ

Permanent loads “G”

Prestressing loads “P”

Seismic loads “A”

Variable – live loads “Q” (factor in EC1)Variable live loads Q (factor in EC1)

Determination of massesDissemination of information for training – Lisbon 10-11 February 2011 29

QG "" kiEikj QG ""

2iEi

Pseudo 3D modelDissemination of information for training – Lisbon 10-11 February 2011 30

Cracked sectionsDissemination of information for training – Lisbon 10-11 February 2011 31

In concrete buildings, in composite steel-b ildi d i b ildi hconcrete buildings and in masonry buildings the

stiffness of the load bearing elements should takeinto account the effect of cracking (Secantinto account the effect of cracking (Secantstiffness to the initiation of yielding of the reinforcement).)

The elastic flexural and shear stiffness properties p pof concrete and masonry elements may be taken to be equal to one-half of the corresponding stiffness of the ncracked elementsstiffness of the uncracked elements.

Cracked sectionsDissemination of information for training – Lisbon 10-11 February 2011 32

Sae (g) Sde (cm)

2 0

2.5

100R NT = 2 TTcr = T √2

1.5

2.0

0.5

1.0 50

0.00 1 2 3

T (s)

0TRTNT Tcr T (s)

Accidental eccentricityDissemination of information for training – Lisbon 10-11 February 2011 33

e i = 0 05 Li

L i th fl di i di l t th

eai = 0.05 Li

Li is the floor-dimension perpendicular to the direction of the seismic action

Methods of analysisDissemination of information for training – Lisbon 10-11 February 2011 34

aSDYNAMICSTATIC a

Modal response spectrum Lateral force

methodLINEAR b

T

analysismethod

Ta combined with response spectrum

b bi d ith b h i f t

Nonlinear response-history analysis

Nonlinear static (pushover) analysis

NONLINEAR

b combined with behaviour factor

Behaviour factorDissemination of information for training – Lisbon 10-11 February 2011 35

Factor used for design purposes to reduce the forces obtained from a linear analysis, in order to y ,account for the non-linear response of a structure, associated with the material, the structural system and the design procedures

Behaviour factor - backgroundDissemination of information for training – Lisbon 10-11 February 2011 36

FF Fe eF DR = = = μμ

y y

R μF D

Fys

d

FR =

F

Fy eμ s

d

FR = = R RF

Fd

uαR R

Eurocode 8

Dd Dy D Du

s1

αR q , R >α

≡

Ductility classesDissemination of information for training – Lisbon 10-11 February 2011 37

FF Fe

Fy2 DCM

Fy1

y

DCH

Dy1 Dy2 D D

Behaviour factorDissemination of information for training – Lisbon 10-11 February 2011 38

OverstrengthDissemination of information for training – Lisbon 10-11 February 2011 39

900

u For

ce 1 F

F

0

0.00 0.15

DisplacementDisplacement

Overstrength factor = u / 1g u 1



Overstrength factorDissemination of information for training – Lisbon 10-11 February 2011 42

Wall- or wall-equivalent dual systems wall systems with only two uncoupled walls perwall systems with only two uncoupled walls per

horizontal direction: u / 1 = 1,0 other uncoupled wall systems: u / 1 =1,1 wall-equivalent dual, or coupled wall systems: u / 1 = 1,2

Irregular in plan: reduced values Pushover analysis: increased values

Lateral force methodDissemination of information for training – Lisbon 10-11 February 2011 43

Regular structures with small influence of higher modes T1 ≤ 4 TC in T1 ≤ 2.0 s

Fb = Sd(T1) m λ

Lateral force methodDissemination of information for training – Lisbon 10-11 February 2011 44

• Approximate formulas for the period T• Approximate formulas for the period T1

• Distribution of horizontal forcesDistribution of horizontal forces

iibi

mzFF

ii

bims

FF

orjj

bi mzFF

jjbi msFF

or

• Accidental eccentricity• Accidental eccentricity

δ = 1 + 1,2 (x/Le)

Le xi

Approximate formulas for T1Dissemination of information for training – Lisbon 10-11 February 2011 45

R l i hRayleigh

jj

jjj

pu

muT

2

1 2j

jj

Empirical formula

34

1 tT C H

Modal response spectrum analysisDissemination of information for training – Lisbon 10-11 February 2011 46

Displacements: Aii

iiDiiii STS 2

2

max 4 ΦΦU

4

aiiii S ΦMFForces:

i

ii M

L

iMsMΦT

iiL

TM ΦMΦ iTiiM ΦMΦ

Number of modesDissemination of information for training – Lisbon 10-11 February 2011 47

The response of all modes of vibration contributing significantly to the global response g g y g pshall be taken into account

the sum of the effective modal masses amounts to at the sum of the effective modal masses amounts to at least 90% of the total mass of the structure

ll d ith ff ti d l t th 5% all modes with effective modal masses greater than 5% of the total mass are taken into account

Effective massesDissemination of information for training – Lisbon 10-11 February 2011 48

iLm2

i

ii Mm

sMΦTiiL i

TiiM ΦMΦii

Mn m

iii

Mmmi j

ji 1 1

Combination of modal responsesDissemination of information for training – Lisbon 10-11 February 2011 49

EE = √ Σ EEi2 (SRSS)

if Tj ≤ 0.9 Ti

Otherwise more accurate procedure such asOtherwise more accurate procedure, such as

CQCCQC

Accidental eccentricityDissemination of information for training – Lisbon 10-11 February 2011 50

Accidental torsional effects

0.05 , 0.05X i X i Y i Y i Y i X iM F L M F L , , , , , ,0.05 , 0.05X i X i Y i Y i Y i X iM F L M F L

Pushover analysisDissemination of information for training – Lisbon 10-11 February 2011 51

N2 method (basic) Target displacement: Annex B (informative)Target displacement: Annex B (informative)

Extended N2 Higher mode effects in plan and elevation Complies with the EC8-3 requirement “4.4.4.5

P d f ti ti f t i l d hi h dProcedure for estimation of torsional and higher mode effects”

Combination of effects of componentsDissemination of information for training – Lisbon 10-11 February 2011 52

E " " 0 30EEEdx "+" 0,30EEdy

0,30EEdx "+" EEdySRSS

E1

E1x

E1x

E2x

Fx Fx

E1y

E1x

E2x

Fy Fy

Vertical seismic actionDissemination of information for training – Lisbon 10-11 February 2011 53

If avg is greater than 0,25 g (2,5 m/s2) the vertical component of the seismic action should be taken into account

for horizontal or nearly horizontal structural b i 20members spanning 20 m or more

for horizontal or nearly horizontal cantilever components longer than 5 mcomponents longer than 5 m

for horizontal or nearly horizontal pre-stressed componentscomponents

for beams supporting columns in base-isolated structures in base-isolated structures

Displacement calculationDissemination of information for training – Lisbon 10-11 February 2011 54

d dds = qd de

d di l t i d d b th d i i i tids displacement induced by the design seismic actionqd behaviour factor for displacements (qd = q, unless

otherwise specified)otherwise specified)de displacement determined by a linear analysis based on

the design response spectrumthe design response spectrum

Upper limit: value from the elastic displacement spectrumTorsional effect are taken into account

Actual displacementsDissemination of information for training – Lisbon 10-11 February 2011 55

F FFe

q = Fe/Fd

D = q DdFy

FFd

Dd Dy D D

Non-structural elementDissemination of information for training – Lisbon 10-11 February 2011 56

Architectural mechanical or electrical element Architectural, mechanical or electrical element, system and component which, whether due to lack of strength or to the way it is connected to thelack of strength or to the way it is connected to the structure, is not considered in the seismic design as load carrying elementy g

Non-structural elementsDissemination of information for training – Lisbon 10-11 February 2011 57

For non-structural elements of great importance or of a particularly dangerous naturep y g Floor-response spectra

For other non-structural elements Simplified procedure

Non-structural elementsDissemination of information for training – Lisbon 10-11 February 2011 58

Simplified analysis

aaaaa / qWSF

Sa = S[3(1 + z/H) / (1 + (1 – Ta/T1)2)-0,5]

Wa weight of the elementγa importance factor for the elementqa behaviour factor for the element

Floor acceleration spectrum (simplified)Dissemination of information for training – Lisbon 10-11 February 2011 59

5

6a

g

Sa S

3

4z = 1.0Hz = 0.5H

2

3 Hz = 0H

0

1

00 1 2 3 4 a

1

TT

Normalized floor acceleration spectrum( 1 1 h i ht t th fl H t t l h i ht(qa = 1, a = 1, z height up to the floor , H total height, Ta period of the element, T1 period of the structure)

Additional measures for masonry infilled framesDissemination of information for training – Lisbon 10-11 February 2011 60

Provisions apply to frame or frame equivalent dual concrete systems of DCH and to steel or steel-concrete composite moment resisting frames of DCH with interacting non-engineered masonry infills Recommendation: adopt also for DCM or DCL concrete steel Recommendation: adopt also for DCM or DCL concrete, steel

or composite structures with masonry infills

I l iti i l ti Irregularities in elevation

Irregularities in plang p

Damage limitation of infills

Friuli 1976Dissemination of information for training – Lisbon 10-11 February 2011 61

Montenegro 1979 Izmit 1999Dissemination of information for training – Lisbon 10-11 February 2011 62

Safety verifications (1) - Ultimate limit stateDissemination of information for training – Lisbon 10-11 February 2011 63

Resistance condition

Ed ≤ Rd

E d d R itEd demand, Rd capacity

P- effects need not be taken into account if

10,0=θtot

rtot hVdP

tot

Safety verifications (2)Dissemination of information for training – Lisbon 10-11 February 2011 64

Global and local ductility conditionSpecific material related requirements shall be satisfied Specific material related requirements shall be satisfied, including, when indicated, capacity design provisions

Prevention of storey mechanismsPrevention of storey mechanisms

RbRc 3,1 MM

Capacity designDissemination of information for training – Lisbon 10-11 February 2011 65

YES ! NO !

Capacity designDissemination of information for training – Lisbon 10-11 February 2011 66




Safety verifications (3)Dissemination of information for training – Lisbon 10-11 February 2011 70

Equilibrium conditionR i t f h i t l di h Resistance of horizontal diaphragms

Resistance of foundations Seismic joint condition

Damage limitation stateDissemination of information for training – Lisbon 10-11 February 2011 71

Limitation of interstorey drifty

• non-structural elements of brittle materialsd ≤ 0 005 h d ≤ 0 01hdr ≤ 0.005 h , dr ≤ 0.01h

• ductile non-structural elementsdr ≤ 0.0075 h

• non-structural elements do not to interfere with structural deformations, or without non-structural elementsdr ≤ 0.010 h dr ≤ 0.02hr r

= 0.4 (importance classes III and IV) = 0.5 (importance classes I in II)

Return period versus (importance) factorDissemination of information for training – Lisbon 10-11 February 2011 72

Return period T (years) Return period T (years)50 0.48

100 0.60200 0.76475 1.001000 1 301000 1.30

10000 2.57

Valid for Slovenia

Test exampleDissemination of information for training – Lisbon 10-11 February 2011 73

RC buildingg6 stories + 2 basements

Description of buildingDissemination of information for training – Lisbon 10-11 February 2011 74

SCHEMATIC SECTION


TYPICAL PLANTYPICAL PLAN


BASEMENTBASEMENT

Seismic actionsDissemination of information for training – Lisbon 10-11 February 2011 77

ELASTIC RESPONSE SPECTRUM

ag = I ·agR = 0.25gimportance class II (I = 1 0) importance class II (I = 1.0)

Soil B, Type 1 S = 1.2,S 1.2, TB = 0.15 s,TC = 0.5 s, TD = 2.0 s

Damping 5%

Vertical actionsDissemination of information for training – Lisbon 10-11 February 2011 78

Permanent loads “G” self weight of the structure + 2 kN/m2self weight of the structure 2 kN/m

Variable – live loads “Q” office building (category B) 2 kN/m2

Vertical loads (G, Q) were distributed to the elements

Seismic masses (1)Dissemination of information for training – Lisbon 10-11 February 2011 79

Masses from permanent loads “G” factor 1.0 Masses from live loads “Q” factor Ei Masses from live loads Q factor Ei

2Ei i

factor = 1.0 (roof storey), = 0.5 (other)factor = 0 3 (category B) factor 2i = 0.3 (category B)

15% (30%) mass from Q is taken into account

Seismic masses (2)Dissemination of information for training – Lisbon 10-11 February 2011 80

Level Storey mass m (ton)

Moment of inertia MMI (ton*m2)

ROOF 372 33951

5 396 36128

4 396 36128

3 396 36128

2 396 36128

1 408 37244

= 2362 ton

2 22 l bMMI m l m

* Only masses above level 0 are taken into account

12sMMI m l m

Structural model – general (1)Dissemination of information for training – Lisbon 10-11 February 2011 81

3D (spatial) model All element are modelled as line elements All element are modelled as line elements

• peripheral walls are modelled with line elements and a rigid beam at the top of the each element

Effective widths of beams (EC2) Rigid offsets are not taken into accountg

• Infinitely stiff elements are used only in relation to walls W1 and W2

Rigid diaphragms at each floor• slabs are not modelled


Masses and mass moments of inertia are lumped at centres of masses

• Only masses above the top of the peripheral walls are taken into account

Cracked elements are considered• 0.5*As, 0.5*I, 0.1*It

All elements are fully fixed in foundation Infills are not considered


Structural model – effective width EC2Dissemination of information for training – Lisbon 10-11 February 2011 84

Structural model – peripheral wallsDissemination of information for training – Lisbon 10-11 February 2011 85

Structural regularityDissemination of information for training – Lisbon 10-11 February 2011 86

Criteria for regularity in elevation

Criteria for regularity in plan

1) slenderness < 4 max 4L1) slenderness < 4

2) eccentricity < 30%* torsional radius

0Direction X: 0.30

Direction Y: 0 30X Xe r

e r

min

4L

2) eccentricity 30% torsional radius

3) torsional radius < radius of gyration

0Direction Y: 0.30Y Ye r

Direction X:Direction Y:

X sr lr l) gy Direction Y: Y sr l

Structural regularity in planDissemination of information for training – Lisbon 10-11 February 2011 87

Structural eccentricity e0 and centre of stiffness 3 static load cases in each storey (FXi = 1, FYi = 1, Mi = 1)3 static load cases in each storey (FXi 1, FYi 1, Mi 1) Loads are applied in centres of mass (CM) Determine rotation RZi due to FXi, FYi and MiZi Xi Yi i

Determine e0i and centres of stiffness (XCRi, YCRi)

, ,

0 , 0 ,,

1( 1)

1

Z i X iX i i X i i

Z i i

R Fe XCR e XCM

R M

R F

, ,

0 , 0 ,,

1( 1)

Z i Y iY i i Y i i

Z i i

R Fe YCR e YCM

R M

Structural regularity in planDissemination of information for training – Lisbon 10-11 February 2011 88

T i l di ( ) Torsional radius (rX, rY) 3 static load cases in each storey (FTXi = 1, FTYi = 1, MTi = 1)

L d li d i t f tif (CR) Loads are applied in centres of stifness (CR) Determine rotations RZi (MTi), displacement UXi (FXi) and UYi (FYi)

Determine torsional (K ) and lateral stiffnesses (K K ) Determine torsional (KM,i) and lateral stiffnesses (KFX,i, KFY,i) Determine rXi and rYi

, , ,, , , , , ,

1 1 1, ,1 1 1M i FX i FY i

Z i T i X i TX i Y i TY i

K K KR M U F U F

, ,, ,

M i M iX i Y i

FY i FX i

K Kr and r

K K, ,FY i FX iK K

Structural regularity - criteriaDissemination of information for training – Lisbon 10-11 February 2011 89

Criteria for regularity in elevation

Criteria for regularity in plan

1) max 4L1)

2) 0Direction X: 0.30X Xe r

max

min

4L

Structure is regular in plan and 2)

3)

0Direction Y: 0.30Y Ye r

Direction X:Direction Y:

X sr lr l

pin elevation

) Direction Y: Y sr l

Irregular in elevation if basement is also considered !?

Structural type of the buildingDissemination of information for training – Lisbon 10-11 February 2011 90

UNCOUPLED WALL SYSTEM The structural system is defined as a wall system when The structural system is defined as a wall system, when

65% (or more) of the shear resistance is contributed by walls

Application of shear resistance is difficult EC8 allows that shear resistance may be substituted by

h fshear forces Base (above basement) shear force taken by walls

amounts to 72% (direction X) and 92% (direction Y)amounts to 72% (direction X) and 92% (direction Y)of the total shear force

Dual wall equivalent system?

Behaviour factor qDissemination of information for training – Lisbon 10-11 February 2011 91

St t l t l d ll t Structural type: uncoupled wall system Ductility class: DCM

0 3.0q

Structural (ir)regularity: regular in elevation - no reduction q0g q0

Factor associated with prevailing failure mode: kw = 1

0 3.0wq k q

Periods, effective masses and modal shapes (1)Dissemination of information for training – Lisbon 10-11 February 2011 92

T M M MMode T(sec)

Meff,UX(%)

Meff,UY(%)

Meff,MZ(%)

1 0.92 80.2 0.0 0.2

2 0 68 0 0 76 3 0 02 0.68 0.0 76.3 0.0

3 0.51 0.2 0.0 75.2

4 0.22 15.0 0.0 0.2

5 0.15 0.0 18.5 0.0

6 0.12 0.2 0.0 17.6

M = 95 7 94 7 93 1 Meff = 95.7 94.7 93.1

ETABS program


1 MODE – predominantly translational in X direction1. MODE – predominantly translational in X direction


2 MODE – translational in Y direction2. MODE – translational in Y direction


3 MODE – predominantly torsional3. MODE – predominantly torsional

Modal response spectrum analysis RSADissemination of information for training – Lisbon 10-11 February 2011 96

Modal response spectrum analysis was performed independently for the ground excitation in two p y ghorizontal direction

Combination of diferent modes – CQCCombination of diferent modes CQC Combination of results in two directions – SRSS Design spectrum was used Design spectrum was used Accidental eccentricity was taken into account

S i i d i it ti Seismic design situation

Accidental torsional effectsDissemination of information for training – Lisbon 10-11 February 2011 97

Results of analysis without accidental torsion (SSRS of two horizontal directions) + envelope of accidental ) ptorsional effects

SRSS (EX, EY) + ENVE(±MX, ± MY)( X Y) ( X Y)

Results of analysis without accidental torsion + id t l t i l ff t f h h i t laccidental torsional effects, for each horizontal

direction. SRSS combination of two horizontal directionsdirections

SRSS (EX ± MX, EY ± MY)

RSA – Accidental torsional effectsDissemination of information for training – Lisbon 10-11 February 2011 98

RSA – shear forcesDissemination of information for training – Lisbon 10-11 February 2011 99

12% of the total 15% of the total %weight weight

RSA - displacementsDissemination of information for training – Lisbon 10-11 February 2011 100

RSA – Damage limitationsDissemination of information for training – Lisbon 10-11 February 2011 101

RSA – second order effectsDissemination of information for training – Lisbon 10-11 February 2011 102

Force distributionDissemination of information for training – Lisbon 10-11 February 2011 103

Direction XDirection X

Lateral force method

Force distributionDissemination of information for training – Lisbon 10-11 February 2011 104

Direction YDirection Y


Shear forcesDissemination of information for training – Lisbon 10-11 February 2011 105

Direction XDirection X


Shear forcesDissemination of information for training – Lisbon 10-11 February 2011 106

Direction YDirection Y


Code designed versus old buildingsDissemination of information for training – Lisbon 10-11 February 2011 107

SPEAR BUILDINGSPEAR BUILDING

Pushover curvesDissemination of information for training – Lisbon 10-11 February 2011 108

3030 Test EC8 H 24

27

30

2427

30

= 6.5 EC8 H

1821

24[%

]

1821

24[%

]

12

15

Fb /

W [

= 3.21215

Fb /

W [

= 3.2

36

9

Test1st yield of beam

3

69 Test

EC8 H1st yield of beam1st yield of columnNC

0

3

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

1st yield of columnNC

03

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

NCDesign force

d n / H [%]d n / H [%]X direction

Determination of seismic capacity (NC)Dissemination of information for training – Lisbon 10-11 February 2011 109

Test Test EC8 H

Probability of “failure”Dissemination of information for training – Lisbon 10-11 February 2011 110

PGA = 0 25 g x 1 15 = 0 29 g (seismic hazard map soil type C)PGA475 = 0.25 g x 1.15 = 0.29 g (seismic hazard map, soil type C)

PGAC = 0.25 g (test building), PGAC = 0.77 g (EC8 building)

PNC = 0.78 x 10-2 or 32% in 50 years (test building)

PNC = 2.67 x 10-4 or 1.3% in 50 years (EC8 building)

Discussion of resultsDissemination of information for training – Lisbon 10-11 February 2011 111

PGAC = 0.77 g “The code is too conservative!?”The code is too conservative!?

P 1 3 %PNC,50 = 1.3 % “The probability is too high!?”

How high is the tolerable probability?How safe is safe enough?

Documents

Modelling and AnalysisModelling and Analysis - Eurocodeseurocodes.jrc.ec.europa.eu/doc/WS_335/S3_EC8-Lisbon_P FAJFAR.pdf · EUROCODE 8 Background and Applications Dissemination of