icossar fp et al

Dam

age and loss evalu

ation in the pe

rform

ance

-based win

d enginee

ring

Francesco PetriniKonstantinos GkoumasFranco Bontempi

ICOSSAR 201311th International Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NY

Sapienza – University of Rome

Francesco Petrini, Ph.D., P.E.Konstantinos Gkoumas, Ph.D., P.E.Franco Bontempi, Ph.D., P.E.

Sapienza - University of RomeDipartimento di Ingegneria Strutturale e Geotecnica

Damage and loss evaluation in the performance-based wind engineering

Dam

age and loss evalu

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Presentation outline

2

• Overview of the Performance Based Wind Engineering (PBWE) procedure

• Models for tall buildings and the assessment of occupant comfort:• Application on a high-rise building• Assessment of the annual probabilities of exceeding

the human perception thresholds

• Vibration and occupant comfort issues• Damage analysis• Loss analysis

• Conclusions and indications for further research

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• Overview of the Performance Based Wind Engineering (PBWE) procedure

• Models for tall buildings and the assessment of occupant comfort• Application on a high-rise building• Assessment of the annual probabilities of exceeding




Dam

age and loss evalu

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Performance-Based Wind Engineering (PBWE)

4

The problem of risk assessment is disaggregated into the following elements:

- site and structure-specific hazard analyses, that is, the assessment of the

probability density functions f(IM), f(SP) and f(IP|IM,SP);

- structural analysis, aiming at the assessment of the probability density function of

the structural response f(EDP|IM,IP,SP) conditional on the parameters characterizing the

environmental actions, the wind-fluid-structure interaction and the structural properties;

- damage analysis, that gives the damage probability density function f(DM|EDP)

conditional on EDP;

- finally, loss analysis, that is the assessment of G(DV|DM), where G(·|·) is a

conditional complementary cumulative distribution function.

G(DV) = ∫…∫ G(DVDM) · f(DMEDP) · f(EDPIM, IP,SP) · f(IPIM,SP) ·

· f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP

Interaction Parameters

Structural Parameters

Intensity measure

IM IP SPEngineering Demand Parameters

EDPDamage Measure

DMDecision Variable

DV

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PBWE procedure flowchart

5

Petrini, F. & Ciampoli M., 2012, Performance-based wind design of tall buildings, Structure & Infrastructure Engineering, 8(10), 954-966.

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis

Structural analysis Damage analysis Loss analysis

IM: intensity measure

IP: interaction parameters

EDP: engineering demand param.

DM: damage measure

DV: decision variable

SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)

Structural characterization

SP: structural system parameters

Structural system

info

Ciampoli M, Petrini, F. & Augusti G., 2011, Performance-Based Wind Engineering: toward a general procedure, Structural Safety, Structural Safety, 33(6), 367-378.

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O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Aerodynamicanalysis

Struc’l analysis Damage analysis Loss analysis



EDP: engineering demand parameters

DM: damage measures DV: decision variables

SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system info

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Aerodynamicanalysis

Struc’l analysis Damage analysis Loss analysis



EDP: engineering demand parameters

DM: damage measures DV: decision variables

SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system info

O, D

g(IM|O,D)

g(IM)

p(EDP|IM)

P(EDP)

p(DM|EDP)

P(DM)

p(DV|DM)

P(DV)

Hazard analysis Struc’l analysis Damage analysis Loss analysis



DM: damage measure


SelectO, D

O: location

D: design

Facility info

Decision-making

O, D

g(IM|O,D)

g(IM)

p(EDP|IM)

P(EDP)

p(DM|EDP)

P(DM)

p(DV|DM)

P(DV)

Hazard analysis Struc’l analysis Damage analysis Loss analysis



DM: damage measure


SelectO, D

O: location

D: design

Facility info

Decision-making

PB

WE

PB

EE

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• Overview of the Performance Based Wind Engineering (PBWE) procedure.





Dam

age and loss evalu

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8

Tam

ura

, Y

. (2

009

).

Win

d an

d ta

ll bu

ildin

gs,

Pro

cee

ding

s of

th

e F

ifth

Eur

ope

an &

Afr

ican

Co

nfe

renc

e on

Win

d E

ngin

eerin

g (E

AC

WE

5),

F

lore

nce,

Ita

ly,

July

19-

23,

200

9..

Vibration frequency

Acc

ele

ratio

n t

hre

sho

lds

for

mo

tion

p

erc

ep

tion

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1B2

H

Loss of serviceability

Loss

of

inte

grity

of

non

-str

uctu

ral

elem

ents

Mot

ion

perc

eptio

n by

bui

ldin

g oc

cupa

nts

Dis

pla

cem

ent

s

Acc

eler

atio

n

Discomfort level in terms of perception thresholds

1

Dam

age and loss evalu

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Loss of serviceability

Loss

of

inte

grity

of

non

-str

uctu

ral

elem

ents

Mot

ion

perc

eptio

n by

bui

ldin

g oc

cupa

nts

Bas

hor,

R

. an

d K

aree

m,

A.

(200

7).

"Pro

babi

listic

P

erfo

rman

ce

Eva

luat

ion

of

Bui

ldin

gs:

An

Occ

upan

t C

omfo

rt P

ersp

ectiv

e",

Pro

c. 1

2th

Inte

rnat

iona

l C

onfe

renc

e on

Win

d E

ngin

eerin

g, 1

-6 J

uly,

Cai

rns,

Aus

tral

ia.

Ava

ilabl

e on

line

at h

ttp://

ww

w.n

d.ed

u/~

nath

az/ [

Acc

esse

d 15

Jun

e 20

10].

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1B2

H

Discomfort level in terms of perception thresholds

Usually Across wind vibration is critical for comfort

The reference period for comfort evaluation is 1 year

1

2

3 1st natural frequency is dominant4

1

10

100

0,1 1

a [

cm/s

2 ]

f [Hz]

Office Apartment

Italian Guidelines

f1

Sca

lar

thre

sho

ld

Dis

pla

cem

ent

s

Acc

eler

atio

n

Dam

age and loss evalu

ation in the pe

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10

Case study structure

Structure•74 floors•Height H=305m•Footprint B1=B2=50m (square)

3d f

ram

e on

the

ext

erna

l pe

rime

ter

cent

ral c

ore

Bracing system

A steel high-rise buildingFinite Element model

FE ModelApproximately•10,000 elements•4,000 nodes•24,000 DOFs

Dam

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Experimental model of Actions

Spe

nce

S.M

.J.,

Gio

ffrè

M.,

Gus

ella

V.,

In

flue

nce

of

high

er m

ode

s on

the

dy

nam

ic r

e-sp

onse

of

irreg

ular

and

re

gula

r ta

ll bu

ildin

gs,

Pro

c. 6

th

Inte

rnat

iona

l C

ollo

quiu

m

on

Blu

ff

Bod

ies

Aer

ody

nam

ics

and

App

lica

tions

(B

BA

A V

I),

Mila

no,

Ital

y, J

uly

20-

24,

2008

.

Boundary Layer Wind Tunnel of the CRIACIV in Prato, Italy

-60

-40

-20

0

20

40

60

80

100

120

140

3000 3200 3400 3600 3800

F [KN]

t [s]

Along Across

1:50

0

Sca

le m

od

el

Response time history

Time domain structural analyses (Experimental actions)

Time domain analyses

Experimental forces

-30

-20

-10

0

10

20

30

3500 3600 3700 3800 3900 4000

aL, aD

[cm/s2]

t [s]Along Across

Dam

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12

)(),(

),,(exp1

),(),(

22

212

2

hSVc

dAdAfA

hSVchS

uumxD

A A

uumxDDD tt

)(),h(S

)(HVc

),h(S)(H),h(S

2uu

22mxD

DD

2

rr tttt

2

0

2

2

20

2

20

2

2

41

1

1)(

mH

rrmp grr rg

Wind action spectra (analytical)

Response spectra

Peak response

Frequency domain response

Response Peak Factor

Analytical model of the buffeting forces

ωfexpωSωSωS jkuuuuuu kkjjkj

kj

2kj

2z

jkzVzV2π

zzCωωf

Cross-spectrum

5.0

0

uu2xu 200

300(x)dxRu

1L

z

where:

5/3

ju

jux2

uuu

/zLf10.3021ω/2π

/zLfσ6.686ωS

jj

2fri0

0

u2u

u1.75)log(zarctan1.16

(n)dnSσ

)z(V2π

zωf

jm

j

Autospectrum

3ew(t)2ev(t)1eu(t))j(zmV)jz(t;jV

α

10m10

zV(z)V

So

lari,

G.

Pic

card

o,

G.

(20

01

). P

rob

ab

ilist

ic 3

-D t

urb

ule

nce

mo

de

ling

fo

r g

ust

bu

ffe

ting

of

stru

ctu

res,

Pro

ba

bili

stic

En

gin

ee

ring

Me

cha

nic

s, (

16

), 7

3–

86

.

Tur

bule

nt w

ind

velo

city

spe

ctra

(a

naly

tical

)

Model of the Vortex shedding forces(variable with the angle of attack)

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

0.000 0.001 0.010 0.100 1.000

PSD

n [Hz]

Total Force spectrumTurbulence force spectrumVortex shedding force spectrum

Dam

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Dam

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Dam

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Hazard analysis

)(10

1)(10

10, exp)(

)(),(f

10

kk

V c

V

c

V

c

kV

The roughness length z0 is characterized by a

lognormal PDF. The mean value μz0 and the standard deviation σz0 of z0 are expressed as function of θ (assuming a slight difference between four sectors, i.e. a mean value of z0 varying between 0.08 m and 0.12 m and a COVz0 equal to 0.30).

V10 and θ are described by their joint probability

distribution function

θ

V10

IM =

θ

V10

z0

Parameters c(θ) and k(θ) are derived from NIST® wind speed database.

(Annual occurrence)

Models for tall buildings and the assessment of occupant comfort

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

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Interaction analysis IP =

gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

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gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info


462.2507.1265.0 2 rg

122if650

122if46

213

45

2

21

.T.

.T.

)Tln(

.

)Tln(

.

windr,e

windr,e

windr,e

windr,e

gr

1690if

690100if

380631 450

r

r

r

r.

r

r,e

q.

.q.

.q.

r

rr

(Obtained from time-domain analyses)

The peak response factor gr is characterized by a Gaussian distribution function

g*r = -0.2562 + 1.507 + 2.462

3.00

3.40

3.80

4.20

4.60

0.5 1 1.5 2 2.5

g*r

[%]

rg

rg

Vanmarcke (1975)

The aerodynamic coefficients CD and CL are characterized by Gaussian distributions. Mean values are expressed as a function of θ, varying from those corresponding to a square shape (for θ = 0) to those corresponding to a rhomboidal shape (for θ = 45); the coefficient of variations of CL and CD are taken equal to 0.07 and 0.05. 0

0.2

0.4

0.6

0.8

1

1.2

-90 -60 -30 0 30 60 90

Mea

n ae

rody

nam

ic c

oeff

icie

nts

θ [deg]mCD mCLμCD μCL

DC

0

0.2

0.4

0.6

0.8

1

1.2

-90 -60 -30 0 30 60 90

Mea

n ae

rody

nam

ic c

oeff

icie

nts

θ [deg]mCD mCLμCD μCL

LC

rrmp grr

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G(EDP) = ∫…∫ G(EDPIM, IP, SP) · f(IPIM,SP) · f(IM) · f(SP) · dIP · dIM · dSPMonte Carlo sim

(5000 runs)

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1B2

H

aLp

Reduced formulation

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

Structural analysis


EDP= aLp

(peak acceleration in the across wind direction)

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Risk Curve. EDP= aLp = peak acceleration in the across wind direction

The annual probabilities of exceeding the human perception thresholds for apartment and office building vibrations are 0.0576 and 0.0148 respectively.

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1B2

H

aLp

G(a

Lp )

aLp [mm/s2]

Ciampoli, M. & Petrini, F., 2012, Performance-Based Aeolian Risk assessment and reduction for tall buildings, Probabilistic Engineering Mechanics, 28 (75–84).


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TMD

Design Parameters

γ = mTMD/mtot

β = ωTMD/ ω1

ξ* = damping of TMD

90

0.125 0.145 0.165 0.185

β = 0.70 ; ξ* = 1% - 10% β = 0.80 ; ξ* = 1% - 10%

β = 0.90 ; ξ* = 1% - 10% β = 1.02 ; ξ* = 1% - 10%

β = 1.10 ; ξ* = 1% - 10% β = 1.20 ; ξ* = 1% - 10%

β = 1.30 ; ξ* = 1% - 10% Uncontrolled

Apartment Office

a Lp

[mm

/s2 ]

n [Hz]

β = ξ* =

β = ξ* =

β = ξ* =β = ξ* =

β = ξ* =

β = ξ* =

β = ξ* =

G(a

Lp )

aLp [mm/s2]

Parametric analysis Effects on risk

γ = 1/150

Aeolian Risk reduction using TMD


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Vibration and occupant comfort issues

Consequences of wind induced vibrations

in high rise buildings

-Fear and alarm

-Discomfort

-Reduced task concentration

-Dizziness, migraine and nausea

Kwok, K.C.S., Hitchcock, P.A. & Burton, M.D., 2009, Perception of vibration and occupant comfort in wind-excited tall buildings, Journal of Wind Engineering and Industrial Aerodynamics, 97(7-8), 368-380

Wind induced vibration−Damage analysis−Loss Analysis

Studies on human perception of vibration and tolerance thresholds

-Field experiments and studies in wind-excited buildings

-Motion simulator tests

-Field experiments conducted in artificially excited buildings

Mitigation measures

-Modifications to the structural system and/or the

aerodynamic shape

-Installation of vibration control devices

- Negative impressions/ publicity

- Eventually they can be an attraction

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

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O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

Damage analysis

Probabilistic damage analysis: assign a probability distribution to the perception thresholdsProcedure: obtain a pdf that assigns at each vibration level a percentage of persons that experience discomfort

Kwok, K.C.S., Hitchcock, P.A., 2008. Occupant comfort test using a tall building motion simulator. In: Proceedings of Fourth International Conference on Advances in Wind and Structures, Jeju, Korea, 28–30 May.


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O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

Loss analysis

Probabilistic loss analysis: assign a cost probability for different damagesIssues: the uncertainty in the cost relies on various factors (e.g. market trend)

DM

Non structural elements

Structural elements

Comfort

SafetyServiceabilitySafety

Serviceability

DVDirect

Indirect

(As a direct damage to the structure)

(As a consequence of the damaged structure)

IM

SPIP EDP DM DV- Direct VS indirect cost that are not

possible to account for in monetary terms.

- Initial VS life-cycle cost. In particular

regarding the evaluation of retrofitting

strategies that could improve the

serviceability performance (e.g. comfort),

by means of vibration mitigation.


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Vibration and occupant comfort issuesLoss analysis for comfort – concept (1)

Limit states implying damages in structural or non-structural components•Direct damages (tangible): costs necessary for retrofitting the structures•Direct damages (non tangible): costs due to service interruption for restoration

Uncertainties are on the unitary costs

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Limit states implying perception of low structural quality (e.g. discomfort) but not implying damages

Our proposal

Cost necessary for improving the quality to an acceptable level, e.g.a.Cost related with a change of the activity in the structure (for example, change from residential to office)

b.Cost of a TMD installation

• Direct losses: DL= ATMD * Ac + TMD installation cost

• Direct losses due to the activity interruption for retrofitting the TMD’s• Account for possible future gains due to attraction factor

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INDIRECT DAMAGES

Depending o whether we consider a new or an existing structure

• Structural design before the construction

• Existing structure

no indirect costs

costs due to service interruption

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Wind occurrence

28


Lifecycle cost analysis

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

Loss analysis

Economic investment

Economic value

Life cycle assessment

MC simulation

With TMD

With TMD retrofitted

Economic losses

Without TMD

Dam

age and loss evalu

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29






Dam

age and loss evalu

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• Occupant comfort is an important issue in the design of tall buildings. Due to the stochastic nature of wind action and wind-induced vibration, deterministic analyses are inadequate for carrying out a comfort assessment.

• The insertion of passive control devices can reduce the vibration perception of building occupants. But the effectiveness of the device must be evaluated in terms of cost (by computing the probability of exceeding acceptable values of an appropriate DV).

• Damage and loss analysis of wind-induced vibrations will be based on corroborated literature studies that provide statistics on the occupant comfort.

30

Conclusions and indications for further research

Dam

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Thank you for your attention

31

Francesco Petrini, Konstantinos Gkoumas, Franco BontempiSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica

Acknowledgements:Prof. Marcello Ciampoli, Prof. Giuliano AugustiThis study is partially supported by StroNGER s.r.l. from the fund “FILAS - POR FESR LAZIO 2007/2013 - Support for the research spin-off”.

Dam

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Additional slides

32

Francesco Petrini, Konstantinos Gkoumas, Franco BontempiSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica

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33



gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

rrmp grr

)T(log

.)T(log

winde

windegr

2

57702 Davenport

(1983)

Reliable results for a broad range of processes

Dam

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34


gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

rrmp grr

)T(log

.)T(log

winde

windegr

2

57702 Davenport

(1983)


- In the Davenport formulation the peak factor does not depend on the bandwidth of the stochastic process.

- Alternative formulations consider this dependence.

122if650

122if46

213

45

2

21

.T.

.T.

)Tln(

.

)Tln(

.

windr,e

windr,e

windr,e

windr,e

gr

)ln(2

577.0)ln(2

,

,

windre

windregT

Tr

Vanmarcke (1975)


Dam

age and loss evalu

ation in the pe

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ance

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35


gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info

rrmp grr

)T(log

.)T(log

winde

windegr

2

57702 Davenport

(1983)


- In the Davenport formulation the peak factor does not depend on the bandwidth of the stochastic process.

- Alternative formulations consider this dependence.

122if650

122if46

213

45

2

21

.T.

.T.

)Tln(

.

)Tln(

.

windr,e

windr,e

windr,e

windr,e

gr

)ln(2

577.0)ln(2

,

,

windre

windregT

Tr

Vanmarcke (1975)


rR12

rB2

rR22

n*Srr

n (Hz)

rR12

rB2

rR22

n*Srr

n (Hz)

Background (broad band process)

Resonant(narrow band

process)

Lightly damped buildings

Highly damped buildings

Dam

age and loss evalu

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36


gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info


rR12

rB2

rR22

n*Srr

n (Hz)

rR12

rB2

rR22

n*Srr

n (Hz)

Background (broad band process)

Resonant(narrow band

process)

Lightly damped buildings

Highly damped buildings

Therefore, the bandwidth parameter, and also the response peak factor must depend on the

structural damping

Dam

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37


gr

CD

CL

O

f(IM|O)

f(IM) f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interactionanalysis





DM: damage measure


SelectO, D

O: location

D: design

Environment info

Decision-making

D

f(SP|D)

f(SP)



Structural system

info


462.2507.1265.0 2 rg

122if650

122if46

213

45

2

21

.T.

.T.

)Tln(

.

)Tln(

.

windr,e

windr,e

windr,e

windr,e

gr

1690if

690100if

380631 450

r

r

r

r.

r

r,e

q.

.q.

.q.

r

rr

(Obtained from time-domain analyses)

The peak response factor gr is characterized by a Gaussian distribution function

g*r = -0.2562 + 1.507 + 2.462

3.00

3.40

3.80

4.20

4.60

0.5 1 1.5 2 2.5

g*r

[%]

rg

rg

Vanmarcke (1975)

icossar fp et al

Technology