Pbwe fp palmeri_barbato

Performance-based wind design of tall buildings equipped with

viscoelastic dampersFrancesco Petrini*, Alessandro Palmeri, Michele Barbato

*Associate Researcher, [email protected]

Sapienza – University of RomeDepartment of Structural and Geotechnical Engineering

Performance-based w

ind design of tall buildings equipped with viscoelastic dam

pers

mailto:[email protected]

Performance-Based Wind Engineering (PBWE) procedure

Intro

Performance-based w


pers

Uncertainty in Wind Engineering

F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.ICOSSAR 2013, Columbia University, New York, 16-20 June 2013

[email protected]

Petrini F.(2009). “A probabilistic approach to Performance-Based Wind Engineering”, Ph.D. dissertation, department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

ENVIRONMENT

Wind action

Structural systems

Non environmental

actions

EXCHANGE ZONE

Site-specific Wind

Aerodynamic and aeroelastic phenomenaWind site

basic parameters

Environmental effects (e.g.

waves)

Structural system as

modified by service loads

STRUCTURAL SYSTEM

Vm

Mean wind velocity profile

Vm+ v(t)Turbulent wind velocity profileVm

Mean wind velocity profile

Vm+ v(t)Turbulent wind velocity profile

ENVIRONMENT EXCHANGE ZONE

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Uncertainty Propagation in Wind EngineeringPerformance-based w


pers


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Types of uncertainties

ENVIRONMENT

Wind action

Structural systems

Non environmental

actions

EXCHANGE ZONE

1. Aleatory2. Epistemic3. Model

Interaction parameters

Structural parameters

Site-specific Wind

Aerodynamic and aeroelastic phenomenaWind site

basic parameters

Intensity measure



Environmental effects (e.g.

waves)

Structural system as

modified by service loads

IM IP SP

STRUCTURAL SYSTEM

SPPIMPSP,IMIPPSP,IP,IMP

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

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PBWE FrameworkPerformance-based w


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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

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

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 IPSP

Engineering Demand Parameters

EDPDamage Measure DM

Decision Variable DV

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

G(·|·) is a conditional

complementary

cumulative

distribution function

f(·|·) is a conditional

probability density

function = progress with respect to the Performance-Based Seismic Design

*

* *

Extension of the Performance-Based

Seismic Design procedure proposed by PEER Research center

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Models for tall buildings and serviceability assessment

1

Serviceability of tall buildings under windPerformance-based w


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Tamura, Y. (2009). Wind and tall buildings, Proceedings of the Fifth European & African Conference on Wind Engineering (EACWE 5), Florence, Italy, July 19-23, 2009..

Loss of serviceability

Loss

of i

nteg

rity

of

non-

stru

ctur

al

elem

ents

Moti

on p

erce

ption

by

bui

ldin

g oc

cupa

nts

Dis

plac

emen

ts

Acce

lera

tions

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

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

X

Z

Y

θ

B1B2

H

7


Past studies (I): Case studyPerformance-based w


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Loss

of i

nteg

rity

of

non-

stru

ctur

al

elem

ents

Moti

on p

erce

ption

by

bui

ldin

g oc

cupa

nts

Dis

plac

emen

ts

Acce

lera

tions

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

Reduced formulation

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

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

cent

ral c

ore

3d fr

ame

on th

e ex

tern

al p

erim

eter

Brac

ing

syst

em

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

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

X

Z

Y

θ

B1B2

H

8


(dr)

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Loss

of i

nteg

rity

of

non-

stru

ctur

al

elem

ents

Moti

on p

erce

ption

by

bui

ldin

g oc

cupa

nts

Dis

plac

emen

ts

Acce

lera

tions

dr samplesMean valuesmean ±st dev

Limit value

10-4 10-2 100

1010

105

100

Experimental

Analytical

n [Hz]

PS

D [

N2 /

Hz]

Vortex shedding effect

G(

dr|θ

=0,

ξ=0.

4%)

(dr)

Annual occurrenceMax drift samples

Past studies (II): integrity

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

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

X

Z

Y

θ

B1B2

H

Ciampoli M, Petrini F. (2011). “Performance-Based Aeolian Risk assessment and reduction for tall buildings”, Probabilistic Engineering Mechanics, 28, 75–84.


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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 i

nteg

rity

of

non-

stru

ctur

al

elem

ents

Moti

on p

erce

ption

by

bui

ldin

g oc

cupa

nts

Dis

plac

emen

ts

Acce

lera

tions

This paper: tall buildings and viscoelastic dampers

[2] Carassale, L., Piccardo, G., Solari, G. (2001), Double modal transformation and wind engineering applications, Journal of Engineering Mechanics 127 (5), pp. 432-439, 2001.

Equivalent cantilever beam model (1)

)(),(

)(),()(),(2

222

hS

HVchSHhS

uu

mxDDDrr tttt

2

0

2

2

20

2

20

2

2

41

1

1)(

mH

Frequency domain response

Structure Wind

0.0025 Hz 0.132 Hz 0.263 Hz

1st

2nd

3rd

Hei

ght (

m)

Hei

ght (

m)

Hei

ght (

m)

Double-modal transformation (2)

[1] Chrysanthakopoulos, C., Bazeos, N., Beskos, D.E. (2006). Approximate formulae for natural periods of plane steel frames. Journal of Constructional Steel Research 62: 592-604

Structure Wind

2

002

12

1

1

214

21

)(

jjjj

j

fffiffifia

fi

fH

jjj

jffiff

fH0

220

2 2

1

4

1)(

Frequency response function in presence of viscoelastic dampers

Assumption: devices are uniformly distributed with the structural stiffness


Methodology, case study, results2

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Case-study and structural modeling techniqueEquivalent cantilever beam model

Chrysanthakopoulos, C., Bazeos, N., Beskos, D.E. (2006). Approximate formulae for natural periods of plane steel frames. Journal of Constructional Steel Research 62: 592-604

Colu

mns

H

EB 4

50

25 @

3m

= 7

5m

7 @ 4m = 28m

Beams IPE 550

Diagonals UPN 140

z

x


ωfexpωSωSωS jkuuuuuu kkjjkj

kj

2kj

2z

jkzVzV2π

zzCωωf

5.0

0

uu2xu 200

300(x)dxRu

1L

z

where:

5/3

ju

jux2

uuu

/zLf10.3021ω/2π

/zLfσ6.686ωS

jj

2fri0

2u u1.75)log(zarctan1.16σ

)z(V2π

zωf

jm

j

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Performance-based w


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Analytical model of the wind turbulence

Dynamic response in the frequency domainSpectral proper transformation

dIM

IMpIMEDPGEDPG

Performance evaluation (M.Carlo)

2

002

12

1

1

214

21)(

jjjj

jfffiffifia

fifH

Presence of viscoelastic dampers

Reduced formulation


τ1 = relaxation time a1j = associated viscoelastic stiffness in the jth mode of vibration

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Single structural analysis (I): eigenvectors

Structure Wind

0.0025 Hz 0.132 Hz 0.263 Hz

1st

2nd

3rd

Hei

ght (

m)

Hei

ght (

m)

Hei

ght (

m)


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Interaction between the wind and the structure (without devices)

Structure Wind

0.0025 Hz 0.132 Hz 0.263 Hz

1st

2nd

3rd

Hei

ght (

m)

Hei

ght (

m)

Hei

ght (

m)

k=1k=2

k=3

1st 2nd 3rd 4th 5th

Structural frequencies Vs Wind power spectra Cross-modal participation matrix

NhM

jPjhjqh

,,2,11

22

Mj

dfffDfHw

j

N

n

N

knkjkjP

,,2,1

)(1 1

222

Standard dev of the structural displacements

Normalized mode shapes

Spectral eigenvalues fkhj


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Parametric analysis for device parameters0.5 s1.01.52.0

Uref=15 m/s

No dissip

5 m/s 10 m/s 15 m/s 20 m/s

τ1=2.0 s

5 m/s 10 m/s 15 m/s 20 m/s

2

002

12

1

1

214

21)(

jjjj

jfffiffifia

fifH

Frequency response function in presence of viscoelastic dampers


A parametric analysis has been conducted in order to assess the optimal value of the parameter τ1. a1,j

has been fixed equal to 5*(2πfj)2

-50%

Effect of viscoelastic dampers


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Structural performance assessment dIM

IMpIMEDPGEDPG

The standard deviation of the displacement at the top of the building is assumed as EDP, while the wind speed at 10m of height from the surface (U10) is chosen as IM.A Weibull distribution with shape and scale parameter 2.02 and 6.2 is adopted for U10.

A total of 500 samples have been generated for evaluating the risk curves G(EDP) for the structure both with and without the presence of dissipative devices.


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Conclusions• The adopted analytical methods are very efficient in terms of computational

costs, especially if the analysis are performed in the frequency domain.

• The use of viscoelastic dampers seems to be very efficient in reducing the displacements of the building under wind.

• Further investigations are required to assess the impact of different assumptions in the analysis process, namely:

• i) neglecting the damping coupling between different modes of vibration (i.e., assuming classical damping);

• ii) having more random variables (e.g., the structural damping, the viscoelastic damping, the drag coefficients);

• iii) selecting different engineering demand parameters (EDPs), associated with various limit states;

• iv) developing the necessary steps for the evaluation of probabilistic evaluation of the performances in monetary terms (loss analysis).

ACKNOWLEDGMENTSThe first author would like to acknowledge the financial support by StroNGER s.r.l. from the fund “FILAS - POR FESR LAZIO 2007/2013 - Support for the research spin-off”


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