1. Performance-based wind design of
tall buildings equipped with
viscoelastic dampers
Francesco Petrini*, Alessandro Palmeri, Michele Barbato
*Associate Researcher, francesco.petrini@uniroma1.it
Sapienza – University of Rome
Department of Structural and Geotechnical Engineering
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers

2. Performance-Based Wind
Engineering (PBWE) procedure
Intro

3. Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
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
francesco.petrini@uniroma1.it
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 profile
river
Vm
Mean wind velocity profile
Vm+ v(t)
Turbulent wind velocity profile
river
river
ENVIRONMENT EXCHANGE ZONE
3

4. Uncertainty Propagation in Wind Engineering
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Types of uncertainties
ENVIRONMENT
Wind
action
Structural
systems
Non
environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parameters
Structural parameters
Site-specific
Wind
Aerodynamic and
aeroelastic
phenomenaWind site
basic
parameters
Intensity measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
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.
4

5. PBWE Framework
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
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
Interaction
analysis
Structural analysis Damageanalysis Loss analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
system parameters
Structural
system
info
G(DV) = ∫…∫ G(DV DM) · f(DM EDP) · f(EDP IM, IP, SP) · f(IP IM,SP) ·
· f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP
Interaction
Parameters
Structural
Parameters
Intensity
measure IM IPSP
Engineering
Demand
Parameters
EDP
Damage
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
5

6. Models for tall buildings and
serviceability assessment
1

7. Serviceability of tall buildings under wind
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
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
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Displacements
Accelerations
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
7

8. Past studies (I): Case study
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Loss of serviceability
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Displacements
Accelerations
G(EDP) = ∫…∫ G(EDP IM, IP, SP) · f(IP IM,SP) · f(IM) · f(SP) · dIP · dIM · dSP
Reduced formulation
Structure
• 74 floors
• Height H=305m
• Footprint B1=B2=50m
FE Model
Approximately
• 10,000 elements
• 4,000 nodes
• 24,000 DOFs
centralcore
3dframeontheexternalperimeter
Bracingsystem
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
8

9. (dr)
9
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Loss of serviceability
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Displacements
Accelerations
dr samples
Mean values
mean st dev
Limit value
10-4 10-2 100
1010
105
100
Experimental
Analytical
n [Hz]
PSD[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
B1
B2
H
Ciampoli M, Petrini F. (2011). “Performance-Based Aeolian Risk assessment and reduction for tall buildings”, Probabilistic Engineering
Mechanics, 28, 75–84.

10. 10
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
Loss of serviceability
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Displacements
Accelerations
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
2
0
2
2
0
2
2
41
1
1
)(
m
H
Frequency domain response
Structure Wind
0.0025 Hz 0.132 Hz 0.263 Hz
1st
2nd
3rd
Height(m)Height(m)Height(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
00
2
1
2
1
1
214
21
)(
jjjj
j
fffiffifia
fi
fH
jjj
j
ffiff
fH
0
22
0
2
2
1
4
1
)(
Frequency response function in
presence of viscoelastic dampers
Assumption: devices are uniformly distributed
with the structural stiffness

11. Methodology, case study, results
2

12. 12
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Case-study and structural modeling technique
Equivalent 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
ColumnsHEB450
25@3m=75m
7 @ 4m = 28m
Beams IPE 550
Diagonals UPN 140
z
x

13. ωfexpωSωSωS jkuuuuuu kkjjkj
kj
2
kj
2
z
jk
zVzV2π
zzCω
ωf
5.0
0
uu2
x
u
200
300(x)dxR
u
1
L
z
where:
5/3
ju
ju
x2
u
uu
/zLf10.3021ω/2π
/zLfσ6.686
ωS jj
2
fri0
2
u u1.75)log(zarctan1.16σ
)z(V2π
zω
f
jm
j
13
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
Analytical model of the wind turbulence
Dynamic response in the frequency domainSpectral proper transformation
dIMIMpIMEDPGEDPG
Performance evaluation (M.Carlo)
2
00
2
1
2
1
1
214
21
)(
jjjj
j
fffiffifia
fi
fH
Presence of viscoelastic dampers
Reduced
formulation
Assumption: devices are uniformly distributed with the structural
stiffness
τ1 = relaxation time
a1j = associated viscoelastic stiffness in the jth mode of vibration

14. 14
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Single structural analysis (I): eigenvectors
Structure Wind
0.0025 Hz 0.132 Hz 0.263 Hz
1st
2nd
3rd
Height(m)Height(m)Height(m)

15. 15
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Interaction between the wind and the structure (without devices)
Structure Wind
0.0025 Hz 0.132 Hz 0.263 Hz
1st
2nd
3rd
Height(m)Height(m)Height(m)
k=1
k=2
k=3
1st 2nd 3rd 4th 5th
Structural frequencies Vs Wind power spectra Cross-modal participation matrix
Nh
M
j
Pjhjqh
,,2,1
1
22

Mj
dfffDfH
w
j
N
n
N
k
nkjkjP
,,2,1
)(
1 1
222

Standard dev of the structural displacements
Normalized mode shapes
Spectral eigenvaluesfk
hj

16. 16
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Parametric analysis for device parameters
0.5 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
00
2
1
2
1
1
214
21
)(
jjjj
j
fffiffifia
fi
fH
Frequency response function in presence of
viscoelastic dampers
Assumption: devices are uniformly distributed with the structural
stiffness
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

17. 17
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
Structural performance assessment
dIMIMpIMEDPGEDPG
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.

18. 18
Performance-basedwinddesignoftallbuildingsequippedwithviscoelasticdampers
F. Petrini. Performance-based wind design of tall buildings equipped with viscoelastic dampers.
ICOSSAR 2013, Columbia University, New York, 16-20 June 2013
francesco.petrini@uniroma1.it
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).
ACKNOWLEDGMENTS
The 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”