Presentation made by Dr. André Barbosa @ University of Porto during the OpenSees Days Portugal 2014 workshop

1. OPENSEES DAYS PORTUGAL 2014
UNCERTAINTY AND SENSITIVITY ANALYSIS
USING HPC AND HTC
André R. Barbosa
(1)
Andre.Barbosa@oregonstate.edu
(1) Assistant Professor, School of Civil and Construction Engineering, Oregon State University
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

2. Design
Alternatives
Hazard
Analysis
Introduction
Structural
Analysis
Damage
Analysis
Loss
Analysis
Decision
Making
L,D
P[IM| X,D]
ν[IM]
P[EDP | IM]
ν[EDP]
P[DM| EDP]
ν[DM]
P[DV| DM]
Select
ν[DV] L,D
Intensity
Measure
L: Location
D: Design
Engineering
Demand Par.
Damage
Measure
Decision
Variable
q Parametric sensitivity studies / optimization / design
(Luis
Celorrio-­‐Barragué)
q Probabilistic seismic demand analysis
Ø Cloud Method
Ø Incremental dynamic analysis (Filipe
Ribeiro)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 2

3. Design
Alternatives
Hazard
Analysis
Introduction
Structural
Analysis
Damage
Analysis
Loss
Analysis
Decision
Making
L,D
P[IM| X,D]
ν[IM]
P[EDP | IM]
ν[EDP]
P[DM| EDP]
ν[DM]
P[DV| DM]
Select
ν[DV] L,D
Intensity
Measure
L: Location
D: Design
Engineering
Demand Par.
Damage
Measure
Decision
Variable
q Parametric sensitivity studies
q Probabilistic seismic demand analysis
Ø Cloud Method
Ø Incremental dynamic analysis
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 3

4. Probabilistic Seismic Hazard Analysis
flt
N
=Σ ∫ ∫ ⎡⎣ > = = ⎤⎦
( ) ( ) ( )
ν im ν P IM im M m R r f m f r dm dr
IM i i i M R
i =
1
R M
Fault j
Site
AAenua8on
rela8ons
R
i i
fR(r)
IM
m0 M mu
,
i i
Magnitude
Source-­‐to-­‐site
distance
fR(r)
IM
m0 M mu
fM(m)
R
Seismic
hazard
curve
M-­‐R
deaggrega8on
IM= Sa (T1 )
Fault i
fM(m)
Fault k
R
R
( ) IM ν im
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

5. Response estimation accounting for modeling uncertainty
q PSDA
equa9on
accoun9ng
for
model
parameter
uncertainty:
ν edp P EDP edp IM f d dν im Θ = ∫ > Θ Θ Θ⋅
q Response
es9ma9on:
XLB
XM
XUB
{ } 1, , | , ,..., k lk P⎡⎣EDP > edp IM = im Θ = θ θ ⎤⎦
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
5
( ) [ | , ] ( ) ( ) EDP IM
IM
EDPLB
EDPM
EDPUB
INPUT NLTH ANALYSIS OUPUT
μθ + aσθ

6. Parameter uncertainty progagation
INPUT
Probability Distribution of RV X
XL B XM X UB
3D NL FE MODEL
TIME HISTORY ANALYSIS
Uncertainty in ground
motion
Intensity Measure (IM)
Ground motion profile (GM)
Uncertainty in structural
properties
Mass
Viscous damping
Strength
Stiffness
OUTPUT
Probability Distribution of EDP j
EDP(XL B ) EDP(XM ) EDP(XU B )
Global EDPs
U : Max Roof Displacement
A : Max Floor Acceleration.
IDR : Max Interstory Drift Ratio
Local EDPs
Member: Curvature
Strains: Reinforcing Steel
Concrete
Faggella
,
Barbosa,
Conte,
Spacone,
Restrepo,
2013
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

7. Parameter uncertainty progagation
3D
NL
FE
MODEL
TIME
HISTORY
ANALYSIS
INPUT
Probability
Distribu9on
of
Variable
X
X
LB
X
M
X
UB
OUTPUT
EDP(X
LB
)
EDP(X
M
)
EDP(X
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
UB
)
Probability
Distribu9on
of
EDP
j
TORNADO
x10 , x50 , x90
FOSM
(First Order Second Moments)
xm-as , xm , xm+as
TORNADO (swing)
EDP(x10) – EDP( x90)
FOSM
mEDP , sEDP
MEAN and STD

8. TORNADO
x10 , x50 , x90
3D NL FE MODEL
TIME HISTORY ANALYSIS
Swing =
EDP(x10) – EDP(x90)
11th value
Tornado sensitivity analysis
Median GM
0 0.5 1 1.5 2 2.5 3
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
EDP
Empirical CDF
XLB XM XUB
Procedure
1. Perform Monte Carlo
Simulation using all ground
motions (GM), fixing all
other variables at their best
estimates (median values)
(e.g. GM = 20)
2. For each EDP, determine
Median GM, and perturbe
all other variables one at a
time about their median
value
Sa
GM
Damping
Mass
Fy
Fc
Es
Ec
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

9. First Order Second Moment (FOSM) sensitivity analysis
q Mean values q Variance-covariance matrix
[ ] Σθ = ⎡⎣ρijσ iσ j ⎤⎦; i, j =1, 2,K , n T
1 2 n = μ , μ ,K , μ θ μ
q Taylor series expansion of the response EDP
( ) ( ) ( ) ( ) lin r r r rθ
θ θ θ μ θ θ θ μ θ μ = ≈ = +∇ ⋅ −
Ø Sensitivity
r r r
∂ = + Δ − − Δ
∂ Δ
Δ =
( θ ) ( μ θ ) ( μ θ
)
i i i i
θ 2
θ
θ σ
i i
a
i θ
i
XLB
μθ + aσθ
XM
XUB
Ø Covariance matrix of the response
n ⎛ ⎞ Σ = Σ ∂ r ⎜ ⎟ ⋅ + ΣΣ
ni
−
⎛ ∂ r ⎞⎛ ∂ r
⎞ ∂ ⎜ ⎟⎜⎜ ⎟⎟ ⋅ ⋅ ⎝ ⎠ ⎝ ∂ ⎠⎝ ∂ ⎠
σθ ρθ θ σθ σθ
2 i ij i j
θ θ θ
EDPLB
EDPM
EDPUB
2 1
2 2
i = 1 i i = 1 j =
1
i j
r
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
9

10. Number of FE runs for TORNADO or FOSM analyses
Median GM
11th value
0 0.5 1 1.5 2 2.5 3
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Number of FE runs:
nruns = GM+ 2⋅RV⋅EDP
( ) runs e.g., n = 20 + 2×7×10 =160
1 med MONTE CARLO
2 IMLB TORNADO
3 dLB TORNADO
4 mLB TORNADO
5 fyLB TORNADO
6 fcLB TORNADO
7 EsLB TORNADO
8 EcLB TORNADO
9 IMUB TORNADO
10 dUB TORNADO
11 mUB TORNADO
12 fyUB TORNADO
13 fcUB TORNADO
14 EsUB TORNADO
15 EcUB TORNADO
10
EZ_erzi
KB_kobj
LP_cor
LP_gav
LP_gilb
LP_lex1
LP_lgpc
LP_srtg
TO_ttr007
TO_ttrh02
CL_clyd
CL_gil6
LV_fgnr
LV_mgnp
MH_andd
MH_clyd
MH_hall
PF_cs05
PF_cs08
PF_temb
EDP 1
EDP 2
GM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
EDP
Empirical CDF
Sa
GM
Damping
Mass
Fy
Fc
Es
Ec
TORNADO
Swing = EDP(x10) – EDP(x90)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

11. Parallelization of the analyses using XSEDE
0.4
0.2
0
-0.2
Parallel Computer -0.4
0 5 10 15 20
Time (sec )
Acceleration (g)
GM 1, Par j
0.4
0.2
0
-0.2
-0.4
0 5 10 15 20
Time (sec )
Acceleration (g)
GM 2, Par j
…
0.4
Acceleration (g) SUPERCOMPUTERS
0.2
0
-0.2
-0.4
0 5 10 15 20
Time (sec )
GM N, Par j
…
OpenSees
Mul9ple
Parallel
Interpreter
(McKenna
and
Fenves
2007)
hVp://opensees.berkeley.edu/OpenSees/parallel/TNParallelProcessing.pdf
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

12. Case study: Bonefro 4 story building
Example 1: Bonefro Italy
Molise 2002 earthquake, Italy
Faggella
et
al.
2008
Severe damage to first story
infills and columns
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

13. Model Variation of the res (pcolanssse) uunndceerrt adiinffteyr ent modeling
assumptions
Bare Frame Stairs Diaphragms (2x2)
NL Infills NL Inf. Bare 1st story NL Shear columns
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

14. Variation of the response under different modeling
Model uncertainty
12
assumptions
2000
1500
Base Shear (KN)
1000
500
0
shell 2x2
infilled
bare frame
stairs
part. infilled
0 50 100 150 200
Top floor displacement (mm)
ADRS Demand Spectrum
Capacity Spectra
infilled
0.71
0.83
part. infilled
0.89
0.15
T C
0.4
2
shell 2x2
1.25
stairs
1.09
1
0.8
0.6
0.4
0.2
0
bare frame
0 0.05 0.1 0.15 0.2
Sde (m)
Se/g , F*/gm*
TH Average
Bare Frame
Diaph.2x2
Stairs
NL Inf. Bare1
NL Infills
NLshear col.
0 50 100 150 200
4
3
2
1
0
Displacements (mm)
Floor
TH Average
0 0.5 1 1.5 2
4
3
2
1
0
Floor
Drift %
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

15. Parameter uncertainty
Uncertainty in structural properties
• Mass
• Viscous damping
• Strength
• Stiffness
Ec
(GPa)
Uncertainty in ground motion
• Intensity Measure (IM)
• Ground motion profile (GM)
Distrib. MCS Logn. Norm. Norm. Logn. Norm. Norm. Norm.
XM On EDP 0.2931 0.03 0.87 451 25 210 28
COV % // 84 40 10 10 6.4 3.3 8
Probability Functions based on
• Seismic hazard
• Values adopted in the literature
• Experimental samples (material testing)
5
Ground motion and structural random variables
GM IM=Sa(T1)
(g)
Damping
(%)
Mass
(ton/m2)
Fy
(MPa)
Fc
(MPa)
Es
(GPa)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

16. 3D Response Engineering Demand Parameters (EDPs)
25
X
Y
Rz
V
G
Outputs (EDPs)
Μ, Χ
LOCAL
Member Sections Curvature
Member Sections Moment
σ , ε Steel
GLOBAL
U : Max Roof Displacement
A : Max Floor Acceleration.
IDR : Max Interstory Drift Ratio
R
Concrete core
Concrete unconf.
4001
3001
2001
1001
4008
3008
2008
121 122
1008
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

17. Median MGM
(11° value)
Outputs (EDPs)
R
Tornado for MGM, all other variables perturbed one at a time about the median
26
Results of MCS and TORNADO analysis
Monte Carlo using 20 ground motions
all other variables at medians
X
Y
Rz
V
G
3D EDPs
Floor DOFs
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

18. A : Max Floor Acceleration.
Member Sections Curvature
Member Sections Moment
Outputs (EDPs)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
25
!
X
Rz
G
Μ, Χ
σ , ε Steel
Concrete core
Concrete unconf.
LOCAL
IDR : Max Interstory Drift Ratio
1001
1008
2001
2008
3001
3008
4001
4008
121 122
R

19. Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 3D Response Engineering Demand Parameters Y
X
Rz
V
G
Μ, Χ
Member Sections Curvature
Member Sections Moment
σ , ε Steel
GLOBAL
U : Max Roof Displacement
A : Max Floor Acceleration.
Concrete core
Concrete unconf.
LOCAL
IDR : Max Interstory Drift Ratio
1001
1008
2001
2008
3001
3008
4001
4008
121 122
R
Outputs (EDPs)

20. PEER PBEE Methodology
Design
Alternatives
Hazard
Analysis
Structural
Analysis
Damage
Analysis
Loss
Analysis
Decision
Making
L,D
P[IM| X,D]
ν[IM]
P[EDP | IM]
ν[EDP]
P[DM| EDP]
ν[DM]
P[DV| DM]
Select
ν[DV] L,D
Intensity
Measure
L: Location
D: Design
Engineering
Demand Par.
Damage
Measure
Decision
Variable
q Parametric sensitivity studies
q Probabilistic seismic demand analysis
Ø Cloud Method
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 20

21. Example 2: NEHRP Building Modeling Approach
g u&&
Ø Walls: Nonlinear truss modeling approach
Ø Columns and beams: Force-based beam-column elements
Ø Diaphragms: Flexible diaphragms allowing for plastic hinge
elongation
NL
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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q Rigid-end zone
modeling for
beam-column
joints
(ASCE41-06)
REZ
NL
NL
NL
NL
q Comprehensive/significant
valida8on
at
system
level
?
…
q Comprehensive/significant
valida8on
at
component
level

22. Observed computational building behavior
EW: 0.44 %
NS: 2.93 %
N
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
22
(%)

23. “Cloud method”: Selection of earthquake records
q NGA database (total 3551 records)
Ø Mechanism: Strike-slip (1004 records)
Ø Magnitude range: 5.5 to 8 (772 records)
Ø Distance: 0 – 40 kms (203 records)
Ø Vs30: C/D range (90 records)
40
35
30
25
20
15
10
5
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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0
5.5 6.0 6.5 7.0 7.5 8.0
Source-to-site distance Rrup
Magnitude Mw
Non-pulse
Pulse
q 90
ground
mo8on
records
selected
from
14
earthquakes
6.0 6.5 7.0 7.5 8.0
Magnitude Mw
Non-pulse
Pulse

24. q Motivation
Ø Perform parametric studies that involve large-scale nonlinear models of structure or
soil-structure systems with OpenSees runs.
q Application Example/Production campaign 1
(1) Probabilistic seismic demand hazard analysis using the “cloud method”
q Some numbers for this application example
Number of NLTH analyses 180
Average duration of NLTH analysis 12 hours
Average size of output data (compressed) 1.4 GB
Estimated clock time on a desktop computer
(180x12)
2,160 hours
90 days
Estimated size of output data (180x1.4) 250 GB
1. OpenSeesMP + Xsede?
2. Local Cluster?
3. Other options?
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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OpenSees and Large Number of Runs
GM1
GM2
GM180
...

25. Possible Parallelization Options
q OpenSeesMP + MPICH2 – useful for Domain
Decomposition + Parameter Studies (addressed by other
talks in this meeting)
q Condor + OpenSees Sequential – Parameter Studies
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

26. HTCondor
q HTCondor (http://research.cs.wisc.edu/htcondor/) is a specialized workload management
system for computational-intensive jobs.
Ø Project started in 1988, directed at users with large computing needs and environments
with heterogeneous distributed resources.
Ø HTCondor is composed of 3 parts:
(1) Submit Node
Submit job
Schedd
(2) Central Manager
Collector
Negotiator
(3) Worker Node
Startd
Get results
GM1
Worker Node
Startd
…
GM180
Worker Node
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

27. Oregon State University: HTCondor + OpenSees
q “Opportunistic” computing resources:
q Student computer labs (used by students mainly during the day, and during the
term …)
q Instruction computer labs (used during the term only during classes …)
q College of Engineering at OSU: 16 computer labs (~1500 cores)
http://monhost.engr.orst.edu/labs/
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

28. Implementation of HTCondor at Oregon State University
(1) Submit Node (3) Worker Nodes
1
• 8 core Intel i7
• Windows Server
• 16 GB RAM
• SSD drive
• 2 TB HDD 15K
• 20 TB NAS
(2) Central Manager
…
• Windows 7
Premium
• 8 GB RAM
• 2 x 1GB cards
• 1 TB 7.2 K
The good news: ~ 1500cores
Communication w/ IT, Dealing w/ Job
recovery, W/O speed, data transfers, …?
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

29. Ø Perform parametric studies that involve large-scale nonlinear models of structure or
soil-structure systems with OpenSees runs.
q Some numbers for this application example
Number of NLTH analyses 180
Average duration of NLTH analysis 12 hours
Average size of output data 1.4 GB
Estimated clock time on a desktop computer
(180x12)
2,160 hours
90 days
Estimated size of output data (180x1.4) 250 GB
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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OpenSees and Large Number of Runs
Clock time
36 hours !!
q Motivation
q Application Example/Production campaign 1
(1) Probabilistic seismic demand hazard analysis using the “cloud method”

30. (a) (b) (c)
Individual Ekqe 2.5- and 97.5-perc Median
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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OpenSees
and
Parameters
Studies
PFD – peak floor displacement; PIDR – peak interstory drift ratio; PFA – peak floor absolute
acceleration

31. HTCondor and Open Science Grid
q HTCondor
(hAp://research.cs.wisc.edu/htcondor/)
is
a
specialized
workload
management
system
for
computa9onal-­‐intensive
jobs.
Ø Project
started
in
1988,
directed
at
users
with
large
compu9ng
needs
and
environments
with
heterogeneous
distributed
resources.
q Open Science Grid is a national, distributed computing grid for data-intensive research.
Ø Consortium of approx. 80 national laboratories and universities.
Ø Version of Condor for the grid
Ø Opportunistic resource usage: resources are sized for peak needs of large experiments
(Atlas, CMS, etc.), OSG allows for non-paying organizations to use their resources.
q NEES and Open Science Grid have been active partners in creating the tools and
infrastructures for making use of opportunistic resources
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 31

32. Response estimation accounting for parameter uncertainty
XLB
XM
GM Damping
XUB
μθ
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
32
EDPLB
EDPM
EDPUB
INPUT NLTH ANALYSIS OUPUT
Uncertainty in structural properties
• Mass
• Viscous damping
• Strength
• Stiffness
Engineering demand parameters
• Roof drift ratio
• Peak floor accelerations
• Shear demand in walls
• Residual deformatios..
μθ + aσθ
(%)
Mass fy
(ksi)
*fc
(ksi)
Es
(ksi)
*Ec
(ksi)
XM MCS 0.02 68.7 6.84 29000 4714
COV % // 40 10 10 10 3.3 8

33. Using Open Science Grid: Production Campaign 2
q Production campaign
(1) Probabilistic seismic demand hazard analysis using the cloud method
(2) Sensitivity of probabilistic seismic demand hazard to FE model parameters
q Some numbers for production campaign 2 (99% complete)
Number of NLTH analyses per parameter
set realization
180
Average duration of NLTH analysis 12 hours
Average size of output data 1.4 GB
Parameters considered 6
Perturbations considered 4
Estimated clock time on a desktop computer
(180x12x[(6x4x2)+1])
105,840 hours
12.1 years
Estimated size of output (compressed) data
(180x1.4x[(6x4x2)+1])
12 TB
Clock time
30 days !!
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
33

34. 30,000
OSG users: André R. Barbosa, Taylor Gugino (UCSD)
OSG support: Gabriele Garzoglio, Marko Slyz (OSG)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
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Wall clock time in HTCondor / OSG
12 clusters of 180 jobs
“Desktop”: 26,000 hours
OSG: 60,000 hours
25,000
20,000
15,000
10,000
5,000
0
Wall Time (hours)
(job
preemp9on)

35. 160,000
120,000
80,000
40,000
0
OSG users: André R. Barbosa, Taylor Gugino (UCSD)
OSG support: Gabriele Garzoglio, Marko Slyz (OSG)
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto
Wall Time (hours)
Wall clock time in HTCondor / OSG

36. Comparison Between Parallelization Options
OpenSeesMP HTCondor
Straight forward implementation of
Domain Decomposition through OpenSees
framework with parallel solving algorithm
like MUMPS
No ready built solution for large problems,
OpenSees sequential does not have
parallel solvers for large problems
MPICH2 networking setup is relatively
easier
Job management easier
Condor pool setup requires some learning
Condor requires maintenance and
administration
Very active user support through
OpenSees user community, most attractive
aspect of using OpenSeesMP
There is no specific user community as
such.
Limited tests show 190 % Speed up from
one processor to two processor
Limited tests show 153 % Speed up from
one processor to two processor
Main complication is compilation of
OpenSeesMP, really really tough!!
But once over it OpenSeesMP is really
powerfull!!!
Global implementation, if want to connect
to other grid systems.
Steep learning curve , knowledge of
networking (Computer science)
Khaled
Mashfiq,
MS
–
La
Sapienza,
Rome
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto

37. Conclusions
37
ü A workflow for running parametric studies that involve
large-scale nonlinear models of structure or soil-structure
systems with large number of parameters and OpenSees
runs has been developed for using NEEShub, Xsede, and
Open Science Grid.
ü HTCondor
ü Pegassus (see Frank Mckenna’s presentation)
ü OpenSees + Condor
q User interfaces for submitting jobs, receiving results
q Data visualization
ü Management and Analysis of Large Research Data Sets
q Where and what to store?
q Post-processing? Data compression algorithms?

38. Andre.Barbosa@oregonstate.edu
Workshop on Multi-Hazard Analysis of Structures using OpenSees – Faculty of Engineering of the University of Porto 38