corso di dottorato su ottimizzazione strutturale: robustezza strutturale - gkoumas
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Introduzione ai concetti legati alla robustezza strutturale nell'ambito del corso di dottorato di OTTIMIZZAZIONE STRUTTURALE Roma, 21 maggio 2015TRANSCRIPT
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
“Structural robustness: definitions, examples and consequence based assessment of structures”
Konstantinos Gkoumas, Ph.D., P.E.
Corso di Dottorato: introduzio ne all'ottimi zzazionestruttural e
Prof.-Ing. Franco Bontempi
Dipartimento di Ingegneria Strutturale e Geotecnica
Dottorato di Ricerca in Ingegneria delle Strutture
Rome, June 21 2014
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Index
Ottimizzazione Strutturale
Ottimizzazione Strutturale
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Personal
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Ronan Point Tower Block– May 16, 1968
Description:- apartments building;
- built between 1966 and 1968;
- 64 m tall with 22 story;
- walls, floors, and staircases was precast
concrete;
- each floor was supported directly by the walls
in the lower stories, (bearing walls system).
The event:- May 16, 1968 a gas explosion blew out an
outer panel of the 18th floor,
- the loss of the bearing wall causes the
progressive collapse of the upper floors,
- the impact of the upper floors’ debris caused
the progressive collapse of the lower floors.
Cause Damage Pr. Collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Description:- apartments building;
- precast concrete wall and floor components
was the structural bearing system;
- ductile detailing and effective ties between
the precast components.
Cause Damage Pr. Collapse
The event:- June 25, 1996 9 tons of
TNTeq detonated in
front of the building;
- the exterior wall was
entirely destroyed;
- collapse did not
progress beyond areas
of first damage.
Khobar Towers Bombing – June 25, 1996
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Description:- office facility for the Deutsche Bank in
Manhattan;
- constructed in the early ‘70s in steel-framed
structure moment connected, 130 m tall, 40
story and 2 subterranean levels;
The event:- On September 11, 2011, the WTC towers
debris impact on a building’s façade,
- heavy damage between the 9th and the 23rd
floor, the column was lost from the 9th and
the 18th floor;
- the framing system was able to support
and redistribute the loads.
Deutsche Bank Building – September 11, 2001
Cause Damage Pr. Collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Probability of progressive collapse from an abnormal event
P(F) = P(D|H) P(F|DH)P(H) x x
damage is caused in
the structure
damage spreads in
the structureoccurrence of
critical event
occurrence of broad
or global collapse
STRUCTURAL INTEGRITY (ISO/FDS 2394)
COLLAPSE RESISTANCE (Starossek&Wolff 2005)
Faber (2006)
STRUCTURALNON STRUCTURAL
MEASURES
HAZARD
References: Ellingwood, B.R. and Dusenberry, D.O. (2005), “Building design for abnormal loads and progressive
collapse”, Comput-Aided Civ. Inf., 20(3), 194-205.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Reference: Bontempi, F. (2005) Frameworks for structural analysis, In: Innovation in Civil and Structural
Engineering Topping, BHV ed., pp. 1-24
HPLCHigh Probability –
Low Consequences
LPHCLow Probability –
High Consequences
ComplexityNon linear issues and
interaction mechanisms
De
sig
n a
pp
roa
ch:
Sto
cha
stic
De
term
inis
tic
QUALITATIVE RISK
ANALYSIS
PROBABILISTIC
RISK ANALYSIS
PRAGMATIC
ANALYSIS OF
RISK SCENARIOS
Secondary
design
Primary
design
Low Probability – High Consequences Events
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References: Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.).
London: Penguin. p. 400. ISBN 1-84614045-5.
A Black Swan is an event with the following three attributes.
1. First, it is an outlier, as it lies outside the realm of regular expectations,
because nothing in the past can convincingly point to its possibility.
Rarity -The event is a surprise (to the observer).
2. Second, it carries an extreme 'impact'.
Extreme “impact” - the event has a major effect.
3. Third, in spite of its outlier status, human nature makes us concoct
explanations for its occurrence after the fact, making it explainable and
predictable.
Retrospective (though not prospective) predictability - After the first
recorded instance of the event, it is rationalized by hindsight, as if it could
have been expected; that is, the relevant data were available but
unaccounted for in risk mitigation programs. The same is true for the
personal perception by individuals.
Black Swans
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
QUALITY
DAMAGE or ERROR
REQUIRED PERFORMANCE
NOMINAL
PERFORMANCE
NOMINAL SITUATION
Structural Robustness
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• Capacity of a construction to exhibit regulardecrease of its structural quality as a consequenceof negative causes.
• It implies:
a) some smoothness of the decrease ofstructural performance due to negativeevents (intensive feature);
b) some limited spatial spread of therupture (extensive feature).
Structural Robustness
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Qualitative definitions of structural robustness
[EN 1991-1-7: 2006 ]: ability of a structure to withstand actions due
to fires, explosions, impacts or consequences
of human errors, without suffering damages
disproportionate to the triggering causes
[SEI 2007,
Beton Kalender 2008]: insensitivity of the structure to local failure
structure B
d
P
s
STRUCTURE B:
P
s
ROBUSTNESS CURVES
P (performance)
structure A
STRUCTURE A
damaged
integer
DP
damaged
more performant, less resistant
integer
(damage level)
DPDP
more performant, less robust less performant, more robust
Structural Robustness
A B
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Co
mm
on
UL
S &
SL
S
Ver
ific
ati
on
Fo
rma
t
Structural Robustness
Assessment
1st level:
Material Point
2nd level:
Element
Section
3rd level:
Structural
Element
4th level:
Structural
System
Structural robustness in design
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
STRUCTURAL DESIGN
PRIMARY SECONDARY TERTIARY
LO
AD
S
DEAD X
LIVE X
SNOW X
EARTHQUAKE X
FIRE X X
EXPLOSIONS X X
“BLACK SWAN” X
Member-basedstructural design
Consequence-basedstructural design
Black Swan event:
- unpredictable,
- large impact on community,
- easy to predict after its occurrence.
References:
Nafday, AM. (2011) Consequence-based structural
design approach for black swan events. Structural
Safety, 33(1): 108-114.
Structural robustness in design
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Uncertainty in the likelihood that
the harmful consequences of a
particular event will be realized
Uncertainty in the consequences
related to the specific event
Primary
designSecondary
design
Tertiary
design
Structural robustness in design
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
STRUCTURE
& LOADS
Collapse
Mechanism
NO SWAY
“IMPLOSION”
OF THE
STRUCTURE
“EXPLOSION”
OF THE
STRUCTURE
is a process in which
objects are destroyed by
collapsing on themselves
is a process
NOT CONFINED
SWAY
Bad VS Good collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Initial load-bearing element failure that
triggers the rigid fall of a part of the
structure onto another and leads to a
sequential impacts on the rest of the
structure, that collapses on itself.
Characteristic feature is the force
redistribution into alternative paths,
impulsive loading due to sudden element
failure and force concentration in elements
to fail next.
Zipper Domino
Section Instability Mixed
Pancake
Initial cross-section cut and stress
concentration that cause the rupture of
further cross-sectional parts (fast fracture)
and failure progression throughout the
entire section.
Initial element rigid overturning and
falling over another element, that, by
means of transformation of potential into
kinetic energy, trigger the overturning of
the following element.
The destabilization of some load-carrying
elements in compression due to an initial
failure of stabilizing elements can trigger a
failure progression throughout the
structure.
Some collapses are less amenable to
generalization because the relative
importance of the contributing basic
categories of collapse can vary and
combine in progression of failures.
- DOMINO + PANCAKE
(e.g. A.P.Murrah Building, Building
during Izmit Earquake)
- ZIPPER + INSTABILITY
(e.g. cable-stayed bridges)
Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapse
susceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)
Collapse types
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Initial load-bearing element failure that
triggers the rigid fall of a part of the
structure onto another and leads to a
sequential impacts on the rest of the
structure, that collapses on itself.
Characteristic feature is the force
redistribution into alternative paths,
impulsive loading due to sudden element
failure and force concentration in elements
to fail next.
Zipper Domino
Section Instability Mixed
Pancake
Initial cross-section cut and stress
concentration that cause the rupture of
further cross-sectional parts (fast fracture)
and failure progression throughout the
entire section.
Initial element rigid overturning and
falling over another element, that, by
means of transformation of potential into
kinetic energy, trigger the overturning of
the following element.
The destabilization of some load-carrying
elements in compression due to an initial
failure of stabilizing elements can trigger a
failure progression throughout the
structure.
Some collapses are less amenable to
generalization because the relative
importance of the contributing basic
categories of collapse can vary and
combine in progression of failures.
- DOMINO + PANCAKE
(e.g. A.P.Murrah Building, Building
during Izmit Earquake)
- ZIPPER + INSTABILITY
(e.g. cable-stayed bridges)
Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapse
susceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)
Collapse types
Islamabad Earthquake 2005
Münsterland, 2005
Viaduct after earthquakeIzmit Earthquake
1999
Tanker S.S. Schenectady, 1941
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
The Boeing B-17 Flying Fortress collided with another aircraft during World War II and, although
sustaining large amount of structural damage, landed safely, due to the high redundancy of the
fuselage connections.
Design Strategy #1: Continuity (robust behavior-redundancy)
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
On July 1945 a B-25 bomber crashed into the Empire State Building, The impact of the plane
created a 5.5x6 m hole in the side of the tower. This crash caused extensive damage to the
masonry exterior and the interior steel structure of the building.
The 278 m building was rocked by the impact but resist the impact in consequence of the
intrinsic redundancy of its framed system.
Plane crash on the Empire
State Building, 1945
Design Strategy #1: Continuity (robust behavior-redundancy)
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Design Strategy #2: Segmentation (Compartmentalization)
A service-induced damage led to explosive decompression and loss of large portion of fuselage
skin when small fatigue crack suddenly linked together. The subsequent fracture was eventually
arrested by fuselage frame structure and the craft landed safely.
Aloha Boeing 737, April 1988
(compartmentalization by strengthening)
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Design Strategy #2: Segmentation (Compartmentalization)
The partial collapse, started in the roof and due design and execution errors, stoped at the two joints
which separated the collapsing section from the adjacent structures.
A higher continuity could have unlikely sustained the forces during collapse, since the construction
deficiencies affected also adjacent sections.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References:
(EN 1991-1-7 2006): "Eurocode 1 – Actions on structures, Part 1-7: General actions – accidental actions." Comité
European de Normalization (CEN).
(Bontempi F, Giuliani L, Gkoumas K, 2007): "Handling the exceptions: robustness assessment of a complex structural
system.“, Invited Lecture, Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.
(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.
Definitions:
1- "The ability of a structure to withstand events like fire, explosions,
impact or the consequences of human error without being damaged to an
extent disproportionate to the original cause." (EN 1991-1-7 2006)
2- "The robustness of a structure, intended as its ability not to suffer
disproportionate damages as a result of limited initial failure, is an
intrinsic requirement, inherent to the structural system organization."
(Bontempi F, Giuliani L, Gkoumas K, 2007)
3- “Robustness is defined as insensitivity to local failure." (Starossek U,
2009)
Structural Robustness
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References:
(ASCE 7-05 2005): "Minimum design loads for buildings and other structures." American Society of Civil Engineers
(ASCE).
(GSA 2003): "Progressive collapse analysis and design guidelines for new federal office buildings and major
modernization projects." General Services Administration (GSA).
(UFC 4-010-01 2003): "DoD minimum antiterrorism standards for buildings." Department of Defense (DoD).
Progressive Collapse
Definitions:
1-"Progressive collapse is defined as the spread of an initial local failure
from element to element resulting, eventually, in the collapse of an entire
structure or a disproportionate large part of it." (ASCE 7-05 2005)
2- "A progressive collapse is a situation where local failure of a primary
structural component leads to the collapse of adjoining members which, in
turn, leads to additional collapse. Hence, the total collapse is
disproportionate to the original cause." (GSA 2003)
3-"Progressive collapse: a chain reaction failure of building members to an
extent disproportionate to the original localized damage." (UFC 4-010-01
2003)
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References:
Arup (2011), Review of international research on structural robustness and disproportionate collapse, London,
Department for Communities and Local Government.
Starossek, U. and Haberland, M. (2010), “Disproportionate Collapse: Terminology and Procedures”, J. Perf. Constr.
Fac., 24(6), 519-528.
Observations:
− A progressive collapse is one which develops in a progressive manner akin to the collapse
of a row of dominos.
− A disproportionate collapse is one which is judged (by some measure defined by the
observer) to be disproportionate to the initial cause. This is merely a judgement made on
observations of the consequences of the damage which results from the initiating events.
− A collapse may be progressive in nature but not necessarily disproportionate in its extents,
for example if arrested after it progresses through a number of structural bays. Vice versa, a
collapse may be disproportionate but not necessarily progressive if, for example, the
collapse is limited in its extents to a single structural bay but the structural bays are large.
− The terms of disproportionate collapse and progressive collapse are often used
interchangeably because disproportionate collapse often occurs in a progressive manner
and progressive collapse can be disproportionate.
Progressive Collapse VS Disproportionate Collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Robustness and collapse resistance in a dependability framework
Sgambi, L., Gkoumas, K. and Bontempi, F. (2012), “Genetic
algorithms for the dependability assurance in the design of a long-
span suspension bridge”, Comput-Aided Civ. Inf., 27(9), 655-675.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
The currently available design strategies and methods to
prevent disproportionate collapse are as follows:
− Prevent local failure of key elements (direct design)
− Specific local resistance
− Non-structural protective measures
− Presume local failure (direct design)
− Alternative load paths
− Isolation by segmentation
− Prescriptive design rules (indirect design)
Reference:
Starossek, U. 2008. Collapse resistance and robustness of bridges. IABMAS’08: 4th International Conference on
Bridge Maintenance, Safety, and Management Seoul, Korea, July 13-17, 2008
Measures against disproportionate collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Reference:
Giuliani, L., 2012. Structural safety in case of extreme actions. International Journal of Lifecycle Performance Engineering
IJLCPE Special Issue on: "Performance and Robustness of Complex Structural Systems", Guest Editor Franco Bontempi, ISSN
(Online): 2043-8656 - ISSN (Print): 2043-8648.
Design strategies against progressive collapse
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
RISK-BASED[Faber, 2005]
R
Iinddir
dirrob
R
R
+=
direct risk
indirect riskDAMAGE-BASED
∑=
=n
1i'
i
i
)K(tr
)K(tr.Deg.Stiff
ithelement stiffness matrix(integer state)
damaged
elements
ithelement stiffness
matrix (damaged state)
[Yan&Chang, 2006] [Biondini &
Frangopol, 2008]
1
0
∆Φ
∆Φρ =Φ
∆ energy between intact
and damaged system
(backward pseudo-loads)
∆ energy between intact
and damaged system
(forward pseudo-loads)
� Indirect
Risk
� Direct
Risk
� Indirect
Risk
� Direct
Risk
Reference:
Olmati, P., Brando, F., Gkoumas, K. “Robustness assessment of a Steel Truss Bridge”, ASCE/SEI Structures Congress,
Pittsburgh, Pennsylvania, May 2-4, 2013.
B
A Withstand actions, events
Withstand damages
Structural Robustness assessment
TOPOLOGY-BASED ENERGY-BASEDOther:
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
[Baker et al. 2008]
R
Iinddir
dirrob
R
R
+=
direct risk
indirect risk
Reference:
Baker J.W., Schubert M., Faber M.H., (2008). On the Assessment of Robustness, Journal of Structural Safety, Volume
30, Issue 3, pp. 253-267, DOI:10.1016/j.strusafe.2006.11.004
“A robust system is considered to be one where indirect
risks do not contribute significantly to the total system
risk”
Rdir˃˃Rind
Rdir: associati con il danni iniziali
Rind: associati con danni successivi
EXBD: Exposure before damage
D � : Damage
D : No Damage
F : Probability of system failure
Cdir : Direct consequences
Cind: Indirect consequences
Risk Based Structural Robustness assessment
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
���������
− ���������
≥ 0member-based design
� − � ≥ 0limit state design
Resistance (probabilistic) Solicitation (probabilistic)
Resistance (design values) Solicitation (design values)
(1 − ���������)��
�������−��
�������≥ 0
Member consequence factor based design
0 ≤ �� ≤ 1
• Cf quantifies the influence that a loss of a structural element has on the load carrying capacity.
• Cf provides to the single structural member an additional load carrying capacity, in function of the
nominal design (not extreme) loads that can be used for contrasting unexpected and extreme loads.
• Essentially, if Cf tends to 1, the member is more likely to be important to the structural system;
instead if Cf tends to 0, the member is more likely to be unimportant to the structural system.
Member consequence factor and robustness assessment
0EγγRγγ kEMEk
1
Rd
1
MR ≥−∑−−
0E)R(*)C1( kEdMEk
1
Rd
1
MRf ≥γγ−γγ− ∑−−
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• The structure is subjected to a set of damage scenarios and the consequence of the
damages is evaluated by the member consequence factor (���������) that for
convenience can be easily expressed in percentage.
• For damage scenario is intended the failure of one or more structural elements.
• Robustness can be expressed as the complement to 100 of ���������, intended as the
effective coefficient that affects directly the resistance.
• ���������is evaluated by the maximum percentage difference of the structural stiffness
matrix eigenvalues of the damaged and undamaged configurations of the structure.
��������� = ���
���� − ��
���
���� 100
� !"#
where, ����and ��
���are respectively the i-th eigenvalue of the structural stiffness
matrix in the undamaged and damaged configuration, and N is the total number of the
eigenvalues.
Member consequence factor and robustness assessment
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• The corresponding robustness index (��������) is therefore defined as:
��������=1 - ���������
• Values of Cf close to 100% mean that the failure of the structural member most
likely causes a global structural collapse.
• Low values of Cf do not necessarily mean that the structure survives after the failure
of the structural member: this is something that must be established by additional
analysis that considers the loss of the specific structural member.
• A value of Cf close to 0% means that the structure has a good structural
robustness.
The proposed method for computing the consequence factors, for different reasons,
should not be used for:
1. Structures that have high concentrated masses (especially non-structural masses) in
a particular zone; and,
2. Structures that have cable structural system (e.g., tensile structures, suspension
bridges).
Member consequence factor and robustness assessment
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Cost of robustness measures ≤ Reduction of failure consequences
• The objective function for optimization may be very complex
and depend on the type of the structural system, robustness
measures, characteristics of failure consequences and
probabilities of occurrence and intensities of various hazards.
• If the total cost of robustness measures exceeds the reduction
in failure consequences, then the system may be considered as
robust but uneconomic. In such a situation, probabilistic
methods of risk assessment may be effectively used
Reference:
COST Action TU0601 Robustness of Structures STRUCTURAL ROBUSTNESS DESIGN FOR PRACTISING
ENGINEERS. EUROPEAN COOPERATION IN SCIENCE AND TECHNOLOGY, Editor T. D. Gerard Canisius.
Robustness in Optimization
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Reference:
Casciati, S. and Faravelli, L. (2008) Building a Robustness Index. Robustness of Structures COST Action TU0601,
1st Workshop, February 4-5, ETH Zurich, Switzerland.
Robustness in Optimization
Example: Hierarchy of the failure modes (“weak beam/strong column”)
...develop the less catastrophic failure
modes first.
...ranking the failure modes in terms of
a hierarchy in such a way that the less
harmful ones are generated at lower
loading levels
Objective function:
Robustness term:Pfi: probability of the i-th failure mode
m: number of failure modes
A robust structure requires the plastic moment of the column, MPc, being larger than the
one of the beam, MPb; that is, Z = MPc– MPb≥ 0
µc, σc, µb, σb: means and the standard deviations of the plastic moments of the columns and
of the beam, respectively.
To ensure robustness, the index I needs to be kept positive. The objective is, therefore, to
minimize FI=-I.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Stiffness matrix
Kun λiun
Eigenvalues
Kdam λidam
Consequence factor
Robustness indexRscenario= 100 - Cfscenario
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
−=
λ
λ−λ=
Structural Robustness assessment - overview
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
ka
kb
x
yK%& =
10 0
0 10
C(!1 = 0% C(*
1 = 30%
R1 = 70%
R1 = 100 − C(1
N: total eigenvalues number
i: single eigenvalue number
a and b: elements
a
b
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
−=
λ
λ−λ=
K./0 =10 0
0 7Scenario 1
Single damage – analytic calculation
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• Single bay frame structure with a diagonal beam brace, composed in total of 5
members
• IPE 300, S235 steel, one meter length, pinned boundary conditions.
The evaluated scenarios consist in the removal of elements 1, 2 and 3 sequentially, so the
damage is cumulative: this means that the each scenario includes the damage from the
previous one.
Cumulative damage – numerical assessment
DSj = Σi=(1-j) di
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Cumulative damage – numerical assessment
• star-shaped structure – 8 members - pipe cross section - 20 centimeters outside
diameter - 20 millimeters thickness - S235 steel.
• members 1, 3, 5, and 7 are 0.5 meters long and members 2, 4, 6, and 8 are 0.7
meters long.All the members are connected to each other by a fixed type connection. Also the boundary
conditions are of the fixed type and the structure is plane.
DSj = Σi=(1-j) di
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• Built 1967
• 3 spans, 1067 feet long
• 1977 – new wearing surface
• 1998 – curbs and railings replaced
I-35 West Bridge, Minneapolis, MN
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
North Downtown
I-35 West Bridge, Minneapolis, MNP
hoto
fro
m a
ircr
aft
flyin
g o
ver
hea
d.
• At 6:05 pm on August 1st 2007 Bridge Collapsed
• 13 People killed & approximately 145 Injured
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 W bridge
I-35 West Bridge, Minneapolis, MN
NTSB 2007
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Undamaged
Damaged
scenario
I-35 West Bridge, Minneapolis, MN – damage scenarios
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN – damage scenarios
3D
2D
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
d1d2d3
d4
d5d7
d6
37
59
42 4535 38
23
63
41
58 5565 62
77
0
20
40
60
80
100
1 2 3 4 5 6 7
Ro
bu
stn
ess
%
ScenarioCf max Robustness
1 2 3 4 5 6 7
ScenarioCf max Robustness
Damage scenariod1 d2 d3 d4 d5 d6 d7
DSj = di
I-35 West Bridge, Minneapolis, MN – single damage
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
d1
d2d3
d4
d5d7
d6
83 87 88
5360
86
64
17 13 12
4740
14
36
0
20
40
60
80
100
1 2 3 4 5 6 7
Ro
bust
nes
s %
ScenarioCf max Robustness
Damage scenariod1 d2 d3 d4 d5 d6 d7
I-35 West Bridge, Minneapolis, MN/ enhanced– single damage
DSj = di
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Black
Swan
Vulnerability
Cause
Damage
Index
• Significant collapse cases
• LPHC events and Black Swans
• Structural robustness in qualitative terms
• Structural robustness in civil engineering
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• Measures against progressive collapse
• Quantification of robustness
• Robustness and optimization
• Member consequence factor
• Assessment of simple structures
• Assessment of complex structures
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References
Alashker, Y., Li, H. and El-Tawil, S. (2011), “Approximations in Progressive Collapse Modeling”, J. Struct. Eng.- ASCE, 137(9), 914-924.
Arup (2011), Review of international research on structural robustness and disproportionate collapse, London: Department forCommunities and Local Government.
ASCE 7-05 (2005), Minimum design loads for buildings and other structures, American Society of Civil Engineers (ASCE).
Biondini, F. and Frangopol, D. (2009), “Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion”,Struct. Saf., 31(6), 483-489.
Biondini, F., Frangopol, D.M. and Restelli, S. (2008), “On structural robustness, redundancy and static indeterminancy”, Proceedings ofthe 2008 Structures Congress, April 24-26, 2008, Vancouver, BC, Canada.
Bontempi, F. and Giuliani, L. (2008), “Nonlinear dynamic analysis for the structural robustness assessment of a complex structuralsystem”, Proceedings of the 2008 Structures Congress, April 24-26, 2008, Vancouver, BC, Canada.
Bontempi, F., Giuliani, L. and Gkoumas, K. (2007), “Handling the exceptions: dependability of systems and structural robustness”, InvitedLecture, Proceedings of the 3rd International Conference on Structural Engineering, Mechanics and Computation (SEMC), Cape Town,South Africa, September 10-12.
Brando, F., Testa, R.B. and Bontempi, F. (2010), “Multilevel structural analysis for robustness assessment of a steel truss bridge”, BridgeMaintenance, Safety, Management and Life-Cycle Optimization - Frangopol, Sause and Kusko (eds), Taylor & Francis Group, London,ISBN 978-0-415-87786-2.
Canisius, T.D.G., Sorensen, J.D. and Baker, J.W. (2007), “Robustness of structural systems - A new focus for the Joint Committee onStructural Safety (JCSS)”, Proceedings of the 10th Int. Conf. on Applications of Statistics and Probability in Civil Engineering(ICASP10), Taylor and Francis, London.
Casciati, S. and Faravelli, L. (2008) Building a Robustness Index. Robustness of Structures COST Action TU0601, 1st Workshop,February 4-5, 2008, ETH Zurich, Zurich, Switzerland.
Cha, E. J. and Ellingwood, B. R. (2012), “Risk-averse decision-making for civil infrastructure exposed to low-probability, high-consequence events”, Reliab. Eng. Syst. Safe., 104(1), 27-35.
Choi, J-h. and Chang, D-k. (2009), “Prevention of progressive collapse for building structures to member disappearance by accidentalactions”, J. Loss Prevent. Proc., 22(6), 1016-1019.
COST (2011), TU0601 - Structural Robustness Design for Practising Engineers, Canisius, T.D.G. (Editor).
Crosti, C. and Duthinh, D. (2012), “Simplified gusset plate model for failure prediction of truss bridges”, Bridge Maintenance, Safety,Management, Resilience and Sustainability - Proceedings of the 6th International Conference on Bridge Maintenance, Safety andManagement, IABMAS 2012, Italy, Stresa, 8-12 July 2012.
Crosti, C., Duthinh, D. and Simiu, E. (2011), “Risk consistency and synergy in multihazard design”, J. Struct. Eng.- ASCE, 137(8), 844-849.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References
DoD - Department of Defense (2009), Unified Facilities Criteria (UFC). Report No. UFC 4-023-03: Design of buildings to resistprogressive collapse. Washington DC: National Institute of Building Sciences.
Ellingwood, B. (2002), “Load and resistance factor criteria for progressive collapse design”, Proceedings of Workshop on Prevention ofProgressive Collapse, National Institute of Building Sciences, Washington, D.C
Ellingwood, B.R. and Dusenberry, D.O. (2005), “Building design for abnormal loads and progressive collapse”, Comput-Aided Civ. Inf.,20(3), 194-205.
Ellingwood, B.R., Smilowitz, R., Dusenberry, D.O., Duthinh, D. and Carino, N.J. (2007), Report No. NISTIR 7396: Best practices forreducing the potential for progressive collapse in buildings. Washington DC: National Institute of Standards and Technology (NIST)
EN 1990 (2002), Eurocode - Basis of structural design.
Faber, M.H. and Stewart, M.G. (2003), “Risk assessment for civil engineering facilities: critical overview and discussion”, Reliab. Eng.Syst. Safe., 80(2), 173-184.
FHWA (2011), Framework for Improving Resilience of Bridge Design, Publication No IF-11-016.
Galal, K. and El-Sawy, T. (2010), “Effect of retrofit strategies on mitigating progressive collapse of steel frame structures”, J. Constr. SteelRes., 66(4), 520-531.
Ghosn, M. and Moses, F. (1998), NCHRP Report 406: Redundancy in Highway Bridge Superstructures, TRB, National Research Council,Washington, D.C.
Giuliani, L. (2012), “Structural safety in case of extreme actions”, Special Issue on: “Performance and Robustness of Complex StructuralSystems”, Int. J. of Lifecycle Performance Engineering (IJLCPE), 1(1), 22-40.
GSA - General Service Administration (2003), Progressive collapse analysis and design guidelines for new federal office buildings andmajor modernization project, Washington DC: GSA.
Hoffman, S. T. and Fahnestock, L. A. (2011), “Behavior of multi-story steel buildings under dynamic column loss scenarios”, SteelCompos. Struc., 11(2), 149-168.
HSE - Health and Safety Executive (2001), Reducing risks, protecting people, HSE’s decision-making process, United King: Crowncopyright.
Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y. and Nethercot, D. A. (2008a), “Progressive collapse of multi-storey buildings due tosudden column loss - Part I: Simplified assessment framework”, Eng. Struct., 30(5), 1308-1318.
Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y. and Nethercot, D. A. (2008b), “Progressive collapse of multi-storey buildings due tosudden column loss - Part II: Application”, Eng. Struct., 30(5), 1424-1438.
Kim, J. and Kim, T. (2009), “Assessment of progressive collapse-resisting capacity of steel moment frames”, J. Constr. Steel Res., 65(1),169-179.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References
Kwasniewski, L. (2010), “Nonlinear dynamic simulations of progressive collapse for a multistory building”, Eng. Struct., 32(5), 1223-1235.
Malla, R.B., Agarwal, P. and Ahmad, R. (2011), “Dynamic analysis methodology for progressive failure of truss structures consideringinelastic postbuckling cyclic member behavior”, Eng. Struct., 33(5), 1503-1513.
Miyachi, K., Nakamura, S. and Manda, A. (2012), “Progressive collapse analysis of steel truss bridges and evaluation of ductility”, J.Constr. Steel Res., 78, 192-200.
Nafday, A.M. (2008), “System Safety Performance Metrics for Skeletal Structures”, J. Struct. Eng.- ASCE, 134(3), 499-504.
Nafday, A.M. (2011), “Consequence-based structural design approach for black swan events”, Struct. Saf., 33(1), 108-114.
Olmati, P., Gkoumas, K., Brando, F., Cao, L. (2013) “Consequence-based robustness assessment of a steel truss bridge”, Steel andComposite Structures, An International Journal, 14(4), 379-395.
Rezvani, F. H. and Asgarian, B. (2012), “Element loss analysis of concentrically braced frames considering structural performancecriteria”, Steel Compos. Struc., 12(3), 231-248.
Saydam, D. and Frangopol, D. M. (2011), “Time-dependent performance indicators of damaged bridge superstructures”, Eng. Struct.,33(9), 2458-2471.
Starossek, U. (2009), Progressive collapse of structures, London: Thomas Telford Publishing.
Starossek, U. and Haberland, M. (2010), “Disproportionate Collapse: Terminology and Procedures”, J. Perf. Constr. Fac. 24(6), 519-528.
Starossek, U. and Haberland, M. (2012), “Robustness of structures”, Special Issue on: “Performance and Robustness of ComplexStructural Systems”, Int. J. of Lifecycle Performance Engineering (IJLCPE), 1(1), 3-21.
Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.). London: Penguin. p. 400. ISBN 1-84614045-5.
Yuan, W. and Tan, K. H. (2011), “Modeling of progressive collapse of a multi-storey structure using a spring-mass-damper system”,Struct. Eng. Mech., 37(1), 79-93.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Acknowledgements
- Luisa Giuliani, PhD. Associate Professor, DTU, Denmark.
- Francesca Brando, PhD. Senior Engineer, Thornton Tomasetti, NY.
- Pierluigi Olmati, PhD. Post-doc, Surrey University, UK.
Corso di Dottorato: Introduzio ne all'o�mi zzazione struttural e Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
“Structural robustness: definitions, examples and consequence based assessment of structures”
Konstantinos Gkoumas, Ph.D., P.E.
Corso di Dottorato: introduzio ne all'ottimi zzazionestruttural e
Prof.-Ing. Franco Bontempi
Dipartimento di Ingegneria Strutturale e Geotecnica
Dottorato di Ricerca in Ingegneria delle Strutture
Rome, June 21 2014