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Structural robustness: context and numerical applications
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www.francobontempi.org
Structural robustness:
issues, applications
and future trends
Konstantinos Gkoumas, Ph.D., P.E.
Franco Bontempi, Ph.D., P.E.
Facoltà di Ingegneria
Sapienza Università di Roma
CORSO DI COSTRUZIONI METALLICHE
1November 20 2014
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Word cloud
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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)
VULNERABILITY ROBUSTNESSEXPOSURE VULNERABILITY ROBUSTNESSEXPOSURE
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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
Des
ign
ap
pro
ach
:
Sto
chas
tic
Det
erm
inis
tic
QUALITATIVE RISKANALYSIS
PROBABILISTICRISK ANALYSIS
PRAGMATICANALYSIS OF
RISK SCENARIOS
Secondary
design
Primary
design
Low Probability – High Consequences Events
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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.
Strengths of Black Swan Theory – Benefits
• Increased awareness of uncertainty in decision making
• New way to deal with risks and uncertainty
Limitations of Black Swan Theory – Disadvantages
• Black Swan is rather extreme
• Theory is not yet mainstream
Assumptions of Black Swan Theory
• Black Swans cannot be predicted because they are rare
• Overestimation of knowledge/Underestimation of randomness
and uncertainty
• Overestimation of skills/underestimation of luck in life
Black Swans
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
QUALITY
DAMAGE or ERROR
REQUIRED PERFORMANCE
NOMINAL
PERFORMANCE
NOMINAL SITUATION
Structural Robustness
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Com
mo
n U
LS
& S
LS
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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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)damagedelements
ithelement stiffnessmatrix (damaged state)
[Yan&Chang, 2006] [Biondini &Frangopol, 2008]
1
0
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-BASEDOther:
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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: related to initial damage
Rind: related to additional damage
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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
𝑅𝑑𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑
− 𝐸𝑑𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑
≥ 0member-based design
𝑅 − 𝐸 ≥ 0limit state design
Resistance (probabilistic) Solicitation (probabilistic)
Resistance (design values) Solicitation (design values)
(1 − 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜)𝑅𝑑
𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑−𝐸𝑑
𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑≥ 0
Member consequence factor based design
0 ≤ 𝐶𝑓 ≤ 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
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 (𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜) 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 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜, intended as the
effective coefficient that affects directly the resistance.
• 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜is evaluated by the maximum percentage difference of the structural stiffness
matrix eigenvalues of the damaged and undamaged configurations of the structure.
𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜 = 𝑚𝑎𝑥
𝜆𝑖𝑢𝑛 − 𝜆𝑖
𝑑𝑎𝑚
𝜆𝑖𝑢𝑛 100
𝑖=1−𝑁
where, 𝜆𝑖𝑢𝑛and 𝜆𝑖
𝑑𝑎𝑚are 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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
• The corresponding robustness index (𝑅𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜) is therefore defined as:
𝑅𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜=1 - 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜
• 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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 and Optimization
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 and 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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
Structural Robustness assessment - overview
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
ka
kb
x
y Kun =10 00 10
Cf11 = 0% Cf2
1 = 30%
R1 = 70%
R1 = 100 − Cf1
N: total eigenvalues number
i: single eigenvalue number
a and b: elements
a
b
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
Kdam =10 00 7
Scenario 1
Single damage – analytic calculation
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
COLLAPSE OF THE BRIDGE ON I 35-W MINNESOTA, AUGUST 1ST 2007
The I-35W Mississippi River Bridge (officially known as Bridge 9340) was an eight-lane, deck
truss bridge, designed by the engineering consulting firm of Sverdrup & Parcel and Associates,
the design plans were approved by the Minnesota Department of Transportation (Mn DOT) on
1965 and opened to traffic on 1967.
http://www.dot.state.mn.us/i35wbridge/ntsb/finalreport.pdf
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
http://www.dot.state.mn.us/i35wbridge/ntsb/finalreport.pdf
• The deck truss comprised in two parallel Warren
trusses (east and west) with verticals.
• The east and west main trusses were spaced 22 m
and were connected by 27 transverse welded floor
trusses spaced 11.6 m on centers and by two floor
beams at the north and south ends.
• Steel gusset plates were used on all the 112
connections of the two main trusses. All nodes had
two gusset plates on either side of the connection.
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
After this tragedy, the Federal Highway Administration (FHWA) focused its attention on all the 465 steel
deck truss bridges present in the National Bridge Inventory [NTSB, 2008].
“The term “fracture critical” indicates that if one main component of a bridge fails, the entire
structure could collapse. Therefore, a fracture critical bridge is a steel structure that is designed
with little or no load path redundancy. Load path redundancy is a characteristic of the design
that allows the bridge to redistribute load to other structural members on the bridge if any one
member loses capacity. “
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
National Transportation Safety Board, NTSB,
2008
“Collapse of I-35 W Highway Bridge,
Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-
916213, Washington D.C. 20594..
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
The primary cause of the collapse was the under-sized gusset plates, with a
thickness of 0.5 inches (13 mm);
U10-W
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1,
2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
FINITE ELEMENT MODEL FOR OUTSIDE WEST GUSSET PLATE AT U10W
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
Stress contours for outside (west) gusset plate at U10W at time of bridge opening in 1967
Yield stress
of 51.5 ksi
South North
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
2 inches (51 mm) of concrete were added to the road surface over the years, increasing
the dead load by 20%;
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
1977, Renovation:
Increased Deck Thickness
1998, Renovation:
Median Barrier, Traffic Railings,
and Anti-Icing System
2007, Repair and Renovation:
Repaving
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
The extraordinary weight of construction equipment and material resting on the bridge just
above its weakest point at the time of the collapse
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
[*]
U10-WNorth South
184 380 lbf (820 kN) of gravel
198 820 lbf (884 kN) of sand
195 535 lbf (870 kN) of parked construction vehicles and personnel
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
FINITE ELEMENT MODEL FOR OUTSIDE WEST GUSSET PLATE AT U10W
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
Stress contours for outside (west) gusset plate at U10W after 1977 and 1998 renovation projects
Yield stress
of 51.5 ksi
South North
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
The extraordinary weight of construction equipment and material resting on the bridge just
above its weakest point at the time of the collapse
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
[*]
U10-WNorth South
Pier 6
184 380 lbf (820 kN) of gravel
198 820 lbf (884 kN) of sand
195 535 lbf (870 kN) of parked construction vehicles and personnel
THE ADDITIONARY CAUSE:
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”
Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
Stress contours for outside (west) gusset plate at U10W on August 1, 2007
Yield stress
of 51.5 ksi
South North
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
FINITE ELEMENT MODEL FOR OUTSIDE WEST GUSSET PLATE AT U10W
Stress contours for outside (west) gusset plate at U10W on August 1, 2007
Yield stress
of 51.5 ksi
8/3112/44 BRIDGE COLLAPSE
8/3113/44 BRIDGE COLLAPSE
8/3114/44 BRIDGE COLLAPSE
8/3115/44 BRIDGE COLLAPSE
8/3116/44 BRIDGE COLLAPSE
8/3117/44 BRIDGE COLLAPSE
8/3118/44 BRIDGE COLLAPSE
8/3119/44 BRIDGE COLLAPSE
8/3120/44 BRIDGE COLLAPSE
8/3121/44 BRIDGE COLLAPSE
8/3121/44 BRIDGE COLLAPSE
8/3122/44 BRIDGE COLLAPSE
8/3123/44 BRIDGE COLLAPSE
8/3124/44 BRIDGE COLLAPSE
/3125/44 BRIDGE COLLAPSE
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN
CASE STUDY
FORENSIC INVESTIGATION
2 inches (51 mm) of concrete were added to the road surface over the years,
increasing the dead load by 20%;
6/67
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August
1, 2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
FORENSIC INVESTIGATION
THE ADDITIONARY CAUSE:
1977, Renovation: Increased Deck Thickness
1998, Renovation:Median Barrier, Traffic Railings,
and Anti-Icing System
2007, Repair and Renovation: Repaving
FINITE ELEMENT MODEL FOR OUTSIDE WEST GUSSET PLATE AT U10W
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August
1, 2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
Stress contours for outside (west) gusset plate at U10W after 1977 and 1998 renovation projects
Yield stress
of 51.5 ksi
FORENSIC INVESTIGATION
South North
The extraordinary weight of construction equipment and material resting on the
bridge just above its weakest point at the time of the collapse
7/67
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August
1, 2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
[*]
U10-WNorth South
FORENSIC INVESTIGATION
184 380 lbf (820 kN) of gravel
198 820 lbf (884 kN) of sand
195 535 lbf (870 kN) of parked construction vehicles and personnel
THE ADDITIONARY CAUSE:
The extraordinary weight of construction equipment and material resting on the
bridge just above its weakest point at the time of the collapse
7/67
[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August
1, 2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.
[*]
U10-WNorth South
FORENSIC INVESTIGATION
Pier 6
184 380 lbf (820 kN) of gravel
198 820 lbf (884 kN) of sand
195 535 lbf (870 kN) of parked construction vehicles and personnel
THE ADDITIONARY CAUSE:
INSPECTION REPORTING FOR I-35W BRIDGE, 2006
GUSSET PLATE???
FORENSIC INVESTIGATION
RESISTANCE OF GUSSET PLATES:
GUSSET PLATES IN TENSION
GUSSET PLATES SUBJECT TO SHEAR
GUSSET PLATES IN COMPRESSION
FHWA GUIDELINES, (2009)
26/67
FORENSIC INVESTIGATION
RESISTANCE OF FASTENERS
SHEAR RESISTANCE OF FASTENERS
PLATE BEARING RESISTANCE AT FASTENERS
http://bridges.transportation.org/Documents/FHWA-IF-09
014LoadRatingGuidanceandExamplesforGussetsFebruary2009rev3.pdf
CRITICAL REVIEW OF THE FHWA GUIDELINES:
• Stiffness of framing members, that increase the ultimate compression capacity of the gusset
plate;
• Influence of the initial imperfections, that decrease the ultimate compression capacity of the
gusset plate;
• Edge buckling vs. Gusset plates buckling, from that the importance of making consideration
not only on the length of the free edge, but also length of equivalent column is important for
buckling
40/67
Framing member stiffness
Gusset Plates
For LRFR and λ ≤ 2.25
(assumes δ ≤ L /1500)
What if δ > L /1500) ?
FORENSIC INVESTIGATION
I-35 West Bridge, Minneapolis, MN
98 Case Study
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
• At 6:05 pm on
August 1st 2007
Bridge Collapsed
• 13 People killed &
approximately 145
Injured
Photo from aircraft flying overhead.
Postcollapse overhead photos of the bridge, view looking east
North
Downtown
North Downtown
D-1
Security Camera video
99 Analysis Procedure
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
N
FIMForensic Investigation Modeling
Thornton Tomasetti was engaged to perform investigation into the causes the collapse by Robins, Kaplan Miller
&Ciresi, a national law firm with offices in Minneapolis, Minnesota. Firm partners recruited and oversaw a
consortium of 17 law firms that agreed to provide pro bono legal services to the survivors of the collapse.
Pier 7
Pier 6
100 Collapse Initiation Area
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
Failure Initiation
North of Pier 6
N
U10-E
U10-W
L9
L11
Pier 7
Pier 6
101 Collapse Initiation Area
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
N
U10-E
U10-W
L9
L11
L11
L9
U10
Failure Initiation
North of Pier 6
Weight
Temp. & Const.
Weight
Temp. & Const.
The upper gusset plate is half as thick as it should
be.
Construction loads increase forces by 3%
Forces due to weight of bridge and traffic
Additional forces due to temperature
(corroded bearings) and construction load
102
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
L11
L9
L11
L9
L11
L9
U10
• Forces due to weight of bridge and traffic
• Additional forces due to temperature
(corroded bearings) and construction load
Failure Initiation
North of Pier 6
Collapse Initiation Area
NTSB Theory – U10 Gusset failed in
a “lateral shifting instability”
Gusset hinges, tears at top and buckles at bottom
103
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
L11L9
L11
L9
L11
L9
U10
Lower chord fails in buckling
• Forces due to weight of bridge and traffic
• Additional forces due to temperature
(corroded bearings) and construction load
• Lower chord fails in buckling
• Gusset hinges, tears at top and buckles at bottom
Failure Initiation
North of Pier 6
Collapse Initiation Area
Gusset plate hinging
BUCKLED
TORN
Rivet hole elongation
U
104
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
L11
L9
U10
• Forces due to weight of bridge and traffic
• Additional forces due to temperature
(corroded bearings) and construction load
• Lower chord fails in buckling
• Gusset hinges, tears at top and buckles at bottom
• Rivet hole elongation
Failure Initiation
North of Pier 6
Collapse Initiation Area
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Postcollapse overhead photos of the bridge, view looking east
North
Downtown
North Downtown
D-1
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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 W bridge
I-35 West Bridge, Minneapolis, MN
NTSB 2007
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
Undamaged
Damaged
scenario
I-35 West Bridge, Minneapolis, MN – damage scenarios
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
I-35 West Bridge, Minneapolis, MN – damage scenarios
3D
2D
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
Robust
nes
s %
ScenarioCf max Robustness
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
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 scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
DSj = di
I-35 West Bridge, Minneapolis, MN – single damage
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
d1
d2d3
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
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 scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
I-35 West Bridge, Minneapolis, MN/ enhanced– single damage
DSj = di
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
(disaster) resilience
Definition (not univocal):
A resilient community is defined as the one having the ability to absorb disaster
impacts and rapidly return to normal socioeconomic activity.
MCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available at
http://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdf
NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technical
report. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdf
MCEER framework for resilience evaluation:
Initial losses Recovery time, depending on:
• Resourcefulness
• Rapidity
Disaster strikes
Systemic
Robustness
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
(disaster) resilience
Definition (not univocal):
A resilient community is defined as the one having the ability to absorb disaster
impacts and rapidly return to normal socioeconomic activity.
MCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available at
http://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdf
NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technical
report. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdf
MCEER framework for resilience evaluation:
Resilience is inversely proportional to the area A.
(dQ/dt)L0
TR
(dQ/dt)0
A
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:
Penguin. p. 519. ISBN 1-400-06782-0.
People/systems/organizations/things/ideas can be described in one
of three ways:
- fragile
- resilient, or
- antifragile
"Some things benefit from shocks; they thrive and grow when
exposed to volatility, randomness, disorder, and stressors and love
adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the
phenomenon, there is no word for the exact opposite of fragile.
Let us call it anti-fragile. Anti-fragility is beyond resilience or
robustness. The resilient resists shocks and stays the same; the
anti-fragile gets better".
“anti-fragility”
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:
Penguin. p. 519. ISBN 1-400-06782-0 .
-----
----
“anti-fragility”
References: Beyond “Sissy” Resilience: On Becoming Antifragile. Available online at
http://www.artofmanliness.com/2013/12/03/beyond-sissy-resilience-on-becoming-antifragile/
Things that are fragile
break or suffer from
chaos and randomness.
The resilient, or
robust, don’t care if
circumstances become
volatile or disruptive
(up to a point).
Things that are anti-
fragile grow and
strengthen from
volatility and stress (to
a point).
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
“anti-fragility”
Fragile people/ systems/
organizations are concave.
As fluctuations increase (x-axis) you
experience more loss.
Anti-fragile things are convex.
As variability increases (x-axis),
gains increase.
References: Beyond “Sissy” Resilience: On Becoming Antifragile. Available online at
http://www.artofmanliness.com/2013/12/03/beyond-sissy-resilience-on-becoming-antifragile/
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Photo Credit: Wikipedia Commons.
Member
consequence
factor
Corso di Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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.
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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 Costruzioni Metalliche Roma, 20 Novembre 2014Prof.-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.
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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.
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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.
Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London: Penguin. p. 519. ISBN 1-400-06782-0
FHWA SETUP**
[**] Iadicola M., Ocel J., Zobel R., “Quantitative Evaluation of Digital Image Correlation for Large-Scale Gusset
Plate Experiments”, IABMAS2012, Stresa, Lake Maggiore, Italy, July 8-12.
NIST PHYSICAL INFRASTRUCTURE PROGRAM
Advanced computing modeling
Hand calculation
7/28
FHWA, 2009
SIMPLIFIED CONNECTION MODEL
Connection element 1 Connection element 3
Connection element 4
n. connection elements: 5
Each connection element has a
6x6 stiffness matrix
N. Nodes: 28330
n. Dof : 169980
n. Elements S4R and S3R: 27670
45/6
7
MODELING OF GUSSET PLATE CONNECTIONS
SUB-STRUCTURING ANALYSIS – SIMPLIFIED LINEAR CONNECTION MODEL
ALL RIGID JOINT
U10 W
ALL RIGID JOINT + 1 SEMI-RIGID JOINT
NorthSouth
3D MODEL OF THE I35-W BRIDGE
3D FINITE ELEMENT MODEL
Nodes: 1172
Beam elements: 1849
56/67
NorthSouth
0
1
2
3
4
5
6
7
-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
Load
Fac
tor
Dz (m)
RIGID JOINTS
SEMI-RIGID JOINT
Node at midspan
18/28
NONLINEAR ANALYSES RESULTS
NONLINEAR ANALYSES RESULTS
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-2.0E+07 -1.0E+07 0.0E+00 1.0E+07 2.0E+07 3.0E+07
Load
Fac
tor
Axial Forces (N)
CONNECTION 1 CONNECTION 2 CONNECTION 3CONNECTION 4 CONNECTION 5 AXIAL CAPACITY CONNECTION 1AXIAL CAPACITY CONNECTION 2 AXIAL CAPACITY CONNECTION 3 AXIAL CAPACITY CONNECTION 4AXIAL CAPACITY CONNECTION 5
57/6319/28
Compression Tension
What is important to underline is not only the possibility to catch the collapse due to the failure of
the connection, but moreover to classify the cause of the collapse which, in this case, happened
because of the achievement for one of the connection elements of the maximum capacity in
compression.
NONLINEAR ANALYSES RESULTS
NONLINEAR ANALYSES RESULTS
Deformed shape (scale displacement of 10)
at the ultimate load (Pu) of 1.2+07 N
62/67
What is important to underline is not only the
possibility to catch the collapse due to the failure of
the connection, but moreover to classify the cause
of the collapse which, in this case, happened
because of the achievement for one of the
connection elements of the maximum capacity in
compression.
CONCLUSIVE CONSIDERATIONS
CONCLUSION
Connection
member
Load
ratio
Tension or
compression
1 0.28 Compression
2 0.56 Tension
3 1.00 Compression
4 0.02 Tension
5 0.41 Tension
I-35W Bridge was subjected constantly to inspection to assess its safety but even with that people
in charge did not notice that the bridge was about to fail. A future work could be to develop
parametric study on some particular shapes of gusset plates in order to identify some “critical”
points where the monitoring of the out-plane displacements, could give to the owners of the
bridges a warning of what it is happening in the connection. An idea of monitoring could have been
done with a technique of monitoring developed by NIST who focuses its research on two areas of
structural health monitoring:
•development of non-destructive techniques; and
•analysis for determining the degraded condition of infrastructural components and their
subcomponents.
FURTHER DEVELOPMENTS
•FEA results•Results from monitoring **
[email protected]@uniroma1.it
CONCLUSION
[**] Iadicola M., Ocel J., Zobel R., “Quantitative Evaluation of Digital Image Correlation for Large-Scale Gusset
Plate Experiments”, IABMAS2012, Stresa, Lake Maggiore, Italy, July 8-12.
•FHWA test
[**] Iadicola M., Ocel J., Zobel R., “Quantitative Evaluation of Digital Image Correlation for Large-Scale Gusset
Plate Experiments”, IABMAS2012, Stresa, Lake Maggiore, Italy, July 8-12.
CONCLUSION
I-35W SAINT ANTHONY FALLS BRIDGE (September 2008)
CONCLUSION
There are 323 sensors that regularly measure bridge conditions
such as deck movement, stress, and temperature
ACKNOWLEDGMENT
The author would like to acknowledge:
•Professor Franco Bontempi and his team, www.francobontempi.org, for the support
and the help,
•the Metallurgy division of the National Institute of Standard and Technology (NIST) in
particular Dr. Dat Duthinh for the support and the help,
•Eng. Piergiorgio Perin for providing the use of the finite element code Straus, and
•NTSB and FHWA for allowing the access to the detailed FE model used in the
investigation of the collapse of the I-35 W Bridge.
CONCLUSION
•100-year life span
•10 lanes of traffic, five in each direction—two lanes wider than the former bridge
•189 feet wide—the previous bridge was 113 feet wide
•13 foot wide right shoulders and 14 foot wide left shoulders, the previous bridge had no
shoulders
•Light Rail Transport-ready which may help accommodate future transportation needs
•Design-build project complete in 339 days.
•Designed to be aesthetically pleasing and fit in with its environment
•There are 323 sensors that regularly measure bridge conditions such as deck
movement, stress, and temperature
•The bridge is equipped with anti-icing sprayers and was constructed with high-strength
concrete.
I-35W SAINT ANTHONY FALLS BRIDGE (September 2008)