Structural robustness and sustainability of structures:concepts and case studies.

Dipartimento di Ingegneria Strutturale e Geotecnica
Dottorato di Ricerca in Ingegneria delle Strutture
“Structural robustness and sustainability of structures:
concepts and case studies”
Konstantinos Gkoumas, Ph.D., P.E.
Corso di Dottorato: introduzione all'ottimizzazione strutturale
Prof.-Ing. Franco Bontempi
Konstantinos Gkoumas Dipartimento di Ingegneria Strutturale e Geotecnica

Konstantinos Gkoumas
06/05/2015
Sustainability of tall buildings:
structural design and intelligent technologies
Page 2
Personal profile
Appointments
2011-’14 Research Fellow (PostDoc), Department of Structural and Geotechnical Engineering - Sapienza
University of Rome.
Research on dependability and energy harvesting for structures and infrastructures.
2009-’10 Postdoctoral Fellow (German Academic Exchange Service), Institut für Numerische und
Angewandte Mathematik, Universität Göttingen, Germany.
2005-’08 Professional Engineer at Co.Re. Ingegneria Srl., Rome.
2004-’07 PhD Student, Department of Hydraulics, Transportation and Roads - Sapienza University of Rome.
1996-‘03 Laurea in Civil Engineering, Transportation Major (5-year degree, equivalent with MEng + MSc) -
Sapienza University of Rome

Roma, 6 Maggio 2015 - Corso di Dottorato: introduzione
all'ottimizzazione strutturale, Prof.-Ing. Franco Bontempi
Konstantinos Gkoumas, PhD, PE
1st part
structural robustness

Word cloud

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

Black
Swan
Vulnerability
Cause
Damage
Index
design
• Collapse types
• Structural robustness and progressive collapse
definitions
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Member
consequence
factor

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

Description:
- apartments building;
- precast concrete wall and floor components
was the structural bearing system;
- ductile detailing and effective ties between
the precast components.
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

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

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 structure
occurrence 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.

Reference: Bontempi, F. (2005) Frameworks for structural analysis, In: Innovation in Civil and Structural
Engineering Topping, BHV ed., pp. 1-24
HPLC
High Probability –
Low Consequences
LPHC
Low Probability –
High Consequences
Complexity
Non linear issues and
interaction mechanisms
Designapproach:
StochasticDeterministic
QUALITATIVE RISK
ANALYSIS
PROBABILISTIC
RISK ANALYSIS
PRAGMATIC
ANALYSIS OF
RISK SCENARIOS
Secondary
design
Primary
design
Low Probability – High Consequences Events

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

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

QUALITY
DAMAGE or ERROR
REQUIRED PERFORMANCE
NOMINAL
PERFORMANCE
NOMINAL SITUATION
Structural Robustness

• Capacity of a construction to exhibit regular
decrease of its structural quality as a consequence
of negative causes.
• It implies:
a) some smoothness of the decrease of
structural performance due to negative
events (intensive feature);
b) some limited spatial spread of the
rupture (extensive feature).

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
A B

CommonULS&SLS
VerificationFormat
Assessment
1st level:
Material Point
2nd level:
Element
Section
3rd level:
Structural
Element
4th level:
Structural
System
Structural robustness in design

STRUCTURAL DESIGN
PRIMARY SECONDARY TERTIARY
LOADS
DEAD X
LIVE X
SNOW X
EARTHQUAKE X
FIRE X X
EXPLOSIONS X X
“BLACK SWAN” X
Member-based
structural design
Consequence-based
structural 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.

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
design
Secondary
design
Tertiary
design

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
design requirements for ductile performance

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

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 earthquake
Izmit Earthquake
1999
Tanker S.S. Schenectady, 1941

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)

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)

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)

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.

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)

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)

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

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.

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

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

RISK-BASED
[Faber, 2005]
R
I
inddir
dir
rob
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


 
 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:

[Baker et al. 2008]
R
I
inddir
dir
rob
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

𝑅 𝑑
𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑
− 𝐸 𝑑
≥ 0
member-based design
𝑅 − 𝐸 ≥ 0limit state design
Resistance (probabilistic) Solicitation (probabilistic)
Resistance (design values) Solicitation (design values)
(1 − 𝐶𝑓
𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜
)𝑅 𝑑
−𝐸 𝑑
≥ 0
Member consequence factor based design
0 ≤ 𝐶 𝑓 ≤ 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  

• The structure is subjected to a set of damage scenarios and the consequence of the
damages is evaluated by the member consequence factor (𝐶𝑓
) 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 𝐶𝑓
, intended as the
effective coefficient that affects directly the resistance.
• 𝐶𝑓
is evaluated by the maximum percentage difference of the structural stiffness
matrix eigenvalues of the damaged and undamaged configurations of the structure.
𝐶𝑓
= 𝑚𝑎𝑥
𝜆𝑖
𝑢𝑛
− 𝜆𝑖
𝑑𝑎𝑚
𝜆𝑖
𝑢𝑛 100
𝑖=1−𝑁
where, 𝜆𝑖
𝑢𝑛
and 𝜆𝑖
𝑑𝑎𝑚
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.

• The corresponding robustness index (𝑅 𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜
) is therefore defined as:
𝑅 𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜=1 - 𝐶𝑓
• 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).

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

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.

Stiffness matrix
Kun λi
un
Eigenvalues
Kdam λi
dam
Consequence factor
Robustness indexRscenario= 100 - Cf
scenario
N1i
un
i
dam
i
un
iscenario
f 100
)(
maxC










Structural Robustness assessment - overview

ka
kb
x
y
Kun
=
10 0
0 10
Cf1
1 = 0% Cf2
1 = 30%
R1 = 70%
R1 = 100 − Cf
1N: 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 0
0 7
Scenario 1
Single damage – analytic calculation

• 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

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

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

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.

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. “

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..

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.

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

2 inches (51 mm) of concrete were added to the road surface over the years, increasing
the dead load by 20%;
1977, Renovation:
Increased Deck Thickness
1998, Renovation:
Median Barrier, Traffic Railings,
and Anti-Icing System
2007, Repair and Renovation:
Repaving

Stress contours for outside (west) gusset plate at U10W after 1977 and 1998 renovation projects
Yield stress
of 51.5 ksi
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
[*]
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

The extraordinary weight of construction equipment and material resting on the bridge just
above its weakest point at the time of the collapse
[*]
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

Stress contours for outside (west) gusset plate at U10W on August 1, 2007
Yield stress
of 51.5 ksi
South North

Stress contours for outside (west) gusset plate at U10W on August 1, 2007
Yield stress
of 51.5 ksi

INSPECTION REPORT FOR I-35W BRIDGE, 1983-2007

GUSSET PLATE???
INSPECTION REPORT FOR I-35W BRIDGE, 1983-2007

BOWED GUSSET PLATE AT NODE U10

RESISTANCE OF GUSSET PLATES:
GUSSET PLATES IN TENSION
GUSSET PLATES SUBJECT TO SHEAR
GUSSET PLATES IN COMPRESSION
RESISTANCE OF FASTENERS
SHEAR RESISTANCE OF FASTENERS
PLATE BEARING RESISTANCE AT FASTENERS
http://bridges.transportation.org/Documents/FHWA-IF-09
014LoadRatingGuidanceandExamplesforGussetsFebruary2009rev3.pdf
FHWA GUIDELINES, (2009)

I-35 West Bridge, Collapse Initiation
Pier 7
Pier 6
Failure Initiation North of Pier 6
N
U10-E
U10-W
L9
L11

Pier 7
Pier 6
N
U10-E
U10-W
L9
L11
L11
L9
U10

Weight
Temp. &
Const.
Weight
Temp. &
Const.
Construction loads increase forces by 3%
Forces due to weight of bridge and traffic
Additional forces due to temperature
(corroded bearings) and construction load
L11
L9
L11
L9
L11
L9
U10
• Additional forces due to temperature
• Forces due to weight of bridge and traffic

Gusset hinges, tears at top and buckles at bottom
L11
L9
L11
L9
L11
L9
U10
Lower chord fails in buckling
• Lower chord fails in buckling
• Gusset hinges, tears at top and buckles at
bottom

BUCKLED
TORN
Rivet hole elongation
U
L11
L9
U10
• Lower chord fails in buckling
• Gusset hinges, tears at top and buckles at
bottom
• Rivet hole elongation

I-35 W bridge
NTSB 2007

Undamaged
Damaged
scenario
I-35 West Bridge, Minneapolis, MN – damage scenarios

I-35 West Bridge, Minneapolis, MN – damage scenarios
3D
2D

d1
d2d3
d4
d5
d7
d6
37
59
42 45
35 38
23
63
41
58 55
65 62
77
0
20
40
60
80
100
1 2 3 4 5 6 7
Robustness%
Scenario
Cf max Robustness
42 45
35 38
23
58 55
65 62
77
3 4 5 6 7
Scenario
Cf max Robustness
83 87 88
53
60
86
64
17 13 12
47
40
14
36
0
20
40
60
80
100
1 2 3 4 5 6 7
Robustness%
Scenario
Cf max Robustness
Damage scenario Damage scenario
d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
DSj = di
I-35 West Bridge, Minneapolis, MN – single damage

d1
d2d3
d4
d5
d7
d6
42 45
35 38
23
58 55
65 62
77
3 4 5 6 7
Scenario
Cf max Robustness
83 87 88
53
60
86
64
17 13 12
47
40
14
36
0
20
40
60
80
100
1 2 3 4 5 6 7
Robustness%
Scenario
Cf max Robustness
Damage scenario Damage scenario
d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
I-35 West Bridge, Minneapolis, MN/ enhanced– single damage
DSj = di

I-35W SAINT ANTHONY FALLS BRIDGE (September 2008)
There are 323 sensors that regularly measure bridge conditions
such as deck movement, stress, and temperature

•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)

Black
Swan
Vulnerability
Cause
Damage
Index
design
• Collapse types
• Structural robustness and progressive
collapse definitions
• What now/next?
• References
Robustness
Collapse
resistance
Progressive
collapse
Member
consequence
factor

(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

(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

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”

References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:
Penguin. p. 519. ISBN 1-400-06782-0 .
-----
----
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).

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/

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 for
Communities 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 of
the 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 structural
system”, 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”, Invited
Lecture, 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”, Bridge
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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 on
Structural 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,
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Choi, J-h. and Chang, D-k. (2009), “Prevention of progressive collapse for building structures to member disappearance by accidental
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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,
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849.

References
DoD - Department of Defense (2009), Unified Facilities Criteria (UFC). Report No. UFC 4-023-03: Design of buildings to resist
progressive 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 of
Progressive 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 for
reducing 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.
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Giuliani, L. (2012), “Structural safety in case of extreme actions”, Special Issue on: “Performance and Robustness of Complex Structural
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GSA - General Service Administration (2003), Progressive collapse analysis and design guidelines for new federal office buildings and
major modernization project, Washington DC: GSA.
Hoffman, S. T. and Fahnestock, L. A. (2011), “Behavior of multi-story steel buildings under dynamic column loss scenarios”, Steel
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References
Kwasniewski, L. (2010), “Nonlinear dynamic simulations of progressive collapse for a multistory building”, Eng. Struct., 32(5), 1223-
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Malla, R.B., Agarwal, P. and Ahmad, R. (2011), “Dynamic analysis methodology for progressive failure of truss structures considering
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Miyachi, K., Nakamura, S. and Manda, A. (2012), “Progressive collapse analysis of steel truss bridges and evaluation of ductility”, J.
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06782-0

2nd part
sustainability of structures

Sustainability: overview
SUSTAINABILITY
SOCIAL
ENVIRONMENTAL
ECONOMIC
SUSTAINABLE DEVELOPMENT:
“Development that meets the needs of the
present without compromising the ability of
future generations to meet their own needs.”
(Brundtland Commission, 1987)

Sustainability: use of steel and structural form
Steel Material
• 40% of resources
from recycling
• Manufacturing
process with
controlled
environmental
impact
• Material durability
• High recycling rate
Construction
Phase
• prefabrication/
offsite manufacture
Design and Service Life
• Weight reduction of structure
• Creation of versatile spaces
• Longevity and robustness of
steel components
• Simple incorporation of
renewable energy generation
systems
End of Life
• Easy dismantling
• Reusability/Reciclability
Source: Foster + Partners Hearst Tower USA, 2000 - 2006
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form

Sustainability: building automation and energy harvesting
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form

Sustainability: integration
SUSTAINABILITY
IN
STRUCTURES
Material
Used
Resource
Efficient
Site
Planning
Non
Pollution
Energy
Efficiency
Structural
Form
Diagrid: double façade - chimney effect

Sustainability: tall buildings
Ali, M. M., Moon, K. S. (2007). Structural Development in Tall Buildings: Current Trends and Future Prospects.
Architectural Science Review, Vol. 50, pp. 205-223.
Interior structuresExterior structures

Diagrid structure: diagrid module
Mele, E., Toreno, M., Brandonisio, G. and Del Luca, A. (2014). Diagrid structures for tall buildings: case studies and design
considerations. The Structural Design of Tall and Special Buildings. Wiley Online Library, Vol. 23, No. 2, pp. 124-145.
effect of gravity load
effect of overturning moment
effect of shear force

Diagrid structure: Initial configuration and diagrid schemes
Outrigger Structure Diagrid Structures
42° 60° 75°
160m
36 m

Diagrid structure: structural configuration
Original Structure:
Outrigger
Improved Structure:
Diagrid
Perimetral
Structure
Internal
Structure

Diagrid structure: analyses and comparisons
SLS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1 1 1 0,7 0,5 1 - - -
COMB6 1 1 1 0,7 0,5 - 1 - -
COMB7 1 1 1 0,7 0,5 - - 1 -
COMB8 1 1 1 0,7 0,5 - - - 1
ULS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1,3 1,3 1,3 1,05 0,75 1,5 - - -
COMB6 1,3 1,3 1,3 1,05 0,75 - 1,5 - -
COMB7 1,3 1,3 1,3 1,05 0,75 - - 1,5 -
COMB8 1,3 1,3 1,3 1,05 0,75 - - - 1,5
Acronym Description Color
Outrigger Outrigger Structure
Diagrid 42°
Diagrid Structure with inclination
of diagonal members of 42°
Diagrid 60°
Diagrid 75°
Outrigger 42° 60° 75°
P
(ton)
8052 6523 5931 5389
Saving
(%)
- 19 26 33
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
P(ton)
Weight

Diagrid structure: modal analysis
T1 T2 T3 T4 T5 T6
Outrigger 3.7 3.6 2.5 1.2 1.1 0.8
Diagrid 42° 3.1 3.1 1.7 1.0 1.0 0.8
Diagrid 60° 3.3 3.3 1.9 1.0 1.0 0.9
Diagrid 75° 3.7 3.6 2.8 1.3 1.2 1.2
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
T(s)
First six periods
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis
Traslational
in Y
direction
Traslational
in X
direction
Rotational
around Z
axis

Diagrid structure: SLS - load combinations
SLS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
COMB5 1 1 1 0,7 0,5 1 - - -
COMB6 1 1 1 0,7 0,5 - 1 - -
COMB7 1 1 1 0,7 0,5 - - 1 -
COMB8 1 1 1 0,7 0,5 - - - 1
HORIZONTAL
DISPLACEMENTS
COMB
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°
Diagrid
42°
Diagrid Structure with inclination of
diagonal members of
42°
Diagrid
60°
diagonal members of
60°
Diagrid
75°
diagonal members of
75°

Diagrid structure: Horizontal displacements
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0
16
32
48
64
80
96
112
128
144
160
U1 (m)
Z(m)
Diagrid 42° Diagrid 60° Outrigger Diagrid 75° SLS limit
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°

Diagrid structure: ULS - load combinations, pushover
Outrigger
Diagrid42°
Diagrid60°
Diagrid75°
Diagrid
42°
diagonal members of
42°
Diagrid
60°
diagonal members of
60°
Diagrid
75°
diagonal members of
75°
ULS Dead Gk Tamp Qk Qn W+X W-X W+Y W-Y
DEAD 1 - - - - - - - -
VERT 1 1 1 - - - - - -
+STATIC PUSHOVER FORCES
PUSHOVER
DEAD VERT

Diagrid structure: Diagrid 60°, Pushover (YZ Sections)
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F(kN)
U1 (m)
Pushover
Step25
Step28
Step37
Step44
Step51
Step67
Step 67Step 51Step 44Step 37Step 25

Diagrid structure: Diagrid 60°, Pushover+Vert (YZ Sections)
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F(kN)
U1 (m)
Pushover+Vert
Step11
Step16
Step39
Step47
Step55
Step 47 Step 55Step 39Step 11
VERT

Diagrid structure: comparison of capacity curves
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F(kN)
U1 (m)
Pushover
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
U1 (m)
Pushover+Vert
Outrigger
Diagrid
42°
Diagrid
60°
Diagrid
75°
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
U1 (m)
Pushover+Dead
DEAD VERT

Diagrid structure: definition of significant properties
R=Fmax
(Strength)
K=Fy/Dy
(Stiffness)
m=Dmax/Dy
(Ductility)

Diagrid structure: comparison of significant properties
Outrigger Diagrid 42° Diagrid 60° Diagrid 75°
Pushover+Vert Pushover+Vert Pushover+Vert Pushover+Vert
Strength
(R) – kN
94775 110185 104972 97131
Stiffness
(K) – kN/m
77143 80615 71306 60897
Ductility
(m)
1,535 3,587 5,681 2,564
Weight
(P) - Ton
8052 6523 5931 5389
Weighted average (W.A.) of significant properties
Pushover+Vert Pushover+Vert Pushover+Vert Pushover+Vert
Strength
(R) – kN
94775 110185 104972 97131
Stiffness
(K) – kN/m
77143 80615 71306 60897
Ductility
(m)
1,535 3,587 5,681 2,564
Weight
(P) - Ton
8052 6523 5931 5389
W.A. 4,20 5,97 7,25 5,08

Diagrid structure: comparison of mechanical properties
0
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R/R0
K/K0
m/m0
1,2 ((P0-
P)/P0+1)
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Diagrid structure: robustness checks
D1,L1
D1,L2
D2,L1
D2,L2
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D3,L2
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U1 (m)
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INTATTA

References
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Dipartimento di Ingegneria Strutturale e Geotecnica
Dottorato di Ricerca in Ingegneria delle Strutture
“Sustainability of structures and structural robustness:
concepts and case studies”
Konstantinos Gkoumas, Ph.D., P.E.
Corso di Dottorato: introduzione all'ottimizzazione strutturale
Prof.-Ing. Franco Bontempi
Konstantinos Gkoumas Dipartimento di Ingegneria Strutturale e Geotecnica

Structural robustness and sustainability of structures:concepts and case studies.

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