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P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
Robustness assessment of a steel truss bridge
P. Olmati & K. GkoumasSapienza University of Rome
F. BrandoThornton Tomasetti, New York
Progressive Collapse and Structural Robustness: An International Perspective
Clay J. Naito, Ph.D., P.E., Associate Professor and Associate ChairKonstantinos Gkoumas, Ph.D., P.E., Associate Researcher
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Introduction1
Consequence factor2
Application3
Conclusions4
Outline
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Introduction1
Consequence factor2
Application3
Conclusions4
Outline
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Structural Robustness
Structural
requirements
Mechanical
properties
Service
properties
Durability
properties
Dependability
Load bearing capacity
Stability
Ductility
Stiffness
Efficient use
Comfort
Appearance
Not degradation of both
mechanical and service
properties
Reliability
Robustness
Maintainability
Prompt response
Introduction
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Structural Robustness
Structural
requirements
Mechanical
properties
Service
properties
Durability
properties
Dependability
Load bearing capacity
Stability
Ductility
Stiffness
Efficient use
Comfort
Appearance
Not degradation of both
mechanical and service
properties
Reliability
Robustness
Maintainability
Prompt response
Introduction
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Structural Robustness
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:
(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." Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.
(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.
Introduction
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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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)
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Structural Robustness
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." Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.
(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.
Introduction
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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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." Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.
(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.
8
Structural Robustness
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)
B
A Withstand actions
Withstand damages
Progressive Collapse and Structural Robustness
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P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
Interstate 90 Grand River bridge, Ohio – October, 1996
Cause Damage Pr. Collapse
Introduction9
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Features:- Deck Warren Truss type bridge built in
1960, 869 feet (265 m) in length and 150 feet
(46 m) in height.
The event:- On May 24, 1996, a gusset plate failed on the
eastbound span.
- The bridge was closed later that day and the
traffic diverted.
- The cause originally was attributed to an
overloaded semi-trailer truck.
I-35W Bridge, MN – August 1st, 2007
Introduction10
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Postcollapse overhead photos of the bridge, view looking east
North
Downtown
North Downtown
D-1
Cause Damage Pr. Collapse
Features:- Continuous Steel Deck Truss Bridge over four
piers
- State of the art bridge when built in 1964.
- High Strength steel which allowed for thin
gusset plates.
- Truss members consisted of welded box built
up section with perforations.
- Geared roller bearings.
The event:- At 6:06 pm on August 1st, 2007, the bridge
suddenly collapsed,
- 13 people died and more than 150 were injured.
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Structural Robustness
Introduction
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Structural
Robustness
Progressive
Collapse
System structural failure System structural property
Factors that affect the Structural Robustness:
1- Redundancy (Geometry – Construction Details)
2- Ductility (Material)
3- Contingency Scenario (Degradation, Existing Damage States)
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Structural Robustness
Assessment Methods:
A relevant issue related to the structural robustness evaluation, is the choice
of appropriate synthetic parameters describing for example the sensitivity of a
damaged structure in suffering a disproportionate collapse.
In literature there are differences in the approaches and indexes towards the
structural robustness quantification.
Introduction
Approach Indexes
- property of the structure or
property of the structure and
the environment
- static or dynamic
- linear or non-linear
- deterministic or probabilistic
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P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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.
13 Introduction
References:
Nafday, AM. (2011) Consequence-based
structural design approach for black swan events.
Structural Safety, 33(1): 108-114.
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Introduction1
Consequence factor2
Application3
Conclusions4
Outline
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Undamaged
Damaged
CfscenarioConsequence factor
Consequence factor
scenario
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Structural Robustness assessment
Stiffness matrix
Kun λiun
Eigenvalues
Kdam λidam
Consequence factor
Consequence factor
Robustness indexRscenario= 100 - Cfscenario
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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17 Consequence factor
Structural Robustness assessment
ka
kb
x
y
N: total eigenvalues number
i: single eigenvalue number
a and b: elements
a
b
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
Scenario 1
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Introduction1
Consequence factor2
Application3
Conclusions4
Outline
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
I-35 West Bridge, Minneapolis, MN
• Built 1967
• 3 spans, 1067 feet long
• 1977 – new wearing surface
• 1998 – curbs and railings
replaced
19 Case Study
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
I-35 West Bridge, Minneapolis, MN
20 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
I-35 West Bridge, Minneapolis, MN
21 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
22 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
23 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
24 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
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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
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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
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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
Structural Robustness assessment – Damage based method
28 Application
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Pier 7
Pier 6
L11
L9
U10
NTSB 2007
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Single damage
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
bu
stn
ess
%
ScenarioCf max Robustness
Damage scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
Application
DSj = di
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Pier 6Pier 7
North
Pier 6
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d1d2d3
d4
d5d7
d6
Single damage
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
Robust
nes
s %
ScenarioCf max Robustness
Damage scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7
Application
DSj = di
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Pier 6Pier 7
North
Pier 6
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Introduction1
Consequence factor2
Application3
Conclusions4
Outline
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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• The consequence coefficient Cf can be used primarily as an index to
establish the critical structural members for the global structural
stability or to compare different structural design solutions from a
robustness point of view.
• The latter implementation of Cf can be helpful for the robustness
assessment of complex structures since it provides an indication on
the key structural elements.
• The method applied in this study aims at increasing the collapse
resistance of a structure, by focusing on the resistance of the single
structural members, and accounting for their importance to the global
structural behavior consequently to a generic extreme event that can
cause a local damage.
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
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Conclusions
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Thank you!
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
Conclusions
d1d2d3
d4
d5d7
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
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
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
Kun λiun
Eigenvalues
Kdam λidam
Consequence factor
Robustness index