MIGLIORAMENTO ED ADEGUAMENTO SISMICO DI STRUTTURE ESISTENTI ATTRAVERSO L’UTIL...
Olmati et al.
1. P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
Robustness assessment of a steel truss bridge
P. Olmati & K. Gkoumas
Sapienza University of Rome
pierluigi.olmati@uniroma1.it
konstantinos.gkoumas@uniroma1.it
F. Brando
Thornton Tomasetti, New York
fbrando@thorntontomasetti.com
Progressive Collapse and Structural Robustness: An International Perspective
Clay J. Naito, Ph.D., P.E., Associate Professor and Associate Chair
Konstantinos Gkoumas, Ph.D., P.E., Associate Researcher
6. 6
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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7. 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)
7
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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8. 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
9. Interstate 90 Grand River bridge, Ohio – October, 1996
Cause Damage Pr. Collapse
Introduction9
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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.
10. 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.
11. 11
Structural Robustness
Introduction
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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)
12. 12
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
13. 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.
13 Introduction
References:
Nafday, AM. (2011) Consequence-based
structural design approach for black swan events.
Structural Safety, 33(1): 108-114.
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16. 16
Structural Robustness assessment
Stiffness matrix
Kun λi
un
Eigenvalues
Kdam λi
dam
Consequence factor
Consequence factor
Robustness indexRscenario= 100 - Cf
scenario
N1i
un
i
dam
i
un
iscenario
f 100
)(
maxC
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17. 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
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19. 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
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20. 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.
North
Downtown
D-1
21. 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.
North
Downtown
D-1
Security Camera video
22. 22 Analysis Procedure
P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone
N
FIM
Forensic 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.
23. 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
24. 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
25. 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
26. 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
L11
L9
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
27. 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
28. Structural Robustness assessment – Damage based method
28 Application
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Pier 7
Pier 6
L11
L9
U10
NTSB 2007
32. 32
• 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.
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Conclusions
