Diapositiva 1

1
STRUCTURE CONGRESS 2008 April 24-26 2008,
Vancouver, Canada
Nonlinear dynamic analysis
for the structural robustness
assessment of a complex
structural system 1Franco Bontempi 2Luisa
Giuliani 1 Full Professor, University of Rome
La Sapienza Department of Structural and
Geotechnical EngineeringVia Eudossiana 18- 00184
Rome ITALYe-mail franco.bontempi_at_uniroma1.it 2
Ph.D. St. at the University of Rome La
Sapienza Department of Structural and
Geotechnical EngineeringVia Eudossiana 18- 00184
Rome ITALYe-mail luisa.giuliani_at_uniroma1.it
UNIVERSITY OF ROME LA SAPIENZA
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Presentation structure
Part II
Introduction
Conclusions
Part I
Safety and structural integrity regulation and
motivation of interest
Requirement of robustness and strategies and
methods of achievement
Robustness assessment of a long suspension bridge
Evaluations and further studies
3
Introduction
Motivation
1/21
Ambiance Plaza collapse, 1987
Meidum Piramide, 5000 a.c.
Skyline plaza collapse, 1973
Oklahoma Federal Building, 1995
Hartford arena roof collapse, 1978
4
Introduction
Motivation
2/21
Regulation
SAFETY
Safety of people
Structural integrity
Safety in SIA260 Building Code
Safety in ISO/FDIS 2394 code

• Structures and structural elements should,
  with proper levels of reliability
• satisfy exercise ultimate state requirements
• satisfy load ultimate state requirements
• satisfy structural integrity requirements

The term SAFETY in the SIA Building Codes is
primarily related to the safety of
people affected by structural failures
5
Introduction
Motivation
3/21
Structural integrity
failure is not to be just prevented, but assumed
as possible the structure response consequent to
a critical event is considered in the design
f lt fadm
Service limit states (SLS)
STIFFNESS
SCTRUCTURAL SAFETY
SECTIONS ELEMENTS
R gt S
RESISTANCE
Ultimate limit states (ULS)
verification on
?
Structural integrity limit state (SILS)
ROBUSTNESS
STRUCTURAL SYSTEM
6
Robustness
4/21
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Strategies
5/21
Strategies and methods for robustness achievement
INDIRECT METHOD
DIRECT METHOD
all those measures that, without requiring any
specific investigation, are aimed to provide the
structure with an high level of
investigation aimed to identify the structure
behavior after the occurrence of failure or a
critical event
Deductive
Inductive
critical event is modeled
critical event is irrelevant

• resistance
• ? invulnerability
• connection
• ? energy dissipation
• ductility
• ? load redistribution

B O T TOM UP
TOP DOWN
Identification of failures at meso-level
(intermediate components)
Identification of failures at micro level
(basic components)
no specific investigation are required but the
efficacy is not granted
FTA Fault Tree Analysis
FMEA Failure, Mode and Effect Analysis
FMECA Failure Mode, Effect and Criticity
Analysis
8
Strategies
6/21
Strategies and methods for robustness achievement
FAULT
FAILURE
SECURITY
INVULNERABILITY
after Starossek and Wolff, 2005
9
Conclusions
A case study
7/21
Robustness assessment of a long span suspension
bridge
Messina Strait Bridge

• Bridge deck
• total deck length 3666 m
• central span length 3300 m
• 3 continuous box-girder
• outer ones highway
• inner one railway
• transversal girder each 30 m

10
Conclusions
A case study
7/21
Robustness assessment of a long span suspension
bridge
Messina Strait Bridge

• Suspension system
• 2 pairs of steel cables
• diameter ?1,24 m
• cables length 5330 m
• 121 pairs of hangers
• hanger ropes spaced 30 m
• 3 different diameter for hanger sections

11
Conclusions
A case study
7/21
Robustness assessment of a long span suspension
bridge
Messina Strait Bridge

• Supporting system
• 2 towers
• height 383 m
• 2 anchoring blocks
• R.C.
• 4 saddles

12
Conclusions
A case study
7/21
Robustness assessment of a long span suspension
bridge
Messina Strait Bridge
Progressive collapse susceptibility of the
suspension system The analyses aim to identify
some meaningful parameter governing the response
of the bridge to an initial damage and that
depends on the particular element organization of
the structural system

• the most sensitive location for the damage for
  the triggering of the collapse (i.e. the minimum
  number of removed hangers is sought, needed to
  cause a subsequent damage in the adjoining ones)
• the most dangerous damage type symmetrical (the
  same hangers are removed on both the bridge
  sides) or asymmetrical (hangers are removed just
  on one side of the bridge
• a possible preferential direction for the
  propagation of the collapse
• some qualitative measure that could possibly lead
  the progressive collapse to an halt

13
Conclusions
Investigation
8/21
Contingency scenarios
ZONE A asymmetrical and symmetrical damage
centered 345 m far from the left tower ZONE B
asymmetrical damage centered 900 m far from the
left tower ZONE C symmetrical damage centered
450 m far from mid-span ZONE D asymmetrical and
symmetrical damage centered at mid-span
MID-SPAN
TOWER
345 m
900 m
450 m
section type 1
section type 2
section type 3
14
Conclusions
Investigation
9/21
Load scenario and bridge modeling
Load scenario

• Hanger failure are assumed to occur on the
  unloaded structure (self-weight only)

north side
Calabria
south side

• Elements one-dimensional frame elements
• Hangers tension-only frame elements with moment
  releases at both ends
• Hangers to be removed equivalent forces

Sicily
Modeling
15
Conclusions
Investigation
10/21
How analyses were performed

• Dynamic parameters
• the hanger failure has been considered by means
  of a sharp ramp function that annul in 1/100
  second the equivalent forces simulating the
  hangers to be removed.
• the dynamic analysis performed consists in a
  direct-integration time-history analysis where no
  damping is assigned and all the previous exposed
  nonlinearities are considered. The time
  integration method used for the time-history
  analysis was the Hilbert-Hughes-Taylor (HHT)
  method (parameter alpha, that can assume value
  in -1/3, 0, was set to zero)
• Restart
• in order to let the hanger failure occurs in a
  self-weight equilibrated configuration, the
  dynamic analysis starts at the end of a previous
  nonlinear static case, that provides for the
  initial conditions of the subsequent time-history
  case.

• Geometric nonlinearities
• the presence of cables required to consider 2nd
  order effects from the beginning
• a full large displacement approach has been
  disregarded (since its influence is limited when
  the deck behaves elastically) and the performed
  analyses are thus limited to the 2nd order theory
• Material nonlinearities
• tension only hangers required to consider
  material nonlinearities starting from the first
  static analysis
• a nonlinear behavior of hangers response is
  considered, by means of axial plastic hinges with
  a tributary hinge length equal to the length of
  the element on which the hinge is assigned. The
  considered hinges have no hardening branch and
  drop load when the ultimate displacement is
  reached.
• in the performed analyses the deck is considered
  to behave elastically and only some qualitative
  considerations about a possible yielding of the
  continuous box-girders of the deck are provided.

16
Conclusions
Results
11/21

• ZONE A - damage centered 345 m far from the left
  tower
• Asymmetrical failure of 9 ? 12 hangers
  
  RH LH yield
  but resist the rupture ? collapse does not
  propagate

Investigation results
17
Conclusions
Results
11/21

• ZONE A - damage centered 345 m far from the left
  tower
• Asymmetrical failure of 9 ? 12 hangers
  
  RH LH yield
  but resist the rupture ? collapse does not
  propagate
• Symmetrical failure of 6 hangers
  
  RH LH yield but
  resist the rupture ? collapse does not propagate

Investigation results
TOWER
MID-SPAN
A
345 m
Section type 1
Section type 2
Section type 3
18
Conclusions
Results
11/21

• ZONE A - damage centered 345 m far from the left
  tower
• Asymmetrical failure of 9 ? 12 hangers
  
  RH LH yield
  but resist the rupture ? collapse does not
  propagate
• Symmetrical failure of 6 hangers
  
  RH LH yield but
  resist the rupture ? collapse does not propagate
• Symmetrical failure of 7 hangers
  
  RH breaks and chain
  rupture is triggered toward the bridge centre
  first and eventually toward the tower (LH
  rupture surmount the failure of 8 RHS) ?
  collapse propagation

Investigation results
TOWER
MID-SPAN
A
345 m
Section type 1
Section type 2
Section type 3
19
Conclusions
Results
11/21

• ZONE A - damage centered 345 m far from the left
  tower
• Asymmetrical failure of 9 ? 12 hangers
  
  RH LH yield
  but resist the rupture ? collapse does not
  propagate
• Symmetrical failure of 6 hangers
  
  RH LH yield but
  resist the rupture ? collapse does not propagate
• Symmetrical failure of 7 hangers
  
  RH breaks and chain
  rupture is triggered toward the bridge centre
  first and eventually toward the tower (LH
  rupture surmount the failure of 8 RHS) ?
  collapse propagation

Investigation results
20
Conclusions
Results
12/21

• ZONE B - damage centered 900 m far from the left
  tower
• Asymmetrical failure of 7 hangers
  
  RH LH yield but
  resit the rupture ? collapse does not propagate

Investigation results
21
Conclusions
Results
12/21

• ZONE B - damage centered 900 m far from the left
  tower
• Asymmetrical failure of 7 hangers
  
  RH LH yield but
  resit the rupture ? collapse does not propagate
• . Asymmetrical failure of 9 hangers
  
  chain ruptures of RHs first and LHs
  later (surmounting the ruptures of 12 RHs)
  trigger ? progressive collapse

Investigation results
22
Conclusions
Results
13/21
ZONE B - Asymmetrical failure of 9 hangers ?
Ruptures propagation

• RH (Right Hangers)
• First rupture occurs in the RH
• Rupture propagation speeds up
• 2 hangers break in 1 sec. then
• 4 break in the following second

• LH (Left Hangers)
• First LH break 3 seconds after the first RH
  rupture, when 12 RHs have already broken
• Rupture propagation does not speed up
• 2 hangers break each second

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Conclusions
Results
14/21

• ZONE C - damage centered 450 m far from the
  midspan
• Symmetrical failure of 5 hangers
  
  chain ruptures trigger
  in RHs first and in LHS some seconds later ?
  progressive collapse

Investigation results
24
Conclusions
Results
14/21

• ZONE C - damage centered 450 m far from the
  midspan
• Symmetrical failure of 5 hangers
  
  chain rupture of RHs
  first and LHS later (surmounting the rupture of )
  trigger ? progressive collapse

Investigation results
25
Conclusions
Results
14/21

• ZONE C - damage centered 450 m far from the
  midspan
• Symmetrical failure of 5 hangers
  
  chain rupture of RHs
  first and LHS later (sormounting the rupture of )
  trigger ? progressive collapse

Investigation results
26
Conclusions
Results
15/21

• ZONE D - damage centered at mid-span
• Symmetrical failure of 5 hangers
  
  chain rupture of RHs
  first and LHS later (sormounting the rupture of )
  trigger ? progressive collapse

Investigation results
27
Conclusions
Results
15/21

• ZONE D - damage centered at mid-span
• Symmetrical failure of 5 hangers
  
  chain rupture of RHs
  first and LHS later (sormounting the rupture of )
  trigger ? progressive collapse
• Asymmetrical failure of 7 hangers
  
  chain rupture of RHs first
  and LHS later (sormounting the rupture of )
  trigger ? progressive collapse

Investigation results
TOWER
MID-SPAN
D
Section type 1
Section type 2
Section type 3
28
Conclusions
Results
16/21
ZONE D - Asymmetrical failure of 7 hangers ?
Ruptures propagation

• RH - LH propagation
• Ruptures trigger and propagate simultaneously in
  the RH LH
• Rupture trigger very soon (in the first one and
  half second) and propagate with an high velocity
  (7 hangers break in 3 seconds) compared with as.
  fail. _at_ B.
• Rupture propagation does not speeds up
• 2 hangers break in each half second
• Progressive collapse doesnt come to an halt
  though, not even when encountering hanger
  greater sections

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Conclusive evaluations
Conclusions
17/21
Characteristics identified in the response
intrinsic to the structural system
most sensitive location

• the minimum number of removed hangers and the
  most sensitive location for the triggering of the
  progressive collapse
• The bridge results to be more sensible to the
  damage at mid-span, where the removal of just 5
  hanger for the symmetrical rupture and 7 hangers
  for the asymmetrical rupture is needed in order
  to trigger the collapse propagation.
• Shifting the initial damage location aside
  (about at 1/3 of the span) the asymmetrical
  rupture of 9 hangers is required for the collapse
  propagation, while moving the initial damage near
  the tower even the asymmetrical removal of 12
  hangers has no global effects on the structure
  and very 7 hangers must be symmetrically removed
  on both sides in order to trigger the propagation
  of the ruptures on the adjoining hangers.

30
Conclusive evaluations
Conclusions
18/21
Characteristics identified in the response
intrinsic to the structural system
collapse propagation
growing element ductility

• preferential direction for the collapse
  propagation
• To the higher damage sensibility of the bridge
  central zone counterpoises a lower acceleration
  of the collapse progression triggered by central
  ruptures, with respect to that one triggered by
  lateral ruptures this effect is due to the
  particular configuration of the structural system
  that requires a growing hanger length from the
  centre to the sides of the bridge when a chain
  rupture trigger, the ultimate elongation required
  to the hangers adjoining the failed ones
  increases as the collapse propagates (because the
  unsupported deck length also increases).
• If the initial damage occurs at mid-span, it
  involves the shortest hangers and the collapse
  propagation is partially slowed down from the
  growing element ductility of sideward hangers.
  On the contrary, a more intense initial damage
  is required sideways to trigger chain ruptures,
  but then the hanger breakdowns speeds up when
  moving toward the centre, where the hanger length
  decreases.

31
Conclusive evaluations
Conclusions
19/21
Characteristics identified in the response
intrinsic to the structural system
ruptures propagate easily
ruptures trigger easily
increasing sections

• qualitative measure that could possibly lead the
  collapse to an halt
• In the case of a central rupture a closer
  increment in the section of the hangers (that
  remain instead the same for about 5/6 of the span
  length) could possibly provide for a collapse
  standstill.
• In the case of a chain rupture triggered in a
  lateral zone the preferential direction showed by
  the progressive collapse would probably make less
  effective such a measure.

32
Conclusive evaluations
Conclusions
20/21
Characteristics identified in the response
intrinsic to the structural system

• Sensibility to modality of damage (asymmetrical
  or symmetrical failure)
• Another consideration about the possible
  collapse standstill concerns the higher
  susceptibility of the bridge to an unsymmetrical
  hanger failure than to a symmetrical one in the
  last case the symmetrical hinge formations
  determines a symmetrical moment increment on the
  deck box-girders, thus possibly allowing for an
  early deck segment detachment that would arrest
  the collapse.

33
Further research
Conclusions
21/21
Further studies are needed to investigate the
effects of

• a possible stiffening of some predetermined
  hangers or a closer increment in the hanger
  sections in order to localize the collapse
  determined by a central rupture
• the role of the deck section ductility and the
  study of a proper design of joint details that
  could provide for an early detachment of the
  deck, in case of a symmetrical failure
• its not sufficient that the deck yields, but it
  is also required that the involved deck segment
  separates early from the rest of the structure,
  avoiding the transmission to the rest of the deck
  of the high stress developed in the three-hinges
  mechanism, that would entangle the deck segment.