Transcript Mitigation of Progressive Collapse in Multi

Imperial College
London
First-Order Robustness,
Higher-Order Mechanics
Bassam A. Izzuddin
Department of Civil & Environmental Engineering
Progressive Collapse…
But Is It Disproportionate?
• Structures cannot be designed to withstand
unpredictable extreme events
• But should be designed for structural robustness:
WTC
Setúbal,
Murrah
Ronan
(2001)
Point
Building
Portugal
(1968)
(1995)
(2007)
the ability of the structure to withstand the action of
extreme events without being
damaged
to an extent
Disproportionate:
Robust
Disproportionate:
structure
No
Yes
?
disproportionate to the original cause
9-12 May 2011
CMM 2011, Warsaw, Poland
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Structural Design – Predictability3
Structure
Codified properties
Statistical data
Site supervision & QA
…
Response
Codified calculations
Simplified analysis
Detailed analysis
… Acceptable?
Actions
Codified loads
Statistical analysis
Event modelling
…
Malicious/terrorist
actions
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CMM 2011, Warsaw, Poland
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First-Order Robustness
• Structure predictability
– Material characteristics, member sizes, connections, …
– Non-structural elements
• Infill panels, glazing, …
• Fire protection
– Structure variability must be considered within a risk assessment
framework
• Construction tolerances and errors
• Statistical data
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CMM 2011, Warsaw, Poland
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First-Order Robustness
• Action (event) predictability
– Intensity, duration and location of initiating event
– Transmission to structure : event to actions
• Blast to overpressures
• Fire to temperatures
• Need for sophisticated event modelling
– Event variability must be considered within a risk assessment
framework
• Statistical data
– Intrinsic unpredictability of terrorist actions
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CMM 2011, Warsaw, Poland
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Higher-Order Mechanics
• Response predictability
– Geometric nonlinearity: large deflections
– Material nonlinearity: inelasticity, rate-sensitivity, elevated
temperatures, fracture, bond-slip,…
– Connection components
– Interaction between structural and non-structural elements
– Effect of localised component failures
– Effect of debris impact and collapse progression
• Poor predictability, even chaotic
• Circumvented with appropriate choice of limit state
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CMM 2011, Warsaw, Poland
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Performance-Based Design for
Robustness
• Structural design for robustness
– Limiting progression of local damage
– Poor predictability, even unpredictability, of extreme events
Structure
Response
Actions
– Prescriptive event-independent local damage scenarios
• Variability may still be considered in terms of location, extent, …
• Damage scenarios must be realistic – e.g. dynamic content
– Performance-based response prediction
– Closer overall to performance-based
than prescriptive
design with
Codified calculations
Codified loads
ofSimplified
realistic
local damage scenarios
analysis
Statistical analysis
Codified properties
Statistical the
data consideration
Site supervision & QA
…
Detailed analysis
…
Event modelling
…
Prescriptive event-independent
local damage scenarios
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CMM 2011, Warsaw, Poland
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Simplified Framework for
Robustness Design
• Robustness limit state for sudden column loss
• Ductility-centred approach
• Application to steel-concrete composite buildings
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CMM 2011, Warsaw, Poland
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Robustness Limit State
• Allow
Designcollapse
goal should
of above
be tofloors
and consider
prevent
collapse
resistance
of above
offloors
lower structure?
• Allowing large deformations
– Impact and debris loading on
– lower
Outside
conventional strength
structure
limit, but within ductility limit
– Top floors sacrificed
• Ductility
limit state
– Even collapse
of one floor is too
ondynamic
lower floor,
causing
– onerous
Maximum
deformed
progressive
collapse
configuration
–
limit state
– Unacceptable
Demand  supply
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CMM 2011, Warsaw, Poland
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Ductility-Centred Approach
• Robustness limit state
– Prevention of collapse of
upper floors
– Ductility: demand  supply
• Two stages of assessment
– Nonlinear static response
accounting for ductility limit
– Simplified dynamic
assessment
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CMM 2011, Warsaw, Poland
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Ductility-Centred Approach
• Maximum gravity
load sustained under
sudden column loss
• Applicable at various
levels of structural
idealisation
• Floors
Planar identical
Reduced
Columns
effects
can
model
resist
are
in
where deformation
re-distributed
components
neglected
and
load is
concentrated
loading
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CMM 2011, Warsaw, Poland
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Ductility-Centred Approach:
Nonlinear Static Response
• Sudden
Need models
column
beyond
loss similar
conventional
to sudden
strength
application
limit, including
of gravity
load to structure
hardening,
tensilewithout
catenary
column
and compressive arching actions
– Maximum dynamic response can be approximated using
amplified static loading (ld P)
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CMM 2011, Warsaw, Poland
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Ductility-Centred Approach:
Simplified Dynamic Assessment
• Based on conservation of energy
• Work done by suddenly applied load equal to
internal energy stored
• Leads to maximum dynamic displacement (also to
load dynamic amplification)
DIF = (ld/l) << 2
• Definition of “pseudo-static” response
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CMM 2011, Warsaw, Poland
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Ductility-Centred Approach:
Simplified Dynamic Assessment
• ‘Pseudo-static capacity’ as a rational
performance-based measure of structural
robustness
– Focus on evaluation of ductility demand and
comparison against ductility limit
 Instead of dynamic amplification of static loads
– Combines redundancy, ductility and energy
absorption within a simplified framework
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CMM 2011, Warsaw, Poland
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Application to Composite Buildings
Gravity
7-storey
Sudden
Assuming
Grillage
Edge
beam
load
approximation:
loss
steel
identical
connections
=offramed
1.0
peripheral
DL+0.25
floors
composite

column
IL building with
simplebeam
assessment
edge
internal
transverse
frame
secondary
primary
atdesign
floorbeams
beam
level of idealisation
6000
Anti-crack mesh
2375
Removed column
6000
Shear stud
50
70
80
60
130
50
40
70
3000
70
70
40
3000
1500
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Supported beam
406 x 140 x 39 UB
Grade S355
Supported beam
406 x 140 x 39 UB
Grade S355
Supporting column
305 x 305 x 118 UC
Grade S355
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Application to Composite Buildings
• Pseudo-static response of individual beams
• Simplified assembly to obtain pseudo-static
capacity of floor system
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CMM 2011, Warsaw, Poland
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Application to Composite Buildings:
Buildings
Individual Beam Responses
150%
125%
Gap closure
15
100%
75%
10
50%
Static resposne, w/ axial restraint
Static response, w/o axial restraint
5
25%
Pseudo-static response, w/ axial restraint
Pseudo-static response, w/o axial restraint
0
0
100
200
Displacement, δ (mm)
300
Percentage of Service Loads (%)
Static/Dynamic Load (kN/m)
20
0%
400
Static and pseudo-static curves for edge beam with ρ = 1.12%
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CMM 2011, Warsaw, Poland
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Application to Composite Buildings:
Buildings
Assembled Floor Grillage
• Assumed deformation mode defines ductility limit
• Case 2 (r=2% with axial restraint) is just about adequate
• Inadequacy of prescriptive tying force requirements
• Infill panels
φj can double resistance of composite buildings to
progressive collapse
Capacity
Po
Capacity/Demand
Deformation
profile
δSB1 P Demand
CaseCase
No. No.
(N)
(N)
ratio
φd,TB (rad)
uis
(mm)
upotentially
ud,IB3 (mm) ud,EB (mm)
• Material rate-sensitivity
significant
d,IB1
d,IB2 (mm)
δanother
SB2
ρmin, EC4,
parameter
598729
741990
1 1
0.0364
54.6
163.7 0.81 272.9
359.3
w/ axial restraint
ρ = 2%,
w/ axial restraint
ρ = 2%,
w/ο axial restraint
Bare-steel frame,
w/ axial restraint
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2
2
3
3
4
4
774358
0.0381
709675
0.0359
741990
57.2
741990
53.8
148530
0.0623
741990
93.5
171.6
δSB3
161.3
280.5
CMM 2011, Warsaw, Poland
1.04 286.0
0.96 268.9
0.20
δMB
467.6
376.5
354.0
615.6
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Conclusions
• Design-oriented ductility-centred approach
– Practical multi-level framework
– Accommodates simplified/detailed nonlinear
structural models
– Simplified dynamic assessment for sudden
column loss
– ‘Pseudo-static capacity’ as a single rational
measure of robustness, combining ductility,
redundancy and energy absorption capacity
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CMM 2011, Warsaw, Poland
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Imperial College
London
First-Order Robustness,
Higher-Order Mechanics
Bassam A. Izzuddin
Department of Civil & Environmental Engineering