First-Order Robustness, Higher-Order Mechanics

1
First-Order Robustness,Higher-Order Mechanics

• Bassam A. IzzuddinDepartment of Civil
  Environmental Engineering

2
Progressive CollapseBut Is It Disproportionate?

• Structures cannot be designed to withstand
  unpredictable extreme events
• But should be designed for structural robustness
• the ability of the structure to withstand the
  action of extreme events without being damaged to
  an extent disproportionate to the original cause

WTC (2001)
Murrah Building (1995)
Ronan Point (1968)
Setúbal, Portugal (2007)
Disproportionate No
Disproportionate ?
Disproportionate Yes
Robust structure
3
Structural Design Predictability3
Structure
Actions
Response
Acceptable?
Malicious/terrorist actions
4
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

5
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

6
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

7
Performance-Based Design for Robustness

• Structural design for robustness
• Limiting progression of local damage
• Poor predictability, even unpredictability, of
  extreme events
• 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 the consideration of
  realistic local damage scenarios

Prescriptive event-independent local damage
scenarios
8
Simplified Framework for Robustness Design

• Robustness limit state for sudden column loss
• Ductility-centred approach
• Application to steel-concrete composite buildings

9
Robustness Limit State

• Allow collapse of above floors and consider
  resistance of lower structure?
• Impact and debris loading on lower structure
• Top floors sacrificed
• Even collapse of one floor is too onerous on
  lower floor, causing progressive collapse
• Unacceptable limit state

• Design goal should be to prevent collapse of
  above floors
• Allowing large deformations
• Outside conventional strength limit, but within
  ductility limit
• Ductility limit state
• Maximum dynamic deformed configuration
• Demand ? supply

10
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

11
Ductility-Centred Approach

• Maximum gravity load sustained under sudden
  column loss
• Applicable at various levels of structural
  idealisation

• Reduced model where deformation is concentrated

• Columns can resist re-distributed load

• Floors identical in components and loading

• Planar effects are neglected

12
Nonlinear Static Response
Ductility-Centred Approach

• Sudden column loss similar to sudden application
  of gravity load to structure without column
• Maximum dynamic response can be approximated
  using amplified static loading (ld P)

• Need models beyond conventional strength limit,
  including hardening, tensile catenary and
  compressive arching actions

13
Simplified Dynamic Assessment
Ductility-Centred Approach

• 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)
• Definition of pseudo-static response

DIF (ld/l) ltlt 2
14
Ductility-Centred ApproachSimplified 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

15
Application to Composite Buildings
7-storey steel framed composite building with
simple frame design
Sudden loss of peripheral column
Assuming identical floors ?assessment at floor
level of idealisation
Grillage approximation
edge beam
internal secondary beams
transverse primary beam
Edge beam connections
Gravity load 1.0 DL0.25 IL
16
Application to Composite Buildings

• Pseudo-static response of individual beams
• Simplified assembly to obtain pseudo-static
  capacity of floor system

17
Application to Composite Buildings
Application to Composite BuildingsIndividual
Beam Responses
18
Application to Composite Buildings
Application to Composite BuildingsAssembled
Floor Grillage

• Assumed deformation mode defines ductility limit
• Case 2 (r2 with axial restraint) is just about
  adequate
• Inadequacy of prescriptive tying force
  requirements
• Infill panels can double resistance of composite
  buildings to progressive collapse
• Material rate-sensitivity is another potentially
  significant parameter

fj
19
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

20
First-Order Robustness,Higher-Order Mechanics

• Bassam A. IzzuddinDepartment of Civil
  Environmental Engineering