Imperial College London First-Order Robustness, Higher-Order Mechanics Bassam A. Izzuddin Department of Civil & Environmental Engineering

May 2011 CMM 2011, Warsaw, Poland Progressive Collapse… But 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) Disproportionate: No Murrah Building (1995) Disproportionate: ? Ronan Point (1968) Disproportionate: Yes Setúbal, Portugal (2007) Robust structure

Structure May 2011 CMM 2011, Warsaw, Poland Structural Design – Predictability 3 ActionsResponse Acceptable? Codified properties Statistical data Site supervision & QA … Codified calculations Simplified analysis Detailed analysis … Codified loads Statistical analysis Event modelling … Malicious/terrorist actions

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 May 2011 CMM 2011, Warsaw, Poland

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 May 2011 CMM 2011, Warsaw, Poland

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 May 2011 CMM 2011, Warsaw, Poland

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 May 2011 CMM 2011, Warsaw, Poland Prescriptive event-independent local damage scenarios Codified calculations Simplified analysis Detailed analysis … StructureActionsResponse Codified properties Statistical data Site supervision & QA … Codified loads Statistical analysis Event modelling …

Simplified Framework for Robustness Design Robustness limit state for sudden column loss Ductility-centred approach Application to steel-concrete composite buildings May 2011 CMM 2011, Warsaw, Poland

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 May 2011 CMM 2011, Warsaw, Poland 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

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 May 2011 CMM 2011, Warsaw, Poland

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 May 2011 CMM 2011, Warsaw, Poland

Nonlinear Static Response Sudden column loss similar to sudden application of gravity load to structure without column –Maximum dynamic response can be approximated using amplified static loading ( d P ) May 2011 CMM 2011, Warsaw, Poland Ductility-Centred Approach: Need models beyond conventional strength limit, including hardening, tensile catenary and compressive arching actions

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 Simplified Dynamic Assessment DIF = ( d / ) << May 2011 CMM 2011, Warsaw, Poland Ductility-Centred Approach:

‘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 9-12 May 2011 CMM 2011, Warsaw, Poland 14 Ductility-Centred Approach: Simplified Dynamic Assessment

Application to Composite Buildings May 2011 CMM 2011, Warsaw, Poland 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 beaminternal secondary beamstransverse primary beam Edge beam connectionsGravity load = 1.0 DL+0.25 IL

Application to Composite Buildings Pseudo-static response of individual beams Simplified assembly to obtain pseudo-static capacity of floor system May 2011 CMM 2011, Warsaw, Poland

Application to Composite Buildings May 2011 CMM 2011, Warsaw, Poland Static and pseudo-static curves for edge beam with ρ = 1.12% Application to Composite Buildings: Individual Beam Responses

Application to Composite Buildings May 2011 CMM 2011, Warsaw, Poland Application to Composite Buildings: Assembled Floor Grillage δ SB3 δ SB1 δ SB2 δ MB φjφj ρ min, EC4, w/ axial restraint ρ = 2%, w/ axial restraint ρ = 2%, w/ο axial restraint Bare-steel frame, w/ axial restraint Assumed deformation mode defines ductility limit Case 2 (  =2% 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

9-12 May 2011 CMM 2011, Warsaw, Poland 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

Imperial College London First-Order Robustness, Higher-Order Mechanics Bassam A. Izzuddin Department of Civil & Environmental Engineering