First-Order Robustness, Higher-Order Mechanics

1. First-Order Robustness,Higher-Order Mechanics Bassam A. IzzuddinDepartment of Civil & Environmental Engineering

2. 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) Setúbal, Portugal (2007) Murrah Building (1995) Ronan Point (1968) Disproportionate: No Robust structure Disproportionate: ? Disproportionate: Yes CMM 2011, Warsaw, Poland

3. Structural Design – Predictability3 Structure Response Actions Acceptable? Codified properties Statistical data Site supervision & QA … Codified calculations Simplified analysis Detailed analysis … Codified loads Statistical analysis Event modelling … Malicious/terrorist actions CMM 2011, Warsaw, Poland

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 CMM 2011, Warsaw, Poland

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 CMM 2011, Warsaw, Poland

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 CMM 2011, Warsaw, Poland

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

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

9. Robustness 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 • 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 CMM 2011, Warsaw, Poland

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 CMM 2011, Warsaw, Poland

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 CMM 2011, Warsaw, Poland

12. Nonlinear Static Response Ductility-Centred Approach: • Need models beyond conventional strength limit, including hardening, tensile catenary and compressive arching actions • 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) CMM 2011, Warsaw, Poland

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) << 2 CMM 2011, Warsaw, Poland

14. 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 CMM 2011, Warsaw, Poland

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 DL+0.25 IL CMM 2011, Warsaw, Poland

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

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

18. δSB1 ρmin, EC4, w/ axial restraint ρ = 2%, w/ axial restraint δSB2 δSB3 ρ = 2%, w/ο axial restraint Bare-steel frame, w/ axial restraint δMB Application to Composite Buildings Application to Composite 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 can double resistance of composite buildings to progressive collapse • Material rate-sensitivity is another potentially significant parameter φj 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 CMM 2011, Warsaw, Poland

20. First-Order Robustness,Higher-Order Mechanics Bassam A. IzzuddinDepartment of Civil & Environmental Engineering