1. Progress towards Structural Design for Unforeseen Catastrophic Events ASME Congress Puneet Bajpai and Ben Schafer The Johns Hopkins University

2. Introduction Unforeseen Hazards PEER Research Program in Performance-Based Earthquake Engineering. Development of enabling methodology and system-level research. Rational models of structural behavior at limit state are needed for simulating performance – Defining Collapse Redundancy and Reliability Integration with decision-making

3. Environmental vs. Unforeseen Hazards (a) P f of foreseen events, goal of traditional environmental hazard governed design (b) P f for unforeseen events, consideration of of design for unknown hazards

4. Modifying PEER framework for unforeseen events IM = Hazard intensity measure spectral acceleration, spectral velocity, duration, … components lost, volume damaged, % strain energy released, … drift Eigenvalues of K tan after loss inter-story drift, max base shear, plastic connection rotation,… EDP = Engineering demand parameter condition assessment, necessary repairs, … DM = Damage measure failure (life-safety), $ loss, downtime, … DV = Decision variable probability of failure (P f ), mean annual prob. of $ loss, 50% replacement cost, … v(DV) = P DV

5. IM: Intensity Measure Inclusion of Unforeseen Hazards through Damage -- Damage-Insertion single member removal multi member removal member weakening strain energy removed Correlation of Damage through the structure concentric damage progression connected member chain roulette wheel selection random member selection Probability distribution – likelihood of IM Categorical definitions or continuous variable descriptions (  IM,  IM ) Damage- Insertion

6. EDP: Engineering Demand Parameter Rational Computationally Efficient Simple Candidates – Inter-story drift Norm of deflection vector Normalized eigenvalue degradation efficiency in computation and reanalysis consistent eigenmode response

7. Case Study: Seattle 3 A SAC building model - 3 story 4 bay frame - is Used to demonstrate the insight into the proposed methodology Gravity loads are considered governing in all the cases with service level lateral load Roulette wheel selection procedure is sought with uniform probability distribution of IM over the structure Load conservative IM: all forces on removed elements are summed and placed at the boundary of the lost element EDP: first eigenvalue normalized with eigenvalue of the intact structure is considered

8. Computational effort Total no. of members in the structure Computational time (sec.) Total no. of ways of inserting damage Explicit member removal Inference: Need to seek efficient sampling method to capture the structure behavior instead of performing explicit calculation

9. Structural performance degradation No. of members removed / Total no. of members in the structure Damage Index (DI = 1 – eig_damaged / eig_intact)

10. Fragility Curve P( <1) – collapse Limit State probability No. of members removed / Total no. of members in the structure

11. Sampling and computational effort Limit State probability Estimate (P[eig<1]) No. of samples Limit state probability converges with inclusion of higher samples in the computation It is also observed that a fair estimate of probabilities can be computed at No. of samples  (total no. of members) 2

12. Redundancy and Reliability Effect of redundancy on the damage tolerance of a structural system and reliability Structure [A] is made redundant by putting cross braces, that possess the same lateral stiffness as A, in one of the bays of the building. [A][B] Fragility curves for the limit state, defined by the collapse condition – eig < 1, are drawn for both structures [A] and [B] Redundant structure [B] is found to have lower probability of failure Limit State probability No. of members removed / Total no. of members

13. Future Directions/Efforts Work is largely underway and exploratory in nature Better IM and IM characterization prob. of loads outside the building codes… more robust metrics than “n”, volume based, load based, energy based??? Better EDP and EDP characterization specific modal response better use of drift measure Efficiencies in analysis Integration with EQ decision-making tools

14. Conclusion Building structural safety must get (1) beyond environmental loads (2) beyond scenario driven loads and instead look more generally and building robustness and redundancy – one way is to perform the type of structural de-constructions suggested here. Fragility curves for unforeseen events can be developed and provide a potential tool for integrating with real decision-making on building structural systems, retrofits, etc. We gratefully and humbly acknowledge the support of this research by the NSF and extend our thanks Dr. Roger Ghanem for his assistance and guidance.

15. Thank you for your attention