Transcript Progress towards Structural Design for Unforeseen
Progress towards Structural Design for Unforeseen Catastrophic Events
ASME Congress
Puneet Bajpai and Ben Schafer The Johns Hopkins University
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
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
Modifying PEER framework for unforeseen events
G DV
|
DM
|
dG DM
|
EDP dG EDP
|
IM
|
d
(
IM
) | IM = Hazard intensity measure EDP = Engineering demand parameter spectral acceleration, spectral velocity, duration, … inter-story drift, max base shear, plastic connection rotation,… components lost, volume damaged, % strain energy released, … drift Eigenvalues of K tan loss after DM = Damage measure DV = Decision variable v(DV) = P DV condition assessment, necessary repairs, … failure (life-safety), $ loss, downtime, … P f probability of failure (P f ), mean annual prob. of $ loss, 50% replacement cost, … G DV EDP | dG EDP IM | d ( IM )
IM: Intensity Measure
Inclusion of Unforeseen Hazards through Damage --
Damage-Insertion
single member removal Damage Insertion 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 )
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
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
Computational effort
Explicit member removal 4000 3000 2000
Inference:
1000 3 0 2 4
Need to seek efficient sampling method to capture the structure behavior instead of
x 10 4 4 6 8 10
performing explicit calculation
12 14 16 2 1 0 2 4 6 8 10 12 Total no. of members in the structure 14 16
Structural performance degradation
1 0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
simulated DI for building mean DI for building 0 0 0.2
0.4
0.6
0.8
No. of members removed / Total no. of members in the structure 1
1 0.8
0.6
0.4
0.2
Fragility Curve
P(
<1) – collapse P[eig < 1] 0 0 0.1
0.2
0.3
0.4
0.5
No. of members removed / Total no. of members in the structure
Sampling and computational effort
1 0.8
0.6
0.4
0.2
Damage Insertion level-2 Damage Insertion level-3 Damage Insertion level-4 Damage Insertion level-5 Damage Insertion level-6 0 2000 4000 No. of samples 6000 8000 10000
•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
Redundancy and Reliability
•Effect of redundancy on the damage tolerance of a structural system and reliability
1 0.8
P[eig < 1] for Non redundant Str. P[eig < 1] for Redundant Str.
•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.
0.6
0.4
[A] [B] •Fragility curves for the limit state, defined by the collapse condition – eig < 1, are drawn for both structures [A] and [B]
0.2
0 0 0.1
0.2
0.3
0.4
No. of members removed / Total no. of members 0.5
•Redundant structure [B] is found to have lower probability of failure
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
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.