Download presentation

Presentation is loading. Please wait.

Published byStephen Larkins Modified over 2 years ago

1
Imperial College London Structural Systems Analysis for Robustness Assessment Bassam A. Izzuddin Department 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) Disproportionate: No Murrah Building (1995) Disproportionate: ? Ronan Point (1968) Disproportionate: Yes Setúbal, Portugal (2007) Robust structure 4 July 2012 Robustness Summer School - COST Action TU0601 2

3
Structure Structural Design – Predictability 3 ActionsResponse Codified properties Statistical data Site supervision & QA … Codified calculations Simplified analysis Detailed analysis … Codified loads Statistical analysis Event modelling … Malicious/terrorist actions Acceptable? 4 July 2012 Robustness Summer School - COST Action TU0601 3

4
Structural robustness (UK Building Regulations, Eurocode EN 1990) –ability to withstand extreme events without being damaged to an extent disproportionate to the original cause UK Building Regulations: A3 Disproportionate Collapse –Class 2B buildings (up to 15 storeys) Prescriptive tying force requirements Notional member removal Key element design –Class 3 buildings (more than 15 storeys) Systematic risk assessment Codified Design for Robustness Invoked if notional member removal leads to excessive damage (15% of floor area or 70m 2 ) No clear guidance Do not guarantee robustness Implicit reliance on tensile catenary action, while ignoring ductility issues Do not allow comparison between alternative designs utilising redundancy, ductility and energy absorption More performance based However, conventional design checks (ignoring large deformations) Ignores dynamic effects Unrealistic designs and damage assessment 4 July 2012 Robustness Summer School - COST Action TU0601 4

5
Probabilistic Risk Assessment Risk = P(H) P(D|H) P(F|D) C(F) Hazard Local damage System failure Vulnerability Damage tolerance Consequences Structural robustness Involve similar types of structural analysis May be considered together depending on event resolution 1.Deterministic evaluation of failure | D = sudden column loss 2.Material related issues (steel and composite structures) 3.Application in probabilistic risk assessment 4 July 2012 Robustness Summer School - COST Action TU0601 5

6
Sudden Column Loss (D) Event-independent scenario More than just a standard test of robustness –Sudden column loss (SCL) vs column damage by blast –Comparison of deformation demands in upper floors –SCL presents an upper bound on floor deformations –SCL can be scaled to correspond to intermediate levels of blast –SCL realistic for multi-storey buildings even considering blast uplift and extended local damage Can be assessed without full nonlinear dynamic analysis Sudden column loss 4 July 2012 Robustness Summer School - COST Action TU0601 6

7
From prescriptive to performance-based design Recent GSA (2003) and DoD (2005) guidance –Consider sudden column loss as a design scenario –Detailed nonlinear dynamic analysis –Simplified equivalent static approach Move to modify and unify GSA/DoD guidance –Important changes in equivalent static approach Sudden Column Loss (D) Too complicated for practical application in design Excessive dynamic amplification factor equal to 2 Conventional design checks 4 July 2012 Robustness Summer School - COST Action TU0601 7

8
Failure limit state at point of collapse of above floors Allowing large deformations –Outside conventional strength limit, but within ductility limit Ductility limit –Maximum dynamic deformed configuration –Demand supply Collapse of above floors and considering 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 –Failure state Failure Limit State (F) 4 July 2012 Robustness Summer School - COST Action TU0601 8

9
Basis of equivalent pushdown static approach proposed for new GSA/DoD guidance Nonlinear static analysis –D–DIF equal to 2 applicable only for linear elastic response –R–Recognition of influence of available ductility on DIF –B–But not the characteristics of nonlinear static response Load Factor Approaches Dynamic responseStatic analysis 4 July 2012 Robustness Summer School - COST Action TU0601 9

10
DIF in terms of ductility for use with nonlinear static analysis in new GSA/DoD guidance Monotonic reduction in DIF with ductility Load Factor Approaches 4 July 2012 Robustness Summer School - COST Action TU0601 10

11
Load Factor Approaches Elastic-plastic static response Dynamic resistance Static resistance DIF = 2 DIF = 1.67DIF = 1.04 Monotonic reduction of DIF with ductilityConsistent with load factor approaches for new GSA/DoD guidance 4 July 2012 Robustness Summer School - COST Action TU0601 11

12
Load Factor Approaches Elasto-plastic static response with hardeningDIF increases with ductility after initial reduction Proposed load factor approaches very unsafe for ductile structures 4 July 2012 Robustness Summer School - COST Action TU0601 12

13
Failure | Sudden Column Loss Limit state: dynamic failure of floors above Two stages of assessment –Nonlinear static response accounting for ductility limit –Simplified dynamic assessment 4 July 2012 Robustness Summer School - COST Action TU0601 13

14
Failure | Sudden Column Loss Maximum gravity load sustained under sudden column loss Applicable at various levels of structural idealisation Reduced model where deformation is concentrated Columns can take re- distributed load Floors identical in components and loading Planar effects are neglected 4 July 2012 Robustness Summer School - COST Action TU0601 14

15
Failure | Sudden Column Loss Benefits of multi-level approach –Low level models can be used to assemble response at higher levels –Realised even if conditions of model reduction are not applicable –Beam models assemble a grillage approximation of floor –Floor model assembles SDOF response of multiple floors, assuming rigid column 4 July 2012 Robustness Summer School - COST Action TU0601 15

16
Nonlinear Static Response Failure | Sudden Column Loss Sudden column removal similar to sudden application of gravity load –Maximum dynamic response can be approximated using amplified static loading ( d P ) 4 July 2012 Robustness Summer School - COST Action TU0601 16

17
4 July 2012 Robustness Summer School - COST Action TU0601 17 Failure | Sudden Column Loss Nonlinear Static Response Proposed framework supports detailed / simplified models Detailed and simplified modelling may be combined –Detailed at lower levels to capture complex nonlinear response (connections, composite action, …) –Simplified assembly at higher levels

18
4 July 2012 Robustness Summer School - COST Action TU0601 18 Failure | Sudden Column Loss Nonlinear Static Response Detailed models, largely based on NLFE –At beam level: geometric and material nonlinearity, connection nonlinearity using component-based approach, composite action, … –At floor level: additionally membrane action, geometric orthotropy, … –At higher levels: additional sophistication, but excessive computational demands

19
4 July 2012 Robustness Summer School - COST Action TU0601 19 Failure | Sudden Column Loss Nonlinear Static Response Simplified modelling –Facilitates practical application in design –Applicable at various levels of structural idealisation –At lowest beam level More sophisticated simplified models needed Can be substituted by detailed models

20
4 July 2012 Robustness Summer School - COST Action TU0601 20 Failure | Sudden Column Loss Nonlinear Static Response Simplified floor grillage model –Assumed SDOF mode, realistic at large deflections –Assume load distributions, but not intensities, on component beams Accuracy of load distribution unimportant at large deflections –Nonlinear load-deflection response of floor system obtained as weighted sum of individual beam responses Simplified / detailed beam models may be used

21
4 July 2012 Robustness Summer School - COST Action TU0601 21 Failure | Sudden Column Loss Nonlinear Static Response Simplified multi-floor model –Assume SDOF mode, realistic if load redistribution between floors well within column capacity –Assume load distributions on floors For practicality, ignore force transferred via line of columns above failed column –Nonlinear load-deflection response of overall system as weighted sum of individual floor responses Simplified / detailed individual floor models

22
4 July 2012 Robustness Summer School - COST Action TU0601 22 Failure | Sudden Column Loss Nonlinear Static Response Ductility limit –Ductility demands in connections and their components related to system displacements –Smallest displacement at which ductility demand exceeds supply in one of the connections –Importance of accounting for rotational and axial deformations –Need for extensive experimental data on connection ductility –Proposed framework accommodates refined data

23
Applicable at various levels of structural idealisation –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 d <<2 Failure | Sudden Column Loss 4 July 2012 Robustness Summer School - COST Action TU0601 23

24
Failure | Sudden Column Loss Simplified Dynamic Assessment Dynamic pseudo-static ( P,u d ) response constructed from corresponding nonlinear static ( P,u s ) response –Represents response to sudden application of gravity load ( P ) –Provides valuable information about influence of different levels of gravity load under sudden column loss –Dynamic analysis would require excessive runs to obtain similar information 4 July 2012 Robustness Summer School - COST Action TU0601 24

25
P max corresponds to (u d =u f ) for monotonic static response Pseudo-static capacity as a rational performance-based measure of structural robustness –Emphasis not on dynamic amplification of static loads with conventional design, but on dynamic demand within ductility limit –Combines redundancy, ductility and energy absorption within a simplified framework Not necessarily for softening static response Failure | Sudden Column Loss Simplified Dynamic Assessment 4 July 2012 Robustness Summer School - COST Action TU0601 25

26
Sudden Component Loss Pseudo-static approach also applicable to sudden loss of other components –Provided dynamic response is dominated by a single mode –Pseudo-static response obtained from nonlinear static response of damaged structure, as before 4 July 2012 Robustness Summer School - COST Action TU0601 26

27
Nonlinear dynamic response under 3 levels of gravity loading Nonlinear static response and pseudo-static response Maximum dynamic displacements from pseudo-static response at three load levels Accounting for initial deflections in pseudo- static response Excellent comparison between pseudo-static approach and nonlinear dynamic analysis Static analysis unsafe and load amplification based on a factor of 2 grossly conservative Truss subject to sudden brace failure (e.g. due to sudden connection failure) Sudden Component Loss 4 July 2012 Robustness Summer School - COST Action TU0601 27

28
Successive Component Losses Further component losses could occur during dynamic response, without necessarily defining overall dynamic system resistance Pseudo-static approach can still be applied: –Single dominant mode –Nonlinear static response of initially damaged structures –Reduction in nonlinear static response due to component failure 4 July 2012 Robustness Summer School - COST Action TU0601 28

29
… for instance following a compressive arching stage Maximum load at intersection between pseudo-static and descending static curves Residual pseudo-static capacity after second component loss …but not with more severe second component loss …unless system ductility and static resistance picks up Static response of undamaged structure Successive Component Losses Structural system subject to initial damage followed by second component loss Static response of initially damaged structure Second component loss Complete system failure Maximum pseudo-static capacity may not even be related to a specific ductility limit 4 July 2012 Robustness Summer School - COST Action TU0601 29

30
Application to Composite Buildings 30 4 July 2012 Robustness Summer School - COST Action TU0601 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 connections

31
Application to Composite Buildings Pseudo-static response of individual beams Simplified assembly to obtain pseudo-static capacity of floor slab Importance of connection ductility, additional reinforcement and axial restraint Inadequacy of prescriptive tying force requirements 31 4 July 2012 Robustness Summer School - COST Action TU0601

32
Application to Composite Buildings 32 4 July 2012 Robustness Summer School - COST Action TU0601 Pseudo-static response curves of internal beams Pseudo-static response curves of transverse beam Pseudo-static response curves of edge beam Static and pseudo-static curves for edge beam with ρ = 1.12% Application to Composite Buildings: Individual Beam Responses

33
Application to Composite Buildings 33 4 July 2012 Robustness Summer School - COST Action TU0601 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

34
Application to Composite Buildings Response of composite beams with partial strength connections dominated by compressive arching in the presence of axial restraint Ductility of partial strength connections typically insufficient to mobilise full catenary action Increasing tying force capacity is helpful but not necessarily via catenary action, unless rotation capacity exceeds 8 º Infill panels can double resistance of composite buildings to progressive collapse Material rate-sensitivity is another potentially significant parameter 34 4 July 2012 Robustness Summer School - COST Action TU0601 ~ 4 º > 8 º Application to Composite Buildings: General Observations

35
Probabilistic Risk Assessment Risk = P(H) P(D|H) P(F|D) C(F) 1.Deterministic evaluation of failure | D = sudden column loss 2.Material related issues (steel and composite structures) 3.Application in probabilistic risk assessment 4 July 2012 Robustness Summer School - COST Action TU0601 35

36
References Izzuddin, B.A., Vlassis, A.G., Elghazouli, A.Y., and Nethercot, D.A., "Progressive Collapse of Multi-Storey Buildings due to Sudden Column Loss Part I: Simplified Assessment Framework, Engineering Structures, Vol. 30, No. 5, May 2008, pp. 1308-1318. Vlassis, A.G., Izzuddin, B.A., Elghazouli, A.Y., and Nethercot, D.A., "Progressive Collapse of Multi-Storey Buildings due to Sudden Column Loss Part II: Application, Engineering Structures, Vol. 30, No. 5, May 2008, pp. 1424-1438. Vlassis, A.G., Izzuddin, B.A., Elghazouli, A.Y., and Nethercot, D.A., "Progressive Collapse of Multi-Storey Buildings due to Failed Floor Impact, Engineering Structures, Vol. 31, No. 7, July 2009, pp. 1522-1534. Gudmundsson, G.V., and Izzuddin, B.A., "The Sudden Column Loss Idealisation for Disproportionate Collapse Assessment, The Structural Engineer, Vol. 88, No. 6, 2010, pp. 22-26. Izzuddin, B.A., "Robustness by Design – Simplified Progressive Collapse Assessment of Building Structures, Stahlbau, Vol. 79, No. 8, August 2010, pp. 556-564. 4 July 2012 Robustness Summer School - COST Action TU0601 36

37
Imperial College London Structural Systems Analysis for Robustness Assessment Bassam A. Izzuddin Department of Civil & Environmental Engineering

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google