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

Imperial CollegeLondon

Structural Systems Analysisfor Robustness Assessment

Bassam A. Izzuddin

Department of Civil & Environmental Engineering

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

Structure

Structural Design – Predictability3

ActionsResponse

Codified properties

Statistical data

Site supervision & QA

…

Codified calculations

Simplified analysis

Detailed analysis

…

Codified loads

Statistical analysis

Event modelling

…

Malicious/terrorist

actions

Acceptable?


• 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 70m2)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


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


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


• 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


• 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)


• Basis of equivalent ‘pushdown’ static approach proposed for new GSA/DoD guidance

• Nonlinear static analysis– DIF equal to 2 applicable only for linear elastic response

– Recognition of influence of available ductility on DIF

– But not the characteristics of nonlinear static response

Load Factor Approaches

Dynamic response Static analysis4 July 2012 Robustness Summer School - COST Action TU0601 9

• DIF in terms of ductility for use with nonlinear static analysis in new GSA/DoD guidance

• Monotonic reduction in DIF with ductility


0.12

0.45DIF 1.04 (Marchand et al. [2008]: Concrete Structures)

m 0.480.76

DIF 1.08 (Marchand et al. [2008]: Steel Structures)m 0.83

DIF 1.44m (Stevens et al. [2008]: Steel Structures

f

y

)

uplastic deformationm 1

yield deformation u



Elastic-plastic static response

Dynamic resistance

Static resistance

DIF = 2

DIF = 1.67 DIF = 1.04

Monotonic reduction of DIF with ductilityConsistent with load factor approaches for new GSA/DoD guidance



Elasto-plastic static response with hardeningDIF increases with ductility after initial reductionProposed load factor approaches very unsafe for ductile structures


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



• 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



• 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


Nonlinear Static ResponseFailure | Sudden Column Loss

• Sudden column removal similar to sudden application of gravity load– Maximum dynamic response can be approximated using

amplified static loading (ld P)



Failure | Sudden Column LossNonlinear 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



• 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



• 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



• 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

i i ii

i i s,i s

P

P , P P (u ) P P(u )



• 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

i ii

i i s,i s

P

P , P P (u ) P P(u )



• 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

• 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

ld<<2l



Failure | Sudden Column LossSimplified Dynamic Assessment

• Dynamic “pseudo-static” (P,ud) response constructed from corresponding nonlinear static (P,us) 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


• Pmax corresponds to (ud=uf) 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 LossSimplified Dynamic Assessment


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


• 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


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


• … 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 responseof undamagedstructure

Successive Component Losses

• Structural system subject to initial damage followed by second component loss

Static response ofinitially damagedstructure

Secondcomponentloss

Completesystemfailure

• Maximum pseudo-static capacity may not even be related to a specific ductility limit


Application to Composite Buildings

304 July 2012 Robustness Summer School - COST Action TU0601

7-storey steel framed composite building with simple frame design

6000 6000

2375

3000

3000

1500

Removed column

504070

70

7040

Supporting column305 x 305 x 118 UCGrade S355

Supported beam406 x 140 x 39 UB

Grade S355

Supported beam406 x 140 x 39 UB

Grade S355

60

7080

50

Anti-crack mesh Shear stud

130

Sudden loss of peripheral columnAssuming identical floors assessment at floor level of idealisationGrillage approximation:edge beaminternal secondary beamstransverse primary beamEdge beam connections


• 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




0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600 700 800 900

Displacement, δ (mm)

Dyn

amic

Loa

d (kN

/m)

0%

25%

50%

75%

100%

Per

cent

age

of S

ervi

ce L

oads

(%

)

ρ = 0.87%, w/ axial restraintρ = 2.00%, w/ axial restraintBare-steel frame, w/ axial restraintρ = 0.87%, w/o axial restraintρ = 2.00%, w/o axial restraintBare-steel frame, w/o axial restraint

• Pseudo-static response curves of internal beams

• Pseudo-static response curves of transverse beam

0

100

200

300

400

500

0.000 0.030 0.060 0.090 0.120 0.150

Rotation, φ (rad)

Dyn

amic

Mom

ent (kN

m)

ρ = 0.45%ρ = 0.87%ρ = 2.00%Bare-steel frame

• Pseudo-static response curves of edge beam

0

5

10

15

20

0 100 200 300 400 500 600 700 800 900

Displacement, δ (mm)

Dyn

amic

Loa

d (kN

/m)

0%

25%

50%

75%

100%

125%

150%

Per

cent

age

of S

ervi

ce L

oads

(%

)

ρ = 0.87%, w/ axial restraint

ρ = 2.00%, w/ axial restraint

Bare-steel frame, w/ axial restraint

ρ = 0.87%, w/o axial restraint

ρ = 2.00%, w/o axial restraint

Bare-steel frame, w/o axial restraint

• Static and pseudo-static curves for edge beam with ρ = 1.12%

0

5

10

15

20

0 100 200 300 400Displacement, δ (mm)

Stat

ic/D

ynam

ic L

oad

(kN/m

)

0%

25%

50%

75%

100%

125%

150%

Per

cent

age

of S

ervi

ce L

oads

(%)

Static resposne, w/ axial restraint

Static response, w/o axial restraint

Pseudo-static response, w/ axial restraint

Pseudo-static response, w/o axial restraint

Gap closure

Application to Composite Buildings:Individual Beam Responses



Application to Composite Buildings:Assembled Floor Grillage

Deformation profile Case No.

φd,TB (rad) ud,IB1 (mm) ud,IB2 (mm) ud,IB3 (mm) ud,EB (mm)

1 0.0364 54.6 163.7 272.9 359.3

2 0.0381 57.2 171.6 286.0 376.5

3 0.0359 53.8 161.3 268.9 354.0

4 0.0623 93.5 280.5 467.6 615.6

δSB3

δSB1

δSB2

δMB

φj

ρmin, EC4, w/ axial restraintρ = 2%, w/ axial restraintρ = 2%, w/ο axial restraintBare-steel frame,w/ axial restraint

Case No. Capacity P

(N)

Demand Po

(N)

Capacity/Demand

ratio

1 598729 741990 0.81

2 774358 741990 1.04

3 709675 741990 0.96

4 148530 741990 0.20

• Assumed deformation mode defines ductility limit

• Case 2 (r=2% with axial restraint) is just about adequate

• Inadequacy of prescriptive tying force requirements


• 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 8º

• Infill panels can double resistance of composite buildings to progressive collapse

• Material rate-sensitivity is another potentially significant parameter


~ 4º

> 8º

Application to Composite Buildings:General Observations

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


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.


Imperial CollegeLondon

Structural Systems Analysisfor Robustness Assessment

Bassam A. Izzuddin

Department of Civil & Environmental Engineering

Documents

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