Robustness assessment for multiple column loss scenarios

M. Pereira and B. A. Izzuddin

Department of Civil and Environmental Engineering

Multiple Damage Scenarios

Robustness assessment framework

Robustness Assessment

Damage Scenarios

Single Damage Scenario

Sudden single column loss

Sudden single column loss

Sudden two adjacent column loss

Column loss scenario – Main Stages

(i) Nonlinear static response of the damaged structure under gravity loading

(ii) Simplified dynamic assessment to establish the maximum dynamic response under column loss scenarios

(iii)Ductility assessment of the connections/structure

Dynamic response of a SDOF system – Point Load

-

=

M u + K u = P

Dynamic response of a SDOF system – UDL

M u + K u = wL

-

=

Dynamic response of a MDOF system – UDL

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Pseudo-static response of a MDOF system

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dd n k

N u

n k s kk

U P u

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N N

n n k d n k n k d n kk k

W P u P u

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0, , ,1

dd n k

N u

k s kk

n k n n N

k d n kk

P uW U

P u

Simplified Dynamic Assessment – Case Study

Floor system Service Load

Edge: 406UB38 (Floor), 305UB28 (Roof)Internal: 305UB25 (Floor), 152UB16 (Roof)Transverse: 356UC153 (Floor), 254UC107 (Roof)

Floor Dead Load: 4.2 kN/m2 (factored 1)Floor Live Load: 5.0 kN/m2 (factored 0.25)Edge Floor (Facade) Dead Load: 8.3 kN/mRoof Loads : ½ of Floor Loads

Individual beam level – Longitudinal edge beam

Rigid Column

Flexible Column

Longitudinal edge beam - Rigid Column

2 Point Load Uniformly Distributed Load

• Accurate approximation of the dynamic response for both loading cases• Slight overestimation as expected in the static analysis more visible for 2 point load (concentrated masses)

• High frequencies excitation for uniformly distributed mass case

Longitudinal edge beam - Flexible Column

Uniformly Distributed Load

• Good approximation of the dynamic response for a case with variable deformation mode during loading• Slight overestimation in the static analysis

• High frequencies excitation

Individual floor level

Detailed Floor Grillage Model Simplified Floor Grillage Model

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dd n k

N u

k s kk

k n n Nn

k d n kk

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Compatibility between members assuming a governing mode

and

• Vertical displacement point of zero system acceleration (maximum static displacement) corresponds to point of exact vertical reaction prediction as expected

• Under/overestimation of vertical support reaction is observed for total down/upwards acceleration

Individual floor

(Pseudo) Static vs. Dynamic Detailed Model

(Pseudo) Static Detailed vs. Simplified Models

• Accurate approximation of the dynamic response

• Dominant trapezoidal mode of deformation for floor system

• Additional rotational restraint given by transverse beams torsional stiffness

• Better approximation of structural response from assembling individual beams with rigid columns, rather than flexible columns

• Use of longitudinal edge beam for governing member and imposed compatibility in remaining floor members

• Good approximation of floor vertical support reaction from individual beams (rigid columns) vertical reaction profiles

Conclusions

• Successful extension of the multi-level simplified dynamic assessment to structures subjected to two adjacent columns loss

• Dominant trapezoidal mode observed even for asymmetric load/structural configuration

• Consideration of reaction transmitted to surrounding structure for alternate load path assessment (including column resistance / connection shear failure)

• Further studies on effect of high frequency excitation in instantaneous system failure

Conclusions

Comparing the dynamic and pseudo-static responses:

• Validity of the assumption of zero kinetic energy at maximum dynamic displacement for MDOF system;

• Conservative assumption of the inertial forces distribution for determination of dynamic vertical support reaction.

Comparing detailed and simplified assembly models responses:

• Simplified models are feasible for structures exhibiting constant deformation mode during loading.

Multiple floors level

Detailed Multiple Floors Model

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dd n k

N u

k s kk

k n n Nn

k d n kk

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P u

Compatibility between members assuming a governing mode

and

Simplified Multiple Floor Model

Multiple floors

(Pseudo) Static vs. Dynamic Detailed Model

(Pseudo) Static Detailed vs. Simplified Models

• Accurate approximation of the dynamic response

• Dominant trapezoidal mode of deformation for multiple floor system

• Vertical displacement point of zero system acceleration (maximum static displacement) corresponds to point of exact vertical reaction prediction as expected

• Under/overestimation of vertical support reaction is observed for total down/upwards acceleration

• Good approximation of structural response either using detailed floors assembly or starting from individual beams assembly.

• Equally satisfactory approximation using either 1st Floor or Roof longitudinal edge beams as governing members

• Satisfactory approximation of floor vertical support reaction from individual beams (rigid columns) vertical reaction profiles taking into account moderate load redistribution between floors