1. Robustness assessment for multiple column loss scenarios
M. Pereira and B. A. Izzuddin
Department of Civil and Environmental Engineering

2. Robustness assessment framework
Damage Scenarios
Single Damage Scenario
Multiple Damage Scenarios
Sudden single column loss
Sudden single column loss
Sudden two adjacent column loss

3. Column loss scenario – Main Stages
Nonlinear static response of the damaged structure under gravity loading
Simplified dynamic assessment to establish the maximum dynamic response under column loss scenarios
Ductility assessment of the connections/structure

4. Dynamic response of a SDOF system – Point Load- =

5. Dynamic response of a SDOF system – UDL- =

6. Dynamic response of a MDOF system – UDL- =

7. Pseudo-static response of a MDOF system

8. 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/m
Roof Loads : ½ of Floor Loads

9. Individual beam level – Longitudinal edge beam
Rigid Column
Flexible Column

10. Longitudinal edge beam - Rigid Column
2 Point Load
Uniformly Distributed Load
Slight overestimation as expected in the static analysis more visible for 2 point load (concentrated masses)
High frequencies excitation for uniformly distributed mass case
Accurate approximation of the dynamic response for both loading cases

11. Longitudinal edge beam - Flexible Column
Uniformly Distributed Load
Slight overestimation in the static analysis
High frequencies excitation
Good approximation of the dynamic response for a case with variable deformation mode during loading

12. Individual floor level
Detailed Floor Grillage Model
Simplified Floor Grillage Model
Compatibility between members assuming a governing mode
and

13. Individual floor (Pseudo) Static vs. Dynamic Detailed Model
(Pseudo) Static Detailed vs. Simplified Models
Good approximation of floor vertical support reaction from individual beams (rigid columns) vertical reaction profiles
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
Accurate approximation of the dynamic response
Dominant trapezoidal mode of deformation for floor system
Additional rotational restraint given by transverse beams torsional stiffness
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

14. 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

15. 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.

16. Multiple floors level Detailed Multiple Floors Model
Simplified Multiple Floor Model
Compatibility between members assuming a governing mode
and

17. Multiple floors (Pseudo) Static Detailed vs. Simplified Models
(Pseudo) Static vs. Dynamic Detailed Model
Satisfactory approximation of floor vertical support reaction from individual beams (rigid columns) vertical reaction profiles taking into account moderate load redistribution between floors
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
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