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

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

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

Dynamic response of a SDOF system – Point Load - =

Dynamic response of a SDOF system – UDL - =

Dynamic response of a MDOF system – UDL - =

Pseudo-static response of a MDOF system

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

Individual beam level – Longitudinal edge beam Rigid Column Flexible Column

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

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

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

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

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 Simplified Multiple Floor Model Compatibility between members assuming a governing mode and

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