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

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

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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

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Dynamic response of a SDOF system – Point Load - =

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Dynamic response of a SDOF system – UDL - =

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Dynamic response of a MDOF system – UDL - =

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Pseudo-static response of a MDOF system

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Simplified Dynamic Assessment – Case Study Floor systemService Load Edge: 406UB38 (Floor), 305UB28 (Roof) Internal: 305UB25 (Floor), 152UB16 (Roof) Transverse: 356UC153 (Floor), 254UC107 (Roof) Floor Dead Load: 4.2 kN/m 2 (factored 1) Floor Live Load: 5.0 kN/m 2 (factored 0.25) Edge Floor (Facade) Dead Load: 8.3 kN/m Roof Loads : ½ of Floor Loads

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Individual beam level – Longitudinal edge beam Rigid Column Flexible Column

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Longitudinal edge beam - Rigid Column 2 Point LoadUniformly 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

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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

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

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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

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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

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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.

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

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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 1 st 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

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