# Risk optimization of a RC frame under column loss scenario

## Palavras-chave:

kriging, progressive collapse, reinforced concrete, reliability analysis, risk optimization## Resumo

The sudden loss of a single supporting element in a RC frame may lead to the disproportionate partial

or total structural collapse if its design fails to confine the initial damage through resisting mechanisms, like

compressive arch action, Vierendeel action, and catenary action. Since uncertainties related to material properties

and geometrical parameters plays a major role in the behavior of these resisting mechanisms, and consequences

are highly significant for such failure events, the risk optimization is a very convenient approach to optimize the

balance between economy and safety. This is shown herein by the optimization of a RC frame, considering the

cross sections and the steel rebar areas of the beam and columns as design variables. Failure consequences are

considered for serviceability, beam bending, shear failure, flexo-axial compression of the columns, and steel

rupture at and before catenary action. A physical and geometrical nonlinear static analysis is employed, in which

the sample points are submitted to pushdown analysis. Material behavior is represented by an elastoplastic model

with isotropic hardening for the steel rebars, and by combination of Mazars μ model with the modified Park-Kent

model for the confined concrete. Failure probabilities are evaluated by the Weighted Average Simulation Method,

and the Risk optimization is done by the Firefly Algorithm. In order to reduce the computational cost due to the

nonlinearities involved and the high number of sample points required, Kriging is used to generate a sufficiently

accurate metamodel for the limit states and reliability indexes. It is shown that the adopted formulation leads to

more allocation of material when a column loss scenario starts to be significant in terms of safety x economy.