Risk optimization of a RC frame under column loss scenario

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.