Risk optimization of RC beam under column loss scenario

Resumo

The sudden column 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.
Since uncertainties like material properties and geometrical parameters plays a major role in the behavior of the
resisting mechanisms, and consequences are highly significant for such failure events, the risk optimization is a
very convenient tool to optimize the balance between economy and safety. This is shown herein by the
optimization of a RC beam sub assemblage, considering the beam height, longitudinal steel rebar areas, stirrup
cross section area and stirrup spacing as design variables. Failure consequences are included for service limit state,
ultimate limit state of confined concrete at snap-through instability, and ultimate limit state of the steel rebars at
catenary action stage. A physical and geometrical nonlinear static analysis is employed, in which the samples are
submitted to pushdown displacement control over the removed column. 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 for the system failure probabilities. It is
shown, for the analyzed problem, that the confinement of concrete plays the major role in providing structural
safety, since a design that survives the initial stages but fails in the instability stage is sudden, not allowing the
occurrence of catenary action.