Response of shear critical RC beam under transverse impact using improved linear complementarity

Abstract

The numerical formulation in the form of a linear complementarity problem (LCP) can easily accommodate the plastic interaction between the bending moment and the shear force at the point of impact. The earlier LCP interaction model cannot be used for simulating RC skeletal structures if the bending shear interaction is desired at more than one location. The current study presents an improved LCP formulation for determining the dynamic response of shear critical RC beams under impact loading. This model is developed from an enhanced kinetic and kinematic description combined with rigid-plastic constitutive relations incorporating bending-shear interaction through rectangular yield criterion. The approach enables numerous computations of impacted simply supported beams, whose maximum deflections are statistically compared with the available experimental data. For the comparison, a database of 46 simply supported RC beams is drawn that experience either flexure shear or shear failures. A thorough assessment of deflections of these 46 RC beams demonstrates a superior predictive capability of the improved LCP model (coefficient of determination R2 = 95%). Because of the inherent limitation of the rigid-plastic model, an empirically based formulation of the peak impact force is developed. Finally, the performance of the improved LCP formulation is verified against the commercial software ABAQUS. As far as the computational cost and efficiency are concerned, the improved LCP formulation is competitive with the commercially available FE softwares.