Rigid Plastic Modelling of RC Beams under Impact Loading

Abstract

A numerical model is produced herein for predicting the dynamic plastic structural responses of RC skeletal structures under drop-weight impact loading. The numerical formulation has the mathematical form of a linear complementarity problem (LCP) that incorporates the strain-rate sensitivity. This formulation offers a systematic numerical process that is automatic from the commencement until the dynamic response termination. The maximum deflection obtained from the viscoplastic LCP of midspan impacted simply supported beam is statistically compared to the experimental dataset of RC beams. So, an extensive experimental database of 118 simply supported RC beams under midspan impact is selected. All cases within the database experiencing either flexure or flexure-shear failure, whereas only shear failure cases are excluded. Similarly, another numerical model is developed here having the same mathematical form of a linear complementarity problem (LCP) but the only difference from the previous one is that it incorporates bending shear interaction obeying the square yield criterion. The maximum deflection as a result output obtained from this interaction-based LCP of midspan impacted simply supported reinforced concrete beam is statistically compared to the experimental dataset of tested RC beams carried out by different researchers available in the Literature. For this purpose, an extensive experimental database of 46 simply supported reinforced concrete (RC) beams under midspan impact has been constructed. All cases within the database experienced either flexure-shear or shear failures, whereas those specimen which failed in pure bending are excluded. For structures and load-bearing members under extreme impact loading, the prediction of peak impact force is the most challenging task. Owing to the non-uniqueness in the acceleration field of the rigid-plastic model, the peak impact force is also non-unique, therefore, an efficient and accurate empirical model is produced to estimate this force for the particular case of a simply supported (RC) beam under drop-weight impact. A gene expression programming (GEP) approach is employed to formulate this empirical model reflecting the contribution of various material and geometric factors like compressive strength of concrete, shear span to depth ratio, and strength and area of tensile reinforcement. The effect of other factors including the impact velocity and impactor weight is also investigated. A database containing 126 impact force experiments of the simply supported RC beams is analyzed statistically on the basis of variation of these factors and is used to develop the proposed models. This model is also compared statistically and analyzed with the available proposed models. Numerical confirmation of the empirical model of peak impact force is obtained by reference to finite element (FE) code ABAQUS with plane stress elements. Overall, the proposed model offers highly promising results, which can be applied to predict the shear force and bending moment diagrams, thus rendering it ideal for practical application.