Contribution to the exact three-dimensional analysis of static and dynamic behaviours of functionally graded concrete beams

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Abstract

The static and vibration behaviours of functionally graded concrete (FGC) structures are attractive topics for structural design researchers in attempts to meet two main objectives. The first objective is addressing economic and environmental concerns using secondary products, specifically industrial waste from abandoned areas, as a substitute for traditional aggregates in concrete formulations. The second objective is incorporating the properties of such FGC into calculation methods, while striving to minimize the complexity of the problem. This study conducted a precise three-dimensional (3D) analysis of FGC beams with thickness-dependent steel slag reinforcement, using a refined beam theory (RBT) based on the 3D Saint-Venant solution and enriched with out-of-plane distortional modes of the cross-section (RBT*), employed within a one-dimensional finite element model to reduce the problem. This theory is suitable for the rational analysis of beams with arbitrary cross-sections. It considers normal and distortional deformations, derived from the 3D Saint-Venant solution, using eigenmodes based on the material properties and cross-sectional geometry. The strategy is enhanced through the utilisation of cross-sectional analysis and beamforming techniques. The mechanical properties of FGC vary with the thickness according to a power law. The properties of steel slag were obtained via the inverse Mori-Tanaka method. The results showed the economic and environmental benefits of using abundant steel slag as an alternative to conventional aggregates in FGC. The RBT* theory was able to describe the 3D displacement, deformation, and stress fields.