Flexural behavior of voided reinforced concrete beams in different truss configurations: Topology optimization basis

This study advances sustainable reinforced concrete (RC) design by performing structural optimization, and embodied CO₂, while maintaining code-compliant strength, serviceability, and ductile failure behavior under bending stress. Full-scale experimental tests are combined with finite element analyses to investigate RC beams incorporating inclined stirrups and arranged voids forming truss-like configurations, including Vierendeel, Warren (30°, 45°, and 60° inclination angles), Warren with verticals, Pratt, and Howe layouts. Beams with spans between 3 m and 7 m are designed according to Eurocode 2, showing comparable yielding force, failure, and deflection to a solid benchmark RC beam. Performance indicators such as first-crack load, yielding and ultimate load, and corresponding displacements are evaluated. Embodied CO₂ is quantified through life-cycle assessment (LCA) (modules A1-A5 and C1-C4), and the structural efficiency under is expressed via a strength-to-carbon efficiency (SCE). The results show that the first-crack force decreases by 8.6%, with the reductions observed mostly for the Vierendeel and Warren 30° layouts. Warren configurations with 45°–60°, with or without verticals, improve crack distribution and limit stiffness loss, while solid beams with alternative stirrup layouts exhibit comparable crack initiation. Vierendeel layouts concentrate stresses and may fail in shear-compression, whereas Warren 45°, Warren 60°, Warren with verticals, Pratt and Howe reach 90–105% of the benchmark capacity with ductile response. Void alignment with principal stress trajectories is critical; diagonals and/or verticals support strut-and-tie flow and become increasingly beneficial for longer spans. CO₂ savings are driven by reduced concrete in A1-A3; Warren 45° achieves 10.8% to 22.9% savings (A1-A5 +C1-C4) and SCE gains up to 27.7%, increasing with span. Warren 60°, Warren with verticals, Pratt, or Howe layouts are recommended for spans exceeding 4 m, while Warren 45° or Warren 60° without verticals are suitable for shorter spans. A hybrid layout, transitioning from Warren 45° near midspan to Warren 60° and subsequently to Warren with verticals, Pratt, or Howe towards the supports, emerges as a design strategy. The conclusions are limited to flexure-dominated response under four-point bending; future work should evaluate shear-dominated and combined bending-shear-torsion actions, uniformly distributed loading, long-term deformation and durability, and joint behavior including load placement relative to joints.