Shear force and Torsion in reinforced concrete linear elements: theoretical analysis based on Brazilian Standard Code ABNT NBR 6118:2007

Resumen

Reinforced concrete beam elements are submitted to applicable loads along their life cycle that cause shear and torsion. These elements may be subject to only shear, pure torsion or both, torsion and shear combined. The Brazilian Standard Code ABNT NBR 6118:2007 [1] fixes conditions to calculate the transverse reinforcement area in beam reinforced concrete elements, using two design models, based on the strut and tie analogy model, first studied by Mörsch [2]. The strut angle θ (theta) can be considered constant and equal to 45° (Model I), or varying between 30° and 45° (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45° and 90°. When the equilibrium torsion is required, a resistant model based on space truss with hollow section is considered. The space truss admits an inclination angle θ between 30° and 45°, in accordance with beam elements subjected to shear. This paper presents a theoretical study of models I and II for combined shear and torsion, in which ranges the geometry and intensity of action in reinforced concrete beams, aimed to verify the consumption of transverse reinforcement in accordance with the calculation model adopted As the strut angle on model II ranges from 30° to 45°, transverse reinforcement area (Asw) decreases, and total reinforcement area, which includes longitudinal torsion reinforcement (Asℓ), increases. It appears that, when considering model II with strut angle above 40°, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.