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

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 45º (Model I), or varying between 30º and 45º (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45º and 90º. 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 30º and 45º, 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 30º to 45º, 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 40º, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.

Shear strength of reinforced concrete circular cross-section beams

A proposed adequation of NBR 6118, Item 7.4, related to shear strength of reinforced concrete beams is presented with aims to application on circular cross-section. The actual expressions are most suitable to rectangular cross-section and some misleading occurs when applied to circular sections at determination of VRd2, Vc and Vsw, as consequence of bw (beam width) and d (effective depth) definitions as well as the real effectiveness of circular stirrups. The proposed adequation is based on extensive bibliographic review and practical experience with a great number of infrastructure elements, such as anchored retaining pile walls, where the use of circular reinforced concrete members is frequent.

Upper crustal earthquake swarms in São Caetano: reactivation of the Pernambuco shear zone and trending branches in intraplate Brazil

Seismogenic fault reactivation of continental-scale structures has been observed in a few intraplate areas, but its cause is still amatter of debate. The objective of the present study is to analyze two seismic swarms that occurred along the EW-trending Pernambuco ductile shear zone and in a NE-trending branch, in 2007 and 2010 in São Caetano County, Northeastern Brazil.We studied both epicentral areas using a nine- and a seven-station network during 180 and 54 days, respectively. The results indicate that the 2007 swarm correspond to a right-lateral, strike–slip fault with a normal component of slip (strike 74°, dip 60°, and rake−145°) and the 2010 swarmcorresponds to a normal fault (strike 265°, dip 79°, and rake −91°). The former reactivated a NE-trending branch, whereas the latter reactivated the main E-W-trending mylonitic belt of the Pernambuco shear zone. These results are consistent with seismogenic reactivation of this major structure, generated by the present-day EW-trending compression and NS-trending extension, as observed by previous studies. This shear zone was reactivated as rift faults in the Cretaceous during the South America–Africa breakup. However, our study confirms that the basement fabric such as continental-scale ductile shear zones, show evidence of crustal weakness outside areas of previous rifting, and it reveals the potential for large earthquakes along dormant rift segments associated with major basement shear belts.