Shear strength of beams with loads near the supports

Abstract

In reinforced concrete beams subjected to concentrated loads, the shear resisted increases considerably as the loads approach to the support. There is not a consensus in the current codes of practice about any simple design formulation which adequately considers this phenomenon. A mechanical model has been developed at the Polytechnic University of Barcelona, which predicts the shear strength of beams. The mo del is originally applicable to slender beams (a/d >2.0 - 2.5), and is under consideration for adoption into the Eurocodes. The model deals with shear - flexure failure, in which flexural cracks develop inclined through the web and stabilized near the neutral axis. Failure is assumed to happen when this flexural crack develops inside the compression chord, subjected to normal and shear stresses, which takes place when the stresses reach the biaxial failure envelope of Kupfer. The model has been extended to ca ses where the loads are applied near the supports. In this case, the Bernoulli assumption (Plane sections remain plane) is no longer valid, and the problem must be faced as a typical discontinuity “D” region, because the dimensions (a/d<2) and because the vertical stresses introduced by the vertical loads by means of the bearing plates interact with the state of stresses of the compression chord. The extension of the model proposed at UPC consists on incrementing the neutral axis depth as the load approach es the supports and including the vertical stresses due to the applied concentrated loads, as confinement stresses in the concrete, thus changing the state of principal stress in the failure envelope from tension - compression to compression - compression, thu s enhancing the shear capacity In this thesis, a data base of beams with loads near the supports, with and without stirrups, has been collected. A comparison between the predictions of the proposed model and the predictions of the Eurocodes has been made , using the collected data base of 121 short - span beams which failed in shear. 43 of the beams had stirrups, while the last 78 were not transversally reinforced, all the beams have a/d - ratios of less than 2.5. The results obtained in this thesis are appro ximate to the results achieved in other literature. The proposed model compares favourably to the Eurocode for beams with and without shear reinforcement. In addition, some of the assumptions of the new model have been investigated using a 2D finite elemen t model. The results obtained with the 2D FEM confirm the assumptions used in the model.