Behavior Predictions of Deep Beams with Short Straight Bar Anchorages using Strut-and-Tie Models and Nonlinear Analysis

  • Rafael Alves de Souza Universidade Estadual de Maringá
  • Sergio F. Breña University of Massachusetts Amherst


This paper investigates the laboratory test results of 12 deep beams available in the literature, where the longitudinal reinforcement was anchored into the support using short straight bar anchorages. Four different specimen groups with three different shear span-to-depth ratios (a/d) were selected and most of the deep beams failed by strut crushing after yielding of the main longitudinal reinforcement. In order to investigate the behavior of the selected deep beams, an enhanced strut-and-tie model assuming geometrical adaptability (possibility of update in the dimensions of the struts and ties as the main tie starts to yield) is proposed. The analytical results obtained using this approach may be considered as much as accurate than some conducted complex nonlinear analysis considering smeared fixed cracking model and bond-slip behavior. However, an improvement on the effective strength factor of bottle-shaped struts by means of an iterative strut-and-tie model is needed, once the effective strength factor prescribed by NBR6118 (2014) has shown to be over conservative for all ranges of span-to-depth ratio (a/d) investigated. Finally, the obtained results indicated that short bar anchorages did not seem to influence significantly the shear strength of the deep beams investigated, especially the strength of bottled-shaped struts when appropriate crack control reinforcement is present.

Author Biographies

Rafael Alves de Souza, Universidade Estadual de Maringá
Departamento de Engenharia Civil Estruturas em Concreto
Sergio F. Breña, University of Massachusetts Amherst
College of Engineering Department of Civil and Environmental Engineering Structural Concrete