Mechanical behaviour and non-linear analysis of short beams using softened truss and direct strut & tie models


ENGINEERING STRUCTURES, vol.27, no.4, pp.639-651, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2005
  • Doi Number: 10.1016/j.engstruct.2004.12.003
  • Page Numbers: pp.639-651


This paper discusses the application of the softened truss and strut and tie models on short beams. The softened truss model originally proposed by Hsu is based on three fundamental principles of mechanics of materials, i.e., stress equilibrium, strain compatibility, and constitutive laws of materials. The model has two important characteristics. The first is the non-linear association of stress and strain. The second is the softening of concrete in compression due to tensile strains in the perpendicular direction. For short beams, one of the most important factors influencing behaviour is the effective transverse compression, which is dependent on the shear-span-to-depth (a/d) ratio. In this study, the softened truss model is revised so that the model gives more accurate predictions of the shear strength of short beams. The revised softened truss model (RSOTM) has three differences from the original model. In the RSOTM, it is shown that the effective transverse compression is not only dependent on the a/d ratio but also on the reinforcement ratio in the longitudinal direction as well as the size of the specimen. Second, it is shown that the softening phenomenon in short beams is more severe than that assumed in the original model. The third difference is that the effective transverse compression will be zero when a/d ratio exceeds 1.5. The ROSTM is compared with ACI318-2002, which recommends that short and deep beams should be designed by strut and tie models. ACI318-2002 and the final draft of Eurocode 2 do not provide specific guidance on suitable strut and tie models for different cases. In this study on short beams, a strut and tie model which consists of three mechanisms is recommended: a direct strut mechanism to account for the contribution of concrete and two truss mechanisms to account for the contributions of the horizontal and vertical shear reinforcements to the shear strength. It is imperative that ACI318-2002 and the final draft of Eurocode 2 should be modified so that they should stress the existence of these three mechanisms in short and deep beams. (c) 2005 Elsevier Ltd. All rights reserved.