Fire Design of Concrete Structures based on a Levels-of-Approximation Approach

Keywords: Concrete structures Shear strength Aggregate interlock Residual tensile strength of concrete Dowel action Arching action Critical Shear Crack Theory Size effect Strain effect a b s t r a c t Many theories and empirical formulae have been proposed to estimate the shear strength of reinforced concrete members without transverse reinforcement. It can be noted that these approaches differ not only in the resulting design expressions, but also on the governing parameters and on the interpretation of the failure mechanisms and governing shear-transfer actions. Also, no general consensus is yet available on the role that size and strain effects exhibit on the shear strength and how should they be accounted. This paper reviews the various potential shear-transfer actions in reinforced concrete beams with rectangular cross-section and discusses on their role, governing parameters and the influences that the size and level of deformation may exhibit on them. This is performed by means of an analytical integration of the stresses developed at the critical shear crack and accounting for the member kinematics. The results according to this analysis are discussed, leading to a number of conclusions. Finally, the resulting shear strength criteria are compared and related to the Critical Shear Crack Theory. This comparison shows the latter to be physically consistent, accounting for the governing mechanical parameters and leading to a smooth transition between limit analysis and Linear Elastic Fracture Mechanics in agreement to the size-effect law provided by Bažant et al. Design for shear of one-and two-way slabs without transverse reinforcement has been a topic where significant efforts have been devoted in the past. For beams and girders with stirrups, consistent equilibrium-based models as strut-and-tie models or stress fields can be applied [1]. However, with reference to the shear strength of beams and slabs without transverse reinforcement, no general agreement on the parameters and phenomena governing shear strength is yet found in the scientific community. This lack of agreement is also reflected in codes of practice, whose provisions for shear design are often based on empirical formulas [2,3]. Some approaches based on mechanical models consider a given shear transfer action as governing, neglecting the influence of the others. For instance, for one-way slabs without transverse reinforcement , shear carried by the compression chord is identified as the most significant parameter influencing the shear strength by Zararis [4]. On the contrary, aggregate interlocking can be considered as the governing shear transfer …