International Concrete Abstracts Portal

Behavior of RC deep beams is very complex, and several factors influence its shear strength. This paper discusses on analytical investigations on the shear strength of reinforced concrete (RC) deep beams. An expression for estimating the ultimate shear strength of RC deep beams provided with shear reinforcement, considering the beam depth including all other influencing parameters has been developed. The proposed ultimate shear strength estimation also considers the shear transfer mechanism of RC deep beams through a refined strut-and-tie model retaining the generic form of the modified Bazant’s size effect law, using a large selected experimental data base. The shear strength of RC deep beams has been predicted accurately using the square root of beam depth. The proposed size dependent equation is simple and accurate for RC deep beams with a/d ratio less than 2.0. Various parameters such as strut angle, flexural reinforcement ratio, shear reinforcement, both vertical and horizontal and beam depth have been accurately accommodated in the present size dependent shear strength expression using refined strut-andtie model. The prediction of the shear strength of RC deep beams has been observed to be reasonably agreeable with the experimental observations.

This article presents a computational fracture mechanics analysis of reinforced concrete deep beams using nonlinear fracture mechanics to study load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement. The article describes the development of a numerical model that includes the nonlinear processes that contributes to the strength of any concrete beam such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. Because the complexities that are present during the meshing when multiple cracks are in the system, the development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.

Accurate prediction of the shear strength of reinforced concrete beams is of paramount importance for shear-critical structures. Despite the complexity of failure mechanisms, shear failure can be comprehensively investigated by means of nonlinear cohesive (or quasibritle) fracture mechanics. This paper presents a review of recent works on shear failure of reinforced concrete beams at Northwestern University and shows that 1) the incorporation of fracture mechanics in concrete shear failure leads to correct prediction of the size effect on the shear strength; 2) the size effect in concrete shear can be analytically described by Bažant’s size effect law for nominal strength of geometrically similar structures made of quasibrittle materials and failing after stable crack growth; 3) an approximate semi-empirical formula for shear strength can be derived by asymptotic matching after establishing the small- and large-size asymptotes, and its parameters can be identified by fitting the existing large database after minimizing the statistical bias; and 4) the size effect formula can be extended to beams with shear reinforcement. When compared with the compiled database and computational studies, the theoretical analysis based on cohesive fracture mechanics shows a satisfactory agreement with tests as well as finite element simulations. Furthermore, as shown by statistical analysis, if the size effect in shear strength is ignored or described by an unrealistic formula, a significant reduction of the structural safety margin, manifested by a change of failure probability from 10¯6 to as high as 10¯3, must be expected for beams of large sizes, regardless of whether the shear reinforcement is added or not.

This paper reviews a recently developed finite weakest link model of strength of concrete structures, which fail under controlled load at macro-crack initiation from one representative volume element (RVE). The probability distribution of RVE strength is derived from the well-established transition rate theory and a hierarchical multi-scale transition model. The model predicts that the strength distribution of concrete structures depends on the structure size and geometry, transiting from a predominantly Gaussian distribution to a Weibull distribution as the structure size increases. It is shown that the present model agrees well with the strength histograms of Portland cement mortar measured by Weibull, which consistently deviate from the classical Weibull distribution. The importance of size effect for the reliability analysis of large concrete structures is then demonstrated through the analysis of the failure of the Malpsset Dam. Both the present model and the available experimental data invalidate the three-parameter Weibull distribution for concrete structures.

The basis of all design codes and recommendations that are endorsed by engineering societies are safety concepts which have been formulated with the intent to meet a society’s safety demands. These demands are expressed in terms of failure probabilities, differentiating between structural safety and serviceability, accounting for the expected service life and the potential loss of life and assets. While in the last century safety formats were mainly based on experience, newer code developments are supported by fully probabilistic concepts and reliability engineering tools. Nonetheless, a realistic assessment of structural performance, and in consequence the expected service life, is in many cases impaired due to oversimplified design assumptions, the elastic determination of internal forces applying the principle of superposition, and a lack of understanding regarding the relevant stochastic models. While the ‘elastic’ design has merit in many design situations, its limitations are quickly reached if a realistic assessment of bearing capacity or serviceability are to be performed. Within this contribution the role of fracture mechanics in the reliability analyses of reinforced and pre-stressed concrete structures will be presented. After providing a review of the relevant concepts, examples are given to illustrate the significance of fracture mechanics as well as point out existing short-comings and the need for additional research.