Discusses the shear design problem in concrete in the context of mixed mode crack propagation in concrete structures. Shear behavior and fracture of precast concrete segmental bridges are presented as a design case study. Joints between the precast segments of these bridges are critical locations through which large shear stresses, combined with normal stresses, must be transmitted. Crack initiation and propagation at these locations represent a mixed mode concrete fracture problem. General concepts for the representation of mixed mode fracture in concrete are briefly discussed, and a combined analytical and experimental methodology is presented for predicting this cracking behavior. Finally, using the developed fracture mechanics approach, a preliminary design concept is proposed for the shear design of prestressed concrete elements.

The fracturing phenomenon in reinforced concrete structures has a profound effect on their flexural stiffness. Consequently, the effect of cracking in reinforced concrete has been the subject of intensive investigation for many years. Because of the complexities associated with the development of feasible methodologies, analytical procedures continue in many respects to investigate and verify with experimental results. Historically, a series of rational analytical procedures have evolved to incorporate various methodologies such as material nonlinear models, failure criteria, and layered finite elements to account for the effect of cracking. However, it is to complex and expensive to apply such approached in design practice. For practical purposes, the Direct Design Method and the Equivalent Frame Method are often adopted in accordance with ACI 318 to design two-way reinforced concrete slabs. But the effect of cracking in concrete is not included in those two methods. Hence, an incremental-iterative procedure is implemented as a tool to design reinforced concrete slabs. The proposed incremental-iterative proceduce follows Section 9.5.2.3 as defined in ACI 318 to treat the effect of cracking in reinforced concrete slabs. Although the use of ACI 318 Eq. (9-7) is primarily provided for flexural members, it is permitted for application for two-way slabs as well. In essence, cracks are smeared and assumed to propagate in in-plane directions determined by the maximum principal moment in a finite element. The effective slab stiffnesses are modified accordingly as progressive cracking is detected under increasing loads. Analytical results from design cases are presented to demonstrate its applicability. In addition, a modified procedure is presented to include the ACI 446.1R, based on fracture mechanics of concrete. Further investigations are also recommended for the future developments in the analysis and design of reinforced concrete slabs.

The fracture mechanics size effect in unreinforced concrete beams has been clearly demonstrated by Bazant. The effect of reinforcement on the fracture mechanics size effect has not been demonstrated quite as clearly. The bending failure of a singly reinforced concrete beam serves to illustrate the effect of reinforcement in the fracture mechanics size effect. The effect of prenotched and unprenotched beams is also considered. A simple analytical model has been developed for the behavior (up to peak load and beyond) of a singly reinforced concrete beam. This model takes into account the existence of an initial traction-free crack and assumes linear elastic behavior of concrete, elastic-plastic response of the steel, crushing of concrete, and simplified bond-slip between the steel and concrete. The model employs the fictitious crack model to determine the crack growth in small beams and linear elastic fracture mechanics to determine crack growth in large beams. The model demonstrates a size effect which starts with a high nominal strength for low values of á (small beams) and a low nominal strength for high values of á (large beams). Between these shelves, in the neighborhood of log(á) = 0, there is an S-shaped transition region, but not well-approximated by a line with a slope of negative one-half, as for unreinforced, prenotched concrete beams. Example problems show the importance of the size effect in design.

Proposes a fracture mechanics approach to crack control design of reinforced concrete beams in flexure (Mode I). The model yields the minimum area of tension steel required of a concrete beam of rectangular cross section to safely sustain a design moment within the prescribed limit of permissible crack height. An iterative procedure is developed by satisfying simultaneously the fracture criterion of crack growth and the equilibrium condition at incipient fracture.

Reviews recent theoretical and experimental results on the size effect in brittle failures of reinforced concrete structures caused by the release of stored energy After summarizing the size effect law and explaining the novel concept of a brittleness number, the results of recent tests of diagonal shear failure, punching shear failure, torsional failure, and pullout failure are discussed. These results, which were obtained on geometrically similar specimens with a broad range of sizes, are found to be in excellent agreement with the theoretical size effect law. The experimental evidence is much stronger than that which was previously obtained by analyzing a large amount of test results from the literature, which were not obtained on geometrically similar specimens and were limited to a narrow size range. It is also pointed out that the test data on diagonal shear disagree with the classical Weibull-type theory of size effect, thus strengthening the theoretical argument against using this theory for the size effect in concrete structures whose maximum load is much larger than the cracking initiation load. The test results indicate that the presently considered fracture mechanics size effect ought to be incorporated into the formulas for the contribution of concrete to the ultimate load capacity in brittle failures of concrete structures. It is shown that such formulas can be based on the brittleness number. For any given structure shape, this number can be determined from size effect tests. However, prediction of this number without such test data will require some further research.