At the Fall meeting of the American Concrete Institute in Philadelphia in 1990, ACI Committee 446 sponsored a technical paper session entitled "Design Based on Fracture Mechanics." The purpose of the session was to present recent advances in our understanding or fracture in concrete in such a way that practitioners could understand and use it, and also to identify ways in which practitioners can make use of fracture mechanics in design of concrete structures. Currently, designers in the United States use the ACI 318 Building Code, which currently makes absolutely no use of fracture mechanics concepts. To enable designers to use fracture mechanics, a logical next step would be to incorporate these concepts into a revised building code. Note: The individual papers are also available as .pdf downloads.. Please click on the following link to view the papers available, or call 248.848.3800 to order. SP134

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.

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.

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.

Progressive microcracking and crack closure effects are the most important phenomena which need to be described in finite element calculations of reinforced concrete structures subjected to cyclic or seismic loads. Microcracking produces a loss of stiffness which is usually modeled with continuous damage mechanics. Crack closure effects such as inelastic deformations and stiffness recovery remain features that must be incorporated in the constitutive relations describing the response of concrete under cyclic loadings. These effects are introduced into a novel damage model in a rigorous, consistent fashion. An attempt to derive the constitutive relations for fiber reinforced concrete using this model is also described. The implementation of these constitutive relations into a layered beam finite element code is discussed, and computations on medium-size bending beams and a beam-column joint subjected to cyclic loading are compared with experiments. Although the computational method remains simple and sufficiently fast for engineering applications, the good agreement obtained with test data shows that the constitutive relations capture very well the main characteristics of the behavior of concrete.