International Concrete Abstracts Portal

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.

The recent introduction of epoxy coating to reinforcing steel has made the study of bond, and the effect of this coating, all the more important. A recent large scale study of bond performance of epoxy-coated and uncoated reinforcement conducted at the University of Kansas using modified cantilever beam-end specimens has shown the effects of various parameters on bond. These specimens placed the bar and surrounding concrete in tension, simulating the situation in actual members. A prescribed bond test region, the bonded length, was placed at a discrete distance, the lead length, from the front of the specimen to prevent surface effects from interfering with the test region. The experimental work has provided ample evidence of the fundamental fracture mechanics aspects of bond failure and the subsequent specimen failure. Splitting failure of the beam-end specimens was observed consistently in all tests where a fracture plane formed above the bond test region and propagated quickly through the tension region of the specimen. Tests indicated that the bonded length of the bar, the value of the lead length, and the amount of cover were all important parameters. The paper presents the results of an analytical evaluation of the bond process and specimen fracture that was observed in the laboratory, using nonlinear finite element analysis to study the effects of interface properties on the fracture behavior and failure load. The majority of the beam-end specimen was modeled using linear elastic elements representing one-half of the symmetric experimental specimen. The actual bar-concrete interface was modeled using link elements and a Mohr-Coulomb failure model. Rod elements joined the specimen to the specified crack plane located at the center line of the specimen. The fracture process was modeled using Hillerborg's fictitious crack model. The behavior observed in the laboratory for coated and uncoated bars has been accurately predicted using this procedure. The fracture process and resulting overall bond performance has been studied analytically to assess the effects of interface properties on the fracture behavior. The analytical studies confirmed that coating reduced the relative bond strength with respect to that of an uncoated bar, while the absolute bond strength was found to increase with additional cover and lead length.

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.

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

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.