Size Effect in Reinforced Flexural Members


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Title: Size Effect in Reinforced Flexural Members

Author(s): W. H. Gerstle, P. Rahulkumar, P. P. Dey, and M. Xie

Publication: Special Publication

Volume: 134


Appears on pages(s): 25-46

Keywords: beams (supports); bending; cracking (fracturing); models; crack propagation; failure; flexural strength; fracture properties; modulus of elasticity; reinforced concrete; strength; Design

Date: 9/1/1992

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.