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Computers and Concrete
  Volume 18, Number 6, December 2016, pages 1175-1194

Minimum reinforcement and ductility index of lightly reinforced concrete beams
Alessandro P. Fantilli, Bernardino Chiaia and Andrea Gorino

    Nonlinear models, capable of taking into account all the phenomena involved in the cracking and in the failure of lightly reinforced concrete beams, are nowadays available for a rigorous calculation of the minimum reinforcement. To simplify the current approaches, a new procedure is proposed in this paper. Specifically, the ductility index, which is lower than zero for under-reinforced concrete beams in bending, is introduced. The results of a general model, as well as the data measured in several tests, reveal the existence of two linear relationships between ductility index, crack width, and the amount of steel reinforcement. The above relationships can be applied to a wide range of lightly reinforced concrete beams, regardless of the geometrical dimensions and of the mechanical properties of materials. Accordingly, if only a few tests are combined with this linear relationships, a new design-by-testing procedure can be used to calculate the minimum reinforcement, which guarantees both the control of cracking in service and the ductility at failure.
Key Words
    lightly reinforced concrete beams; bending moment; minimum reinforcement; ultimate limit state; serviceability limit state; ductility index
Alessandro P. Fantilli, Bernardino Chiaia and Andrea Gorino: Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

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