Abstract
To study the brittle/ductile behavior of concrete beams reinforced with low amounts of rebar and fibers, a new multi-scale model is presented. It is used to predict the flexural response of an ideal Hybrid Reinforced Concrete (HRC) beam in bending, and it is validated with the results of a specific experimental campaign, and some tests available in the technical literature. Both the numerical and the experimental measurements define a linear relationship between the amount of reinforcement and the Ductility Index (DI). The latter is a non-dimensional function depending on the difference between the ultimate load and the effective cracking load of a concrete beam. As a result, a new design-by-testing procedure can be established to determine the minimum reinforcement of HRC elements. It corresponds to DI = 0, and can be considered as a linear combination of the minimum area of rebar (of the same reinforced concrete beam) and the minimum fiber volume fraction (of the same fiber-reinforced concrete beam), respectively.
Highlights
In the technical literature, there is a strong interest in the use of Hybrid Reinforced Concrete (HRC)structures, reinforced by both steel bars and discrete fibers randomly dispersed in the cementitious matrix [1,2,3,4,5]
It corresponds to Ductility Index (DI) = 0, and can be considered as a linear combination of the minimum area of rebar and the minimum fiber volume fraction, respectively
The brittle/ductile flexural behavior of hybrid reinforced concrete beams HRC can be described by the ductility index DI, which, in turn, depends on the difference between the ultimate load and the effective cracking load of a beam; The hybrid reinforcement of lightly reinforced concrete beams can be quantified by means of r, which is a linear combination of the area of rebar and the volume of fibers, both normalized with respect to the minimum reinforcement of Lightly Reinforced Concrete (LRC) and Fiber-Reinforced Concrete (FRC) beams, respectively; Both numerical and experimental investigations performed on HRC beams reveal the existence of a range in the DI vs. r diagram
Summary
There is a strong interest in the use of Hybrid Reinforced Concrete (HRC). If the minimum reinforcement of HRC beams is evaluated as in those LRC are, the resisting true in the case of massive structures, when the computation of As,min , performed in accordance with contribution of fibers is not exploited, making the use of fiber-reinforcement useless This is building code rules, leads to a large amount of steel rebar [8]. The transition from the brittle to ductile behavior of HRC members was investigated deeply by of reducing the amount of steel rebar in presence of fibers, a simple and univocal criterion for Chiaia et al [35], Liao et al [3] and Mobasher et al [36] They demonstrated the possibility evaluating the minimum reinforcement of HRC beams cannot be found in the current literature. A new general is introduced to predict the flexural behavior of HRC beams
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