Steel Free Hybrid Reinforcement System for Concrete Bridge Decks ...

4 s
τ / τ (1 ) 0.5
m
= − e
(2.4)
where s = slip corresponding to the bond stress (τ ) . This model correlates well
with the data obtained in their tests. It is only applicable, however, to this particular type of
GFRP under similar conditions.
These member-scale models are quite useful in addressing realistic structural
problems, as they deal with larger structural systems. The chief limitation of these models is
not that they are empirical, but what Cox refers to as the “scale of empiricism,” which
restricts the application of these models to problems with similar or identical elements, under
similar conditions. Smaller scale models, such as the rib-scale, have much greater predictive
capacity, meaning they can be used to predict the results of untested material combinations
more effectively.
In a rib-scale model, the surface intricacies of a deformed bar are explicitly modeled,
leading to great complexity. Thus, few attempts at modeling at this scale have been done.
With the greater complexity, though, comes a greater understanding of the mechanics
involved in the bond. Cox reviewed several rib-scale analyses in his paper. The first, done
by Yonezawa (1993), who attempted to optimize the surface characteristics of FRP bar to
maximize bond strength. A two-dimensional finite element model was constructed of a
trapezoidal deformation on the surface of a bar, leading to qualitative conclusions on how
changing the rib geometry influenced bond strength. Due to the simplicity of the model, the
conclusions were not widely applicable.
Cox also presented the analysis by Boothby et al (1995). Axissymmetric finite
element models of a bar with a single rib were developed, and it was concluded that the
transverse strength and stiffness of the FRP material could change the failure mechanism of
the bond. Also, as was proven with so many experiments, the failure was shown to be likely
the result of material failure of the FRP, rather than crushing of the concrete.
The conclusion was made that while potentially useful, the rib-scale models are
currently too computationally demanding to accurately depict the effect of bond at a large
scale. Also, there is great difficulty in modeling two anisotropic materials, FRP and
concrete, at a small scale, where modeling either as homogeneous could cause significant
error. The intermediate scale of modeling, bar-scale, provides a reasonable compromise, and
can both predict failure and be used to model larger scale problems.
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