119 © 2012 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 13 (2012), No. 2
The predominant failure mode of concrete members reinforced
with fibre-reinforced polymer (FRP) bars is flexural, due to either
concrete crushing or FRP rupture. Many design tools have been
developed for the flexural design of FRP-reinforced concrete.
These tools are sufficiently accurate, but an iterative procedure
is required when dealing with flexural failure due to FRP rupture.
In addition, despite the fact that the design concepts involved are
similar to those used for conventional steel-reinforced concrete,
the changes in the design philosophy and the linear behaviour up
to rupture of the FRP bars lead to the sectional properties having
a different influence on the design, which not everyone may be
familiar with. Therefore, this study proposes a general methodol-
ogy for evaluating the design flexural capacity of FRP-reinforced
concrete sections. This methodology is based on the design pro-
visions of Eurocode 2 and comprises non-dimensional, closed-
form equations, derived independently of the concrete and FRP
characteristics. The proposed methodology can be used to derive
universal dimensionless design charts as well as tables. The ac-
curacy of the proposed design tools has been verified by compar-
ing the predictions with the experimental results of 98 beams,
which are available in the published literature.
Keywords: design, reinforced concrete, FRP bars, flexural capacity,
FRP rupture, concrete crushing
1 Introduction
Since the early 1980s, fibre-reinforced polymer (FRP) bars
have emerged as an alternative type of internal reinforce-
ment for concrete structures exposed to aggressive envi-
ronments and normally reinforced with conventional steel
bars [1, 2]. In addition to improving the durability of rein-
forced concrete, FRP bars have been used in structural
concrete applications where magnetic neutrality or good
cutting characteristics are required [3, 4].
The major differences between steel-reinforced con-
crete (SRC) and FRP-reinforced concrete (FRP RC) arise
from the mechanical properties of FRP bars, which behave
linearly up to failure. As a result, FRP RC members fail in
a brittle manner and this leads to a change in the predom-
inant mode of failure, i. e. flexure, assumed by limit state
design [3–6].
FRP RC members fail in flexure either due to con-
crete crushing (compressive failure type) or rupture of the
FRP bars (tensile failure type). Although existing design
guidelines for FRP RC (e. g. [3, 7–8]) accept both types of
flexural failure, concrete crushing failure is marginally
more desirable since it is more progressive and has a high-
er degree of deformability [9]. Nevertheless, design prac-
tice indicates that for some members, e. g. bridge deck
FRP RC slabs, the amount of reinforcement provided is
usually lower than the theoretical limit required to achieve
a balanced flexural failure; the design can therefore be
governed by tensile failure of the reinforcement [10].
Various studies of the flexural behaviour of FRP RC
members have been carried out over the years, e. g.
[11–27], and it may be generally stated that the design
methodologies adopted by existing guidelines for FRP RC
(e. g. [3, 7–8, 28]) predict the moment capacity of FRP RC
sections with sufficient accuracy. These methodologies
utilize the assumptions made for SRC which are modified
to account for the specific mechanical properties of FRP
bars, and the proposed design equations are based on
equivalent rectangular compressive stress block proce-
dures. A similar approach is proposed by fib task group 9.3
[4, 29], which adopted the equivalent rectangular stress
block procedure of Eurocode 2 [30].
When FRP rupture governs the design, a rigorous
calculation of the moment capacity leads to an iterative
process, which is required to determine the depth of the
compressive stress block. To avoid this iteration, simpli-
fied procedures can be adopted, such as the proposal of
ACI440.1R [3]. In this case, the nominal moment capacity
of the FRP RC section is approximated by using the equiv-
alent rectangular stress block of a balanced FRP RC sec-
tion. This simplification is regarded as conservative and
assumes a constant maximum value for the depth of the
compressive stress block [10] without taking into account
the possible variation in the lever arm which may result
when there is a change in the geometrical and mechanical
properties of the FRP RC section.
Furthermore, despite the fact that the concepts in-
volved in the design of FRP RC sections are similar to
those for SRC sections, the changes in the design philoso-
phy and the linear behaviour up to rupture of the FRP bars
lead to the sectional properties having a different influ-
ence on the design, which not everyone may be familiar
with.
Articles
Design procedure and simplified equations
for the flexural capacity of concrete members
reinforced with fibre-reinforced polymer bars
Lluis Torres*
Kyriacos Neocleous
Kypros Pilakoutas
DOI: 10.1002/suco.201100045
* Corresponding author: lluis.torres@udg.edu
Submitted for review: 26 September 2011
Revised: 16 December 2011
Accepted for publication: 28 January 2012