Ijciet 10 02_057

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 02, February 2019, pp. 574-602, Article ID: IJCIET_10_02_057
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=02
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
EFFECTS OF BARS SLIPPAGE ON THE PRE-
AND POST-HEATING FLEXURAL BEHAVIOR
OF FRP REINFORCED CONCRETE BEAMS:
EXPERIMENTAL AND THEORETICAL
INVESTIGATIONS
Rami J.A. Hamad
International College of Engineering and Management,
P.O. Box 2511, C.P.O Seeb, P.C. 111, Oman
M. A. Megat Johari
School of Civil Engineering, Universiti Sains Malaysia,
Engineering Campus, 14300 Nibong Tebal, Pulau Pinang, Malaysia
Rami H. Haddad
Department of Civil Engineering, Jordan University of Science and Technology,
P.O. Box 3030, 22110 Irbid, Jordan
ABSTRACT
Using fiber reinforced polymer (FRP) bars as an alternative to traditional steel
reinforcement solves durability problems in reinforced concrete structures. This study
investigated the effects of bar slippage on the pre- and post-heating flexural response
of concrete beams reinforced with different FRP and conventional steel bars. A total
of twenty-four control and heat-damaged concrete beams with different FRP/steel
bars were loaded (in triplicates) under a four-point loading configuration to evaluate
their mechanical performance and failure modes while acquiring strains in tension
steel and compression concrete. A new theoretical method was proposed to predict
the load capacities of the beams with consideration of slippage between the FRP bars
and surrounding concrete. The results were then compared with the load capacities
computed using the ACI code that assumes a prefect bond between FRP bars and
concrete. The post-heated concrete beams failed at a relatively low load capacity.
They also presented an increase in deflection and ductility and a decrease in stiffness
and total absorbed energy. The theoretical ultimate load of the FRP-RC beams,
computed on the basis of the ACI code, was overestimated relative to the
corresponding measured values. By contrast, the computations based on the actual

Effects of Bars Slippage on the Pre- and Post-Heating Flexural Behavior of FRP Reinforced
Concrete Beams: Experimental and Theoretical Investigations
pre- and post-heating mechanical properties of the FRP bars and concrete and their
bond characteristics provided reasonably reliable results.
Keywords: FRP bars, High Temperature, Bond, Slippage, Flexural, deflection,
Stiffness, Ductility, Analytical Model.
Cite this Article: Rami J.A. Hamad, M. A. Megat Johari and Rami H. Haddad,
Effects of Bars Slippage on the Pre- and Post-Heating Flexural Behavior of FRP
Reinforced Concrete Beams: Experimental and Theoretical Investigations,
International Journal of Civil Engineering and Technology, 10(2), 2019, pp. 574-602.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=02
1. INTRODUCTION
Existing reinforced concrete (RC) structures deteriorate when exposed to an aggressive
chloride attack in marine structures or when deicing agents infiltrate the concrete. Hence,
steel reinforcement inside concrete would corrode in the presence of oxygen and water,
leading to concrete cracking and loss in the structural capacity of steel-corroded concrete
elements. The maintenance and rehabilitation of concrete structures damaged by corrosion
are costly and sometimes complicated [1]. Nonmetallic fiber reinforced polymer (FRP) bars
have been recommended as an alternative to traditional steel reinforcement in RC structures
in aggressive environments to overcome reinforcing steel problems [2].
FRP composites consist of strong reinforcing organic/inorganic fibers embedded in a
resin matrix. The fiber component of FRP composites transfers stress and provides stiffness
and strength to the FRP composites, which are commercially manufactured using different
types of fibers, such as glass (GFRP), carbon (CFRP), and basalt (BFRP). In comparison with
traditional reinforcing steel, FRP bars possess higher resistance to electrochemical corrosion,
tensile stresses, fatigue, and electromagnetic waves; lighter weight and lower elastic
modulus; lower resistance to high temperature; and higher cost [1, 3-6]. FRP bars can be
practically used either as internal reinforcing bars inside concrete sections or as externally
bonded reinforcement sheets/plates using epoxy resin adhesives [1]. FRP-RC beams show
non-ductile flexural behavior and higher deflection and cracking than beams reinforced with
conventional steel do because of the brittle behavior of FRP bars [7-9]. Hence, the design of
FRP-RC structures has shifted from the consideration of strength requirements to the regard
for serviceability limit states to ensure functionality and safety during the expected life of
these structures. Furthermore, these structures are designed as over-reinforced to achieve
concrete failure (crushing of concrete) prior to FRP rebars’ failure [8, 10-14].
Extensive research on the structural behavior of FRP-RC elements has been carried out
with an emphasis on the potential of using FRP composites as reinforcement materials. The
results of theoretical and experimental works show contradicting conclusions with regard to
the significance of using FRP in structural concrete elements [15-16]. Using FRP bars as
replacement of traditional steel reinforcement in concrete beams improves the flexural
capacity of these beams but reduces their ductility [7, 11, 17]. Al-Sunna et al. found that
shear cracking, shrinkage, and loss of bond have a significant contribution to the overall
deflection of FRP reinforced structures [13].
Recently, various studies have shown that the FRP–concrete bond behavior depends on
bar diameter, surface treatment, embedment length, FRP modulus, concrete strength, concrete
cover, and the properties of the polymer matrix at the bar surface [5, 18-25]. The mechanism
of the FRP bar– concrete bond depends on the bar’s mechanical interlocking and the friction
between their surfaces and the surrounding concrete. Hence, special surface treatments, such

Rami J.A. Hamad, M. A. Megat Johari and Rami H. Haddad
as sand coating, helical wrapping, molded deformations, or combinations of different surface
treatments, are recommended to enhance bars’ bonds with concrete [26]. Although the bond
between FRP and concrete is questionable, most of the available design codes for FRP
reinforced structures assume a perfect bond between the FRP reinforcement and the
surrounding concrete at ambient temperature [27].
Although the behavior of FRP-RC structures is satisfactory at low temperatures, the
application of combustible FRP materials in commercial, industrial, and residential buildings
requires further research to evaluate structural performance in fire situations [11]. The failure
of any FRP-RC element depends on three parameters that should be considered during the
design of FRP-RC members under fire conditions: strength of FRP, maximum rebar’s
temperature, and the FRP rebar’s anchorage length that is not directly subjected to fire [28].
The reduced material properties of concrete and FRP and their bond characteristics as a
function of temperature and time should be evaluated to gauge FRP-RC structures’ fire
resistance and post-heating residual strength [29-30].
Two different critical temperatures were recognized for any FRP-RC member exposed to
fire. The first temperature causes the softening or burning of FRP bars at an early stage,
which causes interface cracking and de-bonding with concrete [4, 6, 11, 31-32]. The second
critical temperature, which is not precisely estimated, leads to a 50% reduction in FRP rebars’
ambient temperature strength, hence their failure under fire [15, 33-35]. Various studies have
identified the second critical temperature to be in the range of 250 °C–500 °C [15, 28, 37-40].
Hamad et al. [41] stipulated that such a critical temperature corresponds to 325 °C. Concrete
cracking along FRP bars due to concrete thermal cracking and incompatibility of the
coefficients of thermal expansion (CTE) of the FRP and concrete result in further degradation
in the bond behavior between FRP bars and the surrounding concrete; hence structural
performance of flexural members [2]. The type of FRP and its surface characteristics shape
the bond with unheated and heated concrete.
The outlined literature indicates a lack of understanding of the post-fire behavior of FRP
reinforced structures [36, 42]. As a result, a comprehensive study was undertaken to
investigate the flexural performance of heat-damaged concrete beams reinforced with three
different types of FRP bars (glass, basalt, and carbon fibers). The post-heating mechanical
behavior of FRP bars and the bond between heat-damaged concrete and FRP bars were
further investigated [41]. In the present work, the experimental results related to the flexural
behavior of FRP-RC beams before and after heating are reported and discussed. Furthermore,
an analytical prediction of the flexural performance of FRP-RC beams was performed, and
the results were compared with the experimental outcomes. Predictions were carried out with
consideration of the perfect bond as well as slippage between FRP bars and concrete. The
empirical models developed by the authors on the basis of direct pullout bond tests were
employed to account for the slippage between FRP bars and concrete [41].
2. EXPERIMENTAL PROGRAM
2.1. Materials
2.1.1. Reinforcement bars
Three types of helically wrapped GFRP and BFRP and sand-coated CFRP bars, in addition to
deformed steel bars with two nominal diameters (6 and 10 mm) were used to reinforce the
beams in the current study. Figure 1 shows the geometry of the bars. FRP and steel bars with
a 10 mm diameter were used for main tensile reinforcement, whereas steel bars with a 6 mm

diameter were used as stirrups. The properties of the FRP bars based on the supplier’s
technical data sheets are summarized in Table 1.
The mechanical properties of the conventional steel bars were identified in the laboratory.
The latter yield strength, ultimate tensile strength, and maximum elongation at failure were
570 MPa, 638 MPa, and 8.48%, respectively.
Table 1 Mechanical properties of different FRP bars used as per manufacturer data sheet
Type
fuf
MPa
uf
%
Ef
GPa
αT
x10-6
/°C
αL
x10-6
/°C
F
%
Type of
matrix
CFRP-6 mm 2068 1.7 124 89 -0.9 70% VER
CFRP-10 mm 1896 1.6 124 89 -0.9 70% VER
GFRP-6 mm 900 2.1 40 22 5.4 N.A. UP
GFRP-10 mm 800 2.1 40 22 5.4 N.A. UP
BFRP-6 mm 1100 2.1 65 23 6 N.A. EPR
BFRP-10 mm 1000 2.1 65 23 6 N.A. EPR
fuf , maximum tensile strength; uf , maximum strain at ultimate strength; Ef, FRP’s modulus
of elasticity; F%, fiber to matrix volume ratio; αL, Longitudinal coefficient of thermal
expansion; αT, Transverse coefficient of thermal expansion; VER, Vinyl Ester Resin; UP,
Unsaturated Polyester; EPR, Epoxy Polymer Resin; N.A., not applicable.
Figure 1 Different reinforcement bars used in present study.
2.1.2. Concrete
Normal strength concrete with a 28-day compressive strength of 40 MPa was used. The 90±2
mm measured slump enabled good compaction without excess bleeding. Crushed granite
coarse aggregates with 10 mm maximum size and natural river sand with a specific gravity of
2.7 and moisture content of 0.6% were used. The proportions of water, ordinary Portland
cement, coarse aggregates, and fine aggregates were 207, 416, 1139, and 619 kg/m3
,
respectively.

2.2. RC Beams Preparation
A total of 26 concrete beams (130 mm × 180 mm × 1200 mm) with different types of
reinforcement (BFRP, CFRP, GFRP, and steel bars) were cast in a 10 mm-thick plywood
mold and then cured for 28 days. Two RC beams were cast with K-type thermocouples to
obtain the temperature profile across the beams’ depth during the heating process. The
remaining 24 beams were either kept at room temperature or exposed to 500 °C for 90 min
before testing for flexural response and modes of failure. The FRP-RC beams were designed
according to ACI 440.1R-15 [43] as over-reinforced with a reinforcement ratio (ρ =
0.008391) greater than the balanced reinforcement ratio (ρb), whereas the beams reinforced
with conventional steel were designed according to ACI 318R-05 [44] as under-reinforced
with (ρ = 0.008391) lower than (ρb). The calculated balanced reinforcement ratios (ρb) of the
beams reinforced with CFRP, GFRP, BFRP, and steel bars were 0.003324, 0.008104,
0.006453, and 0.0223, respectively. For all cast beams, 210 and 26 mm bars were used for
tensile reinforcement and top reinforcement, respectively. Steel stirrups of 6 mm were used
for shear reinforcement at a spacing of 70 mm (Figure 2). Special steel spacers were
positioned underneath and at the sides of the reinforcement cages to achieve a cover of 25
mm.
Figure 2 Reinforcement details and assemble reinforcement cages.

Prior to the placement of the reinforcement cages in the molds, a special type of high
temperature strain gauge with a 3.0 mm gauge length and resistance of up to 300 °C was
attached to the mid-length of one of the main reinforcement bars. This strain gauge was then
sequentially coated with silicone sealant, ceramic paste layer, ceramic wool layer, and Teflon
tape. At least 25 mm of protection on both sides of the fixed gauge was maintained to reduce
the temperature that reaches the gauge by 100 °C–150 °C. An additional strain gauge was
fixed to the other main reinforcement bar of the specimens already subjected to heating. This
strain gauge served as a backup in case the one installed prior to heating failed. For this
purpose, a small hole of approximately 30 mm × 30 mm × 30 mm was created during casting
at the main reinforcement level and then later filled with ceramic wool to protect the
adjoining FRP bar during heating (Figure 3). After the burning of the RC beams, the ceramic
wool was removed prior to the installation of the strain gauge in the reinforcement bar and
coating of the silicone sealant. Finally, the hole was filled with concrete and allowed to cure
for two weeks before testing. Another strain gauge measuring 40.0 mm was fixed at the
middle of the top surface of all concrete beams prior to flexural testing. Special protection
layers were used to prevent potential damage of strain gauges during flexural testing. The
temperature changes across each beam’s depth during heating were determined by placing
four K-type thermocouples measuring 1.0 m in length at different locations across the depth
of two steel RC beams prior to casting (Figure 5). Through this placement, the temperature
variations across the beams at 500 °C for 4 h were obtained.
(a) Hole created (b) Hole filled with ceramic wool
Figure 3 Hole at bottom of RC beam used for later fixation of strain gauges
Figure 4 Fixation of strain gauge after burning of RC beam

Figure 5 Locations of thermocouples across the depth of two beams.
2.3. Mixing, casting and curing
A titling drum mixer with a 0.15 m3
capacity was used to mix the concrete ingredients
according to the ASTM standards [45]. The slump was measured to be approximately 90 mm
according to the ASTM standards [46]. The concrete was cast in wooden molds in three
layers (Figure 6) and consolidated via an electrical internal poker vibrator to achieve good
compaction. After 24 h, the beam specimens were de-molded and cured for 21 days at room
temperature by spraying water daily and covering them tightly with a plastic membrane to
reduce the evaporation of the sprayed water from the concrete surface (Figure 7). After 21
days, the specimens were left in the laboratory a week prior to testing. Standard concrete
cylinders and cubes were cast, cured, and tested for compression and tensile strengths before
and after exposure to high temperatures to control the quality of the concrete used to make
the beams.
2.4. Beam specimen heating
A gas furnace with internal dimensions of 1.0 × 1.0 × 1.0 m3
and a movable top tight cover
was used in this experiment. The furnace was lined internally with insulating bricks. The
proper heat distribution inside the furnace and equal heating of the beams at all directions
(bottom, sides, and top) were obtained using gas-fired nozzle burners and fixed
thermocouples at all sides of the furnace. The average temperature from the four
thermocouples was closely monitored and adjusted to meet the target heating regime inside
the beam specimens. Therefore, two RC beams were cast with K-type thermocouples. With
consideration of furnace occupancy, the two beams were diagonally placed inside the furnace
and heated simultaneously up to 500 °C and kept constant for 4 h to define the temperature
distribution across the beams’ depth during the heating process. Figure 8 shows the measured
temperature readings from all thermocouples.
Figure 6 RC beams before and after casting in the wooden molds

Figure 7 De-molded RC beams with start of water spray curing
Figure 8 Temperature profile for RC beams heated to 500°C for four hours.
The beams reached a uniform temperature of approximately 460 °C at the end of the
heating duration, and the temperature at the location of the main bottom reinforcement
reached 325 °C after 92 min of heating. According to Hamad et al. [41], significant
degradation in the mechanical properties of FRP reinforcement can be avoided by
maintaining the reinforcement bars’ temperature below 325 °C, which can be achieved by
applying a maximum heating temperature of 500 °C for 90 min for all heated beams.
Hence, the heating regime depicted in Figure 9 was applied to all heated beam specimens
after moist curing for 21 days and air drying in the laboratory for a week. A standard cube
and cylinder, cast from the same concrete and cured for the same period as the beams, were
heated in the same furnace. The beam, cube, and cylinder specimens were air-dried after
heating.
Nigro et al. [28] stated that the temperature rise in rebars can be further delayed by using
a large concrete cover. Abbasi and Hogg [47] showed that the temperature of a main
reinforcement bar could reach 326 °C after a 90 min exposure to ISO 834 standard fire if a 50
mm concrete cover is used. Approximately 50 mm concrete cover is required to maintain a
reinforcement bar’s temperature below the critical level (325 °C) upon exposure to standard
fire (ISO 834).

Figure 9 Heating time-temperature schedule.
2.5. Flexural response test
All beams were tested as simply supported at a center-to-center span of 1050 mm and pure
bending moment span of 350 mm around the middle of the beams (refer to Figure 2 for
details on the geometric dimensions of the test beams). A load actuator with a 500 kN
capacity was applied manually at an approximate average rate of 0.1 kN/s. The measurements
from three linear variable displacement transducers (LVDTs) and strain gauges (attached to
the compression concrete and steel) were acquired using a data acquisition system. Three
LVDTs were placed under the beams to measure deflection (Figure 10). Crack propagation
was visually observed, marked, and photographed while load was increased until failure.
Figure 10 Flexural test arrangement, setup and positioning of the LVDT’s
3. EXPERIMENTAL RESULTS AND DISCUSSION
3.1. Concrete residual mechanical properties
The compressive and splitting strengths of concrete were determined using concrete cylinders
(100 mm × 200 mm) according to the ASTM test methods C39 and C496, respectively [48-
49]. Table 2 presents the averages of the tests carried out before and after a 90 min exposure
to a high temperature of 500 °C. The experimental average compressive strength of the
cylinders decreased by 26% following the exposure of the cylinders to heating at 500 °C. The

corresponding average strain at ultimate stress increased from 0.00260 before heating to
0.00649 after heating. The experimental average splitting tensile strength decreased by 48%
after the exposure of the cylinders to a temperature of 500 °C.
Table 2 Compressive and tensile strength of concrete before and after exposure to 500°C.
Temperature fc' (MPa) c % fsp (MPa)
23°C 33.98 ± 1.57 0.2635 ± 0.0233 3.265 ± 0.71
500°C 25.24 ± 2.76 0.6489 ± 0.0451 1.706 ± 0.27
fc': concrete cylinder compressive strength at 28 days, c: Strain at fc', fsp: splitting tensile
strength.
3.2. Flexural performance of RC beams
3.2.1. Flexural performance of control RC beams
The load–deflection curves of the different FRP reinforced beams consisted mainly of two
main linear segments, followed by a nonlinear segment prior to failure (Figure 11). The first
linear portion of the load–deflection curves at lower loads was related to the linear uncracked
behavior of concrete, whereas the second linear portion thereafter reflected concrete cracking.
At a certain point prior to the ultimate load, the cracked beams showed unreasonable
nonlinear behavior until their failure possibly because of the significant slippage between the
FRP bars and the concrete.
The first linear portions of the load–deflection curves were matched because the
deflections below the cracking load were related directly to the almost equal uncracked
rigidity of the different concrete beams. By contrast, the second linear portions of the beams
varied with the FRP bars because the rigidity of the cracked concrete beams was dictated by
FRP properties and their bond with the surrounding concrete. The load–deflection curves,
depicted in Figure 11 for beams with different types of reinforcement, reflected the typical
behavior observed for triplicate beams (Figure 12). The repeated drops in load values in the
different curves were related to the consecutive cracking of concrete upon load increase.
Meanwhile, the load–deflection curve for the triplicate beams with conventional steel showed
a typical behavior of being linear and non-linear sequentially; designating steel yielding
without signs of possible bar slippage from concrete (Figure 12).
Figure 11 Typical load-deflection curve of control beams with different reinforcement bars.

Figure 12 Load-deflection behavior of control RC beams with different reinforcement bars
3.2.2. Flexural performance of heat–damaged concrete beams
The results of the load versus the mid-span deflection response of the triplicate beams with
different bars exposed to 500 °C were obtained and are presented in Figure 13. Accordingly,
typical load versus mid-span deflection diagrams representing beams with different bars are
presented in Figure 14. Upon exposure to 500 °C, the concrete beams with FRP
reinforcement exhibited a nonlinear load–deflection response, as well as a dramatic increase
in mid-span deflection at low load levels due to the loss of the bond between the FRP bars
and the surrounding concrete.
Hamad et al. [41] stated that the mechanical properties of FRP bars and their bond with
concrete deteriorate dramatically after their exposure to high temperatures; the deterioration
adversely affects the flexural performance of the concrete beams with FRP bars when
exposed to 500 °C. The negative effects of high temperature on the behavior of FRP
reinforced beams were more pronounced in those with GFRP and BFRP than in those with
CFRP because of the higher susceptibility of the GFRP and BFRP bars to elevated
temperatures, as confirmed by Hamad et al. [41].
3.3. Characteristics of load deflection diagram of RC beams with different bars
The characteristics of the load–deflection curves of the control and heat-damaged beams,
namely, ultimate load capacity, mid-span deflection, stiffness, and ductility, were affected by
the type of reinforcement bar, as described below. The characteristics of the load versus
deflection of the beams with different bars were obtained on the basis of the average of three
readings from triplicate specimens and then summarized in Table 3.

Figure 13 Load-deflection response of concrete beams with different reinforcement bars after
exposure to 500°C
Figure 14 Typical load-deflection response of beams with different reinforcement bars before and
after exposure to 500°C

Table 3 Characteristics of load-deflection diagram for RC beams with different FRP bars
Beam
Type
Temp.
(°C)
Pexp-ult
(kN)
Δexp-ult
(mm)
Pexp-cr
(kN)
Δexp-cr
(mm)
Δexp-s
(mm)
I.S.
(kN/m)
S.2nd
(kN/m)
S.R
Etotal
(kN.mm)

GFRP
23 32.638 13.280 10.762 0.804 6.554 12543 4370 65% 285.6 2.430
500
6.853
(21%)
19.969
(150%)
1.501
(14%)
0.376
(47%)
N.A.
4071
(32%)
853
(20%)
79%
(122%)
90.80
(32%)
4.708
(194%)
BFRP
23 38.569 11.983 11.938 0.923 6.860 13440 3892 71% 279.8 1.954
500
7.262
(19%)
15.860
(132%)
1.620
(14%)
0.490
(53%)
N.A.
3277
(24%)
1428
(37%)
56%
(79%)
84.70
(30%)
3.489
(179%)
CFRP
23 89.973 11.437 13.667 0.802 2.728 18147 9260 48% 609.7 1.291
500
31.969
(36%)
16.418
(144%)
1.584
(12%)
0.413
(51%)
9.513
(349%)
3851
(21%)
2087
(23%)
46%
(96%)
312.3
(51%)
1.265
(98%)
Steel
23 76.137 11.123 20.667 1.376 1.587 15888 11496 26.5% 625.5 N.A.
500
69.420
(91%)
13.686
(123%)
2.919
(14%)
0.321
(23%)
2.730
(172%)
9990
(63%)
8247
(72%)
15.79%
(59%)
632.5
(101%)
N.A.
Pexp-ult, experimental ultimate load, Δexp-ult, measured mid-span deflection at ultimate load,
Pexp-cr, experimental cracking load, Δexp-cr, measured mid-span deflection at cracking load,
I.S, initial stiffness, S.2nd
, stiffness after cracking, S.R. Reduction in stiffness, Δexp-s, mid-span
deflection at theoretical service load, Etotal, total absorbed energy, , ductility index, N.A., not
available.
3.3.1. Ultimate load capacity and corresponding mid-span deflection
Hamad et al. [41] showed that CFRP bars have the highest bond strength with concrete
among all reinforcement types. This property positively affects the flexural performance of
the beams with CFRP bars. Hence, the beams with CFRP bars showed the highest ultimate
load capacity at 89.9 kN followed sequentially by those with steel, BFRP, and GFRP bars at
76.1, 38.6, and 32.6 kN, respectively. The post-heating ultimate load capacities of the BFRP,
GFRP, and CFRP beams were 7.26, 6.85, and 31.9 kN, representing 18.8%, 20.9%, and
35.5% of the controls, respectively. As a result of the minor effect of heating on the tensile
strength of the steel bars and the bond between the steel bars and the concrete, the reduction
in load capacity upon heating at 500 °C was low at 8.8%, as explained by Hamad et al. [41].
The load–deflection curves’ characteristics (Table 3) indicate that the FRP reinforced beams
showed larger mid-span deflections than the steel RC beams did due to the formers’ lower
modulus of elasticity and bond strength relative to steel bars. The mid-span deflections at the
ultimate load of the GFRP, BFRP, CFRP, and steel RC beams were 13.28, 11.98, 11.44, and
11.13 mm, respectively. The FRP bars’ modulus of elasticity and the bond between the FRP
bars and the concrete were affected negatively upon beam’s exposure to 500 °C. As a result,
beam stiffness was reduced, and the mid-span deflection at relatively low load levels
increased. All the post-heated FRP reinforced beams failed at small loads and large
deflections. The mid-span deflections of the heated GFRP, BFRP, and CFRP beams

increased by 50.4%, 32.4%, and 43.5% to reach 19.97, 15.86, and 16.42 mm measured at
relatively low loads of 6.85, 7.26, and 31.97 kN, respectively.
3.3.2. Stiffness
The rigidity for the first and second linear portions and the post-cracking reduction
percentage were computed as the average readings from triplicate specimens. The results are
summarized in Table 3. The highest initial rigidity was observed in the beams with CFRP
bars at 18.15 MN/m, followed sequentially by those with BFRP and GFRP bars at 13.44 and
12.54 MN/m, respectively. Rigidity was reduced after first cracking by 48%, 71%, and 65%,
respectively. As expected, the lowest reduction in stiffness after first cracking (27%) was
observed among the steel reinforced beams. Upon exposure to 500 °C, the different beams
suffered from reduced stiffness. Although the concrete beams with CFRP bars showed the
highest initial stiffness among the FRP reinforced beams at normal temperature, they
experienced the highest degradation in their stiffness after exposure to 500 °C. The initial
stiffness values of the heated GFRP, BFRP, CFRP, and steel reinforced beams were 4.07,
3.28, 3.851 and 9.99 MN.m, which represent 32.5%, 24.4%, 21.2%, and 62.8% of their
unheated beam’s stiffness, respectively. After cracking, the corresponding beams suffered
stiffness reduction at 79%, 56%, 46%, and 16%.
3.3.3. Serviceability
Serviceability is defined as the ability to maintain structural usability over the life of a
structure. The present service load values were computed on the basis of the recommendation
of Vesey and Bischoff, that is, a service load between 35% and 45% of the flexural member’s
capacity would limit deflection to L/240, where L is the beam span [50]. In the study, the
service load, Ps, was taken as 35% of the theoretical member capacity; upon which the mid-
span deflections were interpolated. The results are presented in Table 3. The beams with
CFRP bars showed a lower serviceable mid-span deflection than the beams with BFRP and
GFRP did due to the former beams’ higher stiffness. The mid-span deflections at the service
load of the beams with GFRP, BFRP, and CFRP bars were 6.55, 6.86, and 2.728 mm,
respectively. After exposure to 500 °C, the maximum load capacities of the GFRP and BFRP
reinforced beams were significantly decreased to levels lower than the defined service loads.
Therefore, the serviceable mid-span deflection could not be measured. By contrast, the
serviceable mid-span deflection of the CFRP reinforced beams peaked by 250% to reach 9.53
mm. As a result of their high stiffness, the beams with steel bars showed lower serviceable
mid-span deflections than those with the FRP bars did in the pre- and post-heating cases. The
measured serviceable mid-span deflection of the steel reinforced beams increased from 1.587
mm to 2.73 mm upon exposure to 500 °C because of the effect of heating on the reduction of
beam stiffness.
3.3.4. Ductility: Energy based approach
The ductility index, μ, can be calculated according to Equation (1) using elastic and total
absorbed energy, as defined by Naaman and Jeong [51]. The schematics of Figure 15 present
that the total energy is calculated as the total area under the load–deflection curve, whereas
elastic energy is the area of a right triangle formed at failure load with a hypotenuse slope
equal to the weighted average slope of the two initial straight lines of the load–deflection
curve. The hypotenuse slope (S) was computed using Equation (2) in terms of P1 and P2, and
the slopes S1 and S2 are defined in the latter figure. In some cases, idealizing the load–
deflection curves into three segments was difficult. In such cases, P1 and P2 values and their
corresponding slopes S1 and S2, respectively, were estimated. As per Canadian Highways

Bridge Design Code, a minimum ductility index value of 4 is considered enough to have a
ductile failure mode [52], whereas New Zealand standards recommend a ductility index of
more than six for a perfect ductile failure mode [53].
Ductility Index  =
1
2
(
𝐸𝑒𝑙 + 𝐸𝑖𝑛𝑒𝑙
𝐸𝑒𝑙
+ 1) (1)
𝑆 =
𝑃1 𝑆1 + (𝑃2 − 𝑃1)𝑆2
𝑃2
(2)
The results of the ductility index computation according to Equation 2 are summarized in
Table 3, in which the results represent the average of three specimens. The ductility indices
for all control FRP reinforced beams were less than the lower limit at 4, indicating non-
ductile failure mode and greening with actual failure observed experimentally. The GFRP
reinforced beams showed the highest ductility at 2.43, followed sequentially by the BFRP
and CFRP reinforced beams at 1.954 and 1.291, respectively. The procedure for computing
ductility index is applicable only to FRPs but not to conventional beams; hence, the
corresponding value for steel reinforced beams is not provided in Table 3. The CFRP beams,
among all the FRP beams, had the lowest ductility index, but they exhibited the highest
absorbed total energy until failure. The total absorbed energy for the GFRP, BFRP, CFRP,
and steel reinforced beams averaged 286, 280, 610, and 625.5 kN.mm, respectively. This
result showed that the beams reinforced with conventional steel were more ductile than those
with FRP bars.
Figure 15 Ductility index as computed by Naaman and Jeong, [51]
The ductility indices of the GFRP and BFRP beams under 500 °C were increased by 94%
and 79% to reach 4.708 and 3.489, respectively. Those of the CFRP reinforced beams slightly
decreased from 1.291 to 1.265. As a result of the major reduction in the load capacities of the
heated FRP beams, the total absorbed energy of the GFRP, BFRP, and CFRP reinforced
beams dropped to 90.8, 84.7, and 312.3 kN.mm, representing 32%, 30%, and 51% of that of
the control FRP reinforced beams, respectively. The total absorbed energy of the steel
reinforced beams increased from 625.5 kN.mm to 632.5 kN.mm upon exposure to 500 °C,
indicating that the behavior of the steel reinforced beams was more ductile than that of the
FRP-RC beams.

3.4. Modes of failure, induced strains and cracking patterns
3.4.1. Strain induced in reinforcement and compression concrete
The applied loads versus strain curves of concrete and FRP bars are illustrated graphically in
Figures 16 and 17. Table 4 summarizes the strain readings of concrete and reinforcement at
ultimate load capacities, representing the average for three specimens. Increased
reinforcement tensile strain was evident at first cracking of the control FRP reinforced beams,
followed by an almost linear response up to failure. At ultimate load, the average measured
strains of concrete and reinforcement bars for control GFRP, BFRP, and CFRP reinforced
beams were 0.001412 and 0.005419, 0.001707 and 0.005075, and 0.002740 and 0.007144,
respectively. These values indicated that the failure of the beams with GFRP and BFRP bars
occurred due to the loss of bond between the FRP bars and the concrete and before concrete
crushing strain stipulated at 0.003 was reached or the FRP bars ruptured. Shear failure
occurred in the beams with CFRP bars just before the ultimate crushing strain in concrete was
reached. Upon exposure to 500 °C, the bonds between the FRP bars and the concrete were
weakened; hence, the load versus tensile strain curves of the GFRP and BFRP beams suffered
from high nonlinearity. The load–tensile strain relationship of the post-heated CFRP
reinforced beams showed a clear linear behavior up to failure. The post-heated steel
reinforced beams suffered from steel reinforcement yielding before failing by concrete
crushing.
Figure 16 Strains in concrete and reinforcement bars in different control RC beams

Figure 17 Strains in concrete and reinforcement bars in different RC beams, after exposure to 500°C
Table 4 Average strain readings (x10-6) of concrete and different reinforcing bars at ultimate loads.
Temp
GFRP BFRP CFRP Steel
c r c r c r c (ult) r (ult) c (yield) r (yield)
23 1412 5419 1707 5075 2740 7144 5418 6910 2885 2996
500 1075 1644 1443 1869 3255 2835 6201 N.A 3279 2360
f, FRP strain at ultimate load, c, concrete strain at ultimate or yield load, s, steel strain at
yield or ultimate load
3.4.2. Failure mode and cracking pattern of FRP reinforced beams
Tensile forces are transferred from concrete to reinforcement bars upon first cracking in
regions where tensile stress bypasses concrete’s tensile strength. If not controlled properly,
cracks could propagate toward the compression zone and cause concrete crushing failure at
relatively low loads. Improper cracking control could occur due to the loss of bond between
FRPs and concrete, as observed in the control beams with GFRP and BFRP bars. However, if
an intact bond is maintained, as in the case of the control beams with CFRP bars, then shear
failure may occur because the neutral axis can be stabilized as the load increases given the
high strength of CFRP bars. As expected, the steel reinforced beams in this study experienced
the yielding of the steel bars before failing by concrete crushing.
Figures 18–20 show that the first flexural cracks in the control GFRP, BFRP and CFRP
reinforced beams were initiated in the high bending moment zone at average cracking loads
of 10.7, 11.94, and 13.7 kN, respectively; followed by the formation of main flexural cracks
as the applied load further increases. Sudden load drops were noticed concurrently with the
formation of new flexural cracks, which were more visible in the cases of the GFRP and
BFRP beams. In these cases, a maximum of two additional flexural cracks could form below

the loading points and then widen rapidly as the load increases until bond failure prior to
concrete crushing or FRP rupture. In the case of the CFRP reinforced beams, a maximum of
five new vertical cracks were developed along the beam’s span and then branched and
propagated deeply toward the compression zone. Prior to the failure of the latter beams, new
inclined shear cracks were developed near the support and extended diagonally toward the
top loading points that caused sudden shear failure. At failure, the number of cracks in the
beams with CFRP bars was higher than that in the beams with GFRP and BFRP bars.
Upon heating to 500 °C, the GFRP, BFRP, and CFRP beams initially cracked at the
average low loads of 1.5, 1.62, and 1.58 kN, respectively, which are 12%–14% of those of
the control FRP reinforced beams. Cracking was initially formed in the high moment zone
and then followed immediately by the formation of two new flexural cracks located below the
two loading points. These locations were mainly considered as the weak points at which bond
failure starts (Figures 18–20). The cracks widened rapidly with a small increase in load.
Failure occurred upon the sudden increase of the cracks’ width and deflection without any
increase in load due to the total loss of the bond between the FRP bars and the concrete. In
the case of the CFRP reinforced beams, the main flexural cracks were branched with
increasing load and then extended and propagated deeply toward the compression zone, along
with the formation of additional vertical cracks in the nearby zone.
Figure 18 Typical cracking pattern of concrete beams with GFRP bars before (top) and after (bottom)
exposure to 500°C
Figure 19 Typical cracking pattern of concrete beams with BFRP bars before (top) and after (bottom)
exposure to 500°C

Figure 20 Typical cracking pattern of concrete beams with CFRP bars before (top) and after (bottom)
exposure to 500°C
3.4.3. Failure mode and cracking pattern of steel beam
The first flexural crack of the beams with steel bars initiated in the middle zone at the average
cracking load of 20.67 kN and then extended toward the compression zone with increasing
load. Furthermore, six to eight vertical flexural cracks formed along the beam with a high
concentration in the middle high moment zone. At high loads, the flexural cracks in the high
moment zone branched and grew toward the compression zone while the cracks in the high
shear zone were developed with inclined branches that extended diagonally toward the
loading points until the occurrence of concrete crushing failure at a strain of 0.0054 with a
reinforcement strain of 0.0069. Figure 21 shows that the number of cracks in the steel
reinforced beams was higher than that in the beams with FRP bars; however, their average
widths were small.
Post-heated steel reinforced beams cracked at a low cracking load of 2.92 kN,
representing 14.1% of the control steel reinforced beams. Six to eight main flexural cracks
were formed along the beam, extending toward the compression zone with increasing load.
Additional inclined shear cracks at high loads, were formed near the support because of the
reduction in concrete shear strength upon heating; the cracks were extended diagonally
toward the loading points up to failure (Figure 21).
Figure 21 Typical cracking pattern of concrete beams with steel bars before (top) and after (bottom)
exposure to 500°C.

4. ANALYTICAL PREDICTION OF FLEXURAL STRENGTH OF FRP
REINFORCED BEAMS
According to ACI440.1R, flexural concrete sections with FRPs should be designed or
analyzed as over-reinforced with a reinforcement ratio (ρf) that is greater than the balance
reinforcement ratio (ρb), at which point the concrete crushing failure mode is expected.
Failure by the rupture of the FRP bars occurs when the reinforcement ratio (ρf) is lower than
the balance reinforcement ratio (ρb). In general, most concrete FRP reinforced beams,
especially those subjected to elevated temperatures, undergo bond failure prior to concrete
compression or tensile reinforcement failure. Hence, knowledge of bond stress–slip
relationship becomes essential for the precise prediction of beams’ mechanical performance.
The following steps describe how the flexural capacity of the control and heat-damaged FRP
reinforced beams is computed.
1. The FRP bar’s tensile force (T) is calculated as follows with consideration of concrete
crushing failure before FRP rupture:
𝑇 = A 𝑓 𝑓𝑓 = A 𝑓 (√(
𝐸𝑓 𝜀 𝑐𝑢
2
)
2
+ (
0.85𝛽1 𝑓𝑐
′ 𝐸𝑓 𝜀 𝑐𝑢
𝜌 𝑓
) −
𝐸𝑓 𝜀 𝑐𝑢
2
) ≤ A 𝑓 𝑓𝑢𝑓. (3)
2. The maximum bond force capacity (F) between the FRP bars and the surrounding concrete
is calculated on the basis of the schematics of Figure 22 according to Equation (4)
Figure 22 Critical Section for bonding failure (dimensions in mm).
𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝐵𝑜𝑛𝑑 𝐹𝑜𝑟𝑐𝑒 (F) = number of bars × 𝜋 𝜏 𝑚𝑎𝑥 𝑑 𝑏 𝑆 (4)
where τmax is the average bond strength capacity between different FRPs and concrete, as
determined by Hamad et al. and listed in Table 5 [41].
3. Two cases are considered when computing nominal flexural capacities depending on
whether the force (T) in the FRP bars is smaller, equal to, or greater than the calculated bond
force capacity (F).
If T < 𝐹; 𝑀 𝑛 = 𝑇 𝑑 (1 −
0.59𝜌 𝑓 𝑓𝑓
𝑓𝑐
′ ) (5)
𝐼𝑓 𝑇 ≥ 𝐹; 𝜀𝑓 =
𝐹
𝐴 𝑓 𝐸 𝑓
(6)

The maximum strain in FRPs (f) at bond failure level is calculated from Equation (6).
Then, assuming a linear strain distribution of strain across the beam depth, the strain in the
compression concrete was determined through triangle similarity and the schematic of Figure
23. The strain in concrete is related to compressive stresses according to Equation (7),
representing the model by Hognestad [54]. Equilibrium requires the compressive force in
concrete to be equal to that of the reinforcement (F) on the basis of the location of the neutral
axis, c, as given in the equation (8). The location of the neutral axis is determined by
considering internal equilibrium and applying trial and error. Finally, the nominal moment
and load capacity are calculated according to Equation (9). In the case of the post-heated
concrete, its strain is related to the compressive stresses based on Equation (10), as proposed
by Eurocode 2 [55] instead of that proposed by Hognestad. The results of moment capacity
computation for various FRP reinforced beams and exposure before and after exposure to 500
°C are listed in Table 6.
𝑓𝑐 =
{
𝑓𝑐
′
(
𝜀 𝑐
𝜀 𝑜
) (2 −
𝜀 𝑐
𝜀 𝑜
) 𝑖𝑓 𝜀 𝑐 ≤ 𝜀 𝑜 =
1.8𝑓𝑐
′
4700√𝑓𝑐
′
; 𝜀 𝑐 =
𝑐𝜀𝑓
𝑑 − 𝑐
𝑓𝑐
′
[1 − (0.15 ×
𝜀 𝑐 − 𝜀 𝑜
𝜀 𝑐𝑢 − 𝜀 𝑜
)] 𝑖𝑓 𝜀 𝑜 =
1.8𝑓𝑐
′
4700√𝑓𝑐
′
< 𝜀 𝑐 ≤ 𝜀 𝑐𝑢 ; 𝜀 𝑐 =
𝑐𝜀𝑓
𝑑 − 𝑐
(7)
𝑐 =
3𝐹
2𝑓𝑐 𝑏
(8)
Figure 23 Stresses and Internal Forces of FRP-RC Rectangular Section
𝑀 𝑛 = 𝐹(𝑑 − 0.4𝑐); 𝑃𝑛 =
6𝑀 𝑛
𝐿
(9)
𝑓𝑐,500 = (
3𝜀 𝑐,𝑇 𝑓𝑐,500
′
0.015 [2 + (
𝜀 𝑐,𝑇
0.015
)
3
]
) (10)

Table 5 Mechanical properties Steel/FRP reinforcement and their bond strength with concrete as
determined by Hamad et al. [41].
Reinforcement
Type
Bar Temp.
°C
CE
Ef
MPa
fuf*
MPa
fuf
MPa
uf*
mm/mm
uf
mm/mm
τm
MPa
Carbon
23 0.9 119,000 1572 1414 0.0167 0.01503 8.339
325 0.9 80,410 700 630 0.0094 0.00846 1.542
Glass
23 0.7 47,140 816 571 0.0215 0.01505 2.014
325 0.7 37,390 452 316 0.0148 0.01036 0.419
Basalt
23 0.8 65,850 940 752 0.0206 0.01648 2.628
325 0.8 51,890 510 408 0.0141 0.01128 0.554
Es
MPa
fy
MPa
fu
MPa
ult
mm/mm
εR
mm/mm
Steel
23 228,300 571 638 0.0848 0.1054 11.31
325 209,210 547 628 0.0923 0.1097 8.24
CE, environmental reduction factor, Ef, FRP modulus of elasticity, fuf*, FRP ultimate
tensile strength, fuf, design tensile strength of FRP, uf*, FRP ultimate tensile strain, uf, FRP
design strain, fc’, concrete compressive strength, N.A. , τm, average bond strength, fy: steel
yield strength, fu: steel ultimate tensile strength, ult: steel strain at ultimate tensile strength,
εR: steel elongation at rupture, Es: steel modulus of elasticity.
Table 6 shows that the theoretical flexural capacities of the FRP reinforced beams (Pth-ult),
calculated according to ACI440 and under the assumption of a perfect bond between bars and
concrete up to failure, were compared with the predicted flexural capacities on the basis of
the experimental bond test results (Ppre-ult) and the experimental load capacities (Pexp-ult). The
experimental load capacities of the control beams with GFRP, BFRP, and CFRP bars were
49.1%, 50.8%, and 104.7% of their theoretical load capacities and 83.4%, 76.6%, and
104.7% of the predicted load capacities based on actual bond strength results, respectively.
These results indicate that a bond loss failure occurred in the GFRP and BFRP beams before
concrete crushing. Upon 500 °C exposure, the experimental load capacities of the beams with
GFRP, BFRP, and CFRP bars were measured to be 19.5%, 16.4%, and 48.4% of their
theoretical load capacities and 91.8%, 75.2%, and 123.9% of the predicted load capacities
with consideration of FRP bars’ concrete slippage, respectively.
The experimental load-carrying capacity of control and heated-damaged steel reinforced
beams was 112.5% and 110% of their theoretical values, respectively, thereby confirming the
intact bond between steel bars and surrounding concrete. The above results prove that the
proposed calculations for predicting the flexural load capacities of FRP reinforced beams on
the basis of actual bond strength results are reasonably well and present a good agreement
with the experimental results.

Table 6 Comparison between beams’ theoretical and experimental load capacities
Beam Type Temp.°C
Pth-ult
(kN)
Ppre-ult
(kN)
Pexp-ult
(kN)
Pexp-
ult/Ppre-ult
Pexp-ult/Pth-
ult
Ppre-ult/Pth-
ult
GFRP-RC
23 66.51 39.14 32.64 0.83 0.49 0.59
500 35.16 7.46 6.85 0.92 0.19 0.21
BFRP-RC
23 75.94 50.42 38.6 0.77 0.51 0.66
500 44.32 9.66 7.26 0.75 0.16 0.22
CFRP-RC
23 85.74* 85.74* 89.97 1.05 1.05 1.00
500 66.05 25.81 31.97 1.24 0.48 0.39
Steel-RC
23 67.66 76.14 1.13 1.00
500 63.1 69.42 1.10 1.00
Pth-ult, theoretical ultimate load capacity based on ACI440 assumptions, Ppred-ult, predicted
ultimate load capacity based on actual bond test result, Pexp-ult, experimental ultimate load
capacity, * shear load capacity of the beams.
The experimental load carrying capacity of control and heated-damaged steel reinforced
beams was 112.5% and 110% of their theoretical values, respectively, which confirmed that
the bond between steel bars and surrounding concrete was intact. Based on the above results,
the proposed calculations for predicting the flexural load capacities of FRP reinforced beams,
based on actual bond strength results were reasonably well and showed a good agreement
with the experimental results.
The theoretical modes of failure based on the assumption of either a perfect bond or a
direct bond tests, were compared with experimentally observed failure modes. A summary of
the results are listed in Table 7. The observed failure modes represented in FRP bar slippage
matched those predicted. Therefore, FRP bar slippage should be accounted for in the
evaluation of the flexural behavior of FRP reinforced beams prior to and after being exposed
to elevated temperatures.
Table 7 Theoretical, expected and observed failure modes
Beam Type T (°C) Theoretical FM Expected FM Observed FM
CFRP-RC
23
S S S
GFRP-RC CC BS BS
BFRP-RC CC BS BS
CFRP-RC
500
CC BS BS
GFRP-RC FR BS BS
BFRP-RC FR BS BS
FM, failure mode, CC, concrete crushing, FR, FRP rupture, S, shear failure, EC, end cap,
BS, bond slip.

5. CONCLUSIONS
The following conclusions can be stated on the basis of the above discussion.
1. The beams with steel bars showed pure flexural failure before and after heating, along
with a high number of cracks and lower average crack sizes relative to those of
similar beams with FRP bars.
2. The strains measured in a high moment region in the concrete and FRP reinforcement
confirmed the occurrence of a bond–slip failure or shear failure before the concrete
and FRP bars reached their ultimate strain capacities.
3. The initial stiffness of all concrete beams was reduced after cracking. Beams with
BFRP bars had the highest reduction, followed sequentially by the GFRP, CFRP, and
steel bars.
4. Control concrete beams with GFRP and BFRP bars failed prior to reaching theoretical
load capacity due to bond failure. The measured load capacity values for these beams
were 49.1% and 50.8% of the theoretical ones computed, assuming a perfect bond
between concrete and FRP bars according to the ACI440 code.
5. The experimental load capacity of CFRP bars was 104.9% of the theoretical values
owing to the satisfactory surface characteristics of CFRP bars, which imparted an
intact bond with concrete.
6. Upon exposure to 500 °C for 90 minutes, the RC beams with FRP bars failed at
relatively low load levels due to the degradation of the bars’ tensile strength and the
loss in bond between the FRP bars and the surrounding concrete.
7. The heated FRP-RC beams experienced significant deflection and loss in stiffness and
total absorbed energy, but their ductility increased.
8. The detrimental impact of similar heating on the ultimate load capacity, stiffness,
deflection, and ductility of the RC beams with steel bars was minimal and less than
that of heated beams with FRP bars.
9. The beams with CFRP bars displayed superior flexural behavior relative to those with
the GFRP and BFRP bars under elevated temperatures because of the former bars’
higher resistance to heating.
10. The theoretical ultimate load for the control and heat-damaged FRP-RC beams,
computed using the ACI code that assumes a prefect bond between FRP bars and
concrete, was overestimated relative to the corresponding measured values.
11. The method proposed for predicting the load capacity of FRP-RC beams, based on the
actual pre- and post-heating mechanical properties of the FRP bars and concrete and
their bond characteristics, gave reasonably reliable results.
12. A reduced discrepancy between the theoretical and experimental values for the beams
with GFRP and BFRP was observed upon consideration of the slippage between the
FRPs and concrete.
Conflict of Interest:
On behalf of all authors, the corresponding author states that there is no conflict of
interest.
Funding and Acknowledgement:
This research work was financially supported by the Universiti Sains Malaysia (USM)
through the Research University Grant Scheme [Grant number: 1001/PAWAM/814191]

Notations
b = concrete section width,
d= distance from extreme compression fiber to centroid of tension bars,
Af= Area of FRP bars in tension region,
Ef= FRP modulus of elasticity, GPa,
fc' = compressive strength of concrete, MPa,
fuf = design tensile strength of FRP,
ff = tensile stress of FRP, MPa,
ρb = balance reinforcement ratio,
ρf = reinforcement ratio,
db= main reinforcement bar diameter, mm,
cu = crushing strain of concrete, and
uf = maximum strain of FRP.
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