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EFFECTS OF GFRP REINFORCING REBARS ON SHRINKAGE ANDTHERMAL STRESSES IN CONCRETE
Roger H. L. Chen
1
and Jeong-Hoon Choi
2
ABSTRACT
The use of Glass Fiber Reinforced Polymer (GFRP) rebars instead of conventional steel rebars as thereinforcement in Continuously Reinforced Concrete Pavement (CRCP) gives solutions to the problemscaused by corrosion of reinforcement. However, it is necessary to know what effect this replacement hason the development of concrete cracks, which is inevitable in CRCP. Concrete shrinkage and temperaturevariations are known to be the principal factors for early-age crack formation in CRCP. By employing ananalytical model, this study presents the shrinkage and thermal stress distributions in concrete due to therestraint provided by GFRP rebars in comparison with that provided by steel rebars. It reveals theadvantages of using GFRP rebars as reinforcement in CRCP in terms of internal tensile stress reduction inconcrete. Numerical calculation of the concrete stress distribution in a GFRP reinforced CRCP sectionsubjected to thermal change is also presented.
Keywords:
GFRP rebars, CRCP, cracks, concrete shrinkage, thermal stress
INTRODUCTION
Other than the advantage of eliminating steel corrosion, thermal and stiffness compatibility between GFRP and concrete may also offer possible advantages when GFRP rebars are used inreinforced concrete pavements. Traditional CRCP reinforced by steel rebars has been applied for a few decades (AASHTO, 1986), and the CRCP behavior has been reported (Won
et al
., 1991;Kim
et al.
, 2001). However, up to this point, there is no precedent for the use of GFRP asreinforcement in CRCP, and little related work has been done. It is therefore necessary to studythe mechanical behavior of CRCP reinforced with GFRP rebars. The effects of the GFRPreinforcing rebars on shrinkage and thermal stresses in CRCP were investigated at the onset of this study, and will be discussed in this paper. The results of this study will eventually contributeto the development of the design of CRCP with GFRP reinforcement.Shrinkage and thermal stresses in concrete have been known to be principal factors for theincipient cracking in concrete pavements or bridge decks. Understanding the development of these stresses is essential to properly controlling cracking, which may ultimately determine the performance and longevity of the concrete structure. In the case of a freely supported concreteslab subjected to shrinkage or temperature variation, the concrete stresses are produced because
1
Prof., Dept. of Civ. and Envir. Engrg., West Virginia Univ., Morgantown, WV 26506. E-mail: hchen@wvu.edu
2
Grad. Res. Asst., Dept. of Civ. and Envir. Engrg., West Virginia Univ., Morgantown, WV. E-mail: jchoi@wvu.edu
2of the restraints provided by the reinforcements. While concrete shrinkage causes tensile stressesin concrete (Zhang
et al
., 2000), the temperature variation can cause either tensile or compressivestresses in concrete. The thermal stresses are depending on whether the temperatures drop or riseand the relationship between the coefficients of thermal expansion (CTE) of the concrete and thereinforcement used. The CTE of concrete varies with different coarse aggregate types, and theCTE of the GFRP depends on the composite materials used. In this paper, analytical results are presented to describe the effect of GFRP reinforcing rebars on shrinkage and thermal stresses inconcrete slabs.
ANALYTICAL MODEL
To approximate the developments of shrinkage and thermal stresses in a concrete slab, arepresentative concrete prismatic model containing a longitudinal reinforcing rebar at its center with width (or reinforcing space in CRCP)
B
, height (or thickness in CRCP)
H
, length
L
, andrebar diameter 2
r
r
is considered. Then, as a matter of analytical convenience, the model ismodified into an equivalent cylindrical one with the corresponding equivalent diameter 2
R
, where
π
/
HB R
=
, accompanied by the same length and rebar diameter as those for the prismaticmodel. The schematic details of the models are shown in Fig. 1.Adopting the shear-lag theory (Cox, 1952), there are several assumptions made for thisanalysis: 1) the concrete and reinforcement exhibit elastic behavior, 2) the bond betweenconcrete and reinforcement is perfect at an infinitely thin interface, 3) the stiffness of the concreteand the reinforcement in the radial (
r
-) direction are the same, 4) the strain in the concrete,
ε
c
at adistance
R
from the
x
-axis is equivalent to the restraint-free concrete strain due to the shrinkage or temperature variation, and 5) the temperature distribution in the concrete and reinforcement areuniform in the radial direction. The effect of concrete radial shrinkage on the concrete stressdevelopment in the longitudinal direction is neglected. Also, effects from the CTE discrepancies between the concrete and the reinforcement in the radial direction are neglected.When the concrete is subjected to a strain,
ε
c
in the longitudinal (
x
-) direction, the rate of transfer of load from concrete to reinforcement can be assumed as
dP
/
dx = C
o
(
u-v
), where
P
isthe load of the reinforcement, and
C
o
is a constant.
v
and
u
are the axial displacements at
r = R
and
r = r
r
, respectively. It is also known from force equilibrium that
dP/dx
=
2
π
r
τ
. Integratingthe shear strain along the radial direction one gets
(
u-v
)
= dP
/
dx
ln(R
/
r
r
)
/
(
2
π
G
c
)
,
where
G
c
is theshear modulus of concrete. Hence,
)/ln(2
r co
r RGC
π
=
(1)Also,
dv/dx =
ε
c
and
du/dx =
ε
r
. Therefore,
( )
cr o
C dx P d
εε
−=
22
(2)The restraint-free concrete axial strain,
ε
c
, in the above equation can be substituted with either shrinkage strain at any time
t
(in days)
ε
c,s
(
t
) or thermal strain
ε
c,t
which are given by
ult sc sc
t t t
)(35)(
,,
εε
+−=
and
ct c
T
αε
∆=
,
(3a)where (
ε
c,s
)
ult
= ultimate shrinkage strain for drying at 40% RH;
∆
T
= temperature variation; and
α
c
= CTE of concrete.
ε
c,s
(
t
) is an empirical equation (Mindess and Young, 1981) for moist curedconcrete. The reinforcement axial strain due to concrete shrinkage,
ε
r,s
or due to temperature
3variation,
ε
r,t
are shown as:
r r sr
E A P
=
,
ε
and
r r r t r
E A P T
+∆=
αε
,
(3b)where
A
r
= reinforcement cross-sectional area,
E
r
= Young’s modulus of reinforcement, and
α
r
=CTE of reinforcement.Substituting Eq. (3) into Eq. (2) gives the governing differential equation for
P
, and then, bysolving the differential equation with boundary conditions that
P
= 0 at
x
= 0 and
x
=
L
, thereinforcement force,
P(x)
, can be obtained. The axial force equilibrium with the average axialconcrete stress, (
σ
c
)
avg
must also be satisfied at any
x
location:
0)(
=+
cavg c
A P
σ
,
where
A
c
is theconcrete cross-sectional area. Hence, the average axial concrete stress can be given as follows:
−−+=
2cosh2cosh1)(35)(
,
L x Lt t E
ult scr avg c
ββερσ
(Concrete Shrinkage) (4a)and
( )
−−−∆−=
2cosh2cosh1)(
L x LT E
r cr avg c
ββααρσ
(Temperature Variation) (4b)where
ρ
= reinforcing ratio (
A
r
/
A
c
), and
)/ln(/2
2
r r r c
r Rr E G
=
β
(5)The negative sign in front of Eq.(4b) indicates compressive axial stresses in concrete. Themaximum axial stress in concrete can be simply found at
x
=
L/2
.
MATERIAL PARAMETERS
In the shrinkage stress analysis, Young’s modulus of concrete,
E
c
, as well as concreteshrinkage strain,
ε
c,s
(
t
), are employed as a time-dependent properties, and therefore, the elapsedtime,
t
(days) is the only variable. The time-dependent Young’s modulus of concrete can beevaluated by (Mosley and Bungey, 1990)
[ ]
EtEt
cc
()..ln()
,
= +
28
052015
for
t
≤
28 (6a)
EtE
cc
().
,
=
1019
28
for t > 28 (6b)where
E
c
,28
= Young’s modulus of concrete at 28 days. In the thermal stress analysis, the concretestresses at 28 days are estimated for different temperature variations; a value of
E
c
,28
is employedhere. Table 1 lists a set of model parameters and material properties used in this study.
RESULTS AND DISCUSSION
In Fig. 1, the maximum average tensile stresses in the concrete due to the concrete shrinkageare estimated over a period of time. The stresses with either steel or GFRP reinforcements areshown in this figure, and they are compared with each other. In the comparison, # 5 rebars with aradius of 0.3125
in.
(
ρ
= 0.00519) are employed for the model length of
L
= 60
in
. From the
4figure, it can be seen that the maximum concrete stress level created by GFRP rebar is about one-fifth of that by steel rebar. This ratio is about the same as that of the longitudinal GFRP rebar’selastic modulus to steel rebar’s elastic modulus.
TABLE 1. Model Parameters and Material Properties Used in Analysis
Parameter and PropertiesValueWidth,
B
, (
in.
)6Height,
H
, (
in.
)10Length,
L
, (
in.
)60Ultimate Concrete Shrinkage Strain, (
ε
c,s
)
ult
, (
µε
) 800Elastic Modulus of Concrete at 28 days,
E
c,28
, (
Msi
)4.8
(1)
, and 5
(2)
Poisson’s Ratio of Concrete,
ν
c
0.2Young’s Modulus of Steel Rebar (
Msi
)29Longitudinal Young’s Modulus of GFRP Rebar (
Msi
)5.8CTE of Concrete,
α
c
, (
µε
/
o
F
)5.7
(1)
and 8.0
(2)
CTE of Steel Rebar,
α
r,s
, (
µε
/
o
F
)6.6CTE of GFRP Rebar,
α
r,g
, (
µε
/
o
F
)5.2(note: (1) granite aggregate and (2) siliceous river gravel coarse aggregate used)
Fig. 1. Max. Avg. Tensile Stress in Concrete vs. Time (
ρρ
= 0.00519 and
L
= 60
in.
)
Different sizes of GFRP rebars, #3 through #6 (
ρ
= 0.00184 through 0.00739), are also studied inFig. 2, showing that the maximum concrete stress increases with an increase in the reinforcingratio. GFRP rebars with a lower Young’s modulus provide the concrete with less restraint than
00.020.040.060.080.10.12050100150200250300350400450
Time (
days
)
M a x . A v g . T e n s i l e S t r e s s (
k s i
)
SteelGFRP
Lr xr
r
R B L H x y z
Representative Prism

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