sustainability

Article
Parametric Study on Steel–Concrete Composite Beams
Strengthened with Post-Tensioned CFRP Tendons
Ahmed H. Elbelbisi 1,2 , Alaa A. El-Sisi 3, * , Hilal A. Hassan 2 , Hani A. Salim 1 and Hesham F. Shabaan 2

1 Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211, USA
2 Department of Structural Engineering, Zagazig University, Zagazig 44519, Egypt
3 Department of Civil Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA
* Correspondence: aelsisi@siue.edu

Abstract: A sustainable environment can be achieved by strengthening the existing building to avoid
new construction and by replacing the construction materials with long-lasting sustainable materials
such as a fiber-reinforced polymer (FRP). Using post-tensioned (PT) FRP systems has proven to be an
effective technique in strengthening the structure and decreasing cracks and deformability. In this
study, a 3-D finite element model was built to investigate the flexural behavior of composite beams
strengthened with external PT FRP tendons. Limited research studied the use of FRP tendons to
enhance the structural behavior of composite beams. This paper represents a comprehensive study
of the effect of several parameters that control the design of the FRP tendons. Parameters such as
PT level, tendon material, tendon length, degree of shear connection (DOSC), and tendon profile
shape were considered under loading. The 3-D model’s correctness is validated using published
experimental data. It was observed that of all FRP materials, carbon FRP is the best type for upgrading
the beam strength, and it was recommended to use a 30 to 40% PT level. In addition, applying external
PT over the full length of the beam increases the ultimate load capacity significantly. However, due
to the difficulty of construction, it was recommended to use 90% of the beam span length since the
Citation: Elbelbisi, A.H.; El-Sisi, A.A.;
difference in beam capacity does not exceed 5%. Finally, adding PT tendons with a trapezoidal and
Hassan, H.A.; Salim, H.A.; Shabaan,
parabola profile to composite beams significantly increases the yield load and the beam capacity.
H.F. Parametric Study on
Steel–Concrete Composite Beams
Strengthened with Post-Tensioned
Keywords: composite beams; CFRP; tendon profile; shear connector; post-tension; finite element; ANSYS
CFRP Tendons. Sustainability 2022, 14,
15792. https://doi.org/10.3390/
su142315792
1. Introduction
Academic Editor: Enzo Martinelli
In terms of sustainability, strengthening using post-tension is a structural method that
Received: 15 October 2022 not only speeds up construction but also significantly decreases CO2 emissions because less
Accepted: 18 November 2022 concrete is used while rebuilding [1–3]. In addition, environmental effects can be reduced
Published: 28 November 2022 by recycling composites and recovering and reusing fibrous materials [4].
Publisher’s Note: MDPI stays neutral The post-tensioning technique has become one of the most popular strengthening
with regard to jurisdictional claims in technologies during the past 20 years. By reducing deflection and enhancing the stiffness
published maps and institutional affil- and carrying capacity of the structural elements, this technology allows designers and
iations. engineers to use materials more effectively. Several studies investigated this strengthening
approach and focused on its effectiveness in improving the behavior of structural elements
when exposed to various types of stresses [5,6].
Ayyoub et al. conducted an experimental study on external post-tensioning compos-
Copyright: © 2022 by the authors. ite beams (CBs) [7]. It was reported that straight tendon profiles are preferred because
Licensee MDPI, Basel, Switzerland. they are economical; however, draped tendon profiles fared better in terms of capacity
This article is an open access article
and deflection.
distributed under the terms and
Chen et al. provided experimental results from testing a CB fortified with external
conditions of the Creative Commons
post-tensioning tendons under the influence of positive moments [8]. It was found that
Attribution (CC BY) license (https://
adding post-tensioning tendons enhanced yield load and ultimate resistance by around 49%
creativecommons.org/licenses/by/
and 53%, respectively. It was also found that the ultimate moment of the non-strengthened
4.0/).

Sustainability 2022, 14, 15792. https://doi.org/10.3390/su142315792 https://www.mdpi.com/journal/sustainability

 Sustainability 2022, 14, x FOR PEER REVIEW 2 of 17
theythey are economical;
are economical; however, however, draped draped tendon tendon profiles profiles faredfared better betterin terms in terms of capacity
of capacity
and anddeflection.
deflection.
theyChen are
Cheneteconomical;
al.etprovided
al. provided however,
experimental draped
experimental tendon
results resultsfrom profiles
fromtesting fared
testinga CBbetter
a fortified in terms
CB fortified withwith of capacity
external external
and they are economical;
deflection.
post-tensioning
post-tensioning tendons tendons however,
under under draped
the influence
the influence tendon
of positive profiles
of positive moments fared
moments better
[8]. It inItterms
[8].was was
found ofthat
found capacity
that
Sustainability 2022, 14, 15792 andChendeflection.
et al. provided experimental results from testing a CB fortified with 2external
of 16
adding addingpost-tensioning
post-tensioning tendons tendons enhancedenhanced yieldyield loadload and and ultimate ultimate resistance
resistance by aroundby around
49% 49%
and and Chen
post-tensioning
53%,53%, et al.
respectively.provided
tendons
respectively. It experimental
under wasItthewas influence
also also
found results
found of
that from
positive
that
the the testing
moments
ultimate ultimate a moment
CB[8]. fortified
It was
moment of the with
found
of the external
non- that
non-
post-tensioning
adding
strengthened
strengthenedpost-tensioning
specimensspecimenstendons tendons
approximated under
approximated the
enhanced influence
the plastic yield
the plastic ofload
moment positive
moment and of the moments
ultimate
ofsteel
the steel [8].
resistance
section. It
section. was by
In addition, found
around
In addition, that
the49%
specimens adding
ultimate
the ultimate post-tensioning
andapproximated
53%,
moment respectively.
moment the
of strengthened tendons
plasticIt was
of strengthened enhanced
moment also
beams beamsfound
of the
varied yield that
steel
varied fromload the
section.
from and
1.03 toultimate
ultimate
1.03 In moment
addition,
1.11
to 1.11
from resistance
from
the of
theyield the
ultimate
the by
yield
mo- around
non-mo-
moment
ment 49%
strengthened
ment and
ofat
at which 53%,
strengthened
which the therespectively.
specimens
compression approximated
beams
compression Itflange-initiated
varied was from
flange-initiated also
the 1.03 found
plastic to 1.11
yield. yield.that
moment from the of
the ultimate
the steelmoment
yield moment
section. at of
In the non-
addition,
which
thethe strengthened
ultimate
compression
Nie Nie moment
et al.etstudied specimens
flange-initiated
al. studied both both approximated
of strengthened yield.
analytical
analytical and beams the plastic
and varied
experimental
experimental moment
from 1.03 ofto
investigations the 1.11
investigations steel tosection.
from tothe
look look In addition,
yield
into into
the mo- the
ment
behavior the
Nie ultimate
et
at
behavior al.
which studied
of pre-stressed moment
the
of pre-stressed both
compression of strengthened
analytical
steel–concrete and
flange-initiated
steel–concrete CBs CBs beams
experimental
[9]. It[9]. wasvaried
yield.
It was
suggested from
suggested 1.03
investigations
to use to 1.11
to ause to from
reducedlook
a reduced the
into yield
stiffness the
stiffness mo-
behavior
approach ment
Nie
approachof atpre-stressed
et which
al.
to calculate
to calculate the
studied steel–concrete
compression
both
the deflection, analytical
the deflection, CBs
yield, [9].
flange-initiated
and
yield,
and and It was
experimental
ultimate suggested
yield.
ultimate moments to use
investigations
moments a
of pre-stressed reducedto
of pre-stressed lookstiffness
CBs.CBs.into
The Thethe
approach
slipbehavior
slip
impact toon
Nie
impact ofcalculate
et
yield
on al.yield
pre-stressed the
studied
moment deflection,
moment both
steel–concrete
and and yield,
analytical
deflection CBs
deflection and
was [9].wasultimate
experimental
It was
found found moments
tosuggested
greatly
to greatly toof
investigations
improve use pre-stressed
improve to
a analytical
reduced look
analytical CBs.into
stiffness
pre- pre-the
The
dictionslip
dictionimpact
behavior
approach accuracy. toof on
accuracy. yield
pre-stressed
calculate
Finally, moment
the
Finally, the theand
steel–concrete
deflection,
following deflection
followingyield, CBs
equationsand
equationswas
[9]. Itfound
ultimate
could wascould toused
moments
be greatly
suggested
be toofto
used improve
touse
pre-stressed
representrepresent analytical
a reducedtheCBs. thestiffness
yield The
yield
prediction
slip
moment ofaccuracy.
approach
impact
moment theofonto yield
pre-stressed
the Finally,
calculate moment
pre-stressed the the following
deflection,
and
continuous deflection
continuous equations
yield,
steel–concrete and found
was
steel–concrete could
ultimate
CB: to bemoments
CB: used to
greatly represent
of pre-stressed
improve the yield
analytical CBs.pre- The
moment slipof
diction the pre-stressed
impact
accuracy. on yield Finally, continuous
moment the following steel–concrete
and deflection equations was CB: found
could to be greatly
used toimprove represent analytical
the yield pre-
dictionofaccuracy.
moment the pre-stressed Finally,continuousthe following Mpysteel–concrete
M= ξpy ×=M
equationsξ y× My could CB: be used to represent the (1) yield
(1)
moment × My
Mpy = ξsteel–concrete (1)
where where
ξ is ξthe isofcoefficient
thethecoefficient
pre-stressed of slip of continuous
slip
effect effect
accounted
Maccounted
py = ξ × My
for the CB:pre-stressed
for pre-stressed
the continuous
continuous steel– steel–
(1)
concrete
concreteCB, CB,
and and
M y isM the
y is calculated
where ξ is the coefficient of slip effect accounted the calculated yield yield
moment moment
Mpy = for by
ξ × the My pre-stressed continuous steel– and
transformed
by transformed section sectionmethod, method, and (1)
thiswhere
concretethis
could ξbeisdetermined
could
CB,
the
andbe M coefficient
determined
y is the from of
from slipEquation
Equation
calculated
effect(2);
yield
accounted
(2);
moment by
for the pre-stressed continuous steel–
transformed section method, and
where CB,
concrete ξ isand the M coefficient
y is the calculated of slip effect yieldaccounted
moment by fortransformed
the pre-stressed section continuous
method, and steel–
this could be determined from Equation My(2); =Myield
W(ɛy = iW(ɛ ɛyi)E
+moment + sɛy)Esby transformed section method, (2) and (2)
this concrete
could be CB, and My is from
determined the calculated
Equation (2);
where this
W could
where isW the be
thedetermined
isequivalent equivalent section from
section Equation
modulus,
M ymodulus,
=M W( ɛ (2);
+ ɛ )Ei is strain i is strain at the atbottom
the bottom of steelof steel
caused caused
(2) (2)
y =i W(ɛyi + sɛy)Es
by tendon
by tendon before before casting casting the concrete
the concrete slab,M slab,
and ɛ
andy isɛthe
y = W(ɛi + ɛy)Es
y is yieldthe yieldstrain strainof theof steel
the steel
beam, beam, (2)
wherewhere W
respectively. Wis
respectively. is
the the
The The equivalent
equivalent
provided provided section
section
formulae formulae modulus,
modulus,
demonstrated ɛ
demonstrated i is strain is
a significant
i strain
at the
a significant at the
bottom
agreementbottom
agreementof of
steel steel
withwith caused caused
the ex- the ex-
by by where
tendon
tendon
perimental
perimental Wbefore
before isresults,
results, the equivalent
castingcasting
indicating thethe
indicating section
concrete
concrete
that that
theythey modulus,
slab,
may slab, and ɛy utilized
andutilized
may
be be ɛy the
is isyield
isproperly
i the strain
yield
properly atstrain
strain
for the
the
for ofbottom
of
thethe
design
the steel
design of
and steel
steelbeam,
and
anal- caused
beam,anal-
by
respectively.
ysis ysis tendon
respectively.
of pre-stressed The
of pre-stressed before
The
provided
CBs.CBs.casting
provided formulae the
formulae concrete
demonstrated slab,
demonstrated and
a ɛa
significant
y is the
significant yield
agreement strain
agreement with of the
with
the steel
the
experi- beam,
ex-
mental respectively.
De results,
perimentalLee
De Lee et results,
al. The
indicating
etcarried provided
thatan
indicating
al. carried out they
out formulae
anmay
that they
experimental be may
experimental demonstrated
utilized properly
be study
study utilized
on three on aproperly
significant
for
three
full-scaled foragreement
thefull-scaled
design the and
designanalysis
non-pre-stressed with
and anal-
non-pre-stressed the ex-
of
pre-stressed
andysis perimental
and
pre-stressed CBs.results,
ofpre-stressed
pre-stressed CBs CBs CBs.
with indicating
with
corrugated that webs
corrugated theywebs may
under be flexural
under utilized flexural properly
loads [10].for
loads [10].
The theThe design
test test
analysisand
analysisanal-
showed De
ysis
showedLee
De of et
that,that, al.
pre-stressed
Lee et
before carried
al. carried
before out
CBs.
compositing outan
compositing experimental
an experimental
withwith concrete, study study
concrete, on
the the three
on three
accordion full-scaled
accordion full-scaled
effect non-pre-stressed
effect non-pre-stressed
significantly
significantly in- in-
and and
creasedpre-stressed
creasedtheDeintroduced
pre-stressed
the CBs
Leeintroduced
et al.CBs with
carried
with corrugated
pre-stress out an
corrugated
pre-stress in the webs
experimental
in webs
top
the under
top
and under
and flexural
study
bottom on
flexural
bottom loads
three
flanges loads
flanges [10].
of ofThe
full-scaled
[10].
the The
steel
the test
steel analysis
non-pre-stressed
test
beam. analysis
beam. The The
showed
flexural andthat,
showed
flexural
strength before
pre-stressed
that,
strength before
and compositing
and CBs
stiffness with
compositing
stiffness of with
corrugated
the concrete,
with
of pre-stressed
the webs thespecimens
concrete,
pre-stressed accordion
under the flexural
specimens effect
accordion
were weresignificantly
loads
superioreffect [10].
superior to The increased
significantly
those
to test
those
of the analysis
ofin-
the
the introduced
showed
creased
non-pre-stressed thethat,
non-pre-stressed pre-stress
introduced before
specimens specimens in the
compositing
pre-stress top
afterafter being and
in
being bottom
with
the
composite top
composite flanges
concrete,
and with bottom
with of
concrete. the
the concrete. steel
accordion
flanges of effect beam. the steelThe flexural
significantly
beam. Thein-
strength and stiffness
creased
flexural
El-Zohairy
El-Zohairytheetintroduced
strength . ofcreated
aland
et
the pre-stressed
. created
alstiffness pre-stress
a 3-D ofathe3-D
finite
specimens
in the top
pre-stressed
finite
element element
were
and
specimens
(FE) (FE)
superior
bottom
model modelwere
to
to those
flanges of the
tosuperior
simulate simulate
of the
theto steelnon-pre-
those beam.
nonlinear
the of the
nonlinear The
stressed specimens
flexural
non-pre-stressed strength after and
specimens beingstiffnesscomposite
after of the
being with
compositeconcrete.
pre-stressed specimens
with concrete. were superior to those of the
flexural
flexural
behavior behavior of steel–concrete
of steel–concrete CBs CBs strengthened
strengthened withwith post-tensioned
post-tensioned tendons tendons [11].[11].
The The
El-Zohairy
non-pre-stressed
El-Zohairy
nonlinear
nonlinear
et al.
material et al
material .
created
specimens
created
behavior
a 3-D
behavior aafter
3-Dfinite
and and being
finite element
geometrical composite
element
geometrical
(FE) (FE)
analysis
model
with
analysis model
werewere
to simulate
concrete. to simulate
performedperformed
thethe
using
nonlinear
nonlinear
usingincre- incre-
flexural
flexural behavior
mental–iterative El-Zohairy
behavior
mental–iterative loadof et
load al.techniques.
of steel–concrete createdCBs
steel–concrete
techniques. Thea 3-D strengthened
CBs
The
resultsfinite ofelement
strengthened
results the
with (FE)
of FE
post-tensioned
theanalysis
FEwith model to
post-tensioned
analysis are compared
tendonstendons
aresimulate
compared
[11]. nonlinear
totheexperi-
The [11].
to experi-
nonlinear flexuralmaterial behavior behavior of and geometrical
steel–concrete CBs analysis were performed using incremental–
The
mental nonlinear
mental
results. results.The material
The
overall behavior
overallbehavior behavior and
of the of thestrengthened
geometrical
strengthened
strengthened analysis
beam with
beamwaspost-tensioned
were was performed
studied, studied, as well astendons
usingwell
as the as [11].
incre- the
iterative The load
nonlinear
mental–iterative techniques. material
load The
techniques. results
behavior The of
and the
results FE
geometrical analysis
of the FE are
analysis compared
analysis were are to experimental
performed
compared using
to experi- incre-
effect effect
of external
of external post-tensioning
post-tensioning on stiffness,
on stiffness, induced induced stresses, stresses,slippage slippage between between the con- the con-
results.
mental The overallThe
mental–iterative
results. behavior
load
overall ofbehavior
the strengthened
techniques. The
of theresults beam
strengthened of the wasFE studied,
beam analysiswas as studied,
well as the
are compared asthateffect
well toas of
experi-
the
crete crete
slab slab
and and
steelsteel beam, beam,and and
shear shear
connector
connector moments. moments. The The
authors authors indicated indicated that
add- add-
external
effect post-tensioning
mentalof results.
external The on
post-tensioning stiffness,
overall behavior
oninduced of
stiffness, thestresses,
strengthened
induced slippage
stresses, between
beam was
slippage the concrete
studied,
between as slab
well
the as
con- the
ing external
ing external post-tensioning
post-tensioning tendons tendons in the in positive
the positive moment moment areaarea of steel–concrete
of steel–concrete CBs CBs
andcretesteel
effectbeam,ofand and
external shear connector
post-tensioning moments.
on stiffness, The authors
induced indicated
stresses, that adding external
improved slab
improved their their steel
ultimate beam,
ultimate capacityand
capacity shear
by 25%, by connector
25%,
stiffness moments.
stiffness by 33%, by 33%, The
and and the slippage
authors the indicated
overall overall between
performance thatthe
performance add- con-
post-tensioning
ing crete
externalslab tendons
and steelsystem
post-tensioning in the positive
beam, and
tendonsshear moment
inconnector
the area moments.
positive of steel–concrete
moment The area CBs
authors improved
indicatedtheir
of steel–concrete that CBsadd-
of the
ultimateof bridge
the bridge
capacity structural
structural system
by 25%, stiffnesstendons significantly
significantly
by 33%, improved.improved.
ing Fiber-reinforced
improved external
Fiber-reinforced theirpost-tensioning
ultimate
polymer capacity
polymer (FRP) by
(FRP) 25%,
materials inand
materials the
stiffness
the overall
arepositive
areby
made made moment
33%,
up of
performance
upand
twoof two areaoverall
the
main of
main
of the bridge CBs
steel–concrete
components: performance
components: fi- fi-
structural system significantly improved.
of improved
the
ber materials
ber bridge their
structural ultimate system capacity by
significantly 25%, stiffness
improved. by 33%, and the overall performance
Fiber-reinforced polymer (FRP) materials are made up of two main components: fibermost
materials and and
matrix matrix materials.
materials. Carbon Carbon fiber, fiber,
glass glass
fiber, fiber,
and and
aramid aramid fiber fiber
are the
are most
the
of Fiber-reinforced
the bridge structural polymer system (FRP) significantly
materials improved.
are made up of two main components: fi-
materialsfiber
common common andfiber materials,
matrix materials, whereas
materials. whereas resins
Carbon resins
are
fiber,the
areglass
most
the most
common
fiber, common
andmatrix aramid matrixmaterials
fibermaterials
are[12].the[12].
Glass
most Glass
andber and
carbon Fiber-reinforced
materials
carbon fiber and
fiber
have matrix
have
nearly polymer
materials.
nearlyperfect (FRP)
perfect Carbon
linear materials
linear fiber,
failure failure arebehavior.
glass
behavior. made
fiber, up and ofaramid
twodeformation
mainfibercomponents:
are the most fi-
common fiber materials, whereas resins are the most commonCreep matrix Creepdeformation
materials [12]. becomes becomes
Glass
ber
common
increasingly materials
increasingly fiber
critical and
materials,
critical matrix
in nearly
mostin most FRP materials.
whereas FRP resins
composites Carbon
composites are the fiber,
most
at high-stress
atbehavior. glass
common
high-stress fiber,
levels, and
matrix
levels,
high aramid
high materials
temperatures,fiber
temperatures, are
[12]. the
Glass
or a or most a
and carbon fiber have perfect linear failure Creep deformation becomes
and common
combination carbon
combination of fiber
theof materials,
have
two.
the two.nearly
Creep whereas
Creepwillperfect
will
not resins
belinear
not a be are
significant
a the
failure most
significant behavior.
concern common
concern Creep
if the matrix
if structure’s
the materials
deformation
structure’s loads [12].
becomes
loads
are Glass
are
increasingly critical in most FRP composites at high-stress levels, high temperatures, or
andwithin
increasinglycarbon fiber
critical have
in most nearlyFRP perfect
composites linear at failure
high-stress behavior. levels, Creephighdeformation
temperatures, becomes
orma-a
akept kept
within
combination theof manufacturer’s
thethemanufacturer’s
two. Creep suggested
willsuggested
not be stressa stress
levels
significant levels[13]. [13].
FRP
concern FRP
outperforms
if outperforms
the structure’s metallic metallic ma-
loads
terials increasingly
combination
terials
inwithin
terms
in terms of critical
the
of fatigue two.
of fatigue in most
Creep
resistance FRP
will
resistance composites
not
[13].[13].be a
Although at
significant
Although high-stress
therethere concern
has has levels,
been if the high temperatures,
structure’s loads in ina
are or
are kept the manufacturer’s suggested stress levels [13]. FRPbeen minimal
outperformsminimal research research
metallic
kept
bigger combination
biggerwithin
structures, the of the
manufacturer’stwo. Creep will
suggested not be
is auncommon
stress significant
levelsexcept [13]. concern
FRPjoints,atifminimal
the
outperforms structure’smetallic loads ma-are
materials instructures,
terms fatigue fatigue
of fatigue failure failure
resistance in FRPin[13].
FRP
is uncommon
Although there except hasatbeen joints,
connections,
connections,
research and in and
kept
terials inwithin
terms the manufacturer’s suggested stress levels [13]. FRP outperforms metallic ma-
anchoring
bigger anchoring details.
structures, fatigue failure in FRP is uncommon except at joints, connections, and in
details. of fatigue resistance [13]. Although there has been minimal research
terials
bigger
anchoring details. in
structures,terms of
fatiguefatigue failureresistance
in FRP [13].
is Although
uncommon there
except hasat been
joints, minimal
connections, research and in
bigger
anchoring structures,
details. fatigue failure in FRP is
FRPs have recently been popular in civil engineering, especially for structural reinforce- uncommon except at joints, connections, and
ment,anchoring
because ofdetails. their light weight, high strength, and corrosion resistance [14–16]. The
use of FRP tendons greatly increased the flexural strength, fatigue life, and serviceability of
the beams [17–19].
Some researchers studied the shear and flexural performance of reinforced concrete
beams reinforced using FRP materials and discovered some interesting reinforcing effects.
 The use of FRP tendons greatly increased the flexural strength, fatigue life, and servicea
bility of the beams [17–19].
Some researchers studied the shear and flexural performance of reinforced concret
beams reinforced using FRP materials and discovered some interesting reinforcing effects
Sustainability 2022, 14, 15792 Hawileh et al. investigated the influence of externally bonded carbon fiber reinforced
3 of 16
polymer (CFRP) sheets on the shear strength of shear-deficient reinforced concrete beam
connected to the soffit of the beam [20]. They reported that the shear strength of reinforce
concrete
Hawilehbeams
et al. improved
investigatedby the10–70%
influenceasofcompared to control
externally bonded carbonspecimens. They also re
fiber reinforced
ported (CFRP)
polymer that the flexural
sheets on thelongitudinal
shear strengthreinforcement
of shear-deficientratio had anconcrete
reinforced impactbeams on the shea
connected to the soffit of the beam
strength of reinforced beams [21,22]. [20]. They reported that the shear strength of reinforced
concrete beams
Grace andimproved by 10–70%
Abdel-Sayed as compared
examined to control
four bridge specimens.
models under They alsorepeated,
static, reported and ul
that the flexural longitudinal reinforcement ratio had an impact on the shear strength of
timate loads using internally bonded and externally unbonded draped CFRP tendons [23
reinforced beams [21,22].
Two of the bridges were right-angle bridges, while the others were skew bridges. None o
Grace and Abdel-Sayed examined four bridge models under static, repeated, and
the externally
ultimate draped
loads using tendons
internally bonded ruptured duringunbonded
and externally testing. The
draped prestressing
CFRP tendons force in the ex
[23].
ternal tendons increased to almost double the original values
Two of the bridges were right-angle bridges, while the others were skew bridges. None at the maximum.
of the Limited
externallyresearch
draped has studied
tendons the use
ruptured of FRP
during tendons
testing. Theto enhance the
prestressing structural
force in the behav
ior of composite
external beams. to
tendons increased This paper
almost represents
double a comprehensive
the original study of the effect of sev
values at the maximum.
eralLimited research
parameters that has studiedthe
control thedesign
use of FRP tendons
of the FRP to enhance The
tendons. the structural behaviorof this re
main objective
of composite beams. This paper represents a comprehensive study of
search is to develop a numerical model to simulate the behavior of the steel–concrete the effect of several CBs
parameters that control the design of the FRP tendons. The main objective of this research
with FRP external post-tension tendons, studying the effects of several parameters suc
is to develop a numerical model to simulate the behavior of the steel–concrete CBs, with
as tendon materials, tendon eccentricity, tendon length, degree of shear connectio
FRP external post-tension tendons, studying the effects of several parameters such as
(DOSC),
tendon post-tension
materials, tendonlevel, and tendon
eccentricity, tendonprofile
length,in the behavior
degree of the CBs.(DOSC),
of shear connection Several tendo
materials were used, such as steel, CFRP, aramid fiber-reinforced
post-tension level, and tendon profile in the behavior of the CBs. Several tendon materials polymer (AFRP), an
glassused,
were fiber-reinforced
such as steel, polymer
CFRP, aramid (GFRP) with different
fiber-reinforced post-tensioning
polymer (AFRP), and(PT) glasslevels.
fiber- ANSY
FE software
reinforced (v18.1,
polymer Ansys,
(GFRP) Canonsburg,
with PA, USA) was
different post-tensioning (PT)used
levels.inANSYS
this study to create a non
FE software
(v18.1,
linearAnsys,
FE modelCanonsburg,
(FEM) for PA,the
USA) was used in this
post-tensioned CBs study to create
using CFRPatendons
nonlinear[24].
FE model
The FEM wa
(FEM) for the
validated bypost-tensioned
comparing theCBs FEM using CFRP
result withtendons [24]. The FEM
the experimental was validated by
work.
comparing the FEM result with the experimental work.

2.2.Finite
FiniteElement
Element Model
Model
InInthis
this study,
study, thethe ANSYS
ANSYS FE program
FE program was employed.
was employed. Seven different
Seven different element element
types type
wereused
were used toto model
model thethe concrete
concrete slab,slab,
steelsteel I-beam,
I-beam, steel reinforcement,
steel reinforcement, shear connectors
shear connectors,
theinterface
the interface between
between thethe concrete
concrete slab slab andsteel
and the the I-beam,
steel I-beam,
and theand the external
external post-tensio
post-tension
tendons
tendons[24]. Figure
[24]. 1 shows
Figure the FEM
1 shows meshmesh
the FEM of theof
composite cross-section.
the composite cross-section.

Figure1.1.The
Figure TheFEM mesh
FEM for for
mesh the composite cross-section.
the composite cross-section.

The
TheSOLID65
SOLID65 element waswas
element usedused
to model the concrete.
to model This element
the concrete. has eighthas
This element nodes
eight node
with three degrees of freedom at each node, i.e., translations in the nodal x,
with three degrees of freedom at each node, i.e., translations in the nodal x, y, andy, and z di- z direc
rections. These elements are capable of developing plastic deformation, cracking
tions. These elements are capable of developing plastic deformation, cracking in three orin three
orthogonal directions, and crushing [25]. The capability of cracking and crushing makes
thogonal directions, and crushing [25]. The capability of cracking and crushing makes th
the model able to simulate the post-beak behavior of the concrete by reducing the compres-
model able to simulate the post-beak behavior of the concrete by reducing th
sive strength gradually after the peak. LINK180 is a 3-D spar element used to model the
reinforcing bars and external post-tensioning tendons. It has two nodes with three degrees
of freedom, i.e., translations in the nodal x, y, and z directions [26].
The interface between the upper steel flange and the slab was represented by using
surface-to-surface contact; the element consists of 4 nodes [27].
Sustainability 2022, 14, 15792 4 of 16

The SOLID185 element was used for steel I-beam and loading plates. It is defined by
eight nodes having three degrees of freedom at each node, i.e., translations in the nodal x, y,
and z directions. The element has plasticity, hyper-elasticity, stress stiffening, creep, large
deflection, and large strain capabilities. The uniaxial beam element, BEAM23, was used to
simulate the shank of the shear connector.
The unidirectional spring element, COMBINE39, was used to simulate the shear
slippage behavior of the shear connector. The shear-slippage curve of the stud was used as
a force deformation relation for the spring element, i.e., ANSYS element real contact.
For the headed studs, the constitutive relationship introduced by Ollgaard et al. [28]
was used to generate the shear slippage curve of the shear connector [19,29,30]. The
analytical relation between the shear force, Fj, and the slip, Sj, of the generic stud can be
found in Equation (3). Reasonable results were obtained with a curve with the values 0.558
and 1.0 of α and β, respectively [30].

Fj = PU (1 − e − β× Sj )α (3)

Fj: Shear force

PU : Ultimate strength of the shear connectors
Sj: Slip between the slab and the steel profile
α & β: Parameters manage the initial slope and the shape of the curve.
Real constants
To simulate the post-tensioning initial force, effect temperature load was used. The
initial temperature, which is computed as provided by Equation (4), defines the relationship
between the temperature load and the tension force.

Initial temperature = F/αEAp (4)

F: The post-tension force.

E: Tendon modulus of elasticity.
α: Coefficient of thermal expansion.
Ap : Cross section of the tendon.

2.1. Material Modeling

The concrete was modeled to be homogeneous and initially isotropic. ANSYS requires
the
Sustainability 2022, 14, x FOR PEER REVIEW
uniaxial stress–strain curve of the concrete in compression as an input. A multilinear
5 of 17
curve was used in which a simplified stress–strain curve was created by connecting nine
points, as illustrated in Figure 2a [31,32].

36

−σ
30 Compression
−fu
−fy
24
Stress (MPa)

18 εu εy
−εy −εu
12

fy
6 fu
Tension
+σ
0
0 600 1,200 1,800 2,400 3,000 3,600
Strain (με)
(a) (b)
Figure
Figure2.
2. Material Models: (a)
Material Models: (a)Concrete
Concrete compression
compression stress–strain
stress–strain curve
curve andSteel
and (b) (b) material
Steel material
model.
model.

Because the steel bars and tendons are slender, they may be considered to transfer
primarily axial forces only [33,34]. Similar to the steel beam, a bilinear isotropic hardening
model was used for the steel rebar.
 fy
6 fu
Tension
+σ
0
0 600 1,200 1,800 2,400 3,000 3,600
Strain (με)
Sustainability 2022, 14, 15792 5 of 16
(a) (b)
Figure 2. Material Models: (a) Concrete compression stress–strain curve and (b) Steel materia
model.
The bilinear isotropic hardening model was used to simulate the nonlinear behavior
of the steel beam. The required parameters are the elastic modulus and yield stress which
Because the
were evaluated steel bars and
experimentally; tendons
see Figure 2b.are slender, they may be considered to transfe
primarily
Because axial
the forces only
steel bars and[33,34]. Similar
tendons to the steel
are slender, beam,
they may beaconsidered
bilinear isotropic hardening
to transfer
primarily axial forces only [33,34].
model was used for the steel rebar. Similar to the steel beam, a bilinear isotropic hardening
modelTo was used for the
simulate the steel rebar.
brittle behavior of the FRP tendon, a linear elastic material mode
To simulate the brittle behavior of the FRP tendon, a linear elastic material model was
was used. The solution was tracked to make sure that the maximum strain of the tendon
used. The solution was tracked to make sure that the maximum strain of the tendon did
did not exceed the failure strain. Figure 3 shows the stress–strain relation of the used ten
not exceed the failure strain. Figure 3 shows the stress–strain relation of the used tendon
don compared
compared to the stress–strain
to the stress–strain relation
relation of of the steel.
the steel.

4,000
CFRP
3,500 Steel
AFRP
GFRP
3,000
Tensile Strength (MPa)

2,500

2,000

1,500

1,000

500

0
0 6,000 12,000 18,000 24,000 30,000
Strain (με)

Figure3.3.Stress–strain
Figure Stress–strainbehavior of the
behavior of tendon materials
the tendon (tendons).
materials (tendons).

2.2.Verification
2.2. Verification
Experimental
Experimental work
workperformed
performedby Chen et al. et
by Chen [8]al.
and[8]Emam [35] was
and Emam chosen
[35] was from
chosenthefrom th
literature to validate the FEM. For Chen et al., the dimensions, details, and profiles
literature to validate the FEM. For Chen et al., the dimensions, details, and profiles of th of the
post-tensioned
post-tensioned tendons for the
tendons forinvestigated beams are
the investigated shownare
beams in Figure
shown 4a,b
in[8]. The beams
Figure 4a,b [8]. Th
under consideration had a total length of 5150 mm with a simply supported span (L) of
beams under consideration had a total length of 5150 mm with a simply supported span
5000 mm. The beam height (H) is equal to 200 mm and tendon elevation (He) is equal to
(L) of 5000 mm. The beam height (H) is equal to 200 mm and tendon elevation (He) i
30 mm. They were tested using a four-point bending setup. Two rows of shear studs with
equal
an 8 mmto radius
30 mm. andThey were
65 mm tested
height using
were welded a four-point bending
to the flange. setup. Two
The transversal rows of shea
spacing
studs with
between the an
two8 rows
mm radius
was 76 and 65 mm
mm with height of
a spacing were
200 welded
mm alongto the
thebeam
flange. TheThe
span. transversa
concrete slabs were reinforced in two orthogonal directions with 8 deformed bars with
8 mm diameters. A straight tendon profile was positioned 30 mm above the bottom flange.
The material properties of all the beam elements are listed in Table 1.
Table 1. Summary of material properties for Chen et al. experiment [8].

Post-Tension Tendons Concrete Steel I-Beam

Fy (MPa) Fu (MPa)
Fy (MPa) Fu (MPa) Ap (mm2 ) PU (kN) Fc (Mpa)
Web Flange Web Flange
1680 1860 137.4 112.6 35 327.7 406.5 492.6 593.6
Fy and Fu are the yield and ultimate strengths of the material, and PU is the tendon’s ultimate resistance. Fc is the
concrete compression strength.
 spacing between the two rows was 76 mm with a spacing of 200 mm along the beam span.
The concrete slabs were reinforced in two orthogonal directions with 8 deformed bars
Sustainability 2022, 14, 15792 with 8 mm diameters. A straight tendon profile was positioned 30 mm above the bottom
6 of 16
flange. The material properties of all the beam elements are listed in Table 1.

(a)

(b)
Figure 4. The
Figure geometrical
4. The characteristics
geometrical of the
characteristics of simply supported
the simply CB tested
supported by Chen
CB tested (all dimensions
by Chen (all dimensions
in mm): (a) Cross Section and (b) Elevation of the beam.
in mm): (a) Cross Section and (b) Elevation of the beam.

Table 1. Summary of material properties for Chen et al. experiment [8].

As shown in Table 2 and Figure 5, the verification is based on the ultimate moment
provided by the model
Post-Tension as well as the deformation
Tendons Concrete of the CB. Steel I-Beam
Fy (MPa) Fu (MPa)
Fy Table
(MPa)2. Moments
Fu (MPa)andAdeflections
p (mm2) P (kN) Fc (Mpa)
ofUexperimental and FE analysis.
Web Flange Web Flange
1680 1860
Model 137.4 112.6 35
Mu (kN·m) 327.7 406.5 492.6
∆u (mm)593.6
Fy and Fu are the yield and ultimate strengths of the material, and PU is the tendon’s ultimate re-
Experimental Results 350 55
sistance. Fc is the concrete compression strength.
Sustainability 2022, 14, x FOR PEER REVIEW FEM Results 335 53 7 of 17
As shownAccuracy
in Table 2 and Figure 5, the verification
96% is based on the ultimate
96% moment
provided by the model as well as the deformation of the CB.
The comparison between the FEM and experimental results obtained by Chen et al.
400 that the FEM was able to predict the experimental results with a 4% difference.
[8] showed
FEM
360 Chen, 2005
320

280
Moment (kN·m)

240

200

160

120

80

40

0
-6 0 6 12 18 24 30 36 42 48 54
Deflection (mm)

Comparison between
Figure 5. Comparison
Figure between mid-span
mid-span Moment–Deflection
Moment–Deflectioncurve
curvefor
forthe
the Chen
Chen et
et al.
al. [8]
[8] and
and the
the
current
current FEM.

Table 2. Moments and deflections of experimental and FE analysis.

Model Mu (kN·m) Δu (mm)

Experimental Results 350 55
 Deflection (mm)

Figure 5. Comparison between mid-span Moment–Deflection curve for the Chen et al. [8] and the
current FEM.

Table 2. Moments and deflections of experimental and FE analysis.

Sustainability 2022, 14, 15792 7 of 16
Model Mu (kN·m) Δu (mm)
Experimental Results 350 55
The comparison between the FEM and experimental results obtained by53Chen et al. [8]
FEM Results 335
Accuracy
showed that the FEM 96% results with a 4%
was able to predict the experimental 96%difference.
For Emam’s experimental work, the model is a CB with an externally pre-stressed
For Emam’s
CFRP plate to predict experimental
the ultimate work, the model
flexural response. is a The
CB with an externally
dimensions, pre-stressed
details, and profiles
CFRP plate to predict the ultimate flexural response. The dimensions,
of the pre-stressed CFRP plate of the beams studied are illustrated in Figure details, and profiles
6a,b. The
of the
beam hadpre-stressed
a total length CFRP platemm
of 6000 of the andbeams studiedsupported
was simply are illustrated
over in Figure
a 5600 mm 6a,b. TheThe
span.
beam had a total length of 6000 mm and was simply supported over a 5600 mm span. The
beam was loaded symmetrically at two points. Two rows of 16 mm diameter by 28.56 mm
beam was loaded symmetrically at two points. Two rows of 16 mm diameter by 28.56 mm
length shear studs were welded to the top flange, with a transverse spacing of 30 mm and
length shear studs were welded to the top flange, with a transverse spacing of 308 mm
Sustainability 2022, 14, x FOR PEER REVIEW
and
of diameter
17
a longitudinal spacing of 90 mm. The concrete slab was reinforced with 4.1 mm
a longitudinal spacing of 90 mm. The concrete slab was reinforced with 4.1 mm diameter
bars in two orthogonal directions. The pre-stressed plate consists of one layer attached
bars in two orthogonal directions. The pre-stressed plate consists of one layer attached to
to the bottomsteel
the bottom steelflange
flange with
with a thickness
a thickness of 1.2of
mm 1.2with
mm80with
mm 80 mmalong
width widththealong the full
full length
length of the steel I beam. Epoxy, Sikadurr 30 is the adhesive that bonded
of the steel I beam. Epoxy, Sikadurr 30 is the adhesive that bonded the plate with the the plate with
thetension
tensionflange
flangeofofsteel
steelI beam;
I beam;itsitsthickness
thicknessis 1 mm with young’s modulus of 4.5 GPa as as
is 1 mm with young’s modulus of 4.5 GPa
shown
shownin in
Figure
Figure7b.7b.The
Themechanical
mechanical properties
properties of ofthe
thematerials
materialsused
used are
are given
given in Table
in Table 3. 3.

(b)
Figure 6. The geometrical characteristics of the CB were tested by Emam (all dimensions in mm)
[35]: (a) Cross Section and (b) Elevation of the beam.

Table
Sustainability 2022, 14, x FOR PEER 3. Summary of material properties for Chen et al. experiment [8].
REVIEW 8 of 17

CFRP Plate Concrete Steel I-Beam

(a)
Fy (MPa) Fu (MPa)
Fu (MPa) E (GPa) Fc (Mpa)
Web Flange Web Flange
2565 153.8 48 352 454

In general, it is observed that the FEM agrees well with the experimental results. In
the linear range, the FEM moment–deflection response coincides with that from the ex-
perimental results. When the moment–deflection curve transitioned from linear to non-
linear, the yielding of the beam started. After this point, the stiffness of the FEM was
slightly higher than the experimental beam, owing to the difference in the behavior of the
shear connector between the experimental and(b)theoretical models as shown in Figure 7.
The verification
Figure
Figure 6. The
6. The of the FEM
geometrical
geometrical results was accomplished
characteristics
characteristics ofofthe
theCB
CBwere with
were a by
tested
tested good agreement
byEmam
Emam of 96% with
(alldimensions
(all dimensions inmm)
in mm)[35]:
the [35]:
experimental resultsand
(a) Cross Section of (b)
Emam [35] as
Elevation of shown
the beam.in Table 4.
(a) Cross Section and (b) Elevation of the beam.
Table 3. Summary of material properties for Chen et al. experiment [8].
150
Emam,Plate
CFRP 2007 Concrete Steel I-Beam
FEM
125 Fy (MPa) Fu (MPa)
Fu (MPa) E (GPa) Fc (Mpa)
Web Flange Web Flange
100 2565 153.8 48 352 454
Load (kN)

In general, it is observed that the FEM agrees well with the experimental results. In
75
the linear range, the FEM moment–deflection response coincides with that from the ex-
perimental results. When the moment–deflection curve transitioned from linear to non-
50
linear, the yielding of the beam started. After this point, the stiffness of the FEM was
slightly higher than the experimental beam, owing to the difference in the behavior of the
shear
25 connector between the experimental and theoretical models as shown in Figure 7.
The verification of the FEM results was accomplished with a good agreement of 96% with
the experimental results of Emam [35] as shown in Table 4.
0
-30 0 30 60 90 120 150
Deflection (mm)
150
Emam, 2007
Comparisonbetween
Figure7.7.Comparison
Figure betweenthe
themid-span
mid-spanmoment–deflection
moment–deflection curve
curve forfor theEmam
the Emam [35]
[35] and
and the FEM.
the
FEM
FEM. 125

100
N)
Sustainability 2022, 14, 15792 8 of 16

Table 3. Summary of material properties for Chen et al. experiment [8].

CFRP Plate Concrete Steel I-Beam

Fy (MPa) Fu (MPa)
Fu (MPa) E (GPa) Fc (Mpa)
Web Flange Web Flange
2565 153.8 48 352 454

In general, it is observed that the FEM agrees well with the experimental results.
In the linear range, the FEM moment–deflection response coincides with that from the
experimental results. When the moment–deflection curve transitioned from linear to
nonlinear, the yielding of the beam started. After this point, the stiffness of the FEM was
slightly higher than the experimental beam, owing to the difference in the behavior of the
shear connector between the experimental and theoretical models as shown in Figure 7.
The verification of the FEM results was accomplished with a good agreement of 96% with
the experimental results of Emam [35] as shown in Table 4.

Table 4. Moments and deflections of Emam [35] experimental work and FE analysis.

Model Load (kN) ∆u (mm)

Emam Results 130 145
FEM Results 135 146
Accuracy 96% 99%

3. Parametric Study
The model developed to simulate the experimental work performed by Chen et. al.
was used to perform the parametric study by changing both the geometric and material
characteristics; Figure 4. Twenty-four models divided into six groups were developed in
this study to investigate the effect of different parameters, i.e., groups A to F. The details of
the parametric study are found in Table 5. The table shows the limitation of this study.
The objective of the first group A is to study the effect of tendon material. Five models
were created with the names ST, CT, AT, GT, and WT where various tendon materials
were used. Steel, CFRP, AFRP, and GFRP materials were used for the ST, CT, AT, and
GT models, respectively. However, no post-tensioning was used in the WT model. The
material properties of the used tendons are found in Figure 3. Group B contains models
CT1, CT2, CT3, and CT4. Each model has different post-tension levels ranging from
20 to 50% of the ultimate strength of the tendon (PU ) as shown in Table 5.
In group C, CH1, CH2, CH3, and CH4 models were created with different tendon
positions from the bottom face of the steel I-beam flange, as shown in Table 5. The tendon
position was taken as a percent of the steel beam depth. Group D consists of four models
with names TL1, TL2, TL3, and TL4. Each model has a different tendon length, as shown in
Table 5. In order to study the effect of the DOSC, group E was created. In this group E, four
models were built with names D1, D2, D3, and D4. Each model has a different DOSC by
changing the number of shear connectors as shown in Table 5.
Group F has three models, i.e., TP1, TP2, and TP3, to study the effect of tendon profile.
Models TP1, TP2, and TP3 have straight, trapezoidal, and parabolic tendon profiles as
shown in Table 5 and Figure 8a–c.
Sustainability 2022, 14, 15792 9 of 16

Table 5. Parametric study details and limitations.

Groups Model Material PT Level Height (He) Length DOSC Profile

WT ~ ~ ~ ~ ~
ST Steel
Group A CT CFRP 100%
20% PU 10% H 100% L Straight
AT AFRP
GT GFRP
CT1 20% PU
CT2 30% PU
Group B CFRP 10% H 100% L 100% Straight
CT3 40% PU
CT4 50% PU
CH1 10% H
CH2 15% H
Group C CFRP 20% PU 100% L 100% Straight
CH3 20% H
CH4 25% H
TL1 40% L
TL2 60% L
Group D CFRP 20% PU 10% H 100% Straight
TL3 70% L
TL4 80% L
Sustainability 2022, 14, x FOR PEER REVIEW 10 of 17
D1 40%
D2 60%
Group E CFRP 20% PU 10% H 100% L Straight
D3 80%
with names TL1, TL2, TL3, and TL4. Each model has a different tendon length, as shown
D4 100%
in Table 5. In order to study the effect of the DOSC, group E was created. In this group E,
TP1 four models were built with names D1, D2, D3, and D4. Each model has a different DOSC Straight
TP2 by changing the number of shear connectors as shown in Table 5. Trapezoidal
Group F CFRP 20% PU 10% H 100% L 100%
Group F has three models, i.e., TP1, TP2, and TP3, to study the effect of tendon pro-
TP3 Parabola
file. Models TP1, TP2, and TP3 have straight, trapezoidal, and parabolic tendon profiles
as shown in Table 5 and Figure 8a–c.

(a)

(b)

(c)

Figure 8. Figure 8. The geometry of group (F) models: (a) Straight tendon, (b) Trapezoidal tendon, and (c)
The geometry of group (F) models: (a) Straight tendon, (b) Trapezoidal tendon, and
Parabola tendon.
(c) Parabola tendon.
4. Results
The results of the numerical modeling, including mid-span moment–deflection
curves and load-slippage relationships will be reviewed in this part.

4.1. Effect of Tendon Material

 Sustainability 2022, 14, 15792 10 of 16

4. Results
The results of the numerical modeling, including mid-span moment–deflection curves
and load-slippage relationships will be reviewed in this part.

4.1. Effect of Tendon Material

Figure 9a shows the mid-span moment–deflection curves of beams ST, CT, AT, and
GT in comparison with model WT. It is observed that model CT has the highest capacity
(380 kN·m) compared with other models. Therefore, the CFRP tendon increases the CB
capacity by 50% as shown in Figure 9b. However, the GT model has the lowest capacity
(234 kN·m) with the smallest deflection compared to others, and there was a sudden rupture
22, 14, x FOR PEER REVIEW 11 of 17
in the tendon. Thus, the glass fiber tendon decreases the ductility and the load-carrying
capacity of the beam. In addition, it was found that the ST beam capacity is higher than
the AT by 19%. Table 6 shows the mid-span moment, deflections, and the force in the
the FRP tendons; tendon
however, for the
eachmode
model.
ofThe mode
failure wasof failure for crushing
concrete models CTinand AT was
models STaand
rupture in the
WT. FRP tendons; however, the mode of failure was concrete crushing in models ST and WT.

450
360
400
350
Beam Capacity (kN·m)

300

300
Moment (kN·m)

240
250
180 200

120
150
CT
ST 100
AT
60 GT 50
WT
0 0
-5 0 5 10 15 20 25 30 35 40 45 50 55
Deflection (mm)
CT ST AT GT WT
(a) (b)
Figure 9. Effect of tendon
Figure material:
9. Effect of(a) Mid-span
tendon Moment–Deflection
material: curves and (b)curves
(a) Mid-span Moment–Deflection Beamand
capac-
(b) Beam capacity.
ity.

Table 6. Result of group A.

Table 6. Result of group A.
Upward Max.
No. Model Upward Max. Deflection (mm) TendonsTendons
No. Model Deflection (mm) Moment (kN·m)Deflection (mm) Ultimate Force (kN)
Deflection (mm) Moment (kN·m) Ultimate Force (kN)
1 WT ~ 255 45 ~
1 WT ~ 255 45 ~
2 ST 0.9 333 50 223
2 ST 0.9 333 50 223
3 CT 1 380 25 331
3 CT 1 380 25 331
4 AT 1.2 279 14 284
4 AT 1.2 279 14 284
5 GT 1.5 234 11 230
5 GT 1.5 234 11 230

4.2. Effect ofLevel

4.2. Effect of Post-Tensioning Post-Tensioning Level
In this group, post-tension ranging from 20% to more than 50% of tendon ultimate
In this group, post-tension ranging from 20% to more than 50% of tendon ultimate
strength is studied. Model CT1 has the maximum moment capacity (385 kN·m) with a
strength is studied. Model of
deflection CT1 has the
28 mm, maximum
as shown moment
in Figure 10a. Forcapacity
model (385 the ·maximum
CT2, kN m) with amoment is
deflection of 28 mm, as shown in Figure 10a. For model CT2, the maximum
380 kN·m which is higher than the maximum moment of model CT3 by 5%. moment is However,
380 kN·m which is higher
model CT4than thelowest
has the maximum
momentmoment
capacityof(352.2
model kNCT3 by 5%.
·m) with However,
a deflection of 13.28 mm.
model CT4 has the lowest moment capacity (352.2 kN·m) with a deflection of 13.28 mm.
Therefore, model CT1 increases the beam moment capacity by 10% higher than
model CT4. In general, by increasing the level of post-tensioning, early collapse occurs in
the concrete. Yet by decreasing the level of post-tensioning, the moment capacity and the
022, 14, x FOR PEER REVIEW 12 of 17
Sustainability 2022, 14, 15792 11 of 16

400 400
CT1
350 CT2 350
CT3
CT4
300 300
Moment (kN·m)

Moment (kN·m)
250 250

200 200

150 150

100 100 CT1

CT2
50 50 CT3
CT4
0 0
-3 0 3 6 9 12 15 18 21 24 27 30 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Deflection (mm) Slippage (mm)
(a) (b)
400

350

300
Moment (kN·m)

250

200

150

100 CT1
CT2
50 CT3
CT4
0
0 200 400 600 800 1000 1200
Moment on Shank (N·m)
(c)
Figure 10. Results of models
Figure group (B);
10. Results (a) Mid-span
of models Moment–Deflection
group (B); curves, (b) The
(a) Mid-span Moment–Deflection moment–
curves, (b) The moment–
slippage curves at the center
slippage of the
curves at CB, and (c)
the center of Mid-span
the CB, andMoment–Moment on the shank.
(c) Mid-span Moment–Moment on curves
the shank. curves
Shank moment on the shank.
Shank moment on the shank.

4.3. Effect of Tendon Position Elevated

Therefore, model CT1 increases the beam moment capacity by 10% higher than model
CT4. In general,
The moment–deflection by increasing
responses for thethe level of post-tensioning,
strengthened early collapse
beam with different occurs in the
tendon
concrete.
positions are shown Yet by
in Figure 11a.decreasing
Model CH1 the has
levelthe
of maximum
post-tensioning,
beamthe moment
capacity kN· and the
capacity
(380
m) compared with ductility
other of the beam
models increase.
with maximum deflections of 30 mm. For model CH2
Figure 10b shows the moment–slippage curves at the center of the CB with various
and model CH3, the ultimate moment was 324.2 kN·m and 306.02 kN·m, respectively.
degrees of post-tension level. It is noticed that by increasing the post-tension level, the
However, model slippage
CH4 hasbetween
the lowest moment capacity which is 279.1 kN·m, as shown in
the concrete and steel top flange decreases. In addition, the slippage
Figure 11b. Therefore,
between CH1 beam moment
the concrete and steelcapacity
top flangeiscauses
36% moments
higher than model
on the shear CH4; in which is
connector
general, by decreasing the tendon position, the
maximum at the base of the shank. beam moment capacity increases.
Figure 10c shows the moment on the shank for the four models with several post-
tension levels. It can be observed that model CT4 has the highest moment on the shank,
however, model CT1 has the lowest moment on the shank compared with other models.
Therefore, it can be concluded that by increasing the post-tension levels, the moments on
the shank decrease. it is recommended to use a 20% to 30% post-tension level.
 Sustainability 2022, 14, 15792 12 of 16

4.3. Effect of Tendon Position Elevated

The moment–deflection responses for the strengthened beam with different ten-
don positions are shown in Figure 11a. Model CH1 has the maximum beam capacity
Sustainability 2022, 14, x FOR PEER REVIEW 13 of 17
(380 kN·m) compared with other models with maximum deflections of 30 mm. For model
CH2 and model CH3, the ultimate moment was 324.2 kN·m and 306.02 kN·m, respectively.
However, model CH4 has the lowest moment capacity which is 279.1 kN·m, as shown
in Figure
Sustainability 2022, 14, x FOR PEER REVIEW
400 11b. Therefore, CH1 beam moment capacity 450is 36% higher than model13CH4;
of 17in
CH1
general, by decreasing the tendon position, the beam moment capacity increases.
350 CH2 400
CH3
CH4 350

Capacity (kN·m)
300
400 450
CH1 300
Moment (kN·m)

250 CH2 400

350
CH3 250
CH4 350

Beam(kN·m)
200
300 200
150 300
Moment (kN·m)

250 150

Beam Capacity
100
250
200 100
200
50
150
50
150
0 0
100 -3 0 3 6 9 12 15 18 21 24 27 30 100
Deflection (mm)
CH1 CH2 CH3 CH4
50
(a)
50 (b)
0 0
Figure 11.
-3 Effect
0 3 of6tendon
9 12 position elevated;
15 18 21 (a) Mid-span Moment–Deflection curves and (b) Beam
24 27 30
Deflection (mm)
CH1 CH2 CH3 CH4
capacity.
(a) (b)
4.4. Effect of Tendon Length
Figure
Figure11.11.
Effect of tendon
Effect position
of tendon elevated;
position (a) Mid-span
elevated; Moment–Deflection
(a) Mid-span curves andcurves
Moment–Deflection (b) Beam
and
Figure 12a shows the moment–deflection curves at the center of the strengthened
capacity.
(b) Beam capacity.
beam with various tendon lengths. For model TL1, the maximum moment is 335 kN·m
withEffect
4.4. a maximum
of Tendondeflection
Length of 20 mm which is the lowest moment capacity compared
4.4. Effect
with other of TendonThe
models. Length
maximum moment for models TL2 ·m and 375
Figure 12a shows the moment–deflection curves at theand TL3 of
center is 350
the kNstrengthened
kN · m Figure 12a
respectively. shows the
However, moment–deflection
model TL4 has the curves
maximum at the
beam with various tendon lengths. For model TL1, the maximum moment is 335 kN center
beam of
moment the strengthened
capacity (385
·m
kN·m)
beam
with with
a with various
a deflection
maximum tendon lengths.
of 24of
deflection mm, For
Figure
20 mm model TL1, the maximum moment
12b. is the lowest moment capacity compared
which is 335 kN ·m
withItawas maximum
observed deflection
that of 20 mm
increasing which is
the length the lowest moment
of the tendons capacity compared with
with other models. The maximum moment for models TL2 and helps
TL3 isto350increase
kN·m and the ulti-
375
otherstrength
mate models.ofThethemaximum
composite moment
section for models
and improve TL2theand TL3 behavior
overall is 350 kNof ·mthe
and 375 kN·m
reinforced
kN·m respectively. However, model TL4 has the maximum beam moment capacity (385
respectively.
beam. However, However,
because model TL4 has the
ofmaximum beamit ismoment capacitythat kN·of
(38590% m)
kN ·m) with a deflection ofof
24the
mm,difficulty
Figure 12b.construction, recommended
with
the a deflection
beam span be of 24 mm, Figure 12b.
used.
It was observed that increasing the length of the tendons helps to increase the ulti-
mate strength of the composite section and improve the overall behavior of the reinforced
beam.400However, because of the difficulty of construction, 390 it is recommended that 90% of
TL4
the beam350
span be TL3used. 380
TL2
TL1
Capacity (kN·m)

300 370
400 390
TL4
Moment (kN·m)

250 TL3 360

350 380
TL2
TL1 350
Beam(kN·m)

200
300 370
150 340
Moment (kN·m)

250 360
Beam Capacity

100 330
200 350
50 320
150 340
0 310
100 -3 0 3 6 9 12 15 18 21 24 27
330
Deflection (mm)
TL1 TL2 TL3 TL4
50 320
(a) (b)
0 310
Figure
Figure12.
-312.(a)
0(a)Mid-span
3 6 9 Moment–Deflection
Mid-span 12 15 18 21 24 27
Moment–Deflectioncurves
curvesand
and(b)
(b)Beam
Beamcapacity.
capacity.
TL1
Deflection (mm)
TL2 TL3 TL4
(a)
4.5. Degree of Shear Connection (DOSC) (b)
FigureFigure
12. (a) 13a shows
Mid-span the midspan moment–deflection
Moment–Deflection responses
curves and (b) Beam capacity. of a CB with varying
DOSC. Model D1 has the lowest moment capacity (290 kN·m) with a deflection of 18 mm
andDegree
4.5. the failure happened
of Shear in the
Connection studs. The highest moment of Models D2 and D3 is 345
(DOSC)
Sustainability 2022, 14, x FOR PEER REVIEW 14 of 17
Sustainability 2022, 14, 15792 13 of 16

using 100% DOSC in D4 increases the ultimate capacity of the CB by 23% compared to D1.
It wasasobserved
In general, thatofincreasing
the degree the length
shear connection of the tendons
increases, the CBhelps to increase
capacity the ultimate
increases, Figure
strength
13b. of the composite section and improve the overall behavior of the reinforced beam.
However, because of the difficulty of construction, it is recommended that 90%
Figure 13c illustrates the midspan moment–slippage responses of a CB with varying of the beam
span be used.
degrees of shear connection. In comparison to the others, model D4 has the highest
strength with minimum slippage. As a result, increasing the degree of shear connection
4.5. Degree of Shear Connection (DOSC)
reduces slippage between the concrete and steel top flanges. The moment vs. bottom
flangeFigure 13a shows
stress curves at thethecenter
midspan moment–deflection
for the steel–concrete CBresponses of adegrees
with several CB withofvarying
shear
DOSC. Model D1 has the lowest moment capacity (290 kN · m) with a deflection
connection is shown in Figure 13d. The beam capacities are controlled by the shear of 18con-
mm
and the failure happened in the studs. The highest moment of Models D2 and
nection capacity. The low shear connection capacity of model D1 results in premature D3 is 345 and
failure compared to the other beams with a higher degree of shear connection. In order ·to
364 kN · m, respectively. However, model D4 has the maximum beam capacity (385 kN m)
among all models and the failure was crushing in the concrete. It was observed
fully profit from employing externally post-tensioned tendons, it is recommended to that using
100% DOSC in D4 increases the ultimate capacity of the CB by 23% compared to D1. In
achieve a degree of composite action of 80% or higher between the concrete flange and
general, as the degree of shear connection increases, the CB capacity increases, Figure 13b.
the steel beam.

400 450
D4
350 D3 400
D2
D1 350

Beam Capacity (kN·m)

300
300
Moment (kN·mm)

250
250
200
200
150
150
100 100
50 50
0 0
-3 0 3 6 9 12 15 18 21 24
Deflection (mm)
D1 D2 D3 D4
(a) (b)
400 400
D4
350 350 D3
D2
D1
300 300
Moment (kN·m)

Moment (kN·m)

250 250

200 200

150 150

100 D4 100
D3
50 D2 50
D1
0 0
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -100 0 100 200 300 400
Slippage (mm) Bottom flange stress (MPa)
(c) (d)
Figure
Figure13.
13.Effect
Effectof
of DOSC:
DOSC: (a) Mid-span Moment–Deflection
(a) Mid-span Moment–Deflectioncurves,
curves,(b)
(b)Beam
Beam capacities,
capacities, (c) (c) Mo-
Moment
ment slippage relation, and (d) Moment vs. Bottom flange stress relation.
slippage relation, and (d) Moment vs. Bottom flange stress relation.

4.6. Effect of Tendon Profile

Figure 13c illustrates the midspan moment–slippage responses of a CB with varying
The of
degrees moment–deflection
shear connection. In curves at the center
comparison of the steel–concrete
to the others, model D4 has theCB highest
with different
strength
tendon profiles are
with minimum shown in
slippage. AsFigure 14a.
a result, The maximum
increasing moment
the degree of theconnection
of shear model TP1reduces
is 380
kN ·m andbetween
slippage the maximum deflection
the concrete is 24 top
and steel mm. The highest
flanges. moment
The moment vs.for models
bottom TP2 stress
flange and
TP3 is 490 and 500 kN · m, respectively, with deflections of 21 mm and 20 mm.
curves at the center for the steel–concrete CB with several degrees of shear connection is
shown in Figure 13d. The beam capacities are controlled by the shear connection capacity.
 Sustainability 2022, 14, 15792 14 of 16

The low
Sustainability 2022, 14, x FOR PEER REVIEW shear connection capacity of model D1 results in premature failure compared 15 of 17to
the other beams with a higher degree of shear connection. In order to fully profit from
employing externally post-tensioned tendons, it is recommended to achieve a degree of
composite action of 80% or higher between the concrete flange and the steel beam.
It can be seen that the strengthened beams move upward initially in the same way
and
4.6.behave
Effect ofquite similarly
Tendon Profile during the elastic zone. In comparison to the other profiles, the
beam with the straight profile has superior ductility after yielding.
The moment–deflection curves at the center of the steel–concrete CB with different
TP3 has the highest moment capacity with minimal deflection compared to the other
tendon profiles are shown in Figure 14a. The maximum moment of the model TP1 is
models. In general, post-tensioned tendons with a trapezoidal and parabolic shape can
380 kN·m and the maximum deflection is 24 mm. The highest moment for models TP2 and
reduce the deflection and greatly increase the yield load and the ultimate load of CBs by
TP3 is 490 and 500 kN·m, respectively, with deflections of 21 mm and 20 mm.
125 and 130%, respectively: Figure 14b.

550 600
TP1
500 TP2
450 TP1 500

Beam Capacity (kN·m)

400
400
Moment (kN·m)

350
300
300
250
200
200
150
100 100
50
0 0
-6 -3 0 3 6 9 12 15 18 21 24 27
Deflection (mm)
TP1 TP2 TP3
(a) (b)
Figure
Figure14.
14.Effect
Effectofoftendon
tendonprofile:
profile:(a)(a)Mid-span
Mid-spanMoment–Deflection
Moment–Deflectioncurves
curvesofofmodels
modelsgroup
groupand
and
(b) Beam capacity.
(b) Beam capacity.

5. Conclusions
It can be seen that the strengthened beams move upward initially in the same way
andInbehave
this paper, a numerical
quite similarly model
during the was developed
elastic to study thetouse
zone. In comparison theof FRPprofiles,
other post-ten-the
sioned tendons in composite construction. The model
beam with the straight profile has superior ductility after yielding. was validated by using two differ-
ent experimental
TP3 has theworks. highestThe
momentmodelcapacity
was used withto minimal
study thedeflection
effect of different
comparedparameters
to the other
onmodels.
the performance
In general, ofpost-tensioned
steel–concrete CBs strengthened
tendons by post-tensioned
with a trapezoidal tendons.
and parabolic A par-
shape can
ametric
reducestudy that investigated
the deflection and greatlythe increase
effects ofthetendon
yieldmaterials,
load and thepost-tension
ultimate loadlevel,oftendon
CBs by
length,
125 and degree
130%,ofrespectively:
shear connection,
Figureand14b.tendon profile was performed. The results of this
study might be useful for both residential buildings and infrastructure such as bridges.
5. Conclusions
From this paper, the following findings may be drawn:
• AIngood
this paper, a numerical
agreement model was
of the proposed developedFEM
non-linear to study
withthe
theuse of FRP experimental
literature post-tensioned
tendons in composite
data was achieved. construction. The model was validated by using two different
• experimental
The CFRP tendons improve the capacity of the CB by 50%, which is the higheron
works. The model was used to study the effect of different parameters the
im-
performance of
provement ratio. steel–concrete CBs strengthened by post-tensioned tendons. A parametric
• study
By that investigated
increasing the of
the level effects of tendon materials,
post-tensioning, post-tension
early collapse occurs level,
in thetendon
tendon. length,
Yet
degree of shear connection, and tendon profile was performed.
when the level of FRP post-tensioning is decreased, the composite system capacity The results of this study
might be useful for both residential buildings and infrastructure such as bridges.
increases; therefore it is recommended to use a 20 to 30% post-tension level.
From this paper, the following findings may be drawn:
• The ultimate load capacity and the ductility of the strengthened steel–concrete CB
• withA good
CFRP agreement of the proposed
tendon decreases non-linear
by increasing FEM with
the tendons the literature
elevated from the experimental
bottom sur-
data
face ofwas achieved.
the steel beam flange.
• • Applying
The CFRP tendons
external PTimprove
through the the capacity
full length ofofthetheCB by 50%,
beam which
increases theisultimate
the higher im-
load
provement ratio.
capacity. Due to the construction difficulty, it is recommended to use 90% of the beam
• spanBy increasing
length. the level of post-tensioning, early collapse occurs in the tendon. Yet
• As the degree of of
when the level FRPconnection
shear post-tensioning is decreased,
decreases, the beam’s thestiffness
compositeandsystem
ultimate capacity
load
increases; therefore it is recommended to use a 20 to 30%
capacity decrease. However, as the degree of shear connection decreases, stud post-tension level.
stresses and interface slippage increase.
• It is recommended that post-tension strengthening is utilized for bridges and struc-
tures with at least an 80% degree of shear to ensure the best performance.
Sustainability 2022, 14, 15792 15 of 16

• The ultimate load capacity and the ductility of the strengthened steel–concrete CB with
CFRP tendon decreases by increasing the tendons elevated from the bottom surface of
the steel beam flange.
• Applying external PT through the full length of the beam increases the ultimate load
capacity. Due to the construction difficulty, it is recommended to use 90% of the beam
span length.
• As the degree of shear connection decreases, the beam’s stiffness and ultimate load
capacity decrease. However, as the degree of shear connection decreases, stud stresses
and interface slippage increase.
• It is recommended that post-tension strengthening is utilized for bridges and structures
with at least an 80% degree of shear to ensure the best performance.
• Adding post-tensioned tendons with trapezoidal and parabola profiles to CBs en-
hances yield and ultimate loads by 125 and 130%, respectively, with less deflection.

Author Contributions: Conceptualization, A.H.E., A.A.E.-S. and H.F.S.; Data curation, A.H.E. and
A.A.E.-S.; Funding acquisition, H.A.S.; Project administration, H.F.S. and H.A.H.; Supervision, H.A.S.,
H.F.S. and H.A.H.; Writing—original draft, A.H.E. and A.A.E.-S.; Writing–review & editing, A.A.E.-S.,
H.A.S. and A.H.E. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data that supported the findings of this study are available from
the corresponding author upon reasonable request.
Conflicts of Interest: The authors declare no conflict of interest.

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