TianQiao Liu a, Peng Feng a,⇑, Xiao Lu b, Jia-Qi Yang a, Yuwei Wu a
aKey Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing, 100084, Chinab School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China
A R T I C L E I N F O
Keywords:Hybrid GFRP‐concrete beamGFRP composite materialFlexural behaviorWeb local buckling
A B S T R A C T
A novel hybrid beam consisting of pultruded GFRP three‐cell box‐section and concrete slab was proposed forpedestrian bridges. The flexural behavior of the proposed beam was investigated through experimental andanalytical studies. First, material characterization tests were conducted to evaluate the mechanical propertiesof the GFRP material. Second, four‐ and three‐point bending tests were carried out on four beams with varyingspan lengths. The flexural and shear stiffness of the beams were calculated and evaluated based on the exper-imental results. Design equations were proposed to predict the ultimate flexural strength of the hybrid beam.Finite element (FE) models were constructed to validate the effectiveness of the proposed hybrid beam. A goodcorrelation was found between the experimental results, the analytical predictions from the proposed designequation, and the numerical results from FE modeling. The combined bolted and bonded connection providedeffective shear transfer between GFRP and concrete, ensuring a good composite action of the hybrid beam.Additionally, the proposed three‐cell box‐beam increased the web local buckling strength of GFRP beams sub-jected to a concentrated load, avoiding the premature buckling failure of the entire beam. The proposed hybridGFRP‐concrete beam provides an effective approach to increase the span length of GFRP structures.
1. Introduction
Glass fiber‐reinforced polymer (GFRP) composite materials havebeen increasingly used in civil infrastructures due to their advantagesover conventional materials, such as high strength‐to‐weight ratiosand excellent corrosion resistance [1,55,57]. At present, pultrudedGFRP profiles are widely seen in pedestrian bridges, cooling towersand frame structures [2–4]. Despite of those applications, GFRP struc-tures are often limited by deflection and stability limit states ratherthan the strength limit state, resulting in an inefficient use of the mate-rial and an increased cost of the project. GFRP beams, in particular,may exhibit a relatively large deflection and serious local/global buck-ling under service load, potentially leading to sudden failure of theentire structure [5–9]. To make the most effective use of materialand to widen the applicability of pultruded GFRP profiles, hybridGFRP‐concrete beams have drawn attention in the field. In hybridbeam, the concrete slab is able to contribute a considerable amountof compressive strength and stiffness to the beam, and a full restraintis also provided to the compressive flange of the GFRP beams (GFRP I‐and box‐beams, for instance); moreover, the GFRP beam, with the neu-tral axis adjusted, could exhibit an enhanced flexural performance. In
this regard, many studies have been conducted to investigate the struc-tural performance of the hybrid GFRP‐concrete beams.
The earliest study may date back to 1990s when Saiidi et al. [10]tested two types of hybrid GFRP‐concrete beams and observed theweb shear failure in GFRP beams. In addition, the bonded connectionbetween GFRP and concrete was found to have a significant impact onthe flexural behavior of the hybrid beam. Later, Deskovic et al. [11]proposed a simplified analysis method for hybrid GFRP‐concretebeams, and the failure modes of these beams were identified. In theirtests, the concrete slab was observed to be able to restrain the com-pression flange of the GFRP box‐beam, thus preventing the flange localbuckling failure. In addition to the buckling of flange plate, Canninget al. [12] proposed a doubled‐web GFRP‐concrete beam in order toprevent the possible web local buckling. More importantly, in theirstudy six different connections between GFRP and concrete weretested, including adhesively bonded, horizontally bolted, resininjected, vacuum‐assisted resin injected and adhesively wet‐bondedconnections. Through comparison, the adhesively bonded connectionwas found to provide the best composite action.
Indeed, a good composite action between GFRP beam and concreteslab is the critical factor in determining the overall flexural perfor-
a shear span length in the four‐point bending test configura-tion
A cross‐sectional area of the beamAfi cross‐sectional area of the ith flange plate; i = 1, 2, 3 and 4
in this caseAw cross‐sectional area of the web plate; subscripts c and t
indicate a part of the web plate is subjected to compressionand tension, respectively
b GFRP section widthbc concrete slab widthDb flexural stiffness of the beam; subscript exp indicates exper-
imentally determined stiffnessDs shear stiffness of the beam; subscript exp indicates experi-
mentally determined stiffnessEc modulus of elasticity of the concreteEL longitudinal modulus of elasticity of the GFRPET transverse modulus of elasticity of the GFRPf0c compressive strength of the concreteFC compressive strength of the hybrid GFRP‐concrete beamFLT in‐plane shear strength of the flange plate of the GFRP
beamGLT in‐plane shear modulus of elasticity of the GFRP beamh GFRP section heighthc concrete slab thicknessH total beam heightI moment of inertiak shear correction factor; calculated as Aw/A
l length of the coupon in the material characterization testL total span length of the beam in the four‐ and three‐point
bending test configurationsMu ultimate moment capacity; subscripts exp and pred indicate
experimentally and analytically determined moments,respectively
N axial load of the beamP external load; subscript u indicates the ultimate load,
whereas subscripts exp and pred indicate experimentallyand analytically determined loads, respectively
t plate thickness of the GFRP beam; thickness of the steelblock
tw web thickness of the GFRP beam; typically, tw = tw section width of the beam; width of the steel blockyfi distance from the extreme top fiber of the beam to the cen-
ter of the ith flange plate; i = 1, 2, 3 and 4 in this caseyNA location of the neutral axis of the beam, measured from the
extreme top fiber of the beamδload‐point vertical deflection of the beam; subscripts load‐point and
midspan indicate displacements at the load‐point and mid-span of the beam, respectively
εcu ultimate compressive strain in the concreteνc Poisson’s ratio of the concreteνLT major Poisson’s ratio of the GFRPνTL minor Poisson’s ratio of the GFRP; νTL = νLTET/ELΦ diameter of the steel bolt (steel rebar)
T. Liu et al. Composite Structures 250 (2020) 112606
mance of the hybrid GFRP‐concrete beam. With that said, manyresearchers have explored the possible connection methods for GFRPbeam and concrete slab. Fam and Skutezky [13] tested the perfor-mance of sand‐coated GFRP dowels, as the shear connectors, and goodslip resistance and composite action were found. Correia et al. [14,15]analytically and experimentally investigated the flexural behavior ofhybrid GFRP‐concrete beams. In their study, steel bolts and adhesivebonds were proposed as the shear connectors. Then, Fam and Honick-man [16] proposed to use the conventional steel shear connectors incombination with the epoxy adhesive to connect GFRP and concrete.An excellent composite action was observed. Similarly to [16], Chenand El‐Hacha [17] used the GFRP shear studs and epoxy adhesive totransfer the shear force between GFRP and ultrahigh performance con-crete (UHPC) and a good fatigue behavior was reported. Later, El‐Hacha and Chen [18] further studied the static flexural behavior ofthe proposed hybrid beam. The combination of epoxy adhesive andcoarse silica sand aggregates was found to provide a better bondstrength than the conventional adhesively bonded connection, as theaggregates could provide some extent of mechanical interlockingbetween the GFRP and the UHPC. In addition to the studies on hybridGFRP‐UHPC beam, Nguyen et al. [19] experimentally studied the com-bination of steel bolt shear connectors and epoxy adhesive and identi-fied that the connection method was essential in achieving the fullcomposite action. More importantly, in their study a pseudo‐ductilebehavior was observed, which was realized by the progressive crackpropagation in the concrete slab.
Additionally, Manalo et al. [20], in their hybrid FRP‐concretebeams, investigated the use of U‐shaped steel bolts, gravel chips andepoxy resin as the shear connectors, and a full composite action wasreportedly achieved. Recently, Neagoe et al. [21] proposed two typesof hybrid GFRP‐concrete beams and carried out bending tests to inves-tigate the flexural behavior of the beams. Their experimental resultswere found to have a good agreement with the analytical solutions
2
proposed by Neagoe and Gil [22]. Koaik et al. [23] also conductedexperimental tests to assess the flexural behavior of hybrid GFRP‐concrete beams, in which the bolted, bonded and combined connec-tions were studied.
In addition to the hybrid beams, many analytical and experimentalstudies have focused on the hybrid GFRP‐concrete bridge deck systems[24–39,54,56]. The use of GFRP profiles as bridge decks provides anumber of advantages, including a stay‐in‐place form for concrete,high corrosion resistance, light weight and ease of installation. Addi-tionally, in those studies the design of composite decks, full or partialcomposite action, shear and normal tensile stress at the interface, andshear connections and slippage between GFRP and concrete were sys-tematically investigated. Their findings are also adopted in this workto guide the design the new hybrid beam.
Previous studies have clearly shown that the connection betweenGFRP and concrete is a critical factor in achieving the desired flexuralbehavior of hybrid GFRP‐concrete beams and decks. Various types ofconnection approaches have been proposed, which generally can becategorized into three groups: (1) adhesively bonded connections,(2) steel or FRP bolted connections, and (3) combinations of bondedand bolted connections [40–43]. Previous studies have shown thatthe combined bolted and bonded connection may provide the best per-formance; therefore, this connection approach is adopted in this work.
Moreover, for hybrid GFRP‐concrete beams, nine failure modeshave been identified, including: (1) web local buckling [15,16,18],(2) web crushing [14,18,21], (3) flange‐web junction shear failure[14,21], (4) web shear failure [14,35], (5) end bearing failure [presentwork], (6) slipping failure between GFRP and concrete [16,17,19,29],(7) concrete compressive failure [16,18,19,23,36], (8) concrete shearfailure [20], and (9) concrete uplift failure [44]. All the nine failuremodes are schematically shown in Fig. 1. Among these failure modes,the flange‐web junction shear failure and the web local buckling/crushing are the most critical ones as they could lead to the sudden
Fig. 1. Failure modes of hybrid GFRP-concrete beam.
T. Liu et al. Composite Structures 250 (2020) 112606
failure of the entire beam [18,21]. Thus, there is a need to optimize theGFRP profiles so as to eliminate the possible failures at the flange‐webjunction and/or the web. In this regard, the primary motivation of thiswork is to propose a new type of GFRP‐concrete beam capable of pre-venting the shear failure of the flange‐web junction and the crushing/buckling of the web plate.
2. Hybrid Three-Cell GFRP-Concrete beam
In this work, a novel hybrid GFRP‐concrete beam is proposed, asshown in Fig. 2. A GFRP three‐cell box‐section with two web outstandsis used as the beam, and a concrete slab is added to enhance the flex-ural strength and stiffness. A combined steel bolted and adhesivelybonded connection is used between GFRP and concrete. The develop-ment and experimental tests of the hybrid beam is presented in the fol-lowing sections.
It is worth noting that multiple hybrid beams can be assembledtogether using the prestressed steel rebars to make a beam system,thereby achieving a higher strength and stiffness. The prestressedrebar was designed to be installed at the bottom cell in order to pre-vent the beams from splitting apart in transverse direction of thebridge as well as providing a joint for connecting the bridge hangers.All the steel rebars in the hybrid beams were fabricated with anti‐corrosion treatments in order to achieve a uniform durability betweensteel and GFRP materials. In addition, the concrete slab can provide anexcellent platform for future pavement. Using the proposed hybridGFRP‐concrete beam, the authors’ team has designed two pedestrianbridges in Hebei Province, China, as shown in Fig. 3. The hybrid beamsystem was used as the main girder of the two bridges, and the routineinspections have identified that the proposed beam exhibited an excel-lent performance. Thus, the proposed hybrid GFRP‐concrete beam isbelieved to have a great potential to be widely used in bridges and sim-ilar types of structures in the future.
3. Experimental test
Two sets of experimental tests were conducted to evaluate the flex-ural performance of the proposed hybrid beam, including a materialcharacterization test and a full‐scale beam bending test. It is worth not-ing that one specimen with a clear span length of 11.4 m was success-
Fig. 2. Hybrid three-cell
3
fully tested, which is the longest span of its type in the availableliterature.
3.1. Material characterization test
Material characterization tests were first conducted to evaluate themechanical properties of the GFRP material and to investigate the pos-sible failure modes of the box‐section being addressed. It is noted thatthe full‐section axial‐compression test was conducted to obtain thecompressive modulus of elasticity used throughout the calculationsof this work; the shear test was carried out to measure the punchingshear strength of the material with the purpose of simulating a tempo-rary loading condition, that is, on construction site the beams may bestacked on top of each other or subjected to a random concentratedload; and the vertical‐compression test was primarily to investigatethe possible failure modes of the proposed GFRP section. . The test set-ups are shown in Fig. 4. The specimen geometries and measuredmechanical properties are presented in Table 1. In addition, a5000 kN loading machine was used to apply loads to the specimens,and strain gauges were used to measure the changes in strain.
The full‐section axial‐compression test was conducted in accor-dance with GB/T 31539 [45]. In this test, strain gauges were installedin both the longitudinal (L) and the transverse (h) directions of thespecimen, as shown in Fig. 4a. The longitudinal strain, together withthe applied load and transverse strain, were used to calculate the mod-ulus of elasticity and the major Poisson’s ratio of the GFRP material.The test results showed that the GFRP material exhibited a linearbehavior, and no evident buckling was observed.
In addition, to evaluate the punching shear strength of the GFRPmaterial, a shear test was conducted to measure the in‐plane shearstrength of the top flange, near the flange‐web junction (see Fig. 4b).To apply the concentrated shear force, a steel block with dimensionsof 200 mm × 200 mm × 70 mm (l × w × t) was used to transferthe load. The dimension of the steel block was designed to fit inbetween of the two web outstands. In addition, a rubber pad with athickness of 5 mm was used between the GFRP specimen and the steelblock to prevent possible stress concentration. In this test, a longitudi-nal crack along the flange‐web junction was observed at a load of95 kN, indicating shear failure of the top flange (see Fig. 4d). The shearstrength in the through‐thickness plane, FLT, was approximately calcu-
GFRP-concrete beam.
Fig. 3. Two pedestrian bridges in Hebei Province, China.
T. Liu et al. Composite Structures 250 (2020) 112606
lated by Eq. (1). Although this test was not a standard test, theobtained result could be used to support the constructionorganizations.
FLT ¼ P2� t � l
ð1Þ
where P is the applied load, t is the thickness of the top flange, and lis the specimen length.
Moreover, a vertical‐compression test was conducted on the hybridGFRP‐concrete beam to investigate the possible failure modes, asshown in Fig. 4c. The results showed that two longitudinal cracksoccurred at the flange‐web junctions in the lower section when loadedat 225 kN, and then, evident out‐of‐plane deflection was identified,leading to the entire failure of the specimen, as shown in Fig. 4d.The compressive strength of the hybrid GFRP‐concrete beam, FC,was calculated by Eq. (2). Similarly to the above shear strength, thiscompressive strength was not used in any calculations of this work.
FC ¼ Pl
ð2Þ
where P is the applied load and l is the specimen length. It is worthnoting that the observed failure mode – local shear failure at theflange‐web junction in the bottom flange – indicates a weakness ofthe box‐section. This GFRP box‐section was originally used as thebridge deck, and the fillet region (see Fig. 4d) was designed for con-nection purpose. In this regard, in practice a special design shouldbe conducted to ensure the local bearing capacity of the GFRP box‐beam.
4
In addition, the compressive strength of concrete, though notspecifically discussed, was measured using three150 mm × 150 mm × 150 mm blocks. Through the tests, the average
compressive strength of concrete, f0c, was found to be 24 MPa with a
coefficient of variation (COV) of 0.12. The modulus of elasticity, Ec,was then calculated as 23,115 MPa per ACI 318–14 [46].
3.2. Full-scale specimens and test setups
Four beams, including two GFRP beams (control specimens) andtwo hybrid GFRP‐concrete beams, were tested with four‐ and three‐point bending test configurations. The geometries of the four beamsand the test configurations are presented in Table 2 and Figs. 5 and6. The hybrid GFRP‐concrete beams, B3 and B4, were manufacturedby combining two GFRP box‐beams with a concrete slab. Epoxy adhe-sive was used to provide the bonding between the GFRP beams. A con-crete slab was added onto the top flange of the GFRP beams to enhancetheir compressive strength and stiffness.
To achieve a good composite action, a combination of steel boltedand adhesively bonded connections was used between GFRP and con-crete, as shown in Figs. 5b and 7. In particular, steel rebars withΦ = 10 mm were used as the steel bolts in this work, and both endsof the rebars were bent 135 degrees to form two hooks. In addition,steel rebars with Φ = 6 mm were horizontally installed at the mid‐section of the concrete slab and fixed with steel bolts at their top hooksevery 600 mm, providing an additional connection between GFRP andconcrete. Steel bolts and horizontal rebars were spaced at 600 mm and
Fig. 4. Material characterization tests and failure modes.
T. Liu et al. Composite Structures 250 (2020) 112606
200 mm, respectively. Moreover, to enhance the bonding behaviorbetween GFRP and concrete, epoxy adhesive was used together withsmall aggregates, as shown in Fig. 7b. Surface treatment was appliedon the top flange of the GFRP using a sanding machine before instal-ling the rebars and applying the epoxy adhesive, as shown in Fig. 7a.
Each beam was tested in a four‐point bending test configuration:B1, B2 and B3 were loaded until ultimate failure occurred, whereas
Table 1Mechanical properties of the GFRP and concrete materials.
1 Specimen geometry is expressed as l × h × w, as shown in Fig. 4a.
Table 2Specimen geometries and test configurations (units: mm).
Specimen B1GFRP
Total beam height, H 560GFRP section height, h 560GFRP section width, b 250GFRP plate thickness, t 10Concrete slab thickness, hc –
Concrete slab width, bc –
Test configuration Total span, L 5400Flexure span 3000Shear span, a 1200
5
B4 was only loaded to 2P of 170 kN to evaluate its flexural stiffness,and then the test was stopped. Then, B4 was tested in a three‐pointbending configuration to the ultimate failure in order to obtain theultimate flexural strength. During the tests, five linear variable differ-ential transformers (LVDTs) were used to measure the vertical dis-placements near the two end supports (LVDT‐1 and LVDT‐5), at thetwo loading points (LVDT‐2 and LVDT‐4) and at the midspan (LVDT‐
Fig. 5. Cross-sectional geometries of the specimens (units: mm).
Fig. 6. Test configurations.
T. Liu et al. Composite Structures 250 (2020) 112606
3), as shown in Fig. 6. The measured displacements from the four‐point bending tests were further used to calculate the flexural andshear stiffness of all four beams. In the case of sudden catastrophic fail-ure of B4 in the three‐point bending test, only the initial stage, up to atotal load P of 141 kN, was monitored with the LVDTs, and after 141kN, the LVDTs were removed, and only the strains and loads weremeasured.
3.3. Experimental results
The measured load–displacement curves showed that all specimensbehaved in a linear manner until failure, as shown in Fig. 8. It is notedthat B1, B2, and B3 were loaded to failure in the four‐point bending
6
test setups, and B4 was loaded to failure in the three‐point bending testsetup. In particular, continuous displacement of B4 was only measuredto P of 141 kN and the ultimate displacement was then measured at Pof 505 kN when the beam failed. In Fig. 8, linear interpolation wasused to estimate the complete load–displacement curve. SpecimensB1‐GFRP beam and B3‐hybrid beam were failed at loads 2P of 405and 796 kN, respectively, due to the local shear failure of the flange‐web junction at the bottom of the beam at the end supports, as shownin Fig. 9a. The fillet at the flange‐web junction (see Fig. 4d) couldresult in a reduced bearing strength, as the flange‐web junction isessentially subjected to shear force rather than compressive force.The failure modes of B1 and B3 match those observed in the materialcharacterization tests (shear and vertical‐compression tests, shown in
Fig. 7. Connection between the GFRP and the concrete.
Fig. 8. Load-displacement curves at the midspan of the beam.
T. Liu et al. Composite Structures 250 (2020) 112606
Fig. 4d). To eliminate the local shear failure of the flange‐web junctionat the end supports, wood blocks were added to specimens B2 (GFRPbeam) and B4 (hybrid beam), as shown in Fig. 9b. With the end sec-tions strengthened, specimens B2 and B4 did not show any local bear-ing failure at the end supports. In addition, specimen B2 was failed dueto excessive deflection at 2P of 202 kN. The vertical deflection mea-sured at the midspan reached 157 mm, which was 1/70 of the spanlength, and then, the test was stopped. No other failure mode of thematerial was observed. In contrast, specimen B4 with a concrete slabhad an enhanced flexural stiffness and correspondingly exhibited asmaller deflection as compared to B2 at the same load level. B4 wassubjected to a three‐point bending test and failed due to the compres-sive failure of the concrete slab at an ultimate load P of 505 kN andmid‐span displacement of 249 mm (see Fig. 9c). Additionally, the mea-sured ultimate compressive strain in the concrete was found to be0.0066, which is greater than the design value of 0.0033, by a factorof 2. Such strengthening effect on the concrete was attributed to theGFRP box‐section having two web outstands, which were able to pro-vide some extent of biaxial compression to the concrete slab. Theincreased concrete compressive strain also indicates that the boltedand bonded connection used in the hybrid beam provided a good sheartransfer. No web local buckling was observed throughout the tests.
The experimentally determined ultimate load Pu,exp and flexuralstrength Mu,exp are presented in Table 3. Although B1‐GFRP and B3‐hybrid failed due to local bearing failure, it still can be seen that withthe proposed beam configuration the flexural strength increased about
7
97%. As for B2‐GFRP and B4‐hybrid having a longer span length, it isthe deflection limit state that controls the design, instead of thestrength limit state. Assuming a deflection limit state of L/50, the flex-ural strength of the two beams were calculated via regression of thelinear load–displacement curves (see Fig. 8). The calculated load andflexural strength at displacement of L/50 are shown in Table 4. Itcan be seen that at the same deflection limit state the flexural strengthof the proposed hybrid beam is substantially greater than that of theGFRP beam, by 183%.
In addition, the strains along the height of GFRP section wereobtained for B1, B2 and B3 in the four‐point bending tests and forB4 in the three‐point bending test. Fig. 10 shows the strain distributioncurves of B1, B2 and B3 measured under one of the load points and thecurve of B4 measured at 3800 mm of the span. Despite that some straingages were damaged during the tests (B3 and B4, for instance), theplane‐section assumption can still be confirmed for all the beams. Acomparison of specimens B2 and B4, and B1 and B3 shows that withthe addition of a concrete slab, the neutral axis slightly moved up, indi-cating an effective composite action between the GFRP beam and theconcrete slab.
4. Analytical study
4.1. Flexural and shear stiffness
To evaluate the effectiveness of the hybrid beam, the flexural andshear stiffness of all four beams (B1, B2, B3 and B4) were calculatedusing Eqs. (3) and (4) [47] and the displacements measured in four‐point bending tests. As aforementioned, the displacement of B4‐hybrid was only measured to P of 170 kN.
δmidspan ¼ Pa24Db
3L2 � 4a2� �þ Pa
Dsð3Þ
δload�point ¼ Pa6Db
3La� 4a2� �þ Pa
Dsð4Þ
where δmidspan is the vertical displacement at the midspan of thebeam, which is taken as the value measured by LVDT‐3; δload‐point isthe vertical displacement at the load‐point of the beam, which is takenas the mean value of the two displacements measured by LVDT‐2 and−4; P is the external load, which is taken as the mean value of the twomeasured loads; a is the shear span length; and L is the total spanlength.
Combining Eqs. (3) and (4), Db and Ds of all four specimens werecalculated. The flexural stiffness‐load curves were obtained, as shownin Fig. 11. The average Db within a certain load range was taken as Db,-exp and was used to calculate Ds,exp. The results are presented in Table 3.Table 3 shows that the concrete slab could significantly increase the
Fig. 10. Strain distribution curve of the beams.
Fig. 9. Typical failure modes.
T. Liu et al. Composite Structures 250 (2020) 112606
8
Table 3Experimentally and analytically determined flexural strength and stiffness.
Specimen Total span length (mm) Experimental results Analytical predictions
a Pu,exp indicates 2P for B1, B2 and B3 in four-point bending, and P for B4 in three-point bending.b The design strain 0.0033 of concrete was used in analytical and numerical calculations of Mu,pred.c The measured strain 0.0066 of concrete was used in analytical and numerical calculations of Mu,pred.
Table 4Comparison of GFRP and hybrid beams at deflection limit state.
Specimen Span length L (mm) Deflection limit state L/50 (mm) Total loada (kN) Flexural strength M (kNm) MB4-hybrid/MB2-GFRP
a Total load indicates 2P for B2-GFRP and P for B4-hybrid.
T. Liu et al. Composite Structures 250 (2020) 112606
flexural stiffness of the GFRP beam: the Db of both B1 and B2 was145% higher than that of B3 and B4.
In addition, the longitudinal compressive modulus EL and the in‐plane shear modulus GLT of the GFRP material can be calculated usingDb,exp and Ds,exp of specimen B1 as follows:
Db;exp ¼ ELI ð5Þ
Ds;exp ¼ kGLTA ð6Þwhere k is the shear correction factor, which is taken as Aw/A, and I
is the moment of inertia of the GFRP box‐section. The calculated EL is49872 MPa, and GLT is 2656 MPa. The value of EL obtained in the four‐
Fig. 11. Flexural stiffness-load curves (loa
9
point bending test is similar to that obtained from the material charac-terization test (see Table 1), and the difference is approximately 6%.
4.2. Flexural strength
In this work, a set of design equations was proposed to assist thedesign of the hybrid beam in practice. Assuming a full compositeaction between GFRP and concrete, the location of the neutral axiscan be determined by Eqs. (7) and (9), and then, the ultimate flexuralstrength can be calculated by Eqs. (8) and (10). It is noted that whenneutral axis is located at the interface between GFRP and concrete,namely yNA = hc, Eqs. (7) and (8) are applicable. The material proper-
d range used in stiffness calculations).
Fig. 12. Typical meshing of FE model.
T. Liu et al. Composite Structures 250 (2020) 112606
ties were used in accordance with those presented in Section 3.1 andTable 1.
Case 1: neutral axis located at the GFRP box‐section, i.e., yNA ≥ hc.
∑N ¼ 0:8hcbcf0c
þ ELɛcuyNA
∑4
i¼1Afi yNA � yfi
� �þ 12AwcyNA þ 1
2Awt yNA � hð Þ
� �¼ 0
Mu ¼ 0:8hcbcf0c yNA � 0:4hcð Þ
þ ELɛcuyNA
∑4
i¼1Afi yNA � yfi
� �2þ 13Awcy2NA þ 1
3Awt yNA � hð Þ2
� �ð8Þ
Case 2: neutral axis located at the concrete slab, i.e., yNA < hc.
∑N ¼ 0:8yNAbcf0c
þ ELɛcuyNA
∑4
i¼1Afi yNA � yfi
� �þ 12AwcyNA þ 1
2Awt yNA � hð Þ
� �¼ 0 ð9Þ
Mu ¼ 0:48y2NAbcf0c
þ ELɛcuyNA
∑4
i¼1Afi yNA � yfi
� �2þ 13Awcy2NA þ 1
3Awt yNA � hð Þ2
� �ð10Þ
where εcu is the ultimate compressive strain in the concrete, whichis often taken as 0.0033 in design, whereas in this case, it was alsotaken as the measured value of 0.0066; yNA is the location of the neu-tral axis of the hybrid beam, which was measured from the top of thebeam; Afi is the cross‐sectional area of the ith flange plate, whereini = 1, 2, 3 and 4 in this case; yfi is the distance from the top of thebeam to the center of the ith flange plate, wherein i = 1, 2, 3 and 4;h is the GFRP section height, which for this case h = H; and Awc andAwt are the cross‐sectional areas of the web plates subjected to com-pressive and tensile stress, respectively. These cross‐sectional areascan be expressed as follows:
Awc ¼ yNAtwandAwt ¼ ðh� yNAÞtw ð11Þwhere tw is the total thickness of all web plates; tw = 40 mm in this
case. In addition, the fillet regions were neglected in the calculations.Using the proposed design equations, it was found that the neutral axiswas located at the GFRP beam; thus, Eq. (8) was used in this case.Then, the predicted ultimate flexural strength was calculated, as pre-sented in Table 3. It is seen that using the design concrete compressivestrain of 0.0033, the prediction is conservative as compared to theexperimental result. Additionally, using the measured concrete strainof 0.0066 the predicted flexural strength is slightly higher than theexperimental result, by 15%. Thus, it can be first concluded that usingthe design concrete compressive strain the proposed design equation isable to provide a conservative prediction of the ultimate flexuralstrength for the hybrid beam; and also, considering the full compositeaction assumed by the design equation as well as the actual concretestrain of 0.0066, a ratio of 1.15, between predicted and experimentalresults, could generally confirm the excellent shear transfer providedby the bolted and bonded connection between GFRP and concrete.
5. Finite element modeling
5.1. Prediction of flexural strength
Specimen B4‐hybrid was modeled with the finite element (FE)package ABAQUS [48]. The pultruded GFRP profile was modeled with4‐node shell elements (S4). The concrete in B4 was modeled with 8‐node hexahedron elements (C3D8). For simplicity, the fillets at theflange‐web junctions of the GFRP sections were neglected. GFRP andconcrete were assumed to be linear elastic materials. For the GFRPmaterial, the longitudinal compressive modulus EL obtained from thematerial characterization test was used (see Table 1). In addition,the in‐plane shear modulus GLT of 2656 MPa, which was obtained from
10
the four‐point bending test of B1, was adopted. Note that ET was notmeasured in the material characterization test; thus, the design valuereported by the manufacturer was used, which is 12607 MPa. More-over, the elastic modulus of the concrete Ec was set to 23115 MPa,as reported in Table 1, and the Poisson’s ratio of the concrete νc wastaken as 0.2 [49]. In particular, the design and measured concretecompressive strains, 0.0033 and 0.0066, respectively, were alladopted. The FE model was loaded under the three‐point bending testconfiguration.
Mesh convergence test was first conducted on specimen B4. Char-acteristic element size was varied from 100, 50, 25 and 10 mm, andcorrespondingly, the total number of elements was increased from6222, 19,588, 89,648 to 850,780. The mid‐span deflection started toconverge at the element size of 50 mm. In order to achieve a goodaccuracy as well as saving the computational cost, the characteristicelement size was determined as 10 mm for specimen B4 to calculateits flexural strength and stiffness, and the element size of 25 mmwas selected for those models in parametric studies. The FE meshingof B4 is shown in Fig. 12.
In the experimental tests, combined bolted and bonded connectionswere used as the shear connector for specimen B4, and a good compos-ite action was observed between GFRP and concrete. Therefore, in theFE model for specimen B4, the interface between GFRP and concretewas set as tied, assuming there was no slip between the two materials;that is, a full composite action was assumed.
Through FE modeling, the ultimate flexural strength of specimenB4 were obtained, as shown in Table 3. The load–displacement curveof specimen B4 (with measured concrete compressive strain 0.0066)was also obtained, as shown in Fig. 8. The load–displacement curveshows a good correlation between FE modeling and experimentalresults. The ratios between the flexural strength obtained by FE mod-eling and from the tests were 0.60 and 1.19 for the two cases with con-crete compressive strains of 0.0033 and 0.0066, respectively. Again,using the design strain 0.0033 the FE model could provide a conserva-tive prediction, and using the measured strain 0.0066 the numericalprediction is slightly higher than experimental result, by 19%. More-over, an excellent agreement was found between the analytical predic-tion (Eq. (8)) and the FEM result. The difference between Eq. (8) andFEM is about 4% when both compared to the experimental result. Thisfinding, again, demonstrates that the proposed design equation is ableto predict the ultimate flexural strength for the proposed hybrid GFRP‐concrete beam with a satisfactory accuracy.
5.2. Parametric study on concrete slab thickness
In the proposed hybrid GFRP‐concrete beam, the concrete slab cansignificantly increase the flexural stiffness and strength of the beam.To further assess the effectiveness of the concrete slab, a parametricstudy was conducted through FE modeling. In total, six FE models,
Table 5Parametric study on concrete slab thickness.
Case number hc (mm) h (mm) H (mm) L (mm) yNA* (mm) Mu (kNm)
* The neutral axis yNA is measured from the extreme top fiber of the GFRP beam (h = 560 mm).
Fig. 13. Strain distribution at the midspan of the GFRP box-beam.
T. Liu et al. Composite Structures 250 (2020) 112606
denoted as cases 1, 2, 3, 4, 5 and 6 in this study, were constructedusing six different concrete slab thicknesses: 60, 90, 120, 150, 180and 210 mm. The material properties of the models were the sameas those of the previous FE model except that the ultimate compressivestrain in the concrete was taken as the design value of 0.0033. In addi-tion, the dead load (DL) of the concrete slab was considered, and themoment due to the DL was excluded from the ultimate flexuralstrength of the beam. The results of FE modeling are shown in Table 5.Additionally, the strain distributions at the midspans of the six beamswere obtained, as shown in Fig. 13. The neutral axis moves up as theconcrete slab thickness increases, leading to an increased flexuralstrength of the hybrid beam. Comparing case 1 (hc = 60 mm) withcase 6 (hc = 210 mm), the neutral axis moved from 218 mm to48 mm, and such an adjustment in the neutral axis led to a 63%increase in flexural strength, as shown in Table 5. Thus, the proposed
Fig. 14. Deflection and flexural stiffness vs. concrete slab thickness.
11
hybrid GFRP‐concrete beam can potentially further increase the flexu-ral strength and the span length of the GFRP structures.
In addition to the improved flexural strength, the effect of increas-ing the concrete slab thickness on the deflection of the beam was alsoinvestigated, as the deflection limit state often controls the design ofGFRP beams. The concrete slab thickness was varied from 0 to600 mm. The design equations, Eqs. 7–10, were used to calculatethe ultimate flexural strength of the hybrid beams having varying con-crete slab thickness, and then, the corresponding deflections were cal-culated assuming that the beams were subjected to a uniformlydistributed load. The calculated deflections are shown in Fig. 14. Inaddition, the flexural stiffness of the hybrid beams with varying con-crete slab thickness is shown in Fig. 14.
Fig. 15. Web compression buckling strength of one- and three-cell box-sections.
Fig. 16. Compressive-tensile stress distribution in the one- and three-cell box-beams.
Fig. 17. Web flexural local buckling strength vs. GFRP section height of one-and three-cell box-beams.
T. Liu et al. Composite Structures 250 (2020) 112606
Fig. 14 shows that when the concrete slab thickness increased from0 to 90 mm, the deflections substantially decreased. When the con-crete slab thickness increased from 90 to 350 mm, the deflectionsremained approximately constant, although the flexural stiffness dra-matically increased. In this range, the DL of the added concrete coun-teracted the increased flexural stiffness, leading to high deflections.When the concrete slab thickness exceeded 350 mm, the deflectionsdecreased linearly with the increased flexural stiffness. Thus, a con-crete slab thickness less than 90 mm is recommended for the hybridGFRP‐concrete beam addressed in this work, as in this range, theincreased flexural stiffness from the concrete slab could effectivelycontribute to reducing the adverse deflection of the beam.
5.3. Parametric study on web compression buckling
The primary motivation of using the three‐cell box‐beam in thiswork is to reduce the unrestrained depth of the web to increase theweb local buckling strength of the beam, as local buckling often con-trols the design of pultruded GFRP beams and hybrid GFRP‐concretebeams [5,9,21,50]. In particular, web local buckling (see Fig. 1a) isoften critical when a highly concentrated load is directly applied onthe GFRP beam. To investigate the effectiveness of three‐cell box‐sections in improving web local buckling strength, a parametric studywas conducted. A one‐cell box‐section having the same amount ofmaterial as the three‐cell box‐section was assumed; thus, the tw ofthe one‐cell box‐section was calculated as 10+(230 × 10)/500 = 14.6 mm. The design equation from ASCE [51] was adopted to calculatethe web compression buckling strength, as shown in Eq. (12). The cal-culated buckling strength values are shown in Fig. 15.
f wcr ¼π2t2w6b2w
ðffiffiffiffiffiffiffiffiffiffiELET
pþ ETvLT þ 2GLTÞ ð12Þ
In the three‐cell box‐section, the bottom cell with the largest webdepth has the lowest buckling strength and controls the bucklingstrength of the entire section. Fig. 15 shows that although the one‐cell box‐section has a thicker web, the buckling strength is 59 MPa.The three‐cell box‐section with a shorter depth has a buckling strengthof 184 MPa. The web compression buckling strength of the three‐cellbox‐section is 212% higher than that of the one‐cell box‐section withthe same amount of material. Thus, it is demonstrated that using amulticell box‐section, the GFRP beam could achieve an improvedbuckling strength, particularly when the beam is subjected to a highconcentrated load at the supports or at any location along the beam.
5.4. Parametric study on web flexural local buckling
In addition to the web compression buckling due to a concentratedcompressive load, the web flexural local buckling induced by the flex-ural behavior of the beam was also investigated. The design equations
12
from ASCE [51], EUR27666 [52] and Kollár [53] are typically used tocalculate the web flexural local buckling strength of GFRP beams.Using these equations, it is assumed that the web plate is subjectedto a symmetrical compressive‐tensile stress distribution, as shown inFig. 16a. Nonetheless, in the three‐cell box‐section, the webs of thethree cells are subjected to different asymmetrical stress distributions,as shown in Fig. 16b. Thus, the existing design equations cannot bedirectly adopted. In this regard, FE modeling was conducted to evalu-ate the web local buckling strength of the three‐cell box‐beam.
In total, five one‐cell box‐beams (control specimens) and five three‐cell box‐beams were constructed. The heights of the five one‐ andthree‐cell beams were 440, 500, 560, 620 and 680 mm, and the webthickness of all five three‐cell box‐beams was 10 mm. For the one‐and three‐cell beams with the same height, their cross‐sectional areas,namely the amount of material, were assumed to be the same; forexample, for the beams with a height of 560 mm, the web thicknessof the three‐cell box‐beam was 10 mm, and the web thickness of theone‐cell box‐section was therefore 14.6 mm (=10+(230 × 10)/500mm), as shown in Fig. 16a. In addition, the concrete slab thicknesswas taken as 60 mm, and the span length was 1200 mm for all theone‐ and three‐cell box‐beams. A three‐point bending test configura-tion was used. The lateral displacement of the concrete slab was com-pletely restrained. The concrete compressive failure and other possiblefailure modes were set not to control the failure of the beam, as thisstudy was focused on the web local buckling of the GFRP box‐section.
Through FE modeling, the web flexural local buckling strength wasobtained, as shown in Fig. 17. The results show that when the GFRP
T. Liu et al. Composite Structures 250 (2020) 112606
section height is less than 500 mm, the one‐cell box‐beam has a higherweb local buckling strength, which is due to the thicker and relativelyshorter web plate of the beam. When the GFRP section height becomesgreater than 500 mm, the three‐cell box‐beam is found to have ahigher web local buckling strength; in this case, the three‐cell box‐section, in which each web plate is shortened, is able to improve theweb local buckling behavior of the beam by up to 10% over the one‐cell box‐beam. Moreover, such an increase in web local bucklingstrength is expected to become more prominent when the height ofGFRP section increases. Thus, it is validated that the proposed three‐cell box‐section could effectively enhance the web flexural local buck-ling strength of the GFRP beam.
6. Recommendations for future work
In light of the parametric studies presented in above sections, somegaps between existing design methods and practical applications of theproposed hybrid beam are identified. Thus, in this section some futurework is recommended.
First, in calculation of the web local buckling strength of a GFRPthree‐cell box‐beam, the existing design equations, including thosefrom ASCE [51], EUR27666 [52] and Kollár [53], are not applicable,as these equations assume that the stress distribution is symmetrical.However, in the multicell box‐beam, each web plate might be sub-jected to an asymmetrical stress distribution. Thus, there is a need todevelop design equations for predicting the web local bucklingstrength of GFRP multicell box‐beams in the future.
In addition, the geometries of the common GFRP profiles mimic therolled steel shapes, such as I‐, C‐ and box‐sections. However, manystudies have revealed that steel shapes might not be the most appropri-ate for GFRP materials, as GFRPs have a relatively high anisotropy andlow elastic modulus. In this work, a pultruded GFRP three‐cell box‐section was proposed, and the hybrid GFRP‐concrete beam exhibiteda good structural performance. In light of the multicell box‐sectionproposed in this work, future work is needed to investigate and opti-mize the geometries of the GFRP profiles that could accommodatethe unique mechanical properties of GFRP materials.
7. Conclusions
In this work, a novel hybrid GFRP‐concrete beam was proposed,and its flexural behavior was investigated through experimental andanalytical programs. First, material characterization tests were con-ducted to evaluate the structural behavior and the failure modes ofthe proposed pultruded GFRP three‐cell box‐section. Then, four‐ andthree‐point bending tests were carried out, and the flexural behaviorof the beams was obtained. Moreover, design equations were proposedto predict the ultimate flexural strength of the hybrid beams. Finally,an FE model was constructed to validate the effectiveness of the pro-posed hybrid beam, and three parametric studies were conducted toinvestigate the effects of the concrete slab thickness, web compressionbuckling and web flexural local buckling on the performance of thehybrid beams. The following conclusions can be drawn from this work:
(1). The proposed GFRP three‐cell box‐section provides an effectiveapproach for the hybrid GFRP‐concrete beams. A span length of11.4 m was successfully achieved, which is the longest span ofbeam with pultruded profile in the available literature. In addi-tion, multiple hybrid beams can be assembled together to makea beam system, permitting a greater span of the structure.
(2). The proposed three‐cell box‐beam has two web outstands,through which the shear transfer between GFRP and concretecan be achieved; minimal work was required to install the steelbolts of the bolted connection. Moreover, the web outstands andthe hybrid connection could provide some extent of biaxial
13
compression to the concrete; thus, a higher ultimate compres-sive strain in the concrete (0.0066, in this case) can beachieved.
(3). The box‐beam having three cells could increase the web localbuckling strength due to both compression and flexure. Thethree‐cell box‐beam provided 212% higher web compressionbuckling strength and up to 10% higher web flexural bucklingstrength as compared to the conventional one‐cell box‐beam.
(4). With the concrete slab added, the proposed hybrid GFRP‐concrete beam exhibited 183% and 145% increases in flexuralstrength and stiffness at deflection limit state, respectively.Moreover, a greater increase in flexural strength and stiffnesscan be expected if using a concrete material with higherstrength and stiffness, such as UHPC.
(5). In addition to experimental tests, FE modeling was conducted tovalidate the effectiveness of the proposed hybrid beam. Theresults showed that the combined bolted and bonded connec-tion provided excellent shear transfer between concrete andGFRP, thereby permitting an effective composite action of thehybrid beam and ensuring the most effective use of thematerial.
Data availability
All data, models, and code generated or used in this study appear inthe submitted article.
The authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influ-ence the work reported in this paper.
Acknowledgements
This work was supported by grants from the China National KeyResearch and Development – China Plan Project(No.2017YFC0703000) and the National Natural Science Foundationof China (No. 51522807). The authors would give special thanks toBeijing Golden Bridge (Composites) Tech Co., LTD., for providingthe GFRP materials. Their support is highly appreciated.
References
[1] Liu T, Liu X, Feng P. A comprehensive review on mechanical properties ofpultruded FRP composites subjected to long-term environmental effects. Compos BEng 2020;191:107958.
[2] Feng P, Tian Y, Qin Z. Static and dynamic behavior of a truss bridge made of FRPpultruded profiles. Industrial Constr. 2013;43(6):36–41 (In Chinese).
[3] Sundar RU, Gm Kumar. Structural analysis for modified fibre reinforced plasticindustrial cooling tower – A case study. J Intell Fuzzy Syst 2017;33(2):841–51.
[4] Liu T. Stability behavior of pultruded glass-fiber reinforced polymer I-sectionssubject to flexure PhD Dissertation University of Pittsburgh; 2017.
[5] Liu T, Harries KA. Flange local buckling of pultruded GFRP box beams. ComposStruct 2018;189:463–72.
[6] Liu T, Vieira J, Harries KA. Lateral torsional buckling and section distortion ofpultruded GFRP I-sections subject to flexure. Compos Struct 2019;225:111151.
[7] Liu T, Yang JQ, Feng P, Harries KA. Determining rotational stiffness of flange-webjunction of pultruded GFRP I-Sections. Compos Struct 2020;236:111843.
T. Liu et al. Composite Structures 250 (2020) 112606
[8] Yang JQ, Liu T, Feng P. Enhancing flange local buckling strength of pultrudedGFRP open-section beams. Compos Struct 2020;244(2):112313.
[9] Liu T, Vieira JD, Harries KA. Predicting flange local buckling capacity of pultrudedGFRP I-sections subject to flexure. J Compos Constr 2020;24(4):4020025.
[10] Saiidi M, Gordaninejad F, Wehbe N. Behavior of graphite/epoxy concretecomposite beams. J Struct Eng 1994;120(10):2958–76.
[11] Deskovic N, Triantafillou TC, Meier U. Innovative design of FRP combined withconcrete: short-term behavior. J Struct Eng 1995;121(7):1069–78.
[12] Canning L, Hollaway L, Thorne AM. An investigation of the composite action of anFRP/concrete prismatic beam. Constr Build Mater 1999;13(8):417–26.
[13] Fam A, Skutezky T. Composite T-beams using reduced-scale rectangular FRP tubesand concrete slabs. J Compos Constr 2006;10(2):172–81.
[14] Correia JR, Branco FA, Ferreira JG. Flexural behaviour of GFRP–concrete hybridbeams with interconnection slip. Compos Struct 2007;77(1):66–78.
[15] Correia JR, Branco FA, Ferreira JG. Flexural behaviour of multi-span GFRP-concrete hybrid beams. Eng Struct 2009;31(7):1369–81.
[16] Fam A, Honickman H. Built-up hybrid composite box girders fabricated and testedin flexure. Eng Struct 2010;32(4):1028–37.
[17] Chen D, El-Hacha R. Behaviour of hybrid FRP–UHPC beams in flexure underfatigue loading. Compos Struct 2011;94(1):253–66.
[18] El-Hacha R, Chen D. Behaviour of hybrid FRP–UHPC beams subjected to staticflexural loading. Compos B Eng 2012;43(2):582–93.
[19] Nguyen H, Mutsuyoshi H, Zatar W. Hybrid FRP-UHPFRC composite girders: Part 1– Experimental and numerical approach. Compos Struct 2015;125:631–52.
[20] Manalo AC, Aravinthan T, Mutsuyoshi H, Matsui T. Composite behaviour of ahybrid FRP bridge girder and concrete deck. Adv Struct Eng 2012;15(4):589–600.
[21] Neagoe CA, Gil L, Pérez MA. Experimental study of GFRP-concrete hybrid beamswith low degree of shear connection. Constr Build Mater 2015;101:141–51.
[22] Neagoe CA, Gil L. Analytical procedure for the design of PFRP-RC hybrid beamsincluding shear interaction effects. Compos Struct 2015;132:122–35.
[23] Koaik A, Bel S, Jurkiewiez B. Experimental tests and analytical model of concrete-GFRP hybrid beams under flexure. Compos Struct 2017;180:192–210.
[24] Keller T, Gürtler H. Composite action and adhesive bond between fiber-reinforcedpolymer bridge decks and main girders. J Compos Constr 2005;9(4):360–8.
[25] Keller T, Schollmayer M. In-plane tensile performance of a cellular FRP bridgedeck acting as top chord of continuous bridge girders. Compos Struct 2006;72(1):130–40.
[26] Keller T, Schaumann E, Vallée T. Flexural behavior of a hybrid FRP andlightweight concrete sandwich bridge deck. Compos A Appl Sci Manuf 2007;38(3):879–89.
[27] Warn GP, Aref AJ. Sustained-load and fatigue performance of a Hybrid FRP-concrete bridge deck system. J Compos Constr 2010;14(6):856–64.
[28] Mendes PJD, Barros JAO, Sena-Cruz JM, Taheri M. Development of a pedestrianbridge with GFRP profiles and fiber reinforced self-compacting concrete deck.Compos Struct 2011;93(11):2969–82.
[29] He J, Liu Y, Chen A, Dai L. Experimental investigation of movable hybrid GFRPand concrete bridge deck. Constr Build Mater 2012;26(1):49–64.
[30] Sebastian WM, Ross J, Keller T, Luke S. Load response due to local and globalindeterminacies of FRP-deck bridges. Compos B Eng 2012;43(4):1727–38.
[31] King L, Toutanji H, Vuddandam R. Load and resistance factor design of fiberreinforced polymer composite bridge deck. Compos B Eng 2012;43(2):673–80.
[32] Gonilha JA, Correia JR, Branco FA, Caetano E, Cunha Á. Modal identification of aGFRP-concrete hybrid footbridge prototype: experimental tests and analytical andnumerical simulations. Compos Struct 2013;106:724–33.
[33] Nelson M, Fam A. Full bridge testing at scale constructed with novel FRP stay-in-place structural forms for concrete deck. Constr Build Mater 2014;50:368–76.
[34] Nelson M, Eldridge A, Fam A. The effects of splices and bond on performance ofbridge deck with FRP stay-in-place forms at various boundary conditions. EngStruct 2013;56:509–16.
14
[35] Zuo Y, Mosallam A, Xin H, Liu Y, He J. Flexural performance of a hybrid GFRP-concrete bridge deck with composite T-shaped perforated rib connectors. ComposStruct 2018;194:263–78.
[36] Zuo Y, Liu Y, He J. Experimental investigation on hybrid GFRP-concrete deckswith T-shaped perforated ribs subjected to negative moment. Constr Build Mater2018;158:728–41.
[37] Zou X, Feng P, Wang J. Bolted shear connection of FRP-concrete hybrid beams. JCompos Constr 2018;22(3):04018012.
[38] Zhang D, Gu XL, Yu QQ, Huang H, Wan B, Jiang C. Fully probabilistic analysis ofFRP-to-concrete bonded joints considering model uncertainty. Compos Struct2018;185:786–806.
[39] Zou X, Wang J. Experimental study on joints and flexural behavior of FRP truss-UHPC hybrid bridge. Compos Struct 2018;203:414–24.
[40] Zhang P, Wu G, Zhu H, Meng S, Wu Z. Mechanical performance of the wet-bondinterface between FRP plates and cast-in-place concrete. J Compos Constr 2014;18(6):04014016.
[41] Mendes PJD, Barros JAO, Sena-Cruz J, Teheri M. Influence of fatigue andaggressive exposure on GFRP girder to SFRSCC deck all-adhesive connection.Compos Struct 2014;110:152–62.
[42] Zou X, Feng P, Wang J. Perforated FRP ribs for shear connecting of FRP-concretehybrid beams/decks. Compos Struct 2016;152:267–76.
[43] Zou X, Feng P, Wang J, Wu Y, Feng Y. FRP stay-in-place form and shear keyconnection for FRP-concrete hybrid beams/decks. Compos Struct2018;192:489–99.
[44] Li T. Study on Mechanical Performance and Design Method of FRP-Concrete.Master Thesis. Tsinghua University; 2007.
[45] GB/T 31539 2015. Pultruded fiber reinforced polymer composites structuralprofiles. China Association for Engineering Construction Standardization (CECS)(In Chinese).
[46] ACI Committee 318-14. Building Code Requirements for Structural Concrete andCommentary. American Concrete Institute 2014.
[47] Timoshenko SP, Gere JM. Theory of Elastic Stability. Tokyo: McGrawHill-Kogakusha Ltd; 1961.
[48] Simulia, D. S. Abaqus 6.14 documentation 2014. Providence, Rhode Island, US.[49] Yang JQ, Smith ST, Wang Z, Lim YY. Numerical simulation of FRP-strengthened
RC slabs anchored with FRP anchors. Constr Build Mater 2018;172:735–50.[50] Vieira J, Liu T, Harries KA. Flexural stability of pultruded GFRP I-sections. Proc
Inst Civil Eng – Struct Build 2018;171(11):855–66.[51] American Society of Civil Engineers. (ASCE). Pre-Standard for Load and Resistance
Factor Design (LRFD) of Pultruded Fiber Reinforced Polymer (FRP) Structures2010.
[52] Ascione L, Caron JF, Godonou P, van IJselmuijden K, Knippers J, Mottram T, OppeM, Gantriis Sorensen M, Taby J, Tromp L. Prospect for new guidance in the designof FRP; EUR27666 2016.
[53] Kollár LP. Local buckling of fiber reinforced plastic composite structural memberswith open and closed cross sections. ASCE J Struct Eng 2003;129(11):1503–13.
[54] Yang JQ, Smith ST, Feng P. Effect of FRP-to-metal bonded joint configuration oninterfacial stresses: finite element investigation. Thin-Walled Struct2013;62:215–28.
[55] Feng P, Wang J, Wang Y, Loughery D, Niu D. Effects of corrosive environments onproperties of pultruded GFRP plates. Compos B Eng 2014;67:427–33.
[56] Zou X, Feng P, Bao Y, Wang J, Xin H. Experimental and analytical studies on shearbehaviors of FRP-concrete composite section. Eng Struct 2020 (In review).
[57] Feng P, Wang J, Tian Y, Loughery D, Wang Y. Mechanical behavior and design ofFRP structural members at high and low service temperatures. J Compos Constr2016;20(5):4016021.
