The corresponding design ultimate bending moments of the CFDST with regard to the design codes AISC and EC4 were also computed. The results revealed that EC4 and AISC can accurately predict the ultimate moment capacities of the CFDST with shear connector.
Journal of Science and Technology in Civil Engineering NUCE 2019 13 (1): 21–32 EVALUATION OF ULTIMATE BENDING MOMENT OF CIRCULAR CONCRETE–FILLED DOUBLE SKIN STEEL TUBES USING FINITE ELEMENT ANALYSIS Vu Quang Vieta , Hoang Hab , Pham Thai Hoanc,∗ a Faculty of Civil Engineering, Vietnam Maritime University, 484 Lach Tray road, Le Chan district, Hanoi, Vietnam b Vietnam Acapel Architects Ltd Company, Nguyen Huy Tuong street, Thanh Xuan district, Hanoi, Vietnam c Faculty of Building and Industrial Construction, National University of Civil Engineering, 55 Giai Phong road, Hai Ba Trung district, Hanoi, Vietnam Article history: Received 19 November 2018, Revised 04 January 2019, Accepted 04 January 2019 Abstract In this study, the ultimate bending moment of circular concrete-filled double skin steel tubes (CFDSTs) was investigated A CFDSTs made of two concentric circular steel tubes with concrete infill and M16 shear connector system was fabricated The four-point bending test of the 10 m long CFDST consisting of outer and inner steel tubes with 914.4 mm and 514.4 mm in diameter, respectively, was carried out and the ultimate bending moment of the CFDST was investigated A finite element (FE) simulation of the CFDSTs subjected to bending was developed using the commercial software ABAQUS and the accuracy of the developed FE model was verified by comparing to the experimental result The ultimate bending moment of CFDSTs was then evaluated with respect to different concrete infill compressive strengths and yield strengths of the steel tubes The corresponding design ultimate bending moments of the CFDST with regard to the design codes AISC and EC4 were also computed The results revealed that EC4 and AISC can accurately predict the ultimate moment capacities of the CFDST with shear connector Keywords: ultimate bending moment; concrete-filled double skin tube; shear connector system; finite element analysis https://doi.org/10.31814/stce.nuce2019-13(1)-03 c 2019 National University of Civil Engineering Introduction Fully concrete-filled steel tubes (CFST) have been widely used in the past few decades due to their better structural performance than that of pure steel or pure reinforced concrete While the hollow steel tube acts as formwork as well as reinforcement for the concrete, the concrete infill eliminates or delays the local buckling of steel hollow tube, and increases significantly the ductility of the section The use of CFST in construction has proven to be economic in material as well as leading to rapid construction process and thus additional cost savings [1] Recently, concrete-filled double skin steel tubes (CFDST), which not only provide the advantages of concrete-filled steel tubes (CFST) but also supplement the weaknesses of CFST, have been extensively developed CFDST sections consist of two steel tubes, an outer and an inner tube, with concrete ∗ Corresponding author E-mail address: hoanpt@nuce.edu.vn (Hoan, P T.) 21 Hoan, P T., et al / Journal of Science and Technology in Civil Engineering sandwiched between the tubes Advantages of CFDST tubes are over CFST include: increase in section modulus; enhancement in stability; lighter weight; good damping characteristics and better cyclic performance It is expected that the CFDST columns can obtain a higher fire resistance period than the CFST columns, due to the inner tubes of the composite columns being protected by the sandwiched concrete during the fire It is thus expected that CFDST has a potential of being used in building structures Furthermore, the space in the inner tube can be utilized for other purposes such as for electrical cables Thus, researches related to CFDSTs have been widely implemented For instance, experimental researches on beams, columns, and beams-columns made of CFDSTs with various cross-sections were conducted by Tao and Han [2] Eom et al [3] performed an experimental investigation on CFDSTs with and without a joint subjected to bending Experiment and analysis studies on CFDSTs under cyclic and long-term sustained loadings were implemented by Han [4, 5] By performing experimental researches, Wang [6] and Huang [7] investigated the behavior of CFDSTs under collision and torsion loads, respectively Regarding analytical studies, Pagoulatou [8] examined the behavior of CFDST stub columns under concentric axial and then he suggested new expression for Journal of Science andcompression Technology loads, in Civil Engineering - NUCEa 2018 evaluation of the strength of CFDSTs corresponding to EC4 [9] By using finite element analysis (FEA), Huang [10] investigated the effects of important parameters which are used to determine sectional capacities of CFDST stub columns In the other hand, many researchers have investigated the 2.1 Design of CFDST CFDST subjected to only pure bending [11–15], however, comprehensive studies in ultimate bending moment especially with a full CFDST, haveinnot been reported so CFDST far Fig.of1CFDST, illustrates the design of scale CFDST used this study The with the This study aims to investigate the behavior of a full scale CFDST by conducting a four-point length of 10 m consists of outer and inner steel tubes with the diameter of 914.4 mm bending test The developed FE model is used to evaluate the ultimate bending moment capacity of and respectively The designed thicknessesstrengths of theand outer innerof steel this 514.4 CFDSTmm, with respect to different concrete infill compressive yieldand strengths the steel tubes corresponding designrespectively ultimate bendingAmoments according to AISC andconcrete EC4 are also tubes wereThe mm and mm, layer of 200-mm-thick was computed for the purpose of comparison filled into the space between the outer and inner steel tubes A shear connector system of M16 studs was designed and used in order to cause the composite action between Experimental program the concrete and steel tubes On the cross-section of the tubes, sixteen studs were 2.1 Design of CFDST welded between the inner and outer steel tubes, while along the longitudinal section of Fig illustrates the design used in this study CFDST with the lengthdesign of 10 mof the tubes, studs were placedof atCFDST 250 mm spacing as The shown in Fig The consists of outer and inner steel tubes with the diameter of 914.4 mm and 514.4 mm, respectively CFDST including the shear connector system conforms to the requirement of the steel The designed thicknesses of the outer and inner steel tubes were mm and mm, respectively A structure design standards [9, 17] Figure Geometry description description of CFDST Figure Geometry of CFDST 22 Hoan, P T., et al / Journal of Science and Technology in Civil Engineering layer of 200-mm-thick concrete was filled into the space between the outer and inner steel tubes A shear connector system of M16 studs was designed and used in order to cause the composite action between the concrete and steel tubes On the cross-section of the tubes, sixteen studs were welded between the inner and outer steel tubes, while along the longitudinal section of the tubes, studs were placed at 250 mm spacing as shown in Fig The design of CFDST including the shear connector system conforms to the requirement the steel structure designofstandards Figure 1.ofGeometry description CFDST[9, 16] FigureFigure Detail of of thethesteel andshear shear connector Detail steel tubes tubes and connector systemsystem The material properties of the concrete and the steel tubes are shown in Table The material properties of the concrete and the steel tubes are shown in Table Tensile coupon Tensile coupon to tests were employed obtain the steel material properties, tests were employed obtain the steel materialtoproperties, whilst concrete cylinder tests werewhilst used to concrete cylinder tests properties were used to CFDST obtain the concretespecimens materialwere properties obtain the concrete material of the The concrete tested atof 28 the days after casting.The concrete specimens were tested at 28 days after casting CFDST Materialproperties properties of tubes and and concrete TableTable Material ofsteel steel tubes concrete Item Item YieldYield strength Ultimate strength Compressive strength Young strength Ultimate strength Compressive Youngmodulus modulus Fy (MPa) F (MPa) f’ (MPa) E (MPa) u c Fy (MPa) Fu (MPa) strength fc (MPa) E (MPa) Outer steel tube (8 mm) Inner steel tube (6 mm) Concrete 486.5 467.6 - 533.9 517.8 - 48.9 205000 205000 - 2.2 Experimental setup and result Four-point bending test was carried out to evaluate the ultimate bending moment of the designed CFDST The specimen was tested by hydraulic jacks with a loading capacity of 5000 kN The loads were applied on the specimen at two positions of 750 mm away from the center of the CFDST on both sides Loading and boundary pads with the same 25 mm of thickness were placed to prevent stress concentration at the loading positions and the supporting ends Three Linear Variable Displacement Transducers (LVDT) were placed along the bottom of the specimens in a pure bending segment to measure the mid-span vertical displacement of the tube Hinge and roller conditions were applied to the bottom of the boundary pads The configuration and arrangement of the experimental setup are illustrated in Fig The bending experiment was undertaken with displacement control at the velocity of mm/min in the elastic region and mm/min in the plastic region until the specimen collapsed The applied 23 loading positions and the supporting ends Three Linear Variable Displacement Transducers ((LVDT) were placed along bottom of the specimens in a pure bending Transducers LVDT) were Transducers LVDT) were placed along thethe bottom thespecimens specimens a pure bending Transducers ((LVDT) were placed along the bottom ofofthe inina pure bending segment measure mid-span vertical displacement of the tube Hinge and roller segment to measure the segment to to measure thethe mid-span vertical displacement thetube tube Hinge and roller segment to measure the mid-span vertical displacement ofofthe Hinge and roller conditions were applied to bottom of boundary pads The configuration conditions were applied conditions were applied to the thethe bottom thethe boundary pads The configuration andand conditions were applied to bottom ofofthe boundary pads The configuration and arrangement of the experimental setup are illustrated in arrangement of the experimental arrangement of the theHoan, experimental setup are illustrated Fig Engineering P T., et al / Journal ofare Science and Technology inFig Civil arrangement of experimental setup illustrated ininFig P/2 P/2 P/2 P/2 4.25m m 4.25 4.25m m 4.25 P/2 P/2 P/2 P/2 1.5m m 1.5mm1.5 1.5 4.25 m m 4.25 4.25 4.25 mm 10m m 10 1010mm Mn Mn Mn Mn (a) Loading diagram (a) Loading Loading diagram (a)(a) Loading diagram (a) Loading diagram (b) Experimental arrangement (b) Experimental arrangement (b)Experimental Experimental arrangement (b) arrangement Journal of Science and Technology in Civil Engineering - NUCE 2018 Journal of Science and Technology in Civil Engineering - NUCE 2018 the mid-span section was also computed based on the loading diagram in Fig 3a, as follows: the mid-span section was also computed based on the loading diagram in Fig 3a, as P sw (1) Mfollows: = l1 + l2 (c) Roller support end (d) Hinge support end (c) Roller support end (d) Hinge support end (c) Roller support Roller support end Hinge support (c)(c) Roller (d)(d) Hinge support endend P support sw end (1) M = l1 + l22 3.3.Experimental on CFDST where l1 = 4.25 m, l2Figure = Figure 10 m,3.Experimental and sw setup issetup the self-weight Figure 8Figure Experimental setup on CFDST setup on CFDST of the CFDST (sw = 13.5 Figure Experimental on CFDST kN/m) The bending undertaken displacement at(sw where l1 = experiment 4.25 m, l2 =was 10was m, and sw is with the self-weight of thecontrol CFDST =the13.5 The bending experiment The bending experiment was undertaken with displacement control atthe The bending experiment undertaken with displacement control at the load P and vertical displacement at theregion mid-span of4 CFDST were measured during the test the and the velocity 2of mm/min in the elastic mm/min ininthe plastic region until kN/m) Fig of shows the failure mode andand Fig mm/min presents the bending moment-vertical velocity mm/min mm/min in the velocity of mm/min in the elastic region and mm/min the plastic region until thethe velocity of in elastic region and in the plastic region until corresponding bendingThe moment M atload the mid-span section displacement was also computed based on the loading specimen collapsed applied P and vertical at the mid-span of specimen collapsed The applied load P and vertical displacement at the mid-span displacement curve at the mid-span the specimen It the canbending be from these specimen collapsed load P of and vertical displacement at seen the mid-span of offigures specimen collapsed The 43(a), shows theapplied failure mode and Fig presents moment-vertical diagram inFig Fig asThe follows: CFDST were measured during the test and the corresponding bending moment M at sw Pand CFDST were measured during the the moment M CFDST measured during themid-span test and corresponding moment Mfigures atsteel CFDST were measured that thewere CFDST specimen collapsed due the localIt buckling the outer displacement curve at the ofl1the the specimen canbending bebending seenoffrom these +to l22corresponding (1)at tube Mtest = and the that corresponding failure collapsed load is due 2,486 kN The applied load at steel the tube failure is the CFDST specimen to the local buckling of the outer where l1 = 4.25 m, l2 = 10 m, and sw is the self-weight of the CFDST (sw = 13.5 kN/m) is CFDST the the corresponding load 2,486thekN The applied load the failure isin this considered ultimate bending load of obtained from theatexperiment Fig 4and shows failure mode failure and Fig 5the presents bending moment-vertical displacement 4 considered ultimate bending the obtained from in this curve atleading the mid-span of the specimen Itload can of bemoment seenCFDST fromof these figures that the the experiment CFDST specimen study, to the ultimate bending 5299 kNm study, leading to the ultimate bending moment of 5299 kNm Failure mode mode ofof CFDST FigureFigure Failure mode CFDST Figure Failure of CFDST Figure 5 behavior Figure 5.Moment-displacement Moment-displacement behavior Figure Moment-displacement behavior 24 Finite element simulation Finite3.element simulation 3.1.element Finite element modeling 3.1 Finite modeling Hoan, P T., et al / Journal of Science and Technology in Civil Engineering collapsed due to the local buckling of the outer steel tube and the corresponding failure load is 2486 kN The applied load at the failure is considered ultimate bending load of the CFDST obtained from the experiment in this study, leading to the ultimate bending moment of 5299 kNm Finite element simulation 3.1 Finite element modeling In order to investigate and evaluate the ultimate bending moment of CFDSTs with respect to different concrete infill compressive strength and steel tubes yield strength regardless to conducting such uneconomic experiments, the commercial software ABAQUS [17] was used to simulate the four-point bending test of CFDST, which was carried out in the present study For finite element (FE) model, 8-node solid elements (C3D8R) were used for the steel tubes, steel pads, and concrete of CFDST, whereas truss elements (T3D2) were used to model the M16 shear connector system The appropriate element mesh size of 50 mm was chosen for the FE model by performing the sensitivity analysis The interaction between concrete and steel tubes was modeled using the *CONTACT PAIR option, which is a surface-to-surface contact type available in ABAQUS [12] Two types of surfaces including slave and master surfaces were required to define this contact option It was suggested that the slave surface should be assigned to a softer material in order to limit the numerical errors, thus the steel tubes were assigned as master surfaces while the concrete was set as slave surfaces The normal and tangent behavior between the slave and master surfaces were modeled by adopting the hard contact and the Coulomb friction model with a friction coefficient of 0.1, respectively For the contact between the shear connectors and the concrete, the M16 studs were assumed to be completely bonded to the concrete and were simulated using the EMBEDDED option In addition, the contact between the pads and outer steel tubes was modeled by using the TIE option The loads were applied in one row at the top middle of the loading pads, which were installed at 750 mm away from the center of the CFDST on both sides The hinge and roller conditions were applied to the middle points (reference points) of the boundary pads Fig shows the detail modeling of the components and the FE model Concerning the material models, the plasticity model was used for steel tubes and the concrete damaged plasticity model was utilized for concrete infill Noted that the concrete damaged plasticity model proposed by Lubiner et al [18] and by Lee and Fenves [19], which can model the inelastic response of concrete, is available in ABAQUS Fig shows the stress-strain curves of materials used in this study, where the material parameters obtained from the coupon tests in Table were adopted The stress-strain curve of concrete was constructed by using T’sai concrete model [20] It is worth noting that the missing parameters of concrete material from the coupon test, such as strain values at compressive strength (εc ) and at failure (εc1 ) and Young modulus (E), were taken based on the concrete compressive strength according to EC2 [9] as 0.002, 0.003, and 37 GPa, respectively The Poisson’s ratio was taken to be 0.2 for concrete and 0.3 for steel 3.2 Finite element analysis result During the FE analysis, the stress distributions on the whole CFDST can be captured and the relationship between the bending moment and displacement at the mid-span of the CFDST can be obtained Fig shows the stress contour of the whole CFDST at the failure, while Fig presents the comparison of the bending moment-displacement at mid-span behavior obtained from FE analysis and experiment As can be seen from Fig that the bending moment-displacement curve from FE 25 theThe concrete and were simulated using thethe EMBEDDED option In addition, the were applied in one row at top middleofof the loading pads,which which were The loads were applied in simulated one row at the top middle the loading the loads concrete and were using the EMBEDDED option In pads, addition, the were contact between the pads and outer steel tubes was modeled by using the TIE option installed at 750 away from center the CFDSTon onboth bothsides sides The hingeand and contact between the pads and outer steel tubes was modeled by using the TIE option installed at 750 mmmm away from thethe center of of the CFDST The hinge The The loadsloads werewere applied in one row at the top middle of the loading pads, which were applied in onetorow atmiddle the top points middle of(reference the loading pads, which roller conditions were applied to middle points(reference points) thewere boundary roller conditions were applied thethe points) ofofthe boundary installed at 750 mm away from the center of the CFDST on both sides The hinge andand installed at 750 mm away from the center of the CFDST on both sides The hinge pads shows the detail modeling componentsand and theFE FEmodel model pads Fig.Fig shows the modeling of of thethe components the Hoan,detail P T., et al / Journal of Science and Technology in Civil Engineering rollerroller conditions werewere applied to the middle points (reference points) of the boundary conditions applied to the middle points (reference points) of the boundary pads.pads Fig Fig shows the detail modeling of the components and the FE model shows the detail modeling of the components and the FE model (a) Finite element model (a)element Finite element model (a)(a) Finite model (a)Finite Finite element model element model Journal of Science and Technology in Civil Engineering - NUCE 2018 Journal of Science and Technology in Civil Engineering - NUCE 2018 the material material parameters parameters obtained obtainedfrom fromthe thecoupon coupontests testsininTable Table1 1were wereadopted adopted The the The stress-strain curve curve of of concrete concretewas wasconstructed constructedbybyusing usingT’sai T’saiconcrete concretemodel model[21] [21] stress-strain It It is worth worth noting noting that that the themissing missingparameters parametersofofconcrete concretematerial materialfrom fromthethecoupon coupon test, is test, such as as strain strain values values atat compressive compressive strength strength(e(ce)c)and andatatfailure failure(e(c1e)c1)and andYoung Young such modulus (E), (E), were were taken takenbased basedon onthe theconcrete concretecompressive compressivestrength strengthaccording according EC2 modulus toto EC2 Shear connector (c)Loading Loading pads (d) Boundary (b) Shear connector (c) pads Boundary (b)(b)Shear connector (c) Loading pads (d) (d) Boundary padpad pad [9] as as(b)0.002, 0.002, 0.003, and37 37GPa, GPa,respectively respectively ThePoisson’s Poisson’sratio ratio wastaken taken Shear0.003, connector (c) Loading pads (d) Boundary pad [9] and The was toto bebe 0.20.2 Figure Details of of components and FE model(d) Boundary pad Figure Details components model Figure Details ofLoading components FEFE model concrete and 0.3 0.3 for steel (b)concrete Shear connector padsandand for and for steel Figure (c) Details of components and FE model Concerning the material models, plasticity model used steel tubes Concerning the Figure material theofthe plasticity model waswas used for for steel tubes andand 6.models, Details components and FE model Concerning the material models, the plasticity model was used for steel tubes and the concrete damaged plasticity model utilized concrete infill Noted the concrete damaged plasticity model waswas utilized for for concrete infill Noted thatthat thethe the concrete damaged plasticity model was utilized infill Noted the concrete damaged plasticity model proposed Lubiner et concrete at Lee andthatand Concerning the material models, the plasticity model was used forby steel concrete damaged plasticity model proposed by by Lubiner etfor at [19][19] andand by Lee andtubes Fenves which can model the inelastic response concrete, is available concrete damaged plasticity model proposed by Lubiner et at.isinfill [19] and by Lee the and Fenves [20],[20], which can model the inelastic of concrete, available in in the concrete damaged plasticity model wasresponse utilized forof concrete Noted that ABAQUS Fig shows the stress-strain curves of materials used in this study, where Fenves [20], canstress-strain model inelastic response ofinat concrete, is available in ABAQUS Fig which shows the curves of by materials usedet this[19] study, where concrete damaged plasticity model the proposed Lubiner and by Lee and ABAQUS Fig shows the stress-strain curves of materials used in this study, where Fenves [20], which can model the inelastic response of concrete, is available in ABAQUS Fig shows the stress-strain of materials used in this study, where 6 curves 6 (a) Stress-strain curve of concrete (a) (a) Stress-strain Stress-straincurve curveof ofconcrete concrete (b) Stress-strain curve of steel (b) steel (b)Stress-strain Stress-straincurve curveofof steel Figure Material models Figure Figure7.7.Material Materialmodels models 3.2 Finite element analysis result 3.2 Finite element analysis result analysis is in good agreement with that obtained from the experiment of CFDST Not only the shape of the curve but also the ultimate moment Mu.ana = 5461 kNm obtained from FE analysis agrees During During the the FE FE analysis, analysis, the the stress stressdistributions distributionsononthe thewhole wholeCFDST CFDSTcan canbebe 26bending moment and displacement at the captured captured and and the the relationship relationship between betweenthe the bending moment and displacement at the mid-span of the CFDST can be obtained Fig whole mid-span of the CFDST can be obtained Fig.88shows showsthe thestress stresscontour contourofofthethe whole CFDST at the failure, while Fig presents the comparison of the bending momentCFDST at the failure, while Fig presents the comparison of the bending moment- Hoan, P T., et al / Journal of Science and Technology in Civil Engineering Journal of Science and Technology in Civil Engineering - NUCE 2018 well with that of the experiment with a Technology relative error of 3.1% The observed Journal of Science and in Civil Engineering - NUCEresult 2018 indicates that the developed FE model can be used to accurately simulate the four-point bending test of CFDST Figure Stress distributions of the CFDST Figure8.8.Stress Stressdistributions distributions of the CFDST Figure CFDST Figure Comparisonbetween between FE andand experiment resultresult Figure Comparison FEanalysis analysis experiment Figure Comparison between FE analysis and experiment result Ultimate bending moment of CFDST Ultimate bending moment of CFDST Ultimate bending moment of CFDST In to order to evaluate the bending ultimatemoment bendingof moment of CFDST with respect to In order evaluate the ultimate CFDST with respect to different concrete In order to evaluate the ultimate bending moment of CFDST with respect compressive steel yield strengths, simulations of strengths, four-point bending test of CFDST differentstrengths concreteand compressive strengthsFE and steel yield FE simulations ofto with variousconcrete values ofcompressive concrete steel yield conducted To FE examine the yield effect different strengths and steelwere yield strengths, simulations ofof four-point bending test ofand CFDST withstrengths various values of concrete and steel concrete compressive strength on the ultimate bending moment of CFDST, four different values four-point test of CFDST withthevarious values of concrete andstrength steel yield strengths bending were conducted To examine effect of concrete compressive on of 40 MPa, 60 MPa, 80 MPa, and 100 MPa were utilized, while the yield strengths of steel tubes were strengths werebending conducted To examine thefour effect of concrete the ultimate moment of CFDST, different valuescompressive of 40 MPa, 60strength MPa, 80on kept unchanged as the value obtained from the steel coupon tests In contrast, the effect of the yield 100 MPa were utilized, the yield strengths ofof steel tubes 60 were kept80 theMPa, ultimate moment of CFDST, four different values 40 MPa, MPa, strength of and steelbending tubes was considered by while varying these strength values while keeping the concrete unchanged the value thethe steel coupon tests In the were effectkept of MPa, and 100asMPa wereobtained utilized,from while yield strengths of contrast, steel tubes 27 the yield strength of steel tubes was by varying these whileof unchanged as the value obtained fromconsidered the steel coupon tests In strength contrast,values the effect the concrete material parameters unchanged Sincethese the higher yield strength thekeeping yield strength of steel tubes was considered by varying strength values while keeping the concrete material parameters unchanged Since the higher yield strength Journal of Science and Technology in Civil Engineering - NUCE 2018 of steel when compared to the used steel materials in the test may lead to the high Hoan, P T., et al / Journal of Science and Technology in Civil Engineering strength steel type, which shows different stress-strain behavior, only lower yield material parameters the higher yieldDue strength of fact steelthat when the used strength values unchanged were used Since in parametric study to the thecompared values oftoyield steelstrength materialsofin outer the testand mayinner lead to the high different stress-strain steel tubesstrength used insteel thetype, test which were shows different, the reduced behavior, only lower yield strength values were used in parametric study Due to the fact that the ratios of 1.2, 1.4, and 1.6 for both steel yield strengths of outer and inner tubes were values of yield strength of outer and inner steel tubes used in the test were different, the reduced ratios used order to both obtain meaningfull Noted thatwere the used chosen concrete of 1.2, 1.4,inand 1.6 for steela yield strengthscomparison of outer and inner tubes in order to obtain compressive strengthNoted and that reduced ratios of steel yield strength to ratios the of a meaningful comparison the chosen concrete compressive strengthrepresent and reduced properties of commonly used concrete and steel materials in real structures steel yield strength represent to the properties of commonly used concrete and steel materials in real structures 4.1 Effect of concrete compressive strength 4.1 EffectFig of concrete compressive strength moment-displacement curves of CFDST with 10 presents the bending different concrete compressive strengths obtained from the FE with analyses Table listscomFig 10 presents the bending moment-displacement curves of CFDST different concrete the material usedthe in FE FEanalyses analysesTable and the corresponding ultimate bending pressive strengths properties obtained from lists the material properties used in FE analyses and the ultimate bending moments of CFDST moments ofcorresponding CFDST 10 Effect of concretecompressive compressive strength moment-displacement curve curve FigureFigure 10 Effect of concrete strengthonon moment-displacement Table Ultimate bending moments with respect to different concrete strengths Table Ultimate bending moments with respect to different concrete strengths Fy/ Fu of outer steel tube Fy/ Fu of inner steel tube f’c (MPa) Mu (kNm) (MPa) (MPa) Fy /Fu of outer steel tube (MPa) Fy /Fu of inner steel tube (MPa) 40 48.9 486.5/ 533.9 486.5/ 533.9 467.6/ 517.8 467.6/ 517.8 60 80 100 fc (MPa) 40 48.9 60 80 100 Mu (kNm) 5092 5092 5461 5461 5644 5644 6024 6372 6024 6372 As canAsbe can seenbe in Fig thatTable while thethat shapes of moment-displacement curve at seen10inand Fig.Table 10 2and while the shapes of momentmid-span of CFDST are almost similar, the ultimate bending moment of CFDST increases with displacement curve at mid-span of CFDST are almost similar, the ultimate bending the increment of concrete compressive strength The similar shapes of moment-displacement curve at moment of CFDST increases with the increment of concrete compressive strength mid-span of CFDST indicate that the concrete infill has strong influence on the bending behavior of Theinsimilar shapes moment-displacement curve atto mid-span ofthe CFDST CFDST both elastic and of plastic regions It is also interesting observe that increaseindicate of ultimate bending moment of CFDST with respect to the increasing concrete compressive strength is almost linear, as shown in Fig 11 28 elastic plasticinfill regions It is also interesting to observe the increase of ultimate that theand concrete has strong influence on the bending that behavior of CFDST in both bending moment of CFDST with respect to the increasing concrete compressive elastic and plastic regions It is also interesting to observe that the increase of ultimate strength almost linear, as shown Fig 11 to the increasing concrete compressive bending ismoment of CFDST within respect strength is almost Fig 11 Hoan,linear, P T., etas al shown / Journal in of Science and Technology in Civil Engineering Figure 11 Effect of concrete compressive strength on ultimate bending moment Figure 11 Effect of concrete compressive strength on ultimate bending moment 11.yield Effect of concrete compressive strength on ultimate bending moment 4.2.Figure Effect of strength of steel tubes Effect of shows yield strength of tubes steel tubes Fig 12 theofmoment-displacement curves of CFDST with different yield 4.2 4.2 Effect of yield strength steel strength values ofmoment-displacement outer inner steel tubesofobtained from the FE analyses Table of Fig 12 the shows the and moment-displacement curves of CFDST with different yield Fig 12 shows curves CFDST with different yield strength values presents the material properties used FEanalyses analyses and ultimate outer and inner steel tubes obtained from theinFE Table 3the presents material properties strength values of outer and inner steel tubes obtained from thecorresponding FE the analyses Table usedbending in FE analyses and the corresponding ultimate bending moments of CFDST moments of CFDST presents the material properties used in FE analyses and the corresponding ultimate bending moments of CFDST 12 Effect of yield strength of steel tubes on moment-displacement curve FigureFigure 12 Effect of yield strength of steel tubes on moment-displacement curve Figure 12 Effectbending of yieldmoments strength with of steel tubestoondifferent moment-displacement curve Table Ultimate respect strengths of steel tubes Table Ultimate bending moments with respect to different strengths of steel tubes Table Ultimate bending moments to different of steel tubes Reduced ratio of with Fy/respect Fu of outer Fy/ Fstrengths u of inner f’c (MPa) Fyratio steel tube (MPa) Fysteel (MPa) ReducedReduced Fyof/Fu of /F of inner Fouter Fy/u Ftube y/ Fu of outer u of inner fc (MPa)f’c (MPa) ratio of Fy steel tubesteel (MPa) tube (MPa) Fy tube533.9 (MPa) steel steel tube (MPa) 48.9 486.5/ 467.6/ 517.8 48.9 48.9 1.2 1.4 1.6 486.5/ 533.9 486.5/ 533.9 405.4/ 444.9 347.5/ 381.4 10 304.1/ 333.7 10 467.6/ 517.8 467.6/ 517.8 389.7/ 431.5 334.0/ 369.9 292.3/ 323.6 Mu (kNm) u (kNm) MuM(kNm) 5461 5461 5461 4764 4281 3905 It is seen from Table and Fig 12 that the ultimate bending moment of CFDST decreases as the yield strength of steel tubes decreases, whereas the load-displacement curves at mid-span of CFDST 29 It is seen from Table and Fig 12 that the ultimate bending moment of CFDST decreases as the yield strength of steel tubes decreases, whereas the load-displacement curves at mid-span of CFDST in the elastic region are almost identical This observed result reveals that the yield strength of outer and inner steel tubes has strong influence Hoan, P T., et al / Journal of Science and Technology in Civil Engineering on the ultimate bending moment of CFDST but the influence just appears in the in the elasticregion, region while are almost This observed result revealsofthat thetubes yield shows strengthtrivial of outer plastic in theidentical elastic region the yield strength steel and effect inner steel tubes has strong influence on the ultimate bending moment of CFDST influence on the bending behavior of CFDST It is also worth to mention thatbut thethe reduced just appears in the plastic region, while in the elastic region the yield strength of steel tubes shows ratio of ultimate bending moment, which represents the decreasing ratio of ultimate trivial effect on the bending behavior of CFDST It is also worth to mention that the reduced ratio bendingbending moments of CFDST the yield strength of steel decreases, exhibits of of ultimate moment, whichwhen represents the decreasing ratio of tubes ultimate bending moments an exactly linear decrease respect the decreasing yield strengthlinear of steel tubes,with CFDST when the yield strengthwith of steel tubestodecreases, exhibits an exactly decrease as illustrated in Fig.yield 13 strength of steel tubes, as illustrated in Fig 13 respect to the decreasing 13.Journal Effect of yield strength steel tubes onEngineering reduced ultimate bending moment FigureFigure 13 Effect of yield strength ofofsteel tubes reduced bending moment of Science and Technology in Civilon -ultimate NUCE 2018 4.3 Recommendation on the design bending moment capacity of CFDST 4.3 Recommendation on the design bending moment capacity of CFDST equals to popular the total design of tensile stresses of steel4in(EC4) tension The nominal Both codes Eurocode [9]zone and (lower AISC part) [17] provide parallel Both popular design codes Eurocode (EC4) [9] and AISC [16] provide parallel two methods moment capacity Mu evaluation of the cross-section is determined based on theoftotal moment two methods for the of the nominal moment capacity fully concrete for thecaused evaluation of thestresses nominal moment of fully concrete filled steel tube (CFST), which by tube these in both upper lower parts with respect to plastic neutral filled steel (CFST), which arecapacity theandstrain compatibility method (SCM) and the are theaxis strain compatibility method (SCM) and the plastic stress distribution method (PSDM) Using called Mp) by multiplying by a load andthe resistance factor forofbending fb for plastic (so stress distribution method (PSDM) Using same principle the codes the same principle of the codes for CFST, the PSDMs in both aforementioned codes were utilized According to EC4,intheboth compressive stress ofcodes concrete in utilized compression zone isthe taken as CFST, thenominal PSDMs aforementioned were predict nominal to predict the moment capacity of CFDST in this study Notedtothat the nominal moment compressive strength of concrete, both compressive tensile stresses of steel are of moment capacity of CFDST in this study Noted thatand the nominal moment capacity of a cross-section corresponds to the bending ultimate moment of the tube (Mcapacity ) in this study u taken as yield strength of steel, while the load and resistance factor for bending is 0.9 Fig.a14 illustrates thecorresponds calculation principle of nominal moment capacity on the stress cross-section to the bending ultimate moment ofbased the tube (Mplastic u) in this The PSDM inprovided AISC is same The withplastic that in EC4axis except theofcompressive stressof of distribution method in EC4 neutral (PNA) the cross-section the study Fig 14 illustrates the calculation principle of nominal moment capacity basedtube concrete is taken as 0.95 compressive strength (0.95f’c) Fy N.A 445.17 11 Fy 276.8 Fy 26.31 Concrete 97 P.N.A 177.06 on the plastic stress distribution method provided in EC4 The plastic neutral axis ' (PNA) of the cross-section of the tubeFydivides fcthe section into two parts, where the total of compressive stresses of steel and concrete in compression zone (upper part) Figure 14.14 Plastic ofCFDST CFDST (EC4) Figure Plasticstress stress distribution distribution of (EC4) In present study, the nominal moment capacity of the designed CFDST was 30 predicted using the aforementioned method according to both EC4 and AISC codes The geometric parameters of the CFDST and the properties of materials used in the test were utilized in the calculation The computed nominal moment capacity (so Hoan, P T., et al / Journal of Science and Technology in Civil Engineering divides the section into two parts, where the total of compressive stresses of steel and concrete in compression zone (upper part) equals to the total of tensile stresses of steel in tension zone (lower part) The nominal moment capacity Mu of the cross-section is determined based on the total moment caused by these stresses in both upper and lower parts with respect to plastic neutral axis (so called M p ) by multiplying by a load and resistance factor for bending φb According to EC4, the compressive stress of concrete in compression zone is taken as compressive strength of concrete, both compressive and tensile stresses of steel are taken as yield strength of steel, while the load and resistance factor for bending is 0.9 The PSDM in AISC is same with that in EC4 except the compressive stress of concrete is taken as 0.95 compressive strength (0.95 fc ) In present study, the nominal moment capacity of the designed CFDST was predicted using the aforementioned method according to both EC4 and AISC codes The geometric parameters of the CFDST and the properties of materials used in the test were utilized in the calculation The computed nominal moment capacity (so called ultimate bending moment) of the CFDST according to both codes are listed in Table 4, together with those obtained from the test and FE analysis result It is seen from this table that the ultimate bending moments calculated using both codes EC4 and AISC are in good agreement with that obtained from the experiment The prediction recommended by EC4 method is slightly closer to the test result than that recommended by AISC method since EC4 method presumes that the concrete stress is fc instead 0.95 fc used in the AISC method Table Ultimate bending moment of CFDST ∗ Method Mu (kNm) Mu /Mu.exp Experiment FE analysis AISC EC4 5299∗ 5461 4947 4973 1.00 1.03 0.93 0.94 Mu.exp : the ultimate bending moment obtained from experiment Conclusions In this study, a concrete-filled double circular skin steel tubes was designed The flexural behavior and bending ultimate moment of the CFDST were investigated through the experiment and FE analysis The following conclusions can be withdrawn: - The developed FE model can be used to accurately simulate the four-point bending test of CFDST - The infilled concrete strength has strong influence on the bending behavior of CFDST in both elastic and plastic regions The increase of bending ultimate moment of CFDST with respect to the increasing concrete compressive strength is almost linear - The yield strength of outer and inner steel tubes has strong influence on the bending ultimate moment of CFDST but the influence just appears in the plastic region, while in the elastic region the yield strength of steel tubes shows trivial effect on the bending behavior of CFDST The reduced ratio of bending ultimate moment exhibits an exactly linear decrease with respect to the decreasing yield strength of steel tubes - The nominal moment capacity of the CFDST predicted by EC4 method is slightly closer to the test result than that predicted by AISC method 31 Hoan, P T., et al / Journal of Science and Technology in Civil Engineering Acknowledgement The study presented in this paper was financially supported by National University of Civil Engineering through Grant 75-2019/KHXD and XD-2019-29 The financial support is greatly appreciated References [1] Han, L.-H., Huang, H., Tao, Z., Zhao, X.-L (2006) Concrete-filled double skin steel tubular (CFDST) beam–columns subjected to cyclic bending Engineering Structures, 28(12):1698–1714 [2] Tao, Z., Han, L.-H (2006) Behaviour of concrete-filled double skin rectangular steel tubular beam– columns Journal of Constructional Steel Research, 62(7):631–646 [3] Eom, S.-S., Vu, Q.-V., Choi, J.-H., Park, H.-H., Kim, S.-E (2019) Flexural behavior of concrete-filled double skin steel tubes with a joint Journal of Constructional 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FE analysis and experiment result Ultimate bending moment of CFDST Ultimate bending moment of CFDST Ultimate bending moment of CFDST In to order to evaluate the bending ultimatemoment bendingof... moment 11.yield Effect of concrete compressive strength on ultimate bending moment 4.2.Figure Effect of strength of steel tubes Effect of shows yield strength of tubes steel tubes Fig 12 theofmoment-displacement... reduced ratio bendingbending moments of CFDST the yield strength of steel decreases, exhibits of of ultimate moment, whichwhen represents the decreasing ratio of tubes ultimate bending moments an