Flexural behaviour of concrete-filled CHS X-joints with curved chord under out-of-plane bending

Engineering Structures 145 (2017) 254–272

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Flexural behaviour of concrete-filled CHS X-joints with curved chord under out-of-plane bending Ran Feng a, Yu Chen b,⇑, Tao Chen c a

School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China School of Urban Construction, Yangtze University, Jingzhou 434023, China c College of Civil Engineering, Huaqiao University, Xiamen 361021, China b

a r t i c l e

i n f o

Article history: Received 3 September 2015 Revised 2 May 2017 Accepted 11 May 2017

Keywords: CHS X-joints Concrete-filled Curved chord Out-of-plane bending Parametric study Strain distribution

a b s t r a c t This paper presents experimental and numerical investigations on empty and concrete-filled circular hollow section (CHS) X-joints with curved chord under out-of-plane bending. A total of 16 specimens were fabricated by hot-rolled bending the chord members into curvature with three different radii to apply out-of-plane bending to the brace members, in which 6 specimens were tested with empty curved chord, 6 specimens were tested with concrete filled in the curved chord only, and 4 traditional empty and concrete-filled CHS X-joints with straight chord were also tested for comparison. The typical failure modes, axial load-vertical displacement curves, bending moment-chord deformation curves, bending moment-rotation curves and strain distribution curves of all specimens are reported. The effects of curvature radius of chord member and concrete filled in the chord member on the joint strength and behaviour under out-of-plane bending were evaluated. It is shown from the comparison that the ultimate strengths of the CHS X-joints with curvature radius of chord less than 12d0 under out-of-plane bending are closer to those of the traditional CHS X-joints with straight chord with the increase of the curvature radius of chord member. Whereas, the ultimate strengths of the CHS X-joints with curvature radius of chord less than 12d0 under out-of-plane bending are generally similar to those of the traditional CHS X-joints with straight chord. Furthermore, the out-of-plane flexural behaviour of CHS X-joints are improved with the increase of the b ratio. Whereas, filling the concrete in the chord member cannot enhance the ultimate strengths of CHS X-joints under out-of-plane bending. The joint strengths obtained from the experimental investigation are compared with the design strengths calculated using the current design rules for traditional CHS X-joints with straight chord under out-of-plane bending, which were demonstrated to be quite conservative. In addition, the corresponding finite element analysis was also performed and calibrated against the test results. The design equations are proposed based on the test and numerical results for empty and concrete-filled CHS X-joints with curved chord under out-ofplane bending, which were verified to be more accurate. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Circular hollow section (CHS) tubular structures nowadays are commonly used in railway station, airport terminal, great theatre, sports stadium, exhibition hall and many other long-span and spatial structures due to their aesthetic appearance, uniform flexural rigidity and superior static and dynamic behaviour. The CHS X-joint is one of the widely used connection types, which is fabricated by welding CHS brace members to the continuous CHS chord member. While the chord members are usually bent into curvature with certain radius for architectural and structural purposes. ⇑ Corresponding author. E-mail address: [email protected] (Y. Chen). http://dx.doi.org/10.1016/j.engstruct.2017.05.025 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

Concrete filling is one of the commonly used strengthening methods for tubular connections with inadequate resistance and its primary hollow section members cannot be changed, which is particularly appealing for architecturally exposed steelwork. Extensive tests and theoretical analyses have been performed on welded tubular joints subjected to out-of-plane bending. It was shown that the local buckling failure and material yielding failure usually occurred at the brace and chord intersection region, which eventually affected the overall behaviour of tubular structures. Experimental and numerical investigations were conducted by Wang et al. [1] on the behaviour of thick-walled CHS X-joints under cyclic out-of-plane bending. It was found that CHS X-joints with large brace to chord diameter ratio (b) demonstrated better ductility and energy dissipation capacity compared to CHS

R. Feng et al. / Engineering Structures 145 (2017) 254–272

255

Nomenclature Notation d0 outer diameter of chord outer diameter of brace d1 L chord length a chord length coefficient Ec elastic modulus of concrete elastic modulus of steel Es fcu concrete cube strength fu ultimate tensile stress of steel fy tensile yield stress of steel yield stress of chord fy0 h distance between displacement transducers D3 and D5 as well as D6 and D8 M bending moment Mc ultimate strength of CHS X-joints with curved chord MCFF design strength of CHS X-joints subjected to chord face failure Mmin minimum of MCFF, MPSF and MPTB Mop design strength of traditional CHS X-joints with straight chord under out-of-plane bending Mop,c design strength of concrete-filled CHS X-joints with curved chord under out-of-plane bending Mop,e design strength of empty CHS X-joints with curved chord under out-of-plane bending MPSF design strength of CHS X-joints subjected to punching shear failure MPTB plastic out-of-plane bending moment of total crosssection of brace Ms ultimate strength of traditional CHS X-joints with straight chord Mtest test strength MYBE yield out-of-plane bending moment of brace edge N axial load Nu ultimate strength Mu ultimate moment strength (Mu = Nu/2
0.25 in test) R curvature radius of chord

X-joints with small b ratio under cyclic out-of-plane bending. Fatigue life of out-of-plane gusset welded joints was predicted by Choi and Choi [2] using strain energy density factor approach. The fatigue crack growth analysis was performed to evaluate the effects of initial crack shape, initial crack length and stress ratio. The behaviour of bird-beak square hollow section (SHS) X-joints under out-of-plane bending was studied by Chen et al. [3]. The birdbeak SHS X-joints demonstrated better out-of-plane flexural behaviour than the traditional SHS X-joints. A total of 23 complete tubular trusses were tested by Kurobane [4–6], in which 4 specimens are composite trusses with concrete filled in the chords, 4 specimens are composite lattice girders with concrete slabs, and 2 specimens are space trusses. No significant influence from different boundary conditions between actual joints in truss and isolated joints was found. It was shown that the ultimate strengths of Kjoints were governed by either localized shell bending deflection of the chord wall or local buckling of the compression brace in the region adjacent to the joint. The modified beam models were developed by Moazed et al. [7] at substantially reduced computational effort in comparison with the complicated finite element models built of shell or solid elements. The accurate results including the stresses, displacements, reaction forces and natural frequencies were obtained from the structural analysis. The strain and stress concentration factors (SCFs) of T-joints under in-plane bending were studied by Mashiri [8–10], which include CHS-toplate, CHS-to-CHS and SHS-to-plate joints. The SCFs of completely

t t0 t1 b

cM5

2c d d1 d2 d3 d4

ef ei ey e1 e2 e3 m h1

s u uconcave uconvex

w wc we D

thickness of thinner part between brace and chord wall thickness of chord wall thickness of brace brace to chord diameter ratio (d1/d0) partial safety factor chord diameter to thickness ratio (d0/t0) chord deformation flange indentation at the compression area of chord concave side flange indentation at the tension area of chord concave side flange indentation at the compression area of chord convex side flange indentation at the tension area of chord convex side elongation of steel after fracture strain yield strain first principal strain second principal strain third principal strain Poisson’s ratio Inclined angle between brace and chord Brace to chord thickness ratio (t1/t0) out-of-plane rotation angle rotation angle of chord concave side (uconcave = (d2  d1)/ h) rotation angle of chord convex side (uconvex = (d4  d3)/ h) correction factor correction factor for concrete-filled CHS X-joint with curved chord correction factor for empty CHS X-joint with curved chord vertical displacement

overlapped tubular joints under lap brace out-of-plane bending were investigated by Gao [11]. It was found that the existing parametric equations of T- and Y-joints are inappropriate for the SCF predictions. The aforementioned literatures were all conducted on traditional tubular joints fabricated with straight brace members welded to the continuous straight chord members. There is little research being carried out on CHS joints with curved chord under out-of-plane bending. The research on the out-of-plane flexural behaviour of concrete-filled CHS joints with curved chord is far scarce. This study is a further development of empty and concrete-filled CHS X-joints with curved chord that mainly focuses on the strength and behaviour of empty and concrete-filled CHS Xjoints with curved chord under out-of-plane bending. Effective length of curved chords under out-of-plane bending is decided by mechanical behaviour of joints with curved chords under outof-plane bending. The ultimate strengths, failure modes, joint deformations and strain distributions of empty and concretefilled CHS X-joints with curved chord under out-of-plane bending are reported in this study. The joint strengths obtained from the experimental investigation were compared with the design strengths calculated using the current design specifications. Furthermore, the finite element analysis was also performed to evaluate the effects of curvature radius of chord member, crosssection dimension of brace member and concrete infill on the out-of-plane flexural behaviour of CHS X-joints with curved chord.

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The design equations are also proposed for empty and concretefilled CHS X-joints with curved chord under out-of-plane bending. 2. Experimental study 2.1. Test specimens The out-of-plane bending tests were conducted on empty and concrete-filled CHS X-joints with curved chord. A total of 16 specimens were tested by applying out-of-plane bending to the brace members, in which 6 specimens were tested with empty curved chord, 6 specimens were tested with concrete filled in the curved chord along its full length only, and 4 traditional empty and concrete-filled CHS X-joints with straight chord were also tested for comparison. All specimens were fabricated with brace members fully welded at right angles to the opposing sides of the continuous chord members. The 10 mm-thick steel plates were welded at the end of brace members and two steel blocks with height of 80 mm were welded symmetrically at the end of chord member, which are perpendicular to the uniplanar brace and chord members and 80 mm away from the end of chord member for the loading and boundary conditions. The chord members were made of hot-rolled seamless steel tube with identical cross-section of CHS 140
5.0, which has the nominal diameter (d0) of 140 mm and the wall thickness (t0) of 5.0 mm. The chord members were further processed by hot-rolled bending into curvature with three different radii (R) of 420 mm, 840 mm and 1260 mm. The length of chord member was chosen as 600 mm (>4d0) to ensure that the stresses at the brace and chord intersection region are not affected by the ends of the chord. The brace members were made of hotrolled seam steel tube with two different cross-sections of CHS 114
3.0 and CHS 89
2.5, which have the nominal diameter (d1) of 114 mm and 89 mm, respectively, as well as the wall thickness (t1) of 3.0 mm and 2.5 mm, respectively. The distance between end plate welded to the end of brace member and the centroid of chord member was limited to 250 mm to avoid the overall buckling of brace members, which cannot reveal the true ultimate capacity of tubular joints. The specimen dimensions including brace members and chord members as well as geometric parameters b = d1/d0, s = t1/t0 and 2c = d0/t0 are all summarized in Table 1, using the nomenclature defined in Fig. 1 for empty and concrete-filled CHS X-joints with curved chord. It is very difficult to control small vertical loading for joint with long length of the chord, so a very short effective length of the chord is designed in

specimens. At the same time, there will be big errors of strength of joints under small vertical loading in order to generate out-ofplane bending. The strength of typical experimental joints XB114
3.0 under out-of-plane bending increased as the ratio a of chord length to chord diameter increased in a numerical investigation, as shown in Fig. 2, in which L was chord length and a was chord length coefficient. When ratio a is larger than 4.0, the effect of a on strength of X-joints under out-of-plane bending is little. The selected so-called short chord length (4.3d0) does not impose an adverse effect on the X-joints strength. The welds connecting brace and chord members were designed according to American Welding Society (AWS D1.1/1.1 M) Specification [12] and laid using shielded metal arc welding. The type of welding between the brace and the chord was complete penetration because the angle between the brace and the chord is 900. The weld sizes in the test specimens are all greater than the larger value of 1.5t and 3 mm, where t is the thickness of thinner part between brace and chord members. The 3.0 mm and 3.5 mm electrodes of type E4303 with nominal 0.2% proof stress, tensile strength and elongation of 350 MPa, 450 MPa and 35%, respectively, were used for welding carbon steel specimens. All welds consisted of 2 to 3 runs of welding to guarantee that failure of specimens occurred in the brace or chord members rather than the welds. 2.2. Specimen labelling The specimens are labelled according to their joint configuration, cross-section dimensions of brace members, curvature radius of chord members and concrete infill. For example, the label ‘XB89
2.5R420F’ defines the following CHS X-joint:  The first letter ‘x’ denotes X-joint  The second letter ‘B’ denotes brace member and the following expression ‘89
2.5’ indicates the cross-section dimensions of the CHS brace members, which have the nominal diameter (d1) of 89 mm and the wall thickness (t1) of 2.5 mm.  The following notation ‘R420’ indicates the curved chord with the curvature radius of 420 mm. If the notation is not shown, the chord is straight. The prefix letter ‘R’ refers to radius.  The last letter ‘F’ indicates concrete was filled in the chord member only. If there is no ‘F’ in the label, it means there is no concrete in the chord member.

Table 1 Details of test specimens. Specimen

XB89
2.5R420 XB89
2.5R840 XB89
2.5R1260 XB89
2.5 XB89
2.5R420F XB89
2.5R840F XB89
2.5R1260F XB89
2.5F XB114
3.0R420 XB114
3.0R840 XB114
3.0R1260 XB114
3.0 XB114
3.0R420F XB114
3.0R840F XB114
3.0R1260F XB114
3.0F

Brace

Chord

d 1
t1 (mm)

d0
t0 (mm)

R (mm)

Concrete infill

b = d1/d0

s = t1/t0

2c = d0/t0

89
2.5

140
5.0

420 840 1260 1 420 840 1260 1 420 840 1260 1 420 840 1260 1

No

0.636

0.5

28

0.814

0.6

114
3.0

Geometric parameter

Yes

No

Yes

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chord brace

chord

brace

Fig. 1. Schematic diagram of test specimens.

Mu/kN·m 14

Table 2 Material properties of steel tubes.

12

Specimen (mm)

10

CHS CHS CHS CHS

8 6

140
5.0 (Hot-rolled bending) 140
5.0 89
2.5 114
3.0

fy (MPa)

fu (MPa)

fy/fu

298 275 278 310

350 330 340 365

0.85 0.83 0.82 0.85

ef (%) 17.9 18.7 19.2 18.9

4 2 0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

=L/d0 Fig. 2. Mu-a curves of XB114
3.0 under out-of-plane bending.

/MPa 400 350 300 250 200

The chord member of all specimens is CHS 140
5.0, which has the nominal diameter (d0) of 140 mm and the wall thickness (t0) of 5 mm. The brace members of all specimens are CHS 89
2.5 and CHS 114
3.0, which have the nominal diameter (d1) of 89 mm and 114 mm, respectively, as well as the wall thickness (t1) of 2.5 mm and 3.0 mm, respectively. 2.3. Material properties All specimens including both brace and chord members were fabricated by using Chinese Standard Q235 steel (nominal yield stress fy = 235 MPa). Tensile coupon tests were conducted to determine the mechanical properties of the CHS brace and chord members. The coupons were taken from the center face in the longitudinal direction of the untested specimens and prepared according to the recommendations of the Chinese Code of Metallic Materials-Tensile Testing at Ambient Temperature (GB/T 2282002) [13]. The tensile coupon tests were conducted by using a MTS displacement controlled testing machine. The strain gauges were positioned to measure the longitudinal strains during the tests. The material properties obtained from the tensile coupon tests are summarized in Table 2, which include the tensile yield stress (fy), the ultimate tensile stress (fu), and the elongation after fracture (ef). It is shown from the comparison that the material properties of the straight and curved CHS are quite similar. It seems that the process of the hot-rolled bending slightly enhanced the material strength, but deteriorated the material ductility. The typical stress-strain curves of the straight and curved CHS are plotted in Fig. 3. The concrete-filled CHS X-joints were fabricated by filling the concrete with nominal cube strength of 30 MPa in the chord member along its full length only. The material properties of concrete

Straight CHS Curved CHS

150 100 50 0 0

2000

4000

6000

8000

10000 /

12000

Fig. 3. Stress-strain curves of straight and curved CHS.

were determined from the compressive concrete cube tests. The standard concrete cubes with the nominal length of 150 mm were prepared and tested based on the recommendations of Chinese Standard for Test Method of Mechanical Properties on Ordinary Concrete (GB/T 50081-2002) [14]. The material properties of the standard concrete cubes are summarized in Table 3, which include the elastic modulus (Ec) of 30.1 GPa, and the mean value of the measured concrete cube strength (fcu) of 32.4 MPa. 2.4. Test procedure All specimens were installed in the same loading machine, as shown in Fig. 4a–d for front view, end view, top and photo, respectively. The reaction frame and supports were connected to the strong floor firmly by anchor bolts. A 1000 kN capacity hydraulic jack was used to apply the axial compression to the test specimens and monitored by the load cell, which was positioned concentrically between the hydraulic jack and the reaction frame. The compression force was applied using a spreader beam at two steel blocks welded at the end of chord member symmetrically as the loading points. Local stiffeners were weld in spreader beam in order to avoid premature failure near this connection. The connec-

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R. Feng et al. / Engineering Structures 145 (2017) 254–272

Table 3 Material properties of concrete. Nominal concrete strength (MPa)

Specimen

Elastic modulus Ec (GPa)

Compressive cube strength fcu (MPa)

Mean value fcu (MPa)

30

C-1 C-2 C-3

30.1

31.2 33.4 33.6

32.4

tion between the spreader beam and the chord were the two steel rollers. Local stiffeners do not contribute to the strength of the nearby brace-to-chord connection because the spread beam with local stiffeners was separated with connection by steel rollers. The steel rollers were used at the loading points to simulate the simply supported boundary conditions, while the end plates of horizontal brace members were simply supported by using the steel rollers as the end supports. Thus, the out-of-plane bending was generated at the joint intersection region of the test specimens. A total of eight displacement transducers (D1-D8) were used to record the vertical displacement and chord face deformation of each specimen during the test, in which D1 and D2 were positioned on the end plate of steel blocks welded at the end of chord member to measure the vertical displacement of the specimens at the loading points, D3, D4 and D5 were positioned on the chord concave side along the half of brace and chord intersection region to measure the flange indentation (d1) of chord concave side, and

D6, D7 and D8 were positioned on the chord convex side along the half of brace and chord intersection region to measure the flange indentation (d2) of chord convex side, as shown in Fig. 5a and b for front view and end view, respectively. Three-element rosettes strain gauges which enable strain values in three different directions at 450 interval to be measured simultaneously were used to investigate the strain distribution of each specimen under out-of-plane bending. A total of 12 threeelement rosettes strain gauges (T1-T12) were attached along the half of brace and chord intersection region by taking advantage of symmetry in geometry, loading application and boundary conditions, in which T1, T2 and T3 were positioned at the root of brace member connected to the chord concave side, T4, T5 and T6 were positioned on the flange of chord member (concave side), T7, T8 and T9 were positioned on the flange of chord member (convex side), and T10, T11 and T12 were positioned at the root of brace member connected to the chord convex side, as shown in Fig. 6. All strain gauges were positioned roughly 15 mm away from the weld to exclude the influence of welding.

3. Test results 3.1. Failure modes There are four typical failure modes observed from the tests of empty and concrete-filled CHS X-joints with curved chord and traditional empty and concrete-filled CHS X-joints with straight chord, namely Local Buckling of Brace (LBB), Tearing failure along

Reaction frame

Load cell

Reaction frame

Hydraulic jack

Spreader beam Spreader beam

Brace Brace

Chord Support

Chord

Brace

Support

Support

(a) Front view

(b) End view

Support

Support

Brace Chord (c) Top view

(d) Photo Fig. 4. Test setup.

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R. Feng et al. / Engineering Structures 145 (2017) 254–272

D2

D2 1

D3(D6) D6(D8)

D5(D8)

D3(D5)

D4(D7)

D4

D7

D1

1 D1

(a) Front view

(b) End view

Fig. 5. Arrangement of displacement transducers.

chord brace

T3(T12)

T6(T9) T8 T5 T2 T9(T7) T12(T10) T6(T4) T3(T1) T11

T2(T11) brace

T5(T8)

T1(T10)

T4(T7) chord

Fig. 6. Arrangement of strain gauges.

the circumference of brace (TFB), Fracture of Welding (FW) and Chord Plastification (CP), as shown in Fig. 7a–d, respectively. It should be noted that Local Buckling of Brace (LBB) occurred for almost all specimens, as summarized in Table 4, which means the strengths of the empty and concrete-filled CHS X-joints are generally governed by the strengths of brace members rather than the joint strengths. Whereas, Chord Plastification (CP) occurred for empty CHS X-joints only, which means concrete filled in the chord member greatly enhanced the stiffness of the chord member, and there is no damage for the concrete filled in the chord member in the ultimate limit state. 3.2. Vertical load-vertical displacement curves The axial load (N) versus vertical displacement (D) curves of all specimens are plotted in Fig. 8a–d for empty CHS X-joints with brace member of CHS 89
2.5, concrete-filled CHS X-joints with brace member of CHS 89
2.5, empty CHS X-joints with brace member of CHS 114
3.0, and concrete-filled CHS X-joints with brace member of CHS 114
3.0, respectively. The complete curves consist of the elastic stage, elasto-plastic stage, plastic stage and unloading stage, in which the horizontal axis represents the vertical displacement (D) of chord member obtained from the average readings of displacement transducers D1 and D2, and the vertical axis represents the axial load (N) applied to the loading points at two steel blocks welded at the end of chord member. It is shown from the comparison that the initial stiffness of empty CHS Xjoints with identical cross-section dimensions but different curva-

ture radii of chord member are quite similar, which may probably result from the similar out-of-plane rotation capacity of brace members. Furthermore, the initial stiffness of concrete-filled CHS X-joints with identical cross-section dimensions but different curvature radii of chord member are also quite similar, except for specimens XB89
2.5R420F and XB114
3.0R420F. The pronounced hot-rolled bending applied to these two specimens with the least curvature radius of concrete-filled chord member may weaken the out-of-plane rotation capacity of brace members. For empty CHS X-joints with b = 0.64, the ultimate strength and ductility are improved with the increase of the curvature radius of chord member, and the traditional specimen with straight chord has the least ultimate strength, but the largest ductility. For empty CHS Xjoints with b = 0.81, the ultimate strength and ductility are generally improved with the increase of the curvature radius of chord member, and the traditional specimen with straight chord has the least ultimate strength, but comparatively larger ductility. For concrete-filled CHS X-joints with b = 0.64, the specimen with the curvature radius of chord member of 420 mm has the least ultimate strength, initial stiffness and ductility, the specimen with the curvature radius of chord member of 840 mm has comparatively larger ultimate strength and ductility, and the traditional specimen with straight chord has the largest ultimate strength and ductility. For concrete-filled CHS X-joints with b = 0.81, the specimen with the curvature radius of chord member of 420 mm has the least ultimate strength and initial stiffness, but comparatively larger ductility, the specimen with the curvature radius of chord member of 1260 mm has the largest ultimate strength and ductility, and the

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R. Feng et al. / Engineering Structures 145 (2017) 254–272

Local buckling of brace

Tearing failure along the circumference of brace

(a) Local buckling of brace (LBB) (b) Tearing failure along the circumference of brace (TFB)

Fracture of welding Chord plastification

(c) Fracture of welding (FW)

(d) Chord plastification (CP)

Fig. 7. Failure modes of test specimens.

Table 4 Ultimate strengths and failure modes of test specimens. Specimen

Curvature radius of chord R (mm)

Failure mode

Ultimate strength Nu (kN)

XB89
2.5R420 XB89
2.5R840 XB89
2.5R1260 XB89
2.5 XB89
2.5R420F XB89
2.5R840F XB89
2.5R1260F XB89
2.5F XB114
3.0R420 XB114
3.0R840 XB114
3.0R1260 XB114
3.0 XB114
3.0R420F XB114
3.0R840F XB114
3.0R1260F XB114
3.0F

420 840 1260 1 420 840 1260 1 420 840 1260 1 420 840 1260 1

LBB LBB + TFB LBB CP LBB + FW LBB LBB + TFB LBB LBB CP LBB + FW + CP TFB + CP LBB + TFB LBB LBB + TFB LBB + FW

49.8 50.4 56.9 50.1 47.9 56.6 53.7 61.2 92.1 117.9 115.6 84.6 79.6 118.4 120.5 117.6

Note: LBB = Local Buckling of Brace; TFB = Tearing failure along the circumference of brace; FW = Fracture of Welding; CP = Chord Plastification.

traditional specimen with straight chord has comparatively larger ultimate strength, but the least ductility. On the other hand, the ultimate strengths of empty and concrete-filled CHS X-joints under out-of-plane bending are increased with the increase of the b ratio, and filling the concrete in the chord member cannot enhance the ultimate strengths of CHS X-joints under out-of-plane bending since most of specimens failed by Local Buckling of Brace. 3.3. Bending moment-chord deformation curves The rotations of brace members under out-of-plane bending resulted in one side of the chord member in compression, while the other side of the chord member in tension. Therefore, the inward deformations were generated at the compression side of the chord member, while the outward deformations were gener-

ated at the tension side of the chord member, which can be used to evaluate the out-of-plane flexural rigidity of the joint intersection. The bending moment (M) versus chord deformation (d) curves of typical empty CHS X-joints are plotted in Fig. 9, in which the flange indentation at the compression area of chord concave side (d1) was obtained from the readings of displacement transducer D3, the flange indentation at the tension area of chord concave side (d2) was obtained from the readings of displacement transducer D5, the flange indentation at the compression area of chord convex side (d3) was obtained from the readings of displacement transducer D6, the flange indentation at the tension area of chord convex side (d4) was obtained from the readings of displacement transducer D8, while the bending moment (M) was calculated using the axial load applied to the loading points (half of the load cell reading) multiplied by the nominal brace length (half of the distance between the ends of brace members). The flange inward indentation is defined as negative chord deformation, while the flange outward indentation is defined as positive chord deformation. It is shown from the comparison that the concave and convex deformations of all specimens under out-of-plane bending are generally symmetric in the elastic range, and the concave deformations of all specimens under out-of-plane bending developed extensively in the plastic range. On the other hand, the flange inward indentations of most of specimens are generally larger than the flange outward indentations at both chord concave side and chord convex side. It should be noted that the chord deformation curves of concrete-filled CHS X-joints could not be shown on the graphs due to the negligible chord flange indentation and chord web deflection in the ultimate limit state. The reinforcement of the chord member with concrete infill significantly enhanced the radial stiffness of chord member, which resulted in the failure of either brace members or welding material. 3.4. Bending moment-rotation curves The out-of-plane bending behaviour could be most directly reflected by the bending moment-rotation curves. Therefore, the

261

60

80

45

60

N/kN

N/kN

R. Feng et al. / Engineering Structures 145 (2017) 254–272

30 XB89

15 0

0

2.5R420

40 XB89

2.5R420F

XB89

2.5R840F

XB89

2.5R840

XB89

2.5R1260

XB89

2.5R1260F

XB89

2.5

XB89

2.5F

10

20

20

30

0

40

0

5

10

/mm

15

20

/mm

150

150

120

120

90

90

N/kN

N/kN

(a) Empty CHS X-joints with brace CHS 89×2.5 (b) Concrete-filled CHS X-joints with brace CHS 89×2.5

60 30 0

0

XB114

3.0R420

XB114

3.0R840

XB114

3.0R1260

XB114

3.0

10

20

60

XB114 XB114 XB114 XB114

30

30

40

0

0

5

/mm

(c) Empty CHS X-joints with brace CHS 114×3.0

3.0R420F 3.0R840F 3.0R1260F 3.0F 10 /mm

15

20

(d) Concrete-filled CHS X-joints with brace CHS 114×3.0

Fig. 8. Axial load-vertical displacement curves of test specimens.

Fig. 9. Bending moment-chord deformation curves.

bending moment versus rotation curves of all specimens are plotted in Fig. 10, in which the rotations include rotation angle of chord concave side (uconcave) and rotation angle of chord convex side (uconvex). The horizontal axis represents the out-of-plane rotation angle (u) between the brace and chord members, which can be calculated as uconcave = (d2  d1)/h and uconvex = (d4  d3)/h, where h is the distance between displacement transducers D3 and D5 as well as D6 and D8, and the vertical axis represents the bending moment (M) calculated using the axial load applied to the loading points (half of the load cell reading) multiplied by the nominal brace length (half of the distance between the ends of brace members). Some displacement transducers cannot measure real deformation value because of big convex deformation before failure for some

joint. So, the peak moment do not remain the same when the moment is plotted against the concave rotation or the convex rotation for some joint. It is shown from the comparison that the bending momentrotation curves of all specimens generally developed more gently with the increase of the curvature radius of chord member, which means the CHS X-joints with larger curvature radius of chord member have better out-of-plane bending behaviour. On the other hand, the rotation angles of chord concave side (uconcave) of all specimens are greater than the rotation angles of chord convex side (uconvex), except for specimen XB114
3.0, which means the chord concave side of CHS X-joints with curved chord is more easily failed under out-of-plane bending. The tearing failure along

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Fig. 10. Bending moment-rotation curves.

the circumference of brace connected to the chord convex side for specimen XB114
3.0 resulted in the larger rotation angle of chord convex side. Once again, the rotation curves of concrete-filled CHS X-joints could not be shown on the graphs due to the negligible rotation angles of chord concave side and chord convex side in the ultimate limit state.

3.5. Strain distribution curves Strain distributions at the joint intersection region were derived from the readings of three-element rosettes strain gauges, in which T1, T4, T7 and T10 were positioned on the tension side of the joint intersection, T3, T6, T9 and T12 were positioned on the compres-

R. Feng et al. / Engineering Structures 145 (2017) 254–272

sion side of the joint intersection, and T2, T5, T8 and T11 were positioned on between. The strains at the measuring points of strain gauges under different load levels of all specimens are plotted in Fig. 11, in which the horizontal axis represents the measuring points of strain gauges (as shown in Fig. 4), the vertical axis represents the strain (ei), and the dashed line represents the yield strain (ey) of the materials used to identify the material yielding. The strain (ei) could be calculated as follows:

ei

pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ¼ ðe1  e2 Þ2 þ ðe2  e3 Þ2 þ ðe3  e1 Þ2 3

263

ð1Þ

where e1, e2 and e3 are the first, second and third principal strains, respectively, which were obtained from three-element rosettes strain gauges along the joint intersection region. It is shown from the comparison that the brace member of all specimens usually yielded prior to the chord member. Most of

Fig. 11. Strain distribution curves of test specimens.

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R. Feng et al. / Engineering Structures 145 (2017) 254–272

Fig. 11 (continued)

measuring points of strain gauges on the brace member yielded in the ultimate limit state, whereas only few measuring points of strain gauges on the chord member yielded. In addition, the strains at the measuring points of strain gauges (T4-T9) on the chord member and the strains at the measuring points of strain gauges (T10-T12) at the root of brace member connected to the chord convex side for CHS X-joints with curvature radius of chord member of 420 mm are all in the elastic range of the materials in the ultimate limit state. Whereas, the measuring points of strain gauges (T1-T3)

at the root of brace member connected to the chord concave side yielded, which led to the failure of the specimens. For empty CHS X-joints, the absolute values of strains at the brace member connected to the chord concave side are generally greater than those at the brace member connected to the chord convex side, in which the measuring points of strain gauges T1 (positioned on the tension side) and T3 (positioned on the compression side) at the root of brace on concave side of chord member yielded first. In particularly for empty CHS X-joints with small cur-

R. Feng et al. / Engineering Structures 145 (2017) 254–272

265

Fig. 11 (continued)

vature radius of chord member, most of the measuring points of strain gauges at the root of brace on concave side of chord member yielded, whereas the measuring points of strain gauges at the root of brace on convex side of chord member are all in the elastic range of the materials in the ultimate limit state. Furthermore, the absolute values of strains at the chord convex side are generally greater than those at the chord concave side, in which few measuring points of strain gauges on convex side of chord member yielded. It means the brace member connected to the chord concave side

and convex side of chord member of CHS X-joints with curved chord are more easily failed under out-of-plane bending. For concrete-filled CHS X-joints, the absolute values of strains at the brace member connected to the chord concave side are generally greater than those at the brace member connected to the chord convex side, in which the measuring points of strain gauges T1 (positioned on the tension side) and T3 (positioned on the compression side) at the root of brace on concave side of chord member yielded first, whereas few measuring points of strain gauges at the

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R. Feng et al. / Engineering Structures 145 (2017) 254–272

Fig. 11 (continued)

brace member connected to the chord convex side yielded. In addition, the strains at the measuring points of strain gauges (T4-T9) on the chord member for almost all specimens are in the elastic range of the materials in the ultimate limit state due to the reinforcement of the chord member with concrete infill. 4. Comparison of test strengths with design strengths The load carrying capacities of the empty and concrete-filled CHS X-joints under out-of-plane bending obtained from the tests

(Mtest) were compared with those calculated using the design rules given in the Eurocode 3 [15] for traditional CHS X-joints with straight chord subjected to chord face failure (MCFF) and punching shear failure (MPSF), respectively, the yield out-of-plane bending moment of the brace edge (MYBE), the plastic out-of-plane bending moment of the total cross-section of the brace (MPTB) and the minimum (Mmin) of the MCFF, MPSF and MPTB, as shown in Table 5. A quantitative analysis on the joint strength with respect to the brace yield moment capacity was made in Table 5. Test strengths increased average 38.46 percentage of over-strength comparing

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R. Feng et al. / Engineering Structures 145 (2017) 254–272 Table 5 Comparison of test strengths with design strengths for test specimens. Specimen

XB89
2.5R420 XB89
2.5R840 XB89
2.5R1260 XB89
2.5 XB89
2.5R420F XB89
2.5R840F XB89
2.5R1260F XB89
2.5F XB114
3.0R420 XB114
3.0R840 XB114
3.0R1260 XB114
3.0 XB114
3.0R420F XB114
3.0R840F XB114
3.0R1260F XB114
3.0F Average

MYBE (kNm)

MPTB (kNm)

Mmin (kNm)

(Mtest-MPTB)/MPTB
100 (%)

Mtest/Mmin

6.81

3.52

4.57

3.69

11.18

7.78

10.09

6.73

36.32 37.86 55.58 36.98 31.07 54.92 46.83 67.40 14.07 46.09 43.21 4.86 -1.39 46.68 49.26 45.69 38.46

1.67 1.71 1.92 1.68 1.62 1.91 1.82 2.07 1.71 2.19 2.15 1.57 1.48 2.20 2.24 2.18 1.88

Mtest (kNm)

Eurocode 3 MCFF (kNm)

MPSF (kNm)

6.23 6.30 7.11 6.26 5.99 7.08 6.71 7.65 11.51 14.74 14.45 10.58 9.95 14.80 15.06 14.70

3.69

6.73

to the brace total cross-section yield moment by filling the chord with concrete. The strength of concrete filled joints under out-ofplane bending obtained from the tests (Mtest) is larger than the plastic out-of-plane bending moment of the total cross-section of the brace (MPTB). It should be noted that there is no design rule for CHS X-joints with curved chord, let alone concrete-filled CHS X-joints with curved chord. Therefore, the design strengths of empty CHS X-joints with curved chord under out-of-plane bending were also calculated using the design equations for traditional empty CHS X-joints with straight chord by ignoring the effect of curvature radius of chord member. The joint strengths of traditional CHS X-joints with straight chord under out-of-plane bending subjected to chord face failure (MCFF) and punching shear failure (MPSF) can be calculated using the design equations given in the Eurocode 3 [15] as follows:

M op;1;Rd ¼

f y0 t20 d1 2:7 kp =cM5 sin h1 1  0:81b

ðEurocode 3 ½15Þ

ð2Þ

It is shown from the comparison that the current design rules are quite conservative for the design of empty and concrete-filled CHS X-joints with curved and straight chord under out-of-plane bending. The conservative is generally more pronounced with the increase of the curvature radius of chord member. Furthermore, the out-of-plane flexural strengths of empty and concrete-filled CHS X-joints with curvature radius of chord member of 420 mm are all smaller than their counterparts with large curvature radius

of chord member, which means the out-of-plane flexural strengths are greatly weakened by hot-rolled bending the chord members into curvature with small radius. 5. Finite element analysis 5.1. Finite element models The general purpose finite element program ABAQUS was used for the nonlinear numerical analysis of empty and concrete-filled CHS X-joints with curved chord under out-of-plane bending. Three-dimensional eight-node solid element with additional variables relating to the incompatible modes (C3D8I) was used in this study to model the CHS brace and chord members as well as the concrete infill. The welding seams were not considered in the finite element models due to its negligible effect on the out-of-plane bending behaviour of the joints. Convergence studies were carried out to obtain the optimum finite element mesh density. The welding area along the joint interaction region are finely meshed to capture the high stress gradient, whereas the mesh size at the location away from the interest area is gradually coarse in order to save computational cost. The typical finite element mesh generations are shown in Fig. 12a and b for empty and concrete-filled CHS X-joints, respectively. Both material and geometric nonlinearities have been taken into account in the finite element models. The bilinear material model based on the elastic modulus and

Concrete

Fig. 12. Finite element mesh of empty and concrete-filled CHS X-joints with curved chord.

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R. Feng et al. / Engineering Structures 145 (2017) 254–272 Table 7 Comparison between test and FEA results for CHS X-joints under out-of-plane bending.

y 1.0

0.5

0.0

1.0

u

/

c

x

Fig. 13. Stress-strain model used for confined concrete.

post-yield tangent modulus of steel obtained from the tensile coupon tests was used for the material modelling of steel tube, while the Von-Mises yield criterion was applied. Constitutive model of concrete used steel tube confined based on the test of mechanical properties of concrete. The Ottosen multi-linear isotropic hardening model [16,17] was adopted for the material modelling of concrete infill, in which the initial part of the multi-linear stress-strain curve represents the elastic property up to the measured concrete cube strength (fcu) of 22.3 MPa, and Poisson’s ratio (v) equals to 0.2, while the elastic modulus and uniaxial stress-strain relationship were obtained from the provisions of Chinese Code for Design of Concrete Structures (GB50010-2010) [18]. The uniaxial stress-strain curve of confined concrete can be obtained from the Chinese Code [18] as shown in Fig. 13. For x  1

Y ¼ aa x þ ð3  2aa Þx2 þ ðaa  2Þx3

ð3Þ

For x > 1

y ¼ x=ðad ðx  1Þ2 þ xÞ

ð4Þ

x ¼ e=ec

ð5Þ

Y ¼ r=fc

ð6Þ

where fc and ec are the uniaxial compressive ultimate stress and strain, respectively. aa and ad are the parameters that account for the rising and falling stage of uniaxial compressive stress-strain curve of concrete, respectively. The elastic modulus of concrete is shown in Table 6. The median value of elastic modulus can be calculated by using the linear interpolation method. 5.2. Verification of finite element models A comparison between the test and finite element analysis results was carried out in terms of the ultimate strengths, failure modes and axial load-vertical displacement curves to verify the finite element models. The comparison of the ultimate strengths of all specimens obtained from the tests and finite element analyses is shown in Table 7. Good agreement between the test and

Specimen

Test results (kN)

FEA results (kN)

Error (%)

XB89
2.5R420 XB89
2.5R840 XB89
2.5R1260 XB89
2.5 XB89
2.5R420F XB89
2.5R840F XB89
2.5R1260F XB89
2.5F XB114
3.0R420 XB114
3.0R840 XB114
3.0R1260 XB114
3.0 XB114
3.0R420F XB114
3.0R840F XB114
3.0R1260F XB114
3.0F

49.8 50.4 56.9 50.1 47.9 56.6 53.7 61.2 92.1 117.9 115.6 84.6 79.6 118.4 120.5 117.6

51.2 54.7 55.5 54.3 52.8 60.4 55.7 66.9 90.7 120.3 125.4 85.0 84.8 134.9 130.9 122.0

-3% -8% 3% -8% -9% -6% -4% -8% 2% -2% -8% -0.5% -6% -12% -8% -4%

finite element analysis results was achieved with the maximum difference of 12%. The typical failure modes of empty and concrete-filled CHS X-joints observed in the experimental investigation were also verified by the finite element models, as shown in Fig. 14a and b for local buckling of brace and chord plastification, respectively. On the other hand, the axial load-vertical displacement curves obtained from the tests and finite element analyses were also compared in Fig. 15a–d for empty and concrete-filled CHS X-joints with curved chord of the specimens ‘XB89
2.5R420’, ‘XB89
2.5R840F’, ‘XB114
3.0R1260’ and ‘XB114
3.0R1260F’, respectively. It is shown from the comparison that the finite element analysis results generally agreed well with the test results. The reason why there are clear differences between experimental and numerical results is that bond-slip between concrete and steel tube and concrete crack were not considered in FEA model. If bond-slip and concrete crack were taken into consideration, it would cost much more time on computation. Therefore, it was demonstrated that the newly developed finite element models successfully predicted the structural behaviour of empty and concrete-filled CHS X-joints with curved chord under out-ofplane bending.

5.3. Parametric study It is shown that the verified finite element models can accurately predict the strength and behaviour of empty and concretefilled CHS X-joints with curved chord under out-of-plane bending. Therefore, an extensive parametric study was carried out to investigate the effects of main influential factors, especially the curvature radius of chord member and concrete strength filled in the chord member on the out-of-plane flexural behaviour of empty and concrete-filled CHS X-joints with curved chord. A total of 120 CHS X-joints which were selected from the range of practical applications were analyzed in the parametric study. The design values of the main influential factors including the nondimensional geometric parameters b and 2c, and the curvature radius (R) of chord member and concrete strength (fcu) filled in the chord member are summarized in Table 8. The outer diameter

Table 6 Elastic modulus of concrete (GPa). Concrete strength

C15

C20

C25

C30

C35

C40

C45

C50

C55

C60

Ec

22.0

25.5

28.0

30.0

31.5

32.5

33.5

34.5

35.5

36.0

R. Feng et al. / Engineering Structures 145 (2017) 254–272

269

(a) Local buckling of brace

(b) Chord plastification Fig. 14. Comparison of test and FEA failure modes for CHS X-joints with curved chord under out-of-plane bending.

(d0) of the chord of all specimens in the parametric study was chosen as 140 mm, the chord length of all specimens in the parametric study was chosen as 600 mm, and the brace length of all specimens in the parametric study was chosen as 500 mm. The bilinear material model of steel including the elastic modulus (Es) of 206 GPa, the tensile yield stress (fy) of 235 MPa and the Poisson’s ratio (m) of 0.3 was used for the material modelling in the parametric study. The non-dimensional ultimate strength-curvature radius of chord member curves of all specimens obtained from the parametric study are compared in Fig. 16a and b for empty and concretefilled CHS X-joints with curved chord, respectively, in which the horizontal axis represents the ratio of curvature radius (R) of chord to outer diameter (d0) of chord, and the vertical axis represents the ratio of ultimate strengths (Mc) of CHS X-joints with curved chord to ultimate strengths (Ms) of traditional CHS X-joints with straight chord. It is shown from the comparison that the difference of ultimate strengths between empty and concrete-filled CHS X-joints with curved chord and traditional empty and concrete-filled CHS X-joints with straight chord are decreased with the increase of the curvature radius of chord member provided the curvature radius (R) of chord member is less than 12d0. The ultimate strengths of empty and concrete-filled CHS X-joints with curved chord are similar to those of traditional empty and concretefilled CHS X-joints with straight chord regardless of the value of

curvature radius (R) of chord member provided the curvature radius (R) of chord member is greater than 12d0. On the other hand, the effects of the non-dimensional geometric parameters b and 2c on the difference of the ultimate strengths between empty CHS Xjoints with curved chord and traditional empty CHS X-joints with straight chord are decreased with the increase of the curvature radius of chord member since the behaviour of these two types of CHS X-joints are closer to each other with the increase of the curvature radius of chord member. However, the nondimensional geometric parameters b and 2c have little influence on the difference of the ultimate strengths between concretefilled CHS X-joints with curved chord and traditional concretefilled CHS X-joints with straight chord since these two types of CHS X-joints failed by either brace members or welding material. 5.4. Proposed design equations Based on the test and FEA results, design equations were proposed by using the curve fitting technique for empty and concrete-filled CHS X-joints with curved chord under out-ofplane bending. The joint strengths of empty and concrete-filled CHS X-joints with curved chord under out-of-plane bending can be calculated using the design strengths of the corresponding tra-

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Fig. 15. Comparison of test and FEA axial load-vertical displacement curves for CHS X-joints with curved chord under out-of-plane bending.

Table 8 Design values of influential factors in the parametric study. Parameter

Design value

b 2c fcu (MPa) R (mm)

0.5 20 30 1

0.8 28 6400

40 4000

4800

3200

1.05

Mc/MS

Mc/MS

8000

1.00 0.95

=0.5,2 =0.8,2 =0.5,2 =0.8,2

0.90

=28 =28 =20 =20

50 1200

1600

800

700

600

1.00 0.95 =0.5,2 =0.8,2 =0.5,2 =0.8,2

0.90

=28 =28 =20 =20

0.85

0.85 0.80

2400

0.80 0

10

20

30

40

50 60 R/d0

0

10

20

30

40

50

60 R/d0

Fig. 16. Non-dimensional ultimate strength-curvature radius of chord member curves in the parametric study.

ditional CHS X-joints with straight chord multiplied by a correction factor w, which mainly depends on the geometric parameters b and 2c as well as the curvature radius of chord member (R) and concrete filled in the chord member. The proposed design equations were derived from the regression analysis by using Matlab. Therefore, the joint strengths of empty and concrete-filled CHS X-joints with curved chord can be calculated as follows:

M op;e ¼ we  M op

ð7Þ

M op;c ¼ wc  M op

ð8Þ

where we and wc are the correction factors for empty and concretefilled CHS X-joints with curved chord, respectively, which can be calculated as follows:

8   < ðR=d Þ14 1 þ ðb0:9Þ2 ðR=d0 6 12Þ 0 b we ¼ : ð1:5  bÞc0:4 ðR=d0 > 12Þ

8 pffiffi   < c ðR=d Þ14 1 þ ðb0:9Þ2 ðR=d0 6 12Þ 0 3 b wc ¼ : 1 ð1:5  bÞc0:9 ðR=d0 > 12Þ 3

ð9Þ

ð10Þ

R. Feng et al. / Engineering Structures 145 (2017) 254–272 Table 9 Comparison of FEA results with design strengths for empty and concrete-filled CHS X-joints with curved chord under out-of-plane bending. A total of 120 CHS X-joints with curved chord

Empty CHS X-joints

Concrete-filled CHS X-joints

Max Min Mean COV

1.03 0.73 0.91 0.005

1.04 0.72 0.90 0.006

out-of-plane bending, respectively. Therefore, the proposed design equations were verified to be accurate and reliable for empty and concrete-filled CHS X-joints with curved chord under out-ofplane bending. 6. Conclusions An experimental investigation was conducted in this study on the static behaviour of empty and concrete-filled CHS X-joints with curved chord under out-of-plane bending. The joint strengths, failure modes, local deformations and strain distributions of all specimens were reported. In addition, the corresponding finite element analysis was also performed and the validated finite element models were used for the parametric study to evaluate the effects of main influential factors on the behaviour of empty and concretefilled CHS X-joints with curved chord under out-of-plane bending. Based on the experimental and numerical investigations, the following conclusions can be drawn:

12

Mu/kN·m

271

10 8 6 4 2 0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0

0.2

0.4

0.6

0.8

1.0

n=N0/NPL,0 Fig. 17. Out-of-plane bending moment strength-chord axial stress function curves of XB114
3.0.

and Mop is the design strengths of the traditional CHS X-joints with straight chord under out-of-plane bending, which can be obtained from the current CIDECT code equation [19] as follows: For chord punching shear: 2

M op ¼

f y0 t 0 d1 3 þ sin h1 pffiffiffi  =cM5 4 sin h1 3

ð11Þ

For chord plastification:

f y0 t20 d1 =cM5 sin h1

ð12Þ

 1þb c0:15 1  0:7b

ð13Þ

M op ¼ Q u Q f  Q u ¼ 1:3

Q f ¼ ð1  jnjÞC1 n¼

N0 M0 þ Npl;0 M pl;0

ð14Þ in connecting face

ð15Þ

C 1 ¼ 0:45  0:25b in chord compression stress

ð16Þ

C 1 ¼ 0:20 in chord tension stress

ð17Þ

The design strengths (Mop,e and Mop,c) of empty and concretefilled CHS X-joints with curved chord under out-of-plane bending calculated using Eqs. (7) and (8), respectively, were compared with the FEA results, as shown in Table 9. Chord stress function n is considered in Eq. (12). With the increase of compression or tension in chord the ultimate out-of-plane bending moment of X-joints decreased, as shown in Fig. 17. Both compression and tension in chord decreased the strength of CHS X-joints under out-of-plane bending. A good agreement was obtained with the mean values of FEA strength-to-design strength ratios of 0.91 and 0.90, and the corresponding coefficients of variation (COVs) of 0.005 and 0.006, for empty and concrete-filled CHS X-joints with curved chord under

1) The initial stiffness of empty and concrete-filled CHS Xjoints with identical cross-section dimensions but different curvature radii of chord member are generally similar. Furthermore, the ultimate strengths of empty and concretefilled CHS X-joints under out-of-plane bending are increased with the increase of the b ratio, and filling the concrete in the chord member cannot enhance the ultimate strengths of CHS X-joints under out-of-plane bending. 2) The concave and convex deformations of all specimens under out-of-plane bending are generally symmetric in the elastic range, and the concave deformations of all specimens under out-of-plane bending developed extensively in the plastic range. In addition, the flange inward indentations of most of specimens are generally larger than the flange outward indentations at both chord concave side and chord convex side. 3) The brace member of all specimens usually yielded prior to the chord member. Most of measuring points of strain gauges on the brace member yielded in the ultimate limit state, whereas only few measuring points of strain gauges on the chord member yielded. 4) The current design rules are quite conservative for the design of empty and concrete-filled CHS X-joints with curved and straight chord under out-of-plane bending. The conservative is generally more pronounced with the increase of the curvature radius of chord member. 5) The difference of ultimate strengths between empty and concrete-filled CHS X-joints with curved chord and traditional empty and concrete-filled CHS X-joints with straight chord are decreased with the increase of the curvature radius of chord member provided the curvature radius (R) of chord member is less than 12d0. The ultimate strengths of empty and concrete-filled CHS X-joints with curved chord are similar to those of traditional empty and concrete-filled CHS X-joints with straight chord regardless of the value of curvature radius (R) of chord member provided the curvature radius (R) of chord member is greater than 12d0. 6) The proposed design equations were demonstrated to be accurate and reliable for empty and concrete-filled CHS Xjoints with curved chord under out-of-plane bending.

Acknowledgements This research work was supported by the National Natural Science Foundation of China (No. 51478047). The authors are also

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thankful to Fuan Steel Structure Engineering Co., LTD for the fabrication of test specimens. The tests were conducted in Fujian Key Laboratory on Structural Engineering and Disaster Reduction at Huaqiao University. The support provided by the laboratory staff is gratefully acknowledged.

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