Tests of concrete-filled circular hollow section X-joints with curved chord under in-plane bending

Abstract

This article presents the static tests on bare and concrete-filled circular hollow section X-joints with curved chord under in-plane bending. A total of 16 specimens were fabricated by hot-rolled bending the chord members into curvature with three different radii to apply in-plane bending to the brace members, in which six specimens were tested with bare curved chord, six specimens were tested with concrete filled in the curved chord only, and four traditional bare and concrete-filled circular hollow section X-joints with straight chord were also tested for comparison. The effects of curvature radius of chord member, concrete filled in the chord member and cross-section dimension of brace member on the joint strength, and behaviour under in-plane bending were evaluated. The curvature radius of chord member generally has insignificant influence on the in-plane flexural behaviour of circular hollow section X-joints with large radius. However, the ultimate strengths of circular hollow section X-joints under in-plane bending are greatly weakened by hot-rolled bending the chord members into curvature with small radius. Furthermore, the reinforcement of filling the concrete in the chord member has insignificant influence on the in-plane flexural behaviour of circular hollow section X-joints. On the other hand, the cross-section dimension of brace member has significant effect on the ultimate strengths of circular hollow section X-joints under in-plane bending. In addition, the current design rules are quite conservative for the design of bare and concrete-filled circular hollow section X-joints with curved and straight chord under in-plane bending loading.

Keywords

circular hollow section X-joints concrete-filled curved chord in-plane bending strain distribution

Introduction

Circular hollow section (CHS) tubular structures nowadays are widely used in long-span and spatial structures, such as railway station, airport terminal, sports stadium and exhibition centre, due to their aesthetic appearance, uniform flexural rigidity and excellent performance under static and fatigue loadings. The CHS X-joint, which is fabricated by welding CHS brace members to the continuous CHS chord member, is one of the commonly used tubular connections. The chord members are usually bent into curvature with certain radius for architectural and structural purposes. Connection reinforcement is normally used when a tubular connection has an inadequate resistance and its primary hollow section members cannot be changed. One of the commonly used methods of strengthening is to fill the hollow section with concrete or grout, which is particularly appealing for architecturally exposed steelwork. Up to the authors’ knowledge, there is no design rule for CHS joints with curved chord under in-plane bending, let alone concrete-filled CHS joints with curved chord under in-plane bending.

Extensive tests and theoretical analyses have been performed on welded tubular joints subjected to in-plane bending. A large-scale tubular doubler plates reinforced T-joint under in-plane bending was tested by Hoon et al. (2001). A plastic mechanism analysis was performed by Mashiri and Zhao (2004) for welded thin-walled T-joints made up of CHS braces and square hollow section (SHS) chords under in-plane bending. The static strengths of doubler plate and collar plate reinforced CHS X-joints loaded by in-plane bending were studied by Choo et al. (2004a, 2004b). It was found that the strength enhancement provided by the doubler plate reinforcement is up to 240% for unreinforced CHS X-joints within the range of geometric parameters. The collar plate reinforcement was found to be more effective than its doubler plate counterpart for the joint strength enhancement. A design equation was derived by Lee and Gazzola (2006) for overlap tubular K-joints under in-plane bending using nonlinear regression analysis techniques. Fatigue behaviour of thin CHS-plate T-joints under cyclic in-plane bending was experimentally investigated by Mashiri and Zhao (2007). An appropriate design S-N curve was adopted for the design of thin CHS-Plate T-joints. CHS joints with different curvature chord were experimentally investigated by Tong and Wang (2007). A finite element analysis was conducted by Christitsas et al. (2007) for conventional and square bird-beak SHS joints subjected to in-plane bending. A systematic finite element study was carried out by Qian et al. (2007) on the static strengths of thick-walled CHS X-joints subjected to brace moment loadings. A new chord stress function which incorporates the effects of geometric dependency and tensile chord stress was proposed. An in-plane fatigue loading was applied by Mashiri and Zhao (2010) to the braces of SHS T-joints with concrete-filled chords. It was found that the composite SHS T-joints have better fatigue behaviour than their empty counterpart. An experimental investigation of a fatigue-cracked and pre-notched CHS X-joints fabricated from high-strength steels under in-plane bending was performed by Qian et al. (2013). Strength definition for the cracked joints imposed a significant effect on the shape of the failure assessment curve.

This research study is a further development of bare and concrete-filled CHS X-joints with curved chord that mainly focuses on the strength and behaviour of bare and concrete-filled CHS X-joints with curved chord under in-plane bending. The ultimate strengths, failure modes, joint deformations and strain distributions of bare and concrete-filled CHS X-joints with curved chord under in-plane bending are reported in this study. The effects of curvature radius of chord member and concrete infill on the ultimate strength and initial stiffness of all specimens were evaluated. Furthermore, the joint strengths obtained from the experimental investigation were compared with the design strengths calculated using the current design specifications.

Experimental study

Test specimens

The in-plane bending tests were conducted on bare and concrete-filled CHS X-joints with curved chord. A total of 16 specimens were tested by applying in-plane bending to the brace members, in which six specimens were tested with bare curved chord, six specimens were tested with concrete filled in the curved chord along its full length only, and four traditional bare and concrete-filled CHS X-joints with straight chord were also tested for comparison. Chord members of specimens were processed by hot-rolled bending into curvature. The electromagnetic induction generated by intermediate frequency bender was used to heat the CHS tubes in the radial direction with the heating width of 1.5−2.0t, where t is the thickness of the CHS tubes. Then, the CHS tubes were pushed under specified elevated temperatures and bent into curvature with specified radii followed by the water cooling.

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 one 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, 840 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. This is because the points of contraflexure on the chord due to the applied load occur sufficiently far away from the intersection region. The brace members were made of hot-rolled 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 and 89 mm, respectively, as well as the wall thickness (t₁) of 3.0 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 β = d₁/d₀, τ = t₁/t₀ and 2γ = d₀/t₀ are all summarized in Table 1, using the nomenclature defined in Figure 1 for bare and concrete-filled CHS X-joints with curved chord and traditional bare and concrete-filled CHS X-joints with straight chord.

Table 1.

Details of test specimens.

Specimen	Brace	Chord			Geometric parameter
Specimen	d ₁ × t₁ (mm)	d ₀ × t₀ (mm)	R (mm)	Concrete infill	β = d₁/d₀	τ = t₁/t₀	2γ = d₀/t₀
XB89 × 2.5R420	89 × 2.5	140 × 5.0	420	No	0.636	0.5	28
XB89 × 2.5R840			840
XB89 × 2.5R1260			1260
XB89 × 2.5			∞
XB89 × 2.5R420F			420	Yes
XB89 × 2.5R840F			840
XB89 × 2.5R1260F			1260
XB89 × 2.5F			∞
XB114 × 3.0R420	114 × 3.0		420	No	0.814	0.6
XB114 × 3.0R840			840
XB114 × 3.0R1260			1260
XB114 × 3.0			∞
XB114 × 3.0R420F			420	Yes
XB114 × 3.0R840F			840
XB114 × 3.0R1260F			1260
XB114 × 3.0F			∞

Figure 1.

Schematic diagram of test specimens.

The welding seams between brace and chord members were designed according to Chinese Code for Welding of Steel Structures (GB 50661-2011) and laid using shielded metal arc welding. The 3.5 and 4.0 mm electrodes of type E4300 with nominal 0.2% proof stress, tensile strength, and elongation of 380 MPa, 520 MPa, and 35%, respectively, were used for welding low strength carbon steel specimens (Q235 type in China). All welds consisted of two to three runs of welding to guarantee that failure of specimens occurred in the brace or chord members rather than the welds.

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 the 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.

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 and 114 mm, respectively, as well as the wall thickness (t₁) of 2.5 and 3.0 mm, respectively.

Material properties

All specimens including both brace and chord members were fabricated using Chinese Standard Q235 steel (nominal yield stress f_y = 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 centre 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 228-2002:2002, 2002). The tensile coupon tests were conducted using a Mechanical Testing & Simulation (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 (f_y), the ultimate tensile stress (f_u) and the elongation after fracture (ε_f). 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.

Table 2.

Material properties of steel tubes.

Specimen (mm)	f_y (MPa)	f_u (MPa)	f_y/f_u	ε_f (%)
CHS 140 × 5.0 (hot-rolled bending)	298	350	0.85	17.9
CHS 140 × 5.0	275	330	0.83	18.7
CHS 89 × 2.5	278	340	0.82	19.2
CHS 114 × 3.0	310	365	0.85	18.9

Hot-rolled bending could enhance the strength, hardness and wear resistance of steel tubes under appropriate heating temperature, whereas the plasticity and toughness are decreased.

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 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 50081-2002:2003, 2003). The material properties of the standard concrete cubes are summarized in Table 3, which include the elastic modulus (E_c) of 30.1 GPa, and the mean value of the measured concrete cube strength (f_cu) of 32.4 MPa.

Table 3.

Material properties of concrete.

Nominal concrete strength (MPa)	Specimen	Elastic modulus E_c (GPa)	Compressive cube strength f_cu (MPa)	Mean value f_cu (MPa)
30	C-1	30.1	31.2	32.4
	C-2		33.4
	C-3		33.6

Test procedure

All specimens were installed in the same loading machine, as shown in Figure 2(a)–(c) for end view, front view and photo, respectively. The self-balance 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 self-balance reaction frame. The compression force was applied at the end plate of vertical chord member as the loading point, while the end plates of horizontal brace members were simply supported using the steel rollers as the end supports. Thus, the in-plane bending was generated at the joint intersection region of the test specimens.

Figure 2.

Test setup: (a) end view, (b) front view and (c) photo.

Six displacement transducers (D1–D6) were used to record the displacements and deformations during the tests, in which D1 and D2 were positioned on the end plate welded to the vertical chord member to measure the vertical displacements of the loading end plate of chord member, D3 and D4 were positioned at the centre of the chord side wall to record the deflection of chord web, and D5 and D6 were positioned on the chord concave side and chord convex side, respectively, to measure the chord flange indentation, as shown in Figure 3(a) and (b) for front view and end view, respectively.

Figure 3.

Arrangement of displacement transducers: (a) front view, (b) end view and (c) photo.

Three-element rosettes strain gauges which enable strain values in three different directions at 45° interval to be measured simultaneously were used to investigate the strain distribution of each specimen under in-plane bending. Length of rosettes strain gauges is about 10 mm. The measuring capacity of rosettes strain gauges is about 30,000 µε.

A total of 12 three-element rosettes strain gauges (T1–T12) were attached along the half of brace and chord intersection region by taking the 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 Figure 4. All strain gauges were positioned roughly 15 mm away from the weld to exclude the influence of welding.

Figure 4.

Arrangement of strain gauges.

Test results

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 elephant foot buckling of brace (EBB), local buckling of brace (LBB), fracture of welding (FW) and tensile fracture of brace (TFB), as shown in Figure 5. It should be noted that all specimens were failed by either brace members or welding material, which may probably result from larger thickness of CHS chord compared to CHS braces or the reinforcement of the chord member with concrete infill, as summarized in Table 3. Furthermore, there is no damage for the concrete filled in the chord member in the ultimate limit state, which means the strengths of the empty and concrete-filled CHS X-joints are governed by the strengths of brace members rather than the joint strengths.

Figure 5.

Failure modes of test specimens: (a) elephant foot buckling of brace, (b) local buckling of brace, (c) fracture of welding and (d) tensile fracture of brace.

Axial load–vertical displacement curves

The joint deformations of all specimens are equivalent to the overall deformations of a rigid frame structure, as shown in Figure 6, due to the minimal rotations at the joint intersection region resulted from the negligible deformations of the chord member. The vertical displacement of the rigid frame structure can be calculated using the design equation as follows

RF = \frac{P a^{3}}{12 EI}

(1)

where P is the axial load applied at the end plate of vertical chord member, a is the overall length of brace member and EI is the flexural rigidity of brace member.

Figure 6.

Rigid frame structure.

The axial load (P) versus vertical displacement (Δ) curves of all specimens are plotted in Figure 7(a)–(d), (e)–(h), (i)–(l) and (m)–(p) for bare CHS X-joints with brace member of CHS 89 × 2.5, concrete-filled CHS X-joints with brace member of CHS 89 × 2.5, bare 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 vertical displacements of concave side and convex side of chord member were obtained from the readings of displacement transducers D1 and D2, respectively. It is shown from the comparison that the vertical displacements of concave side and convex side of chord member for CHS X-joints with curved chord are quite different due to its asymmetry shape, in which the vertical displacements of concave side of chord member are greater than those of convex side of chord member. Whereas the vertical displacements of both sides of chord member for traditional CHS X-joints with straight chord are similar due to its symmetric shape. On the other hand, the deformations of chord member for bare CHS X-joints are increased with the increase in the β and τ ratios, which generated the rotations at the joint intersection region. Therefore, the joint deformations of bare CHS X-joints deviated from the overall deformations of the rigid frame structure. However, the deformations of chord member for concrete-filled CHS X-joints are quite small due to its enhanced radial stiffness by filling the concrete in the chord, which restrained the rotations at the joint intersection region. Therefore, the joint deformations of concrete-filled CHS X-joints are equivalent to the overall deformations of the rigid frame structure.

Figure 7.

Axial load–vertical displacement curves of test specimens: (a) XB89 × 2.5R420, (b) XB89 × 2.5R840, (c) XB89 × 2.5R1260, (d) XB89 × 2.5, (e) XB89 × 2.5R420F, (f) XB89 × 2.5R840F, (g) XB89 × 2.5R1260F, (h) XB89 × 2.5F, (i) XB114 × 3.0R420, (j) XB114 × 3.0R840, (k) XB114 × 3.0R1260, (l) XB114 × 3.0, (m) XB114 × 3.0R420F, (n) XB114 × 3.0R840F, (o) XB114 × 3.0R1260F and (p) XB114 × 3.0F.

Axial load–chord deformation curves

The rotations of brace members under in-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 generated at the tension side of the chord member, which can be used to evaluate the in-plane flexural rigidity of the joint intersection. The axial load (P) versus chord deformation (Δ) curves of specimens XB89 × 2.5R420 and XB114 × 3.0R840 are plotted in Figure 8(a) and (b), respectively, in which the chord web deflections were obtained from the average readings of displacement transducers D3 and D4, and the flange indentations of chord concave side and chord convex side were obtained from the readings of displacement transducers D5 and D6, respectively. The flange inward indentation is defined as positive chord deformation, while the flange outward indentation and web outward deflection are defined as negative chord deformation. It should be noted that the chord deformation curves of other specimens, especially the 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.

Figure 8.

Axial load–chord deformation curves of bare CHS X-joints: (a) XB89 × 2.5R420 and (b) XB114 × 3.0R840.

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 compression 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 Figure 9, in which the horizontal axis represents the measuring points of strain gauges (as shown in Figure 4), the vertical axis represents the strain (ε_i), the dash line represents the yield strain of the materials used to identify the material yielding. The strain (ε_i) could be calculated as follows

ε_{i} = \frac{\sqrt{2}}{3} \sqrt{{(ε_{1} - ε_{2})}^{2} + {(ε_{2} - ε_{3})}^{2} + {(ε_{3} - ε_{1})}^{2}}

(2)

where ε₁, ε₂ and ε₃ are the first, second and third principal strains, respectively, which were obtained from three-element rosettes strain gauges along the joint intersection region.

Figure 9.

Strain distribution curves of test specimens: (a) XB89 × 2.5R420, (b) XB89 × 2.5R840, (c) XB89 × 2.5R1260, (d) XB89 × 2.5, (e) XB89 × 2.5R420F, (f) XB89 × 2.5R840F, (g) XB89 × 2.5R1260F, (h) XB89 × 2.5F, (i) XB114 × 3.0R420, (j) XB114 × 3.0R840, (k) XB114 × 3.0R1260, (l) XB114 × 3.0, (m) XB114 × 3.0R420F, (n) XB114 × 3.0R840F, (o) XB114 × 3.0R1260F and (p) XB114 × 3.0F.

It is shown from the comparison of strains at all measuring points of strain gauges for bare CHS X-joints that the absolute values of strains at concave side of chord member are all greater than those at convex side of chord member, in which the measuring points of strain gauges T1 and T3 at the root of brace on concave side of chord member yielded first (T1 positioned on the tension side yielded first, followed by T3 positioned on the compression side), followed by the measuring points of strain gauges T4 and T6 on the flange of concave side of chord member (T4 positioned on the tension side yielded first, followed by T6 positioned on the compression side). However, few strain gauges on convex side of chord member yielded. On the other hand, the strain distributions on both sides of chord member for traditional CHS X-joints with straight chord are symmetric due to its symmetric shape and loading and boundary conditions.

It is shown from the comparison of strains at all measuring points of strain gauges for concrete-filled CHS X-joints that the absolute values of strains at concave side of chord member are all greater than those at convex side of chord member, in which the measuring points of strain gauges (T1–T3) at the root of brace on concave side of chord member yielded first. However, few strain gauges at the root of brace on convex side of chord member yielded. On the other hand, the strains at the measuring points of strain gauges (T4–T9) on the chord member are all in the elastic range of materials in the ultimate limit state due to the reinforcement of the chord member with concrete infill.

Effects of influential factors

It is demonstrated from the tests that all specimens including bare and concrete-filled CHS X-joints with curved and straight chord failed by either brace members or welding material. The in-plane flexural behaviour of CHS X-joints depends on the curvature radius of chord member, concrete filled in the chord member and cross-section dimension of brace member. The effect of curvature radius of chord member on the strength and behaviour of bare and concrete-filled CHS X-joints was evaluated, as summarized in Table 5. It is shown from the comparison that the ultimate strengths of the CHS X-joints with curved chord are generally similar (within 10%) to those of the traditional CHS X-joints with straight chord under in-plane bending, except for specimens with curvature radius of chord member of 420 mm, whose ultimate strengths are decreased up to 27%. Therefore, the comparatively large curvature radius of chord member has insignificant influence on the in-plane flexural behaviour of CHS X-joints. The ultimate strengths of CHS X-joints under in-plane bending are greatly weakened by hot-rolled bending the chord members into curvature with small radius (Tables 4 and 5).

Table 4.

Ultimate strengths and failure modes of test specimens.

Specimen	Curvature radius of chord	Failure mode	Ultimate strength
Specimen	R (mm)	Failure mode	P_u (kN)
XB89 × 2.5R420	420	EBB	44.2
XB89 × 2.5R840	840	EBB+FW	54.4
XB89 × 2.5R1260	1260	EBB	53.1
XB89 × 2.5	∞	EBB+LBB+FW	57.1
XB89 × 2.5R420F	420	EBB	44.9
XB89 × 2.5R840F	840	EBB+LBB	51.4
XB89 × 2.5R1260F	1260	EBB+LBB	56.8
XB89 × 2.5F	∞	EBB+TFB	53.5
XB114 × 3.0R420	420	EBB	83.3
XB114 × 3.0R840	840	EBB	103.8
XB114 × 3.0R1260	1260	EBB+LBB	116.0
XB114 × 3.0	∞	EBB+LBB	113.7
XB114 × 3.0R420F	420	EBB	97.0
XB114 × 3.0R840F	840	EBB	109.6
XB114 × 3.0R1260F	1260	EBB	110.4
XB114 × 3.0F	∞	EBB	120.1

EBB: elephant foot buckling of brace; LBB: local buckling of brace; FW: fracture of welding; TFB: tensile fracture of brace.

Table 5.

Comparison of ultimate strengths between CHS X-joints with curved chord and traditional CHS X-joints with straight chord.

Bare CHS X-joints
Curvature radius of chord	Specimen	Ultimate strength	Comparison	Specimen	Ultimate strength	Comparison
R (mm)	Specimen	P_u (kN)	P_uc/P_us	Specimen	P_u (kN)	P_uc/P_us
420	XB89 × 2.5R420	44.2	0.77	XB114 × 3.0R420	83.3	0.73
840	XB89 × 2.5R840	54.4	0.95	XB114 × 3.0R840	103.8	0.91
1260	XB89 × 2.5R1260	53.1	0.93	XB114 × 3.0R1260	116.0	1.02
∞	XB89 × 2.5	57.1	1.00	XB114 × 3.0	113.7	1.00
Concrete-filled CHS X-joints
Curvature radius of chord	Specimen	Ultimate strength	Comparison	Specimen	Ultimate strength	Comparison
R (mm)		P_u (kN)	P_uc/P_us		P_u (kN)	P_uc/P_us
420	XB89 × 2.5R420F	44.9	0.84	XB114 × 3.0R420F	97.0	0.81
840	XB89 × 2.5R840F	51.4	0.96	XB114 × 3.0R840F	109.6	0.91
1260	XB89 × 2.5R1260F	56.8	1.06	XB114 × 3.0R1260F	110.4	0.92
∞	XB89 × 2.5F	53.5	1.00	XB114 × 3.0F	120.1	1.00

On the other hand, the effect of concrete filled in the chord member on the strength and behaviour of CHS X-joints with curved chord and traditional CHS X-joints with straight chord was also evaluated, as summarized in Table 6. It is shown from the comparison that the ultimate strengths of the concrete-filled CHS X-joints are generally similar (up to 16%) to those of the bare CHS X-joints under in-plane bending. Therefore, the reinforcement of filling the concrete in the chord member has insignificant influence on the in-plane flexural behaviour of CHS X-joints.

Table 6.

Comparison of ultimate strengths between bare CHS X-joints and concrete-filled CHS X-joints.

Brace	CHS 89 × 2.5
Curvature radius of chord R (mm)	420	840	1260	∞
Bare CHS X-joints	XB89 × 2.5R420	XB89 × 2.5R840	XB89 × 2.5R1260	XB89 × 2.5
Ultimate strength P_ub (kN)	44.2	54.4	53.1	57.1
Concrete-filled CHS X-joints	XB89 × 2.5R420F	XB89 × 2.5R840F	XB89 × 2.5R1260F	XB89 × 2.5F
Ultimate strength P_uf (kN)	44.9	51.4	56.8	53.5
Comparison P_uf/P_ub	1.02	0.94	1.07	0.94
Brace	CHS 114 × 3.0
Curvature radius of chord R (mm)	420	840	1260	∞
Bare CHS X-joints	XB114 × 3.0R420	XB114 × 3.0R840	XB114 × 3.0R1260	XB114 × 3.0
Ultimate strength P_ub (kN)	83.3	103.8	116.0	113.7
Concrete-filled CHS X-joints	XB114 × 3.0R420F	XB114 × 3.0R840F	XB114 × 3.0R1260F	XB114 × 3.0F
Ultimate strength P_uf (kN)	97.0	109.6	110.4	120.1
Comparison P_uf/P_ub	1.16	1.06	0.95	1.06

In addition, the effect of cross-section dimension of brace member on the strength and behaviour of bare and concrete-filled CHS X-joints with curved and straight chord was also evaluated, as summarized in Table 7. It is shown from the comparison that the cross-section dimension of brace member has significant effect on the ultimate strengths of CHS X-joints under in-plane bending, which attributes to the failure of all specimens by brace members. For bare CHS X-joints under in-plane bending, the ultimate strengths of specimens with large brace member of CHS 114 × 3.0 are enhanced up to 118% compared to those of specimens with small brace member of CHS 89 × 2.5. For concrete-filled CHS X-joints under in-plane bending, the ultimate strengths of specimens with large brace member of CHS 114 × 3.0 are enhanced up to 124% compared to those of specimens with small brace member of CHS 89 × 2.5. The enhancement of the ultimate strengths of bare CHS X-joints with larger brace member under in-plane bending is generally a little bit smaller than their concrete-filled counterparts.

Table 7.

Comparison of ultimate strengths between CHS X-joints with brace member of CHS 89 × 2.5 and CHS 114 × 3.0.

Specimen	Ultimate strength	Specimen	Ultimate strength	Comparison
Specimen	P_u (kN)	Specimen	P_u (kN)	P ₁₁₄/P₈₉
XB89 × 2.5R420	44.2	XB114 × 3.0R420	83.3	1.88
XB89 × 2.5R840	54.4	XB114 × 3.0R840	103.8	1.91
XB89 × 2.5R1260	53.1	XB114 × 3.0R1260	116.0	2.18
XB89 × 2.5	57.1	XB114 × 3.0	113.7	1.99
XB89 × 2.5R420F	44.9	XB114 × 3.0R420F	97.0	2.16
XB89 × 2.5R840F	51.4	XB114 × 3.0R840F	109.6	2.13
XB89 × 2.5R1260F	56.8	XB114 × 3.0R1260F	110.4	1.94
XB89 × 2.5F	53.5	XB114 × 3.0F	120.1	2.24

Comparison of test strengths with design strengths

The load-carrying capacities of the bare and concrete-filled CHS X-joints under in-plane bending obtained from the tests (M_test) were compared with those calculated using the design rules given in the EN 1993-1-8:2005 for traditional CHS X-joints with straight chord subjected to chord face failure (M_CFF) and punching shear failure (M_PSF), respectively, the yield in-plane bending moment of the brace edge (M_YBE), the plastic in-plane bending moment of the total cross section of the brace (M_PTB) and the minimum (M_min) of the M_CFF, M_PSF and M_PTB, as shown in Table 8. 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 bare CHS X-joints with curved chord under in-plane bending were also calculated using the design equations for traditional bare 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 in-plane bending subjected to chord face failure (M_CFF) and punching shear failure (M_PSF) can be calculated using the design equations given in the EN 1993-1-8:2005 as follows:

Chord face failure

M_{CFF} = 4.85 \frac{f_{y 0} t_{0}^{2} d_{1}}{\sin θ_{1}} \sqrt{γ} \frac{β k_{p}}{γ_{M 5}}

(3)

For n_{p} > 0 (compression) : k_{p} = 1 - 0.3 n_{p} (1 + n_{p})

(4)

For n_{p} < 0 (tension) : k_{p} = 1.0

(5)

n_{p} = \frac{(σ_{p, Ed} / f_{y 0})}{γ_{M 5}}

(6)

Punching shear failure

M_{PSF} = \frac{f_{y 0} t_{0} d_{1}^{2}}{\sqrt{3}} \frac{(1 + 3 \sin θ_{1} / 4 \sin^{2} θ_{1})}{γ_{M 5}}

(7)

where f_y₀ is the yield stress of CHS chord; t₀ is the thickness of CHS chord; d₁ is the diameter of CHS chord; θ₁ is the angle between brace and chord; β is the CHS brace to CHS chord diameter ratio; γ is the chord diameter to 2 times thickness ratio; σ_p,Ed is the value of σ_0,Ed excluding the stress due to the components parallel to the chord axis of the axial forces in the braces at that joint; γ_M₅ is the resistance factor.

Table 8.

Comparison of test strengths with design strengths for test specimens.

Specimen	M_test (kN m)	EN 1993-1-8:2005, 2005		M_YBE (kN m)	M_PTB (kN m)	M_min (kN m)	M_test/M_min
Specimen	M_test (kN m)	M_CFF (kN m)	M_PSF (kN m)	M_YBE (kN m)	M_PTB (kN m)	M_min (kN m)	M_test/M_min
XB89 × 2.5R420	5.53	7.65	6.81	3.52	4.57	4.57	1.21
XB89 × 2.5R840	6.80						1.49
XB89 × 2.5R1260	6.64						1.45
XB89 × 2.5	7.14						1.56
XB89 × 2.5R420F	5.61						1.23
XB89 × 2.5R840F	6.43						1.41
XB89 × 2.5R1260F	7.10						1.55
XB89 × 2.5F	6.69						1.46
XB114 × 3.0R420	10.41	12.55	11.18	7.78	10.09	10.09	1.03
XB114 × 3.0R840	12.98						1.28
XB114 × 3.0R1260	14.49						1.44
XB114 × 3.0	14.21						1.41
XB114 × 3.0R420F	12.13						1.20
XB114 × 3.0R840F	13.70						1.36
XB114 × 3.0R1260F	13.80						1.37
XB114 × 3.0F	15.01						1.49

It is shown from the comparison that the current design rules are quite conservative for the design of bare and concrete-filled CHS X-joints with curved and straight chord under in-plane bending. The minimum (M_min) of the M_CFF, M_PSF and M_PTB is much less than the test strengths for all specimens except for specimens with curvature radius of chord member of 420 mm, whose design strengths are comparatively closer to their test strengths since the in-plane flexural strengths are greatly weakened by hot-rolled bending the chord members into curvature with small radius.

Conclusion

An experimental investigation was conducted in this study on bare and concrete-filled CHS X-joints with curved chord under in-plane bending. Some conclusions can be drawn from the test results as follows:

The curvature radius of chord member generally has insignificant influence on the in-plane flexural behaviour of CHS X-joints with large radius. However, the ultimate strengths of CHS X-joints under in-plane bending are greatly weakened by hot-rolled bending the chord members into curvature with small radius. On the other hand, the reinforcement of filling the concrete in the chord member has insignificant influence on the in-plane flexural behaviour of CHS X-joints. In addition, the cross-section dimension of brace member has significant effect on the ultimate strengths of CHS X-joints under in-plane bending. The enhancement of the ultimate strengths of bare CHS X-joints with larger brace member under in-plane bending is generally a little bit smaller than their concrete-filled counterparts.

The vertical displacements of concave side of chord member for CHS X-joints with curved chord are greater than those of convex side of chord member. However, the vertical displacements of both sides of chord member for traditional CHS X-joints with straight chord are similar.

For bare CHS X-joints, the measuring points of strain gauges at the root of brace on concave side of chord member yielded first, followed by the measuring points of strain gauges on the flange of concave side of chord member. However, few strain gauges on convex side of chord member yielded. For concrete-filled CHS X-joints, the measuring points of strain gauges at the root of brace on concave side of chord member yielded first. However, few strain gauges at the root of brace on convex side of chord member yielded. The strains at the measuring points of strain gauges on the chord member are all in the elastic range of materials in the ultimate limit state.

Both in-plane behaviour and out-of-plane behaviour are very important for concrete-filled CHS X-joints with curved chord. The test and finite element analysis (FEA) of out-of-plane behaviour of concrete-filled CHS X-joints with curved chord have been completed in our research group.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research work was supported by the National Natural Science Foundation of China (Nos. 51278209 and 51478047).

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