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Tests of CHS-to-SHS tubular connections in stainless steel
Engineering Structures 199 (2019) 109590
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Tests of CHS-to-SHS tubular connections in stainless steel a,b,⁎
Ran Feng a b c
a
, Yuexin Liu , Jihua Zhu
c,⁎⁎
T
School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China College of Civil Engineering, Shenzhen University, Shenzhen 518060, China
A R T I C LE I N FO
A B S T R A C T
Keywords: CHS-to-SHS tubular connection Circular brace Square chord Stainless steel T-connection X-connection Y-connection
A test program was conducted in this study on hybrid tubular T-, Y- and X-connections made of circular hollow section (CHS) braces and square hollow section (SHS) chord in stainless steel. A total of 18 specimens including 4 T-, 5 Y- and 9 X-connections were tested by applying axial compression to the end of circular brace. The failure modes, failure strengths and deformation curves of all specimens were obtained from experimental investigation. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/ chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the load-carrying capacities of CHS-to-SHS tubular connections in stainless steel were carefully evaluated. Experimental results show that the initial stiffnesses and the failure strengths of hybrid tubular T-, Y- and X-connections increased with the increment of the β value, and increased with the decrement of the θ value. However, the influences of other geometrical parameters of τ and 2γ on the initial stiffnesses and the failure strengths are insignificant. Furthermore, the test strengths are compared with the nominal design strengths calculated using the design formulae of the current design specifications including CIDECT, Eurocode 3 (EC3), Australian/New Zealand Standard (AS/NZS) and Chinese Code, in which AS/NZS is the only design guideline for stainless steel structures. The comparison indicates that the design formulae of CIDECT, EC3 and Chinese Code are all conservative, in which the design formulae of EC3 are most conservative with the largest scatter of predictions. While, the design formulae of AS/NZS are generally appropriate for CHS-to-SHS tubular connections in stainless steel.
1. Introduction Tubular structures are one of the widely used structural forms employed in the on-shore and off-shore structures, in which circular, square and rectangular hollow sections (CHS, SHS and RHS) are the most commonly used tubes in tubular structures. The tubular connections at the intersection of tubular members are the most critical components govern the failure of tubular structures. There are various forms of tubular connections in connection of various shapes of tubular members, in which the CHS tubular connection was formed at the intersection of CHS tubes, the SHS or RHS tubular connection was formed at the intersection of SHS or RHS tubes, and the hybrid tubular connection was formed at the intersection of CHS and SHS or RHS tubes. It is worth noting that the CHS-to-SHS or RHS tubular connection fabricated from CHS (circular) brace members and SHS (square) or RHS (rectangular) chord member exhibits some unique advantages. Compared to the CHS tubular connection, no complex intersecting line
⁎
cutting is required for the circular brace members of this form of hybrid tubular connection. Compared to the SHS or RHS tubular connection, better fatigue life can be achieved due to less stress concentrations occurred at this form of hybrid tubular connection. Nowadays, stainless steel is being used increasingly for structural purposes because of its advantages over carbon steel, such as attractive appearance, better corrosion resistance, excellent durability, ease of maintenance and low cost in service life. However, design guidelines for stainless steel tubular structures are really rare, especially in China, the increasing use of stainless steel tubes in tubular structures and the lack of researches on stainless steel tubular connections are in sharp contrast. The behaviour of carbon steel tubular connections were extensively investigated and the design formulae of connection resistances were given in different design specifications. The researches were ever performed on tubular T-, Y- and X-connections in carbon steel at various loading conditions of static loading [1], combined static loading actions [2] and fatigue loading [3,4], as well as chord preload at elevated
Corresponding author at: School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China. Corresponding author. E-mail addresses: [email protected] (R. Feng), [email protected] (J. Zhu).
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https://doi.org/10.1016/j.engstruct.2019.109590 Received 6 April 2019; Received in revised form 16 August 2019; Accepted 25 August 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Structures 199 (2019) 109590
R. Feng, et al.
Notation
CIDECT Nominal design strength obtained from design formulae of EC3 Nmax Maximum connection strength NTest Test strength N1%b0 Connection strength at a chord deformation of 1%b0 N3%b0 Connection strength at a chord deformation of 3%b0 Qf, kn, ψn Influential factor for chord stress in the connecting face t0 Wall thickness of chord t1 Wall thickness of brace β Brace diameter/chord width ratio (d1/b0) εf Elongation after fracture γM5 Partial safety factor 2γ Chord width/thickness ratio (b0/t0) φ Strength reduction factor θ Inclined angle between brace and chord σu Ultimate tensile stress σ0.2 0.2% tensile proof stress τ Brace/chord thickness ratio (t1/t0) ϕ Resistance factor NnEC
b0 d1 E f fb, fk fy0 L0 L1 NA/N NCC NCI NEC NnA/N NnCC NnCI
Outer width of square chord Outer diameter of circular brace Young’s modulus Design value of compression, tension and flexural strength Flexural buckling stress of chord web Yield stress of chord (0.2% tensile proof stress) Overall length of chord Overall length of brace Design strength obtained from design formulae of AS/NZS Design strength obtained from design formulae of Chinese Code Design strength obtained from design formulae of CIDECT Design strength obtained from design formulae of EC3 Nominal design strength obtained from design formulae of AS/NZS Nominal design strength obtained from design formulae of Chinese Code Nominal design strength obtained from design formulae of
steel tubular connections in both ultimate and serviceability limit states. Since 2008, a series of researches were conducted by Feng and Young [13–18] on SHS and RHS tubular T- and X-connections in stainless steel under static loading. The experimental, numerical and theoretical analyses were performed to evaluate the effects of critical parametric variables. Reasonable design guidelines were provided for the failure criteria, connection strengths and stress concentrations of stainless steel tubular connections. However, few studies were reported on hybrid tubular connections, let alone hybrid tubular connections in stainless steel. The previous literatures include some researches on CHS-to-SHS tubular connections with circular brace welded to square
temperature [5]. Furthermore, the researches were also performed on carbon steel tubular connections reinforced with concrete infill [6], doubler plate [7,8] and fiber reinforced polymer (FRP) [9,10]. Whereas, the researches on stainless steel tubular connections are relatively few, and the design rules for load-carrying capacities of stainless steel tubular connections are scarce. In 2001, the experimental work was conducted by Rasmussen et al. [11,12] on SHS and CHS tubular X- and K-connections in stainless steel, respectively. The specimens were tested in compression and tension with different geometrical parameters to obtain the failure modes and connection strengths and deformations. Design recommendations were given for stainless
(a) T-connection
(b) Y-connection
(c) X-connection ( =90°)
(d) X-connection ( =45°)
Fig. 1. Schematic diagrams of different forms of tubular connections. 2
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of its outer diameter to prevent the premature overall buckling of circular brace prior to the connection failure. All specimens were precisely fabricated with the axes of braces passing through the center of chord axis. The manual arc welding with the input voltage of 380 V, the output voltage of 24–28 V and the current of 180-200A was employed for the fabrication, while the stainless steel electrode type HOCr20Ni10Ti with the nominal diameter of 3.2 mm and the groove size of 3 × 3 mm was used for welding. The measured specimen sizes are summarized in Table 1, which also include the key geometrical parameters of β ranged from 0.54 to 0.88, τ ranged from 0.75 to 1.03, 2γ of 50 and θ of 45° and 90°.
chord [19–21] and SHS-to-H tubular connections with SHS brace welded to H-shaped chord [22]. Nevertheless, the aforementioned studies on hybrid tubular connections mainly focused on carbon steel materials. Based on the authors' knowledge, no research was ever conducted on hybrid tubular connections in stainless steel. An experimental investigation was conducted in this study on CHSto-SHS tubular T-, Y- and X-connections fabricated from circular braces and square chord in stainless steel. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the axial compressive capacities of hybrid tubular connections in stainless steel were evaluated. The test strengths are compared with the nominal design strengths calculated using the design formulae of the current design specifications including CIDECT [23], Eurocode 3 (EC3) [24], Australian/New Zealand Standard (AS/NZS) [25] and Chinese Code [26], in which CIDECT [23], EC3 [24] and Chinese Code [26] are applicable to carbon steel structures only, while AS/NZS [25] provides the design guidelines for stainless steel structures.
2.2. Labelling system The labelling system of the specimens is established based on the connection form and cross-section sizes of circular brace and square chord. For instance, the labels ‘T-C150 × 3-B108 × 3’, ‘Y-C150 × 3B108 × 3-R’ and ‘X-C150 × 3-B108 × 3-45°’ define the hybrid tubular connections as follows:
• The first letter ‘T’, ‘Y’ and ‘X’ indicates T-, Y- and X-connection, respectively. • The second part of the labelling system represents the cross-section
2. Experimental work 2.1. Connection specimens According to the previous researches on hybrid tubular connections, there are three main factors that govern the failure modes and failure strengths of hybrid tubular connections, which include (1) the brace diameter/chord width ratio (β = d1/b0); (2) the brace/chord thickness ratio (τ = t1/t0); (3) the chord width/thickness ratio (2γ = b0/t0). In addition, the inclined angle (θ) between brace and chord also affects the failure strengths of hybrid tubular connections. There are 18 hybrid tubular connections in stainless steel in the test program, which include 4 T-, 5 Y- and 9 X-connections (5 X-connections with θ of 90° and 4 Xconnections with θ of 45°) with the schematic diagrams displayed in Fig. 1. The cross-section sizes of the square chord are SHS 150 × 3 and SHS 200 × 4 having the outer width (b0) of 150 and 200 mm and wall thickness (t0) of 3 and 4 mm, respectively, while the cross-section sizes of the circular brace are CHS 108 × 3 and CHS 133 × 3 having the outer diameter (d1) of 108 and 133 mm and wall thickness (t1) of 3 mm, respectively. The overall length of square chord (L0) is roughly 6 times of its outer width to ensure that the stress distributions at the tubular connections are free from the influence of the boundary conditions of square chord. The overall length of circular brace (L1) is around 3 times
• • •
sizes of square chord with the outer width and wall thickness of 150 and 3 mm, respectively. The third part of the labelling system represents the cross-section sizes of circular brace with the outer diameter and wall thickness of 108 and 3 mm, respectively. For X-connection, in particular, the notation ‘45°’ indicates that the inclined angle between brace and chord is 45°. If this notation is not shown in the labelling system, it means that the inclined angle between brace and chord is 90°. The letter ‘R’ at the end of the labelling system indicates the repeated specimen.
2.3. Mechanical properties The circular brace and square chord of all specimens were made from austenitic stainless steel AISI 304. The tensile coupon tests were conducted to obtain the mechanical properties of the stainless steel SHS and CHS tubes, from which the coupon specimens were extracted at the locations with a quarter and semi-perimeter away from the seam weld, as displayed in Fig. 2. The coupon specimens were prepared and tested
Table 1 Measured specimen sizes and geometrical parameters of hybrid tubular connections in stainless steel. Specimen
T-C150 × 3-B108 × 3 T-C150 × 3-B133 × 3 T-C200 × 4-B108 × 3 T-C200 × 4-B133 × 3 Y-C150 × 3-B108 × 3 Y-C150 × 3-B108 × 3-R Y-C150 × 3-B133 × 3 Y-C200 × 4-B108 × 3 Y-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3 X-C150 × 3-B133 × 3 X-C150 × 3-B133 × 3-R X-C200 × 4-B108 × 3 X-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3-45° X-C150 × 3-B133 × 3-45° X-C200 × 4-B108 × 3-45° X-C200 × 4-B133 × 3-45°
Chord (mm)
Brace (mm)
Geometrical parameter
b0
t0
L0
d1
t1
L1
β
τ
2γ
150.23 149.99 200.15 199.79 150.57 150.05 149.80 199.56 199.44 149.93 149.81 149.80 199.90 199.44 150.05 149.71 200.06 199.58
3.014 3.022 3.957 3.815 2.906 2.991 3.000 3.949 3.993 2.960 2.966 2.958 3.971 3.975 3.007 2.956 3.970 4.038
900 900 1200 1200 900 900 900 1200 1200 900 900 900 1200 1200 900 900 1200 1200
108.43 132.08 108.83 131.23 108.29 108.32 131.72 108.39 132.16 108.39 131.76 131.83 108.42 131.44 107.86 132.12 108.50 131.61
3.044 3.036 3.094 2.884 2.845 2.792 3.046 3.044 3.031 3.048 3.001 2.999 3.065 3.016 2.828 2.995 3.058 3.032
325 400 325 400 325 325 400 325 400 325 400 400 325 400 325 400 325 400
0.72 0.88 0.54 0.66 0.72 0.72 0.88 0.54 0.66 0.72 0.88 0.88 0.54 0.66 0.72 0.88 0.54 0.66
1.01 1.00 0.78 0.76 0.98 0.93 1.02 0.77 0.76 1.03 1.01 1.01 0.77 0.76 0.94 1.01 0.77 0.75
49.84 49.63 50.58 52.37 51.81 50.17 49.93 50.53 49.95 50.65 50.51 50.64 50.34 50.17 49.90 50.65 50.39 49.43
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Table 2 Mechanical properties of stainless steel tubes.
(a) SHS tube
(b) CHS tube
Section
E (MPa)
σ0.2 (MPa)
σu (MPa)
εf (%)
σ0.2/σu
□150 × 3 □200 × 4 ○108 × 3 ○133 × 3
207,009 188,370 232,622 229,172
430.27 423.71 441.15 433.96
780.20 758.11 750.12 753.36
57.34 54.34 54.52 63.17
0.55 0.56 0.59 0.58
include the Young’s modulus (E), the yield stress (σ0.2) and the ultimate stress (σu) of the material, and the elongation after fracture (εf).
Fig. 2. Locations of coupon specimens for SHS and CHS tubes.
2.4. Test setup
according to the design guidelines of Chinese Code [27]. A 100 kN capacity SANS electronic universal testing machine was used for the tensile coupon tests with the strain gauges being attached at the midlength of both sides of the coupon specimens for the real-time measurements. The full testing curves of stainless steel material were then obtained by using the displacement control in the tests with the applied loads and strains being recorded by the data acquisition equipment. The complete static stress-strain curves of stainless steel SHS and CHS tubes are shown in Fig. 3, which exhibit the distinct nonlinearity and rounded curve of stainless steel material without clear yield plateau compared to carbon steel material. The mechanical properties of stainless steel SHS and CHS tubes with the average values for all coupon specimens in the tensile coupon tests are listed in Table 2, which
The compression tests were conducted on all specimens by using a 50 T loading capacity hydraulic jack. Prior to axial loading, the hybrid tubular connections should be installed in the loading devices accurately with the axes of hydraulic jack, load cell and brace members of the specimens being coaxial in the vertical direction. The reaction frame fixed on the ground floor was movable to accommodate different sizes of connection specimens. The test setup of different forms of CHSto-SHS tubular connections in stainless steel is given in Fig. 4. For hybrid tubular T- and Y-connections, the hydraulic jack was vertically placed on the top end plate of circular brace to apply axial compression with a load cell placed in between to monitor the applied loads. Both ends of the square chord were pin-connected to the bottom
Fig. 3. Stress-strain curves of stainless steel SHS and CHS tubes. 4
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(a) T-connection
(b) Y-connection
(c) X-connection ( =90°)
(d) X-connection ( =45°) Fig. 4. Test setup of hybrid tubular connections in stainless steel.
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For hybrid tubular X-connections with θ of 90° as illustrated in Fig. 7, the chord flange indentations were captured by four displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the edge faces of circular braces. For hybrid tubular X-connections with θ of 45° as illustrated in Fig. 8, the chord flange indentations were captured by two displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the root of upper and lower circular braces, respectively.
supports by the high strength steel hinges, which were fixed on the ground floor by anchor bolts. Hence, the boundary conditions that both ends of the square chord could rotate along the in-plane direction in the compression tests were effectively implemented. Unlike hybrid tubular T- and Y-connections, both ends of the square chord of hybrid tubular X-connections are free. The hydraulic jack was vertically placed on the top end plate of upper brace member to apply axial compression with a load cell placed in between to monitor the applied loads. While, the bottom end plate of lower brace member was bolted on a fixed-ended spherical bearing, which was specially designed to ensure that the loading application on hybrid tubular X-connections was pure axial compression without bending moment. Prior to axial loading, the specially designed spherical bearing was free to rotate without any restraint. The hydraulic jack was slowly extended to achieve the full contact among the reaction frame, the hydraulic jack, the load cell and the hybrid tubular connections until an initial load of 1–3 kN was reached. After that, the rotation of the spherical bearing was restrained by both horizontal and vertical bolts, which became a fixed-ended bearing.
2.6. Testing procedure The compression tests were conducted by using the multi-stage loading procedure for all specimens, which were loaded monotonically first by load control prior to the reach of the ultimate strengths and followed by displacement control in the post-ultimate stage. The load level of each loading stage in the load control procedure was estimated to be 10% of the ultimate strengths with the time interval of 2 mins. The displacement level of each loading stage in the displacement control procedure was roughly 1–3 mm with the time interval of 2 mins. The readings of load cell and displacement transducers were collected by the data acquisition equipment when the compression force was stable. The tests were stopped when the hybrid tubular connections severely damaged or generated excessive deformations.
2.5. Arrangement of displacement transducers The arrangements of displacement transducers in the compression tests are displayed in Figs. 5–8 for CHS-to-SHS tubular T-, Y- and Xconnections in stainless steel, respectively, in which, two displacement transducers located at the top end plate of circular brace diagonally were used to measure the axial displacements, while another two displacement transducers positioned at the center of chord webs were used to record the lateral deformations, from which the chord web deflections of all specimens were determined. For hybrid tubular T-connections as illustrated in Fig. 5, the chord flange indentations were captured by four displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the edge faces of circular brace. While, another three displacement transducers were evenly placed at the bottom flange of square chord with a quarter-span interval to record the vertical deflections of square chord along the longitudinal direction, from which the bending curvatures of square chord during the tests were obtained. For hybrid tubular Y-connections as illustrated in Fig. 6, the chord flange indentations were captured by two displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the root of circular brace and mid-span of square chord, respectively. While, another two displacement transducers were placed at the bottom flange and located at the quarter-span of square chord. Hence, a total of three displacement transducers were arranged evenly at the bottom flange of square chord with a quarter-span interval to record the vertical deflections of square chord along the longitudinal direction, from which the bending curvatures of square chord during the tests were obtained.
3. Test results and discussions 3.1. Failure modes The observed failure modes of chord face plastification and chord side wall failure are presented in Figs. 9–12 for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel, respectively, which are also listed in Table 3 for all specimens, except for the specimen X-C150 × 3B133 × 3–45° that subjected to premature failure. The failure modes of hybrid tubular connections with circular braces and square chord in stainless steel can be roughly classified into two categories according to the brace diameter/chord width ratio (β) as follows: (1) Chord face plastification: This failure mode usually occurred for hybrid tubular connections with the β value ranged from 0.6 to 0.8. The plastic zone of chord flange was fully developed with the occurrence of the stress redistribution, which resulted in the failure of the chord face. (2) Chord side wall failure: This failure mode usually occurred for hybrid tubular connections with the β value close to 1. The loads applied to the braces were transmitted directly to the chord webs, which eventually resulted in the chord side wall failure. It is found from Table 3 that most of the specimens failed by chord
(a) Front view
(b) Top view
Fig. 5. Arrangement of displacement transducers for tubular T-connections. 6
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(a) Front view
(b) Top view
Fig. 6. Arrangement of displacement transducers for tubular Y-connections.
(a) Front view
(b) Top view
Fig. 7. Arrangement of displacement transducers for tubular X-connections (θ = 90°).
(a) Front view
(b) Top view
Fig. 8. Arrangement of displacement transducers for tubular X-connections (θ = 45°).
the chord flange. While, some other specimens of T-C150 × 3-B133 × 3, Y-C150 × 3B133 × 3, X-C150 × 3-B133 × 3 and X-C150 × 3-B133 × 3-R failed by chord side wall. The compression forces were mainly undertaken by chord webs, which resulted in the slight lateral convex deformations of chord webs. By increasing the applied loads, the lateral convex deformations of chord webs further developed, which demonstrated the distinct characteristics of chord side wall failure.
face plastification since their β values are within the range of 0.6–0.8. At the early stage of loading, the concave and convex deformations generated at the chord flange and chord webs, respectively, simultaneously. The connection strengths relied on the bending and shear capacity of chord flange to take the applied loads as well as the bearing capacity of chord webs to transmit the applied loads. The membrane force in the chord flange was not formed, while the chord webs were in the combination of compression and bending. By increasing the applied loads, the region produced the maximum stresses first yielded and gradually became a plastic zone, while the membrane force in the chord flange gradually developed, which resulted in the further increase of the compression forces. The large deformations of chord flange and webs prior to the chord face failure caused the stress redistribution in
3.2. Deformation curves The deformation curves of axial load versus axial displacement, axial load versus chord flange indentation and axial load versus chord 7
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(a) Chord face plastification
(b) Chord side wall failure Fig. 9. Failure modes of tubular T-connections.
(a) Chord face plastification
(b) Chord side wall failure Fig. 10. Failure modes of tubular Y-connections. 8
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(a) Chord face plastification
(b) Chord side wall failure Fig. 11. Failure modes of tubular X-connections (θ = 90°).
3.3. Failure strengths
web deflection are illustrated in Figs. 13–16 for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel, respectively. In the testing curves, the convexity is defined as positive deformation, while the concavity is defined as negative deformation. It is found from Figs. 13–16 that the deformation curves of hybrid tubular connections with the β value of 0.88 exhibit the clear peak load, whereas there is no clear peak load in the deformation curves of hybrid tubular connections with the β value less than 0.88, which may attribute to the post-yield response caused by the membrane force in the chord flange and strain hardening property of stainless steel material. Furthermore, the initial stiffnesses of hybrid tubular connections increased with the increment of the β value, but insignificantly influenced by other geometrical parameters of τ and 2γ. This may attribute to the increase of the brace stiffness with the increment of the β value, whereas the variations of the τ and 2γ designed in the tests were limited.
It is shown from Figs. 13–16 that the deformation curves of most of the specimens do not have the clear peak load. Hence, the failure strengths of hybrid tubular connections were determined according to the recommendations of Lu et al. [28] with the results listed in Table 3. For the hybrid tubular connections with no clear peak load, the failure strengths were determined as the minimum value of 1.5 N1%b0 and N3%b0, where N1%b0 and N3%b0 are the connection strengths at the chord deformations of 1%b0 and 3%b0, respectively. For the hybrid tubular connections with clear peak load, the failure strengths were determined as the minimum value of Nmax and N3%b0. The influences of the key geometrical parameters on the failure strengths of hybrid tubular connections were investigated in Fig. 17. It is found that the failure strengths of hybrid tubular connections increased with the increment of the β value, which resulted in the change of the failure modes. For the hybrid tubular connections with small β value, the loads applied to the
Chord face plastification Fig. 12. Failure modes of tubular X-connections (θ = 45°). 9
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Table 3 Test strengths and comparison with nominal design strengths for hybrid tubular connections in stainless steel. Specimen
T-C150 × 3-B108 × 3 T-C150 × 3-B133 × 3 T-C200 × 4-B108 × 3 T-C200 × 4-B133 × 3 Y-C150 × 3-B108 × 3 Y-C150 × 3-B108 × 3-R Y-C150 × 3-B133 × 3 Y-C200 × 4-B108 × 3 Y-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3 X-C150 × 3-B133 × 3 X-C150 × 3-B133 × 3-R X-C200 × 4-B108 × 3 X-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3-45° X-C150 × 3-B133 × 3-45° X-C200 × 4-B108 × 3-45° X-C200 × 4-B133 × 3-45° Mean COV
β
0.72 0.88 0.54 0.66 0.72 0.72 0.88 0.54 0.66 0.72 0.88 0.88 0.54 0.66 0.72 0.88 0.54 0.66
Test result
Comparison
Failure mode
NTest (kN)
NTest/NnCI
NTest/NnEC
NTest/NnA/N
NTest/NnCC
A B A A A A B A A A B B A A A — A A
42.28 74.71 53.82 66.65 61.24 60.02 119.31 68.51 113.98 38.92 85.17 80.34 48.03 53.06 68.92 — 72.65 102.32
1.08 1.20 1.25 1.28 1.02 0.95 1.16 1.01 1.23 1.03 1.47 1.39 1.11 0.94 1.08 — 1.06 1.08 1.14 0.148
1.20 1.34 1.39 1.42 1.14 1.05 1.29 1.13 1.37 1.15 1.63 1.55 1.23 1.04 1.19 — 1.18 1.21 1.27 0.165
0.98 0.83 1.13 1.15 0.92 0.85 0.77 0.91 1.11 0.93 0.98 0.93 1.00 0.85 0.97 — 0.96 0.97 0.96 0.104
1.20 1.03 1.39 1.43 1.14 1.05 1.01 1.12 1.36 1.15 1.31 1.24 1.23 1.04 1.20 — 1.18 1.20 1.19 0.126
Note: A = Chord face plastification; B = Chord side wall failure.
braces were transmitted to the chord flange, which caused the development of the large deformations and the membrane force in the chord flange and eventually resulted in the failure of the chord face. The increment of the β value enhanced the brace stiffness, which transmitted the applied loads from the chord flange to the chord webs and eventually resulted in the combination of chord face failure and chord side wall failure. Therefore, the failure strengths of hybrid tubular connections were enhanced. The comparison also shows that the failure strengths of hybrid tubular Y-connections are larger than those of hybrid tubular T-connections with the same geometrical sizes. In addition, the failure strengths of hybrid tubular X-connections with θ of 45° are larger than those of hybrid tubular X-connections with θ of 90° with the same geometrical sizes. Therefore, the failure strengths of hybrid tubular connections increased with the decrement of the θ value. This may attribute to the smaller vertical loads transmitted to the chord flange and webs with the decrement of the θ value.
4. Design guidelines 4.1. General Researches on carbon steel tubular connections are relatively mature. Various design guidelines are available for carbon steel tubular connections. However, studies on stainless steel tubular connections are rare. This paper introduces four different design guidelines namely CIDECT [23], Eurocode 3 [24], Australian/New Zealand Standard (AS/ NZS) [25] and Chinese Code [26] to determine the load-carrying capacities of hybrid tubular connections fabricated from circular braces and square chord. Among these design guidelines, CIDECT [23], EC3 [24] and Chinese Code [26] were designed for carbon steel structures, while AS/NZS [25] was designed for stainless steel structures. The validity range of geometrical parameters in these design guidelines are presented in Table 4. It should be noted that the geometrical parameters designed in the tests are out of the validity range of those given in these design guidelines.
(a) Axial displacement
(b) Chord deformation
Fig. 13. Axial load versus chord deformation curves of tubular T-connections. 10
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(a) Axial displacement
(b) Chord deformation
Fig. 14. Axial load versus chord deformation curves of tubular Y-connections.
carrying capacities, fk is the flexural buckling stress of chord web, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. It should be noted that the load-carrying capacities need to be limited by a reduction factor of 0.9 under the condition of fy0 > 355 N/mm2.
4.2. Design formulae of CIDECT [23] This design guideline is suitable for hot-finished, cold-formed steel and cold-formed stress-relieved hollow sections. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
2β ⎛ + For β ⩽ 0.85 NCI = ⎜ (1 − β ) sin θ ⎝
2
4 ⎞ πf y0 t0 Qf 1 − β ⎟⎠ 4 sin θ
πf t0 2d For β = 1.0 NCI = ⎛ 1 + 10t0 ⎞ Qf k sin θ 4 sin θ ⎝ ⎠ For 0.85 < β < 1.0
4.3. Design formulae of EC3 [24]
(1)
This design guideline is applicable to the steel tubular structures with material grades of S235, S275, S355 and S460 that under predominantly static loading. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
(2)
Linearly interpolate between the
load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0 (chord side wall failure)
For β ⩽ 0.85 NEC =
(3)
πkn f y0 t02
⎛ 2β + 4 1 − β ⎞ 4(1 − β ) sin θ ⎝ sin θ ⎠
where Qf = 1 is the influential factor for chord stresses on the load-
(a) Axial displacement
(b) Chord deformation
Fig. 15. Axial load versus chord deformation curves of tubular X-connections (θ = 90°). 11
γM 5
(4)
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R. Feng, et al.
(a) Axial displacement
(b) Chord deformation
Fig. 16. Axial load versus chord deformation curves of tubular X-connections (θ = 45°).
For β = 1.0 NEC =
πfb t0 2d1 ⎛ + 10t0⎞ γM 5 4 sin θ ⎝ sin θ ⎠
(5)
For 0.85 < β < 1.0 Linearly interpolate between the load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0(chord side wall failure)
(6)
where kn = 1 is the influential factor for chord stresses on the loadcarrying capacities, γM5 = 1.0 is the partial safety factor, fb is the flexural buckling stress of chord web, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. It should be noted that the load-carrying capacities need to be limited by a reduction factor of 0.9 under the condition of fy0 > 355 N/mm2.
Fig. 17. Comparison of failure strengths of hybrid tubular connections with different key geometrical parameters.
4.4. Design formulae of AS/NZS [25] This design guideline provides the design rules for cold-formed stainless steel tubular structures. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be Table 4 The validity range of geometrical parameters in current design specifications. Geometrical parameter
CIDECT [23]
β = d1/b0 (for CHS brace)
β ≥ 0.1 + 0.01b0/t0 and 0.25 ≤ β ≤ 0.8
d1/t1 (for CHS brace)
Compression
Tension
Compression
Tension
For Class 1
2γ ≤ 40
For Class 1
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
c0 t0 ⩽ 33
235 f y0
d1 t1 ⩽ 50
235 f y0
d1 t1 ⩽ 70
0.4 ≤ β ≤ 0.8
235 f y0
d1 t1 ⩽ 50
and 2γ ≤ 40 For Class 2
c0 t0 ⩽ 38
235 f y1
For Class 2
For Class 2
c0 t0 ⩽ 38
EC3 [24]
θ
2γ = b0/t0 (for SHS chord)
235 f y1
and d1/t1 ≤ 50 For Class 1
AS/NZS [25]
0.4 ≤ β ≤ 0.8
and 10 ≤ 2γ ≤ 35 2γ ≤ 40
Chinese Code [26]
0.4 ≤ β ≤ 0.8
2γ ≤ 35
235 f y1
d1 t1 ⩽ 1.5
d1 t1 ⩽ 44
E f y1 235 f y1
Note: Class 1 = Cross-sections can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance; Class 2 = Crosssections can develop plastic moment resistance, but have limited rotation capacity because of local buckling; c0 = Clear width of SHS chord. 12
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EC3 [24] are most conservative with the largest value of COV. Furthermore, the design formulae of CIDECT [23] and EC3 [24] are quite conservative for the specimens subjected to the chord side wall failure. Whereas, the design formulae of AS/NZS [25] are quite unconservative for the specimens subjected to the chord side wall failure, which may attribute to the validity range of the β ratio limited by 0.85 in AS/NZS [25]. In general, the design formulae of AS/NZS [25] are appropriate for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel with the smallest value of COV.
obtained from the design formulae as follows:
For β ⩽ 0.85 NA
N
=
πf y0 t02
⎛ 2β + 4(1 − β )0.5⎞ kn ⎛ φ ⎞ 4(1 − β ) sin θ ⎝ sin θ ⎠ ⎝ 0.9 ⎠ (7)
where kn = 1 is the influential factor for chord stresses on the loadcarrying capacities, φ = 0.9 is the strength reduction factor, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, and t0 is the wall thickness of square chord. In this paper, the loadcarrying capacities of the specimens with β = 0.88 were also obtained from the design equation for hybrid tubular connections with β ≤ 0.85.
6. Conclusions A test program was conducted in this study on CHS-to-SHS tubular T-, Y- and X-connections fabricated from circular braces and square chord in stainless steel. A total of 18 specimens including 4 T-, 5 Y- and 9 X-connections were tested by applying axial compression to the end of circular brace. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the load-carrying capacities of hybrid tubular connections in stainless steel were investigated. The failure modes, failure strengths and deformation curves of all specimens were obtained. Two failure modes including chord face plastification and chord side wall failure were observed during the compression tests. The chord face plastification usually occurred for hybrid tubular connections with the β value ranged from 0.6 to 0.8. The plastic zone of chord flange was fully developed with the occurrence of the stress redistribution, which resulted in the failure of the chord face. While, the chord side wall failure usually occurred for hybrid tubular connections with the β value close to 1. The loads applied to the braces were transmitted directly to the chord webs, which eventually resulted in the chord side wall failure. Experimental results show that the initial stiffnesses and the failure strengths of hybrid tubular connections increased with the increment of the β value due to the increase of the brace stiffness. While, the failure strengths of hybrid tubular connections also increased with the decrement of the θ value, which may result from the smaller vertical loads transmitted to the chord flange and webs. However, the influences of other geometrical parameters of τ and 2γ on the initial stiffnesses and the failure strengths are insignificant. Most of the specimens failed by chord face plastification and no clear peak load was observed from the deformation curves, which may attribute to the post-yield response caused by the membrane force in the chord flange and strain hardening property of stainless steel material. Whereas, some other specimens with the large β value failed by chord side wall and the clear peak load was obtained from the deformation curves. The test strengths are compared with the nominal design strengths calculated using the design formulae of CIDECT, EC3 and Chinese Code for carbon steel tubular connections, as well as AS/NZS for stainless steel tubular connections. The comparison indicates that the design formulae of CIDECT, EC3 and Chinese Code are all conservative, in which the design formulae of EC3 are most conservative with the largest scatter of predictions. Furthermore, the design formulae of CIDECT and EC3 are quite conservative in calculating the nominal design strengths of the specimens failed by the chord side wall. Whereas, the design formulae of AS/NZS are quite unconservative for the specimens subjected to the chord side wall failure, which may attribute to the validity range of the β ratio limited by 0.85 in AS/NZS. In general, the design formulae of AS/NZS are appropriate for CHS-to-SHS tubular connections in stainless steel.
4.5. Design formulae of Chinese Code [26] This design guideline provides the most updated design rules for carbon steel structures under static or dynamic loading. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
πt02 f β ψn For β ⩽ 0.85 NCC = 1.8 ⎜⎛ + 2⎟⎞ 0.5 0.5 ⎝ (1 − β ) sin θ ⎠ 4(1 − β ) sin θ
(8)
πt0 fk d For β = 1.0 NCC = 2.0 ⎛ 1 + 5t0 ⎞ ψn sin θ 4 ⎝ ⎠ sin θ
(9)
For 0.85 < β < 1.0
Linearly interpolate between the
load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0 (chord side wall failure)
(10)
where ψn = 1 is the influential factor for chord stresses on the loadcarrying capacities, fk is the flexural buckling stress of chord web, f is the design value of compression, tension and flexural strengths of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. 5. Assessment of current design guidelines By comparing the design formulae given in the aforementioned design guidelines, it can be generally concluded that the design formulae of CIDECT [23], EC3 [24] and AS/NZS [25] are identical, while the design formulae of Chinese Code [26] are similar with a little bit different coefficients. Hence, the identical design strengths can be obtained from CIDECT [23], EC3 [24] and AS/NZS [25], while the similar design strengths can be obtained from Chinese Code [26]. The nominal design strengths were determined from the current design guidelines for comparison. In CIDECT [23], the nominal design strengths (NnCI) can be calculated from the design strengths (NCI) by dividing the resistance factor ϕ = 0.9 as NnCI = NCI/ϕ. In EC3 [24], the nominal design strengths (NnEC) can be calculated from the design strengths (NEC) by multiplying the partial safety factor γM5 = 1.0 as NnEC = NEC × γM5. In AS/NZS [25], the nominal design strengths (NnA/N) can be calculated from the design strengths (NA/N) by dividing the strength reduction factor φ = 0.9 as NnA/N = NA/N/φ. In Chinese Code [26], the nominal design strengths (NnCC) can be calculated by replacing f with fy0, where fy0 is the yield stress of square chord. The comparison of test strengths (NTest) with nominal design strengths (NnCI, NnEC, NnA/N and NnCC) determined by the design formulae of CIDECT [23], EC3 [24], AS/NZS [25] and Chinese Code [26], respectively, is summarized in Table 3. The mean values of test/nominal design strength ratios (NTest/NnCI, NTest/NnEC, NTest/NnA/N and NTest/ NnCC) are 1.14, 1.27, 0.96 and 1.19, with the coefficients of variation (COVs) of 0.148, 0.165, 0.104 and 0.126 for CIDECT [23], EC3 [24], AS/NZS [25] and Chinese Code [26], respectively. The comparison indicates that the design formulae of CIDECT [23], EC3 [24] and Chinese Code [26] are all conservative, in which the design formulae of
Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any 13
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R. Feng, et al.
nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
[9] Lesani M, Bahaari MR, Shokrieh MM. Experimental investigation of FRP-strengthened tubular T-joints under axial compressive loads. Constr Build Mater 2014;53(3):243–52. [10] Lesani M, Bahaari MR, Shokrieh MM. FRP wrapping for the rehabilitation of Circular Hollow Section (CHS) tubular steel connections. Thin-Walled Struct 2015;90:216–34. [11] Rasmussen KJR, Young B. Tests of X- and K-joints in SHS stainless steel tubes. J Struct Eng, ASCE 2001;127(10):1173–82. [12] Rasmussen KJR, Hasham AS. Tests of X- and K-joints in CHS stainless steel tubes. J Struct Eng, ASCE 2001;127(10):1183–9. [13] Feng R, Young B. Experimental investigation of cold-formed stainless steel tubular T-joints. Thin-Walled Struct 2008;46(10):1129–42. [14] Feng R, Young B. Tests and behaviour of cold-formed stainless steel tubular X-joints. Thin-Walled Struct 2010;48(12):921–34. [15] Feng R, Young B. Design of cold-formed stainless steel tubular T- and X-joints. J Constr Steel Res 2011;67(3):421–36. [16] Feng R, Young B. Design of cold-formed stainless steel tubular joints at elevated temperatures. Eng Struct 2012;35:188–202. [17] Feng R, Young B. Stress concentration factors of cold-formed stainless steel tubular X-joints. J Constr Steel Res 2013;91(12):26–41. [18] Feng R, Young B. Theoretical analysis of cold-formed stainless steel tubular joints. Eng Struct 2015;83:99–115. [19] Gandhi P, Stig B. Fatigue behavior of T-joints: Square chords and circular braces. J Struct Eng, ASCE 1998;124(4):399–404. [20] Bian LC, Lim JK. Fatigue strength and stress concentration factors of CHS-to-RHS Tjoints. J Constr Steel Res 2003;59(5):627–40. [21] Mashiri FR, Zhao XL. Plastic mechanism analysis of welded thin-walled T-joints made up of circular braces and square chords under in-plane bending. Thin-Walled Struct 2004;42(5):759–83. [22] Chen Y, Ying Wu. Behaviour of square hollow section brace-H-shaped steel chord Tjoints under axial compression. Thin-Walled Struct 2015;89:192–204. [23] CIDECT Guide No. 3. Design guide for rectangular hollow section (RHS) Joints under predominantly static loading. 2nd edition, Comité International pour le Développement et l’Étude de la Construction Tubulaire (CIDECT), Geneva, Switzerland; 2009. [24] Eurocode 3 (EC3). Design of steel structures − Part 1-8: Design of joints. European Committee for Standardization, EN 1993-1-8: 2005, CEN. Brussels, Belgium; 2005. [25] Australian/New Zealand Standard (AS/NZS). Cold-Formed Stainless Steel Structures. AS/NZS 4673: 2001, Sydney, Australia; 2001. [26] Chinese code. Code for design of steel structures. GB 50017-2017, Beijing, China; 2017. (in Chinese). [27] Chinese code. Metallic materials − Tensile testing − Part 1: Method of test at room temperature. GB/T 228.1-2010, Beijing, China, 2010. (in Chinese). [28] Lu HL, Winkel GD, Yu Y, Wardenier J. Deformation limit for the ultimate strength of hollow section joints. In: Proceedings of the sixth international symposium on tubular structures, Melbourne, Australia; 1994. p. 341–349.
Acknowledgements The authors are grateful for the financial support from National Natural Science Foundation of China (Grant No. 51528803), Natural Science Foundation of Guangdong Province of China (Grant No. 2018A030313208), State Key Laboratory of Subtropical Building Science (South China University of Technology, Grant No. 2018ZA02), and Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen Durability Center for Civil Engineering (Shenzhen University, Grant No. GDDCE 18-5). The tests were conducted in Anhui Key Lab on Structure and Material of Civil Engineering at Hefei University of Technology. The support provided by the laboratory staff is gratefully acknowledged. References [1] Zhao XL. Deformation limit and ultimate strength of welded T-joints in cold-formed RHS sections. J Constr Steel Res 2000;53(2):149–65. [2] Zhao XL, Hancock GJ. T-Joints in rectangular hollow sections subject to combined actions. J Struct Eng, ASCE 1991;117(8):2258–77. [3] Chiew SP, Lee CK, Lie ST, Ji HL. Fatigue behaviors of square-to-square hollow section T-joint with corner crack. I: Experimental studies. Eng Fract Mech 2007;74(5):703–20. [4] Lee CK, Chiew SP, Lie ST, Ji HL. Fatigue behaviors of square-to-square hollow section T-joint with corner crack. II: Numerical modeling. Eng Fract Mech 2007;74(5):721–38. [5] Shao YB, Zheng YJ, Zhao HC, Yang DP. Performance of tubular T-joints at elevated temperature by considering effect of chord compressive stress. Thin-Walled Struct 2016;98:533–46. [6] Chen Y, Feng R, Ruan XF. Behaviour of steel-concrete-steel SHS X-joints under axial compression. J Constr Steel Res 2016;122:469–87. [7] Nassiraei H, Lotfollahi-Yaghin MA, Ahmadi H. Static strength of doubler plate reinforced tubular T/Y-joints subjected to brace compressive loading: Study of geometrical effects and parametric formulation. Thin-Walled Struct 2016;107:231–47. [8] Nassiraei H, Lotfollahi-Yaghin MA, Ahmadi H. Static performance of doubler plate reinforced tubular T/Y-joints subjected to brace tension. Thin-Walled Struct 2016;108:138–52.
14
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Tests of CHS-to-SHS tubular connections in stainless steel a,b,⁎
Ran Feng a b c
a
, Yuexin Liu , Jihua Zhu
c,⁎⁎
T
School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China College of Civil Engineering, Shenzhen University, Shenzhen 518060, China
A R T I C LE I N FO
A B S T R A C T
Keywords: CHS-to-SHS tubular connection Circular brace Square chord Stainless steel T-connection X-connection Y-connection
A test program was conducted in this study on hybrid tubular T-, Y- and X-connections made of circular hollow section (CHS) braces and square hollow section (SHS) chord in stainless steel. A total of 18 specimens including 4 T-, 5 Y- and 9 X-connections were tested by applying axial compression to the end of circular brace. The failure modes, failure strengths and deformation curves of all specimens were obtained from experimental investigation. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/ chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the load-carrying capacities of CHS-to-SHS tubular connections in stainless steel were carefully evaluated. Experimental results show that the initial stiffnesses and the failure strengths of hybrid tubular T-, Y- and X-connections increased with the increment of the β value, and increased with the decrement of the θ value. However, the influences of other geometrical parameters of τ and 2γ on the initial stiffnesses and the failure strengths are insignificant. Furthermore, the test strengths are compared with the nominal design strengths calculated using the design formulae of the current design specifications including CIDECT, Eurocode 3 (EC3), Australian/New Zealand Standard (AS/NZS) and Chinese Code, in which AS/NZS is the only design guideline for stainless steel structures. The comparison indicates that the design formulae of CIDECT, EC3 and Chinese Code are all conservative, in which the design formulae of EC3 are most conservative with the largest scatter of predictions. While, the design formulae of AS/NZS are generally appropriate for CHS-to-SHS tubular connections in stainless steel.
1. Introduction Tubular structures are one of the widely used structural forms employed in the on-shore and off-shore structures, in which circular, square and rectangular hollow sections (CHS, SHS and RHS) are the most commonly used tubes in tubular structures. The tubular connections at the intersection of tubular members are the most critical components govern the failure of tubular structures. There are various forms of tubular connections in connection of various shapes of tubular members, in which the CHS tubular connection was formed at the intersection of CHS tubes, the SHS or RHS tubular connection was formed at the intersection of SHS or RHS tubes, and the hybrid tubular connection was formed at the intersection of CHS and SHS or RHS tubes. It is worth noting that the CHS-to-SHS or RHS tubular connection fabricated from CHS (circular) brace members and SHS (square) or RHS (rectangular) chord member exhibits some unique advantages. Compared to the CHS tubular connection, no complex intersecting line
⁎
cutting is required for the circular brace members of this form of hybrid tubular connection. Compared to the SHS or RHS tubular connection, better fatigue life can be achieved due to less stress concentrations occurred at this form of hybrid tubular connection. Nowadays, stainless steel is being used increasingly for structural purposes because of its advantages over carbon steel, such as attractive appearance, better corrosion resistance, excellent durability, ease of maintenance and low cost in service life. However, design guidelines for stainless steel tubular structures are really rare, especially in China, the increasing use of stainless steel tubes in tubular structures and the lack of researches on stainless steel tubular connections are in sharp contrast. The behaviour of carbon steel tubular connections were extensively investigated and the design formulae of connection resistances were given in different design specifications. The researches were ever performed on tubular T-, Y- and X-connections in carbon steel at various loading conditions of static loading [1], combined static loading actions [2] and fatigue loading [3,4], as well as chord preload at elevated
Corresponding author at: School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China. Corresponding author. E-mail addresses: [email protected] (R. Feng), [email protected] (J. Zhu).
⁎⁎
https://doi.org/10.1016/j.engstruct.2019.109590 Received 6 April 2019; Received in revised form 16 August 2019; Accepted 25 August 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Structures 199 (2019) 109590
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Notation
CIDECT Nominal design strength obtained from design formulae of EC3 Nmax Maximum connection strength NTest Test strength N1%b0 Connection strength at a chord deformation of 1%b0 N3%b0 Connection strength at a chord deformation of 3%b0 Qf, kn, ψn Influential factor for chord stress in the connecting face t0 Wall thickness of chord t1 Wall thickness of brace β Brace diameter/chord width ratio (d1/b0) εf Elongation after fracture γM5 Partial safety factor 2γ Chord width/thickness ratio (b0/t0) φ Strength reduction factor θ Inclined angle between brace and chord σu Ultimate tensile stress σ0.2 0.2% tensile proof stress τ Brace/chord thickness ratio (t1/t0) ϕ Resistance factor NnEC
b0 d1 E f fb, fk fy0 L0 L1 NA/N NCC NCI NEC NnA/N NnCC NnCI
Outer width of square chord Outer diameter of circular brace Young’s modulus Design value of compression, tension and flexural strength Flexural buckling stress of chord web Yield stress of chord (0.2% tensile proof stress) Overall length of chord Overall length of brace Design strength obtained from design formulae of AS/NZS Design strength obtained from design formulae of Chinese Code Design strength obtained from design formulae of CIDECT Design strength obtained from design formulae of EC3 Nominal design strength obtained from design formulae of AS/NZS Nominal design strength obtained from design formulae of Chinese Code Nominal design strength obtained from design formulae of
steel tubular connections in both ultimate and serviceability limit states. Since 2008, a series of researches were conducted by Feng and Young [13–18] on SHS and RHS tubular T- and X-connections in stainless steel under static loading. The experimental, numerical and theoretical analyses were performed to evaluate the effects of critical parametric variables. Reasonable design guidelines were provided for the failure criteria, connection strengths and stress concentrations of stainless steel tubular connections. However, few studies were reported on hybrid tubular connections, let alone hybrid tubular connections in stainless steel. The previous literatures include some researches on CHS-to-SHS tubular connections with circular brace welded to square
temperature [5]. Furthermore, the researches were also performed on carbon steel tubular connections reinforced with concrete infill [6], doubler plate [7,8] and fiber reinforced polymer (FRP) [9,10]. Whereas, the researches on stainless steel tubular connections are relatively few, and the design rules for load-carrying capacities of stainless steel tubular connections are scarce. In 2001, the experimental work was conducted by Rasmussen et al. [11,12] on SHS and CHS tubular X- and K-connections in stainless steel, respectively. The specimens were tested in compression and tension with different geometrical parameters to obtain the failure modes and connection strengths and deformations. Design recommendations were given for stainless
(a) T-connection
(b) Y-connection
(c) X-connection ( =90°)
(d) X-connection ( =45°)
Fig. 1. Schematic diagrams of different forms of tubular connections. 2
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of its outer diameter to prevent the premature overall buckling of circular brace prior to the connection failure. All specimens were precisely fabricated with the axes of braces passing through the center of chord axis. The manual arc welding with the input voltage of 380 V, the output voltage of 24–28 V and the current of 180-200A was employed for the fabrication, while the stainless steel electrode type HOCr20Ni10Ti with the nominal diameter of 3.2 mm and the groove size of 3 × 3 mm was used for welding. The measured specimen sizes are summarized in Table 1, which also include the key geometrical parameters of β ranged from 0.54 to 0.88, τ ranged from 0.75 to 1.03, 2γ of 50 and θ of 45° and 90°.
chord [19–21] and SHS-to-H tubular connections with SHS brace welded to H-shaped chord [22]. Nevertheless, the aforementioned studies on hybrid tubular connections mainly focused on carbon steel materials. Based on the authors' knowledge, no research was ever conducted on hybrid tubular connections in stainless steel. An experimental investigation was conducted in this study on CHSto-SHS tubular T-, Y- and X-connections fabricated from circular braces and square chord in stainless steel. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the axial compressive capacities of hybrid tubular connections in stainless steel were evaluated. The test strengths are compared with the nominal design strengths calculated using the design formulae of the current design specifications including CIDECT [23], Eurocode 3 (EC3) [24], Australian/New Zealand Standard (AS/NZS) [25] and Chinese Code [26], in which CIDECT [23], EC3 [24] and Chinese Code [26] are applicable to carbon steel structures only, while AS/NZS [25] provides the design guidelines for stainless steel structures.
2.2. Labelling system The labelling system of the specimens is established based on the connection form and cross-section sizes of circular brace and square chord. For instance, the labels ‘T-C150 × 3-B108 × 3’, ‘Y-C150 × 3B108 × 3-R’ and ‘X-C150 × 3-B108 × 3-45°’ define the hybrid tubular connections as follows:
• The first letter ‘T’, ‘Y’ and ‘X’ indicates T-, Y- and X-connection, respectively. • The second part of the labelling system represents the cross-section
2. Experimental work 2.1. Connection specimens According to the previous researches on hybrid tubular connections, there are three main factors that govern the failure modes and failure strengths of hybrid tubular connections, which include (1) the brace diameter/chord width ratio (β = d1/b0); (2) the brace/chord thickness ratio (τ = t1/t0); (3) the chord width/thickness ratio (2γ = b0/t0). In addition, the inclined angle (θ) between brace and chord also affects the failure strengths of hybrid tubular connections. There are 18 hybrid tubular connections in stainless steel in the test program, which include 4 T-, 5 Y- and 9 X-connections (5 X-connections with θ of 90° and 4 Xconnections with θ of 45°) with the schematic diagrams displayed in Fig. 1. The cross-section sizes of the square chord are SHS 150 × 3 and SHS 200 × 4 having the outer width (b0) of 150 and 200 mm and wall thickness (t0) of 3 and 4 mm, respectively, while the cross-section sizes of the circular brace are CHS 108 × 3 and CHS 133 × 3 having the outer diameter (d1) of 108 and 133 mm and wall thickness (t1) of 3 mm, respectively. The overall length of square chord (L0) is roughly 6 times of its outer width to ensure that the stress distributions at the tubular connections are free from the influence of the boundary conditions of square chord. The overall length of circular brace (L1) is around 3 times
• • •
sizes of square chord with the outer width and wall thickness of 150 and 3 mm, respectively. The third part of the labelling system represents the cross-section sizes of circular brace with the outer diameter and wall thickness of 108 and 3 mm, respectively. For X-connection, in particular, the notation ‘45°’ indicates that the inclined angle between brace and chord is 45°. If this notation is not shown in the labelling system, it means that the inclined angle between brace and chord is 90°. The letter ‘R’ at the end of the labelling system indicates the repeated specimen.
2.3. Mechanical properties The circular brace and square chord of all specimens were made from austenitic stainless steel AISI 304. The tensile coupon tests were conducted to obtain the mechanical properties of the stainless steel SHS and CHS tubes, from which the coupon specimens were extracted at the locations with a quarter and semi-perimeter away from the seam weld, as displayed in Fig. 2. The coupon specimens were prepared and tested
Table 1 Measured specimen sizes and geometrical parameters of hybrid tubular connections in stainless steel. Specimen
T-C150 × 3-B108 × 3 T-C150 × 3-B133 × 3 T-C200 × 4-B108 × 3 T-C200 × 4-B133 × 3 Y-C150 × 3-B108 × 3 Y-C150 × 3-B108 × 3-R Y-C150 × 3-B133 × 3 Y-C200 × 4-B108 × 3 Y-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3 X-C150 × 3-B133 × 3 X-C150 × 3-B133 × 3-R X-C200 × 4-B108 × 3 X-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3-45° X-C150 × 3-B133 × 3-45° X-C200 × 4-B108 × 3-45° X-C200 × 4-B133 × 3-45°
Chord (mm)
Brace (mm)
Geometrical parameter
b0
t0
L0
d1
t1
L1
β
τ
2γ
150.23 149.99 200.15 199.79 150.57 150.05 149.80 199.56 199.44 149.93 149.81 149.80 199.90 199.44 150.05 149.71 200.06 199.58
3.014 3.022 3.957 3.815 2.906 2.991 3.000 3.949 3.993 2.960 2.966 2.958 3.971 3.975 3.007 2.956 3.970 4.038
900 900 1200 1200 900 900 900 1200 1200 900 900 900 1200 1200 900 900 1200 1200
108.43 132.08 108.83 131.23 108.29 108.32 131.72 108.39 132.16 108.39 131.76 131.83 108.42 131.44 107.86 132.12 108.50 131.61
3.044 3.036 3.094 2.884 2.845 2.792 3.046 3.044 3.031 3.048 3.001 2.999 3.065 3.016 2.828 2.995 3.058 3.032
325 400 325 400 325 325 400 325 400 325 400 400 325 400 325 400 325 400
0.72 0.88 0.54 0.66 0.72 0.72 0.88 0.54 0.66 0.72 0.88 0.88 0.54 0.66 0.72 0.88 0.54 0.66
1.01 1.00 0.78 0.76 0.98 0.93 1.02 0.77 0.76 1.03 1.01 1.01 0.77 0.76 0.94 1.01 0.77 0.75
49.84 49.63 50.58 52.37 51.81 50.17 49.93 50.53 49.95 50.65 50.51 50.64 50.34 50.17 49.90 50.65 50.39 49.43
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Table 2 Mechanical properties of stainless steel tubes.
(a) SHS tube
(b) CHS tube
Section
E (MPa)
σ0.2 (MPa)
σu (MPa)
εf (%)
σ0.2/σu
□150 × 3 □200 × 4 ○108 × 3 ○133 × 3
207,009 188,370 232,622 229,172
430.27 423.71 441.15 433.96
780.20 758.11 750.12 753.36
57.34 54.34 54.52 63.17
0.55 0.56 0.59 0.58
include the Young’s modulus (E), the yield stress (σ0.2) and the ultimate stress (σu) of the material, and the elongation after fracture (εf).
Fig. 2. Locations of coupon specimens for SHS and CHS tubes.
2.4. Test setup
according to the design guidelines of Chinese Code [27]. A 100 kN capacity SANS electronic universal testing machine was used for the tensile coupon tests with the strain gauges being attached at the midlength of both sides of the coupon specimens for the real-time measurements. The full testing curves of stainless steel material were then obtained by using the displacement control in the tests with the applied loads and strains being recorded by the data acquisition equipment. The complete static stress-strain curves of stainless steel SHS and CHS tubes are shown in Fig. 3, which exhibit the distinct nonlinearity and rounded curve of stainless steel material without clear yield plateau compared to carbon steel material. The mechanical properties of stainless steel SHS and CHS tubes with the average values for all coupon specimens in the tensile coupon tests are listed in Table 2, which
The compression tests were conducted on all specimens by using a 50 T loading capacity hydraulic jack. Prior to axial loading, the hybrid tubular connections should be installed in the loading devices accurately with the axes of hydraulic jack, load cell and brace members of the specimens being coaxial in the vertical direction. The reaction frame fixed on the ground floor was movable to accommodate different sizes of connection specimens. The test setup of different forms of CHSto-SHS tubular connections in stainless steel is given in Fig. 4. For hybrid tubular T- and Y-connections, the hydraulic jack was vertically placed on the top end plate of circular brace to apply axial compression with a load cell placed in between to monitor the applied loads. Both ends of the square chord were pin-connected to the bottom
Fig. 3. Stress-strain curves of stainless steel SHS and CHS tubes. 4
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(a) T-connection
(b) Y-connection
(c) X-connection ( =90°)
(d) X-connection ( =45°) Fig. 4. Test setup of hybrid tubular connections in stainless steel.
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For hybrid tubular X-connections with θ of 90° as illustrated in Fig. 7, the chord flange indentations were captured by four displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the edge faces of circular braces. For hybrid tubular X-connections with θ of 45° as illustrated in Fig. 8, the chord flange indentations were captured by two displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the root of upper and lower circular braces, respectively.
supports by the high strength steel hinges, which were fixed on the ground floor by anchor bolts. Hence, the boundary conditions that both ends of the square chord could rotate along the in-plane direction in the compression tests were effectively implemented. Unlike hybrid tubular T- and Y-connections, both ends of the square chord of hybrid tubular X-connections are free. The hydraulic jack was vertically placed on the top end plate of upper brace member to apply axial compression with a load cell placed in between to monitor the applied loads. While, the bottom end plate of lower brace member was bolted on a fixed-ended spherical bearing, which was specially designed to ensure that the loading application on hybrid tubular X-connections was pure axial compression without bending moment. Prior to axial loading, the specially designed spherical bearing was free to rotate without any restraint. The hydraulic jack was slowly extended to achieve the full contact among the reaction frame, the hydraulic jack, the load cell and the hybrid tubular connections until an initial load of 1–3 kN was reached. After that, the rotation of the spherical bearing was restrained by both horizontal and vertical bolts, which became a fixed-ended bearing.
2.6. Testing procedure The compression tests were conducted by using the multi-stage loading procedure for all specimens, which were loaded monotonically first by load control prior to the reach of the ultimate strengths and followed by displacement control in the post-ultimate stage. The load level of each loading stage in the load control procedure was estimated to be 10% of the ultimate strengths with the time interval of 2 mins. The displacement level of each loading stage in the displacement control procedure was roughly 1–3 mm with the time interval of 2 mins. The readings of load cell and displacement transducers were collected by the data acquisition equipment when the compression force was stable. The tests were stopped when the hybrid tubular connections severely damaged or generated excessive deformations.
2.5. Arrangement of displacement transducers The arrangements of displacement transducers in the compression tests are displayed in Figs. 5–8 for CHS-to-SHS tubular T-, Y- and Xconnections in stainless steel, respectively, in which, two displacement transducers located at the top end plate of circular brace diagonally were used to measure the axial displacements, while another two displacement transducers positioned at the center of chord webs were used to record the lateral deformations, from which the chord web deflections of all specimens were determined. For hybrid tubular T-connections as illustrated in Fig. 5, the chord flange indentations were captured by four displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the edge faces of circular brace. While, another three displacement transducers were evenly placed at the bottom flange of square chord with a quarter-span interval to record the vertical deflections of square chord along the longitudinal direction, from which the bending curvatures of square chord during the tests were obtained. For hybrid tubular Y-connections as illustrated in Fig. 6, the chord flange indentations were captured by two displacement transducers, which were positioned at the top and bottom flanges of square chord and located at the measuring points of 30 mm away from the root of circular brace and mid-span of square chord, respectively. While, another two displacement transducers were placed at the bottom flange and located at the quarter-span of square chord. Hence, a total of three displacement transducers were arranged evenly at the bottom flange of square chord with a quarter-span interval to record the vertical deflections of square chord along the longitudinal direction, from which the bending curvatures of square chord during the tests were obtained.
3. Test results and discussions 3.1. Failure modes The observed failure modes of chord face plastification and chord side wall failure are presented in Figs. 9–12 for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel, respectively, which are also listed in Table 3 for all specimens, except for the specimen X-C150 × 3B133 × 3–45° that subjected to premature failure. The failure modes of hybrid tubular connections with circular braces and square chord in stainless steel can be roughly classified into two categories according to the brace diameter/chord width ratio (β) as follows: (1) Chord face plastification: This failure mode usually occurred for hybrid tubular connections with the β value ranged from 0.6 to 0.8. The plastic zone of chord flange was fully developed with the occurrence of the stress redistribution, which resulted in the failure of the chord face. (2) Chord side wall failure: This failure mode usually occurred for hybrid tubular connections with the β value close to 1. The loads applied to the braces were transmitted directly to the chord webs, which eventually resulted in the chord side wall failure. It is found from Table 3 that most of the specimens failed by chord
(a) Front view
(b) Top view
Fig. 5. Arrangement of displacement transducers for tubular T-connections. 6
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(a) Front view
(b) Top view
Fig. 6. Arrangement of displacement transducers for tubular Y-connections.
(a) Front view
(b) Top view
Fig. 7. Arrangement of displacement transducers for tubular X-connections (θ = 90°).
(a) Front view
(b) Top view
Fig. 8. Arrangement of displacement transducers for tubular X-connections (θ = 45°).
the chord flange. While, some other specimens of T-C150 × 3-B133 × 3, Y-C150 × 3B133 × 3, X-C150 × 3-B133 × 3 and X-C150 × 3-B133 × 3-R failed by chord side wall. The compression forces were mainly undertaken by chord webs, which resulted in the slight lateral convex deformations of chord webs. By increasing the applied loads, the lateral convex deformations of chord webs further developed, which demonstrated the distinct characteristics of chord side wall failure.
face plastification since their β values are within the range of 0.6–0.8. At the early stage of loading, the concave and convex deformations generated at the chord flange and chord webs, respectively, simultaneously. The connection strengths relied on the bending and shear capacity of chord flange to take the applied loads as well as the bearing capacity of chord webs to transmit the applied loads. The membrane force in the chord flange was not formed, while the chord webs were in the combination of compression and bending. By increasing the applied loads, the region produced the maximum stresses first yielded and gradually became a plastic zone, while the membrane force in the chord flange gradually developed, which resulted in the further increase of the compression forces. The large deformations of chord flange and webs prior to the chord face failure caused the stress redistribution in
3.2. Deformation curves The deformation curves of axial load versus axial displacement, axial load versus chord flange indentation and axial load versus chord 7
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(a) Chord face plastification
(b) Chord side wall failure Fig. 9. Failure modes of tubular T-connections.
(a) Chord face plastification
(b) Chord side wall failure Fig. 10. Failure modes of tubular Y-connections. 8
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(a) Chord face plastification
(b) Chord side wall failure Fig. 11. Failure modes of tubular X-connections (θ = 90°).
3.3. Failure strengths
web deflection are illustrated in Figs. 13–16 for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel, respectively. In the testing curves, the convexity is defined as positive deformation, while the concavity is defined as negative deformation. It is found from Figs. 13–16 that the deformation curves of hybrid tubular connections with the β value of 0.88 exhibit the clear peak load, whereas there is no clear peak load in the deformation curves of hybrid tubular connections with the β value less than 0.88, which may attribute to the post-yield response caused by the membrane force in the chord flange and strain hardening property of stainless steel material. Furthermore, the initial stiffnesses of hybrid tubular connections increased with the increment of the β value, but insignificantly influenced by other geometrical parameters of τ and 2γ. This may attribute to the increase of the brace stiffness with the increment of the β value, whereas the variations of the τ and 2γ designed in the tests were limited.
It is shown from Figs. 13–16 that the deformation curves of most of the specimens do not have the clear peak load. Hence, the failure strengths of hybrid tubular connections were determined according to the recommendations of Lu et al. [28] with the results listed in Table 3. For the hybrid tubular connections with no clear peak load, the failure strengths were determined as the minimum value of 1.5 N1%b0 and N3%b0, where N1%b0 and N3%b0 are the connection strengths at the chord deformations of 1%b0 and 3%b0, respectively. For the hybrid tubular connections with clear peak load, the failure strengths were determined as the minimum value of Nmax and N3%b0. The influences of the key geometrical parameters on the failure strengths of hybrid tubular connections were investigated in Fig. 17. It is found that the failure strengths of hybrid tubular connections increased with the increment of the β value, which resulted in the change of the failure modes. For the hybrid tubular connections with small β value, the loads applied to the
Chord face plastification Fig. 12. Failure modes of tubular X-connections (θ = 45°). 9
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Table 3 Test strengths and comparison with nominal design strengths for hybrid tubular connections in stainless steel. Specimen
T-C150 × 3-B108 × 3 T-C150 × 3-B133 × 3 T-C200 × 4-B108 × 3 T-C200 × 4-B133 × 3 Y-C150 × 3-B108 × 3 Y-C150 × 3-B108 × 3-R Y-C150 × 3-B133 × 3 Y-C200 × 4-B108 × 3 Y-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3 X-C150 × 3-B133 × 3 X-C150 × 3-B133 × 3-R X-C200 × 4-B108 × 3 X-C200 × 4-B133 × 3 X-C150 × 3-B108 × 3-45° X-C150 × 3-B133 × 3-45° X-C200 × 4-B108 × 3-45° X-C200 × 4-B133 × 3-45° Mean COV
β
0.72 0.88 0.54 0.66 0.72 0.72 0.88 0.54 0.66 0.72 0.88 0.88 0.54 0.66 0.72 0.88 0.54 0.66
Test result
Comparison
Failure mode
NTest (kN)
NTest/NnCI
NTest/NnEC
NTest/NnA/N
NTest/NnCC
A B A A A A B A A A B B A A A — A A
42.28 74.71 53.82 66.65 61.24 60.02 119.31 68.51 113.98 38.92 85.17 80.34 48.03 53.06 68.92 — 72.65 102.32
1.08 1.20 1.25 1.28 1.02 0.95 1.16 1.01 1.23 1.03 1.47 1.39 1.11 0.94 1.08 — 1.06 1.08 1.14 0.148
1.20 1.34 1.39 1.42 1.14 1.05 1.29 1.13 1.37 1.15 1.63 1.55 1.23 1.04 1.19 — 1.18 1.21 1.27 0.165
0.98 0.83 1.13 1.15 0.92 0.85 0.77 0.91 1.11 0.93 0.98 0.93 1.00 0.85 0.97 — 0.96 0.97 0.96 0.104
1.20 1.03 1.39 1.43 1.14 1.05 1.01 1.12 1.36 1.15 1.31 1.24 1.23 1.04 1.20 — 1.18 1.20 1.19 0.126
Note: A = Chord face plastification; B = Chord side wall failure.
braces were transmitted to the chord flange, which caused the development of the large deformations and the membrane force in the chord flange and eventually resulted in the failure of the chord face. The increment of the β value enhanced the brace stiffness, which transmitted the applied loads from the chord flange to the chord webs and eventually resulted in the combination of chord face failure and chord side wall failure. Therefore, the failure strengths of hybrid tubular connections were enhanced. The comparison also shows that the failure strengths of hybrid tubular Y-connections are larger than those of hybrid tubular T-connections with the same geometrical sizes. In addition, the failure strengths of hybrid tubular X-connections with θ of 45° are larger than those of hybrid tubular X-connections with θ of 90° with the same geometrical sizes. Therefore, the failure strengths of hybrid tubular connections increased with the decrement of the θ value. This may attribute to the smaller vertical loads transmitted to the chord flange and webs with the decrement of the θ value.
4. Design guidelines 4.1. General Researches on carbon steel tubular connections are relatively mature. Various design guidelines are available for carbon steel tubular connections. However, studies on stainless steel tubular connections are rare. This paper introduces four different design guidelines namely CIDECT [23], Eurocode 3 [24], Australian/New Zealand Standard (AS/ NZS) [25] and Chinese Code [26] to determine the load-carrying capacities of hybrid tubular connections fabricated from circular braces and square chord. Among these design guidelines, CIDECT [23], EC3 [24] and Chinese Code [26] were designed for carbon steel structures, while AS/NZS [25] was designed for stainless steel structures. The validity range of geometrical parameters in these design guidelines are presented in Table 4. It should be noted that the geometrical parameters designed in the tests are out of the validity range of those given in these design guidelines.
(a) Axial displacement
(b) Chord deformation
Fig. 13. Axial load versus chord deformation curves of tubular T-connections. 10
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(a) Axial displacement
(b) Chord deformation
Fig. 14. Axial load versus chord deformation curves of tubular Y-connections.
carrying capacities, fk is the flexural buckling stress of chord web, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. It should be noted that the load-carrying capacities need to be limited by a reduction factor of 0.9 under the condition of fy0 > 355 N/mm2.
4.2. Design formulae of CIDECT [23] This design guideline is suitable for hot-finished, cold-formed steel and cold-formed stress-relieved hollow sections. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
2β ⎛ + For β ⩽ 0.85 NCI = ⎜ (1 − β ) sin θ ⎝
2
4 ⎞ πf y0 t0 Qf 1 − β ⎟⎠ 4 sin θ
πf t0 2d For β = 1.0 NCI = ⎛ 1 + 10t0 ⎞ Qf k sin θ 4 sin θ ⎝ ⎠ For 0.85 < β < 1.0
4.3. Design formulae of EC3 [24]
(1)
This design guideline is applicable to the steel tubular structures with material grades of S235, S275, S355 and S460 that under predominantly static loading. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
(2)
Linearly interpolate between the
load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0 (chord side wall failure)
For β ⩽ 0.85 NEC =
(3)
πkn f y0 t02
⎛ 2β + 4 1 − β ⎞ 4(1 − β ) sin θ ⎝ sin θ ⎠
where Qf = 1 is the influential factor for chord stresses on the load-
(a) Axial displacement
(b) Chord deformation
Fig. 15. Axial load versus chord deformation curves of tubular X-connections (θ = 90°). 11
γM 5
(4)
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(a) Axial displacement
(b) Chord deformation
Fig. 16. Axial load versus chord deformation curves of tubular X-connections (θ = 45°).
For β = 1.0 NEC =
πfb t0 2d1 ⎛ + 10t0⎞ γM 5 4 sin θ ⎝ sin θ ⎠
(5)
For 0.85 < β < 1.0 Linearly interpolate between the load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0(chord side wall failure)
(6)
where kn = 1 is the influential factor for chord stresses on the loadcarrying capacities, γM5 = 1.0 is the partial safety factor, fb is the flexural buckling stress of chord web, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. It should be noted that the load-carrying capacities need to be limited by a reduction factor of 0.9 under the condition of fy0 > 355 N/mm2.
Fig. 17. Comparison of failure strengths of hybrid tubular connections with different key geometrical parameters.
4.4. Design formulae of AS/NZS [25] This design guideline provides the design rules for cold-formed stainless steel tubular structures. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be Table 4 The validity range of geometrical parameters in current design specifications. Geometrical parameter
CIDECT [23]
β = d1/b0 (for CHS brace)
β ≥ 0.1 + 0.01b0/t0 and 0.25 ≤ β ≤ 0.8
d1/t1 (for CHS brace)
Compression
Tension
Compression
Tension
For Class 1
2γ ≤ 40
For Class 1
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
d1/t1 ≤ 50
θ ≥ 30°
c0 t0 ⩽ 33
235 f y0
d1 t1 ⩽ 50
235 f y0
d1 t1 ⩽ 70
0.4 ≤ β ≤ 0.8
235 f y0
d1 t1 ⩽ 50
and 2γ ≤ 40 For Class 2
c0 t0 ⩽ 38
235 f y1
For Class 2
For Class 2
c0 t0 ⩽ 38
EC3 [24]
θ
2γ = b0/t0 (for SHS chord)
235 f y1
and d1/t1 ≤ 50 For Class 1
AS/NZS [25]
0.4 ≤ β ≤ 0.8
and 10 ≤ 2γ ≤ 35 2γ ≤ 40
Chinese Code [26]
0.4 ≤ β ≤ 0.8
2γ ≤ 35
235 f y1
d1 t1 ⩽ 1.5
d1 t1 ⩽ 44
E f y1 235 f y1
Note: Class 1 = Cross-sections can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance; Class 2 = Crosssections can develop plastic moment resistance, but have limited rotation capacity because of local buckling; c0 = Clear width of SHS chord. 12
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EC3 [24] are most conservative with the largest value of COV. Furthermore, the design formulae of CIDECT [23] and EC3 [24] are quite conservative for the specimens subjected to the chord side wall failure. Whereas, the design formulae of AS/NZS [25] are quite unconservative for the specimens subjected to the chord side wall failure, which may attribute to the validity range of the β ratio limited by 0.85 in AS/NZS [25]. In general, the design formulae of AS/NZS [25] are appropriate for CHS-to-SHS tubular T-, Y- and X-connections in stainless steel with the smallest value of COV.
obtained from the design formulae as follows:
For β ⩽ 0.85 NA
N
=
πf y0 t02
⎛ 2β + 4(1 − β )0.5⎞ kn ⎛ φ ⎞ 4(1 − β ) sin θ ⎝ sin θ ⎠ ⎝ 0.9 ⎠ (7)
where kn = 1 is the influential factor for chord stresses on the loadcarrying capacities, φ = 0.9 is the strength reduction factor, fy0 is the yield stress of chord, θ is the inclined angle between brace and chord, and t0 is the wall thickness of square chord. In this paper, the loadcarrying capacities of the specimens with β = 0.88 were also obtained from the design equation for hybrid tubular connections with β ≤ 0.85.
6. Conclusions A test program was conducted in this study on CHS-to-SHS tubular T-, Y- and X-connections fabricated from circular braces and square chord in stainless steel. A total of 18 specimens including 4 T-, 5 Y- and 9 X-connections were tested by applying axial compression to the end of circular brace. The influences of the key geometrical parameters including the brace diameter/chord width ratio (β), the brace/chord thickness ratio (τ), the chord width/thickness ratio (2γ) and the inclined angle (θ) between brace and chord on the load-carrying capacities of hybrid tubular connections in stainless steel were investigated. The failure modes, failure strengths and deformation curves of all specimens were obtained. Two failure modes including chord face plastification and chord side wall failure were observed during the compression tests. The chord face plastification usually occurred for hybrid tubular connections with the β value ranged from 0.6 to 0.8. The plastic zone of chord flange was fully developed with the occurrence of the stress redistribution, which resulted in the failure of the chord face. While, the chord side wall failure usually occurred for hybrid tubular connections with the β value close to 1. The loads applied to the braces were transmitted directly to the chord webs, which eventually resulted in the chord side wall failure. Experimental results show that the initial stiffnesses and the failure strengths of hybrid tubular connections increased with the increment of the β value due to the increase of the brace stiffness. While, the failure strengths of hybrid tubular connections also increased with the decrement of the θ value, which may result from the smaller vertical loads transmitted to the chord flange and webs. However, the influences of other geometrical parameters of τ and 2γ on the initial stiffnesses and the failure strengths are insignificant. Most of the specimens failed by chord face plastification and no clear peak load was observed from the deformation curves, which may attribute to the post-yield response caused by the membrane force in the chord flange and strain hardening property of stainless steel material. Whereas, some other specimens with the large β value failed by chord side wall and the clear peak load was obtained from the deformation curves. The test strengths are compared with the nominal design strengths calculated using the design formulae of CIDECT, EC3 and Chinese Code for carbon steel tubular connections, as well as AS/NZS for stainless steel tubular connections. The comparison indicates that the design formulae of CIDECT, EC3 and Chinese Code are all conservative, in which the design formulae of EC3 are most conservative with the largest scatter of predictions. Furthermore, the design formulae of CIDECT and EC3 are quite conservative in calculating the nominal design strengths of the specimens failed by the chord side wall. Whereas, the design formulae of AS/NZS are quite unconservative for the specimens subjected to the chord side wall failure, which may attribute to the validity range of the β ratio limited by 0.85 in AS/NZS. In general, the design formulae of AS/NZS are appropriate for CHS-to-SHS tubular connections in stainless steel.
4.5. Design formulae of Chinese Code [26] This design guideline provides the most updated design rules for carbon steel structures under static or dynamic loading. The load-carrying capacities of hybrid tubular connections with circular braces and square chord can be obtained from the design formulae as follows:
πt02 f β ψn For β ⩽ 0.85 NCC = 1.8 ⎜⎛ + 2⎟⎞ 0.5 0.5 ⎝ (1 − β ) sin θ ⎠ 4(1 − β ) sin θ
(8)
πt0 fk d For β = 1.0 NCC = 2.0 ⎛ 1 + 5t0 ⎞ ψn sin θ 4 ⎝ ⎠ sin θ
(9)
For 0.85 < β < 1.0
Linearly interpolate between the
load − carrying capacities at β = 0.85 (chord face plastification) and at β = 1.0 (chord side wall failure)
(10)
where ψn = 1 is the influential factor for chord stresses on the loadcarrying capacities, fk is the flexural buckling stress of chord web, f is the design value of compression, tension and flexural strengths of chord, θ is the inclined angle between brace and chord, d1 is the outer diameter of circular brace, and t0 is the wall thickness of square chord. 5. Assessment of current design guidelines By comparing the design formulae given in the aforementioned design guidelines, it can be generally concluded that the design formulae of CIDECT [23], EC3 [24] and AS/NZS [25] are identical, while the design formulae of Chinese Code [26] are similar with a little bit different coefficients. Hence, the identical design strengths can be obtained from CIDECT [23], EC3 [24] and AS/NZS [25], while the similar design strengths can be obtained from Chinese Code [26]. The nominal design strengths were determined from the current design guidelines for comparison. In CIDECT [23], the nominal design strengths (NnCI) can be calculated from the design strengths (NCI) by dividing the resistance factor ϕ = 0.9 as NnCI = NCI/ϕ. In EC3 [24], the nominal design strengths (NnEC) can be calculated from the design strengths (NEC) by multiplying the partial safety factor γM5 = 1.0 as NnEC = NEC × γM5. In AS/NZS [25], the nominal design strengths (NnA/N) can be calculated from the design strengths (NA/N) by dividing the strength reduction factor φ = 0.9 as NnA/N = NA/N/φ. In Chinese Code [26], the nominal design strengths (NnCC) can be calculated by replacing f with fy0, where fy0 is the yield stress of square chord. The comparison of test strengths (NTest) with nominal design strengths (NnCI, NnEC, NnA/N and NnCC) determined by the design formulae of CIDECT [23], EC3 [24], AS/NZS [25] and Chinese Code [26], respectively, is summarized in Table 3. The mean values of test/nominal design strength ratios (NTest/NnCI, NTest/NnEC, NTest/NnA/N and NTest/ NnCC) are 1.14, 1.27, 0.96 and 1.19, with the coefficients of variation (COVs) of 0.148, 0.165, 0.104 and 0.126 for CIDECT [23], EC3 [24], AS/NZS [25] and Chinese Code [26], respectively. The comparison indicates that the design formulae of CIDECT [23], EC3 [24] and Chinese Code [26] are all conservative, in which the design formulae of
Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any 13
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nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.
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Acknowledgements The authors are grateful for the financial support from National Natural Science Foundation of China (Grant No. 51528803), Natural Science Foundation of Guangdong Province of China (Grant No. 2018A030313208), State Key Laboratory of Subtropical Building Science (South China University of Technology, Grant No. 2018ZA02), and Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen Durability Center for Civil Engineering (Shenzhen University, Grant No. GDDCE 18-5). The tests were conducted in Anhui Key Lab on Structure and Material of Civil Engineering at Hefei University of Technology. The support provided by the laboratory staff is gratefully acknowledged. References [1] Zhao XL. Deformation limit and ultimate strength of welded T-joints in cold-formed RHS sections. J Constr Steel Res 2000;53(2):149–65. [2] Zhao XL, Hancock GJ. T-Joints in rectangular hollow sections subject to combined actions. J Struct Eng, ASCE 1991;117(8):2258–77. [3] Chiew SP, Lee CK, Lie ST, Ji HL. Fatigue behaviors of square-to-square hollow section T-joint with corner crack. I: Experimental studies. Eng Fract Mech 2007;74(5):703–20. [4] Lee CK, Chiew SP, Lie ST, Ji HL. Fatigue behaviors of square-to-square hollow section T-joint with corner crack. II: Numerical modeling. Eng Fract Mech 2007;74(5):721–38. [5] Shao YB, Zheng YJ, Zhao HC, Yang DP. Performance of tubular T-joints at elevated temperature by considering effect of chord compressive stress. Thin-Walled Struct 2016;98:533–46. [6] Chen Y, Feng R, Ruan XF. Behaviour of steel-concrete-steel SHS X-joints under axial compression. J Constr Steel Res 2016;122:469–87. [7] Nassiraei H, Lotfollahi-Yaghin MA, Ahmadi H. Static strength of doubler plate reinforced tubular T/Y-joints subjected to brace compressive loading: Study of geometrical effects and parametric formulation. Thin-Walled Struct 2016;107:231–47. [8] Nassiraei H, Lotfollahi-Yaghin MA, Ahmadi H. Static performance of doubler plate reinforced tubular T/Y-joints subjected to brace tension. Thin-Walled Struct 2016;108:138–52.
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