Experimental and numerical investigations on collar plate and doubler plate reinforced SHS T-joints under axial compression

Thin–Walled Structures 110 (2017) 75–87

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Experimental and numerical investigations on collar plate and doubler plate reinforced SHS T-joints under axial compression ⁎

Ran Fenga, Yu Chenb, , Dongfen Chenc a b c

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

A R T I C L E I N F O

A BS T RAC T

Keywords: Axial compression Collar plate Doubler plate Ductility Initial stiffness Load carrying capacity Reinforced SHS T-joint Strain distribution

This paper presents the experimental and numerical investigations on collar plate and doubler plate reinforced square hollow section (SHS) T-joints under axial compression. A total of eleven SHS T-joints with different brace to chord width ratio (β) was tested, in which four specimens were reinforced with collar plate, four specimens were reinforced with doubler plate and three specimens were unreinforced for comparison. The joint strengths, failure modes, load-deformation curves and load-strain distribution curves of all specimens are reported. The effects of brace to chord width ratio (β), reinforcement type and reinforced plate thickness on the structural behaviour of SHS T-joints under axial compression were evaluated. It is shown from the comparison that the reinforced plates including both collar plate and doubler plate significantly increase the load carrying capacity of SHS T-joints under axial compression. The joint strength and initial stiffness benefit from the increase of the β ratio, but the ductility is deteriorated. Furthermore, the joint strength, initial stiffness and ductility of collar plate reinforced SHS T-joints under axial compression are improved with the increase of the collar plate thickness. Whereas, the increase of the doubler plate thickness has detrimental effect on the joint strength and ductility of doubler plate reinforced SHS T-joints under axial compression. The corresponding finite element analysis (FEA) was also performed and calibrated against the test results. The new design equations were proposed based on the test and numerical results for collar plate and doubler plate reinforced SHS T-joints, which were verified to be more accurate.

1. Introduction Square hollow sections (SHS) nowadays are widely used in stadium, bridge, and long-span roof due to welding accessibility [1]. In these structures, the SHS brace members are usually welded directly to the SHS chord member to form a welded SHS joint [2]. The chord member is normally subjected to loadings in the radial direction resulted from the welded brace members under axial loadings [3]. It is worth noting that the stiffness of the SHS tube in the radial direction is much smaller than that in the axial direction, which causes the chord member to be weak in resisting the loadings in the radial direction. Therefore, chord face plastification or punching shear failure often occurred at the chord flange around the brace and chord intersection region [4]. For a full width SHS joint, the buckling failure of chord side wall usually occurred in resisting the loadings transferred from the brace members. Internal and external reinforcement are two main ways to improve the load carrying capacity of SHS joints. Internal ring reinforcement, local chord thickness reinforcement and grouted chord reinforcement

⁎

are the most representative internal reinforcing methods. Many researches [5–12] were conducted on joints with internal reinforcement by using the experimental investigation and finite element analysis. On the other hand, doubler plate and collar plate reinforcement are two typical external reinforcing methods. The experimental and finite element analyses [13–17] were conducted on the static strength and fatigue behaviour of doubler plate reinforced joints under axial compression or in-plane bending. It was demonstrated that the load carrying capacity of joints was greatly improved with reinforcement of the doubler plate. Furthermore, the stress concentration factors of the doubler plate reinforced joints were found to be lower than those of the unreinforced joints. The static and hysteretic performances of the collar plate reinforced joints were also introduced in the previous literatures [18–26] based on the experimental and numerical investigations. The test and finite element analysis results reveal a significant enhancement of the load carrying capacity for collar plate reinforced joints in comparison with the unreinforced joints. In addition, it was shown that the collar plate reinforced joints under

Corresponding author. E-mail address: [email protected] (Y. Chen).

http://dx.doi.org/10.1016/j.tws.2016.10.017 Received 22 April 2016; Received in revised form 20 October 2016; Accepted 24 October 2016 Available online 01 November 2016 0263-8231/ © 2016 Elsevier Ltd. All rights reserved.

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Py P3%b0 tr t0 t1 w β δu δy εf εi ε1 ε2 ε3 λ ν τ ψc ψd Δ

Nomenclature br b0 b1 COV E fu fy fy0 ki kpy Lr L0 L1 PFEA PTest Pu Puc Pud Puu

Reinforced plate width Chord width Brace width Coefficient of variation Elastic modulus Ultimate tensile stress Tensile yield stress Yield stress of chord member Initial stiffness Post-yield stiffness Reinforced plate length Chord length Brace length Joint strength obtained from finite element analysis Joint strength obtained from test Ultimate load Design strength of collar plate reinforced joint Design strength of doubler plate reinforced joint Design strength of unreinforced joint

Yield load Joint strength at deformation of 3% of chord width (b0) Reinforced plate thickness Chord wall thickness Brace wall thickness Weld size Brace to chord width ratio (b1/b0) Vertical displacement corresponding to ultimate load Vertical displacement corresponding to yield load Elongation after fracture Strain First principal strain Second principal strain Third principal strain Reinforced plate to chord wall thickness ratio (tr/t0) Poisson's ratio Brace to chord wall thickness ratio (t1/t0) Correction factor for collar plate reinforced SHS T-joint Correction factor for doubler plate reinforced SHS T-joint Reinforced plate to brace width ratio (br/b1)

nominal overall length (Lr) of 180 mm. The dimensions of test specimens are shown in Table 1, using the nomenclature defined in Figs. 1a–c for unreinforced joints, collar plate reinforced joints and doubler plate reinforced joints, respectively. The welds connecting brace and chord members, as well as reinforced plate and SHS tube were designed according to the American Welding Society (AWS D1.1/1.1 M) Specification [27] and laid using shielded metal arc welding. The weld sizes (w) in the test specimens are all greater than the larger value of 1.5t and 3 mm as specified in the AWS specification, where t is the thickness of thinner part between brace and chord members or reinforced plate and SHS tube. The 3.0 mm and 3.5 mm electrodes of type E4303 with nominal 0.2% proof stress, tensile strength, and elongation of 355 MPa, 447 MPa, and 38%, respectively, were used for welding low strength carbon steel specimens. All welds consisted of 2 to 3 runs of welding to guarantee that failure of specimens occurred in the brace or chord members rather than the welds. The measured weld sizes (w) of all specimens are also shown in Table 1.

cyclic loading could dissipate more energy before failure, which means the collar plate reinforcement could also improve the ductile behaviour of joints. It is easier to reinforce joints with external reinforcement rather than internal reinforcement. Hence, the collar plate and doubler plate reinforcement are widely used in practical applications. It should be noted that the aforementioned researches on the collar plate and doubler plate reinforced joints mainly focused on the circular hollow section (CHS) joints. There is little research being carried out on the SHS joints reinforced with the collar plate and doubler plate. Therefore, the experimental and numerical investigations were conducted in this study on the collar plate and doubler plate reinforced SHS T-joints under axial compression. The corresponding unreinforced counterparts were also investigated for comparison. 2. Experimental investigation 2.1. Test specimens

2.2. Specimen labelling

A total of eleven SHS T-joints including three unreinforced joints, four collar plate reinforced joints and four doubler plate reinforced joints was tested. For the unreinforced SHS T-joints, the brace member was fully welded at right angle to the center of the continuous chord member, as shown in Fig. 1a. For the collar plate reinforced SHS Tjoints, the specimens were fabricated in the similar way, but subsequently by welding two collar plates at brace and chord intersection region, as shown in Fig. 1b. For the doubler plate reinforced SHS Tjoints, the brace member was first welded with a doubler plate through penetration welds. Then the doubler plate was welded to the center of the continuous chord member by using fillet welds, as shown in Fig. 1c. The chord member of all specimens is a square hollow section of SHS 150×6, which has the nominal overall width of 150 mm, the nominal wall thickness of 6 mm, and the nominal overall length (L0) of 1000 mm. The brace members of all specimens are square hollow sections with different cross sections, which have the identical nominal wall thickness of 5 mm, and the identical nominal overall length (L1) of 500 mm. The overall lengths of chord and brace members were designed to be at least three times the overall widths of SHS tubes in order to eliminate the effect of boundary conditions [9]. The reinforced plates of all reinforced joints including both collar plate and doubler plate is rectangular plates with different thicknesses, which have the identical nominal overall width (br) of 140 mm, and the identical

The specimens are labelled according to their joint configuration, shape and dimensions of cross sections, type and dimensions of reinforcement. For example, the label ‘TSCB80‘P6’ defines the following SHS T-joint:

• • • • •

The first letter ‘T’ denotes T-joint. The second letter ‘S’ denotes square hollow section. The third letter indicates the type of reinforcement, where ‘U’ refers to the unreinforced joint, ‘C’ refers to the collar plate reinforced joint, and ‘D’ refers to the doubler plate reinforced joint. The following part of the label ‘B80’ denotes the brace member with the nominal overall width of 80 mm. The last part of the label ‘P6’ denotes the reinforced plate with the nominal overall thickness of 6 mm.

2.3. Material properties The test specimens were fabricated by using Chinese Standard Q235 steel (Nominal yield stress fy=235 MPa). Tensile coupon tests were conducted to obtain the mechanical properties of the seamless 76

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2.4. Test procedure All specimens were installed in the same loading machine, as shown in Figs. 2a–b for elevation and end view, respectively. The reaction frame and supports were connected to the strong floor firmly by anchor bolts. The 1000 kN capacity hydraulic jack was used to apply the axial compression to the brace members of test specimens and monitored by the load cell, which was positioned concentrically between the hydraulic jack and the reaction frame. Two steel bearing plates were welded at the end of chord member as the supporting points to simulate the simply supported boundary conditions. Four displacement transducers (D1-D4) were positioned to record the displacements and deformations during the tests, in which D1 and D2 were used to monitor the vertical displacements of the end plate welded to brace member under axial compression, and D3 and D4 were used to measure the inward deformation of the chord flange for the unreinforced joints, and the inward deformation of the reinforced plate for the reinforced joints during the tests, as shown in Fig. 3a. For a tubular joint, the deformation is defined as the displacement difference between the top surface of the chord and the mid-height of the side wall of the chord at the intersection. This definition is widely used in most published studies. D3 and D4 displacement transducers were directly used to measure the deformation of chord because one side is located at the top surface of chord and another side is located at the mid-height of side wall of chord. Three-element rosettes strain gauges, which enable strain values in three different directions at 45° interval to be measured simultaneously were used to investigate the strain distribution of each specimen under axial compression. A total of 10 three-element rosettes strain gauges (T1-T10) was attached along the quarter of brace and chord intersection region by taking advantage of symmetry in geometry, loading application and boundary conditions, in which T1 and T2 were positioned on the chord flange for the unreinforced joints and on the reinforced plates for the reinforced joints, T3-T6 were positioned on the chord side wall, and T7-T10 were positioned at the root of brace member, as shown in Fig. 3b. All strain gauges were positioned roughly 15 mm away from the weld to exclude the influence of welding. The location of the strain rosettes to be 15 mm from the weld toe was determined by a point 15 mm perpendicular to the welding seam using vernier caliper. Stress and strain distribution of heat affected area around welding was very complicated, so all tri-element rosettes strain gauges were certainly positioned away from the weld. 3. Test results 3.1. Failure modes The typical failure modes of unreinforced SHS T-joints, collar plate reinforced SHS T-joints and doubler plate reinforced SHS T-joints were observed from the tests, as shown in Figs. 4a, b and d, respectively. All specimens were failed by chord plastification with comparatively large deformations, either chord flange inward indentation or chord side wall outward deflection, except for the specimen TSCB100P6 who was suddenly failed by fracture of chord side wall away from the joint intersection region before reaching the ultimate strength because of welding defects in the butt weld, as shown in Fig. 4c. The chord member of this special specimen was fabricated by welding two short SHS tubes together through fillet welds, which resulted in the defects of chord side wall at the welds. For the reinforced SHS T-joints, both collar plate and doubler plate were obviously bent in the ultimate limit state.

Fig. 1. Schematic diagram of SHS T-joints.

steel tube and reinforced plate. The coupons were taken from the center face of the untested specimens in the longitudinal direction and prepared based on the requirements of the Chinese Code of Metallic Materials (GB/T 228–2002) [28]. The tensile coupon tests were conducted by using a MTS displacement controlled testing machine. The strain gauges were positioned to measure the longitudinal strains during the tests. The material properties obtained from the tensile coupon tests are summarized in Table 2, which include the elastic modulus (E), tensile yield stress (fy), ultimate tensile stress (fu), Poisson's ratio (ν) and elongation after fracture (εf).

3.2. Load-displacement curves The axial load versus vertical displacement curves of all specimens are plotted in Figs. 5a–c for unreinforced SHS T-joints, collar plate 77

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Table 1 Dimensions of test specimens. Specimen

TSUB80 TSUB100 TSUB120 TSCB80P6 TSCB80P8 TSCB100P6 TSCB120P6 TSDB80P6 TSDB80P8 TSDB100P6 TSDB120P6

Chord

Brace

Reinforced plate

Weld

b0 (mm)

t0 (mm)

L0 (mm)

b1 (mm)

t1 (mm)

L1 (mm)

br (mm)

tr (mm)

Lr (mm)

w (mm)

150 150 150 150 150 150 150 150 150 150 150

6 6 6 6 6 6 6 6 6 6 6

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

80 100 120 80 80 100 120 80 80 100 120

5 5 5 5 5 5 5 5 5 5 5

500 500 500 500 500 500 500 500 500 500 500

– – – 140 140 140 140 140 140 140 140

– – – 6 8 6 6 6 8 6 6

– – – 180 180 180 180 180 180 180 180

8.1 8.2 8.4 9.2 12.2 9.4 9.3 9.3 12.3 9.2 9.1

β

τ

0.53 0.67 0.80 0.53 0.53 0.67 0.80 0.53 0.53 0.67 0.80

0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83

whereas, the initial stiffness is enhanced remarkably with the increase of the doubler plate thickness, as shown in Fig. 5c. Because the doubler plate reinforced SHS T-joints has large compressive stiffness, the effect of the doubler plate thickness on ultimate load of joints is unobvious.

reinforced SHS T-joints and doubler plate reinforced SHS T-joints, respectively. The complete curves consist of the elastic stage, elastoplastic stage, plastic stage and unloading stage, in which the vertical displacements were obtained from the readings of displacement transducers D1 and D2. The initial stiffness (ki), vertical displacement (δy) corresponding to the yield load, vertical displacement (δu) corresponding to the ultimate load and ductility ratio (δu/δy) based on the Kurobane criterion [29] are all summarized in Table 3. It is shown from the comparison that the initial stiffness and ultimate load of SHS T-joints are enhanced remarkably with the increase of brace to chord width ratio (β), but the ductility is deteriorated. For the collar plate reinforced SHS T-joints, the initial stiffness, ultimate load, vertical displacement corresponding to the ultimate load and ductility are improved remarkably with the increase of the collar plate thickness, as shown in Fig. 5b. For the doubler plate reinforced SHS T-joints, the ultimate load, vertical displacement corresponding to the ultimate load and ductility decreased with the increase of the doubler plate thickness,

3.3. Load-deformation curves The axial load versus chord flange deformation curves of all

Table 2 Material properties of steel. Specimen (mm)

E (GPa)

fy (MPa)

fu (MPa)

εf (%)

ν

□150×150×6 □120×120×5 □100×100×5 □80×80×5 −180×6 −180×8

208 201 199 202 197 205

327 334 350 402 310 325

418 426 421 489 411 423

24.89 29.73 25.27 22.38 26.66 27.70

0.30 0.26 0.29 0.24 0.27 0.29

Fig. 2. Test setup of SHS T-joints.

Fig. 3. Arrangement of displacement transducers and strain gauges.

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Fig. 4. Failure modes of SHS T-joints in the tests.

SHS T-joints. On the other hand, when β ratio is small (β=0.53), the enhancement of ultimate loads of SHS T-joints reinforced with collar plate and doubler plate are almost identical. When β ratio is large (β≥0.67), the reinforcement of doubler plate is more pronounced than that of collar plate in ultimate load, as illustrated in Figs. 6d–f for SHS T-joints with different β ratios.

specimens are plotted in Fig. 6, which could be used to evaluate the joint stiffness. It is shown from the comparison that the ultimate loads of SHS T-joints are enhanced significantly by reinforcing with collar plate and doubler plate, and the initial stiffness of SHS T-joints are also improved remarkably with the increase of β ratio, as shown in Figs. 6a– c for unreinforced SHS T-joints, collar plate reinforced SHS T-joints and doubler plate reinforced SHS T-joints, respectively. Furthermore, the initial stiffness of unreinforced SHS T-joints and doubler plate reinforced SHS T-joints are almost identical, both of which are larger than that of collar plate reinforced SHS T-joints. The initial stiffness of unreinforced and doubler plate reinforced SHS T-joints are larger than that of collar plate reinforced SHS T-joints because intersection between brace and chord cannot be welded in collar plate reinforced

3.4. Strain distribution curves Strain distributions at the joint intersection region were derived from the readings of three-element rosettes strain gauges and the failure mechanism of SHS T-joints was studied. The strains at the measuring points of strain gauges under different load levels of all 79

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Table 3 Test results of SHS T-joints. Specimen

β

tr (mm)

Pu (kN)

ki (kN/ mm)

δy (mm)

δu (mm)

δu/δy

TSUB80 TSUB100 TSUB120 TSCB80P6 TSCB80P8 TSCB100P6 TSCB120P6 TSDB80P6 TSDB80P8 TSDB100P6 TSDB120P6

0.53 0.67 0.80 0.53 0.53 0.67 0.80 0.53 0.53 0.67 0.80

– – – 6 8 6 6 6 8 6 6

102.5 119.0 205.1 198.9 228.6 161.6 235.4 193.1 180.8 229.5 282.9

21.82 30.23 32.48 37.27 46.91 36.61 35.44 31.31 29.29 35.19 44.78

3.54 3.23 3.93 3.76 3.51 – 5.38 4.45 5.32 4.67 4.69

54.14 30.45 53.70 40.69 28.68 – 30.55 31.48 25.58 22.75 40.08

15.29 9.43 13.66 10.82 8.17 – 5.68 7.07 4.81 4.87 8.55

the ultimate limit state; ‘Py’ represents the yield load; and ‘Pu’ represents the ultimate load. It is shown from the comparison that the yield load (Py) of SHS Tjoints increased by reinforcing with both collar plate and doubler plate. For unreinforced SHS T-joints, the measuring points of strain gauges (T3-T4) on the chord side wall around the joint intersection region are yielded first. In the ultimate limit state, most of the measuring points of strain gauges (T1-T6) on the chord member are yielded, whereas the measuring points of strain gauges (T7-T10) at the root of brace member are not yielded, except for the specimen of TSUB120. The axial load applied to the brace member of this specimen mainly transferred to the chord side wall due to the large β ratio. Therefore, the measuring points of strain gauges at the root of brace member are all yielded in the ultimate limit state. For collar plate reinforced SHS Tjoints, the measuring points of strain gauges on the chord side wall around the joint intersection region (T3-T4) and at the root of brace member (T7-T10) are yielded first. In the ultimate limit state, most of the measuring points of strain gauges (T1-T6) on the chord member are yielded, except for that (T5) on the neutral axis of chord side wall, while the measuring points of strain gauges (T7-T10) at the root of brace member are yielded. For doubler plate reinforced SHS T-joints with small β ratio (β=0.53), the measuring point of strain gauges (T2) at the corner of the doubler plate is yielded first. All measuring points of strain gauges (T1-T10) are yielded in the ultimate limit state. For other doubler plate reinforced SHS T-joints with large β ratio (β≥0.67), the measuring points of strain gauges on the chord side wall around the joint intersection region (T3-T4) and at the root of brace member (T7T10) are yielded first. The measuring points of strain gauges on the doubler plate (T1-T2), on the chord member (T3-T4) and at the root of brace member (T7-T9) are yielded in the ultimate limit state. 4. Finite element analysis Fig. 5. Load-displacement curves.

4.1. General specimens are plotted in Fig. 7, in which the horizontal axis represents the measuring point of strain gauges (as shown in Fig. 2a), the vertical axis represents the strain (εi), and the dash line represents the strain corresponding to the yield load. The strain (εi) could be calculated as follows [30,31]:

εi =

2 3

(ε1 − ε2 )2 + (ε2 − ε3)2 + (ε3 − ε1)2

The general purpose finite element program ABAQUS [32] was used for the nonlinear numerical analysis of the unreinforced SHS Tjoints, collar plate reinforced SHS T-joints and doubler plate reinforced SHS T-joints under axial compression. Both material and geometric nonlinearities have been taken into account in the finite element models. In order to provide accurate results with reasonable computational cost, the element type and mesh size of the SHS tube, the reinforced plate, the bearing plate and the welding material were carefully determined by the convergence studies for the simulation of reinforced SHS T-joints. The modelling of materials and welds, the interfaces between SHS tubes and reinforced plates as well as SHS tubes and bearing plates, the loading and boundary conditions were all considered in the finite element analysis. The finite element models were developed based on the measured geometrical dimensions of experimental SHS T-joints.

(1)

where ε1, ε2 and ε3 are the first, second and third principal strains, respectively, which were obtained from three-element rosettes strain gauges along the joint intersection region. Plastic development of the SHS T-joints under distinct axial loads are summarized in Table 4, in which ‘Position ‘A’ represents the measuring points of strain gauges where the stresses go into the plastic range of materials first; ‘Position 'B’ represents the measuring points of strain gauges where the stresses are in the elastic range of material in 80

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Fig. 6. Load-deformation curves.

4.2. Element type and mesh size

4.3. Material modelling

Three-dimensional eight-node solid element with additional variables relating to the incompatible modes (C3D8I) was used in this study to model the SHS brace members, chord members and reinforced plates. The welding seams were not considered in the finite element models due to its negligible effect on the axial compressive behaviour of SHS T-joints [33]. The bearing plates were modelled by using an analytical rigid plate with a reference point. The convergence studies were carried out to obtain the optimum finite element mesh size. The welding area along the joint interaction region are fine meshed to capture the high stress gradient, whereas the mesh size at the location away from the interest area is gradually coarse in order to save computing cost. The typical finite element mesh of SHS T-joints is shown in Fig. 8.

The bilinear material model in the ABAQUS library was used in the finite element analysis. The initial part of the bilinear curve represents the elastic property up to the tensile yield stress (fy) with measured elastic modulus (E) and Poisson's ratio. The post-yield response of the bilinear material model was developed based on the measured ultimate tensile stress (fu) and elongation after fracture (εf) obtained from the tensile coupon tests, while the Von-Mises yield criterion and kinematic hardening model were applied. The material nonlinearity behaviour was included in the finite element models.

4.4. Loading and boundary conditions The loaded bearing plate welded to the top end of brace member 81

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Fig. 7. Strain distribution curves.

force. However, they are not allowed to penetrate each other under the effect of compressive force.

was restrained against all degrees of freedom, except for the displacement at the loaded end in the direction of the applied load. The nodes other than the loaded end were free to translate and rotate in any directions. The static uniform loads were applied in increments by means of displacement at each node of the loaded end, which was identical to the experimental test setup. The nonlinear geometry parameter (*NLGEOM) was used for the consideration of the large displacement analysis. The interfaces between the bearing plates welded to the ends of chord member and the supports were modelled by using the contact interaction. An analytic rigid contact interaction between the bearing plates and the supports was established by using a ‘master-slave’ algorithm available in the ABAQUS library. The contact interaction allows the surfaces to separate under the effect of tensile

4.5. Verification of finite element models A comparison between the test and finite element analysis results was carried out to verify the finite element models. The joint strengths and failure modes of all specimens were investigated. The comparison of the joint strengths obtained from the tests (PTest) and finite element analysis (PFEA) is shown in Table 5. Good agreement between the test and finite element analysis results was achieved with the maximum difference of 4.8%. On the other hand, the typical failure modes of SHS T-joints observed in the experimental investigation were also verified

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Table 4 Plastic development of SHS T-joints. Specimen

Reinforcement

Position A

Py (kN)

Position B

Pu (kN)

TSUB80 TSUB100 TSUB120 TSCB80P6 TSCB80P8 TSCB120P6 TSDB80P6 TSDB80P8 TSDB100P6 TSDB120P6

Unreinforced Unreinforced Unreinforced Collar plate Collar plate Collar plate Doubler plate Doubler plate Doubler plate Doubler plate

T3, T4 T1, T3, T8 T4, T2 T2, T4, T4,

74.5 75.7 149.8 149.8 151.4 202.5 99.9 151.2 199.7 248.6

T5, T7-T10 T5, T8-T10 T10 T1, T2, T5, T9 – T5, T7, T9 T7 T10 T1, T5, T7, T10 T1, T5, T10

102.5 119.0 205.1 198.9 228.6 235.4 193.1 180.8 229.5 282.9

T4 T3, T4 T8 T6, T9 T8, T9 T8 T6, T7

Note: Position A=Measuring points of strain gauges where the stresses go into the plastic range of materials first; Position B=Measuring points of strain gauges where the stresses are in the elastic range of material in the ultimate limit state; Py=Yield load; Pu=Ultimate load.

Fig. 8. Typical finite element mesh of SHS T-joints.

Table 5 Validation of finite element models for SHS T-joints. Specimen

PTest (kN)

PFEA (kN)

Error (%)

TSUB80 TSUB100 TSUB120 TSCB80P6 TSCB80P8 TSCB120P6 TSDB80P6 TSDB80P8 TSDB100P6 TSDB120P6

102.5 119.0 205.1 198.9 228.6 235.4 193.1 180.8 229.5 282.9

106.9 120.9 212.3 208.4 231.3 238.5 195.4 189.5 239.4 289.7

4.3 1.6 3.5 4.8 1.2 1.3 1.2 4.8 4.3 2.4

Fig. 9. Failure modes of SHS T-joints in the finite element analysis.

4.6. Parametric study It is shown that the verified finite element models can accurately predict the strength and behaviour of reinforced SHS T-joints under axial compression. Therefore, an extensive parametric study was carried out to investigate the effects of main geometric parameters on the structural behaviour of reinforced SHS T-joints under axial compression. A total of 48 collar plate reinforced SHS T-joints and 48 doubler plate reinforced SHS T-joints was analyzed in the parametric study. The SHS chord member of all specimens is taken to be SHS300×300×10, which has the nominal width (b0) of 300 mm and nominal wall thickness (t0) of 10 mm. The SHS brace member consisted of large range of section sizes, which were selected from the range of practical applications. The corresponding non-dimensional geometric parameters including brace to chord width ratio (β=b1/b0), reinforced plate to brace width ratio Δ=br/b1) and rein-

by the finite element models, as shown in Figs. 9a–c for unreinforced SHS T-joints, collar plate reinforced SHS T-joints and doubler plate reinforced SHS T-joints, respectively. Therefore, it was demonstrated that the newly developed finite element models successfully predicted the structural behaviour of unreinforced SHS T-joints, collar plate reinforced SHS T-joints and doubler plate reinforced SHS T-joints under axial compression. 83

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and tests are purposely designed beyond the validity range of those defined in the current design specifications. The bilinear material model of steel including the elastic modulus (E) of 206 GPa, tensile yield stress (fy) of 235 MPa and Poisson's ratio (ν) of 0.3 was used in the parametric study. The failure loads were newly defined for reinforced SHS T-joints which attribute to the occurrence of new types of failure modes and deformation curves obtained from the parametric study. For the deformation curves of reinforced SHS T-joints with clear peak load, the peak load was used as the failure load. For the deformation curves of reinforced SHS T-joints with no clear peak load, the joint strength P3%b0 at the deformation of 3% of the chord width (b0), which is equal to 9 mm, was considered to be the failure load [29]. There are two typical failure modes obtained from the parametric study of reinforced SHS T-joints under axial compression. One failure mode involved large deformations for both reinforced plate and chord flange due to insufficient stiffness of the reinforced plate, as shown in Fig. 10a. This failure mode usually occurred for specimens with large β and Δ ratios, but small λ ratio. The other failure mode involved large deformation for chord flange only, whereas the deformation of the reinforced plate is negligible which attributes to its comparatively large stiffness, as shown in Fig. 10b. This failure mode usually occurred for specimens with small β and Δ ratios, but large λ ratio. The effects of the critical geometric parameters including β, Δ and λ on the strength and behaviour of reinforced SHS T-joints were carefully investigated. It is shown from the comparison that the ultimate loads of reinforced SHS T-joints are enhanced with the increase of the β ratio, as shown in Fig. 11. For the reinforced SHS T-joints with β=0.3, the ultimate loads of reinforced joints are enhanced significantly with the increase of Δ ratio under the condition of λ≥1.5, whereas, the enhancements of ultimate loads of reinforced joints are minimal with the increase of Δ ratio under the condition of λ < 1.5, as shown in Figs. 12a–b. For the reinforced SHS T-joints with β > 0.3, the effects of Δ ratio on the ultimate loads of reinforced joints are always pronounced, as shown in Figs. 12c and d. On the other hand, for the reinforced SHS T-joints with β=0.3, the ultimate loads of reinforced joints are slightly enhanced with the increase of λ ratio, as shown in Figs. 13a–b. This may attribute to the relatively small reinforced area, which resulted in the minor increase of the radial stiffness of chord member with the increase of the reinforced plate thickness. For the reinforced SHS T-joints with β > 0.3, the ultimate loads of reinforced joints are significantly enhanced with the increase of λ ratio, as shown in Figs. 13c and d. This may attribute to the relatively large reinforced

Table 6 Validity range of geometric parameters. Geometric parameter

β=b1/b0

Δ=br/b1

λ=tr/t0

CIDECT [2] Eurocode 3 [34] Parametric study and test

≥0.1+0.01b0/t0, but≥0.25 ≤0.85 [0.3–0.9]

– br≥b0−2t0 [1.5–3.0]

– – [1.0–2.5]

Fig. 10. Failure modes of reinforced SHS T-joints in the parametric study.

forced plate to chord wall thickness ratio (λ=tr/t0) were evaluated. The validity range of these geometric parameters defined in the CIDECT [2] and Eurocode 3 [34] design rules, as well as those in the parametric study and tests are summarized in Table 6. It is shown from the comparison that some geometric parameters in the parametric study

Fig. 11. Effect of β on ultimate loads of reinforced SHS T-joints.

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Fig. 12. Effect of Δ on ultimate loads of reinforced SHS T-joints.

doubler plate reinforced SHS T-joints, respectively, which can be calculated as follows:

area, which resulted in the major increase of the radial stiffness of chord member with the increase of the reinforced plate thickness.

For β ≤ 0.30: 5. Proposed design equations It should be noted that the design rules given in the current design specifications for welded tubular joints are applicable to the unreinforced tubular joints only. There is no design rule currently used for the reinforced tubular joints. Therefore, the design rules for the collar plate and doubler plate reinforced SHS T-joints were proposed in this study based on the design rules for the unreinforced SHS T-joints by introducing the correction factors ψc and ψd, respectively, which depend on the β and Δ ratios. The joint strengths of collar plate and doubler plate reinforced SHS T-joints under axial compression can be calculated as follows:

Puc = ψc *Puu

(2)

Pud = ψd *Puu

(3)

ψc = 1.1Δ − 0.65;

ψd = 0.97Δ − 0.7

For 0.30 < β ≤ 0.85:

ψc = 0.4Δ + 1.5;

For 0.85 < β ≤ 1.0:

ψc = 0.02Δ + 0.45;

ψd = 0.19Δ + 0.5 ψd = 0.06Δ + 0.4

(4) (5) (6)

where Puu is the design strength of the unreinforced SHS T-joints under axial compression, which can be obtained from the design equation given in the current Eurocode 3 [34] as follows:

Puu =

fy0 t02 1−β

(2β + 4 1 − β )

(7)

The design strengths (Puc and Pud) of the collar plate and doubler plate reinforced SHS T-joints under axial compression calculated using Eqs. (2) and (3), respectively, were compared with the joint strengths obtained from the parametric study, as shown in Table 7. A good agreement was reached with the mean values of design strength-toFEA result ratios of 0.91 and 0.91, and the corresponding coefficient of

where ψc and ψd are the correction factors for the collar plate and 85

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Fig. 13. Effect of λ on ultimate loads of SHS T-joints.

this study on the static behaviour of the collar plate and doubler plate reinforced SHS T-joints under axial compression. Some conclusions can be drawn as follows:

Table 7 Comparison of design strengths with FEA results for collar plate and doubler plate reinforced SHS T-joints. Specimen

Comparison

A total of 48 collar plate reinforced SHS T-joints and 48 doubler plate reinforced SHS T-joints

Puc/PFEA

Pud/PFEA

Mean COV

0.91 0.023

0.91 0.024

variations (COVs) of 0.023 and 0.024, for the collar plate and doubler plate reinforced SHS T-joints under axial compression, respectively. Therefore, the proposed design equations were verified to be accurate for the design of collar plate and doubler plate reinforced SHS T-joints under axial compression.

(1) The initial stiffness and ultimate strengths of SHS T-joints are enhanced remarkably with the increase of brace to chord width ratio. (2) The initial stiffness and ultimate load of SHS T-joints are enhanced significantly by reinforcing with the collar plate and doubler plate. (3) when brace to chord width ratio is small (β=0.53), the enhancement of ultimate loads of SHS T-joints reinforced with collar plate and doubler plate are almost identical. When brace to chord width ratio is large (β≥0.67), the reinforcement of doubler plate is more pronounced than that of collar plate in ultimate loads. (4) The proposed design equations for the collar plate and doubler plate reinforced SHS T-joints under axial compression were verified to be accurate and safe.

6. Conclusions

Acknowledgements This research work was supported by the National Natural Science

The experimental and numerical investigations were conducted in 86

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