Hysteretic performance of high-strength steel square hollow section T joints considering fracture behavior

Abstract

The performance of high-strength steel (HSS) welding joints is crucial for tubular structure design. This paper investigates the hysteretic performance of HSS square hollow section (SHS) T joints considering fracture behaviors. The hysteresis and tensile tests of the HSS SHS T joints and a comparative analysis of failure modes and bearing capacity are conducted. Parameter analysis is conducted based on the validated FE model considering fracture and elastoplastic constitutive relationship with a wide range of parameters covered, including the cross-sectional width ratio and the wall thickness ratio between brace and chord, and the width-thickness ratio of the chord, and the seam weld size of the joint connection. The results show that fracture behavior can affect the failure mode and bearing capacity of the joints, and it cannot be ignored in the hysteresis analysis process. The energy consumption capacity and the ductility coefficients increase when β increases from 0.2 to 1.0, τ increases from 0.3 to 1.0 and 2γ decreases from 40 to 20. Meanwhile, joints’ failure modes and residual strength vary with the above parameters. It is necessary to use the damage fracture constitutive model of steel in numerical simulation.

Keywords

tubular T-joints HSS square hollow section ductile damage fracture hysteretic performance parametric analysis

Introduction

In the steel structures, the properties of the joints play an essential role in the structure’s safety, hence the mechanical properties and failure modes of the steel tubular joints is a critical issue. With the advancement of material technology, high-strength steel (HSS) has gradually been used in steel tubular joints. Due to the change in microstructure and forming process, the strength of HSS is much higher than that of traditional low-carbon steel such as Q235 and Q345. Meanwhile, it has the advantages of lightweight, low cost, corrosion resistance, and high weldability, and has been widely used in civil engineering (Javidan et al., 2016; Li et al., 2016). Due to the use of HSS, the mechanical properties and failure modes of the HSS tubular joints may be different.

At present, many researchers have conducted research on the static performance of high-strength steel tubular joints. For example, Pandey et al. (2019; 2021) conducted mechanical performance tests on cold-formed high-strength T-shaped square steel tubular joints under compression loads. The results show that the equations in Eurocode (2005) and CIDECT Design Recommendations (2009) poorly predict the strength of cold-formed HSS square hollow section T joints. Lan et al. (2021) conducted experimental research on mechanical properties and several parameter analyses on HSS circular hollow section T joints under predominantly static loading. The results show that the CIDECT design suggestion (Wardenier, 2008) is more accurate in predicting the strength of the S460 steel circular hollow section T joints. Cai et al. (2021) conducted experimental research on the mechanical properties of HSS circular hollow section X joints. The results showed that the joint geometric parameters affect their strength. Based on the experiments and parameter analysis results, a new joint strength prediction equation was proposed. Lan et al. (2021) compared and analyzed the strength of S960 HSS X joints using different bearing capacity equations. Yan et al. (2023) analyzed the applicability of the material coefficient and yield strength ratio of HSS tubular joints to the joint bearing capacity. The results show that if the HSS tubular joints are calculated using the suggested equation of the Eurocode (2005), the requirements of the material coefficient and the yield strength ratio do not need to be considered.

Regarding the hysteresis performance of steel tubular joints. Zhao et al. (2022) proposed a hysteretic model of circular hollow section X joints under in-plane bending based on test results and FE model analysis. Shao et al. (2017) compared the energy dissipation capacity, ductility, and skeleton curves of circular hollow section T joints under high-temperature and normal-temperature fields. However, the hysteresis performance of HSS tubular joints is also worth studying, because there are differences in material properties between HSS and ordinary strength steel. Further analysis is needed to determine whether the conclusions obtained based on the hysteresis performance of ordinary strength steel joints are still applicable to HSS joints. Furthermore, the joints ductility will decrease as the strength of HSS increases (Zhao et al., 2013), which may lead to HSS joints being prone to fracture under reciprocating loads (Li et al., 2016).

In this paper, the hysteretic behavior of high-strength square hollow section (HSS SHS) T joints with a yield strength of 460 MPa is studied. Low cycle reciprocating and tensile tests are carried out on HSS SHS T-joints, and the failure modes and bearing capacity are compared and analyzed. Then, numerical simulation and parameter analysis are conducted to analyze the hysteresis performance of HSS SHS T-joints by considering the fracture constitutive model of HSS.

Experimental program

Details of the specimens

The main geometric parameters of the joints include the cross-sectional width ratio β and the wall thickness ratio τ between brace and chord, and the width-thickness ratio 2γ as shown in equations (1)∼(3). For the convenience of model production and testing, the experimental specimen only considers changes in parameter β, while other parameters were analyzed through numerical simulations. Six HSS SHS T-joints were designed, three for cyclic testing and three for monotonic tensile comparison testing. Referring to the study of HSS X joints by CAI (2021), the chord’s length is 5b₀, and the brace’s length is 2b₁ + 40. The details of the HSS SHS T joint are shown in Figure 1, and the parameters of the T-joint specimens are shown in Table 1.

β = b_{1} / b_{0}

(1)

τ = t_{1} / t_{0}

(2)

2 γ = b_{0} / t_{0}

(3)

Figure 1.

Schematic view of the T-joint specimens.

Table 1.

Parameters of the T-joint Specimens.

Specimen Serial number	Parameter of chord(mm)			Parameter of brace(mm)			Geometric parameters
Specimen Serial number	b₀/mm	t₀/mm	l₀/mm	b₁/mm	t₁/mm	l₁/mm	β	τ	2γ
SJ-1-H	100	6	500	40	6	120	0.4	1.0	16.67
(Cyclic loading)	100	6	500	40	6	120	0.4	1.0	16.67
SJ-1-T	100	6	500	40	6	120	0.4	1.0	16.67
(Tension)	100	6	500	40	6	120	0.4	1.0	16.67
SJ-2-H	100	6	500	80	6	200	0.8	1.0	16.67
(Cyclic loading)	100	6	500	80	6	200	0.8	1.0	16.67
SJ-2-T	100	6	500	80	6	200	0.8	1.0	16.67
(Tension)	100	6	500	80	6	200	0.8	1.0	16.67
SJ-3-H	100	6	500	100	6	240	1.0	1.0	16.67
(Cyclic loading)	100	6	500	100	6	240	1.0	1.0	16.67
SJ-3-T	100	6	500	100	6	240	1.0	1.0	16.67
(Tension)	100	6	500	100	6	240	1.0	1.0	16.67

Material properties

The material properties test specimens were designed concerning GB/T 228.1-2010 (2011), as shown in Figure 2(a). The specimens in Figure 2(b) were named SK-1∼SK-3, respectively, and the tensile test was carried out on the loading platform, as shown in Figure 2(c). The engineering stress and strain curve of Q460 steel is shown in Figure 2(d), and the critical parameters are shown in Table 2.

Figure 2.

Test specimens and results.

Table 2.

Mechanical properties of high-strength steel.

	σ _y	E ₀	σ _u	ε _u	σ _f	ε _f
serial number	(MPa)	(GPa)	(MPa)	mm/mm	(MPa)	mm/mm
SK-1	571.99	200.2	658.59	0.164	510.40	0.254
SK-2	546.21	201.1	637.01	0.180	466.01	0.317
SK-3	575.90	200.4	674.03	0.176	506.18	0.284

Note: Subscript f indicated fracture

Testing procedures

The testing was controlled by displacement in this paper. Servo actuator applied hysteresis displacement load to the T joints through the upper plate, as shown in Figure 3. The vertical displacement was measured using a displacement instrument. The hysteretic displacement and cyclic curve are shown in Figure 4. The tests are loaded step by step according to the displacement amplitude, with one cycle per stage.

Figure 3.

Experimental setup.

Figure 4.

Loading schemes.

Test results and analysis

Hysteresis test results

The hysteresis curves of specimens SJ-1-H∼3-H are shown in Figure 5. It can be seen that the hysteresis curve of specimen SJ-1-H is relatively plump and fusiform. The maximum positive and negative displacement of the joint was 10.4 mm and 27 mm. The joints produced an initial fracture when compressed to around 2.5 mm. It can be seen from Figure 5(b) and (c) that the hysteresis curves of specimens SJ-2-H and SJ-3-H are similar to SJ-1-H. For SJ-2-H, the maximum positive and negative displacement was 12.5 mm and 22.9 mm. When the tensile displacement was about −10 mm, an initial fracture occurred, as shown in the “initial crack” in the Figure 5(b). For SJ-3-H, the maximum and negative positive displacement was 11.3 mm and 15.3 mm, an initial fracture occurred when the tension displacement was near 2.5 mm. When the joints were stretched to about 10 mm, the crack penetrates, causing the specimen SJ-1-H to break at the connection of the brace chord and the corner of the chord. When the joints SJ-2-H and SJ-3-H were compressed to about 7.5 mm, the joints break at the corners of the connection.

Figure 5.

Hysteresis curves.

Failure modes comparison

The failure mode comparison is shown in Figure 6. Specimen SJ-1 had a large convex deformation at the flange of chord. However, different from the tension state, the joint had a large crack in local areas under hysteretic load. The failure modes of specimens SJ-2 and SJ-3 were similar, and the chord had a noticeable bending phenomenon. In addition, the bottom of the chord of specimen SJ-2 had apparent concave deformation, while specimen SJ-3 had local cracks at the flange of chord. Different from the failure mode under tensile load, under hysteretic load, the specimens SJ-2 and SJ-3 did not show apparent chord bending phenomenon and obvious cracks occurred at the joint connections.

Figure 6.

Failure mode comparison.

Skeleton curve comparison

The skeleton curves are shown in Figure 7. According to the geometric drawing method (Feng et al., 2017), the yield load, yield displacement, ultimate load, and ultimate displacement can be obtained, as shown in Table 3. It can be seen that the stiffness and strength increase with the increase of parameter β. This is related to the mechanical model of the joint. When β is small, the failure mode of joint is the yield line mode. Each yield line at the flange of the chord rotated accordingly and caused deformation. When the parameter β is large, the failure model is mixed. In addition to the local yield deformation at the flange of the chord, the corner and side walls of the chord also buckled locally. It can be seen that the deformation capacity of the joints under monotonic tension was much higher than that under reciprocating loads. The ductility coefficients under reciprocating loads are 2.3, 2.8, and 3.0, respectively. However, the three joints under monotonic tension are 4, 11, and 9.6, respectively, as shown in Table 3.

Figure 7.

Skeleton curves of hysteresis and tensile tests.

Table 3.

Characteristic parameters.

Specimen Number	P_y/kN	Δ_y/mm	P_u/kN	Δ_u/mm	μΔ_u/Δ_y	P_u*/kN	P_u*/P_u	Failure mode (Hysteretic)	Failure mode (Tension)
SJ-1-H(+)	160	5.8	160	13.1	2.3	—	—	1 + 2 + 3-H	3-T
SJ-1-H(−)	160	5.2	154	28.2	5.4	—	—	1 + 2 + 3-H	3-T
SJ-1-T	130	7	—	28	4	230	1.4	—	—
SJ-2-H(+)	308	4.64	273	12.7	2.8	—	—	4-H	5 + 6-T
SJ-2-H(−)	273	4.37	253	23.6	5.4	—	—	4-H	5 + 6-T
SJ-2-T	294	4.28	—	47	11	339	1.2	—	—
SJ-3-H(+)	336	4.3	293	12.5	3	—	—	4-H	4 + 6-T
SJ-3-H(−)	289	4.3	271	16.5	3.8	—	—	4-H	4 + 6-T
SJ-3-T	281	4.5	—	43	9.6	338	1.2	—	—

Numerical simulation and parameter analysis

Constitutive relationship based on damage and fracture

Referring to the fracture model calibration method of high-strength structural steel by Yang et al. (2020), ABAQUS was used to calibrate the relationship between the damage variable and the damage plastic strain in this paper. The material fracture constitutive model analysis was based on the data of material properties test results. Before the necking, the true stress and strain were calculated from the engineering stress and strain, as shown by Equations (4) and (5) (the ones with subscript n are engineering stress and strain). After necking, the true stress-strain was calculated using the linear-power hardening equation proposed by Yun et al. (1996), as shown in equation (6), where ε is the true strain converted by equation (5). Among them, a = σ_t,u is the true stress at the necking point, n = ε_t,u is the true strain at the necking point, b = a(1-n), K = a/nⁿ, W is the weighting factor. After multiple assignments and ABAQUS modeling and calculation, it was converted into engineering stress and strain curves and determined based on the test material properties curves.

σ = σ_{n} (1 + ε_{n})

(4)

ε = \ln (1 + ε_{n})

(5)

σ = W (a ε + b) + (1 - W) K ε^{n}

(6)

{\bar{u}}_{p l}^{f} = L (ε_{p l}^{f} - ε_{p l}^{0})

(7)

Where,

u_{p l}^{f}

the effective plastic displacement, L is the characteristic length of the element. For the C3D8R element, L is its side length,

ε_{p l}^{f}

is the plastic strain of the material at fracture, and

ε_{p l}^{0}

is the plastic strain of the material at the necking point.

After multiple adjustments, calculations, and comparisons, as shown in Figure 8(a) the weight factor with a high degree of agreement with the original engineering stress and strain curve can be obtained as W = 0.05. Then, Equations (4)∼(6) was used to generate the real stress and strain of the material before and after necking. The reaction force and displacement curve of the specimen was obtained and converted into an engineering stress and strain curve, which was consistent with the original test engineering stress and strain. The curve corresponds to each other, as shown in the “SK-1 TEST” and “FEM-no fracture” curves in Figure 8(b).

Figure 8.

Weight factor W correction and results.

In the Yang model and ABAQUS model, the damage variable Di is used to represent material degradation and damage, and the damage variable Di can be calculated and determined by equation (7) and the actual damage stress. According to the stress triaxiality equivalent plastic strain curve, the equivalent plastic strains corresponding to the onset of necking point damage and fracture are 0.1625 and 0.8488, respectively as shown in Figure 9. Meanwhile, compare the corresponding strains of the “SK-1 TEST” and “FEM-no fracture” curves at the time of fracture, the plastic strain at this point of the “FEM-no fracture” curve was 0.2226 according to equation (7). The failure displacement of the material was calculated as ${\bar{u}}_{p l}^{f} = 0.0601 mm$ when the characteristic mesh length L = 1 mm. According to the above parameters, the damage variable Di can be calculated. Figure 9(b) shows the damage evolution law for the investigated steel, which is the relationship between the damage variable Di and the damage plastic strain for the steel. The critical damage variable D_cr is 0.415 as marked in Figure 9(b), it is utilized to realize the element removal function in ABAQUS.

Figure 9.

Determination of fracture parameters.

In addition, it is worth noting that the constitutive model of steel under cyclic loading is different from that under monotonic loading. Generally, in numerical simulation, the Ramberg-Osgood model was often used to fit the cyclic skeleton curve, and the cyclic strengthening parameters were obtained through experimental calibration. Then, finite element software can be used for numerical simulation. For the high-strength steel Q460, the material properties test results of Shi (2012) show that there was not much difference between the cyclic skeleton curve and the monotonic skeleton curve. The maximum difference in yield strength was 4%, and the maximum difference in ultimate strength was 6%. Therefore, when analyzing cyclic loads, the authors use the constitutive model obtained from monotonic experiments in this paper. In addition, using monotonic tensile test results can make it more convenient to use Yang’s fracture model for numerical simulation.

FE model and validation

In order to save computational resources, finite element models can be simplified based on symmetry, for example, Chang (2014) and Xia et al. (2017) used a 1/4 analysis model for joints analysis. The joints in this paper were analyzed using a 1/2 model based on symmetry, as shown in Figure 10. For the weld seam, a sweeping method was used to establish the weld seam model according to Zhu’s simulation method (Zhu et al., 2013), and solid elements C3D8R were used for finite element division of all the weld seam, the chord and brace. It should be noted that the thickness of the weld, chord, and brace is the same, and the value is 6 mm, just like the previous specimens. Furthermore, During the production of the specimens, AristoRod 69 was used for welding with a yield strength of 715 MPa and an ultimate strength of 805 MPa. Due to its main mechanical parameters being greater than the base steel material, the same constitutive relationship as the base steel material was used for numerical simulation. The simulation results of hysteresis curves are shown in Figure 10. The comparison between the failure results is shown in Figure 11.

Figure 10.

FE model.

Figure 11.

Comparison of FEM results and test results.

From Figure 11, it can be seen that the hysteresis curves of the simulation and experiment are basically consistent. The finite element simulation results of specimens SJ-1 to SJ-3 are in good agreement with the positions of the maximum compression tension point, initial fracture point, and crack penetration point in the experimental hysteresis curves. The failure modes of specimens SJ-1∼3 are basically similar (Figure 12). For specimen SJ-1, fractures occurred on the inner wall of the chord corner and around the connection of the brace and chord, which was consistent with the test phenomenon. The failure positions of specimen SJ-2 were the same as that of the test results, and occurred at the corners of the connection between the brace and chord. However, for specimen SJ-3, the joint fracture only occurred in the local area of the weld at the connection, and the penetration phenomenon was not apparent.

Figure 12.

Comparison between simulated results and tested phenomena.

Parameter analysis of hysteresis performance

Details of the specimens

Four geometric parameters are considered during parameter analysis, including β, τ, 2γ, and h_f (the weld foot size). The parametric analysis specimens are divided into four groups A, B, A-EP, and A-SW. EP means that the “NO fracture” curve in Figure 8 is used for the elasto-plastic analysis of group A. SW means changing the fillet size of the seam weld for some joints in Group A. Referring to GB 50017-2017 (2017), the size of the seam weld leg should not be larger than twice the wall thickness of the brace, therefore, it is set as h_f, 1.5h_f, and 2h_f. The details of the specimens are shown in Table 4.

Table 4.

Detailed parameters for Parametric Analysis.

Specimen Group	Brace Section		Chord Section		Geometric parameters			Brace Length	Chord Length	Seam Weld Size
Specimen Group	b₁/mm	t₁/mm	b₀/mm	t₀/mm	β	τ	2γ	l ₁/mm	l₀/mm	h_f/mm
A/A-EP	20	5.40	100	6.00	0.2	0.9	16.67	80	650	5.40
	40	5.40	100	6.00	0.4	0.9	16.67	120	650	5.40
	60	5.40	100	6.00	0.6	0.9	16.67	160	650	5.40
	80	5.40	100	6.00	0.8	0.9	16.67	200	650	5.40
	100	5.40	100	6.00	1.0	0.9	16.67	240	650	5.40
	40	1.80	100	6.00	0.4	0.3	16.67	120	650	1.80
	40	3.00	100	6.00	0.4	0.5	16.67	120	650	3.00
	40	4.20	100	6.00	0.4	0.7	16.67	120	650	4.20
	40	5.40	100	6.00	0.4	0.9	16.67	120	650	5.40
	40	6.00	100	6.00	0.4	1.0	16.67	120	650	6.00
	40	2.25	100	2.50	0.4	0.9	40	120	650	2.25
	40	2.57	100	2.86	0.4	0.9	35	120	650	2.57
	40	3.00	100	3.33	0.4	0.9	30	120	650	3.00
	40	3.60	100	4.00	0.4	0.9	25	120	650	3.60
	40	4.50	100	5.00	0.4	0.9	20	120	650	4.50
B	40	7.20	200	9.00	0.2	0.8	22.2	120	1150	7.20
	80	7.20	200	9.00	0.4	0.8	22.2	200	1150	7.20
	120	7.20	200	9.00	0.6	0.8	22.2	280	1150	7.20
	160	7.20	200	9.00	0.8	0.8	22.2	360	1150	7.20
	200	7.20	200	9.00	1.0	0.8	22.2	440	1150	7.20
	100	2.70	200	9.00	0.5	0.3	22.2	240	1150	2.70
	100	4.50	200	9.00	0.5	0.5	22.2	240	1150	4.50
	100	6.30	200	9.00	0.5	0.7	22.2	240	1150	6.30
	100	8.10	200	9.00	0.5	0.9	22.2	240	1150	8.10
	100	9.00	200	9.00	0.5	1.0	22.2	240	1150	9.00
	100	4.00	200	5.00	0.5	0.8	40	240	1150	4.00
	100	4.57	200	5.71	0.5	0.8	35	240	1150	4.57
	100	5.33	200	6.67	0.5	0.8	30	240	1150	5.33
	100	6.40	200	8.00	0.5	0.8	25	240	1150	6.40
	100	8.00	200	10.00	0.5	0.8	20	240	1150	8.00
A-SW	60	5.40	100	6.00	0.6	0.9	16.67	160	650	5.40
										8.10
										10.80
	40	4.20	100	6.00	0.4	0.7	16.67	120	650	4.20
										6.30
										8.40
	40	3.60	100	4.00	0.4	0.9	25	120	650	3.60
										5.40
										7.20

Failure modes

During numerical simulation, all specimens were subjected to reciprocating loads until fracture occurred, and the partial results are shown in Figure 13. When β increased, the joint failure mode changed accordingly. When β was in the range of 0.2 to 0.6, the fracture modes of the joints were roughly similar, and they all occurred at the connection of brace and chord, accompanied by local yielding of the flange and cracking of chord corner. The joint fracture area changed when the parameter β increased from 0.6 to 1. When τ is in the range of 0.3 to 0.5, the fracture modes of the joints are similar, and they all occurred at the bottom of brace, accompanied by buckling of the brace bottom and cracking of the chord corner. When τ increases from 0.5 to 1, fractures occurred at the connections of joints. When 2γ decreases, the joint failure modes do not change significantly.

Figure 13.

Failure modes of group A joints.

Hysteresis curve comparison

Hysteresis curves of the typical specimens in all groups are shown in Figure 14. It can be seen that the increase of parameter β improves the energy consumption capacity of joints. When β = 0.2 and 0.4, the hysteresis curve had an apparent pinching phenomenon, the cracks in the joints caused a severe decrease of the joint stiffness, bearing capacity and deformation capacity, which in turn leads to a decrease in the energy dissipation capacity. When β increases to 0.8, the pinching phenomenon of the curve was relatively improved. The joint did not completely fracture during the loading process, the joints’ stiffness, bearing capacity, and deformation capacity were still partially retained. Meanwhile, the increase of parameter β also affects the maximum displacement and peak load. For example, in group A, when β is 0.2, the maximum positive (positive means tension and negative means compression) displacement of the joints was 13.5 mm, the maximum negative displacement was 13.5 mm, the maximum tensile load was 169 kN, and the maximum compressive load was 130 kN. When β increases to 1.0, the maximum positive and negative displacements were 30 mm and 27 mm respectively. The maximum tensile and compressive loads were 392 kN and 361 kN respectively. It can be seen that when the parameter β increases, the maximum positive and negative displacements increase by 100% to 122%; the positive and negative peak loads increase by 132% to 178%. Parameters τ and 2γ have a similar impact pattern, but their impact was relatively small compared to parameter β.

Figure 14.

Hysteresis curves of typical specimens.

Energy consumption comparison

In order to further study the changing law of energy consumption capacity of joints, the cumulative energy consumption area Q_u and cumulative energy consumption ratio η_tot can be used for analysis. The parameter η_tot was proposed by Zhao et al. (2019) when they studied the hysteresis performance of X joints. A larger η_tot leads to the better energy dissipation capacity of the joint. The definition of the ratio is as follows.

η_{t o t} = E_{t o t} / E_{y} = \sum_{i = 1}^{n} E_{i} / 0.5 (P_{y (+)} Δ_{y (+)} + P_{y (-)} Δ_{y (-)})

(8)

Where, P_y and Δ_y are the joints’ yield load and yield displacement, which can be determined according to the geometric drawing method (Feng et al., 2017) based on the skeleton curves as shown in Figure 15. The detailed results are shown in Table 5.

Figure 15.

Skeleton curves.

Table 5.

Hysteretic Curves Index.

Specimen Serial number	P_y(+)/kN	Δ_y(+)/mm	P_y(−)/kN	Δ_y(−)/mm	P_u(+)/kN	Δ_u(+)/mm	P_u(−)/kN	Δ_u(−)/mm	Q_u/kN·mm	η _tot	μ₍₊₎Δ_u(+)/Δ_y(+)	μ₍₋₎Δ_u(−)/Δ_y(−)
A-β = 0.2	125.12	7.55	92.56	5.40	144.06	13.50	110.93	13.50	6531.99	9.04	1.79	2.50
A-β = 0.4	185.66	6.62	133.95	3.68	207.08	13.50	136.83	10.52	8247.68	9.58	2.04	2.86
A-β = 0.6	268.74	5.27	218.93	3.54	269.95	13.50	205.02	13.59	13151.08	12.00	2.56	3.84
A-β = 0.8	321.96	4.56	303.27	3.76	311.43	16.39	278.06	18.75	55196.47	42.34	3.60	4.98
A-β = 1.0	343.41	4.30	331.80	3.72	333.77	15.09	307.34	18.63	58400.34	43.08	3.51	5.01
A-τ = 0.3	131.57	4.89	102.26	2.95	137.14	9.00	94.49	7.30	3085.58	6.54	1.84	2.48
A-τ = 0.5	179.57	7.88	121.86	4.24	202.90	13.50	131.03	13.50	8492.45	8.79	1.71	3.18
A-τ = 0.7	185.52	7.23	129.35	3.77	208.75	13.50	132.62	12.16	8390.18	9.17	1.87	3.23
A-τ = 0.9	190.07	6.69	136.55	3.72	211.92	13.50	139.90	9.78	8201.94	9.22	2.02	2.63
A-τ = 1.0	193.07	6.52	139.11	3.56	214.72	13.50	143.63	11.72	8514.68	9.71	2.07	3.30
A-2γ = 40	73.97	12.85	48.68	12.00	65.60	15.53	45.74	13.50	2632.63	3.43	1.20	1.13
A-2γ = 35	86.84	12.44	55.48	11.01	79.05	14.90	55.36	13.50	2995.58	3.54	1.20	1.23
A-2γ = 30	102.17	11.75	62.43	9.53	96.90	14.22	67.58	13.50	3711.59	4.14	1.21	1.42
A-2γ = 25	117.78	9.80	66.46	6.32	121.81	13.50	78.84	13.50	4102.80	5.21	1.38	2.13
A-2γ = 20	155.86	8.45	91.18	4.02	170.68	13.50	97.36	10.67	6010.73	7.14	1.60	2.65
B-β = 0.2	333.45	14.84	236.35	11.78	343.82	20.66	264.89	19.50	18132.33	4.69	1.39	1.66
B-β = 0.4	464.10	12.38	321.50	8.42	503.29	20.39	367.34	19.50	27545.23	6.52	1.65	2.31
B-β = 0.6	703.70	9.96	503.34	6.02	751.12	20.93	516.50	20.95	40783.54	8.13	2.10	3.48
B-β = 0.8	1067.75	8.19	888.47	5.80	1051.79	28.14	811.40	21.06	159010.45	22.88	3.44	3.63
B-β = 1.0	1201.12	7.46	986.95	5.98	1157.77	32.09	931.56	32.02	291689.06	39.25	4.30	5.36
B-τ = 0.3	409.12	9.17	299.78	6.20	420.71	15.63	305.84	13.00	10417.60	3.71	1.70	2.10
B-τ = 0.5	532.70	12.70	363.91	7.96	673.32	26.00	398.79	20.99	52419.47	10.85	2.05	2.64
B-τ = 0.7	539.77	11.41	380.39	7.24	587.90	21.31	405.71	19.50	43297.63	9.72	1.87	2.69
B-τ = 0.9	556.95	10.87	387.40	6.44	607.41	21.00	406.39	19.50	41440.56	9.69	1.93	3.03
B-τ = 1.0	569.84	10.80	397.36	6.41	623.09	21.06	417.93	19.50	41906.88	9.63	1.95	3.04
B-2γ = 40	307.81	21.73	172.10	15.08	290.74	26.74	176.84	26.69	18067.16	3.89	1.23	1.77
B-2γ = 35	310.69	16.61	191.51	12.78	300.58	23.89	214.37	22.77	21577.87	5.67	1.44	1.78
B-2γ = 30	372.96	14.65	226.88	9.96	386.37	21.97	266.01	20.36	27701.36	7.17	1.50	2.04
B-2γ = 25	459.25	12.28	303.34	8.12	493.15	21.58	339.68	19.50	36458.22	9.00	1.76	2.40
B-2γ = 20	645.70	10.34	468.87	6.24	699.89	20.69	557.40	19.50	50297.36	10.48	2.00	3.12

Note:+ indicates tension,- indicates compression.

The impact of parameters on the energy consumption capacity of joints in groups A and B is shown in Figure 16. It should be noted that the parameters Q_u and η_tot are normalized. It can be seen that the increase of parameter β improves the energy consumption capacity of joints. When the parameter β increases from 0.2 to 0.6, the cumulative energy consumption Q_u and the cumulative energy consumption ratio η_tot of joints increase relatively slowly. When the parameter β increases from 0.6 to 1, they increase relatively quickly. When the parameter β varies between 0.2 and 0.6, the joints’ main stress-bearing parts and energy-consuming areas are the yield line areas at the flange of the chord. However, compared with the flange area of the chord, the punching shear strength of the joint connection area at the bottom of the brace is insufficient, so it is easy to crack at the joint connection under the action of low cycle reciprocating load, forming through cracks and weakening the energy consumption capacity of the joint. Parameters τ and 2γ have a similar impact pattern, but their impact is relatively small compared to parameter β.

Figure 16.

Energy consumption.

Ductility

The positive and negative ultimate loads, ultimate displacements, yield displacements, and ductility coefficients of joints are shown in Table 5. The results are shown in Figure 17. When β increases, the overall improvement rate of the joint ductility coefficient is 96%∼223%. The increase of the parameter has a more significant effect on the joint ductility coefficient. This indicates a significant increase in tensile deformation capacity. When τ increases, it shows that the joints’ ductility coefficient improvement rate is 13%∼44%. When 2γ is reduced, the increase rate of the ductility coefficient is 33%∼135%. The relative increase of the chord wall thickness can improve the deformation ability of the joint. It indicates that the relative increase of the chord wall thickness can improve the deformation ability of the joint.

Figure 17.

Ductility coefficient.

The ductility influence coefficient can be used to quantitatively analyze each parameter’s influence on the joint’s deformation capacity. The ductility influences coefficients of parameters β, τ and 2γ are shown in Equations (9)–(11).

k_{β - μ} = Δ_{μ} / Δ_{β}

(9)

k_{τ - μ} = Δ_{μ} / Δ_{τ}

(10)

k_{2 γ - μ} = Δ_{μ} / Δ_{2 γ}

(11)

Where Δ_μ indicates the difference between the ductility coefficients of the starting and the ending points of each polyline in Figure 17, Δ_β and Δ_τ and Δ_2γ indicates the difference between the geometric parameters of the starting and the ending points. After calculation, kβ-μ = 2.89, kτ-μ = 0.34, k_2γ-μ = 0.03 can be obtained when the joints are under tension. When the joints are under compression, kβ-μ = 4.63, kτ-μ = 1.34, k_2γ-μ = 0.07. It can be seen that the mechanical model of the joints has the most significant influence on the improvement of deformation capacity, followed by the relative thickness of brace and finally the relative thickness of chord. In order to further analyze the influence of the fracture behavior on the ductility of the joints. Comparison of the ductility coefficients of groups A and A-EP is shown in Figure 18. It can be seen that μ_A-EP/μ_A is generally greater than 1, indicating that only considering the elasto-plastic constitutive model for analysis will overestimate the actual deformation capacity of joints.

Figure 18.

Comparison of group A and A-EP joints.

Conclusion

This paper has presented an investigation on the hysteretic performance of HSS SHS T joints. The hysteresis and tensile tests were carried out, and the comparison analysis was conducted. Meanwhile, parameter analysis was carried out based on the validated FE model.

(1) There are differences in the failure mode, ultimate load, and deformation capacity of HSS SHS T joints under cyclic load and monotonic tensile load. The joint ductility under cyclic loading is significantly lower than that under tensile loading. Under cyclic loading, multiple cracks at the T joint connections rapidly penetrate, weakening the joint’s bearing capacity and deformation capacity, resulting in damage to the joint and a decrease in ultimate load.

(2) The increment of parameters β and τ and the decrement of 2γ increase the energy consumption capacity and ductility coefficients of the HSS SHS T joints. Meanwhile, the change of the above parameters leads to different failure modes due to the changing of mechanical model and resistance of chord hollow sections. With the increase of parameter β, fracture extends from the connection of the joint to the side and bottom of the chord, with the increase of parameter τ, fracture extends from the bottom of the brace to the connection of the joint. Furthermore, the increase of seam weld size can delay the joint fracture trend and ensure the joints’ residual strength.

(3) Under reciprocating loads, the HSS SHS T joints are more prone to damage or even fracture, it is necessary to use the damage fracture constitutive model of HSS in numerical simulation.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China; 52278471.

ORCID iD

Shicai Chen

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