Design of CHS brace-to-H-shaped chord T-joints under axial compression

Thin-Walled Structures 98 (2016) 274–284

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Design of CHS brace-to-H-shaped chord T-joints under axial compression Yu Chen a,b, Ran Feng c,n, Lin Wei b a

School of Urban Construction, Yangtze University, Jingzhou 434023, China College of Civil Engineering, Huaqiao University, Xiamen 361021, China c School of Civil Engineering, Hefei University of Technology, Hefei 230009, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 9 July 2015 Received in revised form 7 October 2015 Accepted 7 October 2015

This paper presents a finite element model of circular hollow section (CHS) brace-to-H-shaped chord T-joints under axial compression, which was verified by the corresponding test results. The parametric study was carried out to reveal the failure modes and plasticity propagation of tubular joints. The effects of CHS brace diameter to H-shaped chord flange width ratio (β), H-shaped chord flange width to thickness ratio (2γ), and CHS brace to H-shaped chord flange thickness ratio (τ) on the ultimate strengths of tubular joints were evaluated. The typical failure modes were obtained from the finite element analysis, which include local buckling failure of CHS brace (LBFB), local buckling failure of flange and web of H-shaped chord (LBFF þLBFW), and local buckling failure of CHS brace and H-shaped chord flange (LBFB þLBFF). The validity range of main geometric parameters was recommended to be β Z0.7, 2γ ¼ 20– 30, and τ ¼ 0.25–0.5. The design equations are proposed by using multiple linear regression for CHS brace-to-H-shaped chord T-joints under axial compression based on the current design rules given in the Eurocode 3. Current Eurocode 3 is dangerous for predicting the ultimate strengths of CHS brace-to-Hshaped chord T-joints under axial compression. It is shown from the comparison that the joint strengths calculated using the proposed design equations agreed well with the finite element analysis results, which means the proposed design equations are verified to be accurate. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Axial compression CHS brace Finite element analysis H-shaped chord T-joints equations

1. Introduction Circular hollow section (CHS) brace-to-H-shaped chord joints nowadays are increasingly used in spatial structures due to its distinct merits over traditional CHS joints, as shown in Fig. 1. The flat surface can be provided by the H-shaped chord flange for installation of purlin and profiled sheet. Furthermore, it is much easier to fabricate CHS brace-to-H-shaped chord joints since the intersection region located at the flat plane. Literature reviews show that extensive research works were conducted on traditional CHS T-joints. The fatigue behavior of very high strength (VHS) steel tubes to steel plate T-joints under cyclic in-plane bending was investigated by Jiao et al. [1]. An experimental study was conducted into the static behavior of axially loaded CHS T-joints in compression and reinforced with FRP composites by Lesani et al. [2]. A finite element model validated by experimental results is developed to numerically study the failure modes and energy dissipation mechanism of tubular T-joint n

Corresponding author. E-mail address: [email protected] (R. Feng).

http://dx.doi.org/10.1016/j.tws.2015.10.005 0263-8231/& 2015 Elsevier Ltd. All rights reserved.

impacted by a drop hammer with the initial velocity of 7–10 m/s by Qu et al. [3]. Reinforced CHS T-joints with external stiffeners were numerically investigated by Zhu et al. [4]. The joint strength increased significantly as the size of the stiffener increased. The reinforcement effect is more dependent on the stiffener length than on the stiffener height. A numerical and experimental research program conducted on CHS T-and Y- joints was performed by Lesani et al. [5]. The FRP wrapping had significant influence on the ultimate load capacity of the connections and had proven to highly improve joints behavior. The fire resistant performance of circular hollow section (CHS) T-joint stiffened with internal rings under axial compression at elevated temperatures was experimentally and numerically investigated by Chen et al. [6]. The internal rings enhance the fire resistant performance of CHS T-joint by decreasing the temperature of chord efficiently and prolonging the fire-resistant time. SCF of thin-walled concrete-filled CHS T-, Y, K-, and KT-joints subjected to axial tension loading was experimentally investigated by Xu et al. [7]. The stress distribution was mainly determined by joint type, while the chord thickness had little effect on it. A series of tests were conducted on bare and concrete-filled CHS T-joints with concave chord under axial

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

tw r h h1 t1

Notation CHS FEA E fy fu

ν εf

fy0 fy1 bf bw Peff tf

Circular hollow section Finite element analysis Elastic modulus Tensile yield stress Ultimate tensile stress Poisson's ratio Elongation after fracture Yield stress of H-shaped chord Yield stress of CHS brace; Flange width of H-shaped chord flange Effective width of H-shaped chord web Effective width of CHS brace Thickness of H-shaped chord flange

θ1

Pu Pug

γM5 β 2γ

τ

275

Thickness of H-shaped chord web Corner radius of H-shaped chord Overall height of H-shaped chord External diameter of CHS brace Thickness of CHS brace Angel between CHS brace and H-shaped chord Ultimate strengths Yield strengths of CHS brace Resistance factor CHS brace diameter to H-shaped chord flange width ratio H-shaped chord flange width to thickness ratio CHS brace thickness to H-shaped chord flange thickness ratio

t

h

r

t

θ

b

Fig. 1. CHS brace-to-H-shaped chord T-joints.

compression by Chen et al. [8]. The ultimate strengths of the CHS T-joints with concave chord were generally larger than those of the traditional CHS T-joints with straight chord. The ultimate strengths of CHS T-joints with concave chord were significantly enhanced by filling the concrete in the chord member only, and the enhancement of the ultimate strengths of the CHS T-joints with large β was much more pronounced than that of the CHS T-joints with small β. The Zero Point Structural Stress (ZPSS) approach was improved to calculate the structural stress for the fatigue life assessment of tubular joints by Liu et al. [9]. The fire resistance behavior of tubular T-joints reinforced with collar and doubler plates was experimentally and numerically investigated by Gao et al. [10,11]. Up to the authors’ knowledge, only Eurocode 3 [12] provided comprehensive equation for CHS brace-to-Hshaped chord T-joints under axial compression in brace. There are no comprehensive design formulae given in the current design codes [13–17] for CHS brace-to-H-shaped chord joints, which have been further investigated in this study. This paper mainly focuses on the nonlinear finite element

analyses of CHS brace-to-H-shaped chord T-joints under axial compression. Accurate finite element models were developed to reveal the mechanical behavior of this type of joints, which were verified by the corresponding test results. An extensive parametric study was carried out using the verified finite element models to evaluate the effects of main geometric parameters on the failure modes and ultimate strengths of CHS brace-to-H-shaped chord T-joints under axial compression. The design equations are proposed for the joint strengths based on the numerical results.

2. Finite element analysis 2.1. FEA model The specimen dimensions of CHS brace-to-H-shaped chord T-joints in the finite element analysis are detailed in the corresponding experimental work [18]. Details of specimens are shown in Table 1. Geometric parameters are located in the range of

Table 1 Details of specimens. Specimen

CT10 CT11 CT20 CT21 CT30 CT31

Chord

Brace

a

b

(mm  mm  mm  mm)

(mm  mm)

(mm)

(mm)

HW200  200  8  12 HW200  200  8  12 HW200  200  8  12 HW200  200  8  12 HW200  200  8  12 HW200  200  8  12

Ф60  3.5 Ф60  3.5 Ф121  3.2 Ф121  3.2 Ф140  3.0 Ф140  3.0

550 550 550 550 550 550

350 350 350 350 350 350

Detail

Unstiffened Stiffened Unstiffened Stiffened Unstiffened Stiffened

276

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

Table 2 Material properties of steel. Specimen

Ф60  3.5 Ф121  3.2 Ф140  3.0 Flange of H200  200  8  12 Web of H200  200  8  12

E

fy

fu

εf

ν

(GPa)

(MPa)

(MPa)

(%)

210 207 205 201 203

455 390 400 293 280

505 460 495 438 405

28.76 22.80 24.05 21.89 23.78

0.29 0.30 0.29 0.26 0.22

practical project application of joints. It is universally acknowledged that the effect of chord length on ultimate capacity of joints can be ignored when the chord length is five times longer than the H-shaped chord height. In the consider of economy, the chord length of specimens was designed as five and half times as long as chord height in experimental research. 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). Tensile setup of steel coupon specimens and coupon specimens before tensile tests are shown in Figs. 2a and b, respectively. There are two types of boundary conditions for the finite element modeling of CHS brace-to-H-shaped chord T-joints under axial compression, which are identical to the experimental investigation. One of the boundary conditions is to provide pin support to both ends of the chord only in specimens CT10, CT11, CT20 and CT22, which used in horizontal truss resisting vertical roof loading, as shown in Fig. 3a. The other boundary condition is to provide surface constraint to the bottom flange of H-shaped chord only in specimens CT30 and CT31, which used in vertical truss resisting horizontal wind loading, as shown in Fig. 3b. The boundary condition of T-joints in FEA is the same with that in tests. The static uniform loads were applied by means of displacement at each node of the loaded end. The true experimental stress–strain curves from tensile coupon tests are used in ABAQUS, as shown in Fig. 4. Three-dimensional eight-node solid element with additional variables relating to the incompatible modes (C3D8I) given in the finite element program ABAQUS [19] was used in this study to model the CHS brace and H-shaped chord. This element is free of shear locking and leads to precise displacement and stress. The structural meshing method was adopted in the finite element modeling by controlling the element size. The welding area along the joint intersection region is 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 side length of control solid element of H-shaped chord and CHS brace far from intersection at chord and brace was arranged at about 6 mm. The side length of control solid element of at the chord and brace intersection region was arranged at about 2 mm. The welding seam at the intersection was omitted in FE models. Arc length was a selected solution method to calculate load–displacement curves of experimental specimens. The typical finite element mesh of CHS brace-to-H-shaped chord T-joint is shown in Fig. 5.

2.2. Verification of FEA model A comparison between the test and finite element analysis results was carried out to verify the finite element model. The typical failure modes obtained from finite element analysis were verified by those observed in the experimental investigation, as shown in Fig. 6. The minor deviation between the FEA and test results is from the symmetric deformed shape, which attributes to the difference between the ideal FEA model and practical experimental work with inevitable eccentric loading and specimen imperfections. Furthermore, the crack of parent metal is out of the scope of the FEA model, which is a continuum. In general, the failure modes of the specimens observed in the tests were closely simulated by the finite element analysis. The load–displacement curves obtained from the finite element analysis and tests are compared in Fig. 7 for all specimens with different failure modes. It is shown from the comparison that good agreement between the FEA and test results was obtained. However, it is worth noting that the initial stiffness of the specimens obtained from the FEA is all slightly greater than that from the tests, which may attribute to the stronger boundary conditions provided in the finite element model that lead to the smaller displacements of the specimens in the elastic range. The ultimate strength of CHS brace-to-H-shaped T-joints under axial compression is determined by the peak load. The comparison of the joint strengths obtained from the finite element analysis and tests is summarized in Table 3. Good agreement between the FEA and test results was achieved with the maximum difference of 10.55%. Therefore, it was demonstrated that the newly developed finite element model successfully predicted the structural behavior of the CHS brace-to-H-shaped chord T-joints under axial compression.

Fig. 2. Coupon tests of steel tube.

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

277

Fig. 3. Boundary conditions of T-joints in finite element models.

σ

ε Fig. 4. Stress-strain curve of steel coupon.

analyzed in the parametric study, which were selected from the range of practical applications, as shown in Table 4. The FEA results of the CHS brace-to-H-shaped chord T-joints in the parametric study are summarized in Table 5, which include the ultimate strengths (Pu) of T-joints, failure modes, yield strengths of CHS brace (Pug), and efficiency of joints in terms of Pu/Pug. There are three typical failure modes obtained from the parametric study, namely Local Buckling Failure of CHS Brace (LBFB), Local Buckling Failure of Flange and Web of H-shaped chord (LBFF þLBFW), and Local Buckling Failure of CHS Brace and H-shaped chord Flange (LBFBþ LBFF), which are identical to those observed in the experimental investigation, as shown in Figs. 8a–c, respectively. The failure of the specimens was determined by the deformations and stress contours of the CHS brace and H-shaped chord. On the other hand, the efficiency of joints was evaluated by comparing the ultimate strengths of joints with yield strengths of CHS brace. How closer this ratio is to unit represents whether the CHS brace is fully utilized. 3.2. Plastic development

Fig. 5. Finite element mesh of CHS brace-to-H-shaped chord T-joints.

3. Parametric study 3.1. Influential factors and failure modes The effects of main geometric parameters on the behavior of CHS brace-to-H-shaped chord T-joints were carefully evaluated in the parametric study, which include CHS brace diameter to H-shaped chord flange width ratio (β), H-shaped chord flange width to thickness ratio (2γ), and CHS brace to H-shaped chord flange thickness ratio (τ). The H-shaped chord of all specimens is taken to be H200  200  8  tf, which has the nominal overall height (h) of 200 mm, the nominal flange width (bf) of 200 mm, the nominal web thickness (tw) of 8 mm, and the varying flange thickness (tf). Pin supports to both ends of the chord were used in the parametric study. The effect of chord length on ultimate capacity of joints is unobvious when the chord length is five times longer than the H-shaped chord height. The chord length is designed as six times as long as chord height in parametric study. A total of 64 T-joints with different non-dimensional geometric parameters (β ¼0.3–0.9, 2γ ¼16–30 and τ ¼0.25–1.00) were

The plastic development of T-joints under axial compression is different for specimens with different geometric parameters. For specimens with small values of 2γ and τ, the stresses at the root of CHS brace step into the plastic range first. The stresses of full cross section of CHS brace gradually step into the plastic range with the increase of axial compression. Then the plasticity developed towards the joint intersection region along the CHS brace. Eventually the CHS brace at the joint intersection region is fully in plastic range at the ultimate limit state, whereas the H-shaped chord is almost in elastic range, as shown in Fig. 9. For other specimens, the stresses at the root of CHS brace step into the plastic range first. Then the plasticity developed slowly until large deformations occurred at the joint intersection region. The stresses of H-shaped chord flange gradually step into the plastic range with the increase of axial compression, which was followed by H-shaped chord web. Eventually the CHS brace at the joint intersection region, H-shaped chord flange and web are partly in plastic range at the ultimate limit state, as shown in Fig. 10. The typical load–displacement curves of CHS brace-to-Hshaped chord T-joints under axial compression are shown in Fig. 11 for specimens with different plastic development and subjected to different failure modes. 3.3. Occurrence of different failure modes A total of 64 T-joints with different geometric parameters were analyzed in the parametric study. Different failure modes were obtained from the finite element analysis of CHS brace-to-Hshaped chord T-joints under axial compression. It can be generally concluded from the FEA results that 26.56% of specimens failed by Local Buckling Failure of CHS Brace (LBFB), 51.56% of specimens

278

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

Fig. 6. Comparison of failure modes obtained from FEA and tests.

failed by Local Buckling Failure of Flange and Web of H-shaped chord (LBFF þLBFW), and 21.88% of specimens failed by Local Buckling Failure of CHS Brace and H-shaped chord Flange (LBFB þLBFF), as shown in Fig. 12. (1) For Local Buckling Failure of CHS Brace (LBFB), the specimens with small β value or with medium β value and small τ value usually failed by this failure mode. The small diameter of CHS brace for specimens with small β value resulted in the weaker CHS brace compared to H-shaped chord, which led to the local buckling failure of CHS brace. Furthermore, the small thickness of CHS brace for specimens with small τ value resulted in the weaker CHS brace compared to H-shaped chord, which also led to the local buckling failure of CHS brace. (2) For Local Buckling Failure of Flange and Web of H-shaped chord (LBFF þLBFW), the specimens with large τ value usually failed by this failure mode. The large thickness of CHS brace for specimens with large τ value led to the local buckling failure of H-shaped chord flange at the joint intersection region under large concentrated force, which was followed by the local buckling failure of H-shaped chord web. Whereas, the deformations of CHS brace at the ultimate limit state are quite small. (3) For Local Buckling Failure of CHS Brace and H-shaped chord Flange (LBFB þLBFF), the specimens with medium β and τ value or large β value and small τ value usually failed by this failure mode. The equivalent buckling resistances of CHS brace and H-shaped chord led to the failure of CHS brace and H-shaped chord flange at the joint intersection region under large concentrated force almost

simultaneously. There are coherent deformations at the root of CHS brace and connected H-shaped chord flange, which were resulted from local buckling failure simultaneously. 3.4. Effects of geometric parameters The effects of non-dimensional geometric parameters (β, 2γ and τ) on the ultimate strengths of CHS brace-to-H-shaped chord T-joints were carefully evaluated in the parametric study, as shown in Fig. 13. For specimens with fixed 2γ and τ value, the ultimate strengths increased with the increase of β value, as shown in Fig. 13a. It is worth noting that the increase of β value leads to variation of failure modes. The failure mode of local buckling failure of CHS brace (LBFB) occurred for specimens with small β value, whereas the failure mode of local buckling failure of flange and web of H-shaped chord (LBFFþLBFW) or local buckling failure of CHS brace and H-shaped chord flange (LBFBþ LBFF) occurred for specimens with large β value. For specimens with τ ¼0.25, the ultimate strengths linearly increased with the increase of β value from 0.3 to 0.7, while the ultimate strengths greatly increased with the increase of β value from 0.7 to 0.9. For specimens with τ 40.25, the ultimate strengths linearly increased with the increase of β value. For specimens with fixed β and τ value, the ultimate strengths linearly decreased with the increase of 2γ value, as shown in Fig. 13b. This may attribute to the decrease of H-shaped chord flange thickness resulted from the increase of 2γ value, which led to the decrease of flexural rigidity of H-shaped chord. For specimens with fixed β and

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

250

F(kN)

350

279

F(kN)

300

200

250

150

200

100

150

Test result

Test result

100

FEA result

FEA result

50 50

Δ(mm)

0

Δ(mm)

0

0

400

1

2

3

4

5

6

7

8

0

450

F(kN)

350

400

300

350

2

4

6

8

10

12

14

16

18

F(kN)

300

250

250

200

200

150 Test result

100

FEA result

50

150

Test result

100

FEA result Δ(mm)

50

Δ(mm)

0

0

0

500

5

10

15

20

25

30

0

600

F(kN)

2

4

6

8

10

12

14

16

F(kN)

450

500

400

350

400

300

300

250 200

Test result

150

200

Test result

FEA result

100

FEA result

100

Δ(mm)

Δ(mm)

50

0

0 0

2

4

6

8

10

12

14

16

0

18

5

10

15

20

25

30

35

40

Fig. 7. Comparison of load-displacement curves obtained from FEA and tests.

Table 3 Comparison of ultimate strengths obtained from FEA and tests.

Table 4 Geometric parameters in the parametric study.

Specimen

FEA result (kN)

Test result (kN)

Error (%)

CT10 CT11 CT20 CT21 CT30 CT31

220 312 385 417 443 533

199 295 365 398 471 539

10.55 5.76 5.48 4.77  5.94  1.11

2γ value, the ultimate strengths greatly increased with the increase of τ value from 0.25 to 0.5, and the increment of the ultimate strengths decreased with the increase of β value, as shown in Figs. 13c and d. Whereas, the influence of τ on the ultimate

Geometric parameter

Validity range

β 2γ τ

0.30 16.00 0.25

0.50 20.00 0.50

0.70 25.00 0.75

0.90 30.00 1.00

strengths is insignificant with the increase of τ value from 0.5 to 1.0. This may attribute to the weaker CHS brace compared to H-shaped chord for specimens with small τ value. The stresses at the CHS brace are much larger than those at the H-shaped chord at the ultimate limit state. The increase of CHS brace thickness effectively

280

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Table 5 Comparison of ultimate strengths obtained from FEA and yield strengths of CHS brace. β

2γ

τ

Pu (kN)

Failure mode

Pug (kN)

Pu/Pug

0.3

16 16 16 16 20 20 20 20 25 25 25 25 30 30 30 30 16 16 16 16 20 20 20 20 25 25 25 25 30 30 30 30 16 16 16 16 20 20 20 20 25 25 25 25 30 30 30 30 16 16 16 16 20 20 20 20 25 25 25 25 30 30 30 30

0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00

276 476 466 474 224 401 453 457 177 353 400 414 129 252 297 359 425 521 527 532 248 480 499 497 231 400 451 467 170 287 367 397 291 550 576 576 269 500 513 530 254 423 465 480 116 298 383 414 473 578 601 612 361 517 542 548 257 436 476 518 129 303 383 422

LBFB LBFB LBFB LBFB LBFB LBFB LBFF þ LBFW LBFF þ LBFW LBFB LBFB LBFB þ LBFF LBFF þ LBFW LBFB LBFB LBFB LBFF þ LBFW LBFB LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFB LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFB LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFB LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFB LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFB LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFB þ LBFF LBFB þ LBFF LBFF þ LBFW LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFF þ LBFW LBFB þ LBFF LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFB þ LBFF LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW LBFB þ LBFF LBFB þ LBFF LBFF þ LBFW LBFF þ LBFW

244 463 656 823 205 393 563 714 166 320 463 594 125 244 357 463 416 806 1170 1509 348 679 991 1286 280 549 806 1052 211 416 614 806 587 1149 1684 2194 491 964 1420 1857 394 777 1149 1509 297 587 871 1149 759 1492 2199 2880 634 1250 1848 2429 509 1006 1492 1966 383 759 1128 1492

1.13 1.03 0.71 0.58 1.09 1.02 0.81 0.64 1.07 1.10 0.86 0.70 1.03 1.03 0.83 0.78 1.02 0.65 0.45 0.35 0.71 0.71 0.50 0.39 0.83 0.73 0.56 0.44 0.81 0.69 0.60 0.49 0.50 0.48 0.34 0.26 0.55 0.52 0.36 0.29 0.64 0.54 0.40 0.32 0.39 0.51 0.44 0.36 0.62 0.39 0.27 0.21 0.57 0.41 0.29 0.23 0.51 0.43 0.32 0.26 0.34 0.40 0.34 0.28

0.5

0.7

0.9

delayed the plastic development of CHS brace, which enhanced the ultimate strengths of joints. The buckling resistances of CHS brace and H-shaped chord for specimens with large τ value are similar. The increase of CHS brace thickness for these specimens has insignificant influence on the ultimate strengths of joints.

3.5. Design recommendations It should be noted that the CHS brace-to-H-shaped chord T-joints under axial compression usually failed by local buckling failure of CHS brace (LBFB) or local buckling failure of flange and web of H-shaped chord (LBFF þLBFW). However, the local buckling failure of CHS brace and H-shaped chord flange (LBFB þLBFF) is the ideal failure mode in the practical application, which could make full use of the strengths of CHS brace and H-shaped chord simultaneously. Therefore, the validity range of main geometric parameters was recommended to be β Z0.7, 2γ ¼20–30, and τ ¼0.25–0.5 in the joint design to ensure the CHS brace-to-Hshaped chord T-joints under axial compression failed by local buckling failure of CHS brace and H-shaped chord flange (LBFBþ LBFF).

4. Design equations The proposed design equations of CHS brace-to-H-shaped chord T-joints under axial compression were derived from the regression analysis by using SPSS software. Design equations of CHS brace-to-H-shaped chord T-joints under axial compression are given in different failure modes, which mainly include local buckling of chord flange and Local buckling of brace. Therefore, the design equations are proposed in this study based on the FEA results using curve fitting technique for CHS brace-to-H-shaped chord T-joints under axial compression subjected to different failure modes as follows: Local buckling of chord flange:

N1, Rdc =

bw =

1.05f y0 tw b w sin θ1

/γM5

h1 + 5( tf + r) sin θ1

b w ≤ 2t1 + 10 ( t f + r )

(1)

(2)

(3)

Where, fy0 — Yield stress of H-shaped chord; tf — Thickness of H-shaped chord flange; tw — Thickness of H-shaped chord web; bw — Effective width of H-shaped chord web; r — Corner radius of H-shaped chord; h1 — External diameter of CHS brace; t1 — Thickness of CHS brace; θ1 — Angel between CHS brace and H-shaped chord; γM5 — Resistance factor. Local buckling of brace:

N1, Rdb = 1.74f y1 t1Peff /γM5

(4)

Peff = tw + 2r + 7t f f y0 /f y1

(5)

Peff ≤ 2h1 − 2t1

(6)

Where, fy1 — Yield stress of CHS brace; Peff — Effective width of CHS brace; h1 — External diameter of CHS brace.

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

281

Fig. 8. Typical failure modes.

{

}

N1, Rd = min N1, Rdc , N1, Rdb

(7)

The ultimate strengths of CHS brace-to-H-shaped chord T-joints under axial compression calculated using the proposed design equations were compared with those obtained from the finite element analysis in the parametric study, as shown in Table 6. A good agreement was obtained with the mean value of proposed design strength-to-FEA result ratio of 0.82, and the corresponding coefficient of variation (COV) of 0.028, for CHS brace-to-H-shaped chord T-joints under axial compression. The design equations of ultimate strengths for CHS brace-to-Hshaped chord T-joints under axial compression in the current

Eurocode 3 [12] subjected to different failure modes as follows: Chord web yielding:

N1, Rdc =

f y0 tw b w sin θ1

/γM5

(8)

Brace failure:

N1, Rdb = 2f y1 t1Peff /γM5

(9)

Furthermore, the comparison of the ultimate strengths of CHS brace-to-H-shaped chord T-joints under axial compression calculated using the proposed design equations and design equations given in the current Eurocode 3 [12] with the FEA results is clearly

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Fig. 9. Plastic development for specimens with β ¼0.3, 2γ ¼ 16 and τ ¼0.25.

500 450 400 350 300 250 200 150 100 50 0

450 400 350

F(kN)

F(kN)

Fig. 10. Plastic development for specimens with β ¼ 0.7, 2γ ¼20 and τ ¼1.0.

300

250 200

150 100

50 0

0

20

40

60

80

100

0

10

20

30

40

50

60

Δ(mm)

Δ(mm) Fig. 11. Load–displacement curves.

shown in Fig. 14. It can be generally concluded from the comparison that the values of most proposed design strength-to-FEA result ratio are within the range of 0.8–0.9 and 0.9–1.0, which means the proposed design equations are more accurate with less scatter of predictions compared to the design equations given in the current Eurocode 3 [12]. It is noted that design equations given in

the current Eurocode 3 is dangerous for predicting the ultimate strengths of CHS brace-to-H-shaped chord T-joints under axial compression.

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

LBFB+LB FF 21.88%

283

Table 6 Statistics of comparison between design strengths and FEA results.

LBFB 26.56%

Specimen

Comparison

A total of 64 T-joints

Max Min Mean COV

LBFF+LB FW 51.56%

1.19 0.55 0.82 0.028

25

Proposed design equations 20

5. Conclusions (1) The typical failure modes obtained from the finite element analysis of CHS brace-to-H-shaped chord T-joints under axial compression mainly include local buckling failure of CHS brace (LBFB), local buckling failure of flange and web of H-shaped chord (LBFF þLBFW), and local buckling failure of CHS brace and H-shaped chord flange (LBFB þLBFF). (2) For specimens with small values of 2γ and τ, the CHS brace at the joint intersection region is fully in plastic range at the ultimate limit state, whereas the H-shaped chord is almost in elastic range. For other specimens, the CHS brace at the joint intersection region, H-shaped chord flange and web are partly in plastic range at the ultimate limit state. (3) The validity range of main geometric parameters was

600

Pu kN

No. of specimens

Fig. 12. Occurrence of different failure modes.

Eurocode3 15 10 5

0 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2

Ratio of design strength to FEA result Fig. 14. Comparison of ultimate strengths obtained from design equations and FEA.

Pu(kN)

600

500

500

2γ

β

400

0.3 0.5

300

400

16 20

300

0.7 200

0.9

100

25

200

30

100

0

τ

0 0.25

0.5

0.75

1

β

Pu(kN)

500 450 400 350 300 250 200 150 100 50 0

700

τ

0.25 0.5 0.75 1

0.3

0.5

0.7

0.9

Pu(kN)

600

τ

500

0.25

400

0.5

300

0.75 1

200 100

2γ

0

16

20

25

30

2γ 16

20

Fig. 13. Effects of main geometric parameters on the ultimate strengths.

25

30

284

Y. Chen et al. / Thin-Walled Structures 98 (2016) 274–284

recommended to be β Z0.7, 2γ ¼ 20–30, and τ ¼ 0.25–0.5 in the design of CHS brace-to-H-shaped chord T-joints under axial compression. (4) Design equations are proposed in this study for CHS braceto-H-shaped chord T-joints under axial compression subjected to different failure modes, which mainly include chord yielding and brace failure. The minimum of the design strengths calculated based on these two failure modes is adopted as the ultimate strength of CHS brace-to-H-shaped chord T-joints under axial compression.

Acknowledgments This research work was supported by the National Natural Science Foundation of China (Nos. 51278209 and 51478047), Program for New Century Excellent Talents in Fujian Province University (No. 2014FJ-NCET-ZR03), Incubation Programme for Excellent Young Science and Technology Talents in Fujian Province Universities (No. JA13005) and the Research Grant for Young and Middle-aged Academic Staff of Huaqiao University (No. ZQNPY110). The authors are also thankful to Fuan Steel Structure Engineering Co., Ltd. for the fabrication of test specimens. The tests were conducted in Fujian Key Laboratory on Structural Engineering and Disaster Reduction at Huaqiao University. The support provided by the laboratory staff is gratefully acknowledged.

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