Residual stresses in welded high-strength steel I-Beams

Journal of Constructional Steel Research xxx (xxxx) xxx

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Residual stresses in welded high-strength steel I-Beams Tuan Le a, Anna Paradowska b, Mark A. Bradford a, *, Xinpei Liu c, Hamid R. Valipour a a

Centre for Infrastructure Engineering, School of Civil and Environmental Engineering, UNSW, Sydney, NSW, 2052, Australia Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, 2234, Australia c School of Civil Engineering, The University of Sydney, NSW, 2006, Australia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 July 2019 Received in revised form 31 October 2019 Accepted 2 November 2019 Available online xxx

This study investigates a unified residual stress model applicable for welded high-strength steel (HSS) Ibeams. In the experimental program, the homogeneous specimens including two prismatic I-beam samples and a web-tapered I-beam fabricated from Australian BISPLATE-80 and BISPLATE-100 steel plates having nominal yield stresses of 690 MPa and 890 MPa respectively were inspected to determine their residual stress distribution using a non-destructive neutron diffraction technique. Details of this neutron diffraction method for measuring residual stresses are presented. It is shown that the technique can achieve high spatial resolution of the residual stresses as well as capturing the high stress gradient in the heat-affected zone, as a consequence of the deep penetration of the neutron particles into the material. The pattern of residual stresses in the specimens reveals that the tensile stresses peak at the flange-web junctions at an average of 70% of the parent material yield stresses, and that the compressive residual stresses have an approximately uniform distribution that dominates large regions of the flange and web. The test results reconfirm the compressive residual stresses being related to the geometry of the cross-section and independent of the steel grade. The interaction of the residual stresses in the flanges and web was found to be negligible for both prismatic and web-tapered beams. A residual stress model applicable for welded thin-walled I-section members for steel grades between 460 MPa and 1000 MPa is proposed by fitting the test results and collective data available in the literature. This representation was incorporated into a detailed finite element (FE) model and it is shown that the FE predictions are in good agreement with the results of experiments conducted on a wide range of HSS Isection beams tested to failure caused by buckling and/or yielding. © 2019 Published by Elsevier Ltd.

Keywords: Buckling Flexural strength High strength steel I-section Neutron diffraction Residual stress

1. Introduction High-strength steels (HSS) having a nominal yield stress fy greater than 450 MPa and with good weldability and notch toughness have received much recent interest within the construction industry. The use of HSS in construction produces lighter structures that can be erected more rapidly with lower labour costs in comparison to normal-strength steels (NSS). Using HSS as a replacement for NSS reduces undesirable emissions and waste during steel manufacture because less of it is needed, and the lighter structural frame needs less emissions-produced concrete in the foundations. Successful applications of HSS in buildings and bridges worldwide [1] have spawned research interest into the behaviour of such structures and component members, particularly the assessment of residual stresses which are a major influence on

* Corresponding author. E-mail address: [email protected] (M.A. Bradford).

the ultimate strength limit states design of steel structures. Studies of residual stresses induced during the process of shaping, mostly by welding, have been reported extensively for wide flange I-sections having steel grades up to 690 MPa. However, very little experimental data is available on the magnitude and distribution of residual stresses in I-sections with yield stresses exceeding 690 MPa. The measurement of residual stresses in quenched and tempered (QT) ASTM A514 steel welded I-sections (fy ¼ 690 MPa or 100 ksi) was reported initially by Odar, Nishino and Tall [2,3] some five decades ago. Two different sections were investigated using the method of sectioning. The tensile residual stresses were predominantly at the flange-web junction, whilst the compressive stresses having a uniform distribution were mostly in the middle regions of the flanges and web. The peak tensile stresses developed in the heat-affected zone (HAZ) at the weld locations, and their magnitude was slightly less than the yield strength of the parent plate, decreasing with a high gradient to become compressive residual stresses outside of the HAZ. The magnitude of the compressive

https://doi.org/10.1016/j.jcsr.2019.105849 0143-974X/© 2019 Published by Elsevier Ltd.

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residual stresses was slightly higher than those of the I-section fabricated from ASTM A47 steel (fy ¼ 250 MPa), indicating a much smaller ratio of the compressive residual stresses to the yield strength in HSS members and consequently an expectation of a less pronounced effect of these stresses on the dimensionless compression strength curve with HSS members. Rasmussen and Hancock [4,5] measured the compressive residual stresses in four Isections fabricated with Australian BISPLATE-80 steel plates (fy ¼ 690 MPa) using the section method, which is a QT low-alloy HSS equivalent to ASTM A514. It was observed that the residual stresses decreased with an increase of the slenderness of the crosssection. In a study of the flexural strength of HSS I-beams fabricated from Slovenian QT NIONICRAL-70 steel plates (fy ¼ 700 MPa), Beg and Hladnik [6] presented the magnitude and distribution of the compressive residual stresses in the flanges of two I-sections, while Lee et al. [7] measured the residual stresses in an I-section fabricated from Korean HSA800 steel having a nominal tensile strength of fu ¼ 800 MPa using the instrumented indentation method. Wang et al. [8] investigated the residual stresses in three I-sections fabricated from Chinese Q460 steel (fy ¼ 460 MPa) using both the sectioning and hole drilling techniques. Further studies on welded Q460 HSS were carried out by Ban et al. [9]. Eight different I-sections were tested using the sectioning method and it was observed that the magnitude of the compressive residual stresses was dependent largely on the cross-sectional dimensions rather than the yield strength of the parent material. By approximating the lower bound to the experimental data, a residual stress model in which the compressive stresses depended on the slenderness and thickness of the component plates was proposed [9]. This model was then modified by Ban et al. [10] to extend the applicability to steel grades with a yield strength up to 960 MPa. Li et al. [11] investigated the residual stresses in three Q690 HSS welded I-sections (fy ¼ 690 MPa) and concluded that the residual tension zones were approximately identical under the same heat input intensity, parent material properties and thicknesses. Yang et al. [12] reported the residual stress distribution in Q460GJ HSS plates and welded I-sections, in which five doubly symmetric and three singly symmetric I-shapes were investigated using the sectioning method. The cross-sectional depth to width ratio (H/B) varied from 1.5 to 2.5, and high tensile stresses up to the yield stress were distributed at the edge of the flame-cut plates initially, but compressive stresses rather than tensile stresses were observed at these regions after the fabricating process. Investigations of residual stresses in medium-walled and thick-walled Q460GJ HSS Isections were also presented in Refs. [13,14]. While sectioning and other destructive methods such as slotting or hole drilling are commonly employed to assess the residual stresses in steel sections, non-destructive approaches using X-ray, synchrotron X-ray and neutron diffraction (ND) are also available [15e17]. Although each technique may suit a specific structural component and measurement objective, non-destructive methods are seemingly more attractive regarding the preservation of the specimens as well as providing high spatial resolution and accuracy in measuring residual stresses. In particular, the chargeless particles in ND can penetrate several centimetres into the interior of a crystalline material [18,19], and so is a robust method for measuring the residual stresses induced in steel sections. Practical aspects of the ND method have been reviewed in Ref. [20] and documented in ISO/TS 21432 [21]. Recently, Khan et al. [22] successfully employed the ND procedure to measure the residual stresses in welded HSS box-sections. Because very little experimental data is available for sections with a steel grade higher than 690 MPa, more research on the residual stresses in such structural components is needed. In addition, previous models for residual stresses [9e11] may only be applicable to HSS I-section columns (with wide flanges) rather than

I-section beams in which the flange tip regions develop compressive stresses after the cooling process [12]. Because of this, a reliable residual stress model applicable to HSS I-beams is much needed, as is a reliable measurement of the tensile stress distribution in the HAZ because the results obtained from the sectioning technique can vary due to the difficulty of accessing the weld region. To this end, an assessment of the residual stresses in welded BISPLATE-80 (fy ¼ 690 MPa) and BISPLATE-100 (fy ¼ 890 MPa) I-beam sections is reported in this study using the ND technique. A high spatial resolution of the stresses in the cross-section is obtained, and especially the high stress gradient in the weld bead, which is not possible to capture accurately using the section procedure. The accuracy of the ND measurements is demonstrated through their condition of self-equilibrium. By interpolating the ND results and additional data obtained from the literature, a residual stress model appropriate for welded I-section members is recommended. The proposed distribution of residual stresses is incorporated in ABAQUS [23] finite element models of full-scale HSS beams and the accuracy of the model for predicting the ultimate flexural strength of HSS I-beams is demonstrated [6,7,24]. 2. Neutron diffraction method The principle of the diffraction method utilising neutrons is based on the assumption that the distance between atomic planes hkl in a crystalline material, the so-called lattice spacing dhkl, corresponds to the state of strain in the stressed material. Accordingly, the elastic strain εhkl in a sample can be obtained from

εhkl ¼

dhkl  d0;hkl ; d0;hkl

(1)

Fig. 1. Schematic of Bragg's law in neutron diffraction.

Fig. 2. The neutron diffraction measurement technique.

Please cite this article as: T. Le et al., Residual stresses in welded high-strength steel I-Beams, Journal of Constructional Steel Research, https:// doi.org/10.1016/j.jcsr.2019.105849

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The measurement gauge volume is an intersection of incident and diffracted beams, and the gauge volume size is defined by the height and width of incident-beam slits and the collimator on the detector side. Typically, the gauge volume is fixed in space by fixing the incident and diffracted beams while the measuring position inside the sample is brought into the gauge volume by using a computer-controlled table capable of rotation and moving in three orthogonal directions. The peak of intensity shown on the detector correlates the diffraction angle as shown in Fig. 3. To calculate the principal residual stresses (sxx, syy, szz) in accordance with the generalised Hooke's law

8 9 > < sxx > = > : Fig. 3. Determination of strain from diffraction angle shift.

where dhkl and d0,hkl are the lattice spacing in a stressed sample and a stress-free reference sample respectively. The lattice spacing can be determined by Bragg's law, which asserts that reflection of electromagnetic radiation on a crystalline lattice plane has a strong emission at a certain orientation [20], as illustrated in Fig. 1. The diffraction Bragg's law is formulated as

l ¼ 2dhkl sinqhkl ;

2

1  nhkl

6 hkl syy ¼ 4 nhkl > ; ð1 þ nhkl Þð1  2nhkl Þ szz nhkl E

8 9 > < εxx > = εyy ; > > : ; εzz

3

nhkl nhkl 1  nhkl nhkl 7 5 nhkl 1  nhkl

(3) the residual strains in the three principal directions (εxx, εyy, εzz) need to be measured. In Eq. (3), (x, y, z) is the principal coordinate system and Ehkl and nhkl the elastic constants of the crystal lattice plane.

(2) 3. Experimental programme

where l is the wavelength of the electromagnetic radiation and qhkl the Bragg angle. Neutron radiation can penetrate several centimetres into the thickness of the sample with spatial resolution of less than 1 mm, so that measuring strains deep inside the component is possible [20]. An outline of the ND measuring technique is shown in Fig. 2.

3.1. Specimen preparation The prismatic samples I-690 and I-890 were fabricated from BISPLATE-80 (fy ¼ 690 MPa) and BISPLATE-100 (fy ¼ 890 MPa) plates respectively, while the web-tapered beam TB-890 was made

Fig. 4. Geometry of prismatic I-beams and the principle coordinate system ðxyzÞ.

Fig. 5. Geometry of the web-tapered specimen and location of cross-sections considered for residual stress measurement.

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Table 1 Specimen dimensions. No.

Notation

fy

H, H1 (mm)

H2 (mm)

B (mm)

tf (mm)

tw (mm)

lf

lw

L (m)

1 2 3

I-690 I-890 TB-890

690 890 890

354 354 354

e e 184

160 160 160

11.77 11.80 11.80

7.70 7.95 7.95

6.47 6.44 6.44

42.92 41.56 41.56

1.00 0.80 3.00

Table 2 Material properties of component plates. BISPLATE

t (mm)

fy (MPa)

sy (MPa)

su (MPa)

E (GPa)

εy (%)

εu (%)

εe (%)

80

8 12 8 12

690 690 890 890

791 851 1003 998

862 914 1070 1078

191 195 198 198

0.41 0.44 0.51 0.50

5.28 5.08 3.77 3.84

10.70 12.90 9.30 9.70

100

Note: t ¼ nominal plate thickness, sy ¼ yield stress (0.2% proof stress), su ¼ tensile stress, E ¼ elastic modulus, εy ¼ yield strain, εu ¼ tensile strain, εe ¼ elongation in 100 mm gauge length.

Table 3 Specifications of gas metal arc welding (GMAW). Fillet weld

Single pass 6 mm

Shielding gas Electrode Voltage Current Travel speed Preheat temperature

18% CO2 in Argon AWS A5.28 ER110S-1 (1.2 mm wire) 27 V 260 A 40 cm/min 150  C

from BISPLATE-100 plates. Figs. 4 and 5 illustrate the geometry of the specimens with the actual dimensions given in Table 1. The material properties of the BISPLATE-80 and BISPLATE-100 plates are given in Table 2. In fabricating the specimens, the plate components were flamecut and welded together following the provisions of AS/NZS1554.42010 [25], and the gas metal arc welding (GMAW) with the specifications given in Table 3 was employed. The plate components were first aligned and assembled by tack welds and steel rods. The flange-web intersection regions were then preheated to about 150  C prior to the welding, which was performed by two accredited welding technicians on opposite sides at the same time in order to reduce the distortion caused by the unbalanced hear transfer (Fig. 6). The strain scanning was undertaken at the mid-span of the prismatic specimens, whilst the residual stresses in the tapered beam were measured in three cross-sections along the axis of the

specimen as indicated in Fig. 5. The spatial restraint of the strain scanner (Fig. 8b) necessitated saw cutting the tapered beam into three segments, whose mid-spans were considered for the residual stress measurements. The specimens as shown in Fig. 7a were differentiated in the size and shape. A BISPLATE-100 stress-free sample (Fig. 7b) was also prepared by cutting a 5 mm thin slice from a sample identical to the I-890 specimen in the longitudinal direction to reduce the longitudinal stresses. The process of electrodischarge machining was employed to minimise the undesirable thermal and mechanical effects. 3.2. Experimental procedure The test was conducted using the Kowari Strain Scanner (Fig. 8b) located at The Centre for Neutron Scattering in The Australian Nuclear Science and Technology Organisation in Sydney. The specimens were scanned for membrane residual strains distributed at the mid-plane of the flanges and web. At regions of high stress gradient such as the flange-web junctions, weld beads and the flange tip regions, the measurement was repeated every 5 mm; however, in the compressive stress regions the measurements were repeated at 10e20 mm intervals. Based on the thickness of the component plates and the proposed spatial resolution, an experimental gauge volume of 3  3  3 mm3 was chosen to optimise the scanning time, and the measured strain was the average within the gauge volume. The incident neutron beam having a wavelength of 1.67 Å was extracted from the Kowari monochromator. The scattering plane was a-Fe

Fig. 6. Fabrication process.

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Fig. 7. Residual stress specimens and a stress-free reference sample.

Fig. 8. Test set-up (a) SScanSS for virtual sample and test simulation, and (b) sample positioned for neutron diffraction measurement in the longitudinal orientation.

Fig. 9. Orientation program for scanning residual strains in the flange, (a) longitudinal, (b) through-thickness, and (c) transverse directions.

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Fig. 10. Orientation program for scanning residual strains in the web, (a) longitudinal, (b) transverse, and (c) through-thickness directions.

needed to be reoriented several times. The three principal strains in the stress-free reference sample were also measured in a similar fashion. 3.3. Test results and discussion 3.3.1. Residual stresses in prismatic I-beams The diffracted neutron signals scattered but concentrated at a certain point in the detector. This neutron scattering can by fitted with a normal distribution (Fig. 3) in which the mean value defines

Fig. 11. Lattice spacing in the flange of BISPLATE 100 stress-free sample and specimen I-890.

(211) with E211 ¼ 223.8 GPa and n211 ¼ 0.27, and the diffraction angle 2q211 ¼ 90 was positioned according to the specifications of the ISO/TS 21432 [21]. A virtual laboratory simulation was carried out prior to the test. For this, a 3-D model of the sample was generated using a coordinate measuring machine fitted with a laser arm scanner and cooperated with SScanSS, the virtual Kowari instrument software for strain scanning simulation (Fig. 8). The sample was then placed on the Kowari computer-controlled table in the position at which the scattering vector was parallel to a principal strain as shown in Figs. 9 and 10. Next, this position was mapped into SScanSS through fiducial points and the test simulation was run within the SScanSS software, based on which a script for the computer-controlled table orienting the movement of the sample in order to bring the measuring points into the gauge volume was constructed. This allows the scanning process to be ascertained as operating smoothly without collisions or off-target points. The script was executed in the Kowari control software GumTree to run the actual test. The scanning time of each position was dependent on the geometry and the expected attenuation, with a longer time being applied where high attenuation was expected (mostly in the weld beads). In addition, it can be seen from Figs. 9 and 10 that in order to obtain the three principal strains, the sample

Fig. 12. Residual stresses in the specimen I-890.

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determined thereby from

d0 ¼

  ð1  nÞd0x þ n d0y þ d0z : 1þn

(4)

The value of d0 obtained along the flange of the stress-free sample is plotted in Fig. 11 and compared with the value measured along the top flange of the I-890 specimen. It is seen that the distribution of d0 is almost flat compared with those of the sample with residual stresses, and that this flat profile of d0 implies a stress-free condition. The mean value of d0 was taken as the reference lattice spacing for the strain calculation, based on which the residual stresses in specimen I-890 were calculated. The distribution of these stresses is plotted in Fig. 12, which shows that the longitudinal stresses srsx (in the x-direction) are more significant than those in the transverse and through-thickness directions. Because of this, longitudinal residual stresses are the only stresses considered in the analysis of steel structures. It is also noteworthy that the throughthickness stresses in the flange srsy and web srsz approach zero outside the HAZ. This observation confirms the assumption of through-thickness residual stresses in thin-walled sections as being negligible. An alternative approach can therefore be used to obtain the stress-free lattice spacing by assigning the through-thickness stress outside the HAZ to be zero, so that the stress-free lattice spacing can be derived as

df0 ¼

ð1  nÞdy þ nðdx þ dz Þ 1þn

(5)

for the flange and as

dw 0 Fig. 13. Residual stresses in the specimen I-690.

the diffraction angle. With the diffraction angle and radiation wavelength available, Eq. (2) can be invoked to determine the lattice spacing dhkl. The BISPLATE-100 reference sample was scanned to obtain the reference lattice spacing (d0x, d0y, d0z) in the three principal directions. The longitudinal stresses in the reference sample were released, i.e. s0xx ¼ 0, and the stress-free crystal lattice spacing was

  ð1  nÞdz þ n dx þ dy ¼ 1þn

(6)

for the web, where (dx, dy, dz) are the lattice spacings measured in the stressed sample. Using the alternative method, the residual stress distribution in the specimen I-690 was determined and the results are plotted in Fig. 13. Figs. 12 and 13 show the high tensile stress gradient determined at the flange-web junctions. The peak tensile stresses induced in the I-690 flanges were 789 MPa and 504 MPa, and those in the I890 flanges were 774 MPa and 487 MPa. On the other hand, the

Fig. 14. Residual stresses in the specimen TB-890.

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Table 4 Average peak tensile residual stresses srsxt in the longitudinal direction. Sample

Component

fy (MPa)

sy (MPa)

srsxt (MPa)

srsxt =fy

srsxt =sy

I-690

Flange Web Flange Web Flange Web Web Web

690 690 890 890 890 890 890 890

851 791 998 1003 998 1003 1003 1003

647 542 631 698 845 e 690 606

0.94 0.79 0.71 0.78 0.95 e 0.78 0.68 0.803

0.76 0.69 0.63 0.70 0.85 e 0.69 0.60 0.702

I-890 TB-890-1 TB-890-2 TB-890-3 Average

Fig. 17. Residual stress self-balancing deviation in the specimen I-890.

Fig. 15. Measurement positions in the weld beads of the specimen I-890, (a) top flange-web, and (b) bottom flange-web intersections.

Table 5 Longitudinal tensile residual stress srsxt in the weld bead of the I-890 specimen. Node

fy (MPa)

srsxt (MPa)

srsxt/fy

1 2 3 4 5 6 7 8 9 Average

890 890 890 890 890 890 890 890 890

504 465 574 365 793 442 358 702 347 506

0.57 0.52 0.64 0.41 0.89 0.50 0.40 0.79 0.39 0.57 Fig. 18. Residual stress model.

compressive stresses are distributed more uniformly outside of the region near the flange-web junction. The flange tip stresses are compressive rather than tensile because of the significant effect of restrained shrinkage during the cooling process of these I-beam sections. The average magnitudes of the compressive stresses in the flanges of the specimens I-690 and I-890 were 118 MPa and 109 MPa respectively. The tensile stresses in the web peaked at the ends of the web at the weld region, with a magnitude of 542 MPa for I-690 and 713 MPa and 683 MPa for I-890. The residual stresses decrease rapidly away from the HAZ and the compressive stresses are

Table 6 Compressive residual stress parameters.

Fig. 16. Residual stress self-balancing deviation in the specimen I-690.

a0

a1

a2

a3

b0

b1

b2

b3

140

16

0.4

820

115

10

0

2100

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fy Notation Edge (MPa)

H B tf tw (mm) (mm) (mm) (mm)

H/ lf B

lw

460

RH3

168

156

21.4

11.5

1.1 3.4

2

460

RH5

244

225

21.2

11.3

3

460

RH7

320

314

21.2

460

RI1

110

130

5

460

RI2

150

6

460

RI3

7

460

RI4

8

460

RI5

9

460

RI6

10

460

RI7

11

460

RI8

460

H1

13

460

H2

14

460

H3

15

460

H7

16

460

H8

690 690

W-A WeB

690

WeC

690 690 690 690

I1RS I2RS I3RS IRS

No. Ref. 1

4

[8]

[9]

12 [12]

17 [2] 18

Grade Q460

Q460

Q460GJ

A514

19 20 [4] 21 22 23 [5]

Bisplate80

Bisplate80

24 [6]

Nionicral70 690

B

690

D

690

RH6

27

690

RH7

28

690

RH8

29 Present Bisplate80

690

I-690

25 26 [11]

Q690

Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Sheared Flamecut Flamecut Sheared Sheared Sheared Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut Flamecut

srfc1 (MPa) Eq. srfc1/ (8) srfc*

srfc2 (MPa)

srfc2/ srfc*

Test

srwc1 (MPa) Eq. srwc1/ srwc*

srwc2 (MPa)

[10]

(9)

[10]

srwc2/ srwc*

10.9 189

224

1.19

278

1.47

77

193

2.51

239

3.10

1.1 5.0

17.8 126

143

1.13

188

1.49

119

120

1.01

162

1.36

11.6

1.0 7.1

23.8 90

96

e

134

e

66

87

e

129

e

10.0

10.0

0.8 6.0

9.0

277

157

e

276

e

234

248

e

290

e

150

10.0

10.0

1.0 7.0

13.0 207

137

e

253

e

208

177

e

215

e

210

210

14.0

14.0

1.0 7.0

13.0 93

112

e

190

e

124

137

e

196

e

150

290

10.0

10.0

0.5 14.0 13.0 164

79

e

187

e

214

177

e

215

e

276

348

12.0

12.0

0.8 14.0 21.0 51

64

e

150

e

65

95

e

140

e

300

220

12.0

10.0

1.4 8.8

27.6 80

99

1.24

190

2.38

75

91

1.21

126

1.68

360

280

12.0

10.0

1.3 11.3 33.6 78

78

1.00

166

2.13

91

78

0.86

111

1.22

150

150

10.0

10.0

1.0 7.0

13.0 191

137

e

253

e

142

177

e

215

e

270

180

10.0

8.0

1.5 8.6

31.3 112

115

1.03

229

2.04

102

102

1.00

133

1.30

360

180

10.0

8.0

2.0 8.6

42.5 113

115

1.02

229

2.03

101

84

0.83

114

1.13

450

180

10.0

8.0

2.5 8.6

53.8 98

115

1.17

229

2.34

75

74

0.99

103

1.37

429

200

10.0

10.0

2.1 9.5

40.9 98

106

1.08

218

2.22

77

66

0.86

100

1.30

432

250

16.0

10.0

1.7 7.5

40.0 84

96

1.14

162

1.93

15

68

4.53

101

6.73

178 178

152 152

12.7 12.7

9.5 9.5

1.2 5.6 1.2 5.6

16.0 145 16.0 131

147 147

1.01 1.12

239 239

1.65 1.82

131 131

151 151

1.15 1.15

187 187

1.43 1.43

267

229

19.1

12.7

1.2 5.7

18.0 121

125

1.03

180

1.49

48

105

2.19

154

3.21

132 162 192 158

96 116 136 140

6.0 6.0 6.0 7.7

6.0 6.0 6.0 7.7

1.4 1.4 1.4 1.1

20.0 25.0 30.0 18.4

168 148 134 136

1.10 1.19 0.92 1.01

392 369 353 294

2.56 2.98 2.42 2.18

100 76 69 32

160 139 125 152

1.60 1.83 1.81 4.75

200 178 163 185

2.00 2.34 2.36 5.78

246

270

12.4

10.4

0.9 10.5 21.3 73

81

e

167

e

e

110

e

147

e

246

220

12.4

10.4

1.1 8.5

21.3 123

100

0.81

188

1.53

e

110

e

147

e

206

209

16.2

16.2

1.0 5.9

10.7 105

124

e

192

e

21

149

e

226

e

240

240

16.1

16.1

1.0 7.0

12.9 60

104

e

171

e

49

117

e

192

e

258

262

16.3

16.3

1.0 7.5

13.9 80

94

e

159

e

9

104

e

179

e

354

160

12.0

8.0

2.2 6.3

41.3 118

135

1.14

231

1.96

48

86

1.79

116

2.42

7.5 9.2 10.8 8.6

srfc* (MPa) Test

153 124 146 135

srwc* (MPa)

T. Le et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

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Table 7 Experiment data for compressive residual stresses in I-sections.

(continued on next page) 9

2.35 1.45 61.63

2.64

1.77 1.07 60.66

156 2.10 124 1.10 0.12 10.94

2.05 0.40 19.44

59 231 e 8.0 160 212

12.0

1.3 6.3

23.5 e

135

e

1.74 134 1.35 104 77 231 e 8.0 160 269

12.0

1.7 6.3

30.6 e

135

e

2.47 121 1.86 91 49 231 1.32 8.0 160 326

12.0

2.0 6.3

37.8 102

135

2.26

116 1.72 86 50 231 1.24 8.0 160

890

890

32

33

Average Standard deviation CoV (%)

890 31

3.3.2. Residual stresses in web-tapered beam The residual stress distributions in the three cross-sections of the specimen TB-890 are plotted in Fig. 14. At the smallest section TB-890-1, the peak tensile stress at the top flange-web junction was 845 MPa and the average magnitude of the compressive stresses in the top flange was 102 MPa. It can be seen that the difference between the stresses in the flanges of the tapered specimen TB-890 and the prismatic specimen I-890 is insignificant and so the effect of tapering on the residual stresses can be ignored. Because of this, the stress measurements in sections TB890-2 and TB-890-3 were only made for the webs of these sections. It is also noticeable that the compressive stresses in the web increase slightly along the direction of the taper as the web slenderness decreases [4,5]. The average of the peak tensile residual stresses srsxt in the flanges and webs of the specimens and their ratio when normalised with respect to the nominal yield strength fy and measured yield stress sy are summarised in Table 4. In general, the peak tensile residual stresses for the BISPLATE-100 specimens was slightly higher than those for the BISPLATE-80 specimens. With reasonable accuracy, the average of the peak tensile stresses can be taken as 80% of the nominal yield strength fy, or as 70% of the measured yield stress sy, which are approximately similar to the recommendation of Ban et al. [9] for I-sections welded from 460 MPa plates, being 75% of the nominal yield strength and 68% of the actual strength.

3.3.4. Error of measurements The accumulated error due to the experimental uncertainty was derived using the error propagation method [27]. Details of calculating the deviation of the residual stress vector (Dsxx, Dsyy, Dszz) are provided in Khan et al. [22]. The uncertainty of the measured residual stresses was calculated to be within the range [18 MPa, 28 MPa] with an average of 21 MPa which is a typical deviation of residual stresses in steel sections obtained by using neutron diffraction method [28].

I-890 Bisplate100 890 30

approximately uniform over a large middle portion of the web, the average values of which are 48 MPa for I-690 and 50 MPa for I890. It thereby reconfirms that the effect of the steel grade on the compressive residual stresses is not significant, as was noted in Refs. [2,3,7,9].

3.3.3. Residual stresses in weld bead In addition to the stress distribution in the flange and web of the HSS sections, the residual stresses induced in the weld bead of the specimen I-890 were investigated. The locations at which the stresses were measured are illustrated in Fig. 15. The magnitude of the measured tensile stresses in the weld bead, which are tabulated in Table 5, was averaged as 506 MPa, which is about 60% of the nominal yield strength of the BISPLATE-100 plate. It is noteworthy that the nominal yield and tensile strengths of the filler material AWS A5.28:ER110S-1 were 660 MPa and 760 MPa respectively [26].

Flamecut TB-890- Flame1 cut TB-890- Flame2 cut TB-890- Flame3 cut

354

12.0

2.2 6.3

41.3 109

135

2.12

[10]

srwc2 (MPa)

srwc1 (MPa) Eq. srwc1/ srwc* (9)

srwc* (MPa)

Test

srfc2/ srfc* [10]

srfc2 (MPa)

srfc1 (MPa) Eq. srfc1/ srfc* (8) Test

srfc* (MPa) lw

H/ lf B H B tf tw (mm) (mm) (mm) (mm) fy Notation Edge (MPa) Grade No. Ref.

Table 7 (continued )

2.32

T. Le et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

srwc2/ srwc*

10

3.3.5. Equilibrium conditions Since the internal stresses distributed across the cross-section of a sample are naturally self-equilibrating, the measured residual stress verification requires this equilibrium condition to be satisfied. The self-balancing deviations for the stresses in the specimens I-690 and I-890 are plotted in Figs. 16 and 17 respectively, with the errors in the whole sections being less than 3% of the nominal yield strength, which represents high accuracy of the measurement technique. It is worth noting that the counterpart deviations of the residual stresses in almost all component plates is less than 5% of the yield stress, so that the interaction between

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11

[10] introduced a unified stress model for welded wide-flange Isections with steel grades between 460 MPa and 960 MPa and so are mainly applicable to I-section column profiles for which the flange tip stresses are tensile. However, in I-section shapes with H/ B > 1, compressive tip residual stresses have been reported [12], as have the stresses measured in the current study. Accordingly, the idealised pattern of longitudinal residual stresses in Fig. 18 can be recommended for welded HSS I-section beams with the magnitude of tensile and compressive stresses obtained from





srft ¼ srwt ¼ 0:7sy or 0:8fy ; .

srfc ¼ a0 þ a1 tf þ a2 t 2f þ a3 lf

(7)

 20 MPa

(8)

and

Fig. 19. Compressive residual stresses in the flange.

the flanges and web can be considered negligible. This is not the case for hot-rolled normal-strength steel sections [29] as well as welded medium and thick-walled sections [13,14], and the residual stress closing error of individual plates of some Q460 I-section samples reported in Ref. [12] was considerable. The residual stress distributions in welded steel sections are complex and largely affected by many factors such as the fabricating procedure, welding sequence and measurement methods. Therefore, more experiments and analytical investigations for the residual stress pattern in steel sections considering various crosssectional dimensions with different steel grades are necessary, which are the interest for future studies.

4. Residual stress model 4.1. Proposed formulation Residual stress models for hot-rolled and welded normalstrength I-section steel members have been widely reported in the literature (e.g. Refs. [29e32]), but far fewer residual stress formulations for welded HSS I-sections have been proposed, with limited application to some particular cases [8,9,11,12]. Ban et al.

srwc ¼ b0 þ b1 tw þ b2 t 2w þ b3 =lw

 20 MPa;

(9)

in which srft and srwt are the peak tensile residual stresses and srfc and srwc the magnitude of the uniform compressive stresses in the flange and web respectively. In Eqs. (8) and (9), the dimensions tf and tw are in units of mm and the stresses in MPa. The magnitude of the compressive residual stresses depends only on cross-sectional properties, being the sum of a parabolic function of the plate thicknesses and the inverse of the slenderness ratios lf ¼ bf/tf and lw ¼ hw/tw. The test data of residual stress distribution in steel sections are often scattered depending on the fabricating procedure, welding sequences and measurement methods. Accordingly, it is appropriate to estimate the magnitudes of residual stresses by approximating the upper bound of the test data. Ban et al. [9,10] presented a formulation for compressive residual stresses in the flange and web with respect to the slenderness and thickness of component plates of HSS I-sections, unfortunately, the proposed model may be too conservative for HSS I-section beam profiles with H/B > 1. In the present study, the coefficients a1, a2, a3 and b1, b2 and b3 in Eqs. (8) and (9) were obtained by fitting the functions to the upper bound of the magnitudes of compressive residual stresses induced in HSS Isection beams obtained from the test herein as well as other experimental data in the literature and are given in Table 6. The experimental data for compressive stresses in I-sections welded from steel plates with yield stresses between 460 MPa and 1000 MPa are summarised in Table 7. The plate thicknesses vary from 6 mm to 21 mm and the plate slendernesses from 3.4 to 53.8. The predicted residual stresses for the flange and web are compared with experimental data in Figs. 19 and 20 respectively. It can be seen that the magnitude of the compressive stress decreases rapidly with an increase of the slenderness and, for the same value of the slenderness, the compressive stresses are comparatively lower for thicker plates. In addition, the magnitude of the compressive stresses in the component plates are never less than 20 MPa. The deviations of the test data and predictions are quantitated in Table 7, which demonstrates that a good approximation of the tests has been achieved, especially for specimens having H/ B > 1. Noting that there is negligible interaction between the residual stresses in the flanges and web, the stress patterns can be determined by substituting Eqs. (7)e(9) into the expressions

∬ srf dA ¼ 0

(10)

Af

Fig. 20. Compressive residual stresses in the web.

and

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12

T. Le et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Table 8 Flexural strength of HSS I-beams. No.

Ref.

Grade

1 [7] HSB800 2 3 4 5 6 HSA800 7 8 9 10 11 12 13 14 15 16 17 [24] Q460GJ 18 19 20 21 22 23 24 25 [6] NIONICRAL-70 26 27 28 29 Average Standard deviation

Notation

H (mm)

B (mm)

tf (mm)

tw (mm)

Mp (kNm)

Mm/Mp

Failure mode (Test)

MFE/Mp

Failure mode (FEM)

MFE/Mm

I-1 I-2 I-3 I-4 I-5 II-1 II-2 II-3 II-4 II-5 II-6 II-7 II-8 II-9 II-10 II-11 C1 C2 C3 C4 C5 C6 C7 C8 A B C D E

400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 270 270 270 270 450 450 450 450 245 245 245 245 245

500 220 220 220 220 650 240 240 200 200 200 160 160 240 240 200 180 180 180 180 180 180 180 180 300 270 250 220 200

17.60 17.60 21.10 17.60 17.60 17.60 15.00 15.00 20.00 20.00 20.00 20.00 20.00 15.00 15.00 20.00 10.48 10.49 10.43 10.40 10.47 10.40 10.47 10.47 12.50 12.50 12.50 12.50 12.50

17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 9.01 9.00 8.82 8.74 8.79 8.90 8.84 8.38 10.40 10.40 10.40 10.40 10.40

3915 2048 2104 2048 2048 4648 1889 1889 1907 1907 1907 1632 1632 1889 1889 1907 330 330 330 330 654 654 654 654 859 723 661 663 568

0.99 1.14 1.21 1.07 1.12 0.82 1.06 1.07 1.10 1.12 1.10 1.12 1.14 1.07 1.07 1.07 1.02 0.99 0.95 0.83 0.97 0.89 0.84 0.74 0.82 0.97 0.98 0.97 0.99

LB TF TF LTB TF LB LB TF LB TF LB LB þ TF LB þ LB þ LB þ LTB LTB LTB LTB LTB LTB LTB LTB LB LB LB LB LB

0.92 1.09 1.13 1.00 1.00 0.84 1.07 1.08 1.12 1.14 1.11 1.14 1.15 0.98 0.98 1.05 1.05 0.99 0.91 0.82 0.94 0.81 0.74 0.69 0.86 0.90 0.95 0.94 0.98

LB LB LB LB LB LB LB LB LB LB LB LTB LTB LB LB LB LTB LTB LTB LTB LTB LTB LTB LTB LB LB LB LB LB

0.93 0.96 0.94 0.94 0.89 1.03 1.01 1.01 1.02 1.02 1.01 1.02 1.01 0.91 0.91 0.98 1.03 1.00 0.95 1.00 0.97 0.91 0.88 0.92 1.05 0.93 0.97 0.96 0.99 0.97 0.05

LTB LTB LTB LTB

Note: Mp ¼ plastic moment, Mm ¼ maximum flexural strength of specimens, MFE ¼ maximum flexural strength of specimens by FE analysis, LB ¼ local buckling, LTB ¼ lateraltorsional buckling, TF ¼ tensile fracture.

Table 9 Material properties of steel plates. Grade

t (mm)

sy (MPa)

su (MPa)

εy (%)

εu (%)

HSB800

17.6 21.1 15 17.6 20 8 10 10 (A, B, C) 10 (D, E) 12 (A, D) 12 (B, E) 12(C)

991 879 956 937 903 541 525 775 830 873 797 776

1040 945 1037 1037 961 669 613 814 864 883 808 808

0.50 0.44 0.48 0.47 0.45 0.27 0.28 0.39 0.42 0.44 0.40 0.39

6.50 6.50 6.50 6.50 6.50 9.67 11.55 6.50 6.50 6.50 6.50 6.50

HSA800

Q460GJ NIONICRAL-70

Fig. 21. Material model.

∬ srw dA ¼ 0;

(11)

Aw

where Af and Aw are the flange and web areas. 4.2. Verification In order to demonstrate the appropriateness and feasibility of the proposed residual stress model, the predictions obtained from Eqs. (8) and (9) are compared with the estimations of Ban et al. [10] for specimens with H/B > 1. In particular, the mean of the ratio of the proposal to tests for the flange and web are 1.10 (with a CoV ¼ 10.9%) and 2.05 (CoV ¼ 60.7%) respectively, whilst the counterpart values from Ban et al. [10] are 1.77 (CoV ¼ 19.4%) and

2.35 (CoV ¼ 61.6%). As the residual stresses would affect the bending and buckling strength of steel beams [7,24,33], further validation of the residual stress model has been performed by integrating it with a FE model to simulate the behaviour and flexural capacity of HSS beams reported to have failed under laboratory testing by yielding or buckling using ABAQUS simulation [23]. The geometry and dimensions of the specimens are given in Table 8 and details of the test span and restraint conditions can be found in Refs. [6,7,24]. The elastic modulus was taken as E ¼ 200 GPa and Poisson's ratio as n ¼ 0.25. The multi-linear stress-strain model in Fig. 21 along with the material properties in Table 9 and von Mises' yield criterion were adopted in the non-linear inelastic analysis, using the linear shell element SR4 with reduced integration. The geometric imperfections were applied based on the fundamental eigenmode obtained from an elastic buckling analysis, with the maximum value of the out-of-plumb magnitude taken as max (span/1000,

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13

Fig. 22. Deformed configurations of the specimen at failure in the numerical simulation: (a) specimen HSA800-II-6, (b) specimen Q460GJ-C5, and (c) specimen NIONICRAL70-E.

3 mm) and the maximum value of the flange local imperfection taken as the tolerances specified in the Australian steel standard [34]. The flexural strength of the specimens predicted by the FE model with the residual stresses proposed are given in Table 8 and they show good agreement with the test data, with the average error being less than 3% with a standard deviation of 2%. The deformed configuration at of the typical specimens at the critical load is plotted in Fig. 22. A comparison of the experimental and theoretical results is shown in Fig. 23 and any discrepancy appears to be independent of the steel grade.

 The peak tensile stresses at the flange-web junction were on average 70% of the measured yield stress, or 80% of the nominal yield stress of the parent material.  The tensile stresses in the weld bead were on average 60% of the nominal yield strength of the parent steel.  Compressive residual stresses were located outside of the heat affected zone and were independent of the steel grade. In deference to wide flange column-type sections, the residual stresses at the flange tips were compressive.  Interaction of the flange and web were found to be insignificant regarding their residual stresses, so each of these elements could be assumed to be self-equilibrating. The effect of tapering had negligible effect on the residual stresses.

5. Conclusions The magnitude and distribution of the residual stresses in welded HSS I-sections obtained using the technique of neutron diffraction have been presented in this study. Specifically, prismatic and web-tapered beams with nominal yield strengths of 690 MPa and 890 MPa were investigated, with the following conclusions being drawn.

Based on the test results and augmented with further test data in the literature, a model of the residual stresses in HSS I-section flexural members was proposed, in which the compressive residual stresses were formulated as a function of the section thickness and slenderness. The proposal correlated well with test results and was particularly accurate when the beam depth exceeded the flange width, which is representative of bending members, and when used in a FE simulation, it predicted the failure modes of HSS members reported elsewhere. This proposed formulation can be used in numerical modelling for steel of grade 460 MPa and greater. Acknowledgement This study was supported by the Australian Research Council (ARC) through a Discovery Project (DP150100446) and funding from the Australian Nuclear Science and Technology Organisation (ANSTO) through Proposals 6397 and 7531. This support is gratefully acknowledged. References

Fig. 23. FE results versus test data.

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