Mechanical properties of headed studs at low temperatures in Arctic infrastructure

Mechanical properties of headed studs at low temperatures in Arctic infrastructure

Journal of Constructional Steel Research 149 (2018) 130–140 Contents lists available at ScienceDirect Journal of Constructional Steel Research Mech...

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Journal of Constructional Steel Research 149 (2018) 130–140

Contents lists available at ScienceDirect

Journal of Constructional Steel Research

Mechanical properties of headed studs at low temperatures in Arctic infrastructure Jian Xie a,b, Guan-Ru Zhu a,b, Jia-Bao Yan a,b,⁎ a b

School of Civil Engineering, Tianjin University, Tianjin 300350, China Key Laboratory of Coast Civil Structure Safety of Ministry of Education, Tianjin University, Ministry of Education, Tianjin 300350, China

a r t i c l e

i n f o

Article history: Received 2 April 2018 Received in revised form 24 July 2018 Accepted 27 July 2018 Available online xxxx Keywords: Mechanical properties Steel materials Low temperature Arctic structures Headed studs Composite structure Design equations

a b s t r a c t The increasing engineering applications of steel–concrete composite structures in the Arctic or other cold regions have brought challenges for the mechanical properties of headed studs at low temperatures. This study experimentally investigated the mechanical properties of headed studs used in steel–concrete composite structures at low temperatures. A total of 56 tensile tests were performed on headed studs at low temperatures ranging from −80 °C to +20 °C. The mechanical properties of headed studs at low temperatures were reported, analysed, and discussed, including their strain–stress behaviour; yield and ultimate strengths; and yield, ultimate, and fracture strains. Based on the experimental results, regression analyses were also carried out to develop empirical prediction equations for the yield and ultimate strengths of headed studs at low temperatures from 20 °C to −80 °C. Finally, empirical prediction equations were proposed, and their accuracy was validated through a comparison with the predictions of experimental results. © 2018 Elsevier Ltd. All rights reserved.

1. Introduction Steel–concrete composite (SCC) structures that combine the advantages of steel and concrete have become popular in engineering infrastructure. Recently, this structural system has been used in a wide variety of engineering constructions in cold regions and harsh environments, e.g. ice-resistant walls in offshore platforms for oil and gas exploration in the Arctic, steel–concrete composite bridges and other infrastructure in cold regions (see Fig. 1), liquefied natural gas (LNG) containers, prestressed concrete (PC) structures, and nuclear cooling towers [1–4]. SCC structures built in cold regions are exposed to harsh environmental conditions, particularly the low temperatures in those regions. As reported by Serreze and Barry [5], the lowest temperatures in Arctic regions can reach −70 °C. For other cold regions, e.g. Canada, Greenland, Tibet, and Northeast China, the lowest recorded temperature is about −60 °C [6, 7]. Headed studs are the most commonly used shear connectors, and are thus key components in determining the structural performance of SCC structures. Owing to their important role, the mechanical properties of headed studs in SCC structures built

Abbreviations: COV, coefficient of variation; LNG, liquefied natural gas; RC, reinforced concrete; PC, prestressed concrete. ⁎ Corresponding author at: School of Civil Engineering, Tianjin University, Tianjin 300350, China. E-mail address: [email protected] (J.-B. Yan).

https://doi.org/10.1016/j.jcsr.2018.07.028 0143-974X/© 2018 Elsevier Ltd. All rights reserved.

in the Arctic and other cold regions need to be carefully investigated and evaluated for the design of these SCC structures. Extensive studies have been carried out to investigate the shear behaviour of headed studs used in SCC structures. Ollgaard et al. [8], Lam [9], and Xue et al. [10] experimentally investigated the shear behaviour of headed studs embedded in concrete simulating the working scenario in SSC structures. Han et al. [11] experimentally studied the influence of the rubber content on the shear behaviour of headed studs. The shear and tensile behaviours of headed studs at room temperature were investigated by Pallares and Hajjar [12, 13]. Mirza and Uy [14] and Shahabi et al. [15] investigated the shear behaviour of headed studs at elevated temperatures. Hanswille et al. [16, 17] experimentally and analytically studied the fatigue behaviour of headed studs. Yan et al. [18] applied the finite element method to investigate the shear behaviour of headed studs at Arctic low temperatures. However, these studies mainly focused on the structural behaviour of headed studs at ambient and elevated temperatures, or only studied the behaviour of headed studs at low temperatures numerically. Few experiments have been carried out to investigate the structural behaviour of headed studs at low temperatures. Recently, some studies have explored the mechanical properties of construction materials at low temperatures. Elices et al. [19] investigated the behaviours of cold-stretched and hot-rolled steel at cryogenic temperatures reaching −180 °C. They found that the strength of both cold-stretched and hot-rolled steel increased with decreasing temperature, and low temperatures have a more significant influence on the

J. Xie et al. / Journal of Constructional Steel Research 149 (2018) 130–140

Nomenclature A0 Au D Es H T T0 a, b fy fu fy0 fu0 fyT fuT α, β ψ εy εu εF σ

original cross-sectional area of the headed stud smallest cross-sectional area of the headed stud at the fracture point diameter of the headed stud elastic Young's modulus of the headed studs length of the headed studs low temperatures ambient temperature constants which can be calculated from the tests results, in 1/°C yield strength of the headed studs ultimate strength of the headed studs yield strength of the headed studs at ambient temperature ultimate strength of the headed studs at ambient temperature yield strength of the headed studs at low temperatures ultimate strength of the headed studs at low temperatures sensitivity coefficients for the yield and ultimate strengths to different low temperature levels, in 1/K reduction in the cross-sectional area of headed studs yield strain of the headed studs ultimate strain of the headed studs fracture strain of the headed studs tensile stress of the headed studs

ductility of hot-rolled steel than cold-stretched steel. The mechanical properties of steel reinforcements at temperatures of +20 °C, −60 °C, −110 °C, and −165 °C were investigated by Lahlou et al. [20], and significant increases in both the yield and ultimate strengths of mild steel reinforcements with decreasing temperature were observed. Yan and Xie [3] carried out 63 tensile tests on hot-rolled mild steel reinforcements at low temperatures from +20 °C to −165 °C. The test results indicated that both the yield and ultimate strength of the steel reinforcements increased significantly with the decrease in temperature to −165 °C, but the ductility of the steel was reduced. Yan et al. [21] also experimentally studied the mechanical properties of high and normal strength steel plates at Arctic temperatures ranging from +20 °C to −80 °C. They found that the yield and ultimate strength of the steel plates increased significantly, whereas the fracture strain was not markedly affected by the low temperature. However, these previous tests only concentrated on the tensile stress–strain behaviour of construction materials at low temperatures, particularly focusing on steel reinforcements in RC or PC structures and steel plates in steel structures. Because headed studs have different production processes, chemical compositions, and microstructures than steel reinforcements and steel plates, the mechanical properties of headed studs used in SCC structures at low temperatures are still not fully understood. Thus, it is important to carry out experimental studies to obtain necessary information on the mechanical properties of headed studs at low temperatures relevant to cold environments. These experimental results can then be used as input data and will contribute to the design of SCC structures and the numerical analysis of their structural behaviour at low temperatures. This study first establishes a testing programme to investigate the mechanical properties of representative headed studs used in SCC structures at low temperatures ranging from an ambient temperature of +20 °C to −80 °C. This testing programme utilises 56 headed stud specimens, which are tested at five temperatures: −80 °C, −60 °C, −30 °C, 0 °C, and +20 °C. The mechanical properties of the headed studs at

131

these low temperatures are investigated, including the stress–strain behaviour, elastic modulus, yield and ultimate strengths, reduction in cross-sectional area (ψ), yield strain (εy), ultimate strain (εu), and fracture strain (εF). Then, the influence of low temperatures on these mechanical properties is analysed and discussed. Finally, empirical prediction formulae are developed to describe the mathematical relationship between the mechanical properties of mild steel headed studs and the low temperatures of their environment. 2. Testing programme 2.1. Details of test specimens To investigate the mechanical properties of headed studs at low temperatures, a total of 56 specimens were prepared for tensile testing. Fig. 2 shows a typical specimen for the tensile tests. This representative specimen consists of one headed stud welded to a bottom welded holding steel plate. This bottom steel plate has a width of 100 mm and thickness of 30 mm, and was used to hold the root of the stud during the tests. The headed studs were made of mild steel, and their chemical compositions are listed in Table 1. The parameters investigated with this testing programme are different low temperatures and varying diameters of the headed studs. Headed studs with diameters of 13, 16, 19, and 22 mm were prepared for the tests. Thus, the 56 specimens can be grouped into four categories. In each category, 15 specimens were tested at five target temperatures, i.e. −80 °C, −60 °C, −30 °C, 0 °C, and +20 °C, with three identical specimens tested at each temperature level. As reported by Serreze and Barry [5], the lowest temperature on record in the Arctic region is approximately −70 °C during winter. In addition, lowest recorded temperatures in Tibet and Northeast China are approximately −50 °C [7]. Thus, the temperature range for this test programme is from +20 °C to −80 °C. 2.2. Test setup Fig. 2 shows the typical setup for the tensile tests on headed studs, consisting of a hydraulic-servo loading system, a cooling chamber, and a data acquisition system. All specimens were tested under this servo-hydraulic testing frame with a capacity of 100 tons. The specimens were anchored to the testing frame with two steel clamps (see Fig. 2). Simulation of the low-temperature environment in the Arctic and cold regions was achieved using a sealed cooling chamber surrounding the specimens accompanied by injection of liquid nitrogen. This cooling chamber has dimensions of 450 × 400 × 600 mm (length × width × height). Four PT100 thermocouples were installed inside the cooling chamber to monitor the environmental temperature during the tests. 2.3. Loadings and measurements Cooling of the specimens was performed after their installation on the loading machine. The cooling rate of the environmental temperature in the chamber was 2–4 °C/min [22]. To monitor the temperature of the specimens, two PT100 thermocouples were installed at their middle regions. After achieving the target temperature, an additional 30 min were required to ensure the average distribution of the target low temperature according to GB/T 13239-2006 [23], and the PT100 readings were used to assist in controlling the temperature. Once the target low temperature was achieved, the tensile tests were performed. Tensile loading on the headed studs was performed in a displacement-controlled mode, and the corresponding reaction forces at each displacement increment were monitored by a load cell attached to the reaction frame. The displacement loading rate was 0.04 mm/min before the yield point and 0.4 mm/min after yielding, according to ASTM: A370-13 [24]. Two linear strain gauges were mounted on the middle surface of the headed stud to measure the strains, particularly those

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Fig. 1. Application of headed studs in steel-concrete composite structures.

before the yield point. An extensometer with a measuring range of ± 50% and a gauge length of 100 mm was also used to measure the plastic strain of the headed studs during the tests. All of the monitored data, including the temperature, reaction forces, and strains at different loading levels were recorded with a data acquisition system running on a controlled PC with a recording frequency of 50 Hz.

3. Test results and discussions 3.1. General Tests results for the mechanical properties of headed studs at low temperatures (−80 °C, −60 °C, −30 °C, 0 °C, and +20 °C) include the tensile stress–strain behaviour, elastic modulus, yield and ultimate strengths and their corresponding strains, fracture strain, and reduction in cross-sectional area.

3.2. Tensile stress–strain curves Fig. 3(a)–(d) shows the typical tensile stress–strain curves for headed studs at different low temperatures with diameters of 13 mm, 16 mm, 19 mm, and 22 mm, respectively. The results show that the stress–strain curves for headed studs at different low temperatures exhibit similar behaviour, and no obvious yielding plateaus are observed. Fig. 4 shows the general stress–strain curve for headed studs at low temperatures, which illustrates that the typical stress–strain curve for headed studs at low temperatures contains three working stages: the elastic stage, strength hardening stage, and strength recession stage. The stress initially exhibits a positive linear increase with increasing strain until the yield strength is reached. After that, it enters the strength hardening stage, and the stress increases nonlinearly in a quadratic manner with increasing strain until the ultimate value is reached. This strength hardening is due to dislocation movements and dislocation generation within the crystal structure of the headed studs at low

J. Xie et al. / Journal of Constructional Steel Research 149 (2018) 130–140

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Fig. 2. Test setup for tensile on headed stud specimens at low temperatures.

temperatures [25]. In the recession stage, necking was first observed, and finally fractures appeared in the headed studs. 3.3. Elastic modulus As the experimental tensile stress–strain curves for headed studs at different low temperatures exhibit no obvious yielding plateaus, the ‘0.2% offset method’ recommended in ASTM: 370-13 [24] was used in this study to determine their elastic modulus and yield strength (see Fig. 4). Table 2 summarises the elastic modulus values obtained for all the tested specimens. Fig. 5(a) depicts the relationship between the elastic modulus and low temperatures for headed studs with different diameters. These results indicate that as the temperature decreased from +20 °C to −80 °C, the elastic modulus of the headed studs increased slightly for all diameters; the average increase was 3.1%, 2.0%, 1.9%, and 2.5% for headed studs with diameters of 13 mm, 16 mm, 19 mm, and 22 mm, respectively. However, it should be noted that the correlation coefficients for the relationship between the temperature (T) and elastic modulus (Es) were only 0.07, 0.17, 0.07, and 0.02 for headed studs with diameters of 13 mm, 16 mm, 19 mm and 22 mm, respectively. This implies that the elastic modulus of the headed studs correlates weakly with the temperature. Similar findings were reported by Table 1 Chemical compositions of the headed stud. Diameter C (%)

Si (%) Mn (%) S (%)

P (%)

Alt (%) Cr (%) Cu (%) Ni (%)

13mm 16mm 19mm 22mm

0.040 0.060 0.040 0.040

0.006 0.016 0.016 0.012

0.035 0.037 0.051 0.045

0.150 0.150 0.160 0.140

0.410 0.360 0.420 0.420

0.006 0.007 0.005 0.007

— 0.025 0.140 0.030

— 0.010 0.020 0.010

— 0.010 0.090 0.010

Yan and Xie [3] and Liu et al. [26]. Based on these experimental results, it can be concluded that the effect of low temperatures on the Es of headed studs made of mild steel are marginal and can likely be neglected. 3.4. Yield and ultimate strength Both the yield strength, fy, and ultimate strength, fu, were determined from the tensile stress–strain curves (see Fig. 4), and the resulting values are listed in Table 2. To evaluate the influence of low temperatures, increase factors for fy and fu due to low temperatures were adopted. The increase factor for the yield strength, IfyT, was defined as the ratio of the yield strength at any low temperature, fyT, to the yield strength at ambient temperature, fy0, i.e. IfyT = fyT/ fy0. Similarly, the increase factor for the ultimate strength due to low temperature, IfuT, was defined as the ratio of fuT to fu0, i.e. IfuT = fuT/ fu0. The values obtained for IfyT and IfuT in these experiments are listed in Table 2. Fig. 5(b) and (c) shows the effect of low temperatures, T, on the IfyT and IfuT of headed studs, respectively. The results indicate that both fy and fu increased with decreasing temperature from +20 °C to −80 °C. In other words, as the temperature decreased from the ambient temperature to 0 °C, −30 °C, −60 °C, and −80 °C, the fu of the Φ13 mm headed stud increased by 3.0%, 5.6%, 12.2%, and 19.9%, respectively. As the temperature decreased from +20 °C to −80 °C, the fy (or fu ) of the Φ13 mm, Φ16 mm, Φ19 mm, and Φ22 mm headed studs increased by 18.8% (19.9%), 14.3% (22.3%), 18.1% (21.8%), and 17.4% (20.1%), respectively. These increases in the fy and fu of headed studs at low temperatures may be explained by the decrease in thermal vibration of atoms as the temperature decreases, thus requiring higher energy to overcome the interatomic force [27]. The test results also show that

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Fig. 3. Stress-strain curves of the headed stud specimens at low temperatures.

low temperatures have a more significant effect on the ultimate strength than on the yield strength of headed studs. This may be attributed to a face-centred cubic element (Ni, Cu) added to the headed stud [28]. Fig. 5(b) and (c) also show that the correlation coefficients, R2, between fy (or fu) and T are 0.82 (0.92), 0.88 (0.94), 0.90 (0.95), and 0.91 (0.96) for the Φ13 mm, Φ16 mm, Φ19 mm, and Φ22 mm headed studs, respectively. These high correlation coefficients indicate that low temperatures have a significant effect on the yield strength and ultimate strength of headed studs, which definitely needs to be considered. The scatter in IfyT and IfuT of headed studs with different diameters at low temperatures, i.e. Fig. 5(b) and (c), suggests that the diameter of the headed studs had a quite limited influence on IfyT and IfuT as the temperature decreased from +20 °C to −80 °C. 3.5. Reduction in cross-sectional area The reduction in cross-sectional area, ψ, was used as an index to describe the ductility of the headed studs. This index reflects the difference

Fig. 4. General stress-strain curve of headed studs.

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135

Table 2 Details and tensile test results of headed studs. Item

T (°C)

A0 (mm2)

Es (GPa)

εy (%)

εu (%)

εF (%)

Au (mm2)

ψ (%)

‾ψ (%)

fu (MPa)

‾fu (MPa)

fy (MPa)

‾fy (MPa)

IfuT

IfyT

A-T1-1 A-T1-2 A-T1-3 A-T2-1 A-T2-2 A-T2-3 A-T3-1 A-T3-2 A-T3-3 A-T4-1 A-T4-2 A-T4-3 A-T5-1 A-T5-2 A-T5-3 B-T1-1 B-T1-2 B-T2-1 B-T2-2 B-T2-3 B-T3-1 B-T3-2 B-T3-3 B-T4-1 B-T4-2 B-T4-3 B-T5-1 B-T5-2 B-T5-3 C-T1-1 C-T1-2 C-T1-3 C-T2-1 C-T2-2 C-T2-3 C-T3-1 C-T3-2 C-T3-3 C-T4-1 C-T4-2 C-T4-3 C-T5-1 C-T5-2 C-T5-3 D-T1-1 D-T1-2 D-T1-3 D-T2-1 D-T2-2 D-T2-3 D-T3-1 D-T3-2 D-T4-1 D-T4-2 D-T5-1 D-T5-2

20 20 20 0 0 0 −30 −30 −30 −60 −60 −60 −80 −80 −80 20 20 0 0 0 −30 −30 −30 −60 −60 −60 −80 −80 −80 20 20 20 0 0 0 −30 −30 −30 −60 −60 −60 −80 −80 −80 20 20 20 0 0 0 −30 −30 −60 −60 −80 −80

128.1 128.3 128.1 126.7 127.9 127.1 127.3 128.1 127.5 127.3 127.7 128.1 127.9 127.7 127.7 196.3 196.1 195.1 195.3 194.3 195.3 195.3 195.8 195.6 196.1 195.3 195.3 195.1 196.1 274.9 275.5 271.7 275.5 275.5 274.6 276.1 276.1 276.7 276.1 275.8 275.5 277.6 274.9 274.6 372.6 372.2 373.6 372.9 372.9 372.9 372.6 371.9 373.3 370.5 372.9 373.3

210.3 183.0 200.9 197.6 198.8 209.4 209.1 188.9 195.1 210.1 196.9 208.9 202.6 206.5 202.4 183.3 184.0 185.9 182.1 184.7 181.8 188.2 187.6 189.3 185.4 187.3 191.2 180.7 187.6 194.0 184.4 188.7 196.6 189.6 196.1 201.1 189.8 189.4 194.2 195.3 196.3 196.3 189.8 190.6 180.2 189.0 183.8 184.0 184.5 191.2 184.8 184.2 182.0 183.0 187.6 190.0

0.378 0.395 0.381 0.383 0.372 0.386 0.395 0.394 0.385 0.403 0.406 0.411 0.410 0.408 0.407 0.381 0.375 0.376 0.381 — 0.388 0.386 0.388 0.394 0.390 0.391 0.396 0.395 0.394 0.376 0.380 0.370 0.380 0.382 0.376 0.373 0.381 0.388 0.390 0.389 0.392 0.405 0.408 0.398 0.377 0.370 0.379 0.377 0.378 0.375 0.381 0.383 0.393 0.391 0.400 0.403

6.41 6.53 6.57 7.79 6.98 7.31 7.94 7.79 7.67 8.54 8.11 8.67 8.88 8.45 8.46 9.60 10.51 9.11 9.39 9.59 10.01 11.47 10.17 11.90 11.30 11.96 11.65 12.47 11.81 9.50 9.55 10.50 9.19 9.74 9.71 10.51 10.62 10.57 11.41 11.15 11.99 11.62 11.68 12.12 10.74 10.47 10.83 11.07 10.88 11.07 11.38 11.07 12.32 12.40 13.15 11.91

14.66 15.24 14.96 15.07 14.79 16.29 16.69 16.19 15.78 18.11 18.70 18.04 19.05 20.23 20.14 20.15 20.24 20.89 20.97 21.99 21.01 21.38 21.41 24.52 24.79 23.94 24.65 24.09 24.63 24.47 24.78 22.89 24.04 23.57 21.85 23.81 24.85 24.59 28.27 30.06 27.97 29.07 28.93 29.17 26.39 26.40 26.58 27.08 28.99 28.16 28.64 28.53 29.24 28.56 29.32 30.83

57.0 56.5 56.6 57.7 58.6 57.0 58.4 58.0 57.7 58.9 59.4 60.7 61.4 60.4 60.0 83.2 87.4 83.6 83.8 83.3 84.3 84.5 84.1 84.3 85.4 85.4 85.9 86.4 87.1 118.4 118.2 117.3 119.8 118.4 119.4 120.4 121.2 120.6 121.7 121.5 121.7 122.3 121.7 121.3 162.0 161.5 161.5 160.6 162.6 161.5 163.5 164.0 166.5 165.6 167.6 167.2

55.49 54.72 55.78 54.46 54.15 55.14 54.15 54.03 54.03 53.72 54.19 53.16 53.62 53.44 53.55 57.64 — 57.12 56.68 57.12 56.84 56.76 57.03 56.90 56.42 56.26 56.01 55.70 55.50 56.92 57.08 57.11 56.52 56.59 56.52 56.40 56.12 56.43 55.91 55.93 55.82 55.93 55.79 55.99 56.53 56.61 56.77 56.63 56.39 56.69 56.10 55.90 55.39 55.31 55.04 55.41

55.33

504.5 489.9 488.9 510.3 510.4 507.6 526.9 522.6 516.7 553.9 560.7 549.2 598.1 593.8 586.4 458.0 452.6 470.5 469.0 472.5 492.0 484.8 478.3 519.9 523.1 520.9 563.1 554.7 553.0 469.1 460.3 438.2 478.0 477.6 480.8 497.4 492.6 500.7 525.7 520.1 522.7 553.4 554.0 558.5 455.5 453.3 458.0 472.1 471.7 466.9 481.1 490.6 514.2 518.2 543.1 551.4

494.4

365.2 360.0 359.2 369.4 368.2 350.2 375.5 349.7 374.7 381.9 399.1 386.0 428.7 430.0 429.3 316.2 321.3 328.8 317.2 325.2 335.7 333.3 328.8 358.5 344.7 362.5 372.4 361.8 359.4 344.8 337.0 323.4 348.0 340.9 342.9 355.4 357.2 361.6 372.5 368.3 366.6 395.9 393.8 397.8 316.0 313.7 318.1 324.1 327.8 326.9 330.0 335.0 342.9 349.5 363.7 373.5

361.5

1.02 0.99 0.99 1.03 1.03 1.03 1.07 1.06 1.05 1.12 1.13 1.11 1.21 1.20 1.19 1.01 0.99 1.03 1.03 1.04 1.08 1.06 1.05 1.14 1.15 1.14 1.24 1.22 1.21 1.03 1.01 0.96 1.05 1.05 1.05 1.09 1.08 1.10 1.15 1.14 1.15 1.21 1.22 1.23 1.00 0.99 1.01 1.04 1.04 1.02 1.06 1.08 1.13 1.14 1.19 1.21

1.01 1.00 0.99 1.02 1.02 0.97 1.04 0.97 1.04 1.06 1.10 1.07 1.19 1.19 1.19 0.99 1.01 1.03 1.00 1.02 1.05 1.05 1.03 1.12 1.08 1.14 1.17 1.14 1.13 1.03 1.01 0.97 1.04 1.02 1.02 1.06 1.07 1.08 1.11 1.10 1.09 1.18 1.18 1.19 1.00 0.99 1.01 1.03 1.04 1.03 1.04 1.06 1.09 1.11 1.15 1.18

54.58

54.07

53.69

53.54

57.64 56.97

56.88

56.53

55.73

57.04

56.55

56.32

55.89

55.90

56.64

56.57

56.00 55.35 55.23

509.4

522.1

554.6

592.8

455.3 470.7

485.0

521.3

556.9

455.9

478.8

496.9

522.8

555.3

455.6

470.2

485.9 516.2 547.3

368.8

375.1

389.0

429.3

318.8 323.7

331.7

355.2

364.5

335.1

348.7

358.1

369.1

395.8

314.1

328.0

332.5 346.2 368.6

A0, Au are the area of the original cross section of the headed studs and the area of the smallest cross section at the fracture point, respectively; Es is Young’s modulus of headed studs; εy, εy, εF are yield, ultimate, and fracture strain, respectively; ψ,‾ψ are reduction in cross-sectional area and average values of reduction in cross-sectional area, respectively; fu,‾fu are ultimate strength, average ultimate strength, respectively; fy,‾fy are yield strength, average yield strength, respectively; IεF, IfyT, IfuT equal to fracture strain, yield strength and ultimate strength at different low temperature levels to their corresponding values at ambient temperature, respectively.

between the cross-sectional area at the fracture point and the original cross-sectional area. It can be calculated using the following equation as specified in ASTM: 370-13 [24]:

ψ¼

A0 ‐Au  100% A0

ð1Þ

where A0 denotes the original cross-sectional area of the headed stud, and Au is the smallest cross-sectional area of the headed stud at the fracture point. Table 2 lists the resulting ψ values, and Fig. 5(d) shows the influence of the T on ψ. These results show that ψ decreased slightly as the temperature decreased from +20 °C to −80 °C. For instance, the headed studs with a diameter of 22 mm had average values of ψ at +20 °C, 0

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Fig. 5. Effect of low temperatures on the mechanical properties.

°C, −30 °C, −60 °C, and −80 °C of 56.6%, 56.5%, 56.0%, 55.4%, and 55.2%, respectively. This indicates that the average value of ψ is only reduced by 2.5% as the temperature decreased from an ambient temperature of +20 °C to −80 °C. Similarly, there were no significant decreases in ψ for the Φ13 mm, Φ16 mm, or Φ19 mm headed studs within the temperature range of +20 °C to −80 °C. This implies that changes in temperature within the range of +20 °C to −80 °C have a limited influence on the ψ of headed studs. Fig. 6 presents the typical fracture modes of headed studs at different temperatures (+20 °C, 0 °C, −30 °C, −60 °C, and −80 °C). For all of the headed studs tested, necking occurred before final fracture, and no brittle failure was observed in these tests [21]. 3.6. Yield strain, ultimate strain, and fracture strain The yield strain, εy, ultimate strain, εu, and fracture strain, εF, were determined from the tensile stress–strain curves for headed studs at different temperatures according to ASTM: A370-13 [24], and the resulting values are listed in Table 3. Fig. 7 shows the effect of low temperatures on εy, εu, and εF. These results show that as the temperature decreased from 20 °C to −80 °C, the εy, εu, and εF values all increased almost linearly with the decreasing temperature. As the temperature decreased from 20 °C to 0 °C, −30 °C, −60 °C, and −80 °C, the average εy values increased by 0.1%, 1.8%, 4.5%, and 6.3%, respectively. Similarly, the increase in εu (or εF) was 1.6% (2.7%), 9.3% (5.8%), 19.7% (18.0%), and 22.1% (22.0%) at 0 °C, −30 °C, −60 °C, and −80 °C, respectively. This comparison also reveals that decreasing the temperature has a more significant beneficial influence on εu and εF. These increases in εy, εu,

and εF are likely caused by the addition of nickel to the mild steel for headed studs, which can improve the dislocation glide between the crystals at low temperatures [29]. Thus, it can be concluded that the ductility of the headed studs was not compromised as the temperature decreased from 20 °C to −80 °C. Similar experimental results were reported by Paik et al. [30] and Ehlers and Østby [31]. 4. Regression analysis of fy and fu at low temperatures The experimental results show that low temperatures have a significant effect on the mechanical properties of headed studs, particularly on the yield and ultimate strengths. Thus, to incorporate the effects of low temperatures on the yield and ultimate strengths of headed studs, regression analyses were carried out to develop mathematical relationships between the low temperatures and the mechanical properties of headed studs. General exponential models were used in these regression analyses, which consider the low temperature, T, as the main predictor. The resulting increase in the yield and ultimate strengths at low temperatures can be proposed as follows [32]: f y ¼ f yT eα ð1=T 0 −1=T Þ

ð2Þ

f u ¼ f uT eβð1=T 0 −1=T Þ

ð3Þ

where T is the low temperature (K); fy is the yield strength (MPa) at the ambient temperature, T0; fu is the ultimate strength (MPa) at the ambient temperature, T0; fyT is the yield strength (MPa) at low temperature T; fuT is the ultimate strength (MPa) at low temperature T; and α and

J. Xie et al. / Journal of Constructional Steel Research 149 (2018) 130–140

137

Fig. 6. Fracture modes of headed studs at different low temperatures.

β are sensitivity coefficients for the yield and ultimate strength to different low temperatures, respectively (1/K). The relationship between α and β can be expressed as follows [32]: β ¼ Aα

ð4Þ

where A is a constant which can be calculated from the testing data. It should be noted that the temperatures in Eqs. (2) and (3) are given in units of Kelvin (K), which is inconvenient for engineering applications. Thus, equations expressing T in °C are also given to simplify Eqs. (2) and (3), as follows: f y ¼ f yT eaðT−T 0 Þ

ð5Þ

f u ¼ f uT ebðT−T 0 Þ

ð6Þ

b ¼ Ba

ð7Þ

where a, b, and B are constants that can be calculated from the testing data. Because the predictive equations (i.e. Eqs. (2)–(7)) focus on mechanical properties at low temperatures, results of the tests at −30 °C, −60 °C, and −80 °C were used to estimate the average values for constants α, β, a, and b. From the test data in Table 2, the coefficients of α, β, a, and b used in this analysis model were determined, and the results

are listed in Table 3. Eqs. (8) and (9) are thus proposed: f y ¼ f yT e76:94ð1=T 0 −1=T Þ

ð8Þ

Table 3 Coefficients of α, β, a and b obtained from the regression analysis. Diameter

T (°C)

α

β

a

b

13mm 13mm 13mm

−30 −60 −80 Mean −30 −60 −80 Mean −30 −60 −80 Mean −30 −60 −80 Mean

52.59 57.20 97.25 69.01 60.34 84.42 75.81 73.52 94.40 75.46 94.19 88.02 72.93 71.45 87.25 77.21

77.54 89.64 102.61 89.93 90.08 105.60 113.93 103.20 122.63 106.87 111.53 113.68 91.54 97.42 103.65 97.54

0.0007 0.0009 0.0016 0.0011 0.0008 0.0014 0.0012 0.0011 0.0013 0.0012 0.0015 0.0013 0.0010 0.0011 0.0014 0.0012

0.0011 0.0014 0.0016 0.0014 0.0013 0.0017 0.0018 0.0016 0.0017 0.0017 0.0018 0.0017 0.0013 0.0016 0.0017 0.0015

16mm 16mm 16mm 19mm 19mm 19mm 22mm 22mm 22mm

The average values of α, β, a and b are 76.94, 101.09, 0.0012 and 0.0016, respectively.

138

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Fig. 7. Effect of low temperatures on yield, ultimate, and fracture strain.

Table 4 Predicted results by the developed equation. Item

fy (MPa)

fu (MPa)

fyA (MPa)

fuA(MPa)

fy / fyA

fu / fuA

fyB (MPa)

fuB (MPa)

fy / fyB

fu / fuB

A-T1-1 A-T1-1 A-T1-2 A-T1-3 A-T2-1 A-T2-2 A-T2-3 A-T3-1 A-T3-2 A-T3-3 A-T4-1 A-T4-2 A-T4-3 A-T5-1 A-T5-2 A-T5-3 B-T1-1 B-T1-2 B-T2-1 B-T2-2 B-T2-3 B-T3-1 B-T3-2 B-T3-3 B-T4-1 B-T4-2 B-T4-3 B-T5-1 B-T5-2 B-T5-3 C-T1-1 C-T1-2 C-T1-3 C-T2-1 C-T2-2 C-T2-3 C-T3-1 C-T3-2 C-T3-3 C-T4-1 C-T4-2 C-T4-3 C-T5-1 C-T5-2 C-T5-3 D-T1-1 D-T1-2 D-T1-3

365.2 365.2 360.0 359.2 369.4 368.2 350.2 375.5 349.7 374.7 381.9 399.1 386.0 428.7 430.0 429.3 316.2 321.3 328.8 317.2 325.2 335.7 333.3 328.8 358.5 344.7 362.5 372.4 361.8 359.4 344.8 337.0 323.4 348.0 340.9 342.9 355.4 357.2 361.6 372.5 368.3 366.6 395.9 393.8 397.8 316.0 313.7 318.1

504.5 504.5 489.9 488.9 510.3 510.4 507.6 526.9 522.6 516.7 553.9 560.7 549.2 598.1 593.8 586.4 458.0 452.6 470.5 469.0 472.5 492.0 484.8 478.3 519.9 523.1 520.9 563.1 554.7 553.0 469.1 460.3 438.2 478.0 477.6 480.8 497.4 492.6 500.7 525.7 520.1 522.7 553.4 554.0 558.5 455.5 453.3 458.0

361.5 361.5 361.5 361.5 368.5 368.5 368.5 381.6 381.6 381.6 399.0 399.0 399.0 414.2 414.2 414.2 318.8 318.8 325.0 325.0 325.0 336.5 336.5 336.5 351.8 351.8 351.8 365.3 365.3 365.3 335.1 335.1 335.1 341.6 341.6 341.6 353.7 353.7 353.7 369.8 369.8 369.8 383.9 383.9 383.9 315.9 315.9 315.9

494.4 494.4 494.4 494.4 507.1 507.1 507.1 530.8 530.8 530.8 562.8 562.8 562.8 591.2 591.2 591.2 455.3 455.3 467.0 467.0 467.0 488.8 488.8 488.8 518.3 518.3 518.3 544.4 544.4 544.4 455.9 455.9 455.9 467.6 467.6 467.6 489.4 489.4 489.4 519.0 519.0 519.0 545.1 545.1 545.1 455.6 455.6 455.6

1.01 1.01 1.00 0.99 1.00 1.00 0.95 0.98 0.92 0.98 0.96 1.00 0.97 1.04 1.04 1.04 0.99 1.01 1.01 0.98 1.00 1.00 0.99 0.98 1.02 0.98 1.03 1.02 0.99 0.98 1.03 1.01 0.97 1.02 1.02 1.03 1.00 1.01 1.02 1.01 1.00 0.99 1.03 1.03 1.04 0.99 1.00 1.01

1.02 1.02 0.99 0.99 1.01 1.01 1.00 0.99 0.98 0.97 0.98 1.00 0.98 1.01 1.00 0.99 1.01 0.99 1.01 1.00 1.01 1.01 0.99 0.98 1.00 1.01 1.01 1.03 1.02 1.02 1.03 1.01 0.96 1.02 1.02 1.03 1.02 1.01 1.02 1.01 1.00 1.01 1.02 1.02 1.02 1.00 0.99 1.01

361.5 361.5 361.5 361.5 370.3 370.3 370.3 383.9 383.9 383.9 397.9 397.9 397.9 407.6 407.6 407.6 318.8 318.8 326.5 326.5 326.5 338.5 338.5 338.5 350.9 350.9 350.9 359.4 359.4 359.4 335.1 335.1 335.1 343.2 343.2 343.2 355.8 355.8 355.8 368.9 368.9 368.9 377.8 377.8 377.8 315.9 315.9 315.9

499.5 494.4 494.4 494.4 510.5 510.5 510.5 535.6 535.6 535.6 561.9 561.9 561.9 580.2 580.2 580.2 455.3 455.3 470.1 470.1 470.1 493.2 493.2 493.2 517.5 517.5 517.5 534.3 534.3 534.3 455.9 455.9 455.9 470.7 470.7 470.7 493.9 493.9 493.9 518.2 518.2 518.2 535.0 535.0 535.0 455.6 455.6 455.6

1.01 1.01 1.00 0.99 1.00 0.99 0.95 0.98 0.91 0.98 0.96 1.00 0.97 1.05 1.06 1.05 0.99 1.01 1.01 0.97 1.00 0.99 0.98 0.97 1.02 0.98 1.03 1.04 1.01 1.00 1.03 1.01 0.97 1.01 1.01 1.02 1.00 1.00 1.02 1.01 1.00 0.99 1.05 1.04 1.05 0.99 1.00 1.01

1.02 1.02 0.99 0.99 1.00 1.00 0.99 0.98 0.98 0.96 0.99 1.00 0.98 1.03 1.02 1.01 1.01 0.99 1.00 1.00 1.01 1.00 0.98 0.97 1.00 1.01 1.01 1.05 1.04 1.04 1.03 1.01 0.96 1.02 1.01 1.02 1.01 1.00 1.01 1.01 1.00 1.01 1.03 1.04 1.04 1.00 0.99 1.01

J. Xie et al. / Journal of Constructional Steel Research 149 (2018) 130–140

139

Table 4 (continued) Item

fy (MPa)

fu (MPa)

fyA (MPa)

fuA(MPa)

fy / fyA

fu / fuA

fyB (MPa)

fuB (MPa)

fy / fyB

fu / fuB

D-T2-1 D-T2-2 D-T2-3 D-T3-1 D-T3-2 D-T4-1 D-T4-2 D-T5-1 D-T5-2 Mean COV

324.1 327.8 326.9 330.0 335.0 342.9 349.5 363.7 373.5

472.1 471.7 466.9 481.1 490.6 514.2 518.2 543.1 551.4

322.0 322.0 322.0 333.4 333.4 348.6 348.6 361.9 361.9

467.3 467.3 467.3 489.1 489.1 518.6 518.6 544.8 544.8

1.02 1.02 1.03 1.00 1.01 0.99 1.01 1.01 1.04 1.00 0.02

1.01 1.01 1.00 0.98 1.00 0.99 1.00 1.00 1.01 1.00 0.01

323.6 323.6 323.6 335.4 335.4 347.7 347.7 356.2 356.2

470.4 470.4 470.4 493.5 493.5 517.8 517.8 534.7 534.7

1.01 1.02 1.03 0.99 1.00 0.99 1.01 1.03 1.05 1.00 0.03

1.00 1.00 0.99 0.97 0.99 0.99 1.00 1.02 1.03 1.00 0.02

fyA, fuA, fyB and fuB are calculated by Eq. (8), Eq. (9), Eq. (10) and Eq. (11), respectively.

f u ¼ f uT e101:09ð1=T 0 −1=T Þ

ð9Þ

where T is given in Kelvin, and 193 K ≤ T ≤ 293 K. If the temperature, T, is given in °C, the following equations can be used to predict the yield and ultimate strengths of headed studs at low temperatures: f y ¼ f yT e0:0012ðT−T 0 Þ

ð10Þ

f u ¼ f uT e0:0016ðT−T 0 Þ

ð11Þ

where T is the low temperature in °C, and −80 °C ≤ T ≤ +20 °C. The mean values and coefficients of variation (COV) of the test-toprediction ratios were used to evaluate the accuracy of the proposed prediction equations (Eqs. (8)–(11)). Table 4 compares the test results for the yield strength and ultimate strength at different temperatures (+20 °C, 0 °C, −30 °C, −60 °C, and −80 °C) with the predicted values

Fig. 8. Comparisons of predictions with experimental results.

Fig. 9. Comparisons between the predictions and experimental results.

140

J. Xie et al. / Journal of Constructional Steel Research 149 (2018) 130–140

calculated using Eqs. (8)–(11). Figs. 8 and 9 show comparisons between the predicted and tested results for the yield and ultimate strength, respectively. These results show that the errors for the predicted yield and ultimate strengths are less than 10%, and the COV for the test-to-prediction ratios obtained with Eq. (8), Eq. (9), Eq. (10), and Eq. (11) are 0.02, 0.01, 0.03, and 0.02, respectively. This implies that the proposed prediction equations give a reasonable estimation of the increase in the yield and ultimate strengths due to low temperatures with limited error. Thus, the prediction equations proposed in Eqs. (8)–(11) can be used to estimate the yield and ultimate strengths of headed studs at low temperatures with a given strength at ambient temperature. However, these predictive equations were developed based on limited test data, and additional experimental results will be required for validation purposes. 5. Conclusions This study experimentally investigated the mechanical properties of headed studs at low temperatures relevant to cold regions and Arctic environments using a 56-specimen testing programme. Then, the stress–strain behaviour, yield and ultimate strengths, reduction in cross-sectional area, and yield, ultimate, and fracture strains obtained from these tests were analysed and discussed. Finally, regression analyses were performed on the yield and ultimate strengths of the headed studs to develop empirical prediction equations. Based on the results of these tests and analyses, the following conclusions can be drawn: (1) Low temperatures within the range of +20 °C to −80 °C exhibited marginal effects on the elastic modulus of headed studs, whereas the yield and ultimate strengths of headed studs with all diameters increased almost linearly with the decreasing temperature from +20 °C to −80 °C. As the temperature decreased from +20 °C to −80 °C, the yield and ultimate strengths were increased by an average of approximately 17% and 20%, respectively. However, the diameter of the headed studs exhibited a quite limited influence on fy and fu when the temperature decreased from +20 °C to −80 °C. (2) The decrease in temperature slightly decreased the reduction in cross-sectional area, ψ; however, the influence of low temperatures in the range of +20 °C to −80 °C on ψ is less than 3.5%. The yield strain, εy, ultimate strain, εu, and fracture strain, εF, all increased with decreasing temperature. As the temperature decreased from +20 °C to −80 °C, εy, εu, and εF increased by an average of 6.3%, 22.1%, and 22.0%, respectively. This may be due to the presence of nickel in the headed studs. (3) Empirical prediction equations, i.e. Eqs. (8)–(11), were proposed to predict the fy and fu of headed studs at low temperatures ranging from −80 °C to +20 °C with given yield and ultimate strengths at ambient temperatures. Validation of the predicted results obtained with the proposed prediction equations shows that the prediction errors were all less than 10%, confirming the accuracy of the predictions.

The proposed prediction equations were based on limited test data, and validation of their accuracy will require further experiments. Acknowledgements This work was funded by the National Natural Science Foundation of China (Grant No. 51608358) and Seed Foundation of Tianjin University,

China (Grant No. 2018XRG-0019). The authors gratefully express their gratitude for the financial support. References [1] J.B. Yan, X. Qian, J.Y.R. Liew, et al., Damage plasticity based numerical analysis on steel–concrete–steel sandwich shells used in the Arctic offshore structure, Eng. Struct. 117 (2016) 542–559. [2] A. Palmer, K. Croasdale, Arctic Offshore Engineering, World Scientific Publishing, Singapore, 2013. [3] J.B. Yan, J. Xie, Experimental studies on mechanical properties of steel reinforcements under cryogenic temperatures, Constr. Build. Mater. 151 (2017) 661–672. [4] Prestressed Concrete Institute (PCI), PCI Design Handbook, 6th ed. Precast/ Prestressed Concrete Institute, Chicago (IL), 2004. [5] M.C. Serreze, R.G. Barry, The Arctic Climate System, Cambridge University Press, London, 2014. [6] N.A. Stjpanova, On the lowest temperatures on earth, Monthly Weather Rev. (1985) 6–10. [7] Y. Qiao, H. Wang, L. Cai, et al., Influence of low temperature on dynamic behavior of concrete, Constr. Build. Mater. 115 (2016) 214–220. [8] J.G. Ollgaard, R.G. Slutter, J.W. Fisher, Shear strength of stud connectors in lightweight and normal-weight concrete, AISC Eng. J. 8 (2) (1971) 55–64. [9] D. Lam, Capacities of headed stud shear connectors in composite steel beams with precast hollowcore slabs, J. Constr. Steel Res. 63 (9) (2007) 1160–1174. [10] W.C. Xue, M. Ding, H. Wang, et al., Static behavior and theoretical model of stud shear connectors, J. Bridg. Eng. 13 (6) (2008) 623–634. [11] Q.H. Han, Y.H. Wang, J. Xu, et al., Static behavior of stud shear connectors in elastic concrete–steel composite beams, J. Constr. Steel Res. 113 (2015) 115–126. [12] L. Pallarés, J.F. Hajjar, Headed steel stud anchors in composite structures, Part I: Shear, J. Constr. Steel Res. 66 (2) (2010) 198–212. [13] L. Pallarés, J.F. Hajjar, Headed steel stud anchors in composite structures, Part II: Tension and interaction, J. Constr. Steel Res. 66 (2) (2009) 213–228. [14] O. Mirza, B. Uy, Behaviour of headed stud shear connectors for composite steel–concrete beams at elevated temperatures, J. Constr. Steel Res. 65 (3) (2017) 662–674. [15] S. Shahabi, N. Sulong, M. Shariati, et al., Performance of shear connectors at elevated temperatures—a review, Steel Compos. Struct. 20 (1) (2016) 185–203. [16] G. Hanswille, M. Porsch, C. Ustundag, Resistance of headed studs subjected to fatigue loading: part i: experimental study, J. Constr. Steel Res. 63 (4) (2007) 475–484. [17] G. Hanswille, M. Porsch, C. Ustundag, Resistance of headed studs subjected to fatigue loading: part ii: analytical study, J. Constr. Steel Res. 63 (4) (2007) 485–493. [18] J.B. Yan, W. Zhang, J.Y.R. Liew, et al., Numerical studies on shear resistance of headed stud connectors in different concretes under Arctic low temperature, Mater. Des. 112 (2016) 184–196. [19] M. Elites, H. Comes, J. Planas, Behavior at cryogenic temperatures of steel for concrete reinforcement, ACI Struct. J. 83 (3) (1986) 405–411. [20] D. Lahlou, K. Amar, K. Salah, Behavior of the reinforced concrete at cryogenic temperatures, Cryogenics 47 (2007) 517–525. [21] J.B. Yan, J.Y.R. Liew, M.H. Zhang, et al., Mechanical properties of normal strength mild steel and high strength steel S690 in low temperature relevant to Arctic environment, Mater. Des. 61 (9) (2014) 150–159. [22] J.M. Pei, Experimental Study on Mechanical Properties of Reinforcement at Cryogenic TemperatureMaster Thesis Tianjing University, China, 2012. [23] GB/T 13239-2006, Metallic Materials – Tensile Testing at Low Temperature, China Standards Press, Beijing, 2006. [24] ASTM, A370-13. Standard Test Methods and Definitions for Mechanical Testing of Steel Products, ASTM International, West Conshohocken, United States, 2013. [25] E.P. Degarmo, J.T. Black, R.A. Kohser, Materials and Processes in Manufacturing, 9th ed. Darvic Associates, 2003. [26] S. Liu, X.L. Gu, Q.H. Huang, Experimental study on mechanical properties of steel bars at super-low temperature, J. Build. Struct. 29 (2008) 47–51. [27] K. Lonsdale, Thermal vibrations of atoms and molecules in crystals, Rev. Mod. Phys. 30 (1) (1958) 168–170. [28] S.F. Ding, Research on Structure Safety of Large LNG Carrier under Ultra-low TemperaturePh.D Thesis Shanghai JiaoTong University, China, 2010. [29] Z.H. Yang, Investigation of Effect Mechanism of Si and Ni in as-cast Ferrite Ductile iron by Electronic TheoryPh.D dissertation Shenyang Ligong University, China, 2017. [30] J.K. Paik, B.J. Kim, D.K. Park, et al., On quasi-static crushing of thin-walled steel structures in cold temperature: Experimental and numerical studies, Int. J. Impact Eng. 38 (1) (2011) 13–28. [31] S. Ehlers, E. Østby, Increased crashworthiness due to arctic conditions – The influence of sub-zero temperature, Mar. Struct. 28 (1) (2012) 86–100. [32] Y.Q. Wang, X.Z. Wang, Y.M. Wu, The experimental study on the main mechanical parameters of structural steel under low temperature, Indust. Construct. 31 (12) (2001) 63–66.