Behavior of welded hollow spherical joints after exposure to ISO-834 standard fire

Journal of Constructional Steel Research 140 (2018) 108–124

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Journal of Constructional Steel Research

Behavior of welded hollow spherical joints after exposure to ISO-834 standard fire Jie Lu a,b,c, Hongbo Liu a,b,⁎, Zhihua Chen a,b a b c

State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Department of Civil Engineering, Tianjin University, Tianjin 300072, China Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, United States

a r t i c l e

i n f o

Article history: Received 22 December 2016 Received in revised form 6 October 2017 Accepted 21 October 2017 Available online xxxx Keywords: Welded hollow spherical joints Post-fire Residual behavior Load-bearing capacity Initial axial stiffness

a b s t r a c t Welded hollow spherical joints are extensively used as a connection pattern in space lattice structures. Provided that structural collapse does not occur after a fire, a reliable evaluation of the residual performances of the structures is necessary to decide whether the structures should be dismantled, repaired, or directly reused. Thus, understanding the post-fire residual behavior of welded hollow spherical joints, which act as key connection elements, is crucial for fire damage assessment of the space lattice structures. In this paper, experimental and numerical studies were conducted to reveal the residual structural behavior of welded hollow spherical joints after fire exposure. Axial compressive tests were performed on eight joint specimens after exposure to the ISO-834 standard fire (including both heating and cooling phases), and three highest fire temperatures, i.e., 600 °C, 800 °C, and 1000 °C, were considered. The temperature distributions in the specimens during the heating and cooling process and the related mechanical behavior of the specimens, such as axial load– displacement curves, initial axial stiffness, yield loads, load-bearing capacities, ductility level, and strain distributions, were obtained and analyzed. Finite element analysis (FEA), including both heat transfer and stress analysis, were also developed using the ABAQUS software. Having validated the FE models against the experimental results, a design method was proposed on the basis of parametric studies to predict both the residual loadbearing capacity and initial axial stiffness of welded hollow spherical joints after fire exposure. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction As a typical large-span structural form, space lattice structures are formed by a large number of tension and compression bars connected with joints. The joints widely used in space lattice structures mainly include MERO joints [1,2], Temcor joints [3], bolt–ball joints [4], socket joints [5], and welded hollow spherical joints etc. The welded hollow spherical joints were initially developed by X. L. Liu and first applied in the Science and Technology Hall in Tianjin, China [6]. This joint pattern possesses such advantages as light weight, high stiffness, simple in construction, easy to connect, and absence of node eccentricity. Thus, this joint pattern has been extensively used in space lattice structures, particularly in China. Structures involving the use of welded hollow spherical joints may be exposed to elevated temperatures in the event of a severe fire hazard, which is typically considered as one of the main disasters causing damages to building structures. Nevertheless, provided that a sufficiently high design safety factor and proper fire insulation are provided, structural collapse of the entire space lattice ⁎ Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Liu).

https://doi.org/10.1016/j.jcsr.2017.10.026 0143-974X/© 2017 Elsevier Ltd. All rights reserved.

structure is unlikely to occur in a real fire. If the response of the structure is satisfactory during and immediately following a fire event, then its post-fire residual performance must be evaluated accurately to determine whether the structure should be dismantled, repaired, or reused directly. Therefore, as an important basis of assessing the fire damage of the entire structure, the post-fire residual behavior of the welded hollow spherical joints, which act as key connection members, must be investigated first. Extensive studies have been conducted to investigate the mechanical behavior of welded hollow spherical joints at ambient temperature without fire exposure. Chen [7] and Zhou [8] conducted both theoretical and experimental studies on the collapse mechanism and load-bearing capacity of welded hollow spherical joints with different diameters. Han et al. [9–11] proposed formulas to calculate the load-bearing capacity and stiffness of welded hollow spherical joints subjected to compression, tension, and bending moment via theoretical and numerical analysis. Dong [12] and Tang [13] investigated the load-bearing capacity of welded hollow spherical joints under eccentric loads and developed a practical calculation method. Wan [14] and Wang et al. [15,16] conducted finite element analysis (FEA) to investigate the axial and rotational stiffness of welded hollow spherical joints and proposed the calculation formulas. Zhang et al. [17] investigated the axial and rotational stiffness

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124 Table 1 Details of the test specimens. Specimen no.

Th (°C)

th (min)

Steel grade

J345-20 J345-600 J345-800 J345-1000 J235-20 J235-600 J235-800 J235-1000

– 600 800 1000 – 600 800 1000

– 5.9 22.7 86.4 – 5.9 22.7 86.4

Q345 Q345 Q345 Q345 Q235 Q235 Q235 Q235

10 30

220 140

30 10

process. Axial compressive tests were subsequently performed on the specimens at ambient temperature to investigate their post-fire fundamental behavior. Related mechanical properties, such as axial load–displacement curves, initial axial stiffness, yield loads, loadbearing capacities, ductility level, and strain distributions, were obtained. Furthermore, finite element analysis, including both the heat transfer and stress analysis, were developed using ABAQUS software. On the basis of parametric studies, a design method was proposed to predict the residual load-bearing capacity and initial axial stiffness of welded hollow spherical joints after fire exposure.

2. Experimental investigation 2.1. Test specimens A total of eight welded hollow spherical joint specimens were tested. The key parameters considered were the highest exposure fire temperatures (corresponding to the heating time based on the ISO-834 standard temperature–time curves) and the steel grades of the specimens. Details of the specimens are shown in Table 1, where Th and th refer to the highest exposure fire temperatures and corresponding heating time, respectively. An example of the naming method of the test specimen is as follows: J345-20, where J refers to the welded hollow spherical joint; the next three digits refer to the steel grade of the specimen, i.e., Q345 or Q235 steel (with nominal yield strengths of 345 and 235 N/mm2, respectively); and the following number refers to the highest exposure fire temperature experienced, i.e., 600 °C, 800 °C, or 1000 °C; whereas number 20, which was the ambient temperature of the laboratory, denotes the specimens without fire exposure. For all test specimens, the external diameter (D) and thickness of the hollow sphere (t) and the external diameter of the steel tube (d) maintained 400 mm, 14 mm, and 140 mm, respectively, which are the commonly used dimensions in practical projects. The corresponding ratios of D/t and D/d are 28.57 and 2.86, respectively, which are in accordance with the recommendations in JGJ 61-2003. Relatively thick steel tubes with a thickness of 10 mm were used for all specimens to obtain the failure modes and load-bearing capacity of the hollow sphere. Two enlarged end plates with a thickness of 30 mm were welded to the top and bottom ends of the steel tubes. The quality of the butt weld connecting the steel tube and the hollow sphere meets the requirements of JGJ 61-2003. The test specimen details are shown in Fig. 1.

30

of welded hollow spherical joints and established a bilinear load– displacement model. Furthermore, design guides, such as JGJ 61-2003: Technical Specification for Latticed Shells [18] and JGJ 7-2010: Technical Specification for Frame Structures [19], also provide the design methods for welded hollow spherical joints. According to the brief literature review, previous studies have all focused on the mechanical behavior of welded hollow spherical joints at ambient temperature. However, it is known that the mechanical properties of structural steels will significantly change after exposure to elevated temperatures, which will lead to obvious changes in the behavior of welded hollow spherical joints further. What's more, some geometric imperfections induced by heating-cooling process might also be introduced in the welded hollow spherical joints, which will also influence the post-fire behavior of the joints. Hence, it is not appropriate to directly apply the research results obtained from ambient temperature to the assessment of the performance of welded hollow spherical joints after fire exposure. Nevertheless, no reported research on their mechanical performance after fire exposure has been found. Furthermore, no current design guide has provided applicable recommendations for the post-fire residual performance of the welded hollow spherical joints. Generally, without comprehensive knowledge of the mechanical performances of welded hollow spherical joints after fire exposure, the post-fire assessment on the behavior of the structures involving the use of these joints is unconvincing. Such results will lead to an uneconomical consequence or potential safety problem. This paper presents the details of the experimental and numerical studies on the post-fire behavior of the welded hollow spherical joints. Eight joint specimens were initially exposed to the ISO-834 standard fire [20] (including both heating and cooling phases) with three different highest fire temperatures of up to 1000 °C. The temperature distributions in the specimens were measured during the heating and cooling

100

30

30

Steel tube Hollow sphere

14 Á 0¡

400 100 30

End plate

660

0 ¦ µ4

Rib plate

109

(a) Details of the specimen (mm) Fig. 1. Test specimen.

(b) Specimen photograph

110

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

Fig. 2. Dimensions of tensile coupons (mm).

2.2. Material properties The structural steels used to manufacture the joint specimens are Q235 and Q345 hot-rolled steels, which are suggested by JGJ61-2003. The quality of the Q235 and Q345 steels utilized is in accordance with GB/T 700 [21] and GB/T 1591 [22], respectively. Tensile coupon tests were conducted on three Q345 and three Q235 standard coupons, which are produced from the same batch of steels used to manufacture the joint specimens, to determine the mechanical properties of the steels. The shapes and dimensions of the standard coupons accord with GB/T 228.1-2010 [23], as shown in Fig. 2. The dimensions of each coupon were measured with a vernier caliper at three points within the gauge length, and the average values of the measured dimensions were used to determine the mechanical properties of the steels. During the test process, the tensile load was applied at tensile stress rate of 10 MPa/s during the elastic stage and at a constant strain rate of 0.001/s during yielding. Thereafter, loading was applied at a constant displacement rate of 10 mm/min until failure occurred. These loading rates satisfied the requirements of GB/T 228-2010. The test results are listed in Table 2, where tc is the thickness of the steel coupon; Es is the elastic modulus; fy and fu refer to the yield strength and ultimate strength, respectively; δu is the fracture strain; and εy denotes the yield strain. The failure modes and obtained stress–strain relationships of the steel coupons are shown in Figs. 3 and 4, respectively. Both Q345 and Q235 steels showed obvious ductile failure modes with necking, whereas higher-grade Q345 steel exhibited higher yield strength, ultimate strength, and yield ratio than those of Q235 steel. 2.3. Test conditions and procedure The entire experimental process comprised two steps, i.e., fire exposure and structural testing. The unloaded joint specimens were heated in a furnace specially built for testing building structures in Tianjin Fire Research Institute, Tianjin, China [24], as shown in Fig. 5(a), which has a 4.0 m × 4.0 m floor area and a height of 2.5 m. A total of 12 gas burners were placed in the furnace chamber, each of which can be adjusted individually to generate a uniform temperature. The pressure in the furnace chamber was controlled automatically and was set according to the ISO-834 standard fire [20] and Chinese Standard GB/T 9978-2008 [25]. A total of 12 thermocouples were installed at various heights to measure furnace temperatures. The ambient temperature at

Table 2 Test results of Q345 and Q235 steel coupons.

Fig. 3. Failure modes of the tensile coupons.

the start of the tests was nearly 20 °C. The furnace temperature was increased following the ISO-834 standard temperature–time curve [20], including both heating and cooling phases. Three highest fire exposure temperatures, i.e., 600 °C, 800 °C, and 1000 °C, were considered, which correspond to the heating time of 5.9 min, 22.7 min, and 86.4 min, respectively, according to the ISO-834 standard fire curve. Type K chromel–alumel sheathed thermocouples with a diameter of 5.0 mm and a temperature data logger were used to measure the temperature distribution of each joint specimen during the process of heating and cooling. The thermocouples were anchored on the spherical surface using an innovative fixed device specially designed for this study. The locations of the thermocouples and the equipment used for the temperature measurement are shown in Fig. 6. Axial compressive loading was then applied to the specimens using a 10,000 kN hydraulic compression machine, as shown in Fig. 5(b). The top end of the machine was fixed, whereas the bottom end could move upward. The loading rate was set as 2 kN/s up to approximately 80% of the expected load-bearing capacity, which is obtained via finite element analysis before the test. Subsequently, the rate was controlled by a displacement rate of 2 mm/min. Four linear variable displacement transducers (LVDTs), eight strain gauges, and ten strain rosettes were used to record the axial displacement and the strain distributions of the specimen (the strain rosettes 9–12 and 17–18 are attached on the intersection of the steel tube and the hollow sphere, while strain rosettes 13–16 are attached along the sphere longitude and evenly spaced). The layouts of the instruments used for structural testing are shown in Fig. 7. 3. Experimental results and discussions

Coupon no.

tc (mm)

Es (GPa)

fy (MPa)

fu (MPa)

δu (%)

fy/fu

εy (με)

Q345-1 Q345-2 Q345-3 Average Q235-1 Q235-2 Q235-3 Average

14.24 14.02 14.20 14.15 14.04 14.19 14.01 14.08

209.6 208.7 208.5 208.9 206.2 204.2 202.5 204.3

447 457 459 454 342 341 347 343

560 566 555 560 469 464 473 469

40.2 41.2 40.6 40.7 40.8 40.6 41.8 41.1

0.8161 0.8074 0.8270 0.8168 0.7292 0.7349 0.7336 0.7326

2133 2190 2201 2175 1659 1670 1714 1681

3.1. Temperature–time curves The measured temperature–time curves of the furnace closely follow the ISO-834 standard temperature–time curve, as shown in Fig. 8. The temperatures of the specimens during the entire heating and cooling process are presented in Fig. 9. Nearly no difference was observed between the measured temperatures of J345 and J235 specimens exposed to the same highest furnace temperature. Thus, only the results

600

600

500

500

Stress (MPa)

Stress (MPa)

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

400 300 200

0 0.0

400 300 200

Q345-1 Q345-2 Q345-3

100

111

Q235-1 Q235-2 Q235-3

100 0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

Strain

0.3

0.4

0.5

Strain

(a) Q345 steel

(b) Q235 steel

Fig. 4. Stress–strain curves of the steels used in the experiment.

of J345 specimens were shown. The temperatures of the specimens clearly depended on the furnace temperature, which initially rose and then dropped. However, varying degrees of reduction in the maximum temperature value and delay of the temperature rise were shown. For

specimens exposed to 600 °C and 800 °C fire temperatures, the maximum temperatures of the specimen are 404 °C and 751 °C (with a reduction of 196 °C and 49 °C), achieved at 12 and 27 min (with a delay of 6.1 min and 4.3 min), respectively; whereas for specimens

(b) Compression machine

(a) Fire furnace Fig. 5. General view of the experimental setup.

(a)Location of the thermocouples

(b)Test setup

Fig. 6. Layouts of the instruments used for fire exposure.

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J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

L3 A

S1 S9

S2 (S4) S3 S11 S10 S13 S14 S15 S16

L4 S12

A

L1

L2

Cross section A-A S17 L1

S5

S18

S6 (S8)

S7

In plane LVDT L2

Out of plane LVDT Strain gauge

Axial load

significant increase of heating time, which allowed a complete heat transfer. Moreover, almost the same temperature–time curves were presented for different locations of the specimen, which indicated that the temperatures of the specimen are uniformly distributed during the heating and cooling stages. The temperature of the tube was not measured during the test because it is the core component of the joint. However, according to the obtained temperature distribution results of the sphere, it is not difficult to speculate that the temperature distribution of the tube is almost the same to that of the sphere and also uniformly distributed, which is attributed to the good heat conductivity of the steel.

Strain rosettes

Fig. 7. Layouts of the instruments used for structural tests.

exposed to 1000 °C fire temperatures, nearly no reduction in the maximum temperature value and delay of the temperature rise were presented. This phenomenon was attributed to the relatively short heating time of the 600 °C and 800 °C fire exposure, where the fire temperature cannot transfer to the specimens completely. While under 1000 °C fire exposure, the phenomenon diminished owing to the

3.2. Failure modes Based on the theoretical and experimental studies, Han et al. [9] concluded that the failure modes of welded hollow spherical joints under axial compression are an elastoplastic buckling collapse of the steel tube and the hollow sphere. In this study, axial compression tests were performed on the joint specimens after fire exposure thus the failure modes were obtained, as shown in Fig. 10. For comparison, the failure modes of the specimens without fire exposure were also included. Under axial compression load, both J345 and J235 specimens exhibited obvious buckling of the steel tube and local dent of the hollow sphere at the zone near the steel tube, on either one side or both sides of the specimens, regardless of how high the fire temperature they had been exposed to. Moreover, similar failure modes are presented for both the specimens with or without fire exposure, which all belong

Fig. 8. Comparisons of measured furnace temperature with the ISO-834 standard fire curve.

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

113

Fig. 9. Measured and predicted temperatures of the specimens.

to an elastoplastic buckling collapse proposed in Ref. [9]. Furthermore, all specimens exhibited fairly ductile behavior with considerable deformation before the final failure, regardless of the exposure temperatures, which is positive for the post-fire reuse of the joint. It is worth to be mentioned that obvious oxide films with colors of dark grey and light grey were observed on the surface of specimens after exposure to 800 °C and 1000 °C, respectively. Under relatively high load level, obvious surface flaking of the oxide film was presented. 3.3. Load–axial displacement relationships Four LVDTs were set at the load end to measure the vertical deformation, and the average value was adopted as the displacement of the joint specimen. The post-fire load–axial displacement responses of the specimens are illustrated in Fig. 11. In general, the initial behavior was linear elastic up to the yield load (approximately 0.8 times of the peak load), followed by a decreased stiffness to the peak load; after which, the load dropped gradually. However, the characteristics of the postfire load–axial displacement relationships differed considerably with respect to the highest exposure temperatures. For J345 specimens, the load–axial displacement curve of the specimen after exposure to fire temperature of 600 °C (J345-600) was almost the same to that of specimen without fire exposure (J345-20). However, when the exposure temperature increased to 800 °C (J345-800), the load–axial displacement curve obviously decreased, indicating a significant reduction in load-bearing capacity. Thereafter, when the exposure temperature continues increasing to 1000 °C (J345-1000), remarkable changes in

all load-bearing capacity, initial axial stiffness, and ductility occurred. By contrast, the load–axial displacement curves of J235 specimens showed similar change trends with respect to increasing exposure temperatures, whereas the load-bearing capacities were obviously lower than those of J345 specimens. 3.4. Initial axial stiffness The initial axial stiffness of the welded hollow spherical joint is defined as the initial ratio of the axial load to the vertical displacement at the intersection of the hollow sphere and the steel tube on one side [15]. The vertical displacement at the intersection of welded hollow spherical joint and steel tube was calculated as half of the difference between the total axial displacement measured by the LVDTs and the deformation of the steel tube. The steel tube deformation can be calculated as the product of the average longitude strain (measured by the strain gauges attached) and the length of the steel tube. The post-fire initial axial stiffness (KN, PT) obtained in this experiment are listed in Table 3 and plotted in Fig. 12(a). Stiffness residual factors are defined as the ratios of the initial axial stiffness after fire exposure (KN, PT) to that at ambient temperature without fire exposure (KN), which are also plotted in Fig. 12(b), to describe the deterioration in the mechanical performance of the welded hollow spherical joint after fire. The initial axial stiffness of both J345 and J235 specimens kept almost unchanged after exposure to fire temperatures until 800 °C. However, when the exposure temperature continued to grow, a significant decreasing trend of the initial axial stiffness was observed for both J345 and J235

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J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

Fig. 10. Failure modes of the test specimens.

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

115

Fig. 11. Post-fire load–axial displacement curves of test specimens.

specimens, which could be attributed to the considerable reduction in elastic modulus of structural steels after exposure to elevated temperatures exceeding 800 °C [26]. Furthermore, the variations of J345 specimens were very similar to those of J235 specimens. Almost equal reductions of 13.1% and 11.6% in the initial axial stiffness were observed for J345 and J235 specimens, respectively, after exposure to fire temperature of 1000 °C, which indicates the variations of initial axial stiffness due to fire exposure were not affected by the steel grade of the welded hollow spherical joints.

in Fig. 14(a) and (b), respectively. Yield load and load-bearing capacity residual factors are defined as the ratios of the yield load and loadbearing capacity after fire exposure (Ny,PT, Np,PT) to that at ambient temperature without fire exposure (Ny, Np), respectively, which are plotted in Fig. 15(a) and (b), respectively. The yield loads and load-bearing capacities of the specimens were almost unaffected after exposure to temperature of 600 °C. Thereafter, significant decreases of both the yield loads and load-bearing capacities were observed with increasing exposure temperatures, whereas the decreasing rate of yield load was higher than that of load-bearing capacity. Considering the J345

3.5. Yield load and load-bearing capacity The determination of the yield load and load-bearing capacity (peak load) of the specimens is shown in Fig. 13. “The furthest point method” proposed by Feng et al. [27] was employed to determine the yield point. The post-fire yield loads (Ny, PT) and the load-bearing capacities (Np,PT) obtained in this experiment are listed in Table 3 and are also plotted

Table 3 Summary of the experimental results of the test specimens. Steel grade

Specimen no.

KN,PT (kN/mm)

Ny,PT (kN)

Δy,PT (mm)

Nu, PT (kN)

Δu,PT (mm)

μΔ, PT

Q345

J345-20 J345-600 J345-800 J345-1000 J235-20 J235-600 J235-800 J235-1000

2240 2208 2195 1947 2238 2225 2220 1978

1348 1349 1146 947 1047 1043 954 772

3.13 2.94 2.92 2.87 2.56 2.46 2.45 2.42

1600 1587 1411 1231 1288 1295 1175 998

28.9 27.7 28.1 32.8 33.3 33.1 34.4 36.6

9.23 9.42 9.63 11.42 13.00 13.45 14.04 15.12

2800

Fig. 13. Determination of the key characteristics of test specimens.

1.1

J345 J235

2400

0.994

1.0

0.986

2000

Residual factor

Intitial axial stiffness (kN/mm)

Q235

1600 1200

0

0.884 0.869

0.8 0.7

J345 J235

0.6 0.5 20 °C

600 °C

800 °C

Exposure temperature (°C)

(a) Initial axial stiffness

1000 °C

0.980

0.9

800 400

0.992

0

200

400

600

800

Exposure temperature (°C)

(b) Residual factors

Fig. 12. Post-fire initial axial stiffness and corresponding residual factors.

1000

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J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

(b) Load-bearing capacity

(a) Yield load

Fig. 14. Post-fire yield load and load-bearing capacity of the test specimens.

Fig. 15. Post-fire yield load and load-bearing capacity residual factors.

specimens for example, reductions of 14.9% and 29.7% in yield load were observed after exposure to temperatures of 800 °C and 1000 °C, respectively; while for load-bearing capacities, the corresponding reductions were 8.8% and 22.5%. In addition, similar decreasing trends of both yield load and load-bearing capacity were presented for J345 and J235 specimens. 3.6. Ductility level Ductility index (μΔ) is an indicator reflecting the deformation capacity of the structures or structural members, which is defined as the ratio

of the ultimate deformation to the yield deformation, as shown in Eq. (1) [28]: μΔ ¼

Δu ; Δy

ð1Þ

where Δu refers to the displacement at the point beyond which strength degradation is no longer tolerable (herein 85% of the maximum resistance was selected), and Δy refers to the displacement at the yield load. Similarly, in this study, the post-fire ductility index (μΔ, PT) of the joint specimen is defined as the ratio of the ultimate deformation

Fig. 16. Post-fire ductility index and corresponding residual factors.

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

(Δu, PT) to the yield deformation (Δy, PT) of the specimens, which have been exposed to fire. The experimentally obtained Δu, PT, Δy, PT and the calculated μΔ,PT are listed in Table 3. Post-fire ductility residual factors are defined as the ratios of the ductility index after fire exposure (μΔ,PT) to that at ambient temperature without fire exposure (μΔ). The post-fire ductility indexes (μΔ,PT) and the corresponding residual factors are also plotted in Fig. 16(a) and (b), respectively. The ductility level of the joint specimens showed a gradually increasing trend after exposure to temperatures exceeding 600 °C, which indicates that welded hollow spherical joints may not lose much ductility after fire exposure. Moreover, similar increasing trends of ductility were presented for J345 and J235 specimens. 3.7. Strain analysis In order to analyze the development of strains in the specimens during the loading process, four strain gauges were bonded to each steel tube to measure its longitudinal strains, whereas 10 strain rosettes were bonded to measure the strains of the hollow sphere (Fig. 7). The strain rosettes consisted of strain gauges at angles of 0°, 45°, and 90°. The 0° and 90° strain gauges were placed in the latitudinal and longitudinal direction of the sphere, respectively. The latitudinal strains, longitudinal strains, and shear strains can be calculated by the following equations [28]: 8 < εx ¼ ε0 εy ¼ ε90 : γ ¼ 2ε −ε −ε 45 0 90 xy

;

ð2Þ

where εx and εy refer to the latitudinal strain and longitudinal strain of the welded hollow spherical joint, respectively; γxy is the shear strain; and ε45 is the strain obtained from the 45° strain gauge. Since the thickness of hollow sphere is significantly lower than that of the diameter of the sphere, the stress along the sphere thickness is not the control stress

117

compared with the in-plane stress. Thus, the equivalent in-plane strain εe, which was adopted in this study to describe the strain intensity of the hollow sphere, can be calculated from the following equation [29]:

εe ¼

pffiffiffirffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 2  ε x −ε y þ εx 2 þ εy 2 þ γxy 2 2 3

ð3Þ

Fig. 17 shows the typical axial load–strain relationships at different locations of the joint specimens after exposure to various fire temperatures, of which the longitudinal strains of the steel tube (location 1) and the equivalent strains of the hollow sphere (locations 2, 3, 4, 5, and 6) calculated by Eq. (3) were adopted. For comparison, the results of the specimen without exposure to fire were also included. Since the strain development of J235 specimens showed similar trends to those of J345 specimens, only the analysis results of J345 were presented. The yield strains of the steel after exposure to various temperatures were calculated based on the experimental results reported by Lu et al. [26]. Generally, the strain development is closely related to the locations of the specimen and the highest exposure temperature. The highest strain levels under a certain axial load were observed on the regions of steel tube (location 1) and the connection part of steel tube and hollow sphere (location 2), which was in accordance with the failure modes shown in Fig. 10. Along the longitudinal direction of the hollow sphere, i.e., from location 2 to 6, the strain value showed a significant decreasing trend. Furthermore, the strains of the specimen developed obviously faster with increasing exposure temperatures, which lead to the earlier yielding of the specimens. For the specimens without fire exposure (J345-20) and after exposure to temperature of 600 °C (J345-600), only the steel tube (location 1) and the connection region of the steel tube and the hollow sphere (location 2) entered the yielding stage under the peak load, whereas other regions were still elastic. With the growth of the exposure temperatures, however, the yielding zone

Fig. 17. Axial load–strain curves of J345 specimens after fire exposure.

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J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

significantly increased. For specimens J345-800 and J345-1000, all the steel tubes and the sphere regions near locations 2, 3, and 4 entered the yielding stage under the peak load. This observation can be explained by the significant reduction in both the stiffness and strengths of the steel after exposure to elevated temperatures. The values and directions of the principal strains of the hollow sphere can be calculated by the following equations [28]: εx þ εy ε1  ¼ ε2 2

tg2θp ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε −ε 2 γ 2 x y xy þ 2 2

γxy εx −ε y

4.1. Material properties For the heat transfer analysis, the high-temperature thermal property models of structural steels specified in EC3 [31] including the density, heat conduction, and specific heat were employed. For subsequent nonlinear stress analysis, a stress–strain model of structural steels after exposure to elevated temperatures, which was proposed by Tao et al. [32], was adopted for the post-fire stress analysis of the welded hollow spherical joint. The stress–strain model is as follows:

ð4Þ

ð5Þ

where ε1 is the first principal strain, ε2 is the second principal strain, and θp is the angle between the direction of the first principal strain and the latitudinal direction of the sphere. The calculated values of θp at different locations of the specimen varied irregularly with increasing axial load and exposure temperature, but ranged from 0° to 15°, which indicates that the direction of the first principal strain ε1 was almost along the latitudinal line of the hollow sphere. Thus, the direction of the second principal strain ε2 was almost along the longitude line. In addition, the first principal strains ε1 of the specimen were positive, whereas the second principal strains ε2 were negative, indicating that the latitudinal direction of the hollow sphere was generally under tension while the longitudinal direction were under compression. 4. Finite element analysis A 3D finite element model was established using the ABAQUS software to investigate both the thermal and structural behavior of the welded hollow spherical joint after fire exposure, as shown in Fig. 18. A transient heat transfer analysis was first performed to study the temperature distributions of the joint during the exposure to the ISO-834 standard fire (including both the heating and cooling phases), and subsequently the temperature distribution results were imported into the nonlinear stress analysis as a predefined field [30].

σ¼

8 EsT ε > > > > < f yT

   ε −ε p uT > f uT − f uT −f yT  > > −ε pT ε > uT : f uT

0≤ε b εyT εyT ≤ ε b ε pT εpT ≤ ε b ε uT

ð6Þ

ε Nε uT

where EsT, fyT, and fuT refer to the post-fire residual elastic modulus, residual yield strength, and residual ultimate strength, respectively; εyT is the yield strain, εyT =fyT/EsT; εpT is the strain at the onset of strain hardening; εuT is the ultimate strain corresponding to the residual ultimate strength; and p is the strain-hardening exponent, which can be determined by

p ¼ EpT 

εuT −ε uT f uT −f yT

! ð7Þ

where EpT is the residual initial elastic modulus at the onset of strain hardening. As shown, six parameters (EsT, fyT, fuT, εpT, εuT, and EpT) are required to define the full-range stress–strain relationship after exposure to a certain highest temperature T. Previous studies [26,32–36] indicate that the post-fire mechanical properties of structural steels depend primarily on the maximum temperature attained during the heating and cooling phases. Thus, EsT, fyT, and fuT can be determined by introducing the post-fire residual factors to the mechanical properties of the steel without fire exposure. In this study, the residual factors specially proposed for Q235 and Q345 steels [26] based on the experimental data were adopted. The post-fire elastic modulus residual factors of both Q235 and Q345 steels were taken as EsT ¼ Es



1:0 2:148−2:15  10−3 T þ 9:02  10−7 T 2

20 ° C ≤ T ≤ 800 ° C 800 ° C b T ≤1000 ° C ð8Þ

The post-fire yield strength residual factors of both Q235 and Q345 steels were taken as f yT ¼ fy



1:0 1:6−8:88  10−4 T

20 ° C ≤T ≤700 ° C 700 ° C b T ≤1000 ° C

ð9Þ

The post-fire ultimate strength residual factors of both Q235 and Q345 steels were taken as f uT ¼ 0:999 þ 1:59  10−4 T−2:89  10−7 T 2 20 ° C≤T ≤1000 ° C fu

ð10Þ

where Es, fy, and fu are the elastic modulus, yield strength, and ultimate strength, respectively, of the structural steel at ambient temperature, and T is the highest temperature that the steels have been exposed to. As for other parameters, εpT, εuT, and EpT can be calculated by following equations as suggested in Ref. [32]: ( εpT ¼ Fig. 18. Finite element model of the welded hollow spherical joint.

15ε yT h  i 15−0:018 f y −300 εyT

f y ≤300 MPa 300 b f y ≤ 800 MPa

ð11Þ

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

( εuT ¼

100εyT h  i 100−0:15 f y −300 εyT

f y ≤300 MPa 300 b f y ≤ 800 MPa

EpT ¼ 0:02EsT

ð12Þ

5. Parametric studies and design method 5.1. Load-bearing capacity

ð13Þ

The Poisson's ratio was assumed to be 0.3 for both the steels with or without fire exposure. 4.2. Heat transfer analysis The thermal response of the welded hollow spherical joint under fire exposure is a transient heat transfer process. The heat is transmitted from the fire to the outer surface of the steel tube and the hollow sphere by convection and radiation, which is then transferred within the joint by conduction. In this study, the convective heat transfer coefficient and resultant emissivity were taken as 25 W/(m2·K) and 0.5 [37], respectively. The ambient temperature was set as 20 °C, and the ISO-834 standard fire condition [20], including both heating and cooling phases, was applied as a thermal load. The three-dimensional eight-noded continuum solid element (DC3D8) was used to establish the model. 4.3. Stress analysis The lowest buckling mode obtained by eigenvalue buckling analysis was introduced into FE model as the shape of the initial geometrical imperfection. Subsequently, nonlinear elastoplastic analysis was performed to investigate the post-fire mechanical behavior of welded hollow spherical joint. As discussed above, the post-fire properties of the steels depend on the maximum temperatures reached during the heating and cooling phases. Due to the excellent thermal conductivity of the steel, the maximum temperature of the entire joint was achieved at almost the same time. Thus, the maximum nodal temperatures can be easily extracted from the results of the heat transfer analysis and imported into the stress analysis model as a predefined field. The finite element meshes of the stress analysis were the same as those of the corresponding heat transfer analysis to read the nodal temperatures efficiently. The three-dimensional eight-noded solid element with reduced integration (C3D8R) was used to mesh the joint. The grids were densified in the region near the intersection of steel tube and hollow sphere, where the stress level is high. A total of 30,248 elements were meshed for the entire model. 4.4. Validation of the FE model Both the heat transfer analysis and stress analysis models were validated by comparing their results with the experimental results of welded hollow spherical joint obtained in this study. The comparisons of the temperature–time curves, strain development, typical failure modes, and load–axial displacement curves are presented in Figs. 9, 17, 19, and 20, respectively, which show good agreement between the predictions of the finite element analysis and the experimental results.

(a) FEA of J235-20

119

According to extensive theoretical and experimental studies [7–10], the load-bearing capacity of the welded hollow spherical joint is closely related to the thickness of the hollow sphere t, external diameter of the steel tube d, the external diameter ratio of the steel tube to the hollow sphere d/D, and the yield strength of the steel fy. Furthermore, a practical formula is given in JGJ61-2003 [18] to calculate both compressive and tensile load-bearing capacity of the welded hollow spherical joint without fire exposure, which is as follows: Nu ¼

  d 0:32 þ 0:6 η πtdf y D d

ð14Þ

where Nu is the load-bearing capacity (for both compression and tension) of the welded hollow spherical joint under the axial load (N), D is the external diameter of the hollow sphere (mm), t is the thickness of the hollow sphere (mm), d is the external diameter of the steel tube (mm), fy is the yield strength of the steels (N/mm2), and ηd is the enhancing coefficient which is equal to 1.4 when the joint has a stiffener or equal to 1.0 when the stiffener doesn't exist. For practical use, a design method maintaining consistency with the above formula widely used was proposed to calculate the residual loadbearing capacities of the welded hollow spherical joint after exposure to the ISO-834 standard fire by introducing a post-fire residual loadbearing capacity factor ηPT into Eq. (14), which is as follows: Nu;PT ¼ ηPT Nu

ð15Þ

where Nu,PT is the residual load-bearing capacities of the welded hollow spherical joint under axial load after fire exposure (N), and Nu is the axial load-bearing capacity of the welded hollow spherical joint at ambient temperature without fire exposure (N), which can be calculated by Eq. (14). Parametric studies were undertaken to extend the ranges of the key parameters to investigate their influence on ηT. The considered parameters include the highest exposure temperature Th (corresponding to the heating time th based on the ISO-834 standard temperature–time curves), external diameter ratio of the steel tube to hollow sphere d/D, thickness of the hollow sphere t, external diameter of the steel tube d, and the yield strength of the steel fy. The values of these parameters are listed in Table 4, where the dimension parameters are all in the ranges suggested by JGJ61-2003. The influences of these key parameters on ηPT are shown in Fig. 21. The post-fire residual load-bearing capacity factor ηPT can be seen to decrease significantly when the highest exposure temperature exceeded 700 °C owing to the deterioration of material properties at elevated temperatures, whereas the influences of the dimension parameters such as d/D, t, and d, which significantly affect the load-bearing capacity of the welded hollow spherical joint, are insignificant compared with the effects of

(b) Experimental results of J235-20

Fig. 19. Comparisons of the typical failure mode predicted by FEA with the experimental results.

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Fig. 20. Comparisons of the load–axial displacement curves predicted by FEA with the experimental results.

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

121

exposure temperature Th, is proposed for the post-fire residual loadbearing capacity factor ηPT:

Table 4 Values of studied parameters. Parameter

Values

Fixed value

Th (°C) d/D t (mm) d (mm) fy (N/mm2)

20, 600, 700, 800, 900, 1000 0.33, 0.35, 0.37, 0.39, 0.41 10, 12, 14, 16, 18 108, 140, 180, 219 343 (Q235 in this study), 454 (Q345 in this study)

– 0.35 14 140 454

exposure temperature thus they can be ignored. Furthermore, ηPT was almost unchanged for both the Q235 steel and Q345 steel, indicating that the influences of the yield strength on ηPT can also be neglected for these commonly used structural steels. Thus, a piecewise formula for practical use, which is developed as a function of the highest

ηPT ¼

1 20 ° CbT h ≤700 ° C 14:071−4:5010−2 T h þ 5:1410−5 T h 2 −1:9710−8 T h 3 700 ° CbT h ≤1000 ° C

ð16Þ where Th can be also expressed in the form of heating time th based on the ISO-834 standard temperature–time curve. After having known ηPT, Eq. (15) can be used to predict the residual load-bearing capacities of the welded hollow spherical joint after fire exposure. Comparisons of the predicted residual load-bearing capacity using the design method presented in Eq. (15) with both the FEA results and the experimental results obtained in this study are listed in

Fig. 21. Influences of the key parameters on the post-fire residual load-bearing capacity factor ηPT.

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Fig. 22. Comparisons of the predicted load-bearing capacity with the results of the FEA and experiments.

Fig. 22, and a good agreement is observed, which confirms the validity of the design method. 5.2. Initial axial stiffness Wang et al. [15,16] and Zhang et al. [17] revealed that the initial axial stiffness of the welded hollow spherical joint without fire exposure mainly depends on the external diameter ratio of the steel tube to hollow sphere d/D and the thickness of the hollow sphere t via the method of FEA. Based on the theoretical analysis, Han et al. [11] developed a practical formula to calculate the initial axial stiffness of the welded hollow spherical joint without fire exposure, which are given as follows:   td t3 d K N ¼ 2πE 0:34 þ 66:8 3 D D

ð17Þ

where KN is the initial axial stiffness of the welded hollow spherical joint (kN/mm), E is the elastic modulus of the steel, and the nomenclatures of D, t, and d are the same to those of Eq. (14). Similar to load-bearing capacity, a post-fire residual stiffness factor κPT is introduced into Eq. (17) to evaluate the initial axial stiffness of the welded hollow spherical joint after exposure to the ISO-834 standard fire: K N;PT ¼ κ PT K N

ð18Þ

where KN, PT is the residual initial axial stiffness of the welded hollow spherical joint after fire exposure (kN/mm), and KN is the initial axial stiffness of the welded hollow spherical joint at ambient temperature without fire exposure (kN/mm), which can be determined by Eq. (17). Parametric studies were conducted to investigate the influences of key parameters on κPT. The considered parameters include the highest exposure temperatures Th, the external diameter ratio of the steel tube to the hollow sphere d/D, and the thickness of hollow sphere t. The values of these parameters are listed in Table 5. Similarly, the dimension parameters are all in accordance with the ranges suggested by JGJ61-2003. The influences of the studied parameters on κPT are shown in Fig. 23. The results show that the post-fire residual stiffness factor κPT remained

Table 5 Values of studied parameters. Parameter

Values

Fixed value

Th (°C) d/D t (mm)

20, 600, 700, 800, 900, 1000 0.33, 0.35, 0.37, 0.39, 0.41 10, 12, 14, 16, 18

– 0.35 14

unchanged after exposure to temperatures up to 800 °C, whereas a linear decreasing trend was observed thereafter owing to the deterioration of the elastic modulus of the steel after exposure to elevated temperatures. However, the effects of dimension parameters d/D and t on κPT are insignificant. Thus, a practical piecewise formula, which is also developed as a function of the highest exposure temperature Th, is proposed for the calculation of κPT: κ PT ¼

1 1:518−6:50  10−4 T h

20 ° C b T h ≤800 ° C 800 ° C b T h ≤1000 ° C

ð19Þ

where Th can be also expressed in the form of heating time th according to the correspondence between them based on the ISO-834 standard temperature–time curve. After having known κPT, Eq. (18) can be used to calculate the residual initial axial stiffness of the welded hollow spherical joint after fire exposure. The predicted residual initial axial stiffness using the design method presented in Eq. (18) are compared with the results of both the FEA and experiments obtained in this study, as shown in Fig. 24. Again, a good agreement was presented. In practical application of post-fire estimation, engineers can obtain the spatial temperature field of the structure which is subjected to fire exposure via numerical simulation [38], or they can speculate the fire temperature by observing the remains of the fire site and measuring the residual strength of the steel material [39]. Subsequently, the engineers can apply the residual factors ηPT and κPT proposed in this paper to assess the post-fire load-bearing capacity and initial axial stiffness of the welded hollow spherical joints. 6. Conclusion This paper presented the experimental and numerical studies on the post-fire behavior of welded hollow spherical joints, which are extensively used as key connections in space lattice structures. Eight joint specimens were initially exposed to the ISO-834 standard fire (including both heating and cooling phases) with three different highest fire temperatures of up to 1000 °C, and the temperature distributions in the specimens were measured during the heating and cooling process. Axial compressive tests were subsequently performed on the specimens at ambient temperature to investigate their post-fire fundamental behavior. Related mechanical behavior, such as load–axial displacement curves, initial axial stiffness, yield loads, load-bearing capacities, ductility level, and strain distributions, were obtained. Sequentially coupled thermal-stress finite element analysis including both heat transfer and stress analysis, were developed using the ABAQUS software. On the basis of parametric studies, a design method for predicting the residual load-bearing capacity and initial axial stiffness of welded hollow spherical

J. Lu et al. / Journal of Constructional Steel Research 140 (2018) 108–124

123

Fig. 23. Influences of the key parameters on the post-fire residual stiffness factor κPT.

joints after fire exposure was proposed. The following conclusions can be drawn based on these studies: (1) The temperatures of the specimen clearly depend on the furnace temperature. However, when the exposure temperature was relatively low, varying degrees of reduction in the maximum temperature value and delay of the temperature rise were observed owing to the short heating time, which limited the heat transfer between the fire and the specimen. This phenomenon diminished with increasing heating time. Moreover, the temperatures of the specimen are uniformly distributed during the heating and cooling stages.

(2) The failure modes of welded hollow spherical joints under axial compression were all elastoplastic buckling collapses of the steel tube and the hollow sphere, regardless of whether or not the joints had been exposed to fire. Moreover, all specimens exhibited fairly ductile behavior with considerable deformation before the final failure, which is positive for the post-fire reuse of the joint. (3) Generally, all the initial axial stiffness, yield load, and loadbearing capacity of the welded hollow spherical joint decreased with increasing exposure fire temperatures owing to the deterioration of material properties at elevated temperatures, whereas the reduction of yield load and load-bearing capacity occurred

Fig. 24. Comparisons of the predicted initial axial stiffness with the results of the FEA and experiments.

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earlier (at temperatures exceeding 600 °C) than that of initial axial stiffness (at temperatures exceeding 800 °C). Furthermore, the ductility level of the joints showed a gradually increasing trend after fire exposure. (4) The strain development was closely related to the locations of the specimen and the highest exposure temperature. Under a certain axial load, the highest strain levels were observed on the regions of the steel tube and the connection part of the steel tube and hollow sphere. Furthermore, the strains of the specimen developed obviously faster with increasing exposure temperatures, which lead to the earlier yielding of the specimen. (5) A design method for predicting the residual load-bearing capacity and initial axial stiffness of welded hollow spherical joints after standard fire exposure was proposed by introducing the residual factors ηPT and κPT. The application of the method can be used in the assessment of the post-fire residual performance of space lattice structures involving the use of welded hollow spherical joints. Acknowledgments This study was financially supported by the National Natural Science Foundation of China (Grant No. 51678404). The authors also appreciate the financial support provided by the Chinese Scholarship Council (File No. 201706250068), which enabled the authors to collaborate with Prof. Huiming Yin at Columbia University. References [1] T. See, R.E. Mcconnel, Large displacement elastic buckling of space structures, J. Struct. Eng. 112 (5) (1986) 1052–1069. [2] F.A. Fathelbab, The Effect of Joints on the Stability of Shallow Single Layer Lattice DomesPh.D. Thesis University of Cambridge, 1987. [3] S. Xu, Z. Chen, X. Wang, et al., Hysteretic out-of-plane behavior of the Temcor joint, ThinWalled Struct. 94 (2015) 585–592. [4] H.H. Ma, F. Fan, S.Z. Shen, Numerical parametric investigation of single-layer latticed domes with semi-rigid joints, J. Int. Assoc. Shell Spat. Struct. 49 (158) (2008) 99–110. [5] F. Fan, H. Ma, G. Chen, et al., Experimental study of semi-rigid joint systems subjected to bending with and without axial force, J. Constr. Steel Res. 68 (1) (2012) 126–137. [6] X.L. Liu, Design and Construction of Plate Grid Structures, Press of Tianjin University, Tianjin, China, 2000 (In Chinese). [7] Z.H. Chen, Analysis of Collapse Mechanism and Experiment Study on Load Capacity of Welded Hollow Sphere Joint in Space GridsMaster Thesis Tianjin University, 1990 (In Chinese). [8] X.J. Zhou, Analysis of Collapse Mechanism of Super Large Welded Hollow Spherical Joint in Space Trusses and Experimental Research of Its Bearing CapacityMaster Thesis Tianjin University, 1996 (In Chinese). [9] Q.H. Han, X.L. Liu, Ultimate bearing capacity of the welded hollow spherical joints in spatial reticulated structures, Eng. Struct. 26 (1) (2004) 73–82. [10] Q.H. Han, Q.Z. Zhou, Y. Chen, Ultimate bearing capacity of hollow spherical joints welded with circular pipes under eccentric loads, Trans. Tianjin Univ. 13 (1) (2007) 28–34.

[11] Q. Han, Y. Liu, Y. Xu, Stiffness characteristics of joints and influence on the stability of single-layer latticed domes, Thin-Walled Struct. 107 (2016) 514–525. [12] S.L. Dong, H.J. Tang, Y. Zhao, Load-carrying capacity and practical calculation method for welded hollow spherical joints subject to combined axial force and bending moment, Chin. Civil Eng. J. 38 (1) (2005) 21–30 (In Chinese). [13] H.J. Tang, Load-carrying Capacity and Practical Calculation Method of Welded Hollow Spherical Joints Subjected to Combined Axial Force and Bending MomentMaster Thesis Zhejiang University, 2005 (In Chinese). [14] H.Y. Wan, Finite element analysis of axial flexibility and flexural stiffness of welded hollow spherical joints of space trusses structure, J. Anhui Inst. Archit. 6 (4) (1998) 31–34 (In Chinese). [15] X. Wang, S.L. Dong, H.Y. Wan, Finite element analysis of the welded hollow spherical joints' stiffness, J. Zhejiang Univ. (Eng. Sci.) 34 (1) (2000) 77–82 (In Chinese). [16] F. Wang, X. Wang, Study on the stiffness of welded hollow spherical joints with rib stiffeners, Spat. Struct. 19 (1) (2013) 91–96. [17] J. Liao, Y.G. Zhang, The study of bilinear model for loading-deformation curve of welded hollow spherical joints, Spat. Struct. 16 (1) (2010) 31–38 (In Chinese). [18] JGJ 61-2003, Technical Specification for Latticed Shells, Ministry of Construction of the People's Republic of China, Beijing, 2003 (In Chinese). [19] JGJ 7-2010, Technical Specification for Frame Structures, Ministry of Construction of the People's Republic of China, Beijing, 2010 (In Chinese). [20] ISO-834, Fire Resistance Tests—Elements of Building Construction, International Organization for Standardization, Switzerland, 1975. [21] GB/T 700-2006, Carbon Structural Steels, Standards Press of China, Beijing, 2006 (In Chinese). [22] GB/T 1591-2008, High Strength Low Alloy Structural Steels, Standards Press of China, Beijing, 2008 (In Chinese). [23] GB/T 228-2010, Metallic material-tensile testing, Part 1: Method of Test at Room Temperature, Standards Press of China, Beijing, 2010 (In Chinese). [24] Q.F. Han, T.T. Lie, H.J. Wu, Column fire resistance test facility at the Tianjin fire research institute, NRC-CNRC Internal Report, No. 648. Ottawa, Canada, 1993. [25] GB/T 9978-2008, Test Standard for Fire Resistance of Construction Members, Standard Press of China, Beijing, 2008 (In Chinese). [26] J. Lu, H. Liu, Z. Chen, et al., Experimental investigation into the post-fire mechanical properties of hot-rolled and cold-formed steels, J. Constr. Steel Res. 121 (2016) 291–310. [27] P. Feng, H. Qiang, L. Ye, Discussion and definition on yield points of materials, members and structures, J. Eng. Mech. 34 (3) (2017) 36–46 (In Chinese). [28] Z.X. Li, Theory and Technique of Engineering Structure Experiments, Tianjin University Press, Tianjin, 2004 (In Chinese). [29] H.F. Chen, A.F. Salipu, Elasticity and Plasticity, China Architecture & Building Press, Beijing, 2005 (In Chinese). [30] SIMULIA, ABAQUS/Standard Version 6.9 Analysis User's Manual, Hibbit, Karlsson & Sorenson, Inc, Pawtucket, Rhode Island, 2009. [31] Eurocode 3, Design of steel structures, Part 1–2: General Rules-structural Fire Design, CEN, 2005. [32] Z. Tao, X.Q. Wang, B. Uy, Stress-strain curves of structural and reinforcing steels after exposure to elevated temperatures, J. Mater. Civ. Eng. 25 (9) (2012) 1306–1316. [33] J. Outinen, Mechanical Properties of Structural Steels at High Temperatures and After Cooling DownPh.D. Thesis Helsinki University of Technology, Helsinki, Finland, 2007. [34] X. Qiang, F.S.K. Bijlaard, H. Kolstein, Post-fire mechanical properties of high strength structural steels S460 and S690, Eng. Struct. 35 (2012) 1–10. [35] X. Qiang, F.S.K. Bijlaard, H. Kolstein, Post-fire performance of very high strength steel S960, J. Constr. Steel Res. 80 (2013) 235–242. [36] S. Gunalan, M. Mahendran, Experimental investigation of post-fire mechanical properties of cold-formed steels, Thin-Walled Struct. 84 (2014) 241–254. [37] F. Liu, L. Gardner, H. Yang, Post-fire behaviour of reinforced concrete stub columns confined by circular steel tubes, J. Constr. Steel Res. 102 (11) (2014) 82–103. [38] Y. Yin, T. Yuan, Z. Chen, et al., Numerical study on the behaviour of a lattice shell structure under fire and damage estimation, Chin. Civil Eng. J. 43 (8) (2010) 51–56 (In Chinese). [39] J. Chen, P. Cao, T. Zhou, et al., Estimation methods of fire temperature for steel structure, Build. Sci. 29 (9) (2010) 67–70 (In Chinese).