- Email: [email protected]
Calculation method for the residual stability bearing capacity under axial compression of steel tube members exposed to a high temperature
Thin-Walled Structures 132 (2018) 475–493
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Full length article
Calculation method for the residual stability bearing capacity under axial compression of steel tube members exposed to a high temperature
T
⁎
Rui Mab, Hongbo Liua,b, , Zhihua Chena,b a b
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Department of Civil Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Elevated temperature Steel tube Stability bearing capacity Experiment Numerical analysis
Fire accidents occur occasionally when grid structures are extensively applied, although many grid structures do not suffer general failure after fire disasters and can be used again after reasonable evaluation and reinforcement. To reasonably evaluate the residual load bearing capacity of grid structures, this paper investigated stability bearing capacity of steel tube members in grid structures after fire disasters through axial compression experiment and numerical simulation. Axial compression experiments performed on 32 steel tubes after exposure to the ISO-834 standard fire, and three highest fire temperatures were considered, including 600 °C， 800 °C and 1000 °C. The temperature distributions in the specimens during the heating and related mechanical properties such as load-displacement curves, ultimate loads and strain distributions of the specimens, were obtained and analyzed. Finite element analysis was also conducted by using ABAQUS software. Then, the main factors influencing the residual stability bearing capacities of the steel tube members exposed to high temperatures were obtained through a lot of numerical analysis. Based on the results of experiments and numerical analysis, the formula for the computation of the residual stability bearing capacities of the steel tube members after fire disasters was presented. And calculated results using the formulas accorded well with experimental results.
1. Introduction Owing to their superior load-bearing properties and high-efficiency assembling, grid structures have been extensively applied in various fields of civil engineering, as a kind of grid structure shown in Fig. 1. Building fire significantly threatens the safety of human life and national property. In most fire accidents, significant local damage is frequently observed in spatial grid structures after a fire. However, general structural collapse accidents are uncommon because of certain fireproof protection, high indeterminate degrees, and collaborative spatial load bearing of members, as shown in Fig. 2. After damage detection, restoration, and reinforcement, most grid structures can be used again for fire damage reduction. Therefore, studying the evaluation method of residual mechanical properties of grid structures after a fire disaster and proposing reasonable suggestions about demolition, reconstruction, restoration, and reinforcement are of great theoretical significance and have great engineering application values. Currently, the residual mechanical properties of materials constituting grid structures exposed to high temperatures have been extensively studied, such as ordinary steel [1–10], high-strength
⁎
steel [11–20] and stainless steel [21,22]. However, studies on the members, joints, and overall structures of these structures are lacking. Some researchers [23–26] studied the overall stability performance of axial compressed steel columns exposed to high temperatures. They analyzed the influences of fire temperature and cooling mode and then provided a simplified computing method for residual stability bearing capacity. Furthermore, considering the combined effects of explosion and fire, Ding Y. et al. [27,28] found that fire duration was the main factor influencing the residual stability bearing capacity of a steel column. Then proposed a damage evaluation method. Meanwhile, Lu J. et al. [29,30] explored the influence of different cooling modes on the basic study of the mechanical properties of welded hollow sphere joints at ambient by Han Q.H. and Liu X.L. [31] and at high temperatures by Qlu L.B. et al. [32]. Their study indicated that residual bearing capacities of welded hollow sphere joints after spray cooling was higher than those observed after natural cooling. Some scholars studied the mechanical properties of overall grid structures after a fire disaster. For instance, Wang X. et al. [33] and Wang G. et al. [34] analyzed and computed the post-fire displacement and internal force distribution laws of steel grid structures. Cui J. et al. [35] proposed a quasi-
Corresponding author. E-mail address: [email protected] (H. Liu).
https://doi.org/10.1016/j.tws.2018.09.011 Received 9 April 2018; Received in revised form 25 June 2018; Accepted 3 September 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Nomenclature
T Δ δ L0 A D/t λ φ φT α
Es fy fy, T fu ηEs η fy η fu NcrE NcrS NcrF Ncr, T
fire temperature residual deformation value residual deformation coefficient computed specimen length member section sectional diameter-thickness ratio slenderness ratio stability coefficient post-fire stability coefficient stability reduction coefficient
elasticity modulus yield strength post-fire yield strength tensile strength post-fire reduction coefficients of elasticity modulus post-fire reduction coefficients of yield strength post-fire reduction coefficients of tensile strength experimental stability bearing capacity FEM result of stability bearing capacity formula result of stability bearing capacity Post-fire stability bearing capacity
sandwich panel method for a simplified computation of the post-fire midspan displacement of grid structures. Yin Y. et al. [36] and Liu Z. et al. [37] presented post-fire structural reinforcement schemes for specific engineering projects. However, present studies on the post-fire residual bearing capacities of circular steel tube members commonly used by grid structures are limited. In this paper, residual stability bearing capacities of such members were studied through experiment and numerical analysis. A calculation method of the residual stability bearing capacity of steel tube members after exposure to high temperature was proposed. Results provided a scientific basis for the evaluation of post-fire residual load bearing capacities of grid structures. 2. Experiment investigation 2.1. Specimen design
Fig. 2. Post-fire grid structure.
Eight groups of specimens were selected, each of which consisted of two commonly used steel materials (Q235B and Q345B), three slenderness ratios (60, 80, and 100), and two steel tube specifications (ϕ60 × 3.5 and ϕ89 × 4 ), as shown in Table 1. Each group had four specimens. A study on the axial compression of steel tubes after a hightemperature treatment of 600 °C, 800 °C, and 1000 °C and those not experiencing high-temperature treatment was carried out. Specimens in these groups were named in accordance with “material-cross sectionslenderness ratio-fire temperature.” For example, Q235 in Q23589–60–1000 expresses the Q235 steel material, 89 represents the section size ϕ89 × 4 , 60 is the slenderness ratio, and 1000 denotes that the specimen was subjected to 1000 °C treatment. Specimens not experiencing high-temperature treatment were expressed by 20.
Table 1 Specimen design information. Member no.
Material
Section
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
Q235B Q235B Q235B Q235B Q345B Q345B Q345B Q345B
ϕ60 ϕ60 ϕ60 ϕ89 ϕ60 ϕ60 ϕ60 ϕ89
× × × × × × × ×
3.5 3.5 3.5 4 3.5 3.5 3.5 4
Length/mm
Slenderness ratio
1200 1600 2000 1800 1200 1600 2000 1800
60 80 100 60 60 80 100 60
temperature effect in fire disasters. The high-temperature furnace is shown in Fig. 3(a). Three target temperatures—600 °C, 800 °C, and 1000 °C—were designed. The furnace was heated to target temperatures and was kept for 30 min in order to insure that specimens reached target temperatures. Then, specimens were naturally cooled to ambient temperature. Thermocouples were installed on specimens such that temperature changes during the high-temperature treatment, as shown in Fig. 3(b).
2.2. High-temperature treatment The ISO-834 standard heating curve was used for the high-temperature treatment of the specimens to simulate the actual high-
2.3. Material property test Material coupons were taken from steel tube specimens along the longitudinal direction after high-temperature treatment and the shapes and dimensions were in accordance with GB/T228.1–2010 [38], as shown in Figs. 4 and 5. Then, one-way static stretching was conducted. The elasticity modulus Es , yield strength fy , and tensile strength fu of specimen materials after high-temperature treatment and those not going through high-temperature treatment were obtained through material property test.
Fig. 1. Grid structure. 476
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 3. High-temperature treatment device and specimens. Fig. 4. Location of coupons for tensile test.
Fig. 5. Dimensions of material coupons (mm).
2.4. Axial compression experiment
3. Experimental results
An NYL-500 5000 kN long-column hydraulic compression machine was used for axial compression loading. Axis pins were set on both sides of the members to simulate hinge joint constraints. A pressure sensor with 500 kN measuring range was arranged at the upper end of the shaft stool of the bearing pin. The experimental apparatus are shown in Fig. 6. Fig. 7 presents the measuring point arrangement of strain and displacement. Four one-way strain gauges were arranged along the section on the member quartile. A total of 12 gauges were arranged to measure axial strains at points on the section. Displacement meters (VL1–VL2) were installed at the top and bottom of members for the measurement of axial displacement. Guyed displacement meters were arranged along the free (HL1) and constraint (HL2) directions in members midspan for the measurement of lateral displacement.
3.1. High-temperature treatment The specimen temperature-time curves during the high-temperature treatment were obtained, as shown in Fig. 8, and the highest temperatures of the specimens were 563 °C，790 °C and 972 °C respectively. All specimens experienced residual deformations at different degrees, as shown in Fig. 9. Residual deformation in each specimen midspan of each direction was measured, as shown in Fig. 10, and the residual deformation value Δ was calculated by the formula (1)–(3), where Δx1, Δx2 donate the distance between the tube and end plate at the each end of specimen along the free direction, Δx3 donates the distance at midspan and Δx donates the residual deformation in the free direction, while Δy1, Δy2 , Δy3 and Δy have the same meaning in the constraint direction. The deformation values are listed in Table 2.
Δx = Δx 3 − (Δx1 + Δx 2 )/2
477
(1)
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 6. Experimental apparatus.
Fig. 7. Schematic diagram of measuring points for axial compression experiment.
Δy = Δy3 − (Δy1 + Δy2 )/2
(2)
(Δx )2 + (Δy )2
(3)
Δ=
significantly increased after the temperature exceeded 800 °C. The δ values of specimens with the same slenderness ratio but different sections were basically identical after the same high-temperature treatment. Meanwhile, the δ values of the specimens with the same section but different slenderness ratios increased as the slenderness ratio increased.
Then the residual deformation coefficients δ = Δ/ L0 were computed. In the formula, Δ denotes the residual deformation value and L0 is the computed specimen length. Fig. 11 presents the change in residual deformation coefficient δ with treatment temperature. As fire temperature increased, δ presented an increasing trend and
478
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
stability bearing capacities of steel tube members after treatment below 600 °C were basically not weakened. When the fire temperature was higher than 600 °C, the initial stiffness of the post-fire specimens reduced as fire temperature increased. Load-lateral displacement curves bore influence from initial imperfection and residual deformation, and the greater the residual deformation, the higher the increasing rate of lateral displacement with load. The load-strain curves of specimens in Q235-60–60 group are shown in Fig. 17. Strains of measuring points experienced out-of-sync change as the load increased due to the initial imperfection and residual deformation. The greater the residual deformation, the greater the strain variation difference between measuring points. Compressive strain continuously increased before the stability bearing capacity was reached. The midspan section experienced a yield when the stability bearing capacity was reached. Strain values at measuring points suddenly increased, and tensile strain happened to some measuring points. Most of the other sections remained within the elasticity scope.
3.2. Material property test The test results of the specimen material test are listed in Table 3, where T is the highest fire temperature of the specimen, Es denotes the elasticity modulus, fy represents the yield strength, fu signifies the tensile strength, and ηEs , η fy , and η fu refer to the post-fire reduction coefficients of elasticity modulus, yield strength, and tensile strength, respectively. The stress–strain relationships of the steel coupons and the comparison between the obtained results and predictor formula [16] results are shown in Figs. 12 and 13. The predictor formula fits well with the test results.
3.3. Axial compression experiment All 32 specimens in eight groups experienced overall lateral instability. The instability direction presented significant correlation with the direction of residual deformation. The instability pattern of typical specimen Q345-60–80 are shown in Fig. 14. Table 4 presents the experimental values NcrE of stability bearing capacities of the specimens. Fig. 15 reveals that NcrE changed with parameter change. Experimental results indicated that in the same group, NcrE of specimens after 600 °C high-temperature treatment did not experience considerable change compared with those not experiencing high-temperature treatment. NcrE of specimens after 800 °C treatment slightly decreased compared with those not experiencing high-temperature treatment. NcrE of specimens after 1000 °C treatment significantly decreased compared with those not experiencing high-temperature treatment. NcrE of specimens with the same material and section size after the same high-temperature treatment decreased as slenderness ratio increased. The NcrE values of the specimens with large sections were higher than those with small sections after the same high-temperature treatment when they had the same material and slenderness ratio. The load-displacement curves of specimens in the groups are shown in Fig. 16. Some specimens failed to acquire displacement change in the test due to sensor fault, and load-displacement curves were not provided. Load-axial displacement curves of all specimens presented the same variation trend. The slope of curves basically remained unchanged before stability bearing capacity was reached but became a negative value after stability bearing capacity was reached. Then, overall lateral instability would occur. Load-axial displacement curves of specimens experiencing 600 °C treatment basically overlapped with those not experiencing high-temperature treatment. This result indicated that
4. Numerical analysis and model verification 4.1. Finite element model ABAQUS finite element software was used to establish a numerical analysis model of axial compression behaviors of steel tube members after exposure to high temperature and to conduct a nonlinear stability analysis. Steel density was 7800 kg/m3. An ideal elastoplastic model was used for constitutive relation. Elasticity modulus and yield strength values after different fire temperatures were determined in accordance with Table 3. Poisson's ratio was 0.3. The steel tube model, which had been extensively applied to a large strain analysis, was established using S4R elements. Because finite element results are sensitive to element meshes, the tube of Q235-60–89–20 and 5 kinds of element size were selected to test mesh sensitive and test results are listed in Table 5. When the element size is larger than 0.02 mm, the result is not accurate. Long computing time is needed when the element size is smaller than 0.02 m with slightly difference between results. The element size was set as 0.02 m × 0.02 m in the subsequent analysis. Parameters adopted in the numerical model are listed in Table 6 and the Q235-60–60-20 finite element model is shown in Fig. 18. Two ends of the steel tube were coupled to a reference point as shown in Fig. 19. One end of the steel tube model was constrained by a fixed hinged support, whereas the other end was constrained by a sliding hinged support. Axial compression simulation was performed by applying axial load to the reference point. The numerical analysis included eigenvalue and nonlinear buckling analyses. The first-order buckling mode obtained through eigenvalue buckling analysis was used as the initial imperfection model. The measured residual deformation value was taken as maximum imperfection value, and initial imperfection was introduced. In consideration of material and geometric nonlinearities, the failure mode, stability bearing capacity, and load-displacement curves of the specimens were obtained through nonlinear bucking analysis. 4.2. Model verification All 32 specimens experienced overall lateral instability, which was similar to the tested failure mode. The FEM results NcrS and the comparison between NcrS and NcrE are shown in Table 4 and Table 7, respectively. FEM results accorded well with experimental results. The error was within ± 10%, and variance was within 0.005. Meanwhile, FEM results of specimen load-displacement curves accorded well with experimental results as shown in Figs. 20–27.
Fig. 8. Temperature change during high-temperature treatment of specimens.
479
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 9. Specimens after high-temperature treatment. Note: Photos from left to right successively show specimens not experiencing high-temperature treatment and those experiencing high-temperature treatments of 600 °C,800 °C, and1000 °C.
The stability bearing capacity of axial compressed steel tube after exposure to high temperature could be calculated in accordance with the following formula:
4.3. Parametric analysis The stability bearing capacity Ncr of axial compressed steel tube was related to the stability coefficient φ , member section A , and material yield strength fy . The computational formula (formula 4) of the stability bearing capacity of the axial compressed steel tube was obtained from Design Code for Steel Structures [39]. The stability coefficient φ could be determined in accordance with the look-up table of the slenderness ratio of steel tube members and steel yield strength.
Ncr = φAfy
Ncr, T = φT Af y, T ,
(5)
where Ncr, T is the stability bearing capacity (N) of axial compressed steel tube members after exposure to high temperature, φT denotes the stability coefficient after high-temperature treatment, and fy, T represents the steel yield strength after exposure to high temperature (N/ mm2). The ratio of stability coefficient φT of steel tube members after exposure to high temperature to φ at an ambient temperature was defined as the stability reduction coefficient α after high-temperature treatment. The following can be obtained in accordance with formulas (4) and (5):
(4)
α= Fig. 10. Measure of residual deformation.
480
φT Ncr, T Ncr Ncr, T fy Ncr, T / = = ⋅ = , φ Afy, T Afy Ncr fy, T Ncr η fy , T
(6)
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 2 Residual deformation Δ and residual deformation coefficient δ of specimens. Member no.
Temp. 20 °C
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
600 °C
800 °C
1000 °C
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
4.0 3.0 3.0 6.0 3.5 5.0 1.0 4.0
3.33 1.88 1.50 3.32 2.92 3.12 0.50 2.21
3.0 5.0 4.0 5.0 2.5 6.0 2.0 1.0
2.50 3.12 2.00 2.76 2.08 3.75 1.00 0.55
4.0 8.0 8.0 7.0 4.5 7.0 7.5 6.5
3.33 5.00 4.00 3.87 3.75 4.38 3.75 3.59
9.0 33.0 52.0 9.0 15.0 30.0 80.0 29.0
7.50 20.62 26.00 4.98 12.50 18.75 40.00 16.03
Fig. 11. Maximum residual deformation-treatment temperature curves.
where η fy , T is the material yield strength reduction coefficient after high-temperature treatment. The material yield strength reduction coefficient reflects the influence of the highest fire temperature on stability bearing capacities of steel tube members and can be determined in accordance with the formula provided in literature [16]:
Table 3 Test results of material property. Material no.
T ( oC )
Es (GPa)
η Es
fy (MPa)
η fy
fu (MPa)
η fu
Q235–60
20 600 800 1000 20 600 800 1000 20 600 800 1000 20 600 800 1000
200 192 208 185 205 204 190 180 195 190 162 174 194 189 184 176
1.000 0.960 1.040 0.925 1.000 0.995 0.927 0.878 1.000 0.974 0.831 0.892 1.000 0.974 0.948 0.907
438 436 387 364 383 382 326 325 444 457 391 333 400 394 312 270
1.000 0.995 0.884 0.831 1.000 0.997 0.851 0.848 1.000 1.029 0.881 0.750 1.000 0.985 0.779 0.676
579 572 524 508 526 515 483 476 582 589 528 489 505 504 499 466
1.000 0.988 0.905 0.877 1.000 0.979 0.918 0.905 1.000 1.012 0.907 0.840 1.000 0.998 0.988 0.923
Q235–89
Q345–60
Q345–89
η fy , T = 1 20°C ≤ T ≤ 700°C ⎧ 4 − ⎨ η fy , T = 1.6 − 8.88 × 10 T 700°C < T ≤ 1000°C ⎩
(7)
A finite element model after verification was used for parametric analysis. The influences of parameters, such as steel type fy , sectional diameter-thickness ratio D / t , slenderness ratio λ , fire temperature T , and residual deformation coefficient (δ = Δ/ L0 ), on the reduction coefficient α of stability bearing capacity after high-temperature treatment were analyzed. Parameter values all met JGJ7–2010 [40] requirements, as detailed in Table 8. Fig. 28 presents the influences of the parameters. Fig. 28 (a) shows that the steel type and the highest fire temperature had minor influences on α , which slightly increased as the slenderness ratio λ increased. Moreover, α ≈ 1.0 when λ was not greater 481
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 12. Stress-strain curves of 4 group coupons.
residual deformation coefficient δ . On the basis of numerical calculation results, a simplified calculated formula of α was formulated through regression as follows:
than 80, α ≈ 1.1 when λ was greater than 80 but smaller than or equal to 120, and α ≈ 1.2 when λ was greater than 120 but smaller than or equal to 180, as shown in Fig. 28(b). Fig. 28 (c) shows that the diameter-thickness ratio D / t nearly had no effect on α . Thus, α did not change because of the differences among the sectional forms but changed considerably when δ changed. Therefore, the main factors influencing α after exposure to high temperature were λ and δ .
α = α (λ )⋅α (δ ),
where α (λ ) is the expression related to the influence of the slenderness ratio on the reduction coefficient α of the stability bearing capacity. α was set as 1.0, 1.1, and 1.2 when λ ≤ 80 , 80 < λ ≤ 120 , and 120 < λ ≤ 180 , respectively. α (δ ) denotes the influence of the residual deformation coefficient on the reduction coefficient α of the stability bearing capacity, specifically as follows:
5. Calculation method After combining formulas (4)–(6), the residual stability bearing capacity of steel tube members after exposure to high temperature can be calculated as follows:
Ncr, T = αη fy , T φAfy
(9)
α (δ ) = 1.07 − 81.46δ + 4330.64δ 2 − 91658.56δ 3 (0.001 ≤ δ ≤ 0.02) (10)
(8)
Formulas (7)–(10) were used to calculate residual stability bearing capacities of 32 steel tube specimens after high-temperature treatment under axial compression experiment, and the results obtained from formula NcrF are shown in Table 4. The formula calculation values NcrF were compared with experimental results NcrE as shown in Table 6. Differences between the calculated results using formulas and the
Therefore, the key to determine the residual stability bearing capacity relied on the determination of the reduction coefficient α of the stability bearing capacity. In accordance with the previous analysis, a large quantity of finite element analysis and computation models were established for the main factors influencing α , slenderness ratio λ and
482
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 13. Comparison between test results of material property and results of predictor formula.
Fig. 14. Pictures of Q345-60–80 after failure.
483
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 4 Stability bearing capacity results. Member no.
Temp. /°C 20
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
600
800
1000
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
192 159 134 270 244 209 153 280
188 154 123 259 232 213 159 287
191 159 132 248 220 205 140 278
227 162 141 256 253 197 154 278
206 160 144 260 236 204 161 283
209 151 130 242 234 197 142 278
205 167 95 247 234 203 113 269
192 159 90 240 223 190 105 258
192 153 93 226 211 192 110 248
128 69 38 175 92 111 36 187
125 64 41 175 97 108 33 174
126 62 37 173 92 100 34 168
Note: NcrS is FEM result of stability bearing capacity. NcrF is formula result of stability bearing capacity.
Fig. 15. Stability bearing capacity.
484
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. Load-displacement curves of Q235-60–60 specimens.
485
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. (continued)
486
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. (continued)
were overall bending instability. 3) Stability bearing capacities of steel tube members after high-temperature treatment were almost not weakened when the fire temperature was lower than 700 °C. Influenced by the degradation of material mechanical properties and residual deformation, residual stability bearing capacity of steel tube members after high-temperature treatment significantly reduced. Residual stability bearing capacities could be reduced by 35% at maximum when the fire temperature exceeded 700 °C. 4) The highest fire temperature, slenderness ratio, and residual deformation coefficient after high-temperature treatment were the main influential factors of residual bearing capacities of steel tube members after exposure to high temperature. 5) After the introduction of material yield strength and stability reduction coefficients after high-temperature treatment, calculated formulas of residual stability bearing capacities of steel tube members after exposure to high temperature were proposed. Calculated results using the formulas accorded well with experimental results.
experimental results were within 10%. Calculated results were smaller to experimental results, which certified that the formulas proposed in this paper could conservatively calculate residual stability bearing capacities of steel tube members after exposure to high temperature. 6. Conclusions 1) After different high-temperature treatments, residual deformations of different degrees happened to steel tube specimens. The higher the temperature and the greater the slenderness ratio, the greater the generated residual deformation. When the fire temperature was lower than 800 °C, the residual deformation value was approximately 1/200 of the length of the steel tube specimen. However, the residual deformation value could reach 1/25 of the length of the specimen when the fire temperature reached 1000 °C. 2) The failure mode of axial compressed steel tube members after hightemperature treatment was the same as that of steel tube members not experiencing high-temperature treatment. Both failure modes
487
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 17. Load-strain curves of Q235-60–60 specimens.
Table 5 Mesh sensitive test results. Element size / m Result / kN
0.01 292
0.015 289
0.02 287
0.025 280
0.03 277
Fig. 18. Finite element model of steel tube.
Table 6 Parameters adopted in the numerical model. Parameters
Values
Steel density Constitutive relation Elasticity modulus Yield strength Poisson's ratio Element Element size
7800 kg/m3 Ideal elastoplastic model According to Table 3. According to Table 3. 0.3 S4R 0.02 m × 0.02 m
Fig. 19. Reference point.
488
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 7 Comparison of results of stability bearing capacities. Group
Treatment temperature /°C 20
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60 Average Variance
600
800
1000
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
0.98 0.97 0.92 0.96 0.95 1.02 1.04 1.02 0.98 0.0017
0.95 0.96 0.94 0.91 0.93 0.99 0.93 0.99 0.95 0.0008
0.91 0.99 1.02 1.02 0.93 1.04 1.05 1.02 1.00 0.0026
0.91 0.98 0.92 0.99 0.92 0.99 0.91 1.00 0.95 0.0017
0.94 0.95 0.95 0.97 0.95 0.94 0.93 0.96 0.95 0.0002
0.94 0.96 0.98 0.94 0.91 0.90 0.91 0.92 0.93 0.0008
0.98 0.93 1.08 1.00 1.05 0.97 0.92 0.93 0.98 0.0034
0.91 0.91 1.00 0.99 0.99 0.90 1.00 0.91 0.95 0.0022
Fig. 20. Comparison between finite element and experimental results of load-displacement curves of Q235-60–60 specimens.
Fig. 21. Comparison between finite element and experimental results of load-displacement curves of Q235-60–80 specimens.
489
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 22. Comparison between finite element and experimental results of load-displacement curves of Q235-60–100 specimens.
Fig. 23. Comparison between finite element and experimental results of load-displacement curves of Q235-89–60 specimens.
Fig. 24. Comparison between finite element and experimental results of load-displacement curves of Q345-60–60 specimens.
490
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 25. Comparison between finite element and experimental results of load-displacement curves of Q345-60–80 specimens.
Fig. 26. Comparison between finite element and experimental results of load-displacement curves of Q345-60–100 specimens.
Fig. 27. Comparison between finite element and experimental results of load-displacement curves of Q345-89–60 specimens.
491
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 8 Parameter values in parametric analysis. Parameter
Value
Fixed value
fy (N/mm2)
235, 345
235
D/t λ
15.9, 17.1, 19.9, 22.2, 28.5 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180 600, 700, 800, 900, 1000
17.1 60 1000
0.001, 0.002, 0.005, 0.01, 0.02
0.001
T ( οC) δ
Fig. 28. Main parameters influencing α .
Acknowledgments
temperatures and after cooling down, Fire Mater. 28 (2–4) (2004) 237–251. [3] F. Ding, Z. Yu, H. Wen, Experimental research on mechanical properties of Q235 steel after high temperature treatment], J. Build. Mater. 02 (2006) 245–249. [4] J. Chen, B. Young, Experimental investigation of cold-formed steel material at elevated temperatures, Thin-Walled Struct. 45 (1) (2007) 96–110. [5] J.M. Atienza, M. Elices, Behavior of prestressing steels after a simulated fire: fireinduced damages, Constr. Build. Mater. 23 (8) (2009) 2932–2940. [6] N.D. Kankanamge, M. Mahendran, Mechanical properties of cold-formed steels at elevated temperatures, Thin-Walled Struct. 49 (1) (2011) 26–44. [7] S. Gunalan, M. Mahendran, Experimental investigation of post-fire mechanical properties of cold-formed steels, Thin-Walled Struct. 84 (2014) 241–254. [8] F. Mccann, L. Gardner, S. Kirk, Elevated temperature material properties of coldformed steel hollow sections, Thin-Walled Struct. 90 (2015) 84–94. [9] 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
This study was financially supported by the National Natural Science Foundation of China (No. 51678404) and the Fok Ying Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151072). References [1] J. Outinen, J. Kesti, P. Mäkeläinen, Fire design model for structural steel S355 based upon transient state tensile test results, J. Constr. Steel Res. 42 (3) (1997) 161–169. [2] J. Outinen, P. Makelainen, Mechanical properties of structural steel at elevated
492
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
[25] S. Fan, L. Zhang, W. Sun, et al., Numerical investigation on fire resistance of stainless steel columns with square hollow section under axial compression, ThinWalled Struct. 98 (2016) 185–195 (Part A). [26] W. Wang, T. Liu, Experimental and numerical study on post-fire behavior of highstrength Q460 steel columns[J], Adv. Struct. Eng. 19 (12) (2016) 1873–1888. [27] Y. Ding, M. Wang, Z.X. Li, et al., Damage evaluation of the steel tubular column subjected to explosion and post-explosion fire condition[J], Eng. Struct. 55 (2013) 44–55. [28] Y. Ding, Y. Chen, Y. Shi, Damage evaluation of a restrained steel column subjected to indoor blast and fire[J], Zhendong yu Chongji/J. Vib. Shock. 36 (5) (2017) 79–86. [29] J. Lu, H. Liu, Z. Chen, Behavior of welded hollow spherical joints after exposure to ISO-834 standard fire, J. Constr. Steel Res. 140 (Supplement C) (2018) 108–124. [30] H. Liu, J. Lu, Z. Chen, Residual behavior of welded hollow spherical joints after exposure to elevated temperatures, J. Constr. Steel Res. 137 (2017) 102–118. [31] 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. [32] L.B. Qlu, S.D. Xue, M. Feng, Fire performance of space grid structures. International Association for Shell and Spatial Structures, 2009. [33] X. Wang, H. Sun, Y. Du, et al., Experimental research on fire response and post-fire performance of prestressed steel truss structures, J. Build. Struct. 08 (2013) 46–55. [34] W. Guangyong, W. Xinggiang, L. Guangwei, Fire and post-fire performance of space grid structures, Appl. Mech. Mater. 238 (2012) 621–624. [35] J. Cui, X. Guo, L. Yin, Calculation method based on equivalent sandwich plate method for grid structures in conditions of evaluated temperature and post fire, Spat. Struct. 02 (2016) 37–43. [36] Y. Yin, T. Yuan, Z. Chen, et al., Numer. Study Behav. a Lattice Shell Struct. fire Damage Estim. 08 (2010) 51–56. [37] Z. Liu, Y. Liu, Y. Zhou, et al., Analysis and evaluation of safety of a lattice truss structure after fire accident, Steel Constr. 07 (2007) 89–91. [38] GB/T 228.1-2010, Metallic materials-tensile testing at ambient temperature, Standards Press of China, Beijing, 2002. [39] GB50017-2017, Code for design of steel structure, Standards Press of China, Beijing, 2017. [40] JGJ7-2010, Technical Specification for Frame Structures, Ministry of Construction of the People’s Republic of China. Beijing. (In Chinese), 2010.
(2016) 291–310. [10] S. Kesawan, M. Mahendran, Post-fire mechanical properties of cold-formed steel hollow sections, Constr. Build. Mater. 161 (2018) 26–36. [11] 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. [12] 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. [13] X. Qiang, F.S.K. Bijlaard, H. Kolstein, et al., Experimental study on high strength structural steel S460 in fire and after cooling down, IES J. Part A: Civil. Struct. Eng. 6 (2) (2013) 104–111. [14] W.Y. Wang, G.Q. Li, Y. Ge, Residual stress study on welded section of high strength Q460 steel after fire exposure[J]. advanced Steel, Construction 11 (2) (2015) 150–164. [15] W. Wang, T. Liu, J. Liu, Experimental study on post-fire mechanical properties of high strength Q460 steel, J. Constr. Steel Res. 114 (2015) 100–109. [16] W. Wang, T. Liu, Study on mechanical properties of high strength Q460 steel after cooling from high temperature, Jianzhu Cailiao Xuebao/J. Build. Mater. 19 (1) (2016) 171–176. [17] X. Qiang, N. Wu, X. Jiang, et al., Experimental study on post-fire mechanical properties of very high strength steel S960, Tongji Daxue Xuebao/J. Tongji Univ. 44 (7) (2016) 1076–1083. [18] G.Q. Li, H. Lyu, C. Zhang, Post-fire mechanical properties of high strength Q690 structural steel, J. Constr. Steel Res. 132 (2017) 108–116. [19] C. Siwei, J. Shaokun, G. Houzuo, et al., Mechanical and ductile fracture performances of high strength structural steel Q690 after a fire: experimental investigation, Procedia Eng. 210 (2017) 496–503. [20] F. Azhari, A. Heidarpour, X. Zhao, et al., Post-fire mechanical response of ultra-high strength (Grade 1200) steel under high temperatures: linking thermal stability and microstructure, Thin-Walled Struct. 119 (2017) 114–125. [21] Y. Huang, B. Young, Post-fire behaviour of ferritic stainless steel material, Constr. Build. Mater. 157 (2017) 654–667. [22] X. Gao, X. Zhang, H. Liu, et al., Residual mechanical properties of stainless steels S30408 and S31608 after fire exposure, Constr. Build. Mater. 165 (2018) 82–92. [23] Liu Tianzi, Study on Post-fire Mechanical Behavior of High Strength Q460 Steel Columns[D]. Chongqing University, 2015. [24] Ge Yong, Study on Fire Resistance of Restrained High Strength Q460 Steel Column [D]. Chongqing University, 2012.
493
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Full length article
Calculation method for the residual stability bearing capacity under axial compression of steel tube members exposed to a high temperature
T
⁎
Rui Mab, Hongbo Liua,b, , Zhihua Chena,b a b
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Department of Civil Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Elevated temperature Steel tube Stability bearing capacity Experiment Numerical analysis
Fire accidents occur occasionally when grid structures are extensively applied, although many grid structures do not suffer general failure after fire disasters and can be used again after reasonable evaluation and reinforcement. To reasonably evaluate the residual load bearing capacity of grid structures, this paper investigated stability bearing capacity of steel tube members in grid structures after fire disasters through axial compression experiment and numerical simulation. Axial compression experiments performed on 32 steel tubes after exposure to the ISO-834 standard fire, and three highest fire temperatures were considered, including 600 °C， 800 °C and 1000 °C. The temperature distributions in the specimens during the heating and related mechanical properties such as load-displacement curves, ultimate loads and strain distributions of the specimens, were obtained and analyzed. Finite element analysis was also conducted by using ABAQUS software. Then, the main factors influencing the residual stability bearing capacities of the steel tube members exposed to high temperatures were obtained through a lot of numerical analysis. Based on the results of experiments and numerical analysis, the formula for the computation of the residual stability bearing capacities of the steel tube members after fire disasters was presented. And calculated results using the formulas accorded well with experimental results.
1. Introduction Owing to their superior load-bearing properties and high-efficiency assembling, grid structures have been extensively applied in various fields of civil engineering, as a kind of grid structure shown in Fig. 1. Building fire significantly threatens the safety of human life and national property. In most fire accidents, significant local damage is frequently observed in spatial grid structures after a fire. However, general structural collapse accidents are uncommon because of certain fireproof protection, high indeterminate degrees, and collaborative spatial load bearing of members, as shown in Fig. 2. After damage detection, restoration, and reinforcement, most grid structures can be used again for fire damage reduction. Therefore, studying the evaluation method of residual mechanical properties of grid structures after a fire disaster and proposing reasonable suggestions about demolition, reconstruction, restoration, and reinforcement are of great theoretical significance and have great engineering application values. Currently, the residual mechanical properties of materials constituting grid structures exposed to high temperatures have been extensively studied, such as ordinary steel [1–10], high-strength
⁎
steel [11–20] and stainless steel [21,22]. However, studies on the members, joints, and overall structures of these structures are lacking. Some researchers [23–26] studied the overall stability performance of axial compressed steel columns exposed to high temperatures. They analyzed the influences of fire temperature and cooling mode and then provided a simplified computing method for residual stability bearing capacity. Furthermore, considering the combined effects of explosion and fire, Ding Y. et al. [27,28] found that fire duration was the main factor influencing the residual stability bearing capacity of a steel column. Then proposed a damage evaluation method. Meanwhile, Lu J. et al. [29,30] explored the influence of different cooling modes on the basic study of the mechanical properties of welded hollow sphere joints at ambient by Han Q.H. and Liu X.L. [31] and at high temperatures by Qlu L.B. et al. [32]. Their study indicated that residual bearing capacities of welded hollow sphere joints after spray cooling was higher than those observed after natural cooling. Some scholars studied the mechanical properties of overall grid structures after a fire disaster. For instance, Wang X. et al. [33] and Wang G. et al. [34] analyzed and computed the post-fire displacement and internal force distribution laws of steel grid structures. Cui J. et al. [35] proposed a quasi-
Corresponding author. E-mail address: [email protected] (H. Liu).
https://doi.org/10.1016/j.tws.2018.09.011 Received 9 April 2018; Received in revised form 25 June 2018; Accepted 3 September 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Nomenclature
T Δ δ L0 A D/t λ φ φT α
Es fy fy, T fu ηEs η fy η fu NcrE NcrS NcrF Ncr, T
fire temperature residual deformation value residual deformation coefficient computed specimen length member section sectional diameter-thickness ratio slenderness ratio stability coefficient post-fire stability coefficient stability reduction coefficient
elasticity modulus yield strength post-fire yield strength tensile strength post-fire reduction coefficients of elasticity modulus post-fire reduction coefficients of yield strength post-fire reduction coefficients of tensile strength experimental stability bearing capacity FEM result of stability bearing capacity formula result of stability bearing capacity Post-fire stability bearing capacity
sandwich panel method for a simplified computation of the post-fire midspan displacement of grid structures. Yin Y. et al. [36] and Liu Z. et al. [37] presented post-fire structural reinforcement schemes for specific engineering projects. However, present studies on the post-fire residual bearing capacities of circular steel tube members commonly used by grid structures are limited. In this paper, residual stability bearing capacities of such members were studied through experiment and numerical analysis. A calculation method of the residual stability bearing capacity of steel tube members after exposure to high temperature was proposed. Results provided a scientific basis for the evaluation of post-fire residual load bearing capacities of grid structures. 2. Experiment investigation 2.1. Specimen design
Fig. 2. Post-fire grid structure.
Eight groups of specimens were selected, each of which consisted of two commonly used steel materials (Q235B and Q345B), three slenderness ratios (60, 80, and 100), and two steel tube specifications (ϕ60 × 3.5 and ϕ89 × 4 ), as shown in Table 1. Each group had four specimens. A study on the axial compression of steel tubes after a hightemperature treatment of 600 °C, 800 °C, and 1000 °C and those not experiencing high-temperature treatment was carried out. Specimens in these groups were named in accordance with “material-cross sectionslenderness ratio-fire temperature.” For example, Q235 in Q23589–60–1000 expresses the Q235 steel material, 89 represents the section size ϕ89 × 4 , 60 is the slenderness ratio, and 1000 denotes that the specimen was subjected to 1000 °C treatment. Specimens not experiencing high-temperature treatment were expressed by 20.
Table 1 Specimen design information. Member no.
Material
Section
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
Q235B Q235B Q235B Q235B Q345B Q345B Q345B Q345B
ϕ60 ϕ60 ϕ60 ϕ89 ϕ60 ϕ60 ϕ60 ϕ89
× × × × × × × ×
3.5 3.5 3.5 4 3.5 3.5 3.5 4
Length/mm
Slenderness ratio
1200 1600 2000 1800 1200 1600 2000 1800
60 80 100 60 60 80 100 60
temperature effect in fire disasters. The high-temperature furnace is shown in Fig. 3(a). Three target temperatures—600 °C, 800 °C, and 1000 °C—were designed. The furnace was heated to target temperatures and was kept for 30 min in order to insure that specimens reached target temperatures. Then, specimens were naturally cooled to ambient temperature. Thermocouples were installed on specimens such that temperature changes during the high-temperature treatment, as shown in Fig. 3(b).
2.2. High-temperature treatment The ISO-834 standard heating curve was used for the high-temperature treatment of the specimens to simulate the actual high-
2.3. Material property test Material coupons were taken from steel tube specimens along the longitudinal direction after high-temperature treatment and the shapes and dimensions were in accordance with GB/T228.1–2010 [38], as shown in Figs. 4 and 5. Then, one-way static stretching was conducted. The elasticity modulus Es , yield strength fy , and tensile strength fu of specimen materials after high-temperature treatment and those not going through high-temperature treatment were obtained through material property test.
Fig. 1. Grid structure. 476
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 3. High-temperature treatment device and specimens. Fig. 4. Location of coupons for tensile test.
Fig. 5. Dimensions of material coupons (mm).
2.4. Axial compression experiment
3. Experimental results
An NYL-500 5000 kN long-column hydraulic compression machine was used for axial compression loading. Axis pins were set on both sides of the members to simulate hinge joint constraints. A pressure sensor with 500 kN measuring range was arranged at the upper end of the shaft stool of the bearing pin. The experimental apparatus are shown in Fig. 6. Fig. 7 presents the measuring point arrangement of strain and displacement. Four one-way strain gauges were arranged along the section on the member quartile. A total of 12 gauges were arranged to measure axial strains at points on the section. Displacement meters (VL1–VL2) were installed at the top and bottom of members for the measurement of axial displacement. Guyed displacement meters were arranged along the free (HL1) and constraint (HL2) directions in members midspan for the measurement of lateral displacement.
3.1. High-temperature treatment The specimen temperature-time curves during the high-temperature treatment were obtained, as shown in Fig. 8, and the highest temperatures of the specimens were 563 °C，790 °C and 972 °C respectively. All specimens experienced residual deformations at different degrees, as shown in Fig. 9. Residual deformation in each specimen midspan of each direction was measured, as shown in Fig. 10, and the residual deformation value Δ was calculated by the formula (1)–(3), where Δx1, Δx2 donate the distance between the tube and end plate at the each end of specimen along the free direction, Δx3 donates the distance at midspan and Δx donates the residual deformation in the free direction, while Δy1, Δy2 , Δy3 and Δy have the same meaning in the constraint direction. The deformation values are listed in Table 2.
Δx = Δx 3 − (Δx1 + Δx 2 )/2
477
(1)
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 6. Experimental apparatus.
Fig. 7. Schematic diagram of measuring points for axial compression experiment.
Δy = Δy3 − (Δy1 + Δy2 )/2
(2)
(Δx )2 + (Δy )2
(3)
Δ=
significantly increased after the temperature exceeded 800 °C. The δ values of specimens with the same slenderness ratio but different sections were basically identical after the same high-temperature treatment. Meanwhile, the δ values of the specimens with the same section but different slenderness ratios increased as the slenderness ratio increased.
Then the residual deformation coefficients δ = Δ/ L0 were computed. In the formula, Δ denotes the residual deformation value and L0 is the computed specimen length. Fig. 11 presents the change in residual deformation coefficient δ with treatment temperature. As fire temperature increased, δ presented an increasing trend and
478
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
stability bearing capacities of steel tube members after treatment below 600 °C were basically not weakened. When the fire temperature was higher than 600 °C, the initial stiffness of the post-fire specimens reduced as fire temperature increased. Load-lateral displacement curves bore influence from initial imperfection and residual deformation, and the greater the residual deformation, the higher the increasing rate of lateral displacement with load. The load-strain curves of specimens in Q235-60–60 group are shown in Fig. 17. Strains of measuring points experienced out-of-sync change as the load increased due to the initial imperfection and residual deformation. The greater the residual deformation, the greater the strain variation difference between measuring points. Compressive strain continuously increased before the stability bearing capacity was reached. The midspan section experienced a yield when the stability bearing capacity was reached. Strain values at measuring points suddenly increased, and tensile strain happened to some measuring points. Most of the other sections remained within the elasticity scope.
3.2. Material property test The test results of the specimen material test are listed in Table 3, where T is the highest fire temperature of the specimen, Es denotes the elasticity modulus, fy represents the yield strength, fu signifies the tensile strength, and ηEs , η fy , and η fu refer to the post-fire reduction coefficients of elasticity modulus, yield strength, and tensile strength, respectively. The stress–strain relationships of the steel coupons and the comparison between the obtained results and predictor formula [16] results are shown in Figs. 12 and 13. The predictor formula fits well with the test results.
3.3. Axial compression experiment All 32 specimens in eight groups experienced overall lateral instability. The instability direction presented significant correlation with the direction of residual deformation. The instability pattern of typical specimen Q345-60–80 are shown in Fig. 14. Table 4 presents the experimental values NcrE of stability bearing capacities of the specimens. Fig. 15 reveals that NcrE changed with parameter change. Experimental results indicated that in the same group, NcrE of specimens after 600 °C high-temperature treatment did not experience considerable change compared with those not experiencing high-temperature treatment. NcrE of specimens after 800 °C treatment slightly decreased compared with those not experiencing high-temperature treatment. NcrE of specimens after 1000 °C treatment significantly decreased compared with those not experiencing high-temperature treatment. NcrE of specimens with the same material and section size after the same high-temperature treatment decreased as slenderness ratio increased. The NcrE values of the specimens with large sections were higher than those with small sections after the same high-temperature treatment when they had the same material and slenderness ratio. The load-displacement curves of specimens in the groups are shown in Fig. 16. Some specimens failed to acquire displacement change in the test due to sensor fault, and load-displacement curves were not provided. Load-axial displacement curves of all specimens presented the same variation trend. The slope of curves basically remained unchanged before stability bearing capacity was reached but became a negative value after stability bearing capacity was reached. Then, overall lateral instability would occur. Load-axial displacement curves of specimens experiencing 600 °C treatment basically overlapped with those not experiencing high-temperature treatment. This result indicated that
4. Numerical analysis and model verification 4.1. Finite element model ABAQUS finite element software was used to establish a numerical analysis model of axial compression behaviors of steel tube members after exposure to high temperature and to conduct a nonlinear stability analysis. Steel density was 7800 kg/m3. An ideal elastoplastic model was used for constitutive relation. Elasticity modulus and yield strength values after different fire temperatures were determined in accordance with Table 3. Poisson's ratio was 0.3. The steel tube model, which had been extensively applied to a large strain analysis, was established using S4R elements. Because finite element results are sensitive to element meshes, the tube of Q235-60–89–20 and 5 kinds of element size were selected to test mesh sensitive and test results are listed in Table 5. When the element size is larger than 0.02 mm, the result is not accurate. Long computing time is needed when the element size is smaller than 0.02 m with slightly difference between results. The element size was set as 0.02 m × 0.02 m in the subsequent analysis. Parameters adopted in the numerical model are listed in Table 6 and the Q235-60–60-20 finite element model is shown in Fig. 18. Two ends of the steel tube were coupled to a reference point as shown in Fig. 19. One end of the steel tube model was constrained by a fixed hinged support, whereas the other end was constrained by a sliding hinged support. Axial compression simulation was performed by applying axial load to the reference point. The numerical analysis included eigenvalue and nonlinear buckling analyses. The first-order buckling mode obtained through eigenvalue buckling analysis was used as the initial imperfection model. The measured residual deformation value was taken as maximum imperfection value, and initial imperfection was introduced. In consideration of material and geometric nonlinearities, the failure mode, stability bearing capacity, and load-displacement curves of the specimens were obtained through nonlinear bucking analysis. 4.2. Model verification All 32 specimens experienced overall lateral instability, which was similar to the tested failure mode. The FEM results NcrS and the comparison between NcrS and NcrE are shown in Table 4 and Table 7, respectively. FEM results accorded well with experimental results. The error was within ± 10%, and variance was within 0.005. Meanwhile, FEM results of specimen load-displacement curves accorded well with experimental results as shown in Figs. 20–27.
Fig. 8. Temperature change during high-temperature treatment of specimens.
479
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 9. Specimens after high-temperature treatment. Note: Photos from left to right successively show specimens not experiencing high-temperature treatment and those experiencing high-temperature treatments of 600 °C,800 °C, and1000 °C.
The stability bearing capacity of axial compressed steel tube after exposure to high temperature could be calculated in accordance with the following formula:
4.3. Parametric analysis The stability bearing capacity Ncr of axial compressed steel tube was related to the stability coefficient φ , member section A , and material yield strength fy . The computational formula (formula 4) of the stability bearing capacity of the axial compressed steel tube was obtained from Design Code for Steel Structures [39]. The stability coefficient φ could be determined in accordance with the look-up table of the slenderness ratio of steel tube members and steel yield strength.
Ncr = φAfy
Ncr, T = φT Af y, T ,
(5)
where Ncr, T is the stability bearing capacity (N) of axial compressed steel tube members after exposure to high temperature, φT denotes the stability coefficient after high-temperature treatment, and fy, T represents the steel yield strength after exposure to high temperature (N/ mm2). The ratio of stability coefficient φT of steel tube members after exposure to high temperature to φ at an ambient temperature was defined as the stability reduction coefficient α after high-temperature treatment. The following can be obtained in accordance with formulas (4) and (5):
(4)
α= Fig. 10. Measure of residual deformation.
480
φT Ncr, T Ncr Ncr, T fy Ncr, T / = = ⋅ = , φ Afy, T Afy Ncr fy, T Ncr η fy , T
(6)
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 2 Residual deformation Δ and residual deformation coefficient δ of specimens. Member no.
Temp. 20 °C
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
600 °C
800 °C
1000 °C
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
Δ(mm)
δ (10−3)
4.0 3.0 3.0 6.0 3.5 5.0 1.0 4.0
3.33 1.88 1.50 3.32 2.92 3.12 0.50 2.21
3.0 5.0 4.0 5.0 2.5 6.0 2.0 1.0
2.50 3.12 2.00 2.76 2.08 3.75 1.00 0.55
4.0 8.0 8.0 7.0 4.5 7.0 7.5 6.5
3.33 5.00 4.00 3.87 3.75 4.38 3.75 3.59
9.0 33.0 52.0 9.0 15.0 30.0 80.0 29.0
7.50 20.62 26.00 4.98 12.50 18.75 40.00 16.03
Fig. 11. Maximum residual deformation-treatment temperature curves.
where η fy , T is the material yield strength reduction coefficient after high-temperature treatment. The material yield strength reduction coefficient reflects the influence of the highest fire temperature on stability bearing capacities of steel tube members and can be determined in accordance with the formula provided in literature [16]:
Table 3 Test results of material property. Material no.
T ( oC )
Es (GPa)
η Es
fy (MPa)
η fy
fu (MPa)
η fu
Q235–60
20 600 800 1000 20 600 800 1000 20 600 800 1000 20 600 800 1000
200 192 208 185 205 204 190 180 195 190 162 174 194 189 184 176
1.000 0.960 1.040 0.925 1.000 0.995 0.927 0.878 1.000 0.974 0.831 0.892 1.000 0.974 0.948 0.907
438 436 387 364 383 382 326 325 444 457 391 333 400 394 312 270
1.000 0.995 0.884 0.831 1.000 0.997 0.851 0.848 1.000 1.029 0.881 0.750 1.000 0.985 0.779 0.676
579 572 524 508 526 515 483 476 582 589 528 489 505 504 499 466
1.000 0.988 0.905 0.877 1.000 0.979 0.918 0.905 1.000 1.012 0.907 0.840 1.000 0.998 0.988 0.923
Q235–89
Q345–60
Q345–89
η fy , T = 1 20°C ≤ T ≤ 700°C ⎧ 4 − ⎨ η fy , T = 1.6 − 8.88 × 10 T 700°C < T ≤ 1000°C ⎩
(7)
A finite element model after verification was used for parametric analysis. The influences of parameters, such as steel type fy , sectional diameter-thickness ratio D / t , slenderness ratio λ , fire temperature T , and residual deformation coefficient (δ = Δ/ L0 ), on the reduction coefficient α of stability bearing capacity after high-temperature treatment were analyzed. Parameter values all met JGJ7–2010 [40] requirements, as detailed in Table 8. Fig. 28 presents the influences of the parameters. Fig. 28 (a) shows that the steel type and the highest fire temperature had minor influences on α , which slightly increased as the slenderness ratio λ increased. Moreover, α ≈ 1.0 when λ was not greater 481
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 12. Stress-strain curves of 4 group coupons.
residual deformation coefficient δ . On the basis of numerical calculation results, a simplified calculated formula of α was formulated through regression as follows:
than 80, α ≈ 1.1 when λ was greater than 80 but smaller than or equal to 120, and α ≈ 1.2 when λ was greater than 120 but smaller than or equal to 180, as shown in Fig. 28(b). Fig. 28 (c) shows that the diameter-thickness ratio D / t nearly had no effect on α . Thus, α did not change because of the differences among the sectional forms but changed considerably when δ changed. Therefore, the main factors influencing α after exposure to high temperature were λ and δ .
α = α (λ )⋅α (δ ),
where α (λ ) is the expression related to the influence of the slenderness ratio on the reduction coefficient α of the stability bearing capacity. α was set as 1.0, 1.1, and 1.2 when λ ≤ 80 , 80 < λ ≤ 120 , and 120 < λ ≤ 180 , respectively. α (δ ) denotes the influence of the residual deformation coefficient on the reduction coefficient α of the stability bearing capacity, specifically as follows:
5. Calculation method After combining formulas (4)–(6), the residual stability bearing capacity of steel tube members after exposure to high temperature can be calculated as follows:
Ncr, T = αη fy , T φAfy
(9)
α (δ ) = 1.07 − 81.46δ + 4330.64δ 2 − 91658.56δ 3 (0.001 ≤ δ ≤ 0.02) (10)
(8)
Formulas (7)–(10) were used to calculate residual stability bearing capacities of 32 steel tube specimens after high-temperature treatment under axial compression experiment, and the results obtained from formula NcrF are shown in Table 4. The formula calculation values NcrF were compared with experimental results NcrE as shown in Table 6. Differences between the calculated results using formulas and the
Therefore, the key to determine the residual stability bearing capacity relied on the determination of the reduction coefficient α of the stability bearing capacity. In accordance with the previous analysis, a large quantity of finite element analysis and computation models were established for the main factors influencing α , slenderness ratio λ and
482
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 13. Comparison between test results of material property and results of predictor formula.
Fig. 14. Pictures of Q345-60–80 after failure.
483
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 4 Stability bearing capacity results. Member no.
Temp. /°C 20
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60
600
800
1000
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
NcrE
NcrS
NcrF
192 159 134 270 244 209 153 280
188 154 123 259 232 213 159 287
191 159 132 248 220 205 140 278
227 162 141 256 253 197 154 278
206 160 144 260 236 204 161 283
209 151 130 242 234 197 142 278
205 167 95 247 234 203 113 269
192 159 90 240 223 190 105 258
192 153 93 226 211 192 110 248
128 69 38 175 92 111 36 187
125 64 41 175 97 108 33 174
126 62 37 173 92 100 34 168
Note: NcrS is FEM result of stability bearing capacity. NcrF is formula result of stability bearing capacity.
Fig. 15. Stability bearing capacity.
484
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. Load-displacement curves of Q235-60–60 specimens.
485
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. (continued)
486
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 16. (continued)
were overall bending instability. 3) Stability bearing capacities of steel tube members after high-temperature treatment were almost not weakened when the fire temperature was lower than 700 °C. Influenced by the degradation of material mechanical properties and residual deformation, residual stability bearing capacity of steel tube members after high-temperature treatment significantly reduced. Residual stability bearing capacities could be reduced by 35% at maximum when the fire temperature exceeded 700 °C. 4) The highest fire temperature, slenderness ratio, and residual deformation coefficient after high-temperature treatment were the main influential factors of residual bearing capacities of steel tube members after exposure to high temperature. 5) After the introduction of material yield strength and stability reduction coefficients after high-temperature treatment, calculated formulas of residual stability bearing capacities of steel tube members after exposure to high temperature were proposed. Calculated results using the formulas accorded well with experimental results.
experimental results were within 10%. Calculated results were smaller to experimental results, which certified that the formulas proposed in this paper could conservatively calculate residual stability bearing capacities of steel tube members after exposure to high temperature. 6. Conclusions 1) After different high-temperature treatments, residual deformations of different degrees happened to steel tube specimens. The higher the temperature and the greater the slenderness ratio, the greater the generated residual deformation. When the fire temperature was lower than 800 °C, the residual deformation value was approximately 1/200 of the length of the steel tube specimen. However, the residual deformation value could reach 1/25 of the length of the specimen when the fire temperature reached 1000 °C. 2) The failure mode of axial compressed steel tube members after hightemperature treatment was the same as that of steel tube members not experiencing high-temperature treatment. Both failure modes
487
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 17. Load-strain curves of Q235-60–60 specimens.
Table 5 Mesh sensitive test results. Element size / m Result / kN
0.01 292
0.015 289
0.02 287
0.025 280
0.03 277
Fig. 18. Finite element model of steel tube.
Table 6 Parameters adopted in the numerical model. Parameters
Values
Steel density Constitutive relation Elasticity modulus Yield strength Poisson's ratio Element Element size
7800 kg/m3 Ideal elastoplastic model According to Table 3. According to Table 3. 0.3 S4R 0.02 m × 0.02 m
Fig. 19. Reference point.
488
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 7 Comparison of results of stability bearing capacities. Group
Treatment temperature /°C 20
Q235–60–60 Q235–60–80 Q235–60–100 Q235–89–60 Q345–60–60 Q345–60–80 Q345–60–100 Q345–89–60 Average Variance
600
800
1000
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
NcrS NcrE
NcrF NcrE
0.98 0.97 0.92 0.96 0.95 1.02 1.04 1.02 0.98 0.0017
0.95 0.96 0.94 0.91 0.93 0.99 0.93 0.99 0.95 0.0008
0.91 0.99 1.02 1.02 0.93 1.04 1.05 1.02 1.00 0.0026
0.91 0.98 0.92 0.99 0.92 0.99 0.91 1.00 0.95 0.0017
0.94 0.95 0.95 0.97 0.95 0.94 0.93 0.96 0.95 0.0002
0.94 0.96 0.98 0.94 0.91 0.90 0.91 0.92 0.93 0.0008
0.98 0.93 1.08 1.00 1.05 0.97 0.92 0.93 0.98 0.0034
0.91 0.91 1.00 0.99 0.99 0.90 1.00 0.91 0.95 0.0022
Fig. 20. Comparison between finite element and experimental results of load-displacement curves of Q235-60–60 specimens.
Fig. 21. Comparison between finite element and experimental results of load-displacement curves of Q235-60–80 specimens.
489
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 22. Comparison between finite element and experimental results of load-displacement curves of Q235-60–100 specimens.
Fig. 23. Comparison between finite element and experimental results of load-displacement curves of Q235-89–60 specimens.
Fig. 24. Comparison between finite element and experimental results of load-displacement curves of Q345-60–60 specimens.
490
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Fig. 25. Comparison between finite element and experimental results of load-displacement curves of Q345-60–80 specimens.
Fig. 26. Comparison between finite element and experimental results of load-displacement curves of Q345-60–100 specimens.
Fig. 27. Comparison between finite element and experimental results of load-displacement curves of Q345-89–60 specimens.
491
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
Table 8 Parameter values in parametric analysis. Parameter
Value
Fixed value
fy (N/mm2)
235, 345
235
D/t λ
15.9, 17.1, 19.9, 22.2, 28.5 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180 600, 700, 800, 900, 1000
17.1 60 1000
0.001, 0.002, 0.005, 0.01, 0.02
0.001
T ( οC) δ
Fig. 28. Main parameters influencing α .
Acknowledgments
temperatures and after cooling down, Fire Mater. 28 (2–4) (2004) 237–251. [3] F. Ding, Z. Yu, H. Wen, Experimental research on mechanical properties of Q235 steel after high temperature treatment], J. Build. Mater. 02 (2006) 245–249. [4] J. Chen, B. Young, Experimental investigation of cold-formed steel material at elevated temperatures, Thin-Walled Struct. 45 (1) (2007) 96–110. [5] J.M. Atienza, M. Elices, Behavior of prestressing steels after a simulated fire: fireinduced damages, Constr. Build. Mater. 23 (8) (2009) 2932–2940. [6] N.D. Kankanamge, M. Mahendran, Mechanical properties of cold-formed steels at elevated temperatures, Thin-Walled Struct. 49 (1) (2011) 26–44. [7] S. Gunalan, M. Mahendran, Experimental investigation of post-fire mechanical properties of cold-formed steels, Thin-Walled Struct. 84 (2014) 241–254. [8] F. Mccann, L. Gardner, S. Kirk, Elevated temperature material properties of coldformed steel hollow sections, Thin-Walled Struct. 90 (2015) 84–94. [9] 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
This study was financially supported by the National Natural Science Foundation of China (No. 51678404) and the Fok Ying Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151072). References [1] J. Outinen, J. Kesti, P. Mäkeläinen, Fire design model for structural steel S355 based upon transient state tensile test results, J. Constr. Steel Res. 42 (3) (1997) 161–169. [2] J. Outinen, P. Makelainen, Mechanical properties of structural steel at elevated
492
Thin-Walled Structures 132 (2018) 475–493
R. Ma et al.
[25] S. Fan, L. Zhang, W. Sun, et al., Numerical investigation on fire resistance of stainless steel columns with square hollow section under axial compression, ThinWalled Struct. 98 (2016) 185–195 (Part A). [26] W. Wang, T. Liu, Experimental and numerical study on post-fire behavior of highstrength Q460 steel columns[J], Adv. Struct. Eng. 19 (12) (2016) 1873–1888. [27] Y. Ding, M. Wang, Z.X. Li, et al., Damage evaluation of the steel tubular column subjected to explosion and post-explosion fire condition[J], Eng. Struct. 55 (2013) 44–55. [28] Y. Ding, Y. Chen, Y. Shi, Damage evaluation of a restrained steel column subjected to indoor blast and fire[J], Zhendong yu Chongji/J. Vib. Shock. 36 (5) (2017) 79–86. [29] J. Lu, H. Liu, Z. Chen, Behavior of welded hollow spherical joints after exposure to ISO-834 standard fire, J. Constr. Steel Res. 140 (Supplement C) (2018) 108–124. [30] H. Liu, J. Lu, Z. Chen, Residual behavior of welded hollow spherical joints after exposure to elevated temperatures, J. Constr. Steel Res. 137 (2017) 102–118. [31] 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. [32] L.B. Qlu, S.D. Xue, M. Feng, Fire performance of space grid structures. International Association for Shell and Spatial Structures, 2009. [33] X. Wang, H. Sun, Y. Du, et al., Experimental research on fire response and post-fire performance of prestressed steel truss structures, J. Build. Struct. 08 (2013) 46–55. [34] W. Guangyong, W. Xinggiang, L. Guangwei, Fire and post-fire performance of space grid structures, Appl. Mech. Mater. 238 (2012) 621–624. [35] J. Cui, X. Guo, L. Yin, Calculation method based on equivalent sandwich plate method for grid structures in conditions of evaluated temperature and post fire, Spat. Struct. 02 (2016) 37–43. [36] Y. Yin, T. Yuan, Z. Chen, et al., Numer. Study Behav. a Lattice Shell Struct. fire Damage Estim. 08 (2010) 51–56. [37] Z. Liu, Y. Liu, Y. Zhou, et al., Analysis and evaluation of safety of a lattice truss structure after fire accident, Steel Constr. 07 (2007) 89–91. [38] GB/T 228.1-2010, Metallic materials-tensile testing at ambient temperature, Standards Press of China, Beijing, 2002. [39] GB50017-2017, Code for design of steel structure, Standards Press of China, Beijing, 2017. [40] JGJ7-2010, Technical Specification for Frame Structures, Ministry of Construction of the People’s Republic of China. Beijing. (In Chinese), 2010.
(2016) 291–310. [10] S. Kesawan, M. Mahendran, Post-fire mechanical properties of cold-formed steel hollow sections, Constr. Build. Mater. 161 (2018) 26–36. [11] 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. [12] 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. [13] X. Qiang, F.S.K. Bijlaard, H. Kolstein, et al., Experimental study on high strength structural steel S460 in fire and after cooling down, IES J. Part A: Civil. Struct. Eng. 6 (2) (2013) 104–111. [14] W.Y. Wang, G.Q. Li, Y. Ge, Residual stress study on welded section of high strength Q460 steel after fire exposure[J]. advanced Steel, Construction 11 (2) (2015) 150–164. [15] W. Wang, T. Liu, J. Liu, Experimental study on post-fire mechanical properties of high strength Q460 steel, J. Constr. Steel Res. 114 (2015) 100–109. [16] W. Wang, T. Liu, Study on mechanical properties of high strength Q460 steel after cooling from high temperature, Jianzhu Cailiao Xuebao/J. Build. Mater. 19 (1) (2016) 171–176. [17] X. Qiang, N. Wu, X. Jiang, et al., Experimental study on post-fire mechanical properties of very high strength steel S960, Tongji Daxue Xuebao/J. Tongji Univ. 44 (7) (2016) 1076–1083. [18] G.Q. Li, H. Lyu, C. Zhang, Post-fire mechanical properties of high strength Q690 structural steel, J. Constr. Steel Res. 132 (2017) 108–116. [19] C. Siwei, J. Shaokun, G. Houzuo, et al., Mechanical and ductile fracture performances of high strength structural steel Q690 after a fire: experimental investigation, Procedia Eng. 210 (2017) 496–503. [20] F. Azhari, A. Heidarpour, X. Zhao, et al., Post-fire mechanical response of ultra-high strength (Grade 1200) steel under high temperatures: linking thermal stability and microstructure, Thin-Walled Struct. 119 (2017) 114–125. [21] Y. Huang, B. Young, Post-fire behaviour of ferritic stainless steel material, Constr. Build. Mater. 157 (2017) 654–667. [22] X. Gao, X. Zhang, H. Liu, et al., Residual mechanical properties of stainless steels S30408 and S31608 after fire exposure, Constr. Build. Mater. 165 (2018) 82–92. [23] Liu Tianzi, Study on Post-fire Mechanical Behavior of High Strength Q460 Steel Columns[D]. Chongqing University, 2015. [24] Ge Yong, Study on Fire Resistance of Restrained High Strength Q460 Steel Column [D]. Chongqing University, 2012.
493