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Experimental investigation and parametric analysis on overall buckling behavior of large-section aluminum alloy columns under axial compression
Thin-Walled Structures 122 (2018) 585–596
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Full length article
Experimental investigation and parametric analysis on overall buckling behavior of large-section aluminum alloy columns under axial compression
MARK
⁎
Z.X. Wanga, , Y.Q. Wanga, Jeong Sojeonga, Y.W. Ouyangb a b
Department of Civil Engineering, Tsinghua University, Beijing 100084, PR China Shanghai Tongzheng Aluminum Engineering Co., Ltd., Shanghai 200030, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Aluminum alloy Large-section Experimental investigation Parametric analysis Finite element analysis
Experimental investigation was conducted on large-section extruded aluminum alloy columns of I-section and rectangular hollow section (RHS). Altogether seven columns with different slenderness ratios were comprised. The failure modes and stability resistance as well as load-displacement responses were identified. It was found that all tested specimens failed in flexural buckling. An extensive parametric analysis on 180 specimens was carried out with general FEA software ANSYS to evaluate the reliability level of the current design specifications including American aluminum design manual, Eurocode 9 and Chinese code GB 50429. The design stability resistance advised by Eurocode 9 and Chinese code GB 50429 is conservative, while that of American aluminum design manual slightly overestimates the practical stability resistance. Based on the parametric analysis results, a new design method was proposed to improve the design accuracy.
1. Introduction Aluminum alloy members are increasingly applied in constructions since 1950s all over the world because of its good corrosion resistance, light weight, high strength and ease of production [1–3]. Combined with frequently applied large slenderness ratio and its lower Young's modulus (about 70,000 MPa), the buckling behavior usually occurs on aluminum alloy columns. The research on overall buckling behavior of aluminum alloy columns dates back to the middle of the last century. Based on a series of experimental and numerical investigations [4–7], America Aluminum Association promulgated their first edition of the Specification for Aluminum Structures in 1967. European Convention for Constructional Steelwork (ECCS) also proposed their first aluminum alloy design code [8] in 1978 including overall stability design criteria. Since then the overall buckling behavior of aluminum alloy columns has attracted a large number of researchers. Over the past few years, the overall buckling behavior of aluminum alloy columns with different section shapes, including circular hollow sections [9,10], H-sections [11,12], square and rectangular hollow sections [11,13,14], angle sections [15], and irregular shaped cross sections [16], has been intensively experimentally investigated. However, almost all the above researches focused on small-section (section height ≤ 200 mm) aluminum alloy members. And the overall stability design criteria in current design specifications including
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American aluminum design manual [17], Eurocode 9 [18], Australian/ New Zealand Standard [19] and Chinese standards GB50429-2007 [20] are also mainly drawn from investigation on small-section members. The reasons of the extensive study on small-section aluminum alloy members are: (i) large-section members were not necessarily used in practical engineering in the past; (ii) the development of large-section aluminum alloy members was limited by the immature extrusion technology. However, the situation is different right now in that the increasing demand in engineering and the improvement of the extrusion technology has made the large-section aluminum alloy members more widely used. For instance, a large number of 550 mm-sectionheight large-section aluminum alloy members have been used in reticulated shell of Usnisa Palace in Nanjing, China (Fig. 1). Therefore, the lack of experimental work and relevant study on large-section members has been a concern, which is the main focus of the paper. First, experimental investigation on overall buckling behavior of large-section extruded aluminum alloy columns including I-sections and rectangular hollow sections (RHS) was conducted in the paper. Then, the test results and corresponding numerical results were compared with the current design specifications which are American aluminum design manual [17], Eurocode 9 [18] and Chinese code GB 50429 [20]. At last, a more rational design procedure was proposed for large-section aluminum alloy columns failed by overall buckling under axial compression.
Corresponding author. E-mail address: [email protected] (Z.X. Wang).
http://dx.doi.org/10.1016/j.tws.2017.11.003 Received 16 June 2017; Received in revised form 22 October 2017; Accepted 2 November 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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Nomenclature A Aeff B E0 f0.2 fu H iy k L L0 NAA NEC9 NFEA NGB
Nproposed NPA Nu n tf tw ΔV, Δv α εu λ λ λ0 λ0 λn λy θyield ρc
area of cross-section effective area of cross-section overall width of cross-section initial Young's modulus nominal yield stress (0.2% proof stress) ultimate stress overall depth of cross-section inertia radius about y axis stiffness of the rotation springs length of specimen effective length of specimen predicted stability resistance by American Aluminum design manual predicted stability resistance by EC9 numerical value of stability resistance by FEA predicted stability resistance by GB 50429
2. Experimental investigation
predicted stability resistance by proposed design method stability resistance of the parametric analysis stability resistance in the tests exponent in Ramberg-Osgood expression thickness of flange thickness of web overall geometric imperfection imperfection factor ultimate strain at tension failure Slenderness ratio nondimensional slenderness ratio defined in GB 50429 effective flexural slenderness about minor axis limit of horizontal plateau nondimensional slenderness ratio defined in EC9 slenderness ratio about minor axis yield rotation angle of rotation springs local buckling reduction factor
longitudinal direction. There are 12 tension coupons, which is divided into four groups with three identical coupons in each. The tests were conducted on hydraulic universal testing machine in accordance with ASTM E8M-97 standard [21] and GB/T 228.1 [22]. The deformation of the coupons was measured by both strain gauges and extensometer. The coupons tension almost did not result in necking. There was a very sudden failure process with loud sound. The average measured material properties are shown in Table 2, where E0 is the initial Young's modulus, f0.2 is the nominal yield stress (0.2% proof stress), fu is the ultimate stress, n is the exponent in Ramberg-Osgood expression [23] and εu is the ultimate strain at the failure of the tension coupons. The full stress-strain curves of the aluminum alloy are shown in Fig. 4. As shown in Fig. 4, there is a difference between the material properties of I-section columns and RHS columns. The strength of RHS columns is about 20% higher than the strength of I-section columns probably owing to the different extrusion process. However, the material properties of flange and web from same section are nearly the same.
2.1. Test specimens Tests were conducted on 7 large-section aluminum alloy columns including 4 I-section columns and 3 RHS columns, with all the specimens extruded and fabricated by 6061-T6 aluminum alloy. The section height of all the columns is 550 mm which is larger than that in any other existing research. The dimensions of each specimen are shown in Table 1 using the symbols defined in Fig. 2. In Table 1, L is the measured length of the column and A is the area of the cross-section. λy refers to the slenderness ratio about the minor axis ranging from 58.37 to 116.74 for Isection columns and 28.96–48.23 for RHS columns. The specimens were labeled according to the section shape, column length and material type. For example, the label “R-L3510-T6” defines the specimen as follows: the first letter R indicates that the section shape is RHS, while the L3510 indicates the measured length of 3510 mm of the specimen, and the last term T6 indicates that the material of the column is 6061T6. Both ends of the specimens were milled flat by finishing machine to make a uniform distribution of loads.
2.3. Initial geometric imperfection The initial geometric imperfection impinges on the stability resistance of the metallic structures and therefore was measured before testing for all the columns. The imperfection was measured with the combination of optical theodolite and vernier caliper, and this measuring method was successfully applied in steel columns [24,25]. The schematic diagram of the initial geometric imperfection measurement is shown in Fig. 5. The overall geometric imperfection is actually the deviation of the section centroid from the axis connecting the centroid of two end sections, i.e. Δv1, Δv2 and Δv3 in Fig. 5. The measurement was conducted on two ends and the quarter points about both major axis and minor axis. The maximum value of Δv1, Δv2 and Δv3 was taken as the initial geometric imperfection ΔV (shown in Table 3), which would be applied in further numerical investigation. It was found that the ΔV/L of all the columns in both axes are no more than 0.4%, indicating that the extrusion forming could make a smaller initial geometric imperfection.
2.2. Material properties Prior to the loading tests, tensile coupon tests were conducted to determine the material properties of the aluminum alloy. The dimensions of the tension coupons were detailed in Fig. 3. The tension coupons were cut from the web and flange of the specimens along the
2.4. Test configuration All of the columns were loaded by a 12,000 kN servo-control rig between pinned-ended bearings. The test configuration is shown in Fig. 6. Two pole hinges were attached to the testing machine to supply hinged boundary condition which ensured the flexible rotation of the end sections. The distance between each column end and the rotation
Fig. 1. Usnisa Palace on Niushou mountain in Nanjing, China.
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Table 1 Dimensions of specimens. Specimen
H (mm)
B (mm)
tw (mm)
tf (mm)
L (mm)
A (mm2)
λy
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 R-L3510-T6 R-L4675-T6 R-L5845-T6
550.0 550.0 550.0 550.0 550.0 550.0 550.0
220.0 220.0 220.0 220.0 290.0 290.0 290.0
11.0 11.0 11.0 11.0 10.5 10.5 10.5
14.0 14.0 14.0 14.0 12.0 12.0 12.0
2670.0 3560.0 4450.0 5340.0 3510.0 4675.0 5845.0
11,902.0 11,902.0 11,902.0 11,902.0 18,006.0 18,006.0 18,006.0
58.37 77.83 97.28 116.74 28.96 38.57 48.23
Fig. 2. Definition of symbols. Fig. 4. Measured stress-strain curves.
Fig. 5. Imperfection measurement.
Table 3 The value of initial geometric imperfection.
Fig. 3. Dimensions of the tension coupons (mm).
Specimen Table 2 Material properties. Section shape
Location
E0 (MPa)
f0.2 (MPa)
fu (MPa)
n
εu (%)
I-section
Flange (group1) Web (group2) Flange (group3) Web (group4)
73,173.12
240.11
279.96
24.01
13.55
72,237.13
237.73
278.18
23.77
12.32
75,739.76
302.38
334.03
30.24
9.68
72,266.75
304.54
338.46
30.45
9.74
RHS
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 R-L3510-T6 R-L4675-T6 R-L5845-T6
About minor axis
About major axis
ΔV (mm)
L (mm)
ΔV/L (%)
ΔV (mm)
L (mm)
ΔV/L (%)
0.49 0.55 0.72 0.56 1.01 1.32 0.39
2670 3560 4450 5340 3510 4675 5845
0.19 0.16 0.16 0.11 0.29 0.28 0.07
0.90 0.52 0.66 0.45 1.02 0.57 0.31
2670 3560 4450 5340 3510 4675 5845
0.34 0.15 0.15 0.08 0.29 0.12 0.05
1–DG B-4 were installed at end sections to measure the rotation of the end sections; DG C-1 and DG C-2 were installed at the loading end to measure the end shortening, although DG B-3 and DG B-4 have the same function ( Fig. 7). Strain gauges were attached at end sections, quarter-length sections and mid-span section to measure the longitudinal strains, as shown in Fig. 8. The deformation and stress are usually much larger at mid-span section for overall buckling columns. Therefore, there are more strain gauges attached at this section.
center of the pole hinge is 165 mm which should be added to the effective length of the columns in the theoretical and numerical analysis. Geometric centering method was adopted to make the load cross the section centroid of the columns. Prior to the testing, pre-loading was conducted to ensure the full contact of the column and end plates. In the testing process, the load, deformation and strain were collected by IMP Data Acquisition System continuously. In the test, 7 LVDTs (linearly-varying displacement transducers) were installed to measure the in-plane displacements and out-of-plane displacements. The layout of the LVDTs for I-section columns and RHS columns was the same. DG A-1 was installed at the web of mid-span section to measure the out-of-plane displacement (Fig. 6(a)); DG B-
3. Test results and analysis In the loading process, the end plates rotated obviously and all of the columns failed in flexural buckling. The typical failure modes of the columns are shown in Fig. 9. Slight local buckling was observed at mid587
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initial stiffness decreases. The load-lateral displacement (at mid-span section) curves are shown in Fig. 12. It is noted that there is nearly no lateral displacement for short I-section columns I-L2670-T6 and IL3560-T6 until overall buckling failure, indicating inflexible rotation of the pole hinges due to the friction. When buckling failure occurred, because of the instantaneous release of frictional energy, the failure process was too sudden, leading to no data measured for the descending branch. 4. Finite element analysis In order to make up the limitation of the amount of the specimens in the tests, finite element (FE) models were built to carry out an extensive parametric analysis. After verification by the corresponding test results, the FE models will provide basis for the design method and exact prediction of the buckling resistance of the large-section aluminum alloy columns. 4.1. Finite element models
Fig. 6. Test configuration.
Based on FE software ANSYS, three-dimensional FE models of 4 Isection columns and 3 RHS columns were built related to the tested specimens, considering material nonlinearity, geometric nonlinearity and initial geometric imperfection. The dimensions of the specimens in FE models are identical to that of tested specimens which are shown in Table 1. (1) Element and material: Shell element SHELL 181 was adopted to simulate the component plates. SHELL 181 is suitable for the analysis of moderately thick and thick shell structures, involving shear deformation. The mesh size of the element is about 1/20 of the section height, which is precise enough according to sensitivity analysis of mesh size. Material properties applied in the FE model were identical to the corresponding tests, as shown in Fig. 13 described by RambergOsgood expression [23] (Eq. (1)). n
ε=
σ σ + 0.002 ⎛⎜ ⎞⎟ E0 ⎝ f0.2 ⎠
(1)
(2) Boundary and load condition: In the corresponding tests, pole hinges were installed to supply pined-ended boundary condition. However, the hinges did not rotate flexibly in the loading process of I-section columns according to Fig. 12(a). In order to make an accurate simulation of the tests, rotation springs were attached to the ends of I-section columns to simulate the pole hinges with friction, as shown in Fig. 14. According to the corresponding tests, the moment-rotation curve of the rotation springs was defined in Fig. 15. The parameters θyield (yield rotation angle) and k (stiffness of the rotation) of the bilinear rotation springs applied in the FE model were calibrated according to the corresponding tests. For RHS columns, the pole hinges rotated flexibly and continuously about the minor axis. Therefore, perfect pined-ended boundary condition was applied in the FE models of RHS columns. Axial load was applied to the loading end plate of the columns with load eccentricity which determined by the test results. The thickness of end plates is 20 mm for both I-section and RHS columns. The Young's modulus of the end plate is 1000 times [15] larger than that of aluminum alloy in order to simulate a rigid plate. (3) Initial geometric imperfection: The initial geometric imperfections were included in the FE models by geometric modeling in the form of half-sinusoid with zero value on the column edges [27,28]. The imperfection values were identical to the measured values in corresponding tests, as shown in Table 3.
Fig. 7. Layout of the LVDTs.
span section of RHS columns. All of the columns after failure are shown in Fig. 10. The ultimate strengths of all the specimens are summarized in Table 4. λ0 is the effective flexural slenderness about the minor axis (λ0 = L0/y, L0 = L + 2 × 165 mm), Nu is the experimental ultimate strength, Aeff-ec is the effective area based on EC9 and Aeff-gb is the effective area based on GB 50429. The test results were compared with the design provisions in three current design codes which are also listed in Table 4. According to EC9, the slenderness parameters of all the plate elements of I-section and RHS columns exceed the limit value β3. Therefore, the true section should be replaced by an effective one in the calculating process because of the classification of Class 4 [26]. The design provisions underestimate the ultimate strength of I-section columns mainly owing to the friction of the pole hinges which decreases with the increase of the column length. American aluminum design manual [17] makes an opposite prediction of the failure modes of RHS columns. The 3 RHS columns failed in flexural buckling in the tests, while AA predicts local buckling failure. The comparison with design provisions will be discussed in detail later. The load-axial displacement curves of all the columns are shown in Fig. 11. It was found that with the increase of the column length, the 588
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Fig. 8. Layout of strain gauges.
rotation of end plates even the slight buckling of the plate elements in RHS columns are simulated fairly well. The comparison of the stability resistance between FE models and test results is shown in Table 5. NFEA is the numerical value of stability resistance. As shown, the mean value of NFEA/Nu is 0.99 and 0.97 for Isection columns and RHS columns with the corresponding COV (coefficient of variation) of 0.01 and 0.03, respectively. Fig. 17 shows the comparison of the load-axial displacement curves between FE results and test results. Combined with above three aspects of comparison, it is evident that the FE models can make an accurate simulation of the corresponding tests. In order to further validate the FE models, analysis was carried out on the other tests [11] by the FE models. The comparison of the FE results and test results is shown in Fig. 18. The mean value of NFEA/Nu is 0.916 and 0.947 for I-section columns and RHS columns, respectively. And the COV is 0.036 and 0.080, respectively. Therefore, the FE models are verified to accurately predict the buckling behavior of aluminum alloy columns under axial compression.
Fig. 9. Typical failure modes.
4.2. Verification of the FE models The comparison of the failure modes between FE models and tests is shown in Fig. 16. It is found that, the failure modes in FE models are almost the same with the ones in the tests. The flexure of columns, the
5. Parametric analysis and proposed design method The FE models accurately predicted the buckling behavior including Fig. 10. All the columns after failure.
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Table 4 Experimental ultimate strength and comparisons with current design codes. Specimen
λ0
Nu (kN)
NAA/Nu
Aeff-ec (mm2)
NEC9/Nu
Aeff-gb (mm2)
NGB/Nu
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 Mean COV R-L3510-T6 R-L4675-T6 R-L5845-T6 Mean COV
65.6 85.0 104.5 124.0 – – 31.7 41.3 50.9 – –
2231.8 1598.8 968.2 631.0 – – 3370.5 3167.8 2891.2 – –
0.86 0.74 0.81 0.88 0.82 0.08 1.10 1.17 1.28 1.18 0.08
9063.8 9063.8 9063.8 9063.8 – – 12,566.6 12,566.6 12,566.6 – –
0.61 0.59 0.69 0.78 0.67 0.13 1.01 1.00 0.98 1.00 0.02
9140.0 9140.0 9140.0 9140.0 – – 12,256.9 12,256.9 12,256.9 – –
0.52 0.48 0.55 0.61 0.54 0.10 0.96 0.90 0.82 0.89 0.08
Fig. 11. Load-axial displacement curves.
Fig. 12. Load-lateral displacement curves.
40″ defines the column which has I-shape cross section with 6061-T6 aluminum alloy material, 200 mm width flange, 400 mm height section and slenderness ratio of 40. 1/1000 of the column length was adopted as the overall initial geometric imperfection in the parametric analysis. The material property of 6061-T6 in the parametric analysis is identical to that in this paper, as shown in Table 2. In addition to 6061-T6, the paper added 6063-T5 to the parametric analysis which is also usually applied in the engineering structures. The material property of 6063-T5 is identical to the one in a previous research paper [2] with f0.2 = 170.2 MPa, fu = 215.6 MPa, E0 = 63,682 MPa and n = 17. Mesh size, boundary
stability resistance and failure modes of the aluminum alloy columns both in this paper and in other researches. Therefore, an extensive parametric analysis including 180 specimens was conducted by the FE model. The 180 columns consisted of 20 series with different section shapes (I-section and RHS), different section dimensions and different aluminum alloy materials (6061-T6 and 6063-T5), which are shown in Table 6. The symbols B, H, tf, and tw in Table 6 are defined in Fig. 2. Each series includes 9 specimens with different slenderness ratios (about minor axis) varying from 40 to 120. The columns were labeled according to section shape, material type, flange width (B), section height (H) and slenderness ratio. For example, the label “I-T6-200-400590
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Fig. 13. Constitutive relation applied in FE models.
Fig. 14. Diagram of rotation springs.
Fig. 16. Comparison of the failure modes.
condition and load condition in the parametric analysis are same as the ones in the above FE models. The purpose of the parametric analysis conducted in this section is to validate the accuracy of the design methods in the current design specifications. The results of parametric analysis were compared with predicted results by design codes including Eurocode 9 [18], American aluminum design manual [17] and Chinese standards GB 50429-2007 [20], as shown in Table 7 and Table 8.
Fig. 15. Moment-rotation curve of the springs.
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Table 5 Comparison of the stability resistance between FE models and test results. Specimen
λ0
Nu (kN)
NFEA (kN)
NFEA/Nu
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 Mean COV R-L3510-T6 R-L4675-T6 R-L5845-T6 Mean COV
65.6 85.0 104.5 124.0 – – 31.7 41.3 50.9 – –
2231.8 1598.8 968.2 631.0 – – 3370.5 3167.8 2891.2 – –
2207.5 1575.3 945.5 632.2
0.99 0.99 0.98 1.00 0.99 0.01 0.99 0.93 0.99 0.97 0.03
3333.0 2957.8 2855.2 – –
5.1. Eurocode 9 and GB 50429 Fig. 18. Comparison between FE results and test results by Zhai et al.
Eurocode 9: Design of aluminum structures, or EC9 for short, slightly underestimates the stability resistance of the columns. The average value of NEC9/NPA for all the T6 columns (including I-section and RHS specimens) is 0.90, and for all the T5 columns is 0.81. NPA is the stability resistance of the parametric analysis. EC9 adopts Perrytype curve to design the overall stability resistance, with different imperfection factor α and limit of horizontal plateau λ 0 for T6 and T5 aluminum alloy. The local buckling reduction factor ρc is adopted to reduce the thickness of the element. Effective section area Aeff reduced by ρc is applied in the calculation. The design method in GB 50429 is similar to the method in EC9 except for two differences. The first one is the design value of ρc is more conservative. The second one is the α and λ 0 is different from EC9, as shown in Table 9, leading to a more conservative prediction. The average value of NGB/NPA for all the T6 columns is 0.71, and for all the T5 columns is 0.68. Fig. 19 and Fig. 20 show the comparison between the parametric analysis results and the design codes. Nondimensional slenderness ratio λ n = λ / π [(Aeff / A)⋅(f0.2 / E0)]0.5 , λ = λ / π (f0.2 / E0)0.5 are defined in EC9 and GB 50429, respectively. It is obvious that EC9 makes a more reliable prediction than GB 50429. However, both design codes give a more conservative prediction for strong hardening material (6063-T5), because of its more pronounced strain hardening behavior.
advised in AA of calculating overall stability resistance is based on Euler curve. However, AA ignores the interaction of local buckling and overall buckling, leading the overestimation of the code. And the difference of T6 alloy and T5 alloy in the design provisions is also ignored. Fig. 21 shows the comparison of parametric analysis results and AA. 5.3. Proposed design equation based on EC9 According to the results, the accuracy of design codes doesn’t change obviously with the variation of the section size. Nevertheless, without the parametric analysis of section size, the engineers have less confidence to use large-section aluminum alloy members which is much larger than the member sections in almost all the previous existing research work in design. However, the parametric analysis and the comparison with current codes are meaningful, leading to find out that the current design codes are not reliable enough. Based on EC9, a new design equation was proposed to make a more accurate design method. For the design equations in EC9, the main factors affecting the accuracy are the imperfection factor α and limit of horizontal plateau λ 0 which also vary among different design codes. Proposed imperfection factor and limit of horizontal plateau are derived by regression analysis, as shown in Table 10. Based on the proposed design method, the predicted results were compared with parametric analysis results, with obvious improved accuracy, as shown in Fig. 22. The mean value of Nproposed/NPA for all the T6 alloy members is 0.946 with COV of 0.066, the mean value of Nproposed/NPA for all the T5 alloy members is 0.935 with COV of 0.034.
5.2. American aluminum design manual American aluminum design manual (AA) overestimates the stability resistance of the parametric analysis results. NAA/NPA for all the T6 columns is 1.12, and for all the T5 columns is 1.13. The design method
Fig. 17. Comparison of the load-displacement curves.
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Table 6 Dimensions of the specimens in parametric analysis.
I-section
RHS
Series
B/mm
H/mm
tf/mm
tw/mm
Iy/mm4
I-T6/T5-200-400 I-T6/T5-250-500 I-T6/T5-300-600 I-T6/T5-350-700 I-T6/T5-400-800 R-T6/T5-200-400 R-T6/T5-250-500 R-T6/T5-300-600 R-T6/T5-350-700 R-T6/T5-400-800
200 250 300 350 400 200 250 300 350 400
400 500 600 700 800 400 500 600 700 800
10 10 12 16 25 10 10 12 16 25
10 10 12 16 25 10 10 12 16 25
1.34 2.61 5.41 1.15 2.68 8.19 1.64 3.41 7.11 1.59
× × × × × × × × × ×
A/mm2 107 107 107 108 108 107 108 108 108 109
7800 9800 14,112 21,888 38,750 11,600 14,600 21,024 32,576 57,500
Table 7 Comparison of FE results and predicted results by design codes for I-section columns (6061-T6 and 6063-T5). Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
I-T6-200-400-40 I-T6-200-400-50 I-T6-200-400-60 I-T6-200-400-70 I-T6-200-400-80 I-T6-200-400-90 I-T6-200-400-100 I-T6-200-400-110 I-T6-200-400-120 Mean COV I-T6-250-500-40 I-T6-250-500-50 I-T6-250-500-60 I-T6-250-500-70 I-T6-250-500-80 I-T6-250-500-90 I-T6-250-500-100 I-T6-250-500-110 I-T6-250-500-120 Mean COV I-T6-300-600-40 I-T6-300-600-50 I-T6-300-600-60 I-T6-300-600-70 I-T6-300-600-80 I-T6-300-600-90 I-T6-300-600-100 I-T6-300-600-110 I-T6-300-600-120 Mean COV I-T6-350-700-40 I-T6-350-700-50 I-T6-350-700-60 I-T6-350-700-70 I-T6-350-700-80 I-T6-350-700-90 I-T6-350-700-100 I-T6-350-700-110 I-T6-350-700-120 Mean COV I-T6-400-800-40 I-T6-400-800-50 I-T6-400-800-60 I-T6-400-800-70 I-T6-400-800-80 I-T6-400-800-90 I-T6-400-800-100 I-T6-400-800-110 I-T6-400-800-120 Mean COV
0.81 0.81 0.85 0.89 0.91 0.93 0.94 0.94 0.95 0.89 0.063 0.84 0.82 0.82 0.85 0.88 0.91 0.92 0.93 0.94 0.88 0.054 0.84 0.82 0.82 0.84 0.88 0.90 0.92 0.93 0.94 0.88 0.055 0.82 0.79 0.81 0.86 0.89 0.92 0.93 0.94 0.95 0.88 0.069 0.81 0.82 0.85 0.89 0.92 0.93 0.95 0.95 0.96 0.90 0.065
1.11 1.14 1.24 1.16 1.12 1.09 1.08 1.07 1.06 1.12 0.050 1.25 1.30 1.30 1.17 1.13 1.10 1.08 1.07 1.06 1.16 0.084 1.25 1.30 1.29 1.17 1.12 1.10 1.08 1.07 1.06 1.16 0.083 1.17 1.16 1.22 1.15 1.11 1.09 1.08 1.07 1.06 1.12 0.048 0.98 1.04 1.16 1.11 1.09 1.08 1.07 1.06 1.06 1.07 0.046
0.76 0.71 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.71 0.028 0.77 0.68 0.61 0.59 0.59 0.59 0.59 0.59 0.59 0.62 0.101 0.77 0.68 0.61 0.59 0.59 0.59 0.59 0.59 0.59 0.62 0.101 0.76 0.68 0.64 0.64 0.65 0.65 0.65 0.66 0.66 0.67 0.056 0.79 0.77 0.77 0.79 0.80 0.81 0.82 0.82 0.83 0.80 0.027
I-T5-200-400-40 I-T5-200-400-50 I-T5-200-400-60 I-T5-200-400-70 I-T5-200-400-80 I-T5-200-400-90 I-T5-200-400-100 I-T5-200-400-110 I-T5-200-400-120 Mean COV I-T5-250-500-40 I-T5-250-500-50 I-T5-250-500-60 I-T5-250-500-70 I-T5-250-500-80 I-T5-250-500-90 I-T5-250-500-100 I-T5-250-500-110 I-T5-250-500-120 Mean COV I-T5-300-600-40 I-T5-300-600-50 I-T5-300-600-60 I-T5-300-600-70 I-T5-300-600-80 I-T5-300-600-90 I-T5-300-600-100 I-T5-300-600-110 I-T5-300-600-120 Mean COV I-T5-350-700-40 I-T5-350-700-50 I-T5-350-700-60 I-T5-350-700-70 I-T5-350-700-80 I-T5-350-700-90 I-T5-350-700-100 I-T5-350-700-110 I-T5-350-700-120 Mean COV I-T5-400-800-40 I-T5-400-800-50 I-T5-400-800-60 I-T5-400-800-70 I-T5-400-800-80 I-T5-400-800-90 I-T5-400-800-100 I-T5-400-800-110 I-T5-400-800-120 Mean COV
0.76 0.77 0.78 0.80 0.83 0.85 0.87 0.88 0.90 0.83 0.062 0.76 0.72 0.71 0.75 0.78 0.81 0.84 0.86 0.87 0.79 0.075 0.76 0.72 0.71 0.74 0.78 0.81 0.83 0.86 0.87 0.79 0.075 0.73 0.73 0.75 0.77 0.80 0.83 0.85 0.87 0.89 0.80 0.076 0.82 0.82 0.82 0.83 0.85 0.87 0.88 0.90 0.91 0.86 0.042
1.03 1.07 1.13 1.23 1.25 1.19 1.15 1.13 1.11 1.14 0.062 1.12 1.13 1.15 1.25 1.26 1.20 1.16 1.13 1.12 1.17 0.047 1.13 1.14 1.15 1.24 1.26 1.19 1.16 1.13 1.11 1.17 0.044 1.04 1.06 1.13 1.23 1.24 1.19 1.15 1.13 1.11 1.14 0.060 0.99 1.03 1.09 1.20 1.22 1.17 1.14 1.12 1.11 1.12 0.067
0.72 0.71 0.70 0.69 0.69 0.70 0.71 0.71 0.72 0.71 0.016 0.70 0.64 0.60 0.59 0.59 0.60 0.60 0.61 0.61 0.62 0.057 0.70 0.64 0.60 0.59 0.59 0.60 0.60 0.61 0.61 0.62 0.057 0.69 0.66 0.65 0.64 0.65 0.65 0.66 0.67 0.67 0.66 0.023 0.81 0.79 0.77 0.77 0.78 0.79 0.81 0.82 0.83 0.80 0.027
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Table 8 Comparison of FE results and predicted results by design codes for RHS1 columns (6061-T6 and 6063-T5). Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
R-T6-200-400-40 R-T6-200-400-50 R-T6-200-400-60 R-T6-200-400-70 R-T6-200-400-80 R-T6-200-400-90 R-T6-200-400-100 R-T6-200-400-110 R-T6-200-400-120 Mean COV R-T6-250-500-40 R-T6-250-500-50 R-T6-250-500-60 R-T6-250-500-70 R-T6-250-500-80 R-T6-250-500-90 R-T6-250-500-100 R-T6-250-500-110 R-T6-250-500-120 Mean COV R-T6-300-600-40 R-T6-300-600-50 R-T6-300-600-60 R-T6-300-600-70 R-T6-300-600-80 R-T6-300-600-90 R-T6-300-600-100 R-T6-300-600-110 R-T6-300-600-120 Mean COV R-T6-350-700-40 R-T6-350-700-50 R-T6-350-700-60 R-T6-350-700-70 R-T6-350-700-80 R-T6-350-700-90 R-T6-350-700-100 R-T6-350-700-110 R-T6-350-700-120 Mean COV R-T6-400-800-40 R-T6-400-800-50 R-T6-400-800-60 R-T6-400-800-70 R-T6-400-800-80 R-T6-400-800-90 R-T6-400-800-100 R-T6-400-800-110 R-T6-400-800-120 Mean COV
0.83 0.83 0.83 0.86 0.85 0.87 0.87 0.94 0.83 0.86 0.042 1.00 0.97 0.94 0.94 0.92 0.92 0.92 0.94 0.94 0.94 0.028 1.00 1.01 0.99 0.94 0.97 0.86 0.97 0.99 1.00 0.97 0.048 0.96 0.93 0.90 0.90 0.91 0.92 0.94 0.95 0.95 0.93 0.024 0.81 0.79 0.80 0.83 0.85 0.85 0.84 0.82 0.79 0.82 0.029
1.02 1.13 1.17 1.10 1.04 1.02 0.99 1.05 0.92 1.05 0.072 1.23 1.33 1.42 1.26 1.15 1.10 1.07 1.07 1.06 1.19 0.109 1.22 1.38 1.50 1.26 1.22 1.02 1.13 1.12 1.12 1.22 0.121 1.17 1.28 1.30 1.17 1.11 1.09 1.07 1.07 1.06 1.15 0.079 0.99 1.00 1.09 1.04 1.01 0.99 0.95 0.91 0.87 0.98 0.067
0.78 0.74 0.70 0.70 0.68 0.69 0.68 0.73 0.65 0.71 0.055 0.92 0.82 0.73 0.70 0.66 0.64 0.64 0.65 0.64 0.71 0.138 0.92 0.86 0.77 0.69 0.69 0.60 0.67 0.68 0.68 0.73 0.140 0.90 0.82 0.74 0.71 0.70 0.70 0.71 0.71 0.71 0.74 0.093 0.79 0.73 0.72 0.73 0.74 0.74 0.72 0.70 0.68 0.73 0.042
R-T5-200-400-40 R-T5-200-400-50 R-T5-200-400-60 R-T5-200-400-70 R-T5-200-400-80 R-T5-200-400-90 R-T5-200-400-100 R-T5-200-400-110 R-T5-200-400-120 Mean COV R-T5-250-500-40 R-T5-250-500-50 R-T5-250-500-60 R-T5-250-500-70 R-T5-250-500-80 R-T5-250-500-90 R-T5-250-500-100 R-T5-250-500-110 R-T5-250-500-120 Mean COV R-T5-300-600-40 R-T5-300-600-50 R-T5-300-600-60 R-T5-300-600-70 R-T5-300-600-80 R-T5-300-600-90 R-T5-300-600-100 R-T5-300-600-110 R-T5-300-600-120 Mean COV R-T5-350-700-40 R-T5-350-700-50 R-T5-350-700-60 R-T5-350-700-70 R-T5-350-700-80 R-T5-350-700-90 R-T5-350-700-100 R-T5-350-700-110 R-T5-350-700-120 Mean COV R-T5-400-800-40 R-T5-400-800-50 R-T5-400-800-60 R-T5-400-800-70 R-T5-400-800-80 R-T5-400-800-90 R-T5-400-800-100 R-T5-400-800-110 R-T5-400-800-120 Mean COV
0.78 0.77 0.76 0.77 0.79 0.81 0.83 0.85 0.87 0.80 0.049 0.80 0.82 0.79 0.77 0.78 0.79 0.81 0.84 0.85 0.81 0.033 0.85 0.81 0.78 0.77 0.78 0.80 0.82 0.84 0.86 0.81 0.040 0.80 0.77 0.75 0.75 0.77 0.80 0.83 0.85 0.86 0.80 0.052 0.84 0.82 0.79 0.79 0.81 0.83 0.85 0.86 0.88 0.83 0.037
1.04 1.06 1.09 1.17 1.18 1.13 1.10 1.09 1.07 1.10 0.043 1.03 1.16 1.21 1.24 1.23 1.13 1.11 1.09 1.08 1.14 0.064 1.10 1.15 1.20 1.23 1.22 1.15 1.12 1.10 1.08 1.15 0.048 1.06 1.09 1.10 1.17 1.18 1.13 1.10 1.09 1.07 1.11 0.038 1.04 1.05 1.08 1.16 1.17 1.13 1.10 1.08 1.07 1.10 0.042
0.74 0.71 0.68 0.66 0.66 0.67 0.68 0.69 0.70 0.69 0.038 0.73 0.72 0.66 0.62 0.61 0.59 0.60 0.61 0.62 0.64 0.081 0.77 0.71 0.66 0.61 0.60 0.60 0.61 0.62 0.62 0.64 0.092 0.75 0.70 0.66 0.64 0.64 0.65 0.66 0.67 0.68 0.67 0.052 0.81 0.77 0.74 0.72 0.72 0.74 0.75 0.76 0.77 0.75 0.038
displacement response were identified. By general FEA software ANSYS, the simulation of the test process was conducted and verified. An extensive parametric analysis including 180 specimens was carried out based on the verified FE model to evaluate the reliability level of the current design specifications including Eurocode 9, American aluminum design manual and GB 50429-2007. Based on the parametric analysis results, the paper proposed a new design method. According to the investigation, the conclusions can be drawn as follows:
Table 9 Different value of α and λ 0 in EC9 and GB 50429. Material type
Class A (T6) Class B (T5)
Imperfection factor α
Horizontal plateau λ 0
EC9
GB 50429
EC9
GB 50429
0.20 0.32
0.20 0.35
0.10 0.00
0.15 0.10
(1) All of the large-section aluminum alloy columns failed in flexural buckling in the test. The three design specifications generally underestimate the stability resistance of the columns. (2) Three-dimensional FE models were built by ANSYS based on corresponding tests incorporating material nonlinearity and initial geometric imperfection. Rotation springs were attached to the ends
6. Conclusion The paper carried out experimental investigation on 7 large-section aluminum alloy columns including 4 I-section columns and 3 RHS columns. The failure modes and stability resistance as well as load594
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Fig. 19. Comparison of parametric analysis results and EC9.
Fig. 20. Comparison of parametric analysis results and GB 50429.
of I-section columns to simulate the pole hinges with friction. The FE models made accurate simulation of failure modes and stability resistance as well as load-displacement response of the specimens related to tested specimens in this paper and other research work. (3) An extensive parametric analysis including 180 specimens with 20 series classified with different section shapes, different section dimensions and different aluminum alloy materials was conducted by the FE models. The accuracy of design codes doesn’t change obviously with the variation of the section size. Therefore, if a reliable design method is suitable for small-section and thin-walled aluminum alloy columns, it is also suitable for the large-section aluminum alloy columns. This conclusion is meaningful for engineers who can use the large-section aluminum alloy columns in “superstructures” without worry about the applicability of the design method. (4) The results of parametric analysis were compared with predicted results by design codes including BS EN 1999-1-1: 2007 (EC9), American aluminum design manual (AA) and GB 50429. EC9 and GB 50429 adopt Perry-type curve to design the overall stability resistance and apply effective section area to consider local buckling reduction. Because of different imperfection factor and limit of horizontal plateau in GB 50429 from EC9, GB 50429 gives a more conservative prediction. The design method in AA is based on Euler curve ignoring the interaction of local buckling and overall buckling, resulting in an overestimated prediction.
Fig. 21. Comparison of parametric analysis results and AA.
Table 10 Proposed value of α and λ 0 and comparison with parametric results. Material type
Class A (T6) Class B (T5)
Imperfection factor α
Horizontal
Mean value of Nproposed/NPA
COV
plateau λ 0
0.160 0.240
0.280 0.400
0.946 0.935
0.066 0.034
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Fig. 22. Comparison of parametric analysis results and proposed curves. 1978. [9] J.H. Zhu, B. Young, Experimental investigation of aluminum alloy circular hollow section columns, Eng. Struct. 28 (2) (2006) 207–215. [10] Y.J. Wang, F. Fan, S.B. Lin, Experimental investigation on the stability of aluminum alloy 6082 circular tubes in axial compression, Thin-Walled Struct. 89 (2015) 54–66. [11] X.M. Zhai, Y.J. Wang, H. Wu, F. Fan, Research on stability of high strength aluminum alloy columns loaded by axial compressive load, Adv. Mater. Res. 168–170 (2010) 1915–1920. [12] G.O. Adeoti, F. Fan, Y.J. Wang, X.M. Zhai, Stability of 6082-T6 aluminum alloy columns with H-section and rectangular hollow sections, Thin-Walled Struct. 89 (2015) 1–16. [13] J.H. Zhu, B. Young, Tests and design of aluminum alloy compression members, J. Struct. Eng. 132 (7) (2006) 1096–1107. [14] M.N. Su, B. Young, L. Gardner, Testing and design of aluminum alloy cross sections in compression, J. Struct. Eng. 140 (9) (2014) (04014047-1-04014047-11). [15] Y.Q. Wang, Z.X. Wang, X.G. Hu, J.K. Han, H.J. Xing, Experimental study and parametric analysis on the stability behavior of 7A04 high-strength aluminum alloy angle columns under axial compression, Thin-Walled Struct. 108 (2016) 305–320. [16] M. Liu, L. Zhang, P. Wang, Y. Chang, Buckling behaviors of, section aluminum alloy columns under axial compression, Eng. Struct. 95 (2015) 127–137. [17] Aluminum Association (AA), Aluminum Design Manual, AA, Washington, DC., 2010. [18] CEN, Eurocode 9: Design of Aluminum Structures—Part 1-1: General Structural Rules BS EN 1999-1-1, CEN, Brussels, 2007. [19] AS/NZS, Aluminum Structures Part 1: Limit State Design AS/NZS, 1664.1 Standards Australia, Sydney, 1997. [20] MOHURD, Code for design of aluminum structures GB 50429-2007, China Planning Press, Beijing, 2007 (in Chinese). [21] ASTM, Standard Test Methods for Tension Testing of Metallic Materials E8M-97, ASTM, West Conshohocken, 1997. [22] AQSIQ, Metallic Materials-tensile Testing – Part 1: Method of Test at Room Temperatures GB/T228.1, Standards Press of China, Beijing, 2010 (in Chinese). [23] W. Ramberg, W.R. Osgood, Description of Stress-strain Curves by Three Parameters (Technical Note 902), National Advisory Committee for Aeronautics, Washington, DC, 1943. [24] H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Overall buckling behavior of 460 MPa high strength steel columns: experimental investigation and design method, J. Constr. Steel Res. 74 (6) (2012) 140–150. [25] H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Column buckling tests of 420 MPa high strength steel single equal angles, Int. J. Struct. Stab. Dyn. 13 (02) (2013) 1–23. [26] R. Landolfo, F.M. Mazzolani, Different approaches in the design of slender aluminium alloy sections, Thin-Walled Struct. 27 (1) (1997) 85–102. [27] A. Formisano, F.M. Mazzolani, G. Brando, G. De Matteis, Numerical evaluation of the hysteretic performance of pure aluminum shear panels. in: Proceedings of the 5th International Conference on Behavior of Steel Structures in Seismic Areas (STESSA 2006) 211-217, 2006. [28] A. Formisano, G. De Matteis, F.M. Mazzolani, Experimental and numerical researches on aluminum alloy systems for structural applications in civil engineering fields, Key Eng. Mater. 710 (2016) 256–261.
(5) Based on the design methods in EC9, a new design equation was proposed. With proposed imperfection factor α and limit of horizontal plateau λ 0 , the prediction accuracy is substantially improved. The mean value of prediction accuracy (Nproposed/NPA) for all the T6 alloy members is 0.946 with COV of 0.066, while the mean value of prediction accuracy (Nproposed/NPA) for all the T5 alloy members is 0.935 with COV of 0.034. The proposed design method can fairly well describe the stability resistance of aluminum alloy columns of both large-section columns and small columns and will make reference for the investigation of aluminum alloy columns. However, the method still needs to be confirmed by further experimental and numerical research. Acknowledgments The research work described in this paper was supported by National Natural Science Foundation of China (Grant no. 51038006), the Special Research Fund for the Doctoral Program of Higher Education (Grant no. 20110002130002) and Tsinghua Fudaoyuan Research Fund. Thanks are also extended to the Civil Engineering Department, Tsinghua University for the test conditions and equipment provided. References [1] F.M. Mazzolani, Aluminum Alloy Structures, Second edition, Spon Press, London, 1994. [2] Y.Q. Wang, Z.X. Wang, F.X. Yin, L. Yang, Y.J. Shi, J. Yin, Experimental study and finite element analysis on the local buckling behavior of aluminium alloy beams under concentrated loads, Thin-Walled Struct. 105 (2016) 44–56. [3] M. Manganiello, G. De Matteis, R. Landolfo, Inelastic flexural strength of aluminium alloys structures, Eng. Struct. 28 (4) (2006) 593–608. [4] G.S. Gibson, An approximate method for calculating the distortion of welded members, Weld. J. 17 (7) (1938). [5] M. Holt, Tests on build-up columns of structural aluminum alloys, Trans. ASCE 105 (1940) 96–219. [6] R.J. Brungraber, J.W. Clark, Strength of welded aluminum columns, Trans. ASCE 127 (1962) 202–226. [7] J.W. Clark, R.L. Rolf, Design of aluminum tubular members, J. Struct. Div., ASCE ST6 (1964) 259–289. [8] European Convention for Constructional Steelworks (ECCS), European Recommendations for Aluminum Alloy Structures, 1st edition, ECCS, Brussels,
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Full length article
Experimental investigation and parametric analysis on overall buckling behavior of large-section aluminum alloy columns under axial compression
MARK
⁎
Z.X. Wanga, , Y.Q. Wanga, Jeong Sojeonga, Y.W. Ouyangb a b
Department of Civil Engineering, Tsinghua University, Beijing 100084, PR China Shanghai Tongzheng Aluminum Engineering Co., Ltd., Shanghai 200030, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Aluminum alloy Large-section Experimental investigation Parametric analysis Finite element analysis
Experimental investigation was conducted on large-section extruded aluminum alloy columns of I-section and rectangular hollow section (RHS). Altogether seven columns with different slenderness ratios were comprised. The failure modes and stability resistance as well as load-displacement responses were identified. It was found that all tested specimens failed in flexural buckling. An extensive parametric analysis on 180 specimens was carried out with general FEA software ANSYS to evaluate the reliability level of the current design specifications including American aluminum design manual, Eurocode 9 and Chinese code GB 50429. The design stability resistance advised by Eurocode 9 and Chinese code GB 50429 is conservative, while that of American aluminum design manual slightly overestimates the practical stability resistance. Based on the parametric analysis results, a new design method was proposed to improve the design accuracy.
1. Introduction Aluminum alloy members are increasingly applied in constructions since 1950s all over the world because of its good corrosion resistance, light weight, high strength and ease of production [1–3]. Combined with frequently applied large slenderness ratio and its lower Young's modulus (about 70,000 MPa), the buckling behavior usually occurs on aluminum alloy columns. The research on overall buckling behavior of aluminum alloy columns dates back to the middle of the last century. Based on a series of experimental and numerical investigations [4–7], America Aluminum Association promulgated their first edition of the Specification for Aluminum Structures in 1967. European Convention for Constructional Steelwork (ECCS) also proposed their first aluminum alloy design code [8] in 1978 including overall stability design criteria. Since then the overall buckling behavior of aluminum alloy columns has attracted a large number of researchers. Over the past few years, the overall buckling behavior of aluminum alloy columns with different section shapes, including circular hollow sections [9,10], H-sections [11,12], square and rectangular hollow sections [11,13,14], angle sections [15], and irregular shaped cross sections [16], has been intensively experimentally investigated. However, almost all the above researches focused on small-section (section height ≤ 200 mm) aluminum alloy members. And the overall stability design criteria in current design specifications including
⁎
American aluminum design manual [17], Eurocode 9 [18], Australian/ New Zealand Standard [19] and Chinese standards GB50429-2007 [20] are also mainly drawn from investigation on small-section members. The reasons of the extensive study on small-section aluminum alloy members are: (i) large-section members were not necessarily used in practical engineering in the past; (ii) the development of large-section aluminum alloy members was limited by the immature extrusion technology. However, the situation is different right now in that the increasing demand in engineering and the improvement of the extrusion technology has made the large-section aluminum alloy members more widely used. For instance, a large number of 550 mm-sectionheight large-section aluminum alloy members have been used in reticulated shell of Usnisa Palace in Nanjing, China (Fig. 1). Therefore, the lack of experimental work and relevant study on large-section members has been a concern, which is the main focus of the paper. First, experimental investigation on overall buckling behavior of large-section extruded aluminum alloy columns including I-sections and rectangular hollow sections (RHS) was conducted in the paper. Then, the test results and corresponding numerical results were compared with the current design specifications which are American aluminum design manual [17], Eurocode 9 [18] and Chinese code GB 50429 [20]. At last, a more rational design procedure was proposed for large-section aluminum alloy columns failed by overall buckling under axial compression.
Corresponding author. E-mail address: [email protected] (Z.X. Wang).
http://dx.doi.org/10.1016/j.tws.2017.11.003 Received 16 June 2017; Received in revised form 22 October 2017; Accepted 2 November 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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Nomenclature A Aeff B E0 f0.2 fu H iy k L L0 NAA NEC9 NFEA NGB
Nproposed NPA Nu n tf tw ΔV, Δv α εu λ λ λ0 λ0 λn λy θyield ρc
area of cross-section effective area of cross-section overall width of cross-section initial Young's modulus nominal yield stress (0.2% proof stress) ultimate stress overall depth of cross-section inertia radius about y axis stiffness of the rotation springs length of specimen effective length of specimen predicted stability resistance by American Aluminum design manual predicted stability resistance by EC9 numerical value of stability resistance by FEA predicted stability resistance by GB 50429
2. Experimental investigation
predicted stability resistance by proposed design method stability resistance of the parametric analysis stability resistance in the tests exponent in Ramberg-Osgood expression thickness of flange thickness of web overall geometric imperfection imperfection factor ultimate strain at tension failure Slenderness ratio nondimensional slenderness ratio defined in GB 50429 effective flexural slenderness about minor axis limit of horizontal plateau nondimensional slenderness ratio defined in EC9 slenderness ratio about minor axis yield rotation angle of rotation springs local buckling reduction factor
longitudinal direction. There are 12 tension coupons, which is divided into four groups with three identical coupons in each. The tests were conducted on hydraulic universal testing machine in accordance with ASTM E8M-97 standard [21] and GB/T 228.1 [22]. The deformation of the coupons was measured by both strain gauges and extensometer. The coupons tension almost did not result in necking. There was a very sudden failure process with loud sound. The average measured material properties are shown in Table 2, where E0 is the initial Young's modulus, f0.2 is the nominal yield stress (0.2% proof stress), fu is the ultimate stress, n is the exponent in Ramberg-Osgood expression [23] and εu is the ultimate strain at the failure of the tension coupons. The full stress-strain curves of the aluminum alloy are shown in Fig. 4. As shown in Fig. 4, there is a difference between the material properties of I-section columns and RHS columns. The strength of RHS columns is about 20% higher than the strength of I-section columns probably owing to the different extrusion process. However, the material properties of flange and web from same section are nearly the same.
2.1. Test specimens Tests were conducted on 7 large-section aluminum alloy columns including 4 I-section columns and 3 RHS columns, with all the specimens extruded and fabricated by 6061-T6 aluminum alloy. The section height of all the columns is 550 mm which is larger than that in any other existing research. The dimensions of each specimen are shown in Table 1 using the symbols defined in Fig. 2. In Table 1, L is the measured length of the column and A is the area of the cross-section. λy refers to the slenderness ratio about the minor axis ranging from 58.37 to 116.74 for Isection columns and 28.96–48.23 for RHS columns. The specimens were labeled according to the section shape, column length and material type. For example, the label “R-L3510-T6” defines the specimen as follows: the first letter R indicates that the section shape is RHS, while the L3510 indicates the measured length of 3510 mm of the specimen, and the last term T6 indicates that the material of the column is 6061T6. Both ends of the specimens were milled flat by finishing machine to make a uniform distribution of loads.
2.3. Initial geometric imperfection The initial geometric imperfection impinges on the stability resistance of the metallic structures and therefore was measured before testing for all the columns. The imperfection was measured with the combination of optical theodolite and vernier caliper, and this measuring method was successfully applied in steel columns [24,25]. The schematic diagram of the initial geometric imperfection measurement is shown in Fig. 5. The overall geometric imperfection is actually the deviation of the section centroid from the axis connecting the centroid of two end sections, i.e. Δv1, Δv2 and Δv3 in Fig. 5. The measurement was conducted on two ends and the quarter points about both major axis and minor axis. The maximum value of Δv1, Δv2 and Δv3 was taken as the initial geometric imperfection ΔV (shown in Table 3), which would be applied in further numerical investigation. It was found that the ΔV/L of all the columns in both axes are no more than 0.4%, indicating that the extrusion forming could make a smaller initial geometric imperfection.
2.2. Material properties Prior to the loading tests, tensile coupon tests were conducted to determine the material properties of the aluminum alloy. The dimensions of the tension coupons were detailed in Fig. 3. The tension coupons were cut from the web and flange of the specimens along the
2.4. Test configuration All of the columns were loaded by a 12,000 kN servo-control rig between pinned-ended bearings. The test configuration is shown in Fig. 6. Two pole hinges were attached to the testing machine to supply hinged boundary condition which ensured the flexible rotation of the end sections. The distance between each column end and the rotation
Fig. 1. Usnisa Palace on Niushou mountain in Nanjing, China.
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Table 1 Dimensions of specimens. Specimen
H (mm)
B (mm)
tw (mm)
tf (mm)
L (mm)
A (mm2)
λy
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 R-L3510-T6 R-L4675-T6 R-L5845-T6
550.0 550.0 550.0 550.0 550.0 550.0 550.0
220.0 220.0 220.0 220.0 290.0 290.0 290.0
11.0 11.0 11.0 11.0 10.5 10.5 10.5
14.0 14.0 14.0 14.0 12.0 12.0 12.0
2670.0 3560.0 4450.0 5340.0 3510.0 4675.0 5845.0
11,902.0 11,902.0 11,902.0 11,902.0 18,006.0 18,006.0 18,006.0
58.37 77.83 97.28 116.74 28.96 38.57 48.23
Fig. 2. Definition of symbols. Fig. 4. Measured stress-strain curves.
Fig. 5. Imperfection measurement.
Table 3 The value of initial geometric imperfection.
Fig. 3. Dimensions of the tension coupons (mm).
Specimen Table 2 Material properties. Section shape
Location
E0 (MPa)
f0.2 (MPa)
fu (MPa)
n
εu (%)
I-section
Flange (group1) Web (group2) Flange (group3) Web (group4)
73,173.12
240.11
279.96
24.01
13.55
72,237.13
237.73
278.18
23.77
12.32
75,739.76
302.38
334.03
30.24
9.68
72,266.75
304.54
338.46
30.45
9.74
RHS
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 R-L3510-T6 R-L4675-T6 R-L5845-T6
About minor axis
About major axis
ΔV (mm)
L (mm)
ΔV/L (%)
ΔV (mm)
L (mm)
ΔV/L (%)
0.49 0.55 0.72 0.56 1.01 1.32 0.39
2670 3560 4450 5340 3510 4675 5845
0.19 0.16 0.16 0.11 0.29 0.28 0.07
0.90 0.52 0.66 0.45 1.02 0.57 0.31
2670 3560 4450 5340 3510 4675 5845
0.34 0.15 0.15 0.08 0.29 0.12 0.05
1–DG B-4 were installed at end sections to measure the rotation of the end sections; DG C-1 and DG C-2 were installed at the loading end to measure the end shortening, although DG B-3 and DG B-4 have the same function ( Fig. 7). Strain gauges were attached at end sections, quarter-length sections and mid-span section to measure the longitudinal strains, as shown in Fig. 8. The deformation and stress are usually much larger at mid-span section for overall buckling columns. Therefore, there are more strain gauges attached at this section.
center of the pole hinge is 165 mm which should be added to the effective length of the columns in the theoretical and numerical analysis. Geometric centering method was adopted to make the load cross the section centroid of the columns. Prior to the testing, pre-loading was conducted to ensure the full contact of the column and end plates. In the testing process, the load, deformation and strain were collected by IMP Data Acquisition System continuously. In the test, 7 LVDTs (linearly-varying displacement transducers) were installed to measure the in-plane displacements and out-of-plane displacements. The layout of the LVDTs for I-section columns and RHS columns was the same. DG A-1 was installed at the web of mid-span section to measure the out-of-plane displacement (Fig. 6(a)); DG B-
3. Test results and analysis In the loading process, the end plates rotated obviously and all of the columns failed in flexural buckling. The typical failure modes of the columns are shown in Fig. 9. Slight local buckling was observed at mid587
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initial stiffness decreases. The load-lateral displacement (at mid-span section) curves are shown in Fig. 12. It is noted that there is nearly no lateral displacement for short I-section columns I-L2670-T6 and IL3560-T6 until overall buckling failure, indicating inflexible rotation of the pole hinges due to the friction. When buckling failure occurred, because of the instantaneous release of frictional energy, the failure process was too sudden, leading to no data measured for the descending branch. 4. Finite element analysis In order to make up the limitation of the amount of the specimens in the tests, finite element (FE) models were built to carry out an extensive parametric analysis. After verification by the corresponding test results, the FE models will provide basis for the design method and exact prediction of the buckling resistance of the large-section aluminum alloy columns. 4.1. Finite element models
Fig. 6. Test configuration.
Based on FE software ANSYS, three-dimensional FE models of 4 Isection columns and 3 RHS columns were built related to the tested specimens, considering material nonlinearity, geometric nonlinearity and initial geometric imperfection. The dimensions of the specimens in FE models are identical to that of tested specimens which are shown in Table 1. (1) Element and material: Shell element SHELL 181 was adopted to simulate the component plates. SHELL 181 is suitable for the analysis of moderately thick and thick shell structures, involving shear deformation. The mesh size of the element is about 1/20 of the section height, which is precise enough according to sensitivity analysis of mesh size. Material properties applied in the FE model were identical to the corresponding tests, as shown in Fig. 13 described by RambergOsgood expression [23] (Eq. (1)). n
ε=
σ σ + 0.002 ⎛⎜ ⎞⎟ E0 ⎝ f0.2 ⎠
(1)
(2) Boundary and load condition: In the corresponding tests, pole hinges were installed to supply pined-ended boundary condition. However, the hinges did not rotate flexibly in the loading process of I-section columns according to Fig. 12(a). In order to make an accurate simulation of the tests, rotation springs were attached to the ends of I-section columns to simulate the pole hinges with friction, as shown in Fig. 14. According to the corresponding tests, the moment-rotation curve of the rotation springs was defined in Fig. 15. The parameters θyield (yield rotation angle) and k (stiffness of the rotation) of the bilinear rotation springs applied in the FE model were calibrated according to the corresponding tests. For RHS columns, the pole hinges rotated flexibly and continuously about the minor axis. Therefore, perfect pined-ended boundary condition was applied in the FE models of RHS columns. Axial load was applied to the loading end plate of the columns with load eccentricity which determined by the test results. The thickness of end plates is 20 mm for both I-section and RHS columns. The Young's modulus of the end plate is 1000 times [15] larger than that of aluminum alloy in order to simulate a rigid plate. (3) Initial geometric imperfection: The initial geometric imperfections were included in the FE models by geometric modeling in the form of half-sinusoid with zero value on the column edges [27,28]. The imperfection values were identical to the measured values in corresponding tests, as shown in Table 3.
Fig. 7. Layout of the LVDTs.
span section of RHS columns. All of the columns after failure are shown in Fig. 10. The ultimate strengths of all the specimens are summarized in Table 4. λ0 is the effective flexural slenderness about the minor axis (λ0 = L0/y, L0 = L + 2 × 165 mm), Nu is the experimental ultimate strength, Aeff-ec is the effective area based on EC9 and Aeff-gb is the effective area based on GB 50429. The test results were compared with the design provisions in three current design codes which are also listed in Table 4. According to EC9, the slenderness parameters of all the plate elements of I-section and RHS columns exceed the limit value β3. Therefore, the true section should be replaced by an effective one in the calculating process because of the classification of Class 4 [26]. The design provisions underestimate the ultimate strength of I-section columns mainly owing to the friction of the pole hinges which decreases with the increase of the column length. American aluminum design manual [17] makes an opposite prediction of the failure modes of RHS columns. The 3 RHS columns failed in flexural buckling in the tests, while AA predicts local buckling failure. The comparison with design provisions will be discussed in detail later. The load-axial displacement curves of all the columns are shown in Fig. 11. It was found that with the increase of the column length, the 588
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Fig. 8. Layout of strain gauges.
rotation of end plates even the slight buckling of the plate elements in RHS columns are simulated fairly well. The comparison of the stability resistance between FE models and test results is shown in Table 5. NFEA is the numerical value of stability resistance. As shown, the mean value of NFEA/Nu is 0.99 and 0.97 for Isection columns and RHS columns with the corresponding COV (coefficient of variation) of 0.01 and 0.03, respectively. Fig. 17 shows the comparison of the load-axial displacement curves between FE results and test results. Combined with above three aspects of comparison, it is evident that the FE models can make an accurate simulation of the corresponding tests. In order to further validate the FE models, analysis was carried out on the other tests [11] by the FE models. The comparison of the FE results and test results is shown in Fig. 18. The mean value of NFEA/Nu is 0.916 and 0.947 for I-section columns and RHS columns, respectively. And the COV is 0.036 and 0.080, respectively. Therefore, the FE models are verified to accurately predict the buckling behavior of aluminum alloy columns under axial compression.
Fig. 9. Typical failure modes.
4.2. Verification of the FE models The comparison of the failure modes between FE models and tests is shown in Fig. 16. It is found that, the failure modes in FE models are almost the same with the ones in the tests. The flexure of columns, the
5. Parametric analysis and proposed design method The FE models accurately predicted the buckling behavior including Fig. 10. All the columns after failure.
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Table 4 Experimental ultimate strength and comparisons with current design codes. Specimen
λ0
Nu (kN)
NAA/Nu
Aeff-ec (mm2)
NEC9/Nu
Aeff-gb (mm2)
NGB/Nu
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 Mean COV R-L3510-T6 R-L4675-T6 R-L5845-T6 Mean COV
65.6 85.0 104.5 124.0 – – 31.7 41.3 50.9 – –
2231.8 1598.8 968.2 631.0 – – 3370.5 3167.8 2891.2 – –
0.86 0.74 0.81 0.88 0.82 0.08 1.10 1.17 1.28 1.18 0.08
9063.8 9063.8 9063.8 9063.8 – – 12,566.6 12,566.6 12,566.6 – –
0.61 0.59 0.69 0.78 0.67 0.13 1.01 1.00 0.98 1.00 0.02
9140.0 9140.0 9140.0 9140.0 – – 12,256.9 12,256.9 12,256.9 – –
0.52 0.48 0.55 0.61 0.54 0.10 0.96 0.90 0.82 0.89 0.08
Fig. 11. Load-axial displacement curves.
Fig. 12. Load-lateral displacement curves.
40″ defines the column which has I-shape cross section with 6061-T6 aluminum alloy material, 200 mm width flange, 400 mm height section and slenderness ratio of 40. 1/1000 of the column length was adopted as the overall initial geometric imperfection in the parametric analysis. The material property of 6061-T6 in the parametric analysis is identical to that in this paper, as shown in Table 2. In addition to 6061-T6, the paper added 6063-T5 to the parametric analysis which is also usually applied in the engineering structures. The material property of 6063-T5 is identical to the one in a previous research paper [2] with f0.2 = 170.2 MPa, fu = 215.6 MPa, E0 = 63,682 MPa and n = 17. Mesh size, boundary
stability resistance and failure modes of the aluminum alloy columns both in this paper and in other researches. Therefore, an extensive parametric analysis including 180 specimens was conducted by the FE model. The 180 columns consisted of 20 series with different section shapes (I-section and RHS), different section dimensions and different aluminum alloy materials (6061-T6 and 6063-T5), which are shown in Table 6. The symbols B, H, tf, and tw in Table 6 are defined in Fig. 2. Each series includes 9 specimens with different slenderness ratios (about minor axis) varying from 40 to 120. The columns were labeled according to section shape, material type, flange width (B), section height (H) and slenderness ratio. For example, the label “I-T6-200-400590
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Fig. 13. Constitutive relation applied in FE models.
Fig. 14. Diagram of rotation springs.
Fig. 16. Comparison of the failure modes.
condition and load condition in the parametric analysis are same as the ones in the above FE models. The purpose of the parametric analysis conducted in this section is to validate the accuracy of the design methods in the current design specifications. The results of parametric analysis were compared with predicted results by design codes including Eurocode 9 [18], American aluminum design manual [17] and Chinese standards GB 50429-2007 [20], as shown in Table 7 and Table 8.
Fig. 15. Moment-rotation curve of the springs.
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Table 5 Comparison of the stability resistance between FE models and test results. Specimen
λ0
Nu (kN)
NFEA (kN)
NFEA/Nu
I-L2670-T6 I-L3560-T6 I-L4450-T6 I-L5340-T6 Mean COV R-L3510-T6 R-L4675-T6 R-L5845-T6 Mean COV
65.6 85.0 104.5 124.0 – – 31.7 41.3 50.9 – –
2231.8 1598.8 968.2 631.0 – – 3370.5 3167.8 2891.2 – –
2207.5 1575.3 945.5 632.2
0.99 0.99 0.98 1.00 0.99 0.01 0.99 0.93 0.99 0.97 0.03
3333.0 2957.8 2855.2 – –
5.1. Eurocode 9 and GB 50429 Fig. 18. Comparison between FE results and test results by Zhai et al.
Eurocode 9: Design of aluminum structures, or EC9 for short, slightly underestimates the stability resistance of the columns. The average value of NEC9/NPA for all the T6 columns (including I-section and RHS specimens) is 0.90, and for all the T5 columns is 0.81. NPA is the stability resistance of the parametric analysis. EC9 adopts Perrytype curve to design the overall stability resistance, with different imperfection factor α and limit of horizontal plateau λ 0 for T6 and T5 aluminum alloy. The local buckling reduction factor ρc is adopted to reduce the thickness of the element. Effective section area Aeff reduced by ρc is applied in the calculation. The design method in GB 50429 is similar to the method in EC9 except for two differences. The first one is the design value of ρc is more conservative. The second one is the α and λ 0 is different from EC9, as shown in Table 9, leading to a more conservative prediction. The average value of NGB/NPA for all the T6 columns is 0.71, and for all the T5 columns is 0.68. Fig. 19 and Fig. 20 show the comparison between the parametric analysis results and the design codes. Nondimensional slenderness ratio λ n = λ / π [(Aeff / A)⋅(f0.2 / E0)]0.5 , λ = λ / π (f0.2 / E0)0.5 are defined in EC9 and GB 50429, respectively. It is obvious that EC9 makes a more reliable prediction than GB 50429. However, both design codes give a more conservative prediction for strong hardening material (6063-T5), because of its more pronounced strain hardening behavior.
advised in AA of calculating overall stability resistance is based on Euler curve. However, AA ignores the interaction of local buckling and overall buckling, leading the overestimation of the code. And the difference of T6 alloy and T5 alloy in the design provisions is also ignored. Fig. 21 shows the comparison of parametric analysis results and AA. 5.3. Proposed design equation based on EC9 According to the results, the accuracy of design codes doesn’t change obviously with the variation of the section size. Nevertheless, without the parametric analysis of section size, the engineers have less confidence to use large-section aluminum alloy members which is much larger than the member sections in almost all the previous existing research work in design. However, the parametric analysis and the comparison with current codes are meaningful, leading to find out that the current design codes are not reliable enough. Based on EC9, a new design equation was proposed to make a more accurate design method. For the design equations in EC9, the main factors affecting the accuracy are the imperfection factor α and limit of horizontal plateau λ 0 which also vary among different design codes. Proposed imperfection factor and limit of horizontal plateau are derived by regression analysis, as shown in Table 10. Based on the proposed design method, the predicted results were compared with parametric analysis results, with obvious improved accuracy, as shown in Fig. 22. The mean value of Nproposed/NPA for all the T6 alloy members is 0.946 with COV of 0.066, the mean value of Nproposed/NPA for all the T5 alloy members is 0.935 with COV of 0.034.
5.2. American aluminum design manual American aluminum design manual (AA) overestimates the stability resistance of the parametric analysis results. NAA/NPA for all the T6 columns is 1.12, and for all the T5 columns is 1.13. The design method
Fig. 17. Comparison of the load-displacement curves.
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Table 6 Dimensions of the specimens in parametric analysis.
I-section
RHS
Series
B/mm
H/mm
tf/mm
tw/mm
Iy/mm4
I-T6/T5-200-400 I-T6/T5-250-500 I-T6/T5-300-600 I-T6/T5-350-700 I-T6/T5-400-800 R-T6/T5-200-400 R-T6/T5-250-500 R-T6/T5-300-600 R-T6/T5-350-700 R-T6/T5-400-800
200 250 300 350 400 200 250 300 350 400
400 500 600 700 800 400 500 600 700 800
10 10 12 16 25 10 10 12 16 25
10 10 12 16 25 10 10 12 16 25
1.34 2.61 5.41 1.15 2.68 8.19 1.64 3.41 7.11 1.59
× × × × × × × × × ×
A/mm2 107 107 107 108 108 107 108 108 108 109
7800 9800 14,112 21,888 38,750 11,600 14,600 21,024 32,576 57,500
Table 7 Comparison of FE results and predicted results by design codes for I-section columns (6061-T6 and 6063-T5). Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
I-T6-200-400-40 I-T6-200-400-50 I-T6-200-400-60 I-T6-200-400-70 I-T6-200-400-80 I-T6-200-400-90 I-T6-200-400-100 I-T6-200-400-110 I-T6-200-400-120 Mean COV I-T6-250-500-40 I-T6-250-500-50 I-T6-250-500-60 I-T6-250-500-70 I-T6-250-500-80 I-T6-250-500-90 I-T6-250-500-100 I-T6-250-500-110 I-T6-250-500-120 Mean COV I-T6-300-600-40 I-T6-300-600-50 I-T6-300-600-60 I-T6-300-600-70 I-T6-300-600-80 I-T6-300-600-90 I-T6-300-600-100 I-T6-300-600-110 I-T6-300-600-120 Mean COV I-T6-350-700-40 I-T6-350-700-50 I-T6-350-700-60 I-T6-350-700-70 I-T6-350-700-80 I-T6-350-700-90 I-T6-350-700-100 I-T6-350-700-110 I-T6-350-700-120 Mean COV I-T6-400-800-40 I-T6-400-800-50 I-T6-400-800-60 I-T6-400-800-70 I-T6-400-800-80 I-T6-400-800-90 I-T6-400-800-100 I-T6-400-800-110 I-T6-400-800-120 Mean COV
0.81 0.81 0.85 0.89 0.91 0.93 0.94 0.94 0.95 0.89 0.063 0.84 0.82 0.82 0.85 0.88 0.91 0.92 0.93 0.94 0.88 0.054 0.84 0.82 0.82 0.84 0.88 0.90 0.92 0.93 0.94 0.88 0.055 0.82 0.79 0.81 0.86 0.89 0.92 0.93 0.94 0.95 0.88 0.069 0.81 0.82 0.85 0.89 0.92 0.93 0.95 0.95 0.96 0.90 0.065
1.11 1.14 1.24 1.16 1.12 1.09 1.08 1.07 1.06 1.12 0.050 1.25 1.30 1.30 1.17 1.13 1.10 1.08 1.07 1.06 1.16 0.084 1.25 1.30 1.29 1.17 1.12 1.10 1.08 1.07 1.06 1.16 0.083 1.17 1.16 1.22 1.15 1.11 1.09 1.08 1.07 1.06 1.12 0.048 0.98 1.04 1.16 1.11 1.09 1.08 1.07 1.06 1.06 1.07 0.046
0.76 0.71 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.71 0.028 0.77 0.68 0.61 0.59 0.59 0.59 0.59 0.59 0.59 0.62 0.101 0.77 0.68 0.61 0.59 0.59 0.59 0.59 0.59 0.59 0.62 0.101 0.76 0.68 0.64 0.64 0.65 0.65 0.65 0.66 0.66 0.67 0.056 0.79 0.77 0.77 0.79 0.80 0.81 0.82 0.82 0.83 0.80 0.027
I-T5-200-400-40 I-T5-200-400-50 I-T5-200-400-60 I-T5-200-400-70 I-T5-200-400-80 I-T5-200-400-90 I-T5-200-400-100 I-T5-200-400-110 I-T5-200-400-120 Mean COV I-T5-250-500-40 I-T5-250-500-50 I-T5-250-500-60 I-T5-250-500-70 I-T5-250-500-80 I-T5-250-500-90 I-T5-250-500-100 I-T5-250-500-110 I-T5-250-500-120 Mean COV I-T5-300-600-40 I-T5-300-600-50 I-T5-300-600-60 I-T5-300-600-70 I-T5-300-600-80 I-T5-300-600-90 I-T5-300-600-100 I-T5-300-600-110 I-T5-300-600-120 Mean COV I-T5-350-700-40 I-T5-350-700-50 I-T5-350-700-60 I-T5-350-700-70 I-T5-350-700-80 I-T5-350-700-90 I-T5-350-700-100 I-T5-350-700-110 I-T5-350-700-120 Mean COV I-T5-400-800-40 I-T5-400-800-50 I-T5-400-800-60 I-T5-400-800-70 I-T5-400-800-80 I-T5-400-800-90 I-T5-400-800-100 I-T5-400-800-110 I-T5-400-800-120 Mean COV
0.76 0.77 0.78 0.80 0.83 0.85 0.87 0.88 0.90 0.83 0.062 0.76 0.72 0.71 0.75 0.78 0.81 0.84 0.86 0.87 0.79 0.075 0.76 0.72 0.71 0.74 0.78 0.81 0.83 0.86 0.87 0.79 0.075 0.73 0.73 0.75 0.77 0.80 0.83 0.85 0.87 0.89 0.80 0.076 0.82 0.82 0.82 0.83 0.85 0.87 0.88 0.90 0.91 0.86 0.042
1.03 1.07 1.13 1.23 1.25 1.19 1.15 1.13 1.11 1.14 0.062 1.12 1.13 1.15 1.25 1.26 1.20 1.16 1.13 1.12 1.17 0.047 1.13 1.14 1.15 1.24 1.26 1.19 1.16 1.13 1.11 1.17 0.044 1.04 1.06 1.13 1.23 1.24 1.19 1.15 1.13 1.11 1.14 0.060 0.99 1.03 1.09 1.20 1.22 1.17 1.14 1.12 1.11 1.12 0.067
0.72 0.71 0.70 0.69 0.69 0.70 0.71 0.71 0.72 0.71 0.016 0.70 0.64 0.60 0.59 0.59 0.60 0.60 0.61 0.61 0.62 0.057 0.70 0.64 0.60 0.59 0.59 0.60 0.60 0.61 0.61 0.62 0.057 0.69 0.66 0.65 0.64 0.65 0.65 0.66 0.67 0.67 0.66 0.023 0.81 0.79 0.77 0.77 0.78 0.79 0.81 0.82 0.83 0.80 0.027
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Table 8 Comparison of FE results and predicted results by design codes for RHS1 columns (6061-T6 and 6063-T5). Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
Specimen
NEC9/NPA
NAA/NPA
NGB/NPA
R-T6-200-400-40 R-T6-200-400-50 R-T6-200-400-60 R-T6-200-400-70 R-T6-200-400-80 R-T6-200-400-90 R-T6-200-400-100 R-T6-200-400-110 R-T6-200-400-120 Mean COV R-T6-250-500-40 R-T6-250-500-50 R-T6-250-500-60 R-T6-250-500-70 R-T6-250-500-80 R-T6-250-500-90 R-T6-250-500-100 R-T6-250-500-110 R-T6-250-500-120 Mean COV R-T6-300-600-40 R-T6-300-600-50 R-T6-300-600-60 R-T6-300-600-70 R-T6-300-600-80 R-T6-300-600-90 R-T6-300-600-100 R-T6-300-600-110 R-T6-300-600-120 Mean COV R-T6-350-700-40 R-T6-350-700-50 R-T6-350-700-60 R-T6-350-700-70 R-T6-350-700-80 R-T6-350-700-90 R-T6-350-700-100 R-T6-350-700-110 R-T6-350-700-120 Mean COV R-T6-400-800-40 R-T6-400-800-50 R-T6-400-800-60 R-T6-400-800-70 R-T6-400-800-80 R-T6-400-800-90 R-T6-400-800-100 R-T6-400-800-110 R-T6-400-800-120 Mean COV
0.83 0.83 0.83 0.86 0.85 0.87 0.87 0.94 0.83 0.86 0.042 1.00 0.97 0.94 0.94 0.92 0.92 0.92 0.94 0.94 0.94 0.028 1.00 1.01 0.99 0.94 0.97 0.86 0.97 0.99 1.00 0.97 0.048 0.96 0.93 0.90 0.90 0.91 0.92 0.94 0.95 0.95 0.93 0.024 0.81 0.79 0.80 0.83 0.85 0.85 0.84 0.82 0.79 0.82 0.029
1.02 1.13 1.17 1.10 1.04 1.02 0.99 1.05 0.92 1.05 0.072 1.23 1.33 1.42 1.26 1.15 1.10 1.07 1.07 1.06 1.19 0.109 1.22 1.38 1.50 1.26 1.22 1.02 1.13 1.12 1.12 1.22 0.121 1.17 1.28 1.30 1.17 1.11 1.09 1.07 1.07 1.06 1.15 0.079 0.99 1.00 1.09 1.04 1.01 0.99 0.95 0.91 0.87 0.98 0.067
0.78 0.74 0.70 0.70 0.68 0.69 0.68 0.73 0.65 0.71 0.055 0.92 0.82 0.73 0.70 0.66 0.64 0.64 0.65 0.64 0.71 0.138 0.92 0.86 0.77 0.69 0.69 0.60 0.67 0.68 0.68 0.73 0.140 0.90 0.82 0.74 0.71 0.70 0.70 0.71 0.71 0.71 0.74 0.093 0.79 0.73 0.72 0.73 0.74 0.74 0.72 0.70 0.68 0.73 0.042
R-T5-200-400-40 R-T5-200-400-50 R-T5-200-400-60 R-T5-200-400-70 R-T5-200-400-80 R-T5-200-400-90 R-T5-200-400-100 R-T5-200-400-110 R-T5-200-400-120 Mean COV R-T5-250-500-40 R-T5-250-500-50 R-T5-250-500-60 R-T5-250-500-70 R-T5-250-500-80 R-T5-250-500-90 R-T5-250-500-100 R-T5-250-500-110 R-T5-250-500-120 Mean COV R-T5-300-600-40 R-T5-300-600-50 R-T5-300-600-60 R-T5-300-600-70 R-T5-300-600-80 R-T5-300-600-90 R-T5-300-600-100 R-T5-300-600-110 R-T5-300-600-120 Mean COV R-T5-350-700-40 R-T5-350-700-50 R-T5-350-700-60 R-T5-350-700-70 R-T5-350-700-80 R-T5-350-700-90 R-T5-350-700-100 R-T5-350-700-110 R-T5-350-700-120 Mean COV R-T5-400-800-40 R-T5-400-800-50 R-T5-400-800-60 R-T5-400-800-70 R-T5-400-800-80 R-T5-400-800-90 R-T5-400-800-100 R-T5-400-800-110 R-T5-400-800-120 Mean COV
0.78 0.77 0.76 0.77 0.79 0.81 0.83 0.85 0.87 0.80 0.049 0.80 0.82 0.79 0.77 0.78 0.79 0.81 0.84 0.85 0.81 0.033 0.85 0.81 0.78 0.77 0.78 0.80 0.82 0.84 0.86 0.81 0.040 0.80 0.77 0.75 0.75 0.77 0.80 0.83 0.85 0.86 0.80 0.052 0.84 0.82 0.79 0.79 0.81 0.83 0.85 0.86 0.88 0.83 0.037
1.04 1.06 1.09 1.17 1.18 1.13 1.10 1.09 1.07 1.10 0.043 1.03 1.16 1.21 1.24 1.23 1.13 1.11 1.09 1.08 1.14 0.064 1.10 1.15 1.20 1.23 1.22 1.15 1.12 1.10 1.08 1.15 0.048 1.06 1.09 1.10 1.17 1.18 1.13 1.10 1.09 1.07 1.11 0.038 1.04 1.05 1.08 1.16 1.17 1.13 1.10 1.08 1.07 1.10 0.042
0.74 0.71 0.68 0.66 0.66 0.67 0.68 0.69 0.70 0.69 0.038 0.73 0.72 0.66 0.62 0.61 0.59 0.60 0.61 0.62 0.64 0.081 0.77 0.71 0.66 0.61 0.60 0.60 0.61 0.62 0.62 0.64 0.092 0.75 0.70 0.66 0.64 0.64 0.65 0.66 0.67 0.68 0.67 0.052 0.81 0.77 0.74 0.72 0.72 0.74 0.75 0.76 0.77 0.75 0.038
displacement response were identified. By general FEA software ANSYS, the simulation of the test process was conducted and verified. An extensive parametric analysis including 180 specimens was carried out based on the verified FE model to evaluate the reliability level of the current design specifications including Eurocode 9, American aluminum design manual and GB 50429-2007. Based on the parametric analysis results, the paper proposed a new design method. According to the investigation, the conclusions can be drawn as follows:
Table 9 Different value of α and λ 0 in EC9 and GB 50429. Material type
Class A (T6) Class B (T5)
Imperfection factor α
Horizontal plateau λ 0
EC9
GB 50429
EC9
GB 50429
0.20 0.32
0.20 0.35
0.10 0.00
0.15 0.10
(1) All of the large-section aluminum alloy columns failed in flexural buckling in the test. The three design specifications generally underestimate the stability resistance of the columns. (2) Three-dimensional FE models were built by ANSYS based on corresponding tests incorporating material nonlinearity and initial geometric imperfection. Rotation springs were attached to the ends
6. Conclusion The paper carried out experimental investigation on 7 large-section aluminum alloy columns including 4 I-section columns and 3 RHS columns. The failure modes and stability resistance as well as load594
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Fig. 19. Comparison of parametric analysis results and EC9.
Fig. 20. Comparison of parametric analysis results and GB 50429.
of I-section columns to simulate the pole hinges with friction. The FE models made accurate simulation of failure modes and stability resistance as well as load-displacement response of the specimens related to tested specimens in this paper and other research work. (3) An extensive parametric analysis including 180 specimens with 20 series classified with different section shapes, different section dimensions and different aluminum alloy materials was conducted by the FE models. The accuracy of design codes doesn’t change obviously with the variation of the section size. Therefore, if a reliable design method is suitable for small-section and thin-walled aluminum alloy columns, it is also suitable for the large-section aluminum alloy columns. This conclusion is meaningful for engineers who can use the large-section aluminum alloy columns in “superstructures” without worry about the applicability of the design method. (4) The results of parametric analysis were compared with predicted results by design codes including BS EN 1999-1-1: 2007 (EC9), American aluminum design manual (AA) and GB 50429. EC9 and GB 50429 adopt Perry-type curve to design the overall stability resistance and apply effective section area to consider local buckling reduction. Because of different imperfection factor and limit of horizontal plateau in GB 50429 from EC9, GB 50429 gives a more conservative prediction. The design method in AA is based on Euler curve ignoring the interaction of local buckling and overall buckling, resulting in an overestimated prediction.
Fig. 21. Comparison of parametric analysis results and AA.
Table 10 Proposed value of α and λ 0 and comparison with parametric results. Material type
Class A (T6) Class B (T5)
Imperfection factor α
Horizontal
Mean value of Nproposed/NPA
COV
plateau λ 0
0.160 0.240
0.280 0.400
0.946 0.935
0.066 0.034
595
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Fig. 22. Comparison of parametric analysis results and proposed curves. 1978. [9] J.H. Zhu, B. Young, Experimental investigation of aluminum alloy circular hollow section columns, Eng. Struct. 28 (2) (2006) 207–215. [10] Y.J. Wang, F. Fan, S.B. Lin, Experimental investigation on the stability of aluminum alloy 6082 circular tubes in axial compression, Thin-Walled Struct. 89 (2015) 54–66. [11] X.M. Zhai, Y.J. Wang, H. Wu, F. Fan, Research on stability of high strength aluminum alloy columns loaded by axial compressive load, Adv. Mater. Res. 168–170 (2010) 1915–1920. [12] G.O. Adeoti, F. Fan, Y.J. Wang, X.M. Zhai, Stability of 6082-T6 aluminum alloy columns with H-section and rectangular hollow sections, Thin-Walled Struct. 89 (2015) 1–16. [13] J.H. Zhu, B. Young, Tests and design of aluminum alloy compression members, J. Struct. Eng. 132 (7) (2006) 1096–1107. [14] M.N. Su, B. Young, L. Gardner, Testing and design of aluminum alloy cross sections in compression, J. Struct. Eng. 140 (9) (2014) (04014047-1-04014047-11). [15] Y.Q. Wang, Z.X. Wang, X.G. Hu, J.K. Han, H.J. Xing, Experimental study and parametric analysis on the stability behavior of 7A04 high-strength aluminum alloy angle columns under axial compression, Thin-Walled Struct. 108 (2016) 305–320. [16] M. Liu, L. Zhang, P. Wang, Y. Chang, Buckling behaviors of, section aluminum alloy columns under axial compression, Eng. Struct. 95 (2015) 127–137. [17] Aluminum Association (AA), Aluminum Design Manual, AA, Washington, DC., 2010. [18] CEN, Eurocode 9: Design of Aluminum Structures—Part 1-1: General Structural Rules BS EN 1999-1-1, CEN, Brussels, 2007. [19] AS/NZS, Aluminum Structures Part 1: Limit State Design AS/NZS, 1664.1 Standards Australia, Sydney, 1997. [20] MOHURD, Code for design of aluminum structures GB 50429-2007, China Planning Press, Beijing, 2007 (in Chinese). [21] ASTM, Standard Test Methods for Tension Testing of Metallic Materials E8M-97, ASTM, West Conshohocken, 1997. [22] AQSIQ, Metallic Materials-tensile Testing – Part 1: Method of Test at Room Temperatures GB/T228.1, Standards Press of China, Beijing, 2010 (in Chinese). [23] W. Ramberg, W.R. Osgood, Description of Stress-strain Curves by Three Parameters (Technical Note 902), National Advisory Committee for Aeronautics, Washington, DC, 1943. [24] H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Overall buckling behavior of 460 MPa high strength steel columns: experimental investigation and design method, J. Constr. Steel Res. 74 (6) (2012) 140–150. [25] H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Column buckling tests of 420 MPa high strength steel single equal angles, Int. J. Struct. Stab. Dyn. 13 (02) (2013) 1–23. [26] R. Landolfo, F.M. Mazzolani, Different approaches in the design of slender aluminium alloy sections, Thin-Walled Struct. 27 (1) (1997) 85–102. [27] A. Formisano, F.M. Mazzolani, G. Brando, G. De Matteis, Numerical evaluation of the hysteretic performance of pure aluminum shear panels. in: Proceedings of the 5th International Conference on Behavior of Steel Structures in Seismic Areas (STESSA 2006) 211-217, 2006. [28] A. Formisano, G. De Matteis, F.M. Mazzolani, Experimental and numerical researches on aluminum alloy systems for structural applications in civil engineering fields, Key Eng. Mater. 710 (2016) 256–261.
(5) Based on the design methods in EC9, a new design equation was proposed. With proposed imperfection factor α and limit of horizontal plateau λ 0 , the prediction accuracy is substantially improved. The mean value of prediction accuracy (Nproposed/NPA) for all the T6 alloy members is 0.946 with COV of 0.066, while the mean value of prediction accuracy (Nproposed/NPA) for all the T5 alloy members is 0.935 with COV of 0.034. The proposed design method can fairly well describe the stability resistance of aluminum alloy columns of both large-section columns and small columns and will make reference for the investigation of aluminum alloy columns. However, the method still needs to be confirmed by further experimental and numerical research. Acknowledgments The research work described in this paper was supported by National Natural Science Foundation of China (Grant no. 51038006), the Special Research Fund for the Doctoral Program of Higher Education (Grant no. 20110002130002) and Tsinghua Fudaoyuan Research Fund. Thanks are also extended to the Civil Engineering Department, Tsinghua University for the test conditions and equipment provided. References [1] F.M. Mazzolani, Aluminum Alloy Structures, Second edition, Spon Press, London, 1994. [2] Y.Q. Wang, Z.X. Wang, F.X. Yin, L. Yang, Y.J. Shi, J. Yin, Experimental study and finite element analysis on the local buckling behavior of aluminium alloy beams under concentrated loads, Thin-Walled Struct. 105 (2016) 44–56. [3] M. Manganiello, G. De Matteis, R. Landolfo, Inelastic flexural strength of aluminium alloys structures, Eng. Struct. 28 (4) (2006) 593–608. [4] G.S. Gibson, An approximate method for calculating the distortion of welded members, Weld. J. 17 (7) (1938). [5] M. Holt, Tests on build-up columns of structural aluminum alloys, Trans. ASCE 105 (1940) 96–219. [6] R.J. Brungraber, J.W. Clark, Strength of welded aluminum columns, Trans. ASCE 127 (1962) 202–226. [7] J.W. Clark, R.L. Rolf, Design of aluminum tubular members, J. Struct. Div., ASCE ST6 (1964) 259–289. [8] European Convention for Constructional Steelworks (ECCS), European Recommendations for Aluminum Alloy Structures, 1st edition, ECCS, Brussels,
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