Abstract
Five specimens were cut from an aluminum alloy thin-walled hollow column to complete a tensile test, and the strength of the aluminum alloy was measured to be 200.18 MPa. The Ramberg–Osgood model was compared with the stress-strain relationship of the test results, and the fitting regression coefficient was more than 0.99. Four groups of axial compression trials of aluminum alloy thin-walled hollow columns with different heights were accomplished, and the test phenomena and data were concurrently observed and recorded. The results show that the axial compressive bearing capacity of aluminum alloy thin-walled hollow columns does not change with the change in column height, the mean value is 73.72 kN, and the corresponding covariance is only 2.14%. Local buckling failures appeared in all of these columns, and the failure locations were distributed at each height of the test pieces. The stiffness of the column decreased with the increase in height and width ratio, and the varying trend between them obeys exponential distribution. The displacement that corresponds to the ultimate load increased with the increase in the height-width ratio, and the increasing trend follows a linear relationship with the change in column height.
1. Introduction
Aluminum alloys are isotropic metal materials [1] with the advantages of light weight and high specific strength. This material is widely used in industries that require light and high strength materials [2, 3]. In civil engineering, aluminum alloys are mainly used in pedestrian overpasses, portal steel frames, spatial reticulated shell structures, and others. Scholars from Europe and the US conducted large numbers of experimental tests of axial compression members to study the ultimate bearing capacity of aluminum alloy columns from the 1930s to 1970s and compiled aluminum alloy structure design specifications of different nations [5–8]. In recent years, Chinese researchers have implemented experimental studies and numerical simulations on the buckling behavior and ultimate strength of aluminum alloy thin-walled hollow columns [9], large-section columns [10], and irregular section aluminum alloy thin-walled hollow columns [11] under axial compression to study the buckling performance and evaluate the accuracy of existing design methods of standards. Zhao et al. [12, 13] conducted bias tests on 30 aluminum alloy square and circular hollow section members and studied different parameters (length slenderness ratio, eccentricity, width thickness ratio, diameter thickness ratio, etc.) on the bearing capacity of members. Then, by comparing the test results with national codes, it was concluded that the direct strength method is the most accurate method to calculate the bearing capacity of members. Shi et al. [14] and Guo et al. [15] studied the overall stability of aluminum alloy under axial compression through finite element and modulus numerical calculations, respectively, and put forward calculation formulas. Wang et al. [16] conducted relevant experimental research on the stability of aluminum alloy axial compression members and verified the reliability of the design methods of various codes by comparing the test results with the calculation results of Chinese, European, American, and Australian/New Zealand codes.
In this paper, five uniaxial tensile tests of aluminum alloy materials were completed, then the mechanical property parameters of the materials were calculated, and the Ramberg–Osgood model was used to predict the stress-strain relationship of aluminum alloy. Four groups of aluminum alloy hollow thin-walled columns with different lengths were proposed in this paper. The width-to-height ratios of different groups of columns were 1 : 4, 1 : 8, 1 : 12, and 1 : 20. Axial compression tests of hollow thin-walled columns were conducted, and the load-strain and load-displacement curves of each specimen were recorded to compare with national norms.
2. Material Experiment
According to ASTM E8 − E8 M [17], 5 mechanical property test samples of aluminum alloy were cut along the longitudinal direction of the hollow column, which were numbered 1-1-1–5. The tensile test was completed on a 50 kN universal testing machine with a DDL-50 model. The experimental results are summarized in Table 1, where σtu is the ultimate tensile strength of the aluminum alloy specimen, εtu is the ultimate tensile strain, Et is the tensile elastic modulus, A is the elongation at break, and ν is Poisson’s ratio of the aluminum alloy. The calculation formulas for tensile strength σtu, tensile modulus Et, elongation at break A, and Poisson’s ratio ν are as follows:where Ftu is the ultimate tensile bearing capacity of the aluminum alloy specimen; ΔFt and Δεt are the increased load and strain, respectively; ΔFt is 10%∼30% of σtu; and t are the width and thickness of the smallest section, respectively; L0 and l′ are the gauge length and fracture length, respectively; εt and εc are the mean tensile and compressive strain, respectively.
The Ramberg and Osgood models [18] and the three-stage models proposed by Baehre [19] and Mazzolain [20] are widely used in the research of constitutive models of aluminum alloys. Verified by numerous Chinese scholars, the constitutive relationship of domestic aluminum alloy is consistent with the Ramberg–Osgood model, and its expression is as follows:where E is the modulus of elasticity; ƒ0.2 is the stress corresponding to a nonproportional elongation of 0.2%; ƒ0.1 is the stress corresponding to a nonproportional elongation of 0.1%.
The stress-strain relationship of aluminum alloy has no yield stage, and the strengthening stage appears after exceeding the proportional limit. The specification stipulates that the stress corresponding to the nonproportional elongation of 0.2% is defined as the nominal yield strength, i.e., yield strength. The calculation results of ƒ0.1 and ƒ0.2 are shown in Table 1. Substituting the test results in Table 1 into (2) and (3), we obtain
The comparison results between the calculation and the test results are shown in Figure 1, and the fitted regression coefficient R2 > 0.99 indicates that the Ramberg–Osgood model can well describe the constitutive relationship of aluminum alloy in this paper.
3. Test Design and Scheme
3.1. Specimen Design
The test consists of four groups of specimens with different heights. The sample numbers are K360, K720, K1080, and K1800. As shown in Figure 2, the section dimensions of all members are identical; the width (bw) is 90 mm, the wall thickness (t) is 2 mm, the height (H) is 360 mm, 720 mm, 1080 mm, and 1800 mm, and the corresponding width-height ratios are 1 : 4, 1 : 8, 1 : 12, and 1 : 20. Four parallel specimens were set for each test group.
3.2. Test Method
The axial compression experiment of aluminum alloy thin-walled hollow columns was completed in the structural laboratory of the School of Civil Engineering, Nanjing Forestry University. The loading equipment is a 1000 kN fatigue testing machine with an LFV-1000 model produced by Walter + Bai AG, and the loading device is shown in Figure 3(a).
(a)
(b)
One transverse and one longitudinal strain gauge are arranged in the middle of the four sides of the hollow column to measure the deformation of the sample during the test to analyze the real-time state of the sample. Preloading was performed before the test to eliminate the gap of the sample and ensure that the displacement gauge and strain gauge worked normally. The formal loading method of the testing machine was controlled by compression deformation, and the loading speed was 1 mm/min. When the load dropped to 70%–80% of the ultimate bearing capacity, the test piece was considered damaged, and the loading was stopped. The strain, load, and displacement data of the hollow columns of the entire experimental process are collected by the TDS 530 (Tokyo measuring instrument) data acquisition instrument and transmitted to the computer.
4. Test Results
4.1. Ultimate Bearing Capacity and Failure Mode
The failure modes of the aluminum alloy axial compression specimen are shown in Figure 4. Local buckling failures occur in columns with K360, K720, K1080, and K1800. The buckling positions are distributed at stochastic heights of the specimen, and most of the specimens buckle in the middle.
Table 2 provides a summary of the measured ultimate bearing capacity results and failure modes of hollow column axial compression samples. When the height of the hollow column is less than 1800 mm, the ultimate bearing capacity of axial compression does not significantly change with different heights; it is 72.03–75.52 kN with an average of 73.72 kN, on a standard deviation of 1.57 and a covariance of 2.14. Thus, when the height is less than 1800 mm, the bearing capacity only depends on the width-thickness ratio of the member section. When the sample height is increased to 2520 mm, the slenderness ratio of the sample exceeds the limit, and the ultimate bearing capacity of the specimen decreases to 62.02 kN.
4.2. Load-Displacement Relationship
Figure 5 shows the load-displacement relationship of each group of trials. At the initial stage of loading, the curves of each group exhibited a linear relationship. When the load approached the limit state, the load decreased with the displacement growth rate and entered the elastic-plastic stage. When the load reached the ultimate bearing capacity of the hollow column, the load decreased with increasing displacement, and the specimens failed.
Figure 5 shows that the slopes of the load-displacement relation curves of each group are different, which indicates that the compressive stiffness of each group of samples is different, and the stiffness of the hollow column continuously decreases with increasing member height. Assuming that the compressive stiffness of the hollow column with a height of 360 mm is 1, the equivalent stiffness of column K720 is 0.88, and the equivalent stiffness of column K1080 is reduced to 0.7. When the column height is 1800 mm, the equivalent stiffness is 0.51. The stiffness degradation law of each group of hollow columns is shown in Figure 6. The red line is the fitting curve of the equivalent stiffness with increasing sample height, the horizontal axis is the column height, the Y axis represents the equivalent stiffness, the stiffness degradation is linear with increasing column height, and R2 is 0.98.
In addition, with the increase in sample height, the displacement that corresponds to the ultimate load also increases from 1.94 mm of column K360 to 3.48 mm of column K1800. The reason is that the plastic hinge occurs after the local buckling of the test-piece; under identical bearing capacity, a longer column has a greater ultimate displacement. Figure 7 shows that with the continuous increase in height of hollow columns, the displacement corresponding to the ultimate load follows the exponential distribution law, the fitting formula is y = 1.61 e0.0004x, and the fitting regression coefficient is greater than 0.99.
4.3. Load-Strain Relationship
Typical curves were selected from the measured load-strain relationship of each group for analysis, as shown in Figure 8. Each load-strain curve can be roughly divided into three periods. The first stage is the linear elastic stage, where the load linearly increases with increasing strain. The second phase is the elastic-plastic stage. When the load exceeds the proportional limit, the growth rate of the load gradually decreases, and the load-strain presents a nonlinear relationship. The third section is the failure stage, where the stress outstrips the yield limit, the load decreases, and the strain steadily increases.
(a)
(b)
(c)
(d)
At the initial phase of loading, all curves of hollow columns in Figure 8 almost coincide, and the rate of increase in longitudinal strain with load is greater than that in transverse strain, which conforms to the variety rule of Hooke’s law.
5. Comparison with National Specifications
The American aluminum alloy structure design standard ADM-105-2005 [21] (AA), the European Code BS EN-1999-1–1:2007 [22] (EC9), and the Chinese standard for the design of aluminum alloy structures GB50429-2007 [23] (GB) were used to calculate the bearing capacity of hollow aluminum columns. The calculated values were compared with the test results to verify the applicability of national specifications to calculate the studied members.
When the local buckling of bilateral stiffened plates was calculated using the American standard ADM-105-2005 (AA), the design strength of the plates is reduced, and the bearing capacity is calculated. The equation is as follows:wherewhere ϕFL is the design value of stress when the specimen reaches the bearing capacity limit state; ϕy and ϕc are the resistance coefficients, ϕy = 0.95 and ϕc = 0.85, respectively; Fcy is the standard value of compressive yield strength of aluminum alloy; b is the plate width; t is the plate thickness; E is the elastic modulus of aluminum alloy; Bp and Dp are buckling constants; S1 and S2 are calculation parameters; k1 and k2 are constants, k1 = 0.35 and k2 = 2.27.
Both European and Chinese norms adopted plate thickness reduction to analyze the influence of local buckling, but the reduction methods are different. The reduction calculation expression of European Code BS EN-1999-1-1:2007 (ES9) is as follows:where
ρ c is the reduction factor; C1 and C2 are constants, C1 = 29, and C2 = 198; β is the width thickness ratio of the plate; β3 is the width thickness ratio limit, and β3/φ = 22; f0.2 is the nominal yield strength of aluminum alloy.
The computing formula for plate thickness reduction in the Chinese standard GB 50429–2007 (GB) is as follows:where te is the effective thickness of the plate; α1 and α2 are the calculation coefficients and are both equal to 0.9; means the conversion flexibility coefficient of the plate; σcr is the elastic critical buckling stress of the compression plate; ν implies Poisson’s ratio of aluminum alloy.
The ultimate bearing capacities of aluminum alloy thin-walled hollow columns calculated according to specifications AA, EC9, and GB are 76.86 kN, 80.69 kN, and 76.96 kN, respectively, which are 4%, 9%, and 4% larger than the test results, as shown in Table 3. The ratio of the bearing capacity determined by the three groups of standards to the test results is less than 1.1, which indicates that the codes of various countries can accurately predict the axial compressive bearing capacity of aluminum alloy thin-walled hollow columns.
6. Conclusion
The constitutive relationship of aluminum alloy in this paper can be calculated using the Ramberg–Osgood model.
The axial bearing capacity of aluminum alloy thin-walled hollow columns does not alter with the change in column height. The average bearing capacity of each group of columns was 73.72 kN, and the covariance was only 2.14. Local buckling failure occurred in all specimens, and the failure locations were distributed at different heights of the columns.
The stiffness of the column decreases with the increase in the aspect ratio of height to width, and the change trend is linear. The displacement corresponding to the ultimate load increases with the increase in the height-width ratio, and the increasing trend follows an exponential distribution with the change in column height.
The computed results of national standards were compared with the experimental test results. The maximum calculated value of ultimate bearing capacity was determined by EC9, which is 80.69 kN and 9% greater than the experimental results. The calculation results of the other two codes of AA and GB are 4% higher than the observed values, which indicates that all specifications of different nationalities can accurately predict the bearing capacity of aluminum alloy thin-walled hollow columns. [4].
Data Availability
Some or all the data, models, or code generated or used during the study are available from the corresponding author by request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors wish to express their gratitude to the National Natural Science Foundation of China (No. 51778300, 52108150), Key Research and Development Project of Jiangsu Province (No. BE2020703), the Natural Science Foundation of Jiangsu Province (No. BK20191390), the Six Talent Peaks Project of Jiangsu Province (JZ-017), the Qinglan Project of Jiangsu Province, and the Science and Technology Plan Project of Nanjing Construction Industry (Ks2207) for financially supporting this study.