Experiment on aluminum alloy members under axial compression

Abstract

To improve the design methods of Chinese aluminum alloy members, experiment of 63 profiled aluminum alloy members, made of Chinese aluminum alloy 6061-T6, under axial compression is conducted in this paper. Valuable experimental data are obtained. At the same time, in order to obtain the relevant data, a large number of other experimental data from published papers and technical reports are collected and sorted out. 167 valid experimental data points are obtained finally. Furthermore, for the purpose of creating column curves, the aluminum alloy members under the axial compression, used in experiments, are analyzed by means of FEM. Based on the numerical results, 2 column curves are created by means of the numerical fitting method. The column curves are compared with the calculated data according to the experimental results for verification, and also are verified with the curves in design codes of several relevant countries. The numerical results show that the column curves obtained in this paper are valid and reliable.

Keywords

aluminum alloy / column curve / compression members / overall stability coefficient

Introduction

A few experiments on Chinese aluminum alloy members under axial compression have been carried through till now. And several practical design formulas have been proposed accordingly. However, current researches are all focusing on concrete problems of actual projects. The obtained experimental data have not been sorted out for creating generally used design curves or formulas yet. Sorting out the obtained experimental data, it can be found that most of the data are concerned with the flexural buckling of circular tubes and H-section members, and few data can be found from experiments of members with smaller slenderness ratios or members subjected to flexural-torsional buckling. According to now situation, experiments of 63 profiled aluminum alloy members, made of Chinese 6061-T6, under axial compression are conducted in this paper. Based on the experimental results and the data obtained from existing references, the loading behavior and stability characteristics of Chinese aluminum alloy members under axial compression are investigated. The column curves are created. Meanwhile valuable design suggestions are proposed.

Experimental data

Introduction of experiments

63 profiled aluminum alloy members are designed for the axial compression experiment. The members are made of Chinese aluminum alloy 6061-T6.Varied types of cross section, including square section, circular section, H section, T section, L section are adopted in the experiments. Since the current existing experimental data are not enough for investigation of the buckling behavior of members with smaller slenderness ratios, most slenderness ratios of the designed members for experiment in this paper are relatively small. The expected buckling modes of these members are flexural buckling and flexural-torsional buckling. Detailed information of the members is listed in Table 1.

During the experiment process, the members are all assembled vertically and loaded by an oil jack at one end. To simulate the hinge supports effectively, double-knife edge supports are positioned at two ends of a member. The experimental phenomena show that some members fail for flexural-torsional buckling and some for flexural buckling. Only a few members fail for local panel buckling, which is not investigated in this paper. The failure phenomena of the members are described in Table 1. Several photos of buckling members are shown in Fig. 1.

Before conducting the member experiments, tensile specimens for testing material properties of the aluminum alloy are made, cutting from the same profiled aluminum alloy members, and tested. The elastic modulus, E, and non-proportional extension strength, f_0.2, of the aluminum alloy are obtained and shown in Table 2.

Introduction of other experiments

In 1999, a series of experiments of profiled aluminum alloy members, made of Chinese 6061-T6, under axial compression were conducted by Li et al. [ 1, 2] in Tongji University. Cross section shapes of the members were H and circular tube. The double-knife edge support and the spherical hinge support were adopted during experiment. The experimental results show that the critical buckling loads of the members with spherical hinge support were larger than those with double-knife edge support. And all the members failed for flexural buckling. The experimental results are shown in Table 1.

According to the design requirement on the space truss of the conservatory roof in Shanghai Botanical Garden, a series of experiments of profiled aluminum alloy members under axial compression were conducted by Shen et al. [ 3] in Tongji University, 2001. The truss members were made of Chinese aluminum alloy 6061-T6 and 5038-H321. Section shapes of the members included H and circular tube. The double-knife edge support was adopted. All of the members failed for flexural buckling. The experimental results are also shown in Table 1.

In 2001, a series of experiments of aluminum alloy (6061-T6) members under axial compression were conducted by Meng and Gao. [ 4] in China Aeronautical Project & Design Institute. The members were circular tube. Bolted hemisphere hinge supports were adopted, which made the members similar to the actual behavior of the truss members. The experimental results indicated that members of the truss with bolted-sphere joints could be regarded as hinged at both ends. All of the members failed for flexural buckling. The experimental results are shown in Table 1.

In 2004, a series of experiments of aluminum alloy members under axial compression were conducted by Li and Yin [ 5] in Xi’an University of Architecture and Technology. The members were made of Chinese forged aluminum alloy LD2 (equivalent to 6A02). The members were circular tube with relatively small radius and thin wall. The double-knife edge support was adopted in experiments. All members failed for flexural buckling. The experimental results are shown in Table 1.

A series of experiments of profiled aluminum alloy members under axial compression were conducted by Li [ 6] in Xi’an University of Architecture and Technology also in 2004. The members were made of Chinese aluminum alloy 6061-T6 and were circular pipes with relatively small radius and thin wall. The double-knife edge support was adopted for most of members. A few members were fixed on top and spherically hinged on bottom. All members failed for flexural buckling. The experimental results are shown in Table 1.

In 2005, a series of experiments of uniaxial-symmetric members under axial compression were conducted by Jin [ 7] in Tongji University. The members were made of Chinese aluminum alloy 6061-T6 and their section shapes were C, T and L. The knife edge support was adopted during experiment. Some members failed for flexural buckling, and others failed for flexural-torsional buckling. The experimental results are shown in Table 1.

In 2006, an axial compression experiment of an aluminum alloy member with H section was conducted in Tongji University by Zhang [ 8]. The member was made of Chinese aluminum alloy 6061-T6. The double-knife edge support was adopted. The member failed for flexural buckling. The experimental results are shown in Table 1.

A series of experiments of profiled aluminum alloy members under axial compression were conducted by Zhu and Young [ 9] in University of Hong Kong in 2005. The members were made of Chinese aluminum alloy 6063-T5 and 6061-T6. The members were circular pipes with relatively small radius and thin wall. The supports were fixed. Some members failed for yielding, and others failed for overall bulking. The experimental results are shown in Table 1.

The mechanical properties of aluminum alloy were tested or obtained from material suppliers before member experiments [ 1– 9]. The material properties are shown in Table 2.

Sorting out the experimental data

Total 205 experimental data points are obtained from mentioned experiments, including the experiments in this paper. However, some of them are ineffective and useless for research in this paper. After sorted out, following data are ineffective and not considered in this paper: 1) members with spherical hinge supports; 2) members failed for local panel buckling; 3) members whose measured load-bearing capacity is obviously larger than Euler critical load.

After removing the ineffective data, 159 effective data points remain. The effective data points are collected from references, including 8 in Ref. [ 1], 8 in Ref. [ 2], 12 in Ref. [ 3], 9 in Ref. [ 4], 26 in Ref. [ 5], 36 in Ref. [ 6], 3 in Ref. [ 7], 1 in Ref. [ 8], 8 in Ref. [ 8], 8 in Ref. [ 9], with 53 date points in the experiment of this paper. It can be found that 30 data points are from experiments of members with H section, 11 from T section, 16 from L section, 4 from square section and 106 from circular section. The data points are almost evenly distributed over the slenderness ratios. As for failure mode, 4 members failed for yielding, 20 for flexural-torsional buckling and 143 for flexural buckling.

Detailed informations about the effective experimental data is listed in Table 1. The symbols used in Table 1 are explained as follows:

P_u—Ultimate load-bearing capacity of the member, measured from experiments;

\varphi —stability factor, \phi =P_{\mathrm{u}}/A{f}_{\mathrm{0.2}} , calculated according to the measured data;

\overline{\lambda } —regularized slenderness ratio. \overline{\lambda }={\displaystyle \frac{{\lambda }_y}{\pi }}\sqrt{{\displaystyle \frac{f_{\mathrm{0.2}}}{E}}} , for the flexural buckling. \overline{\lambda }={\displaystyle \frac{{\lambda }_{y\omega }}{\pi }}\sqrt{{\displaystyle \frac{f_{\mathrm{0.2}}}{E}}} , for the flexural-torsional buckling;

{\lambda }_y —slenderness ratio about the bending axis of the member for the flexural buckling;

{\lambda }_{y\omega } —equivalent slenderness ratio of the member for the flexural-torsional, which can be obtained according to the typical elastic theory;

A—measured section areas of the members;

f_{\mathrm{0.2}} —non-proportional limit stress of the member material, shown in Tables 2 and 3;

E —elastic modulus of the member material, shown in Tables 2 and 3.

Specifications of the member sections in Table 1 are as follows:

H section — H height × width × web thickness*flange thickness

Circular section —Φ outer diameter × wall thickness

Square section —□ width × wall thickness

L section — L width × wall thickness

T section — T height × width × web thickness × flange thickness

C section —C height × width × web thickness × flange thickness

All obtained data points and the effective data points are marked in \varphi -\overline{\lambda } coordinates and shown in Fig. 2 and Fig. 3 respectively.

Numerical analysis

FE models

With the aim of further study, the numerical analysis program that was devoted to the evaluation of the flexural buckling capacity was performed by means of the nonlinear code ANSYS. It should be noted that the shell 181 element was selected to model the flange and the web of the beam in consideration of varied section types.

Equivalent initial flexures of members

Before conducting the numerical analysis of the aluminum alloy members under axial compression, the equivalent initial flexure of the member should be determined. The upper limits about the initial flexure of a structural member are not always the same in design codes all over the world. In “Code for Design of Steel Structures (GB50017)” [ 10], L/1000 (L is the length of the member and the same thereinafter.) is regarded as the initial flexure of compressed members, and the influence of residual stresses is also considered. In “Technical Code of Cold-formed Thin-wall Steel Structures (GB50018)” [ 11], L/750+ 0.05ρ (ρ is the distance of kern of section) is regarded as the initial flexure of compressed members. In “European Recommendations for Aluminum Alloy Structures” issued by ECCS [ 12], L/1000 is regarded as the initial flexure. For members with closed cross section, centroidal eccentricity of the section caused by 10% thickness deviation is also considered. In codes for design of aluminum alloy structures in other countries, L/1000 is mostly regarded as initial flexure for creating column curves of aluminum alloy members.

In Chinese code “Wrought aluminum alloy extruded profiles for architecture” (GB/T 5237) [ 13], the initial flexure of profiled aluminum alloy members is limited to less than L/1250. Therefore, it is reasonable to take L/1000 as a maximum initial flexure. However, loading eccentricity is unavoidable for members under axial compression. The eccentricity may be caused by deviation of load position, joint structure and deviation of section thickness and so on. The eccentricity is a random variable. Since the eccentricity has no direct relationship with member length, it is not reasonable to take L/1000 of the initial flexure as equivalence of all initial imperfections when the slenderness ratio of the member is small. It may cause unsafe results.

Since there is no a widely accepted limit about the initial flexure in Chinese codes at present, the equivalent initial flexure can only be determined by the experimental results of this paper. Figure 4 shows the relationship between log₁₀(L/ν₀) and the slenderness ratios of members, in which v₀ is the equivalent initial flexure derived from measured strains in the experiments. It can be found from Fig. 4 that the distribution of log₁₀(L/ν₀) is relatively random. However, on the whole, the smaller the length of member is, the smaller the value of log₁₀(L/ν₀) is. The relationship between log₁₀(L/ν₀) and slenderness ratios of members can be regressed with the least square method and expressed as follow:

(1) {\log }_{\mathrm{10}}\left(L/v_{\mathrm{0}}\right)=\mathrm{0.015}\times {\lambda }_y+\mathrm{2.20},

(2) \mathrm{or}L/v_{\mathrm{0}}={\mathrm{10}}^{\mathrm{0.015}\times {\lambda }_y+\mathrm{2.20}}.

Meanwhile, to avoid the initial flexure is too small, following equation is proposed for determining L/ν₀ based on the limit of the initial flexure, L/750, in reference [ 11].

(3) L/v_{\mathrm{0}}=\min \left({\mathrm{10}}^{\mathrm{0.015}*{\lambda }_y+\mathrm{2.20}},\mathrm{750}\right).

From Eq. (3), the general distribution of the equivalent initial flexure can be described, but it cannot be used for all members as the accurate initial imperfection values. However, the caused risk of the member can be eliminated by reliability analysis in design.

Definition of typical cross-sections of members

Thirteen types of typical cross-sections in actual structures are listed in Table 4. The influence of geometric parameters of each type of the section on \varphi -\overline{\lambda } curves is analyzed and compared (Fig. 4). Based on reference [ 14], 52 cross-sections, which are most unfavorable for member stability, are selected as typical cross-sections of members used in investigation of this paper.

Confine of types of aluminum alloy

Four types of aluminum alloy made in China, named 6061-T6, 6063-T6, 6061-T4, and 6063-T5, are adopted in investigation of this paper. The elastic modulus, E, of the aluminum alloy is 68000.0 MPa and f_0.2 is determined according to the Chinese code “Wrought aluminum alloy extruded profiles for architecture” (GB/T 5237) [ 13]. The constitutive relationship models proposed by Ramberg-Osgood [ 15] and Steinhardt suggestion [ 16] are employed.

Numerical results

Following assumptions are adopted in numerical analysis of aluminum alloy members under axial compression: 1) Two ends of a member are hinged, but the plates can warp freely. 2) Residual stresses are not considered, since the residual stress of profiled aluminum alloy is relatively small [ 17], and the unfavorable effect of the residual stress is usually not considered.

Finally, 52 different cross-sections of members, including 13 types of cross-sections made of 4 aluminum alloys, under axial compression are analyzed. The results show that the members with H cross section which is biaxial symmetry finally buckle in lateral flexure on symmetric axes, and the members with H cross section of uniaxial symmetry buckle in lateral flexure on the symmetric axis or fail in flexural-torsional mode. From the numerical results, 252 column curves are obtained totally. For the different types of aluminum alloy, the numerical results are drawn in Fig. 5, in which the vertical axis stands for stability factor, and the horizontal axis represents regularized slenderness ratio \overline{\lambda } .

The fitting formulas

Perry formula is generally used in current design codes of relevant countries for calculating the stability factor of aluminum alloy members under axial compression:

(4) \varphi ={\displaystyle \frac{\mathrm{1}}{\mathrm{2}{\overline{\lambda }}^{\mathrm{2}}}}\left[\left({\overline{\lambda }}^{\mathrm{2}}+\mathrm{1}+{ϵ}_{\mathrm{0}}\right)-\sqrt{{\left({\overline{\lambda }}^{\mathrm{2}}+\mathrm{1}+{ϵ}_{\mathrm{0}}\right)}^{\mathrm{2}}-\mathrm{4}{\overline{\lambda }}^{\mathrm{2}}}\right],

where, ϵ₀ is the coefficient of the equivalent imperfection.

From the compassion of the numerical results and experimental results, it is verified that the FE models are effective and able to analysis the members accurately. In fact, the experimental data are not enough for fitting formulas due to their different sources and non-sequence in date. On the other hand, the numerical results are easy for analysis and data compilation. As results, the numerical data are taken for fitting the formulas for calculation the stability factor.

According to numerical results, after using the least square method, the calculating formulas of ϵ₀ can be obtained by the fitting method as follows:

(5a) \mathrm{Curve}1\mathrm{for}6061-T6\mathrm{and}6063-T6:{ϵ}_0=0.20{\overline{\lambda }}^3-0.50{\overline{\lambda }}^2+0.55\overline{\lambda }-0.05,

(5{{\rm\tf="fp1"\char"0062}}) \mathrm{Curve}2\mathrm{for}6061-T4\mathrm{and}6063-T5:{ϵ}_0=0.13{\overline{\lambda }}^3-0.35{\overline{\lambda }}^2+0.55\overline{\lambda }-\mathrm{0.05.}

In Eq. (5), the regularized slenderness ratio, \overline{\lambda } , is calculated according to the member buckling mode. \overline{\lambda } is calculated according to the flexural slenderness ratio λ_y of which the member buckles in the flexural mode, and according to the flexural-torsional slenderness ratio λ_yω of which the member buckles in the flexural-torsional mode.

The aluminum alloy members, from which the effective experimental data are obtained, are made of not only 6061-T6, but also 6063-T5, 5083-H321 and 6A02. Except 6061-T6 and 6063-T5, both of 5083-H321 and 6A02 are weak-hardening aluminum alloy, but their mechanical properties are close to 6061-T6. Therefore, coefficients of the equivalent imperfection and stability factors of the members, made of aluminum alloy except 6063-T5, can be calculated according to the formula of curve 1. Figure 3 shows the relationship between the calculating points according to the effective experimental data and the fitting curves. The comparison among the calculating points, the fitting curve 1 and the results from design codes of relevant countries is shown in Table 5. Due to limited space, the comparison is limited among the calculating points from the effective experimental data, the curve for weak hardening alloy in European code EC9 [ 18], the C2 curve in British code BS8118 [ 19] and the column curves in Chinese code GB50429 [ 20]. It can be found in Fig. 3 and Table 5 that, the fitting curve of this paper is lower than that in EC9 and BS8118 if the slenderness ratios of members are relatively large, and very close to that in EC9-2 if the slenderness ratios of members are relatively small. The points calculated from the experimental data are mostly located at both sides of the fitting curve. The maximum ratio of measured φ and fitted φ is 1.421, and the minimum is 0.792. Most of the ratios are located between 0.90 and 1.30. The average value, the standard deviation and the coefficient of variation are 1.11699, 0.13331 and 0.11935 respectively (See Fig. 6).

Conclusions

The following investigation about the aluminum alloy members under axial compression has been carried through in this paper:

1) Experiments of 63 profiled aluminum alloy members, made of Chinese 6061-T6, under axial compression are conducted in this paper. Meanwhile a large number of experimental data from published papers and technical reports are collected and sorted out. 213 experimental data points are obtained totally, and 167 of them are available.

2) The equivalent initial flexure of members is determined according to the experimental data obtained in this paper. Based on the parameter analysis method, this paper analyzed the influence of 52 different cross section and 4 types of aluminum alloy with 252 curves of \varphi -\overline{\lambda } .

3) According to numerical results, the Eqs. (5a) and (5b) are obtained by the fitting method based on the least square method. The formulas can be used for calculating the overall stability coefficient of Chinese profiled aluminum alloy members under axial compression.

From the above comparison, following conclusions can be drawn:

1) The fitting curve of this paper is lower than that in EC9 and BS8118 if the slenderness ratios of members are relatively large, but very close to that in EC9-2 if the slenderness ratios are relatively small.

2) The points calculated from the experimental data are mostly located at both sides of the fitting curve. The maximum ratio of measured φ and fitted φ is 1.421, and the minimum is 0.792. Most of the ratios are located between 0.90 and 1.10.

3) As for the statistic parameters, the average value, standard deviation and coefficient of variation are 1.11699, 0.13331 and 0.11935 respectively.

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