Axial compression behavior of edge stiffened C-profile aluminium alloy: a finite element analysis

ABSTRACT

Aluminium alloys find diverse applications in building construction. Specifically, C-profiles being used as various structural elements in the building. Providing Edge stiffeners in the C-profile leads to increase the load carrying capacity. Limited research is available on compression behaviour c-profile with edge stiffeners. Hence, this article aims to study the behaviour of a Finite Element Analysis of aluminium alloy stiffened edge C profiles subjected to axial compression. Two different aluminium alloy materials, namely 6061-T6, and 6063-T5 were investigated. Finite element models were developed and results, including ultimate load, failure modes, and load vs. axial shortening curves, were verified against existing test data. A comprehensive parametric study was carried out based on the verified finite element models, involving variation in the orientation of the edge stiffener, column length, and section thickness. A total of 144 parametric results were compared with the design strengths calculated from Euro code 9.

Keywords:
Aluminium alloys; C-profile; Column; Compression; Euro code 9; Finite Element Analysis

1. INTRODUCTION

Aluminium alloys are lightweight, corrosion resistant, and simple to produce, so that they are commonly used in structural applications. The members are manufactured by rolling, casting, extrusion and drawing techniques. Among these, the extrusion method is more efficient to extrude the different cross section geometries. Over the past few decades, a lot of research is being done in the area of aluminium alloys subjected to compressive loading. ZHU et al. [¹, ²] conducted both experimental and numerical study on the behavior of plain and lipped channel columns made of aluminum alloy. Obtained results were evaluated with the various design specifications from America, Australia/New Zealand, Europe and China. HUYNH et al. [³] studied the stub column behaviour of cold-rolled aluminium alloy column by finite element method. ZHU et al. [¹, ²] developed finite element model of welded aluminium alloy channel columns and validated with existing test results. The strengths obtained from finite element analysis were compared to the design strengths calculated by continuous and direct strength method. PHAM [⁴] and PHAM et al. [⁵] carried out investigation by numerically on aluminium alloy cold-rolled channel column by incorporating geometric imperfections. GEORGANTZIA et al. [⁶] conducted an experimental and numerical investigation on the structural performance of aluminium channel alloy column under fixed and pinned end condition. Also, proposed a design curve subjected to flexural buckling, and evaluated the application of direct strength method for finding the axial capacity of channel column. MAZZOLANI et al. [⁷], WANG et al. [⁸] and ZHANG et al. [⁹] investigated the behaviour of aluminium alloy angle section under axial compression. YUAN and Zhang [¹⁰] studied the buckling behaviour of T-section aluminium alloy column subjected to concentric load. SU et al. [¹¹] conducted compression test on aluminium alloy box sections with and without stiffeners. ZHU and YOUNG [¹²] investigated the strength effect of welding on hollow circular columns made by aluminium alloy. ZHAO et al. [¹³], HU et al. [¹⁴], ALI et al. [¹⁵], LI et al. [¹⁶] carried out the investigation on hollow aluminium alloy section under compression. LIU et al. [¹⁷, ¹⁸, ¹⁹] and CHANG et al. [²⁰] studied the behaviour of aluminium alloy irregular shaped columns. ZHAO and ZHAI [¹³] ZHAO et al. [²¹, ²², ²³] carried out the study on aluminium alloy column subjected to eccentric load. ROY et al. [²⁴, ²⁵] studied the influence of number of screws, thickness of the section and modified slenderness ratio on strength of built-up aluminium slender column alloy by conducting experimental and numerical investigation. The obtained strength was compared with calculated design strength by various design standards for aluminium alloy sections. FANG et al. [²⁶, ²⁷] studied the impact of size of web hole on axial strength of aluminium alloy built-up column fabricated as channel sections. WANG et al. [²⁸] investigated buckling resistance of the aluminium alloy stiffened column under the support condition of fixed and pinned. FENG and YOUNG [²⁹] studied the behaviour of aluminium alloy square stub compression members with circular opening. WANG et al. [⁸, ³⁰, ³¹] investigated the overall buckling failure of alumninium alloy columns. ZIÓŁKOWSKI and IMIEŁOWSKI [³²] carried out the study on buckling and post-buckling behaviour of stocky and slender shape prismatic aluminium columns. YOUNG [³³] carried out the research on Design and numerical investigations of cold-formed steel channel columns with simple lips and inclined edge stiffeners at various angle. WANG et al. [³⁴, ³⁵], ZHANG et al. [³⁶] and MANIKANDAN et al. [³⁷] investigated the effect of simple edge stiffeners on channel subjected to compression. ARUNA et al. [³⁸] conducted test and numerical investigation on cold-formed angle section with different edge stiffeners. So far the research has been carried out on the strength and behaviour of square, rectangular, circular hollow section, plain and lipped channel, T section, irregular, and built-up sections. SANTAPHAN and RAJARAM [³⁹] carried out the test on cold-formed steel frame made with lipped channel column and beam elements subjected to lateral loading. Though channel sections are pleasant in its appearance, good integrity, and can be easily connected, their use in construction has increased. Provision of edge stiffeners to these sections enhances buckling stress and retards distortional buckling.

This research seeks to develop a perfect finite element model and study the strength of fixed-ended aluminium alloy channel columns with various edge stiffeners. Finite element models were developed incorporating geometric and material nonlinearities and verified against existing test results. The verified FE model was then employed for a parametric study. Totally 144 columns were modelled and analysed with variation in parameters such as orientation of edge stiffener, thickness, column length. Furthermore, the column strengths obtained from parametric study were compared with the design column strengths calculated using the Eurocode (EC9) [⁴⁰].

2. FINITE ELEMENT ANALYSIS

2.1. Development of finite element model using existing test data

Finite element analysis was carried out using ABAQUS software, because it is inexpensive and time efficient compared with the experimental investigation. Simulation of fixed-ended aluminium alloy lipped channel columns tested by ZHU et al. [¹, ²] was carried out. Totally 6 specimens of Heat treated aluminium alloys 6061-T6 and 6063-T5 channel lipped sections were taken for the modelling. The nominal dimensions of the specimens were height of web 80 mm, width of web 40 mm, width of lip 15 mm and thickness of specimens 2 mm. Totally, three column lengths were taken such as 300mm, 1350 mm, and 1900 mm for T5 specimens; 300 m, 800 mm and 1350 mm for T6 specimens. Measured dimensions were used for the modelling. Material properties for modelling of the specimens were taken from existing coupon test results presented by ZHU et al. [¹, ²]. For T5 and T6 specimens, Young’s modulus is 63 GPa, and 62 GPa; Yield strength is 175 MPa and 239 Mpa; Ultimate stress is 186 MPa and 239 Mpa; percentage of elongation is 7.2%, and 7.4% respectively. Measured initial geometric imperfections of specimens also considered for the modelling of the specimens.

FEA was carried out in two steps. In the first step, the possible buckling modes of the columns were obtained by Eigen buckling analysis. Following this, the ultimate load and failure modes of the columns were obtained by performing non-linear analysis. Channel columns were modelled by S4R element. The mesh size was chosen as 10 x 10 mm because it simulates the experimental results accurately. Master node was created at centroid of the specimen on the loaded and unloaded end and this node connected to slave nodes, which were on the loaded and unloaded end of the cross section. The fixed-ended condition was modelled by constraining all the degree of freedom of master node at loaded and unloaded end, except translational degree of freedom at loaded end which is the direction of load. The load was applied via master node. Figure 1 shows the finite element modelling of the test specimens. The material non-linearity of aluminium was incorporated in FEA by giving input value of true stress and true strains. The plasticity model was used in ABAQUS to describe the non-linearity of the aluminium alloy and true stress (σ_true) and true plastic strain (ε^Pl_true) were calculating using equ. 1 and 2.

Figure 1
Modelling of the test specimens.

(1) $${\sigma }_{\text{true}}=\sigma (1+\epsilon )$$

(2) $${\epsilon }_{\text{true}}^{\text{Pl}}=\text{ln}\left(1+\epsilon \right)-\frac{{\sigma }_{\text{true}}}{\text{E}}$$

Where E is the Young’s Modulus, σ and ε are engineering stress and strain which were obtained based on original cross section area of the coupon specimens as illustrated in ZHU et al. [¹, ²].

2.2. Verification of finite element model

A total of 6 aluminium lipped alloy column in T5 and T6 series were analysed by finite element analysis. The specimens were labelled such that “T5-1350”, where T5 mentions the normal strength aluminium alloy 6063-T5 and 1350 represents the specimen length in mm. The ultimate load, axial compressive load vs. axial shortening curve obtained from FEA were verified with test results obtained by ZHU et al. [¹, ²] and presented in Figure 2, and 3 respectively. The failure mode obtained from the FEA is depicted in Figure 4 for the specimen T5-1350, which is revealed that the finite element analysis simulate the failure mode of existing test specimen carried by obtained ZHU et al. [¹, ²]. The mean value between ultimate loads obtained from test to FEA is 1 and corresponding coefficient of variation (CoV) is 0.02. Two failure modes were observed, including local buckling and interaction of local and flexural torsional buckling. Comparison of ultimate load, axial load vs. axial shortening and failure modes demonstrates the validity of the FEA predictions.

Figure 2
Comparison of FEM strengths with existing experimental strengths.

Figure 3
Axial load vs. axial shortening curves for specimen T5-1350.

Figure 4
Failure mode of specimen T5-1350.

3. PARAMETRIC STUDY

3.1. Details of the specimens

The strengths and behaviour of tested aluminium alloy lipped channel have been accurately predicted developed FEM. As a result, a detailed parametric investigation was conducted using verified FEM. The effect of variation of orientation of edge stiffeners, length and thickness of the specimens were investigated in the parametric study by analysing 144 number of fixed ended aluminium alloy channel columns. Nomenclature of the cross–sectional element is shown in Figure 5. The stiffened edge were oriented at various angles ranging from 45° to 315° with respect to horizontal plane of the flanges, as depicted in Figure 6. A flange width of 50 mm, web width of 90 mm and lip width of 15 mm were used for all the sections. The specimen thicknesses were 2 mm and 3 mm. High and normal strength aluminium alloy were used to model the material. Totally 6 lengths of the column were taken by varying the length from 400 mm to 3400 mm with an increment of 600 mm. The labelling of the specimen consists of type of aluminium alloy, angle of edge stiffener, length and thickness of the specimen. For example, the label “T6-C-A45-400-2” T6 – refers the high strength aluminium alloy 6063-T5; if “T6” is replaced with “T5”, then it refers the normal strength aluminium alloy 6061-T6, C refers channel section, A45 indicates the edge stiffeners with an angle of 45° with respect to horizontal plane of flanges, 400 refers the nominal length of the specimens and 2 represents the specimens thickness of 2 mm. The initial, local and global geometric imperfection was considered as 16% of specimen thickness and 1/2000 of the column length respectively as per the measurements conducted by ZU and YOUNG [¹², ⁴¹].

Figure 5
Nomenclature of specimen C-A45.

Figure 6
Orientation of edge stiffeners.

3.2. Parametric results and discussion

The failure modes of T5 and T6 specimens with a thickness of 2 mm are illustrated in Figures 7 and 8, respectively. Local, interaction of local-torsional, flexural-torsional, local-flexural, and local-torsional-flexural buckling modes were observed from the parametric study. Graphs depicting the relationship between axial compressive stress and slenderness ratio for T5 and T6 specimens are presented in Figures 8 to 11. Notably, for 2 mm thickness specimens, the channel sections with edge stiffeners oriented at 90 degrees (A270) demonstrated a higher axial resistance capacity compared to other cross sections. Conversely, for 3 mm thickness specimens, channel sections with edge stiffeners oriented at 225 degrees (A225) exhibited a greater axial resistance capacity compared to other cross sections.

Figure 7
Failures modes of T6 specimens of 2 mm thickness.

Figure 8
Axial compressive stress vs. slenderness ratio of T5-2 mm thickness specimens.

Figure 9
Axial compressive stress vs. slenderness ratio T6-2 mm thickness specimens.

Figure 10
Axial compressive stress vs. slenderness ratio T5-3 mm thickness specimens.

Figure 11
Axial compressive stress vs. slenderness ratio T6-3 mm thickness specimens.

4. DESIGN STRENGTH BY EUROCODE 9

The EC9 (2007) states that under axial compression loads structural members may fail via flexual, torsional or flexural torsional and local squashing. The compressive strength of the section is computed using the effective cross-section method. As per EC9, The design strength of the sections determined by following

(3) $$\text{P}=\text{min}({\text{P}}_{\text{C},\text{Rd};}{\text{P}}_{\text{b},\text{Rd},})$$

(4) $${\text{P}}_{\text{C},\text{Rd}}=\text{Ae *fy}$$

(5) $${\text{P}}_{\text{b},\text{Rd}}=\chi {\text{*A}}_{\text{e}}{\text{* f}}_{\text{y}}$$

(6) $$\chi =\frac{1}{\varphi +\sqrt{{\varphi }^2-{\lambda }^2}}<1$$

(7) $$\varphi =0.5\left(1+\alpha \left(\lambda -{\lambda }_0\right)+{\lambda }^2\right)$$

For flexural buckling $\lambda =\left(\frac{\text{KL}}{\text{i}\pi }\right)\sqrt{\raisebox{1ex}{${\text{A}}_{\text{e}}{\text{f}}_{\text{y}}$}\!\left/ \!\raisebox{-1ex}{$\text{AE}$}\right.}$

For torsional or torsional-flexural buckling $\lambda =\sqrt{\raisebox{1ex}{${\text{A}}_{\text{e}}{\text{f}}_{\text{y}}$}\!\left/ \!\raisebox{-1ex}{${\text{P}}_{\text{cr}}$}\right.}$

Where

PC,Rd = Design resistance for compression

Ae = effective area of cross-section

Pb,Rd = design buckling resistance of a compression member without welding

Χ = reduction factor related to the relevant buckling mode

α = imperfection factor

λ = relative slenderness

λ0 = limit of the horizontal plateau in the buckling curves

k = 0.85, buckling length factor for members

Pcr = elastic critical load for torsional buckling

5. COMPARISON OF RESULTS

The Strengths derived from the parametric results were compared with the design strengths computed according to Euro code 9, and findings are detailed in Tables 1 to 4. The mean and CoV of ratio between PFEM/PEC9 for T5 2 mm specimen is 1.78, and 0.14; for T5 3 mm specimens it is 1.748, and 0.123; T6 2 mm specimen is 1.866, and 0.182; for T6 3 mm specimen is 1.823, and 0.159 respectively. It shows that strength predicted by EC9 is more conservative.

Table 1
Comparison of results T5-2 mm specimens.

SPECIMEN ID	SLENDERNESS RATIO	PFEM	FAILURE MODE	PEC9	PFEM/ PEC9
T5-C-A45-2-400	19.14	64.50	L	40.38	1.60
T5-C-A45-2-1000	47.85	53.70	L+T	35.83	1.50
T5-C-A45-2-1600	76.56	42.07	F+T	25.88	1.63
T5-C-A45-2-2200	105.27	29.75	F+T	17.27	1.72
T5-C-A45-2-2800	133.98	24.75	F+T	12.16	2.04
T5-C-A45-2-3400	162.69	21.26	F+T	9.16	2.32
T5-C-A90-2-400	20.12	66.48	L	40.38	1.65
T5-C-A90-2-1000	50.31	62.78	L	34.96	1.80
T5-C-A90-2-1600	80.50	41.27	L+F	24.16	1.71
T5-C-A90-2-2200	110.68	28.81	F+T	15.24	1.89
T5-C-A90-2-2800	140.87	24.35	F+T	11.15	2.18
T5-C-A90-2-3400	171.05	19.49	F+T	8.44	2.31
T5-C-A135-2-400	20.80	67.81	L	40.38	1.68
T5-C-A135-2-1000	52.00	63.62	L	37.25	1.71
T5-C-A135-2-1600	83.19	42.92	L+F	28.76	1.49
T5-C-A135-2-2200	114.39	29.17	F+T	20.06	1.45
T5-C-A135-2-2800	145.59	23.97	F+T	14.27	1.68
T5-C-A135-2-3400	176.79	21.00	F+T	10.75	1.95
T5-C-A225-2-400	23.18	57.89	L	40.38	1.43
T5-C-A225-2-1000	57.96	51.66	L+F	35.56	1.45
T5-C-A225-2-1600	92.74	43.07	L+F	25.18	1.71
T5-C-A225-2-2200	127.51	31.51	F+T	16.56	1.90
T5-C-A225-2-2800	162.29	23.46	F+T	11.54	2.03
T5-C-A225-2-3400	197.07	19.18	F+T	8.61	2.23
T5-C-A270-2-400	21.70	63.19	L	40.38	1.57
T5-C-A270-2-1000	54.24	58.67	L	37.15	1.58
T5-C-A270-2-1600	86.79	48.65	L+F	28.42	1.71
T5-C-A270-2-2200	119.33	36.79	L+F	19.57	1.88
T5-C-A270-2-2800	151.88	26.48	L+F	13.75	1.93
T5-C-A270-2-3400	184.42	21.14	F+T	10.22	2.07
T5-C-A315-2-400	20.53	61.17	L	40.38	1.52
T5-C-A315-2-1000	51.33	53.10	L	37.59	1.41
T5-C-A315-2-1600	82.13	45.73	L+F	29.42	1.55
T5-C-A315-2-2200	112.93	36.44	L+F	20.64	1.77
T5-C-A315-2-2800	143.73	26.74	F+T	14.61	1.83
T5-C-A315-2-3400	174.53	21.55	F+T	10.87	1.98
Mean					1.78
COV					0.14

Table 2
Comparison of results T5-3 mm specimens.

SPECIMEN ID	SLENDERNESS RATIO	PFEM	FAILURE MODE	PEC9	PFEM/ PEC9
T5-C-A45-3-400	19.175	111.17	L	70.71	1.572
T5-C-A45-3-1000	47.936	100.09	L+F	60.88	1.644
T5-C-A45-3-1600	76.698	70.3	L+F+T	42.65	1.648
T5-C-A45-3-2200	105.46	48.96	L+F+T	29.03	1.687
T5-C-A45-3-2800	134.222	40.19	F+T	21.33	1.884
T5-C-A45-3-3400	162.984	35.38	F+T	16.86	2.098
T5-C-A90-3-400	20.052	113.24	L	70.71	1.601
T5-C-A90-3-1000	50.13	101.78	L	59.23	1.718
T5-C-A90-3-1600	80.209	66.83	L+F+T	40.13	1.665
T5-C-A90-3-2200	110.287	47.42	L+F	27.16	1.746
T5-C-A90-3-2800	140.365	39.8	F+T	20.08	1.982
T5-C-A90-3-3400	170.443	35.1	F+T	15.95	2.201
T5-C-A135-3-400	20.534	116.27	L	70.17	1.657
T5-C-A135-3-1000	51.335	106.9	L	64.43	1.659
T5-C-A135-3-1600	82.136	71.9	L+F	49.24	1.46
T5-C-A135-3-2200	112.936	49.63	L+F+T	34.9	1.422
T5-C-A135-3-2800	143.737	40.38	F+T	25.66	1.574
T5-C-A135-3-3400	174.538	35.14	F+T	19.98	1.759
T5-C-A225-3-400	24.054	100.27	L	70.17	1.429
T5-C-A225-3-1000	60.136	94.27	L+F	58.92	1.6
T5-C-A225-3-1600	96.217	76.82	L+F	39.14	1.963
T5-C-A225-3-2200	132.299	52.36	L+F+T	25.82	2.028
T5-C-A225-3-2800	168.381	39.64	F+T	18.57	2.135
T5-C-A225-3-3400	204.462	32.19	F+T	14.33	2.246
T5-C-A270-3-400	21.201	105.37	L	70.17	1.502
T5-C-A270-3-1000	53.003	99.96	L	64.31	1.554
T5-C-A270-3-1600	84.804	85.9	L+F	48.69	1.764
T5-C-A270-3-2200	116.606	58.78	L+F+T	33.86	1.736
T5-C-A270-3-2800	148.407	43.91	L+F+T	24.39	1.8
T5-C-A270-3-3400	180.209	35.17	L+F	18.62	1.889
T5-C-A315-3-400	19.862	108.92	L	70.17	1.552
T5-C-A315-3-1000	49.655	97.46	L	65.05	1.498
T5-C-A315-3-1600	79.448	89.72	L+F+T	50.26	1.785
T5-C-A315-3-2200	109.241	62.87	F+T	35.47	1.772
T5-C-A315-3-2800	139.034	46.33	F+T	25.68	1.804
T5-C-A315-3-3400	168.827	37.26	F+T	19.64	1.897
Mean					1.748
COV					0.123

Table 3
Comparison of results T6-2 mm specimens.

SPECIMEN ID	SLENDERNESS RATIO	PFEM	FAILURE MODE	PEC9	PFEM/ PEC9
T6-C-A45-2-400	19.14	76.82	L	49.83	1.54
T6-C-A45-2-1000	47.85	62.23	L	42.04	1.48
T6-C-A45-2-1600	76.56	45.22	L+F+T	27.77	1.63
T6-C-A45-2-2200	105.27	34.43	F+T	17.73	1.94
T6-C-A45-2-2800	133.98	29.15	F+T	12.30	2.37
T6-C-A45-2-3400	162.69	24.53	F+T	9.20	2.67
T6-C-A90-2-400	20.12	84.86	L	49.83	1.70
T6-C-A90-2-1000	50.31	80.95	L	40.60	1.99
T6-C-A90-2-1600	80.50	44.29	L+F	25.63	1.73
T6-C-A90-2-2200	110.68	33.52	F+T	16.18	2.07
T6-C-A90-2-2800	140.87	26.68	F+T	11.25	2.37
T6-C-A90-2-3400	171.05	20.32	F+T	8.47	2.40
T6-C-A135-2-400	20.80	85.79	L	49.83	1.72
T6-C-A135-2-1000	52.00	81.14	L	44.14	1.84
T6-C-A135-2-1600	83.19	45.10	L+F+T	31.54	1.43
T6-C-A135-2-2200	114.39	33.16	L+F+T	20.82	1.59
T6-C-A135-2-2800	145.59	27.80	L+F+T	14.52	1.91
T6-C-A135-2-3400	176.79	23.86	F+T	10.82	2.21
T6-C-A225-2-400	23.18	69.53	L	49.83	1.40
T6-C-A225-2-1000	57.96	57.33	L	41.54	1.38
T6-C-A225-2-1600	92.74	46.91	L+F	26.88	1.75
T6-C-A225-2-2200	127.51	33.00	L+F+T	16.96	1.95
T6-C-A225-2-2800	162.29	25.56	F+T	11.65	2.19
T6-C-A225-2-3400	197.07	20.85	L+F+T	8.64	2.41
T6-C-A270-2-400	21.70	80.76	L	49.83	1.62
T6-C-A270-2-1000	54.24	76.37	L	43.97	1.74
T6-C-A270-2-1600	86.79	55.66	L+F+T	31.09	1.79
T6-C-A270-2-2200	119.33	38.13	L+F+T	20.27	1.88
T6-C-A270-2-2800	151.88	28.54	F+T	13.97	2.04
T6-C-A270-2-3400	184.42	23.17	F+T	10.29	2.25
T6-C-A315-2-400	20.53	73.31	L	49.83	1.47
T6-C-A315-2-1000	51.33	60.38	L	44.65	1.35
T6-C-A315-2-1600	82.13	49.79	L+F+T	32.45	1.53
T6-C-A315-2-2200	112.93	37.23	F+T	21.49	1.73
T6-C-A315-2-2800	143.73	28.74	L+F	14.87	1.93
T6-C-A315-2-3400	174.53	23.62	F+T	10.96	2.16
Mean					1.866
COV					0.182

Table 4
Comparison of results T6-3 mm specimens.

SPECIMEN ID	SLENDERNESS RATIO	PFEM	FAILURE MODE	PEC9	PFEM/ PEC9
T6-C-E45-t3-400	19.17	142.21	L	91.25	1.56
T6-C-E45-t3-1000	47.94	118.73	L	72.75	1.63
T6-C-E45-t3-1600	76.70	74.95	L+F	45.87	1.63
T6-C-E45-t3-2200	105.46	55.27	L+F+T	29.93	1.85
T6-C-E45-t3-2800	134.22	47.20	L+F+T	21.67	2.18
T6-C-E45-t3-3400	162.98	40.88	F+T	16.97	2.41
T6-C-E90-t3-400	20.05	151.70	L	91.25	1.66
T6-C-E90-t3-1000	50.13	122.34	L	70.01	1.75
T6-C-E90-t3-1600	80.21	71.78	L+F	42.74	1.68
T6-C-E90-t3-2200	110.29	54.36	L+F	27.89	1.95
T6-C-E90-t3-2800	140.36	46.72	F+T	20.36	2.30
T6-C-E90-t3-3400	170.44	40.22	F+T	16.08	2.50
T6-C-E135-t3-400	20.53	156.20	L	91.25	1.71
T6-C-E135-t3-1000	51.33	130.84	L	78.66	1.66
T6-C-E135-t3-1600	82.14	76.02	L+F+T	54.66	1.39
T6-C-E135-t3-2200	112.94	55.10	L+F+T	36.53	1.51
T6-C-E135-t3-2800	143.74	46.53	L+F+T	26.28	1.77
T6-C-E135-t3-3400	174.54	41.01	F+T	20.26	2.02
T6-C-E225-t3-400	24.05	128.71	L	91.25	1.41
T6-C-E225-t3-1000	60.14	108.15	L	69.50	1.56
T6-C-E225-t3-1600	96.22	83.11	L+F+T	41.54	2.00
T6-C-E225-t3-2200	132.30	55.03	L+F+T	26.44	2.08
T6-C-E225-t3-2800	168.38	42.16	L+F+T	18.79	2.24
T6-C-E225-t3-3400	204.46	33.73	L+F+T	14.41	2.34
T6-C-E270-t3-400	21.20	141.45	L	91.25	1.55
T6-C-E270-t3-1000	53.00	123.60	L	78.51	1.57
T6-C-E270-t3-1600	84.80	96.78	L+F	53.89	1.80
T6-C-E270-t3-2200	116.61	61.99	L+F+T	35.34	1.75
T6-C-E270-t3-2800	148.41	46.36	F+T	24.92	1.86
T6-C-E270-t3-3400	180.21	37.26	F+T	18.85	1.98
T6-C-E315-t3-400	19.86	141.79	L	91.25	1.55
T6-C-E315-t3-1000	49.65	113.59	L	79.75	1.42
T6-C-E315-t3-1600	79.45	100.33	F+T	56.12	1.79
T6-C-E315-t3-2200	109.24	65.83	L+F+T	37.19	1.77
T6-C-E315-t3-2800	139.03	49.50	L+F+T	26.29	1.88
T6-C-E315-t3-3400	168.83	40.36	F+T	19.91	2.03
Mean					1.826
COV					0.159

Graphs were drawn between PEC9 and PFEM and shown in Figure 12. Equation was proposed by conducting linear regression analysis such as PEC9 = 0.6068 PFEM with R square value of 0.9621. The suggested equation provides a reasonably accurate prediction for the ultimate strength of aluminium alloy channel sections with diverse edge stiffeners.

Figure 12
PEC9 vs. PFEA.

6. CONCLUSIONS

A finite element analysis of aluminium alloy channel sections with different edge stiffeners subjected to compression are discussed in this paper. Finite element models were developed and verified against the test data. An extensive parametric study was undertaken using these verified finite element models resulting in a total of 144 specimens The study encompassed two different aluminium alloys, namely 6063-T5 and 6061-T6, various edge stiffeners, column lengths ranging from 400 mm to 3600 mm in increments of 400 mm, and different thicknesses. The strengths obtained from the finite element analysis were compared with those calculated using Eurocode 9. It was revealed that, the design strengths anticipated by Eurocode 9 were found to be highly conservative.

7. BIBLIOGRAPHY

• ^[1] ZHU, J.H., LI, Z., SU, M.-N., et al, “Behaviour of aluminium alloy plain and lipped channel columns”, Thin-walled Structures, v. 135, pp. 306–316, 2019. doi: http://doi.org/10.1016/j.tws.2018.11.010.
  » https://doi.org/10.1016/j.tws.2018.11.010.
• ^[2] ZHU, J.H., LI, Z., SU, M.-N., et al, “Numerical study and design of aluminium alloy channel section columns with welds”, Thin-walled Structures, v. 139, pp. 139–150, 2019. http://doi.org/10.1016/j.tws.2019.03.015.
  » https://doi.org/10.1016/j.tws.2019.03.015.
• ^[3] HUYNH, L.A.T., PHAM, C.H., RASMUSSEN, K.J.R., “Numerical simulations of cold-rolled aluminium alloy 5052 channel sections in stub column tests”, In: Proceedings of the 4th Congrès International de Géotechnique, Lecture Notes in Civil Engineering, 2018. doi: http://doi.org/10.1007/978-981-10-6713-6_19.
  » https://doi.org/10.1007/978-981-10-6713-6_19.
• ^[4] PHAM, N.H., “Numerical investigation of sectional buckling behaviors of cold-rolled aluminium alloy channel columns”, Key Engineering Materials, v. 942, pp. 173–180, 2023. doi: http://doi.org/10.4028/p-8lik6b.
  » https://doi.org/10.4028/p-8lik6b.
• ^[5] PHAM, N.H., PHAM, C.H., RASMUSSEN, K.J.R., “Finite element simulation of member buckling of cold-rolled aluminium alloy 5052 channel columns”, In: Proceedings of the 5th International Conference on Geotechnics, Civil Engineering Works and Structures, pp. 263–268, 2020. doi: http://doi.org/10.1007/978-981-15-0802-8_39.
  » https://doi.org/10.1007/978-981-15-0802-8_39.
• ^[6] GEORGANTZIA, E., GKANTOU, M., KAMARIS, G.S., “Aluminium alloy channel columns: Testing, numerical modelling and design”, Thin-walled Structures, v. 182, pp. 110242, 2023. doi: http://doi.org/10.1016/j.tws.2022.110242.
  » https://doi.org/10.1016/j.tws.2022.110242.
• ^[7] MAZZOLANI, F.M., PILUSO, V., RIZZANO, G., “Local buckling of aluminum alloy angles under uniform compression”, Journal of Structural Engineering, v. 137, n. 2, pp. 173–184, 2011. doi: http://doi.org/10.1061/(ASCE)ST.1943-541X.0000289.
  » https://doi.org/10.1061/(ASCE)ST.1943-541X.0000289.
• ^[8] WANG, Y.Q., WANG, Z.X., HU, X.G., et al, “Experimental study and parametric analysis on the stability behavior of 7A04 high-strength aluminum alloy angle columns under axial compression”, Thin-walled Structures, v. 108, pp. 305–320, 2016. doi: http://doi.org/10.1016/j.tws.2016.08.029.
  » https://doi.org/10.1016/j.tws.2016.08.029.
• ^[9] ZHANG, Y., WANG, Y., WANG, Z., et al, “Experimental investigation and numerical analysis of pin-ended extruded aluminium alloy unequal angle columns”, Engineering Structures, v. 215, pp. 110694, 2020. doi: http://doi.org/10.1016/j.engstruct.2020.110694.
  » https://doi.org/10.1016/j.engstruct.2020.110694.
• ^[10] YUAN, L., ZHANG, Q., “Buckling behavior and design of concentrically loaded T-section aluminum alloy columns”, Engineering Structures, v. 260, pp. 114221, 2022. doi: http://doi.org/10.1016/j.engstruct.2022.114221.
  » https://doi.org/10.1016/j.engstruct.2022.114221.
• ^[11] SU, M.-N., YOUNG, B., GARDNER, L., “Testing and design of aluminum alloy cross sections in compression”, Journal of Structural Engineering, v. 140, n. 9, pp. 04014047, 2014. doi: http://doi.org/10.1061/(ASCE)ST.1943-541X.0000972.
  » https://doi.org/10.1061/(ASCE)ST.1943-541X.0000972.
• ^[12] ZHU, J.H., YOUNG, B., “Experimental investigation of aluminium alloy circular hollow section columns”, Engineering Structures, v. 28, n. 2, pp. 207–215, 2006. doi: http://doi.org/10.1016/j.engstruct.2005.07.012.
  » https://doi.org/10.1016/j.engstruct.2005.07.012.
• ^[13] ZHAO, Y., ZHAI, X., “Reliability assessment of aluminum alloy columns subjected to axial and eccentric loadings”, Structural Safety, v. 70, pp. 1–13, 2018. doi: http://doi.org/10.1016/j.strusafe.2017.09.001.
  » https://doi.org/10.1016/j.strusafe.2017.09.001.
• ^[14] HU, Y., RONG, B., ZHANG, R., et al, “Study of buckling behavior for 7A04-T6 aluminum alloy rectangular hollow columns”, Thin-walled Structures, v. 169, pp. 108410, 2022. doi: http://doi.org/10.1016/j.tws.2021.108410.
  » https://doi.org/10.1016/j.tws.2021.108410.
• ^[15] ALI, S., GEORGANTZIA, E., KAMARIS, G.S., et al, “Experimental study of square and rectangular hollow section aluminium alloy columns”, Journal of Physics: Conference Series, v. 2198, n. 1, pp. 012046, 2022. doi: http://doi.org/10.1088/1742-6596/2198/1/012046.
  » https://doi.org/10.1088/1742-6596/2198/1/012046.
• ^[16] LI, B., WANG, Y., ZHI, X., et al, “Testing, modelling and design of 7A04-T6 high-strength aluminium alloy RHS columns under axial compression”, Journal of Building Engineering, v. 57, pp. 104910, 2022. doi: http://doi.org/10.1016/j.jobe.2022.104910.
  » https://doi.org/10.1016/j.jobe.2022.104910.
• ^[17] LIU, M., CHANG, Y., WANG, P., et al, “Buckling behaviors of thin-walled aluminum alloy column with irregular-shaped cross section under axial compression in a fire”, Thin-walled Structures, v. 98, pp. 230–243, 2016. doi: http://doi.org/10.1016/j.tws.2015.02.008.
  » https://doi.org/10.1016/j.tws.2015.02.008.
• ^[18] LIU, M., ZHANG, L., WANG, P., et al, “Buckling behaviors of section aluminum alloy columns under axial compression”, Engineering Structures, v. 95, pp. 127–137, 2015. doi: http://doi.org/10.1016/j.engstruct.2015.03.064.
  » https://doi.org/10.1016/j.engstruct.2015.03.064.
• ^[19] LIU, M., ZHANG, L., WANG, P., et al, “Experimental investigation on local buckling behaviors of stiffened closed-section thin-walled aluminum alloy columns under compression”, Thin-walled Structures, v. 94, pp. 188–198, 2015. doi: http://doi.org/10.1016/j.tws.2015.04.012.
  » https://doi.org/10.1016/j.tws.2015.04.012.
• ^[20] CHANG, Y., LIU, M., WANG, P., et al, “Behaviors and design method for distortional buckling of thin-walled irregular-shaped aluminum alloy struts under axial compression”, Engineering Structures, v. 153, pp. 18–135, 2017. doi: http://doi.org/10.1016/j.engstruct.2017.10.014.
  » https://doi.org/10.1016/j.engstruct.2017.10.014.
• ^[21] ZHAO, Y., ZHAI, X., SUN, L., “Test and design method for the buckling behaviors of 6082-T6 aluminum alloy columns with box-type and L-type sections under eccentric compression”, Thin-walled Structures, v. 100, pp. 62–80, 2016. doi: http://doi.org/10.1016/j.tws.2015.12.010.
  » https://doi.org/10.1016/j.tws.2015.12.010.
• ^[22] ZHAO, Y., ZHAI, X., WANG, J., “Buckling behaviors and ultimate strength of 6082-T6 aluminum alloy columns with square and circular hollow sections under eccentric compression - Part II: Parametric study, design provisions and reliability analysis”, Thin-walled Structures, v. 143, pp. 106208, 2019. doi: http://doi.org/10.1016/j.tws.2019.106208.
  » https://doi.org/10.1016/j.tws.2019.106208.
• ^[23] ZHAO, Y., ZHAI, X., WANG, J., “Buckling behaviors and ultimate strengths of 6082-T6 aluminium alloy columns under eccentric compression - Part I: Experiments and finite element modelling”, Thin-walled Structures, v. 143, pp. 106207, 2019. doi: http://doi.org/10.1016/j.tws.2019.106207.
  » https://doi.org/10.1016/j.tws.2019.106207.
• ^[24] ROY, K., CHEN, B., FANG, Z., et al, “Axial capacity of back-to-back built-up aluminum alloy channel section column”, Journal of Structural Engineering, v. 148, n. 2, pp. 04021265, 2022. doi: http://doi.org/10.1061/(ASCE)ST.1943-541X.0003238.
  » https://doi.org/10.1061/(ASCE)ST.1943-541X.0003238.
• ^[25] ROY, K., CHEN, B., FANG, Z., et al, “Local and distortional buckling behaviour of back-to-back built-up aluminium alloy channel section columns”, Thin-walled Structures, v. 163, pp. 107713, 2021. doi: http://doi.org/10.1016/j.tws.2021.107713.
  » https://doi.org/10.1016/j.tws.2021.107713.
• ^[26] FANG, Z., ROY, K., CHEN, B., et al, “Local and distortional buckling behaviour of aluminium alloy back-to-back channels with web holes under axial compression”, Journal of Building Engineering, v. 47, pp. 103837, 2022. doi: http://doi.org/10.1016/j.jobe.2021.103837.
  » https://doi.org/10.1016/j.jobe.2021.103837.
• ^[27] FANG, Z., ROY, K., CHEN, B., et al, “Effect of the web hole size on the axial capacity of back-to-back aluminium alloy channel section columns”, Engineering Structures, v. 260, pp. 114238, 2022. doi: http://doi.org/10.1016/j.engstruct.2022.114238.
  » https://doi.org/10.1016/j.engstruct.2022.114238.
• ^[28] WANG, H., LI, P., JIAN, B., et al, “Investigation of buckling resistance of cable-stiffened aluminium alloy columns”, Thin-walled Structures, v. 165, pp. 107946, 2021. doi: http://doi.org/10.1016/j.tws.2021.107946.
  » https://doi.org/10.1016/j.tws.2021.107946.
• ^[29] FENG, R., YOUNG, B., “Experimental investigation of aluminum alloy stub columns with circular openings”, Journal of Structural Engineering, v. 141, n. 11, pp. 04015031, 2015. doi: http://doi.org/10.1061/(ASCE)ST.1943-541X.0001265.
  » https://doi.org/10.1061/(ASCE)ST.1943-541X.0001265.
• ^[30] WANG, Y., LIN, S., FENG, F., et al, “Numerical simulation of aluminum alloy 6082-t6 columns failing by overall buckling”, Advances in Structural Engineering, v. 19, n. 10, pp. 1547–1574, 2016. doi: http://doi.org/10.1177/1369433216643899.
  » https://doi.org/10.1177/1369433216643899.
• ^[31] WANG, Z.X., WANG, Y.Q., SOJEONG, J., et al, “Experimental investigation and parametric analysis on overall buckling behavior of large-section aluminum alloy columns under axial compression”, Thin-walled Structures, v. 122, pp. 585–596, 2018. doi: http://doi.org/10.1016/j.tws.2017.11.003.
  » https://doi.org/10.1016/j.tws.2017.11.003.
• ^[32] ZIÓŁKOWSKI, A., IMIEŁOWSKI, S., “Buckling and post-buckling behaviour of prismatic aluminium columns submitted to a series of compressive loads.”, Experimental Mechanics, v. 51, n. 8, pp. 1335–1345, 2011. doi: http://doi.org/10.1007/s11340-010-9455-y.
  » https://doi.org/10.1007/s11340-010-9455-y.
• ^[33] YOUNG, B., “Design of channel columns with inclined edge stiffeners”, Journal of Constructional Steel Research, v. 60, n. 2, pp. 183–197, 2004. doi: http://doi.org/10.1016/j.jcsr.2003.09.001.
  » https://doi.org/10.1016/j.jcsr.2003.09.001.
• ^[34] WANG, C., ZHANG, Y., ZHANG, Z., “Experiments on channel columns with inclined simple edge stiffeners under compression loading”, Frontiers of Architecture and Civil Engineering in China, v. 1, n. 3, pp. 312–321, 2007. doi: http://doi.org/10.1007/s11709-007-0041-z.
  » https://doi.org/10.1007/s11709-007-0041-z.
• ^[35] WANG, C., ZHANG, Y., ZHANG, Z., “Experimental investigation on channel columns with inclined simple edge stiffeners under compression loading.”, Journal of Building Structures, v. 27, n. 3, pp. 1–9, 2006.
• ^[36] ZHANG, Y., WANG, C., ZHANG, Z., “Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners”, Journal of Constructional Steel Research, v. 63, n. 3, pp. 383–395, 2007. doi: http://doi.org/10.1016/j.jcsr.2006.04.008.
  » https://doi.org/10.1016/j.jcsr.2006.04.008.
• ^[37] MANIKANDAN, P., ARUNA, G., BALAJI, S., et al, “Evaluation on effectiveness of cold-formed steel column with various types of edge stiffener”, Arabian Journal for Science and Engineering, v. 42, n. 9, pp. 4157–4168, 2017. doi: http://doi.org/10.1007/s13369-017-2571-6.
  » https://doi.org/10.1007/s13369-017-2571-6.
• ^[38] ARUNA, G., ROY, K., LIM, J.B.P., et al, “Cold-formed steel equal angles with complex edge stiffeners under axial-compression laboratory testing, numerical simulation, and design”, Practice Periodical on Structural Design and Construction, v. 27, n. 2, pp. 04022012, 2022. doi: http://doi.org/10.1061/(ASCE)SC.1943-5576.0000678.
  » https://doi.org/10.1061/(ASCE)SC.1943-5576.0000678.
• ^[39] SANTAPHAN, S.S., RAJARAM, B., “Experimental investigation on cold-formed steel structural frame made with lipped channel column and beam elements subjected to lateral loading coldformed cold formed”, Matéria (Rio de Janeiro), v. 29, n. 3, pp. e20240323, 2024. doi: http://doi.org/10.1590/1517-7076-rmat-2024-0323.
  » https://doi.org/10.1590/1517-7076-rmat-2024-0323.
• ^[40] EUROPEAN COMMITTEE FOR STANDARDIZATION, EUROCODE 9: Design of Aluminium Structures—Part 1–1: General Rules and Rules for Buildings, BS EN 1999-1-1:2007,CEN, 2007.
• ^[41] ZHU, J.H., YOUNG, B., “Numerical investigation and design of aluminum alloy circular hollow section columns”, Thin-walled Structures, v. 46, n. 12, pp. 1437–1449l, 2008. doi: http://doi.org/10.1016/j.tws.2008.03.006.
  » https://doi.org/10.1016/j.tws.2008.03.006.

Publication Dates

• Publication in this collection
  28 Feb 2025
• Date of issue
  2025

History

• Received
  21 Oct 2024
• Accepted
  09 Jan 2025