Structural Behaviour of Aluminium Alloy Angle Sections After Elevated Temperatures

Abstract

This study investigated the post-fire resistances of 6063-T5 aluminium alloy angle section stub columns (SCs). The post-fire mechanical properties of 6063-T5 aluminium alloy were assessed using tensile coupon tests. Instead of exhibiting a yield plateau, the stress–strain curves indicated a shift from an elastic to a strain-hardening phase. The impacts of elevated-temperature exposure on the residual elastic modulus were negligible. Strength properties decreased while ductile properties increased within the elevated-temperature range of 200 to 450 °C, with a subsequent strength increase observed beyond 450 °C. After the SC tests, gradual decreases in ultimate resistance were observed within 200–450 °C, followed by an increase beyond 450–500 °C. These trends in the ultimate resistance closely paralleled those strength characteristics observed in the stress–strain curves. As regards the failure mode, all specimens experienced local buckling after exposure to the range of elevated temperatures. The failure mode, ultimate resistance, and load–end shortening curve were used to evaluate a numerical modelling approach that was created to simulate the residual resistance of SCs after exposure to different elevated temperatures was applied. The EC9, ADM-2020, AS/NZS 1664, and GB 50429-2007 were among the design approaches that were evaluated using the experimental and numerical data. Due to the increased strain-hardening behaviour caused by elevated temperatures, the existing design methods proved excessively conservative when applied to the direct prediction of ultimate resistances of 6063-T5 aluminium alloy angle section SCs. The modified design provisions in light of the observed post-fire strain-hardening behaviour improved the accuracy in predicting the residual bearing capacity of 6063-T5 aluminium alloy angle section SCs, which showed better agreement with test and numerical results, offering enhanced applicability for post-fire design.

1. Introduction

Aluminium alloy is becoming more and more popular in building structures because of the exceptional corrosion resistance, recyclability, and high strength-to-weight ratio [1]. Aluminium alloy components formed by extrusion are widely used in structures servicing corrosive environments, such as angles, channels, and hollow sections. Investigations have been conducted on aluminium alloy stub columns (SCs) with different cross-sections, encompassing hollow sections [2,3], channel sections [4], and I-sections [5]. The suitability of the design methodologies described in the current standards was examined in these investigations. Mazzolani et al. [6] performed many experimental investigations on aluminium alloy angle sections exposed to local buckling to assess the precision of the current design regulations. Wang et al. [7] experimentally and numerically investigated the axial-compression behaviour of 7A04 high-strength aluminium alloy angle columns and demonstrated that existing design methods could not always accurately predict their buckling resistance, prompting the development of a modified design approach. Evangelia et al. [8] provided numerical evidence on the local buckling response and strength of aluminium alloy angle SCs, and showed that the accuracy of existing design methods could be further improved. Nevertheless, the study did not consider behaviour after fire exposure. Su et al. [9] gathered a large amount of test and simulation data on various sections of different members in order to evaluate the slenderness limits in current aluminium alloy design codes. Zhou et al. [10,11] further investigated aluminium alloy columns in composite forms and showed that the structural response and strength were influenced by geometric parameters and concrete strength. However, the extant investigations into aluminium alloy materials, members, and structures have predominantly focused on ambient-temperature conditions. Notably, studies focusing on aluminium alloy members and structures under post-fire conditions have been scarce.

Fire safety remains a paramount concern for metal structures because the elevated temperatures during fires can significantly weaken the mechanical properties of structural alloys [12,13,14]. Understanding the residual capacity of structures following fire exposure, particularly in cases where collapse does not occur, is crucial for post-fire service performance evaluations [15,16,17]. Research on the post-fire mechanical properties of structural steels has garnered considerable attention [18,19]. As regards aluminium alloys, Liu et al. [20] and Chen et al. [21] investigated the post-fire mechanical properties of various grades of aluminium alloys by considering different cooling methods. These scholars devised predictive equations to assess residual mechanical properties, considering the effects of cooling methods and elevated temperatures. Wang et al. [22] studied the residual factors and a two-stage Ramberg–Osgood material model through experimental studies on a heated 7A04-T6 aluminium alloy subject to cooling. Furthermore, Sun et al. [23] studied the mechanical properties of 6063-T5 aluminium alloy after fire exposure, revealing the impacts of the elevated temperatures on key mechanical parameters. Zhong et al. [15,24] examined the post-fire compression behaviour and load-bearing capacity of S700 SCs with rectangular and circular hollow sections via experiments and numerical simulations. Zuo et al. [25] investigated post-fire cold-formed elliptical hollow sections and devised modified design approaches for ultimate resistance. He et al. [26] performed a test involving 16 austenitic stainless-steel circular hollow-section SCs in order to evaluate the applicability of established design approaches for post-fire stainless-steel structures. As regards aluminium alloy SCs, Sun et al. [27] studied the post-fire compressive behaviour of aluminium alloy channel-section SCs and showed that existing design rules were overly conservative because they did not properly account for post-fire strain-hardening. However, studies focusing on the post-fire load-bearing capacity of aluminium alloy angle section SCs are lacking.

On the basis of clarifying the bearing performance of SCs, the bearing performance of slender columns could be revealed by considering the influence of overall buckling. Therefore, the post-fire load-bearing capacity of SCs is the key foundation to assess the post-fire serviceability of aluminium alloy structures after fire exposure. In this context, the present study investigates the post-fire compressive behaviour of 6063-T5 aluminium alloy angle section SCs through experimental and numerical analyses with different geometric dimensions and elevated temperatures.

2. Experimental and Numerical Methods

2.1. Test Specimen Preparation

To examine the post-fire capacity of the 6063-T5 aluminium alloy angle section SCs, a tensile coupon test on the aluminium alloy specimen and an axial-compressive-loading process on the angle section SCs were performed. For the 6063-T5 aluminium alloy angle section SC specimens, the geometric cross-section is shown in Figure 1. The dimensions are listed in

Table 1. Geometric dimensions of the angle section SCs.

Cross-Section	B (mm)	H (mm)	L (mm)	t (mm)	B/t	Classification in EC9
A1	40	40	120	0.8	50	Class 4
A2	50	50	150	2.8	17.9	Class 4

. The length L of the SC is 3B. The primary purpose of the axial-compressive-loading test on SCs is to determine their cross-sectional bearing capacity, which provides a critical foundation for predicting the bearing capacity of slender columns.

Table 2. Chemical composition of the angle section SCs (wt%).

Cross-Section	Cu	Zn	Mg	Cr	Fe	Mn	Ti	Si
A1	0.032	0.0050	0.60	0.0063	0.246	0.014	0.0029	0.427
A2	0.031	0.0051	0.59	0.0066	0.243	0.013	0.0028	0.427

shows the chemical composition of the aluminium alloy specimens in this study. For the design approach in EC9 [28], four classes of cross-sections were considered. For Classes 1, 2, and 3 (non-slender), the yield loading of the cross-section could be achieved. For Class 4 (slender), local buckling occurred before attaining the yield loading. To comprehensively investigate the post-fire resistant capacity of the angle section SCs, the two different slender cross-sections, presented in Table 1, were considered. It should be noted that Class 4 aluminium alloy angle sections were selected in the present study because they are more susceptible to local buckling, which governs their structural response. Therefore, the conclusions drawn herein are mainly applicable to slender sections. The same batch of 6063-T5 aluminium alloy extrusions was used to prepare the angle section SC specimens. Thus, for SCs with the same cross-sections, the material properties were considered to be the same. Hence, elevated-temperature exposure was selected to simulate the impacts of fire. Figure 2 displays the geometry size of the tensile coupon specimens, according to the recommendations in GB/T 228-2021 [29].

2.2. Elevated-Temperature Exposure Treatment

An elevated-temperature exposure process was employed to simulate the effects of fire on 6063-T5 aluminium alloy specimens. The experimental findings reported by Sun et al. [27] suggest that the impacts of elevated temperatures on the post-fire mechanical properties of the 6063-T5 aluminium alloy could be ignored for elevated temperatures that were not higher than 200 °C. The lowest elevated temperature in this study was determined to be 200 °C. There was an evident decrease in the strength characteristics of the 6063-T5 aluminium alloy for elevated temperatures within 200–400 °C. To meticulously examine the post-fire resistant performance of the 6063-T5 aluminium alloy angle section SCs, 250 and 350 °C were included among the elevated temperatures in this study. For the cases of exposure to 500–550 °C, previous test results indicated that the changes among the stress–strain properties for 6063-T5 aluminium alloy were negligible [27]. Accordingly, elevated temperatures of 200, 250, 300, 350, 400, 450, and 500 °C were considered in this study. For each target temperature, two angle section SC specimens and six tensile coupon specimens were prepared, giving a total of 16 aluminium alloy SC specimens and 48 tensile coupon specimens. All specimens were fabricated from the same batch of 6063-T5 aluminium alloy extrusions to ensure material consistency throughout the test programme.

After determining the elevated temperatures, an elevated-temperature exposure treatment was conducted to obtain post-fire SCs and tensile coupons. A N30/85HA (Nabertherm GmbH, Lilienthal, Germany) air circulation box furnace was employed in this experiment (Figure 3). The furnace temperature was increased from ambient temperature to the target temperature at a constant heating rate of 15 °C/min, as this rate can provide a stable temperature increase while ensuring a relatively uniform temperature distribution within the specimens during heating [23]. The tensile coupon and SC specimens were soaked for 30 min after reaching the pre-set elevated temperature to achieve uniform heating. Subsequently, the tensile coupon and SC specimens were removed from the furnace and cooled in an ambient-temperature (25 °C) air environment. This testing methodology has been widely used to investigate post-fire materials and members [30,31].

2.3. Tensile Coupon Test

After the elevated-temperature exposure treatment, a tensile coupon test was performed to quantify the effect of the elevated temperatures on the residual stress–strain responses of the 6063-T5 aluminium alloy specimens with cross-sections A1 and A2 (as shown in Figure 4). A mechanical testing machine (CMT 5305, MTS Industrial Systems (China) Co., Ltd., Shanghai, China) was used to perform the tensile coupon tests. An extensometer with a 50 mm original gauge length was used to record the deformation of the coupon specimen’s test section. The testing machine could provide the requisite tensile loads, and 30 Hz was chosen as the data-gathering frequency. The tensile stress was regulated by displacement at 0.2 mm/min and continued until fracture occurred. Then, by using the experimental results of deformation and tensile loading, the post-fire stress–strain curves of 6063-T5 aluminium alloy were measured.

2.4. Stub Column Test

After exposure to fire, axial-loading tests were conducted on the 6063-T5 aluminium alloy angle section SCs to determine their failure modes and load-bearing capacity. The significance of accounting for the initial geometric imperfection in the SC has been acknowledged by numerous scholars [32,33]. Consequently, before performing the axial-stress test, the initial geometric flaws of the SCs were assessed. The highest plane deflections of the basic plates of the SC specimens with the A1 cross-section were 0.03 mm, and those of the A2 cross-section were 0.05 mm. The experimental setup for axial-loading tests is shown in Figure 5. The axial-loading tests were conducted using the CMT 5105 tester system. The axial end shortening of the specimens was recorded by two linear variable differential transformers. Stiffeners were employed to maintain fixed-end boundary conditions and to suppress local buckling at the specimen ends. Displacement-controlled loading was applied at a constant rate of 0.05 mm/min. The applied load was recorded through the testing system with a data acquisition frequency of 30 Hz. Once the ultimate load was reached, the test was paused for one minute to permit stress relaxation, following recommendations from earlier studies [32,33,34]. Loading ceased when a significant reduction in load was observed after reaching the peak value. Additionally, the failure mode of the SC specimen was carefully documented.

2.5. Numerical Modelling

Numerical analyses of the post-fire 6063-T5 aluminium alloy angle section SCs were performed using ABAQUS 2022, as shown in Figure 6. The stress–strain behaviour of the post-fire alloy was obtained from tensile coupon testing and converted into true stress–strain curves for numerical input. The finite element analysis was performed using a residual-material modelling approach, in which the experimentally obtained post-fire stress–strain curves were directly assigned to the structural model after cooling to ambient temperature. Therefore, thermal expansion, temperature gradients, and thermally induced residual stresses were not considered in the present analysis. The model is intended to evaluate the structural response based on residual-material properties after fire exposure. By utilizing the S4R shell element, 6063-T5 aluminium alloy angle section SC numerical models were constructed, enabling the effective simulation of the elastic buckling pattern. This feature is well-suited for thin-walled components, as widely acknowledged in the literature [32,33,35,36,37,38]. The fixed-end boundary conditions in the axial-loading test were reproduced numerically by coupling the column ends with two reference points. At one reference point, both translational and rotational degrees of freedom were fully constrained, while at the other, axial translation was permitted. Mesh convergence analyses were performed to identify the optimal element size, with mesh densities varying from B/40 to B/3. Relevant results depicted in Figure 7 indicated that a mesh size of B/10 was applicable and was employed in subsequent numerical analyses. The numerical analysis considered the influence of initial geometric imperfections. The initial geometric imperfection profile was derived from the buckling modes predicted by the elastic buckling analysis of perfect numerical models. Relevant results of the virgin angle section SC are presented in Figure 8, showing various initial geometric imperfection distribution forms and amplitudes. Subsequently, the first buckling mode and B/125 imperfection amplitude were deemed appropriate.

3. Results and Parametric Study

3.1. Stress–Strain Curves

The post-fire stress–strain curves of the 6063-T5 aluminium alloy specimens with both A1 and A2 cross-sections are shown in Figure 9. No clear yield plateaus were observed. Strain-hardening is observed after the initial elastic segment. The yield strength f_o is defined as the stress corresponding to a residual strain of 0.2% [39]. As the ultimate stress was achieved, the stress decreased with increasing strain. The elastic moduli of the specimens remained almost the same as the elevated temperatures varied. The specimens with both A1 and A2 cross-sections exhibited similar variation trends for the key mechanical properties. The virgin specimen and the specimen with an elevated temperature of 200 °C showed very little variation in their stress–strain curves. This is also observed in the experimental results presented in the prior study [27]. For 200 °C ≤ T ≤ 400 °C, the strength dropped, while the ductility qualities rose. Thereafter, the strength properties were enhanced for the elevated temperatures within 400–500 °C. The related numerical study of the aluminium alloy angle section SCs with the A1 or A2 cross-section was conducted using the residual stress–strain curves after exposure to elevated temperatures (Figure 9).

3.2. Load–End Shortening Curves

After conducting the axial-loading test, the post-fire load–end shortening curves of the 6063-T5 aluminium alloy angle section SCs were obtained, as illustrated in Figure 10. For instance, the designation A1-T200 indicated the A1 angle section with an elevated temperature of 200 °C. The test findings indicated that the initial resistance stiffness was negligibly affected by the elevated temperatures. All the resistance curves demonstrated a unimodal shape. The ultimate resistance of the specimens after exposure to various elevated temperatures is presented in

Table 3. Test and numerical results of the 6063-T5 aluminium alloy angle section SCs.

Cross-Section	Specimen ID	Nu,test (kN)	δ (mm)	Nu,test/Afo	Nu,FE (kN)	Nu,FE/Nu,test
A1 40 × 40 × 0.8	A1-T25	4.04	0.323	0.361	4.09	1.012
	A1-T200	4.08	0.342	0.356	4.14	1.016
	A1-T250	3.88	0.296	0.385	3.92	1.011
	A1-T300	2.59	0.195	0.470	2.63	1.016
	A1-T350	1.57	0.129	0.568	1.62	1.030
	A1-T400	1.29	0.152	0.588	1.39	1.075
	A1-T450	1.39	0.114	0.583	1.43	1.029
	A1-T500	1.95	0.148	0.536	1.99	1.022
A2 50 × 50 × 2.8	A2-T25	38.39	0.361	0.704	38.55	1.004
	A2-T200	34.93	0.372	0.713	35.83	1.026
	A2-T250	32.85	0.347	0.732	34.22	1.042
	A2-T300	21.54	0.249	0.865	22.60	1.049
	A2-T350	15.31	0.562	1.058	15.66	1.023
	A2-T400	10.83	0.465	1.135	11.07	1.022
	A2-T450	12.20	0.666	1.195	12.71	1.042
	A2-T500	18.18	0.398	1.024	18.46	1.015
	Mean	-	-	-	-	1.027
	COV	-	-	-	-	0.017

. Within 200–400 °C, the ultimate resistance gradually decreased. Subsequently, a rise in ultimate resistance was detected between 400 and 500 °C. The ultimate resistance trends were found to be consistent with the strength behaviour reflected in the stress–strain responses (Figure 9). Both the A1 and A2 cross-sections belong to Class 4 (EC9), and the effects of the elevated temperatures on the resistance curves of the SC specimens with both cross-sections were similar. Specifically, δ represents the end shortening corresponding to the peak load of the specimen. Af_o denotes the axial yield capacity of the cross-section, calculated as the product of the cross-sectional area A and the yield strength f_o. The ratio Nᵤ_,test/Af_o, therefore, represents the normalized ultimate capacity obtained from the test results relative to the cross-sectional yield capacity. Notably, the influence of the elevated temperatures on the ratio N_u,test/Af_o was evident, resulting in differences in the cross-sectional classification of the SCs. As the failure modes of the 6063-T5 aluminium alloy angle section SC specimens, all SCs exposed to different elevated temperatures showed modes of local buckling. The influence of the elevated temperatures on the specimens’ failure modes was comparatively minor.

3.3. Validation

To validate the numerical modelling approach for assessing the post-fire load-bearing capacity of 6063-T5 aluminium alloy angle section SCs, a comparative analysis was conducted on experimental and numerical outcomes. It is noteworthy that a remarkable consistency in the load–end shortening curves from the experiment and numerical analysis was observed (Figure 11), particularly before reaching the peak point. Table 3 presents a comparison of the experimental and numerical ultimate-resistance results. The ratio N_u,FE/N_u,test has a mean value of 1.027 and a coefficient of variation (COV) of 0.017. The numerical modelling method accurately simulated the weakening effects of fire exposure on the residual bearing capacity of 6063-T5 aluminium alloy angle section SCs. The numerical study correctly identified the buckling performance of the SCs after fire exposure with respect to the failure mechanism (Figure 12), with particular emphasis on the local buckling of flanges. Therefore, this study’s numerical modelling approach works well for examining the 6063-T5 aluminium alloy angle section SC’s residual resistance after fire exposure.

3.4. Parametric Study

The experiments were carefully compared with the findings of the study using the numerical modelling approach. The previously indicated numerical modelling technique was then used to perform a parametric analysis. The key parameters considered were the geometric dimensions and elevated temperatures, as outlined in

Table 4. Parametric study of cross-section geometric dimensions.

Cross-Section	H (mm)	B (mm)	t (mm)	T (°C)
Angle section	50	50	3.6, 6.5, 9.1, 11.6	25, 200, 250, 300, 350, 400, 450, 500
	100	100	6.5, 11.8, 16.6, 21
	150	150	8.9, 16, 22.6, 28.7
	200	200	10.8, 19.4, 27.4, 34.7
	240	240	11.8, 21.2, 29.9, 37.9
	280	280	12.5, 22.5, 31.7, 40.2

. The geometric dimensions include the width and thickness of the outer flanges. The outer flange width varied from 50 to 280 mm, and the thickness was in the range of 3.6–40.2 mm. The length was three times the outer flange height in every numerical model. Elevated temperatures ranged from 200 to 500 °C, where the interval was 50 °C. A virgin specimen without exposure to elevated temperatures was also included as a benchmark. In total, 192 numerical models were used in the parametric study. Notably, ε_EC9 = (250/f_o)^0.5, where f_o represented the 0.2% proof strength. ε_EC9 exerted influence on slenderness parameters, thereby affecting cross-section classes. For the 6063-T5 aluminium alloy angle section SCs studied, the threshold value distinguishing Classes 3 and 4 was set to 5.5, as depicted in Figure 13. Variations in the mechanical properties of 6063-T5 aluminium alloy were induced by varying the elevated temperatures. Consequently, different ε_EC9 values were derived from the experimental results of the mechanical properties. All of the numerical models in this parametric investigation had their b/tε_EC9 values calculated. It is clear that this parametric analysis includes the non-slender (Classes 1, 2, and 3) and slender (Class 4) cross-sections listed in EC9 [28]. The effects of the elevated temperatures on the ultimate resistance of 6063-T5 aluminium alloy angle section SCs were comprehensively revealed through a parametric study. The geometric dimensions used for the numerical models in the parametric investigation were thus deemed suitable.

4. Post-Fire Ultimate-Resistance Evaluation

Despite the changes in the mechanical properties of the 6063-T5 aluminium alloy following exposure to elevated temperatures, the nonlinear features of the stress–strain curves remained largely parallel. Notably, research pertaining to 6063-T5 aluminium alloy SCs unaffected by fire exposure served as the foundation for the development of current design codes. Thus, it is imperative to assess whether these current design codes are applicable for predicting the resistance performance of 6063-T5 aluminium alloy SCs after exposure to elevated temperatures. This assessment considered the design codes outlined in EC9 [28], ADM-2020 [40], AS/NZS 1664 [41], and GB 50429-2007 [42].

4.1. Eurocode (EC9)

The EC9 [28] provides design methods for aluminium alloy structures without exposure to elevated temperatures. The SC’s ultimate resistance was determined using the cross-section categorization framework (Classes 1 through 4), with the flange used to establish the cross-section classification for the angle section. Cross-sectional yield resistance can be attained for members with Class 1, 2, and 3 cross-sections prior to local buckling. However, for Class 4 cross-sections, local buckling developed prior to attaining the cross-sectional yield resistance. Consequently, the design compressive strength for Class 1–3 sections was calculated by Equation (1), with a partial factor γ_M1 of 1.1. For Class 4 sections, the ultimate resistance was evaluated using the effective area A_eff, defined as the sum of the component plate areas based on the effective thickness t_eff. Because of the local buckling, the t_eff = ρ_ct. Equation (2) was used to calculate the local buckling factor ρ_c, where ψ = 1. Notably, for flat outstand parts in asymmetrical cross-sections, the ρ_c value should not be larger than the limit in Equation (3). According to EC9 provisions [28], the values of these classification constants C₁ and C₂ for unwelded outstand flanges were taken as 9.5 and 22, respectively. In this study, the 6063-T5 aluminium alloy tubes were classified as buckling class B in EC9 [28]. Subsequently, using the slenderness limits outlined in EC9 [28], the values of β₂/ε and β₃/ε were determined to be 4.5 and 5.5, respectively, for the outstand flange. A class of numerical models can be established with reference to slenderness limits. Subsequently, the ultimate resistance of the 6063-T5 aluminium alloy angle section SC was determined using Equation (1).

The EC9 slenderness boundary distinguishing Class 3 from Class 4 was evaluated by numerical findings, which are presented in Figure 14. For flat outstand elements without stress gradients, β was defined as b/t, and the b/tε_EC9 of the slenderest plate element within the cross-section. In equal-leg angle sections, b was taken as B-t, where B denotes the full width of the plate, and t was the thickness. Here, ε_EC9 = (250/f_o)^0.5. According to EC9, the slenderness limit for outstand plate elements in compression, distinguishing slender from non-slender sections, was 5.5. The nondimensional ratio N_u/Af_o was employed to illustrate the evolution of plastic resistance in the cross-section. In the fire-unexposed numerical model, when the ratio b/tε_EC9 was below 5.5, the ratio N_u/Af_o typically exceeded 1. Conversely, when b/tε_EC9 exceeded 5.5, N_u/Af_o gradually decreased below 1. Thus, the slenderness limit specified in EC9 is applicable for 6063-T5 aluminium alloy angle section SCs without fire exposure. After subjecting the SCs to various elevated temperatures, the aforementioned slenderness limit in EC9 remained deemed appropriate and safe, as depicted in Figure 14. Consequently, the differences in the slenderness limitation for Class 3 and Class 4 sections might be disregarded for the 6063-T5 aluminium alloy angle section SCs after exposure to different elevated temperatures.

A comparison of the numerical, experimental, and EC9-predicted results of the ultimate resistances is illustrated in Figure 15. The mean values and COVs of N_u,FE/N_u,EC9 for the SCs with and without exposure to various elevated temperatures were as follows: 1.25/0.19 (25 °C), 1.24/0.15 (200 °C), 1.23/0.14 (250 °C), 1.35/0.10 (300 °C), 1.66/0.22 (350 °C), 2.04/0.28 (400 °C), 1.98/0.28 (450 °C), and 1.59/0.22 (500 °C). For the ratio N_u,test/N_u,EC9, the mean values and COVs were 3.54/0.59 (25 °C), 3.54/0.61 (200 °C), 3.40/0.59 (250 °C), 2.47/0.47 (300 °C), 1.78/0.25 (350 °C), 1.61/0.20 (400 °C), 1.69/0.17 (450 °C), and 2.05/0.34 (500 °C). Figure 15 indicates that the design approaches outlined in EC9 are suitable for 6063-T5 aluminium alloy angle section SCs without fire. Even after exposure to elevated temperatures of 200 °C and 250 °C, it exhibited good accuracy. However, at temperatures exceeding 300 °C, the accuracy of the EC9 design provisions significantly diminished. When b/tε_EC9 was less than 5.5, the EC9 design approaches were overly conservative for predicting the ultimate resistance of 6063-T5 aluminium alloy angle section SCs after exposure to elevated temperatures. For 6063-T5 aluminium alloy, the strain-hardening behaviour was pronounced as temperatures surpassed 300 °C. Consequently, for specimens with non-slender cross-sections, strain-hardening transpires subsequent to the attainment of yield strength f_o. Thus, values of the ultimate resistances of SCs with non-slender cross-sections were notably higher than the results predicted by the EC9 design approaches when exposed to temperatures exceeding 300 °C. When the b/tε_EC9 value was relatively large, ρ_c was controlled on the basis of Equation (3). The methodology of EC9 [28] was overly conservative for direct application to 6063-T5 aluminium alloy angle section SCs with and without exposure to elevated temperatures.

$$N_{u,EC9}=\left\{\begin{array}{ll}A{f}_o/{\gamma }_{M1}\hfill & \mathrm{for} \mathrm{Class} 1–3 \mathrm{sections}\hfill \\ A_{eff}{f}_o/{\gamma }_{M1}\hfill & \mathrm{for} \mathrm{Class} 4 \mathrm{sections}\hfill \end{array}\right.$$

(1)

$${\rho }_C={\displaystyle \frac{C_1}{\left(\frac{\beta }{\epsilon }\right)}}-{\displaystyle \frac{\left(3+\psi \right)C_2}{4{\left(\beta /\epsilon \right)}^2}} \mathrm{if}{\displaystyle \frac{\beta }{\epsilon }}>{\displaystyle \frac{1}{2}}\left(C_1+\sqrt{C_1^2-C_2\left(3+\psi \right)}\right)$$

(2)

$${\rho }_C\le {\displaystyle \frac{120}{{\left(\beta /\epsilon \right)}^2}}$$

(3)

4.2. American Design Manual (ADM-2020)

For ADM-2020 [40], the ultimate resistance of the aluminium alloy SC was calculated by the full cross-sectional area, as expressed in Equation (4), and P_nc was calculated using Equation (5). A_i represents the area of each constituent plate element i. Further, ϕ_c denotes the resistance factor, set at 0.9. f_c represents the compressive critical stress determined using Equation (6) and is influenced by various factors, including the width-to-thickness ratio of constituent plate β, nominal yield strength f_o, elastic modulus E, and buckling constants B_p and D_p. The values of λ₁ = (B_p − f_o)/(5.0D_p) and λ₂ = C_p/5.0. According to ADM-2020 [40], buckling constants B_p and D_p can be determined using Equations (7) and (8). κ = 6.895 MPa, and C_p is determined using B_p and D_p, as shown in Equation (9). As shown in Figure 16, an evaluation of the slenderness limitation in the ADM-2020 [40] was conducted, where λ₁ = (B_p − f_o)/(5.0D_p) was the slenderness limitation between the slender and non-slender cross-sections. The relevant results indicate that the aforementioned slenderness limitation in ADM-2020 [40] accurately classified slender and non-slender cross-sections for 6063-T5 aluminium alloy angle section SCs without fire exposure. When the elevated temperatures did not exceed 250 °C, the effectiveness and safety of the above slenderness limitation in ADM-2020 [40] persisted. However, at temperatures exceeding 300 °C, the conservative nature of the ADM-2020 [40] was attributed to differences in the post-fire mechanical properties of the 6063-T5 aluminium alloy.

A comparison of the numerical and experimental results and ADM-2020 [40]-predicted results of the ultimate resistance is depicted in Figure 17. The mean values and COVs of N_u,FE/N_u,AADM for the SCs, both without fire and after exposure to various temperatures, were 1.27/0.26 (25 °C), 1.26/0.22 (200 °C), 1.24/0.19 (250 °C), 1.35/0.11 (300 °C), 1.68/0.22 (350 °C), 2.07/0.27 (400 °C), 2.01/0.27 (450 °C), and 1.60/0.23 (500 °C). For the ratio N_u,test/N_u,AADM, the mean values and COVs were 3.82/0.55 (25 °C), 3.82/0.59 (200 °C), 3.66/0.59 (250 °C), 2.67/0.54 (300 °C), 1.95/0.32 (350 °C), 1.77/0.23 (400 °C), 1.89/0.22 (450 °C), and 2.20/0.40 (500 °C). According to ADM-2020, the ultimate resistance of unexposed 6063-T5 aluminium alloy angle SCs could be accurately predicted when b/tλ_AADM < 2. For relatively large b/tλ_AADM, ADM-2020 provided conservative predictions for unexposed 6063-T5 aluminium alloy angle SCs. At elevated temperatures that remained below 300 °C, the ADM-2020 remained suitable for the SCs after exposure to elevated temperatures, when the b/tλ_AADM < 2. However, for temperatures at or above 300 °C, the predictive accuracy of ADM-2020 significantly diminished. For b/tλ_AADM < 1, ADM-2020 was excessively conservative for predicting the ultimate resistance of the 6063-T5 aluminium alloy angle section SCs after exposure to elevated temperatures higher than 300 °C. This prediction error was ascribed to differences in the nonlinear characters of the residual stress–strain responses of the 6063-T5 aluminium alloy after exposure to elevated temperatures.

$$N_{u,AADM}={\varphi }_c{P}_{nc}$$

(4)

$$P_{nc}=\sum _n^{i=1}{f}_{ci}{A}_i+f_o\left(A_g-\sum _n^{i=1}{A}_i\right)$$

(5)

$$f_c=\left\{\begin{array}{ll}{f}_o\hfill & \mathrm{for}{\displaystyle \frac{b}{t}}\le {\displaystyle \frac{B_p-f_o}{5.0D_p}}\hfill \\ B_p-5.0D_p{\displaystyle \frac{b}{t}}\hfill & \mathrm{for}{\displaystyle \frac{B_p-f_o}{5.0D_p}}<{\displaystyle \frac{b}{t}}<{\displaystyle \frac{C_p}{5.0}}\hfill \\ {\displaystyle \frac{{\mathsf{\pi }}^{2}E}{{(5.0b/t)}^2}}\hfill & \mathrm{for}{\displaystyle \frac{b}{t}}\ge {\displaystyle \frac{C_p}{5.0}}\hfill \end{array}\right.$$

(6)

$$B_p=f_o\left[1+{\left({\displaystyle \frac{f_o}{1500\kappa }}\right)}^{{\displaystyle \frac{1}{3}}}\right]$$

(7)

$$D_p={\displaystyle \frac{B_p}{10}}{\left({\displaystyle \frac{B_p}{E}}\right)}^{{\displaystyle \frac{1}{2}}}$$

(8)

$$C_p=0.41{\displaystyle \frac{B_p}{D_p}}$$

(9)

4.3. AS/NZS 1664

The design approaches of AS/NZS 1664 [41] closely resemble those of ADM 2020 [40]. The ultimate resistances of 6063-T5 aluminium alloy angle section SCs were calculated using the uniform compression provisions, as shown in Equation (10), with factors Φ_c = 0.85, Φ_y = 0.95, k_c = 1.12, and buckling constants B_p and D_p from Equations (7) and (8) respectively. Since AS/NZS 1664 [41] adopts the same slenderness limitation for slender cross-sections as ADM-2020 [40], it was not reassessed in this section. A comparison of the numerical and experimental results and the AS/NZS 1664 [41]-predicted results of the ultimate resistance is illustrated in Figure 18. The mean values and COVs of N_u,FE/N_u,AS/NZS for the 6063-T5 aluminium alloy angle section SCs, both without fire and after exposure to various temperatures, were 1.36/0.27 (25 °C), 1.35/0.24 (200 °C), 1.33/0.21 (250 °C), 1.44/0.11 (300 °C), 1.78/0.21 (350 °C), 2.20/0.27 (400 °C), 2.13/0.27 (450 °C), and 1.70/0.22 (500 °C). For the ratio N_u,test/N_u,AS/NZS, the mean values and COVs were 4.18/0.55 (25 °C), 4.18/0.58 (200 °C), 4.01/0.59 (250 °C), 2.91/0.55 (300 °C), 2.12/0.33 (350 °C), 1.93/0.25 (400 °C), 2.05/0.23 (450 °C), and 2.39/0.42 (500 °C). The comparison results for AS/NZS 1664 [41] closely resemble those for ADM 2020 [40], owing to their similar design approaches. However, owing to the presence of k_c and Φ_y, the predicted results using AS/NZS 1664 [41] were smaller than those from ADM 2020 [40]. Thus, for 6063-T5 aluminium alloy angle section SCs with non-slender cross-sections, the design approaches in AS/NZS 1664 [41] yielded more conservativeness. When the b/tλ_AS/NZS ratio was relatively large, the design approaches in AS/NZS 1664 [41] yielded notably conservative results for the ultimate resistance of 6063-T5 aluminium alloy angle section SCs, both with and without exposure to elevated temperatures.

$$\mathsf{\Phi }{F}_{\mathrm{L}}=\left\{\begin{array}{ll}{\displaystyle \frac{{\mathsf{\Phi }}_y{f}_{\mathrm{o}}}{k_c}}\hfill & \mathrm{for}{\displaystyle \frac{b}{t}}\le (B_p-{\displaystyle \frac{{\mathsf{\Phi }}_y{f}_{\mathrm{o}}}{{\mathsf{\Phi }}_c{k}_c}})/5.1D_p\hfill \\ {\mathsf{\Phi }}_c(B_p-5.1D_p{\displaystyle \frac{b}{t}})\hfill & \mathrm{for}(B_p-{\displaystyle \frac{{\mathsf{\Phi }}_y{f}_{\mathrm{o}}}{{\mathsf{\Phi }}_c{k}_c}})/5.1D_p<{\displaystyle \frac{b}{t}}<{\displaystyle \frac{C_p}{5.1}}\hfill \\ {\displaystyle \frac{{\mathsf{\Phi }}_{\mathrm{c}}{\mathsf{\pi }}^{2}E}{{(5.1b/t)}^2}}\hfill & \mathrm{for}{\displaystyle \frac{b}{t}}\ge {\displaystyle \frac{C_p}{5.1}}\hfill \end{array}\right.$$

(10)

4.4. GB 50429-2007

The Chinese code GB 50429-2007 [42], similar to EC9 [28], applies an effective thickness approach. The ultimate resistance of the 6063-T5 aluminium alloy angle section SC was determined using Equation (11), where the A_eff represented the effective cross-section area, and γ_R,GB = 1.2. The effective cross-section thickness t_eff value could be obtained from Equation (12). Given the strong hardening nature of the 6063-T5 AA, calculation coefficients α₁ and α₂ were set to 0.9 each. For biaxially symmetrical sections, t_eff should also conform to Equation (13). The conversion flexibility coefficient is denoted as $\overline{\lambda }$= (f_o/σ_cr)^0.5, where σ_cr is determined using Equation (14). Notably, the code specifies a slenderness limitation of 5ε_GB for slender and non-slender cross-sections, where ε_GB = (240/f_o)^0.5. The evaluation of the slenderness limitation in GB 50429-2007 [42] is presented in Figure 19, showing its appropriateness for a 6063-T5 aluminium alloy angle section SC without elevated-temperature exposure. However, with increasing elevated temperatures, the slenderness limitation for the Class 4 and Class 3 cross-sections in GB 50429-2007 [42] gradually became unsuitable.

A comparison of the numerical and experimental outcomes and the GB 50429-2007 [42] calculations of the ultimate resistance is shown in Figure 20. The mean values and COVs of N_u,FE/N_u,GB for 6063-T5 aluminium alloy angle section SCs, both without fire and after exposure to different temperatures, were 1.44/0.26 (25 °C), 1.43/0.23 (200 °C), 1.40/0.20 (250 °C), 1.50/0.10 (300 °C), 1.82/0.21 (350 °C), 2.23/0.27 (400 °C), 2.17/0.27 (450 °C), and 1.75/0.21 (500 °C). As regards N_u,test/N_u,GB, the mean values and COVs were 4.63/0.58 (25 °C), 4.59/0.62 (200 °C), 4.19/0.61 (250 °C), 3.10/0.52 (300 °C), 2.25/0.34 (350 °C), 1.95/0.26 (400 °C), 2.04/0.23 (450 °C), and 2.53/0.40 (500 °C). The design approaches in GB 50429-2007 [42] exhibited slight conservatism for the 6063-T5 aluminium alloy angle section SC without elevated-temperature exposure. However, with the rise in elevated temperatures, the accuracy of the GB 50429-2007 [42] diminished, particularly for b/tε_GB < 5.0. This is attributable to the enhanced strain-hardening of the post-fire 6063-T5 AA.

$$N_{u,GB}=A_{eff}{\displaystyle \frac{f_o}{{\gamma }_{R,GB}}}$$

(11)

$${\displaystyle \frac{t_{eff}}{t}}={\alpha }_1{\displaystyle \frac{1}{\overline{\lambda }}}-{\alpha }_2{\displaystyle \frac{0.22}{{\overline{\lambda }}^2}}\le 1$$

(12)

$${\displaystyle \frac{t_{eff}}{t}}\le {\displaystyle \frac{1}{{\overline{\lambda }}^2}}$$

(13)

$${\sigma }_{cr}={\displaystyle \frac{k{\pi }^{2}E}{12\left(1-{\nu }^2\right)\cdot {\left(b/t\right)}^2}}$$

(14)

5. Modified Design Approach

Based on the above discussion, it was found that the strain-hardening behaviour of 6063-T5 aluminium alloy after exposure to elevated temperatures led to overly conservative predictions by existing design codes when estimating the residual bearing capacity of aluminium alloy angle section SCs. To improve the predictive accuracy, the design provisions in EC9 [28] and GB 50249-2007 [42]—which are based on similar design principles—were modified in this study.

Following the Direct Strength Method [43], the linear strain-hardening material model of the 6063-T5 aluminium alloy after exposure to elevated temperatures is shown as Equation (15). All key mechanical parameters were derived from the post-fire experimental results of 6063-T5 aluminium alloy tension coupons. The coefficient p was introduced to characterize the post-yield strain-hardening response after fire exposure. Its value was calibrated using the combined database of SC test results and the validated numerical results. Specifically, regression-based calibration was carried out by comparing the predicted ultimate resistances with the corresponding experimental and numerical resistances over the investigated temperature range; analyses and the resulting values of p are summarized in

Table 5. Coefficients in the modified design approaches for EC9 and GB 50249-2007.

T (°C)	p	Nu/Nu,predicted,EC9 Mean	Nu/Nu,predicted,EC9 COV	Nu/Nu,predicted,GB Mean	Nu/Nu,predicted,GB COV
25	17.11	1.09	0.10	1.11	0.10
200	17.90	1.09	0.08	1.11	0.05
250	18.39	1.11	0.09	1.12	0.06
300	28.74	1.15	0.07	1.15	0.06
350	62.78	1.13	0.04	1.14	0.04
400	140.78	1.12	0.05	1.13	0.06
450	124.99	1.11	0.06	1.13	0.08
500	53.95	1.05	0.04	1.07	0.05

.

Considering the influence of the cross-section class of the SC, the ultimate-resistance calculation regulations in EC9 [28] and GB 50249-2007 [42] were modified in a segmented manner according to different member slenderness. The modified equations are given as Equations (16) and (17), in which N_{u,predicted,EC9} and N_{u,predicted,GB} represent the modified ultimate resistance. The λ_EC9 and λ_GB denote the slenderness limitation b/tε_EC9 and b/tε_GB, respectively.

For non-slender sections, the residual bearing capacity was governed by both post-fire material properties and slenderness, whereas for slender sections, it was mainly controlled by the slenderness of the SCs. It was worth noting that for flat outstand parts in non-biaxially symmetric cross-sections, the thickness reduction factors of the cross-section defined in Equations (3) and (13) were found to be overly conservative at high cross-section class values. This issue was also considered in the modified design approaches, in which cross-section class limits are 15 for EC9 [28] and 13 for GB 50249-2007 [42].

To verify the accuracy of the modified equations, comparisons were made against both experimental and numerical results, as shown in Figure 21. The corresponding mean values and COVs of the N_u/N_{u,predicted,EC9} and N_u/N_{u,predicted,GB} ratios are summarized in Table 5. The results confirmed that the modified design methods in EC9 [28] and GB 50249-2007 [42] provided accurate predictions of the post-fire ultimate resistances of 6063-T5 aluminium alloy angle section SCs.

$${\sigma }_{sh}=f_o+{\displaystyle \frac{E}{p}}({\epsilon }_u-{\epsilon }_y)$$

(15)

$$N_{u,predicted,EC9}=\left\{\begin{array}{cc}{\displaystyle \frac{{\sigma }_{sh}}{f_o{\lambda }_{EC9}^{0.6}}}{N}_{u,EC9}& \mathrm{for} {\lambda }_{EC9}\le 5.5\\ {\displaystyle \frac{{\lambda }_{EC9}^{0.4}}{2}}{N}_{u,EC9}& \mathrm{for} 5<{\lambda }_{EC9}\le 15\\ {\displaystyle \frac{{\lambda }_{EC9}}{10}}{N}_{u,EC9}& \mathrm{for} {\lambda }_{EC9}>15\end{array}\right.$$

(16)

$$N_{u,predicted,GB}=\left\{\begin{array}{cc}{\displaystyle \frac{1.1{\sigma }_{sh}}{f_o{\lambda }_{GB}^{0.6}}}{N}_{u,GB}& \mathrm{for} {\lambda }_{GB}\le 5\\ 0.55{\lambda }_{GB}^{0.4}{N}_{u,GB}& \mathrm{for} 5<{\lambda }_{GB}\le 13\\ 0.11{\lambda }_{GB}{N}_{u,GB}& \mathrm{for} {\lambda }_{GB}>13\end{array}\right.$$

(17)

6. Conclusions

This paper investigated the residual capacity of 6063-T5 aluminium alloy angle section SCs after exposure to elevated temperatures through experiments and numerical analyses, the results of which were meaningful for the assessment of the residual resistance performance of aluminium alloy structures after fire. The key findings of this study are as follows:

• A fire exposure treatment was adopted to simulate the influence of fire on the residual load-bearing capacity of 6063-T5 aluminium alloy angle section SCs. The post-fire mechanical properties of the alloys were determined using tensile coupon tests. After exposure to elevated temperatures, the stress–strain curves exhibited no yield plateau, transitioning from an elastic segment to a strain-hardening section. The elevated-temperature exposure generated negligible influences on the post-fire elastic modulus of the 6063-T5 AA. Strength properties decreased while ductile properties increased within 200–450 °C, with subsequent strength increase observed beyond 450 °C.
• Following the SC tests, all load–end shortening curves exhibited a unimodal form. Gradual decreases in ultimate resistance were observed within the range of 200 to 450 °C, followed by an increase beyond 450 to 500 °C. These trends in the ultimate resistance closely paralleled those observed in the strength properties of the stress–strain curves. In the failure mode, all of the 6063-T5 aluminium alloy angle section SCs after exposure to different elevated temperatures manifested local buckling.
• A finite element modelling method was developed to simulate the residual load-bearing performance of 6063-T5 aluminium alloy angle section SCs after exposure to different elevated temperatures, validated by the failure modes, ultimate resistances, and load–end shortening curves obtained from the tests. Based on the validated numerical model together with the experimental results for Class 4 sections, the applicability of current design codes, including EC9, ADM-2020, AS/NZS 1664, and GB 50429-2007, was assessed. These design approaches demonstrated satisfactory accuracy in predicting the ultimate resistances of unexposed 6063-T5 aluminium alloy angle section SCs with non-slender cross-sections. However, with increasing elevated temperatures and cross-sectional slenderness, the accuracy generally decreased. Owing to the enhanced strain-hardening of the alloy after exposure to elevated temperatures, these design approaches were found to be overly conservative for the direct prediction of the ultimate resistances of 6063-T5 aluminium alloy angle section SCs with non-slender cross-sections, based on the accompanying numerical analyses.
• To improve the accuracy of current design codes in predicting the residual bearing capacity of aluminium alloy angle section SCs after exposure to elevated temperatures, the design provisions in EC9 and GB 50249-2007 were revised based on the experimental and numerical findings for 6063-T5 aluminium alloy SCs. The modified formulations considered the strain-hardening effect observed in post-fire materials and demonstrated improved agreement with both experimental and numerical results. The proposed design modifications, therefore, provide a more reliable basis for evaluating the post-fire resistance of 6063-T5 aluminium alloy angle section SCs under axial compression within the investigated parameter range.