Web Crippling Behaviour of High-Strength Aluminium Alloy Channel Sections under Concentrated Loading: Numerical Modelling and Proposed Design Rules

: Two types of high-strength aluminium alloy (HA)—namely, AA-6086 and 7075-T6—have been developed and extensively used in recent years. These high-strength aluminium alloys offer advantages such as lower prices and higher yield strength than traditional alloys. The webs of aluminium channel members under concentrated loads are susceptible to web buckling failure, which restricts their applications. However, no research work has been reported that has evaluated the web buckling performance of high-strength aluminium alloy channel sections subjected to end-two-ﬂange (ETF) loading, and the material characteristics of these high-strength aluminium alloys differ signiﬁcantly from those of conventional aluminium alloys. This work addresses this gap by conducting a detailed numerical investigation. A parametric investigation consisting of 1024 models was performed using the ﬁnite element (FE) models previously developed for traditional aluminium alloys. A wide range of high-strength aluminium alloy sections covering varying web slenderness ratios, internal corner radii, bearing lengths, and aluminium alloy grades were considered in this investigation. It was shown that the latest design recommendations in the Australian and New Zealand Standards (AS/NZ S4600) and (AS/NZS 1664.1) were over-conservative when estimating the web buckling strength of such channel sections. Finally, new web buckling design equations for high-strength aluminium alloy channel sections were proposed through reliability analysis in this investigation.


Introduction
Aluminum alloys are being increasingly used as building materials in structural engineering applications because of their numerous benefits, including being lightweight, highly resistant to deterioration, and easy to manufacture-as illustrated in Figure 1.In recent times, two types of channel sections fabricated by extrusion using high-strength aluminum alloys (HAs) AA-6086 and 7075-T6 have been extensively used due to their lower cost and higher yield strength [1,2].However, the webs of aluminum channel members are prone to web buckling when subjected to concentrated loading, as aluminum alloys have a lower elastic modulus than steel.Therefore, the impact of web buckling on the performance of HA channel sections should be evaluated carefully.
The use of aluminum alloy sections as load-bearing members subjected to different loadings has been investigated by many researchers [3,4].Roy et al. [5,6] and Fang et al. [7,8] numerically and experimentally studied the buckling performance and design of a backto-back built-up aluminum alloy channel section subjected to axial compression, and the impacts of modified slenderness, screw number, and section thickness were evaluated.Feng et al. [9] reported the results of twelve laboratory tests on the flexural capacity of perforated aluminum members subjected to bending, and they found that the current design guidelines are normally over-conservative when estimating the flexural capacity of such channel sections.
Buildings 2023, 13, x FOR PEER REVIEW 2 of 22 perforated aluminum members subjected to bending, and they found that the current design guidelines are normally over-conservative when estimating the flexural capacity of such channel sections.Researchers have carried out a significant number of studies to evaluate the web buckling performance of cold-formed steel (CFS) sections over the last few years.Examples include Uzzaman et al. [10,11], Janarthanan et al. [12,13], Chen et al. [14], and Gunalan and Mahendran [15].Web buckling failure in CFS beams was first experimentally investigated by Winter and Pian [16], and they reported a total of 136 laboratory test results.Following this, Young and Hancock [17] carried out web buckling laboratory testing on CFS beams featuring both restrained and unrestrained flanges.Macdonald et al. [18,19] observed that the web's bearing length, corner radius, and clear height significantly affected the member's web buckling strength.The web buckling performance of CFS hollow flange channel beams under two-flange loading was evaluated by Keerthan and Mahendran [20].Using both laboratory testing and numerical methods, Sundararajah et al. [21,22] developed new design rules in web buckling strength using the Direct Strength Method (DSM).
Limited research works are available regarding the web buckling performance of aluminum channels.Alsanat et al. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] recently evaluated the web buckling failure of aluminum sections with fastened flanges experimentally and numerically; they thoroughly assessed the existing design guidelines and suggested new ones based on their evaluation results.Zhou and Young [28] experimentally evaluated the web buckling performance of aluminum alloy channels, with 340 data points reported.They found that the latest design recommendations were generally unconservative and unreliable for those members with one flange-restrained condition.
However, all of the studies mentioned above were mainly focused on traditional aluminum alloy sections or CFS sections [29], despite the popularity of HA channels.No research study has been reported investigating the web buckling strength of HA channels subjected to end-two-flange (ETF) loading.In a recent study, Alsanat et al. [23] evaluated the web buckling performance of traditional aluminum alloy channels and presented new design recommendations according to their laboratory testing and finite element analysis results.These results, however, may not be appropriate for HA sections.More importantly, the existing standards-such as the Australian and New Zealand Standards (AS/NZ S4600) [30], American Iron and Steel Institute (AISI S100-16) [31], and Australian Standards (AS/NZS 1664.1)[32]-do not include design guidelines for evaluating the web buckling capacity of high-strength aluminum sections.Researchers have carried out a significant number of studies to evaluate the web buckling performance of cold-formed steel (CFS) sections over the last few years.Examples include Uzzaman et al. [10,11], Janarthanan et al. [12,13], Chen et al. [14], and Gunalan and Mahendran [15].Web buckling failure in CFS beams was first experimentally investigated by Winter and Pian [16], and they reported a total of 136 laboratory test results.Following this, Young and Hancock [17] carried out web buckling laboratory testing on CFS beams featuring both restrained and unrestrained flanges.Macdonald et al. [18,19] observed that the web's bearing length, corner radius, and clear height significantly affected the member's web buckling strength.The web buckling performance of CFS hollow flange channel beams under two-flange loading was evaluated by Keerthan and Mahendran [20].Using both laboratory testing and numerical methods, Sundararajah et al. [21,22] developed new design rules in web buckling strength using the Direct Strength Method (DSM).
Limited research works are available regarding the web buckling performance of aluminum channels.Alsanat et al. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] recently evaluated the web buckling failure of aluminum sections with fastened flanges experimentally and numerically; they thoroughly assessed the existing design guidelines and suggested new ones based on their evaluation results.Zhou and Young [28] experimentally evaluated the web buckling performance of aluminum alloy channels, with 340 data points reported.They found that the latest design recommendations were generally unconservative and unreliable for those members with one flange-restrained condition.
However, all of the studies mentioned above were mainly focused on traditional aluminum alloy sections or CFS sections [29], despite the popularity of HA channels.No research study has been reported investigating the web buckling strength of HA channels subjected to end-two-flange (ETF) loading.In a recent study, Alsanat et al. [23] evaluated the web buckling performance of traditional aluminum alloy channels and presented new design recommendations according to their laboratory testing and finite element analysis results.These results, however, may not be appropriate for HA sections.More importantly, the existing standards-such as the Australian and New Zealand Standards (AS/NZ S4600) [30], American Iron and Steel Institute (AISI S100-16) [31], and Australian Standards (AS/NZS 1664.1)[32]-do not include design guidelines for evaluating the web buckling capacity of high-strength aluminum sections.
This study aimed to address these gaps through a comprehensive numerical analysis, and the web buckling performance of HA channel sections undergoing ETF loading was analyzed.This research was built upon the work of Alsanat et al. [23], but focused on HA sections instead of traditional aluminum alloys.Both material grades of AA-6086 and 7075-T6 were considered.The finite element (FE) models were developed and verified using the data obtained from laboratory testing.A parametric investigation was undertaken to examine the impact of various parameters on the web buckling performance of HA sections.Based on the outcomes of the numerical investigation, the accuracy of the latest design recommendations in the AS/NZ S4600 [30] and AS/NZS 1664.1 [32] was assessed.Moreover, this study presented new design calculations for evaluating the web buckling strength of HA channel sections through reliability analysis.

Material Characteristics of High-Strength Aluminum Alloys 2.1. 7075-T6 Aluminum Alloy
Zhi et al. [1] carried out 16 tensile coupon tests using the coupons cut from the flange and web of columns.Four different nominal thicknesses-which were 4, 5, 6, and 8 mm-were considered, and each thickness was tested four times.
An extensometer was employed to record strain during laboratory testing, which were carried out on a 1000 kN testing machine.Figure 2a depicts stress-strain curves related to aluminum alloy 7075-T6.Table 1 summarizes its crucial material characteristics, including the 0.2% proof stress (f 0.2 ), ultimate strength (f u ), and elongation after failure with an initial gauge length of 80 mm (δ), as well as variables in the two-stage Ramberg-Osgood model (E 0.2 , n, and m).This study aimed to address these gaps through a comprehensive numerical analysis, and the web buckling performance of HA channel sections undergoing ETF loading was analyzed.This research was built upon the work of Alsanat et al. [23], but focused on HA sections instead of traditional aluminum alloys.Both material grades of AA-6086 and 7075-T6 were considered.The finite element (FE) models were developed and verified using the data obtained from laboratory testing.A parametric investigation was undertaken to examine the impact of various parameters on the web buckling performance of HA sections.Based on the outcomes of the numerical investigation, the accuracy of the latest design recommendations in the AS/NZ S4600 [30] and AS/NZS 1664.1 [32] was assessed.Moreover, this study presented new design calculations for evaluating the web buckling strength of HA channel sections through reliability analysis.

7075-T6 Aluminum Alloy
Zhi et al. [1] carried out 16 tensile coupon tests using the coupons cut from the flange and web of columns.Four different nominal thicknesses-which were 4, 5, 6, and 8 mmwere considered, and each thickness was tested four times.
An extensometer was employed to record strain during laboratory testing, which were carried out on a 1000 kN testing machine.Figure 2a depicts stress-strain curves related to aluminum alloy 7075-T6.Table 1 summarizes its crucial material characteristics, including the 0.2% proof stress (0.2),ultimate strength (u), and elongation after failure with an initial gauge length of 80 mm (), as well as variables in the two-stage Ramberg-Osgood model (0.2,n, and m).

AA-6086 Aluminium Alloy
Zupanič et al. [2] conducted two tensile coupon tests in order to characterize the physical properties of the aluminum alloy AA-6086.The new alloy had a higher silicon, copper, and zirconium content in its material composition.Before being analyzed, the material underwent the processes of being homogenized, extruded, and T6 heat-treated to achieve a desired state.
A mechanical extensometer featuring a 25 mm gauge length and a 100 kN servohydraulic test equipment was utilized.Figure 2b illustrates the stress-strain curves for the AA-6086 aluminum alloy and Table 1 summarizes its material properties.

General
Alsanat et al. [23] recently performed laboratory testing on web buckling for traditional aluminum alloy channels under ITF and ETF loadings.A total of forty test results were reported, which were then employed for validating the FE models.Detailed descriptions of both the laboratory testing and finite element models can be found in Alsanat et al. [23]; however, brief details concerning the laboratory testing methods are summarized below.

Testing Setup and Loading Process
All test specimens were manufactured from the structural aluminum alloy 5052H36.The depth of web section (d) was changed from 100 to 250 mm, while the widths of the flange (bf) was changed from 60.5 to 75 mm.The specimen's total length (L) was calculated

AA-6086 Aluminium Alloy
Zupanič et al. [2] conducted two tensile coupon tests in order to characterize the physical properties of the aluminum alloy AA-6086.The new alloy had a higher silicon, copper, and zirconium content in its material composition.Before being analyzed, the material underwent the processes of being homogenized, extruded, and T6 heat-treated to achieve a desired state.
A mechanical extensometer featuring a 25 mm gauge length and a 100 kN servohydraulic test equipment was utilized.Figure 2b illustrates the stress-strain curves for the AA-6086 aluminum alloy and Table 1 summarizes its material properties.

General
Alsanat et al. [23] recently performed laboratory testing on web buckling for traditional aluminum alloy channels under ITF and ETF loadings.A total of forty test results were reported, which were then employed for validating the FE models.Detailed descriptions of both the laboratory testing and finite element models can be found in Alsanat et al. [23]; however, brief details concerning the laboratory testing methods are summarized below.

Testing Setup and Loading Process
All test specimens were manufactured from the structural aluminum alloy 5052H36.The depth of web section (d) was changed from 100 to 250 mm, while the widths of the flange (b f ) was changed from 60.5 to 75 mm.The specimen's total length (L) was calculated according to AS/NZ S4600 [30].For the ITF condition, the length was calculated as being three times the height of the channel section added to the bearing plate length, and for the ETF condition, as being 1.5-times the height of the channel added together with the bearing plate length.The impact of bearing plate length on web buckling performance was evaluated (N was ranged from 25 mm to 150 mm).It should be noted that the flanges of these specimens were not fastened to the supports.
To carry out web buckling laboratory testing on the CFS sections, the procedures outlined in AS/NZ S4600 [30] were followed.Figure 3 shows the test setup, where a 100 kN Instron piece of testing equipment was utilized to exert a centralized reaction on the specimens.Half-rounds were employed to replicate the top and bottom hinge supports.The test specimens were positioned at the edge and mid-span between two bearing plates for the ETF and ITF loading case, respectively.Three laser displacement transducers (LVDTs) were employed to obtain the lateral displacement of the web in three different positions, while one LVDT was employed to obtain the vertical displacement of the bottom flange.Displacement control was implemented, maintaining a steady speed of 0.05 mm/min.
To carry out web buckling laboratory testing on the CFS sections, the procedures outlined in AS/NZ S4600 [30] were followed.Figure 3 shows the test setup, where a 100 kN Instron piece of testing equipment was utilized to exert a centralized reaction on the specimens.Half-rounds were employed to replicate the top and bottom hinge supports.The test specimens were positioned at the edge and mid-span between two bearing plates for the ETF and ITF loading case, respectively.Three laser displacement transducers (LVDTs) were employed to obtain the lateral displacement of the web in three different positions, while one LVDT was employed to obtain the vertical displacement of the bottom flange.Displacement control was implemented, maintaining a steady speed of 0.05 mm/min.The ABAQUS software (Version 6.14-2) was employed to establish FE models that can simulate the nonlinear behavior and web buckling performance of HA channel sections.The recorded cross-sectional measurements and the aluminum's characteristics gleaned from the coupon tensile tests were adopted in the FE models.Similar modelling methods have been reported by many researchers [33][34][35][36][37][38][39][40][41][42][43].A detailed discussion of the modelling method is presented as follows.

Geometry and Material Characteristics Modelling
In each analysis, the steel's isotropic yielding and plastic hardening were defined using the ABAQUS classical metal plasticity model.The stress-strain curve employed in the FE models was simplified, bilinear, and did not consider strain hardening.The numerical models incorporated the material parameters from coupon testing.The engineering material curve was transformed into an actual stress-strain curve in accordance with the recommended equations provided in the ABAQUS manual [44].The true stress (σ true ) and true strain (ε true ) can be calculated by the following Equations ( 1) and ( 2):

FE Meshing
S4R shell elements were utilized to model channel sections made of the aluminum alloy, while the top and bottom endplates were simulated utilizing rigid quadrilateral shell elements (R3D4).In order to explore how various mesh sizes might impact the capacity of web buckling strength in these members, a mesh sensitivity analysis was undertaken, and the mesh size was varied from 2 mm to 50 mm.The impact of varying mesh element sizes on the ultimate strength of these sections has been studied, revealing that a mesh size of 5 mm was the suitable for simulating the aluminum alloy channel members-being able to provide accurate results.Mesh refinement was applied around the corner between the web and flange to achieve a more accurate FE analysis, as can be seen in Figure 4.
modelling method is presented as follows.

Geometry and Material Characteristics Modelling
In each analysis, the steel's isotropic yielding and plastic hardening were defined using the ABAQUS classical metal plasticity model.The stress-strain curve employed in the FE models was simplified, bilinear, and did not consider strain hardening.The numerical models incorporated the material parameters from coupon testing.The engineering material curve was transformed into an actual stress-strain curve in accordance with the recommended equations provided in the ABAQUS manual [44].The true stress (σtrue) and true strain (εtrue) can be calculated by the following Equations ( 1) and ( 2): (1 ) (2)

FE Meshing
S4R shell elements were utilized to model channel sections made of the aluminum alloy, while the top and bottom endplates were simulated utilizing rigid quadrilateral shell elements (R3D4).In order to explore how various mesh sizes might impact the capacity of web buckling strength in these members, a mesh sensitivity analysis was undertaken, and the mesh size was varied from 2 mm to 50 mm.The impact of varying mesh element sizes on the ultimate strength of these sections has been studied, revealing that a mesh size of 5 mm was the suitable for simulating the aluminum alloy channel membersbeing able to provide accurate results.Mesh refinement was applied around the corner between the web and flange to achieve a more accurate FE analysis, as can be seen in Figure 4.

Boundary Conditions and Loading Procedures
The boundary conditions deployed in the FE models are illustrated in Figure 5.The load in the axial direction was introduced via the reference point of the upper base plate using the displacement control general static method [44].All degrees of freedom on the top surface of the end plates were constrained except for translational flexibility in the Y axis.The surface-to-surface contact option was selected in the modelling of the interface between the end plates and the aluminum alloy section.No object was allowed to pass through these two touching surfaces.
The boundary conditions deployed in the FE models are illustrated in Figure 5.The load in the axial direction was introduced via the reference point of the upper base plate using the displacement control general static method [44].All degrees of freedom on the top surface of the end plates were constrained except for translational flexibility in the Y axis.The surface-to-surface contact option was selected in the modelling of the interface between the end plates and the aluminum alloy section.No object was allowed to pass through these two touching surfaces.

Analysis Methods
Elastic buckling and implicit dynamic analysis were employed to model the aluminum alloy channel sections.The dynamic approach involving implicit time integration was utilized to determine the models' quasi-static responses.

FE Model Validation
A total of 19 laboratory test outcomes for aluminum-lipped channel sections presented by Alsanat et al. [23] were included in Table 2 to validate the numerical modelling methodology adopted in this investigation.Figure 6 depicts the failure modes seen in laboratory testing and FE analysis.It can be observed that the shapes of deformation suggested by the FE models were comparable to the ones discovered through the laboratory testing.Table 2 contrasts the experimental data (PEXP) with the computational findings (PFEA).As displayed in Figure 7, the PEXP/PFEA had a coefficient of variation of 0.09 and a mean of 0.98, showing that the web buckling strength of aluminum alloy channels could be reliably estimated using the FE models developed in this work.Figure 8 presents the load-displacement curves generated from the numerical modelling and laboratory testing, demonstrating a strong agreement.

Analysis Methods
Elastic buckling and implicit dynamic analysis were employed to model the aluminum alloy channel sections.The dynamic approach involving implicit time integration was utilized to determine the models' quasi-static responses.

FE Model Validation
A total of 19 laboratory test outcomes for aluminum-lipped channel sections presented by Alsanat et al. [23] were included in Table 2 to validate the numerical modelling methodology adopted in this investigation.Figure 6 depicts the failure modes seen in laboratory testing and FE analysis.It can be observed that the shapes of deformation suggested by the FE models were comparable to the ones discovered through the laboratory testing.Table 2 contrasts the experimental data (P EXP ) with the computational findings (P FEA ).As displayed in Figure 7, the P EXP /P FEA had a coefficient of variation of 0.09 and a mean of 0.98, showing that the web buckling strength of aluminum alloy channels could be reliably estimated using the FE models developed in this work.Figure 8 presents the load-displacement curves generated from the numerical modelling and laboratory testing, demonstrating a strong agreement.

Parametric Study for High-Strength Aluminum Alloys
After the verification of the FE models for conventional aluminum alloy channel sections, a detailed parametric investigation was undertaken to create a comprehensive database for HA sections.A total of 1024 simulation results were generated, in which 256 FE results were for AA-6086 aluminum alloy lipped channel sections, 256 FE results were for AA-6086 aluminum alloy unlipped channel sections, 256 FE results were for 7075-T6 aluminum alloy lipped channel sections, and the remaining 256 FE results were for 7075-T6 aluminum alloy unlipped channel sections.
Previous work reported by Chen et al. [29] demonstrated that the web buckling strength of CFS sections is primarily affected by the length of the bearing plate (N), web slenderness ratio (h/tw), and internal corner radii ratio (ri/tw).Therefore, a wide range of

Parametric Study for High-Strength Aluminum Alloys
After the verification of the FE models for conventional aluminum alloy channel sections, a detailed parametric investigation was undertaken to create a comprehensive database for HA sections.A total of 1024 simulation results were generated, in which 256 FE results were for AA-6086 aluminum alloy lipped channel sections, 256 FE results were for AA-6086 aluminum alloy unlipped channel sections, 256 FE results were for 7075-T6 aluminum alloy lipped channel sections, and the remaining 256 FE results were for 7075-T6 aluminum alloy unlipped channel sections.
Previous work reported by Chen et al. [29] demonstrated that the web buckling strength of CFS sections is primarily affected by the length of the bearing plate (N), web slenderness ratio (h/t w ), and internal corner radii ratio (r i /t w ).Therefore, a wide range of HA sections covering varying web slenderness ratios, internal corner radii, bearing lengths, and aluminum alloy grades were examined in the parametric study (Table 3).The web slenderness ratio (h/t w ) was considered at values of 50, 75, 100, and 125.Four bearing plate lengths (N) were selected: 25, 50, 75, and 100 mm.The internal corner radii ratio (r i /t w ) was considered at values of 1.0, 2.0, 3.0, and 4.0.Four distinct web thicknesses of aluminum alloy channels (t w ) were included in the parametric study-namely, 1.0, 2.0, 3.0, and 4.0 mm.Figures 9-11 show the impact of the ratios h w /t, N/t, and r i /t on the web buckling strength of HA sections, correspondingly.When h w /t rose from 50 to 125, a minor reduction in strength was noticed-as illustrated in Figure 9.As depicted in Figure 10, the web buckling strength increased significantly when N/t increased from 25 to 100.The impact of the r/t ratio on the web buckling strength of the HA sections was studied, as illustrated in Figure 11, and it was found that a considerable decrease in strength was observed when r/t increased from 1.0 to 4.0.This indicated that the impact of the r/t ratio on the web buckling strength cannot be ignored.
Figures 9-11 show the impact of the ratios hw/t, N/t, and ri/t on the web buckling strength of HA sections, correspondingly.When hw/t rose from 50 to 125, a minor reduction in strength was noticed-as illustrated in Figure 9.As depicted in Figure 10, the web buckling strength increased significantly when N/t increased from 25 to 100.The impact of the r/t ratio on the web buckling strength of the HA sections was studied, as illustrated in Figure 11, and it was found that a considerable decrease in strength was observed when r/t increased from 1.0 to 4.0.This indicated that the impact of the r/t ratio on the web buckling strength cannot be ignored.

General
The web buckling strength database derived from the parametric analysis was evaluated against the expected web buckling strength calculated by the latest design recom-

General
The web buckling strength database derived from the parametric analysis was evaluated against the expected web buckling strength calculated by the latest design recommendation given in AS/NZS 4600 [30] and AS/NZS 1664.1 [32].AS/NZS 4600 [30] is intended for cold-formed carbon steel, while AS/NZS 1664.1 [32] is a specification for aluminum buildings.It is worth mentioning that the comparison mentioned does not consider the design methods outlined in Eurocode 9 [45] for aluminum structures.These methods are applicable only to aluminum structural sheeting, which involves members with two or more webs.They do not provide design guidelines for determining the web buckling strength of single-web sections such as aluminum channel sections.Additionally, a recent study by Alsanat et al. [23] found that Eurocode 9 [45] was not suitable for estimating the web buckling strength of aluminum single-web sections.

Design Methods in AS/NZ S4600 [30]
The current AS/NZ S4600 [30] and AISI S100-16 [31] guidelines provide design calculations with different specific coefficients for evaluating the web buckling strength of CFS lipped channels.These coefficients are directly related to the loading conditions, types of support, and flange types.The expression for evaluating the web buckling strength is as illustrated below: 5.3.Design Methods in AS/NZS 1664.1 [32] Design calculations are available in AS/NZS 1664.1 [32] for estimating the web buckling strength of aluminum alloy channel sections undergoing ETF and ITF loadings.Additionally, any enhancement in web buckling strength due to the flanges secured to the supports is disregarded in the design guidelines.The design calculations for both flangefastened and unfastened support scenarios are the same.Below is the expression for estimating the web buckling strength under ETF and ITF loading: P AS1664 = (t 2 w sin θ(0.46 f y + 0.02 E f y )(N + C w1 ))/(C w3 + r i (1 − cos θ)) (5)

Comparing the Design Strengths with the Simulation Results
In this section, the accuracy of the existing design methods given in AS/NZ S4600 [30] and AS/NZS 1664.1 [32] were evaluated based on the parametric analysis outcomes.
The design strengths derived from AS/NZ S4600 [30] and AS/NZS 1664.1 [32] were compared to the web buckling strength obtained from the parametric investigation.The comparison was summarized in Table 4.As illustrated in Figure 12, the average design strength calculated by AS/NZ S4600 [30] compared to the simulation results was 1.53 and 1.37 for 7075-T6 and AA-6086, respectively.The web buckling strength predicted by AS/NZS 1664.1 [32] was slightly unconservative by 14% and 2% for 7075-T6 and AA-6086, respectively, compared to simulation results (see Figure 13).This indicates that the existing design methodologies tend to be overly conservative when assessing the web buckling strength of such members.As mentioned previously, the existing design rules are demonstrated to be over conservative when assessing the web buckling strength of such members, and new design rules should be presented in this investigation.The simulation results suggested that the impact of the h w /t, N/t, and r i /t ratios on the web buckling strength of HA sections was significant.This indicates the importance of including the impact of h w /t, N/t, and r i /t ratios when proposing design calculations for estimating the web buckling strength of such members.
In this investigation, new design calculations were presented based on three key parameters (h w /t, N/t, and r i /t ratios), which followed the format of the design calculations given in AS/NZS 4600 [30].Therefore, only new coefficients such as 1.483, 0.01, 0.265, and 0.505 were developed using the bivariate linear regression analysis, based on a total of 1024 numerical results.
For 7075-T6 unlipped channel sections: For AA-6086 lipped channel sections: For AA-6086 unlipped channel sections: As depicted in Figure 14, the simulation results-which were the outcomes from the parametric investigation-and the design strengths, which were derived from the newly presented equations given in this investigation (M-AS/NZ S4600), were comparatively analyzed.Table 4 summarizes the findings from the comparison.The average ratio of design values to simulation results was found to be 0.94, and the coefficient of variation (COV) was 0.24 for 7075-T6 aluminum, while the average ratio was 0.93 and the COV was 0.25 for AA-6086 aluminum.Therefore, it can be concluded that the newly presented design calculations provided in this research (M-AS/NZ S4600) were marginally conservative in comparison to the simulation results.

Reliability Analysis
A reliability assessment was undertaken to determine the accuracy of the newly developed design calculations in web buckling, and the reliability of the proposed formulae was evaluated based on the statistical model recommended by the AS/NZ S4600 [30] and AISI S100-16 [32]: As per AS/NZ S4600 [30] and AISI S100-16 [32], a reliability index (β) value of at least 2.5 indicates reliable design calculations.During the reliability analysis, a loading condition of 1.2DL + 1.6LL was chosen, where DL stands for dead load and LL for live load.The statistical parameters chosen for the material and fabrication properties were based on the averages (M m = 1.10,F m = 1.00) and COVs (V M = 0.10, V F = 0.05) in accordance with AS/NZ S4600 [30] and AISI S100-16 [32].According to Table 4, the values of β were found to be 2.51 and 2.50 for 7075-T6 and AA-6086, respectively, implying that the suggested design method can properly estimate the web buckling strength of such members.More information regarding the reliability analysis is available in AS/NZ S4600 [30] and AISI S100-16 [32].

Conclusions
This study focused on the web buckling performance of high-strength aluminum alloy channel sections subjected to end-two-flange (ETF) loading.Both material grades of AA-6086 and 7075-T6 were investigated.Based on the outcomes of this study, the following conclusions can be drawn: (1) A parametric investigation consisting of 1024 models was performed using the finite element (FE) models previously developed for traditional aluminum alloys.A wide range of high-strength aluminum alloy sections covering varying web slenderness ratios, internal corner radii, bearing lengths, and aluminum alloy grades were considered.The results obtained from the parametric investigation suggested that the impact of h w /t, N/t, and r i /t ratios on the web buckling strength of high-strength aluminum alloy sections was significant.This indicates the importance of including the impact of h w /t, N/t, and r i /t ratios when proposing the design calculations for estimating the web buckling strength of such members.(2) The accuracy of the latest design recommendations provided in the Australian and New Zealand Standards (AS/NZ S4600; 2018) and Australia Standards (AS/NZS 1664.1;1997) was evaluated by comparing them with the parametric analysis results.The results showed that the average design strength calculated by AS/NZ S4600 to the simulation results was 1.53 and 1.37 for 7075-T6 and AA-6086, respectively.The web buckling strength predicted by AS/NZS 1664.1 was slightly unconservative by 14% and 2% for 7075-T6 and AA-6086, respectively, compared to the simulation results.It was shown that the latest design recommendations were over-conservative when estimating the web buckling strength of such channel sections.(3) Four unified web buckling equations with new coefficients for high-strength aluminum alloys were presented based on the simulation results.The same methodology as AS/NZS 4600 (2018) was adopted in developing the new design calculations.The average ratio of design values to simulation results was found to be 0.94, and the coefficient of variation (COV) was 0.24 for 7075-T6 aluminum, while the average ratio was 0.93 and the COV was 0.25 for AA-6086 aluminum.A comparison revealed that the design strengths calculated by the newly presented formulas (M-AS/NZ S4600) were close to the simulation results.(4) The accuracy of the new design calculations presented in this work were evaluated through a reliability analysis.The reliability index values (β) for 7075-T6 and AA-6086 were determined to be 2.51 and 2.50, respectively, indicating that the new design calculations can closely estimate the web buckling strength of such channel sections.

Figure 1 .
Figure 1.Aluminum alloy sections used as load-bearing members in engineering applications.

Figure 1 .
Figure 1.Aluminum alloy sections used as load-bearing members in engineering applications.
(a) ITF loading case (b) ETF loading case

4 .
Development of Numerical Models and Parametric Study 4.1.General

Figure 4 .
Figure 4. Mesh size employed in the FEMs.

Figure 4 .
Figure 4. Mesh size employed in the FEMs.

Figure 5 .
Figure 5. Boundary conditions applied in the FEMs.

Figure 5 .
Figure 5. Boundary conditions applied in the FEMs.

Figure 7 .
Figure 7.Comparison of ultimate strength between the laboratory tests [23] and numerical analysis.

Figure 7 .
Figure 7.Comparison of ultimate strength between the laboratory tests [23] and numerical analysis.

Figure 7 .Figure 8 .
Figure 7.Comparison of ultimate strength between the laboratory tests [23] and numerical analysis.

Figure 8 .
Figure 8. Load-displacement relationship between the laboratory tests [23] and numerical analysis.

Figure 10 .
Figure 10.Web buckling strength versus the bearing length ratio (N/t).Figure 10.Web buckling strength versus the bearing length ratio (N/t).

Figure 11 .
Figure 11.Web buckling strength versus the inside bent radius ratio (r/t).

Figure 11 .
Figure 11.Web buckling strength versus the inside bent radius ratio (r/t).

Figure 12 .
Figure 12.Comparison between simulation results and design strength calculated by AS/NZS 4600 [30].Figure 12.Comparison between simulation results and design strength calculated by AS/NZS 4600 [30].

Figure 13 .
Figure 13.Comparison between the simulation results and design strength calculated by AS/NZS 1664.1 [32].

Figure 13 .
Figure 13.Comparison between the simulation results and design strength calculated by AS/NZS 1664.1 [32].
calculations provided in this research (M-AS/NZ S4600) were marginally conservative in comparison to the simulation results.(a) 7075-T6 (b) AA-6086

Figure 14 .
Figure 14.Comparison between the simulation results and design strength calculated by proposed design formulas.Figure 14.Comparison between the simulation results and design strength calculated by proposed design formulas.

Figure 14 .
Figure 14.Comparison between the simulation results and design strength calculated by proposed design formulas.Figure 14.Comparison between the simulation results and design strength calculated by proposed design formulas.

Table 2 .
Comparison [23]he ultimate strength predicted from laboratory tests[23]and numerical analysis.WebFlange Lip Thickness Length Bearing WidthTest Result FEA Result

Table 2 .
[23]arison of the ultimate strength predicted from laboratory tests[23]and numerical analysis.

Table 3 .
Details of the parametric analysis.

Table 4 .
Comparison of the simulation results with the design strength.