Web crippling investigation of perforated aluminium lipped channels under interior-one-flange loading condition

Abstract

This study investigates the web crippling performance of roll-formed aluminium-lipped channels (ALCs) made of 5052-H36 aluminium alloy. The influence of web perforations on the crippling resistance of webs subjected to Interior-One-Flange (IOF) loading was examined. Laboratory tests were conducted on ALCs with and without circular openings at the mid-depth of the web. Finite element (FE) models were then developed and validated against the experimental results, ensuring their accuracy. To explore the influence of various parameters on the web crippling resistance, a parametric study was carried out. The parameters considered in the study include opening diameter, section depth, inside bent radius, bearing length, and aluminium grade. Using the data obtained from the parametric study, a comprehensive assessment of the available design guidelines for cold-formed steel and stainless steel was performed. New equations in the form of reduction factors were developed to accurately predict the reduction in the web crippling strength, showing their applicability to predict the reduction in the web crippling resistance due to web openings and statistically verifying their reliability.

Keywords

aluminium lipped channels interior-one-flange loading condition web crippling perforated web design guidelines

Introduction

Roll-formed aluminium lipped channels (ALC’s) are used in the building sector for applications such as roof purlins, floor joists, and rafters. Their popularity stems from their advantages, including low density, lightweight, high strength-to-weight ratio, excellent corrosion resistance, durability, and high ductility, making them ideal for low-rise buildings and portal frames, especially in humid environments.

Aluminium alloys possess yield strengths comparable to that of mild steel, though their lower elastic modulus increases susceptibility to buckling instabilities. Current design guidelines outlined in the Australian/New Zealand Standard (AS/NZS) (1997a, 1997b), Eurocode (CEN, 2006, 2007), and The Aluminum Association (2015) for ALC sections are limited mainly due to incomplete research in this field. However, recent studies (Alsanat et al., 2019a, 2019b, 2020a, 2020b, 2022; Fang et al., 2022a, 2022b; Huynh et al., 2019; Nguyen et al., 2022a, 2022b; 2020a, 2020b, 2021) have been conducted to investigate the behaviour of ALC under web crippling, shear, and combined failure actions.

Holes in the web of sections are typically used for the installation of plumbing and electrical systems and can have a significant impact on their web crippling resistance. Studies by Lian et al. (2017, 2016a, 2016b) and Uzzaman et al. (2020a, 2020b, 2017, 2013, 2012a, 2012b, 2012c) mainly concerned cold-formed steel sections. Experiments followed by numerical parametric analyses examined the effects of perforations on the web crippling capacity under various loading conditions, including end-one-flange (EOF), end-two-flange (ETF), interior-one-flange (IOF), and interior-two-flange (ITF) loading. Yousefi et al. (2017a, 2017b, 2017c, 2016) focused on stainless-steel press braked channel sections, under different loading conditions. For sections made of aluminium, research by Zhou and Young (2010) investigated extruded hollow sections made of 6061-T6 heat-treated aluminium alloy whereas Alsanat et al. (2021a) studied ALC’s, manufactured by roll forming 5052-H36 aluminium alloy sheets. Both examined ETF and ITF loading conditions and developed reduction factor coefficients to account for the influence of web perforations on the web crippling resistance. Fang et al. (2022a, 2022b, 2022c, 2021) studied 5052-H32 aluminium unlipped channels under ITF loading conditions. Through experimental, numerical, and deep-learning techniques, they developed new design equations.

Recent studies have increasingly focused on the buckling behavior of thin-walled cold-formed aluminium sections, particularly under conditions where distortional buckling is likely to govern failure. Investigations, such as those by Huynh et al. (2021), have demonstrated the significance of initial geometric imperfections and material inelasticity in predicting distortional buckling behavior accurately. These studies emphasize the importance of using detailed finite element (FE) models, calibrated against experimental data, to extend the applicability of design methods. Additionally, the development of new design guidelines based on parametric studies has been highlighted as a critical step in optimizing the performance of cold-rolled aluminium sections under various loading conditions.

Pham et al. (2021) have shown that existing design standards, such as AS/NZS 1664.1 and the American Aluminium Design Manual, often fail to accurately predict the buckling behavior of cold-rolled aluminium sections, especially when global and distortional buckling modes interact. This research highlights the need for refined design provisions that better account for these interactions, particularly in beams where such effects are critical. Pham et al. (2022) developed new design guidelines for cold-rolled aluminium alloy channel beams subject to global buckling, validating their approach through experimental and finite element (FE) analyses. Their study demonstrated that the Direct Strength Method (DSM) from the AS/NZS 4600 standard, typically used for cold-formed steel, provides accurate predictions for aluminium beams. This research underscores the potential for applying DSM design rules to cold-rolled aluminium sections, highlighting the need for refined guidelines in this area. Furthermore, Pham et al. (2024) conducted comprehensive compression tests on cold-rolled aluminium alloy channel columns, highlighting the limitations of current design standards in predicting buckling behavior, particularly for sections where local-global interaction buckling modes are critical. Their findings underscore the need for refined design guidelines that better capture the complex buckling responses of cold-rolled aluminium members, especially for intermediate and slender sections. On the other hand, in the research series, Nguyen et al. (2024a) conducted full-scale tests on cold-rolled aluminium portal frames with unbraced columns, highlighting the susceptibility of such systems to flexural-torsional buckling under vertical and combined loading scenarios. Their study provided valuable insights into the mechanical properties and buckling behavior of cold-rolled aluminium structural members, emphasizing the critical role of adequate bracing in enhancing the ultimate load capacity of these systems. This work contributes to the understanding of buckling phenomena in cold-rolled aluminium structures, particularly in the context of unbraced configurations. Also, Nguyen et al. (2024b) explored the impact of bracing and structural enhancements on the performance of long-span cold-rolled aluminium portal frames. Their experimental program demonstrated that braced columns and the inclusion of rafter ties and sleeve stiffeners significantly improve the strength and ductility of these structures. The study highlighted that while unbraced columns were prone to flexural-torsional buckling, braced configurations achieved higher load capacities and better overall performance. This work provides critical insights into optimizing the design of cold-rolled aluminium portal frames and underscores the importance of lateral bracing and structural reinforcements.

However, IOF loading conditions have not yet been thoroughly investigated and it is necessary to re-evaluate the proposed empirical design guidelines to verify their suitability in determining the web crippling capacity of ALC sections under IOF loading conditions. This study concentrates on the interior-one-flange (IOF) loading condition, considering both unfastened and fastened flange scenarios. It involves experimental tests and non-linear finite element (FE) parametric analyses using the Abaqus/Explicit solver. Parameters include section depth, opening diameter, bearing length, inside bent radius, and aluminium grade. The obtained data is used to evaluate the appropriateness of reference design guidelines. New design formulae are developed to estimate the reduction in web crippling resistance of roll-formed ALC’s under the IOF loading condition.

It’s worth mentioning that the primary focus of this study is on evaluating the reduction factor for aluminum lipped channels (ALCs) with perforations. The presence of holes significantly affects the web crippling strength, and this research aims to quantify this reduction through a parametric analysis. The discussion of web crippling capacity for ALCs without perforations is beyond the scope of this paper. However, a comprehensive analysis of ALCs without holes, including the derivation of reduction factors, has been covered in a separate study by the authors (Alsanat et al., 2021b).

Experimental investigation

Test specimens and material properties

Tests were conducted on specimens made of 5052-H36 aluminium alloy grade. A total of ten specimens, both with and without web openings, were tested under the IOF loading condition. Circular holes located at the centre of the web, with nominal diameters (a) equal to 20%, 50%, and 80% of the clear web depth (h) were perforated using waterjet cutter. The web slenderness ratio, defined as the clear web depth (h) to thickness (t) ratio, was 83.3. The internal channel corner radius (r_i) was 5 mm. The length of the specimens (L) followed the recommendations of AISI S909 (A.I. and S. Institute, 2008), i.e. L = 3N + 3h, where N is the bearing length and h is the clear web depth. Table 1 provides a summary of the nominal dimensions of the specimens, with each specimen labelled as illustrated in Figure 1.

Table 1.

Geometric and mechanical properties of tested ALC’s.

Specimen	N (mm)	d (mm)	a (mm)	t (mm)	b_f (mm)	r_i (mm)	l_b (mm)	L (mm)	E (MPa)	f_y (MPa)	P_Exp. (kN)
U-IOF-300-3-A0(a)	100	297.0	0.0	2.99	109.80	4.50	28.80	1114.70	68109	223	24.69
U-IOF-300-3-A0(b)	100	296.0	0.0	2.99	110.09	4.75	27.08	1110.80	68109	223	24.55
U-IOF-300-3-A0.2	100	295.5	60.0	2.99	110.28	4.75	25.70	1114.90	68109	223	24.20
U-IOF -300-3-A0.5	100	295.5	125.0	2.99	109.70	4.75	26.19	1114.65	68109	223	23.50
U-IOF -300-3-A0.8	100	295.5	230.0	2.99	109.64	4.75	26.24	1114.85	68109	223	19.16
F-IOF -300-3-A0(a)	100	294.5	0.0	2.99	109.86	4.75	26.53	1115.00	68109	223	26.43
F-IOF -300-3-A0(b)	100	295.1	0.0	2.99	109.85	5.00	26.45	1100.80	68109	223	26.17
F-IOF -300-3-A0.2	100	297.0	60.0	2.99	109.53	5.00	26.27	1115.10	68109	223	25.72
F-IOF -300-3-A0.5	100	296.5	125.0	2.99	109.50	4.75	28.95	1114.90	68109	223	25.28
F-IOF -300-3-A0.8	100	296.5	230.0	2.99	109.50	4.75	28.95	1114.90	68109	223	20.23

Note: specimen names ending with (a) or (b) were repeated tests.

Figure 1.

Specimen nomenclature.

The material properties of 5052-H36 aluminium alloy grade were determined through tensile coupon tests conducted in accordance with AS 1391 (Standards Australia, 2007). Three coupons were extracted from the upper, centre, and bottom regions of the web in the longitudinal direction. Tensile testing was performed using an Instron displacement-controlled testing machine (5980 Series), and stress and strain data were recorded, using static clip-on extensometer, at regular intervals during the tests. The resulting data was used to generate the engineering stress-strain curve, depicted in Figure 2. The average value of the elastic modulus (E₀) is 68301 MPa, the 0.2% tensile proof stress ( $σ_{0.2}$ ) is 226 MPa, ultimate tensile strength ( $σ_{u}$ ) is 277 MPa and the strain at fracture ( $ε$ _u) is 0.078.

Figure 2.

Engineering stress-strain curve for 5052-H36 aluminium alloy grade.

Test rig and procedure

Following AISI S909 test method, a pair of specimens were tested together to prevent lateral movement, positioning them face-to-face, forming a box shape as shown in Figures 3 and 4. They are connected using four 15 × 15 × 5 mm angles, screwed to the top and bottom flanges of the samples, to allow for flange rotation during testing.

Figure 3.

Web crippling test set-up under IOF.

Figure 4.

Experimental test set-up under IOF.

To replicate the IOF loading condition, three identical high-strength steel bearing plates are connected to half rounds, which enable them to freely rotate during the test, simulating a simply supported beam scenario. To prevent failure at the beam boundaries and guarantee its occurrence at mid-span, 10 mm thick steel plates are rigidly attached, using M14 bolts, to both ends of the web. In the fastened flange scenario, the specimens were connected to the bearing plates using M12 bolts as indicated in Figure 4(b). The loading cross-head of the testing machine is moving at a constant rate of 2 mm/min until failure. The applied load and vertical displacement were recorded using the displacement cross head with ±0.1 N and ±0.02 mm accuracy.

The web crippling strengths (PExp.) for the unfastened and fastened IOF tests are summarized in Table 1. The results showed minimal variation, with a 1.3% difference for the U-IOF-300-3-A0 test and a 0.6% difference for the F-IOF-300-3-A0 test.

Failure modes for the unfastened and fastened scenarios are shown in Figure 5. Generally, plastic deformation occurred in the form of a yield arc beneath the loading plate, with size (width (L_w) and depth (L_d)) noticeably increasing with the hole size. Intersection between the yield arc and the hole perimeter was observed for holes with diameters of 0.5h and 0.8h, while no intersection occurred for samples with a hole diameter of 0.2h.

Figure 5.

Experimental failure modes for IOF ALC’s samples.

Figures 6 and 7 display the load versus displacement curves. Generally, similar behaviour was observed for all samples; first, the sample behaved elastically, and the applied load increased linearly with increasing vertical displacement. Then, the behaviour (elastic-plastic) started to become non-linear and the load kept increasing until it reached the ultimate load. Subsequently, plastic deformation was initiated, and the load started to decrease slightly. Notably, a significant reduction in web crippling capacity was observed for samples with a hole diameter of 0.8h, which considerably intersects with the failure region, as shown in Figure 5(d).

Figure 6.

Comparison of experimental and FE load versus vertical displacement curves - unfastened condition.

Figure 7.

Comparison of experimental and FE load versus vertical displacement curves - fastened condition.

Numerical analysis

Finite-element model development

Finite element (FE) models were developed to simulate the experimental tests using ABAQUS software, version 6.14, using a quasi-static analysis with the explicit solver. The model was meshed using S4R 2D shell elements for the lipped channels, and R3D4 rigid shell element for the bearing plates, and included a contact model to capture the interaction between them.

A sensitivity analysis led to selecting a mesh size of 5 × 5 mm for the lipped channels, with a finer mesh of 1 × 5 mm used for the corners and of 3 mm × 3 mm for the middle region of the model to capture concentration of stresses near the loading plate and hole, see Figure 8. The full stress-strain curve was inputted to fully capture the material nonlinearity. The ALC’s corners were modelled with considering residual stresses effects generated due to cold-forming process. The yield stress at the corner was increased by 10% and the ultimate strengths increase 7% (Huynh et al., 2019). As suggested by Rossi, the residual stresses effects were defined to the corners and the adjacent flat parts by a distance approximately equal to 2t (Zhao et al., 2015).

Figure 8.

Mesh size distribution in lipped channel cross-section.

Figure 9 depicts the boundary conditions used in the FE models under unfastened and fastened conditions. In both cases, the top and bottom plates were constrained to prevent translational movements along the X and Y axes (U_x and U_y) as well as rotations around the Y and Z axes (R_y and R_z). The top plate was permitted to move along the Y axis (U_y). Additionally, one of the bottom plates was fixed along the Z axis (U_z) to avoid rigid body motion.

Figure 9.

Boundary conditions assigned to the FE models.

Contact between the channel and bearing plates was modelled through surface-to-surface contact algorithm. In the case of fastened conditions, the bolts connecting the bearing plates with the channel flanges were simulated using the multi-point constraint (MPC) algorithm. Tie type constraint was assigned to rigidly connect the hole perimeter to the bearing plate. The explicit analysis was conducted with a displacement rate of 25 mm/s, with step time period of 1. No geometrical imperfections were considered in the FE models, as they have minimal influence on the overall web crippling capacity since the load is applied with a relatively large eccentricity to the flat portion of the web due to corner radius (Natário et al., 2014).

Model validation

To evaluate the accuracy of the FE results, a comparison was made between the ultimate web crippling capacities, load versus vertical displacement responses, and failure modes obtained from the experiments and the FE simulations. Table 2 indicates that the FE simulations provide an accurate estimation of the ultimate capacities, with mean experimental-to-numerical values and corresponding Coefficients of Variation (COV) of 0.94 and 0.035, respectively.

Table 2.

Ultimate web crippling loads from experiments and FE analysis.

Specimen	P_Exp. (kN)	P_FEA (kN)	P _Exp. /P _FEA
U-IOF-300-3-A0	24.66	26.73	0.93
U-IOF-300-3-A0.2	24.20	26.61	0.92
U-IOF -300-3-A0.5	23.50	23.82	1.00
U-IOF -300-3-A0.8	19.16	19.15	1.01
F-IOF -300-3-A0	26.25	28.08	0.94
F-IOF -300-3-A0.2	25.72	27.11	0.96
F-IOF -300-3-A0.5	25.28	27.18	0.94
F-IOF -300-3-A0.8	20.23	22.03	0.93
Mean			0.94
COV			0.035

Figures 6 and 7 illustrate the comparison of the experimental and numerical load-displacement curves, indicating reasonable agreement. The comparison of web crippling failure modes for specimens with different web opening sizes is presented in Figures 10 and 11, for unfastened and fastened conditions, respectively, indicating high similarity between the experimental and FE-captured failure modes under the IOF loading condition.

Figure 10.

Experimental failure modes for samples with 0.8h hole diameter.

Figure 11.

Failure modes comparison between experimental tests and FE analysis for fastened samples.

To assess the accuracy of the FE simulations, this section compared the ultimate web crippling capacities, load-displacement responses, and failure modes with the experimental results. As presented in Table 2, the FE model provides an accurate estimation of the ultimate capacities, achieving a mean experimental-to-numerical ratio of 0.94 and a Coefficient of Variation (COV) of 0.035, demonstrating good predictive performance.

Figures 6 and 7 compare the experimental and numerical load-displacement curves, which show reasonable agreement, despite minor discrepancies. The average difference between experimental and FE results is only 6%, with a COV of 0.035 (as shown in Table 2), underscoring the consistency of the FE results across different specimens.

Additionally, Figures 10 and 11 present the comparison of web crippling failure modes for specimens with varying web opening sizes under both unfastened and fastened conditions. The close agreement between the experimental and FE-captured failure modes under the IOF loading condition further validates the robustness of the FE model in simulating complex mechanical behavior.

Parametric study

This section presents the details of the FE parametric study conducted to study web crippling resistances. A total of 576 models were generated based on the validated FE models, covering key parameters such as the slenderness ratio (h/t) varied from 27.7 to 131.0, the inside bent radii (r_i) ranged from 3 mm to 8 mm, and the bearing lengths (N) ranged from 50 mm to 150 mm, the perforations, with the a/h ratios ranging from 0.2 to 0.8 (including no perforation as well), as summarized in Table 3.

Table 3.

Summary of examined key parameters and their corresponding range.

Section notation	N (mm)	h/t	a/h	r_i (mm)	Number of models
100-3.0	50, 100, 150	27.7-31.0	0, 0.2, 0.5, 0.8	3, 5, 8	72
200-2.5	50, 100, 150	73.6-77.6	0, 0.2, 0.5, 0.8	3, 5, 8	72
300-2.5	50, 100, 150	113.6-117.6	0, 0.2, 0.5, 0.8	3, 5, 8	72
400-3.0	50, 100, 150	127.7-131.0	0, 0.2, 0.5, 0.8	3, 5, 8	72
Tests (Section “Test rig and procedure”)				5
FE validation (Section “Model Validation”)				4
Total				297
Total (IOF-unfastened and fastened, two aluminium grades)				594

In addition to varying this set of key parameters, all simulations were run for two different aluminium alloy grades, 5052 with H32 and H36 tempers, were considered. The nominal material parameters for these tempers were obtained from AS/NZS 1664.1 (AS/NZS1664.1, 1997), indicated in Table 4. To capture material nonlinearity, the predictive method proposed by Su et al. (2016) was employed. A bi-linear stress-strain curve, consisting of an elastic region defined by the elastic modulus (E) and a strain hardening region defined by the strain hardening slope (E_sh), was defined using the following equations:

E_{s h} = \frac{f_{u} - f_{y}}{0.5 ε_{u} - ε_{y}}

(1)

ε_{u} = 0.13 (1 - \frac{f_{y}}{f_{u}}) + 0.059

(2)

where

f_{u}

is the ultimate strength (MPa) and

ε_{y}

is the strain at yield point.

Table 4.

Comparison of mean and COV Values of R_Exp-FEA/R_Predicted.

Equation	Flange condition	Mean	COV	$ϕ_{w}$	$β_{0}$
Lian et al. [21]	Unfastened	1.10	0.070	0.85	3.25
Lian et al. [21]	Fastened	1.08	0.090	0.85	3.05
Yousefi et al. [35]	Unfastened	1.08	0.080	0.85	2.90
Yousefi et al. [35]	Fastened	1.06	0.060	0.85	3.10
Proposed	Unfastened	0.99	0.038	0.92	2.50
	Fastened	1.00	0.043	0.93	2.50

Figure 12 presents the impact of web opening ratios (a/h) on the reduction factor (R), i.e., the ratio between the web crippling resistances of samples with perforated web and their equivalents without perforations. The unfastened and fastened conditions are shown in Figure 12(a) and (b), respectively, both exhibiting a nonlinear relationship. Generally, smaller a/h (e.g., a/h = 0.2) have a negligible effect on R, while at higher ratio (e.g., a/h = 0.8) a significant reduction in the web crippling capacity is observed, up to 25%. The influence of the a/h ratio also increases when the bearing plate length decreased for both fastened and unfastened scenarios.

Figure 12.

Changes in reduction factors as a function of web opening ratio for U/F-FTF-100-3 ALC’s.

Figure 13 illustrates the effect of the web slenderness ratio (h/t) on R, indicating minimal impact both unfastened and fastened conditions. Figure 14 provides the influence of the N/h ratio on the reduction factor is shown. Increasing the N/h ratio resulted in an increase in the reduction factor particularly for sections with large perforations (a = 0.8). Figure 14 illustrates the influence of the N/h ratio on the reduction factor. It shows that increasing the N/h ratio results in a slight increase in the reduction factor, particularly for sections with larger perforations (a = 0.8). However, for smaller perforations (a ≤ 0.5), the effect of the N/h ratio is negligible. This trend is consistent for both fastened and unfastened sections. Therefore, due to the minimal influence of N/h on the reduction factor, especially for smaller perforations, this parameter will not be included in the proposed equation in the current study.

Figure 13.

Changes in reduction factors with web slenderness for U/F-ITF-100-3 ALC’s (H32).

Figure 14.

Changes in reduction factors with N/h ratio for ITF-100-3 ALC’s (H32).

Figure 15 illustrates the influence of unfastened and fastened flanges on the reduction of web crippling strength. The mean value of the R_Unfastened /R_Fastened ratios is 0.99 and the COV value is 0.036 indicating the negligible influence of fastening the flanges on the reduction in web crippling strength. The influence of unfastened and fastened flanges on the reduction of web crippling strength is illustrated in Figure 15. A mean value of 0.99 for the R_Unfastened /R_Fastened ratio, along with a Coefficient of Variation (COV) of 0.036, is observed, indicating that the effect of fastening the flanges on the reduction of web crippling strength is negligible.

Figure 15.

Reduction factor comparison between FE-results for unfastened and fastened conditions.

Assessment of existing design methods

The development of accurate design equations is key to enabling reliable use of cold-rolled aluminium members in loads-bearing applications. However, the existing web crippling design guidelines for ALCs with web openings in international codes, such as European (CEN, 2006, 2007), AS/NZS1664, 1997a, 1997b) and The Aluminum Association (2015) codes, are limited in scope.

In the scientific literature however, Lian et al. (2017) and Yousefi et al. (2016) investigated the influence of web openings on the web crippling strength of channels under IOF loading condition, proposing empirical design rules primarily developed for cold-formed carbon steel and stainless steel sections. The suitability of these design rules for ALCs with web openings is presently assessed.

Lian et al. (2017) proposed reduction factor formulae applicable to web crippling of cold-formed steel channels with web openings centred beneath the bearing plate. The reduction factor formulae for both unfastened and fastened flange conditions are provided in equations (3) and (4), respectively.

For the case where the flange is not affixed to the bearing plate,

R = 0.98 - 0.26 (\frac{a}{h}) + 0.06 (\frac{N}{h}) \leq 1

(3)

For the case where the flange is affixed to the bearing plate,

R = 0.95 - 0.06 (\frac{a}{h}) + 0.01 (\frac{N}{h}) \leq 1

(4)

The predicted reduction factors (R_Predicted) based on Lian et al. (2017) were compared with the results from both experimental and parametric studies (R_Exp.-FEA) (see Figure 16). Table 4 provides the mean and COV values for equations (3) and (4), indicating slight overestimation with acceptable scatter. The reliability index ( $β_{0}$ ) values for R_Exp-FEA/R_Predicted, calculated according to AISI S100 (AISI, 2007) with a capacity reduction factor $ϕ_{w}$ value of 0.85 equals 3.25, or 3.05, for unfastened and fastened respectively, beyond its target value of 2.50, reflecting the models’ reliability.

Figure 16.

Reduction factor comparison between R_Exp.-FEA and R_Predicted using (a) equation (3) for unfastened condition and (b) equation (4) for fastened condition (Lian et al., 2017).

Similarly, Yousefi et al. (2016) proposed the following two equations for stainless steel sections:

For the case where the flange is not affixed to the bearing plate,

R = 1.15 - 0.36 (\frac{a}{h}) - 0.1 (\frac{N}{h}) \leq 1

(5)

For the case where the flange is affixed to the bearing plate,

R = 1.1 - 0.28 (\frac{a}{h}) - 0.05 (\frac{N}{h}) \leq 1

(6)

Comparisons of the data obtained against the results from equations (5) and (6) are presented in Figure 17, while the means and coefficients of variation (COVs) are outlined in Table 4. The mean and COV values for the unfastened scenario are 1.08 and 0.08, respectively, reflecting relatively high mean and COV values. Similar patterns were observed for the fastened scenario, with mean and COV values equal to 1.06 and 0.06, respectively. The reliability indices (β₀) for unfastened and fastened conditions are 2.9 and 3.1, respectively, indicating over-conservatism in predicting the web crippling reduction factor.

Figure 17.

Reduction factor comparison between R_Exp.-FEA and R_Predicted using (a) equation (5) for unfastened condition and (b) equation (6) for fastened condition (Yousefi et al. [35]).

Proposed design equation

Utilizing FE parametric data, the current paper proposes design equations in the form of reduction factors for web crippling strength. Among the parameters studied, the distance between the hole and the top of the web (x=(h-a)/2) emerges as the most influential. Equation (7) delineates the reduction in web crippling strength under unfastened and fastened IOF loading conditions:

R_{p} = 1.08 - 0.027 (\frac{h}{x}) \leq 1

(7)

In developing the proposed equation (7), the parameter x, defined as (h−a)/2, was introduced as a key factor influencing the web crippling strength. This approach was found to provide a more accurate representation of the behavior compared to using the (a/h) ratio directly. By incorporating x, the influence of the perforation size relative to the web height is effectively captured. Additionally, as discussed earlier, the parameter (N/h) was excluded from the equation due to its negligible effect on the reduction factor, as evidenced by the findings in this study. In Figure 18, the results of experiments and parametric studies are depicted alongside the proposed reduction factor equations, demonstrating improved agreement. Table 4 presents the statistical summary, where equation (7) exhibits mean values of 0.99 and unity for unfastened and fastened conditions, respectively, with corresponding COV values of 0.038 and 0.042. Calculations for the capacity reduction factor ϕ_w, aiming for a reliability index β₀ of 2.5, yield values of 0.92 and 0.93 for unfastened and fastened conditions. Consequently, a recommended capacity reduction factor of 0.90 is suggested for web design of ALCs with web openings under the IOF load case.

Figure 18.

Reduction factor comparison between R_Exp.-FEA and R_Predicted using the proposed design equation.

It is important to note that the proposed equations are applicable within the specified ranges: a/h ≤ 0.8, h/t ≤ 131, and N/h ≤ 1.81. Furthermore, they are suitable for aluminium alloy grades of 5052 with H32 and H36 tempers.

Conclusions

The paper investigates the resistance of Aluminium Lipped Channels (ALCs) with webs when subjected to web crippling under Interior-One-Flange loading. Both unfastened and fastened sections (where lateral movement is prevented) were examined in the study. Ten experiments were conducted on ALCs with three different opening diameters. The experimental results were then used to validate a finite element model, which was subsequently employed for a parametric study. Various parameters, including opening size, web slenderness, and bearing length, were considered for two aluminium grades, resulting in a total of 596 data points. The study revealed that restraining the flanges has minimal impact on the web crippling reduction factor.

The collected data was utilized to evaluate the performance of two reference formulas from the literature, which provide the reduction factor R. This factor represents the ratio between the web crippling resistances of sections with perforated webs and their equivalents without perforations. The analysis indicated that these formulas are generally overly conservative. Consequently, new design equations were proposed to accurately predict the reduction in the web crippling capacity of aluminum-lipped channels with web openings under Interior-One-Flange loading conditions.

Footnotes

Acknowledgments

This research project is funded by Al-Hussein Bin Talal (AHU) University (Project No. 2021/185). The authors would like to thank AHU University for the financial support, Permalite Australia Building Solutions Pty Ltd for the supply of channel specimens, Griffith University for providing the test facilities to conduct the laboratory work and Mr Mohammad Esam Husni Abu Al Zait for his work on numerical simulations.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Al-Hussein Bin Talal University; Project No. 2021/185.

ORCID iDs

Mahmoud Alrsai

Keerthan Poologanathan

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