1 Introduction

Cold-formed steel (CFS) channel sections have been considered a viable alternative to hot rolled steel channels because of their superior strength to weight ratio and ease of fabrication. These channel sections are used widely in CFS building components. Despite the popularity of CFS channel sections, these remain susceptible to local, distortional, flexural, and flexural–torsional buckling failures (Loughlan and Yidris 2014; Hancock et al. 1994; Wang et al. 2016; Zhang et al. 2007; Young and Hancock 2003).

Buckling behaviour of CFS channel sections has been studied extensively in the last two decades, with focus on code conservativeness. Heva et al. (2012) conducted compression tests on CFS channel sections under flexural–torsional buckling at both ambient and elevated temperatures and showed that Australia-New Zealand standard (AS/NZS 4600) design guidelines were conservative when predicting the axial capacity of CFS channels. On the other hand, Kandasamy et al. (2016) provided the optimum size of lip considering the flexural–torsional buckling interaction for CFS channel beams under restrained boundary conditions. Martins et al. (2015) have presented a critical review on the non-linear behavior and design of CFS columns under local-distortional buckling interaction. Other work in the area includes Gunalan and Mahendran (2013), who investigated the axial capacity of fixed ended CFS channel section columns subjected to flexural–torsional buckling interaction. This study showed how current design guidelines by the American Iron and Steel Institute and Australia-New Zealand standards (AS/NZS 4600) are over-conservative. Most recently, Ye et al. (2018) reported an experimental investigation on local-flexural interactive buckling behaviour of CFS channel section columns. Here, a total of 36 axial compression tests on CFS channel sections of three different lengths (1 m, 1.5 m and 2 m) and four different cross-sections were conducted under pin-ended boundary conditions (Ye et al. 2018).

Interaction between local, distortional, and overall buckling modes plays an important role in determining the section capacities of CFS channel sections under axial compression. However, very limited research is available in the literature for understanding the effect of buckling interactions on the axial capacity of CFS channels. Santos et al. (2012) conducted experimental tests on lipped channels undergoing local-distortional-global buckling interactions. Their study showed that the intermediate columns are susceptible to buckling interactions (Santos et al. 2012).

The Direct Strength Method (DSM) includes the effect of buckling interactions. However, the DSM does not have provisions to include the shift of effective centroid when compressive force is applied to pin-ended columns. Young (2004, 2005, 2006) and Rhodes and Harvey (1977) explained that the shift of effective centroid is caused by the asymmetric redistribution of longitudinal stress due to local buckling. This leads to an eccentricity of the applied load in pin-ended columns.

In terms of CFS angle section columns, significant research is available in the literature. Popovic et al. (1999) investigated the compression capacity of CFS steel angle section columns. In their tests, the primary failure mode for most of the angle sections was overall buckling and flexural–torsional buckling. It was concluded that the Australia-New Zealand standard (AS/NZS 4600) design guidelines were conservative for shorter columns but un-conservative for slender columns (Popovic et al. 1999). Young (2004, 2005) performed experimental tests on angle section columns and showed that the Australia-New Zealand standard (AS/NZS 4600) design rules are over-conservative. Young (2004, 2005) then proposed a new design rule for axially loaded fixed ended CFS plain angle section columns. This was verified by Silvestre et al. (2012) when estimating the member capacity of columns, with more accurate results obtained. On the other hand, Shifferaw and Schafer (2011) found that fixed ended plain and lipped angles exhibited post-buckling strength. Rasmussen and Hancock (1994) studied the flexural buckling behavior of CFS channel section columns and showed that the Australia-New Zealand standard (AS/NZS 4600) design guidelines are conservative for intermediate and long columns under fixed ended condition.

There is limited research available on the axial capacity of CFS channels undergoing local-overall buckling interaction failure. The issue is addressed in the present paper, offering results of 40 experiments on CFS channel sections under axial compression. Prior to compression testing, the material properties and initial imperfections were measured for all test specimens. A non-linear FE model was also developed, which showed good agreement with the experimental test results, both in terms of failure modes and axial capacities. The validated FE model was then used to conduct a parametric study to determine the axial capacity of CFS channels, undergoing local-overall buckling interaction. Four different steel grades, two different cross sections and four different thicknesses were considered. The results obtained from the parametric study were compared against design strengths calculated using current guidelines AISI (2016), AS/NZS (2018), and Eurocode (2006). Having compared FE and test results against the design strengths calculated in accordance with the AISI (2016) and AS/NZS (2018), improved design rules are proposed in this study for predicting accurately the axial capacity of CFS channel section columns undergoing local-overall buckling interaction.

2 Current Design Guidelines

2.1 AISI (2016) Specification and AS/NZ Standard (2018)

The axial capacities obtained from the experiments (as described in Sect. 3) were compared against the un-factored design strengths calculated in accordance with the AISI (2016) and AS/NZS (2018) standards. It should be noted that design strengths calculated from both the AISI (2016) and AS/NZS (2018) depend on the effective area of the cross-sections. For channel sections, the un-factored design strength of axially loaded compression members can be calculated by the Equations given next.

$${\text{P}}_{{{\text{AISI }}\& {\text{ AS}}/{\text{NZS}}}} = {\text{A}}_{{\text{e}}} {\text{F}}_{{\text{n}}}$$
(1)

The critical buckling stress (Fn) can be calculated by using Eqs. (2) and (3), as given next.

$${\text{For}},{\uplambda }_{{\text{c}}} \le \, 1.5:{\text{F}}_{{\text{n}}} = (0.658 {\uplambda }_{{\text{c}}}^{2} ){\text{ F}}_{{\text{y}}}$$
(2)
$${\text{For}},{\uplambda }_{{\text{c}}} > 1.5,{\text{F}}_{{\text{n}}} = \left( {\frac{0.877}{{{\uplambda }^{2}_{{\text{c}}} }}} \right){\text{F}}_{{\text{y}}}$$
(3)

where Ae is the effective area of the section, Fn is the critical buckling stress, λc is the non-dimensional slenderness ratio.

The non-dimensional critical slenderness (\({\uplambda }_{{\text{c}}}\)) can be calculated by using Eq. (4) as given next.

$${\uplambda }_{{\text{c}}} = \sqrt {\frac{{{\text{F}}_{{\text{y}}} }}{{{\text{F}}_{{\text{n}}} }}}$$
(4)

where Fn is the least of the applicable elastic flexural, torsional, and flexural–torsional buckling stresses. Further details regarding the current design guidelines can be found in the AISI (2016) and AS/NZS (2018) standards.

2.2 Eurocode (EN 1993-1-3) (2006)

Design strength of axially loaded compression members calculated using the Eurocode (PEN) depends on the effective area of the section. According to EC3 (BSEN1993-1-3) (2018), the axial strength (PEN) is calculated as follows:

$${\text{P}}_{{{\text{EN}}}} = {\chi A}_{{\text{e}}} {\text{F}}_{{\text{y}}} { }$$
(5)

where \({\text{A}}_{{\text{e}}}\) is the effective area of the section. \({\text{F}}_{{\text{y}}}\) is the yield stress. \({\upchi }\) is the reduction factor for the relevant buckling mode

$${\upchi } = \frac{1}{{\phi + \sqrt {\phi^{2} - {\overline{\lambda }}^{2} } }}\,\,\,\,\,{\text{but}}\,\,\,\,{\upchi } \le 1.0$$
(6)
$$\phi = 0.5\left[ {1 + {\upalpha }\left( {{\overline{\lambda }} - 0.2} \right) + {\overline{\lambda }}^{2} } \right]$$
(7)
$${\overline{\lambda }} = \sqrt {\frac{{{\text{A}}_{{\text{e}}} {\text{F}}_{{\text{y}}} }}{{{\text{N}}_{{{\text{cr}}}} }}} = \frac{{{\text{L}}_{{{\text{cr}}}} }}{{\text{i}}}\frac{{\sqrt {{\text{A}}_{{\text{e}}} /{\text{A}}_{{\text{g}}} } }}{{{\uplambda }_{1} }}$$
(8)
$${\uplambda }_{1} = {\uppi }\sqrt {\frac{{\text{E}}}{{{\text{F}}_{{\text{y}}} }}}$$
(9)

where \({\text{L}}_{{{\text{cr}}}}\) is in plane buckling length, i is the radius of gyration for the particular axis, dependent on cross sectional properties. \({\uplambda }\) is the imperfection factor and \({\text{N}}_{{{\text{cr}}}}\) is the elastic critical force, calculated by using cross sectional properties.

3 Experimental Investigation

3.1 Test Specimens

Figure 1 shows the details of the CFS channel sections considered in the experimental program. These are referred to as C75 and C90. The measured specimen dimensions are shown in Tables 1 and 2 for C75 and C90, respectively. In Tables 1 and 2, the overall web length of sections is defined by the notation “A”. The flange width and lip width of channel sections are defined by “B” and “C”, respectively. The length and thickness of channel sections are defined as “L” and “t”, respectively. The test program comprised 40 specimens; 20 each for C75 and C90 channel sections, subdivided into four different column heights: 300 mm, 500 mm, 1000 mm, and 2000 mm.

Fig. 1
figure 1

Details of cold-formed steel channel columns investigated in this study

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Table 1 Experimental test results: C75
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Table 2 Experimental test results: C90
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All columns were tested with pin-ended boundary conditions, apart from the 300 mm (stub) column which was tested as a fixed ended column. In Tables 1 and 2, the specimens have been sub-divided into stub (300 mm long), short (500 mm long), intermediate (1000 mm long) and slender (2000 mm long) columns for C75 and C90 sections, respectively. In the experimental program, five different nominal thicknesses were considered for all four heights: 1.2 mm, 1.5 mm, 2 mm, 2.5 mm, and 3 mm.

3.2 Determination of Material Properties

Tensile coupon tests were carried out to determine the material properties of the test specimens. The tensile coupons were cut from the center of the web plate in the longitudinal direction of the untested specimens. Five coupons were cut from the longitudinal direction of the coupons for each of the thicknesses for both the C75 and C90 channels. The tensile coupons were tested according to the British Standard for Testing and Materials for the tensile testing of metals BS EN (2001) using 12.5 mm wide coupons of a gauge length 50 mm. The coupons were tested in an MTS displacement-controlled testing machine using friction grips. Two strain gauges and a calibrated extensometer of 50 mm gauge length were used to measure the longitudinal strain. The average stress–strain curve of the steel used in this research is shown in Fig. 2a, b for full and initial curves, respectively. As can be seen from Fig. 2, the Young’s modulus and yield stress of the steel were 207 GPa and 560 N/mm2, respectively. The average values of the material properties are also reported in Table 3.

Fig. 2
figure 2

Average stress–strain curves of CFS used in this research (average of C75 and C90 sections)

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Table 3 Material properties obtained from the tensile coupon tests
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3.3 Specimen Labelling

The test specimens were labelled such that the cross section of channel section, nominal length of specimen and specimen number were expressed by the label. Figure 3 shows an example of the specimen labelling used in this study. The channel sections are denoted by their web depth, i.e. 75 in the label (Fig. 3). The column length is stated at the end of the label as ‘L’. The number “1” at the end of the label refers to the specimen number.

Fig. 3
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Specimen labelling

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3.4 Test-Rig and Testing Procedure

Figure 4 shows a photograph of the test set-up for stub (300 mm long) and intermediate (1000 mm long) columns. In order to record the axial load, the external load cell was positioned at the base of the columns. Two Linear Variable Displacement Transducers (LVDTs) were positioned at the web and a third LVDT was positioned at the top. LVDT positions are numbered as 1, 2 and 3, as shown in Fig. 4a for stub columns and 1, 2, 3,4 5 and 6 for intermediate column tests (Fig. 4b). The axial load was applied to the specimens via a 600 kN capacity GOTECH, GT-7001-LC60 Universal Testing Machine (UTM). The machine was displacement controlled and the loading rate was kept below 25 kg/cm2/s for all test specimens. The columns were centered and aligned so that the load could be applied through the centroid of the sections.

Fig. 4
figure 4

Photograph of a test set-up

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3.5 Measurement of Initial Imperfections

Figure 5a shows the set-up used to measure initial geometric imperfections for all test specimens. The test specimens were placed on a level surface with one end fixed using a G-clamp. A level was used to ensure surface integrity. A LVDT with an accuracy of 0.01 mm was used to record the readings at 20 mm along the length of the sections at the center of the web, flanges, and edge of the lips. Gridlines with 20 mm spacings were drawn on the outer surface of every test specimen to guide the movement of the LVDT along a straight line. The locations of LVDTs are shown in Fig. 5b. A typical plot of the measured initial imperfections versus the channel column length is shown in Fig. 5c for C75-L300-1. In Fig. 5d, another plot of initial imperfections versus the length is shown for C75-L2000-1. The highest imperfections of the investigation samples were 0.21 mm for a 300 mm long column, 0.24 mm for a 500 mm long column, 0.42 mm for a 1000 mm long column and 0.60 mm for a 2000 mm long column.

Fig. 5
figure 5figure 5

Details of imperfection measurements

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3.6 Experimental Results

The dimensions of test specimens and the experimental failure loads (PEXP) are shown in Tables 1 and 2 for C75 and C90, respectively. Tables 1 and 2 also shows the axial capacity of channel sections calculated in accordance with the AISI (2016), AS/NZS (2018) and Eurocode (2006). The non-dimensional slenderness of the CFS channel sections were calculated and shown in Tables 1 and 2 for C75 and C90, respectively. As can be seen from Tables 1 and 2, the AISI (2016) and AS/NZS (2018) standards are conservative by around 10% for columns which failed in local-overall buckling interaction. In contrast, Eurocode (2006) design rules lead to considerably more conservative predictions of the column axial load capacity of CFS channels. In almost all cases, the Eurocode (2006) predictions were lower than the actual strength values obtained from the experimental tests of CFS channels failed in local-overall buckling interactions (the average ratios of test results to predicted values were 1.20 and 1.15, for C75 and C90 columns).

Different failure modes were observed as the length of channel sections varied. Almost all stub and short columns of C75 and C90 channels failed by local buckling. Local-overall buckling interaction was observed for all slender columns except C90-L2000-1 and C90-L2000-2, which were failed only by overall buckling. For most of the slender columns, overall buckling was observed with a large curved deformation at the mid-height. However, after the ultimate load was reached, localized deformation was visible near the mid-height of the compression side of the test specimens.

4 Numercial Study

4.1 General

The FE program ABAQUS (2018) was used to develop a numerical model in order to evaluate the axial capacities of CFS channel columns. The FE model was analyzed via two steps. The first analysis step was to conduct a linear perturbation analysis (Eigen-value analysis) to obtain the buckling modes (Eigen-modes). The second analysis step was to perform a load–displacement analysis to obtain the axial capacities, using the “general-static” method.

4.2 Geometry and Material Properties

The full geometry of the CFS channel sections was modelled. The material non-linearity was incorporated in the FE model by specifying the ‘true’ values of stresses and strains. The ABAQUS (2018) classical metal plasticity model was adopted for the purposes both of validation and for the parametric study (described in Sect. 5 of this paper). In order to define the isotropic yielding and plastic hardening of the steel, the von Mises yield surface was used in the classical metal plasticity model. The material properties were taken from the results of the tensile coupon tests (described in Sect. 3.2 of this paper) and included in the FE models. As per the ABAQUS manual (2018), the engineering material curve was converted into a true material curve by using the following Equations:

$${\upsigma }_{{{\text{true}}}} = {\upsigma }\left( {1 + {\upvarepsilon }} \right)$$
(10)
$${\upvarepsilon }_{{{\text{true}}\left( {{\text{pl}}} \right)}} = \ln (1 + {\upvarepsilon }) - \frac{{{\upsigma }_{{{\text{true}}}} }}{{\text{E}}}$$
(11)

where E is the Young’s modulus, σtrue is the true stress, σu is the tensile ultimate strength, and σ and \({\upvarepsilon }\) are the engineering stress and strain, respectively in ABAQUS (2018). The modulus of elasticity was taken as 207 GPa, and the elastic Poisson’s ratio, v, was assumed as 0.30. Plastic material properties of the CFS channels, used in the FE model are shown in Table 4.

Table 4 Plastic material properties used in the FE model
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4.3 Element Type and Finite Element Meshing

The channel sections were modelled using the linear 4-noded quadrilateral thick shell elements (S4R5). To choose the optimum size of the FE meshing, a mesh sensitivity study was completed. The mesh sensitivity analysis revealed that a mesh size of 5 × 5 mm is suitable, given consideration to both computation time and accuracy of the numerical results. Figure 6a shows a typical FE mesh for C75-L500-2.

Fig. 6
figure 6figure 6

Details of the finite element model developed for CFS channel column

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4.4 Boundary Conditions and Load Application

The CFS channel section columns investigated in this study were pin-ended, other than the stub which was fixed–fixed. To simulate the upper and lower pin-ended supports, the displacements and rotations (boundary conditions) were assigned to the upper and lower ends of the CFS channel sections through reference points. The load was applied to the center of gravity (CG) of the cross-section with the help of reference points, as shown in Fig. 6b. The distance between two reference points were equal to the effective length of the CFS channel section columns between the two hinged supports. The displacement control was used to load the channels, following the general-static (*STATIC) method. The non-linear geometric parameters (*NLGEOM) were activated in the FE model to consider large displacements in the simulation.

4.5 Imperfection Modeling

Initial geometric imperfections were included in the FE model by conducting elastic buckling analysis to determine the contours of such imperfect geometries. The scaled estimations of the general imperfections, as specified in Sect. 3.5 of this paper, were incorporated in the FE model. Moreover, the local imperfections having a magnitude of 0.5% of the channel thickness was used based on the recommendations of Ellobody and Young (2005). The same magnitude of local imperfections was also used by Roy et al. (2018) for modeling back-to-back built-up CFS channel section columns under axial compression. The application of eigenvalue analysis enabled the achievement of overall and local buckling failure modes, as shown in Fig. 6c for C75L500-2.

4.6 Validation of the FE Model

The load–displacement behaviour obtained from the FE model are compared against the experimental failure load, as shown in Fig. 7a, b for specimens C75- L500-2 and C90-L500-2, respectively. Figure 8 shows the failure modes of stub, short, intermediate, and slender columns from both the FE model and experiments. Tables 1 and 2 compare the experimental failure loads to the failure loads determined from the FE analysis for C75 and C90, respectively. As can be seen, the experimental and FE results show good agreement, both in terms of ultimate strength and failure modes.

Fig. 7
figure 7

Comparison of experimental failure load against the FEA results

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Fig. 8
figure 8figure 8figure 8

CFS channels at failure

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5 Parametric Study

5.1 General

A parametric study, comprising 70 FE models, was conducted using the validated FE model. Both cross sections, i.e. C75 and C90, were considered in the parametric study (Fig. 1). The length of CFS channel sections was varied from 100 to 3000 mm (Tables 5, 6). Four different grades of steel were considered in the parametric study, i.e. G250, G450, G500, and G550. Also, four different thicknesses were considered: 0.95 mm, 1.20 mm, 2.20 mm and 2.40 mm.

Table 5 Comparison of axial capacities obtained from the FEA, AISI (2016), AS/NZS (2018) and Eurocode (2006): C75
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Table 6 Comparison of axial capacities obtained from the FEA, AISI (2016), AS/NZS (2018) and Eurocode (2006): C90
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5.2 Parametric Study Results

In Tables 5 and 6, the FE strengths of the CFS channel sections obtained from the parametric study are shown. For comparison, the design strengths calculated in accordance with the current AISI (2016) and AS/NZS (2018) are shown in Tables 5 and 6 for C75 and C90, respectively. As can be seen from both the Tables 5 and 6, the AISI (2016) and AS/NZS (2018) underestimates the axial capacity of CFS channel section columns by 10% on average for all channels which failed by local-overall buckling interaction. The comparison of experimental strengths against the design strengths calculated in accordance with the AISI (2016) and AS/NZS (2018) standards are also shown in Fig. 9a, b for C75 and C90, respectively. Tables 5 and 6 also show the comparison of FE strengths against the design strengths calculated from Eurocode (2006), which reveals that the Eurocode (2006) design strengths are considerably more conservative for determining the axial capacity of lipped channels failed in local-overall buckling interaction. The non-dimensional slenderness (λc) values reported in Tables 5 and 6 were calculated from Eqs. (2)–(4), found in current design codes, i.e. AISI (2016) and AS/NZS (2018) for CFS channel section columns.

Fig. 9
figure 9

Comparison of experimental strengths against the design strengths from current design guidelines [AISI (2016) and AS/NZS (2018) standards]

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6 Proposed Design Rules

There are mainly two regions in the design curve of AISI (2016) and AS/NZS (2018). The first region is for stub columns (where the non-dimensional slenderness (λc) ≤ 1.5). The second region is for slender columns (where the non-dimensional slenderness (λc) > 1.5). These are defined by Eqs. (2) and (3), respectively, as given in this paper. Tables 1 and 2 compare the experimental and FEA results with existing design equations for C75 and C90 columns, respectively. As can be seen from Tables 1 and 2, the AISI (2016) and AS/NZS (2018) is conservative by 10% on average for intermediate and slender columns which failed through local-overall buckling interaction. This highlights the need for improved design rules. The present paper proposes Eq. (12) for calculating the value of Fn when the non-dimensional slenderness (λc) is greater than 1.5. This is because the intermediate and slender columns are mainly susceptible to local-overall buckling interaction. For stub and short columns, the non-dimensional slenderness (λc) is less than or equal to 1.5, and the failure modes are mainly local or distortional buckling. Therefore, it is recommended to use the same equation of Fn as given in the AISI (2016) and AS/NZS (2018) [Eq. (2)], when the non-dimensional slenderness (λc) is less than or equal to 1.5.

$${\text{For}},\,{\uplambda }_{{\text{c}}} > 1.5,\,{\text{F}}_{{\text{n}}} = \left( {\frac{0.94}{{ {\uplambda }_{{\text{C}}}^{1.92} }}} \right){\text{F}}_{{\text{y}}}$$
(12)

As shown in Tables 1 and 2, the comparison of axial capacities from FEA and design strengths is calculated using Eq. (12) for C75 and C90, respectively. As can be seen from Tables 1 and 2, where design Eq. (12) was used, the design strengths are very close to the FE strengths.

7 Capacity Reduction Factor

The AISI standard (2016) recommends a statistical model to determine the capacity reduction factors. This model accounts for the variations in material, fabrication, and the loading effects. The capacity reduction factor \(\phi\) is given by the following Equation:

$$\phi = 1.52{\text{M}}_{{\text{m}}} {\text{F}}_{{\text{m}}} {\text{P}}_{{\text{m}}} {\text{e}}^{{ - {\upbeta }_{0} \sqrt {{\text{V}}_{{\text{m}}}^{2} + {\text{V}}_{{\text{f}}}^{2} + {\text{C}}_{{\text{p}}} {\text{V}}_{{\text{p}}}^{2} + {\text{V}}_{{\text{q}}}^{2} } }}$$
(13)

where \({\text{M}}_{{\text{m}}}\) and Vm are the mean and coefficient of variation of the material factor 1.1, 0.1; \({\text{F}}_{{\text{m}}}\), and Vf are the mean and coefficient of variation of the fabrication factor 1, 0.05; Vq is the coefficient of variation of load effect 0.21; β0 is the target reliability index 2.5; \({\text{C}}_{{\text{p}}}\) is the correction factor depending on the number of tests; \({\text{P}}_{{\text{m}}}\) is the mean value of the tested to predicted load ratio; and Vp is the coefficient of variation of the tested to predicted load ratio. Vp and Pm values must be determined from experiments or analyses. In this investigation, ultimate loads obtained from FEA were considered. Hence Vp and Pm are the mean and coefficient of variation of the ratio of ultimate loads from FEA and design standards. The substitution of all the above values leads to the following Equation.

$$\phi = 1.615{\text{P}}_{{\text{m}}} {\text{e}}^{{ - 2.5\sqrt {0.0566 + {\text{C}}_{{\text{p}}} {\text{V}}_{{\text{p}}}^{2} } }}$$
(14)

Equation (14) was used to determine the capacity reduction factors for the values obtained from the current AISI (2016) and AS/NZS (2018) and the proposed design rules. The AS/NZS (2018) recommends a capacity reduction factor of 0.85 for compression members. Tables 1 and 2 compare the test and FEA results with design strengths calculated from the existing design equations of AISI (2016) and AS/NZS (2018) and the proposed design equation [Eq. (7)]. The capacity reduction factor according to the current AISI (2016) and AS/NZS (2018), using Eq. (3) is 0.92, for CFS channel section columns undergoing local-overall buckling interaction. This slightly higher value of capacity reduction factor emphasizes the need of improved design rules. The capacity reduction factor is 0.86 when following proposed design Eq. (12). Therefore, Eq. (7) is recommended instead of Eq. (3), for determining Fn, and calculating the axial capacity of CFS channel section columns undergoing local-overall buckling interaction.

8 Conclusions

This paper presents an experimental and finite element (FE) investigation to determine the axial capacity of CFS channel section columns subjected to local-overall buckling interaction. In total, 40 experimental tests on CFS channel section columns subjected to axial load were conducted and reported in this paper. Prior to the compression tests, initial imperfections were measured for all test specimens. The failure modes and deformed shapes of CFS channel section columns undergoing local-overall buckling interaction were discussed.

An elasto-plastic FE model was developed to include material non-linearity and geometric imperfections. The von Mises yield surface was defined in the classical metal plasticity model, which was adopted to incorporate isotropic yielding and plastic hardening of the steel. The FE model was validated against the test results. The validated FE model was then used to conduct an extensive parametric study (comprising 70 models) considering four different steel grades and thicknesses, as well as two different cross-sections of CFS channels.

This study has also reviewed the accuracy of the current AISI (2016), AS/NZS (2018) and Eurocode (EN 1993-1-3) design guidelines for determining the axial capacity of CFS channel sections undergoing local-overall buckling interaction failure. The FE and experimental results were compared against the design strengths calculated in accordance with the AISI (2016) and AS/NZS (2018) and Eurocode (EN 1993-1-3). It was found that the current design guidelines as per the AISI (2016) and AS/NZS (2018) standards underestimate the axial capacity by 10% on average for pin-ended CFS channel section columns undergoing local-overall buckling interaction. Eurocode (EN 1993-1-3) design rules lead to considerably more conservative predictions of the column axial load capacity for CFS channels. This paper has, therefore, proposed modifications to the current design rules of AISI (2016) and AS/NZS (2018). The accuracy of proposed design rules was verified using the FE analysis and test results of CFS channel section columns undergoing local-overall buckling interaction.