Keywords

1 Introduction

Cold-formed steel structures have been progressively used in buildings due to their convenience in manufacturing, fabrication, transportation and assembly. Their applications are seen in industrial or commercial buildings. More details of the applications can be found in Yu et al. [1]. Cold-formed channel section is a popular product that has been available in the worldwide market for decades. This section has a wide and flat web that is very sensitive to local buckling. This drawback subsequently has been solved by adding stiffeners in this web to create a new section called SupaCee. This SupaCee section will be considered in this investigation.

In terms of design for cold-formed steel structures, Direct Strength Method (DSM) can be seen as a new design method that has attracted the mentions of researchers and designers due to its advantages compared to the traditional effective width method (EWM) [2,3,4]. The new method allows the designers to easily determine the capacities of complex section shapes such as the SupaCee section. This method has been regulated in the Australian/New Zealand Standard AS/NZS 4600:2018 [5]. Elastic buckling analyses are compulsory for the application of this DSM method that can be carried out by using commercial software packages such as CUFSM [6] or THIN-WALL-2 [7, 8]. The design procedure was reported by Pham and Vu [9]. The DSM method will be used for the investigation in this paper.

In literature, a huge number of studies on channel or SupaCee sections under flexure have been available. Almost of the studies are flexure about the strong-axis [4, 10,11,12,13,14,15] whereas these on flexure about the weak-axis remained limited [16, 17]. Impacts of web stiffeners on the capacities of SupaCee sections under bending about the strong axis were studied in previous works [18] whereas their impacts on the weak-axis were not reported. Flexure about the weak axis of SupaCee sections can be found in numerous cases and this has a specific influence on the flexural capacities of SupaCee sections. The strength and behaviour of SupaCee sections under bending about the weak-axis are investigated in this paper. The distances between web stiffeners are subsequently varied in order to study their distance impacts on the flexural capacities about the weak-axis.

2 Sectional Capacities of Cold-Formed Steel Sections Under Bending Using the Direct Strength Method

In this paper, global buckling failures are prevented by using bracing systems as illustrated in Fig. 1 and discussed in Pham and Vu [9]. The member capacities can be determined as the sectional capacities with the replacement of the global buckling moment by the yield moment in the design formulae using the DSM method regulated in the Australian/New Zealand Standard AS/NZS 4600:2018 [5]. The flexural capacity is the smaller of the local buckling moment (Mbl) and the distortional buckling moment (Mbd) as follows:

$$ M_{s} \, = {\text{ Min }}(M_{bl} , \, M_{bd} ) $$
(1)
$$ M_{bl} = \left\{ {\begin{array}{*{20}l} {M_{y} } \hfill & {{\text{for}}\;\lambda_{{\text{l}}} \le {0}{\text{.776}}} \hfill \\ {\left[ {1 - 0.15\left( {\frac{{M_{ol} }}{{M_{y} }}} \right)^{0.4} } \right]\left( {\frac{{M_{ol} }}{{M_{y} }}} \right)^{0.4} M_{y} } \hfill & {{\text{for}}\;\lambda_{{\text{l}}} { > 0}{\text{.776}}} \hfill \\ \end{array} } \right. $$
(2)
$$ M_{bd} = \left\{ {\begin{array}{*{20}l} {M_{y} } \hfill & {{\text{for}}\;\lambda_{{\text{d}}} \le {0}{\text{.673}}} \hfill \\ {\left[ {1 - 0.22\left( {\frac{{M_{od} }}{{M_{y} }}} \right)^{0.5} } \right]\left( {\frac{{M_{od} }}{{M_{y} }}} \right)^{0.5} M_{y} } \hfill & {{\text{for}}\;\lambda_{{\text{d}}} { > 0}{\text{.673}}} \hfill \\ \end{array} } \right. $$
(3)
Fig. 1
A diagram presents a rectangular-shaped plate with 2 lateral bracings on either side.

The arrangement of lateral bracing systems

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where \(\lambda_{l} = \sqrt {M_{y} /M_{ol} }\); \(\lambda_{d} = \sqrt {M_{y} /M_{od} }\); My is the yield moment; Mol and Mod are the elastic local and distortional buckling moments respectively and are determined as presented in Sect. 3.

3 Behaviour and Strength of SupaCee Sections Under Flexure About the Weak Axis

SupaCee sections for the investigation are selected from the commercial sections provided by BlueScope Lysaght [19] as listed in Table 1, and their dimensions are illustrated in Fig. 2. Each section is labelled on the basis of its depth and thickness. For instance, “SC25015” means that: “SC” stands for SupaCee; “250” shows the nominal depth of 250 mm; “15” indicates the thickness of 1.5 mm. The grade G450 is used for the investigation as regulated in the Australian Standard AS1397 [20] including yield stress fy = 450 MPa; Young’s modulus E = 200 GPa.

Table 1 The nominal dimensions of SupaCee sections
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Fig. 2
A cross-sectional view of a beam, which has t between 2 S with the inner radius r subscript 1 and r subscript 2, angles of alpha subscript 1 and alpha subscript 2, length L subscript 1 and L subscript 2, with dimensions D, G S, and B.

Nomenclature for SupaCee sections

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Due to the asymmetry of SupaCee sections about the weak axis, the bending directions are considered in the investigation with the directions regulated in Fig. 3. Elastic buckling analyses are conducted by using the software program THIN-WALL-2 [7, 8]. The elastic buckling stresses are obtained and given in Table 2 for both two bending directions. For the negative direction, two lips are in tension whereas web areas are in compression. This leads to the observation of local buckling in the web as illustrated in Fig. 4a, and distortional buckling does not occur in this situation. For the positive direction, tension is found in the webs and compression is observed in the lips and flange areas adjacent to the lips. Local buckling is seen in the flange areas and distortional buckling is also observed, as illustrated in Fig. 4b, c. Based on the obtained elastic buckling stresses, the flexural capacities of the investigated SupaCee sections are determined according to the DSM method as presented in Sect. 2. The results are given in Table 3. It is found that the local buckling occurs for the negative moment direction and this is distortional buckling for the positive direction.

Fig. 3
2 diagrams present a rectangular-shaped steel beam, which has several lines along its length. Arrows indicate local buckling that occurs with negative and positive bending directions.

The conventions of bending directions

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Table 2 Sectional buckling stresses of SupaCee sections under flexure about the weak-axis
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Fig. 4
3 graphs plot load factor at buckling versus buckle half-wave length. They plot a decreasing curve with fluctuations. There are 3 contour plots of the beam in a color gradient scale and 3 diagrams of the beam with different bending directions.

The behaviours of the investigated sections with the variation of bending directions

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Table 3 Flexural capacities of SupaCee sections about the weak-axis (Unit: kNm)
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Table 3 shows that the capacities in the positive direction (M(+)) are significantly higher than those in the negative direction (M(−)). Also, it is found that the ratios M(+)/M(−) are seen as a downward trend when the section thicknesses increase. This is explained that the increase in the thickness allows the webs to become more stable which has significant impacts on the negative moments M(−).

The negative moment is the detrimental case for the flexural capacities of SupaCee sections about the weak-axis, and this moment is also significantly affected by stiffeners. Therefore, the negative direction is used to investigate the impacts of web stiffener locations on the flexural capacities of SupaCee sections about the weak-axis, as presented in Sect. 4.

4 Effects of Web Stiffener Locations on the Flexural Capacities of SupaCee Sections About the Weak-Axis

As seen in Fig. 2, SupaCee has two couples of stiffeners, and these couples are close to the flanges. The distance between two couples is termed “GS”. In this paper, two couples of stiffeners will reach the centroid of the webs; it means that the distance “GS” will decrease, as given in Table 4.

Table 4 Flexural capacities of SupaCee sections under flexure about the weak-axis
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In terms of elastic buckling analyses, elastic buckling stresses are also determined by using the commercial software program THIN-WALL-2 for the negative bending direction, as listed in Table 4. These buckling stresses are utilised for the determination of flexural capacities of SupaCee sections as presented in Table 4.

Table 4 shows the increase in the negative moments if the distances “GS” decrease. It means that the flexural capacities of SupaCee sections become more beneficial if two couples of stiffeners are towards the centroid of the webs. The moment improvements are more significant for sections with small thicknesses. This improvement is about 6% for SC25015, but this is only about 3.6% for SC25024.

5 Conclusions

The paper investigates the behaviour of SupaCee sections under flexure about the weak-axis and the impacts of the distances between web stiffeners of these SupaCee sections on their flexural capacities. Based on the investigated results, several remarks are given as follows:

  • The behaviour of SupaCee sections under bending about the weak-axis depends on the moment directions due to the asymmetry of these sections.

  • The failures of SupaCee sections are governed by the local buckling for the negative moment direction, and they are governed by distortional buckling for the positive moment direction. In general, the flexural capacities of SupaCee sections about the weak-axis are taken as the negative direction moments.

  • As the couples of stiffeners reach toward the centroid of the webs, the negative moments become more beneficial. These stiffener couples should be kept close to the centroid of the webs.