Keywords

1 Introduction

The usability of hot-rolled steel sections become inefficient for the steel structures which are supposed to carry the light and moderate loads and also for the short span structural members. Hence, the study on the behaviour of cold-formed steel members is inevitable due to their lightness, high yield strength, long-term durability, high load resistance, long-span capability, ease of prefabrication and construction. For the economic utilization of steel and for the larger loads, the individual components are not sufficient to satisfy the required design strength. So the built-up sections are often used in this case to fulfil the stiffness requirements. In general, built-up sections are made up of connecting two or more individual components by either lacings or batten plates. Thus, this paper reports the behaviour and strength of the cold-formed steel built-up battened columns. The built-up columns possessed of two identical web-stiffened cold-formed steel lipped channel sections positioned face to face at differing spacing connected by using batten plates. The web stiffeners are provided in order to improve the buckling resistance of the web. The end conditions are considered as the pinned–pinned. The space between the chords has been chosen to have moment of inertia about minor axis equals that 3 times and 1.5 times the moment of inertia about major axis.

Based on the previous investigation, numerous research work has been conducted in the area of built-up cold-formed steel columns, and the results were reported by Roy et al., Zhang and Young, Craveiro et al. and Dubino et al. On the other hand, Anbarasu and Dar studied the upgraded design method for built-up cold-formed steel battened columns possessed of four lipped angles. Dabaon et al. and Anbarasu et al. conducted an investigation on the built-up cold-formed steel battened columns. In the research works reported, limited research is available for built-up battened columns placed face to face. There is no investigation about the effect of web stiffeners in face-to-face built-up CFS battened columns. Hence, this investigation concentrated on the effect of web stiffeners in the buckling behaviour of battened columns.

2 Finite-Element Analysis and Validation

Finite-element analysis (FEA) is a process of mathematical modelling performed that having ability to predict the ultimate moments and complex failure modes of cold-formed steel structural members. The perfectly linear elastic–plastic material was considered. In the numerical modelling, the material properties and geometric nonlinearity properties were considered. Initially, the linear analysis was carried out to predict the buckling loads and their buckling modes. The nonlinear analysis was followed by elastic analysis to obtain the ultimate load capacity.

The columns were modelled using shell S4R elements having which exhibits an exact solution for number of application. Thus, the fine mesh sized 10 mm (length to width) was used throughout the section for adequate accuracy in results. The end condition of the built-up column considered in this study was pinned–pinned. The upper and lower ends are constrained with the “rigid body” constraints. The “tie constraints” were used to connect the batten plates and the channel section by selecting the inner surface of flanges as master surface and outer surface of battens as slave surface. The load was enforced to the end conditions using the static RIKS method.

The perfect elastic–plastic behaviour for the material was considered. Due to the cold forming, the strain hardening of the corners has been neglected. The Young’s modulus and Poisson’s ratio of the section considered was 2 × 105 N/mm2 and 0.3. The residual stresses were not incorporated in order to avoid the complexity in analysis. The imperfection factors are depending on width-thickness ratio, depth-thickness ratio, local buckling length, slenderness ratio and also the number of batten plates. Thus, the overall imperfections were taken as L/1000, and the initial local imperfections were considered as 0.34% times the section thickness.

2.1 Nonlinear Analysis

Plastic analysis is more precise when compared to linear analysis because it enrols geometric nonlinearity and static analysis to obtain the buckling loads. In the elastic analysis, the initial local and global imperfections were modelled by insisting initial out-of-plane deflections to the section. The lowest Eigen vale buckling mode shapes were used to create geometric imperfections for the nonlinear analysis.

2.2 Validation

Finite-element modelling procedure is validated through the published results reported in the literature [6]. Five specimens of cold-formed built-up steel sections have modelled for validation. By comparing the numerical modelling results obtained with the already existing experimental results reported by Dabaon et al. [6], it is clear that the results are in good agreement with each other. Hence, the same procedure will be followed to carry out the parametric study. Table 1 shows the comparison between the experimental results reported in literature validated and the results obtained from carried out numerical analysis.

Table 1 Validating finite-element analysis results with experimental results reported by Dabaon et al. [6]
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The experimental failure mode and the finite-element model deformed shape of B2B25-300 specimen were compared and shown in Fig. 1. The failure mode obtained from the numerical simulation in finite-element analysis is the same as that of failure mode obtained experimentally.

Fig. 1
A. A photograph of a tall column with 5 rectangular gaps in the center. The top portion of the column is slightly bent. B. A contour mesh model presents the maximum stress in the bent section of the bar. C. A closer view of the mesh model depicts the maximum stress in the deformed section.

Comparison of deformed shapes of B2B25-300 specimen

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3 Sections

3.1 General

As per AISI-S100-2016 Specification for the design of cold-formed steel structural member 2016 edition, the dimensional limitations are available for an individual section only. Based on the individual section limitations, face-to-face web-stiffened built-up section was selected.

3.2 Section Geometric Details

The geometric details of the selected web-stiffened built-up columns were represented in Table 2.

Table 2 Section geometric details
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The cross-section and elevation of the web-stiffened built-up battened columns chosen for this study were shown in Fig. 2.

Fig. 2
2 diagrams. A presents the 2 V-shaped inward bends on the vertical sides. The dotted line over the top and bottom depicts the batten plate. B presents a tall bar with 5 horizontal rectangular blocks. The labels include the loading plate, the intermediate batten, and the end batten.

a Cross-sectional view. b Elevation

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4 Parametric Study

The parametric study was designed to investigate the web stiffener effect and varying the overall slenderness ratio on the axial strength of built-up battened columns. A detailed parametric study has been carried for different cross-section geometries with pinned end conditions. Two cross-section 50 × 90 × 15 and 60 × 150 × 15 with thickness 1.2 mm were selected for this study. The thickness of the batten plates was the same as that of the thickness of the lipped channels. Spacing between the batten plates was selected based on the codal specifications. The column length was taken as varying the slenderness ratio from 20 to 120. The nominal axial compression capacity of the battened column is evaluated based on the design equations provided in North American Specification AISI S100-2016. It depends on the guidelines provided in the AISI S100-2016 to predict design strength for web-stiffened lipped channel sections, the DSM was computed in this study. The deformed shape and its closure view of the battened columns for section 50 × 90 × 15 mm of slenderness ratio 30 and 40 obtained from finite-element modelling were shown in Fig. 3.

Fig. 3
2 contour mesh models of the tall blocks along with their magnified views present the maximum stress at deformity in the center section. The left contours present the outward bent and the right contours present the inward bent.

Deformed shape and the closure view of failure mode of cross-section 50 × 90 × 15 of slenderness ratio 30 and 40

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The curve was plotted between the axial displacement and ultimate load capacity for the cross-section 50 × 90 × 15 mm of the slenderness ratio 20 and 120 was shown in Figs. 4 and 5.

Fig. 4
A line graph of axial load versus axial shortening plots an initial linear rise followed by a concave upward decline. The peak is at (1.8, 138), approximately.

Load versus axial shortening curve of 50 × 90 × 15—slenderness ratio 20

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Fig. 5
A line graph of axial load versus axial shortening plots an initial linear rise followed by a decline. The peak is at (5, 65), approximately.

Load versus axial shortening curve of 50 × 90 × 15—slenderness ratio 120

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Figure 6 represents the finite-element modelling results for two different cross-sections with varying slenderness ratio.

Fig. 6
A grouped bar chart plots a decline in the value of load with an increase in the slenderness ratio. It has a higher value of load for 60 cross 150 cross 15 millimeters compared to 50 cross 90 cross 15 millimeters.

FEA design strength results

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The ultimate loads obtained from finite-element modelling and direct strength method (DSM) were compared for different cross-sections and represented in Figs. 7 and 8.

Fig. 7
A line graph of the load versus slenderness ratio plots a decline in the trend. It has a higher value for finite element modeling compared to the direct strength method.

Comparison of FEM and DSM results of specimen 50 × 90 × 15 mm

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Fig. 8
A line graph of the load versus slenderness ratio plots a decline in the trend. It has a higher value for finite element modeling compared to the direct strength method.

Comparison of FEM and DSM results of specimen 60 × 150 × 15 mm

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Based on the above comparisons, it is clear that the finite-element modelling results are unconservative for both the cross-sections. For the cross-section 50 × 90 × 15, the numerical analysis results are slightly unconservative with the theoretical results, while for a cross-section 60 × 150 × 15, the numerical modelling results are totally unconservative with the predicted theoretical results.

5 Conclusion

This study deals with the behaviour and strength of the web-stiffened built-up cold-formed steel battened columns. The numerical model was validated by means of comparison with the experimental results reported by Dabaon et al. [6]. A total of 22 numerical analyses was performed with the validated finite-element model. Based on this study, the following conclusions are drawn:

  1. 1.

    For a section having slenderness ratio 20–40, the failure mode was local buckling, and for a section having slenderness ratio 50–120, the failure mode obtained was global buckling.

  2. 2.

    In general, the ultimate compression load decreases by increasing the overall slenderness ratio.

  3. 3.

    By providing web stiffeners in the built-up columns, it delays/prevents the occurrence of local buckling of slender web elements.

  4. 4.

    It is found that the plate slenderness significantly affects the ultimate compression capacity of the built-up battened columns.

  5. 5.

    The ultimate load-carrying capacity of web-stiffened built-up battened columns computed from numerical analysis (PFEM) shows proximate results with DSM equations in AISI S100-2016 with mean 1.04 and standard deviation 0.017.