Structural behaviour of built-up I-shaped CFS columns | Scientific Reports

Scientific Reports volume 14, Article number: 25628 (2024) Cite this article

Metrics details

The utilization of cold-formed thin-walled members as structural members has gained significant popularity due to their advantages in fabrication, cost-effectiveness, and transportation convenience. However, the reduced thickness of the used sections poses challenges such as global, local, and distortional member buckling, leading to a decrease in their axial strength. This study focuses on addressing these challenges by connecting the channels together using screws as an alternative to welding, considering the cost, time, and ease of implementation. Conducting finite element analysis on structural columns built-up from cold-formed double C steel channels and subjected to axial loads, this paper verifies the numerical models used against experimental tests known from the literature. A comparison of experimental results with nonlinear FEA and AISI & AS/NZ standards reveals commendable agreement, particularly in predicting the buckling behavior of the built-up I-shaped CFS columns. While the results of the finite element analysis show an overestimation of approximately 3.6% compared to the experimental tests, the AISI and AS/NZS standards demonstrate a conservatism of about 3.0%. Furthermore, the current study investigates the influence of screw spacing on axial strength of built-up cold-formed steel columns. The findings are derived from 175 finite element experiments, evaluating seven different cross-sectional profiles with twelve distinct screw spacings. These spacings correspond to the half-wavelength of local, distortional, and global buckling, divided by values ranging from one to four. The screw spacing determined by half the local buckling half-wavelength along the webs’ centerline resulted in enhancements of 22%, 7%, 13%, and 11% in the critical elastic local, distortional, and global column buckling loads, as well as the nominal axial strength, respectively. These increases were even more pronounced for double-lane fasteners with the same spacing, yielding improvements of 25%, 46%, 17%, and 12%, respectively. For economic considerations, it is advisable to utilize single-lane fasteners with a half-wavelength equal to half the local buckling half-wavelength.

Cold-formed steel is becoming increasingly popular in construction due to its low cost1, light weight2, high strength-to-weight ratio3,4, and ease of manufacturing. The built-up I-shaped CFS column is an example of a cold-formed steel component used in trusses5,6, residential and commercial construction. By examining different C-section configurations and varying screw spacings, the study determines the optimal screw spacing, resulting in improved strength characteristics. Using the Abaqus software, the effects of screw quantity on the structural behavior of a I-shaped CFS column will be investigated. The results of this study will be beneficial for designing cold-formed steel structures and will allow engineers to make more informed design choices.

Screws that self-taper and self-drill are the two most common varieties. For better load bearing capability or to make the fastening self-sealing, most screws will be used in combination with washers. Certain varieties feature plastic heads or plastic caps, which are available for added corrosion protection and/or color matching7. By drawing the screw out of the plate (pull-out), dragging material over the screw head and washer (pull-over), or by tension-fracturing the screw8, demonstrated how screw connections exposed to tension might fail9. Illustrated how fastener efficacy is substantially influenced by the end support conditions of built-up sections. The spacing, placement, and stiffness of fasteners, as well as changes in the bending moment and axial force diagrams, all affect the effective flexural rigidity, which is not a constant throughout the length of the beam. The10 states that while the distance between screw centers must be at least three times the nominal screw diameter (df), it must also allow room for screw washers. A screw must have a minimum distance from the center to the edge of any section of 1.5 df. So, 3.0 mm ≤ df ≤ 7.0 mm. Nevertheless11, suggests that 2.03 mm ≤ df ≤ 6.35 mm. Moreover, in accordance with12, screw fasteners should be deemed to be 80% effective in steel-to-steel connections when the center-to-center spacing is less than 3 times the nominal diameter but larger than or equal to 2 times the nominal diameter.

In the case of compression members with two sections in contact13, a modified slenderness approach may be used:

where ri is the minimum radius of gyration of the whole unreduced cross-sectional area of a certain form in a built-up member, a is the intermediate fastener or spot weld spacing, K is the effective length factor, laterally unbraced length of member, radius of gyration of full unreduced cross-section about axis of buckling, and \(\:{\left(\frac{\text{K}\text{L}}{\text{r}}\right)}_{\text{o}}\) is the overall slenderness ratio of the entire section about the built-up member axis. According to research14, the modified Direct Strength Method (DSM) offers more accurate predictions than the present DSM. The study’s validation was completed by15. Experimental values were discovered to be 1.072 times the FEM values from the validation research, and DSM values to be 0.97 times the FEM values. The suggested design guideline and the modified DSM value are appropriate for designing back-to-back stiffened columns based on the important study findings.

According to the findings of research16, the direct strength method’s real global buckling equation is already adequate to account for the distortional-global (DG) buckling interaction in the case of lipped channel columns4. demonstrated that single-channel sections failed due to local buckling, which started from the flanges towards the web, as well as flexural buckling after the yielding limit was reached. The axial capacity obtained from the tests and FEA also demonstrated that design in accordance with the (DSM) is accurate and conservative by only 4% on average17. Claimed that the plate buckling at the mid-height causes the doubly symmetric plain section bolted back-to-back to fail. As18 predicted, lipped channels utilize the material more effectively than plain channels over the whole range of lengths, thicknesses, and load eccentricities.

The objective of this research is to analyze the influence of screw spacing and configuration to provide valuable insights for optimizing the axial load capacity of built-up cold-formed steel (CFS) C-section columns. The findings indicate that both the quantity and spacing of screws play a significant role in enhancing the strength of built-up I-shaped CFS columns, particularly with regard to their buckling resistance.

The finite element (FE) and finite strip (FS) methods are the predominant numerical techniques used for analyzing the buckling behavior of CFS structural members. Two separate kinds of CFS member behaviors have been investigated throughout the finite element method. Initially, the linear elastic buckling analysis is used to calculate the crucial elastic buckling loads. Furthermore, a nonlinear elastic buckling analysis is performed in order to accurately capture the post-buckling behavior19. An analysis of the buckling characteristics of built-up I-shaped CFS columns subjected to compressive loads indicates three possible modes of failure: global (G), which includes flexural, torsional, or flexural-torsional buckling; local (L) buckling; and distortional (D) buckling. Alternatively, failure might arise from the combined effect of all three types20.

Plate buckling at mid-height is a potential failure mode for built-up I-shaped CFS columns17. Regardless of the space between connectors, it has been discovered that contact pressure between components has only a little impact on the final capacity, despite other factors being taken into account21. The average values for dynamic coefficients of friction for combinations in air, such as “coated steel,” vary between 0.14 and 0.42. These values are influenced by the amount of contact pressure22. Furthermore, both experimental testing and finite element analysis have shown that thin fixed-ended beam-column members usually are not affected by torsional or flexural-torsional buckling modes23. In conclusion, within the scope of this paper, the analysis conducted on the 175 Finite Element Method (FEM) models reveals comprehensive consideration of both normal and tangential behaviors in the contact property section.

The modified slenderness ratio given by Eq. (1) is useful mainly in areas with minimal fastener spacing, as Mahar et al.24 found. However, when fastener spacing grows, their investigation shows that it becomes too cautious. On the other hand, results from25 demonstrate that for built-up back-to-back CFS columns with short screw spacing, the modified slenderness approach, when applied to global buckling, results in dangerous ultimate strength predictions.

Furthermore, as shown by26, the local buckling strength of built-up I-shaped CFS columns is about double that of the equivalent C-section components. This conclusion is consistent with the evidence presented in27, which shows that the ultimate strength and stiffness of built-up I-shaped members that fail as a result of the interplay between local, distortional, and overall buckling are highly influenced by the slenderness ratio. Additionally, a few effects on the assembled I-shaped members break down in the presence of the local-distortional buckling interaction.

End fastener groups (EFGs) must be positioned longitudinally at a maximum spacing of four times the diameter of applied screws and over a distance equivalent to 1.5 times the maximum dimension of the built-up Sects13,28. Nevertheless, studies have shown that EFG could be too cautious and redundant in cases where the end supports are either fixed or pinned, and warping is already addressed29. When the load is applied using inflexible end platens, both sets of fasteners and welds at the ends show little impact30. In addition, the spacing between screws and the presence of EFG have little effect on the compression behavior and capacity of NC members, as stated in reference31.

Furthermore, the use of EFGs may boost capacity by up to 33%. However, it may also elevate member reliability indices in comparison to columns that lack EFGs. However, when local buckling and global buckling interact, both the capacity for buckling and the deformations caused by bending suffer a slight decrease, and the effectiveness of the EFG is also reduced32. The impact of the EFG becomes more prominent when shear slip decreases, resulting in an elevation of composite action28.

Although EFGs and other configurations of built-up back-to-back CFS section connecting by fasteners (built-up stud fasteners) may greatly increase the overall resistance to buckling28,33, it is important to recognize that these layouts and the degree of composite action they provide do not improve the capacities for local and distortional buckling9,33,20.

For various column kinds, the AISI11,13 and AS/NZ10 Standards show differing degrees of conservatism in their projections. In particular, these criteria are shown to be non-conservative for stub columns34,35, since they failed due to local buckling. Their conservatism, on the other hand, is clearly seen in short, intermediate, and slender columns when failure is caused by a combination of global and local buckling.

In contrast, the AISI and AS/NZS standards exhibit a distinct conservative trend, as shown in36. By around 12%, they are considered non-conservative when stubs and short columns fail because of local buckling. For the strength of intermediate and slender columns, these criteria, however, turn out to be too cautious, failing mostly due to global member buckling36.

Additional findings, as described in35, show that the AISI and AS/NZS standards over-conserve about 15% of the time when built-up columns collapse due to global buckling. On the other hand, these guidelines are around 8% less cautious for built-up columns that collapse mainly because of local buckling. When examining face-to-face built-up columns, the degree of conservatism in the criteria differs according to the failure mechanism. They are about 15% more cautious for global buckling and about 5% less conservative for local buckling37.

When the Direct Strength Method’s modified strength formula is applied, it is found that this method accurately predicts the ultimate strength of intermediate slender columns, which experience a combination of local and distortional buckling before failing in the distortional mode38.

It is determined that this technique offers good forecasts of the failure load for CFS lipped channel columns experiencing local-distortional-global buckling interaction39,40, while evaluating the efficacy of the presently codified DSM design curve against local-global interactive buckling.

When completely composite buckling behavior is guaranteed, the modified AISI slenderness formula, see Eq. (1), is shown to be conservative by around 10% when looking at the buckling load prediction for built-up Sect41.

In the end, it is shown that for columns with intermediate fastener spacing less than the appropriate local buckling half wavelength, the design forecasts are ultimately conservative. For columns with wide connectivity spacing, on the other hand, they are non-conservative42.

The failure mechanisms of steel-to-steel screw connections include screw hole bearing failure, screw shear failure and screw pull-out from steel plates. There is a link between the failure modes and the thicknesses of steel plates and the diameters of screws43. Furthermore, the placement and configuration of fasteners are significant factors in ascertaining the failure load of members. Nevertheless, accurate calculations using current experimental data continue to pose a challenge44. It is worth mentioning that the ultimate strength of built-up I-shaped CFS columns can be significantly influenced by the spacing of screws and the configuration of the end fastener group. This effect is particularly pronounced in columns that have encountered global buckling mode27.

According to the specified guidelines8,10,11,12,13,45, it is necessary for the center-to-center spacing between fasteners (such as screws and bolts) to be a minimum of three times the diameter of the fasteners. Additionally, the distance between the first and last fasteners from the initial and terminal edges of the structural members, as well as the separation between fasteners from the junction of the web and flanges, should not be less than 1.5 times the diameter of the fasteners. Conversely, to mitigate the risk of end bearing failure, it is advised in the recommendations46 that the distance between the first and last screws and the edges be maintained at a minimum of 20 mm.

The findings emphasize that decreasing the ratio of fastener spacing greatly improves the ability of built-up sections to resist buckling. This phenomenon is especially noticeable in both the global and local buckling areas of constructed open Sect47. Furthermore, it is clear that the buckling behavior of back-to-back aluminum alloy channel section columns is affected by the distance between the screws. Specifically, a smaller screw spacing results in the channels staying intact until failure48.

Moreover, the research49 shows that the spacing of screws in between has a significant influence, with its effect depending on the failure mode of CFS-built-up cross-sections. Overall, the test findings demonstrate a significant impact of the spacing between intermediate screws on both the maximum load capacity and the manner in which double C-section CFS-built-up columns fail. More precisely, a rise in the ratio of local slenderness (\(\:{\varvec{\uplambda\:}}_{\text{l\:}}\)) and the distance between screws (a) is linked to an increased probability of local-global interaction buckling49.

Moreover, the rotational rigidity of the connection between the flange and the web is improved when the distance between the webs that link the fasteners is reduced. It is important to mention that the maximum strength of sections with wide interior webs in relation to their thickness drops dramatically when the space between connecting fasteners increases. However, sections with narrow webs in relation to their thickness only exhibit a little sensitivity to fastener spacing50.

The impact of screw spacing varies depending on the column slenderness. When it comes to stub columns, adding more screws has a little impact on strength. However, for short and intermediate slender columns, the strength is greatly influenced by the number of screws. Specifically, when the screw spacing is doubled, the strength of short columns is reduced by around 5–10%, while intermediate slender columns see a decrease of 10–15%. Nevertheless, thin columns do not exhibit any notable disparity in strength since their failure is mostly caused by global buckling34.

Additionally, the axial strength of columns shows an average increase of 10% for plain parts, when the number of screws is increased from 2 to 5 48. By connecting webs in back-to-back CFS members using fasteners, it is possible to achieve composite action, resulting in a capacity increase of up to 21% 51. This composite action mostly happens when there is solitary global buckling in the flexural behavior32.

The study also examines the effect of spring spacing, finding that it does not affect local buckling, has a small impact on distortional buckling, and has a significant influence on global buckling when the spring spacing is equal to or less than four times the length of critical global buckling52. As stated in reference41, in order to achieve complete composite action, the spacing between fasteners should be less than or equal to the length of the member divided by five. However, reference19 implies that a fastener spacing of s = L/2 is enough to improve the overall buckling load capacity, where L is the built-up column length, coming close to attaining complete composite levels.

It is crucial to acknowledge that when the distance between screws exceeds the local buckling half-wavelength of the corresponding C-section portions, it is not possible to prevent local buckling in cold-formed I-section columns26,21,42. However, studies conducted by to37,29,20 argue that the distance between screws has a little impact on the axial strength of cross-sections.

Numerous authoritative sources provide methodologies for determining the nominal buckling load and moment of thin-walled sections, including standards such as those established by AISI S100-16 11,13, AISI S240 12, AISI D100-08 45, AS/NZS 4600 10, Eurocode 3 Part 1–3 7, and the book titled Cold-Formed Steel Design8, written by Wei-Wen Yu et al.

The following equations are utilized to determine the buckling resistance of cold-formed steel (CFS) columns11,13:

where

and where Fcre is the elastic global (flexural, torsional, or flexural-torsional) buckling stress, Pcre is the elastic global column buckling force, Ag is the gross area, Fy is the yield stress and Fn is the compressive strength.

For the local buckling resistance of cold-formed steel (CFS) columns has to be calculated in the following way11,13:

where

and where Pcrl is the elastic local buckling force.

The following equations are employed to determine the distortional buckling resistance of cold-formed steel (CFS) columns11,13:

where

and where Py is the column axial yield strength, Pcrd is the elastic distortional column buckling force.

Finally, the nominal column resistance is11,13:

and the design column resistance is \(\:{{\upvarphi\:}}_{\text{C}}{\text{P}}_{\text{n}}\) where \(\:{{\upvarphi\:}}_{\text{c}}=0.85\:\).

In the process of validating Finite Element Analysis (FEA) through experimental tests, this study employed two identical C-section columns, connected back-to-back to form an I-section column using self-drilling screws. To secure the columns, 15 mm thick steel end plates were welded to both ends of the test members26. In contrast, test members’ end plates were affixed to specially designed devices to simulate pin-pin ends. Shell elements represented all columns, while analytical rigid elements were employed for the base plates. The simply supported boundary conditions at the end supports were consistently applied across all Finite Element (FE) models of back-to-back channel (BC) members.

Initially, TIE (weld) constraints were applied to each end cross-section, connecting them to the respective base plates. Subsequently, all displacements (Ux, Uy, and Uz) and rotation (URz) of the bottom reference point (RP-1) were constrained, as illustrated in Fig. 1. The top reference point (RP-2) underwent a similar treatment, except for the axial displacement (Uz), which was released. Displacement control was implemented to apply axial compression loading via RP-2. Both reference points were strategically located at the center of gravity (c.g.) of the members. Determination of (c.g.) involved meticulous calculations using AutoCAD, as opposed to conventional methods such as ETABS, SAP200, or Revit, which are commonly employed for this purpose. It is noteworthy that AutoCAD was specifically chosen for its precision in establishing (c.g.).

Comparison between experimental26 and finite element modeling (FEM) of back-to-back built-up columns.

The test specimens were systematically labeled following a standardized convention to denote their section type, cross-sectional dimensions, and trial number. The adopted labeling format for the specimens was represented as “wCx-y-Az,” where each character conveys specific information about the specimen.

“w” indicates the length category: “L” represents long lengths, “M” represents intermediate lengths, and “S” represents short lengths.

“C” denotes the column configuration.

“x” specifies the section type: “1” refers to single-channel sections, and “3” refers to back-to-back built-up channel sections.

“y” represents the cross-sectional dimension, with “90” corresponding to a web depth of approximately 90 mm, and “140” indicating a web depth of approximately 140 mm.

“Az” signifies the trial number, with “A1” denoting the first trial, “A2” the second trial, and “A3” the third trial.

For instance, the label “LC3-90-A1” represents a long back-to-back built-up channel section with a web depth of approximately 90 mm, used in the first trial.

When the section thickness is less than one-tenth of an elemental dimension, it is advisable to model the section as shell elements53. The S4R element, known for its computational efficiency, proves suitable for a diverse array of applications, especially in the analysis of thin-walled structures. In this study, a mesh size of 5 mm × 5 mm was determined through a careful convergence study.

Additionally, a “surface-to-surface” contact approach was employed to accurately simulate the interaction between individual C-sections. This strategy guaranteed a precise depiction of the physical interactions taking place throughout the loading process.

The cold-formed column under investigation, with thicknesses of 1.2 mm (LC3-90) and 1.5 mm (LC3-140), is composed of Chinese Q235 steel. Material properties, including yield and ultimate strengths and elastic modulus, were derived from standard tensile coupon specimens extracted along the longitudinal direction of the web of the tested sections.

For the 1.2 mm thick columns, measured yield and ultimate strengths were 321.5 MPa and 374.1 MPa, with an elastic modulus of 216 MPa. Similarly, for the 1.5 mm thick columns, the measured values were 305.4 MPa and 369.7 MPa for yield and ultimate strengths, respectively, with an elastic modulus of 205 MPa. In this investigation, three trials are conducted for each specific thickness. Subsequently, the resultant data from each trial is averaged. However, it is important to note that the averaging process is limited to the data collected up to the First Rapture within each of the three trials, (as illustrated Fig. 2).

Stress (σ) – Strain (ε) curves.

The Poisson’s ratio for the material was established at 0.3. The stress versus strain curve for Q235 steel, obtained from the tensile coupon tests, guided the development of the corresponding true stress versus strain curve applied in the finite element models.

In the pursuit of a solver capable of providing accurate capacities and deformations aligned with experimental results, the dynamic-implicit solver in ABAQUS was selected for this study, employing a quasi-static application type54. To ensure convergence for both sheathed and unsheathed specimens, an equilibrium adjustment coefficient of 0.005 times the strain energy, following Rasmussen’s proposal55, was implemented. Additionally, in adherence to Schafer’s recommendation56, the displacement load was set at approximately 1.5 times the ultimate displacement, with initial and maximum loading steps established at 0.01 and 0.02, respectively. This comprehensive approach aimed to enhance calculation accuracy in the numerical simulations.

In conducting this study, fourteen experimental laboratory tests were conducted26. A comprehensive comparative analysis was performed using various analytical methods, namely AISI & AS/NZS Elastic Linear analysis and Finite Element (FE) nonlinear analysis, as outlined in Table 1. A comparison of experimental results with nonlinear finite element analysis (FEA) and the American Iron and Steel Institute and Australian and New Zealand standards (AISI & AS/NZS) reveals commendable agreement, particularly in predicting the buckling behavior of the columns built-up from cold-formed double C steel channels. While the results of the finite element analysis show over estimate of approximately 3.6% with a corresponding sample standard deviation (S) of 0.045 compared to experimental tests, the AISI and AS/NZ Standards demonstrate a conservatism of about 3.0% with a corresponding sample standard deviation (S) of 0.054. The relatively small standard deviation values indicate the accuracy and reliability of the analytical methods employed.

On the other hand, upon examining the axial displacement and applied load graphs for both Finite Element Method (FEM) and experimental testing (refer to Fig. 3), notable congruence in results is observed. The graphs depict a consistent trend, showcasing a Pu value being attained with a 1.5 mm axial displacement in both FEM and experimental tests. This implies a parallelism in the outcomes generated by the two methodologies.

Comparing the experimental results26 with Finite Element Analysis (FEA) findings.

Experimental testing and Direct Strength Method (DSM) calculations have confirmed that stub columns (SC3-90) exhibit local buckling, whereas long columns (LC3) experience global buckling. The buckling behavior observed in the ‘SC3-90-A3’ specimen was consistent in both experimental and finite element (FE) models, as depicted in Fig. 4. The visual comparison of these models demonstrates a strong correlation in buckling patterns.

The buckling shape for both experimental26 and FE models.

It is noteworthy that the findings from both FEM and American Iron and Steel Institute (AISI) align closely with those obtained through experimental testing. Nevertheless, a subtle distinction arises, indicating that AISI tends to adopt a more conservative approach in comparison to FEM when evaluated against experimental results.

The experimental investigations, AISI linear analysis, and FE nonlinear analysis collectively contribute to a comprehensive understanding of the behavior of the tested structures. The agreement between the methods substantiates the reliability of both AISI and FEM, with nuanced variations that warrant consideration in specific analytical contexts.

In both ABAQUS and CUFSM, the material is “S355” steel, characterized by specific mechanical properties including a yield stress (Fy) of 355 MPa, a mass density of 7.849\(\:\times\:{10}^{-9}\)\(\:\raisebox{1ex}{$\text{g}$}\!\left/\:\!\raisebox{-1ex}{${\text{m}\text{m}}^{3}$}\right.\), a Young’s Modulus of 210,000 MPa, and a Poisson’s ratio of 0.3. Conforming to AISI S100 11,13 specifications, the screw diameter is mandated to fall within the range of greater than or equal to 2.03 mm and less than or equal to 6.35 mm. Furthermore, the specifications dictate that the minimum distance between screws and edges or ends should be at least one and a half times the screw diameter, while the minimum distance between screws must be a minimum of three times the screw diameter. In the present investigation, the nominal screw diameter (ds) is established at 4.8 mm, with edge and end distances set at 20 mm for two lanes of screws, as illustrated in Fig. 8. When employing a single lane of screws, the edge distance equals half of the web depth (D/2).

To establish appropriate boundary conditions, coupling constraints were initially applied to both end cross-sections of the structure. Subsequently, all degrees of freedom (displacements U1, U2, and U3, as well as rotation UR3) were restrained at the bottom reference point (RP-2). At the top reference point (RP-1), similar constraints were imposed, with the exception of the axial displacement (U3), which was left free to allow for the application of axial compression loading, as illustrated in Fig. 5. This loading was introduced through displacement control at RP-1. Both reference points were strategically positioned at the centroids of their respective members to ensure accurate representation of the structural behavior.

Boundary conditions of finite element model.

The finite element models were developed using Abaqus/CAE 2024 57. For the buckling analysis, the “Linear Perturbation - Buckle” analysis step was utilized. A total of 200 eigenvalues were requested, with 208 vectors used per interaction, and a maximum of 100,000 iterations allowed. Linear buckling analysis (LBA) is a structural analysis technique employed to determine the critical load at which a structure or component, modeled as a linear elastic material, reaches a state of neutral stability between its unbuckled and buckled configurations.

The selection of mesh size in finite element analysis (FEA) plays a crucial role in determining both the accuracy and computational efficiency of the simulation. A coarse mesh may fail to capture essential geometric details and loading conditions, thus compromising the reliability of the results. In this study, a mesh size of 5 mm by 5 mm was employed for the columns, as illustrated in Fig. 6. When the section thickness is less than one-tenth of the element size, the use of shell elements is recommended53 to ensure accurate representation of the structural behavior. The S4R element55,58 is particularly appropriate for this application, given its computational efficiency and suitability for analyzing thin-walled structures.

Finite element model of CFS built-up section member.

The cross-sections of the specimens used in this study are defined by the following equation: (2CD * B * d * t). In this equation, the coefficient “2” reflects the double back-to-back column configuration. “C” represents the C-section profile, “D” denotes the web depth, “B” indicates the flange width, “d” corresponds to the lip length, and “t” refers to the thickness of the cold-formed steel (CFS) sections. A schematic representation of the cross-sectional geometry is presented in Fig. 7.

Cross-section geometry and parameters.

Concerning the junctions between webs and flanges and between lips and flanges, the inside radius is set to twice the thickness of the respective cross-sections, while the outside fillet radius is established at three times the cross-section thickness of the specimen cross-sections (see Table 2).

The seven cross-sections defined in Table 2 are categorized into three groups. Initially, the first category encompasses three cross-sections characterized by identical web depth, flange width, and lip depth, but with varying thickness. Moving on to the second category, it comprises three specimens with consistent web depth, lip length, and thickness, yet differing in flange width. Finally, the third category includes three specimens with the same flange width, lip depth, and thickness, but exhibiting variations in web depth (refer to Table 2; Fig. 7).

The seven cross-sections were utilized solely as columns, subjected exclusively to axial loading. Each column was formed by connecting two C-sections with screws. The columns were categorized into two types based on the screw arrangement: (1) columns with a single row of screws, where the back-to-back C-sections were connected along the midline of their webs, and (2) columns with two rows of screws, where the back-to-back C-sections were connected by two rows of screws, each located 20 mm from the outer edge of the flanges (see Fig. 8a and b).

Screw Arrangement Comparison: Double-Layer vs. Single-Layer.

The objective is to determine the optimal screw spacing that yields the maximum nominal axial strength Pn according to Eq. (13). Within each column configuration, thirteen different screw spacings are examined (see Table 3). The research incorporates a total of 175 modules with simply-supported columns created using Abaqus software (see Fig. 5). There are seven distinct back-to-back c-section columns, each comprising 25 screw spacings. These 25 spacings are categorized as follows: initially, no screws are utilized, followed by twelve different screw spacings in a single line, and finally, twelve different screw spacings across two lines.

Schafer et al. introduced a software tool titled CUSFM59, serving as an implementation of the Effective Width Method (EWM). This software serves the purpose of identifying various half-wave lengths. This software was used to compute the half-wave lengths shown in the Table 3, where the specimens investigated in this study are comprehensively described.

Additionally, the lengths of local buckling (Lcre), distortional buckling (Lcrd), and global buckling (Lcre) of each column were determined using CUFSM59, a software utilizing the finite strip method (FSM) to compute various types of buckling lengths. To provide a comprehensive comparison, an evaluation is conducted among all the results obtained from the Abaqus and CUFSM computations.

In illustrating spacing considerations, a straightforward model can be employed, denoted as (Lcr/n), where Lcr represents the half-wavelength associated with global (Lcre), distortional (Lcrd), and local (Lcrl) buckling phenomena, respectively. Here, n takes on values of 1, 2, 3, and 4, corresponding to each type of buckling mode. Furthermore, the notation 0 S indicates that no screws are utilized for connecting sections see Table 3.

This study employs finite element analysis to determine the critical elastic buckling loads (local, distortional, and global) for all column configurations. Subsequently, established design codes (AISI S100 and AS/NZS 4600) are utilized, with Eqs. (2) to (12), to convert the critical elastic loads into their corresponding nominal counterparts. Finally, Eq. (13) is applied to ascertain the overall elastic nominal buckling load for each type of built-up column, where single c-sections are not connected with screws. Detailed results are presented in Table 4.

When built-up back-to-back C-sections, comprising large webs and flanges, are assembled by screwing them together in a single line, the Pcrl increases significantly, accompanied by increments in Pcrd, Pcre, and Pn. However, when employing two lines of screws for connection and subsequently reducing the screw spacing, Pcrl experiences a substantial surge, while Pcrd sees a pronounced increase, along with enhancements in Pcre and Pn.

Changes in the thickness of these members, exemplified by (2*C200*75*20*t), lead to variations in load-carrying capacity without altering the buckling type. Similarly, modifications in screw spacing do not influence the buckling type but exert a notable impact on load-carrying capacity, as depicted in Tables 5, 6 and 7.

For instance, when considering (2*C200*75*20*1.5) with zero screws, the Nominal Axial Strength is measured at 124 kN. However, augmenting the thickness of the built-up section by 33.33% and 66.67% correspondingly increases the Nominal Axial Strength by 63.71% and 137.1%, respectively, as outlined in Table 4.

When built-up back-to-back c-Sect. (2*C150*B*20*2) which is screwed together, there is a discernible impact on structural behavior. Initially, when it is screwed together with one line of screws, then by reducing screw spacing, Pcrl increases significantly along with notable increases in Pcrd, Pcre, and Pn. Moreover, upon employing two lines of screws to connect C-sections, reducing the screw spacing exhibits a profound effect: it substantially elevates Pcrl, markedly augments Pcrd, and boosts Pcre and Pn. These alterations in screw configurations underscore the critical role of fastening mechanisms in load distribution and structural integrity.

Additionally, changes in the flange width of these members (2*C150*B*20*2) provoke notable variations in load carrying capacity and buckling behavior. Likewise, modifications in screw spacing exert a tangible influence on buckling characteristics and load-carrying capacity. This interplay of factors is elucidated in Tables 8, 9 and 10, providing a comprehensive understanding of how design parameters affect structural performance.

Transitioning to the specific case of (2*C150*50*20*2), the absence of screws yields a Nominal Axial Strength of 116 kN. However, as the flange width of this built-up section increases by 30% and 50% respectively, the Nominal Axial Strength experiences substantial increments of 61.21% and 93.1% correspondingly. For detailed insights, refer to Table 4, which highlights the direct correlation between flange width adjustments and axial strength enhancement.

When built-up back-to-back c-Sect. (2*CD*75*20*2) are screwed together, the arrangement significantly impacts the structural integrity. Initially, when connected with a single line of screws, a reduction in screw spacing results in a notable increase in Pcrl, thereby affecting Pcrd, Pcre, and Pn. Moreover, employing two lines of screws for connection intensifies this effect, particularly augmenting Pcrl and Pcrd, followed by subsequent increases in Pcre and Pn.

Alterations in the web depth of these members (2*CD*75*20*2) invariably alter their load-carrying capacity. Furthermore, adjustments in screw spacing influence the buckling behavior, especially noticeable when utilizing smaller screw spacings as exemplified in (2*C100*75*20*2). These variations are elucidated in detail within Tables 6, 8 and 11.

In scenarios where (2*CD*75*20*2) is employed and the screw count reaches zero, the Nominal Axial Strength amounts to 244 kN. However, as the web depth of the built-up section increases by 50% and 100%, the Nominal Axial Strength experiences a respective decrease of 8.2% and 16.8%, as outlined in Table 4.

In terms of results, a notable enhancement in nominal axial strength (Pn) is observed. Specifically, for one lane of screws, the increase is 15%, 13%, 11%, 5%, 6%, 6%, and 5% for the corresponding screw spacings mentioned earlier. Conversely, for the configuration with two lanes of screws, Pn experiences increases of 15%, 14%, 12%, 8%, 8%, 8%, and 7%, respectively. See Table 12.

For economic reasons, it is advisable to avoid the utilization of Lcrl/4 and Lcrl/3 screw spacings. The rationale behind this recommendation is that these configurations necessitate a substantial number of screws, resulting in closely spaced screws. Consequently, steering clear of these two spacing types is deemed optimal.

As depicted in Fig. 8b, employing a single lane of screws along the centerline of the webs can significantly enhance the critical elastic local buckling load (Pcrl). This enhancement is particularly noteworthy when the spacing is equal to Lcrl/n, where n takes values of 1, 2, 3, and 4. With each incremental value of n, there is a notable surge in Pcrl, accompanied by a marginal increase in Pn.

Referencing in Fig. 8a, an alternative approach involves employing two lanes of screws, leading to an improvement in the critical elastic distortional buckling strength (Pcrd). This improvement is especially pronounced when the spacing equals Lcrl/n, with n ranging from 1 to 4. Notably, as n increases, there is a substantial rise in (Pcrd) and a gradual uptick in (Pn).

For economic considerations, it is recommended to opt for a single lane of screws and adopt a screw spacing equal to S10 or Lcrl/2. This configuration results in significant increases across critical elastic local buckling load (Pcrl), critical elastic distortional buckling strength (Pcrd), critical elastic distortional-torsional buckling strength (Pcre), and Pn. Specifically, there is a remarkable increase of 22%, 7%, 13%, and 11%, respectively.

Screw spacing, denoted as ‘Si,’ is characterized by the interval when ‘i’ ranges from 0 to 12. Additionally, Lcr/n is defined for ‘n’ values spanning from 1 to 4.

Referring to Fig. 9a and b, when the value is 0, it corresponds to ‘S0,’ indicating that no screws are utilized. The subsequent values, 1 through 4 on the graph, represent ‘S1,’ ‘S2,’ ‘S3,’ and ‘S4,’ corresponding to Lcre/1, Lcre/2, Lcre/3, and Lcre/4, respectively.

Examining the correlation between column load and screw spacing, considering both critical and nominal loads.

Similarly, values 5 through 8 on the graph, namely 5, 6, 7, and 8, correspond to ‘S5,’ ‘S6,’ ‘S7,’ and ‘S8,’ aligning with Lcrd/1, Lcrd/2, Lcrd/3, and Lcrd/4, respectively. Furthermore, values 9 through 12 on the graph, specifically 9, 10, 11, and 12, correspond to ‘S9,’ ‘S10,’ ‘S11,’ and ‘S12,’ representing Lcrl/1, Lcrl/2, Lcrl/3, and Lcrl/4, respectively.

This study conducted a comprehensive finite element analysis (FEA) of 175 models to investigate the axial behavior of back-to-back cold-formed steel (CFS) channel section columns connected with fasteners. The analysis focused on local, distortional, and global buckling modes, examining seven unique channel cross-sections and twelve different screw connection configurations. The FE model’s accuracy in predicting axial load capacities and failure modes was validated through comparison with experimental test results. Additionally, the consistency between FEA, direct strength method (DSM) results, and experimental findings further confirmed the model’s reliability. Specifically, the average ratios of nonlinear FEA and DSM capacities to experimental axial load capacity were found to be 1.04 and 0.97, respectively.

Following the establishment of the credibility of the finite element models, a parametric study was conducted to explore the impact of screw spacing on various critical buckling loads and the nominal axial strength of back-to-back built-up cold-formed steel lipped channel sections. The analysis revealed that employing a small screw spacing along the centerline of the webs in a single lane significantly enhances the critical elastic local buckling load. In contrast, utilizing a small screw spacing along two lines notably improves the critical elastic distortional buckling strength. Specifically, the critical elastic local, distortional, and global column buckling loads, along with the nominal axial strength, were enhanced by 22%, 7%, 13%, and 11%, respectively, when the screw spacing along the webs’ centerline was set to half the local buckling half-wavelength. Additionally, with double-lane fasteners spaced at the same distance, these improvements were even more pronounced, achieving enhancements of 25%, 46%, 17%, and 12%, respectively.

For practical and economic considerations, it is recommended to use single-lane fasteners with a spacing equivalent to half the local buckling half-wavelength.

It is recommended that future researchers and readers investigate the impact of screw spacing on the performance of built-up closed sections, as well as its effect on assemblies consisting of three or four C-sections.

All data generated or analysed during this study are included in this published article and its supplementary information files.

Samuel, J. et al. Composite Cold-formed steel beams with diagonal rebars for earthquake-resistant buildings. Materials 16, (2023).

Fang, Z., Roy, K., Uzzaman, A. & Lim, J. B. P. Numerical simulation and proposed design rules of cold-formed stainless steel channels with web holes under Interior-one-flange loading. Eng. Struct. 252, (2022).

Sam, V. S., Nammalvar, A., Andrushia, D., Gurupatham, B. G. A. & Roy, K. Flexural Behavior of Galvanized Iron Based Cold-Formed Steel Back-to-Back Built-Up Beams at Elevated Temperatures. Buildings 14, (2024).

Gurupatham, B. G. A., Roy, K., Raftery, G. M. & Lim, J. B. P. Influence of Intermediate Stiffeners on Axial Capacity of Thin-Walled Built-Up Open and Closed Channel Section Columns. Buildings 12, (2022).

Roy, K., Chui Huon Ting, T., Ho Lau, H. & Lim, P. J. B. Experimental Investigation into the Behavior of Back-to-Back Gapped Built-up Cold-Formed Steel Channel Sections under Compression. https://scholarsmine.mst.edu/isccss

Roy, K., Lau, H. H. & Lim, J. B. P. Finite element modelling of back-to-back built-up cold-formed stainless-steel lipped channels under axial compression Finite element modelling of back-to-back built-up cold. https://doi.org/10.12989/scs.2019.33.1.037

Dubina, D., Ungureanu, V. & Landolfo, R. Eurocode 3: Part 1–3 (ECCS – European Convention for Constructional Steelwork, 2012).

Wei-Wen Yu, Roger, A. LaBoube & Helen Chen. Cold-Formed Steel Design, 5th Edition. (Wiley, 2020).

Fratamico, D. C., Torabian, S., Rasmussen, K. J. R., Schafer, B. & Schafer, B. W. Experimental Investigation of the Effect of Screw Fastener Spacing on the Local and Distortional Buckling Behavior of Built-Up Cold-Formed Steel Columns. https://www.researchgate.net/publication/305568137 (2016).

AS/NZS. AS/NZS 4600: 2018. (2018).

AISI. AISI S100-16 (R2020) w/S3-22. vol. 3. (2016).

AISI. AISI S240-20. (2020).

AISI. AISI S100-16 (2020) w/S2-20. vol. 2. (2016).

Wang, L. & Young, B. Design of cold-formed steel channels with stiffened webs subjected to bending. Thin-Walled Struct. 85, 81–92 (2014).

Article ADS CAS Google Scholar

Mohan, M., Ramachandran, A., Amran, M. & Borovkov, A. Determination of buckling behavior of web-stiffened cold-formed steel Built-Up column under Axial Compression. Materials 15, (2022).

de Lazzari, J. A. & de Batista, E. Distortional-global buckling interaction relevance in cold-formed steel lipped channel columns. Latin Am. J. Solids Struct. 17, 1–29 (2020).

Article Google Scholar

Beulah Gnana Ananthi, G. & Ashvini, B. Experimental theoretical and numerical studies on cold-formed steel stub channel columns with stiffeners. Asian J. Civil Eng. 20, 171–185 (2019).

Article Google Scholar

Mojtabaei, S. M., Becque, J. & Hajirasouliha, I. Structural size optimization of single and Built-Up cold-formed Steel Beam-Column members. J. Struct. Eng.147, (2021).

Khezri, M., Abbasi, M. & Rasmussen, K. J. R. Application of the compound strip method in buckling analysis of cold-formed steel built‐up sections. ce/papers 1, 1667–1676 (2017).

Vy, S. T., Mahendran, M. & Sivaprakasam, T. Built-up back-to-back cold-formed steel compression members failing by local and distortional buckling. Thin-Walled Struct. 159, (2021).

Meza, F. J. & Becque, J. Numerical modelling of cold-formed steel built-up columns. Thin-Walled Struct. 188, (2023).

Pijpers, R. J. M. & H.M. Slot. Friction coefficients for steel to steel contact surfaces in air and seawater.

Vy, S. T. & Mahendran, M. DSM design of fixed-ended slender built-up back-to-back cold-formed steel compression members. J. Constr. Steel Res. 189, (2022).

Mahar, A. M., Jayachandran, S. A. & Mahendran, M. Global buckling strength of discretely fastened back-to-back built-up cold-formed steel columns. J. Constr. Steel Res. 187, (2021).

Zhou, T., Li, Y., Wu, H., Lu, Y. & Ren, L. Analysis to determine flexural buckling of cold-formed steel built-up back-to-back section columns. J. Constr. Steel Res. 166, (2020).

Lu, Y., Zhou, T., Li, W. & Wu, H. Experimental investigation and a novel direct strength method for cold-formed built-up I-section columns. Thin-Walled Struct. 112, 125–139 (2017).

Article Google Scholar

Yao, X. Experimental Study and Direct Strength Method for Cold-Formed Steel Built-Up I-Sectional Columns under Axial Compression. Math. Probl. Eng. (2021).

Fratamico, D. C., Torabian, S., Rasmussen, K. J. R. & Schafer, B. W. Buckling and Collapse Behavior of Screw-Fastened, Built-Up Cold-Formed Steel Columns of Varying Cross-Section Size: Experimental Investigation.

Vy, S. T. & Mahendran, M. Behaviour and design of slender built-up nested cold-formed steel compression members. Eng. Struct. 241, (2021).

Rasmussen, K. J. R., Khezri, M., Schafer, B. W. & Zhang, H. The mechanics of built-up cold-formed steel members. Thin-Walled Struct.154, (2020).

Vy, S. T. & Mahendran, M. Design of Built-up Nested Cold-Formed Steel Channel Compression Members.

Fratamico, D. C., Torabian, S., Zhao, X., Rasmussen, K. J. R. & Schafer, B. W. Experiments on the global buckling and collapse of built-up cold-formed steel columns. J. Constr. Steel Res. 144, 65–80 (2018).

Article Google Scholar

Fratamico, D. C. & Schafer, B. Numerical studies on the Composite Action and buckling behavior of Built-Up cold-formed Steel columns Experimental and Numerical Study on the Behavior and Design of Screw Connected built-up CFS Chord Studs View Project Family Optimization of Cold-Formed Steel Lipped-Channel sections using two-level optimization Scheme with Strength and Stiffness constrains due to cross-sectional instabilities View Project. https://www.researchgate.net/publication/262315483 (2014).

Ting, T. C. H., Roy, K., Lau, H. H. & Lim, J. B. P. Effect of screw spacing on behavior of axially loaded back-to-back cold-formed steel built-up channel sections. Adv. Struct. Eng. 21, 474–487 (2018).

Article Google Scholar

Roy, K., Ting, T. C. H., Lau, H. H. & Lim, J. B. P. nonlinear behavior of axially loaded back-to-back built-up cold-formed steel un-lipped channel sections. Steel Compos. Struct. 28, 233–250 (2018).

Google Scholar

Roy, K., Ting, T. C. H., Lau, H. H. & Lim, J. B. P. Effect of thickness on the behaviour of axially loaded back-to-back cold-formed steel built-up channel sections - experimental and numerical investigation. Structures 16, 327–346 (2018).

Article Google Scholar

Roy, K. & Lim, J. B. P. Numerical investigation into the buckling behaviour of face-to-face built-up cold-formed stainless steel channel sections under axial compression. Structures 20, 42–73 (2019).

Article Google Scholar

Kwon, Y. B., Kim, B. S. & Hancock, G. J. Compression tests of high strength cold-formed steel channels with buckling interaction. J. Constr. Steel Res. 65, 278–289 (2009).

Article Google Scholar

Young, B., Dinis, P. B. & Camotim, D. CFS lipped channel columns affected by L-D-G interaction. Part I: experimental investigation. Comput. Struct. 207, 219–232 (2018).

Article Google Scholar

Dinis, P. B., Camotim, D., Young, B. & Batista, E. M. CFS lipped channel columns affected by L-D-G interaction. Part II: Numerical simulations and design considerations. Comput. Struct. 207, 200–218 (2018).

Article Google Scholar

Mahar, A. M., Sanjeevi, A. J., Mahar, M. & Arul Jayachandran, A. S. & Research Scholar, P. D. Global Buckling Behaviour of Intermittently Fastened Cold-formed Steel Built-up Columns. In: Indian Structural Steel Conference (ISSC). (2020).

Selvaraj, S. & Madhavan, M. Structural behaviour of Cold-Formed Steel Built-Up closed cross-section columns - assessing the influence of parameters and design methods. Eng. Struct. 294, (2023).

Wu, H., Sui, L., Liu, X., Liang, S. & Zhou, T. Shear-slip constitutive model of screw-fastened connections and application in numerical analysis of built-up back-to-back cold-formed steel columns. Thin-Walled Struct. 186, (2023).

Li, Y., Li, Y., Wang, S. & Shen, Z. Ultimate load-carrying capacity of cold-formed thin-walled columns with built-up box and i section under axial compression. Thin-Walled Struct. 79, 202–217 (2014).

Article Google Scholar

AISI D100-08. (American Iron and Steel Institute, (2008).

Muftah, F., Sani, M., Muda, H. & Mohammad, S. M. F. Assessment of Connection Arrangement of built-up cold-formed steel section under axial compression. in Advanced Materials Research vol. 1043 252–257. Trans Tech Publications Ltd, (2014).

Abbasi, M., Khezri, M., Rasmussen, K. J. R. & Schafer, B. W. Elastic buckling analysis of cold-formed steel built-up sections with discrete fasteners using the compound strip method. Thin-Walled Struct. 124, 58–71 (2018).

Article Google Scholar

Fang, Z. et al. Effect of the web hole size on the axial capacity of back-to-back aluminium alloy channel section columns. Eng. Struct. 260, (2022).

Selvaraj, S. & Madhavan, M. Design of cold-formed steel built-up columns subjected to local-global interactive buckling using direct strength method. Thin-Walled Struct. 159, (2021).

Tawfic, M. & Amoush, E. Compressive strength of axially loaded built-up Sigma Cold formed sections columns. Future Eng. J. 1.

Fratamico, D. C., Torabian, S., Zhao, X., Rasmussen, K. J. R. & Schafer, B. W. Experimental study on the composite action in sheathed and bare built-up cold-formed steel columns. Thin-Walled Struct. 127, 290–305 (2018).

Article Google Scholar

Post, B. FASTENER SPACING STUDY OF COLD-FORMED STEEL WALL STUDS USING FINITE STRIP AND FINITE ELEMENT METHODS. (2012).

Karthik Vishweswaran, C. & Srisanthi, V. G. Experimental Study on Cold-formed Steel Built-up Column Sect. (2021).

Kechidi, S., Fratamico, D. C., Schafer, B. W., Miguel Castro, J. & Bourahla, N. Simulation of screw connected built-up cold-formed steel back-to-back lipped channels under axial compression. Eng. Struct. 206, (2020).

yao Kim, Z. Jr Finite Element Modelling and Parametric Studies of Perforated Thin-Walled Steel Columns. http://sydney.edu.au/civil (2014).

Schafer, B. W., Li, Z. & Moen, C. D. Computational modeling of cold-formed steel. Thin-Walled Struct. 48, 752–762 (2010).

Article Google Scholar

Dassault Systèmes, A. B. A. Q. U. S. Preprint at https://www.3ds.com/products/simulia/abaqus.

Cristopher, D., Moen & Schafer, B. W. Direct Strength Design of Cold-Formed Steel Members with Perforations. https://scholarsmine.mst.edu/ccfss-aisi-spec/34/?utm_source=scholarsmine.mst.edu%2Fccfss-aisi-spec%2F34&utm_medium=PDF&utm_campaign=PDFCoverPages (2009).

Schafer, B. W. & Ádány, S. Buckling analysis of cold-formed steel members using CUFSM: conventional and constrained finite strip methods. In: 18th International Specialty Conference on Cold-Formed Steel Structures. Orlando, Florida, (2006).

Download references

Department of Structural Engineering and Geotechnics, Széchenyi István University, Egyetem Tér 1, Győr, 9026, Hungary

Ardalan B. Hussein

You can also search for this author in PubMed Google Scholar

I wish to formally notify you that, as a researcher affiliated with Széchenyi István Egyetem, I serve as the sole author of the manuscript submitted herewith. Consequently, all the research and content therein are solely attributed to my efforts.

Correspondence to Ardalan B. Hussein.

The authors declare no competing interests.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Below is the link to the electronic supplementary material.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

Hussein, A.B. Structural behaviour of built-up I-shaped CFS columns. Sci Rep 14, 25628 (2024). https://doi.org/10.1038/s41598-024-77455-x

Download citation

Received: 24 April 2024

Accepted: 22 October 2024

Published: 27 October 2024

DOI: https://doi.org/10.1038/s41598-024-77455-x

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative