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Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression

The practice of utilizing cold-drawn steel for structural and non-structural elements has expanded nowadays due to it being lighter in weight, economic section, desirable in fabrication, and its preferred post-buckling behavior over hot rolled sections. The cold-drawn steel section back to the back-lipped channel section has a wide application as a structural member. The fasteners are provided at regular intervals for the long-span structure to prevent individual failures. This study is concerned with the inadequacy of research addressing the behavior of built-up columns. The relevant built-up column section is chosen based on the AISI-S100:2007 specification. Thirty-six specimens were designed and tested by varying web, flange, lip dimensions, spacing between the chords, and battened width experimentally subjected to an axial compression. Comparing 36 experimentally buckled specimens with the model generated by Finite Element Method accompanied with ASI-recommended two direct strength methods (DSMs). The DSM comprises the step-by-step procedure incorporated with the elastic, critical, and global distortional interaction. Based on the performed reliability analysis, such as the experimental, analytical, and theoretical studies, the failure load, buckling mode, the economic section, and design rules were proposed. Four suitable sections were selected from the proposal, and the validation study was carried out. From the validation study, experimental values were found to be 1.072 times the FEM values, and DSM values were found to be 0.97 times the FEM values. Based on the significant findings of this study, the proposed design recommendation and the corrected value for DSM are suitable for designing back-to-back stiffened columns.


Introduction
In modern construction, the usage of cold-formed steel sections is needed. The coldformed steel structural members such as beams, columns, and joists are widely used. The main advantage of the cold-formed steel (CFS) is the post-buckling behavior where the hot rolled steel section fails early during axial loading in the single section member. Hence, the area is modified by placing two-lipped chords at a certain distance. Those two chords are connected back-to-back by batten with bolted connection to perform like a single member during loading. The failure mode of the column was influenced predominantly by the local buckling mode. However, there are some limitations in predicting the column's buckling mode by varying the specifications such as the size of the battened plate, dimensions of the section, and the slenderness ratio during the experimental investigation. There is a need for conducting a parametrical study. So that area chosen for our research was selected from carrying capacity is 19% more than the commercially available section and was agreeable with the EC 3-Part 1 [12]. Aswathy and Kumar's [26] study on stiffened and unstiffened lipped channel sections shows the decrease in stiffness or depth of the lip will increase the chance for distortional buckling. The study gave clear information about the distortional buckling in the stiffened lipped channel section during axial loading and predicted that the limiting case for distortional buckling is a partially stiffened element.
The work progresses by performing the validation study similar to the observation reported by Kumar and Kalyanaraman [27]. That work shows the strength of CFS lipped channel compression members reducing its power by the member interaction between the buckling modes during axial loading. This study demands the need for the DSM approach for individual buckling modes to predict the accurate load and buckling interaction. In this study, short columns are selected for experimental study rather than slender columns based on Numerical investigation performed by Dar et al. [28]. The work proves that the ultimate capacity of the column goes on reduced by an increase in toe-toe spacing and slenderness ratio, which even affect the behavior of battens in the built-up column during loading. Dar et al.'s [29] and Vijayanand and Anbarasu's [30] validation studies predicted that North American Specification and Euro standards are found to be unconservative by 15 to 30 %; the slenderness ratio needs to be restricted by 75 to avoid lateral drifting and large lateral displacements. The reason for choosing the open section rather than the closed section is based on the main findings of the research reported by Kherbouche and Megnounif [29]. The nonlinear finite element analysis is performed on both open and closed channels connected by battened plates. The study showed that the stability of the column is influenced by spacing between the channels 'web to length ratio. The open sections are found to be conservative, and failure is influenced by local buckling. Moreover, the closed sections failed by global buckling, and the results are found to be un-conservative. The limitation of the spacing between the chords is chosen based on the recommendation of Vijayanand and Anbarasu's [31] validation study stated that the increase in spacing between the chords and varying slenderness ratio from 20 to 120 would influence column strength and found the conservative DSM method predicted the column strength. Anbarasu's [32] work on four lipped channel sections shows that a column with a lower chord slenderness ratio significantly affects the axial load compression. In that work, the predicted FEA models were agreeable with the experimental test results.
Zhang and Young [33] conducted a CFS column investigation. It is revealed that stiffener facing inwards has more buckling strength against axial loading and defines the need for conducting regression line analysis to predict the relationship between the failure load of the FEA and DSM approach for the validation study. The modified value of the failure load using DSM has been adopted and applied for numerical investigation from the validation study. The concept of the corrected value of failure load is adopted from Gunalan and Mahendran [33] and preceded. The reason behind choosing the pinned end connection is based on the recommendation of Martins et al. [34] regarding the investigation subjection to flexural-torsional buckling. The work shows good performance of pinned end condition under warping, and NAS prediction for failure load under DSM is found to be closely agreeable by modifying the equation using the reduction factor. The pre-analysis using Generalized Beam Theory at the University of Lisbon (GBTUL) was referred to by Martins et al. [35], and Cava et al. [36] reported pre-analysis works on cold-formed steel columns with a lipped channel to find out the local-distortional interaction effects on its design and behavior. The study reveals the web triggered the L-D interaction. The failure load availed from L-D interaction was quite agreeable with DSM results and the need for carrying over-generalized beam theory for post-buckling analysis. Manikandan and Arun [37] demand the provision of intermediate stiffeners, and the ratio of center to center of the spacer plate to the length of the column will influence the torsional rigidity for the partially closed sections. The values of DSM were found to be conservative. Ref. [38] detailed learning reveals the need for conducting regression line analysis for the CFS section subjected to axial loads. From [39,40] performed work outcomes, the numer-ical investigation and strengthening techniques are adopted for effective section design Roy, K. et al. [41] suggestions are incorporated into the FEA analysis and modeling. Liang, H. et al. [42] is a review on CFS members, which ensures better structural and thermal performance for the chosen section.
Anbarasu et al. [18] and Muthuraman et al. [19] work on the unstiffened built-up section by parametric validation and numerical analysis. This work advances by converting the unstiffened section in Muthuraman and Anuradha [19] to a stiffened section by providing intermediated stiffener in both sections. Based on the limitation of AISI-S100 [1], six different cross-sections are experimentally and analytically tested in this study. In a repetition pattern by varying the slenderness ratio and batten width, 36 specimens were analyzed. A parametric study was carried out from the recommendation proposed by the validation work. The parametric study comprises about two different sections. By varying its battened width and slenderness ratio, a total of 40 specimens were analyzed using FEM and compared with DSM results. Based on the outcomes, a suitable design method is said to be proposed to predict the failure load for the CFS web-stiffened column using the DSM.

Selection of Specimen
Based on the AISI-S100 [1] recommendation in Table 1, six models on three times repeatability patterns, for a total of 36 web-stiffened lipped channel sections, were tested by varying geometrical specifications, as shown in Table 2. The channels are connected by battened plates using self-drilling screws as per AISI-S100 [1] guidelines. The span, web, flange, and lip thickness dimensions varied and underwent local bucking, distortion bucking, and overall bucking during axial loading. The selected specimen was analyzed based on the GBTUL code provisions [37]. Based on previous work reported by Muthuraman et al. [19], the validation study on unstiffened built-up sections, the selected section is modified to a stiffened built-up section by varying the web, flange, and geometrical specification. Finally, experimental, analytical, and theoretical work is performed. Table 1. Geometric limitation as per AISI-S100 [1] specification.

Lipped c-Section with Web Stiffener
One or Two Intermediate Stiffeners: values of DSM were found to be conservative. Ref. [38] detailed learning reveals the need for conducting regression line analysis for the CFS section subjected to axial loads. From [39,40] performed work outcomes, the numerical investigation and strengthening techniques are adopted for effective section design Roy, K. et al. [41] suggestions are incorporated into the FEA analysis and modeling. Liang, H. et al. [42] is a review on CFS members, which ensures better structural and thermal performance for the chosen section. Anbarasu et al. [18] and Muthuraman et al. [19] work on the unstiffened built-up section by parametric validation and numerical analysis. This work advances by converting the unstiffened section in Muthuraman and Anuradha [19] to a stiffened section by providing intermediated stiffener in both sections. Based on the limitation of AISI-S100 [1], six different cross-sections are experimentally and analytically tested in this study. In a repetition pattern by varying the slenderness ratio and batten width, 36 specimens were analyzed. A parametric study was carried out from the recommendation proposed by the validation work. The parametric study comprises about two different sections. By varying its battened width and slenderness ratio, a total of 40 specimens were analyzed using FEM and compared with DSM results. Based on the outcomes, a suitable design method is said to be proposed to predict the failure load for the CFS web-stiffened column using the DSM.

Selection of Specimen
Based on the AISI-S100 [1] recommendation in Table 1, six models on three times repeatability patterns, for a total of 36 web-stiffened lipped channel sections, were tested by varying geometrical specifications, as shown in Table 2. The channels are connected by battened plates using self-drilling screws as per AISI-S100 [1] guidelines. The span, web, flange, and lip thickness dimensions varied and underwent local bucking, distortion bucking, and overall bucking during axial loading. The selected specimen was analyzed based on the GBTUL code provisions [37]. Based on previous work reported by Muthuraman et al. [19], the validation study on unstiffened built-up sections, the selected section is modified to a stiffened built-up section by varying the web, flange, and geometrical specification. Finally, experimental, analytical, and theoretical work is performed.

Properties of the Specimen
The selected specimen is a web-stiffened lipped channel section with a thickness of around 2 mm, whose percentile value of elongation, failure stress, and maximum yield stress shown in Table 2 agree with the ASTM C 370 [38] standard specification. Since the cold-formed steel members will tend to yield by that failure load can be found, and the failure stress of the section can be found by the offset method.
Based on [1] the limitation, the specimen studied satisfies the specification for tensile stress and failure stress, which vary from 289 to 581 N/mm 2 and 72 to 482 N/mm 2 , respectively. Similarly, the proportion of tensile strength to the yield strength ranges from 12 to 27. The detailed geometrical specifications and properties, such as failure stress, maximum stress, percentage of elongation, and modulus of elasticity are stated in Table 2. The specification for the individual section is mentioned in Table 3. The labelling is done as shown in Figures 1 and 2.

Validation of the Selected Specimen with GBTUL
Based on the GBTUL codal specification, the single unstiffened section is selected, and Anbarasu and Murugapandian [43] performed validation work as a reference to the material properties. From the analysis of the section, Figure 1 shows the change in critical

Validation of the Selected Specimen with GBTUL
Based on the GBTUL codal specification, the single unstiffened section is selected, and Anbarasu and Murugapandian [43] performed validation work as a reference to the material properties. From the analysis of the section, Figure 1 shows the change in critical buckling for the column BBSC-20-105-2-1. Usually, the column fails by three variants of failure mode depending upon the span. For a length L < 600 mm, the column will exhibit local buckling, the distortional buckling occurs where the length L lies in between 600 < L <1960 mm, and the flexural buckling occurs when L < 1960 mm. It shows the column's buckling behavior (local, global, and flexural) for their corresponding length.
The buckling curve diagram indicates that for the 1960 mm accord and with D-G critical loads of P crd = 170 kN with P cre = 178 kN for the chosen section, the critical load analysis shows that the failure mode changes from distortion buckling way to global buckling for 1960 mm, as shown in Figure 3. The D-G interaction influenced the postbuckling behavior of the column, as shown in Figure 4. Hence, for the experimental work, the single chord section is placed back-to-back and connected with a batten to improve the post-buckling behavior under loading. To calculate the effective length, the actual distance summed off with both pinned ends (i.e.) 1960 + 37 mm for a non-loading part at the bottom end + 25 mm loading part at the top end equals an effective span of 2022 mm. Specifications in Table 3 (1,2,3) indicate the repetition of the specimen to obtain accurate results.

Testing of Specimen
The sheets used for testing are of 2 mm thickness cold rolled sheets made up of pressed brake form as per AISI-S100 [1] specification. The sheet profiles of horned edges

Testing of Specimen
The sheets used for testing are of 2 mm thickness cold rolled sheets made up of pressed brake form as per AISI-S100 [1] specification. The sheet profiles of horned edges whose edge radius is negotiable. The corners of both sides connected by the plates are

Testing of Specimen
The sheets used for testing are of 2 mm thickness cold rolled sheets made up of pressed brake form as per AISI-S100 [1] specification. The sheet profiles of horned edges whose edge radius is negotiable. The corners of both sides connected by the plates are made of carbon of 10 mm, as shown in Figure 5. To provide uniform load transmission during axial loading and avoid confined warping at the ends; for achieving the pinned end condition, round-shaped 60 mm balls between the endplates, along the top and bottom of the flat plate. The experimental setup is chosen from Anbarasu and Murugapandian's [39] investigation of cold-formed steel specimens. The maximum loads and their failure modes obtained from the test are shown in Table 4. All the specimens are found to fail from the trial by the combination of local and distortional buckling (local and flexural buckling), as shown in Table 4. The buckled models after loading are shown in Figure 7.   Before loading, the LVDT is fixed in a specific place to determine the deflection at all three axes. It includes placing one at half the span of the column, the second one at the middle of the web, and the third one at the center of the flange. The applied loads are captured by the transducer at suitable intervals with the help of a data logger, as shown in Figure 6. The maximum loads and their failure modes obtained from the test are shown in Table 4.
All the specimens are found to fail from the trial by the combination of local and distortional buckling (local and flexural buckling), as shown in Table 4. The buckled models after loading are shown in Figure 7.   The loading has been started incrementally by initially applying 2-5 kN as pre-load to ensure the specimen end is well connected with the endplates. The gradual loading is conducted by employing jack works hydraulically until the column achieves the failure. The maximum loads and their failure modes obtained from the test are shown in Table 4. All the specimens are found to fail from the trial by the combination of local and distortional buckling (local and flexural buckling), as shown in Table 4. The buckled models after loading are shown in Figure 7.

DSM (Direct Strength Method) Approach
The AISI-S100 [1] specification provides an effective method for finding the maximum load-carrying capacity of the stiffened cold-formed steel column subjected to local distortion overall buckling. Changing the slenderness ratio and providing the fasteners at regular intervals are mentioned in AISI-S100 [1] Recommendation D 1.2 described in Equations (1)- (7).
where (KL/r) O -total slenderness ratio of the specimen; K-effective length of the member; L-unbraced member length; a-spacing between intermediate fastener or spot weld; r i -minimum radius of gyration of the full unreduced cross-sectional area of an individual shape in the built-up member.
For the DSM design approach for calculating the axial load-carrying capacity of the member, the minimum value of the nominal member capacity, such as local buckling (P nl ), distortional buckling (P nd ), and flexural torsional or torsional buckling (P ne ). P n -Minimum (P nl , P nd , P ne ). The nominal axial resistance P ne for the flexural and torsional buckling is calculated as shown below: where λ c = P y /P cre and P y = a f y P y (3) f y -stress due to local buckling; P cre represents the minimum critical elastic buckling load in flexural and torsional buckling; a-Total cross-sectional area; P y -squash load.
For the local buckling, the nominal axial resistance P nl can be find out by the following equation.
where: P ne -obtained from Equations (3) and (4); P crl -critical elastic column buckling load. For calculating the nominal axial resistance P nd under distortion, buckling can be calculated as follows: where: P crd -Critical Elastic buckling load of the column under distortion mode; P crd -Af od , f od represents stress under elastic buckling of distortional mode. From the above equations, the desired failure loads under local distortion and flexural buckling have been found, and taking the minimum of them as the failure load under DSM (P DSM ) will be considered for the validation study. The finite element method is carried out for all the specimens to perform a numerical investigation of the experimentally tested model. The elastic and nonelastic mode behavior study deal with the analysis performed in ABAQUS [44]. The modeling was carried out by generating a stiffened back-to-back section. The properties of the FEM generated model are chosen from Table 2 of the properties of the experimental model for validating the experimental results with FEM results. As Schafer (23) stated, the load-carrying capacity of the area was influenced by residual stresses while analyzing a channel section. After carrying over the linear analysis, nonlinear analysis was only performed after feeding the imperfection details and residual stresses. Finally, the plotted load-carrying capacity versus the shortening graph gives the maximum load-carrying ability of the section for parametric validation.

Incorporation of Material Parameter
As reported by Anbarasu et al. [18], the approach for the model in the material comprises choosing the type of the element and size of the mesh. The ABAQUS model classified several nodes as S4R5 thin segments with six degrees of freedom for an individual node for the convergence studies. Initially, for the selected specimen, the length to the breadth ratio is said to be chosen as one for obtaining accurate outcomes and reducing the analysis duration. The minimum area of the mesh should be 100 mm 2 (10 mm × 10 mm) for the practice. The analysis carried a nonlinear analysis on Stiffened sections with lip edges. The global imperfection quantity is identified from one of the thousandth spans from the middle portion of the column. Both local and global imperfections are (0.006 W × T) and (1.0 t), respectively. Therefore, the first minimum Eigen value obtained from the analysis is taken as the overall failure mode for the flexible approach. The determined value is said to be superposed to find out the inelastic performance of the section.

Selecting the End Condition and Loading
The specimen loading load ends are restricted against translation and rotation along the x, y and z axes, respectively. As shown in Figure 8, all nodes need to connect with an individual tie called MPC (multi-point constraint). Because the edges have to behave as a single one during loading, the generated MPC point must be at the center of gravity point of the geometrical section. As mentioned in Table 2, the specifications (including linearity of the specimen and geometric of the unit) and end conditions are similar to the experimental setup and other attributes that proved Roy et al.'s [7] claim that the in-built stress has less impact to be omitted. The applied load must pass through the C.G. points of the specimen. The loading pattern must be in the form incremental manner using the RIKS method, and the buckling of the column was discovered, as shown in Figure 9. single one during loading, the generated MPC point must be at the center of gravity point of the geometrical section. As mentioned in Table 2, the specifications (including linearity of the specimen and geometric of the unit) and end conditions are similar to the experimental setup and other attributes that proved Roy et al.'s [7] claim that the in-built stress has less impact to be omitted. The applied load must pass through the C.G. points of the specimen. The loading pattern must be in the form incremental manner using the RIKS method, and the buckling of the column was discovered, as shown in Figure 9.

Validation of Experimentally Tested Specimen with FEM and DSM
The built-up section subjected to axial loading undergoes lateral deflection and buckles based on the load incrementation. Based on the cross-section, slenderness ratio, and material properties, load-bearing behavior varies along with failure modes, as discussed in detail.
The experimentally tested specimen was validated with FEM results, as shown in Figure 10. The test specimens were assembled in FEM, similar to the experimental setup. The screws of 8mm self-drill screws were made like the experimental models to provide

Validation of Experimentally Tested Specimen with FEM and DSM
The built-up section subjected to axial loading undergoes lateral deflection and buckles based on the load incrementation. Based on the cross-section, slenderness ratio, and material properties, load-bearing behavior varies along with failure modes, as discussed in detail.
The experimentally tested specimen was validated with FEM results, as shown in Figure 10. The test specimens were assembled in FEM, similar to the experimental setup. The screws of 8mm self-drill screws were made like the experimental models to provide the connection between the batten plate and the section. The end plate conditions are ensured to be restricted against warping due to loading. The failure load during the experiment (P EXP ), finite element analysis (P FEA ), and direct strength method (P DSM ) results are tabulated in Table 4. The standard deviation and coefficient of variation of FEA to the experimental specimen are 1.072, 0.030, and 0.028. Moreover, FEA to the DSM is 0.971, 0.027, and 0.028, respectively. Therefore, from the performed FEA and experimental work, it can be inferred that using FEA, the probable buckling mode and the buckling behavior of the CFS stiffened column under experimental load subjection can be derived irrespective of slenderness ratio and geometrical specification [41].

Load Bearing Capacity vs. Axial Shortening Performance
The DSM approach results mentioned in Table 4 predicted the design strength under service load for the back-to-back stiffened CFS column. From the above testing, 85% of the specimen was failed by its maximum load. The column's post-buckling behavior was enhanced by increasing axial shortening for the built-up section during the nonlinear analysis. Whatever the geometrical specification (slenderness ratio and thickens), the load increases gradually and decreases in regular intervals. The slope of the curve goes on, increasing rapidly from the initial stage. Table 4 for the back-to-back stiffened section of 2 mm thickness for the specimen BBSC-132.5×78.75×16.75×2-1 records the maximum ultimate load of 264 kN and FEA and DSM of 273,276, respectively. The FEA results were found agreeable with the experimental results. The failure load obtained by FEA is found to be 3% more than the obtained experimental value. Moreover, obtained DSM value is found to be 2.7 % more than the predicted FEA value. Among the 36 tested specimens, 6 specimens of slenderness ratio 20 failed by local buckling and 30 specimens of slenderness ratios 30 and 40 failed by a combination of both local and distortion buckling. The load-versus-shortening curve for the boundary conditions 1, 2, 3, 4, 5, and 6 are shown in Figures 11-13.

Comparison of DSM vs. FEM
After comparing the yield load obtained from the experimentally tested model with the load availed from FEA model. The conventional DSM for predicting the failure load predicted by Muthuraman et al. [16] is adopted as a reference DSM. The failure load calculated using DSM was compared with FEM output. The comparison shows that the DSM approach was found to be a firm method for predicting the load-carrying capacity of the column. The load behavior of the DSM was found to be similar to that of the FEA predicted load. The results go on varies based on the geometrical specification. From the comparison, it is predicted that the failure load of FEM is found to be equal to 0.986 times the failure load of DSM and a difference of 3.65 (PFEA = 0.986 PDSM − 3.65) along with an R square value of 0.99 (1 − (Residual sum of squares/corrected Sum of squares)), as shown in Figure 14. The obtained equation can be used for all CFS stiffened built-up battened columns to predict the maximum load-carrying capacity [42,43,45].

Comparison of DSM vs. FEM
After comparing the yield load obtained from the experimentally tested model with the load availed from FEA model. The conventional DSM for predicting the failure load predicted by Muthuraman et al. [16] is adopted as a reference DSM. The failure load calculated using DSM was compared with FEM output. The comparison shows that the DSM approach was found to be a firm method for predicting the load-carrying capacity of the column. The load behavior of the DSM was found to be similar to that of the FEA predicted load. The results go on varies based on the geometrical specification. From the comparison, it is predicted that the failure load of FEM is found to be equal to 0.986 times the failure load of DSM and a difference of 3.65 (P FEA = 0.986 P DSM − 3.65) along with an R square value of 0.99 (1 − (Residual sum of squares/corrected Sum of squares)), as shown in Figure 14. The obtained equation can be used for all CFS stiffened built-up battened columns to predict the maximum load-carrying capacity [42,43,45].

Comparison of DSM vs. FEM
After comparing the yield load obtained from the experimentally tested model with the load availed from FEA model. The conventional DSM for predicting the failure load predicted by Muthuraman et al. [16] is adopted as a reference DSM. The failure load calculated using DSM was compared with FEM output. The comparison shows that the DSM approach was found to be a firm method for predicting the load-carrying capacity of the column. The load behavior of the DSM was found to be similar to that of the FEA predicted load. The results go on varies based on the geometrical specification. From the comparison, it is predicted that the failure load of FEM is found to be equal to 0.986 times the failure load of DSM and a difference of 3.65 (PFEA = 0.986 PDSM − 3.65) along with an R square value of 0.99 (1 − (Residual sum of squares/corrected Sum of squares)), as shown in Figure 14. The obtained equation can be used for all CFS stiffened built-up battened columns to predict the maximum load-carrying capacity [42,43,45].

Parametric Study Buckling Mode
Two different types of stiffened cross-sections were selected and varied in batten width, similar to the performed experimental work taken for parametric study. This work is detailed by studying the buckling mode of members by both analytical and theoretical (FEM and DSM) approaches. The selected section must satisfy the AISI-S100 [1] specification for the lipped stiffened section. The specification for the selected section is shown in Table 5. To find out the performance of the stiffened section, its strength obtained from analytical (P FEM ) was compared with the load obtained theoretically (P DSM ), and the proposed load for the experimental work can be achieved from the above-performed work in Table 4. The proposed relation shows that P EXP = 0.933 times P FEM is was selected as the corrected load (P corrected ) for predicting the load using DSM. The geometrical specification of the specimen taken for the parametric study is shown in Table 5. A parametric study was carried out by varying the slenderness ratio to find out the effectiveness of the stiffener and thickness. The failure load obtained by FEA and DSM and the corrected values were compared, and the precise prediction was made from the performed work. The obtained buckling modes of the columns are shown in Figure 15. The ultimate load-carrying capacity versus axial shortening is shown in Figures 16 and 17.

Parametric Study
Buckling Mode Two different types of stiffened cross-sections were selected and varied in batten width, similar to the performed experimental work taken for parametric study. This work is detailed by studying the buckling mode of members by both analytical and theoretical (FEM and DSM) approaches. The selected section must satisfy the AISI-S100 [1] specification for the lipped stiffened section. The specification for the selected section is shown in Table 5. To find out the performance of the stiffened section, its strength obtained from analytical (PFEM) was compared with the load obtained theoretically (PDSM), and the proposed load for the experimental work can be achieved from the above-performed work in Table 4. The proposed relation shows that PEXP = 0.933 times PFEM is was selected as the corrected load (Pcorrected) for predicting the load using DSM. The geometrical specification of the specimen taken for the parametric study is shown in Table 5. A parametric study was carried out by varying the slenderness ratio to find out the effectiveness of the stiffener and thickness. The failure load obtained by FEA and DSM and the corrected values were compared, and the precise prediction was made from the performed work. The obtained buckling modes of the columns are shown in Figure 15. The ultimate load-carrying capacity versus axial shortening is shown in Figures 16 and 17.

Results of Parametric Study
By FEA analysis, it can be inferred from the Table 6 that for a slenderness ratio between 20 and 60, the failure mode is the local, distortional, and flexural mode of failure (N L + N D + N E ), and above 60, the failure mode is the flexural and distortional mode of failure (N D + N E ). This study enumerates the importance of failure by distortional buckling, which could influence the capacity of the chord members. From the comparison of FEA, DSM, and the corrected values, the ratio of P DSM to P FEA and P Corrected values to P FEA are 1.10 and 0.978. This method was found to reliably predict the exact failure load of DSM using FEA and obtained agreeable results, as shown in Figures 18 and 19. By the regression line analysis in Figure 20, the load-carrying capacity of FEM is equal to the difference between the product of 0.96 times DSM and 12.21, and the R square value is 0.971. Therefore, this equation can be applicable for all other types of stiffened cold-formed steel built-up section columns to determine the failure load under axial loading if an analytical load is known. The load variation adapted from the following actual method P DSM /P FEA to the corrected method P Corrected /P FEA varies according to the slenderness ratio shown in Figure 21.

Discussion
From the above work, the following outcomes are discussed. 1. The experimental method shows that the load-carrying capacity is governed by residual stress, slenderness ratio, and battened width. 2. The buckling mode started with local buckling and ended up with a combination of local and distortional with respect to slenderness ratio. The buckling mode started with local buckling and ended up with the combination of local and distortional for slenderness ratio. 3. Increasing the slenderness ratio from 20 to 30 and 30 to 40, the resistance against loading decreased by the nominal verge of 10 percent for the experimental specimen. The failure of the column is predicted for a lower slenderness ratio (≤30) may be local or a combination of local and flexural buckling. For the higher-order slenderness ratio (>30), the buckling will combine local, distortional, and flexural buckling modes. 4. The experimental specimen subjected to buckling mode was matched with the FEA specimen from the validation study. Therefore, for the tedious situation, such as for the CFS back-to-back stiffened column, the observed value for a larger slenderness ratio can be predicted by finding out the product of 1.072 with PFEM (analytical value). 5. From the theoretical study, it can be inferred that the DSM analysis is found to be conservative with the inclusion of service load and predicted the column's strengthen equation, which calculates the failure load irrespective of the thickness and slenderness ratio.

Conclusions
In this study, a total of 36 specimens were examined experimentally, analytically, and theoretically to predict the load-carrying property and buckling behavior of CFS stiffened built-up columns under axial loading. From the outcomes of the validation study, a relationship was established between the FEA predicted load and DSM loads. The parametric study is carried out for the selected four different sections. The numerical investigation is performed by varying the slenderness ratio from 20 to 120 for boundary conditions 1 and 2 and 20 to 100 for boundary conditions 3 and 4. We investigated the failure load under FEA (PFEM), DSM (PDSM), and corrected values (Pcorrected) of failure load for DSM obtained

Discussion
From the above work, the following outcomes are discussed. 1.
The experimental method shows that the load-carrying capacity is governed by residual stress, slenderness ratio, and battened width.

2.
The buckling mode started with local buckling and ended up with a combination of local and distortional with respect to slenderness ratio. The buckling mode started with local buckling and ended up with the combination of local and distortional for slenderness ratio.

3.
Increasing the slenderness ratio from 20 to 30 and 30 to 40, the resistance against loading decreased by the nominal verge of 10 percent for the experimental specimen. The failure of the column is predicted for a lower slenderness ratio (≤30) may be local or a combination of local and flexural buckling. For the higher-order slenderness ratio (>30), the buckling will combine local, distortional, and flexural buckling modes. 4.
The experimental specimen subjected to buckling mode was matched with the FEA specimen from the validation study. Therefore, for the tedious situation, such as for the CFS back-to-back stiffened column, the observed value for a larger slenderness ratio can be predicted by finding out the product of 1.072 with P FEM (analytical value).

5.
From the theoretical study, it can be inferred that the DSM analysis is found to be conservative with the inclusion of service load and predicted the column's strengthen equation, which calculates the failure load irrespective of the thickness and slenderness ratio.

Conclusions
In this study, a total of 36 specimens were examined experimentally, analytically, and theoretically to predict the load-carrying property and buckling behavior of CFS stiffened built-up columns under axial loading. From the outcomes of the validation study, a relationship was established between the FEA predicted load and DSM loads. The parametric study is carried out for the selected four different sections. The numerical investigation is performed by varying the slenderness ratio from 20 to 120 for boundary conditions 1 and 2 and 20 to 100 for boundary conditions 3 and 4. We investigated the failure load under FEA (P FEM ), DSM (P DSM ), and corrected values (P corrected ) of failure load for DSM obtained using the relationship taken from the validation study. By making a complete closed section with the battened connection, investigation under axial load is considered the scope for future work.