Experimental analysis of built-up cold-formed steel lipped channel stub column

Abstract

This article reports the results of experimental tests conducted on built-up cold-formed steel (CFS) stub columns, composed of double lipped channel members connected with self-drilling screws, which will be applied as the chord members of laced columns. These experiments aim to quantify the effect of four distinct web fastener layouts on the composite action, including the ultimate strength, buckling modes and collapse mechanism for built-up CFS members. The tested stub columns are of 480mm length, double 88x86x40x42x12mm lipped channel cross-section and 0.8mm thickness. The built-up CFS lipped channel members were analyzed with help of the Generalized Beam Theory in order to identify their buckling loads and modes. The Direct Strength Method (DSM) was adopted to obtain the analytical strength of the built-up members, to be compared with the experimental results. The axially compressed built-up members displayed local and distortional buckling, negligible composite behavior and minor effect of number and distribution of the screws. The results indicate (i) inefficient behavior of the self-drilling screws for composite condition purposes and (ii) the DSM rules for non-composite CFS are able to estimate the ultimate strength of this type of built-up lipped channel section.

Keywords:
buckling; cold formed steel; column; built-up section; compression tests

1. Introduction

Cold-formed steel built-up sections are applied as structural members in the construction industry for more structurally efficient cross-section shapes, when higher capacity is required. Two or more single CFS members are connected for a built-up section in order to carry higher loads as well as to cross a larger span. Built-up sections are commonly designed as chords of spatially laced columns, with several applications, such as industrial buildings, offering advantages of lightness, fast production, transportation and erection. This article is part of a study concerning the stability of spatial laced built-up columns, with chords composed of double lipped channels (Bastos, Batista, 2018). The main design standards and specifications do not present methods for designing this type of cold-formed steel built-up section.

Research conducted by Fratamico et al. (2018) indicated that composite action could develop in built-up sections, with axial compression and bending behavior capacity higher than the sum of the individual sections. These authors studied the composite action and the achievable capacities over a range of built-up column cross-section types, practical column end conditions and fastening arrangements for application to CFS framing. The tested capacities were compared with nominal strength estimates based on rational analysis extension of the Direct Strength Method, DSM (Schafer, Peköz, 1998).

Liu and Zhou (2017) tested screw-connected T-section columns with the help of three lipped channel sections, for three different lengths. The failure modes of long columns and intermediate long columns were flexural-torsional buckling, while the failure modes of short columns were distortional buckling.

Zhang and Young (2012, 2015) studied the pertinence of the DSM for built-up open CFS members under axial compression, by comparing the results of a FEM parametric study with the experimental results of axial compression tests on I-shaped, open-section cold-formed steel with edge and web stiffeners. Based on rational buckling analysis, it was concluded that the current DSM could be used for the design of built-up open CFS columns.

Liao et al. (2017) studied multi-limb, built-up cold-formed steel stub columns with three different section forms and observed that the failure modes were local and distortional buckling. The screw spacing has little effect on local and distortional buckling capacities and ultimate loads.

Young and Chen (2008) also conducted experiments on built-up CFS closed sections with intermediate stiffeners, with fixed-ended columns and different lengths. The authors concluded that DSM using a single section to obtain the local and distortional elastic buckling stresses is generally conservative and reliable, as composite action was not significant during tests. The failure modes were local and distortional buckling of the webs and flexural buckling.

This article presents the experimental analysis of a built-up cold-formed steel lipped channel stub column submitted to axial compression and a comparison between experimental and theoretical results. The main objectives were: (i) quantify the effect of four distinct web fastener layouts on the composite action, including the ultimate strength, buckling modes and collapse mechanism for built-up CFS members; and (ii) check the applicability of DSM, as the method does not cover this type of built-up section used in laced columns.

2. Experimental program

The experimental program included full-scale tests carried out on built-up cold-formed steel columns, composed of double lipped channels connected with 4.8mm diameter self-drilling screws, as shown on Figure 1. The measured dimensions (average) of a single lipped channel cross-section are 88x86x40x42x12mm and 0.8mm thickness. The tested columns are 480mm in length, with a composite asymmetric cross-section composed of members A and B as shown on Figure 1. The flange of member B was in contact with part of the web of member A. Different arrangements of screws were tested, with two, three, four and five screws, as shown on Figure 2.

Figure 1
Tested CFS stub columns: (a) single section, (b) built-up section (members A and B).

Figure 2
Tested built-up arrangements, with, 2, 3, 4 and 5 self-drilling 4.8mm screws.

A total number of eight built-up columns were tested at the Structures and Material Laboratory of COPPE, at the Federal University of Rio de Janeiro. The built-up columns were previously prepared with 9mm plates Tig-welded at both extremities. Table 1 shows the columns IDs.

Table 1
Built-up columns IDs: 2 lipped channel CFS 88x86x40x42x12mm, t=0.8mm.

Column ID	Number of self-drilling 4.8mm screws
CP1-03, CP2-13	2
CP3-14, CP4-16	3
CP5-09, CP6-18	4
CP7-17, CP8-10	5

Figure 3 shows the built-up columns before and after welding the end plates.

Figure 3
Tested built-up columns: a) built-up cross-section; b) built-up column before welding the end plates; c) built-up column with Tig-welded 9mm thick end plates.

2.1 Testing procedure and measuring devices

The built-up columns were tested in a displacement control condition, with compression load applied by a servo controlled hydraulic actuator. The actuator was placed in a rigid frame, as shown in Figure 4a), programed at a 0.004mm/s rate smooth displacement control. The end condition for the axial compression test was rigid type for flexural rotations (constrained ends), as confirmed by the recorded experimental measurements of test set-up templates, described further on. The identification of bottom and top templates are, respectively, Template 1 and 2.

Figure 4
Experimental set-up: a) Testing frame arrangement; b) displacement transducers DTs for (i) vertical and horizontal measurements at bottom template 1 (V1 and V3, H2 and H4)) and (ii) at the column mid-length (H5, H6 and H8 – see Fig. 5a)).

Displacement transducers (DTs H5, H6 and H8) were applied for flange deflection measurements at the mid-length of the column, as shown in Figure 5a). Additional DTs were placed to follow displacements and rotations at the top template 2 (V7) and bottom template 1 (V1, V3, H2 and H4). These measurements allow end condition control, in order to confirm the constrained condition at the templates, which must be assured by the rotation-fixing bolts indicated in Figure 4b). Figure 4b) shows the DTs placed at the test machine bottom template 1 (V1, H2, V3 and H4) and at column mid-length (H5, H6 and H8). Longitudinal strain gages were placed externally and internally in the webs of both lipped channels, at the mid-length of the column, thus performing two couples of strain gages addressed to record the onset of local buckling deformation. Figure 5b) displays the distribution of strain gages.

Figure 5
Measurement devices placed at the mid-length section of the columns: a) displacement transducers DTs H5, H6 and H8, b) longitudinal couples of strain gages E1-E2 and E3-E4

The process adopted for centering the specimens in the testing set up followed a graphic scheme. This method consisted of stamping the cross-section of the columns on graph paper (for both ends). The geometric characteristics were computed through the actual cross-section geometry drawn, including the position of the centroid. Next, the centroid of each section was marked over the original drawing, as well as the actual principal axis of inertia. The graph paper with the stamped cross-section was fixed over the end plates, coinciding its centroids, defining the TIG-welding position. Finally, the end plates of the column were bolted to the top and bottom templates. Figure 6a) shows the TIG-welding process and Fig.6b) the finished welded end plate fixed with bolts to testing set-up template. A laser level device was used to check column position and verticality.

Figure 6
Built-up column with welded end plates: a) TIG welding of the 9mm end plate; b) built-up column fixed with bolts to the test set top template.

2.2 Material Properties

The columns were manufactured with structural steel (commercial identification ZAR345) with nominal yield stress f_y =345MPa. The steel mechanical properties were measured through standard tensile tests of 6 coupons extracted from the same coil of the built-up columns (extraction from flat sheet before cold-forming). The geometry of the coupons and the testing procedure were based on the guidance provided by ISO 6892 standard (ABNT, 2013). The average result of yield stress f_y, ultimate stress f_u, Young modulus E and residual strain after failure ε_r are given in Table 2.

Table 2
Average results of six standard tensile tests.

	Yield Stress fy (MPa)	Ultimate Stress fu (MPa)	Young Modulus E (GPa)	εr %
Average	370	455	198	29
Standard deviation	3.1	3.8	13	6
Coefficient of variation	0.84%	0.83%	6.75%	19.35%

3. Test results

During the tests of the built-up columns, it was possible to observe (by naked eye) the development of the typical local buckling deformation mode along the webs of the members (A and B) before collapse. Although the web of member A was partially fixed to the flange of member B, local and distortional buckling deformation was clearly observed and measured, showing that the screw connection was not fully effective. Figure 7 shows the local and distortional buckling semi-waves developed during the test for CP8-10 and CP4-16. Table 3 describes the approximate position of the collapse mechanism for the tested built-up columns. Figure 8 shows the collapse mechanism for CP2-13 and CP3-14.

Figure 7
Test results of columns CP8-10 and CP4- 16: a) seven local buckling semi-waves in the web combined with single distortional buckling observed in member A of CP8- 10; b) local buckling semi-waves observed along the web of member B of CP4-16.

Table 3
Registered position of thecollapse mechanisms.

Column ID	Member A	Member B
CP1-03	quarter-length	mid-length
CP2-13	quarter-length	mid-length
CP3-14	quarter-length	quarter-length
CP4-16	mid-length	mid-length
CP5-09	mid-length	top (end 2)
CP6-18	top (end 2)	mid-length
CP7-17	top (end 2)	top (end 2)
CP8-10	bottom (end 1)	bottom (end 1)

Figure 8
Collapse mechanism: a) CP2-13: (i) mid-length combined local and distortional buckling for member B and (ii) top quarter length typical local buckling collapse mechanism for member A; b) CP3-14: typical local buckling collapse mechanism at top quarter length for members A and B.

The flanges of members A and B deformed inward (closing) during the tests, as may be seen in Fig.7a). Figure 9a) shows the horizontal displacements recorded by DTs H5, H6 and H8 at the mid-length of column CP1-03, indicating the non-linear behavior for loads greater than 30kN. This behavior was similar for all tested columns, indicating the presence of a distortional buckling. Experimental measurements from the DTs V1, H2, V3, H4 and V7, placed at bottom and top set-up templates, registered minor displacements (less than 0.6mm for vertical DTs and less than 0.05mm for horizontal DTs), confirming the constrained ends.

Figure 9
a) Load vs. displacement recorded at the column mid-length for built-up column CP1-03; b) load vs. strain measurements (με) at mid-length section of the built-up column CP1-03.

The mid-length longitudinal couples of strain gages registered linear (compression) behavior until the onset of local buckling. Figure 9b) shows the strain gage results for the built-up column CP1-03, where near linear behavior can be observed until (approx.) 11kN applied load. The beginning of the local buckling effect was recorded for member B, in accordance with measurements of couple of strain gages E1/E2. The registered collapse load was 53.9kN.

Finally, Table 4 shows a summary of the results for the tested built-up columns, including the records of (i) the collapse load P_uexp, and (ii) the loading level (approx.) for which the onset of local buckling was identified P_Lexp, with the help of strain gage measurements.

Table 4
Experimental results of tested built-up columns.

Column ID	Number of screws	Collapse load Puexp(kN)	Local buckling onset PLexp (kN)
CP1-03	2	53.90	11.00
CP2-13	2	55.40	13.00
CP3-14	3	56.05	13.00
CP4-16	3	55.25	13.00
CP5-09	4	56.30	16.00
CP6-18	4	54.55	15.00
CP7-17	5	55.60	15.00
CP8-10	5	53.70	23.00
Average		55.09	14.88
Standard deviation		0.96	3.64
Coef. of variation		1.7%	24.5%

As observed in the results of the tests, although improved results of the onset of the local buckling were recorded during the tests, especially for the case of 4 and 5 screw connections (see Table 4), the ultimate load (column strength) was marginally affected. The explanation for this performance is the fact that the local buckling mode is mainly affected at the connected elements and develops almost freely in the other plate elements. This statement is confirmed by the fact that the experimentally observed local buckling shape, especially in the web element not restricted by the fasteners (see Fig. 7 and Fig.10d)), strictly corresponds to the theoretical one computed for a single column member with the help of the generalized beam theory (seven local buckling semi-waves with 69mm length). The collapse load values (P_uexp) were very similar between the tested built-up columns, regardless of the number of screws adopted to connect members A and B. The average value was 55.1kN with negligible standard deviation.

Figure 10
a) GBTUL fully-composite section (double thickness in the contact portion) and constrained ends condition (C-C) for specimen CP6-18; b) local buckling deformation mode; c) distortional buckling deformation mode; d) seven local buckling semi-waves along 480mm length.

4. Design methods

The direct strength method (DSM) proposed by Schafer and Peköz (1998) and considered in the North American standard (AISI, 2016) was included in Annex C of the Brazilian code NBR 14762 (ABNT, 2010), for the design of cold-formed steel structural members. However, the DSM does not cover the design of built-up members, as is the case of the chords of the present case of the investigated laced column. The present study adopted DSM to obtain the strength of the built-up members, composed of a two lipped channel, as shown in Fig. 1(b), in order to compare with experimental results.

The Young modulus was assumed as E =198 GPa and the yield strength f_y =370MPa, according with standard tensile test results included in Table 2. Poisson ration is admitted as ν = 0.3.

Cross-section elastic buckling analysis

The analysis of the buckling modes and the corresponding critical buckling load P_cr is the first step for the design calculation using DSM. Buckling analysis was performed taking into account a constrained ends condition, using the generalized beam theory with the help of the GBTUL computational program, Camotim and Basaglia (2010). The actual screw connection condition between the CFS members was admitted as fully effective (fully-composite) and transformed into a double thickness (2t) plate element in the portion of contact between the web and flange of the element members A and B, respectively. In addition, a non-composite condition was admitted, considering the single section of members A and B, for comparison. The analyses performed with GBTUL considered the actual dimensions of each specimen, with imperfections. Figure 10 shows, as an example, the GBTUL fully-composite section, with double thickness at the contact between the flange of member B with the web of member A, for specimen CP6-18.

Figure 11 shows the GBTUL non-composite section (members A and B computed separately), for specimen CP6-18. The deformation modes for local buckling are shown in Figures 10b) and 11b), and distortional buckling in Figures 10c) and 11c).

Figure 11
GBTUL non-composite section (members A and B) for column specimen CP6-18; b) local buckling deformation mode; c) distortional buckling deformation mode.

Compression strength according with the direct strength method (DSM)

The DSM design rules for columns are described below, equations (1) to (6). The column strength (P_n) is taken as the lowest value provided by local-global LG buckling interaction (P_nLG) or the distortional buckling (P_nD). In the following equations, P_crG is the elastic global buckling load; P_crL is the elastic local buckling load and P_crD is the elastic distortional buckling load.

(1) $\begin{array}{cc}{\mathit{P}}_{\mathit{nG}}=\left(0.{658}^{{\mathit{\lambda }}_0^2}\right){\mathit{Af}}_{\mathit{y}}& \mathrm{for}{\mathit{\lambda }}_0\le 1.5\end{array}$

(2) $\begin{array}{cc}{\mathit{P}}_{\mathit{nG}}=\left(\frac{0.877}{{\mathit{\lambda }}_0^2}\right){\mathit{Af}}_{\mathit{y}}& \mathrm{for}{\mathit{\lambda }}_0\le 1.5\mathrm{where}{\lambda }_0={\left(\frac{{\mathit{Af}}_{\mathit{y}}}{{\mathit{P}}_{\mathit{crG}}}\right)}^{\mathit{0}\mathit{.}\mathit{5}}\end{array}$

(3) $\begin{array}{cc}{\mathit{P}}_{\mathit{nLG}}={\mathit{P}}_{\mathit{nG}}& \mathrm{for}{\mathit{\lambda }}_{\mathit{L}}\le 0.776\end{array}$

(4) ${\begin{array}{cc}{\mathit{P}}_{\mathit{nLG}}=\left(1-\frac{0.15}{{\lambda }_{\mathit{L}}^{0.8}}\right)\frac{{\mathit{P}}_{\mathit{nG}}}{{\lambda }_{\mathit{L}}^{0.8}}& \mathrm{for}{\mathit{\lambda }}_{\mathit{L}}\le 0.776\mathrm{where}{\lambda }_{\mathit{L}}=\left(\frac{{\mathit{P}}_{\mathit{nG}}}{{\mathit{P}}_{\mathit{crL}}}\right)\end{array}}^{\mathit{0}\mathit{.}\mathit{5}}$

(5) $\begin{array}{cc}{\mathit{P}}_{\mathit{nD}}={\mathit{Af}}_{\mathit{y}}& \mathrm{for}{\mathit{\lambda }}_{\mathit{D}}\le 0.561\end{array}$

(6) ${\begin{array}{cc}{\mathit{P}}_{\mathit{nD}}=\left(1-\frac{0.25}{{\lambda }_{\mathit{D}}^{1.2}}\right)\frac{{\mathit{Af}}_{\mathit{y}}}{{\lambda }_{\mathit{D}}^{1.2}}& \mathrm{for}{\mathit{\lambda }}_{\mathit{D}}\le 0.561\mathrm{where}{\lambda }_{\mathit{D}}=\left(\frac{{\mathit{Af}}_{\mathit{y}}}{{\mathit{P}}_{\mathit{crD}}}\right)\end{array}}^{\mathit{0}\mathit{.}\mathit{5}}$

The values of P_crL and P_crD were obtained from GBTUL considering a constrained-constrained (C-C) end condition. Table 5 presents the values of λ_L, P_crL, λ_D and P_crD for CP6-18, considering the single U (member A, Figure 11) and the double U (member A + member B, Figure 10). As the CPs are stub columns, the global buckling loads (PnG) were much higher. The values of λ_L, P_crL, λ_D and P_crD were computed for both ends and were very similar for all CPs.

Table 5
Elastic buckling for CP6-18: local (λ_L, P_crL) and distortional (λ_D, P_crD).

CP6-18	PcrL (kN)	PcrD (kN)	λL	λD	RλDL = λL / λD
Single U	12.92	56.03	2.02	0.99	0.49
Double U	24.50	136.40	1.98	0.90	0.46

According to Matsubara et al. (2019), for the case of CFS lipped channel columns with DL slenderness ratio R_λDL = λ_D / λ_L less than 0.45, the local mode is predominant, and for R_λDL greater than 1.05, the distortional mode is predominant. Lipped channel columns with a slenderness ratio R_λDL ranging between 0.45 and 1.05 developed a local and distortional buckling mode interaction, LD. In the present case, the ratio slenderness ratio is R_λDL = 0.49 for single U and 0.46 for double composite U, indicating probable (weak) interaction between local and distortional modes.

As the local buckling was predominant (remember that global buckling is excluded in the present investigation), Table 6 shows the values of the local buckling critical load P_crL, for the non-composite section (member A and B) and fully-composite section (the lowest value obtained between the measured cross-section geometries of the column top and bottom ends). Table 6 shows also the collapse load P_uth obtained from DSM, for the non-composite section (A+B) and fully-composite section, as well as the ratio between them. The ratio fully/non-composite was 1.04 (average) for the collapse load P_uth. As the members A and B are connected with screws at discrete points, the actual condition may be considered in between the non-composite and fully-composite values.

Table 6
Computed values for elastic local buckling P_crL and DSM-based collapse load P_uth.

Column ID	PcrL (kN) - GBTUL			Puth (kN) - DSM
	Member A	Member B	Fully composite	Non composite (A+B)	Fully composite	Fully / Non
CP1-03	12.60	12.35	28.05	54.98	57.63	1.05
CP2-13	12.99	12.78	28.67	55.70	58.09	1.04
CP3-14	12.68	12.57	27.91	55.01	57.04	1.04
CP4-16	12.52	12.06	27.77	55.09	57.95	1.05
CP5-09	12.68	12.83	27.71	55.44	57.56	1.04
CP6-18	12.60	12.92	27.50	55.08	57.44	1.04
CP7-17	12.45	12.95	27.21	55.00	56.85	1.03
CP8-10	12.38	12.66	27.22	54.74	56.82	1.04
Average	12.62	12.65	27.74	55.19	57.48	1.04
Standard deviation	0.29	0.24	0.66	0.50	0.76	0.01
Coef. of variation	2.3%	1.9%	2.4%	0.9%	1.3%	0.6%

5. Comparison of experimental and DSM results

From the experimental tests, it can be observed that members A and B developed a local buckling mode with seven semi-waves and distortional buckling modes with a single wave. The buckling modes were similar to the modes obtained from GBTUL for the non-composite section presented in Figure 11. Figure 9b shows the local buckling in the web of member A started afterwards, with an approximate applied load of 25kN, registered by strain gage E4. Meanwhile, for member B, the on-set of local buckling was 11kN, registered by s.g. E1. The observed performance is explained by the web of member A, partially constrained by the flange of member B (observe Figures 1 and 10).

Table 7 shows the experimental and DSM-based theoretical collapse loads for the tested built-up columns, considering non-composite and fully-composite, as well as the ratio between results. It can be observed that theoretical non-composite hypothesis is in very good agreement with the experimental collapse loads, with an average value of 55.1kN and insignificant standard deviation. These results are sustained by the evidence that the connection between member A and B was not fully effective, as observed during the test.

Table 7
Comparison between experimental and theoretical loads of the built-up lipped channel columns, considering non-composite and fully-composite members.

Column ID	Experimental		Theoretical DSM strength Puth
	Number of screws	Collapse load Puexp	Non composite (members A+B)	Experim. / Non -comp.	Fully composite	Experim. / Fully comp.
CP1-03	2	53.90	54.98	0.98	57.63	0.94
CP2-13	2	55.40	55.70	0.99	58.09	0.95
CP3-14	3	56.05	55.01	1.02	57.04	0.98
CP4-16	3	55.25	55.09	1.00	57.95	0.95
CP5-09	4	53.60	55.44	1.02	57.56	0.98
CP6-18	4	54.55	55.08	0.99	57.44	0.95
CP7-17	5	55.60	55.00	1.01	56.85	0.98
CP8-10	5	53.70	54.74	0.98	56.82	0.95
Average		55.09	55.19	1.00	57.48	0.96
Standard deviation		0.96	0.50	0.02	0.76	0.02
Coef. of variation		1.7%	0.9%	1.5%	1.3%	1.8%

6. Conclusions

Elastic buckling analysis of steel built-up columns was performed with a numerical GBTUL computational program, considering the composite and non-composite hypothesis. The experimental results indicate marginal influence of the connection between members A and B regarding the column strength, with almost no influence of the number of self-drilling screws. These results indicate that the elastic buckling load may be accessed considering non-composite members.

Experimental results clearly indicate not only the presence of local buckling during the tests, but also a distortional mode, as registered by DTs H5, H6 and H8. The collapse load (P_uexp) was very similar between built-up columns, regardless of the number of screws. The average value was 55kN with negligible standard deviation.

The analytical built-up column strength was computed with the help of DSM equations. As the interaction between local and distortional mode can be ignored, with a slenderness ratio R_λDL = λ_D / λ_L = 0.49, quite close to the lower limit value 0.45 stipulated by Matsubara et al. (2019), the DSM rules (Eqs. 1 to 6) are able to estimate the column strength of the built-up lipped channel section. The results indicate accurate comparison between the computed and experimental data with P_uexp / P_uth average value 1.0 and minor coefficient of variation 1.5% (Table 7) for non-composite CFS. It must be observed that the better results of the computed column strength were obtained for the non-composite built-up CFS, following experimental evidence of local buckling mode.

The authors estimate the obtained results contribute to the improvement of design procedures for the case of laced columns composed of built-up thin-walled CFS. The simplified design procedure taking double thickness in the connected elements for the numerical computation of the critical buckling load proved to be useless, other than the actual behavior of the built-up member.

Acknowledgments

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brasil (CAPES) - Finance Code 001, and National Council for Research and Technology, CNPq (Process 161975/2015-1). The authors would like to thank GYPSTEEL Company for the supply of the CFS lipped channels and ARMCO STACO for the supply of the steel end plates.

References

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Publication Dates

• Publication in this collection
  16 Sept 2019
• Date of issue
  Oct-Dec 2019

History

• Received
  09 Feb 2019
• Accepted
  10 June 2019