Experimental study on cold-formed steel lipped channel medium-long columns strengthened longitudinally by steel strips or steel bars

Abstract

Based on the existing methods of reinforcing cold-formed steel lipped channel column, this paper proposed that reinforced the cold-formed steel lipped channel column longitudinally with steel strips or steel bars for the first time. In order to study the influence of section forms and initial stress ratio on axial compression behavior of columns, a series of pin-pin ends axial compression tests were conducted. The experiment specimens contained 20 concentrically loaded specimens with two cross-section shapes, four initial stress ratios, respectively. It was shown that when reinforcing column longitudinally with the reinforcement, under axial compression, the ultimate bearing capacity of the specimens could significantly increase with little change in the quantity of steel. Moreover, the reinforcing effect of the column decreased linearly with an increase in the initial stress ratio (β) of the load-strengthened specimens. Here, unloading or partial unloading reinforcement was recommended, and the initial stress ratio should be lower than 0.3. Finally, the experimental results were compared with the calculation results for the axial bearing capacities of the column based on the current Chinese standard (GB50018-2002) and North American standard (AISI). It indicated that for the section prone to local-global interactive buckling, the result calculated by GB50018-2002 is more accurate, but has a large deviation in calculating the section prone to distortional buckling. Results of direct strength method of AISI are the opposite to the result of GB50018-2002.

Keywords

axial compression experiment cold-formed steel initial stress lipped channel columns load-carrying properties longitudinally reinforced with steel strips or steel bars

Introduction

In recent years, with the vigorous promotion of light steel green building, cold-formed steel lipped channels have been increasingly used as the main load-bearing members of buildings. Over time, ageing, damage, and changes in the service function of the structure in service appear. The carrying capacity of the structure in service may not comply with the current requirements. Therefore, it is necessary to strengthen and transform it.

Anbarasu and Murugapandian (2015) tested 15 webs stiffened lipped channel compression members under pin ended with warping restrained end condition and compared the experimental results with the direct strength method (DSM) in Appendix 1 of the North American Specifications (AISI S100-2012, 2012). Manikandan and Arun (2016) performed a numerical simulation by using finite element analysis software ANSYS and conducted a parametric study of the effects of cross section geometry on the ultimate strength and buckling behavior of cold-formed steel lipped channel columns. Chen et al. (2020) concerned the behavior and ultimate strength of cold-formed steel web-flange-stiffened and web stiffened lipped channel columns undergoing local-distortional buckling interaction.

Yang and Yao (2007) adopted the connecting bars between the two lips are added to improve the distortional buckling load of cold-formed steel lipped channel. Zhang et al. (2017) based on the failure mode of cold-formed thin-walled lipped channel steel purlin, the structure reinforced method by batten plate connected is put forward and the mechanical property of a flexural member is analyzed. Zhou and Chen (2018) found that the batten sheets exert significant influence on both the buckling modes and the ultimate strength of the cold-formed steel lipped channel under positive eccentric loading and axial loading conditions, while they just have few impacts on that of the specimens under negative eccentric compression.

Cold-formed steel (CFS) structures are extensively used in various industries; the structural forms include CFS trusses, space frames, and portal frames (Roy et al. 2019a, 2019c; Taheri et al., 2019). Roy et al. (2018a, 2018b) performed on back-to-back built-up cold-formed steel channel sections under compression. In addition, the axial capacities obtained from the numerical study were used to assess the performance of the American Iron and Steel Institute and Australian and New Zealand Standards. Roy et al. (2018a) and Ting et al. (2018) carried out relevant experimental studies and finite element parameter analysis of CFS columns to consider the influence of section form and other factors on the strength of CFS columns. Selvaraj and Madhavan (2021) studied the influence of slenderness of the section, length and intermediate spacing between self-drilling screws on back-to-back built-up cold-formed steel channel sections. The test results indicate that the axial ultimate strengths of the built-up columns are governed by buckling of the individual channel section and an unstiffened flange element due to higher local buckling stress resulting in an interactive buckling.

Rozylo et al. (2020) presented research was a thin-walled composite column made of CFRP. Also, experimental and numerical tests for the loss of stability and load-carrying capacity of the composite construction were carried out. Kalavagunta et al. (2013) observed that there was significant increase in strength due to CFRP strengthening and proposed the design procedures for the axial load capacity of cold formed steel lipped channel columns strengthened with carbon fiber reinforced polymer (CFRP). Sun et al. (2020) studied the effects of CFRP reinforcement layers, CFRP direction, and CFRP reinforcement position on the ultimate load of CFRP-strengthened cold-formed thin-walled steel lipped channel column. Furthermore, a method for calculating the bearing capacity of the CFRP-strengthened cold-formed thin-walled steel lipped channel column was proposed based on the direct strength methods (DSM).

According to the above literature review, it can be seen that some researches concerning the ultimate bearing capacity of cold-formed steel lipped channel columns after reinforcement have been conducted in the past decades. These reinforcement measures can improve the ultimate bearing capacity of the steel column to a certain extent. However, there are still some points worth to be mentioned, which can be summarized as follows: first of all, V-shaped stiffening will change the shape of the section when the web and flange were rolled longitudinally and the processing technology was more complicated than cold-formed steel lipped channel. What’s more, in actual engineering, the initial imperfections are inevitably randomly distributed on the surface of the experimental piece. Therefore, the reinforcement method of adding a connecting rod at the crest or trough of the half wavelength was likely to fail to achieve the expected reinforcement effect. In addition, built-up cold-formed steel channel sections can improve the ultimate bearing capacity by increasing the amount of steel, so the economic benefit was poor. Finally, for CFRP reinforcement technology, it is urgent to settle the problems of the long processing cycle, poor plasticity, and high cost of CFRP materials.

Given the above, this paper proposed that reinforced the cold-formed steel lipped channel column longitudinally with steel strips or steel bars for the first time. That is to say, in view of the common reinforcement problem of cold-formed steel lipped channel column, put forward a kind of reinforcement method that does not change the original section shape of the member, only reinforced the cold-formed steel lipped channel columns longitudinally by steel strips or steel bars. For the section which prone to distortional (D) buckling, increasing the external constraint of the flange plate can improve the axial bearing capacity of the specimen effectively. So, the solution of HPB400φ6 round steel bars placed longitudinally along with the middle of the crimping edge has been proposed; By limiting the width-thickness ratio of the specimen, the local instability of the specimen can be prevented effectively and then the global instability can be inhibited. In addition, steel strips were used to reinforce inside the web, which can increase the contact area between reinforcement material and specimen to facilitate construction. So, for the section which prone to local-global (LG) interactive buckling, a solution of steel strips placed longitudinally along with the inner three-point of the web has been proposed. In order to understand the effect of reinforcement and the bearing capacity of the reinforced member, the following experimental studies were conducted.

Experimental program

Test specimens

The characteristics of cold-formed steel lipped channels are wide-limbed thin walls and the slenderness ratio has a significant impact on the axial bearing capacity and failure mode. This research was mainly concerned with medium-long columns. The length of the axial compression specimen was 1200 mm. Among them, the MC100 type column mainly studies the distortional (D) buckling, HPB400φ6 round steel bars placed longitudinally along with the middle of the crimping edge has been proposed; the MC90 type column mainly studies the local-global (LG) interactive buckling, a solution of 12 mm × 1.5 mm Q235b steel strips placed longitudinally along with the inner three-point of the web has been proposed. In order to facilitate the reinforcement construction and give full play to the synergistic work of the reinforcement material and specimen, the length of the steel bars and steel stirps had to be reduced by 10 mm at both ends of the specimen (Figure 1).

Figure 1.

Specimen size and reinforcement scheme: (a) cross section details, (b) MC90 type column, and (c) MC100 type column.

The experimental members were carefully labeled so that the section type, reinforcement type and repetition number of the specimen could be included, as shown in Figure 2. MC indicated the length of the specimen; the first number indicated web size of the section; the second number indicated the initial stress ratio of load; the letter a and b at the end meant the two column specimens with the same design parameters, respectively. For example, MC90-2-b is the column with a web size of 90 mm reinforced by a load under the initial stress ratio of 0.2, which has a number b.

Figure 2.

Labeling rule of specimens.

According to GB 50550-2010 (2010), in order to study the influence on the axial compression performance of the column strengthened by steel bars or steel strips under initial stresses, this paper selected initial stress ratios (β) of 0, 0.2, 0.3, and 0.4 to experiment.

Before the experiment, vernier calipers were used to measure the width and thickness of each panel at both ends and the middle of the component. Also, the average value was taken as the actual size of the panel, as recorded in Table 1.

Table 1.

Actual dimensions of MC type column.

Specimens	$H / mm$	$B / mm$		$d / mm$		$t / mm$	$D / mm$	$L / mm$	Geometric imperfection
Specimens	$H / mm$	Left	Right	Left	Right	$t / mm$	$D / mm$	$L / mm$	$δ_{g} / mm$	$δ_{d} / mm$
MC100-a	99.8	99.8	99.7	11.8	11.7	1.47	–	1200.3	0.541	1.245
MC100-b	99.8	99.9	99.6	11.6	11.7	1.49	–	1200.1	0.52	1.324
MC100-0-a	99.9	99.4	99.8	11.6	11.8	1.48	6.22	1200.4	0.496	−1.892
MC100-0-b	99.8	99.8	99.9	11.9	11.8	1.48	6.19	1199.8	0.488	−1.785
MC100-2-a	99.4	99.8	99.7	11.8	11.6	1.48	6.21	1199.9	0.502	1.021
MC100-2-b	99.7	99.9	99.8	11.9	11.7	1.48	6.21	1199.7	0.496	1.156
MC100-3-a	99.5	99.5	99.7	11.6	11.5	1.49	6.19	1200.5	0.511	1.564
MC100-3-b	99.6	99.8	99.9	11.8	11.5	1.47	6.18	1200.4	0.504	1.365
MC100-4-a	99.8	99.7	99.6	11.7	11.7	1.48	6.21	1200.3	0.482	−1.452
MC100-4-b	99.9	99.7	99.5	11.6	11.5	1.49	6.22	1201.1	0.468	−1.257
MC90-a	89.2	40.2	40.3	13.6	13.5	1.48	–	1199.8	−0.334	–
MC90-b	89.3	40.8	40.7	13.6	13.7	1.49	–	1201.3	−0.414	–
MC90-0-a	89.5	40.3	40.5	13.3	13.2	1.48	–	1199.8	0.512	–
MC90-0-b	89.4	40.4	40.3	13.5	13.5	1.48	–	1199.6	0.498	–
MC90-2-a	89.6	40.3	40.1	13.6	13.8	1.47	–	1199.4	0.458	–
MC90-2-b	89.8	40.8	40.9	13.8	13.7	1.49	–	1200.7	0.487	–
MC90-3-a	89.1	40.3	40.1	13.4	13.6	1.48	–	1199.8	−0.502	–
MC90-3-b	89.6	40.7	40.6	13.8	13.8	1.49	–	1200.8	−0.511	–
MC90-4-a	89.4	40.6	40.7	13.3	13.2	1.48	–	1200.2	−0.421	–
MC90-4-b	89.5	40.8	40.9	13.9	13.8	1.48	–	1199.5	−0.452	–

t is the thickness of the steel strip, D means the diameter of the reinforcement, L is the length of the specimen, $δ_{g}$ represents global geometrical imperfections, and $δ_{d}$ represents distortional geometrical imperfections.

Material properties

The structural steel of the cold-formed steel lipped channel column investigated in this study was Chinese Q235B steel. The reinforcement steel strips with a nominal thickness of 1.5 mm were obtained along the longitudinal direction of the web of the tested section by cutting with a plate shearing machine, and the steel bars were HPB400φ6 round steel. The material properties were determined using standard specimen tensile tests. The specimens were processed using the same batch of materials. Based on GB/T 228.1-2010 (2010), three standard tensile plate samples and three circular section samples were used in the reinforcement material properties test. The tensile test was carried out using a universal testing machine. Table 2 summarizes the material information derived from the experimental results. T1.5 means that the thickness is 1.5 mm, G6 means that the diameter is 6 mm. The second number refers to the repeated number. For steel bars, substitute $σ_{0.2}$ for $f_{y}$ . Adhesive materials used for reinforcement were special structural adhesives for epoxy resin quick-setting adhesive steel reinforcement. It’s material performance indexes list in Table 3 (Peng et al., 2012).

Table 2.

Experiment results for material properties of cold-formed thin-walled lipped channel and steel bars.

Specimens	Yield stress		Ultimate tensile stress		Elastic module		Elongation (%)
Specimens	$f_{y} / MPa$	Mean value	$f_{u} / MPa$	Mean value	$E / 10^{5} MPa$	Mean value	Elongation (%)
T1.5-1	274.76	285.44	341.39	353.22	2.04	2.03	29.93
T1.5-2	287.74		355.68		2.02		24.41
T1.5-3	293.81		362.6		2.02		24.28
G6-1	346.65	347.85	500.18	502.19	2.1	2.11	17.65
G6-2	347.94		501.24		2.11		18.98
G6-3	348.97		505.15		2.12		20.01

Table 3.

Performance indexes of structural adhesives.

Elasticmodule $(10^{5} MPa)$	Tensilestrength $(MPa)$	Compressionstrength $(MPa)$	Shearstrength $(MPa)$	Usagetemperature $(° C)$	Positioningtime $(min)$	Curingtime $(h)$
2.48	43.70	85.10	20.10	−60 to 100	5–10	2

Geometric imperfections

The initial imperfections have a significant effect on the bearing capacity of the column. Therefore, the initial imperfections of the experimental piece must be measured before the experiment. For the MC100 type column, the initial bending geometrical imperfections and distortional geometrical imperfections were measured. For the MC90 type column, only the initial bending geometrical imperfections were measured. The initial global measurements were performed on the surface of the experimental members, as illustrated in Figure 3(a). A displacement transducer with an accuracy of 0.01 mm, which attached to a guide, was used to perform the measurements. When experimenting with the global initial geometrical imperfections, the cross sections were measured at intervals of 100 mm for each specimen along the longitudinal direction. The measured maximum absolute values of global geometrical imperfections ( $δ_{g}$ ) for the columns are listed in Table 1 (Roy et al., 2019b). When measuring distortional geometric imperfections, a vernier caliper was used to measure the width of the channel steel web, which was recorded as $b_{1}$ . In addition, the width of the opening direction of the channel steel was measured, which was recorded as $b_{2}$ . The measured maximum absolute values recorded ( $δ_{d} = b_{2} - b_{1}$ ) for the column are listed in Table 1. Positive timing was considered an outward expansion, while the negative was an inward contraction (Figure 3(b)). For example, the initial geometrical imperfections along the length of MC100-a and MC90-a can be seen in Figures 4 and 5.

Figure 3.

Measurement positions for initial geometric imperfections: (a) measurement of initial global imperfections and(b) measurement of initial distortional imperfections.

Figure 4.

Initial geometrical imperfections along the length of MC100-a.

Figure 5.

Initial geometrical imperfections along the length of MC90-a.

Initial stress

In the experiment, load strengthening on structural adhesive needed a certain amount of ageing time to reach the use strength was considered and the load retaining reinforcement was needed in the experiment. The exact process was as follows: Firstly, the specimen was placed on the electro-hydraulic servo pressure experimenting machine with the capacity of the hydraulic jack was 300 kN (Figure 6) and connected to the acquisition system. Secondly, force control was adopted in order to load the specimen to the load corresponding until the initial stress ratios (β) of 0.2, 0.3, and 0.4, respectively. Then, the reinforcement material was bonded to the specimen and the load was kept until the structural adhesive reaches the use strength. Finally, the test was continued.

Figure 6.

Experiment set-up.

Test setup and arrangement of strain gauges and LVDTS:

The uniaxial compression test was conducted for the investigated members on the test rig shown in Figure 6. In order to fix the column, steel end plates with a thickness of 16 mm were welded to the ends of all the test members. The end plates of test members were connected to a designed condition device to model the pin-pin ends (See Figure 7). As a result, the calculating length for MC type columns was assumed to be $L_{0} = l + 242$ mm, where l is the length of the specimen. Since there were L-shape holes on the top plate of the bidirectional hinged supports, it was not difficult to center the MC type columns.

By referring to the pre-experiment finite element analysis and prediction, in this paper, the strain gauges and displacement measurements (LVDTs) of MC type column were positioned at the middle height, 1/3 height and 2/3 height of the column, respectively. A LVDT was arranged vertically at the bottom steel end plate. The numbers and positions of the strain gauges for the MC90 type column and MC100 type column were slightly different. They were used to measure the local deformation and distortion, respectively. The corresponding strain gauge was arranged at the corresponding position of the reinforcement material to observe whether the specimen deform in coordination with the reinforcement material. The specific arrangement and numbering of the strain gauge and LVDTS were shown in Figure 8.

Figure 7.

Bidirectional hinged support: (a) configuration of the support and (b) connections between the support and experimental members.

Figure 8.

Gauge arrangement.

The compressive load was applied on the bottom end of the column by using a capacity servo-controlled hydraulic jack with an approximate 1 kN/min loading rate. The load, deflections, and strains were measured simultaneously by a data acquisition system and recorded on a computer.

Test results

MC100 type column

In this paper, the MC100 type column which prone to distortional (D) buckling was selected for the test. For the MC100 type column, the solution of HPB400φ6 round steel bars placed longitudinally along with the middle of the crimping edge has been proposed. As an example, Figure 9 shows the typical failure modes of the MC100 type column, respectively.

Figure 9.

Failure mode photos of MC100 type column: (a) MC100-b, (b) MC100-0-b, (c) MC100-2-b, (d) MC100-3-b, and (e) MC100-4-b.

The experimental results show that the MC100 type column has no bending along the weak axis and two flanges all have distortional (D) buckling in opposite directions. Under the action of axial pressure, the specimens are deformed by two half waves (Figure 9). In addition, it can be seen that there were two modes of distortional buckling: outward-expanding distortional (OD) buckling and inward-contracting distortional (ID) buckling (Figure 10(a) and (b)). What’s more, the flange-edging assembly will produce large plastic deformation at the most concave deformation and result in failure. In the end, the reinforcement materials do not fall off all the time in the whole loading process, which indicates that the method of HPB400φ6 round steel bars placed along with the middle of the crimping edge longitudinally for the MC100 type column is feasible (Figure 10(c)). To sum up, for the MC100 type column, the failure modes of unreinforced and reinforced members were D buckling and the MC100 type column displayed a significant post-buckling strength, which is due to the large inertia moment and small slenderness ratio of the MC100 type column, so the global buckling does not take place.

Figure 10.

Deformation photos of MC100: (a) outward-expanding distortional buckling, (b) inward-contracting distortional buckling, and (c) joint deformation of reinforcement.

As can be seen from Figure 11, the specimen deformation is not obvious at the initial stage of loading. When the load increased to about 50% of the ultimate load, the deformation begins to appear and develop rapidly. For the MC100-a, the values of LVDT4 and LVDT6 increase negatively while the values of LVDT7 and LVDT 9 increase positively when the load reaches the ultimate load. On the contrary, for all the other specimens, the values of LVDT4 and LVDT6 increase positively while the values of LVDT7 and LVDT9 increase negatively when the load reaches the ultimate load (Figure 11). It indicates that for MC100-a, the maximum outward-expanding distortional (OD) buckling occurs near the 1/3 height of the specimen, while the maximum inward-contracting distortional (ID) buckling of the specimen occurs near the middle height of the specimen. In contrast, the maximum OD buckling of other specimens occurs near the middle height of the specimen, while the maximum ID buckling occurs near 1/3 height of the specimen. In addition, the final values of LVDT4 and LVDT6 at the middle height of the specimen and the values of LVDT7 and LVDT9 at the 1/3 height of the specimen are relatively close before reinforcement and the final deformation amount is relatively large. However, the maximum deformation is smaller than that of the unreinforced specimen. It demonstrates that for the MC100 type column, the method of HPB400φ6 round steel bars placed longitudinally along with the middle of the crimping edge can improve the axial bearing capacity and restrict the deformation of the experimental piece.

Figure 11.

Load-lateral displacement curve of MC100 type column: (a) MC100-b, (b) MC100-0-b, (c) MC100-2-b, (d) MC100-3-b, and (e) MC100-4-b.

In order to observe the strain development law of reinforced material and original member material under load. The load-strain curves of the crimping edge and steel bars of MC100-3-a at the same section are recorded, as shown in Figure 12. It can be seen that during the loading of the specimen, with the load increases, the strain of the steel and the steel bars at the same position changes synchronously. It demonstrates that the steel bars and the specimen deform in coordination during the whole loading process. Also, there is no slipping or even falling off the steel bars, which shows the reliability of the paste again.

Figure 12.

Load-strain curve of MC100-3-a at reinforcement of coil edge.

The load vs. axial displacement curves of the MC100 type column are illustrated in Figure 13. The experimental results of the same group of “a” and “b” specimens were similar. In this paper, only the corresponding curves of the serial number of each section “b” specimen are given. First of all, As shown in the graph, after the column was reinforced, the extreme point of the curve is obviously higher than that of the unreinforced column. It indicates that the ultimate bearing capacity of the strengthened column is increased to some extent. What’s more, when the ultimate bearing capacity of the specimen is achieved, the curve drops rapidly. Before the extreme point in the Figure, the slope of the curves of the reinforced columns are larger than that of the unreinforced column. It is shown that after the column was reinforced, the stiffness of the member increases obviously, the buckling failure of the member has been delayed and its ultimate bearing capacity improves greatly. The reinforcement effect was also realised.

Figure 13.

Load versus axial displacement curves of MC100 type column.

The experimental results of the MC100 type column are listed in Table 4. It can be observed that after the column was reinforced, the amount of steel used by members only increased by 11.7% and the ultimate bearing capacity of the members increases significantly, with the maximum increase of 35.1%. In addition, with the increase of the initial stress (β) of the original steel columns strengthened by load, the increased amplitude of the stiffness, bearing capacity and deformation capacity of the column strengthened by reinforcement decreased. When the initial stress ratio (β) is 0.4, the increase of bearing capacity of reinforced steel columns is only 4.44%. In the end, the method of reinforcement is equivalent to setting a small column at the crimping edge, which increases the external constraints of the flanges and improves the bearing capacity of the specimens effectively.

Table 4.

Experimental results of MC100 type column.

Specimens	$P / kN$	$P_{1} / kN$	Load mode	Failure mode	Mean value	$Δ P / %$	$A / kg$	$Δ A / %$	$Δ P / Δ A$
MC100-0-a	52.80	–	No pre-load	D	52.96	–	4.493	–	–
MC100-0-b	53.11	–	No pre-load	D	52.96	–	4.493	–	–
MC100-1-a	71.36	–	No pre-load	D	71.55	35.1	5.017	11.7	3.00
MC100-1-b	71.73	–	No pre-load	D	71.55	35.1			3.00
MC100-2-a	65.12	10.36	Pre-load	D	65.76	24.17			2.07
MC100-2-b	66.41	10.42	Pre-load	D	65.76	24.17			2.07
MC100-3-a	60.21	15.54	Pre-load	D	60.44	14.12			1.21
MC100-3-b	60.67	15.63	Pre-load	D	60.44	14.12			1.21
MC100-4-a	55.58	20.72	Pre-load	D	55.31	4.44			0.38
MC100-4-b	55.04	20.84	Pre-load	D	55.31	4.44			0.38

P represents the ultimate load of the specimen; $P_{1}$ represents initial load before reinforcement; $Δ P$ represents the percentage increase in carrying capacity; $D$ represents distortional buckling; A represents the amount of steel used for a single specimen; $Δ A$ represents a percentage increase in steel usage; $Δ P / Δ A$ represents the carrying capacity-to-weight ratio.

MC90 type column

In this paper, the MC90 type column which prone to local-global (LG) interactive buckling was selected for the test. For the MC90 type column, the solution of steel strips placed longitudinally along with the inner three-point of the web has been proposed. The experimental results show that the deformation of the MC90 type column is mainly concentrated in the middle height of the specimen. Also, the ultimate failure mode of the unreinforced specimens is local buckling of the web and flange and the global instability of the specimens. For reinforced specimens, there are two failure modes, one is local-global (LG) interactive buckling, the other is distortional-global (DG) interactive buckling. Figure 14 shows the typical failure modes of the MC90 type column, respectively. As can be seen from Figure 14, The failure mode of the unreinforced specimen is local-global (LG) interactive buckling, when the initial stress (β) of the original steel columns strengthened by load reaches 0.2, the failure mode of the reinforced specimen changes to distortional-global (DG) interactive buckling.

Figure 14.

Failure mode photos of MC90 type column: (a) MC90-b, (b) MC90-0-b, (c) MC90-2-b, (d) MC90-3-b, and (e) MC90-4-b.

It can be seen from Figure 15 that under the action of axial pressure, the value of LVDT5 rises vertically along the vertical axis at the initial stage of loading. It indicates that no bending displacement around the weak axis at this stage and the specimen is well aligned. With the increase of load, for the specimens with DG interactive buckling, the values of LVDT5, LVDT4, and LVDT6 increased positively, resulting in outward-expanding distortional (OD) buckling. On the contrary, for the specimens with LG interactive buckling, the LVDT5 increases negatively and the values of LVDT4 and LVDT6 increases positively, resulting in OD buckling. In addition, the value of LVDT5 at the web increases gradually with the load increasing, while the values of LVDT4 and LVDT6 at the flange hardly change before the load reaching the limit load. After reaching the ultimate load, the values of LVDT4 and LVDT6 increase rapidly. It is shown that the global (G) buckling precedes the distortional (D) buckling and the local (L) buckling. So, the final ultimate failure mode is interactive buckling.

Figure 15.

Load-lateral displacement curve of MC90 type column: (a) MC90-b, (b) MC90-2-b, (c) MC90-3-b, and (d) MC90-4-b.

As can be seen from Figure 16, the strain of the web and steel strip changes synchronously at the same position during the initial loading of the specimen. With the increase of load, the specimen begins to exhibit G buckling, the strain gauges are reversed, the compressive strain on the web continued to increase, while the tensile strain on the steel strip continued to increase. Because of the L buckling occurred at the middle height of the specimen, the tensile strain of the steel strip and the compressive strain of the web are the largest.

Figure 16.

Load-strain curve of MC90-3-a at reinforcement of steel belt.

It can be viewed on Figure 17 that the material strength and the ultimate capacity of the MC90 type column are significantly improved after been reinforced and the effect of reinforcement is significant. The law is similar to that of MC100 type column.

Figure 17.

Load versus end shortening curves of MC90 specimens.

The experimental results of the MC90 type column are listed in Table 5. It can be seen that after the column was reinforced, the amount of steel used by members only increases by 12.15% and the ultimate bearing capacity of the members increases significantly, with the maximum increase of 31.74%. Furthermore, with the increase of the initial stress (β) of the original steel columns strengthened by load, the increased amplitude of the bearing capacity of the column strengthened by steel strips decreased. When the initial stress ratio is 0.4, the bearing capacity of the reinforced steel column increases by only 2.94%. Finally, for the MC90 type column, the moment of inertia is compact and the slenderness ratio is large relatively. The failure of the specimens is accompanied by G buckling. It is found that the MC90 type column is finally destroyed by the interactive buckling in the experiment.

Table 5.

Experimental results of MC90 type column.

Specimens	$P / kN$	$P_{1} / kN$	Load mode	Failure mode	Mean value	$Δ P / %$	$A / kg$	$Δ A / %$	$Δ P / Δ A$
MC90-a	51.55	–	No pre-load	LG	51.39	–	2.741	–	–
MC90-b	51.22	–	No pre-load	LG	51.39	–	2.741	–	–
MC90-0-a	67.54	–	No pre-load	DG	67.70	31.74	3.074	12.15	2.61
MC90-0-b	67.86	–	No pre-load	DG	67.70	31.74			2.61
MC90-2-a	61.83	10.31	Pre-load	DG	61.62	19.91			1.64
MC90-2-b	61.41	10.24	Pre-load	DG	61.62	19.91			1.64
MC90-3-a	59.19	15.47	Pre-load	LG	58.85	14.52			1.20
MC90-3-b	58.50	15.37	Pre-load	LG	58.85	14.52			1.20
MC90-4-a	52.50	20.62	Pre-load	LG	52.90	2.94			0.24
MC90-4-b	53.29	20.49	Pre-load	LG	52.90	2.94			0.24

P represents the ultimate load of the specimen; $P_{1}$ represents initial load before reinforcement; $Δ P$ represents the percentage increase in carrying capacity; $D$ represents distortional buckling; $G$ represents global buckling; $L$ represents local buckling; A represents the amount of steel used for a single specimen; $Δ A$ represents a percentage increase in steel usage, $Δ P / Δ A$ represents the carrying capacity-to-weight ratio.

Current design rules

GB50018-2002

At present, the effective width method of Chinese (CEWM) to calculate the ultimate load of cold-formed thin-wall channel steel and the effective width method is written into GB 50018-2002 (2002). GB 50018-2002 (2002) use $P_{n}^{1}$ , which can be calculated according to equation (1):

P_{n}^{1} = φ A_{e} f

(1)

b_{e} = {\begin{matrix} b b / t < 18 α ρ \\ (\sqrt{\frac{21.8 α ρ}{b / t}} - 0.1) b 18 α ρ < b / t < 38 α ρ \\ \frac{25 α ρ}{b / t} b b / t > 38 α ρ \end{matrix}

(1a)

k_{1} = {\begin{matrix} \frac{1}{ξ} ξ < 1.1 \\ 0.11 + \frac{0.93}{{(ξ - 0.05)}^{2}} ξ > 1.1 \end{matrix}

(1b)

where

ξ = \frac{c}{b} \sqrt{\frac{k}{k_{c}}}, ρ = \sqrt{\frac{205 k_{1} k}{σ_{1}}}, σ_{1} = φ f

(1c)

In accordance with equation (1), the coefficient of calculation $α = 1.0$ and the coefficient of uneven distribution of compressive stress $ψ = 1$ . The coefficient for the compressive stability of the web is taken into account according to the reinforced plate, with a value such as $k = 4$ for the MC100 type column. The coefficient of compressive stability for the flange is taken into account according to the reinforced plate, with a value such as $k = 4$ for the MC90 type column. The coefficient of compressive stability for the flange is taken into account according to a partially reinforced plate, with a value such as $k = 0.98$ . The coefficient of compressive stability for an edge is taken into account according to a non-reinforced plate, with a value such as $k = 0.425$ .

AISI

In the North American AISI code, the effective width method of American (AEWM) is used to calculate the axial bearing capacity ( $P_{n}^{2}$ ) of cold-formed thin-walled steel members as follows:

p_{n}^{2} = A_{e} F_{n}

(2)

b_{e} = {\begin{matrix} b λ < 0.673 \\ \frac{1}{λ} (1 - \frac{0.22}{λ}) b λ > 0.673 \end{matrix}

(2a)

F_{n} = {\begin{cases} ({0.658}^{λ_{c}^{2}}) F_{y} λ_{c} < 1.5 \\ (\frac{0.877}{λ_{c}^{2}}) F_{y} λ_{c} > 1.5 \end{cases}

(2b)

where

λ = \frac{1.052}{\sqrt{k}} (\frac{b}{t}) \sqrt{\frac{f}{E}}, λ_{c} = \sqrt{\frac{F_{y}}{F_{e}}}, F_{e} = \frac{π^{2} E}{{(KL / r)}^{2}}

(2c)

In 1998, after Schafer et al. proposed the direct strength method (Hancock, 2003; Schafer, 2002, 2008), the North American cold-formed steel specification also adopted the calculation equation of the direct strength method. The current direct strength method (DSM), adopted in AISI S100-2012 (2012), takes global (G) buckling, distortional (D), buckling and local-global (LG) interaction buckling into account, which yields the following:

P_{n}^{3} = min (ϕ_{c} P_{ne}, ϕ_{c} P_{nl}, ϕ_{c} P_{nd})

(2c)

Where $ϕ_{c}$ is the resistance coefficient of the axial compression member, set at 0.85;

P_{ne} = {\begin{cases} (0 {. 658}^{λ_{c}^{2}}) P_{y} λ_{c} \leq 1.5 \\ (\frac{0.877}{λ_{c}^{2}}) P_{y} λ_{c} > 1.5 \end{cases}

(3a)

P_{nl} = {\begin{matrix} P_{ne} λ_{l} \leq 0.776 \\ [1 - 0.15 {(\frac{P_{crl}}{P_{ne}})}^{0.4}] {(\frac{P_{crl}}{P_{ne}})}^{0.4} P_{ne} λ_{l} > 0.776 \end{matrix}

(3b)

P_{nd} = {\begin{matrix} P_{y} λ_{d} \leq 0.561 \\ [1 - 0.25 {(\frac{P_{crd}}{P_{y}})}^{0.6}] {(\frac{P_{crd}}{P_{y}})}^{0.6} P_{y} λ_{d} > 0.561 \end{matrix}

(3c)

where $λ_{c} = \sqrt{P_{y} / P_{cre}}$ , $P_{y} = A F_{y}$ $λ_{l} = \sqrt{P_{ne} / P_{crl}}$ , $P_{crl} = A f_{crl}$ , $λ_{d} = \sqrt{P_{y} / P_{crd}}$ , $P_{crd} = A f_{crd}$ , and A is the gross cross-sectional area. $P_{cre}$ , $P_{crl}$ , and $P_{crd}$ are the elastic critical local, distortional, and overall buckling loads, respectively. $P_{ne}$ , $P_{nle}$ , and $P_{nd}$ are the nominal overall buckling strength, local-global interaction buckling strength, and distortional strength, respectively.

Since one has $P_{nle} \leq P_{ne}$ , the actual nominal strength of the column always corresponds to the lower of the two values between the local-global interactive ( $P_{nle}$ in equation (3b)) and distortional ( $P_{nd}$ in equation (3c)) failure loads.

Comparison of results from experiment and design method

The CEWM, AEWM, and DSM were used to calculate the axial capacity of the MC90 type column and the MC100 type column. The performance of the three methods was compared and verified by using the test results in this study. As listed in Table 6, the calculation results of unreinforced columns specifications were in good agreement with the experimental results. As for MC90-0, the results calculated by CEWM were in good agreement with the experimental results, while the calculation results of the AEWM and DSM were biased toward safety. However, for MC100-0, the results calculated by CEWM and the AEWM were much higher than the experimental results, which were unsafe. This was due to the fact that distortional (D) duckling was calculated as a local buckling in terms of AEWM and the D buckling was lower than the post-buckling strength of the local (L) buckling. Although CEWM did not directly put forward the concept of D buckling, based on the consideration of the relevant role of plate sets, in the calculation of effective width, the constraint coefficient of plate group ( $k_{1}$ ) was introduced. Nevertheless, the $k_{1}$ was the same for the calculation of CEWM, so there was a big gap in the calculation of complex section types. To sum up, for the MC90 type column with interactive buckling, the calculation results of CEWM were more accurate. For the MC100 type column with D buckling, the calculation results of DSM were more accurate.

Table 6.

Comparison of the results of axial pressure calculation and experiment between Chinese and American codes.

Specimens	P	$P_{n}^{1}$	$P / P_{n}^{1}$	$P_{n}^{2}$	$P / P_{n}^{2}$	$P_{n}^{3}$	$P / P_{n}^{3}$
MC90	51.39	49.99	1.028	45.25	1.136	47.7	1.077
MC90-0	67.7	66.42	1.019	50.63	1.337	60.44	1.120
MC90-2	61.62	66.42	0.928	50.63	1.217	60.44	1.020
MC100	52.96	51.23	1.034	54.96	0.964	50.87	1.041
MC100-0	71.55	91.1	0.785	88.1	0.812	69.24	1.033
MC100-2	65.76	91.1	0.722	88.1	0.746	69.24	0.950

P represents the ultimate load of the specimen, $P_{n}^{1}$ represents the ultimate load of specimen calculated by GB50018-2002, $P_{n}^{2}$ represents the ultimate load of specimen calculated by the effective width method of AISI, $P_{n}^{3}$ represents the ultimate load of specimen calculated by the direct strength method of AISI.

It can be seen from Figure 18 that with the increase of the initial stress ratio (β), the bearing capacity of the experimental axial compression decreased linearly. However, the calculation results of the above specifications were independent of the initial stress ratio, which indicated that there was no relevant regulation on the load reinforcement class members. Therefore, it is necessary to study this kind of component especially.

Figure 18.

Comparison of axial pressure calculation and experiment between Chinese and American codes: (a) reinforcement of MC90 type column and (b) reinforcement of MC100 type column.

Conclusions

In this paper, the axial bearing capacity of the cold-formed steel lipped channel medium-long columns were studied through experiments. Two types of typical specimens, the MC100 type column prone to distortional buckling and the MC90 type column prone to local-global interactive buckling, were selected for the axial compression tests. The effects of the initial imperfections before reinforcement and initial stresses of the members under load reinforcement were considered, with the following conclusions.

The MC90 type column and the MC100 type column adopted the different method of reinforcement respectively, which can improve the ultimate bearing capacity and restrain the deformation of the specimens. Consequently, the longitudinal transfixion stiffening position shall be selected according to the deformation characteristics of the original specimens.

With the increase of the initial stress ratio, the increase of the axial bearing capacity of the reinforced column decreased and the strength utilization ratio of the newly reinforced material is reduced. Therefore, when the structure is strengthened, the original structure should be unloaded or partially unloaded to reduce the initial stress ratio as far as possible. So that the steel column after reinforced can work in coordination with the reinforced material. In this paper, it is suggested that the initial stress ratio should not exceed 0.3 for strengthening MC type column.

The effective width method of Chinese was more accurate in calculating the MC90 type column that is prone to local-global interactive buckling, but had a large deviation in calculating the MC100 type column that is prone to distortional buckling. In addition, when using the effective width method of American to calculate, there was a considerable deviation for the calculation results of these two kinds of column. What’s more, when using the direct strength method to calculate, the calculation results of the MC90 type column were conservative and the calculation results of the MC100 type column were in good agreement. Finally, there was no regulation for load-strengthened members. So, it is necessary to conduct special research on the calculation of such members.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are sincerely appreciated to the financial support as following: 1. The Natural Science Foundation of Shaanxi Province China 2019JM-522; 2. The Fundamental Research Funds for the Central Universities, CHD 300102289104.

ORCID iD

Jianfeng Chen

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