Twenty-six cold-formed steel lipped channel columns with and without slotted web holes were tested to failure. The overall view of axially-compressed columns tests arrangement is shown in Fig. (1). -The column specimens bear directly to the steel plates to simulate the fixed-fixed support. The columns compression tests were performed with 200kN hydraulic jack testing machine. Near the 90% ultimate strength, the static load was paused for half minute and loaded again. This allowed the stress relaxation with the occurrence of the plastics. A data acquisition system was used to record the displacement and load during the tests. Displacement control was adopted to drive the hydraulic actuator a constant rate of 0.3 mm/min for the axially-compressed tests. Three displacement transducers were positioned at the flange and web to measure the distortional buckling and local buckling. One transducer was positioned at the top support plate to record the vertical displacement of specimen.

The four kinds of slotted web hole types Fig. (2) are selected to test for the axially compressed members, where the location of holes for the specimens with one row holes is at the mid-height of the columns, and the location of holes for the specimens with two rows holes is at the 1/3 and 2/3 height of the columns. The nominal length (L_h) and width (H_h) of the slotted hole are 25mm and 14mm and the nominal vertical (S₁) and transverse (S₂) distance of holes are 250 and 50mm.

Fig. (2). Holes type of the web for specimens.

The dimensions and nomenclature for each specimen are presented in Fig. (3), and the measured value was recorded at the 1/4 and 1/2 length points for every specimen, so there were three measurement locations for each specimen. The measured mean values for specimens are summarized in Table 1. The inside bend radius of specimens is 2t, where t is the base thickness of members. The test specimens were labeled with characteristic information so that each column can be easily identified. For example, the label “AC-12-SH-1”, where “AC” means axially-compressed member, “12” refers that the holes type is two holes in one row, “SH” means slotted hole, If a test was repeated, then a symbol of “1” was added which means different repeated group.

Fig. (3). Specimen measurement nomenclature.

Fig. (4). Local buckling mode.

Tension tests were carried out following the provisions of Metallic materials--Tensile testing--Part 1: Method of test at room temperature (GB/T228.1-2010) [18]. Six tensile coupons were cut from two ends of a test member including the web flat and two flanges flat. A 200kN capacity testing machine was used for applying loading. The mean value of six coupons test results is calculated. The specimen yield stress, f_y, is 295 MPa, the steel elastic modulus, E, is assumed as 2.072x10⁵ Mpa, and the elongation of the specimens is 31.85%.

The thin shell finite element non-linear analysis in ABAQUS was employed to simulate the experimental behavior of lipped channel compressed members with slotted web holes. At the two ends of the member, the fixed-fixed boundary condition was used.

The material model was based directly on the coupon tests. The ideal elastic-plastic curve was used based on the experimental steel elastic modular and yield stress which were the average values of the test results for simplifying finite element analysis. Residual stresses, residual strains and cold-work of forming effects were not included in the finite element model.

The ABAQUS S9R5 thin shell element was adopted to model compressed members with web holes. The element aspect ratio was kept below 3:1 along the length direction. In the cross-section, 6, 24, 2, and 2 elements were used for the flange, web, lip, and corner, respectively. The ABAQUS solution control employed was the modified Riks method and the arc length method.

Imperfection sensitivity was considered in the finite element analysis. The magnitudes of the geometric imperfections adopted were L/750 according to Chinese cold-formed steel specification, where L is the length of member. The shape of the geometric imperfection was obtained from the first buckling mode shape of the finite element Eigen buckling analysis. The finite element model for specimen and the mesh of the slotted web holes are depicted in (Fig. 7).

The critical elastic local buckling strength (P_crl), distortional buckling strength (P_crd), and ultimate yield strength (P_y) are provided in Table 3 for compressed columns with different hole types and without hole. The nominal dimensions are used in the Eigen-value elastic buckling analysis.

Fig. (7). Finite element model.

Fig. (8). Comparison on local buckling mode.

The comparison in Table 3 illustrates that the slotted web hole has a little influence on elastic local buckling strength for axially compressed columns, but the effect is not significant because the ratio of the width of hole to the width of web is 0.14 approximately. Because the local buckling occur mainly at the proximity of holes for members with larger cross-sectional area of holes as shown in Fig. (8), the elastic buckling strengths of AC-12-SH and AC-22-SH are higher than AC-11-SH and AC-21-SH. However, the slotted web holes have a significant influence on elastic distortional buckling strength of axially compressed columns, especially for columns with wider web holes cross-sectional area . The elastic distortional buckling strengths of AC-11-SH and AC-21-SH are higher than AC-12-SH and AC-22-SH because the web with wider holes area has lower torsional stiffness for flange.

The first local buckling and distortional buckling shapes for axially-compressed columns with different hole types and without hole are compared in (Figs. 8 and 9).

Fig. (9). Comparison on distortional buckling mode.

The comparisons in Figs. (8 and 9) illustrate that the web holes have no significant effect on elastic local and distortional buckling half-wave length when the ratio of the width of hole is very small for the axially compressed columns, but the deformation of cross section located at the holes of column is bigger than that of other cross sections.

Fig. (10). Failure modes of columns with slotted holes.

The buckling modes for the typical specimens obtained by the FEM are presented in Fig. (10), which is agreed to the test failure modes depicted in Figs. (4 and 5) The local and distortional buckling can occur for the columns with slotted web holes. This observation suggests that the FE model can model the buckling mode of columns with slotted holes.

The ultimate compressed capacities (P_ABA) obtained from the FEM are compared with the experimental ultimate capacities (P_t) as shown in Table 4 for each specimen. The mean value of the FEM-to-experimental ultimate compressed capacities ratio is 1.0172 with the corresponding coefficient of variation of 0.015 for all compressed specimens. The comparisons of the ultimate capacities demonstrate that the ultimate compressed capacities obtained from the FEM are close to the experimental ultimate capacities and the FE model can also predict the ultimate compressed capacity.

The load-compressed deformation curves for different holes analyzed using finite element method are illustrated in Fig. (11), where the cross-sectional dimensions of columns are the nominal section dimensions. As shown in Fig. (11), the holes have no effect on the stiffener of columns with slotted web holes because the local buckling occurs at the end of the column and the distortional buckling approaches near to the global flexural buckling. But the holes can decrease the load-carrying capacities.

The Mises stress graph and load-compressed deformation curves of columns with different holes dimension are shown in Figs. (12 and 13). The height of holes is 50mm and the total transverse width of holes is 50mm,but the space of holes is different. For example, as shown in Fig. (12a), the width of holes is 10mm, the space of holes is 30mm because the total width of holes is 50mm. As shown in Fig. (12), the distortional buckling occurs for all columns and the maximum stress occurs at the middle height. As shown in Fig. (13), the width of single hole has less effect on ultimate strength if the total width of all transverse holes of column is same. So the ultimate strength of column with multiple transverse holes approximates to equal to the ultimate strength of column with single hole which has the same transverse width to the multiple holes. The multiple holes have a little effect on the stiffeness of column with slotted web holes. The wider the net width of whole holes is, the lower the stiffeness of axially-compressed column is.

Fig. (11). Load- compressed deformation curves for columns with different holes in nominal dimension.

Fig. (12). Mises stress graph of columns with different width of single hole.

Two calculated method are used to predict the ultimate capacity of each specimen and evaluate every design method: (1) The Chinese cold-formed steel specification GB5018-2002, (2) The North America cold-formed steel specification AISI-S100 (2016).

The ultimate capacities of every specimen calculated using Chinese cold-formed steel specification and North America cold-formed steel specification are provided in Table 4, including ratios of predicted-to-test capacities of each specimen for two design methods, Where P_CI and P_C are the ultimate capacity predicted using Chinese cold-formed steel specification considering the interaction of the elements and without considering the interaction of the elements, P_N is the calculated results using North America cold-formed steel specification.

The mean values of the ratios of calculated compressive capacities to test results P_CI and P_C obtained using Chinese specification considering the interaction of the elements and without considering the interaction of the elements are 1.0225 and 1.0663, respectively. The comparison results indicate that the current Chinese cold-formed steel specification is not safe to predict the ultimate capacity of column with slotted web holes because the code doesn’t consider the effect of the holes. So the proposed method for predicting the ultimate capacity of compressed column with slotted web holes should be analyzed and put forward based on the Chinese cold-formed steel specification.

However the mean value of the ratios of calculated compressive capacities to test results using North America cold-formed steel specification is 0.9466 with the corresponding coefficient of variation of 0.0321 for columns with holes. The comparison demonstrates that North America cold-formed steel specification takes into account the effect of slotted web holes and is conservative.

Fig. (13). Load-compressed deformation curves of columns with different width of single hole.

The model proposal should be investigated based on the existing EWM in Chinese cold-formed steel specification in order to consider the reduction of capacity because of the influence of slotted web holes of axially compressed columns.

The effective width of the web with slotted holes proposed for Chinese cold-formed steel specification can be determined using Eq.1 based on Chinese cold-formed steel specification and calculated method for the effective width of the element with slotted holes in North America cold-formed steel specification when the compressive strength of columns with the slotted web holes are calculated.

(1)

Where b_enh is the effective width of the web without considering the influence of the slotted holes, and b_eh is the effective width of the web considering the influence of slotted holes.

b_enh is calculated using Eq.2 based on Chinese cold-formed steel specification.

(2)

where b and t are the width and thickness of the element, respectively; α is a coefficient, and α=1.15-0.15ψ, ψ is an uneven coefficient of the compression stress distribution (for axially-compressive members, ψ=1); b_c is the compressive width of the plate; ρ is a calculating coefficient, k₁ is the interaction coefficient due to the adjacent element, k₁ equals to 1 when the interaction effect of plates is ignored, k is the stability coefficient of the element under compression, k equals 4 for the web of the axially compressed members when the influence of slotted holes is not considered.

b_eh is estimated using Eq.2 based on Chinese cold-formed steel specification, but the plates adjacent to the slotted hole or multiple slotted holes are as the unstiffened strip and k of the unstiffened strip should be calculated using Eq.3 when the influence of slotted holes is considered [11] refer to the North America cold-formed steel specification.

(3)

Where L_h and b_u are the length of slotted hole and the width of unstiffened strip.

Meanwhile, the effective width of web with slotted holes should be less than the net section width of web as Eq.4.

(4)

Where b_h is the total width of the slotted holes.

The ultimate capacities of each specimen calculated using proposed method are provided in Table (4), P_S1 and P_S2 are the ultimate capacity calculated using proposed method considering the interaction of the plates and without considering the interaction of the plates, respectively. The mean values of ratios of predicted results P_S1 and P_S2 using the proposed method to test results are 0.883 and 0.9277 with the corresponding coefficient of variation of 0.0545 and 0.0514, respectively. The comparisons indicate that the proposed method is conservative and can be used to calculate the ultimate capacity of the specific compressive column with slotted web holes studied in this paper.