Distortional buckling behaviour of intermediate coldformed steel lipped channel section with various web stiffeners under compression
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Abstract
The aim of the study is to investigate the distortional buckling behaviour of intermediate coldformed lipped channel section under pinned end condition subjected to axial compression. An extensive test and numerical investigation of coldformed lipped channel column with various types of intermediate web stiffeners is presented. In this study, three types of intermediate web stiffeners are chosen such as V, U and Σ. The entire crosssectional dimensions meet with the prequalified column dimension given in Direct Strength Method for coldformed steel structures. Totally, 12 columns are tested and results are compared with the numerical analysis. Numerical analysis is carried out using software ABAQUS. Material and geometric imperfections are incorporated in the FE model. Selected section dimensions met with the distortional buckling mode. Good correlation is achieved between experiment and finite element analysis. All the results are compared with the Direct Strength Method specifications for coldformed steel structures. Based on the comparison of results, a suitable design modification is proposed. Furthermore, results are verified with the existing results which are available from the literature.
Keywords
Distortional buckling Intermediate column Lipped channel column Web stiffeners Design equationIntroduction
The primary advantages of the coldformed steel section are high strength to weight ratio, low self weight, easy lifting and fabrications, etc. Open sections are normally used in the industry. The basic failure modes are local buckling, distortional buckling, flexural buckling, torsional buckling or interaction between them. The buckling characteristics depend on the shape and the slenderness ratio of the crosssectional profile.
Hancock (1985) studied the distortion mode of buckling. Kwon and Hancock (1992) described a design curve for sections undergoing distortional buckling. Schafer and Pekoz (1998a, b) adopted a new procedure for calculating the effective width of stiffened elements with multiple longitudinal intermediate stiffeners. Yan and Young (2002) discussed the behaviour of coldformed steel channels with complex stiffeners subjected to pure axial compression. Yang and Hancock (2004) described a series of compression tests on lipped channel section columns fabricated from coldreduced highstrength steel of thickness 0.42 mm with nominal yield stress 550 MPa. The test results show that distortional buckling and the interaction of local and distortional buckling may have a significant effect on the strength of the section. Zhang et al. (2007) were presented an investigation on coldformed channels with inclined simple edge stiffeners under compression. Liu (2008) presented a crashworthiness design of regular multicorner thinwalled columns with different types of cross sections and different profiles, including straight octagonal columns and curved hexagonal columns.
Kwon et al. (2009) described a series of compression tests on coldformed simple lipped channels and lipped channels with intermediate stiffeners in the flanges and web. Nguyen and Kim (2009) studied the buckling of thinwalled composite columns in hat sections and lipped channel sections reinforced with web stiffener under axial compression. Chen et al. (2010) conducted a series of stub column tests on complex sections with intermediate stiffeners. It was shown that the intermediate stiffeners could effectively enhance the local buckling stress sections. Yap and Hancock (2011) described the design and testing of webstiffened highstrength steel coldformed lipped channel sections with web stiffener. If a section failing in the distortional mode and subjected to the interaction of local and distortional buckling modes, the test results showed that the sections failed prematurely and the DSM distortional strength curve was inadequate to account for such interactions.
He et al. (2014) examined the design and loadcarrying capacity of fixedended webstiffened lipped channel columns eroded by mode interaction behaviour combined with distortional and local deformations. Anil Kumar and Kalyanaraman (2014) presented about distortional buckling of CFS stiffened lipped channel compression members. Zhang and Young (2015) investigate the behaviour of coldformed steel builtup open section columns with edge and web stiffeners. Zhou et al. (2015) offered explicit analytical formulae to provide distortional critical stress estimates for coldformed steel Csection columns. Aruna et al. (2015) described a series of experiments conducted in coldformed builtup square sections with intermediate flange and web stiffeners under axial compression with hinged end conditions. Wang et al. (2016) conducted a series of pinended compression tests and numerical analysis of channels with complex edge stiffeners and two different types of web stiffeners.
From the literature, it is observed that edge stiffeners and intermediate web stiffeners are improving the distortional and local buckling strength, respectively. Though many of the literatures pertaining strength and behaviour of simple coldformed steel channel column with edge and intermediate web stiffeners. However, the results are scattered. Hence, in this study, lipped coldformed steel channel column with various types of intermediate web stiffeners are selected.
In this study, coldformed steel lipped channel sections with various types of intermediate web stiffeners are analysed. The dimensions of the cross sections are arrived based on the North American Specifications (NAS) for the coldformed steel structures. The crosssectional dimensions also satisfy the prequalified section profile Direct Strength Method (DSM) for the coldformed steel structures. In this study, a series of 12 specimens are fabricated from the locally available coldrolled sheets with a pressbraking operations. The strength of the sections is calculated from the DSM and NAS for coldformed steel structures. The strength obtained from the experiments is being compared with the strength of the section calculated from the DSM and NAS for coldformed steel structures. From the comparability of the results, modifications of the design specifications are being suggested. The main aim of this study is to investigate the strength and buckling behaviour of coldformed steel lipped channel column with various types of intermediate web stiffeners.
Experimental programme
Details of the specimen and material properties
Specimen labelling
In this study, four crosssectional geometries are chosen. From the specimen label, the crosssectional geometry and length of the section are easily identified. For an example, “LCV500”, first letter defines the type of cross section (LClipped channel), the second letters defines the type of intermediate stiffener, second is lipped channel with Vshaped intermediate stiffener (LCV), third is lipped channel with Ushaped intermediate stiffener (LCU) and fourth is lipped channel with Σshaped intermediate stiffener (LCΣ), and a third letter defines the length of the column in mm.
Design of specimen
Measured section dimensions
S. No.  Specimen ID  Section dimension (mm)  

H  B  W  L  t  
H _{1}  H _{2}  H _{3}  
1  LC500  150  50  20  500  1.6  
2  LC700  150  50  20  700  1.6  
3  LC1000  150  50  20  1000  1.6  
4  LCV500  55  20  –  50  20  500  1.6 
5  LCV700  55  20  –  50  20  700  1.6 
6  LCV1000  55  20  –  50  20  1000  1.6 
7  LCU500  45  20  20  50  20  500  1.6 
8  LCU700  45  20  20  50  20  700  1.6 
9  LCU1000  45  20  20  50  20  1000  1.6 
10  LCΣ500  40  20  30  50  20  500  1.6 
11  LCΣ700  40  20  30  50  20  700  1.6 
12  LCΣ1000  40  20  30  50  20  1000  1.6 
Material properties
Average results of coupon test
S. No.  Yield stress (Mpa)  Young’s modulus (Mpa)  Ultimate stress (Mpa)  Elongation 

1  276  2.05 × 10^{5}  350  13% 
Experimental setup
Finite element modelling
The numerical modelling is thorough in the commercial finite element software ABAQUS. The finite element program ABAQUS is used to simulate the experimental behaviour of the four types of members. An Eigenvalue elastic buckling analysis is first conducted to establish probable buckling modes (Eigen modes) of the specimens. A nonlinear buckling analysis is then performed to predict the ultimate loads, deformations and failure modes of the specimens.
In this study, geometric non linearity is not measured. However, the scaled imperfection value is considered in the FE model (Schafer and Pekoz 1998a, b). The Eigen mode 1 scaled by a factor is used to obtain the geometric imperfection for the nonlinear buckling analysis. According to the buckling type of Eigen mode 1, the magnitude of the geometric imperfection of local, distortional and overall which from Schafer and Pekoz (1998a, b) is 0.34 t, 0.9 t and L/1000, respectively, used to specify the factor.
Results and discussion
Comparison of results between experiment and finite element analysis
S. No.  Specimen ID  Ultimate load (kN)  P _{EXP}  P _{EXP}  P _{FEM}  Failure modes  

P _{EXP}  P _{FEM}  P _{DSM}  P _{FEM}  P _{DSM}  P _{DSM}  
1  LC500  41.33  45.11  49.23  0.92  0.84  0.92  L 
2  LC700  32.11  42.16  47.89  0.76  0.67  0.88  D + L 
3  LC1000  30.09  39.11  41.11  0.77  0.73  0.95  D + L 
4  LCV500  69.78  72.07  75.03  0.97  0.93  0.96  L 
5  LCV700  68.30  66.30  71.33  1.03  0.96  0.93  D 
6  LCV1000  60.30  62.13  66.56  0.97  0.91  0.93  D + L 
7  LCU500  70.11  77.32  82.02  0.91  0.85  0.94  L 
8  LCU700  69.15  71.06  73.21  0.97  0.94  0.97  D 
9  LCU1000  64.32  65.11  69.32  0.99  0.93  0.94  D 
10  LCΣ500  80.13  86.16  90.11  0.93  0.89  0.96  D 
11  LCΣ700  79.14  84.32  83.24  0.94  0.95  1.01  D 
12  LCΣ1000  72.65  80.98  79.76  0.90  0.91  1.02  D 
Mean  0.92  0.88  0.95  
Standard deviation  0.08  0.09  0.04 
There are four series of section are chosen. The first series is lipped channel column without intermediate stiffener; the second series is lipped channel column with Vshaped intermediate stiffener; third series is lipped channel column with Ushaped intermediate stiffener and fourth series is lipped channel column with Σshaped intermediate stiffener. All the series, three different lengths are chosen such as 500, 700, 1000 mm. In this study, all the specimens are having equal crosssectional area. All the specimens having 500 mm length fail by local buckling, whereas specimen LCΣ500 fails by distortional buckling. Likewise the specimens having 700 mm length, except specimen LC700, fail by pure distortional buckling, whereas specimen LC700 fails by interaction of local and distortional buckling. Similarly, the specimens having 1000 mm length, such as specimen LC1000 and LCV1000, fail by interaction of local and distortional buckling, whereas all other remaining specimens fail by pure distortional buckling.
Loadcarrying capacities of LC500, LCV500, LCU500 and LCΣ500 are 41.33, 69.78, 70.11, and 80.11 kN, respectively. Similar improvement of loadcarrying capacity is observed for all other length variations, and the corresponding results are presented in Table 3. From this study, it is observed that an intermediate stiffener significantly affects the strength and behaviour of the specimens. And also noted that, a specimen with Σtype intermediate stiffeners provides better performance compared to all other types of intermediate stiffeners.
Theoretical investigations
Based on the specification of direct strength method (DSM) for coldformed steel design, the capacity of members in axial compression (P_{n, DSM}) shall be minimum of local buckling (P_{nl}), distortional buckling (P_{nd}) and flexural torsional buckling (P_{ne}),
λ_{c} = \( \sqrt {P_{\text{y}} /P_{\text{cre}} } \)and P_{y} = Af_{y}.P_{y} is the squash load.
λ_{1} = \( \sqrt {P_{\text{ne}} /P_{\text{crl}} } \).
λ_{d} = \( \sqrt {P_{\text{y}} /P_{\text{crd}} } \).
Verification of design equation [Yan and Young (2002)]
Specimen ID as per literature  Load (kN)  P _{EXP}  

P _{EXP}  P _{DSM}  P _{Design}  P _{prop}  
T1.5F120L0500  168.90  164.70  165.04  1.02 
T1.5F120L3000  131.30  133.30  130.82  1.00 
T1.5F120L3500  127.40  123.20  119.81  1.06 
T1.9F120L2000  225.20  217.30  222.38  1.01 
T1.9F120L2500  220.20  206.50  210.61  1.05 
T1.9F120L3000  209.40  193.00  195.89  1.07 
T1.9F120L3500  194.60  178.20  179.76  1.08 
Mean  1.04  
Standard deviation  0.03 
Summary and conclusions

Results obtained from the numerical investigation agreed well with the experimental investigation.

Local buckling, distortional buckling and interaction between local and distortional buckling are observed experimentally and compared well numerically.

Strength and stiffness of the member increase with modifying the crosssectional geometries. A specimen with Σtype intermediate stiffeners provides better performance compared to all other types of intermediate stiffeners.

Intermediate stiffener significantly affects the strength and behaviour of the sections.

The average and standard deviation of P_{EXP}/P_{FEM} are 0.92 and 0.08, respectively.

The mean values of P_{EXP} and P_{DSM} and P_{FEM} and P_{DSM} are 0.88 and 0.95, respectively. Similarly, standard deviations of P_{EXP} and P_{DSM} and P_{FEM} and P_{DSM} are 0.09 and 0.04, respectively.

From this comparison, it is observed that DSM specification predicts the strength almost equal to the experiment and finite element analysis. However, all the values are below to the one.

Hence, a new design expression is proposed and also verified with the results available from the literature.

The mean and standard deviation of P_{EXP}/P_{Prop} are 1.04 and 0.03, respectively. From the results, it is concluded that the proposed design equation reasonably predicts the strength of the lipped channel column with and without intermediate stiffener.
Notes
References
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