Failure modes and buckling coefficient of partially stiffened cold-formed sections in bending
Introduction
Cold-formed section strength is not only controlled by material yielding but also by lateral, lateral–torsional, local and distortional buckling. In lateral buckling the whole section deflects laterally. In lateral–torsional buckling, the whole section twists and bends without any changes in the section's shape. In local buckling, the plate element buckles without any deformation of the web-flange juncture. In distortional buckling, the shape of the cross-section is changed and the flange element rotates around the web-flange intersection.
A compression element with an edge stiffener is called a partially stiffened element, and is susceptible to distortional buckling failure mode. The buckling behaviour of a partially stiffened element, depending on the edge stiffener size, varies between unstiffened and stiffened elements. Therefore, the plate buckling coefficient, k, of a partially stiffened element varies between 0.43 and 4. Desmond et al. [8] conducted analytical and experimental studies on partially stiffened elements. They concluded that the buckling behaviour of an element with an adequate size of stiffener (and therefore its effective width), is similar to a stiffened element that has the same material and dimensions. The outcome of the research by Desmond et al. [8] led to the design rules for calculating the buckling coefficients of uniformly compressed partially stiffened elements in AS/NZS 4600 [2] and AISI-S100 [1].
Schafer et al. [14] studied the effect of complex edge stiffeners on the distortional buckling behaviour of thin-walled members. They concluded that Open thin-walled members benefit substantially from the use of edge stiffeners. However, an increase in the length of the stiffener could cause local instability for the section.
Bambach [6] illustrated that if the lip-to-flange ratio for an element with a simple stiffener exceeds 0.16, the element will behave as a stiffened element. Bambach also concluded that the lip-to-flange ratio should not exceed 0.25. This is due to the fact that a large stiffener initiates buckling itself and will reduce the theoretical buckling stress of the whole element.
It is to be noted that the AISI-S100 [1] and AS/NZS 4600 [2] calculations are based on the Winter equation. To verify the Winter equation for partially stiffened elements, Kwon and Hancock [9] have performed compression tests on cold-formed channel sections with edge stiffeners. Their test results indicated that sections without adequate edge stiffeners, and a flange buckling coefficient of less than 4, will fail due to distortional buckling. Therefore, the critical value of an element's theoretical buckling stress (fcr) should be equal to the theoretical distortional buckling stress. Based on distortional buckling failure, Kwon and Hancock [9] compared their test results with the Winter equation results and concluded that the Winter equation provides an un-conservative design capacity for partially stiffened elements.
Bambach [6] modified the Winter equation for edge-stiffened elements. Bambach's modification was purely based on an empirical approach using finite element analysis, and his modified equations are as follows:where λ is the slenderness ratio and is determined using Eq. (9).
From Kwon and Hancock [9] and Bambach [6], it can be concluded that distortional buckling failure is not clearly addressed in the effective width method (EWM). Bambach [5] verified Eqs. (1), (2) by testing 30 plates, which were simply supported on three sides, with the remaining (longitudinal) edge stiffened with an edge stiffener. Bambach [5] illustrated that increasing the stiffness of the edge stiffener (Is) can provide considerable improvement in strength of a compression element. It is to be noted that all Bambach's samples had the same width with various stiffener sizes. In his study, the interaction effect between the web and flange was not considered as the tested samples were only solo elements. However, Yu and Yan [18], have shown in their research that web to flange ratio is an effective factor in determining the plate buckling coefficient in C and Z sections.
Using the finite strip method (FSM), Schafer and Pekoz [15] illustrated that the boundary condition has a great effect on the distortional buckling coefficient. In addition, Seif and Schafer [16] showed that the section geometry can be a controlling factor for determining the local plate buckling coefficient. However, in all design standards, such as AS 4100 [4], the web and flange slenderness limits are assumed to be independent of the restraining element.
The aim of this study is two-fold. Firstly, to investigate the effect of web, flange and edge stiffener interactions on the failure deformations of the sections. Secondly, using an extensive experimental analysis of 42 cold-formed channel sections, revise the existing formula for the plate buckling coefficient of partially stiffened elements.
Section snippets
Experimental setup and test specimens
The channel sections were brake-pressed from four different steel G450 sheets of 1500 mm length. In the design of the section dimensions, theoretical buckling stresses were calculated using the finite strip software Thin-wall [12]. The theoretical buckling stress of the tested sections is the minimum value of the local and distortional buckling stress of the sections based on their effective length. By introducing the size of the section and the loading pattern to the Thin-Wall program, the
Effect of web and flange interaction on the failure mode of a partially stiffened compression element
It has been proven that increasing the stiffness of the edge stiffener (Is) can provide considerable improvement in strength of a solo compression element [6]. However, the interaction effects between the web and flange have not been investigated in Bambach's study. The focus of this study is to discuss the effect of web and flange interaction on the failure mode of a partially stiffened compression element.
To inform the analysis of the failure mode of each tested section, two dimensions were
Comparing test results with existing design rules on edge stiffened elements
Maduliat et al. [11] proved that in some cold-formed channel sections, the ultimate curvature can exceed the yield curvature. These sections buckle elastically, and show post-buckling moment capacity significantly beyond the yield curvature. Fig. 11, Fig. 12 explain the development of this inelastic behaviour in slender sections further, using Section 13 as an example.
In the first stage, the section behaves as a fully effective section due to the small stress on the compression flange (Fig. 12
Proposed revision of plate buckling coefficient for partially stiffened elements
The experimental buckling coefficients were back-calculated from the experimental buckling stresses and compared with the EWM results in Fig. 13. It is shown that the EWM over-predicts the buckling coefficients of the partially stiffened element due to the large aspect ratios of the sections.
Therefore, the existing method to calculate the buckling coefficients of the partially stiffened elements is revised. The revised method is aligned with the existing method for the sections with aspect
Conclusions
By reviewing the range of literature on the study of designing cold-formed channel sections with edge stiffeners, a number of conclusions are evident. The common observed failure modes from the tests are identified and discussed, and are outlined as follows:
- 1.
For sections where the width-to-depth ratio is less than 0.5, the distortional buckling failure mode is more pronounced when compared to the local buckling failure mode.
- 2.
For the sections with width-to-depth ratios from 0.5 to 0.7, the
Acknowledgment
The writers are grateful to Dr. Mike Bambach and Prof. Xiao-Ling Zhao for their assistance in the experimental program at Monash University. The tests were conducted at the Structural Engineering Laboratory, Monash University.
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