Method Considered Distortional-local Interaction Buckling for Bearing Capacity of Channels with Complex Edge Stiffeners and Web Stiffeners under Axial Compression

Using the current direct strengths method to predict the bearing capacity of channels with complex edge stiffeners and stiffeners in the web, it will make the excessively conservative results to the test data for it couldn’t account for the interaction between distortional and local buckling. In order to study the method for bearing capacity of channels with complex edge stiffeners and web stiffeners under axial compression, the paper revised the current direct strengths method and new proposals considered distortional and local interaction buckling were made. The proposed method was verified by the finite element analysis results and the test results. It shows that the member strength predicted by the proposed method is more accurate than the present method and agrees well with the test data. Furthermore, compared with the results of the finite element method and hand method, the hand method for calculating elastic buckling critical stress of web-stiffened lipped channels with complex edge stiffeners was validated.


Introduction
Cold-formed steel sections are commonly used in a variety of applications including residential construction.With the reduction in thickness and variation in sections, distortional buckling modes have become control actions in structural instabilities gradually.Effective width method is the common approach in current codes for all countries, but the process of calculation is too complicated and the influence of distortional buckling is not considered.Direct strength method (DSM) developed recently is able to handle both local and distortional effects and has simple but accurate calculation.However, its application to members affected by distortional-local interaction buckling is still under development.Widely accepted DSM for channels with complex edge stiffeners and web stiffeners is lacking.
In recent years, the study on calculation method of the stiffened members' bearing capacity has been carried out in China and abroad.But about channels with complex edge stiffeners and web stiffeners under axial compression, there is no well established method.The paper deals with the ultimate strength and design of pin-ended channel columns with complex edge stiffeners and web stiffeners under axial compression.The aim of this paper is to put forward a method considered distortional-local interaction buckling.

Current Direct Strength Method
The DSM provides an efficient approach to estimate the ultimate strength of cold-formed steel columns considered failing in local-global interactive and distortional-global interactive modes [1].The formula for calculation is as follows.The domestic method considered local-global interaction buckling [2] is determined by The domestic method considered distortional-global interaction buckling is identical to Eq. 2, but the integral stability coefficient of specimen is determined by domestic code.
The current method only considered local-global interactive and distortional-global interactive buckling, but the buckling mode of specimen with web stiffener mostly is interaction of local, distortional and overall buckling modes.The formula proposed by Yap [3] is suitable for fixed-ended lipped channel columns, but for pin-ended complex lipped channel it is necessary to study the direct strength method of the bearing capacity of channels with complex edge stiffeners and web stiffeners under axial compression.

The Elastic Buckling Stress of Channels with Complex Edge Stiffeners and Web Stiffeners
The elastic buckling stress is essential for the calculation of direct strength method.The finite strip program of CUFSM was used to calculate the elastic buckling stress of channel columns with complex edge stiffeners and web stiffeners under axial compression.The results of the finite strip and hand methods were compared with each other, and the hand method of elastic buckling critical stress was validated.The buckling stress of channels with complex edge stiffeners and interactive V type stiffeners has been studied by Wang Chungang [4] and with complex edge stiffeners and interactive type stiffeners was studied in this paper.
The cross section forms used for analysis are shown in Fig. 1.There are three kind of specimen length(L=1m, 2m, 3m); two kind of thickness(t=1mm, 2mm); two kind of web height(H=180mm 220mm); E=2.06×10 5 MPa; ȣ=0.3; f y =345MPa; the flange width B=90mm, the first lip width d=25mm, the second lip width a=15mm.In the specimen label, C2 means channels with complex edge stiffeners and interactive type stiffeners and C3 means with complex edge stiffeners and interactive V type stiffeners.L and the number then represents effective length; the letter s and h means H=180mm, H=220mm respectively; the number 1 and 2 means t=1mm, t=2mm; the letter a to e in C2 section means H 1 /H 2 =0.

The local buckling stress
The hand method of elastic local buckling stress proposed by Schafer [5] is suited for channels with interactive V type stiffeners.As shown in Table 1, the results of hand method coincided with the analysis results approximately, and the elastic local buckling critical stress of channels with type section is also predicted by this simplified formula.

The distortional buckling stress
It is found that the influence of the interactive V type stiffener on the distortional stress of the section is very small.The formula proposed by Hancock [6] is suited for channels with interactive V type stiffeners.The comparison result of distortional stress of channels with Ȉ type section calculated by hand method and software analysis is shown in Table 2.

The Global Buckling Stress
Setting up the middle stiffeners doesn't have a significant effect on the overall stability.The method of global buckling stress was introduced in literature [7].

Proposed Design Method for bearing capacity of channels with complex edge stiffeners and web stiffeners under axial compression
As shown in Table 3.Using present direct strengths method to predict the bearing capacity of channels with complex edge stiffeners and stiffeners in the web, it will make the excessively conservative results to the test data.
In order to consider the enhancement of bearing capacity by stiffening, the magnification factor has been introduced into P nd .
nd uf P P is used as ordinate and crd n / P P l is used as abscissa.The results are showed in Fig2.It's obvious that regularities of distribution seem to be linear.The fitting equation is: y 0.04527x+1.12599,recommended formula: y 0.045x 1.1.The proposed design methods for bearing capacity are as follows:

3.
The column nominal strength (P n ) is the lower of P nl and P nld .
In order to validate the accuracy of proposed method, the proposed method is verified by the finite element analysis results and the test results from literature [8].As shown in Table 4 and Table 5.The contrast results are in good agreement.(1) The hand methods of the elastic local and distortional buckling stress are also suited for the channels with complex edge stiffeners and web stiffeners.
(2) The ultimate bearing capacity of the members can be improved effectively after stiffening and the failure mode mainly are distortional or distortional-local interactive buckling.The result of the present direct strength method is often inaccurate and conservative.
(3) Based on the current DSM, a method considered distortional-local interaction buckling for bearing capacity of channels with complex edge stiffeners and web stiffeners under axial compression was proposed and verified by the finite element analysis results and the test results.

Acknowledgements
This work described in this paper was supported by Natural Science Foundation of Liaoning Province (2015020575), their supports are gratefully acknowledged.

V
;and ı crl means local critical buckling stresses; P ne means overall stability bearing capacity.means distortional critical buckling stresses.The column nominal strength is the lower of the local-global interactive and distortional-global interactive failure stresses.
Fig. 1 Cross section form and geometric parameters definition of test specimen and P nd are obtained from Eq. 2 and Eq.

Table 2 The
Elastic Distortional Buckling Critical Stress Of Channels With Ȉ Type Section

Table 3
The Results Of The Present Dsm Contrast To The Experimental Results