1. Thin-Walled Column Design Considering Local, Distortional and Euler Buckling Ben Schafer Asst. Professor Johns Hopkins University

2. Overview Introduction Elastic Buckling Ultimate Strength Column Design Methods Performance of Methods Conclusion

3. Introduction

4. Elastic Buckling Prediction Numerical Methods –finite element, finite strip (www.ce.jhu.edu/bschafer) Hand Methods (for use in a traditional Specification) –Local Buckling Element methods, e.g. k=4 Semi-empirical methods that include element interaction –Distortional Buckling Proposed (Schafer) method, rotational stiffness at web/flange juncture Hancock’s method AISI (k for Edge Stiffened Elements per Spec. section B4.2)

5. Elastic Buckling Comparisons 1 * *For members with slender webs and small flanges the Lau and Hancock (1987) approach conservatively converges to a buckling stress of zero (these members are ignored in the summary statistics given above) 1 For a wide variety of cold-formed steel lipped channels, zees and racks

6. Ultimate Strength Numerical Studies (nonlinear FEA) –Analysis of isolated flanges –Parametric studies on lipped channels Existing Experimental Data (pin ended, concentrically loaded columns) –100+ tests on lipped channels –80+ tests on lipped zees –40 tests on rack columns (variety of stiffeners)

7. Numerical Studies on Ultimate Strength Primarily focused on differences in the behavior and in the failure mechanisms associated with local and distortional buckling. Key findings in this area: –distortional buckling may control the failure mechanism even when the elastic distortional buckling stress (f crd ) is higher than the elastic local buckling stress (f cr l ) –distortional failures have lower post-buckling capacity and higher imperfection sensitivity than local failures

8. Experiments on Distortional Buckling Failures High Strength Rack Columns (U. of Sydney) Eq. 16 not predicted by AISI Spec.

9. Considered Design Methods Effective Width Methods –AISI Design Specification (1996) –Element by element effective width approach, local and distortional buckling treated separately Direct Strength Methods –Hand solutions for member elastic buckling –Numerical solutions (finite strip) for elastic buckling Varying levels of interaction amongst the failure modes considered (see paper for full discussion)

10. Effective Width Methods * * for Euler (long column) interaction f=F cr of the column curve used in AISC Spec. (the notation for f is F n in the AISI Spec. but the same column curve is employed)

11. Direct Strength Methods Local Distortional

12. Performance of Effective Width Methods (for subset of tests on lipped Zees)

13. Performance of Direct Strength Methods (for subset of tests on lipped Zees)

14. Overall Performance (Direct Strength)

15. Conclusions Must consider local, distortional, and Euler modes, but closed- form and numerical methods are accurate and available Current effective width based design methods ignore local web/flange interaction and distortional buckling, leading to systematic error and inflexibility in dealing with new shapes A direct strength method using separate column curves for local and distortional buckling: –provides a consistent and accurate treatment of the relevant buckling modes –avoids lengthy effective width calculations –demonstrates the effectiveness of directly using numerical elastic buckling solutions –opens the door to rational analysis methods –provides greater potential innovation in cold-formed shapes