1. DSM Design Guide

2. Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development Design Examples

3. Using the Guide (pg. 1)

4. DSM Advantages Practical advantages of DSM: –no effective width calculations, –no iterations required, and –uses gross cross-sectional properties. Theoretical advantages of the DSM approach: –explicit design method for distortional buckling, –includes interaction of elements (i.e., equilibrium and compatibility between the flange and web is maintained in the elastic buckling prediction), and –explores and includes all stability limit states. Philosophical advantages to the DSM approach: –encourages cross-section optimization, –provides a solid basis for rational analysis extensions, –potential for much wider applicability and scope, and –engineering focus is on correct determination of elastic buckling behavior, instead of on correct determination of empirical effective widths. (pg. 2)

5. DSM Limitations Limitations of DSM (as implemented in AISI 2004) –No shear provisions –No web crippling provisions –No provisions for members with holes –Limited number/geometry of pre-qualified members –No provisions for strength increase due to cold-work of forming Practical Limitations of DSM approach –Overly conservative if very slender elements are used –Shift in the neutral axis is ignored Limitations of finite strip method –Cross-section cannot vary along the length –Loads cannot vary along the length (i.e., no moment gradient) –Global boundary conditions at the member ends are pinned (i.e., simply- supported) –Assignment of modes sometimes difficult, particularly for distortional buckling (pg. 6)

6. DSM Design Guide Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development Design Examples

7. (pg. 10)

8. variation along the member length half-wavelength 5 in. Local 25 in. Distortional 200 in. Lateral-torsional 5 Applied stress on the section indicates that a moment about the major axis is applied to this section. All results are given in reference to this applied stress distribution. Any axial stresses (due to bending, axial load, warping torsional stresses, or any combination thereof) may be considered in the analysis. Minima indicate the lowest load level at which a particular mode of buckling occurs. The lowest M cr /M y is sought for each type of buck- ling. An identified cross-section mode shape can repeat along the physical length of the member. Half-wavelength shows how a given cross-section mode shape (as shown in the figure) varies along its length. Mode shapes are shown at the identified minima and at 200 in.. Identification of the mode shapes is critical to DSM, as each shape uses a different strength curve to connect the elastic buckling results shown here to the actual ultimate strength. In the section, local buckling only involves rotation at internal folds, distortional buckling involves both rotation and translation of internal fold lines, and lateral-torsional buckling involves rigid-body deformation of the cross- section without distortion. Understanding Finite Strip Analysis Results variation along the member length half-wavelength 5 in. Local 25 in. Distortional 200 in. Lateral-torsional 5 Applied stress on the section indicates that a moment about the major axis is applied to this section. All results are given in reference to this applied stress distribution. Any axial stresses (due to bending, axial load, warping torsional stresses, or any combination thereof) may be considered in the analysis. Minima indicate the lowest load level at which a particular mode of buckling occurs. The lowest M cr /M y is sought for each type of buck- ling. An identified cross-section mode shape can repeat along the physical length of the member. Half-wavelength shows how a given cross-section mode shape (as shown in the figure) varies along its length. Mode shapes are shown at the identified minima and at 200 in.. Identification of the mode shapes is critical to DSM, as each shape uses a different strength curve to connect the elastic buckling results shown here to the actual ultimate strength. In the section, local buckling only involves rotation at internal folds, distortional buckling involves both rotation and translation of internal fold lines, and lateral-torsional buckling involves rigid-body deformation of the cross- section without distortion. (pg. 12)

9. Elastic buckling upperbounds Beams –if M cr > 1.66M y then no reduction will occur due to local buckling –if M crd > 2.21M y then no reduction will occur due to distortional buckling –if M cre > 2.78M y then no reduction will occur due to global buckling Columns –if Pcr > 1.66P y then no reduction will occur due to local buckling –if Pcrd > 3.18P y then no reduction will occur due to distortional buckling –if Pcre > 3.97P y a 10% or less reduction will occur due to global buckling –if Pcre > 8.16P y a 5% or less reduction will occur due to global buckling –if Pcre > 41.64P y a 1% or less reduction will occur due to global buckling (pg. 9)

10. DSM Design Guide Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development Design Examples

11. Elastic buckling examples C, Z, angle, hat, wall panel, rack post, sigma.. (pg. 16)

12. Z-section with lips (pg. 26)

13. Z-section with lips modified (pg. 28)

14. Comparison (pg. 26 and 28)

15. Comparison (pg. 26 and 28)

16. DSM Design Guide Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development Design Examples

17. Overcoming FSM difficulties The discussions in the following section are intended to provide the design professional with a means to apply engineering judgment to an elastic buckling analyses. When in doubt of how to identify a mode, or what to do with modes that seem to be interacting, or other problems; remember, it is easy to be conservative. Select the lowest bucking value (i.e., Pcr, Mcr) of all mode shapes which includes some characteristics of the mode of interest. This ensures a lowerbound elastic buckling response. However, this may be too conservative in some cases, and the challenge, often, is to do better than this and use judgment to determine a more appropriate (and typically higher) approximation. (pg. 42)

18. Multiple modes (pg. 46)

19. Global modes at short L (pg. 47)

20. DSM Design Guide Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development Design Examples

21. Beam Chart (pg. 58)

22. AISI (2002) Design Manual (pg. 61)

23. Column Chart (pg. 64)

24. DSM Design Guide Introduction Elastic Buckling Member elastic buckling –examples –overcoming difficulties Beam, Column, and Beam-Column Design Product Development (later today) Design Examples

25. C-section with lips,C-section with lips C-section with lips modified,C-section with lips modified C-section without lips (track section),C-section without lips (track section) C-section without lips (track section) modified,C-section without lips (track section) modified Z-section with lips,Z-section with lips Z-section with lips modified,Z-section with lips modified Equal leg angle with lips,Equal leg angle with lips Equal leg angle,Equal leg angle Hat section,Hat section Wall panel section,Wall panel section Rack post section, and aRack post section Sigma section.Sigma section Beam chart construction and Column Chart constructionBeam chartColumn Chart