Direct Strength Design for Cold-Formed Steel Members with Perforations

1. Direct Strength Design for Cold-Formed Steel Members with Perforations Progress Report 1 C. Moen and B.W. Schafer AISI-COS Meeting February 21, 2006

2. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals, plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

3. Objective Development of a general design method for cold-formed steel members with perforations.

4. Perforation patterns in CFS

5. Direct strength prediction Pn = f (Py, Pcre, Pcrd, Pcrl)? • Input • Squash load, Py • Euler buckling load, Pcre • Distortional buckling load, Pcrd • Local buckling load, Pcrl • Output • Strength, Pn

6. Direct strength for members with holes Pn = f (Py, Pcre, Pcrd, Pcrl)? Does fstay the same? Explicitly model hole(s)? Accuracy? Efficiency? Identification? Just these modes? Gross or net, or some combination?

7. DSM for columns without holes 267 columns , b = 2.5, f = 0.84

8. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals, plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

9. Project Update • Originally proposed as a three year project. Year 1 funding was provided, we are currently ½ way through year 1. • Project years 1: Benefiting from existing data 2: Identifying modes and extending data 3: Experimental validation & software

10. Project year 1 Focus has primarily been on compression members with isolated holes in the first 6 mos.

11. Project year 2

12. Project year 3

13. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals, plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

14. ABAQUS Element Accuracy • Motivation • For the student to learn and understand sensitivity of elastic (eigen) stability response to FE shell element solutions • In particular, to explore FE sensitivity in members with holes • To take the first tentative steps towards providing practicing engineers real guidance when using high level FE software for elastic stability solutions of unusual situations

15. Stiffened element in uniform compression (benchmark: stiffened plate in compression)

16. Linear vs. quadratic elements S4/S4R S9R5 models compared at equal numbers of DOF

17. Number of elements along the length 2.5 elements per half-wave shown

18. S9R5 sensitivity to modeling corners 1 element in corner Use of quadratic shell elements that can have an initially curved geometry shown to be highly beneficial/accurate here. 3 elements in corner

19. FE vs FSM comparisons • SSMA 362S162-33 in pure compression • FE = ABAQUSFSM = CUFSM model length = half-wavelength in ABAQUS (ABAQUS boundary conditions = “pinned ends”)

20. Exploring local buckling difference number of local buckling half-waves in ABAQUS model (physical length of ABAQUS model is increased)

21. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals, plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

22. Mesh sensitivity around holes 4 layers of elements shown SS SS SS SS

23. Mesh sensitivity around holes

24. Mesh sensitivity around holes Do holes decrease local buckling this much??

25. The square plate problem • Much of the fundamental research on plates with holes has been conducted on square plates. • The idea being that one local buckle evenly fits into a square plate. • So, examining the impact of the hole in a square plate examines the impact in a localized fashion? ? =

26. Local buckling in an a/b = 4 plate w = 92.075mm l = 4w Conclusion? Lots of wonderful theoretical studies are not really relevant...

27. “SSMA” hole and varied plate width 4w

28. Local plate stability with a hole Observed loss of local stability much less than in a square plate. We will revisit this basic plot for member local buckling as well.

29. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals,plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

30. SSMAS162-33 w/ hole Member Study L = 1220mm = 48 in.

31. CUFSM elastic buckling (no hole) Pcr/Py half-wavelength (mm)

32. ABAQUS model • Classical FSM style boundary conditions are employed, i.e., pinned free-to-warp end conditions.

33. Local (L) buckling • Pcrl no hole = 0.28Py, with hole = 0.28Py

34. Distortional (D) buckling • Pcrd no hole = 0.64Py, with hole = 0.65Py

35. Distortional (DH) buckling around the hole • Pcrd no hole = 0.64Py, with hole = 0.307Py

36. Antisymm. dist. buckling (DH2) at the hole • Pcrd no hole = 0.64Py, with hole = 0.514Py

37. Global flexural torsional (GFT) buckling • Pcrd no hole = 0.61Py, with hole = 0.61Py

38. Impact of hole location on buckling values

39. GFT mode with hole at midspan Mixed GFT-L-D mode observed with hole near end. BC influence near the ends, under further study.. Hole location impact on GFT

40. SSMAS162-33 w/ hole Member Study 2 b L = 1220mm = 48 in.

41. Hole size and member buckling modes

42. Observed buckling modes L DH GFT D

43. “DH” mode 0.62Py 0.38Py 0.35Py 0.31Py 0.30Py

44. Outline • Objective and challenges • Project overview • FE stability studies • fundamentals, plates and members with holes • Modal identification and cFSM • Existing experimental column data • elastic buckling studies: hole effect, boundary conditions • strength prediction by preliminary DSMstub columns, long columns • Conclusions

45. Modal identification • Mixing of modes (a) complicates the engineers/analysts job (b) may point to post-buckling complications • We need an unambiguous way to identify the buckling modes • A significant future goal of this research is the extension of newly developed modal identification tools to members with holes

46. We can’t effectively use FEM • We “need” FEM methods to solve the type of general stability problems people want to solve today • tool of first choice • general boundary conditions • handles changes along the length, e.g., holes in the section 30 nodes in a cross-section 100 nodes along the length 5 DOF elements 15,000 DOF 15,000 buckling modes, oy! • Modal identification in FEM is a disaster

47. Special purpose finite strip can fail too

48. cFSM • cFSM = constrained finite strip methodThe “constraints” restrict the FSM model to deformations within a selected mode – for instance, only distortional buckling • cFSM adopts the basic definitions of buckling modes developed by GBT researchers • My research group has been developing this method as a means to provide modal decomposition and modal identification • Extension of modal identification to general purpose FE results has a potentially huge impact on our problem

49. modal decomposition

50. modal identification