Direct Strength Design for Cold-Formed Steel Members with Perforations

1. Direct Strength Design for Cold-Formed Steel Members with Perforations Progress Report 2 C. Moen and B.W. Schafer AISI-COS Meeting August 2006

2. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

3. next? Perforation patterns in CFS

4. Objective Development of a general design methodfor cold-formed steel members with perforations. Direct Strength Method Extensions 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?

5. DSM for columns no holes 267 columns , b = 2.5, f = 0.84

6. Progress Report 1 HighlightDSM prediction* for stub columns with holes mean test-to-predicted = 1.04 standard deviation = 0.16 *Pcr by FE reflects test boundary conditions, minimum D mode selected, Py=Py,g

7. Progress Report 1 HighlightGlobal buckling in long columns with holes mean test-to-predicted = 1.14 standard deviation = 0.09

8. Project Update • Year 1 of 3 complete • Project years 1: Elastic buckling studies, identifying modes, benefiting from existing data 2: Ultimate strength studies, modal composition, connecting elastic stability to strength 3: Experimental validation & software

9. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

10. Slotted Hole Spacing in Plates • Motivation • Evaluate influence of hole spacing on elastic buckling of plates • Study buckling modes with multiple holes, observe critical buckling stress as hole spacing changes • Provide code-based recommendations on slotted hole spacing

11. Influence of a single hole (benchmark: stiffened plate in compression)

12. Influence of multiple holes Fixed length plate, vary spacing and quantity of holes (note clear space between holes = S – Lhole) models compared at equal numbers of DOF

13. Influence of multiple holes

14. Elastic buckling study: S/Lhole > 5 implies S > 5Lhole and Sclear > 4Lhole Send > 2.5Lhole and Sclear-end > 2Lhole Old D4 rules on holes... S > 24 in. Sclear-end > 10 in. Lhole < 4.5 in. implies S > 5.3Lhole Sclear-end > 2.2Lhole old rules look reasonable, but we need to non-dimensionalize Comparison of findings on spacing

15. Critical buckling stress equation for S/Lhole > 5

16. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

17. Flange holes in SSMA studs (Western States Clay Products Association Design Guide for Anchored Brick Veneer over Steel Studs)

18. Flange holes and elastic buckling ¼”,½”,¾”, 1”, 1¼” dia. holes in a 1⅝” flange (362S162-33) Local buckling (LH mode) caused by large diameter holes

19. Influence of flange holes on elastic buckling modes Keep bhole/b < 0.5 in this study to avoid problems

20. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

21. Evaluate nonlinear solution methods • Motivation • Gain experience with nonlinear FEM analysis using ABAQUS • Use modified Riks method (arc length or work method) and artificial damping method to predict the strength of a plate with a hole • Explore solution controls and identify areas of future research (task group only..)

22. Loading and boundary conditions Simply supported plates (task group only..)

23. Modified Riks Solution (task group only..)

24. Artificial Damping Solution (task group only..)

25. Ultimate strength of a plate with a hole • Motivation • Use knowledge gained from solution control study to predict strength and failure modes • What happens at failure when we add a hole? • Study the influence of initial imperfections on strength and load-displacement response (task group only..)

26. Considering initial imperfections fundamental buckling mode of plate initial geometric imperfections fundamental buckling mode mapped to plate with slotted hole (task group only..)

27. Imperfections and strengthPlate WITHOUT a hole (task group only..)

28. Imperfections and strengthPlate WITH a hole (task group only..)

29. Plate strength summary (task group only..)

30. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

31. fundamental buckling mode of plate d SS d SS SS initial geometric imperfections SS SS SS SS d SS fundamental buckling mode mapped to plate with slotted hole d Simply supported plate models

32. Effective width – basic concepts

33. Effective widthPlate WITHOUT hole

34. Effective WidthPlate WITH hole

35. Through thickness stresses in a plate

36. Through thickness stress variation A A A

37. Through thickness effective width Top of Plate Middle of Plate Bottom of Plate

38. Outline • Objective and challenges • Project overview • FE elastic stability studies • slotted hole spacing limits • flange holes in SSMA studs • FE strength studies • nonlinear solution methods (ABAQUS) • isolated plates with holes • studies on effective width • SSMA structural stud with hole (initial study) • Conclusions task group

39. SSMA Structural Stud – Ultimate Strength(362S162-33) Also modeled – fixed-fixed end conditions No warping allowed at member ends!

40. Elastic Buckling Modes Pinned-pinned shown ( fixed-fixed similar)

41. Influence of hole and end conditions on strength baseline response: initial imperfections not considered here

42. SSMA stud failure mechanisms 33 ksi yield stress Yielding occurs in the web, flange, and lip stiffener Fixed ends Pu=0.77Py,g Yielding occurs only at the hole Fixed ends with hole Pu=0.61Py,g Pinned ends Pu=0.64Py,g Pinned ends with hole Pu=0.53Py,g

43. Conclusions • Progress report 1 shows • holes create new mixed buckling modes,for web holes this means triggering distortional buckling earlier • DSM style methods are working in an average sense, when reduced elastic buckling for holes is accounted for • New elastic buckling studies show that • Hole spacing: S/Lhole>5 , Send/Lhole>2.5 to avoid interaction • Flange holes: bhole/b < 0.5 to avoid reduced Pcr in SSMA stud • Ultimate Strength of Plates/Members with holes • Nonlinear FEA is v. sensitive to solution algorithm • Net section “revealed” for stocky sections, small imperfections • Imperfection sensitivity not markedly increased due to hole • Hole impacts “effective width” and through thickness rigidity • Yielding patterns with hole are more “like” distortional buckling mechanisms than local mechanisms suggesting reduced post-buckling capacity and some concern with using DSM local buckling curve for members with holes.

44. What’s Next? • Elastic buckling and nonlinear FEM of COLUMNS with holes • Elastic buckling and nonlinear FEM of BEAMS with holes • Modal decomposition of failure modes with GBT • Laboratory testing of intermediate length SSMA studs with holes • Moving closer to a formal connection between elastic buckling and ultimate strength for cold-formed steel members with holes