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
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 f stay 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, PyPy,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)
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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
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Comparison of findings on spacing

• Elastic buckling study
• S/Lhole gt 5 implies
• S gt 5Lhole and
• Sclear gt 4Lhole
• Send gt 2.5Lhole and
• Sclear-end gt 2Lhole

• Old D4 rules on holes...
• S gt 24 in.
• Sclear-end gt 10 in.
• Lhole lt 4.5 in.
• implies
• S gt 5.3Lhole
• Sclear-end gt 2.2Lhole
• old rules look reasonable, but we need to
  non-dimensionalize

15
Critical buckling stress equation
for S/Lhole gt 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)
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Flange holes and elastic buckling
¼,½,¾, 1, 1¼ dia. holes in a 1? flange
(362S162-33)
Local buckling (LH mode) caused by large diameter
holes
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Influence of flange holes on elastic buckling
modes
Keep bhole/b lt 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
Simply supported plate models
32
Effective width basic concepts
33
Effective widthPlate WITHOUT hole
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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)
No warping allowed at member ends!

• Also modeled fixed-fixed end conditions

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
Yielding occurs in the web, flange, and lip
stiffener
Fixed ends Pu0.77Py,g

• 33 ksi yield stress

Yielding occurs only at the hole
Fixed ends with hole Pu0.61Py,g
Pinned ends Pu0.64Py,g
Pinned ends with hole Pu0.53Py,g
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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/Lholegt5 , Send/Lholegt2.5 to avoid
  interaction
• Flange holes bhole/b lt 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
Whats 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