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Direct Strength Design for Cold-Formed Steel Members
with Perforations
Progress Report 3C. Moen and B.W. Schafer
AISI-COS MeetingFebruary 2007
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Outline• Objective and challenges• Project overview• Column Experiments
– Test procedures– Compressive strength results– Load-deformation response
• Beam Elastic Buckling Study– Finite element modeling– Buckling mode identification– Comparison of DSM predictions to tested results
• Conclusions
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ObjectiveDevelopment of a general design method
for cold-formed steel members with perforations.
Direct Strength Method ExtensionsPn = f (Py, Pcre, Pcrd, Pcrl)?
Does f stay the same?
Gross or net, or some combination?
Explicitly model hole(s)?Accuracy? Efficiency?Identification? Just thesemodes?
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Outline• Objective and challenges• Project overview• Column Experiments
– Test procedures– Compressive strength results– Load-deformation response
• Beam Elastic Buckling Study– Finite element modeling– Buckling mode identification– Comparison of DSM predictions to tested results
• Conclusions
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4P
test
/Py,
g
(Py,g/Pcrl)0.5,(Py,g/Pcrd)0.5
D buckling controlsL buckling controlsDSM Pnl
DSM Pnd
Progress Report 1 HighlightDSM prediction* for stub columns with holes
mean test-to-predicted = 1.04standard deviation = 0.16
*Pcr by FE reflects test boundary conditions, minimum D mode selected, Py=Py g
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4P
test
/Py,
g
Slenderness, (Py,g/Pcre)0.5
Global buckling controls, Pne=Pnl
All Long Column SpecimensDSM Pne
Progress Report 1 HighlightGlobal buckling in long columns with holes
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4
Pte
st/P
ne,g
Slenderness, (Pne/Pcrl)0.5
Local buckling controlsDSM Pnl
mean test-to-predicted = 1.14standard deviation = 0.09
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Progress Report 1 &2 HighlightElastic Buckling Modes
Pcrd=1.15Py,g
Pcrl=0.42Py,g Pcrl=0.42Py,g
Pcrd1=0.52Py,g
Pcrd2=0.54Py,g
Pcrd3=1.16Py,g
D
L L
L+DH
DH2
D+L
Distortional modes unique to a column with a hole
Unique D modes are created with the presence of a hole
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Progress Report 2 HighlightCritical buckling stress equation
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
hhole/h
plat
e bu
cklin
g co
eff.,
k
Data points from eigenbuckling analysis
Fitted curve
44462
≤+⎟⎠⎞
⎜⎝⎛−⎟
⎠⎞
⎜⎝⎛=
hh
hhk holehole
SS/2 Lhole hholeh
for S/Lhole > 5
A simplified elastic buckling equation for a perforated plate
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Progress Report 2 HighlightSSMA stud failure mechanisms
33 ksi yield stress
Yielding occurs only at the hole
Yielding occurs in the web, flange, and lip stiffener
Holes can influence yielding location and failure mechanisms
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Project UpdateWe are halfway through the project now
• Project years1: Elastic buckling studies, identifying modes,
benefiting from existing data2: Beam elastic buckling, column experiments,
Nonlinear FEM ultimate strength studies3: Validating DSM, software, automating and
simplifying modal identification
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Outline• Objective and challenges• Project overview• Column Experiments
– Test procedures– Compressive strength results– Load-deformation response
• Beam Elastic Buckling Study– Finite element modeling– Buckling mode identification– Comparison of DSM predictions to tested results
• Conclusions
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Column Experiments• Motivation
– Observe first hand the influence of holes on elastic buckling and failure mechanisms
– Obtain data to validate future nonlinear finite element modes– Contribute short and intermediate length column results to
existing experimental database
362-1-24-NH 362-1-24-H362-2-24-NH 362-2-24-H362-3-24-NH 362-3-24-H362-1-48-NH 362-1-48-H362-2-48-NH 362-2-48-H362-3-48-NH 362-3-48-H600-1-24-NH 600-1-24-H600-2-24-NH 600-2-24-H600-3-24-NH 600-3-24-H600-1-48-NH 600-1-48-H600-2-48-NH 600-2-48-H600-3-48-NH 600-3-48-H
No Holes Holes
Specimen Names
SSMA 362S162-33
SSMA 600S162-33
Short Column
Intermediate Column
Short Column
Intermediate Column
24 inches
48 inches
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Test SetupMTS Load CellFixed Crosshead
Steel Platen
Novotechnikposition transducers (with magnet tips)
Hydraulic actuator
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End Conditions and Hole Locations
Hole orientations
Column end preparation
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Strength Results
Holes have a small influence on compressive strength here BUT…
Ptest Mean Std. Dev.kips kips kips
362-1-24-NH 10.48362-2-24-NH 10.51362-3-24-NH 10.15362-1-24-H 10.00362-2-24-H 10.38362-3-24-H 9.94362-1-48-NH 9.09362-2-48-NH 9.49362-3-48-NH 9.48362-1-48-H 8.95362-2-48-H 9.18362-3-48-H 9.37600-1-24-NH 11.93600-2-24-NH 11.95600-3-24-NH 12.24600-1-24-H 12.14600-2-24-H 11.62600-3-24-H 11.79600-1-48-NH 11.15600-2-48-NH 11.44600-3-48-NH 11.29600-1-48-H 11.16600-2-48-H 11.70600-3-48-H 11.16
11.29
Specimen
10.38
10.11
9.35
11.34
0.20
0.24
0.23
0.21
0.17
0.27
0.15
0.31
9.17
Hole
Without Hole Short
ColumnsHole
12.04
11.85
Without Hole Long
ColumnsHole
362S162-33
600S162-33
Without Hole Long
ColumnsHole
Without Hole Short
Columns
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362S162-33 Short ColumnPeak Load
hole (unstiffenedstrip)
Peak Load
Holes DO influence column ductility and failure modes.
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362S162-33 Short Column
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2
-14
-12
-10
-8
-6
-4
-2
0
Column axial displacement (inches)
Col
umn
axia
l loa
d (k
ips)
362-2-24-NH362-2-24-H
Slotted hole influences post-peak load path and decreases column ductility.
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600S162-33 Short ColumnPeak Load
Peak Load
Peak Load
Influence of slotted hole on failure mode is not as strong here.
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600S162-33 Short Column
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2
-14
-12
-10
-8
-6
-4
-2
0
Column axial displacement (inches)
Col
umn
axia
l loa
d (k
ips)
600-1-24-NH600-1-24-H
Slotted hole has a small influence on the load-deformation response.
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362S162-33 Intermediate Column
Peak Load
Peak Load
Holes dampen web local buckling.
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2
-14
-12
-10
-8
-6
-4
-2
0
Column axial displacement (inches)
Col
umn
axia
l loa
d (k
ips)
362-3-48-NH362-3-48-H
362S162-33 Intermediate Column
Columns fail in sudden global-torsional buckling.
Holes have a small influence on peak load and ductility.
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600S162-33 Intermediate ColumnPeak Load
Loud snap from local (L) to distortional (D) buckling.
Hole stiffens web and prevents snap from L to D.
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2
-14
-12
-10
-8
-6
-4
-2
0
Column axial displacement (inches)
Col
umn
axia
l loa
d (k
ips)
600-1-48-NH600-1-48-H
600S162-33 Int. Column
L to D snaps in NO HOLE column influence load response.
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Outline• Objective and challenges• Project overview• Column Experiments
– Test procedures– Compressive strength results– Load-deformation response
• Beam Elastic Buckling Study– Finite element modeling– Buckling mode identification– Comparison of DSM predictions to tested results
• Conclusions
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Beam Elastic Buckling Study• Motivation
– Evaluate the influence of web holes on the elastic buckling of beams
– Classify unique hole buckling modes for beam– Compare DSM Predictions to tested results
• This study based on test data from three studies:– Shan and LaBoube (1994)– Schuster (1992)– Batson (1992)
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Test Boundary Conditions
Section a-a
3/4”x3/4”x1/8” angle
Channel 1 Channel 2 Slotted Hole
Tri-slotted Hole
Lhole
hhole
0.5*hhole
Rhole
A total of 72 beam specimens are considered.
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FE Model (for Mcr!)
Beam end restrained in 2 and 3 (v, w=0)
Beam end restrained in 2 and 3 (v, w=0)
Bottom flange restrained in 1 at support (u=0)
* **
**
**
**
Restrain node at midline of top flange in 3 (w=0) (Typ.)
Rigid body connection between top (and bottom) flange midline nodes (Typ.)
1
2
3
Care is taken to simulate tested boundary conditions in eigenbuckling analyses.
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Local Buckling Modes
LHMcrl/Myg=0.77
LH2Mcrl/Myg=0.77
LMcrl/Myg=0.83
L (NO HOLE)Mcrl/Myg=0.82
Beam nominal depth=2.5”
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Distortional Buckling Modes
DMcrd/Myg=2.31Half wavelength=12 inches
DHMcrd/Myg=2.00
DMcrd/Myg=2.31Half wavelength=12 inches
Beam nominal depth=3.625”
Restraints influence location of half-waves
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Distortional Buckling Modes
DMcrd/Myg=1.02Half wavelength=12 inches
DH+LMcrd/Myg=0.88
DMcrd/Myg=1.00Half wavelength=12 inches
Formal modal identification method is needed!!!
Beam nominal depth=8”
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Impact of Hole on Local Buckling
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
hhole/H
Mcrl ,h
ole/M
crl ,n
o ho
le
Largest decrease in critical elastic localbuckling moment occurs at hhole/h= 0.25
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Impact of Hole on Distortional Buckling
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
hhole/H
Mcr
d,ho
le/M
crd,
no h
ole
Holes decrease critical elastic distortionalbuckling moment, modeling required
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Impact of Test Conditions on Dist. Buckling
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250 3000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
H/t
Mcr
d,no
hol
e, A
BAQ
US/M
crd,
CU
FSM
Tested boundary conditions boost critical elastic distortional buckling
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Beam Tests vs. DSM Predictions
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
(Myg/Mcrl)0.5 or (Myg/Mcrd)0.5
Mte
st/M
yg
DSM MnlDSM Mnd
Local buckling controlsDist. buckling controlsYielding controls
Test to Predictedmean=0.998STDV=0.115
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Outline• Objective and challenges• Project overview• Column Experiments
– Test procedures– Compressive strength results– Load-deformation response
• Beam Elastic Buckling Study– Finite element modeling– Buckling mode identification– Comparison of DSM predictions to tested results
• Conclusions
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Conclusions• Column Tests
– Holes had a small influence on the compressive strength in this study, but did influence buckling modes, load-deformation response, and ductility
– Yielding patterns for distortional-sensitive members (362’s) were influenced more by holes than the web local-sensitive members (600’s)
• Beam Elastic Buckling– Holes create unique local and distortional modes – These modes appear related to similar modes in compression members– Holes decrease the L and D critical elastic buckling capacity
• DSM vs. Tested Results– Predictions for local-controlled members are conservative– Predictions for distortional-controlled members exhibit a slightly different
trend than the DSM curve – DSM approach is viable when reduced elastic buckling is considered
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•Nonlinear FEM of COLUMNS and BEAMS with holes
•Automate modal identification with GBT
•Brainstorming for simplified methods of determining Mcr for local and distortional hole modes
•Develop FEM meshing tools for CFS members with holes
•Moving closer to a formal connection between elastic buckling and ultimate strength for cold-formed steel members with holes
What’s Next?
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• extra slides.. not enough time to cover
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Beam Elastic Buckling Study
1 inch mesh spacing (typ.)
Rigid body connection between top (and bottom) flange midline nodes
Rigid body reference node
Channel 1
Channel 2
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Local Buckling Modes
L (NO HOLE)Mcrl/Myg=1.05
LH2Mcrl/Myg=0.87
LMcrl/Myg=1.07
LHMcrl/Myg=0.75
Beam nominal depth=6”
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Beam Tests vs. DSM Predictions
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
local slenderness, (Myg/Mcrl)0.5
Mte
st/M
yg
DSM MnlLocal buckling controls
Test to Predictedmean=1.061STDV=0.096
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Beam Tests vs. DSM Predictions
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
distortional slenderness, (Myg/Mcrd)0.5
Mte
st/M
yg
DSM Mnd
Distortional buckling controls
Test to Predictedmean=0.928STDV=0.098