Direct Strength Design for Cold-Formed Steel Members
with Perforations
Progress Report 2
C. Moen and B.W. SchaferAISI-COS Meeting
August 2006
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
Perforation patterns in CFS
next?
ObjectiveDevelopment of a general design method
for cold-formed steel members with perforations.
Direct Strength Method ExtensionsPn = f (Py, Pcre, Pcrd, Pcr)?
Does f stay the same?
Gross or net, or some combination?
Explicitly model hole(s)?Accuracy? Efficiency?Identification? Just thesemodes?
DSM for columns no holes
267 columns , = 2.5, = 0.84
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 controls
L buckling controlsDSM P
nl
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
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 Specimens
DSM 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 controls
DSM Pnl
mean test-to-predicted = 1.14standard deviation = 0.09
Project Update
• Year 1 of 3 complete
• Project years1: Elastic buckling studies, identifying modes,
benefiting from existing data
2: Ultimate strength studies, modal composition, connecting elastic stability to strength
3: Experimental validation & software
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
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
Influence of a single hole(benchmark: stiffened plate in compression)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
L/Lhole
f cr,h
ole/f cr
,no
hole
hhole
/h=0.66
hhole
/h=0.44
hhole
/h=0.19
hhole
/h=0.26
Lhole
Rholehhole
h
L
(a) (b)(a) (b)
(a) (b)
(a) (b)
Influence of multiple holes
models compared at equal numbers of DOF
SS/2 Lhole hholeh
Fixed length plate, vary spacing and quantity of holes
(note clear space between holes = S – Lhole)
Influence of multiple holes
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
S/Lhole
f cr,h
oles
/f cr,n
o ho
les
hhole
/h=0.66
hhole
/h=0.44
hhole
/h=0.19
hhole
/h=0.26
2 3 4 50.75
0.8
0.85
0.9
S/Lhole
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
S/Lhole
f cr,holes
/f
cr,no holes
hhole/h=0.66
hhole/h=0.44
hhole/h=0.19
hhole/h=0.26
Simply supported plate (all four sides), S=4Lhole shown
S Lhole hholeh
Decrease in fcr when hole spacing becomes small
Comparison of findings on spacing• 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
Critical 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
h
h
h
hk holehole
SS/2 Lhole hholeh
for S/Lhole > 5
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
Flange holes in SSMA studs
(Western States Clay Products Association Design Guide for Anchored Brick Veneer over Steel Studs)
Flange holes and elastic bucklingB
b
bbholeH
R
D
t
r
L
¼”,½”,¾”, 1”, 1¼” dia. holes in a 1⅝” flange (362S162-33)
Local buckling (LH mode) caused by large diameter holes
Influence of flange holes on elastic buckling modes
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
bhole
/b
Pcr
/Py
D
GFT
L
LH
GFT, no hole
D, no hole
L, no holeLH
Keep bhole/b < 0.5 in this study to avoid problems
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
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..)
Loading and boundary conditions
(a) Modifed Riks method -employed with a uniform compressive load applied
to the ends of the plate
(b) Artificial damping method –employed with uniform longitudinal displacement applied at the member ends
h
P
h
PSimply supported plates
(task group only..)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
/t
P/P
y,g
RIKS1
RIKS2
Initial imperfection shape (scale exaggerated)
P
b
P
b
compression
tension 2
3
cannot move past peak load
1
Modified Riks Solution
(task group only..)
Artificial Damping Solution
0 0.25 0.5 0.75 1 1.25 1.5 1.750
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
/t
P/P
y,g
STAB1
STAB2
0.25 0.3 0.350.3
0.34
0.38
/t
P/P
y,g
Highly nonlinear post-peak equilibrium path found with STAB1 and STAB2
Initial imperfection shape (scale exaggerated)
h
P
Displacement control
h
P
(task group only..)
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..)
Considering initial imperfections
fundamental buckling mode mapped to plate with slotted hole
fundamental buckling mode of plate
initial geometric
imperfections
(task group only..)
Imperfections and strengthPlate WITHOUT a hole
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1 1.25 1.5 1.750
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
/t
P/P
y,g
no imperfections
d1/t=0.14
d1/t=0.34
d1/t=0.66
d1/t=1.35
d1/t=3.85
Pn=0.58Py,g
(DSM Prediction)
(task group only..)
Imperfections and strengthPlate WITH a hole
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1 1.25 1.5 1.750
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
/t
P/P
y,g
no imperfections
d1/t=0.14
d1/t=0.34
d1/t=0.66
d1/t=1.35
d1/t=3.85
Pn=0.56Py,g
(DSM Prediction, Pne=Py,g)
Pn=0.38Py,g
(DSM Prediction, Pne=Py,net)
(task group only..)
Plate strength summary
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 3 3.5 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d1/t
Pu/P
y,g
plate without hole
plate with hole
d1
without hole
Pn=0.58Py,g
(DSM Prediction)with hole
Pn=0.56Py,g
(DSM Prediction, Pne=Py,g)
with hole
Pn=0.38Py,g
(DSM Prediction, Pne=Py,net)
*
* *P(∆<d1)=0.50
(task group only..)
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
Simply supported plate models
SSSS
SSSS
SS
SS SS
SS
fundamental buckling mode mapped to plate with slotted hole
fundamental buckling mode of plate
initial geometric
imperfections
Effective width – basic concepts
h
he/2
he/2membrane stress (S11)
yield stress
calculate area under stress curve (A)
distribute area (A) to edges of plate
A/2
A/2
h
0ye11 fthdyst
Effective widthPlate WITHOUT hole
he/2
(a) membrane stress in 1 direction (S11)
Plan view of element
+S11 +S11
Elevation
(b) variation in effective width along plate
h
effective width he/h
average 0.51standard deviation 0.02
max 0.55min 0.48
Effective WidthPlate WITH hole
Plan view of element
+S11 +S11
Elevation
(a) membrane stress in 1 direction (S11)
(b) variation in effective width along plate
h
effective width he/h
average 0.38standard deviation 0.03
max 0.41min 0.34
he/2
Through thickness stresses in a plate
Plan view of element
+S11 +S11
Elevation view of element
Top
Bottom
MidplaneMembrane stress
Membrane stress
Through thickness stress variation
-1.5 -1 -0.5 0 0.5 1 1.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
fplate
/fy
x/h
top of plate
midplane of plate
bottom of plate
Top of plate is fully effective
Tension and compression stresses counteract each other when calculating effective width at the bottom of the plate
Stress distribution used to calculate code-based effective width
TensionCompression
Longitudinal (S11) stress variation across width of plate
SECTION A-A
A
A
A
Through thickness effective width
Top of plate
Midplane of plate
Bottom of plate
Effective width calculated with longitudinal stresses (S11) at top, midplane, and bottom of the plate
Top of Plate
Middle of Plate
Bottom of Plate
ye
h
0
t
011 fthdxdys
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
SSMA Structural Stud – Ultimate Strength(362S162-33)
1
2
3
Rigid translational connection to centroid in 1, 2, and 3 (u, v, and w)
Centroid restrained in
translation:1, 2, and 3 (u=v=w=0)
rotation:4, 6 (Θ1=Θ3=0)
45
6
Centroid restrained in
translation:2 and 3 (v=w=0)
rotation:4, 6 (Θ1=Θ3=0)
Rigid translational connection to centroid in 1, 2, and 3 (u, v, and w)
Displacement control
Pinned End Conditions
Also modeled – fixed-fixed end conditions
No warping allowed at member ends!
Elastic Buckling Modes
Pcrd=1.15Py,g
Pcr=0.42Py,g Pcr=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
Pinned-pinned shown ( fixed-fixed similar)
Influence of hole and end conditions on strength
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1 1.25 1.5 1.750
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
/t
P/P
y,g
Fixed ends Pu=0.77Py,g
Fixed ends with hole Pu=0.61Py,g
Pinned ends Pu=0.64Py,g
Pinned ends with hole Pu=0.53Py,g
Displacement control
baseline response: initial imperfections not considered here
SSMA stud failure mechanisms
33 ksi yield stress
Fixed ends Pu=0.77Py,g
Fixed ends with hole Pu=0.61Py,g
Pinned ends Pu=0.64Py,g
Pinned ends with hole Pu=0.53Py,g
Yielding occurs only at the hole
Yielding occurs in the web, flange, and lip stiffener
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.
•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
What’s Next?