Transcript Slide 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
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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
Perforation patterns in CFS
next?
Objective
Development of a general design method
for cold-formed steel members with perforations.
Direct Strength Method Extensions
Pn = f (Py, Pcre, Pcrd, Pcrl)?
Does f stay
the same?
Gross or net, or
some combination?
Explicitly model hole(s)?
Accuracy? Efficiency?
Identification? Just these
modes?
DSM for columns no holes
267 columns , b = 2.5, f = 0.84
Progress Report 1 Highlight
DSM prediction* for stub columns with holes
1.4
1
D buckling controls
L buckling controls
DSM Pnl
1.2
0.8
DSM Pnd
0.6
0.8
P
test
/P
y,g
1
0.4
0.6
0.4
0.2
mean test-to-predicted = 1.04
0
standard
deviation = 0.16
0.2
0
0
0
0.2
0.5
0.4
1
1.5
0.6
0.8
2
2.5
1
3
(Py,g/Pcrl)0.5,(Py,g/Pcrd)0.5
*P by FE reflects test boundary conditions, minimum D mode selected, P =P
Progress Report 1 Highlight
Global buckling in long columns with holes
1.4
1
Global buckling controls, P ne=Pnl
All Long Column Specimens
DSM Pne
1.2
0.8
1
0.6
0.8
Local buckling controls
DSM Pnl
0.8
1
ne,g
0.6
0.8
/P
test
0.4
0.6
P
test
P
1
1.2
/P
y,g
1.4
0.4
0.6
0.4
0.2
0.2
0.4
0
0.2
0
0
0
0.2
0.5
0.4
1
1.5
0.6
0.8
2
2.5
Slenderness, (P ne/Pcrl)0.5
mean test-to-predicted = 1.14
standard
deviation = 0.09
0
0.2
0
0
0
0.2
0.5
0.4
1
1.5
0.6
0.8
2
Slenderness, (P y,g/Pcre)0.5
2.5
1
3
1
3
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
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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
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)
1.2
1
(a)
f
/f
cr,hole cr,no hole
1
(a)
0.8
0.8
(b)
hhole/h=0.66
0.6
hhole/h=0.44
0.6
hhole/h=0.19
0.4
(a) L
0.4
0.2
(a)
(b)
0
Rhole
(b)
hhole
0
hhole/h=0.26
Lhole
0.2
0
(b)
0
h
0.2
5
0.4
10
0.6
15
L/Lhole
0.8
1
20
25
Influence of multiple holes
S/2
S
Lhole
h
hhole
Fixed length plate, vary spacing and quantity of holes
(note clear space between holes = S – Lhole)
models compared at equal numbers of DOF
Influence of multiple holes
1.2
1
1.2
1
1
/f
f
/f holes
cr,holes
cr,no
cr,holes
cr,no holes
hhole/h=0.44
0.8
1
f
hhole/h=0.66
hhole/h=0.19
0.8
hhole/h=0.26
0.8
0.6
0.9
0.8
0.6
0.6
0.85
0.4
0.6
0.8
0.4
0.4
0.75
0.2 2
0.4
0.2 0.2
0
0.2
0
0
0
0
0
hhole/h=0.66
hhole/h=0.26
5
4
3
S/Lhole
Lhole
S
0.2
0
0
/h=0.44
h
hole
Decrease in fcr when hole
/h=0.19
hhole
small
spacing becomes
0.4
h
0.6
hhole
0.8
Simply supported plate (all four sides), S=4Lhole shown
5 0.2
5
0.6
15
100.4
S/Lhole
15
10
S/Lhole
1
0.8
20
125
20
25
Comparison of findings on spacing
• Elastic buckling study: Old D4 rules on holes...
S/Lhole > 5 implies
• S > 24 in.
• Sclear-end > 10 in.
• S > 5Lhole and
• Lhole < 4.5 in.
• Sclear > 4Lhole
implies
• S > 5.3Lhole
• Send > 2.5Lhole and
• Sclear-end > 2.2Lhole
• Sclear-end > 2Lhole
old rules look reasonable, but we
need to non-dimensionalize
Critical buckling stress equation
Lhole
S
S/2
5
hhole
1Data points from
eigenbuckling analysis
4.5
4
plate buckling coeff., k
h
0.8
3.5
0.6
3
Fitted curve
2.5
2
h 
h 
k  6 hole   4 hole   4  4
 h 
 h 
0.4
2
1.5
for S/Lhole > 5
0.2
1
0.5
0
0
0
0
0.2
0.2
0.4
0.4
0.6
0.6
hhole/h
0.8
0.8
1
1
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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
Flange holes in SSMA studs
(Western States Clay Products Association
Design Guide for Anchored Brick Veneer over Steel Studs)
Flange holes and elastic buckling
B
b
R
L
H
bhole
b
t
D
r
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
1
1
D
GFT
L
LH
0.9
0.8
D, no hole
0.8
0.7
0.6
cr
P /P
y
0.6
0.5
GFT, no hole
0.4
0.4
0.3
0.2
0.2
0.1
0
0
0
L, no hole
0
0.2
0.2
0.4
0.4
0.6
0.6
LH
0.8
0.8
bhole/b
Keep bhole/b < 0.5 in this study to avoid problems
1
1
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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
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
P

h
Simply supported plates



(a) Modifed Riks method employed with a uniform
compressive load applied
to the ends of the plate
P
h
(b) Artificial damping method –
employed with uniform
longitudinal displacement
applied at the member ends
(task group only..)
Modified Riks Solution
1
RIKS1
RIKS2
0.8
0.6
cannot move
past peak load
0.4
P/Py,g
0.2
1
compression
0
tension
2
-0.2
Initial imperfection shape
(scale exaggerated)
P

b
-0.4
-0.6


3
-0.8
-1
-2

-1.5
-1
-0.5
0
/t
0.5
1
1.5
P
b
2
(task group only..)
Artificial Damping Solution
1
0.38
STAB1
STAB2
y,g
0.9
P/P
0.8
0.34
Highly nonlinear post-peak
equilibrium path found with
STAB1 and STAB2
0.7
0.3
0.25
P/P
y,g
0.6
0.3
/t
0.5
0.35
0.4
0.3
0.2

P
h

Displacement control
0.1
0
Initial imperfection shape
(scale exaggerated)
P
h
0
0.25
0.5
0.75
1
1.25
1.5
1.75
/t
(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
of plate
initial geometric
imperfections
fundamental buckling
mode mapped to plate
with slotted hole
(task group only..)
Imperfections and strength
Plate WITHOUT a hole
1
1
no imperfections
d1/t=0.14
0.9
0.8
0.8
d1/t=0.34
Pn=0.58Py,g
(DSM Prediction)
d1/t=0.66
0.7
0.6
P/P
y,g
0.6
d1/t=1.35
d1/t=3.85
0.5
0.4
0.4
0.3
0.2
0.2
0
0.1
0
0
0
0.2
0.25
0.5
0.4
0.75
0.6
1
0.8
1.25
1.5
1
1.75
/t
(task group only..)
Imperfections and strength
Plate WITH a hole
1
1 Pn=0.56Py,g
0.8
0.8
d1/t=0.66
0.6
0.6
y,g
d1/t=0.34
Pn=0.38Py,g
(DSM Prediction, Pne=Py,net)
0.7
P/P
no imperfections
d1/t=0.14
(DSM Prediction, Pne=Py,g)
0.9
d1/t=1.35
d1/t=3.85
0.5
0.4
0.4
0.3
0.2
0.2
0
0.1
0
0
0
0.2
0.25
0.5
0.4
0.75
0.6
1
0.8
1.25
1.5
1
1.75
/t
(task group only..)
Plate strength summary
1
1
plate without hole
plate with hole
0.9
without hole
0.8
0.8
Pn=0.58Py,g
(DSM Prediction)
u
P /P
y,g
0.7
with hole
Pn=0.56Py,g
(DSM Prediction, Pne=Py,g)
0.6
0.6
0.5
0.4
*
*P(∆<d1)=0.50
0.4
*
0.3
0.2
with hole
0.2
0.1
0
0
0
Pn=0.38Py,g
(DSM Prediction, Pne=Py,net)
d1
0
0.5
0.2
1
0.4
1.5
2
d1/t
0.6
2.5
0.8
3
1
3.5
4
(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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
Simply supported plate models
fundamental
buckling mode
of plate


initial geometric
imperfections

fundamental buckling
mode mapped to plate
with slotted hole

Effective width – basic concepts
distribute area (A) to
edges of plate
A/2
he/2
h
t  s11dy  thef y
calculate area under
stress curve (A)
h
0
membrane stress (S11)
he/2
A/2
yield stress
Effective width
Plate WITHOUT hole
+S11
+S11
Plan view of element
Elevation
(a) membrane stress in 1 direction (S11)
h
he/2
(b) variation in effective width along plate
effective width
average
standard deviation
max
min
he/h
0.51
0.02
0.55
0.48
Effective Width
Plate WITH hole
+S11
+S11
Plan view of element
effective width
average
standard deviation
max
min
Elevation
(a) membrane stress in 1 direction (S11)
h
he/2
(b) variation in effective width along plate
he/h
0.38
0.03
0.41
0.34
Through thickness stresses in a plate
+S11
+S11
Plan view of element
Top
Membrane
stress
Midplane
Bottom
Elevation view of element
Membrane
stress
Through thickness stress variation
A
A
A
Longitudinal (S11) stress
variation across width of plate
1
top of plate
midplane of plate
bottom of plate
0.9
0.8
0.7
x/h
0.6
0.5
Top of plate is
fully effective
Stress
distribution used
to calculate
code-based
effective width
0.4
0.3
Tension and compression
stresses counteract each other
when calculating effective width
at the bottom of the plate
0.2
0.1
Compression
0
-1.5
-1
-0.5
Tension
0
fplate/fy
0.5
SECTION A-A
1
1.5
Through thickness effective width
Effective width calculated with
longitudinal stresses (S11) at top,
midplane, and bottom of the plate
Top of Plate
Middle of Plate
Bottom of Plate
ht
  s11dxdy  th ef y
00
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)
task group
isolated plates with holes
studies on effective width
SSMA structural stud with hole (initial study)
• Conclusions
SSMA Structural Stud – Ultimate Strength
(362S162-33)
Centroid restrained in
Rigid translational
connection to centroid in
1, 2, and 3 (u, v, and w)
translation:
2 and 3 (v=w=0)
No warping allowed at
member ends!
rotation:
4, 6 (Θ1=Θ3=0)
Rigid translational
connection to centroid in
1, 2, and 3 (u, v, and w)

Displacement control
2
6
3
5
Pinned End
Conditions
4
Centroid restrained in
translation:
1, 2, and 3 (u=v=w=0)
rotation:
4, 6 (Θ1=Θ3=0)
1
Also modeled – fixed-fixed end conditions
Elastic Buckling Modes
L
Pcrl=0.42Py,g
L
Pcrl=0.42Py,g
L+DH
Distortional modes unique
to a column with a hole
Pcrd1=0.52Py,g
DH2
Pcrd2=0.54Py,g
D
D+L
Pcrd=1.15Py,g
Pcrd3=1.16Py,g
Pinned-pinned shown ( fixed-fixed similar)
Influence of hole and end conditions
on strength
1
1
0.9
0.8
Fixed ends
Pu=0.77Py,g
0.8
0.7
y,g
0.6
P/P
Fixed ends with hole
Pu=0.61Py,g
0.6
0.5
0.4
Pinned ends
Pu=0.64Py,g
0.4
0.3
0.2
0.2

0
0.1
0
0
0
Displacement control
0.2
0.25
0.5
0.4
0.75
Pinned ends with hole
Pu=0.53Py,g
0.8
1
0.6
1
1.25
1.5
1.75
/t
baseline response: initial imperfections not considered here
SSMA stud failure mechanisms
Yielding occurs in
the web, flange,
and lip stiffener
Fixed ends
Pu=0.77Py,g
33 ksi yield stress
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
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 postbuckling capacity and some concern with using DSM local
buckling curve for members with holes.
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