Transcript Slide 1

Direct Strength Design for
Cold-Formed Steel Members
with Perforations
Progress Report 1
C. Moen and B.W. Schafer
AISI-COS Meeting
February 21, 2006
Outline
• Objective and challenges
• Project overview
• FE stability studies
– fundamentals, plates and members with holes
• Modal identification and cFSM
• Existing experimental column data
– elastic buckling studies:
hole effect, boundary conditions
– strength prediction by preliminary DSM
stub columns, long columns
• Conclusions
Objective
Development of a general design method
for cold-formed steel members
with perforations.
Direct strength for members with holes
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?
Project Update
• Originally proposed as a three year
project. Year 1 funding was provided, we
are currently ½ way through year 1.
• Project years
1: Benefiting from existing data
2: Identifying modes and extending data
3: Experimental validation & software
Outline
• Objective and challenges
• Project overview
• FE stability studies
– fundamentals, plates and members with holes
• Modal identification and cFSM
• Existing experimental column data
– elastic buckling studies:
hole effect, boundary conditions
– strength prediction by preliminary DSM
stub columns, long columns
• Conclusions
Local plate stability with a hole
Simply Supported
w
w
R = 19.05mm
h
w = 38.1mm
l = 101.6mm
Simply Supported
4w
305mm
610mm
610mm
SSMAS162-33 w/ hole Member Study
SSMA Designation
362S162-33
H
(mm)
92.1
B1
(mm)
41.3
B2
(mm)
41.3
D1
(mm)
12.7
L = 1220mm = 48 in.
D2
(mm)
12.7
R
(mm)
1.9
t
(mm)
0.88
Local (L) buckling
• Pcrl no hole = 0.28Py, with hole = 0.28Py
2
Distortional (D) buckling
• Pcrd no hole = 0.64Py, with hole = 0.65Py
2
Global flexural torsional (GFT) buckling
• Pcrd no hole = 0.61Py, with hole = 0.61Py
half-wavelength
10
0
0.5
load factor
1
1.5
2
1
10
2
10
3
Distortional (DH) buckling around the hole
• Pcrd no hole = 0.64Py, with hole = 0.307Py
2
2
Hole size* and member buckling modes
1
1
0.9
0.8
0.8
0.7
0.6
D
GFT
DH2
DH
L
cr
P /P
y
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0
0.1
0
0
0
0.2
0.2
0.4
0.4
0.6
b/H
0.6
0.8
0.8
1
1
*this graph depicts effect of a circular hole, not the ‘SSMA’ oval hole
Modal identification
• Mixing of modes (a) complicates the
engineer/analyst work (b) may point to
post-buckling complications
• We need an unambiguous way to identify
the buckling modes
• A significant future goal of this research is
the extension of newly developed modal
identification tools to members with holes
cFSM and modal decomposition
FSM All
L (L1-L8)
1
D (D -D )
1
2
G (G -G )
2
4
0.8
cr
P /P
y
example (a)
0.6
0.4
0.2
0
2
10
3
10
half-wavelength (mm)
10
4
cFSM and modal identification
global
distortional
local
other
1
cr
P /P
y
0.8
0.6
0.4
L
D
0.2
0
2
10
G
3
10
half-wavelength (mm)
4
10
Outline
• Objective and challenges
• Project overview
• FE stability studies
– fundamentals, plates and members with holes
• Modal identification and cFSM
• Existing experimental column data
– elastic buckling studies:
hole effect, boundary conditions
– strength prediction by preliminary DSM
stub columns, long columns
• Conclusions
Study of experimentally tested members
• Collection of experimental column data
Reference
Author
Publication Date
1
Ortiz-Colberg
1981
2
3
4
5
Pekoz and Miller
Sivakumaran
Abdel-Rahman
Pu
1987
1994
1998
1999
Types of Specimens
Stub Column
Long Column
Stub Column
Stub Column
Stub Column
Stub Column
Cross Section
Lipped Channel
Lipped Channel
Lipped Channel
Lipped Channel
Lipped Channel
End Conditions
Fixed-Fixed
Weak Axis Pinned
Fixed-Fixed
Fixed-Fixed
Fixed-Fixed
Fixed-Fixed
• Estimation of elastic buckling Pcrl, Pcrd, Pcre
using FE to capture influence of hole and
reflect test boundary conditions
• Examination of initial DSM strength
predictions for tested sections
Elastic local buckling in stub columns
2.5
1
Stub column data
Unstiffened element approx.
0.8
0.6
1.5
Pcrl,no hole
= pin freeto-warp
boundary
conditions
0.4
1
P
crl,hole
/P
crl,no hole
2
0.2
0.5
0
0
0
0
0.2
0.1
0.4
0.6
0.2
0.3
0.4
hole depth/web width (b/H)
0.8
0.5
increasing hole size
1
0.6
Boundary condition effect: local buckling
1.8
1
Long Columns
Stub Columns
1.6
0.8
1.2
0.6
1
0.4
0.8
0.6
P
crl,test bc
/P
crl,cufsm bc
1.4
0.2
0.4
0.2
0
0
0
0
0.2
0.05
0.4
0.6
0.1
0.15
0.2
0.25
hole depth/member length (b/L)
0.8
0.3
1
0.35
Distortional buckling (effect of holes)
(stub column data)
2.5
1
0.8
0.6
1.5
0.4
1
P
crd,hole
/P
crd,no hole
2
minimum D mode
pure D mode
0.2
0.5
0
0
0
0
0.2
0.1
0.4
0.6
0.2
0.3
0.4
hole depth/web width (b/H)
0.8
0.5
1
0.6
identification of D modes can be challenging, minimum D mode = “DH” mode
Stub column testing restrains
distortional buckling
3
1
0.8
2
1.6 Factor
Suggested by DSM
Design Guide
0.6
1.5
0.4
1
0.2
P
crd,test bc
/P
crd,cufsm bc
2.5
0.5
0
0
0
0
0.2
1
0.4
0.6
2
3
4
web width/flange width (H/B1)
0.8
1
5
6
Global buckling in long columns
(effect of holes)
2.5
1
0.8
0.4
1
P
cre,hole
Effect of holes on global
buckling modes greater than
anticipated, still under study...
0.6
1.5
/P
cre,no hole
2
Long column data
Pnecontrols design, P ne=Pnl
0.2
0.5
0
0
0
0
0.2
0.02
0.4
0.6
0.8
0.04
0.06
0.08
hole length/member length (a/L)
1
0.1
Preliminary DSM for stub columns
• Local strength
Pnl
=
lowest local mode in an FE model with
hole and test boundary conditions


1  0.15 Pcrl
P

 ne





Pne set to Py
Py,net
?
=

 Pcrl
 Pne





0.4
Pne
Pne set to Py
Py,gross
• Distortional strength
Pnd
0.4 
Py,net
?
Py,gross
lowest distortional mode (includes DH)
in an FE model w/ hole and test bc’s
0.6 
0.6






Pcrd   Pcrd 

Py
 1  0.25

Py   Py 


 


P
?
P
P
?
Py,gross
DSM prediction for stub columns
quite a few specimens
have strength
1.4
greater than Py,net
NET
1
D buckling controls
L buckling controls
DSM Pnl
1.2
0.8
DSM Pnd
0.6
0.8
P
test
/P
y,net
1
0.4
0.6
0.4
0.2
mean test-to-predicted = 1.18
standard deviation = 0.16
0.2
0
0
0
0
0.2
0.5
0.4
1
1.5
0.6
0.8
2
2.5
1
3
(Py,net/Pcrl)0.5,(Py,net/Pcrd)0.5
*P by FE reflects test boundary conditions, minimum D mode selected, P =P
DSM prediction* for stub columns
GROSS
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
0.2mean test-to-predicted = 1.04
standard deviation = 0.16
0.2
0
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
2 

2 



Pne =  0.658 c Py
c P

P
=
0
.
658
ne

 y
for  c  1.5




2 

or c > 1.5

for

>
1.5
cPne =  0.658 c Py
for buckling
 c  1.5
Global
 

 0.877 
2
0.877 
1.5 P =Py 0.658  c P

P

Py
for P
ne

for c > 1.5 ne
c
 2ne  
 y
2
  
 c   2

 c 




0.877
.658 c Py
where for
P1.5
ne
y= P0cre
c =cP>
wherePnec  = PyPPycre


 2 
 c 
 0.877 
Local
buckling
for c > 1.5 P  

ne  2 Py
where c = Py Pcre
0.4 
0.4

 c  
 0.877





P 1  0.15 Pcrl   Pcrl  P
P

P
=
y
ne
 P   P 
where ne nl
c  =2 Py Pcre

 ne   ne 
 c 

where c = Py Pcre
Preliminary DSM for long columns
Distortional buckling
Pnd
=
0.6 
0.6






Pcrd   Pcrd 

Py
 1  0.25



Py

 Py 




Global buckling in long columns
1.4
1
Global buckling controls, P ne=Pnl
All Long Column Specimens
DSM Pne
1.2
0.8
0.6
0.8
P
test
/P
y,g
1
0.4
0.6
0.4
0.2
0.2
0
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
Local-global in long columns
1.4
1
Local buckling controls
DSM Pnl
1.2
0.8
0.6
0.8
P
test
/P
ne,g
1
0.4
0.6
0.4
0.2
0.2
0
0
0
0
0.2
0.5
0.4
1
1.5
0.6
0.8
2
Slenderness, (P ne/Pcrl)0.5
2.5
1
3
Preliminary DSM for long columns
1.8
1
Gross Area
Net Area
1.6
0.8
1.4
/P
0.8
test
1
P
n
1.2
0.6
0.4
0.6
0.2
0.4
Gross Area
0 N et Area
0.2
0
0
0
0.2
Standard
D eviation
0.094
0.094
Mean
1.137
1.236
0.4
0.6
5
10
15
member
length/weblength
depth(H/L)
(L/H)
hole depth/member
0.8
1
20
Conclusions
• We are off and running on columns with holes
• Local buckling (a) doesn’t really follow unstiffened
element approximation (at least for elastic buckling)
(b) should be modeled consistent with application, i.e.,
stub column boundary conditions, no square plates
• Distortional buckling is even more of a mess than usual
as it appears to get mixed with local buckling, particularly
around hole locations. What does PcrdPcrl imply? We
need better modal identification tools!
• Global buckling needs further study, Pcre sensitivity to
isolated holes here is a bit surprising
• DSM (preliminary) based on gross section yield instead
of net section yield has the best accuracy, what does this
imply? The boundary conditions of the test and the hole
should be explicitly modeled for finding Pcr.
• Existing data does not cover distortional buckling well.
We need additional experimental work and nonlinear FE
modeling!