Direct Strength Design for Cold-Formed Steel Members with Perforations

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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

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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 DSMstub
  columns, long columns
• Conclusions

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Objective

• Development of a general design method for
  cold-formed steel members with perforations.

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Perforation patterns in CFS
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Direct strength prediction

• Pn f (Py, Pcre, Pcrd, Pcrl)?
• Input
• Squash load, Py
• Euler buckling load, Pcre
• Distortional buckling load, Pcrd
• Local buckling load, Pcrl
• Output
• Strength, Pn

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Direct strength for members with holes

• 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?
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DSM for columns without holes
267 columns , b 2.5, f 0.84
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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 DSMstub
  columns, long columns
• Conclusions

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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

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Project year 1
Focus has primarily been on compression members
with isolated holes in the first 6 mos.
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Project year 2
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Project year 3
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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 DSMstub
  columns, long columns
• Conclusions

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ABAQUS Element Accuracy

• Motivation
• For the student to learn and understand
  sensitivity of elastic (eigen) stability response
  to FE shell element solutions
• In particular, to explore FE sensitivity in
  members with holes
• To take the first tentative steps towards
  providing practicing engineers real guidance when
  using high level FE software for elastic
  stability solutions of unusual situations

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Stiffened element in uniform compression
(benchmark stiffened plate in compression)
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Linear vs. quadratic elements
S4/S4R
S9R5
models compared at equal numbers of DOF
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Number of elements along the length
2.5 elements per half-wave shown
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S9R5 sensitivity to modeling corners
1 element in corner
Use of quadratic shell elements that can have an
initially curved geometry shown to be highly
beneficial/accurate here.
3 elements in corner
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FE vs FSM comparisons

• SSMA 362S162-33 in pure compression
• FE ABAQUSFSM CUFSM

model length half-wavelength in ABAQUS (ABAQUS
boundary conditions pinned ends)
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Exploring local buckling difference
number of local buckling half-waves in ABAQUS
model (physical length of ABAQUS model is
increased)
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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 DSMstub
  columns, long columns
• Conclusions

22
Mesh sensitivity around holes
4 layers of elements shown
SS
SS
SS
SS
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Mesh sensitivity around holes
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Mesh sensitivity around holes
Do holes decrease local buckling this much??
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The square plate problem

• Much of the fundamental research on plates with
  holes has been conducted on square plates.
• The idea being that one local buckle evenly fits
  into a square plate.
• So, examining the impact of the hole in a square
  plate examines the impact in a localized fashion?

?

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Local buckling in an a/b 4 plate
w
92.075mm
l
4w
Conclusion? Lots of wonderful theoretical studies
are not really relevant...
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SSMA hole and varied plate width
4w
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Local plate stability with a hole
Observed loss of local stability much less than
in a square plate. We will revisit this basic
plot for member local buckling as well.
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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 DSMstub
  columns, long columns
• Conclusions

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SSMAS162-33 w/ hole Member Study
L 1220mm 48 in.
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CUFSM elastic buckling (no hole)
Pcr/Py
half-wavelength (mm)
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ABAQUS model

• Classical FSM style boundary conditions are
  employed, i.e., pinned free-to-warp end
  conditions.

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Local (L) buckling

• Pcrl no hole 0.28Py, with hole 0.28Py

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Distortional (D) buckling

• Pcrd no hole 0.64Py, with hole 0.65Py

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Distortional (DH) buckling around the hole

• Pcrd no hole 0.64Py, with hole 0.307Py

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Antisymm. dist. buckling (DH2) at the hole

• Pcrd no hole 0.64Py, with hole 0.514Py

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Global flexural torsional (GFT) buckling

• Pcrd no hole 0.61Py, with hole 0.61Py

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Impact of hole location on buckling values
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Hole location impact on GFT

• GFT mode with hole at midspan
• Mixed GFT-L-D mode observed with hole near end.
• BC influence near the ends, under further study..

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SSMAS162-33 w/ hole Member Study 2
b
L 1220mm 48 in.
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Hole size and member buckling modes
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Observed buckling modes
L
DH
GFT
D
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DH mode
0.62Py 0.38Py 0.35Py 0.31Py 0.30Py
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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 DSMstub
  columns, long columns
• Conclusions

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Modal identification

• Mixing of modes (a) complicates the
  engineers/analysts job (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

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We cant effectively use FEM

• We need FEM methods to solve the type of
  general stability problems people want to solve
  today
• tool of first choice
• general boundary conditions
• handles changes along the length, e.g., holes in
  the section

30 nodes in a cross-section 100 nodes along the
length 5 DOF elements 15,000 DOF 15,000 buckling
modes, oy!

• Modal identification in FEM is a disaster

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Special purpose finite strip can fail too
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cFSM

• cFSM constrained finite strip methodThe
  constraints restrict the FSM model to
  deformations within a selected mode for
  instance, only distortional buckling
• cFSM adopts the basic definitions of buckling
  modes developed by GBT researchers
• My research group has been developing this method
  as a means to provide modal decomposition and
  modal identification
• Extension of modal identification to general
  purpose FE results has a potentially huge impact
  on our problem

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modal decomposition
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modal identification
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at the heart of cFSM are themechanics-based
modal buckling definitions
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1
2
3

• Global modes are those deformation patterns that
  satisfy all three criteria.
• now let us examine these three criteria...

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1
2
3

• 1 membrane strains
• gxy  0, membrane shear strains are zero,
• ex  0, membrane transverse strains are zero, and
  
• v f(x), long. displacements are linear in x
  within an element.

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1
2
3

• 2 warping
• ey ? 0,
• longitudinal membrane strains/displacements
  are non-zero along the length.

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1
2
3

• 3 transverse flexure
• ky  0,
• no flexure in the transverse direction.
  (cross-section remains rigid!)

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1
2
3

• Distortional modes are those deformation patterns
  that satisfy criteria 1 and 2, but do not
  satisfy criterion 3 (i.e., transverse flexure
  occurs).

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1
2
3

• Local modes are those deformation patterns that
  satisfy criterion 1, but do not satisfy
  criterion 2 (i.e., no longitudinal warping
  occurs) while criterion 3 is irrelevant.

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1
2
3

• Other modes (membrane modes ) do not satisfy
  criterion 1. Note, other modes typically do not
  exist in GBT, but must exist in FSM or FEM due to
  the inclusion of DOF for the membrane.

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1
2
3
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lipped channel column example

• FSM DOF 4 per node, total of 24

v
q
u
w
200mm
G4
O10
D2
L8
t2mm
15mm
all deformations
80mm
E210000MPa, n0.3
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G and D deformation modes
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L deformation modes
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O deformation modes
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Modal decomposition

• Begin with our standard stability (eigen) problem
• Now introduce a set of constraints consistent
  with a desired modal definition, this is embodied
  in R
• Pre-multiply by RT and we create a new, reduced
  stability problem that is in a space with
  restricted degree of freedom, if we choose R
  appropriately we can reduce down to as little as
  one modal DOF

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modal decomposition
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modal identification
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Years 2 and 3 of this project...

• extending modal identification to FE is one of
  the keys to creating a general method that all
  can agree upon.
• We need to remove the ambiguity in visual modal
  identification (a small problem for members
  without holes, but a much more important one for
  members with holes!)

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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 DSMstub
  columns, long columns
• Conclusions

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Study of experimentally tested members

• Collection of experimental column data
• 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

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Geometry of available specimens

• Stub columns
• Total of 51 specimens
• Boundary conditions...
• Remember the square plate lesson in local
  buckling
• Distortional restrained

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Geometry of available specimens

• Long columns
• Total of 15 specimens
• Member geometry not varied significantly, but
  hole size range is fairly large

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Length of available tested specimens
more testing needed here to understand what
is going on with holes and distortional buckling..
stub columns
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Histogram of normalized hole size
?
enough specimens with big holes?
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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 DSMstub
  columns, long columns
• Conclusions

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Elastic local buckling in stub columns
Pcrl,no hole pin free- to-warp boundary
conditions
increasing hole size
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Boundary conditions of stub test matter
The bigger the hole and the shorter the specimen
the more important the BC
Local buckling
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Boundary condition effect local buckling
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Effect of isolated holes on local buckling in
long columns?
remember...
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Distortional buckling (effect of holes)
(stub column data)
identification of D modes can be challenging,
minimum D mode DH mode
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Distortional buckling (effect of holes)
(long column data)
identification of D modes can be challenging,
minimum D mode DH mode
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Stub column testing restrains distortional
buckling
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Ends free to warp vs. fixed

• Remember! D modes are defined by the warping
  (longitudinal deformations)

warping distribution defined by cFSM
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Global buckling in long columns(effect of holes)
Effect of holes on global buckling modes greater
than anticipated, still under study...
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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 DSMstub
  columns, long columns
• Conclusions

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Preliminary DSM for stub columns

• Local strength

lowest local mode in an FE model with hole and
test boundary conditions
Pne set to Py
Pne set to Py
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Gross vs. Net Area
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First cut of DSM on Stub Columns
(NET YIELD PyPy,net Local slenderness plotted
for all data)
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First cut of DSM on Stub Columns
(GROSS YIELD PyPy,g Local slenderness plotted
for all data)
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Preliminary DSM for stub columns

• Local strength
• Distortional strength

lowest local mode in an FE model with hole and
test boundary conditions
Pne set to Py
Pne set to Py
lowest distortional mode (includes DH) in an FE
model w/ hole and test bcs
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DSM prediction for stub columns
NET
mean test-to-predicted 1.18 standard deviation
0.16
Pcr by FE reflects test boundary conditions,
minimum D mode selected, PyPy,net
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DSM prediction for stub columns
GROSS
mean test-to-predicted 1.04 standard deviation
0.16
Pcr by FE reflects test boundary conditions,
minimum D mode selected, PyPy,g
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Preliminary DSM for Stub Columns
member length/web depth (L/H)
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Preliminary DSM for long columns
Global buckling
Local buckling
Distortional buckling
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Global buckling in long columns
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Local-global in long columns
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Preliminary DSM for long columns
member length/web depth (L/H)
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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 DSMstub
  columns, long columns
• Conclusions

98
Conclusions

• We are off and running on columns with holes
• Local buckling (a) doesnt 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!

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DH mode as hole location moves
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Beginning of BC study

• Pinned free-to-warp ends, midspan warping
  restrained
• Pinned fixed warping ends, far end is torsion free