direct strength design for with perforations - … holes progress report 3... · direct strength...

Direct Strength Design for Cold-Formed Steel Members

with Perforations

Progress Report 3C. Moen and B.W. Schafer

AISI-COS MeetingFebruary 2007

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

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?




• Conclusions

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

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

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

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

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

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




• Conclusions

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

Test SetupMTS Load CellFixed Crosshead

Steel Platen

Novotechnikposition transducers (with magnet tips)

Hydraulic actuator

End Conditions and Hole Locations

Hole orientations

Column end preparation

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

362S162-33 Short ColumnPeak Load

hole (unstiffenedstrip)

Peak Load

Holes DO influence column ductility and failure modes.

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.

600S162-33 Short ColumnPeak Load

Peak Load

Peak Load

Influence of slotted hole on failure mode is not as strong here.

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


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.

362S162-33 Intermediate Column

Peak Load

Peak Load

Holes dampen web local buckling.

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


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.

600S162-33 Intermediate ColumnPeak Load

Loud snap from local (L) to distortional (D) buckling.

Hole stiffens web and prevents snap from L to D.

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


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.




• Conclusions

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)

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.

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.

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”

Distortional Buckling Modes

DMcrd/Myg=2.31Half wavelength=12 inches

DHMcrd/Myg=2.00


Beam nominal depth=3.625”

Restraints influence location of half-waves

Distortional Buckling Modes


DH+LMcrd/Myg=0.88


Formal modal identification method is needed!!!

Beam nominal depth=8”

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

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

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

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




• Conclusions

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

•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?

• extra slides.. not enough time to cover

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

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”


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



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


direct strength design for with perforations - … holes progress report 3... · direct strength...

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