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?