Strain Distribution in Locally Slender Structural Steel Cross-sections

Seif, M., Schafer, B.W.

CivilEngineeringat JOHNS HOPKINS UNIVERSITY

Acknowledgments

• AISC Faculty Fellowship Program

• Professor Ben Schafer• The thin-walled structures research group at JHU

Overview

• Motivation• Cross-section stability• Design methods• FE parametric study• Strain Distributions• Ongoing work

AISC definition of locally slender

lim

AISC limit:

or 1.49w y

h E

t F

Motivation

AISCQ-factor

AISIEffective

Width

AISIDirect

Strength

App. 1

Qsfy

fy

fy1/2he

Qsfy

fy

fy1/2he

fy

fy ½he

½be

fy

fy ½he

½be

Column curve

c c

c

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

c

Overview

• Motivation• Cross-section stability• Design methods• FE parametric study• Strain Distributions• Ongoing work

ABAQUS elements

S4

10 elements

Residual stresses

--

-

--

+

yc f3.0

)2( fwff

ffct tdttb

tb

----

--

-

--

+

yc f3.0

)2( fwff

ffct tdttb

tb

----

Galambos and Ketter (1959)

Material modeling

fu= 65

fy= 50

Eng

inee

ring

Str

ess (

ksi)

Engineering Strain

y st

Slope, E =29000

Slope, Est=720Slope, Est=720

Slope, E’=145

=0.011

fu= 65

fy= 50

Eng

inee

ring

Str

ess (

ksi)

Engineering Strain

y st

Slope, E =29000

Slope, Est=720Slope, Est=720

Slope, E’=145

=0.011

Barth, White, Righman, & Yang (2005)

Geometric imperfections

Geometric imperfections

Geometric imperfections

100

101

102

103

0

100

200

300

400

500

600

700

800

900

1000

Half wave length

Load

x

x

L

Local

Global

LOCAL slenderness

W14FI: W14x233 with variable Flange thickness, varies Independently from all other dimensions

W14FR: W14x233 with variable Flange thickness, but the web thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W14x233

W36FR: W36x330 with variable Web thickness, but the flange thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W36x330

W36WI: W36x330 section with variable Web thickness, that varies Independently from all other dimensions

c

0 50 100 1500

5

10

15

20

25

30

35

h/tw

b f/2t f

kf=0.1

kw

=36k

f=0.05

kw

=36

kf=0.5

kw

=29

kf=0.5

kw

=29

kf=0.5

kw

=27

kf=0.6

kw

=6.0

kf=1.2

kw

=0.5

kf=0.6

kw

=5.6

kf=0.6

kw

=5.0

kf=0.9

kw

=2.1

pw

rw

pf

rf

W36WI

W36FR

W14FR

W14FI

fy = 50 ksi (345 MPa)

LOCAL slenderness

Results

Columns

1 2 30

0.5

1

W14FI

1 2 30

0.5

1

W14FR

1 2 30

0.5

1

W36FR

1 2 30

0.5

1

W36WI

1 2 30

0.2

0.4

0.6

0.8

1

1 2 30

0.2

0.4

0.6

0.8

1

1 2 30

0.2

0.4

0.6

0.8

1

1230

0.51

AISC

AISI

DSM

ABAQUS

AISI

DSM

AISC

Results

Columns

App. 1

1 2 30

0.2

0.4

0.6

0.8

1

1 2 30

0.2

0.4

0.6

0.8

1

1 2 30

0.2

0.4

0.6

0.8

1

1230

0.51

AISC

AISI

DSM

ABAQUS

AISI

DSM

AISC

Overview

• Motivation• Cross-section stability• Design methods• FE parametric study• Strain Distributions• Ongoing work

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2000

4000

6000

8000

10000

12000

Results

W36x330

x

x

x

W36WI

Thicker

OriginalW36x233

ThinnerDisplacement, in.

Pn,

kip

s

Deformed shape

Thinnerweb

OriginalW36x330

ThickerWeb

Membrane longitudinal stress

Thinnerweb

OriginalW36x330

Thickerweb

~ Zero= Yield

Membrane plastic strain

Thinnerweb

OriginalW36x330

Thickerweb

~ 10y

~ Zero

3D 2D

S4 - Element3D

xx

Thinnerflange

Thickerflange

2D Stress/Strain distributions

2D

Effective Area

NO !!!!

--

-

--

+

yc f3.0

)2( fwff

ffct tdttb

tb

----

--

-

--

+

yc f3.0

)2( fwff

ffct tdttb

tb

----

Equilibrium

Clear height

W14 FI: Strain Energy Distribution

Thinner ThickerOriginalW14x233

SEbending

SEmembrane

SEbending

SEmembrane

SEbending

SEmembrane

W14 FI: Postulated Effective Width Distribution

Thinner ThickerOriginalW14x233

W14 FR: Strain Energy Distribution

Thinner ThickerOriginalW14x233

SEbending

SEmembrane

SEbending

SEmembrane

SEbending

SEmembrane

W14 FR: Postulated Effective Width Distribution

Thinner OriginalW14x233

Thicker

W36 FR: Strain Energy Distribution

Thinner OriginalW36x330

Thicker

SEbending

SEmembrane

SEbending

SEmembrane

SEbending

SEmembrane

W36 FR: Postulated Effective Width Distribution

Thinner OriginalW36x330

Thicker

W36 WI: Strain Energy Distribution

Thinner OriginalW36x330

Thicker

SEbending

SEmembrane

SEbending

SEmembrane

SEbending

SEmembrane

W36 WI: Postulated Effective Width Distribution

Thinner OriginalW36x330

Thicker

Ongoing work

• Strain Distributions

• Effective Areas

• DSM for Structural Steel

Work continues…..more at: www.ce.jhu.edu/bschafer/aisc