Strain Distribution in Locally Slender
Structural Steel Cross-sections
Seif, M., Schafer, B.W.
Civil
Engineering
at 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
Motivation
AISC definition of locally slender
AISC limit:
 h
 or  
 tw 
 1.49
E
Fy
lim
AISC
Q-factor
AISI
Effective
Width
AISI
Direct
Strength
App. 1
½be
Qsfy
fy
fy
fy
1/2he
fy
½he
Column curve

1.2
c
1
c
0.8
0.6
0.4
0.2
c
0
0
0.2
0.4
0.6
0.8
1
c
1.2
1.4
1.6
1.8
Overview
•
•
•
•
•
•
Motivation
Cross-section stability
Design methods
FE parametric study
Strain Distributions
Ongoing work
ABAQUS elements
S4
10
elements
Residual stresses
-
-
-
 c  0. 3 f y


bf t f


+ t  c

 b f t f  t w ( d  2t f ) 
-
-
Galambos and Ketter (1959)
Engineering Stress (ksi)
Material modeling
fu= 65
fy= 50
Slope,
E’=145
Slope,
Est =720
Slope,
E =29000
y
 st =0.011
Engineering Strain
Barth, White, Righman, & Yang (2005)
Geometric imperfections
Geometric imperfections
Geometric imperfections
1000
900
800
700
Load
600
500
400
x
300
Local
200
Global
100
0
0
10
x
1
2
10
3
10
Half wave length
10
L
LOCAL slenderness
W14FI: W14x233 with variable Flange thickness, varies
c
Independently from all other dimensions
W14FR: W14x233 with variable Flange thickness, but
the web thickness set so that the Ratio of the flange-toweb 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
LOCAL slenderness
35
f y = 50 ksi (345 MPa)
30
k f=1.2
k w=0.5
25
20
b /2t
f
rf
k f=0.6
k w=6.0
k f=0.5
k w=29
f
W14FI
W14FR
15
k f=0.9
k w=2.1
10
pf
k f=0.6
k w=5.0
5
0
0
k f=0.5
k w=29
k f=0.6
k w=5.6
k f=0.5
k w=27
W36FR
k f=0.1
k w=36
W36WI
pw 100
50
h/t w
k f=0.05
k w=36
rw
150
W14FI
 
1
W14FR
0.4
1
0.2
AISC
1
2
0
3
0.5
1
2
1
1
3
0.8
0.5

2

1
3
2
1

2
3
3
AISC
1 AISI
0.5 DSM
0
123
ABAQUS
W36WI
0.4
0.2
1
0
AISI

0.6
0
0
0.6
0.4
0.5
W36FR
 
0.8
0.6
0
0
1
0.8
0.2
 
 
1
Results
1
DSM
1
2

0.5

0
1
3

2
3

Columns
 
Results
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0.2
AISC
1
2
3
0
AISI
1

2
3

 
1
0.8
0.6
0.4
0.2
0
App. 1
AISC
1 AISI
0.5 DSM
0
123
ABAQUS
DSM
1

2
3

Columns
Overview
•
•
•
•
•
•
Motivation
Cross-section stability
Design methods
FE parametric study
Strain Distributions
Ongoing work
Results
12000
Thicker
10000
W36WI
x
P , kips
n

8000
6000
Original
W36x233
x
4000
W36x330
x
2000
0
0
0.2
0.4
0.6
0.8
1
1.2
in.
 Displacement,





1.4
1.6
1.8
2
Thinner
Deformed shape
Thinner
web
Original
W36x330
Thicker
Web
~ Zero
= Yield
Membrane longitudinal stress
Thinner
web
Original
W36x330
Thicker
web
~ 10y
~ Zero
Thinner
web
Membrane plastic strain
Original
W36x330
Thicker
web
3D
2D
x
3D
S4 - Element
2D Stress/Strain distributions
Thinner
flange
Thicker
flange
Effective
Area
NO !!!!
2D
Equilibrium
-
-
-
 c  0. 3 f y


bf t f


+ t  c

 b f t f  t w ( d  2t f ) 
Clear height
-
-
W14 FI: Strain Energy Distribution
Thinner
SEbending
SEbending
SEmembrane
SEmembrane
Original
W14x233
SEbending
SEmembrane
Thicker
W14 FI: Postulated Effective Width Distribution
Thinner
Original
W14x233
Thicker
W14 FR: Strain Energy Distribution
Thinner
SEbending
SEbending
SEbending
SEmembrane
SEmembrane
SEmembrane
Original
W14x233
Thicker
W14 FR: Postulated Effective Width Distribution
Thinner
Original
W14x233
Thicker
W36 FR: Strain Energy Distribution
Thinner
SEbending
SEbending
SEbending
SEmembrane
SEmembrane
SEmembrane
Original
W36x330
Thicker
W36 FR: Postulated Effective Width Distribution
Thinner
Original
W36x330
Thicker
W36 WI: Strain Energy Distribution
Thinner
SEbending
SEbending
SEbending
SEmembrane
SEmembrane
SEmembrane
Original
W36x330
Thicker
W36 WI: Postulated Effective Width Distribution
Thinner
Original
W36x330
Thicker
Ongoing work
• Strain Distributions
• Effective Areas
• DSM for Structural Steel
Work continues…..
more at:
www.ce.jhu.edu/bschafer/aisc