CS 3120 USER INTERFACE DESIGN, IMPLEMENTATION AND EVALUATION (UIDIE) Dr. Ben Schafer schafer/3120.
Strain Distribution in Locally Slender Structural Steel Cross-sections Seif, M., Schafer, B.W. Civil...
-
Upload
darlene-grew -
Category
Documents
-
view
212 -
download
0
Transcript of Strain Distribution in Locally Slender Structural Steel Cross-sections Seif, M., Schafer, B.W. Civil...
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