Limit State Response of Composite Columns and beam-columns Part I, Roberto Leon.pdf
Towards a Direct Strength Method for Cold-Formed Steel Beam-Columns
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Towards a Direct Strength Method for Cold-Formed Steel Beam- Columns Structural Stability Research Council Orlando, Florida May 2010 Y.Shifferaw 1 , B.W.Schafer 2 (1),(2) Department of Civil Engineering- Johns Hopkins University C ivil Engineering at JO HN S H O PK IN S U NIV ERSITY C ivil Engineering at JO HN S H O PK IN S U NIV ERSITY
description
Towards a Direct Strength Method for Cold-Formed Steel Beam-Columns. Structural Stability Research Council Orlando, Florida May 2010 Y.Shifferaw 1 , B.W.Schafer 2 (1),(2) Department of Civil Engineering- Johns Hopkins University. Acknowledgments. National Science Foundation. - PowerPoint PPT Presentation
Transcript of Towards a Direct Strength Method for Cold-Formed Steel Beam-Columns
Towards a Direct Strength Method for Cold-Formed Steel Beam-Columns
Structural Stability Research CouncilOrlando, Florida
May 2010Y.Shifferaw1 , B.W.Schafer2
(1),(2) Department of Civil Engineering- Johns Hopkins University
CivilEngineeringat JOHNS HOPKINS UNIVERSITY
CivilEngineeringat JOHNS HOPKINS UNIVERSITY
Overview• Introduction • Basis of DSM: yield and elastic critical
buckling• Finite element collapse analysis in the P-M
space• Direct Strength Method preliminaries for local
and distortional buckling in the P-M space • Conclusion• Future research
Introduction• Current and postulated beam-column design
approaches
0 50 100 150 2000
10
20
30
40
50
60
70
DSM anchor ptsYieldDiscr
Interaction
n
dcr,
y
nP
dcrP ,
nM dcrM ,
Postulated n curve
for all P and M ratios
Postulated for a
given P and M ratio
0 50 100 150 2000
10
20
30
40
50
60
70
DSM anchor ptsYieldDiscr
Interaction
n
dcr,
y
nP
dcrP ,
nM dcrM ,
Postulated n curve
for all P and M ratios
Postulated for a
given P and M ratio
My
Py
Sections considered
3.625 in.
Channel Eave Strut
1.625 in.
1.75 in
1 in.
0.5 in.
6 in.
1.625 in. 2 in.
0.5 in. 1 in.
1.75 in
t=0.08in.
fy=55.9 ksi
250
DSM basis: major axis yielding and elastic buckling
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Mx/Mx,y
P/P
y362Cmajor
First yieldLoccr
Distcr
DSM basis: minor axis yielding and elastic buckling
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Mz/Mz,y
P/P
y362Cminor
First yieldLoccr
Distcr
DSM basis: biaxial yielding and elastic buckling
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Mz/Mz,y
Mx/M
x,y
362Cbiaxial
First yieldLoccr
Distcr
Finite element modeling
• ObjectiveTo study combined P-M collapse loads in CFS beam-columns for local and distortional limit states.
• Method– Material and geometric nonlinear analysis in
ABAQUS using S9R5 shell element models; geometric local and distortional imperfections considered
– Models generated from purpose-built Matlab code
Major axis local for channel
-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
Mx/Mx,y
P/P
y
FE AnalysisUltimate Bounding Surface
-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
Mx/Mx,y
P/P
y
FE AnalysisUltimate Bounding Surface
Major axis local for eave strut
Minor axis distortional for channel section
-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
Mz/Mz,y
P/P
y
FE AnalysisUltimate Bounding Surface
-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
Mz/Mz,y
P/P
y
FE AnalysisUltimate Bounding Surface
Minor axis distortional for eave strut section
Overview• Introduction • Basis of DSM: yield and elastic critical
buckling• Finite element collapse analysis in the P-M
space• Direct Strength Method preliminaries for local
and distortional buckling in the P-M space • Conclusion• Future research
2
dy
dypynd 1MMMM
2
dy
dypynd 1MMMM
Preliminary DSM beam-column strength prediction
5.0
4.04.0
15.01
,776.0
,776.0
cr
y
yy
cr
y
crn
nen
where
if
if
LOCAL
Local DSM vs major axis strength bounds for channel
-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
Mx/Mx,y
P/P
y
DSM vs Strength Bounds-362Cloc,major
FE-LocDSM anchor pts
Yield
Loccr
DSM proposedInteraction
Local DSM vs minor axis strength bounds for channel
-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
Mz/Mz,y
P/P
y
DSM vs Strength Bounds-362Cloc,minor
FE-LocDSM anchor pts
Yield
Loccr
DSM proposedInteraction
Local DSM vs major axis strength bounds for eave
-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
Mx/Mx,y
P/P
y
DSM vs Strength Bounds-Eloc,major
FE-LocDSM anchor pts
Yield
Loccr
DSM proposedInteraction
Local DSM vs minor axis strength bounds for eave
-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
Mz/Mz,y
P/P
y
DSM vs Strength Bounds-Eloc,minor
FE-LocDSM anchor pts
Yield
Loccr
DSM proposedInteraction
2
dy
dypynd 1MMMM
2
dy
dypynd 1MMMM
Preliminary DSM beam-column strength prediction
DISTORTIONAL
spaceMPtheinradiansindirectionangularcba
where
a
cif
cif
dcr
yd
y
b
y
dcrb
y
dcrnd
d
ynd
d
2()^834.0(,2()^2.1(,2()^136.1(
22.01
,673.0
,673.0
5.0
5.05.0
Distortional DSM vs major axis strength bounds for channel
-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
Mx/Mx,y
P/P
yDSM vs Strength Bounds-362Cd,major
FE-Dist
pFE-Dist
n
DSM anchor pts
Yield
Distcr
DSM proposedInteraction
Distortional DSM vs minor axis strength bounds for channel
-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
Mz/Mz,y
P/P
yDSM vs Strength Bounds-362Cd,minor
FE-Dist
pFE-Dist
n
DSM anchor pts
Yield
Distcr
DSM proposedInteraction
Distortional DSM vs major axis strength bounds for eave
-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
Mx/Mx,y
P/P
yDSM vs Strength Bounds-Ed,major
FE-Dist
pFE-Dist
n
DSM anchor pts
Yield
Distcr
DSM proposedInteraction
Distortional DSM vs minor axis strength bounds for eave
-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
Mz/Mz,y
P/P
y
DSM vs Strength Bounds-Ed,minor
FE-Dist
pFE-Dist
n
DSM anchor pts
Yield
Distcr
DSM proposedInteraction
Conclusion• Under combined loading the assumptions in linear
interaction equations are invalidated in CFS members due to– Un-symmetric shapes of common CFS sections– Consideration of cross-section stability
• Finite element models for local and distortional models are developed to examine load-bending collapse envelopes.
• Preliminary Direct Strength Method design expressions for beam-columns in local and distortional buckling as a function of elastic section slenderness are established and compared with the FE models developed.
• Significant efficiency in the proposed DSM approach in comparison with traditional design.
Future work
• Incorporation of recently proposed inelastic bending provisions
• Further preliminary studies including global buckling
• Beam-column tests• Comprehensive FE parametric study• Formal DSM proposals for beam-columns
