Transcript Civil Engineering At JHU

Analysis and Testing of
Cold-Formed Steel Beams
Cheng Yu
Benjamin W. Schafer
The Johns Hopkins University
2003
Overview
• Background
• Experiments
– Local buckling tests
– Distortional buckling tests
• Design methods
• Extensions (FEA)
• Conclusions
Background
Local buckling tests
Testing setup
Range of tested specimens
Experiments on restraint detail
Specimen
8.5Z0735E6W
8.5Z0731E2W
8.5Z0734E3W
8.5Z073-5E6W
Mtest/My
Mtest/Maisi
0.78
0.86
0.80
0.88
0.86
0.96
note
single panel-to-purlin screws - 12" o.c.
single panel-to-purlin screws
on both sides of raised corrugation
paired panel-to-purlin screws
on both sides of raised corrugation
8.5Z073-1E2W
8.5Z073-4E3W
Distortional buckling tests
Comparison of buckling shapes
Local buckling test
11.5Z092-1E2W
Distortional buckling test
D11.5Z092-3E4W
Comparison of load-displacement
Comparison with U.S. Design
1.40
test-to-predicted ratio
1.20
1.00
0.80
0.60
0.40
Local buckling tests
0.20
Distortional buckling tests
0.00
0.40
0.60
0.80
1.00
1.20
1.40
web slenderness = web = (fy/fcr_web)
1.60
0.5
Compared with North American Spec (NAS 2001) prediction
23 local buckling tests, average Mtest/MNAS=1.02
17 distortional buckling tests, average Mtest/MNAS=0.85
1.80
Distortional buckling tests only
test-to-predicted
ratio
1.2
1
0.8
0.6
0.4
Beams with Mcrl>Mcrd
0.2
Beams with Mcrl<Mcrd
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.5
web slenderness = web = (fy/fcr_web)
Compared with North American Spec (NAS 2001) prediction
Direct Strength Method vs. tests
Local buckling
tests
Mtest/MDSL=1.03
Distortional
buckling tests
Mtest/MDSD=1.03*
*formulas similar
to AS/NZ Spec.
Extensions
• Explicit DB check in North American Spec.
• Restraint of existing systems?
• Moment gradient influence on DB?
Extensions via modeling
FEA result of local buckling test of
Z beams h=8.5 in. t=0.12 in.
Simulation @ 25% Imperfection
P25%=17968.2 lbs (102.5% of test)
Real test
Ptest=17524.7 lbs
Simulation @ 75% Imperfection
P75%=16483.8 lbs (94.1% of test)
Conclusion
• Tests that explicitly separate local and
distortional buckling are necessary for
understanding bending strength
• Current North American Specifications are
adequate only for local buckling limit states
• The Direct Strength expressions work well for
strength in local and distortional buckling
• More work on restraint and influence of
moment gradients is needed
Acknowledgments
• Sponsors
– MBMA and AISI
– VP Buildings, Dietrich Design Group and Clark
Steel
• People
–
–
–
–
Sam Phillips - undergraduate RA
Tim Ruth - undergraduate RA
Jack Spangler – technician
James Kelley – technician
Finite strip and LB vs. DB
FE (elastic) and LB vs. DB
single screw pattern,
t=0.073 in. h=8.5 in.
Z beam
panels removed for
visual purposes only
paired screw pattern,
t=0.073 in. h=8.5 in.
Z beam
panels removed for
visual purposes only
Direct Strength Method
Local buckling strength:
   0.776 , MDS = My

 > 0.776, M DS   1  0.15
 =
M
M
y
   
M cr 0.4
My
M cr 0.4
My
(1)
My
(2)
(3)
cr 
Distortional buckling strength:
 d  0.673 , MDSd = My

d > 0.673, M DSd  1  0.22
d =
M
y
M
crd
   
M crd 0.5
My
M crd 0.5
My
(4)
My
(5)
(6)
Local collapse mechanisms
(a) Collapse of 8.5 in. Z, t=0.073 in.
(b) Collapse of 8.5 in. Z, t=0.059 in.
(c) Collapse of 8 in. C, t=0.097 in.
(d) Collapse of 8 in. C, t=0.043 in.