cheng yu, benjamin w. schafer the johns hopkins university february 2004 distortional buckling of c...
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![Page 1: Cheng Yu, Benjamin W. Schafer The Johns Hopkins University February 2004 DISTORTIONAL BUCKLING OF C AND Z MEMBERS IN BENDING Progress Report to AISI](https://reader035.vdocuments.site/reader035/viewer/2022062518/56649e7c5503460f94b7e702/html5/thumbnails/1.jpg)
Cheng Yu, Benjamin W. Schafer
The Johns Hopkins University
February 2004
DISTORTIONAL BUCKLING OF C AND Z MEMBERS IN BENDING
Progress Report to AISI
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Overview
• Test Summary• Notable Tests• Comparison with Local Buckling Tests• Comparison with Design
Specifications• Finite Element Modeling• Conclusions
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Notable Tests
1. Test D8C097 – with lower lateral-torsional buckling strength
Lateral-torsionalDistortionalLocal
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Continued. Test D8C097 – with lower lateral-torsional buckling strength
D8C097-5E4W-standard D8C097-5E4W-angle addedActuator load-displacement
Actuator load P=10350 lbsActuator load P=12751 lbs
84% of DSM_d 99% of DSM_d
Notable Tests - Continued
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Notable Tests - Continued
2. Test D8.5Z059-6E5W – failed outside constant moment region
Beam failed at 83% of distortional strength by DSM
Actuator load-displacementPurlin buckled
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Notable Tests - Continued
3. Test D3.62C054-3E4W – failed by yielding
Mtest= 34 kips-in.
My = 33 kips-in.
McrD = 66 kips-in. (first mode)
Observed large deflection
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Notable Tests - Continued
4. Test D8C033-1E2W – failed in local buckling mode
Mtest= 32.8 kips-in.
My = 40 kips-in.
McrL = 30 kips-in.
McrD = 61 kips-in.
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Direct Comparison with Local Bucking Tests
9 pairs of tests having nominally identical geometry and material yield stresses
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Direct Comparison with Local Bucking Tests - Continued
Test 8.5Z082
Test 8.5Z092
Local buckling test Distortional buckling test
Local buckling test Distortional buckling test
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Direct Comparison with Local Bucking Tests - Continued
Test 12C068
Test 8C043
Local buckling test Distortional buckling test
Local buckling test Distortional buckling test
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0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80
web slenderness = web = (fy/fcr_web)0.5
test
-to
-pre
dic
ted
ra
tio
Local buckling tests
Dirtortional buckling tests
Comparison with Design Codes
Compared with North American Spec (NAS 2001) prediction
Local buckling tests average Mtest/MNAS=1.02Distortional buckling tests average Mtest/MNAS=0.87
(consider controlling specimens only)
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Direct Strength Method vs. tests
Local buckling tests
Mtest/MDSL=1.03
Distortional buckling tests
Mtest/MDSD=1.01*
*formulas similar to AS/NZS Spec.
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Finite Element Modeling
lo a d in g p o in t
displacement control at loading point.
automatic stabilization technique applied.
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Finite Element Modeling - Continued
Solid element (C3D8)Shell element (S4R)
Pin connection between Load
beam and tube
Tie connection between purlin
and tube
Shell element (S4R) Tie connection between purlin
and panel
12
1
2
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Finite Element Modeling - Continued
Link connection between two
nodes to simulate the angle at
tension flanges
• Material properties of beams use tension test results.
• Panel is pure elastic.
• High elastic modulus is assumed for tubesand load beam.
3
3
2
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0.00
0.20
0.40
0.60
0.80
1.00
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
d/t
Pro
babi
lity
(X <
x)
Type 1
Type 2
Type 1 Type 2P(X < x) d/t d/t
0.25 0.14 0.640.50 0.34 0.940.75 0.66 1.550.95 1.35 3.440.99 3.87 4.47 0.50 1.29 0.66 1.07
CDF of Maximum Imperfection
Type 1 Type 2
(local) (distortional)
d
d
Finite Element Modeling – Continuedgeometric imperfection
Geometric imperfection is generated by the superposing two eigenmodes which
are calculated by finite strip method. The magnitudes are corresponding to
25% and 75% CDF of maximum imperfection.
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
web slenderness = web = (fy/fcr_web)0.5
FE
M-t
o-t
est
ra
tio
25% CDF
75% CDF
Finite Element Modeling – Continuedcomparison with tests
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Finite Element Modeling – Continuedselected results
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Conclusions
• Tests that 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
• Local buckling failure could control the strength of beams with loose restraint
• Nonlinear finite element analysis with proper imperfections provides a good simulation
• More work on restraint and influence of moment gradients has been initialized
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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
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Finite Element Modeling - Continued comparison with tests
Test label Ptest(lbs) P25% P25%/Ptest P75%(lbs) P75%/Ptest
8.5Z120-3E2W 17520 17968 103% 16484 94%8.5Z105-2E1W 16720 17294 103% 15806 95%8.5Z092-4E2W 11330 11901 105% 11170 99%8.5Z082-1E2W 10130 11446 113% 10749 106%8.5Z073-4E3W 8341 8770 105% 7309 88%8.5Z065-3E1W 5969 6771 113% 5886 99%8.5Z059-2E1W 6180 6749 109% 5748 93%11.5Z073-2E1W 12120 13956 115% 12396 102%11.5Z082-2E1W 17123 17294 101% 15806 92%11.5Z092-1E2W 22000 23417 106% 19790 90%8.5Z059-4E3W 6275 6855 109% 5763 92%8C097-2E3W 10770 11175 104% 10200 95%8C068-4E5W 6476 6762 104% 5614 87%8C054-1E8W 3492 3849 110% 3233 93%8C043-5E6W 3195 3574 112% 3082 96%6C054-2E1W 2803 2882 103% 2240 80%4C054-1E2W 1731 1720 99% 1365 79%12C068-9E5W 6505 6697 103% 5968 92%3.62C054-1E2W 1263 1170 93% 987 78%12C068-3E4W 8542 9458 111% 8655 101%10C068-2E1W 4381 4233 97% 3937 90%8C068-1E2W 6141 6854 112% 5557 90%8C043-3E1W 2985 3482 117% 3026 101%
mean 106% 93%standard deviation 6% 7%
Ptest: tested actuator load
P25%: load of simulation with 25% CDF
P75%: load of simulation with 75% CDF
Test Label Ptest(lbs) P25% P25%/Ptest P75%(lbs) P75%/Ptest
D8.5Z120-4E1W 15870 16283 103% 14839 94%D8.5Z115-1E2W 14837 16402 111% 13028 88%D8.5Z092-3E1W 9566 10740 112% 8779 92%D8.5Z082-4E3W 7921 9160 116% 7775 98%D8.5Z065-7E6W 5826 6891 118% 6053 104%D11.5Z092-3E4W 16377 16817 103% 14443 88%D8.5Z065-4e5W 4993 5876 118% 5155 103%D11.5Z082-4E3W 14578 15172 104% 14473 99%D12C068-21 6160 8157 132% 7566 123%D8C043-4E2W 2678 3051 114% 2751 103%D12C068-1110 5912 5497 93% 4930 83%D8C033-1E2W 1024 1089 106% 950.8 93%D8C054-7E6W 3032 3363 111% 2919 96%D10C068-4E3W 3185 3235 102% 2746 86%D8C097-5E4W 10350 12353 119% 9985 96%D3.62C054-3E4W 1071 1027 96% 838 78%
mean 110% 95%standard deviation 8% 8%
Local buckling tests Distortional buckling tests
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Comparison with Design Codes - Continued
μ: meanσ: standard deviation
Mtest/ Mtest/ Mtest/ Mtest/ Mtest/ Mtest/ Mtest/
MAISI MS136 MNAS MAS/NZS MEN1993 MDSL MDSd
μ 1.01 1.06 1.02 1.01 1.01 1.03 1.24
σ 0.04 0.04 0.05 0.04 0.06 0.06 0.07
μ 1.00 1.05 1.01 1.00 1.01 1.03 1.24
σ 0.05 0.06 0.07 0.05 0.06 0.07 0.07
μ 0.85 0.91 0.87 1.02 0.96 0.89 1.01
σ 0.11 0.10 0.11 0.09 0.10 0.11 0.08
μ 0.83 0.88 0.85 0.99 0.95 0.87 0.99
σ 0.10 0.10 0.11 0.09 0.11 0.11 0.09
Distortional buckling tests
Controlling specimens
Second specimens
Local buckling tests
Controlling specimens
Second specimens
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Test Summary
Total 19 completed tests were included in the progress report.
9 Z beams 10 C beams
Tensile tests are underway for additional performed 5 tests.
D8.5Z120-4E1W 62ksi D8.5Z115-1E2W 64ksi D8.5Z092-3E1W 58ksi D8.5Z082-4E3W 59ksi D8.5Z065-7E6W 62ksi D8.5Z065-4E5W 60ksi D8.5Z059-6E5W 59ksi D11.5Z092-3E4W 70ksi D11.5Z082-3E4W 72ksi
D8C097-7E6W 85ksi D8C097-5E4W 84ksi D8C068-6E7W 79ksi D8C054-7E6W 41ksi D8C043-4E2W 45ksi D8C033-1E2W 20ksi D12C068-10E11W 33ksi D12C068-1E2W 56ksi D10C068-4E3W 22ksi D3.62C054-3E4W 33ksi
D6C063-2E1W D8C045-1E2W D8C085-2E1W
D10C048-1E2W D10C056-3E4W