Transcript Civil Engineering At JHU

DISTORTIONAL BUCKLING OF
C AND Z MEMBERS IN BENDING
Progress Report to AISI
Cheng Yu, Benjamin W. Schafer
The Johns Hopkins University
February 2004
Overview
•
•
•
•
•
•
Test Summary
Notable Tests
Comparison with Local Buckling Tests
Comparison with Design Specifications
Finite Element Modeling
Conclusions
Notable Tests
1. Test D8C097 – with lower lateral-torsional buckling strength
Local
Distortional
Lateral-torsional
Notable Tests - Continued
Continued. Test D8C097 – with lower lateral-torsional buckling strength
Actuator load-displacement
D8C097-5E4W-standard
D8C097-5E4W-angle added
Actuator load P=10350 lbs Actuator load P=12751 lbs
84% of DSM_d
99% of DSM_d
Notable Tests - Continued
2. Test D8.5Z059-6E5W – failed outside constant moment region
Purlin buckled
Actuator load-displacement
Beam failed at 83% of distortional strength by DSM
Notable Tests - Continued
3. Test D3.62C054-3E4W – failed by yielding
Observed large deflection
Mtest= 34 kips-in.
My = 33 kips-in.
McrD = 66 kips-in. (first mode)
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.
Direct Comparison with Local Bucking Tests
9 pairs of tests having nominally identical geometry and
material yield stresses
Direct Comparison with Local Bucking Tests
- Continued
Test 8.5Z092
Local buckling test
Distortional buckling test
Test 8.5Z082
Local buckling test
Distortional buckling test
Direct Comparison with Local Bucking Tests
- Continued
Test 8C043
Local buckling test
Distortional buckling test
Test 12C068
Local buckling test
Distortional buckling test
Comparison with Design Codes
(consider controlling specimens only)
test-to-predicted ratio
1.20
1.00
0.80
0.60
0.40
Local buckling tests
0.20
Dirtortional buckling tests
0.00
0.40
0.60
0.80
1.00
1.20
1.40
1.60
web slenderness = web = (fy/fcr_web)0.5
Compared with North American Spec (NAS 2001) prediction
Local buckling tests average Mtest/MNAS=1.02
Distortional buckling tests average Mtest/MNAS=0.87
1.80
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.
Finite Element Modeling
loading point
displacement control at loading point.
automatic stabilization technique applied.
Finite Element Modeling - Continued
Shell element (S4R)
Solid element (C3D8)
Pin connection between Load
beam and tube
Tie connection between purlin
1
Shell element (S4R)
and tube
Tie connection between purlin
and panel
2
1
2
Finite Element Modeling - Continued
Link connection between two
nodes to simulate the angle at
tension flanges
3
• Material properties of beams use tension
test results.
• Panel is pure elastic.
3
• High elastic modulus is assumed for tubes
and load beam.
2
Finite Element Modeling – Continued
geometric 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.
1.00
Type 1
d
Type 1
(local)
Type 2
(distortional)
0.80
Probability (X < x)
d
Type 2
0.60
P(X < x)
0.25
0.50
0.75
0.95
0.99


0.40
0.20
Type 1
d/t
0.14
0.34
0.66
1.35
3.87
0.50
0.66
Type 2
d/t
0.64
0.94
1.55
3.44
4.47
1.29
1.07
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
d/t
CDF of Maximum
Imperfection
7.0
Finite Element Modeling – Continued
comparison with tests
1.4
1.2
FEM-to-test ratio
1
0.8
0.6
25% CDF
0.4
75% CDF
0.2
0
0.4
0.6
0.8
1
1.2
1.4
web slenderness =  web = (fy/fcr_web)0.5
1.6
1.8
Finite Element Modeling – Continued
selected results
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
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 Element Modeling - Continued
comparison with tests
Local buckling tests
Ptest(lbs)
Test label
8.5Z120-3E2W
17520
8.5Z105-2E1W
16720
8.5Z092-4E2W
11330
8.5Z082-1E2W
10130
8.5Z073-4E3W
8341
8.5Z065-3E1W
5969
8.5Z059-2E1W
6180
11.5Z073-2E1W
12120
11.5Z082-2E1W
17123
11.5Z092-1E2W
22000
8.5Z059-4E3W
6275
8C097-2E3W
10770
8C068-4E5W
6476
8C054-1E8W
3492
8C043-5E6W
3195
6C054-2E1W
2803
4C054-1E2W
1731
12C068-9E5W
6505
3.62C054-1E2W
1263
12C068-3E4W
8542
10C068-2E1W
4381
8C068-1E2W
6141
8C043-3E1W
2985
mean
standard deviation
Distortional buckling tests
P25%
17968
17294
11901
11446
8770
6771
6749
13956
17294
23417
6855
11175
6762
3849
3574
2882
1720
6697
1170
9458
4233
6854
3482
P25%/Ptest P75%(lbs) P75%/Ptest
103%
16484
94%
103%
15806
95%
105%
11170
99%
113%
10749
106%
105%
7309
88%
113%
5886
99%
109%
5748
93%
115%
12396
102%
101%
15806
92%
106%
19790
90%
109%
5763
92%
104%
10200
95%
104%
5614
87%
110%
3233
93%
112%
3082
96%
103%
2240
80%
99%
1365
79%
103%
5968
92%
93%
987
78%
111%
8655
101%
97%
3937
90%
112%
5557
90%
117%
3026
101%
106%
93%
6%
7%
Ptest(lbs)
Test Label
D8.5Z120-4E1W
15870
D8.5Z115-1E2W
14837
D8.5Z092-3E1W
9566
D8.5Z082-4E3W
7921
D8.5Z065-7E6W
5826
D11.5Z092-3E4W 16377
D8.5Z065-4e5W
4993
D11.5Z082-4E3W 14578
D12C068-21
6160
D8C043-4E2W
2678
D12C068-1110
5912
D8C033-1E2W
1024
D8C054-7E6W
3032
D10C068-4E3W
3185
D8C097-5E4W
10350
D3.62C054-3E4W 1071
mean
standard deviation
P25%
16283
16402
10740
9160
6891
16817
5876
15172
8157
3051
5497
1089
3363
3235
12353
1027
P25%/Ptest P75%(lbs) P75%/Ptest
103%
14839
94%
111%
13028
88%
112%
8779
92%
116%
7775
98%
118%
6053
104%
103%
14443
88%
118%
5155
103%
104%
14473
99%
132%
7566
123%
114%
2751
103%
93%
4930
83%
106%
950.8
93%
111%
2919
96%
102%
2746
86%
119%
9985
96%
96%
838
78%
110%
95%
8%
8%
Ptest: tested actuator load
P25%: load of simulation with 25% CDF
P75%: load of simulation with 75% CDF
Comparison with Design Codes - Continued
Controlling
Local buckling specimens
tests
Second
specimens
Controlling
Distortional specimens
buckling tests Second
specimens
Mtest /
MAISI
Mtest /
MS136
Mtest /
MNAS
Mtest /
MAS/NZS
Mtest /
MEN1993
Mtest /
MDSL
Mtest /
MDSd
1.01
0.04
1.00
0.05
0.85
0.11
0.83
0.10
1.06
0.04
1.05
0.06
0.91
0.10
0.88
0.10
1.02
0.05
1.01
0.07
0.87
0.11
0.85
0.11
1.01
0.04
1.00
0.05
1.02
0.09
0.99
0.09
1.01
0.06
1.01
0.06
0.96
0.10
0.95
0.11
1.03
0.06
1.03
0.07
0.89
0.11
0.87
0.11
1.24
0.07
1.24
0.07
1.01
0.08
0.99
0.09
μ
σ
μ
σ
μ
σ
μ
σ
μ: mean
σ: standard deviation
Test Summary
Total 19 completed tests were included in the progress report.
9 Z beams
D8.5Z120-4E1W
D8.5Z115-1E2W
D8.5Z092-3E1W
D8.5Z082-4E3W
D8.5Z065-7E6W
D8.5Z065-4E5W
D8.5Z059-6E5W
D11.5Z092-3E4W
D11.5Z082-3E4W
10 C beams
62ksi
64ksi
58ksi
59ksi
62ksi
60ksi
59ksi
70ksi
72ksi
D8C097-7E6W
D8C097-5E4W
D8C068-6E7W
D8C054-7E6W
D8C043-4E2W
D8C033-1E2W
D12C068-10E11W
D12C068-1E2W
D10C068-4E3W
D3.62C054-3E4W
Tensile tests are underway for additional performed 5 tests.
D6C063-2E1W D8C045-1E2W D8C085-2E1W
D10C048-1E2W D10C056-3E4W
85ksi
84ksi
79ksi
41ksi
45ksi
20ksi
33ksi
56ksi
22ksi
33ksi