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

2. Overview Test Summary Notable Tests Comparison with Local Buckling Tests Comparison with Design Specifications Finite Element Modeling Conclusions

3. Notable Tests 1. Test D8C097 – with lower lateral-torsional buckling strength Lateral-torsionalDistortionalLocal

4. Continued. Test D8C097 – with lower lateral-torsional buckling strength D8C097-5E4W-standardD8C097-5E4W-angle added Actuator load-displacement Actuator load P=10350 lbsActuator load P=12751 lbs 84% of DSM_d 99% of DSM_d Notable Tests - Continued

5. 2. Test D8.5Z059-6E5W – failed outside constant moment region Beam failed at 83% of distortional strength by DSM Actuator load-displacementPurlin buckled

6. Notable Tests - Continued 3. Test D3.62C054-3E4W – failed by yielding M test = 34 kips-in. M y = 33 kips-in. M crD = 66 kips-in. (first mode) Observed large deflection

7. Notable Tests - Continued 4. Test D8C033-1E2W – failed in local buckling mode M test = 32.8 kips-in. M y = 40 kips-in. M crL = 30 kips-in. M crD = 61 kips-in.

8. Direct Comparison with Local Bucking Tests 9 pairs of tests having nominally identical geometry and material yield stresses

9. Direct Comparison with Local Bucking Tests - Continued Test 8.5Z082 Test 8.5Z092 Local buckling test Distortional buckling test Local buckling testDistortional buckling test

10. Direct Comparison with Local Bucking Tests - Continued Test 12C068 Test 8C043 Local buckling test Distortional buckling test Local buckling testDistortional buckling test

11. Comparison with Design Codes Compared with North American Spec (NAS 2001) prediction Local buckling tests average M test /M NAS =1.02 Distortional buckling tests average M test /M NAS =0.87 (consider controlling specimens only)

12. Direct Strength Method vs. tests Local buckling tests M test /M DSL =1.03 Distortional buckling tests M test /M DSD =1.01* *formulas similar to AS/NZS Spec.

13. Finite Element Modeling displacement control at loading point. automatic stabilization technique applied.

14. 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 1 2 1 2

15. 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 tubes and load beam. 3 3 2

16. CDF of Maximum Imperfection Type 1 Type 2 (local) (distortional) d d 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.

17. Finite Element Modeling – Continued comparison with tests

18. Finite Element Modeling – Continued selected results

19. 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

20. 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

21. Finite Element Modeling - Continued comparison with tests P test : tested actuator load P 25% : load of simulation with 25% CDF P 75% : load of simulation with 75% CDF Local buckling testsDistortional buckling tests

22. Comparison with Design Codes - Continued μ: mean σ: standard deviation

23. Test Summary Total 19 completed tests were included in the progress report. 9 Z beams10 C beams Tensile tests are underway for additional performed 5 tests. D6C063-2E1W D8C045-1E2W D8C085-2E1W D10C048-1E2W D10C056-3E4W