1. Strain Distribution in Locally Slender Structural Steel Cross-sections
Seif, M., Schafer, B.W.
Civil
Engineering
at JOHNS HOPKINS UNIVERSITY

2. Acknowledgments AISC Faculty Fellowship Program Professor Ben Schafer
The thin-walled structures research group at JHU

3. Overview Motivation Cross-section stability Design methods
FE parametric study
Strain Distributions
Ongoing work

4. AISC definition of locally slender
Motivation
AISC definition of locally slender

5. AISC
Q-factor
AISI
Effective
Width
AISI
Direct
Strength
App. 1

6. Column curve

7. Overview Motivation Cross-section stability Design methods
FE parametric study
Strain Distributions
Ongoing work

8. ABAQUS elements S4
10 elements

9. Residual stresses
Galambos and Ketter (1959)

10. Material modeling
Barth, White, Righman, & Yang (2005)

11. Geometric imperfections

12. Geometric imperfections

13. Geometric imperfections

14. LOCAL slenderness c
W14FI: W14x233 with variable Flange thickness, varies Independently from all other dimensions
W14FR: W14x233 with variable Flange thickness, but the web thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W14x233
W36FR: W36x330 with variable Web thickness, but the flange thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W36x330
W36WI: W36x330 section with variable Web thickness, that varies Independently from all other dimensions

15. LOCAL slenderness

16. Results
Columns

17. Results
App. 1
Columns

18. Overview Motivation Cross-section stability Design methods
FE parametric study
Strain Distributions
Ongoing work

19. Results x W36x330 Thicker Original Thinner W36WI Pn, kips W36x233
thicker (recall tw is varied here) specimens develop significant strain hardening (in compression!) while the thinner specimens exhibit less displacement before collapse
Take them through the whole plot
Thinner
Displacement, in.

20. Deformed shape
Thicker
Web
Thinner
web
Original
W36x330

21. Membrane longitudinal stress
~ Zero
= Yield
Shown is the membrane or mid-plane longitudinal stress essentially at peak load/collapse. Areas in blue indicate regions where the applied load is being carried.
In all the section the flange is carrying the load, and basically uniformly. Recall from an AISC standpoint these are all compact flanges
The web carries a variable amount of load; though even in the thick section some local buckling reduction is experienced, not consistent with AISC which says this is a compact web
Overall the notion of an eff. Width for the web seems generally supported by the stress contours
Further reductions in the web and flange are certainly dis-similarl
Original
W36x330
Thicker
web
Thinner
web

22. Membrane plastic strain
~ 10ey
~ Zero
Plastic strain provides a look at collapse again membrane plastic strain
In thin section yielded flanges, but elastically buckling web
In the original section you have yielding in both flange and web, but recall stress was still dominant in the flange
Thicker section shows less yield in the web compared with the original..
RED indicates that the section can chew up a lot of energy
Original
W36x330
Thicker
web
Thinner
web

23. 3D 2D

24. x x 3D
S4 - Element

25. 2D Stress/Strain distributions
Thinner
flange
Thicker
flange

26. Effective Area
NO !!!! 2D

27. Equilibrium
Clear height

28. W14 FI: Strain Energy Distribution
Original
W14x233
Thicker
Thinner

29. W14 FI: Postulated Effective Width Distribution
Original
W14x233
Thicker
Thinner

30. W14 FR: Strain Energy Distribution
Original
W14x233
Thicker
Thinner

31. W14 FR: Postulated Effective Width Distribution
Original
W14x233
Thicker
Thinner

32. W36 FR: Strain Energy Distribution
Original
W36x330
Thicker
Thinner

33. W36 FR: Postulated Effective Width Distribution
Original
W36x330
Thicker
Thinner

34. W36 WI: Strain Energy Distribution
Original
W36x330
Thicker
Thinner

35. W36 WI: Postulated Effective Width Distribution
Original
W36x330
Thicker
Thinner

36. Ongoing work Strain Distributions Effective Areas
DSM for Structural Steel

37. Work continues…..
more at: