1. BEHAVIOR OF COMPOSITE CFT BEAM-COLUMNS
BASED ON NONLINEAR FIBER ELEMENT ANALYSIS
Tiziano Perea, Roberto Leon and Jerome Hajjar
Georgia Institute of Technology, UIUC, UMN
COMPOSITE CONSTRUCTION IN STEEL AND CONCRETE VI July 20-24, 2008, Devil's Thumb Ranch, Colorado, USA

2. Outline Introduction Stress-strain modeling Fiber analysis results
Cross section strength
Beam-column strength
Full-scale testing program
Conclusions

3. Fiber analysis definition & applications
Numerical technique which couples the two ends of a structural element to a discrete cross-section. s-e in each fiber is integrated to get stress-resultant forces and rigidity terms which must satisfy equilibrium and compatibility.
FEA has been widely used to understand/predict behavior of:
+ Steel elements
+ Reinforced concrete elements
+ Composite elements
* Different structural elements (columns, beams, slabs, etc)
* Different shapes (rectangular, circular, T, I, C, etc)
* Different s-e model (EPP, Kent, Popovics, Sakino, etc)
- Monotonic vs. Cyclic

4. Application of Fiber Analysis
NON COMPOSITE
COMPOSITE ELEMENTS
Steel / RC
SRC
CFT
White (1986)
Liew & Chen (2004)
Elnashai & Elghazouli (1993)
Ricles & Paboojian (1994)
El-Tawil & Dierlein (1999)
Tomii & Sakino (1979)
Hajjar & Gourley (1996)
Lakshimi & Shanmugan (2000)
Uy (2000)
Aval et al. (2002)
Fujimoto et al. (2004)
Inai et al. (2004)
Varma et al. (2004)
Lu et al. (2006)
Choi et al. (2006)
Kim & Kim (2006)
Liang (2008)
Taucer et al (1991)
Izzudin et al (1993)
Spacone & Filippou (1995)

5. Frame element with ends coupled to fiber cross-sections1 d
Frame element
Integration points s e

6. Fiber analysis advantages
• Accurate and efficient approach
Complex cross-sections
• Tapered elements
• Complex strength-strain behavior (uniaxial s-e)
• Material nonlinearity (monotonic/cyclic loads)
Residual stresses
Confinement effects in concrete
Local buckling in steel tubes
Concrete-steel slip by adding DOFs
Geometric nonlinearity and initial imperfections captured directly by the frame formulation.

7. Stress-strain modeling
Elastic-perfectly-plastic, or fully-plastic s-e distribution
Fully-plastic stress distribution
Kent-Park
Popovics (Mander)
Sakino-Sun
Others

8.  curves: plain & confined concrete

9.  curve for concrete in CFTs (Sakino-Sun)
Circular CFTs
Rectangular CFTs
D/t=50
b/t=50
D/t=100
b/t=100

10.  curve for steel tubes (Sakino-Sun)
elb
elb
+ Unsymmetrical  for biaxial stresses (Von Mises)
+ Local buckling by a descending branch at lb (calibration)

11. Fiber analysis 18 CFT beam-columns (fc’=5, 12 ksi, L=18’, 26’)
Goal  Obtain the best prediction (strength & ductility) of a set of large full-scale circular and rectangular CFT beam-columns.
18 CFT beam-columns (fc’=5, 12 ksi, L=18’, 26’)
CCFT20x0.25-5ksi HSS20x0.25: A500 Gr. B, Ry=1.4, Fy=42 ksi, Ru=1.3, Fu=58 ksi Concrete strength: 5 ksi D/t=86.0. AISC-05 limit: 0.15Es/Fy=103.6 (Spec & Seismic Provisions)
RCFT20x12x ksi: HSS20x12x0.3125: A500 Gr. B, Ry=1.4, Fy=46 ksi, Ru=1.3, Fu=58 ksi Concrete strength: 5 ksi b/t =65.7. AISC-05 limit: 2.26√Es/Fy=56.7 (Spec) ,√2Es/Fy=35.5 (Seismic)

12. used in concrete fibers
Uniaxial  models
used in concrete fibers c

13. Mf for CCFT20x0.25-5ksi (P=0.2Po)

14. P-M Interaction Diagrams cross-section strength

15. P-M Interaction diagrams for beam-columnMb
Cross-section strength P M Po M Do Dp d Df F
Do: initial out-of-plumbness (L/500)
or eccentricity
PDo Pd
PDf FL
PDp
P(Do+Dp) L
PDo+PDp+FL+PDf P
PDf FL

16. Column curves

17. P-M Interaction Diagrams (beam-column strength)

18. Lateral force vs. Drift (P=0.2Po)

19. Multi-Axial Sub-assemblage Testing system (MAST at University of Minnesota)

20. TEST MATRIX (10 CCFT, 8 RCFT)

21. Lateral force vs. Drift (P=0.2Po)

22. Nonlinear Fiber Analysis (OpenSees) CCFT20x0
Nonlinear Fiber Analysis (OpenSees) CCFT20x0.25, fc’=5ksi, K=2, L=18’, Do=L/500, e=0:1:10”, Load Control

23. Nonlinear Fiber Analysis (OpenSees) CCFT20x0
Nonlinear Fiber Analysis (OpenSees) CCFT20x0.25, fc’=5ksi, K=2, L=18’, Do=L/500, e=5”, Displ. Control

24. Effective stiffness (EIeff)
Mirza and Tikka (1999)
EC-4 (2004)
AISC (2011?)
b = f (creep & shrinkage) = f (r,KL/r) ≤ (RFT-CFT), 0.3 (SRC)
Alternatives:
Concrete-only or a steel-only (not unusual in practice, too conservative!)
Fiber element analysis: Nonlinearity (s-e, P-D, P-d), buckling, confinement (contact enforcement)
Finite element analysis: Local buckling, effective confinement, cracking.
Steel-concrete contact (friction, bond stress, slip, adhesion, interference).

25. EI evolution from Nonlinear Fiber Analysis RCFT12x20x0
EI evolution from Nonlinear Fiber Analysis RCFT12x20x0.3125, fc’=5ksi, K=2, L=18’, e=5, LC 1-
P/Pn
M/My
M2=M1+P(D+d)
M1=P(Do+e)
M2/My
EIt 1-
EIs 1
E / EAISC
f/fy

26. Fiber analysis: CCFT20x0.25-5ksi-18’

27. Fiber analysis: CCFT20x0.25-5ksi-18’
Concrete crack in tension
Steel yield in compression
Steel yield in tension
Concrete crushing
Local buckling / Failure

28. RCFTw20x12x0.3125-18’-5ksi Experimentally: smax ≈ 21.12 ksi
emax ≈ 728 me
dmax ≈ 0.2 in
Analytically:
smax ≈ 25.9 ksi
emax ≈ 893 me
dmax ≈ 0.188in

29. Conclusions
The results shown in this paper were aimed at assessing primarily the overall behavior and stability effects on composite CFT structural elements as a prelude to a large full-scale testing program. Fiber analysis is a very useful technique to predict the overall behavior of composite beam-column elements.
The accuracy on the results is highly dependable on the s-e model coupled to the fiber cross-section: simple stress-strain models predict reasonably the ultimate strength; more complex material models should be assumed to predict ductility and high displacements such that damage is considered.

30. Conclusions
Most of the nonlinearity sources (strength/stiffness degradation, confinement, local buckling and triaxial stresses effects) have to be calibrated experimentally and/or analytically (FEA).
3D FEA can deal with these sources in a straightforward manner. Definition of the concrete- steel contact can consider a more realistic interaction within these materials; confinement, local buckling and triaxial stresses can be directly integrated in the behavior (with no influence on the material model). More computing resources and time will be required though.

31. Multi-Axial Sub-assemblage Testing system (MAST at University of Minnesota)
Thank you