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 VIJuly 20-24, 2008, Devil's Thumb Ranch, Colorado, USA Outline Introduction Stress-strain modeling Fiber analysis results
Cross section strength Beam-column strength Full-scale testing program Conclusions 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 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) Frame element with ends coupled to fiber cross-sections
1 d Frame element Integration points s e 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. Stress-strain modeling
Elastic-perfectly-plastic, or fully-plastic s-e distribution Fully-plastic stress distribution Kent-Park Popovics (Mander) Sakino-Sun Others curves: plain & confined concrete curve for concrete in CFTs (Sakino-Sun)
Circular CFTs Rectangular CFTs D/t=50 b/t=50 D/t=100 b/t=100 curve for steel tubes (Sakino-Sun)
elb elb + Unsymmetrical for biaxial stresses (Von Mises) + Local buckling by a descending branch at lb (calibration) 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: 2.26Es/Fy=56.7 (Spec) ,2Es/Fy=35.5 (Seismic) used in concrete fibers
Uniaxial models used in concrete fibers c Mf for CCFT20x0.25-5ksi (P=0.2Po) P-M Interaction Diagrams cross-section strength P-M Interaction diagrams for beam-column
Mb 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 Column curves P-M Interaction Diagrams (beam-column strength) Lateral force vs. Drift (P=0.2Po) Multi-Axial Sub-assemblage Testing system (MAST at University of Minnesota) TEST MATRIX (10 CCFT, 8 RCFT) Lateral force vs. Drift (P=0.2Po) 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 Nonlinear Fiber Analysis (OpenSees) CCFT20x0
Nonlinear Fiber Analysis (OpenSees)CCFT20x0.25, fc=5ksi, K=2, L=18, Do=L/500, e=5, Displ. Control 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). EI evolution from Nonlinear Fiber Analysis RCFT12x20x0
EI evolution from Nonlinear Fiber AnalysisRCFT12x20x0.3125, 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 Fiber analysis: CCFT20x0.25-5ksi-18 Fiber analysis: CCFT20x0.25-5ksi-18
Concrete crack in tension Steel yield in compression Steel yield in tension Concrete crushing Local buckling / Failure 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 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. 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. Multi-Axial Sub-assemblage Testing system (MAST at University of Minnesota)
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