Seismic Multi Axial Behavior of Concrete Filled Steel Tube Beam - PowerPoint PPT Presentation

Seismic Multi ‐ Axial Behavior of Concrete ‐ Filled Steel Tube Beam ‐ Columns Mark Denavit Tiziano Perea Jerome F. Hajjar Roberto T. Leon University of Illinois at Urbana ‐ Champaign Georgia Institute of Technology Urbana, Illinois Atlanta, Georgia Sponsors: National Science Foundation American Institute of Steel Construction Georgia Institute of Technology University of Illinois at Urbana ‐ Champaign August 14, 2009

Introduction • NEESR ‐ II: System Behavior Factors for Composite and Mixed Structural Systems • Analytical Investigation – Following prior work focusing on RCFT members and extending to CCFT and SRC members – Three ‐ dimensional distributed plasticity mixed beam element formulation – Comprehensive uniaxial cyclic constitutive models for concrete core and steel tube – Parametric Studies • Developing rational system response factors (ATC ‐ 63) • Investigations of beam ‐ column strength • Establishing guidelines for the computation of equivalent composite beam ‐ column rigidity to be used in seismic analysis and design of composite frames • Experimental Investigation

Element Formulation • Three ‐ dimensional distributed plasticity mixed beam element formulation • Mixed basis allows for accurate analysis of material and geometric nonlinearity • Interpolation functions for both element displacements and forces • Formulated in the corotational frame • Implemented within the OpenSees framework • Suitable for static and dynamic analyses • Utilizes built in coordinate transformations and sections

Concrete Backbone Curve Backbone curve in tension and compression Increasing post ‐ peak 100 based on the model by Tsai (1988) degradation with 80 Compression: increasing f’c Stress (MPa) [ ] [ ] f ′ 60 • Initial stiffness: = 3/8 E MPa 8,200 MPa c c ⎛ ⎞ 7.94 f f 40 ′ ′ = − + + − • Peak stress: ⎜ ⎟ l l f f 1.254 2.254 1 2 ⎜ ⎟ ′ ′ cc c f f ⎝ ⎠ c c f'c = 50 MPa; D/t = 50 20 f'c = 60 MPa; D/t = 50 2 = α – Confinement Pressure: f F D t f'c = 70 MPa; D/t = 50 θ − l y 2 f'c = 80 MPa; D/t = 50 f'c = 90 MPa; D/t = 50 0 ( ) α = − ≥ – Hoop Stress Ratio: f'c = 100 MPa; D/t = 50 0.138 0.00174 D t 0 θ 0 0.005 0.01 0.015 0.02 0.025 0.03 Strain (mm/mm) ( ) ( ) • Strain at peak stress: ′ ′ ′ ε = ε + − 70 1 5 f f 1 cc c cc c Post peak factor r : 60 • [ ] ′ ′ ⎧ − ε > ε 50 ⎪ f MPa 5.2 1.9 for − c cc = ⎨ r ) ( ) Increasing ( + ′ ε ≤ ε ′ ⎪ 0.4 0.016 D t f F for 40 ⎩ Stress (MPa) c y cc strength with decreasing D/t 30 20 Increasing post ‐ peak f'c = 50 MPa; D/t = 30 10 f'c = 50 MPa; D/t = 40 degradation with f'c = 50 MPa; D/t = 50 increasing D/t f'c = 50 MPa; D/t = 60 0 f'c = 50 MPa; D/t = 70 f'c = 50 MPa; D/t = 80 -10 0 0.005 0.01 0.015 0.02 0.025 0.03 Strain (mm/mm)

Steel Backbone Curve Plasticity model based on the incremental bounding surface formulation by Shen et 600 al. (1995) with modifications for CCFT Fy = 500 MPa; D/t = 30 Fy = 500 MPa; D/t = 60 Fy = 500 MPa; D/t = 90 members 400 Fy = 500 MPa; D/t = 120 Fy = 500 MPa; D/t = 150 F Local Buckling: D 200 = y R Stress (MPa) t E s 0 ( ) − ε = ε • Strain at initial local buckling: 1.413 0.2139 R lb y -200 ( ) ⎧ > = f R / R for R R 0.17 • Residual stress: = ⎨ lb crit crit f rs ⎩ f otherwise -400 lb • Degradation slope: E K = − s s -600 30 -0.04 -0.03 -0.02 -0.01 0 0.01 Strain (mm/mm) Residual Stresses: Decreasing Decreasing local residual stress buckling strain with increasing • Initial plastic Strain: 0.0006 with increasing D/t D/t

CCFT Model Validation 8000 1200 Yoshioka et al. 1995 7000 CC4 ‐ D ‐ 4 1000 6000 Yoshioka et al 1995 800 CC4 ‐ A ‐ 4 5000 Force (kN) Force (kN) F y = 283 MPa 4000 600 f’ c = 40.5 MPa D/t = 50.4 F y = 283 MPa 3000 400 L/D = 3.00 f’ c = 40.5 MPa 2000 D/t = 152 200 L/D = 3.00 Experiment Experiment 1000 Analysis Analysis 0 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.01 0.02 0.03 0.04 0.05 0.06 Strain (mm/mm) Strain (mm/mm) 3500 2500 Experiment Analysis 3000 2000 O’Shea & Bridge 2500 2000 Force (kN) Force (kN) 1500 R12CF1 2000 Han & Yao 2004 scv2 ‐ 1 1500 F y = 303 MPa 1000 F y = 203 MPa f’ c = 58.5 MPa 1000 f’ c = 110 MPa D/t = 66.7 500 D/t = 171 L/D = 3.00 500 Experiment L/D = 3.48 Analysis 0 0 0 0.002 0.004 0.006 0.008 0.01 0.012 0 0.01 0.02 0.03 0.04 Strain (mm/mm) Strain (mm/mm)

CCFT Model Validation 8 700 7 600 6 500 Wheeler & Bridge 2004 Moment (kN-m) Moment (kN-m) 5 TBP005 400 F y = 351 MPa Elchalakani et al. 2001 4 f’ c = 48.0 MPa CBC0 ‐ C 300 D/t = 71.3 3 F y = 400 MPa L/D = 8.33 200 f’ c = 23.4 MPa 2 D/t = 110 Experiment 100 1 Experiment L/D = 7.28 Analysis Analysis 0 0 0 2 4 6 8 0 20 40 60 80 100 120 Curvature (rad/mm) -4 Mid-Span Deflection (mm) x 10 12 500 10 400 Wheeler & Bridge 2004 Moment (kN-m) 8 Moment (kN-m) TBP002 300 Elchalakani et al 2001 F y = 351 MPa 6 CBC6 f’ c = 40.0 MPa 200 D/t = 63.4 4 F y = 456 MPa L/D = 2.96 f’ c = 23.4 MPa 100 D/t = 23.5 2 Experiment Experiment L/D = 10.5 Analysis Analysis 0 0 0 0.5 1 1.5 0 20 40 60 80 Curvature (rad/mm) -3 Mid-Span Deflection (mm) x 10

CCFT Model Validation 600 300 Kilpatrick & Rangan 1999 500 250 SC ‐ 0 Matsui & Tsuda 1996 400 200 C4 ‐ 5 Load (kN) Load (kN) F y = 414 MPa 300 f’ c = 31.9 MPa 150 F y = 435 MPa D/t = 36.7 f’ c = 58.0 MPa L/D = 4.0 200 100 D/t = 34.5 e/D = 0.625 L/D = 10.6 100 50 Experiment e/D = 0.197 Experiment Analysis Analysis 0 0 0 5 10 15 20 0 10 20 30 40 50 60 Mid-Height Deflection (mm) Mid-Height Deflection (mm) Kilpatrick & Rangan 1999 1200 200 SC ‐ 14 Matsui & Tsuda 1996 1000 C12 ‐ 1 150 800 Load (kN) Load (kN) F y = 410 MPa 600 100 f’ c = 58 MPa F y = 414 MPa D/t = 42.4 f’ c = 31.9 MPa 400 L/D = 19.1 D/t = 36.7 50 e/D = 0.393 L/D = 12.0 200 e/D = 0.125 Experiment Experiment Analysis Analysis 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Mid-Height Deflection (mm) Mid-Height Deflection (mm)

CCFT Model Validation 400 35 350 30 300 25 Nishiyama et al. 2002 Moment (kN-m) Moment (kN-m) 250 EC4 ‐ A ‐ 4 ‐ 035 Ichinohe et al 1991 20 C06F3M 200 F y = 420 MPa 15 F y = 283 MPa 150 f’ c = 64.3 MPa f’ c = 39.9 MPa 10 D/t = 51.5 D/t = 50.7 100 P/P o = 0.30 P/P o = 0.35 5 Experiment Experiment 50 L/D = 2.0 L/D = 3.0 Analysis Analysis 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Curvature (1/mm) Curvature (1/mm) -4 -4 x 10 x 10 400 300 Nishiyama et al. 2002 350 EC4 ‐ D ‐ 4 ‐ 06 250 300 Nishiyama et al. 2002 EC8 ‐ C ‐ 4 ‐ 03 Moment (kN-m) Moment (kN-m) 200 250 F y = 834 MPa f’ c = 40.7 MPa 200 150 D/t = 34.3 F y = 283 MPa 150 P/P o = 0.30 f’ c = 40.7 MPa 100 L/D = 3.0 D/t = 152 100 P/P o = 0.60 50 Experiment Experiment 50 L/D = 3.0 Analysis Analysis 0 0 0 1 2 3 4 5 6 0 1 2 Curvature (1/mm) Curvature (1/mm) -5 -4 x 10 x 10

Cyclic Behavior Concrete Steel Test #3; Marson & Bruneau 2004; Specimen: CFST 64 400 Rule based model by Cyclic plasticity model Horizontal Force (kN) 200 by Shen et al. Chang and Mander (1994) (1995) 0 -200 • Elastic unloading Experiment Analysis • Decreasing elastic zone -400 Smooth nonlinear -8 -6 -4 -2 0 2 4 6 8 Percent Drift • Bauschinger effect unloading, 1000 Bounding stiffness • Base Moment (kN-m) reloading, and Local buckling 500 transition curves degradation 0 κ = γ κ • Elastic range: -500 Experiment κ reduced Analysis • Cyclic tension ⎛ ⎞ -1000 p W -8 -6 -4 -2 0 2 4 6 8 γ = ⎜ − ⎟ ≥ • Opening and closing of 1 15 R 0.05 Percent Drift ⎜ ⎟ k F ⎝ ⎠ Response of Extreme Steel Fiber Response of Extreme Concrete Fiber cracks y 600 Analysis 0 400 Stress (MPa) Stress (MPa) = γ p p E E -10 Plastic modulus: • 200 reduced p E -20 0 ⎛ ⎞ p W γ = ⎜ − ⎟ ≥ -200 -30 1 10 R 0.05 ⎜ ⎟ p E F ⎝ ⎠ -400 -40 Analysis y -0.05 0 0.05 0.1 -0.05 0 0.05 0.1 Strain (mm/mm) Strain (mm/mm) D = 406 mm; t = 5.50 mm; f’ c = 37 MPa; F y = 449 MPa; L = 2,200 mm; P = 1,000 kN

Cyclic Model Validation Test #3; Elchalakani & Zhao 2008; Specimen: F04I1 Test #7; Elchalakani & Zhao 2008; Specimen: F14I3 8 8 6 6 4 4 Moment (kN-m) Moment (kN-m) 2 2 0 0 -2 -2 -4 -4 -6 -6 Experiment Experiment Analysis Analysis -8 -8 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 End Rotation (rad) End Rotation (rad) Response of Extreme Steel Fiber Response of Extreme Concrete Fiber Response of Extreme Steel Fiber Response of Extreme Concrete Fiber 500 Analysis Analysis 400 0 0 Stress (MPa) Stress (MPa) Stress (MPa) Stress (MPa) 200 -10 -10 0 0 -20 -200 -20 -30 Analysis Analysis -400 -500 -0.01 0 0.01 -5 0 5 10 15 -0.01 0 0.01 0.02 -0.01 0 0.01 0.02 Strain (mm/mm) Strain (mm/mm) Strain (mm/mm) Strain (mm/mm) -3 x 10 D = 110 mm; t = 1.25 mm; f’ c = 23.1 MPa; F y = 430 MPa D = 89.3 mm; t = 2.52 mm; f’ c = 23.1 MPa; F y = 378 MPa L = 800 mm L = 800 mm