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

Mark Denavit Jerome F. Hajjar

University of Illinois at Urbana‐Champaign Urbana, Illinois Sponsors: National Science Foundation American Institute of Steel Construction Georgia Institute of Technology University of Illinois at Urbana‐Champaign

Seismic Multi‐Axial Behavior of Concrete‐Filled Steel Tube Beam‐Columns

Tiziano Perea Roberto T. Leon

Georgia Institute of Technology Atlanta, Georgia

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 based on the model by Tsai (1988) Compression:

• Initial stiffness:
• Peak stress:

– Confinement Pressure: – Hoop Stress Ratio:

• Strain at peak stress:
• Post peak factor r:

0.005 0.01 0.015 0.02 0.025 0.03

• 10

10 20 30 40 50 60 70

Strain (mm/mm) Stress (MPa)

f'c = 50 MPa; D/t = 30 f'c = 50 MPa; D/t = 40 f'c = 50 MPa; D/t = 50 f'c = 50 MPa; D/t = 60 f'c = 50 MPa; D/t = 70 f'c = 50 MPa; D/t = 80 0.005 0.01 0.015 0.02 0.025 0.03 20 40 60 80 100

Strain (mm/mm) Stress (MPa)

f'c = 50 MPa; D/t = 50 f'c = 60 MPa; D/t = 50 f'c = 70 MPa; D/t = 50 f'c = 80 MPa; D/t = 50 f'c = 90 MPa; D/t = 50 f'c = 100 MPa; D/t = 50

[ ] [ ]

3/8

MPa 8,200 MPa

c c

E f ′ = 2 2

l y

f F D t

θ

α = − 7.94 1.254 2.254 1 2

l l cc c c c

f f f f f f ⎛ ⎞ ′ ′ = − + + − ⎜ ⎟ ⎜ ⎟ ′ ′ ⎝ ⎠

( )

0.138 0.00174 D t

θ

α = − ≥

( )

( )

1 5 1

cc c cc c

f f ε ε ′ ′ ′ = + −

[ ] ( )(

)

MPa 5.2 1.9 for 0.4 0.016 for

c cc c y cc

f r D t f F ε ε ε ε

−

′ ′ ⎧ − > ⎪ = ⎨ ′ ′ + ≤ ⎪ ⎩ Increasing strength with decreasing D/t Increasing post‐peak degradation with increasing D/t Increasing post‐peak degradation with increasing f’c

Steel Backbone Curve

Plasticity model based on the incremental bounding surface formulation by Shen et

• al. (1995) with modifications for CCFT

members Local Buckling:

• Strain at initial local buckling:
• Residual stress:
• Degradation slope:

Residual Stresses:

• Initial plastic Strain: 0.0006
• 0.04
• 0.03
• 0.02
• 0.01

0.01

• 600
• 400
• 200

200 400 600

Strain (mm/mm) Stress (MPa)

Fy = 500 MPa; D/t = 30 Fy = 500 MPa; D/t = 60 Fy = 500 MPa; D/t = 90 Fy = 500 MPa; D/t = 120 Fy = 500 MPa; D/t = 150

( )

1.413

0.2139

lb y

R ε ε

−

=

y s

F D R t E = 30

s s

E K = −

( )

/ for 0.17

• therwise

lb crit crit rs lb

f R R R R f f ⎧ > = = ⎨ ⎩ Decreasing local buckling strain with increasing D/t Decreasing residual stress with increasing D/t

0.01 0.02 0.03 0.04 500 1000 1500 2000 2500

Strain (mm/mm) Force (kN)

Experiment Analysis 0.002 0.004 0.006 0.008 0.01 0.012 500 1000 1500 2000 2500 3000 3500

Strain (mm/mm) Force (kN)

Experiment Analysis 0.01 0.02 0.03 0.04 0.05 0.06 200 400 600 800 1000 1200

Strain (mm/mm) Force (kN)

Experiment Analysis 0.01 0.02 0.03 0.04 0.05 0.06 1000 2000 3000 4000 5000 6000 7000 8000

Strain (mm/mm) Force (kN)

Experiment Analysis

CCFT Model Validation

Fy = 283 MPa f’c = 40.5 MPa D/t = 152 L/D = 3.00 Yoshioka et al 1995 CC4‐A‐4 Fy = 283 MPa f’c = 40.5 MPa D/t = 50.4 L/D = 3.00 Fy = 203 MPa f’c = 110 MPa D/t = 171 L/D = 3.48 Han & Yao 2004 scv2‐1 Fy = 303 MPa f’c = 58.5 MPa D/t = 66.7 L/D = 3.00 O’Shea & Bridge 2000 R12CF1 Yoshioka et al. 1995 CC4‐D‐4

20 40 60 80 100 200 300 400 500 Mid-Span Deflection (mm) Moment (kN-m) Experiment Analysis 0.5 1 1.5 x 10

• 3

2 4 6 8 10 12 Curvature (rad/mm) Moment (kN-m) Experiment Analysis 20 40 60 80 100 120 100 200 300 400 500 600 700 Mid-Span Deflection (mm) Moment (kN-m) Experiment Analysis 2 4 6 8 x 10

• 4

1 2 3 4 5 6 7 8 Curvature (rad/mm) Moment (kN-m) Experiment Analysis

CCFT Model Validation

Elchalakani et al 2001 CBC6 Wheeler & Bridge 2004 TBP002 Fy = 351 MPa f’c = 40.0 MPa D/t = 63.4 L/D = 2.96 Elchalakani et al. 2001 CBC0‐C Fy = 400 MPa f’c = 23.4 MPa D/t = 110 L/D = 7.28 Wheeler & Bridge 2004 TBP005 Fy = 351 MPa f’c = 48.0 MPa D/t = 71.3 L/D = 8.33 Fy = 456 MPa f’c = 23.4 MPa D/t = 23.5 L/D = 10.5

20 40 60 80 100 50 100 150 200 Mid-Height Deflection (mm) Load (kN) Experiment Analysis 20 40 60 80 100 200 400 600 800 1000 1200 Mid-Height Deflection (mm) Load (kN) Experiment Analysis 10 20 30 40 50 60 50 100 150 200 250 300 Mid-Height Deflection (mm) Load (kN) Experiment Analysis 5 10 15 20 100 200 300 400 500 600 Mid-Height Deflection (mm) Load (kN) Experiment Analysis

CCFT Model Validation

Matsui & Tsuda 1996 C4‐5 Fy = 414 MPa f’c = 31.9 MPa D/t = 36.7 L/D = 4.0 e/D = 0.625 Fy = 435 MPa f’c = 58.0 MPa D/t = 34.5 L/D = 10.6 e/D = 0.197 Fy = 414 MPa f’c = 31.9 MPa D/t = 36.7 L/D = 12.0 e/D = 0.125 Fy = 410 MPa f’c = 58 MPa D/t = 42.4 L/D = 19.1 e/D = 0.393 Kilpatrick & Rangan 1999 SC‐0 Matsui & Tsuda 1996 C12‐1 Kilpatrick & Rangan 1999 SC‐14

1 2 x 10

• 4

50 100 150 200 250 300 Curvature (1/mm) Moment (kN-m) Experiment Analysis 1 2 3 4 5 6 x 10

• 5

50 100 150 200 250 300 350 400 Curvature (1/mm) Moment (kN-m) Experiment Analysis 1 2 3 4 5 6 x 10

• 4

5 10 15 20 25 30 35 Curvature (1/mm) Moment (kN-m) Experiment Analysis 1 2 3 4 5 6 x 10

• 4

50 100 150 200 250 300 350 400 Curvature (1/mm) Moment (kN-m) Experiment Analysis

CCFT Model Validation

Nishiyama et al. 2002 EC4‐D‐4‐06 Nishiyama et al. 2002 EC8‐C‐4‐03 Fy = 834 MPa f’c = 40.7 MPa D/t = 34.3 P/Po = 0.30 L/D = 3.0 Ichinohe et al 1991 C06F3M Fy = 420 MPa f’c = 64.3 MPa D/t = 51.5 P/Po = 0.30 L/D = 2.0 Fy = 283 MPa f’c = 39.9 MPa D/t = 50.7 P/Po = 0.35 L/D = 3.0 Nishiyama et al. 2002 EC4‐A‐4‐035 Fy = 283 MPa f’c = 40.7 MPa D/t = 152 P/Po = 0.60 L/D = 3.0

Cyclic Behavior

Steel Cyclic plasticity model by Shen et al. (1995)

• Elastic unloading
• Decreasing elastic zone
• Bauschinger effect
• Bounding stiffness

Local buckling degradation

• Elastic range:
• Plastic modulus:

Concrete Rule based model by Chang and Mander (1994) Smooth nonlinear unloading, reloading, and transition curves

• Cyclic tension
• Opening and closing of

cracks

reduced κ

κ γ κ = 1 15 0.05

p k y

W R F γ ⎛ ⎞ = − ≥ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

p

p p reduced E

E E γ = 1 10 0.05

p

p E y

W R F γ ⎛ ⎞ = − ≥ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

• 8
• 6
• 4
• 2

2 4 6 8

• 400
• 200

200 400

Percent Drift

Test #3; Marson & Bruneau 2004; Specimen: CFST 64

Horizontal Force (kN)

Experiment Analysis

• 8
• 6
• 4
• 2

2 4 6 8

• 1000
• 500

500 1000

Percent Drift Base Moment (kN-m)

Experiment Analysis

• 0.05

0.05 0.1

• 400
• 200

200 400 600

Strain (mm/mm) Stress (MPa) Response of Extreme Steel Fiber

Analysis

• 0.05

0.05 0.1

• 40
• 30
• 20
• 10

Strain (mm/mm) Stress (MPa) Response of Extreme Concrete Fiber

Analysis

D = 406 mm; t = 5.50 mm; f’c = 37 MPa; Fy = 449 MPa; L = 2,200 mm; P = 1,000 kN

Cyclic Model Validation

• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

• 8
• 6
• 4
• 2

2 4 6 8

End Rotation (rad)

Test #7; Elchalakani & Zhao 2008; Specimen: F14I3

Moment (kN-m)

Experiment Analysis

• 0.01

0.01 0.02

• 500

500

Strain (mm/mm) Stress (MPa) Response of Extreme Steel Fiber

Analysis

• 0.01

0.01 0.02

• 30
• 20
• 10

Strain (mm/mm) Stress (MPa) Response of Extreme Concrete Fiber

Analysis

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2

• 8
• 6
• 4
• 2

2 4 6 8

End Rotation (rad)

Test #3; Elchalakani & Zhao 2008; Specimen: F04I1

Moment (kN-m)

Experiment Analysis

• 0.01

0.01

• 400
• 200

200 400

Strain (mm/mm) Stress (MPa) Response of Extreme Steel Fiber

Analysis

• 5

5 10 15 x 10

• 3
• 20
• 10

Strain (mm/mm) Stress (MPa) Response of Extreme Concrete Fiber

Analysis

D = 110 mm; t = 1.25 mm; f’c = 23.1 MPa; Fy = 430 MPa L = 800 mm D = 89.3 mm; t = 2.52 mm; f’c = 23.1 MPa; Fy = 378 MPa L = 800 mm

Full‐Scale Beam‐Column Tests

• Specimens chosen to fill gaps in prior

experimental research, namely high member slenderness and section slenderness

• Experimentally determine

– Progression of bending stiffness (EIeffective) – Beam‐column interaction strength, including stability effects – Post‐peak behavior and progression of damage of members subjected to large cyclic deformations

• Provide complex set of data for validation of

computational models

MAST Facility

The MAST facility permits the comprehensive testing of a wide range of composite beam‐ columns subjected to three dimensional loading at a realistic scale.

NEES@Minnesota Degree of Freedom Load Stroke/ Rotation X‐Translation ±3,910 kN ±406 mm X‐Rotation ±12,080 kN‐m ±7° Y‐Translation ±3910 kN ±406 mm Y‐Rotation ±12,080 kN‐m ±7° Z‐Translation ±5,870 kN ±508 mm Z‐Rotation ±17,900 kN‐m ±10°

Maximum non‐concurrent capacities of MAST DOFs

Measured Properties

HSS steel Concrete L (mm) t (mm) Fy (MPa) Fu (MPa) Es (MPa) f'c (MPa) Ec (MPa) ft (MPa) Specimen measured measured coupon coupon coupon measured measured measured 1-CCFT5.563x0.134-18ft-5ksi 5,499 3.24 383.4 487.6 193,984 37.92 27,579 7.58 2-CCFT12.75x0.25-18ft-5ksi 5,499 5.80 337.1 446.2 199,162 37.92 27,579 7.58 3-CCFT20x0.25-18ft-5ksi 5,525 5.98 328.0 470.7 200,262 37.92 27,579 7.58 4-RCFTw20x12x0.3125-18ft-5ksi 5,537 7.15 365.4 501.7 202,375 37.92 27,579 7.58 5-RCFTs20x12x0.3125-18ft-5ksi 5,537 7.15 365.4 501.7 202,375 37.92 27,579 7.58 6-CCFT12.75x0.25-18ft-12ksi 5,499 5.80 337.1 446.2 199,162 87.56 41,851 11.38 7-CCFT20x0.25-18ft-12ksi 5,534 5.98 328.0 470.7 200,262 87.56 41,851 11.38 8-RCFTw20x12x0.3125-18ft-12ksi 5,553 7.15 365.4 501.7 202,375 87.56 41,851 11.38 9-RCFTs20x12x0.3125-18ft-12ksi 5,553 7.15 365.4 501.7 202,375 87.56 41,851 11.38 10-CCFT12.75x0.25-26ft-5ksi 7,950 5.80 50.33 35,094 3.79 11-CCFT20x0.25-26ft-5ksi 7,995 5.98 328.0 470.7 200,262 50.33 35,094 3.79 12-RCFTw20x12x0.3125-26ft-5ksi 7,957 7.15 365.4 501.7 202,375 50.33 35,094 3.79 13-RCFTs20x12x0.3125-26ft-5ksi 7,969 7.15 365.4 501.7 202,375 50.33 35,094 3.79 14-CCFT12.75x0.25-26ft-12ksi 7,950 5.80 79.29 37,921 11.03 15-CCFT20x0.25-26ft-12ksi 7,976 5.98 79.29 37,921 11.03 16-RCFTw20x12x0.3125-26ft-12ksi 7,976 7.15 79.29 37,921 11.03 17-RCFTs20x12x0.3125-26ft-12ksi 7,976 7.15 79.29 37,921 11.03 18-CCFT5.563x0.134-26ft-12ksi 7,976 3.24 383.4 487.6 193,984 79.29 37,921 11.03

Setup and Instrumentation

• Strain Gages

– Uniaxial and Rosettes Distributed Along Height – Measurements during concrete pouring and testing

• LVDTs

– Sets of three for biaxial curvature measurement

• String Pots

– Distributed along height

• Krypton Coordinate Measurement

Machine

• Video and Still Images

– Four towers for images of whole specimen as well as base

Typical Load Protocol

y x

T

Load Case 1: Concentric Loading y x y x Load Case 2-3: Uniaxial Cyclic Load Case 4-6: Biaxial Cyclic Load Case 7-8: Torsion

Specimen 8

D = 508 mm B = 305 mm t = 7.15 mm L = 5,553 mm f‘c = 87.56 MPa Fy = 365.4 MPa

Specimen 11

Load Case 2; P = 2,669 kN Load Case 3; P = 1,334 kN Load Case 1

50 100 150 200 250 500 1000 1500 2000 2500 3000 3500 4000

Top Position (mm) (a) Load Case 1: Concentric Loading Axial Force (kN)

Experiment Analysis 200 400 600 800 500 1000 1500 2000 2500 3000 3500 4000

Moment (kN-m) (b) Load Case 1: Concentric Loading Axial Force (kN)

Experiment Analysis

• 300
• 200
• 100

100 200 300 400

• 70
• 60
• 50
• 40
• 30
• 20
• 10

10 20 30

Top Position (mm) (c) Load Case 2: Uniaxial Cyclic Force (kN)

Experiment Analysis

• 400
• 200

200 400

• 1000
• 800
• 600
• 400
• 200

200 400 600 800 1000

Top Position (mm) (d) Load Case 2: Uniaxial Cyclic Moment (kN-m)

Experiment Analysis

• 400
• 200

200 400

• 80
• 60
• 40
• 20

20 40 60

Top Position (mm) (e) Load Case 3: Uniaxial Cyclic Force (kN)

Experiment Analysis

• 400
• 200

200 400

• 1000
• 800
• 600
• 400
• 200

200 400 600 800 1000

Top Position (mm) (f) Load Case 3: Uniaxial Cyclic Moment (kN-m)

Experiment Analysis

D = 508 mm; t = 5.98 mm; L = 7,995 mm; f‘c = 50.33 MPa; Fy = 328.0 MPa

Load Case 4; P = 2,002 kN

• 400
• 200

200 400

• 400
• 300
• 200
• 100

100 200 300 400

X Top Displacement (mm) (g) Load Case 4: Biaxial Cyclic Y Top Displacement (mm)

• 1000
• 500

500

• 800
• 600
• 400
• 200

200 400 600

X Moment (kN-m) (h) Load Case 4: Biaxial Cyclic Y Moment (kN-m)

Experiment Analysis

• 400
• 200

200 400

• 60
• 40
• 20

20 40 60

X Top Displacement (mm) (i) Load Case 4: Biaxial Cyclic X Top Force (kN)

Experiment Analysis

• 400
• 300
• 200
• 100

100 200 300

• 60
• 40
• 20

20 40 60

Y Top Displacement (mm) (j) Load Case 4: Biaxial Cyclic Y Top Force (kN)

Experiment Analysis

• 400
• 200

200 400

• 1000
• 800
• 600
• 400
• 200

200 400 600 800

X Tip Displacement (mm) (k) Load Case 4: Biaxial Cyclic Y Base Moment (kN-m)

Experiment Analysis

• 400
• 200

200 400

• 1000
• 800
• 600
• 400
• 200

200 400 600 800

Y Tip Displacement (in) (l) Load Case 4: Biaxial Cyclic X Base Moment (kN-m)

Experiment Analysis

D = 508 mm; t = 5.98 mm; L = 7,995 mm; f‘c = 50.33 MPa; Fy = 328.0 MPa

Specimen 11

Specimen 3

D = 508 mm; t = 5.98 mm; L = 5,525 mm; f‘c = 37.92 MPa; Fy = 328.0 MPa

• 500

500

• 500

500 1000 2000 3000 4000 5000 6000 7000

My,base (kN-m) Mx,base (kN-m) P (kN)

All Load Cases Experimental Interaction Points

Concluding Remarks

• Experimental and computational research on CCFT and

RCFT beam‐columns

• An accurate nonlinear model has been developed for

the analysis of circular concrete filled steel tubes

– Accuracy confirmed by validation to a broad range of experimental results – Future research includes parametric studies

• Testing of the 18 beam‐column specimens is complete

– More detailed comparisons (e.g., at the section or material level) and conclusions are forthcoming based on more detailed data reduction