Three-Dimensional Distributed Plasticity "Fiber" Finite Element Formulation for RCFT Beam-Columns

Principal Investigator:
Jerome F. Hajjar

Sponsors:
National Science Foundation
American Institute of Steel Construction
Northeastern University
University of Illinois at Urbana-Champaign
University of Minnesota

Graduate Students:
Mark Denavit
Jie Zhang
Cenk Tort
Steven M. Gartner
Brett C. Gourley
Jorge Grauvilardell
Narina Jung
Alexander O. Molodan
Paul H. Schiller
Cenk Tort
Jose Zamudio

Undergraduate Students:
Mahmoud Alloush
Tarik Ata Rafi
Rachel Back
Brian Beck
Wilfred Chan
Mark Chauvin
Kathryna Clarke
Steve Earl
Ryan Hopeman
Ezra Jampole
Saif Jassam
Michael Kehoe
Sarah Keenan
Angela Kingsley
Tyler Krahn
Susan K. La Fore
Gregory S. Lauer
Elisa Livingston
Brett Mattas
Steven Palkovic
Matthew Parkolap
Jill Pinsky
Alston Potts
Abdulrahman Ragab
Alexandra Reiff
Katherine A. Stillwell
Zhuanqiang Tan

Comparison of fiber analysis with interlayer slip to
experimental results from Dunberry:
Transfer of load from steel to concrete

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• Fiber-based stress-resultant based formulation
• Stress-strain behavior tracked at each fiber
• Co-rotational geometric stiffness formulation
  • Small strain, moderate displacements, moderate rotations
• Slip is accounted for between steel and concrete
  • 18 degrees-of-freedom per element to permit separate concrete and steel translational degrees-of-freedom
  • Lagrange multipliers enforce compatibility between steel and concrete of shear degrees-of-freedom
  • Models axial and flexural behavior ranging from complete bond to perfect slip
• Incorporated into frame analysis finite element software
  

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• Virtual work formulation divided explicitly into steel, concrete, and interface components


• Slip causes axial extension due both to axial force and flexure
• Slip stiffness modeled using nonlinear springs at steel-concrete interface
• Bi-linear cyclic load-slip relation. Calibrated parameters:
  • Bond strength
  • Initial bond stiffness
  • Bond stiffness after breach of bond strength
• Calibrated to connection studies of steel I-girders framing into CFTs using shear tabs, racking down on shear tabs (see figure above)
  

Stress-Based Bounding Surface Formulations

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• Stress-based bounding surface formulation used for both steel and concrete material response
• Both formulations include isotropic and kinematic hardening:
• Steel formulation models:
  • Rounded stress-strain curve found in cold-formed steel
  • Decreasing elastic zone with increased cyclic excitation
  • Cyclic hardening
  • Ratcheting
  • Different stress-strain behavior exhibited in corners and flanges of cold-worked steel tubes
  • Calibrated versus monotonic and cyclic coupon tests from cold-formed steel tubes
• Concrete formulation models:
  • Strength and stiffness degradation through the use of a cumulative damage parameter
  • Post-peak behavior of concrete is calibrated to account implicitly for confinement of concrete core by tube
  • Concrete that cycles into tension and then back into compression (crack opening and closing)
  • Calibrated to a wide range of multi-axial monotonic and cyclic concrete material tests
    

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Analysis compared to a series of tests to calibrate and verify slip model parameters

Experimental Test Setup for Calibration of Slip Model

One of Several Calibration Analyses Done to Determine Bond Strength in CFT's, Plotting Slip versus Height

One of Several Calibration Analyses Done to Determine Initial Bond Stiffness in CFT's, Showing Load in Steel and Concrete versus Height

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