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Collapse Assessment of Steel Braced Frames In Seismic Regions

Collapse Assessment of Steel Braced Frames In Seismic Regions. July 9 th -12 th , 2012. Dimitrios G. Lignos, Ph.D. Assistant Professor, McGill University, Montreal, Canada Emre Karamanci , Graduate Student Researcher, McGill University, Montreal, Canada. Outline. Motivation

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Collapse Assessment of Steel Braced Frames In Seismic Regions

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  1. Collapse Assessment of Steel Braced Frames In Seismic Regions July 9th-12th, 2012 Dimitrios G. Lignos, Ph.D. Assistant Professor, McGill University, Montreal, Canada EmreKaramanci, Graduate Student Researcher, McGill University, Montreal, Canada

  2. Outline • Motivation • A Database for Modeling of Post-Buckling Behavior and Fracture of Steel Braces • Calibration Studies • Case #1: E-Defense Dynamic Testing • Case #2: 2-Story Chevron Braced Frame • Collapse Assessment • Summary and Observations

  3. Motivation In the context of Performance-Based Earthquake Engineering, collapse constitutes a limit state associated with complete loss of a building and its content. Understanding collapse is a fundamental objective in seismic safety since this failure mode is associated with loss of lives. Therefore, there is a need for reliable prediction of the various collapse mechanisms of buildings subjected to earthquakes. Dimitrios G. Lignos Quake Summit, San Francisco 2010

  4. Motivation In the case of steel braced frames, one challenge for reliable collapse assessment is to accurately model the post-buckling behavior and fracture of steel braces as parts of a braced frame. Another challenge is to consider other important deterioration modes associated with plastic hinging in steel components that are part of local story mechanisms that develop after the steel braces fracture This could be an issue for steel braced frames designed in moderate or high seismicity regions. The emphasis is on a common collapse mode associated with sidesway instability in which P-Delta effects accelerated by cyclic deterioration in strength and stiffness of structural components fully offset the first order story shear resistance of a steel braced frame and dynamic instability occurs. Dimitrios G. Lignos Quake Summit, San Francisco 2010

  5. Steel Brace Model Model proposed by (Uriz et al. 2008) Gusset Plate flexibility and yield moment are modeled with the model proposed by Roeder et al. (2011) • εoindicates the strain amplitude at which one complete • Cycle of a undamaged material causes fracture • m material parameter that relates the sensitivity of a total strain amplitude of the material to the number of cycles to fracture ?

  6. Steel Brace Database for Model Calibration • Collected Data from 20 different experimental programs from the 1970s to date • 143 Hollow Square Steel Sections • 51 Pipes • 50 W Shape braces • 37 L Shape Braces LH LB LH LB LH LH LB LB LB LH • Digitization of axial load axial displacement relationships • (CalibratorJAVA software , Lignos and Krawinkler 2008)

  7. Steel Brace Database Based on the local slenderness ratios (b/t), the majority of the braces are categorized as Class 1 based on CISC (2010) requirements (Same conclusions based on AISC 2010 Highly ductile braces) Slenderness Parameter

  8. Calibration Process of the Brace Model Mesh Adaptive Search Algorithm (MADS, Abramson et al. 2009) • Objective Function H Fexp: Experimentally measured axial force of the brace Fsimul: Simulated axial force of the brace δi: Axial displacement of the brace at increment i • Non-differentiable  Optimization problem lacks of smoothness. • MADS does not use information about the gradient of H to search for an optimal point compared to more traditional optimization algorithms.

  9. Calibration Process of the Brace Model • Based on a sensitivity study with a subset of 30 braces: • Offset of 0.1% of the brace length is adequate • Eight elements along the length of the steel brace • Five integration points per element • Section level: • Stress strain relationship: • Strain hardening of 0.1% • Radius that defines Bauschinger effect Ro=25 • Based on the calibration study of the entire set of braces • Exponent m =0.3 • Strain amplitude εois a function of KL/r, b/t, fy

  10. Model Parameter Calibrations (Data from Tremblay et al. 2008) (Data from Uriz and Mahin 2008)

  11. Validation with a Chevron CBF tested @ E-Defense • Chevron CBF, 70%-scale • HSS braces: b/t = 19.4, KL/r = 82.5 x: Lateral bracing (Okazaki, Lignos, Hikino and Kajiyara, 2012)

  12. E-Defense Chevron CBF: Test Setup Load Cells Connecting Beam Test Bed Test Bed Specimen Connecting Beam Direction of Shaking N Shake Table (Okazaki, Lignos, Hikino and Kajiyara, 2012)

  13. E-Defense Chevron CBF: Test Setup • JR Takatori • (1995 Kobe EQ) • 10, 12, 14, • 28, 42, 70% • Damping h ≈ 0.03 • inherent in test-bed • system (Okazaki, Lignos, Hikino and Kajiyara, 2012)

  14. Response of Braces: Comparison @ 70% JR Takatori East Brace 42% 70% (Okazaki, Lignos, Hikino and Kajiyara, 2012)

  15. Global Response: Comparison @ 70% JR Takatori (Okazaki, Lignos, Hikino and Kajiyara, 2012)

  16. Case Study #2: 2-Story Chevron Braced Frame 6,096 Beam W24x117 2,743 □ 152x9.5 （A500 Gr. B) □ 152x9.5 （A500 Gr. B) PL 22 (A572 Gr.50) Column W10x45 2,743 □ 152x9.5 （A500 Gr. B) □ 152x9.5 （A500 Gr. B) PL 22 (A572 Gr.50) Reaction Beam Lateral support (Uriz and Mahin, 2008)

  17. Case Study #2: 2-Story Chevron Braced Frame Rigid offset Rigid offset Rigid offset Steel beam & column spring (Bilinear Modified IMK Model) Shear connection spring (Pinching Modified IMK Model) Gusset plate spring (Menegotto-Pinto model)

  18. Case Study #2: 2-Story Chevron Braced Frame Rigid offset Rigid offset Rigid offset Steel beam & column spring (Bilinear Mod. IMK Model) Liu and Astaneh (2004) Shear connection spring (Pinching Mod. IMK Model) Gusset plate spring (Menegotto-Pinto model)

  19. Case Study #2: 2-Story Chevron Braced Frame Rigid offset Rigid offset Rigid offset (Ibarra et al. 2005, Lignos and Krawinkler 2011) Steel beam & column spring (Bilinear Mod. IMK Model) Shear connection spring (Pinching Mod. IMK Model) Gusset plate spring (Menegotto-Pinto model)

  20. Case Study #2: 2-Story Chevron Braced Frame (Lignos and Krawinkler 2011)

  21. Case Study #2: Loading Protocol (Uriz and Mahin, 2008)

  22. Case Study #2: Quasi-Static Analysis-Global Response

  23. Case Study #2: Incremental Dynamic Analysis Based on 2% Rayleigh Damping (damping matrix proportional to initial stiffness) Collapse Capacities seem a bit high Indicates that a closer look of the individual responses in terms of base shear hysteretic response is needed and not just story drift ratios.

  24. Validation of Simulated Collapse-Small Scale Tests Collapse (NEESCollapse) (Lignos, Krawinkler & Whittaker 2007)

  25. Validation of Simulated Collapse-Full Scale Tests Collapse Collapse (Suita et al. 2008) (Lignos, Hikino, Matsuoka, Nakashima 2012)

  26. Canoga Park Record: Story Drift Ratio Histories SF=2.0

  27. Dynamic Analysis: Base Shear-SDR1 Due to Artificial Damping Artificial damping is generated in the lower modes with the effective damping increasing to several hundred percent. Following the change in state of steel braces after fracture occurs, large viscous damping forces are generated. This forces are the product of the post-event deformational velocities multiplied by the initial stiffness and by the stiffness proportional coefficient.

  28. IDA Curves: Damping Based on Current Stiffness Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)

  29. Dynamic Analysis: Story Drift Ratios (SF=2.0)

  30. Dynamic Analysis: Brace Response

  31. Base Shear-First Story SDR @ Collapse Intensity Fracture of East Brace Collapse Fracture of West Brace

  32. First Story Column Behavior @ Collapse Intensity □ 152x9.5 （A500 Gr. B) □ 152x9.5 （A500 Gr. B) PL 22 (A572 Gr.50) □ 152x9.5 （A500 Gr. B) □ 152x9.5 （A500 Gr. B) PL 22 (A572 Gr.50) Lateral support

  33. Summary and Observations • 1. Modeling of Post-Buckling Behavior and Fracture Initiation of Steel Braces is Critical for Evaluation of Seismic Redundancy of Steel Braced Frames. • Proposed steel brace fracture modeling for different types of steel braces is based on calibration studies from 295 tests. • 2. For collapse simulations of sidesway instability, modeling of component deterioration of other structural components is also critical (Beams and Columns) • 3. Non-simulated collapse criteria could be “dangerous”. Story drift in conjunction with base shear of the system needs to be considered. • 4. Modeling of damping can substantially overestimate the collapse capacity of steel braced frames For Rayleigh Damping, damping matrix proportional to current stiffness should be considered.

  34. Acknowledgments • Dr. Uriz and Prof. Steve Mahin (University of California, Berkeley) for sharing the digitized data of individual steel brace components and systems that tested over the past few years. • Professor Benjamin Fell (Sacramento State) for sharing the digitized data of steel brace components that he tested 4 years ago at NEES @ Berkeley.

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