Presentation on theme: "Collapse Assessment of Steel Braced Frames In Seismic Regions"— Presentation transcript:
1Collapse Assessment of Steel Braced Frames In Seismic Regions July 9th-12th, 2012Dimitrios G. Lignos, Ph.D.Assistant Professor, McGill University, Montreal, CanadaEmre Karamanci, Graduate Student Researcher, McGill University, Montreal, Canada
2OutlineMotivationA Database for Modeling of Post-Buckling Behavior and Fracture of Steel BracesCalibration StudiesCase #1: E-Defense Dynamic TestingCase #2: 2-Story Chevron Braced FrameCollapse AssessmentSummary and Observations
3MotivationIn 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. LignosQuake Summit, San Francisco 2010
4MotivationIn 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. LignosQuake Summit, San Francisco 2010
5Steel 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)εo indicates the strain amplitude at which one completeCycle of a undamaged material causes fracturem material parameter that relates the sensitivity of a total strain amplitude of the material to the number of cycles to fracture?
6Steel Brace Database for Model Calibration Collected Data from 20 different experimental programs from the 1970s to date143 Hollow Square Steel Sections51 Pipes50 W Shape braces37 L Shape BracesLHLBDigitization of axial load axial displacement relationships(Calibrator JAVA software , Lignos and Krawinkler 2008)
7Steel Brace DatabaseBased 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
8Calibration Process of the Brace Model Mesh Adaptive Search Algorithm (MADS, Abramson et al. 2009)Objective Function HFexp: Experimentally measured axial force of the braceFsimul: Simulated axial force of the braceδi: Axial displacement of the brace at increment iNon-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.
9Calibration 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 adequateEight elements along the length of the steel braceFive integration points per elementSection level:Stress strain relationship:Strain hardening of 0.1%Radius that defines Bauschinger effect Ro=25Based on the calibration study of the entire set of bracesExponent m =0.3Strain amplitude εo is a function of KL/r, b/t, fy
10Model Parameter Calibrations (Data from Tremblay et al. 2008)(Data from Uriz and Mahin 2008)
11Validation with a Chevron CBF tested @ E-Defense x: Lateral bracingChevron CBF, 70%-scaleHSS braces: b/t = 19.4, KL/r = 82.5(Okazaki, Lignos, Hikino and Kajiyara, 2012)
12E-Defense Chevron CBF: Test Setup Load CellsConnecting BeamTest BedTest BedSpecimenConnectingBeamDirection of ShakingNShake Table(Okazaki, Lignos, Hikino and Kajiyara, 2012)
13E-Defense Chevron CBF: Test Setup JR Takatori(1995 Kobe EQ)10, 12, 14,28, 42, 70%Damping h ≈ 0.03inherent in test-bedsystem(Okazaki, Lignos, Hikino and Kajiyara, 2012)
14Response of Braces: Comparison @ 70% JR Takatori East Brace42%70%(Okazaki, Lignos, Hikino and Kajiyara, 2012)
15Global Response: Comparison @ 70% JR Takatori (Okazaki, Lignos, Hikino and Kajiyara, 2012)
16Case Study #2: 2-Story Chevron Braced Frame （A500 Gr. B)□ 152x9.5ColumnW10x45BeamW24x1172,7436,096ReactionPL 22(A572 Gr.50)Lateral support(Uriz and Mahin, 2008)
17Case Study #2: 2-Story Chevron Braced Frame Rigid offsetRigid offsetRigid offsetSteel beam & column spring (Bilinear Modified IMK Model)Shear connection spring (Pinching Modified IMK Model)Gusset plate spring (Menegotto-Pinto model)
18Case Study #2: 2-Story Chevron Braced Frame Rigid offsetRigid offsetRigid offsetSteel beam & column spring (Bilinear Mod. IMK Model)Liu and Astaneh (2004)Shear connection spring (Pinching Mod. IMK Model)Gusset plate spring (Menegotto-Pinto model)
19Case Study #2: 2-Story Chevron Braced Frame Rigid offsetRigid offsetRigid offsetSteel beam & column spring (Bilinear Mod. IMK Model)(Ibarra et al. 2005,Lignos and Krawinkler 2011)Shear connection spring (Pinching Mod. IMK Model)Gusset plate spring (Menegotto-Pinto model)
20Case Study #2: 2-Story Chevron Braced Frame (Lignos and Krawinkler 2011)
21Case Study #2: Loading Protocol (Uriz and Mahin, 2008)
22Case Study #2: Quasi-Static Analysis-Global Response
23Case 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.
25Validation of Simulated Collapse-Full Scale Tests (Suita et al. 2008)(Lignos, Hikino, Matsuoka, Nakashima 2012)
26Canoga Park Record: Story Drift Ratio Histories SF=2.0
27Dynamic Analysis: Base Shear-SDR1 Due to Artificial DampingArtificial 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.
28IDA Curves: Damping Based on Current Stiffness Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)
32First Story Column Behavior @ Collapse Intensity （A500 Gr. B)□ 152x9.5PL 22(A572 Gr.50)Lateral support
33Summary 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.
34AcknowledgmentsDr. 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 Berkeley.