Modeling Steel Moment Resisting Frames with OpenSees!

Transcription

1 Modeling Steel Moment Resisting Frames with OpenSees! DIMITRIOS G. LIGNOS! ASSISTANT PROFESSOR! MCGILL UNIVERSITY, MONTREAL CANADA! With Contributions By: Ahmed Elkady* and Samantha Walker*! *Graduate Students at McGill University! OpenSees Workshop, University of California, Berkeley! September 26 th 2014! 1

2 Agenda! ² Nonlinear Modeling of Steel MRFs! ² Steel Components for Nonlinear Modeling! ² Distributed and Concentrated Plasticity! ² Nonlinear Force-Based Elements! ² Zero Length Elements (Concentrated Plasticity)! ² Background on Available Steel Materials in OpenSees! ² Examples and Applications! ² Summary Remarks! 2

3 Steel Components for Nonlinear Modeling in MRFs! (Images courtesy of Prof. M. Engelhardt)! 3

4 Steel Components for Nonlinear Modeling in MRFs! Panel Zone (Shear Yielding) Column (Flexural & Axial Yielding) Beam (Flexural Yielding) (Image courtesy of Prof. M. Engelhardt)! 4

5 Steel Components for Nonlinear Modeling in MRFs! -Beam Plastic Hinging! Local buckling of Beams with RBS Lateral torsional buckling of Beams with RBS (Images courtesy of Prof. M. Engelhardt)! 5

6 Steel Components for Nonlinear Modeling in MRFs! -Panel Zone Shear Yielding! (Image courtesy of Prof. M. Engelhardt)! 6

7 Steel Components for Nonlinear Modeling in MRFs! -Column Plastic Hinging! (Image from Suzuki and Lignos 2014)! 7

8 Simulation Approach! Image Source: NIST GSR ! 8

9 Concentrated Plasticity Models! Image Source: NIST GSR ! Advantages! ² Fairly simple! ² Effective for interface effects! ² Computationally efficient! Disadvantages! ² Require the moment rotation relationship! (as opposed to engineering stress-strain)! ² They don t capture P-M interaction! (critical for columns)! 9

10 Distributed Plasticity Models! Advantages! ² Force- and displacement-based element permits spread of plasticity along the element! ² P-M interaction can be captured! Disadvantages! ² Localization! Image Source: NIST GSR ! ² Requires fiber section discretization (# fibers matters)! ² Deteriorating phenomena (local buckling) difficult to capture with available engineering stress-strain models in OpenSees! 10

11 Example for Today s Presentation! m I I I I m I I I I I I I I I I I I I I I I I I I I I I I I H = 16.60m 4.6m 4.0m 4.0m 4.0m Perimeter SMF W21x57 W21x57 W21x73 W21x Leaning Column I I I I Modeled SMF 6.10m ² 4-story building with perimeter steel special moment frames (SMFs)! ² Design location Bulk Center Los Angeles, CA! ² Design provisions: ASCE 7-10, AISC 2010! ² Fully-Restrained Beam-to-Column connections with Reduced Beam Sections (RBS)à See AISC or FEMA-350! ² First mode period: 1.51sec! m Rigid links (Source: Elkady and Lignos 2014)! 11

12 Modeling with Distributed Plasticity! Perimeter SMF W21x57 Leaning Column Node i Node j H = 16.60m 4.6m 4.0m 4.0m 4.0m W21x57 W21x73 W21x m Rigid links x Force- or Displacement- Based Element y z IntegraNon point Fiber element Engineering stress- strain domain 12

13 Steel Material Models Available in OpenSees! Steel01-Simple Bilinear! Steel02-Giuffre Menegotto-Pinto Model with Isotropic Strain Hardening! 13

14 Steel Material Models Available in OpenSees! Utilization of Steel01 for Modeling of Steel Components! 14

15 Steel Material Models Available in OpenSees! Utilization of Steel02 for Modeling of Steel Components! Example Utilization of Steel02 Material Model! From calibranon Moment [kn mm] Simulation Experimental Data Chord Rotation [rad] 15

16 Number of Fibers for Cross Section Discretization! à Follow the recommendations by Kostic & Filippou (2012)! W-Shapes: 12 MP gives remarkable accuracy in terms of local response estimates! Biaxial bending and failures associated with weak axis bending: (40MP) 2x8 fibers (Flange) 1x8 fibers (Web)! 16

17 Steel2.tcl FiberSteelWsection2d! 17

18 Nonlinear Beam-Column Elements in OpenSees! -Use of forcebeamcolumn element! (Neuenhofer and Filippou 1997) à good discussion why you may want to consider using force based elements over displacement-based ones.! Node i Node j x Force- Based Element y IntegraNon point z Only one element is adequate! 5 integration points along the member length are sufficient most of the times for modeling of steel MRFs! Fiber element Recommendations by Kostic & Filippou (2012)! 18

19 Steel2.tcl Procedure: ForceBeamWSection2d! à Uses forcebeamcolumn element! 19

20 model Basic ndm 2 ndf 3! source Steel2d.tcl!! # set some lists containing floor and column line locations and nodal masses! set floorlocs { }; # floor locations in inches! set collocs { }; #column line locations in inches! set massesx { }; # mass at nodes on each floor in x dirn! set massesy{ } ; # in y dirn!! # add nodes at each floor at each column line location & fix nodes if at floor 1! foreach floor { } floorloc $floorlocs massx $massesx massy $massesy {! foreach colline { } colloc $collocs {! node $colline$floor $colloc $floorloc -mass $massx $massy 0.! if {$floor == 1} {fix $colline$floor 1 1 1}! }! }! #uniaxialmaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2 $a1 $a2 $a3 $a4! uniaxialmaterial Steel ; # material to be used for steel elements!! # set some list for col and beam sizes! set colsizes { W24X103 64}; #col sizes stories 1, 2, 3 and 4! set beamsizes {W21x73 W21X73 W21X57 W21x57}; #beams sizes floor 1, 2, 3 and 4!! # add columns at each column line between floors! geomtransf PDelta 1! MRF1.tcl! Same Model in 35 lines! (Tcl Code by F. McKenna)! Selection of material model! Selection of nonlinear force beamcolumn element! foreach colline { } {! foreach floor1 {1 2 3 } floor2 { } {! set thesection [lindex $colsizes [expr $floor1-1]]; # obtain section size for column! ForceBeamWSection2d $colline$floor1$colline$floor2 $colline$floor1 $colline$floor2 $thesection 1 1 nip 5! }! }! #add beams between column lines at each floor! geomtransf Linear 2! foreach colline1 {1 2 3} colline2 {2 3 4} {! foreach floor { } {! set thesection [lindex $beamsizes [expr $floor -2]]; # obtain section size for floor! ForceBeamWSection2d $colline1$floor$colline2$floor $colline1$floor $colline2$floor $thesection 1 2! }! }! 20

21 Panel Zone Modeling! Perimeter SMF W21x57 Leaning Column H = 16.60m 4.6m 4.0m 4.0m 4.0m W21x57 W21x73 W21x m Nonlinear force-beam! column elements! Rigid links d b! Elastic beam! column elements! d c! How to obtain the input parameters?! see Gupta and Krawinkler (1999)! 21

22 Procedure for Modeling Panel Zones! -Available from OpenSees Examples Posted by Dr. L. Eads! 22

23 Base Shear/Seismic Weight, V/W 4-Story SMF Distributed Plasticity Approach! Basic Results Nonlinear Static Procedure! First Mode Lateral Load Pattern! Ω! Without P Delta With P Delta C s! Roof Drift Ratio, /H [rad] Does not capture strength deterioranon of steel components Floor Formation of a 3-story mechanism! Roof r /H = 1% r /H = 2% r /H = 3% r /H = 4% Normalized Floor Displacement [rad] 23

24 4-Story SMF Distributed Plasticity Approach! Basic Results Nonlinear Response History Analysis! Sa (T, 5%) [g] Canoga Park Record! Northridge 1994 Earthquake! Unscaled (SF=1.0)! Floor Roof SF=1.0 SF= T [sec] Story Drift Ratio, SDR [rad] Does not include the effect of cyclic deterioration on flexural strength and stiffness of steel components! 24

25 4-Story SMF Concentrated Plasticity Approach! Perimeter SMF W21x57 Leaning Column Zero Length element (rotational springs)! With idealized moment rotation relationship! H = 16.60m 4.6m 4.0m 4.0m 4.0m W21x57 W21x73 W21x m Rigid links Elastic beam-column element! 25

26 4-Story SMF Concentrated Plasticity Approach! From Steel2d.tcl: Procedure to Create Elastic Beam-Column Element! à Look for Procedure! ElasticBeamSection2d! 26

27 Available Steel Material Models for Modeling the Moment Rotation Relationship of a Steel Component! ² Steel01 (Basic Bilinear)! ² Steel02 (Giuffre Menegotto-Pinto Model with Isotropic Strain Hardening)! ² Modified Ibarra-Medina-Krawinkler (IMK) Deterioration Model with Bilinear Hysteretic Response (or Bilin in OpenSees) à Considers Strength and Stiffness Deterioration of Steel Components! 27

28 The Modified IMK Deterioration Model! -Input Model Parameters! (Image Source: Lignos and Krawinkler 2012)! The deduced moment rotation relationship of the component under consideration is needed for input parameter identification! 28

29 The Modified IMK Deterioration Model! -Considering Slab Effects (see Elkady and Lignos 2014)! Moment (kn-m) Initial Backbone Curve M - r θ- u θ- pc M - c M + y θ+ p M + c Strength Det. Post Cap. Strength Det. Unload. Stiff. Det. M ȳ θ- M - p ref Chord Rotation (rad) N.A! The deduced moment rotation relationship of the component under consideration is needed for input parameter identification! 29

30 Utilizing the Modified IMK Model in OpenSees! Visit: dimitrios.lignos.research.mcgill.ca/databases/steel/! Contains data from more than 300 experiments from steel beams! 30

31 Utilizing the Modified IMK Model in OpenSees! Sample Model Calibrations! Steel Beam (bare) with RBS! Steel Beam (Composite) with RBS! (Sources: Lignos and Krawinkler 2011, 2013)! 31

32 CAS February 2011 Utilizing the Modified IMK Model in OpenSees! Visit: dimitrios.lignos.research.mcgill.ca/databases/component/! Pre-capping plastic rotation, p, for beams with non-rbs connections: D.G. Lignos et al. / Computers and Structures xx p h b f L d cunit F y 1 t w 2 t f d cunit 21" M y M c p Pre-capping plastic rotation, p, for beams with RBS connections: h b f L CAS c b L d unit F y w 2 f y unit 21" t t r d c 7 February 2011 Moment M r K e θ p θ pc Moment No. of Page Post-capping rotation, pc, for beams with non-rbs connections: D.G. Lignos et al. / Computers and Structures xxx (2011) xxx xxx Chord Rotation θ h b f d cunit F y pc Initial (a) backbone curve t w 2 t f cunit 21" 50 BackBone Curve θ u Post-capping rotation, pc, for beams with RBS connections: pc M M c y b f L c b unit F y h 9.62 t w 2 t f r y 50 Moment Reference cumulative plastic rotation,, for beams with non-rbs M connections: r K e t h b f cunit F y 500 M y t w 2 t f 50 Chord Rotation θ θ u (a) backbone curve (Sources: Lignos and Krawinkler 2011, 2013)! θ p θ pc Moment Post Cap. Strength Det. Chord Rotation θ Unload. Stiffness Det. Strength Det. (b) basic modes of cyclic deterioration Fig. 1. Modified Ibarra Krawinkler deterioration model (Lignos and Krawinkler [39]). 32

33 Utilizing the Modified IMK Model in OpenSees! Visit: dimitrios.lignos.research.mcgill.ca/databases/component/! 33

34 4-Story Concentrated Plasticity Approach! Steel2d.tcl: Rotational Spring with SteelWsectionMR! à Look for SteelWSectionMR! Uses the multivariate-regression equations and utilizes the modified IMK model in OpenSees! 34

35 4-Story SMF Concentrated Plasticity- Deterioration! Nonlinear Static Analysis First Mode Lateral Load Pattern! Comparisons with Distributed Plasticity Model! Base Shear/Seismic Weight, V/W Fiber Based,Steel02 Spring Mod. IMK Model Due to! strength deterioration! Roof Drift Ratio, /H [rad] Floor Formation of a 3-story mechanism! (Did not change in this case)! Roof Normalized Floor Displacement [rad] 35

36 4-Story SMF Concentrated Plasticity- Deterioration! Nonlinear Response History Analysis with Canoga Park Record! Comparisons with Distributed Plasticity Model! Roof Canoga Park SF=1.0! Fiber Based,Steel02 Roof Canoga Park SF=1.5! 4 Spring Mod. IMK Model 4 Floor 3 Floor Story Drift Ratio, SDR [rad] 2 Fiber Based,Steel02 Spring Mod. IMK Model Story Drift Ratio, SDR [rad] The effect of cyclic deterioration on the! structural response is minimal for SF = 1.0 (close to design level earthquake)! The effect of cyclic deterioration on the! structural response is significant! 36

37 4-Story SMF Concentrated Plasticity- Deterioration! Nonlinear Response History Analysis with Canoga Park Record! Comparisons with Distributed Plasticity Model! Canoga Park Record SF=1.5! Normalized Base Shear V 1 / W st Story Drift Ratio [rad] Due to strength deterioration! Spring Mod. IMK Model Fiber Based, Steel02 Approaching! dynamic collapse! 37

38 Collapse Assessment of Steel SMFs Using Concentrated Plasticity Approach! Case studies: Archetype office steel buildings with perimeter steel special moment frames designed in Urban California (ASCE 7-10, AISC-2010)! 20 Story Story W21x57 W21x57 W21x73 W21x W21x57 W21x57 W21x73 W21x W21x57 W21x57 W21x73 W21x Story W21x W27x94 W27x W21x W27x94 W27x W21x W27x94 W27x Story W27x9 4 W27x W27x9 4 W27x W27x9 4 W27x W14x500 W14x455 W14x455 W14x370 W14x370 W14x311 W14x283 W14x233 W14x193 W14x132 W36x330 W36x262 W36x232 W27x194 W27x129 W36x395 W36x361 W36x441 W36x487 W36x W33x13 0 W33x13 0 W33x13 0 W33x13 0 W33x15 2 W33x15 2 W33x15 2 W33x15 2 W33x15 2 W33x15 2 W33x15 2 W33x15 2 W33x14 1 W33x14 1 W33x14 1 W33x14 1 W33x13 0 W33x13 0 (Sources: Elkady and Lignos 2014)! Source: National Seismic Hazard Map (USGS 2008)! 38

39 Example: Collapse Risk of 4-Story Steel SMF! Incremental Dynamic Analysis Utilization of 44 Ground Motions! 2.5 IDA Curves! Collapse! 1 Collapse Fragility Curve! Sa (T 1, 5%) [g] Median Collapse Capacity Ŝ CT! Maximum Story Drift Ratio [rad] Probabilty of Collapse S CT = = Simulation Results Lognormal CDF IM = Sa(T, 5%) [g] 1 Source: Elkady and Lignos (2014)! 39

40 Concluding Remarks! ² Modeling Steel Moment Resisting Frames in OpenSees! Ø You can use a number of readily available tools (procedures in tcl, examples, web-based tools, etc)! ² Steel Components to Consider! ü Steel Beams, Columns and Panel Zones! ² Distributed Versus Concentrated Plasticity Approach! ü For low rise code-compliant steel buildings with perimeter MRFs the differences should not be large for design level earthquakes Distributed plasticity models capture cyclic hardening, P-M interaction! ² If Performance Evaluation at Large Deformations is the Objective: Component Deterioration Must be Considered! ü Concentrated Plasticity with Degrading Phenomenological Models will do reasonably well for low- to mid-rise steel MRFs.!! 40

41 Thank you for your kind attention!! References:! For more information visit: dimitrios-lignos.research.mcgill.ca! 1. Elkady, A., Lignos, D.G. (2014). Modeling of the Composite Action in Fully Restrained Beam-to-Column Connections: Implications in the Seismic Design and Collapse Capacity of Steel Special Moment Frames, Earthquake Engineering and Structural Dynamics, EESD, doi: /eqe.2430 (available in early view).! 2. Lignos, D.G., Krawinkler, H. (2013). Development and Utilization of Structural Component Databases for Performance-Based Earthquake Engineering, ASCE, Journal of Structural Engineering, Vol. 139 (NEES 2), pp , doi:10/1061/(asce)st x ! 3. Lignos, D.G., Krawinkler, H. (2011). Deterioration Modeling of Steel Components in Support to Collapse Prediction of Steel Moment Frames, ASCE Journal of Structural Engineering, Vol. 137 (11), pp , doi: /(ASCE)ST X ! 4. Lignos, D.G., Krawinkler, H. (2012). Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations, Report No. TB 177, The John A. Blume Earthquake Engineering Center, Stanford, CA.! 5. Ibarra, L., Medina, R., Krawinkler, H. (2005). Hysteretic Models that Incorate Strength and Stiffness Deterioration, Earthquake Engineering and Structural Dynamics, EESD, Vol. 34(12), pp ! 41