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- 1. OpenSees Days in Portugal @FEUP p. 1 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 OpenSees Days in Portugal @Faculdade de Engenharia at Univ. do Porto DYNAMIC ANALYSIS (Seismic and Tsunami loadings) André R. Barbosa, Ph.D., P.E. July 03, 2014
- 2. OpenSees Days in Portugal @FEUP p. 2 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 2 Outline • Moment-‐interac8on diagrams as an applica8on of sec8on analysis using OpenSees.exe • Modeling a 1-‐bay, 2-‐story RC concrete frame – Nonlinear material and nonlinear geometry • What can else can we do using OpenSees? – Building example – Bridge example – Soil-‐structure-‐fluid-‐interac8on?
- 3. OpenSees Days in Portugal @FEUP p. 3 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Moment interacOon diagrams RC sec8on behavior under Combined Bending and Axial Load https://www.dropbox.com/s/evzcz6er3ep0jen/Ex1_MP_Interaction_Diagram.zip
- 4. Development of M-‐N interac8on diagrams OpenSees Days in Portugal @FEUP p. 4 Dynamic Analysis Notes Interaction Diagram (Failure Envelope) Dr. André R. Barbosa July 03, 2014 Concrete crushes before steel yields Steel yields before concrete crushes Moment Axial Load, P Failure Criterion: ecu = 0.003
- 5. OpenSees Days in Portugal @FEUP p. 5 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 General Procedure – For various levels of axial load, increase curvature of the sec8on un8l a concrete strain of 0.003 is reached. – Files used: • model.tcl • Mp.tcl – Output: • mp.out Moment = f(c) Axial Load, P P M
- 6. OpenSees Days in Portugal @FEUP p. 6 Dynamic Analysis Notes Zero-Length Section ≡ = Δ = Δ Dr. André R. Barbosa July 03, 2014 Zero Length Sec8on Element for RC Sec8on Analysis y z y x L 1 u u L L ε χ = Δ θ = Δ θ
- 7. OpenSees Days in Portugal @FEUP p. 7 Concrete01 $Fy $b*E0 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 $fpcu 2*$fpc/$epsc0 Concrete01 $fpc $epsU $eps0 strain stress $E0 strain stress $Fy $b*E0 y As1 = 4 No. 8 bars As2 = 4 No. 8 bars z y1 -y1 z1 -z1 cover Fiber sec8on Steel01 Core concrete Cover concrete
- 8. Reinforced Concrete: Mechanics and Design (4th Edi8on) by James G. MacGregor, James K. Wight M C y a F y d = ⎛ − ⎞ + − ⎜⎝ ⎟⎠ Σn n i ⎛ ⎞ = ⎜ ⎟ ⎝ − ⎠ s y c d Z OpenSees Days in Portugal @FEUP p. 8 P C F Dynamic Analysis Notes 0.003 ; where = 0.003 i if < i a d else Dr. André R. Barbosa July 03, 2014 Interac8on Diagram = +Σn n c si =1 i ( ) c si 2 i =1 1 1 1 ε ε ε s ε = ⎛ − ⎞0.003 ⎜⎝ ⎟⎠ si c d c = ε ; ≤ si si s si y f E f f 1 = 1.05 0.05 c f psi 1000 β ⎛ ′ ⎞ − ⎜ ⎟ ⎝ ⎠ ( )( ) 1 = 0.85 ′ ; =β c c C f ab a c = (positive in compression) si si si F f A = ( −0.85 ′) si si c si F f f A y = h for symmetric sections 2
- 9. OpenSees Days in Portugal @FEUP p. 9 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Interac8on Diagram
- 10. Modeling a 1-‐bay, 2-‐story RC frame Beam column element with (elas8c) RC OpenSees Days in Portugal @FEUP p. 10 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 fiber sec8on https://www.dropbox.com/s/ove56qgu7dqg54r/Ex2_ElasticFrame.zip
- 11. Lcol = 36 _ OpenSees Days in Portugal @FEUP p. 11 Dynamic Analysis Notes P Dr. André R. Barbosa July 03, 2014 P H/2 1 2 3 4 H 5 6 A A P P (1) (2) (3) (4) (5) (6) Linear Elas8c Steel Concrete Lbeam = 42 _ Lcol = 36 _ Cross-‐sec8ons
- 12. OpenSees Days in Portugal @FEUP p. 12 Dynamic Analysis Notes Pushover Analysis Dr. André R. Barbosa July 03, 2014 Linear geometry PDelta Corotational
- 13. OpenSees Days in Portugal @FEUP p. 13 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 13 Time-history Response Analysis Linear geometry PDelta Corotational
- 14. Modeling a 1-‐bay, 2-‐story RC frame Beam-‐column element with RC OpenSees Days in Portugal @FEUP p. 14 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 nonlinear fiber sec8on https://www.dropbox.com/s/geigqdn3dsrvbyb/Ex3_NonlinearFrame.zip
- 15. Lcol = 36 _ OpenSees Days in Portugal @FEUP p. 15 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 e P P H/2 1 2 3 4 H 5 6 A A P P (1) (2) (3) (4) (5) (6) Lbeam = 42 _ Lcol = 36 _ Cross-‐sec8ons s s e Steel02 Concrete02 Material models
- 16. Pushover Analysis Time History Analysis OpenSees Days in Portugal @FEUP p. 16 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014
- 17. OpenSees Days in Portugal @FEUP p. 17 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Concrete stress-strain response Steel stress-strain response Fiber 2 y z Fiber 1 Pushover Analysis Element 1 Section 5
- 18. Time History Analysis Concrete stress-strain response OpenSees Days in Portugal @FEUP p. 18 Dynamic Analysis Notes Fiber 2 y Dr. André R. Barbosa July 03, 2014 z Steel stress-strain response Element 1 Section 5
- 19. OpenSees Days in Portugal @FEUP p. 19 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Building Example Barbosa, Conte, Restrepo (2011)
- 20. q NEHRP design example (FEMA 451) Barbosa, Conte, Restrepo (2011) Ø Demonstrate the design procedures (ASCE7-‐05, ACI318-‐08) Ø Building was OpenSees Days in Portugal @FEUP p. 20 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 re-‐designed to account for latest Seismic Design Maps and common prac8ces in California Latitude: 37.87N Longitude: -122.29W Plan View Eleva,on Loca,on
- 21. q First…. CHECK AND VALIDATE YOUR MODEL… q The model Ø Walls: Nonlinear truss modeling approach Ø Columns and beams: Force-‐based beam-‐column elements Ø Diaphragms: Flexible diaphragms allowing for plas8c hinge OpenSees Days in Portugal @FEUP p. 21 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Elevation Location elonga8on Barbosa, Conte, Restrepo (2011)
- 22. OpenSees Days in Portugal @FEUP p. 22 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014
- 23. OpenSees Days in Portugal @FEUP p. 23 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Bridge Example Soil-structure interaction: Barbosa, Mason, Romney (2013) Tsunami following earthquake: Carey, Mason, Barbosa, Scott (2014)
- 24. out-of-plane cross sectional area of the quadrilateral element. The earthquake motion is to the model as an equivalent force-time series, which is coupled with the dashpot. equivalent force-time series, FE, is calculated as FE = 2ȡE Vs uլg A, where uլg is the velocity-series of the input earthquake motion. Applying the force-time series at the soil-bedrock requires the soil column to have unconstrained horizontal degrees of freedom, accomplished by modeling soil column bedrock interface with rollers (i.e. the vertical degree-is constrained). OpenSees Days in Portugal @FEUP Barbosa, Mason, Romney (2013) p. 24 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Soil-‐Founda8on-‐Bridge Model q Type-‐I sha q California, Oregon, Washington, USA (a) (b)
- 25. OpenSees Days in Portugal @FEUP p. 25 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Bridge Deck & Abutments • Linear elas8c beam-‐column • 10.36 m W x 1.67 m T x 63.4 m L • Area = 4.56 m2 • Ixx = 5.98x1012 mm4
- 26. OpenSees Days in Portugal @FEUP p. 26 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Bridge Deck & Abutments • Abutment (Shamsabadi et al., 2007, Caltrans SDC) • Silty sand • S8ffness, K = 307 kN/cm/m • Yield Force, Fy = 1397 kN • Ini8al Gap Opening = 2.54 cm
- 27. OpenSees Days in Portugal @FEUP p. 27 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 27 Pile and Column • Moment-‐Curvature Analysis • f’ c = 28 MPa • Fy = 475 MPa • E = 200 GPa • Long. steel ra8o = 1.0% • Fiber-‐sec8on: • Varied number of theta wedges and radial rings
- 28. the Open System for Earthquake Engineering Simulations (OpenSees) finite [10]. The seismic response of the soil-bridge system was analyzed by subjecting seven shallow crustal earthquake motions and seven subduction zone earthquake 1 shows a schematic of the overall soil-bridge system and a cross-section of the bridge column. Barbosa et al. [2] contains more details about the soil-bridge model, of the modeling details have changed, which are documented herein. OpenSees Days in Portugal @FEUP p. 28 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Analysis Methodology • Development of SFB Model • Step 1: Define soil • Step 2: Define structural nodes and elements
- 29. OpenSees Days in Portugal @FEUP p. 29 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Analysis Methodology • Step 3: Gravity (self-‐weight) loads • Soil self-‐weight loading • Connect pile to soil column • Structural self-‐weight loading
- 30. OpenSees Days in Portugal @FEUP p. 30 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Analysis Methodology • Step 4: Nonlinear dynamic analysis using earthquake mo8ons
- 31. response will be dominated by tsunami impact on the much larger deck width. The length tsunami bore is set as twice the open length (defined in Figure 3). The accuracy and PFEM solution depends on the mesh density of the fluid and structure under consideration 3. Schematic of the tsunami bore simulation (Note: pile and soil column are not Tsunami ensure accuracy and stability, the mesh size for the tsunami bore simulation was mm x 175 mm. OpenSees Days in Portugal @FEUP p. 31 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 following Earthquake Modeling q Type-‐I sha q California, Oregon, Washington, USA q In OpenSees, use PFEM: v Zhu and Scott (2014) Carey, Mason, Barbosa, Scott (2014)
- 32. PFEM procedure. At the conclusion of each time step, the fluid, wall, flume and bridge column were re-meshed for the subsequent time steps. Figure 5 shows a schematic of the tsunami simulation. Tsunami-‐Bridge Interac8on Model OpenSees Days in Portugal @FEUP p. 32 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Figure 4. Flow Chart of the three stages comprising the analysis framework.
- 33. Tsunami-‐Bridge Interac8on Model q Type-‐I sha q California, Oregon, Washington, USA Figure 4. Flow Chart of the three stages comprising the analysis framework. 30 30 25 25 20 20 15 15 10 10 5 5 0 0 −5 −5 30 25 20 15 10 5 0 −20 −15 −10 −5 0 5 10 OpenSees Days in Portugal @FEUP p. 33 Analysis at 0.575 Sec Analysis at 0.575 Sec Dynamic Analysis Notes 30 25 20 15 10 5 0 −5 Dr. André R. Barbosa July 03, 2014 Carey, Mason, Barbosa, Scott (2014) Figure 4. Flow Chart of the three stages comprising the analysis framework. (b) 3.1, and (b) tsunami bore during Step 3.2. Initial Bore Time 0 −20 5 10 −20 −15 −10 −5 0 5 10 (a) (b) Figure 5. (a) Tsunami bore at the end of Step 3.1, and (b) tsunami bore during Step 3.2. −5 Initial Bore Time 0 −20 −15 −10 −5 0 5 10 Units in meters
- 34. OpenSees Days in Portugal @FEUP p. 34 Dynamic Analysis Notes Dr. André R. Barbosa July 03, 2014 Andre.Barbosa@oregonstate.edu

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