TRANSPORTATION RESEARCH BOARD. TRB Webinar Program Direct Displacement Based Seismic Design of Bridges. Thursday, June 22, :00-3:30 PM ET

Transcription

1 TRANSPORTATION RESEARCH BOARD TRB Webinar Program Direct Displacement Based Seismic Design of Bridges Thursday, June 22, :00-3:30 PM ET

2 The Transportation Research Board has met the standards and requirements of the Registered Continuing Education Providers Program. Credit earned on completion of this program will be reported to RCEP. A certificate of completion will be issued to participants that have registered and attended the entire session. As such, it does not include content that may be deemed or construed to be an approval or endorsement by RCEP.

3 Purpose Discuss the concepts of Direct Displacement-Based Seismic Design (DDBD) as a methodology suitable for seismic design of bridges. Learning Objectives At the end of this webinar, you will be able to: Understand the fundamentals of DDBD Apply DDBD principles do the design of simple bridges Understand the issues involved in developing more complex structures

4 TRB WEBINAR DISPLACEMENT-BASED SEISMIC DESIGN OF BRIDGES Mervyn J. Kowalsky Professor of Structural Engineering North Carolina State University June 2017

5 Webinar Schedule Introduction and Motivation Seismic Demands for DDBD Fundamentals of DDBD for SDOF systems. Multi-span bridges

6 Traditional Force-Based Design 2π T n = W gk Acc. (g) V Bel = a el * M e V Bel Force Equal Displacement Approximation a el V BD T n Period (s) m V BD = V Bel /R Disp.

7 Forces: Poor Indicators of Damage

8 DESIGN TO ELASTIC ACCELERATION SPECTRA (FORCE-BASED DESIGN) ASSUMPTIONS ARE: Elastic force levels (dependent on initial stiffness) are of prime importance Elastic stiffness is known at the start of design Elastic forces can be reduced by ductility factors, dependent only on material and structural type Maximum transient response is the issue. Residual displacement is irrelevant Displacements are well estimated by elastic response values Safety is increased as strength is increased

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11 1 0.8 ρ l = Stiffness Ratio (EI/EI gross ) ρ l = 0.03 ρ l = 0.02 ρ l = 0.01 ρ l = EI eff = M N /φ y EI eff /EI gross =M N /φ y EI gross Axial Load Ratio (N u /f' c A g ) EFFECTIVE STIFFNESS RATIO FOR CIRCULAR COLUMNS

12 INTERDEPENDENCY OF STRENGTH AND STIFFNESS Stiffness EI = M/φ M M 1 M M 1 M 2 M 2 M 3 M 3 φ y3 φ y2 φ y1 φ φ y φ (a) Design assumption (constant stiffness) (b) Realistic assumption (constant yield curvature INFLUENCE OF STRENGTH ON MOMENT-CURVATURE RESPONSE

13 FORCE-BASED DESIGN ASSUMPTIONS OF SYSTEM DUCTILITY In current force-based design it is assumed that structural systems have a unique ductility capacity, and hence a unique force-reduction factor e.g. Concrete Frame Building: R µ = 6 (depends on country) Concrete Wall Building: R µ = 4 (::) Concrete Bridge: R µ = 3 (::)

14 CONSIDER BRIDGE COLUMNS OF DIFFERENT HEIGHTS y = φ y H 2 / 3 p = φ p L p H H=3m H=8m y + p φ plp µ = = 1+ 3 φ H y y L P = 0.08H+0.022d b f y (a) Squat Column,µ =9.4 (b) Slender Column,µ =5.1 (P/f cag=0.1, Rebar = 2% long., 0.6% transverse

15 T = 2π m / K long Bridge Under Longitudinal Response H A H B H C C A Stiffness: K long B = K A + K B + K C = A, B, C 12EI H 3 Period: T = 2π m / K long Pier Strength: F = i F K K i long What value to use for EI? What ductility? 6

16 Direct Displacement-Based Design: What s Different? Design for a target damage level. Use displacement spectra to define hazard. Consider energy dissipation via equivalent viscous damping. Start with target displacement end with required strength and stiffness.

17 FUNDAMENTALS OF DDBD F m e F u F n h e K e K i y d (a) SDOF Simulation (b) Effective Stiffness K e Damping (%) Elasto-Plastic Steel Frame Concrete Frame Concrete Bridge Hybrid Prestress Displacement (m) d 5% 10% 15% 20% 30% 0 0 T e Displacement Ductility Period (seconds) (c) Equivalent damping vs. ductility (d) Design Displacement Spectra

18 Session 2 Characterization of Seismicity for Displacement-Based Seismic Design

19 Seismicity Outline Time histories Response Spectra Seismic Input for DDBD

20 WHITTIER NARROWS 1987, Mw = 6.0 (15 km) ACCELEROGRAM 0.8 Acceleration (xg) g -0.8 (a) Whittier Earthquake, M W =6.0, Time (sec)

21 NOTRTHRIDGE, 1994, Mw=6.7 (6km) ACCELEROGRAM g Acceleration (xg) (b) Sylmar Record, Northridge Earthquake, M W =6.7, Time (sec)

22 KOBE, 1995, Mw=6.9 (1 km) ACCELEROGRAM 0.8 Acceleration (xg) (c) Kobe Earthquake, M W =6.9, Time (sec) 0.8g

23 Displacement (cm) (a) Whittier Record M W =6.0, Time (sec) GROUND DISPLACEMENT Whittier, 1.0cm Displacement (cm) (b) Sylmar Record, 1994 Northridge Earthquake, M W =6.7 Northridge, 30cm Time (sec) Displacement (cm) (c) Kobe Earthquake 1995, M W =6.9 Kobe, 20cm

24 Time History Observations Acceleration time histories give an incomplete picture of an EQ Frequency content may be influenced by distance to source Displacement time histories expose large differences between earthquakes of comparatively similar PGAs

25 ARS and DRS of Selected Records Spectral acceleration (xg) Spectral acceleration (xg) Spectral acceleration (xg) ξ= Period (seconds) ξ= Period (seconds) ξ= Period (seconds) Spectral displacement (cm) (a) Whittier (M W =6.0) Spectral displacement (cm) (b) Sylmar (Northridge,1994; M W =6.7) Spectral displacement (cm) (c) Kobe (M W =6.9) ξ= Period (seconds) ξ= Period (seconds) ξ= Period (seconds) M6 15 km M6.7 6 km M6.9 1 km

26 Response Spectra Observations ARS do not give the complete picture of damage potential of an EQ EQs with large PGAs do not necessarily indicate large potential for damage. Distance to source plays an important role in defining damage potential of an EQ

27 Seismic Input for DDBD

28 DRS Options Approximate from code ARS Direct calculation from code specified parameters (i.e. EuroCode) Ground motion prediction equations (magnitude-distance relationships) for DRS, or converted from ARS. Site-specific evaluation

29 Option One: DRS from ARS

30 Derived ASCE 7 Displacement Spectra Tc Easy to apply, however, design ARS may be inaccurate in the long period range, likely overestimating response levels.

31 Option Two: Code DRS Ideal option, however, only EuroCode defines DRS directly

32 Option Three: GMPEs Numerous GMPEs for ARS that could be converted to DRS by dividing by ω 2 as in option one. Preferable to use GMPE that directly defines DRS, i.e. Faccioli, 2004 and 2010.

33 DESIGN DISPLACEMENT SPECTRA (4) Based on Faccioli s observations,the corner period T c appears to increase almost linearly with moment magnitude. For earthquakes with M W > 5.7, the following expression seems conservative: ( 5.7) T c M = w Peak displacement at the corner period can be estimated from the following expression (firm ground): δ max = 10 ( M 3.2) W r mm seconds r = nearest distance to fault plane (km)

34 Spectral Displacement (mm) M = 7.5 M = 7.0 M = 6.5 M = Period (seconds) 5% Damped Spectra Resulting from the Equations, at r = 10km

35 Comparison of 2004 Faccioli Model with actual Data < M < km Sd [cm] km km km T [s]

36 SESSION 3 Fundamentals of Displacement-Based Seismic Design

37 FUNDAMENTALS OF DDBD m e F u F F n rk i H e K i K e y d (a) SDOF Simulation (b) Effective Stiffness K e Damping Ratio, ξ Elasto-Plastic Steel Frame Concrete Frame Concrete Bridge Hybrid Prestress Displacement (m) d ξ=0.05 ξ=0.10 ξ=0.15 ξ=0.20 ξ= Displacement Ductility 0 T e Period (seconds) (c) Equivalent damping vs. ductility (d) Design Displacement Spectra

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40 Select target displacement, d Strain, Drift, or Ductility Calculate yield displacement, y Fundamental member property Calculate equivalent viscous damping, ζ Relationships between damping and ductility available and easily obtained Calculate effective period, T eff From Response spectra Calculate effective stiffness, K eff K eff = 4π 2 m/t 2 eff Calculate design base shear force, V b V b = K eff d

41 DIRECT DISPLACEMENT-BASED DESIGN SINGLE-DEGREE-OF-FREEDOM STRUCTURES

42 1. DESIGN DISPLACEMENT FOR S.D.O.F STRUCTURES Depends on Design Limit State Structural displacement limit: Strain related, Ductility related Non-structural displacement limit: Drift related chose critical of structural and non-structural limit displacements

43 EXAMPLE OF STRAIN LIMIT STATES Curvature from concrete compression: φ mc = ε cm /c Curvature from reinforcement tension: φ ms = ε sm /(d-c) Chose lesser of φ mc and φ ms, Design Displacement is: ds = y + p = φ y H 2 /3 + (φ m -φ y )L p H L p = plastic hinge length.

44 2. DUCTILITY Damping depends on the design displacement ductility: µ = d / y NOTE: The yield displacement is independent of strength, and is thus known at the start of the design process (provided section size is known). Hence ductility is known at the start of the design process.

45 DIMENSIONLESS YIELD CURVATURES AND DRIFTS

46 3.EQUIVALENT VISCOUS DAMPING

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48 HYSTERETIC DAMPING INITIAL WORK: JACOBSEN EVD APPROACH

49 RELATIONSHIPS FOR TANGENT-STIFFNESS DAMPING, T e > 1 sec (CORRECTION FACTOR INCLUDED)

50 Example DDBD SDOF H=10m d=2m 875 mm 4 sec. ζ=5% f y =470MPa E s =200GPa W=5000kN θ d =0.035 µ d =4 Target Displacement: Drift: d =(0.035)(10m) = m Ductility: d =µ d y y =φ y H 2 /3 φ y =2.25ε y /D= /m y = m d = 4(0.088) = m

51 Example DDBD SDOF Equivalent Viscous Damping (These expressions all assume 5% tangent stiffness proportional viscous damping and hysteretic damping):

52 Example DDBD SDOF Obtaining Effective Period: Disp (mm) c 5% = 875 mm ζ=5% c 15.5% = 553 mm ζ=15.5% d = 350 mm T eff = 2.53 NOTE: c X% = c 5% R ξ R ξ = T c = ζ Period (sec)

53 Example DDBD SDOF Obtaining Effective Stiffness: Obtaining Design Base Shear:

54 Simplified Base Shear Equation for DDBD α = 0.5 for regular conditions α = 0.25 for velocity pulse conditions NOTE: Damping expressed as ratio in the above equation (not %). NOTE: Equation assumes a linear DRS to the corner point.

55 Sample Problems See Handout

56 Session 4 Longitudinal Design of Bridges Transverse Design of Bridges

57 DDBD OF MDOF BRIDGES Longitudinal Design: If the bridge is straight, this is generally straightforward, but will often dominate design requirements. Effective damping and design displacement are the main issues. Transverse Design: More complex, but often doesn t govern. Displacement shape may not be obvious at start. Design displacement, damping, higher mode effects need to be considered.

58 Obtaining Displaced Shape Displacement Position along bridge Note: Stars are limit state displacements based on strain, ductility, or drift

59 System Displacement and Effective Mass From work balance between MDOF and SDOF systems: From force equilibrium between MDOF and SDOF systems:

60 Base Shear Distribution Force is distributed in proportion to mass and pier top displacement.

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62 Transverse Design Example 40m 50m 50m 40m A 16m C 12m 16m E B (Not to scale) D Estimate proportion of total force carried to abutments: X = 0.5 Target displaced shape (governed by limit state displacement of central column: 40mm; 417mm; 596mm; 417mm; 40mm Pier B and D displacements are assumed to be 70% of Pier C displ.

63 Example, continued System displacement: 485mm Pier ductilities: 1.59; 3.82; 1.59 Pier damping: 10.2%, 15.4%, 10.2% System damping: 8.9% Base shear: kn Lateral force distribution: 115; 2820; 4410; 2820;115 kn Lateral analysis using secant stiffness properties: 43mm; 383mm; 572mm; 383mm; 43mm (actual) 40mm; 417mm; 596mm; 417mm; 40mm (target) Revision of proportion of force carried by abutments. (increase portion of force to abutments slightly) Converge onto X and displaced shape. 40mm; 395mm; 595mm; 395mm; 40mm (final)

64 Sample Design and Analysis Result for MDOF Bridge

65 Other verification results 2, 4, 6 span bridges with 9 different support conditions. Each bridge designed with DDBD and then analyzed with NLTH analysis.

66 6 Span Bridge Results Deck Displacement (m) EQ1 to EQ7 0.1 EQ Avg DDBD_ST Normalize length Deck Displacement (m) Normalize length Deck Displacement (m) Normalize length Case 1 Case 2 Case 3 Deck Displacement (m) Case 4 Normalize length Deck Displacement (m) Normalize length Case 5 Deck Displacement (m) Normalize length Case 6 Deck Displacement (m) Normalize length Case 7 Deck Displacement (m) Normalize length Case 8 Deck Displacement (m) Normalize length Case 9

67 IMPLEMENTATION OF DDBD IN PRACTICE CODES: 1. Chapter 14 is written in code format, as a starting point for code development. 2. Envisaged as being adopted as an alternative design process (i.e. parallel force-based and displacement-based procedures acceptable) 3. POLA has adopted DDBD as the preferred procedure of a dual force-based/displacement-based code (performance defined by limit strains for BOTH approaches. 4. Australia, New Zealand, Europe developing DDBD based codes.

68 IMPLEMENTATION OF DDBD IN PRACTICE WITHIN EXISTING CODES: Many codes permit the use of Time-history analysis as a design tool, hence: 1. Design using DDBD to obtain a rational design 2. Verify response using ITHA. Note that this approach follows the logical procedure of using analysis to verify design, rather than using analysis to DEFINE design (as with multi-modal analysis)

69 To learn more Textbook/papers Occasional short courses Feel free to contact me with any questions or to chat further.

70 Panelists Presentations After the webinar, you will receive a follow-up containing a link to the recording

71 Today s Participants Elmer Marx, Alaska Department of Transportation and Public Facilities, elmer.marx@alaska.gov Mervyn Kowalsky, North Carolina State University, kowalsky@ncsu.edu

72 Get Involved with TRB Getting involved is free! Join a Standing Committee ( Search for AFF50 (Seismic Design and Performance of Bridges) Become a Friend of a Committee Networking opportunities May provide a path to become a Standing Committee member For more information: Create your account Update your profile 97 th TRB Annual Meeting: January 7-11, 2018