Recommended LRFDGuidelines for the SeismicDesign of Highway BridgesCustomary U.S. Units

Requested by:American Association of State Highwayand Transportation Officials (AASHTO)Highway Subcommittee on Bridge and StructuresPrepared by:

Roy A. ImbsenTRC/Imbsen & Associates, Inc.

May 2006The information contained in this report was prepared as part of NCHRPProject 20-07, Task 193, National Cooperative Highway Research Program,Transportation Research Board.

AcknowledgementsThis study was requested by the American Association of State Highway and Transportation Officials(AASHTO), and conducted as part of National Cooperative Highway Research Program (NCHRP) Project 2007(193). The NCHRP is supported by annual voluntary contributions from the state Departments of Transportation.Project 20-07(193) is intended to fund quick response studies on behalf of the AASHTO Standing Committee onHighways. The report is being prepared by Roy Imbsen, TRC Imbsen Sacramento. The work was guided by a taskgroup chaired by Richard A. Pratt which included Ralph E. Anderson, Harry A. Capers, Jugesh Kapur, Michael D.Keever, Richard D. Land, Paul V. Liles, Jr., Derrell A. Manceaux, Joseph Penzien, Kevin J. Thompson, Edward P.Wasserman, and Phil Yen. The project was managed by David B. Beal, P.E., NCHRP Senior Program Officer.

DisclaimerThe opinions and conclusions expressed or implied are those of the research agency that performed the researchand are not necessarily those of the Transportation Research Board or its sponsors. This report has not been reviewed or accepted by the Transportation Research Board's Executive Committee or the Governing Board of theNational Research Council.

Table of ContentsPage No.

Section No.1.

2.

INTRODUCTION....................................................................................................................................... 1-11.1

Background ...................................................................................................................................... 1-1

1.2

Project Organization......................................................................................................................... 1-3

1.3

Flow Charts ...................................................................................................................................... 1-6

1.4

References ...................................................................................................................................... 1-14

SYMBOLS AND DEFINITIONS .............................................................................................................. 2-12.1

3.

4.

Notations .......................................................................................................................................... 2-1

GENERAL REQUIREMENTS .................................................................................................................. 3-13.1

Applicability of Specifications ........................................................................................................ 3-1

3.2

Performance Criteria......................................................................................................................... 3-1

3.3

Earthquake Resisting Systems (ERS) Requirements for SDC C & D.............................................. 3-2

3.4

Seismic Ground Shaking Hazard..................................................................................................... 3-93.4.1

Design Spectra Based on General Procedure ..................................................................... 3-9

3.4.2

Site Effects on Ground Motions....................................................................................... 3-11

3.4.3

Response Spectra Based on Site-Specific Procedures...................................................... 3-19

3.4.4

Acceleration Time-Histories ............................................................................................ 3-20

3.5

Selection of Seismic Design Category SDC................................................................................... 3-21

3.6

Temporary and Staged Construction .............................................................................................. 3-23

3.7

Load Factors ................................................................................................................................... 3-24

ANALYSIS AND DESIGN REQUIREMENTS ........................................................................................ 4-14.1

4.2

4.3

4.4

General ............................................................................................................................................. 4-14.1.1

Balanced Stiffness .............................................................................................................. 4-1

4.1.2

Balanced Frame Geometry................................................................................................. 4-2

4.1.3

Adjusting Dynamic Characteristics.................................................................................... 4-2

4.1.4

End Span Considerations ................................................................................................... 4-3

Selection of Analysis Procedure to Determine Seismic Demands ................................................... 4-44.2.1

Special Requirements for Curved Bridges ......................................................................... 4-5

4.2.2

Limitations and Special Requirements............................................................................... 4-6

Determination of Seismic Lateral Displacement Demands .............................................................. 4-74.3.1

Horizontal Ground Motions ............................................................................................... 4-7

4.3.2

Displacement Modification For Other Than 5% Damped Bridges .................................... 4-7

4.3.3

Displacement Magnification For Short Period Structures.................................................. 4-8

Combination of Orthogonal Seismic Displacement Demands ......................................................... 4-9

NCHRP 20-7(193) Task 12

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Section No.

Page No.

4.5

Design Requirements for Single Span Bridges .............................................................................. 4-10

4.6

Design Requirements for Seismic Design Category A................................................................... 4-10

4.7

Design Requirements for Seismic Design Categories B, C, and D ................................................ 4-10

4.8

4.9

4.7.1

Design Methods for Lateral Seismic Displacement Demands ......................................... 4-10

4.7.2

Vertical Ground Motions, Design Requirements for SDC D.......................................... 4-11

Structure Displacement Capacity for SDC B, C, and D ................................................................. 4-124.8.1

Local Displacement Capacity for SDC B and C .............................................................. 4-12

4.8.2

Local Displacement Capacity for SDC D ........................................................................ 4-13

Member Ductility Requirement for SDC D .................................................................................. 4-14

4.10 Column Shear Requirement for SDC B, C, and D ......................................................................... 4-144.11 Capacity Design Requirement for SDC C and D ........................................................................... 4-154.11.1

Capacity Design ............................................................................................................... 4-15

4.11.2

Inelastic Hinging Forces................................................................................................... 4-15

4.11.3

Single Column and Piers .................................................................................................. 4-16

4.11.4

Bents with Two or More Columns ................................................................................... 4-19

4.11.5

P- Capacity Requirement for SDC C & D .................................................................. 4-20

4.11.6

Analytical Plastic Hinge Length....................................................................................... 4-21

4.11.7

Reinforced Concrete Column Plastic Hinge Region ........................................................ 4-21

4.11.8

Steel Column Plastic Hinge Region ................................................................................. 4-22

4.12 Minimum Seat Width ..................................................................................................................... 4-224.12.1

Seismic Design Category A ............................................................................................. 4-22

4.12.2

Seismic Design Category B, C, D .................................................................................... 4-23

4.13 Support Restraints for SDC B, C AND D ...................................................................................... 4-234.13.1

Expansion Joints within a Span........................................................................................ 4-23

4.13.2

Simple Span Superstructures............................................................................................ 4-24

4.13.3

Detailing Restrainers ........................................................................................................ 4-24

4.14 Superstructure Shear Keys ............................................................................................................. 4-265.

ANALYTICAL MODELS AND PROCEDURES ..................................................................................... 5-15.1

5.2

5.3

GENERAL ....................................................................................................................................... 5-15.1.1

Analysis of a Bridge ERS................................................................................................... 5-1

5.1.2

Global Model ..................................................................................................................... 5-2

Abutments ........................................................................................................................................ 5-35.2.1

General ............................................................................................................................... 5-3

5.2.2

Wingwalls .......................................................................................................................... 5-4

5.2.3

Longitudinal Direction ....................................................................................................... 5-5

5.2.4

Transverse Direction .......................................................................................................... 5-9

Foundations .................................................................................................................................... 5-11

NCHRP 20-7(193) Task 12

ii

Section No.

5.4

5.5

5.6

Page No.

5.3.1

General ............................................................................................................................. 5-11

5.3.2

Spread Footing ................................................................................................................. 5-12

5.3.3

Pile Foundations............................................................................................................... 5-13

5.3.4

Drilled Shafts ................................................................................................................... 5-13

Analytical Procedures..................................................................................................................... 5-145.4.1

General ............................................................................................................................. 5-14

5.4.2

Procedure 1 Equivalent Static Analysis (ESA) ................................................................ 5-14

5.4.3

Procedure 2 Elastic Dynamic Analysis (EDA) ................................................................ 5-14

5.4.4

Procedure 3 Nonlinear Time History Method .................................................................. 5-15

Mathematical Modeling using EDA (Procedure 2)........................................................................ 5-165.5.1

General ............................................................................................................................. 5-16

5.5.2

Superstructure .................................................................................................................. 5-16

5.5.3

Substructure...................................................................................................................... 5-17

Effective Section Properties ........................................................................................................... 5-175.6.1

Effective Section Properties For Seismic Analysis .......................................................... 5-17

5.6.2

E c I eff and GAeff For Ductile Members........................................................................ 5-17

5.6.3

I eff For Box Girder Superstructures............................................................................... 5-22

5.6.4

I eff For Other Superstructure Types............................................................................... 5-22

5.6.5

Effective Torsional Moment of Inertia............................................................................. 5-22

6. FOUNDATION AND ABUTMENT DESIGN REQUIREMENTS ........................................................... 6-16.1

General ............................................................................................................................................. 6-1

6.2

Foundation Investigation ................................................................................................................. 6-1

6.3

6.4

6.2.1

Subsurface Investigation .................................................................................................... 6-1

6.2.2

Laboratory Testing ............................................................................................................. 6-1

6.2.3

Foundation Investigation for SDC A ................................................................................. 6-2

6.2.4

Foundation Investigation for SDC B and C ....................................................................... 6-2

6.2.5

Foundation Investigation for SDC D ................................................................................. 6-2

Spread Footings................................................................................................................................ 6-36.3.1

General ............................................................................................................................... 6-3

6.3.2

SDC B ................................................................................................................................ 6-3

6.3.3

SDC C or D ........................................................................................................................ 6-3

6.3.4

Rocking Analysis ............................................................................................................... 6-3

Pile Cap Foundation ......................................................................................................................... 6-86.4.1

General ............................................................................................................................... 6-8

6.4.2

Foundation with Standard Size Piles.................................................................................. 6-8

6.4.3

Pile Foundations in Soft Soil............................................................................................ 6-11

NCHRP 20-7(193) Task 12

iii

Section No.6.4.4

Other Pile Requirements .................................................................................................. 6-11

6.4.5

Footing Joint Shear SDC C and D ................................................................................... 6-12

6.4.6

Effective Footing Width For Flexure SDC C and D ........................................................ 6-15

6.5

Drilled Shafts.................................................................................................................................. 6-15

6.6

Pile Extensions ............................................................................................................................... 6-16

6.7

Abutment Design Requirements..................................................................................................... 6-16

6.87.

Page No.

6.7.1

Longitudinal Direction Requirements .............................................................................. 6-16

6.7.2

Transverse Direction Requirements ................................................................................. 6-17

6.7.3

Other Requirements for Abutments ................................................................................. 6-18

Liquefaction Design Requirements ................................................................................................ 6-18

SUPERSTRUCTURE STEEL COMPONENTS ........................................................................................ 7-17.1

General ............................................................................................................................................. 7-1

7.2

Performance Criteria ........................................................................................................................ 7-27.2.1

Type 1 ................................................................................................................................ 7-3

7.2.2

Type 2 ................................................................................................................................ 7-3

7.2.3

Type 3 ................................................................................................................................ 7-4

7.3

Materials........................................................................................................................................... 7-4

7.4

Member Requirements for SDC C and D......................................................................................... 7-5

7.5

7.6

7.7

7.4.1

Limiting Slenderness Ratios............................................................................................... 7-5

7.4.2

Limiting Width-Thickness Ratios ...................................................................................... 7-5

7.4.3

Flexural Ductility for Members with Combined Flexural and Axial Load. ....................... 7-6

7.4.4

Combined Axial and Bending ............................................................................................ 7-6

7.4.5

Weld Locations .................................................................................................................. 7-9

7.4.6

Ductile End-Diaphragm in Slab-on-Girder Bridge ............................................................ 7-9

Ductile Moment Resisting Frames and Single Column Structures for SDC C and D.................... 7-107.5.1

Columns ........................................................................................................................... 7-10

7.5.2

Beams............................................................................................................................... 7-11

7.5.3

Panel Zones and Connections .......................................................................................... 7-13

7.5.4

Multi-Tier Frame Bents.................................................................................................... 7-13

Concrete Filled Steel Pipes for SDC C and D ................................................................................ 7-137.6.1

Combined Axial Compression and Flexure .................................................................... 7-14

7.6.2

Flexural Strength.............................................................................................................. 7-14

7.6.3

Beams and Connections ................................................................................................... 7-15

Connections for SDC C and D ....................................................................................................... 7-157.7.1

Minimum Strength for Connections to Ductile Members ................................................ 7-15

7.7.2

Yielding of Gross Section for Connectors to Ductile Members...................................... 7-16

7.7.3

Welded Connections ........................................................................................................ 7-16

NCHRP 20-7(193) Task 12

iv

Section No.

Page No.

7.7.4

Gusset Plate Strength ....................................................................................................... 7-16

7.7.5

Limiting Unsupported Edge Length to Thickness Ratio for a Gusset Plate..................... 7-16

7.7.6

Gusset Plate Tension Strength.......................................................................................... 7-16

7.7.7

Compression Strength of a Gusset Plate .......................................................................... 7-17

7.7.8

In-Plate Moment (Strong Axis)........................................................................................ 7-17

7.7.9

In-Plate Shear Strength .................................................................................................... 7-17

7.7.10

Combined Moment, Shear and Axial Force ..................................................................... 7-18

7.7.11

Fastener Capacity ............................................................................................................. 7-18

7.8

Isolation Devices ............................................................................................................................ 7-19

7.9

Fixed and Expansion Bearings ....................................................................................................... 7-197.9.1

Applicability..................................................................................................................... 7-19

7.9.2

Design Criteria ................................................................................................................. 7-19

7.9.3

Design and Detail Requirements...................................................................................... 7-19

7.9.4

Bearing Anchorage........................................................................................................... 7-20

7.10 Structural Steel Design Requirements for Energy Disipation Components in SDC C and D...... 7-217.10.18.

General ............................................................................................................................. 7-21

REINFORCED CONCRETE COMPONENTS.......................................................................................... 8-18.1

General ............................................................................................................................................. 8-1

8.2

Seismic Design Category A.............................................................................................................. 8-1

8.3

Seismic Design Categories B, C, and D ........................................................................................... 8-1

8.4

8.3.1

General ............................................................................................................................... 8-1

8.3.2

Force Demands SDC B ...................................................................................................... 8-2

8.3.3

Force Demands SDC C & D .............................................................................................. 8-2

8.3.4

Local Ductility Demands SDC D....................................................................................... 8-2

Properties and Applications of Reinforcing Steel, Prestressing Steel and Concretefor SDC B, C, and D ........................................................................................................................ 8-28.4.1

Reinforcing Steel................................................................................................................ 8-2

8.4.2

Reinforcing Steel Modeling ............................................................................................... 8-4

8.4.3

Prestressing Steel ............................................................................................................... 8-5

8.4.4

Concrete ............................................................................................................................. 8-6

8.5

Plastic Moment Capacity for Ductile Concrete Members SDC B, C, and D ................................... 8-7

8.6

Shear Demand and Capacity for Ductile Concrete Members SDC B, C and D ............................... 8-88.6.1

Shear Demand and Capacity .............................................................................................. 8-9

8.6.2

Concrete Shear Capacity SDC B, C and D ........................................................................ 8-9

8.6.3

Shear Reinforcement Capacity......................................................................................... 8-10

8.6.4

Shear Reinforcement Capacity of Interlocking Spirals .................................................... 8-11

8.6.5

Maximum Shear Reinforcement....................................................................................... 8-11

8.6.6

Minimum Shear Reinforcement ....................................................................................... 8-11

NCHRP 20-7(193) Task 12

v

Section No.

8.7

8.8

8.9

Page No.

8.6.7

Pier Wall Shear Capacity in the Weak Direction ............................................................. 8-12

8.6.8

Minimum Vertical Reinforcement in Interlocking Portion .............................................. 8-12

8.6.9

Pier Wall Shear Capacity in the Strong Direction............................................................ 8-12

8.6.10

Pier Wall Minimum Reinforcement ................................................................................. 8-13

Requirements for Ductile Members Design ................................................................................... 8-138.7.1

Minimum Lateral Strength ............................................................................................... 8-13

8.7.2

Maximum Axial Load In A Ductile Member................................................................... 8-13

Longitudinal and Lateral Reinforcement Requirements................................................................. 8-148.8.1

Maximum Longitudinal Reinforcement .......................................................................... 8-14

8.8.2

Minimum Longitudinal Reinforcement........................................................................... 8-14

8.8.3

Splicing of Longitudinal Reinforcement in Columns Subject to Ductility Demandsfor SDC C or D ................................................................................................................ 8-14

8.8.4

Minimum Development Length of Reinforcing Steel for SDC C or D............................ 8-14

8.8.5

Anchorage of Bundled Bars in Ductile Components for SDC C or D............................ 8-15

8.8.6

Maximum Bar Diameter for SDC C, or D ....................................................................... 8-15

8.8.7

Lateral Reinforcement Inside The Plastic Hinge Region for SDC D............................... 8-15

8.8.8

Lateral Column Reinforcement Outside The Plastic Hinge Region for SDC C or D ..... 8-15

8.8.9

Maximum Spacing for Lateral Reinforcement for SDC C or D....................................... 8-16

8.8.10

Development Length for Column Bars Extended into Shafts for SDC C or D................ 8-16

8.8.11

Lateral Reinforcement Requirements For Columns Supported On Oversized Pile Shafts forSDC C or D ...................................................................................................................... 8-16

8.8.12

Lateral Confinement For Oversized Pile Shafts for SDC C or D..................................... 8-16

8.8.13

Lateral Confinement for Non Oversized Strengthened Pile Shafts for SDC C or D........ 8-17

Requriements for Capacity Protected Members ............................................................................. 8-17

8.10 Superstructure Capacity Design for Longitudinal Direction SDC C & D...................................... 8-188.11 Superstructure Capacity Deisgn for Transverse Direction (Integral Bent Cap) SDC C & D........ 8-198.12 Superstructure Design for Nonintegral Bent Cap SDC C and D.................................................... 8-208.13 Superstructure Joint Design SDC C or D ....................................................................................... 8-218.13.1

Joint Performance............................................................................................................. 8-21

8.13.2

Joint Proportioning........................................................................................................... 8-21

8.13.3

Joint Description .............................................................................................................. 8-21

8.13.4

T Joint Shear Design ........................................................................................................ 8-21

8.14 Column Flares SDC C & D ............................................................................................................ 8-298.14.1

Horizontally Isolated Flares ............................................................................................. 8-29

8.14.2

Integral Column Flares..................................................................................................... 8-29

8.14.3

Flare Reinforcement......................................................................................................... 8-29

8.15 Column Shear Key Design SDC C & D......................................................................................... 8-308.16 Concrete Piles................................................................................................................................. 8-30

NCHRP 20-7(193) Task 12

vi

Section No.

Page No.

8.16.1

Transverse Reinforcement Requirements........................................................................ 8-30

8.16.2

Cast-in-Place and Precast Concrete Piles ......................................................................... 8-30

APPENDICESAppendix A

Acceleration Time Histories ..................................................................................................A-1

Appendix B

Provisions for Site Characterization ......................................................................................B-1

Appendix C

Guideline for Modeling of Footings ......................................................................................C-1

Appendix D

Provisions for Collateral Seismic Hazards.............................................................................D-1

Appendix E

Liquefaction Effects and Associated Hazards ....................................................................... E-1

Appendix F

Load and Resistance Factor Design for Single-Angle Members ........................................... F-1

NCHRP 20-7(193) Task 12

vii

List of FiguresFigure No.

Page No.

FIGURE 1.3A

Design Procedure Flow Chart A.............................................................................................. 1-8

FIGURE 1.3B

Design Procedure Flow Chart B.............................................................................................. 1-9

FIGURE 1.3C

Design Procedure Flow Chart C............................................................................................ 1-10

FIGURE 1.3D

Design Procedure Flow Chart D............................................................................................ 1-11

FIGURE 1.3E

Design Procedure Flow Chart E ............................................................................................ 1-12

FIGURE 1.3F

Design Procedure Flow Chart F ............................................................................................ 1-13

FIGURE 1.3G

Design Procedure Flow Chart G............................................................................................ 1-14

FIGURE 3.3.1a

Permissible Earthquake Resisting System (ERS) .................................................................... 3-5

FIGURE 3.3.1b

Permissible Earthquake Resisting Elements (ERE)................................................................. 3-6

FIGURE 3.3.2

Permissible Earthquake Resisting Elements that Require Owners Approval ........................ 3-7

FIGURE 3.3.3

Earthquake Resisting Elements that are not Permitted for New Bridges ................................ 3-8

FIGURE 3.4.1-1

Design Response Spectrum, Construction Using Two-Point Method................................... 3-10

FIGURE 3.4.1-2

Horizontal Spectral Response Acceleration for the Conterminous United Statesof 0.2-Second Period (5 Percent of Critical Damping) with 5 Percent Probabilityof Exceedance in 50 Years .................................................................................................... 3-27

FIGURE 3.4.1-3

Horizontal Spectral Response Acceleration for the Conterminous United Statesof 1.0-Second Period (5 Percent of Critical Damping) with 5 Percent Probabilityof Exceedance in 50 Years .................................................................................................... 3-28

FIGURE 3.4.1-4

Horizontal Spectral Response Acceleration for Region 1 of 0.2-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-29

FIGURE 3.4.1-5

Horizontal Spectral Response Acceleration for Region 1 of 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-30

FIGURE 3.4.1-6

Horizontal Spectral Response Acceleration for Region 2 of 0.2-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-31

FIGURE 3.4.1-7

Horizontal Spectral Response Acceleration for Region 2 of 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-32

FIGURE 3.4.1-8

Horizontal Spectral Response Acceleration for Region 3 of 0.2-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-33

FIGURE 3.4.1-9

Horizontal Spectral Response Acceleration for Region 3 of 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-34

FIGURE 3.4.1-10

Horizontal Spectral Response Acceleration for Region 4 of 0.2-And 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-35

FIGURE 3.4.1-11

Horizontal Spectral Response Acceleration for Hawaii of 0.2-And 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-36

FIGURE 3.4.1-12

Horizontal Spectral Response Acceleration for Alaska of 0.2-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-37

FIGURE 3.4.1-13

Horizontal Spectral Response Acceleration for Alaska of 1.0-Second Period(5 Percent of Critical Damping) with 5 Percent Probability of Exceedance in 50 Years ...... 3-38

NCHRP 20-7(193) Task 12

vii

Figure No.

Page No.

FIGURE 3.4.1-14

Horizontal Spectral Response Acceleration for Puerto Rico, Culebra, Vieques, St. Thomas,St. John, and ST. Croix of 0.2-And 1.0-Second Period (5 Percent of Critical Damping)with 5 Percent Probability of Exceedance in 50 Years.......................................................... 3-39

FIGURE 3.5.1

Seismic Design Category (SDC) Core Flowchart ................................................................. 3-23

FIGURE 4.1

Balanced Stiffness ................................................................................................................... 4-4

FIGURE 4.2

Capacity Design of Bridges Using Overstrength Concepts................................................... 4-18

FIGURE 4.3

Dimension for Minimum Support Length Requirements ...................................................... 4-25

FIGURE 5.1

Elastic Dynamic Analysis Modeling Techniques .................................................................... 5-3

FIGURE 5.2

Design Passive Pressure Zone ................................................................................................ 5-6

FIGURE 5.3

Characterization of Abutment Capacity and Stiffness............................................................. 5-7

FIGURE 5.4

Effective Flexural Stiffness of Cracked Reinforced Concrete Sections [x] .......................... 5-21

FIGURE 6.1

Rocking Equilibrium of a Single Column Bent....................................................................... 6-6

FIGURE 6.2

Flowchart for Design of a New Column on Spread Footing ................................................... 6-7

FIGURE 6.3

Simplified Pile Model for Foundations in Competent Soil ................................................... 6-11

FIGURE 6.4

Effective Joint Width for Footing Joint Stress Calculation ................................................... 6-15

FIGURE 7.1

Seismic Load Path and Affected Components ........................................................................ 7-2

FIGURE 8.1

Steel Stress-Strain Model ........................................................................................................ 8-5

FIGURE 8.2

Prestressing Strand Stress-Strain Model.................................................................................. 8-6

FIGURE 8.3

Concrete Stress-Strain Model .................................................................................................. 8-7

FIGURE 8.4

Moment-Curvature Model ....................................................................................................... 8-8

FIGURE 8.5

Effective Superstructure Width ............................................................................................. 8-19

FIGURE 8.6

Effective Bent Cap Width...................................................................................................... 8-20

FIGURE 8.7

Joint Shear Stresses in T Joints.............................................................................................. 8-24

FIGURE 8.8

Location of Vertical Joint Reinforcement ............................................................................. 8-27

FIGURE 8.9

Joint Shear Reinforcement Details ........................................................................................ 8-27

FIGURE 8.10

Location of Horizontal Joint Shear Steel............................................................................... 8-28

FIGURE 8.11

Additional Joint Shear Steel For Skewed Bridges................................................................. 8-28

NCHRP 20-7(193) Task 12

viii

List of TablesTable No.

Page No.

Table 3.4.2-1:

Site Classification......................................................................................................3-12

Table 3.4.2.3-1:

Values of Fa as a Function of Site Class and Mapped Short-Period SpectralAcceleration ..............................................................................................................3-18

Table 3.4.2.3-2:

Values of Fv as a Function of Site Class and Mapped 1 Second Period SpectralAcceleration ..............................................................................................................3-18

Table 3.5.1:

Partitions for Seismic Design Categories A, B, C and D ..........................................3-21

Table 4.1

Analysis Procedures ...................................................................................................4-5

Table 4.2

Regular Bridge Requirements.....................................................................................4-6

Table 4.3

Values of Characteristic Ground Motion Period, T* ....................................................4-9

Table 5.1

Definition of Foundation Modeling Method ...............................................................5-12

Table 7.1

Limiting Slenderness Parameters ...............................................................................7-7

Table 7.2

Limiting Width-Thickness Ratios.................................................................................7-8

Table 7.3

Limiting Width-to-Thickness Ratios...........................................................................7-12

Table 8.1

Reinforcement Size for Interlocking Portion of Columns ..........................................8-12

NCHRP 20-7(193) Task 12

ix

PrefaceThe seismic design specifications included in the current AASHTO LRFD Bridge Design Specifications, ThirdEdition (2004) with 2006 Interim Revisions and the AASHTO Standard Specifications for Highway Bridges, Division I-A, 17th Edition (2002) with Errata March 2005 are essentially the recommendations that were completed bythe Applied Technology (ATC-6) in 1981 and adopted by AASHTO as a Guide Specification in 1983. In 1990AASHTO adopted the Guide Specification (i.e., ATC-6/Division I-A) as part of the AASHTO Standard Specification for Highway Bridges. Some minor revisions were made for their inclusion into the AASHTO LRFD BridgeDesign Specifications. There have been some significant changes that have occurred in seismic design since theadoption of ATC-6. Recognizing the availability of improvements as documented in NCHRP 12-49, Caltrans Seismic Design Criteria (SDC) 2004, SCDOT Seismic Design Specifications for Highway Bridges, 2002 and relatedresearch projects, the T-3 AASHTO committee for seismic design has, with the financial support of NCHRP, initiated this project to update the Recommended LRFD Guidelines for the Seismic Design of Highway Bridges May2006.

NCHRP 20-7(193) Task 12

x

1. INTRODUCTION

1.1 BACKGROUND

C1.1

The AASHTO LRFD Guidelines for SeismicDesign of Highway Bridges is established inaccordance with NCHRP 20-07/Task 193 Task 6Report. Task 6 contains five (5) Sections as follows:

This commentary is included to provide additional information to clarify and explain the technicalbasis for the specifications provided in the LRFDGuidelines for Seismic Design of Highway Bridges.These guidelines are for the design of new bridges.It is envisioned that the commentary will be expanded and completed at the completion of the TestDesigns being completed by the states that have volunteered to use the new guidelines on the trialdesigns.

SECTION 1 includes a review of the pertinentdocuments and information that were available.SECTION 2 presents the justification for the975-year return period (i.e., 5% probability of exceedance in 50 years as recommended for the seismicdesign of highway bridges.SECTION 3 includes a description of how theno analysis zone is expanded and how this expansion is incorporated into the displacement basedapproach.SECTION 4 describes the two alternative approaches available for the design of highway bridgeswith steel superstructures and concludes with a recommendation to use a force based approach for steelgirder superstructures.SECTION 5 describes the recommended procedure for liquefaction design to be used for highwaybridges. This aspect of the design is influenced bythe recommended hazard level and the no analysiszone covered in Tasks 2 and 3, respectively. Therecommendations proposed are made taking into account the outcome of these two tasks for SeismicDesign Category D.The following recommendations are documented.Task 21.

Adopt the 5% in 50 years hazard levelfor development of a design spectrum.

2.

Ensure sufficient conservatism (1.5safety factor) for minimum seat widthrequirement.This conservatism isneeded to enable to use the reserve capacity of hinging mechanism of thebridge system. This conservatism shallbe embedded in the specifications toaddress unseating vulnerability. At aminimum it is recommended to embedthis safety factor for sites outside ofCalifornia.

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Scope of Commentary

The term shall denotes a requirement for compliance with these Guidelines.The term should indicates a strong preferencefor a given criterion.The term may indicates a criterion that is usable, but other local and suitably documented,verified, and approved criterion may also be used in amanner consistent with the LRFD approach to bridgedesign.The term recommended is used to give guidance based on past experiences. Seismic design is adeveloping field of engineering, which has not beenuniformly applied to all bridge types and thus theexperiences gained to date on only a particular typeare included as recommendations.

3.

Partition Seismic Design Categories(SDCs) into four categories and proceed with the development of analyticalbounds using the 5% in 50 years Hazard level.

Task 3Establish four Seismic Design Categories withthe following requirements.1.

2.

3.

4.

SDC Aa.

No Displacement Capacity CheckNeeded

b.

No Capacity Design Required

c.

SDC A, Minimum Requirements

SDC Ba.

Implicit Displacement CapacityCheck Required (i.e., use a ClosedForm Solution Formula)

b.

No Capacity Design Required

c.

SDC B, Level of Detailing

SDC Ca.

Implicit DisplacementCheck Required

b.

Capacity Design Required

c.

SDC C, Level of Detailing

Capacity

SDC Da.

Pushover Analysis Required

b.

Capacity Design Required

c.

SDC D, Level of Detailing

Task 4Recommend the following for SDC C & D.1.

Adopt AISC LRFD Specifications fordesign of single angle members andmembers with stitch welds.

2.

Allow for three types of a bridge structural system as adopted in SCDOTSpecifications.Type 1 Design a ductile substructurewith an essentially elastic superstructure.Type 2 Design an essentially elasticsubstructure with a ductile superstructure.

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Type 3 Design an elastic superstructure and substructure with a fusingmechanism at the interface between thesuperstructure and the substructure.3.

Adopt a force reduction factor of 3 fordesign of normal end cross-frame.

4.

Adopt NCHRP 12-49 for design ofDuctile End-Diaphragm where aforce reduction factor greater than 3 isdesired.

Task 5The following list highlights the main proposedliquefaction design requirements:1.

Liquefaction design requirements areapplicable to SDC D.

2.

Liquefaction design requirements aredependent on the mean magnitude forthe 5% PE in 50-year event and thenormalized Standard Penetration Test(SPT) blow count [(N1)60].

3.

If liquefaction occurs, then the bridgeshall be designed and analyzed for theLiquefied and Non-Liquefied configurations.

Design requirements for lateral flow are still debatable and have not reached a stage of completionfor inclusion in the Guidelines. Recommendationsfor foundation type are deemed appropriate at thisstage to mitigate lateral flow hazard.

1.2

PROJECT ORGANIZATION

This NCHRP Project was organized to assist theAASHTO T-3 Subcommittee for Seismic Design ofBridges to complete another step towards producingan LRFD Seismic Design Specification for inclusioninto the AASHTO Specifications. The T-3 Subcommittee defined very specific tasks as described inArticle 1.1 above that they envisioned were needed tosupplement the existing completed efforts (i.e.,AASHTO Division I-A, NCHRP 12-49 Guidelines,SCDOT Specifications, Caltrans Seismic DesignCriteria, NYDOT Seismic Intensity Maps and ATC32) to yield an implementable specification forAASHTO. The tasks have now been completed byTRC/Imbsen & Associates, Inc. under the directionof the T-3 Subcommittee and the assistance of theirBoard of Reviewers to yield a stand-alone Guidelinethat can be evaluated by AASHTO and consideredfor adopting in 2007. This project was completed byImbsen Consulting under a subcontract withTRC/Imbsen & Associates, Inc.

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1-3

1.2.1 Project Direction from AASHTO T-3The T-3 Working Group that defined the projectobjectives and directed the project include:

Rick Land, CA (Past chair)

Harry Capers, NJ (Current Co-chair)

Richard Pratt, AK (Current chair)

Ralph Anderson, IL

Jerry Weigel, WA

Ed Wasserman, TN

Paul Liles, GA

Kevin Thompson, CA

The project team members and reviewers thatparticipated in the NCHRP 20-07/193 include:

Roger Borcherdt, USGS

Po Lam, Earth Mechanics, Inc.

Ed V. Leyendecker, USGS

Lee Marsh, Berger/Abam

Randy Cannon, Site Blauvelt

George Lee, MCEER, Chair

Geoff Martin, MCEER

Joe Penzien, HSRC, EQ V-team

John Kulicki, HSRC

Les Youd, BYU

Joe Wang, Parsons, EQ V-team

Lucero Mesa, SCDOT V-team

Derrell Manceaux, FHWA

Peter W. Osborn, FHWA

Alexander K. Bardow, Mass. Highway

Stephanie Brandenberger, Montana DOT

Bruce Johnson, Oregon DOT

Michael Keever, Calif. DOT

Jerry OConnor, MCEER

Roland Nimis, FHWA

W. Phil Yen, FHWA

Firas Ibrhim, FHWA

Shyam Gupta, MODOT

Elmer E. Marx, Alaska DOT & PF

NCHRP 20-7(193) Task 12

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William Crawford, Nevada DOT

Jugesh Kapur, Washington State DOT

John Jordan, Indiana DOT

1.2.2 Technical Assistance Agreement BetweenAASHTO and USGSUnder the agreement the USGS prepared twotypes of products for use by AASHTO. The firstproduct was a set of paper maps of selected seismicdesign parameters for a 5% probability of exceedancein 50 years. The second product was a ground motion software tool to simplify determination of theseismic design parameters.These guidelines use spectral response acceleration with a 5% probability of exceedance in 50 yearsas the basis of the seismic design requirements. Aspart of the National Earthquake Hazards ReductionProgram, the U.S. Geological Surveys NationalSeismic Hazards Mapping Project prepares seismichazard maps of different ground motion parameterswith different probabilities of exceedance. Howevermaps were not prepared for the probability level required for use by these guidelines. These maps wereprepared by the U.S. Geological Survey under aseparate Technical Assistance Agreement with theAmerican Association of State Highway and Transportation Officials (AASHTO), Inc. for use byAASHTO and in particular the Highway Subcommittee on Bridges and Structures.MapsThe set of paper maps covered the fifty states ofthe U.S. and Puerto Rico. Some regional maps werealso included in order to improve resolution of contours. Maps of the conterminous 48 states werebased on USGS data used to prepare maps for a 2002update. Alaska was based USGS data used to prepare a map for a 2006 update. Hawaii was basedUSGS data used to prepare 1998 maps. Puerto Ricowas based on USGS data used to prepare 2003 maps.The maps included in the map package were prepared in consultation with the Subcommittee onBridges and Structures. The package included a series of maps prepared for a short period (0.2 sec)value of spectral acceleration, SS, and a longer period(1.0 sec) value of spectral acceleration S1. The mapswere for spectral accelerations for a reference SiteClass B.

NCHRP 20-7(193) Task 12

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Ground Motion ToolThe ground motion software tool was packagedon a CD-ROM for installation on a PC using a Windows-based operating system. It includes featuresallowing the user to calculate Peak Ground Acceleration, (PGA) and the mapped spectral responseaccelerations as described below:

PGA, SS, and S1 - Determination of the parameters PGA, SS, and S1 by latitudelongitude or zip code from the USGS gridded data. The peak ground acceleration,PGA,

Design values of PGA, SS, and S1 Modification of PGA, SS, and S1 by the site factorsto obtain design values. These are calculated using the mapped parameters and thesite coefficients for a specified site class.

In addition to calculation of the basic parameters, the CD allows the user to obtain the followingadditional information for a specified site:

1.3

Calculation of a response spectrum Theuser can calculate response spectra for spectral response accelerations and spectraldisplacements using design values of PGA,SS, and S1. In addition to the numerical datathe tools include graphic displays of thedata. Both graphics and data can be savedto files.

Maps - The CD also include the 5% in 50year maps in PDF format. A map viewer isincluded that allows the user to click on amap name from a list and display the map.

FLOW CHARTS

It is envisioned that the flow charts will providethe engineer with a simple reference to direct thedesign process needed for each of the four SeismicDesign Categories (SDC).Flow charts outlining the steps in the seismic design procedures implicit in these specifications aregiven in Figures 1.3A to 1.3G.The flow chart in Figure 1.3A guides the designer on the applicability of the specifications andthe breadth of the design procedure dealing with asingle span bridge versus a multi-span bridge and abridge in Seismic Design Category A versus a bridgein Seismic Design Category B, C, or D.

NCHRP 20-7(193) Task 12

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Figure 1.3B shows the core flow chart of procedures outlined for bridges in SDC B, C, and D.Figure 1.3D directs the designer to determine displacement capacity for SDC B or C using implicitprocedures defined in Article 4.8. Since the displacement approach is the main thrust of this criteria,the flow chart in Figure 1.3C directs the designer toFigure 1.3E in order to establish the displacementdemands on the subject bridge and Figure 1.3F and1.3G in order to establish member requirements forSDC C or D based on the type of the structure chosenfor seismic resistance.

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PRELIMINARY DESIGN BRIDGETYPE SELECTION AND DESIGNFOR SERVICE LOADS

APPLICABILITY OFSPECIFICATIONSSECTION 3.1

YESTEMPORARYBRIDGE

SECTION 3.6

NO

PERFORMANCE CRITERIASECTION 3.2

EARTHQUAKE RESISTING SYSTEMS (ERS)REQUIREMENTS FOR SDC C & DSECTION 3.3

DETERMINE DESIGN RESPONSE SPECTRUMSECTION 3.4

DETERMINE SEISMIC DESIGN CATEGORY (SDC)SECTION 3.5

YESSDC A

DETERMINE DESIGN FORCES

NO

SECTION 4.6

YESSINGLE SPANBRIDGE

DETERMINE SEAT WIDTH

DETERMINE DESIGN FORCES

SECTION 4.8.1

NOSEISMIC DESIGN CATEGORY B, C, DFOUNDATION DESIGN

See Figure 1.3B

SECTION 6.2

DESIGN COMPLETE

DETERMINE MINIMUMSEAT WIDTHSECTION 4.8

SEISMIC DESIGNCATEGORY B, C, AND DSee Figure 1.3C

FIGURE 1.3A: Design Procedure Flow Chart A

NCHRP 20-7(193) Task 12

SECTION 4.5

1-8

DESIGN COMPLETE

NoSDC C

Yes

SDC D

Yes

Yes

DEMAND ANALYSIS

DEMAND ANALYSIS

DEMAND ANALYSIS

IMPLICITCAPACITY

IMPLICITCAPACITY

PUSHOVER CAPACITYANALYSIS

DEPENDS ON ADJUSTMENTS

NoSDC B

ADJUST BRIDGECHARACTERISTICS

D

C

1

No

Yes

D

C

No

1Yes

D

C

1

No

Yes

SDC B DETAILING

CAPACITY DESIGN

CAPACITY DESIGN

COMPLETE

SDC C DETAILING

SDC D DETAILING

COMPLETE

COMPLETE

FIGURE 1.3B: Design Procedure Flow Chart B

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SDC B, C, D

SEISMIC DESIGN PROPORTIONINGAND ARTICULATIONRECOMMENDATIONSSECTION 4.1

DETERMINE ANALYSIS PROCEDURESECTION 4.2

YESSDC D

NO

CONSIDER VERTICALGROUND MOTION EFFECTSSECTION 4.7.2

SELECT HORIZONTAL AXESFOR GROUND MOTIONSSECTION 4.3.1

DAMPING CONSIDERATION,SECTION 4.3.2

SHORT PERIOD STRUCTURESCONSIDERATIONSECTION 4.3.3

DETERMINE SEISMIC DISPLACEMENTDEMANDS(See Figure1.3E)

COMBINE ORTHOGONAL DISPLACEMENTS(i.e., LOADS CASES 1 & 2)SECTION 4.4

SDC B OR C DETERMINE C

YESSDC B or C

(See Figure 1.3D)

NOSDC D, DETERMINE C - PUSHOVERSECTION 4.8

GLOBAL STRUCTUREDISPLACEMENT REQUIREMENTC > DSECTION 4.3

P CAPACITY REQUIREMENTSECTION 4.11.5

MEMBER/COMPONENTPERFORMANCE REQUIREMENTSee Figures 1.3F & 1.3G

FIGURE 1.3C: Design Procedure Flow Chart C

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1-10

SDC B or CDETERMINE CSECTION 4.8

C > DYES

NO

RETURN TO SDC DDETERMINE C - PUSHOVERSee Figure 1.3C

SDC CNOYES

CAPACITYvs. P SECTION 4.11.5

NO

YESSATISFY SUPPORT REQUIREMENTSSEAT WIDTHSECTION 4.12

SHEAR KEYSECTION 4.14

FOUNDATION INVESTIGATIONSECTION 6.2

SPREAD FOOTING DESIGNSECTION 6.3

PILE CAP FOUNDATION DESIGNSECTION 6.4

DRILLED SHAFTSECTION 6.5

ABUTMENT DESIGNSECTION 6.7

DESIGN COMPLETE

FIGURE 1.3D: Design Procedure Flow Chart D

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DETERMINE SEISMIC DISPLACEMENTDEMANDS FOR SDC B, C, D

NOSDC C or D

YESDEFINE BRIDGE ERSSECTION 5.1.1SECTION 3.3

SELECT ANALYSIS PROCEDURE 1SECTION 5.4.2

SELECT ANALYSIS PROCEDURE 2SECTION 5.4.3

SELECT ANALYSIS PROCEDURE 3SECTION 5.4.4

SATISFY MODELING REQUIREMENTSSECTION 5.1

SATISFY MATHEMATICAL MODELINGREQUIREMENTS FOR PROCEDURE 2SECTION 5.5

ABUTMENT MODELINGSECTION 5.2

FOUNDATION MODELINGSECTION 5.3

EFFECTIVE SECTION PROPERTIESSECTION 5.6

CONDUCT DEMAND ANALYSISSECTION 5.1.2

DETERMINE DISPLACEMENTDEMANDS ALONGMEMBER LOCAL AXIS

RETURN TO

COMBINE OTHOGONALDISPLACEMENTSSee Figure 1.3C

FIGURE 1.3E: Design Procedure Flow Chart E

NCHRP 20-7(193) Task 12

1-12

Note:1) Type 1 considers concrete substructure2) Type 1* considers steel substructureTYPE 1

TYPE 1*DUCTILE MOMENT RESISTINGFRAMES AND SINGLE COLUMNSTRUCTURES FOR SDC C AND D

yy

3) Type 1** considers concrete filled steel pipessubstructure

TYPE 1DUCTILE SUBSTRUCTUREESSENTIALLY ELASTICSUPERSTRUCTURE

TYPE 1**CONCRETE FILLED STEEL PIPESFOR SDC C AND D

COLUMN REQUIREMNTSFOR SDC C AND D

SATISFY MEMBER DUCTILITYREQUIREMENTS FOR SDC D

COMBINED AXIAL COMPRESSIONAND FLEXURE

SECTION 7.5.1

SECTION 4.9

SECTION 7.6.1

BEAM REQUIREMNTSFOR SDC C AND D

DETERMINE FLEXURE ANDSHEAR DEMANDS

FLEXURAL STRENGTH

SECTION 8.3

SECTION 7.6.2

PANEL ZONES AND CONNECTIONSFOR SDC C AND D

SATISFY REQUIREMENTS FORCAPACITY PROTECTED MEMBERSFOR SDC C AND D

BEAMS AND CONNECTIONS

SECTION 7.5.3

SECTION 8.9

SECTION 7.5.2

SATISFY REQUIREMENTS FORDUCTILE MEMBERS DESIGNFOR SDC C AND DSECTION 8.7

SATISFY LONGITUDINAL ANDLATERAL REINFORCEMENTREQUIREMENTSSECTION 8.8

SUPERSTRUCTURE DESIGN FORLONGITUDINAL DIRECTIONFOR SDC C AND DSECTION 8.10

SUPERSTRUCTURE DESIGN FORTRANSVERSE DIRECTIONINTEGRAL BENT CAPSFOR SDC C AND DSECTION 8.11

NON-INTEGRAL BENT CAPFOR SDC C AND DSECTION 8.12

SUPERSTRUCTURE JOINT DESIGNFOR SDC C AND DSECTION 8.13

COLUMN FLARES FOR SDC C AND DSECTION 8.14

COLUMN SHEAR KEY DESIGNFOR SDC C AND DSECTION 8.15

CONCRETE PILESFOR SDC C AND DSECTION 8.16

SATISFY SUPPORT SEAT WIDTHREQUIREMENTSSee Figure 1.3D

FIGURE 1.3F: Design Procedure Flow Chart F

NCHRP 20-7(193) Task 12

1-13

SECTION 7.6.3

TYPE 2 & 3TYPE 3

TYPE 2

y

ESSENTIALLY ELASTICSUBSTRUCTURE

y

DUCTILE STEELSUPERSTRUCTURE

yyy

ELASTIC SUPERSTRUCTUREELASTIC SUBSTRUCTUREFUSING MECHANISM ATINTERFACE BETWEENSUPERSTRUCTURE ANDSUBSTRUCTURESECTION 7.2

USE REDUCTION FACTORSTABLE 7.2

ISOLATION DEVICESSATISFY MEMBER REQUIREMENTSFOR SDC C AND D

SECTION 7.8

SECTION 7.4

FIXED AND EXPANSION BEARINGSSECTION 7.9

SATISFY CONNECTIONREQUIREMENTS FOR SDC C AND DSECTION 7.7

SATISFY BEARING REQUIREMENTSSECTION 7.9

SATISFY SUPPORT SEAT WIDTHREQUIREMENTSSee Figure 1.3D

Note: Type 2 and Type 3 considers concrete orsteel substructure

FIGURE 1.3G: Design Procedure Flow Chart G

1.4

REFERENCES

AASHTO (2004), LRFD Bridge Design Specifications, Third Edition, with 2006 Interim Revisions,American Association of State Highway and Transportation Officials, Washington, DC.AASHTO, Standard Specifications for HighwayBridges, 17th Edition, with Errata thru March 2005,American Association of State Highway and Transportation Officials, 1996, with current interimsthrough 2000.

NCHRP 20-7(193) Task 12

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AASHTO/AWS D1.5M/D1.5 Bridge WeldingCode, 2002.ACI (1995), Building Requirements for Structural Concrete (ACI 318-95) and Commentary (ACI318R-95), American Concrete Institute, FarmingtonHills, MI.AISC (1992), Seismic Provisions for StructuralSteel Buildings, American Institute of Steel Construction, Chicago, IL.AISC (1993), Load and Factor Design Specification for Structural Steel Buildings, 2nd Ed.,American Institute of Steel Construction, Chicago,IL.AISC (1994), Load and Factor Design Manualof Steel Construction, 2nd Ed., American Institute ofSteel Construction, Chicago, IL.AISC (1997), Seismic Provisions for StructuralSteel Buildings, American Institute of Steel Construction, Chicago, IL.ATC-32, Improved Seismic Design Criteria forCalifornia Bridges: Provisional Recommendations,Applied Technology Council (ATC), 1996Building Seismic Safety Council, 1997, NEHRPRecommended Provisions for Seismic Regulations forNew Buildings and Other Structures, Report FEMA302, Washington D.C.Caltrans (2004), Seismic Design Criteria Version1.4. California Department of Transportation, Sacramento, CA, July 2004.Caltrans (2001), Guide Specifications for Seismic Design of Steel Bridges. California Departmentof Transportation, First Edition, December 2001.Frankel, A., Mueller, C., Barnhard, T., Perkins,D., Leyendecker, E. V., Dickman, N., Hanson, S.,and Hopper, M., 1996, Interim National SeismicHazard Maps: Documentation, U.S. Geological Survey, January, 1996.NCHRP 12-49, Comprehensive Specification forSeismic Design of Bridges, ATC/MCEER, 1998Preistly, M.J.N., Seible, F., and G.M. Calvi,Seismic Design and Retrofit of Bridges, John Wileyand Sons, 1996.South Carolina Department of Transportation,Seismic Design Specifications for Highway Bridges,First Edition 2001, with October 2002 Interim Revisions.

NCHRP 20-7(193) Task 12

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2. SYMBOLS AND DEFINITIONS

2.1

NOTATIONSThe following symbols and definitions apply to these Standards:

A

= Cross-section area of a steel member

Ac

= Area of reinforced concrete column core (in2)

botAcap= Area of bottom reinforcement in the bent cap (in2)topAcap= Area of top reinforcement in the bent cap (in2)

Ae

= Effective shear area (in2)

Aew = Cross-sectional area of pier wallAg

= Gross area of reinforced concrete column (in2)

Agg = Gross area of gusset plate (in2)A jh = The effective horizontal area of a moment resisting joint (in2)A jhftg = The effective horizontal area at mid-depth of the footing, assuming a 45 degree spread away from theboundary of the column in all directions (in2)

An

= Net area of a gusset plate (in2)

Asjv = Area of vertical stirrups required for joint reinforcement (in2)Asjh = Area of horizontal stirrups required for joint reinforcement (in2)

Asj bar = Area of J-dowels reinforcement required for joint reinforcement (in2)Assf = Area of longitudinal side face reinforcement in the bent cap (in2)

Asp = Cross-Sectional area of a hoop or spiral bar (in2)Ast

= Total area of column reinforcement anchored in the joint (in2)

Atg

= Gross area along the plane resisting tension in a gusset plate (in2)

Atn

= Net area along the plane resisting tension in a gusset plate (in2)

NCHRP 20-7(193) Task 12

2-1

Av

= Cross-Sectional area of web reinforcement

Avg = Gross area along the plane resisting shear in a gusset plate (in2)Avn = Net area along the plane resisting shear in a gusset plate (in2)Bc

= Width of a rectangular column (in)

Bcap = Width of a bent cap (in)Beff = Effective width of a bent cap (in)

Beffftg = Effective width of a footing (in)Bo

= Column width or diameter in the direction of bending (ft)

Br

= Footing width orthogonal to direction of rocking

C(i ) pile = Compression force in pile (i) (kips)D

= Core diameter of a column (in)

D C = Displacement Demand to Capacity RatioD t = Diameter to thickness ratio of a tubular member

D*

= Diameter for circular shafts or the cross section dimension in direction being consideredfor oblong shafts (in)

Dc

= Column diameter or depth

Dcj = Column width or diameter parallel to direction of bending

Dc ,max = Largest cross-sectional dimension of the column (in)Deff = Effective yield displacement of soil behind the abutment backwallD ftg = Footing depth (in)Dg

= Abutment gap width

Ds

= Superstructure depth (in)

E

= Structural Steel Elastic Modulus

Ec

= Concrete Elastic Modulus

Ec I eff = Effective flexural rigidity (kips-in2)Es

= Steel elastic modulus (ksi)

F

= Applied force at the superstructure level for a rocking column/footing system

NCHRP 20-7(193) Task 12

2-2

Fa

= Site coefficient defined in Table 3.3.3A based on the site class and the values of the response accelerationparameter SS

Fu

= Specified minimum tensile strength of structural steel (ksi)

Fv

= Site coefficient defined in Table 3.3.3.B based on the site class and the values of the response acceleration

Fy

= Specified minimum yield strength of structural steel (ksi)

Fye = Expected yield strength of structural steel

G

= Soil shear modulus

(GA) eff = Shear stiffness parameterGc

= Concrete shear modulus

Gc J = Torsional rigidity

Gf

= Gap between the isolated flare and the soffit of the bent cap (in)

Gmax = Maximum soil shear modulus

H

= Thickness of soil layer (ft)

H h = Largest column height within the most flexible frame adjacent to the expansion joint, height from top offooting to top of the column (i.e., column clear height, ft.) or equivalent column height for pile extensioncolumn (ft.). For single spans seated on abutments, the term H is taken as the abutment height (ft.).

H o = Height from top of footing to top of the column (i.e., column clear height, ft.).Hr

= Height of column/footing system used for rocking analysis

H w = Wall height (ft)

H = Length of pile shaft/column from point of maximum moment to point of contraflexure above ground (in)I eff

= Effective flexural moment of inertia (in4)

Ig

= Gross flexural moment of inertia (in4)

I p. g . = Moment of inertia of the pile group defined by Equation 6-3J eff = Effective torsional moment of inertia (in4)Jg

= Gross torsional moment of inertia (in4)

K

= Effective length factor used in steel design and given in Article 7.4 (dimensionless)

Ki

= Effective stiffness of abutment soil backwall corresponding to iteration (i)

KL r = Slenderness ratio of a steel member (dimensionless)Kr

= Equivalent stiffness of a rocking system

NCHRP 20-7(193) Task 12

2-3

L

= The length of column from the point of maximum moments to the point of contra-flexure

Lc

= Column clear height used to determine shear demand

LF

= Length of base of footing in the direction of rocking

L ftg = The cantilever length of the pile cap measured from the face of the column to the edge of the footing (in)Lg

= Unsupported edge length of a gusset plate (in)

Lp

= Analytical plastic hinge length (in)

L pr = Plastic hinge region (in)

M

= Flexural moment of a member due to seismic and permanent loads (kip-in)

M g = Moment demand in a gusset plate (kip-in)M n = Nominal moment capacity of a memberM ne = Nominal moment capacity of a reinforced concrete member based on expected materials properties (kipin)

M ng = Nominal moment strength of a gusset plate (kip-in)M ns = Nominal flexural moment strength of a steel member (kip-in)M o = Column over strength moment.

M p = Idealized plastic moment capacity of a reinforced concrete member based on expected material properties(kip-in)

M po = Overstrength plastic moment capacity (kip-in)

M pg = Plastic moment of a gusset plate under pure bending (kip-in)M px = The column plastic moment under pure bending calculated using FyeM r = Restoring moment of a rocking column/footing system

M w = Mean Earthquake Moment MagnitudeM y = Moment capacity of the section at first yield of the reinforcing steelN

= Minimum support length (in)

N

= Average standard penetration resistance for the top 100 ft (blows/ft)+

N ch = Average standard penetration resistance of a cohesionless soil layer for the top 100 ft

Ni

= Standard Penetration Resistance not to exceed 100 blows/ft as directly measured in the field

N p = Total number of piles in the pile group

NCHRP 20-7(193) Task 12

2-4

P

= Axial load of a member due to seismic and permanent loads (kip)

Pac

= Axial force at top of the column including the effects of overturning (kips)

Pb

= Horizontal effective axial force at the center of the joint including prestressing

Pbs

= Tensile strength of a gusset plate based on block-shear (kip)

Pc

= The total axial load on the pile group including column axial load (dead load +EQ load), footing weight,and overburden soil weight

Pcol = Axial force including the effects of overturning at the base of the column (kip)Pdl

= Axial dead load at the bottom of the column (kip)

Pg

= Axial load in a gusset plate (kip)

PI

= Plasticity Index

Pn

= Nominal axial strength of a member (kip)

Png = Nominal compressive or tensile strength of a gusset platePp

= Passive force behind backwall

Pu

= Maximum strength of concentricity loaded steel columns (kips)

Py

= Yield axial strength of a member (kips)

Pyg = Yield axial strength in a gusset plate (kips)

R

= Force reduction factor is obtained by dividing the elastic spectral force by the plastic yield capacity

RD

= Reduction factor to account for increased damping

Rd

= Magnification factor to account for short period structure

Ry

= Overstrength factor of Structural Steel

S

= Site coefficient specified in Article 3.5.1 (dimensionless)

Sa

= The design spectral response acceleration

S1

= The mapped design spectral acceleration for the one second period as determined in Sections 3.4.2 and3.4.3 (for Site Class B: Rock Site)

S D1 = Design spectral response acceleration parameter at one second

S DS = Design short-period (0.2-second) spectral response acceleration parameterSk

= Angle of skew of support in degrees, measured from a line normal to the span

SS

= The mapped design spectral acceleration for the short period (0.2 second) as determined in Sections 3.4.2and 3.4.3 (for Site Class B: Rock Site)

NCHRP 20-7(193) Task 12

2-5

S sm = Elastic section modulus about strong axis for a gusset plate (in2)

T

= Fundamental period of the structure (second)

T1

= Fundamental period from frame 1 (second)

T2

= Fundamental period of frame 2 (second)

Tc

= Column tensile force obtained from a section analysis corresponding to the overstrength column momentcapacity (kips)

TF

= Fundamental Period of the subject bridge

Ti

= Fundamental period of the less flexible frame (second)

T(i ) pile = The tensile axial demand in a pile (kip)

Tj

= Fundamental period of the more flexible frame (second)

T jv

= Critical shear force in the column footing connection (kips)

To

= Structure period defining the design response spectrum as shown in Figure 3.4.1 (second)

TS

= Structure period defining the design response spectrum as shown in Figure 3.4.1 (second)

T*

= Characteristic Ground Motion Period (second)

Vc

= Concrete shear contribution (kip)

Vd

= Shear demand for a column

Vg

= Shear force in a gusset plate (kip)

Vn

= Nominal shear capacity (kip)

Vng = Nominal shear strength of a gusset plate (kip)Vnk

= Nominal shear capacity of a shear key

Vo

= Column shear demand corresponding to column overstrength capacity

Vok

= Overstrength shear capacity of a shear key

V pg = plastic shear capacity of gusset plate (0.58AggFy) (kips)

V po = Overstrength plastic shear demand (kip)Vs

= Transverse steel shear contribution (kip)

Vu

= Maximum shear demand in a column or a pier wall

WCOLUMN = Column weight of a rocking column/footing system

NCHRP 20-7(193) Task 12

2-6

WCOVER = Cover weight of a rocking column/footing systemWFOOTING = Footing weight of a rocking column/footing systemWT

= Total weight of a rocking column/footing system

Ws

= Superstructure weight of a rocking column/footing system

b

= Width of tied column

beff

= Effective joint width for footing joint stress calculation

b t = Width to thickness ratio for a stiffened or unstiffened element

c

= Damping ratio (maximum of 10%)

cx (i ) = Distance from column centerline to pile centerline along x-axis (in)

c y (i ) = Distance from column centerline to pile centerline along y-axis (in)d

= Pier wall depth (in)

d bl

= Longitudinal reinforcement bar diameter (in)

di

= Thickness of any layer between 0 and 100 ft depth (ft)

f c

= Specified compressive strength of concrete (psi or MPa)

f cc

= Compressive strength of confined concrete

f ce

= Expected compressive strength of concrete

fh

= Horizontal effective compressive stress in a joint (ksi)

f ps = Prestressing steel stressf ue

= Expected tensile strength (ksi)

fv

= Vertical effective compressive stress in a joint (ksi)

fy

= Specified minimum yield strength of reinforcing steel (ksi)

f ye = Expected yield strength of reinforcing steel (ksi)f yh = Yield strength of transverse reinforcement (ksi)h t w = Web slenderness ratiokie

= The smaller effective bent or column stiffness

k ej

= The larger effective bent or column stiffness

lac

= The anchorage length for longitudinal column bars (in)

NCHRP 20-7(193) Task 12

2-7

mi

= Tributary mass of column or bent (i)

mj

= Tributary mass of column or bent (j)

n

= The total number of piles at distance cx(i) or cy(i) from the centroid of the pile group

pb

= Ultimate compressive bearing pressure

pc

= Principal compressive stress (psi)

pp

= Passive pressure behind backwall

pt

= Principal tensile stress (psi)

r

= Radius of gyration (in)

ry

= Radius of gyration about weak axis (in)

s

= Spacing of transverse reinforcement in reinforced concrete columns (in)

su

= Average undrained shear strength in the top 100 ft

sul

= Undrained shear strength not to exceed 5000 psf ASTM D2166-91 or D2850-87 (psf)

t

= Thickness of a gusset plate (in)

vc

= Concrete shear stress (psi)

v jv

= Vertical joint shear stress (ksi)

vs

= Average shear wave velocity (ft/sec)

vsi

= Shear wave velocity of layer i (ft/sec)

w

= Moisture content

cc

= Compressive strain for confined concrete corresponding to ultimate stress in concrete

co

= Compressive strain for unconfined concrete corresponding to ultimate stress in concrete

cu

= Ultimate compressive strain in confined concrete

ps

= Prestressing steel strain

ps,EE = Essentially Elastic prestress steel strain

psu = Ultimate prestress steel strain Rps,u = Reduced ultimate strain of prestressing steel reinforcement

sh

= Onset of strain hardening of steel reinforcement

sp

= Ultimate unconfined compression spalling strain

su

= Ultimate strain of steel reinforcement

NCHRP 20-7(193) Task 12

2-8

R su = Reduced ultimate strain of steel reinforcement ye

= Yield strain at expected yield stress of steel reinforcement

= Total Displacement of a rocking column/footing system

b

= Displacement Demand due to flexibility of essentially elastic components, i.e., bent caps

C

= Corresponding displacement capacity obtained along the same axis as the displacement demand

col = The portion of global displacement attributed to the elastic displacement y and plastic displacement pof an equivalent member from the point of maximum moment to the point of contra-flexure

cr + sh = Displacement due to creep and shrinkage D = Displacement along the local principal axes of a ductile member generated by seismic design force appliedto the structural system

eq = Seismic displacement demand of the long period frame on one side of the expansion joint (in.)f

= Displacement demand duct foundation flexibility

fo = Column flexural displacement of a rocking column/footing system ot = Movement attributed to prestress shortening creep, shrinkage and thermal expansion or contraction to beconsidered no less than one inch per 100 feet of bridge superstructure length between expansion joints.(in.)

pc = Plastic displacement capacity pd = Plastic displacement demand p / s = Displacement due to prestress shorteningr

= The relative lateral offset between the point of contra-flexure and the end of the plastic hinge.

ro = Rigid body rotation of a rocking column/footing systemS

= The pile shaft displacement at the point of maximum moment

temp = Displacement due to temperature variationy

= Elastic displacement

ycol = Column yield displacement

= Pile cap displacement

= Fixity factor for a column

= Stability term of a rocking column/footing system

= Shear strength reduction factor (dimensionless)

b

= Resistance factor used for limiting width-thickness ratios

NCHRP 20-7(193) Task 12

2-9

bs

= 0.8 for block shear failure

tf

= 0.8 for fracture in net section

u

= Ultimate curvature

y

= Yield Curvature

= Ductility parameter of a rocking column/footing system

fs

= Transverse reinforcement ratio in a column flare

h

= The ratio of horizontal shear reinforcement area to gross concrete area of vertical section in pier wall

n

= The ratio of vertical shear reinforcement area to gross concrete area of horizontal section pier walls

s

= Volumetric ratio of spiral reinforcement for a circular column (dimensionless)

w

= Web reinforcement ratio in the direction of bending

b

= Slenderness parameter of flexural moment dominant members

bp = Limiting slenderness parameter for flexural moment dominant membersc

= Slenderness parameter of axial load dominant members

cp

= Limiting slenderness parameter for axial load dominant members

mo = Moment overstrength factorp

= Limiting width-thickness ratio for ductile component

r

= Limiting width-thickness ratio for essentially elastic component

D

= Local member ductility demand

= damping ratio (maximum of 0.1)

2.2

DEFINITIONS

Capacity Design A method of component design that allows the designer to prevent damage in certain components by making them strong enough to resist loads that are generated when adjacent components reach theiroverstrength capacity.Capacity Protected Element Part of the structure that is either connected to a critical element or within itsload path and that is prevented from yielding by virtue of having the critical member limit the maximum force thatcan be transmitted to the capacity protected element.Collateral Seismic Hazard Seismic hazards other than direct ground shaking such as liquefaction, fault rupture, etc.Complete Quadratic Combination (CQC) A statistical rule for combining modal responses from an earthquake load applied in a single direction to obtain the maximum response due to this earthquake load.Critical or Ductile Elements Parts of the structure that are expected to absorb energy, undergo significantinelastic deformations while maintaining their strength and stability.Damage Level A measure of seismic performance based on the amount of damage expected after one of thedesign earthquakes.

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Displacement Capacity Verification Seismic Design and Analysis Procedure (SDAP) E A design andanalysis procedure that requires the designer to verify that his or her structure has sufficient displacement capacity.It generally involves a non-linear static (i.e. pushover) analysis.Ductile Substructure Elements See Critical or Ductile ElementsEarthquake Resisting Element (ERE) The individual components, such as columns, connections, bearings,joints, foundation, and abutments, that together constitute the Earthquake Resisting System (ERS).Earthquake Resisting System (ERS) A system that provides a reliable and uninterrupted load path fortransmitting seismically induced forces into the ground and sufficient means of energy dissipation and/or restraint toreliably control seismically induced displacements.Life Safety Performance Level The minimum acceptable level of seismic performance allowed by thisspecification. It is intended to protect human life during and following a rare earthquake.Liquefaction Seismically induced loss of shear strength in loose, cohesionless soil that results from a buildup of pore water pressure as the soil tries to consolidate when exposed to seismic vibrations.Liquefaction-Induced Lateral Flow. Lateral displacement of relatively flat slopes that occurs under thecombination of gravity load and excess porewater pressure (without inertial loading from earthquake). Lateral flowoften occurs after the cessation of earthquake loading.Liquefaction-Induced Lateral Spreading Incremental displacement of a slope that occurs from the combined effects of pore water pressure buildup, inertial loads from the earthquake, and gravity loads.Maximum Considered Earthquake (MCE) The upper level, or rare, design earthquake having ground motions with a 3% chance of being exceeded in 75 years. In areas near highly-active faults, the MCE ground motionsare deterministically bounded to ground motions that are lower than those having a 3% chance of being exceeded in75 years.Minimum Seat Width The minimum prescribed width of a bearing seat that must be provided in a newbridge designed according to these specifications.Nominal resistance Resistance of a member, connection or structure based on the expected yield strength(Fye) or other specified material properties, and the nominal dimensions and details of the final section(s) chosen,calculated with all material resistance factors taken as 1.0.Operational Performance Level A higher level of seismic performance that may be selected by a bridgeowner who wishes to have immediate service and minimal damage following a rare earthquake.Overstrength Capacity The maximum expected force or moment that can be developed in a yielding structural element assuming overstrength material properties and large strains and associated stresses.Performance Criteria The levels of performance in terms of post earthquake service and damage that areexpected to result from specified earthquake loadings if bridges are designed according to this specification.Plastic Hinge The region of a structural component, usually a column or a pier in bridge structures, that undergoes flexural yielding and plastic rotation while still retaining sufficient flexural strength.Pushover Analysis See Displacement Capacity VerificationPlastic Hinge Zone Those regions of structural components that are subject to potential plastification andthus must be detailed accordingly.Response Modification Factor (R-Factor) Factors used to modify the element demands from an elasticanalysis to account for ductile behavior and obtain design demands.Seismic Hazard Level One of four levels of seismic ground shaking exposure measured in terms of the rareearthquake design spectral accelerations for 0.2 and 1.0 second.Service Level A measure of seismic performance based on the expected level of service that the bridge is capable of providing after one of the design earthquakes.Site Class One of six classifications used to characterize the effect of the soil conditions at a site on groundmotion.

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Square Root of the Sum of the Squares (SRSS) Combination In this specification, this classical statisticalcombination rule is used in two ways. The first is for combining forces resulting from two or three orthogonalground motio