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Chapter 4Uploaded by Wenix OniralcoRelated InterestsDeep FoundationGeotechnical EngineeringColumnBeam (Structure)Stress (Mechanics)Rating and Stats0.0 (0)Document ActionsDownloadShare or Embed DocumentEmbedView MoreCopyright: Attribution Non-Commercial (BY-NC)List price: $0.00Download as PDF, TXT or read online from ScribdFlag for inappropriate contentChapter 44.1 4.2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1-1 WSDOT Modifications to AASHTO Guide Specifications for LRFD Seismic Bridge Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-1 4.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-1 4.2.2 Earthquake Resisting Systems (ERS) Requirements for SDCs C and D . . . . . . . . 4.2-1 4.2.3 Seismic Ground Shaking Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-5 4.2.4 Selection of Seismic Design Category (SDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-5 4.2.5 Temporary and Staged Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-5 4.2.6 Load and Resistance Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-6 4.2.7 Balanced Stiffness Requirements and Balanced Frame Geometry Recommendation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-6 4.2.8 Selection of Analysis Procedure to Determine Seismic Demand. . . . . . . . . . . . . . . 4.2-6 4.2.9 Design Requirements for Single-Span Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-6 4.2.10 Member Ductility Requirement for SDCs C and D . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-6 4.2.11 Plastic Hinging Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-8 4.2.12 Minimum Support Length Requirements Seismic Design Category D . . . . . . . . . . 4.2-9 4.2.13 Longitudinal Restrainers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-9 4.2.14 Abutments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-9 4.2.15 Foundation – General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-9 4.2.16 Foundation – Spread Footing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-9 4.2.17 Procedure 3: Nonlinear Time History Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-10 4.2.18 Figure 5.6.2-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-10 4.2.19 Ieff for Box Girder Superstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-10 4.2.20 Foundation Rocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-10 4.2.21 Footing Joint Shear for SDCs C and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-10 4.2.22 Drilled Shafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-12 4.2.23 Longitudinal Direction Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-13 4.2.24 Liquefaction Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-13 4.2.25 Reinforcing Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-13 4.2.26 Plastic Moment Capacity for Ductile Concrete Members for SDCs B, C, and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-13 4.2.27 Shear Demand and Capacity for Ductile Concrete Members for SDCs B, C, and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-14 4.2.28 Concrete Shear Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-14 4.2.29 Shear Reinforcement Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-15 4.2.30 Interlocking Bar Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-15 4.2.31 Splicing of Longitudinal Reinforcement in Columns Subject to Ductility Demands for SDCs C and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-15 4.2.32 Minimum Development Length of Reinforcing Steel for SDCs A and D . . . . . . . 4.2-16 4.2.33 Requirements for Lateral Reinforcement for SDCs B, C, and D . . . . . . . . . . . . . . 4.2-16 4.2.34 Development Length for Column Bars Extended into Oversized Pile Shafts for SDCs C and D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-16 4.2.35 Lateral Reinforcements for Columns Supported on Oversized Pile Shaft for SDCs C and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-16 4.2.36 Lateral Confinement for Oversized Pile Shaft for SDCs C and D . . . . . . . . . . . . 4.2-16 4.2.37 Lateral Confinement for Non-Oversized Strengthened Pile Shaft for SDCs C and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2-16
Page 4-i
WSDOT Bridge Design Manual M 23-50.04 August 2010
4.2.38 4.2.39 4.2.40 4.2.41 4.2.42 4.2.43 4.2.44 4.2.45 4.2.46 4.2.47 4.3
Requirements for Capacity Protected Members. . . . . . . . . . . . . . . . . . . . . . . . . . . Superstructure Capacity Design for Integral Bent Caps for Longitudinal Direction for SDCs B, C, and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superstructure Capacity Design for Transverse Direction (Integral Bent Cap) for SDCs B, C, and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superstructure Design for Non-Integral Bent Caps for SDCs B, C, and D . . . . . . Joint Proportioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum Joint Shear Reinfocing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Longitudinal Cap Beam Reinforcement. . . . . . . . . . . . . . . . . . . . . . . . Horizontal Isolated Flares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Column Shear Key Design for SDCs C and D. . . . . . . . . . . . . . . . . . . . . . . . . . . . Cast-in-Place and Precast Concrete Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2-17 4.2-18 4.2-18 4.2-18 4.2-18 4.2-20 4.2-21 4.2-21 4.2-22 4.2-22
Seismic Design Requirements for Bridge Widening Projects . . . . . . . . . . . . . . . 4.3-1 4.3.1 Seismic Analysis and Retrofit Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3-1 4.3.2 Design and Detailing Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3-3 Seismic Retrofitting of Existing Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Seismic Analysis Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Seismic Retrofit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Computer Analysis Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.5 Earthquake Restrainers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4-1 4.4-1 4.4-1 4.4-1 4.4-1 4.4-1
Seismic Design Requirements for Retaining Walls . . . . . . . . . . . . . . . . . . . . . . . . 4.5-1 4.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5-1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.99-1 Design Examples of Seismic Retrofits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-B1-1 SAP2000 Seismic Analysis Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-B2-1
Appendix 4-B1 Appendix 4-B2
Page 4-ii
Seismic design of new bridges and bridge widenings shall conform to AASHTO Guide Specifications for LRFD Seismic Bridge Design as modified by Sections 4.2 and 4.3 of this manual. Analysis and design of seismic retrofits for existing bridges shall be completed in accordance with Section 4.4 of this manual. Seismic design of retaining walls shall be in accordance with Section 4.5 of this manual. For nonconventional bridges, bridges that are deemed critical or essential, or bridges that fall outside the scope of the Guide Specifications for any other reasons, project specific design requirements shall be developed and submitted to the WSDOT Bridge Design Engineer for approval. The importance classifications for all highway bridges in Washington State are classified as “Normal” except for special major bridges. Special major bridges fitting the classifications of either “Critical” or “Essential” will be so designated by either the WSDOT Bridge and Structures Engineer or the WSDOT Bridge Design Engineer. The performance object for “Normal” bridges is live safety. Bridges designed in accordance with AASHTO Guide Specifications are intended to achieve the live safety performance goals.
Page 4.1-1
WSDOT Bridge Design Manual M 23-50.Seismic Design and Retrofit
Page 4.04 August 2010
4.e. This category is permissible.3-1a. Shear design shall be based on 1.
WSDOT Bridge Design Manual M 23-50. The design criteria for column base with moment reducing detail shall consider all applicable loads at service.2.3 WSDOT Global Seismic Design Strategies: Type 1: Ductile Substructure with Essentially Elastic Superstructure.3-2 Types 6 and 8 are not Permissible for Non-liquefied configuration and Permissible with WSDOT Bridge Design Engineer’s approval for liquefied configuration For ERSs and EREs requiring approval. and which has its own reinforcing cage that is separate from that of the supported column.04 August 2010
Page 4. Figure 3. If the columns or pier walls are designed for elastic forces. For WSDOT projects. 3. strength. Type 3: Elastic Superstructure and Substructure with a Fusing Mechanism Between The Two. the WSDOT Bridge Design Engineer’s approval is required regardless of contracting method (i. Type 2: Essentially Elastic Substructure with a Ductile Superstructure.Person or agency having jurisdiction over the bridge.1 Add the following definitions: Oversized Pile Shaft.3-2.2 times elastic shear force and nominal material strengths shall be used for capacities. regardless of delivery method.2
Earthquake Resisting Systems (ERS) Requirements for SDCs C and D
Guide Specifications Article 3. This category is not permissible. all other elements shall be designed for the lesser of the forces resulting from the overstrength plastic hinging moment capacity of columns or pier walls and the unreduced elastic seismic force in all SDCs.2 WSDOT Modifications to AASHTO Guide Specifications for LRFD Seismic Bridge Design
WSDOT amendments to the AASHTO Guide Specifications for LRFD Seismic Bridge Design are as follows:
4. connection with moment reducing detail should only be used at column base if proved necessary for foundation design. Limitations on the use of ERS & ERE are shown in Figures 3. This category is permissible with WSDOT Bridge Design Engineer’s approval. approval authority is not transferred to other entities).3-1b. Fixed connection at base of column remains the preferred option for WSDOT bridges. the term “Owner” in these Guide Specifications shall be the WSDOT Bridge Design Engineer or/and the WSDOT Geotechnical Engineer.3-3. Figure 3.2. The minimum detailing according to the bridge seismic design category shall be provided.A drilled shaft that is at least 18 inches larger in diameter than the supported column. and 3. Owner.2-1
Guide Specifications Article 2.3-1b Type 6. 3.
4. and extreme event limit states.
Figure 3.2-2 WSDOT Bridge Design Manual M 23-50.Seismic Design and Retrofit
BDM Chapter 4
Plastic hinges in inspectable locations.3-1a Permissible Earthquake-Resisting Systems (ERSs)
BDM Figure 4. Abutment not required in ERS.3
Permissible 2
Abutment resistance not required as part of ERS Knock-off backwalls permissible
Permissible Upon Approval
Isolation bearings accommodate full displacement Abutment not required as part of ERS
Transverse Response
Transverse or Longitudinal Response
4 Permissible Upon Approval
Plastic hinges in inspectable locations Plastic hinges in inspectable locations.04 August 2010 Page 1
Bridge Design Manual M23-50-02
Abutment required to resist the design earthquake elastically Longitudinal passive soil pressure shall be less than 0.2.3-1a
Permissible Earthquake-Resisting Systems (ERSs).2-1 Page 4. breakaway shear keys permissible with WSDOT Bridge Design Engineer’s Approval Transverse or Longitudinal Response Isolation bearings with or without energy dissipaters to limit overall displacements
6 Not Permissible
Multiple simply-supported spans with adequate support lengths Plastic hinges in inspectable locations.70 of the value obtained using the procedure given in Article 5.
Plastic hinges at base of wall piers in weak direction
Spread footings that satisfy the overturning criteria of Article 6.3
Permissible Upon Approval 13
isolation gap optional Columns with architectural flares – with or without an isolation gap See Article 8.2.04 August 2010 Page 4. which behave elastically
Columns with moment reducing or pinned hinge details
Permissible except battered piles are not allowed
Pier walls with or without piles.4
Permissible 12
Seat abutments whose backwall is designed to fuse
Passive abutment resistance required as part of ERS Use 70% of passive soil strength designated in Article 5.3-1b Permissible Earthquake-Resisting Elements (EREs)
BDM Figure 4.2-2 WSDOT Bridge Design Manual M 23-50. including caps with battered piles.14
Permissible – isolation gap is required
Seat abutments whose backwall is designed to resist the expected impact force in an essentially elastic manner
Figure 3.Chapter 4
Plastic hinges below cap beams including pile bents Above ground / near ground plastic hinges
Permissible 4
Tensile yielding and inelastic compression buckling of ductile concentrically braced frames
Seismic isolation bearings or bearings designed to accommodate expected seismic displacements with no damage
Not Permissible 5
Piles with ‘pinned-head’ conditions
Capacity-protected pile caps.
2-4 WSDOT Bridge Design Manual M 23-50.1
Permissible Upon Approval for Liquefied Configuration
Figure 3.2-3 Page 4.. Ensure Limited Ductility Response in Piles according to Article 4 .g .7 .1
Batter pile systems in which the geotechnical capacities and/or in-ground hinging define the plastic mechanisms .7 .7 . Ensure Limited Ductility Response in Piles according to Article 4 .3-2 Permissible Earthquake-Resisting Elements that Require Owner’s Approval
Figure 3.2.3-2 Permissible Earthquake-Resisting Elements that Require Owner’s Approval
BDM Figure 4. integral abutment piles or pile-supported seat abutments that are not fused transversely) Ensure Limited Ductility Response in Piles
Permissible Upon Approval for Liquefied Configuration 8
In-ground hinging in shafts or piles .Seismic Design and Retrofit
Passive abutment resistance required as part of ERS Passive Strength Use 100% of strength designated in Article 5 .1
Plumb piles that are not capacity-protected (e . and are not designed for the Design Earthquake elastic forces Ensure Limited Ductility Response in Piles according to Article 4 .4 .04 August 2010
Foundations permitted to rock Use rocking criteria according to Appendix A
More than the outer line of piles in group systems allowed to plunge or uplift under seismic loadings
Wall piers on pile foundations that are not strong enough to force plastic hinging into the wall.2 .3
Sliding of spread footing abutment allowed to limit force transferred Limit movement to adjacent bent displacement capacity
Ductile End-diaphragms in superstructure (Article 7 .
Selection of Seismic Design Category (SDC)
Guide Specifications Article 3.2.Chapter 4
Bearing systems that do not provide for the expected displacements and/or forces (e .5 Pushover analysis shall be used to determine displacement capacity for both SDCs C and D. the seismic ground shaking hazard shall be determined based on the WSDOT Geotechnical Engineer recommendations.2-4Not Recommended for New Bridges Are
4.6 For bridges that are designed for a reduced seismic demand.3-3 Earthquake-Resisting Elements that Are Not Recommended for New Bridges
BDM Figure Figure 3.2. the contract plans shall include a statement that clearly indicates that the bridge was designed as temporary using a reduced seismic demand.3
Seismic Ground Shaking Hazard
Guide Specifications Article 3.2.g .
Page 4. rocker bearings)
Battered-pile systems that are not designed to fuse geotechnically or structurally by elements with adequate ductility capacity
Figure 3.3-3 Earthquake-Resisting Elements that4.2..
Temporary and Staged Construction
Guide Specifications Article 3.2-5
.4 For bridges that are considered critical or essential or normal bridges with a site class F.
Guide Specifications Article 3. times the tributary permanent load in the restrained direction. as specified in Article 3.2 and 4.2. C. or D. Deviations from balanced stiffness and balanced frame geometry requirements require approval from the WSDOT Bridge Design Engineer. Guide Specifications Article C3.2-6 WSDOT Bridge Design Manual M 23-50.2 Analysis Procedures: • Procedure 1 (Equivalent Static Analysis) shall not be used.7
Balanced Stiffness Requirements and Balanced Frame Geometry Recommendation
Guide Specifications Articles 4.7 Add the following paragraph: Vehicular live loads have not been observed to be in-phase with the bridge structure during seismic events.9 In-ground hinging for drilled shaft and pile foundations may be considered for the liquefied configuration with WSDOT Bridge Design Engineer approval.0 when pushover analysis is used to determine the displacement capacity.
4. the connections between the superstructure and substructure shall be designed to resist a horizontal seismic force not less than the acceleration coefficient.Seismic Design and Retrofit
4. the inertial effect of actual live loads on typical bridges is assumed to be negligible in the dynamic demand analysis and pushover capacity analysis for normal bridges in SDCs C and D. Guide Specifications Article C4.8
Selection of Analysis Procedure to Determine Seismic Demand
Guide Specifications Article 4.9
Design Requirements for Single-Span Bridges
Guide Specifications Article 4.9 Add the following paragraph: The member ductility demand may be determined by M-φ analysis (see Figure 1) and the following equations:
4.7 Revise as follows: • The load factor for live load shall be 0. the live load factor shall be determined on a project-specific basis.2.
4.5 Revise second sentence as follows: However. Use live load factor of 0.10
Member Ductility Requirement for SDCs C and D
Guide Specifications Article 4.1.2. Thus. • Procedure 3 (Nonlinear Time History) shall only be used with WSDOT Bridge Design Engineer’s approval.2. For critical/essential bridges.5 for all other extreme event cases. except as modified for SDC A in Article 4. • Procedure 2 (Elastic Dynamic Analysis) shall be used for all “regular” bridges with two through six spans and “not regular” bridges with two or more spans in SDCs B.1 Balanced stiffness and balanced frame geometry are required for bridges in both SDCs C and D.2. As.4.04 August 2010
8.18 Equivalent analytical plastic hinge length in inches as defined in Article 4.2 5 5 8.18 L =
4.8 1 6.2.13.13.9 4)
(C4 .9 1 6.9 2) (C4.13.9 2) (C4.26 4.13.9 3) (C4.8 1 6.9 4) (C4. µD .40 4.9 1) (C4.5 1 4.4.13 Idealized yield curvature from bilinearization described in Article 8.2.4.9 1 8.13.13.2 4 Figure C 4.Chapter 4
4.9-2) (C4 .2.13.13.11.2.2.4.9 1 4.13.2.9 1) 4.4.2 3 8.40
4.2.) 4.21 4.
4.9 4) (C4.4.13.13.13.2 6 6 8.2.10 4.2.4.2-7
.2 3 8.9 2) (C4.2 1 8.9 2) (C4.4.13.26 8.9 3) (C4.8 1 6.13.5 4.10-1 8.4.2
idealized elasto-plastic behaviour
8.18 Length of column from point of maximum moment to the point of moment contraflexure (in.2 6 8.13.10
(C4.2.2.5 1
4.2 2 8.2 1 8.2 6 8.13.40 8.04 August 2010
Page 4.8 1 6.13.2.13.2 1 1 8.9-4)
Where: 4.5 M ne 1 4.26 8.2 2 8.5 1 8.10 (C4.2.13.9-3) (C4 .2 BDM Figure 4.9 1 Mp 6.2
WSDOT Bridge Design Manual M 23-50.2.2 4 8.2.2 5 8.2 2 2 8.9 4.21
6.13.2 8.2 8.2.13= φcol φyi = 4.9 3) (C4.6 4.2.26 6.2.2.9 4) (C4.2 5 8.13.9-1 Moment-Curvature Diagram 8.2.13 Column curvature demand from "pushover" analysis 4.2.13.13.18 = Lp 4.9 1) (C4.21 4.21
Note that a column with two plastic hinges will have two values of ductility demand.9 3) (C4.2. The larger value controls and must compared against the limits given in Equations 1-6 .2 3 3 8.13 4.10 1) (C4.13.2.40 4.2.2 4 4 8.2.9-1) (C4 .
4.2.04 August 2010
Guide Specifications Article 4.2-1 Capacity Design of Bridges Using Overstrength Concepts
Page 4.11.2-8
WSDOT Bridge Design Manual M 23-50.2.11-1
Figure 4.2-1 Capacity Design of Bridges Using Overstrength Concepts
BDM Figure 4.g .2-1 as follows:
Additional strength to be provided by the bridge deck
2M po Lc
Column overstreng th moment capacity
(a) Longitudinal Response for Nonintegral Abutments
c .Seismic Design and Retrofit 4 BDM Chapter
4.11.11 Plastic Hinging Forces Plastic Hinging Forces (Guide Specifications Article 4.2. of superstructure
d M po
2 M po Lc
(b) Transverse Response for Dual Column Pier
Figure 4.11.2-1 as follows:
Revise Figure 4.2) Revise Figure 4.11.11.
4.26 8. 8.3.2.2 3 8.2 1 Guide Specifications Article C5.13.2. N. With WSDOT Bridge Design Engineer approval.15
4.2 4 8.13.2.2.13.3.7 of this manual. 1 below (using 2 times seismic displacement instead of 1.4.2-9
8.2 Diaphragm Abutment type shown in Figure 5.3 and Section 4.3.1 4.18 Longitudinal restrainers shall not be used at the end piers (abutments).3. Restrainers may be omitted for SDCs C and D where the available seat width exceeds the calculated support length specified in Eq.2-1 shall not be used for WSDOT bridges.2. For determining seismic demand. and drilled shafts shall be based on the WSDOT Geotechnical Engineer’s recommendations.14 Abutments
Guide Specifications Article 5. the abutment may be considered and designed as part of earthquake resisting system (ERS) in the longitudinal direction of a straight bridge with little or no skew and with a continuous deck.2. pile foundations. WSDOT Geotechnical Design Manual Section 6. See the earthquake restrainer design example in the Appendix of this chapter.3-1).1.10 (C4.2. 6.16
4.12.12.2.2 6
.8 1 Participation of the wingwall in the transverse direction shall not be considered in the seismic design of bridges.4 The Iterative Method.2.4. 4.5.3.2.9 1) Longitudinal restrainers shall be provided at the expansion joints between superstructure segments.13.21 4.1 and the WSDOT Geotechnical Engineer’s recommendations.12.2.2.2 .13.2.5 of this manual.13.04 August 2010
Foundation – Spread Footing
8. the support length shall be 150% of the empirical support length.9 2) Structure (FHWA-HRT-06-032) Article 8.4.13.5 1 Guide Specifications Article 5.2 Foundation springs for2spread footings shall be determined in accordance with Section 7. 4.40
4. Restrainers shall be designed in accordance with the FHWA Seismic Retrofitting Manual for Highway (C4.13
Guide Specifications Article 4.13.12
Minimum Support Length Requirements Seismic Design Category D
Guide Specifications Article 4. Restrainers shall be detailed in accordance with the (C4.1
The required foundation modeling method (FMM) and the requirements for estimation of foundation springs for spread footings.9 1
4.2-1.2.13-1)
Omitting restrainers for liquefiable sites shall be approved by the WSDOT Bridge Design Engineer.13
(4 .9 3) requirements of Guide Specifications Article 4.3 Add the following paragraph: For single-span bridges in SDC D. 6.9 4) Eq.
4. specified by Guide Specifications Equation 4.65 as required in (C4. 4.2 5
WSDOT Bridge Design Manual M 23-50. longitudinal passive soil pressure shall not exceed 50% of the value obtained using the procedure given in Article 5.
2 .” Add the following Articles: • 6.4.2 2 For columns with interlocking cores.2 4 8. within the joint is required.13. shall satisfy Eq.9 Foundation rocking shall not be used for the design of WSDOT bridges.2 3 8.4. pt.2 1 Where the principal tension stress in the joint.Seismic Design and Retrofit
4. (8. the transverse  reinforcement ratio in 4.21
Gross moment of inertia shall be used for box girder superstructure modeling. ρs shall be based on the total area of reinforcement of each core.2 5
Page 4.6.2.2-10
8.2. 8.9.13.
4.2-1 for both (a) Circular Sections and (b) Rectangular Sections 4.7 Joint Shear Reinforcement Principal compression stress shall not exceed the limit specified in Article 6.4.5 is less than  .6.3-1) and no additional reinforcement the joint.17
(C4.8.4.3
4.13.40 ρs.3.13.2.5
6.) Delete the last paragraph.2.13.4.18
Figure 5.5 1 Article 8.2. is greater than  .4.2 6
WSDOT Bridge Design Manual M 23-50.18
4.18-1)
Guide Specifications Article 5.4. ρs.8.6.8 and 6.13.6. “Transverse joint reinforcement shall be provided in accordance with 4.13 shall be Axial Load Ratio:
Guide Specifications Article 6. If the principal tension stress in the joint.9 1)
4.19 Ieff for Box Girder Superstructure
(4 .2.2.9 3) used to describe the earthquake loads shall be selected in consultation with the WSDOT Geotechnical Engineer and the WSDOT Bridge Design Engineer.13.2.9 2) Procedure 3: Nonlinear Time History Method
Guide Specifications Article 5.
(C4.04 August 2010
. shall satisfy Eq.21
Footing Joint Shear for SDCs C and D
Guide Specifications Article 6.9 4)
Guide Specifications Article 5.10
(C4. pt. the transverse reinforcement ratio. (8. as specified in Article 6.2. 8. then transverse  reinforcement ratio in the joint.2 The horizontal axis label of Figure 5.4.26 8.8 1
Revise Bc unit as follows: or wall Bc = diameter or width of column6.2.4
The time histories of input acceleration (C4.3-2) and additional joint reinforcement is required as specified in Articles 6.9 1measured normal to the direction of loading (in.
13.2 1 4.13. any force transferred to the bend is directed away from the joint and increase diagonal tension stress within the joint region. which has a total area as defined by Eq.2 5 8.13.13.8-18Vertical Joint Shear Reinforcement Region 8.4.2 4 8.4.2.2
BDM Figure 4.13.
Page 4.9 1
(6 .13.4 .2 3 8.2 2 8.5 Dc away from the face of column.4.40 j v Reinforcing 4 BDM Chapterbars making up the vertical joint reinforcement. From a joint performance viewpoint.4.
8.2 2 8.13. the reinforcement area given by Eq.8 8.2) 6.13.13. As .4. If only X% of the column bars are bent outward.13.13.Chapter 4
• 6.13.13.13. if this is done.2 5 8.9-1.9 1 Ast = Total area of column reinforcement anchored in the joint (in.2.6.2) 4.4. 1 may be reduced proportionately.2 3 8.21 6.2 8 Contractors (and designers. thus making stable platform for 8.2.2 9 supporting the column cage and prevent congestion.2-11
.13.21 the region identified above and Figure 1. Where: = Total area of vertical joint reinforcement required (in.1.2 7 4.8-1)
Figure 6. However. but this will cause undue congestion.2 1 8.13. shall be no larger than #5Retrofit Seismic Design and bars to allow for the top hook to be field bend after placement from the 90° to a 135° as shown in 8. as a matter of habit) prefer to provide anchorage for column longitudinal reinforcement by bending its tails outward.13. within 4.2 7 8.40 Figure 6.2 9 8.2 4 8.2 6 8.4. it is desirable to bend the column bar inward toward the joint.21-1 Figure 6.2. with the remainder bent into the core.2 6 8.8 Vertical Joint Shear Reinforcement Vertical joint reinforcement is required in the region that extends horizontally from the face of column to a distance of 0. The vertical joint reinforcement shall be evenly distributed around the column.2.8-1 Vertical Joint Shear Reinforcement Region
• Add C.13.
2 8 8.9-1) 6.2.Seismic Design and Retrofit
4.8-1 Vertical Joint Shear if straight bar development 8.4.13.13.2 7 8.13.13.2 9
8.13.4.40 is required in both directions.2.2. Reinforcement may be hooked Reinforcement Region is Figure 6.13.2 Ast = Total area of column reinforcement anchored in the joint (in.2 6 8.21 be placed in the top of the footing extending through the joint and for a sufficient distance to develop its yield strength at a1distance beyond 0.2 1 4.4 .13.13.13.2 3 unattainable.2 6 8.21
4.2 8 8.13.2 4 8.2 4 8.2 5 8.13.13.4.9 Horizontal Joint Shear Reinforcement .22
Guide Specifications Article C6.4.13.13.21-2 Joint Shear Reinforcement
4. Bridge WSDOT Geotechnical Engineer Page 14
Page 4.2 2 forces acting both parallel seismic and transverse to the longitudinal axis of the bridge.21
6. The additional area of reinforcement shall 4.2.2-12
WSDOT Bridge Design Manual M 23-50.4.13.13.13.9-1 Footing 4.2 9
8.8 1 4.13.4.2 1 8.2 8 8.13.2 6 8.40
8.9-1 Footing Joint Shear Reinforcement
BDM Figure Figure 6.9 1 8.2.5 The scale factor for p-y curves for large diameter shafts shall not be used for WSDOT bridges unless approved by Design Manual M23-50-02 and WSDOT Bridge Design Engineer.2 7 8.13.04 August 2010
.8 1 • 6.13.4.2 2 8. 6.9 1 in addition to that required to resist other loads.2) 1 6.2 4 8.2 3 8.2 5 8.2.13.4.13.4.2) Since the column to footing connection resists moments from8.13. as shown in Figure 1.2 7 8.9 1 6. 6.40 where: = Total area of vertical joint reinforcement required (in.2 9
Figure 6.2.2 5 8. the additional horizontal reinforcement 4.5 Dc from the column face.2 3 8.8 The additional area of the horizontal steel shall satisfy:
(6 .13. shall be provided Additional horizontal reinforcement in the footing of the total amount.2 2 8.4. 8.2.13.13.
4.5 Revise Figure 8.1 Case 2: Earthquake Resisting System (ERS) with abutment contribution may be used provided that the mobilized longitudinal passive pressure is not greater than 50% of the value obtained using procedure given in Article 5.
Guide Specifications Article 8.4.26
Plastic Moment Capacity for Ductile Concrete Members for SDCs B.4.
4.2.2. and D
Guide Specifications Article 8.2.5-1 as follows:
M ne My
idealized elasto plastic behaviour
Figure 8.2-13
Longitudinal Direction Requirements
Guide Specifications Article 6.2.26-1
WSDOT Bridge Design Manual M 23-50.2.8 Soil liquefaction assessment shall be based on the WSDOT Geotechnical Engineer’s recommendation and WSDOT Geotechnical Design Manual Section 6.
4.3.2.2.24
Liquefaction Design Requirements
Guide Specifications Article 6. Deformed welded wire fabric may be used with the WSDOT Bridge Design Engineer’s approval. Wire rope or strands for spirals.8.7.1 Only ASTM A 706 reinforcing steel shall be used. and high strength bars with yield strength in excess of 75 ksi shall not be used. C. ASTM A 615 reinforcement shall not be used in WSDOT bridges.5-1 Moment-Curvature Model
BDM Figure 4.3.04 August 2010
0075 0.6.2.#10 0.2 1 Reduced Reduced either the concrete strain reaches a magnitude of0. Where: H′ = Length of the pile shaft/column from the ground surface to the point of zero Bridge moment Manual M23-50-02 Design above ground Page 31 Dc = Diameter of pile shaft Bridge Design Manual M23-50-02 Page 31 The shear reinforcement outside of the plastic hinge region need not exceed the required shear reinforcement inside the plastic hinge region.0150 0.4.6.0125 0.2-14
WSDOT Bridge Design Manual M 23-50.0075 0.090 0.#8 #3 .060 0.090 0.120
0.060 0. the expected nominal ultimate steel strain reaches ⅔ su #11 .26 8. For SDC B. with su as defined in Table 8.0023 #3 .090 0.0115 0.40 The expected nominal moment capacity.090
0.3.0150 0.0115 Mmax = sh hardening Ultimate Moment capacity of column (kip-ft) 0. Mne.#18
Guide Specifications Article C8. size and cost of the Table 4.#10 #4 . C.0150 4.0193 sh #10 0.Mp in lieu of development of a moment-curvature0.0023
95 0.2.060 0.0193 0.060 or the reinforcing steel strengths when #4 .5 1 (8 .0050 0.040 0.3.#18
0.0050 components that are concrete #18 #180.060 0. 8.090 The design engineer should use the minimum column section and reinforcing steel that meets the project constraints and satisfies the requirements of the design codes/specifications. for capacity protected 0.28
Guide Specifications Article 8.1 Add the following paragraphs: The shear demand for the non-oversized pile shafts shall be taken as the larger of either the force reported in the soil/pile shaft interaction analysis when the in-ground hinges form or the shear calculated by dividing the overstrength moment capacity of the pile shaft by the length Hs.0050 0.#18 #3 .2 2 strain strain capacity.060 0.#10 0.0150 0.003 0.120 0.#18 95 f ue #3 . and D
Guide Specifications Article 8.0125 0.13.2-1.5-1) #9 #9 0.090
0.2 5 should be actively involved in the aesthetic selection process to encourage the use of economical members.2.120
0.0115 hardening Revise the third paragraph as follows: #14 #140.04 August 2010
.#8 0.120
4.5 Ultimate Ultimate 8.0023
0.0125 0.#18 0.00166
#3 .).2-1 Stress Propertiescap ReinforcingThe design engineer connecting elements (foundations.00166
0.4.0075
4.Expected f tensile strength ue tensile strength Seismic(ksi) Design and Retrofit 6.0023
95 0.13.13.4.060 0.9 Revise Equation 8.#18#11 .090 0.2 6 Shear Demand and Capacity for Ductile Concrete Members for SDCs B.13.0050 connected to the plastic hinge locations shall be based on the expected concrete and reinforcing 8. The design 8.2 4 engineer must keep in mind that using a larger column than necessary can greatly increase the Table 4.090 0.27
Page 4.13.8 1 (ksi) Expected yield Expected yield ye strain strain as follows: 6.040 analysis.#18
95 0.2 Revise the definition as follows: D′ = Diameter of core section for each individual circular core of column measured between the centerline of the hoop or spiral (in.5-1 1
#3 .2 3 tensile strain su Add the following paragraph: tensile strain
#4 . Mne.2-1 Stress Properties of Reinforcing Steel Bars.2.#10 #4 . of beams.0125 Where: of strain Onset Onset of strain #10 & #11 & #11 0.090 0. Hs shall be taken as the smaller of: • H′+ 2Dc • Length of the column/pile shaft from the point of maximum moment in the pile shaft to the point of contraflexural in the column. may be used as #18#11 .). Steel Bars.13.060 0.0075 0.0115 0.090 R R ultimate tensile tensile. 8. moment 8.
The hooks shall engage peripheral longitudinal bars.7 The longitudinal reinforcing bar inside the interlocking portion of column (interlocking bars) shall be Bridge size of bars used outside the Page 1 the sameDesign Manual M23-50-02 interlocking portion.7) 4.6.04 August 2010
Page 4.2-15
. Cross-ties shall have 135° hooks at one end and 90° hooks at the other end as specified in Article 8.8. Splices shall be staggered at least 2 feet.4. The performance object for “Normal” bridges spirals or hoops as shown in the accordance with below (Correal et al. for all highway bridges in Washington State are classified as “Normal” except for special major bridges.3-3 Column Interlocking Spiral and Hoop Details BDM Figure 4. where the length of the rebar cage is less than 60 feet (72 feet for #14 and #18 bars). For nonconventional bridges. Bridges designed in revised Figure C3 AASHTO Guide Specifications are intended the same bar size as the spiral or hoop reinforcement shall be used. Figure C8.30 Interlocking Bar Size (Guide Specifications Article 8.29 Shear Reinforcement Capacity The importance classifications Guide Specifications Article C8.6.accordance with BDM Section 4. Special major bridges fitting the classifications of Add the followingor “Essential” will be so designated by either the WSDOT Bridge and Structures either “Critical” paragraph: Horizontal cross-ties connecting the spirals or hoops should be provided between the interlocking Engineer or the WSDOT Bridge Design Engineer. In general.6.9 (alternate 135° hook every other tie bar).29-1 4. 2004).
WSDOT Bridge Design Manual M 23-50.5.2. bridges that are deemed critical or essential.
4.30 Interlocking Bar Size
Guide Specifications Article 8.3 The splicing of longitudinal column reinforcement outside the plastic hinging region shall be accomplished using mechanical couplers that are capable of developing a minimum tensile strength of 85 ksi. Lap splices shall not be used. no splice in longitudinal reinforcements shall be allowed.8.
Figure C8. The ties shall be spaced to achieve the live safety performance goals. The design engineer shall clearly identify the locations where splices in longitudinal column reinforcement are permitted on the plans.2. vertically at two times the pitch/spacing of the spirals/hoops.2.6.2.2.6.3-3 Column Interlocking Spiral and Hoop Details. Seismic design of retaining walls shall be in accordance with BDM Chapter 4 Section 4. project specific design requirements shall be developed and submitted to the WSDOT Bridge Design Engineer for approval.31
Splicing of Longitudinal Reinforcement in Columns Subject to Ductility Demands for SDCs C and D
Guide Specifications Article 8. or Seismic Design and Retrofit bridges that fall outside the scope of the Guide Specifications for any other reasons. Cross-ties having is live safety.. 4.
based on TRAC Report WA-RD 417.4. the hoop weld splices shall be placed at centerline of pier near centerline of column.1 should be used to limit the reinforcing bar size for a given bridge joint geometry. the hoop weld splices shall be staggered around the column by a minimum distance of ⅓ of the hoop circumference.8.37 Lateral Confinement for Non-Oversized Strengthened Pile Shaft for SDCs C and D
Guide Specifications Article 8. C.04 August 2010
Requirements for Lateral Reinforcement for SDCs B.8.
4.13 Non-oversized column-shaft is not permissible unless approved by the WSDOT Bridge Design Engineer.8. and D
Guide Specifications Article 8.2.2 K of this manual. In the case of prestressed girder structures with integral cap beams.
Page 4. For members that are reinforced with interlocking hoops.2. Eq.32
Minimum Development Length of Reinforcing Steel for SDCs A and D
Guide Specifications Article 8.34
Development Length for Column Bars Extended into Oversized Pile Shafts for SDCs C and D
Guide Specifications Article 8.2.1 and the AASHTO Specifications may be met with a shorter anchorage length.36 Lateral Confinement for Oversized Pile Shaft for SDCs C and D
Guide Specifications Article 8.2.8.
WSDOT Bridge Design Manual M 23-50.35
Lateral Reinforcements for Columns Supported on Oversized Pile Shaft for SDCs C and D
Guide Specifications Article 8.12 The requirement of this article for shaft lateral reinforcement in the column-shaft splice zone may be replaced with Section 7.
4.C of this manual.4 Add C8. the longitudinal reinforcement shall be extended as close as possible to the top of the stage 1 cap beam.11 Add C8.8.2.Seismic Design and Retrofit
4.2.10 Extending column bars into oversized shaft shall be per Section 7.11: The spacing of hoops or pitch of spirals of the column cage may be doubled along the entire embedded length of the column cage into the shaft.1 “Non Contact Lap Splice in Bridge Column-Shaft Connections.4: The longitudinal reinforcing bar should also meet the longitudinal development requirements in the AASHTO LRFD Bridge Design Specifications for all load cases other than seismic loads. Column longitudinal bars shall be extended into the cap beam and footing as close as practically possible to the opposite face of the cap beam or footing even though the develop length required in Eq.”
4.8. The additional length is required to develop favorable bond-strut angles in the column-cap beam and column-footing joint.
4.4.8.8.8.9 Add the following paragraphs: For members that are reinforced with single circular hoops.
Extended pile shafts (same sized column shaft) are designed so the plastic hinges will form below ground in the pile shaft. The point of maximum moment shall be identified based on the moment diagram.11. pile and drilled shaft in-ground hinging may be considered as an ERE. Bridges shall be analyzed and designed for the nonliquefied condition and the liquefied condition in accordance with Article 6. the pile shaft may be strengthened and shall be designed for a expected nominal moment capacity equal to 1. Where in-ground hinging is part of ERS. The capacity protected members shall be designed in accordance with the requirements of Article 4. with the WSDOT Bridge Design Engineer’s approval.Chapter 4
.9 Add the following paragraphs: Oversized pile shafts are designed so the plastic hinge will form at or above the shaft/column interface. that is.25 times the moment demand generated by the overstrength moment of supported column. at any location along the shaft. a factor of 1. To ensure the formation of plastic hinges in columns. The extended pile shafts shall not be used in the WSDOT projects without the WSDOT Bridge Design Engineer’s approval. oversized pile shafts shall be designed for an expected nominal moment capacity. thereby. The design moments below ground for extended pile shaft may be determined using the Nonlinear Static Procedure (pushover analysis) by pushing them laterally to the displacement demand obtained from an elastic response spectrum analysis.25 is used in the design of oversized pile shafts. To avoid the plastic hinge forming below ground. The ductility demand for the pile shaft shall be less than the ductility demand for the column supported by the shaft.8. To ensure the formation of plastic hinges in columns and to minimize the damage to oversized pile shafts. Therefore.9 Add the following paragraphs: For SDCs C and D where liquefaction is identified. but the cross section of the confined core is the same for both the column and the pile shaft. This factor also accommodates the uncertainty associated with estimates on soil properties and stiffness. containing the majority of inelastic action to the ductile column element.2.0 depending on the soil properties and upon the WSDOT Bridge Design Engineer’s approval.
WSDOT Bridge Design Manual M 23-50. Guide Specifications Article C8. the confined concrete core should be limited to a maximum compressive strain of 0.04 August 2010
Page 4. area of transverse and longitudinal reinforcement may change between the column and the pile shaft. The concrete cover. equal to 1. The safety factor of 1. Mne. The moment along a pile shaft is dependent upon the geotechnical properties of the surrounding soil and the stiffness of the shaft.25 may be reduced to 1. oversized pile shafts should be designed to remain elastic. The plastic hinge zone shall be designated as the “No-splice” zone and the transverse steel for shear and confinement shall be provided accordingly.25 times moment demand generated by the overstrength column plastic hinge moment and associated shear force at the base of the column.38 Requirements for Capacity Protected Members
Guide Specifications Article 8. The expected plastic hinge zone shall extend 3D above and below the point of maximum moment.008 and the member ductility demand shall be limited to 4.
(8 . pt: 8. the longitudinal flexural bent cap beam reinforcement shall be continuous.41
Superstructure Design for Non-Integral Bent Caps for SDCs B.13 .13.2 3 8. of the superstructure shall be resisted by girders within the effective width.13. C.40 • For principal compression.13.2-4) (8 .2 5 8.13 .2.40
Superstructure Capacity Design for Transverse Direction (Integral Bent Cap) for SDCs B.13.2. C.D.40 4. pc:
8.13.13.2 3 8.1.13.2 8 8.13.12 Non-Integral Bent Caps shall not be used for continuous concrete bridges in SDC B.2 7
8.121 Revise the last paragraph as follows: For SDCs C and D. See Section 5.2 9 8.3. and the remaining one-third by girders outside the effective width.2 1 8.2-18
WSDOT Bridge Design Manual M 23-50.13. and D
Guide Specifications Article 8.2-2)
(8 .2 4 8.10 Add the following paragraph: For precast prestressed girder bridges.2.2 2 In which: 8.2.2. 1 and Eq.2 6 Average 8.
Joint Proportioning
Guide Specifications Article 8.
4.13.2 7 8. and D except at the expansion joints between superstructure segments.g.13 . Splicing of cap beam longitudinal flexural reinforcement shall be accomplished using mechanical couplers that are capable of developing a minimum tensile strength of 85 ksi.39
Superstructure Capacity Design for Integral Bent Caps for Longitudinal Direction for SDCs B.13. Splices shall be staggered at least 2 feet.13.2-3)
Where: ƒh = ƒv = vjh =
Average axial horizontal stress (ksi) 8.2 1 • For principal tension.4 of this manual for additional details.
4.13.2 4 8.13.Seismic Design and Retrofit
4.13. and D
Guide Specifications Article 8. Lap splices shall not be used. C.13.13.2vertical stress (ksi) axial 6 Average joint shear stress (ksi) 8. 2 4.04 August 2010
Page 4.2 Revise Article 8. two-thirds of the column plastic hinging moment at the c.2 as follows: Moment-resisting joints shall be proportioned so that the principal stresses satisfy the requirements of Eq.2.2 2 8. and D
Guide Specifications Article 8.13 .13.13. C.2-1) (8 .
(8 .13 .13.2 4 8.g.13. the effective width will be the smaller of the value given by the above equations or the cap beam width.) Db 8.2 typically be ignored since there is typically no prestress in the cap.04 August 2010
Page 4.13.2 9
(8 . Figure 8.) Dc = Diameter or cross-sectional dimension of column in the direction of loading (in.g. This level arm may be approximated by Ds. of bottom 8.13. ƒ8.2 5 = Depth of bent cap (in.2 9 longitudinal reinforcement of the cap beam or superstructure (kip-in.13.2.2 4 = Bent cap width (in. of tensile force to c.2 3 response and depth of cap beam for nonintegral bent caps and integral joint under 4.2 7 • For circular columns:
8.13.2 8 8.2.) 8.13.13.40 transverse response (in.2 7 = Column axial force including the effects of overturning (kips) Pc 8.2. using 8.1 shall be modified if the1cap beam does not extend beyond the column exterior face greater 8.
4.13.13.13. Beff = Effective width6of joint (in. For most projects. Mpo. Beff .2 Eq.2 The effective width of joint. 6 8.2 9 than the bent cap depth.13.13 .13.13. depends on the shape of the column framing into the joint and is determined4.2-5)
Beam8.) 8.2 63 8.2.13 . 4.13.13.2-6)
Where: 8.) of superstructure at the bent cap for integral joints under longitudinal Ds = Depth8.2.). Assuming 8.13.2-19
.13.13.13 .13.2-8) (8 .2-9)
The horizontal axial stress is based on the mean axial force at the center of joint.40 Where: Pb =
8.2spread away from the boundary of the column to a plane at mid-depth of a8. in addition to the moment induced due to The column 8 eccentricity between the column plastic hinge location and the c. can be approximated with the following equation: Where: M = 4.2 8.) Bcap =4.21 8.2overstrength moment.g.13 .13.13.13.) Dc 8.2force at the center of the joint including the effects of prestressing axial 2 and the shear associated with plastic hinging (kips) Bcap= Bent cap width (in.13. the average axial stress in the joint is provided by the axial force in the column.241 h can In the vertical direction.2 8 • For rectangular columns: 8.2 2 The average joint shear stress.2 5 hb = The distance from c.13.13.21
WSDOT Bridge Design Manual M 23-50.2 3
(8 .) 8.2-1 clarifies the quantities to be used in this calculation.13.2-7)
For transverse response. of compressive force on the section (in.252 45° the bent cap. vjh.40 Diameter or cross-sectional dimension of column parallel to bent cap (in. the average axial stress is calculated by the following equation:
8.13.2 7 8.2.21 the following equations.2
13.2-1 Effective Joint Width for Shear Stress Calculation.5.4.in this calculation.2 for integral bent cap and Article 8.13.
BDM Figure 4. 4.2-20
WSDOT Bridge Design Manual M 23-50.13.1-1 and Figure 8. Bent cap beams not satisfying these joint geometry and detail requirements shall be designed based upon the strut and tie provisions of the AASHTO LRFD Bridge Design Specifications.13.13.13.2-1-1 to 3 and Figures 8.04 August 2010
Page 4.13.13. The joint reinforcements shall be placed within a distance of 0.) Diameter or width of column or wall measured normal to the direction of loading (in.3 Add commentary C8.2.1 for nonintegral bent cap are based on the tests by Priestley (1996) and Sritharan (2005) for certain standard joints as shown in Figure C8.5 Dc from the column surface.4.2-1 Effective Joint Width for Shear Stress Calculation
Figure 8.2-1-2 using the external strut force transfer method.4.
Seismic Design and Retrofit where:
c Where: Bc =
diameter or width of column or wall measured normal to the direction of loading (in. Consequently.1-1 to 2.5.2.1.)
Figure 8. these specifications are only applicable to the joints that closely match the geometry of test joints as detailed in Figures 8.3 as follows: Additional joint reinforcements specified in Article 8.43 Minimum Joint Shear Reinfocing
Guide Specifications Article 8.13.13.
. The plastic rotation.45
Horizontal Isolated Flares
Guide Specifications Article 8.3-1 Additional Longitudinal Cap Beam Reinforcement for Joint Force Transfer
BDM Figure 4. can be calculated using the moment-area method by integrating the M/EI along the column height.
4.1.13.3 Add the following: This reinforcement shall extend a sufficient distance to develop its yield strength at a distance of 0.5Dc from the column face as shown in Figure 1.5. Delete the entire third paragraph and replace with the following: For SDCs C and D.44 Additional Longitudinal Cap Beam Reinforcement
Guide Specifications Article 8.Chapter 4
4. θy. The total deformation of the flare edge can be calculated by multiplying the total rotation. is given by:
WSDOT Bridge Design Manual M 23-50.44-1
Add C8.2. θp.
Figure 8.3: The additional longitudinal cap beam reinforcement in reinforced concrete “T” joint is based on the force transfer method proposed by Sritharan (2005). the gap shall be large enough so that it will not close during a seismic event.5.2. The gap thickness shall be based on the estimated ductility demand and corresponding plastic hinge rotation capacity. which is the summation of θp and θy.13.1.13.04 August 2010
Page 4.14.1 Delete the last sentence in second paragraph. The yield rotation.2.5. by the distance from the neutral axis of the section at the ultimate curvature to the edge of flare.
8.16. and D. φu = Ultimate curvature as defined in Article 8.75% of Ag shall be provided for CIP piles in SDCs B.1-1)
Where: Lp = Analytical plastic hinge length as determined in Equation 4.13.
4.14 .4 provisions for shear friction using the nominal material strength properties.15 Add the following paragraph: The column hinge shall be designed in accordance with the AASHTO LRFD Bridge Design Specifications Article 5. The thickness of the expansion joint filler shall allow the maximum column rotation without crushing the edge of the column concrete against the cap beam or footing.1 titled “Moment-Reducing Hinge Details for the Based of Bridge Columns” should be used.11. Add C8.2-22
WSDOT Bridge Design Manual M 23-50. The procedure is based on curvature analysis of the section and does not include bond slip and the deflection of the beam.6-3 (in. (2004).2. Longitudinal reinforcement shall be provided for the full length of pile unless approved by the WSDOT Bridge Design Engineer. To prevent the gap closure.).46
Column Shear Key Design for SDCs C and D
Guide Specifications Article 8.2 Minimum longitudinal reinforcement of 0. C.8.
Page 4.2.1: The required gap is determined using Caltrans procedure and the safety factor recommended by Chandane et al.14.47
Cast-in-Place and Precast Concrete Piles
Guide Specifications Article 8.45
4. the calculated gap thickness shall be multiplied by a factor of 3 to determine the required gap. The design procedure and hinge detail per TRAC Report WA-RD 220.5.04 August 2010
However. This policy balances the engineers responsibility to “safeguard life.04 August 2010
Page 4. The Legislature has established the priority of these and other programs. the widening can be designed and constructed without retrofitting existing seismically deficient bridge elements. This policy allows bridge widening projects to be completed without addressing existing seismic risks. A seismic analysis is not required for single-span bridges. This approach maintains the priorities that have been set by the Washington State Legislature. When the addition of the widening has insignificant effects on the existing structure elements. the requirements of the International Building Code (2009 IBC Section 3403. Bridge seismic risks are addressed through bridge seismic retrofit projects that are funded as part of the P2 . and set funding levels accordingly. existing elements of single span bridges shall meet the requirements of AASHTO Guide Specifications for LRFD Seismic Bridge Design Section 4. This policy is based on. However. In many cases. The IBC is the code used throughout the nation for design of most structures other than bridges.” (WAC 196-27A-020 (2)(a)). In this case. specifically when it comes to determining how to address elements of the existing structure that do not meet current design standards.4).3. existing elements of bridges in SDC A shall meet the requirements of AASHTO Guide Specifications for LRFD Seismic Bridge Design Section 4. If the widened capacity/demand ratios are decreased. retrofit of seismically deficient elements is recommended but not required.Mobility Program.6. health. provided “No Harm” is done to the existing structure.3-1
. the requirements of the IBC can be taken to provide an acceptable level of safety that meets the expectations of the public. and property” (WAC 196-27A-020) with their responsibility to “achieve the goals and objectives agreed upon with their client or employer.3-1) has been established to give bridge design engineers guidance on how and when to address structural deficiencies in existing bridges that are being widened.3 Seismic Design Requirements for Bridge Widening Projects
4. Thus. and validated by. A seismic analysis is not required for bridges in SDC A. adding less than 10% mass without new substructure could be considered insignificant. The objective of the I1-Mobility Program is to improve mobility… not to address seismic risks. the seismically deficient existing elements must be retrofitted as part of the widening project. The existing seismic risks are left to be addressed by a bridge seismic retrofit project. Widening elements (new structure) shall be designed to meet current WSDOT standards for new bridges. The decision to retrofit these elements is left to the Region and is based on funding availability. by accomplishing widening (mobility) projects without requiring that retrofit (preservation/ risk reduction) work be added to the scope. the seismic analysis may be waived with the WSDOT Bridge Design Engineer’s approval. Current versions of bridge design specifications/codes do not provide guidance on how to treat existing structures that are being widened. provided the existing structure is not made worse.Structures Preservation Program. This policy upholds the priorities established by the Legislature. If the capacity/demand ratio is not decreased.1 Seismic Analysis and Retrofit Policy
Widening of existing bridges is often challenging.
WSDOT Bridge Design Manual M 23-50.Chapter 4
4. This “Do No Harm” policy requires the bridge engineer to compare existing bridge element seismic capacity/demand ratios for the before widening condition to those of the after widening condition. The Seismic Analysis and Retrofit Policy for Bridge Widening Projects (Figure 4. Most widening projects are funded by the I1 .5.
LEGEND C/DPre = Existing Bridge Element Seismic Capacity Demand Ratio Before Widening C/DPost = Existing Bridge Element Seismic Capacity Demand Ratio After Widening NOTES 1. Generate C/DPre And C/DPost For All Applicable Existing Bridge Elements (Including Foundation Elements).0 No Revise Widening Design (Reduce Mass. Seismic analysis shall account for substandard details of the existing bridge.3-2 WSDOT Bridge Design Manual M 23-50.3-1 Page 4. C/D ratios are evaluated for each existing bridge element. Along With Final Project Scope To Bridge Management Group. (See Notes 1 and 2) Yes C/DPost 1.)
C/DPost C/DPre (See Note 3) Yes
Can Widening Design Be Revised to Result In C/DPost C/DPre No Seismic Performance Made Worse Retrofit Of Element Is Required
Prepare Preliminary Cost Estimates Including: • Widening Plus Recommended Seismic Retrofits Estimate (Widening + Required Seismic Retrofits + Optional Seismic Retrofits) • Base Widening Estimate (Widening + Required Seismic Retrofits) • Bridge Replacement Estimate (Only Required for Widening Projects With Required Seismic Retrofits)
Region Select From The Following Alternatives: • Widen Bridge And Perform Required & Optional Seismic Retrofits • Widen Bridge And Perform Required Seismic Retrofits • Replace Bridge • Cancel Project
Report C/DPre And C/Dpost Ratios. 2. This Information Will Be Used To Adjust The Status Of The Bridge In The Seismic Retrofit Program.3-1 WSDOT Seismic Analysis and Retrofit Policy for Bridge Widening Projects
Figure 4. Increase Stiffness. 3. Etc.
Figure 4.Seismic Design and Retrofit
WSDOT SEISMIC ANALYSIS & RETROFIT POLICY FOR BRIDGE WIDENING PROJECTS
Perform Seismic Analysis Of Existing And Widened Structure.04 August 2010
. Widening elements (new structure) shall be designed to meet current WSDOT standards for New Bridges.
bearing type(s).3. If there is a need for longitudinal restrainers. piers. For example.Chapter 4
4. Tolerance of the superstructure to lateral movement will depend on bridge seat widths. the new structure shall be designed to carry live loads independently at the Strength I limit state. • Safety. • Ride-ability. the type of foundation. relaxation. Where yielding is expected in the crossbeam connection at the Extreme Event limit state. Experience has shown that bridges can and often do accommodate more movement and/or rotation than traditionally allowed or anticipated in design. and the nature of soil (sand or clay). •	Foundation	Types The foundation type of the new structure should match that of the existing structure. • Aesthetics.
WSDOT Bridge Design Manual M 23-50. transverse restrainers or additional support length on the existing structure they shall be included in the widening design. Longitudinal joints between the existing and new structure are not permitted. a shaft foundation may be used in lieu of spread footing.3). Some studies have been made to synthesize apparent response.2
•	Support	Length The support length at existing abutments. Elements subject to inelastic behavior shall be designed and detailed to sustain the expected deformations. •	Differential	Settlement The allowable differential settlement of bridges depends on the type of construction. These studies indicate that angular distortions between adjacent foundations greater than 0. Horizontal movement criteria should be established at the top of the foundation based on the tolerance of the structure to lateral movement.008 (RAD) in simple spans and 0.004 (RAD) in continuous spans should not be permitted in settlement criteria (Moulton et al. The bridge designer shall evaluate. and redistribution of force effects accommodate these movements. Other angular distortion limits may be appropriate after consideration of: • Cost of mitigation through larger foundations. 1985. The geotechnical designer should evaluate the potential for differential settlement between the existing structure and widening structure. realignment or surcharge. Barker et al. However. a different type of foundation may be used for the new structure due to geotechnical recommendations or the limited space available between existing and new structures. DiMillio.2. 1991). structure type. The existing columns shall then be analyzed with the new un-braced length and retrofitted if necessary. with consideration of the column length and stiffness. The angular distortion appears to be the useful criteria for establishing the allowable limits. Additional geotechnical measures may be required to limit differential settlements to tolerable levels for both static and seismic conditions.12. In cases where large differential settlement and/or a liquefaction-induced loss of bearing strength are expected. The horizontal displacement of pile and shaft foundations shall be estimated using procedures that consider soil-structure interaction (see WSDOT Geotechnical Design Manual M 46-03 Section 8.04 August 2010
Page 4. and load distribution effects. Rotation movements should be evaluated at the top of the substructure unit (in plan location) and at the deck elevation.3-3
. Creep. 1982. and. •	Connections	Between	Existing	and	New	Elements Connections between the new elements and existing elements should be designed for maximum overstrength forces. •	Existing	Strutted	Columns The horizontal strut between existing columns may be removed. in-span hinges and pavement seats shall be checked. design and detail all elements of new and existing portions of the widening structure for the differential settlement warranted by the Geotechnical Engineer. the connections may be designed to deflect or hinge in order to isolate the two parts of the structure.
#18 #4 .090 0.04 August 2010
.0075 #18 0.#8 #9 #10 & #11
0. • Deformation capacities of existing bridge members that do not meet current detailing standards shall be determined using the provisions of Section 7.0075 0 .0150 0.0023 #8
0 .040 0.#18 #3 .#4 .00166
40 48 81
#3 .120 0.#10 0.0115 0 .120 0 .#4 .#18 0.0125 0.0050 #18 0 .3-4
WSDOT Bridge Design Manual M 23-50.090
Ultimate Ultimate tensile strain tensile strain
#11 #11 . • In lieu of specific data.090 0. • Joint shear capacities of existing structures shall be checked using Caltrans Bridge Design Aid.0193 0 . FHWA-HRT-06-032.0023
#3 . Deformation capacities of existing bridge members that meet current detailing standards shall be determined using the latest edition of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.0125 #10 & #11 0 .090 0 .090
Table 4.Seismic Design and Retrofit
•	Non-Structural	Element	Stiffness Median barrier and other potentially stiffening elements shall be isolated from the columns to avoid any additional stiffness to the system.0193
0.0050 0 .0023
#3 -#3 .00166
#3 #9 .0115 0 .090 0 .01150 .3.060
0 .#18 #3 .3.120 0 .#18 #3 .0150 0 .#18 0.#18
48 81 0.#10 0.060 0 .090 #11 .090
Table 4. ASTM ASTM A615 ASTM A615
Property Notation Bar Size A706 60 68 95 Grade 60 Grade 40 Specified Property fy minimum yield Notation stress (ksi) Specified minimum Expected yield y fƒye yield stress (ksi) stress (ksi) Expected yieldExpected ƒye stress (ksi) f ue tensile strength (ksi) Expected tensile ƒue strength (ksi) Expected yield ye strain Expected εye yield strain Onset of strain hardening Onset of strain hardening Reduced Reduced ultimate ultimate tensile tensile strain strain
#3 -Bar Size #18
ASTM A706 60 68
ASTM A615 ASTM A615 60 Grade 60 40 Grade 40
68 95 0.120 #10 #11 .2-1 Stress Properties of Reinforcing Steel Bars.01500 .#18 0.0075 #14 0 .0023 0.090 0.0050 0.#18 0 .0125 0 .0150 0.#18 95 #3 .0115 #14 0.040 0 .060 0 .2-1 should be used.060 #10 0.8 of the Retrofitting Manual for Highway Structures: Part 1 – Bridges.3.01250 .#18 0.
Page 4.0075 0.0050 #4 .090 0 . 14-4 BDM Chapter 4 Seismic Design and Retrofit Joint Shear Modeling Guidelines for Existing Structures. the reinforcement properties provided in Table 4.060 .2-1
0.060 0 .060 0.
Once seismically deficient bridge elements have been identified. and Appendices D thru F of the Seismic Retrofitting Manual shall be used in selecting and designing the seismic retrofit measures.4-1
.4.2. • Check the distribution of lateral forces. • Check the mode shapes and verify that structure movements are reasonable. supports. • Calculate fundamental and subsequent modes by hand and compare results with computer results.
WSDOT Bridge Design Manual M 23-50. Table 1-11. Are they consistent with column stiffness? Do small changes in stiffness of certain columns give predictable results?
4. and shall be included in the analysis. Make sure that all the structural components and connections correctly model the actual structure. 11. Seismic capacities shall be determined in accordance with the requirements of the Seismic Retrofitting Manual. Chapters 8. GTSTRUDL/SAP2000 directly calculates the percentage of mass participation. The WSDOT Bridge and Structure Office Seismic Specialist shall be consulted in the selection and design of the retrofit measures.4 Seismic Retrofitting of Existing Bridges
Earthquake Restrainers
Longitudinal restrainers shall be high strength bars in accordance with the requirements of Bridge Special provision BSP022604. • Increase the number of modes to obtain 90% or more mass participation in each direction.
4. 9. Seismic displacement and force demands shall be determined using the Multi-Mode Spectral Analysis of section 5.4.
4. The designer should use the following procedures for model verification: • Using graphics to check the orientation of all nodes. appropriate retrofit measures shall be selected and designed. such as support length. members.4. joint and member releases.1 General
Seismic retrofitting of existing bridges shall be performed in accordance with the FHWA publication FHWA-HRT-06-032. 10. Displacement capacities shall be determined by the Method D2 – Structure Capacity/Demand (Pushover) Method of Section 5. the seismic analysis need only be performed for the upper level (1000-year return period) ground motions with a Life Safety seismic performance level. Seismic Retrofitting Manual for Highway Structures: Part 1 – Bridges. The difference should be less than 5%.4. The initial analysis consists of generating capacity/demand ratios for all relevant bridge components.04 August 2010
Page 4.2 (at a minimum). Prescriptive requirements.4.4.4
Computer Analysis Verification
The computer results shall be verified to ensure accuracy and correctness. shall be considered a demand. • Check dead load reactions with hand calculations.6.2
Seismic Analysis Requirements
The first step in retrofitting a bridge is to analyze the existing structure to identify seismically deficient elements. For most WSDOT bridges.
.Seismic Design and Retrofit
AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO Guide Specifications for Structural Design of Sound Barriers – 1989 & Interims . Gravity Blocks.5-1
.04 August 2010
Page 4. Design per Chapter 3 of this manual .Chapter 4
Exceptions to the cases described above may occur with approval from the WSDOT Bridge Design Engineer and/or the WSDOT Geotechnical Engineer. Once the design acceleration is determined.1 General
All retaining walls shall include seismic design load combinations.5 Seismic Design Requirements for Retaining Walls
4. The design acceleration for retaining walls shall be determined in accordance with the AASHTO Guide Specifications for LRFD Seismic Bridge Design.5.000 yr map design acceleration . the designer shall follow the applicable design specification requirements listed below:
Wall Types Soldier Pile Walls With and Without Tie-Backs Pre-Approved Proprietary Walls Design Specifications AASHTO LRFD Bridge Design Specifications AASHTO LRFD Bridge Design Specifications or the AASHTO Standard Specifications for Highway Bridges17th Edition and 1.
WSDOT Bridge Design Manual M 23-50. AASHTO LRFD Bridge Design Specifications
Non-Preapproved Proprietary Walls Standard Plan Geosynthetic Walls Non-Standard Geosynthetic Walls Standard Plan Reinforced Concrete Cantilever Walls Non-Standard Non-Proprietary Walls Soil Nail Walls Standard Plan Noise Barrier Walls Non-Standard Noise Barrier Walls Pre-Approved and Standard Plan Moment Slabs for SE Walls and Geosynthetic Walls Non-Pre-Approved and Non-Standard Moment Slabs for SE Walls and Geosynthetic Walls Non-Standard Non-Proprietary Walls.
WSDOT Bridge Design Manual M 23-50.
. FHWAHRT-06-032. D. Saiidi. Vol. Bridge Design Aids 14-4 Joint Shear Modeling Guidelines for Existing Structures. and M. FHWA Seismic Retrofitting Manual for Highway Structures: Part 1-Bridges. “Improved Seismic Design Procedure for Concrete Bridge Joints”. 9. CCEER-03-08. 131. Chandane. “Static and Dynamic Performance of RC Bridge Bents with Architectural-Flared Columns.. University of Nevada. 4th Edition. 1st Edition. Caltrans. AASHTO Guide Specifications for LRFD Seismic Bridge Design. Sritharan. S. pp. September 2005. and Interims through 2009. January 2006.” Report No. 2009. 2004.04 August 2010
Page 4.99-1
. California Department of Transportation.99 References
AASHTO LRFD Bridge Design Specifications. August 2008.S. Journal of the Structural Engineering.
WSDOT Bridge Design Manual M 23-50. Reno. ASCE. Publication No. No. Sanders. 1334-1344.Chapter 4
.99-2
0.4 = 0.2Ts =
0.7 / 1.00 '' concrete cover on vertical faces at seat (inch) 1.75 = 0. Example 8.) 1. For new structures.05 design spectrum damping ratio 1.70 long period coefficient 0.00 ksi restrainer yield stress (ksi) 10.00 '' expansion joint gap (inch).08 sec
WSDOT Bridge Design Manual M 23-50. 0.75 short period coefficient 0.Appendix 4-B1
Design Example – Restrainer Design
Design Examples of Seismic Retrofits
FHWA-HRT-06-032 Seismic Retrofitting Manual for Highway Structures: Part 1 . use maximum estimated opening.2 * 0.04 August 2010
Page 4-B1-1
S DS = S D1 = As =
0.00 '' restrainer slack (inch) 5000.00 the stiffness of the more flexible frame (kips) (Frame 2) 2040 the stiffness of the less flexible frame (kips/in) (Frame 1) 510 the stiffness of the more flexible frame (kips/in) (Frame 2) 4.05 '' converge tolerance
"G" =
Fy = E = L = Drs = W1 = W2 = K1 = K2 =
F.00 Target displacement ductility of the frames 386.Bridges.S.00 '' Seat Width (inch) 2.28 effective peak ground acceleration coefficient
S DS S D1
Fa S s Fv S1
= 0.40 acceleration due to gravity (in/sec ) 0.000 restrainer modulus of elasticity (ksi) 18.1 Restrainer Design by Iterative Method
12.00 the weight of the less flexible frame (kips) (Frame 1) 5000.67 safety factor against the unseating of the span 176.00 ' restrainer length (ft.
T2. 3) the frequency ratio of modes.5 ) / PI() = 0.95 /( 4 ) ^ 0.00 sec.8 '' > = 4. eff = 510 / 4 = 127.4 = 4.0.68* 0.69 ''
Calculate Maximum Allowable Expansion Joint Displacement and compare to the available seat width.
T2.67 * 7 = 4.19 ^2* 2 *(1+ 2 )^2) = 0. eff
W1 gK1.19 cd = 1. 2 8 eff (1 12 2 2
2 )2 eff (1 12 = (8 * 0.0. eff D2 cd S a (T2.5 = 2 sec.69 ''
Restrainers are required
Page 4-B1-2
WSDOT Bridge Design Manual M 23-50.4 * 127. eff
0.Design Examples of Seismic Retrofits
Calculate Available seat width.65 '' 2 2 T2. S a (T1.2 ^2)^2 + 4* 0. eff
W2 gK 2.5 = 1 sec. The cross-correlation coefficient.19 + 1 ) + 0. Dr = 1 + 176 * 18 * 12 / 10000 = 4.5 / ( 40 * 0. eff ) g = ( 2 / ( 2*PI()))^2 * 0. K1.52 ''
>=2/3 Das = 4. eff D1 cd S a (T1.65 ^2 + 9.4 = 9.
The effective damping and design spectrum correction factor is: eff = 0.68* 0.
S a (T2. eff ) g = ( 1 / ( 2*PI()))^2 * 0.5 = 0.04 August 2010
.4 * 510) )^0. eff
2.5) )^0.1 .00
sec.2 * 2 = 7 '' as
0.699 0.3 ^2 .35 * 386.68 Determine the frame displacement from Design Spectrum T1.05 + ( 1 . eff
= 2 * PI() *( 5000 / ( 386.5 .3 ) ^ 0.5 kip/in The effective natural period of each frame is given by:
T1. eff = 2040 / 4 = 510 kip/in K 2.69 '' NG Compute expansion joint displacement without restrainers The effective stiffness of each frame are modified due to yielding of frames.2 * 0.3 ''
The relative displacement of the two frames can be calculated using the CQC combination of the two frame displacement as given by equation (Eq.05 * (4 ) ^ 0.19 ^2)*(1 + 2 )*( 2 ^(3/2))/((1 .2 * 4.65 * 9.2
The initial relative hinge displacement
Deq o
= ( 4. eff
= 2 * PI() *( 5000 / ( 386. D Das = 12 . eff ) =
Modified displacement for damping other than 5 percent damped bridges 2 T1.5 = 9.699 * 386. eff = 1.
T2.46 sec.12.94 * 12.21 .21 ) . set 1.4 = 12.21 = 188197.44 B m1 ( K 2.12.44*188197.397
It is customary to describe the normal modes by assigning a unit value to one of the amplitudes.57
2 2 = (-(-13249.52 = 50.21
kip/in (Input a value to start)
T1.5 ) / ( 510 + 127.78 rad/sec 1 = The corresponding natural periods are
0. For the first mode.5)/( 2*167. Sec / in K 2.21 ) = -13249.50
2 2 i )
A m1m2 = 12.52 K1.04 August 2010
Page 4-B1-3
.94 = 167. eff =
127.44) = 18.57 = -80. eff Kr m1
= 193.5)/(2*167. eff
K1.52)^2-4*167.31
rad/sec 1.40 1. r This can be achieve by using Goal Seek on the Tools menu.5 + ( 510 + 127. eff
The relative value (modal shape) corresponding
Kr K1.52) ^2-4* 167. Goal Seek Set Cell $J$104 Cell Address for Deq Dr To Value By Changing Cell $D$104 Cell address for initial guess Apply the Goal Seek every time you use the spreadsheet and Click OK
193. Sec / in kip.22 )^0. Frame 1 mass Frame 2 mass
K1.5 ) * 193.52) +(( -13249.22)^0.00 then -2.4 = 12.8 ) / 9.56
The natural frequencies are 7.40 11 = 21 = The mode shape for the first mode is
-2.44 * 188197.5 ) = 102 kip/in
= 102 * ( 9.Chapter 4
Estimate the Initial restrainer stiffness
K eff mod
K1.78 rad/sec 60.4. eff =
K1. eff
Kr ) = .94 * 60.57 1 = 2 m1 1 = 510 + 193.61 = -2.94 * ( 127.5 + 193. eff
m1 = 5000 / 386.94 m2 = 5000 / 386.00
WSDOT Bridge Design Manual M 23-50.22
The roots of this quadratic are 2 1 = (-( -13249. eff K eff mod ( Deqo Dr )
= ( 510 * 127.21 / -80. eff (K1. eff K 2.44 ) = 60.52 .81
sec. eff ) K r
= 510 * 127.00 ''
Calculate Relative Hinge Displacement from modal analysis. eff K 2.94 * ( 510 + 193.00 kip/in
kip. eff K 2.12.
For mode 1.54 kip/in
Adjust restrainer stiffness to limit the joint displacement to a prescribed value D . eff K r ) m2 ( K1.94
= 510. eff K 2.52-((-13249.
4 = -0. eff
-18.-2.56 2 = 510 + 193.94 * 1 + 12.96
( K 2.08 / 5286.4) ^2 .4 * 1 + ( 127. eff ) =
Page 4-B1-4
WSDOT Bridge Design Manual M 23-50.4 .21 .Design Examples of Seismic Retrofits
For mode 2.480
T2.94 * 1 = -18.2* 193.94 * 2. S a (T1. eff
{a}T { 1}
m2 21 2 K r ) 11
Determine the frame displacement from Design Spectrum T1.08
( K 2.4 = 3.
S a (T2.5 + 193.98 * 3.00 2. eff
= ( 510 + 193.21 ) * ( 2.1 = 1.
43.11 m1 2
4.21 * 1 * 2.4 = 0.81 sec.40
{ 1}T [ M ]{1} { 1} [ K ]{ 1}
({a}T { 1})
{ 1}T [ M ]{1} m1 11 { 1}T [ K ]{ 1} ( K1.21 ) * ( 1 ) ^2 = 5286. eff = 0.4 + 12.96 / 1619.53
{a}T { 2 }
2. set 12 = The mode shape for the 2nd mode is
2.04 August 2010
{ 2 }T [ M ]{1} { 2 } [ K ]{ 2 }
({a}T { 2 })
m1 12 { 2 } [ K ]{ 1} ( K1.867 0.31
Kr K1.46
1.56 = 2 463.98 1 .53 * 1.12.2* 193.4 ) ^2 = 1619.4 + ( 127.4 = 43.21 / 463. eff
{ 2 }T [ M ]{1}
m2 22 2 K r ) 12
For the 2nd mode.21 * -2. eff
= 193.5 + 193.21 ) * (-2. eff
= ( 510 + 193. eff
2 = rad/sec 18.
K1.21 ) * (1) ^2 .94 * -2.4 sec.11 = 0.4 sec. eff Kr
1.94 * 18.
64 ) * (4.00 ksi
( 193.8 = 0 ''
>4. eff T1.8 .77))^0.77)^2+2* 0.81 )^2) = 0. eff .8 ''
Dr = 4.19 ^2)*(1+ 1. eff .0116 * 0.4 = 4.80 '' 0.81 )*( 1.68 * 0.222 ) = 23.05) g
Deq 2 P2 cd S a (T2.26 * ( -2.21 * 4.64)^2 + ( 4. eff
= 176.8 ) / ( 176 * 0.5 = 4.81 = 1. 12 = (8 * 0.77 ''
T2.46 / 0.222
193.8 ''
Go to Step 7 and calculate the number of restrainers
Calculate number of restrainers
K r Dr Fy Ar
4.4.64 '' 0.68 * 0.74 restrainers
WSDOT Bridge Design Manual M 23-50.0.81 ^2)^2+4* 0. 0.81 *(1+1.48 * 386.0379 * 0.81
The cross-correlation coefficient.04 August 2010
Page 4-B1-5
Calculate new relative displacement at expansion joint
Deq1 P1cd S a (T1.26
OK Step 7:
= ( ( -2.81 ^(3/2))/((1 -1.4 = -2.05) g
-0.19 ^2* 1.867 * 386.
Page 4-B1-6
................................. To perform the pushover analysis in the longitudinal direction...........................3 Materials Modeling ...................................................... Note: By producing this example..... Brief Table of Contents of Example: 1.................................................6 2...1 Hinge Definitions and Assignments ............41 5.....................................73 5.......Appendix 4-B2
SAP2000 Seismic Analysis Example
1............1 Overview of Model ....................................... Introduction ..................... This example was created using SAP2000 version 14...................................................... The example does not relieve Design Engineers of their professional responsibility for the software’s accuracy and is not intended to do so...............4 Member Ductility Requirement Check .67 5...........1 Modal Analysis ................................................ Displacement Capacity Analysis ........................................................................................ Displacement Demand Analysis .............................. Model Setup .............................................2 2..........................................6 Balanced Stiffness and Frame Geometry Requirement Check ..................19 2..34 4........................... Design Engineers should verify all computer results with hand calculations........... the Washington State Department of Transportation does not warrant that the SAP2000 software does not include errors........................................ Introduction
This example serves to illustrate the procedure used to perform nonlinear static “pushover” analysis in both the longitudinal and transverse directions in accordance with the AASHTO Guide Specifications for LRFD Seismic Bridge Design using SAP2000............................66 5..22 3..........5 Crossbeam Modeling ............................................. Code Requirements ..............................................................69 5..............23 3. To perform the pushover analysis in the transverse direction...............................................................1 2....................83
WSDOT Bridge Design Manual August 2010
M 23-50............... The example bridge is symmetric and has three spans........................79 5.............................................................2 2................04
Page 4-B2-1
.........................................................................20 2.................................4 Column Modeling ..............................................32 4..........3 2......2 Foundations Modeling ......................................................27 3..............2...................................................................................................................................2 Response-Spectrum Analysis............................................1 P-Δ Capacity Requirement Check ...............................................................................................0........................................................15 2..... A full model of the bridge is used to compute the displacement demand from a response-spectrum analysis..........................7 Gravity Load Patterns ............................................................ the entire bridge is pushed in order to include the frame action of the superstructure and adjacent bents................2 Pushover Analysis ....................5 Column Shear Demand/Capacity Check ..........................6 Superstructure Modeling............34 4.................................3 Structure Displacement Demand/Capacity Check .............................................................23 3.........................3 Displacement Demand . a bent is isolated using the SAP2000 “staged construction” feature......... It is assumed the reader has some previous knowledge of how to use SAP2000................................................................................................................2 Minimum Lateral Strength Check ..............66 5.........................................
Wireframe 3-D View of Model
Figure 2. The X-axis is along the bridge’s longitudinal axis and the Z-axis is vertical. Shell elements are also used to model the end.1-1 shows a view of the model in SAP2000. The following summarizes the bridge being modeled: • All spans are 145’ in length • (5) lines of prestressed concrete girders (WF74G) with 9’-6” ctc spacing • 8” deck with 46’-11” to width • Girders are continuous and fixed to the crossbeams at the intermediate piers • (2) 5’ diameter columns at bents • Combined spread footings – 20’L x 40’W x 5’D at each bent • Abutment longitudinal is free. Model Setup
2. The superstructure is modeled using frame elements for each of the girders and shell elements for the deck. and pier diaphragms. The units used for inputs into SAP2000 throughout this example are kip-in.1 Overview of Model
This example employs SAP2000.04 August 2010
. intermediate. Non-prismatic frame sections are used to model the crossbeams since they have variable depth.SAP2000 Seismic Analysis Example
Page 4-B2-2
WSDOT Bridge Design Manual M23-50. transverse is fixed Figure 2.
These footings are modeled using springs.2.2.04 Page 4-B2-3
.1-2 shows the spread footing joint spring assignments (Assign menu > Joint > Springs).SAP2000 Seismic Analysis Example
Wireframe 2-D View of Bent
Figure 2.35.030.1-1.2.000. The spring values used in the model for the spread footings are shown in Table 2. Degree of Freedom UX UY UZ RX RY RZ Stiffness Value 18.
WSDOT Bridge Design Manual August 2010 M23-50. Rigid links connect the bases of the columns to a center joint that the spring properties are assigned to as shown in Figure 2.700 ksf and ν = 0. The assumed soil parameters were G = 1.2.000.1 Intermediate Piers
Each bent is supported by a combined spread footing that is 20’L x 40’W x 5’D.2.1-1
The soil springs were generated using the method for spread footings outlined in Chapter 7 of the Washington State Department of Transportation Bridge Design Manual.1-1
Joint Spring Values for Spread Footings Figure 2.2 Foundations Modeling
2.000 kip/in 1.810 kip/in 16.1-1.000 kip-in/rad 417.000 kip-in/rad 1.000 kip-in/rad
Table 2.178.2.820 kip/in 18.100.
please note that the AASHTO Guide Specifications for LRFD Seismic Bridge Design require the stiffness of the transverse abutments be modeled.2.2 Abutments
The superstructure is modeled as being free in the longitudinal direction at the abutments in accordance with the policies outlined in the Washington State Department of Transportation Bridge Design Manual.2. Degree of Freedom UX UY UZ RX RY RZ Fixity Free Fixed Fixed Free Free Free
Joint Fixity for Girder Joints at Abutments
Table 2.2. It is also be acceptable to conservatively use fixedbase columns for the capacity model. However.2-1
Page 4-B2-4
WSDOT Bridge Design Manual M23-50.1-2
The springs used in the demand model (response-spectrum model) are the same as the springs used in the capacity model (pushover model). the joints at the ends of the girders at the abutments all have joint restraints assigned to them. The girder joint restraint assignments at the abutments are listed in Table 2.2.2-1. The abutments are fixed in the transverse direction in this example for simplification.04 August 2010
. Since there are five girder lines instead of a spine element.SAP2000 Seismic Analysis Example
Spread Footing Joint Spring Assignments
M23-50.04
Page 4-B2-5
Girder Joint Restraint Assignments at Abutments
Figure 2.SAP2000 Seismic Analysis Example
Figure 2.2.2-1 shows the girder joint restraints at the abutments (Assign menu > Joint > Restraints).
3-1 (Define menu > Materials > select 4000Psi-Deck > click Modify/Show Material button). Section Property Used For Deck Crossbeams & Diaphragms Columns Girders Rebar Other Than Columns Column Rebar
Table 2. nonlinear properties of the column section. Please see the current WSDOT Bridge Design Manual and Bridge Design Memorandums.SAP2000 Seismic Analysis Example
2.3-1 lists the material definitions used in the model and the elements they are applied to (Define menu > Materials). The elastic moduli of the concrete materials used in this example are based on the Washington State Department of Transportation’s policy on concrete densities to be used in the calculations of elastic moduli.3-1
Material Name 4000Psi-Deck 4000Psi-Other 5200Psi-Column 7000Psi-Girder A706-Other A706-Column
Material Type Concrete Concrete Concrete Concrete Rebar Rebar
Material Unit Weight (pcf) For Dead For Modulus Load of Elasticity 155 150 150 150 165 490 490 145 145 155 -
Material Properties Used in Model The “5200Psi-Column” and “A706-Column” material definitions are created to define the expected.
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WSDOT Bridge Design Manual M23-50. The Material Property Data for the material “4000Psi-Deck” is shown in Figure 2. In Version 14 of SAP2000.3 Materials Modeling
SAP2000’s default concrete material properties have elastic moduli based on concrete densities of 144 psf. Table 2. nonlinear material properties for Caltrans sections are no longer defined in Section Designer and are now defined in the material definitions themselves.04 August 2010
Material Property Data for Material “4000Psi-Other”
The Material Property Data for the material “4000Psi-Other” is shown in Figure 2.SAP2000 Seismic Analysis Example
Material Property Data for Material “4000Psi-Deck”
Figure 2.04 Page 4-B2-7
WSDOT Bridge Design Manual August 2010 M23-50.3-2 (Define menu > Materials > select 4000Psi-Other > click Modify/Show Material button).
Page 4-B2-8
WSDOT Bridge Design Manual M23-50.SAP2000 Seismic Analysis Example
The Material Property Data for the material “7000Psi-Girder” is shown in Figure 2.3-3 (Define menu > Materials > select 7000Psi-Girder > click Modify/Show Material button).
Material Property Data for Material “7000Psi-Girder”
Figure 2.04 August 2010
3-4 is checked .3-5 opens.3-4
When the Switch To Advanced Property Display box shown in Figure 2.04
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By clicking the Modify/Show Material Properties button in Figure 2.3-5.
Advanced Material Property Options for Material “5200Psi-Column”
The Material Property Data for the material “5200Psi-Column” is shown Figure 2.
M23-50.
Material Property Data for Material “5200Psi-Column”
Figure 2.3-4 (Define menu > Materials > select 5200Psi-Column > click Modify/Show Material button). the window shown in Figure 2. the window shown in Figure 2.3-6 opens.
4 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.SAP2000 Seismic Analysis Example
Advanced Material Property Data for Material “5200Psi-Column”
Figure 2. the window shown in Figure 2.4. It is seen
Page 4-B2-10 WSDOT Bridge Design Manual M23-50.3-7
Note that in Figure 2.3-6.
Nonlinear Material Data for Material “5200Psi-Column”
. f’c and the Ultimate Unconfined Strain Capacity are set to the values required in Section 8.3-6
By clicking the Nonlinear Material Data button in Figure 2. These unconfined properties are parameters used in defining the Mander confined concrete stress-strain curve of the column core.3-7 the Strain At Unconfined Compressive Strength.3-7 opens.
3-8 shows both the confined and unconfined nonlinear stress-strain relationships. By clicking the Show Stress-Strain Plot button in Figure 2. The Material Property Data for the material “A706-Other” is shown in Figure 2.
M23-50. Mander is selected.
Material Stress-Strain Curve Plot for Material “5200Psi-Column”
Figure 2.3-8
Figure 2.3-9 (Define menu > Materials > select A706-Other > click Modify/Show Material button).SAP2000 Seismic Analysis Example
that under the Stress-Strain Definition Options.04
Page 4-B2-11
.3-8 is displayed.3-7. The user should verify that the concrete stress-strain curves are as expected. a plot similar to that shown Figure 2.
3-10 (Define menu > Materials > select A706-Column > click Modify/Show Material button).3-9
The Material Property Data for the material “A706-Column” is shown in Figure 2.04 August 2010
Page 4-B2-12 WSDOT Bridge Design Manual M23-50.
Material Property Data for Material “A706-Column”
Material Property Data for Material “A706-Other”
By clicking the Nonlinear Material Data button in Figure 2.
Advanced Material Property Options for Material “A706-Column”
Figure 2. Fy = 68 ksi and the Minimum Tensile Stress.
Advanced Material Property Data for Material “A706-Column”
Figure 2. the Fye and Fue inputs in SAP2000 do not serve a purpose for this analysis.2-1 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.4. SAP2000 uses Fy and Fu instead of Fye and Fue to generate the nonlinear stressstrain curve. the window shown in Figure 2. Fu = 95 ksi as required per Table 8.3-12.3-13 opens.3-11 opens. the Minimum Yield Stress.SAP2000 Seismic Analysis Example
When the Switch To Advanced Property Display box in Figure 2.
WSDOT Bridge Design Manual August 2010 M23-50.3-10 is checked.04 Page 4-B2-13
. Therefore.3-12. the window shown in Figure 2.3-11.3-12 opens.3-12
In Figure 2. the window shown in Figure 2.3-11
By clicking the Modify/Show Material Properties button in Figure 2.
the strain at which the stress begins to decrease is εRsu. which the user should verify for correctness.3-14
In Figure 2. Also the box for Use Caltrans Default Controlling Strain Values is checked.SAP2000 Seismic Analysis Example
Nonlinear Material Data for Material “A706-Column”
Page 4-B2-14 WSDOT Bridge Design Manual M23-50.3-14.3-13.3-14 is displayed.
Material Stress-Strain Curve Plot for Material “A706-Column” In Figure 2.3-13 the plot shown in Figure 2.04 August 2010
Figure 2. it is seen that under the Stress-Strain Curve Definitions Options. Park is selected. By clicking the Show Stress-Strain Plot button in Figure 2.
The columns are five feet in diameter and have (24) #10 bars for longitudinal steel. The columns are split into three frame elements. The net clear height of the columns is 29’-2”. Section 5.4 Column Modeling
There are two columns at each bent.4-1 shows the frame section property definition for the column elements (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button).
M23-50.SAP2000 Seismic Analysis Example
2. which amounts to a steel-concrete area ratio of about 1%.4-1
By clicking the Section Designer button in Figure 2.4. Figure 2.
Frame Section Property Definition for Frame Section “COL”
Figure 2. The column elements have rigid end offsets assigned to them at the footings and crossbeams. the window shown in Figure 2.04
Page 4-B2-15
.4-1.4-2 opens. The “COL” frame section is defined using a round Caltrans shape in Section Designer as shown in Figure 2.3 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design requires that columns be split into a minimum of three elements. the columns have confinement steel consisting of #6 spiral bars with a 3.5 inch spacing.4-2. In the hinge zones.
4-2.4-3 shows the parameter input window for the Caltrans shape is shown in Figure 2. Figure 2. the window shown in Figure 2.
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Section Designer View of Frame Section “COL”
By right-clicking on the section shown in Figure 2.04 August 2010
.4-2.4-3 opens.
By clicking the Show button for the Core Concrete in Figure 2.4-3.4-4 opens.04
Page 4-B2-17
M23-50. the window shown in Figure 2.SAP2000 Seismic Analysis Example
Caltrans Section Properties for Frame Section “COL”
4-4 shows the Mander confined stress-strain concrete model for the core of the column. The user should verify that the concrete stress-strain curve is as expected.
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Concrete Model for Core of Frame Section “COL”
An extruded view of the bent is shown in Figure 2.SAP2000 Seismic Analysis Example
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. The crossbeam elements have their insertion points set to the top center (Assign menu > Frame > Insertion Point).5 Crossbeam Modeling
The crossbeams are modeled as frame elements with non-prismatic section properties due to the variable depth of the sections (Define menu > Section Properties > Frame Sections).
Extruded 2-D View of Bent
M23-50.5-1. The pier diaphragm above the crossbeam is modeled with shell elements.
6-2 shows the girder frame element insertion point assignments (Assign menu > Frame > Insertion Point)./2 +3 in.SAP2000 Seismic Analysis Example
2.6 Superstructure Modeling
The girders are Washington State Department of Transportation WF74Gs.6-1
The girders are assigned insertion points such that they connect to the same joints as the deck elements but are below the deck.) above the top of the girder.
Frame Section Parameter Input for Frame Section “WF74G”
. the insertion point is 7 inches (8 in.6-1 (Define menu > Section Properties > Frame Sections > select WF74G > click Modify/Show Property button). Figure 2. Since the deck is 8 inches thick and the gap between the top of the girder and the soffit of the deck is 3 inches. The frame section definition for section “WF74G” is shown in Figure 2.
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WSDOT Bridge Design Manual M23-50.
3 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design requires that a minimum of four segments per span be used.6-3.6-3
The superstructure is broken into five segments per span.6-2
Links connect the girders to the crossbeams which models the fixed connection between these elements.
M23-50. Section 5.4. See the screen shot shown in Figure 2.SAP2000 Seismic Analysis Example
Girder Frame Element Insertion Point Assignments
Wireframe 3-D View of Bent and Superstructure Intersection
Page 4-B2-21
which is applied as an area load to the outermost deck shells.SAP2000 Seismic Analysis Example
The designer should verify the weight of the structure in the model with hand calculations.04 August 2010
.7-1 (Define menu > Load Patterns). The “DC-Barriers” case includes the dead load of the barriers. and “DWOverlay”. “DC-Barriers”.
Dead Load Pattern Definitions
Figure 2.7 Gravity Load Patterns
There are three dead load patterns in the model: “DC-Structure”. The dead load pattern definitions are shown Figure 2.
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WSDOT Bridge Design Manual M23-50. The “DC-Structure” case includes the self weight of the structural components. The “DW-Overlay” case includes the future overlay loads applied to the deck shells.
SAP2000’s Section Designer can be used to compute the effective section properties.1. there are situations where the inclusion of construction sequence effects will significantly alter the analysis.1-1
3. it is found that ICrack = 212. A display of the mass source definition window from SAP2000 is shown in Figure 3.1.044 inch4 (as calculated by SAP2000).907/628.2 Cracking of Columns
M23-50.1-1 (Define menu > Mass Source). However. the inclusion of staging effects would cause the axial load in the columns to vary by less than ten percent.044 = 0. Such a small change in axial load would not significantly alter the results of this analysis. Displacement Demand Analysis
3. For the bridge in this example. the ratio is 212.1.6 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design provides diagrams that can be used to determine the cracked section properties of the columns. the designer should verify that the method of calculation conforms to AASHTO Guide Specifications of LRFD Seismic Bridge Design. The gross moment of inertia is 628. If using Section Designer.250 kips without including the effects of the construction staging.1 Mass Source
All of the dead loads are considered as contributing mass for the modal load case.2-1 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve). The moment-curvature analysis is shown in Figure 3. However.1. By having Section Designer perform a moment-curvature analysis on the column section with an axial load of 1.04
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.SAP2000 Seismic Analysis Example
3.907 inch4. Therefore.250 kips.
Figure 3.1 Modal Analysis
3.34. Therefore.1. engineering judgment should be used when decided whether or not to include the effects of staging. The column axial dead load at mid-height is approximately 1.
2 for columns as required by Section 5.1. The property modifiers are then applied to the column frame elements as shown in Figure 3.
Page 4-B2-24 WSDOT Bridge Design Manual M23-50.2-2 (Assign menu > Frame > Property Modifiers). Designers should verify that SAP2000’s bilinearization is acceptable.
Frame Property Modification Factor for Column Frame Elements
Figure 3.6.5 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.04 August 2010
.1.SAP2000 Seismic Analysis Example
Moment Curvature Curve for Frame Section “COL” at P = -1250 kips
It can be seen in Figure 3.2-2
The torsional constant modifier is 0.2-1 that concrete strain capacity limits the available plastic curvature.1.
3.1.4. the mass is considered to be the same in both directions even though the end diaphragms are free in the longitudinal direction and restrained in the transverse direction. The Modal Participating Mass Ratios table is shown in Figure 3.1.3-1
3.1. By displaying the Modal Participating Mass Ratios table for the “MODAL” load case it is found that the X-direction (longitudinal) reaches greater than 90% mass participation on the first mode shape. while the Y-direction (transverse) reaches greater than 90% mass participation by the seventeenth mode shape.04
Page 4-B2-25
.1.4 Verification of Mass Participation
Section 5.3 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design requires a minimum of 90% mass participation in both directions. This implies that the minimum code requirements could be met by including only seventeen mode shapes.
Load Case Data for Load Case “MODAL”
Figure 3. For this example.4-1 (Display menu > Show Tables > check Modal Participating Mass Ratios > click OK button).3 Load Case Setup
The “MODAL” load case uses Ritz vectors and is defined in SAP2000 as shown in Figure 3.
M23-50.1.31 (Define menu > Load Cases > select MODAL > click Modify/Show Load Case button).
Page 4-B2-26
WSDOT Bridge Design Manual M23-50.4-1 also shows that the first mode in the X-direction (longitudinal) has a period of 0.1.04 August 2010
Modal Participating Mass Ratios for Load Case “MODAL”
Figure 3.95 seconds and the first mode in the Y-direction (transverse) has period of 0. The designer should verify fundamental periods with hand calculations. The designer should also visually review the primary mode shapes to verify they represent realistic behavior.61 seconds.1.
294 g A site class of E is assumed for this example and the site coefficients are: FPGA = 0. The mapped spectral acceleration coefficients are: PGA = 0.919 g SD1 = Fv*S1 = 0.
M23-50. Wash.82 Therefore. per Table 3.2-1 (Define menu > Functions > Response Spectrum > select SC-E > click Show Spectrum button).361 g SDS = Fa*Ss = 0.396 g Ss = 0.
3.1 Seismic Hazard
The bridge is located in Redmond.2 Response-Spectrum Input
The spectrum is defined from a file created using the AASHTO Earthquake Ground Motion Parameters tool.91 Fa = 1.5-1 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design the Seismic Design Category is D.830 g Since SD1 is greater than or equal to 0.883 g S1 = 0.2 Response-Spectrum Analysis
Page 4-B2-27
. A screen shot of the response-spectrum as inputted in SAP2000 is shown in Figure 3.2.SAP2000 Seismic Analysis Example
3.04 Fv = 2. the response-spectrum is generated using the following parameters: As = FPGA*PGA = 0.50.2.
the function appears as shown in Figure 3.2.2-1
When the Convert to User Defined button is clicked.2.2-2.
Response Spectrum Function Definition for Function “SC-E”
Figure 3.SAP2000 Seismic Analysis Example
Response Spectrum Function Definition from File for Function “SC-E”
Figure 3.2.04 August 2010
Page 4-B2-28
Having the response-spectrum function stored as “User Defined” is advantageous because the data is stored within the .2-1 (Define menu > Load Cases > select EY > click Modify/Show Load Case button).2.
Load Case Data for Load Case “EX”
Figure 3. if the .1 Longitudinal Direction
The load case data for the X-direction is shown in Figure 3.2.3 Load Case Setup
Two response-spectrum analysis cases are setup in SAP2000: one for each orthogonal direction.2.3. the response-spectrum function will also be moved.2.3.2.3.3.2. Therefore.2 Transverse Direction
The load case data for the Y-direction is shown Figure 3.04
Page 4-B2-29
3.SDB file.
3.SDB file is transferred to a different location (different computer).3.1-1 (Define menu > Load Cases > select EX > click Modify/Show Load Case button).
3.4.2.4.00 inches.2-1
3. which is located at the top of a column.2.
Page 4-B2-30
Load Case Data for Load Case “EY”
3.4 Response-Spectrum Displacements
The column displacements in this example are tracked at Joint 33.48 inches and U2 = 0.1 Longitudinal Direction
The horizontal displacements at the tops of the columns from the EX analysis case are U1 = 7.2. This is shown in Figure 3. all of the columns have the same displacements in the response-spectrum analyses.1-1 as displayed in SAP2000 (Display menu > Show Deformed Shape > select EX > click OK button).04 August 2010
.2. Since the bridge is symmetric.
4.2 Transverse Direction
The horizontal displacements at the tops of the columns from the EY analysis case are U1 = 0.2.2.1-1
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.55 inches.2-1 as displayed in SAP2000 (Display menu > Show Deformed Shape > select EY > click OK button).2.4.SAP2000 Seismic Analysis Example
Joint Displacement at Joint 33 for Load Case “EX”
M23-50.17 inches and U2 = 3. This is shown in Figure 3.4.
Joint Displacement at Joint 33 for Load Case “EY”
903 = 1.
3.19 > 1.19) + 1/6 = 1.61 = 1. The displacements are tracked as Joint 33.2 Transverse Direction
Compute magnification for the Y-direction (Transverse): TTrans T* / TTrans Rd_Trans = 0.04 August 2010
.16 (Assume μD = 6)
3.95 = 1.13 / 0.919 = 0.1.3.4) = 1.25 * 0.13 / 0.0 => Magnification is required = (1 – 1/μD) * (T* / T) + 1 / μD = (1 – 1/6) * (1.85 > 1.4) = 1.1.61 sec.25 Ts = 1.830 / 0.13 sec.3.3 Displacement Demand
3.0 => Magnification is required = (1 – 1/μD) * (T* / T) + 1 / μD = (1 – 1/6) * (1.3 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design. (see section 3. Compute Ts and T*: Ts = SD1 / SDS = 0.4 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design requires that 100% plus 30% of the displacements from each orthogonal seismic load case be combined to determine the displacement demands.903 sec. which is located at the top of a column.3. (see section 3.
Page 4-B2-32
WSDOT Bridge Design Manual M23-50. = 1.1.2 Column Displacement Demand
Section 4.95 sec.1.1 Displacement Magnification
Displacement magnification must be performed in accordance with Section 4.85) + 1/6 = 1.3.SAP2000 Seismic Analysis Example
3.3.71 (Assume μD = 6)
3.1 Longitudinal Direction
Compute magnification for the X-direction (Longitudinal): TLong T* / TLong Rd_Long = 0.
48 + 0.3 * 1.3 * Rd_Long * 0.16 * 0.1 Longitudinal Direction
For the X-direction (100EX + 30EY): UX (due to EX) = 7.1. ΔLD_Trans = 1.0 * 1. => This is the Displacement Demand for the Y-Dir
M23-50.17 = 8.55 + 0.07 in.71 * 3.17 in. UY (due to EX) = 0.3.00 = 6.48 in.2 Transverse Direction
For the Y-direction (100EY + 30EX): UY (due to EY) = 3.SAP2000 Seismic Analysis Example
3.3. Therefore.1.16 * 7.71 * 0. UX (due to EY) = 0.3 * Rd_Trans * 0.00 = 1.17 = 1.00 in.76 in.48 + 0. ΔLD_Long = 1.3 * 1.0 * Rd_Long * 7.55 + 0.0 * 1. Therefore.04
Page 4-B2-33
.55 in. => This is the displacement demand for the X-Dir
3.0 * Rd_Trans * 3.
4. which means the columns will exhibit behavior similar to a fixed-fixed column.1.1.1-1
From the axial loads displayed for the DC+DW load case it is determined that the axial force at the bottom of the column is approximately 1. which will not be true for most bridges.1 Plastic Hinge Definitions and Assignments
4.2 of this example for a discussion on the inclusion of construction sequence effects on column axial loads).
Page 4-B2-34
WSDOT Bridge Design Manual M23-50. on some bridges the axial loads at the tops and bottoms of the columns may be substantially different or the column section may vary along its height producing significantly different plastic moments at each end.1. However.1 Column Inflection Points
The tops and bottoms of all columns have enough moment fixity in all directions to cause plastic hinging. Figure 4. Due to the symmetry of the bridge in this example.04 August 2010
. Displacement Capacity Analysis
4. The plastic moment capacities of the columns under dead loads will be used to approximate the location of the column inflection points.290 kips and the axial force at the top of the column is approximately 1. the axial loads (due to dead load) at the top and bottom of the columns must be determined. Therefore.1.
Frame Axial Force Diagram for Load Case “DC+DW”
Figure 4. the axial loads are the same for all of the columns.210 kips (see section 3.1-1 shows the axial force diagram for the DC+DW load case as displayed in SAP2000 (Display menu > Show Forces/Stresses > Frames/Cables > select DC+DW > select Axial Force > click OK button). It is expected that the difference in axial load between the tops and bottoms of the columns will not result in a significant difference in the plastic moment.
Moment Curvature Curve for Frame Section “COL” at P = -1290 kips
Figure 4.1.SAP2000 Seismic Analysis Example
The moment-curvature analysis of the column base is shown in Figure 4.04
Page 4-B2-35
.1-2 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve).1-2 that the plastic moment capacity at the base of the column is 79.186 kip-inches (with only dead load applied). The moment-curvature analysis of the column top is shown in Figure 4.1-2
It is seen in Figure 4.1.1.1.1-3 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve).
Moment Curvature Curve for Frame Section “COL” at P = -1210 kips
It is seen in Figure 4.1.1-3 that the plastic moment capacity at the top of the column is 77,920 kip-inches (with only dead load applied). The clear height of the columns is 350 inches; therefore: L1 = Length from point of maximum moment at base of column to inflection point (in.) = 350 x Mp_col_base / (Mp_col_base + Mp_col_top) = 350 x 79186 / (79186 + 77920) = 176 in. = Length from point of maximum moment at top of column to inflection point (in.) = 350 – L1 = 350 – 176 = 174 in.
4.1.2 Plastic Hinge Lengths
The plastic hinge lengths must be computed at both the tops and bottoms of the columns using the equations in Section 4.11.6 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design. The hinge length is computed as follows: Lp
Page 4-B2-36
= 0.08L + 0.15fyedbl ≥ 0.3fyedbl
WSDOT Bridge Design Manual M23-50.04 August 2010
Where: L = length of column from point of maximum moment to the point of moment contraflexure (in.) = L1 at the base of the columns (L1Long = L1Trans = 176 in.) = L2 at the top of the columns (L2Long = L2Trans = 174 in.) = expected yield strength of longitudinal column reinforcing steel bars (ksi) = 68 ksi (ASTM A706 bars). = nominal diameter of longitudinal column reinforcing steel bars (in.) = 1.27 in. (#10 bars) = Plastic hinge length at base of column = 0.08*176 + 0.15*68*1.27 ≥ 0.3*68*1.27 = 27.03 ≥ 25.91 = 27.0 in. = Plastic hinge length at top of column = 0.08*174 + 0.15*68*1.27 ≥ 0.3*68*1.27 = 26.87 ≥ 25.91 = 26.9 in.
fye dbl Lp1
In this example, the plastic hinge lengths in both directions are the same because the locations of the inflection points in both directions are the same. This will not always be the case, such as when there is a single column bent.
4.1.3 Assign Plastic Hinges
In order to assign the plastic hinges to the column elements, the relative locations of the plastic hinges along the column frame elements must be computed. For the bases of the columns: Relative Length = [Footing Offset + (Hinge Length / 2)] / Element Length = [30 + (27.0 / 2)] / 146 = 0.30 For the tops of the columns: Relative Length = [Element Length – Xbeam Offset – (Hinge Length / 2)] / Element Length = [146 – 58 – (26.9 / 2)] / 146 = 0.51 The hinges at the bases of the columns are assigned at relative distances as shown in Figure 4.1.3-1 (Assign menu > Frame > Hinges).
Page 4-B2-37
Frame Hinge Assignments for Column Bases
By selecting the Auto P-M3 Hinge Property in Figure 4.1.3-1 and clicking the Modify/Show Auto Hinge Assignment Data button, the window shown in Figure 4.1.3-2 opens. Figure 4.1.32 shows the Auto Hinge Assignment Data form with input parameters for the hinges at the bases of the columns in the longitudinal direction. Due to the orientation of the frame element local axes, the P-M3 hinge acts in the longitudinal direction.
Auto Hinge Assignment Data for Column Bases in Longitudinal Direction
By selecting the Auto P-M2 Hinge Property in Figure 4.1.3-1 and clicking the Modify/Show Hinge Assignment Data button in Figure 4.1.3-1, the window shown in Figure 4.1.3-3 opens. Figure 4.1.3-3 shows the Auto Hinge Assignment Data form with input parameters for the hinges at the bases of the columns in the transverse direction. Due to the orientation of the frame element local axes, the P-M2 hinge acts in the transverse direction.
Page 4-B2-38
In Figures 4.1.34 (Assign menu > Frame > Hinges).3-5 opens. the Use Idealized (Bilinear) Moment-Curvature Curve box is checked. and the Drops Load After Point E option is selected. the window shown in Figure 4.1. Figure 4. the P-M3 hinge acts in the longitudinal direction.04
Page 4-B2-39
. The hinges at the tops of the columns are assigned at relative distances as shown in Figure 4.1.3-4 and clicking the Modify/Show Auto Hinge Assignment Data button.1.1.0 inches. Due to the orientation of the frame element local axes.1.3-4
By selecting the Auto P-M3 Hinge Property in Figure 4.35 shows the Auto Hinge Assignment Data form with input parameters for the hinges at the tops of the columns in the longitudinal direction.
Frame Hinge Assignments for Column Tops
M23-50.1.SAP2000 Seismic Analysis Example
Auto Hinge Assignment Data for Column Bases in Transverse Direction
Figure 4.3-2 and 4.3-3 it is seen that the Hinge Length is set to 27.1.
1. the Use Idealized (Bilinear) Moment-Curvature Curve box is checked.
Page 4-B2-40
Auto Hinge Assignment Data for Column Tops in Longitudinal Direction
Figure 4.1.3-6 opens.3-5
By selecting the Auto P-M2 Hinge Property in Figure 4.3-6 it is seen that the Hinge Length is set to 26.
Auto Hinge Assignment Data for Column Tops in Transverse Direction
Figure 4. Figure 4.1.04 August 2010
.3-5 and 4.1.1.1. the P-M2 hinge acts in the transverse direction. the window shown in Figure 4.1.9 inches.3-6
In Figures 4.3-4 and clicking the Modify/Show Hinge Assignment Data button.3-6 shows the Auto Hinge Assignment Data form with input parameters for the hinges at the tops of the columns in the transverse direction. and the Drops Load After Point E option is selected. Due to the orientation of the frame element local axes.
1.2.1.2 Transverse Direction
The lateral load distribution used in this example for the pushover analysis in the transverse direction consists of a horizontal load applied at the equivalent of the centroid of the superstructure. Figure 4. This load distribution is used to mimic a direct horizontal acceleration on the superstructure mass.1 Lateral Load Distributions
4.1. A special load pattern must be created for the column dead loads since the entire structure is not in place during the pushover analysis. The load is applied this way because the bent is isolated using staged construction and the superstructure is not present for the transverse pushover load case. Also.2 Pushover Analysis
4.1.2. The column dead load moments in the transverse direction are small and can be neglected.
M23-50.2.
“Dead-Col_Axial” Load Pattern Definition
The column axial loads are 1. the dead load can be applied as previously defined since the entire structure is present during the pushover analysis. a lateral load distribution proportional to the fundamental mode shape in the transverse direction is also acceptable provided that at least 75% of the structure mass participates in the mode.
4. It should be noted that a lateral load distribution proportional to the fundamental mode shape in the longitudinal direction is also acceptable provided that at least 75% of the structure mass participates in the mode.2.2.SAP2000 Seismic Analysis Example
4.2-1 (Define menu > Load Patterns).1. A new load pattern called “Dead-Col_Axial” is added as shown in Figure 4.1 Longitudinal Direction
The lateral load distribution used in this example for the pushover analysis in the longitudinal direction is a direct horizontal acceleration on the structure mass. As mentioned above. This recommendation is derived from provisions in FEMA 356: Prestandard and Commentary for the Seismic Rehabilitation of Buildings.2.04
Page 4-B2-41
.2-2 shows the joint forces assignment window for the “Dead-Col_Axial” load pattern (Assign menu > Joint Loads > Forces).250 kips (average of top and bottom).
1.1.2.2-4 (Define menu > Load Patterns).1.2-2 have been assigned.1.SAP2000 Seismic Analysis Example
Joint Force Assignment for Load Pattern “Dead-Col_Axial”
Wireframe View of Assigned Forces for Load Pattern “Dead-Col_Axial”
Page 4-B2-42
WSDOT Bridge Design Manual M23-50. they can be viewed as shown in Figure 4.2-3.1. a new load pattern called “Trans_Push” is added as shown in Figure 4.2-3
To define the transverse pushover analysis lateral load distribution.2.2.2.04 August 2010
After the forces defined in Figure 4.
2. there is no joint in the plane of the bent located at the centroid of the superstructure.83 = 5.
M23-50. The centroid of the superstructure is located 58. the load distribution for the transverse pushover analysis is an equivalent horizontal load consisting of a point load and a moment applied at the center crossbeam joint. As a result.1.2.1.04
Page 4-B2-43
.2-6. The joint forces are assigned to the crossbeam center joint as shown in Figure 4.2.2-5 have been assigned.1.1.1.SAP2000 Seismic Analysis Example
“Trans_Push” Load Pattern Definition
Figure 4.2.883 kip-inches is used.2-5 (Assign menu > Joint Loads > Forces).2-5
After the forces defined in Figure 4.83 inches above the center joint. they can be viewed as shown in Figure 4. Therefore.
Joint Force Assignment for Load Pattern “Trans_Push”
Figure 4. a joint force with a horizontal point load of 100 kips and a moment of 100*58.2.2-4
Since the superstructure is not defined as a spine element. Special care should be taken to ensure that the shear and moment are applied in the proper directions.
1 Longitudinal Direction
The dead load (DC+DW) must be applied prior to performing the pushover analysis. another load case can continue from it with the loads stored in the structure.2.2 Load Case Setup
4. a new load case is created called “LongPushSetup”.2-6
4. In this load case.
Page 4-B2-44
WSDOT Bridge Design Manual M23-50.2.2. By running the load case as a nonlinear analysis type.1-1 (Define menu > Load Cases > select LongPushSetup > click Modify/Show Load Case button). the dead load (DC+DW) is applied and the case is run as a nonlinear analysis.2.1.04 August 2010
. The Load Case Data form for the “LongPushSetup” load case is shown in Figure 4.2.2. To do so in the longitudinal direction.SAP2000 Seismic Analysis Example
Wireframe View of Assigned Forces for Load Pattern “Trans_Push”
A new load case is now created called “LongPush”.1-1
It is seen in Figure 4.2.2. the Load Case Type is Static.2. The Load Case Data form for the “LongPush” load case is shown in Figure 4.2.1-2 (Define menu > Load Cases > select LongPush > click Modify/Show Load Case button). and the Geometric Nonlinearity Parameters are set to None.2.SAP2000 Seismic Analysis Example
Load Case Data for Load Case “LongPushSetup”
Figure 4. the Analysis Type is set to Nonlinear.04
Page 4-B2-45
M23-50. which will actually be the pushover analysis case.1-1 that the Initial Conditions are set to Zero Initial Conditions – Start from Unstressed State.
2.2.2.1-2.1-2 that the Initial Conditions are set to Continue from State at End of Nonlinear Case “LongPushSetup”. the window shown in Figure 4.
Load Application Control for Load Case “LongPush”
Figure 4.2. and the Geometric Nonlinearity Parameters are set to None. the Load Type is set to Accel in the UX direction with a Scale Factor equal to -1. the Load to a Monitored Displacement Magnitude of value is set at 11 inches which is greater than the longitudinal displacement demand of 8.2. the Load Case Type is Static. Applying the acceleration in the negative X-direction results in a negative base shear and positive X-direction displacements.04 August 2010
. the Analysis Type is Nonlinear.1-3 opens. By clicking the Modify/Show button for the Load Application parameters in Figure 4.2.1-3
Page 4-B2-46
WSDOT Bridge Design Manual M23-50. It is seen in Figure 4.1-3 that the Load Application Control is set to Displacement Control.SAP2000 Seismic Analysis Example
Load Case Data for Load Case “LongPush”
Figure 4.2. Under Loads Applied.2. the DOF being tracked is U1 at Joint 33.2.2.76 inches.2.2. Also.1-2
It is seen in Figure 4.
Also.1-4 opens.2. Figure 4.2.1-2. and one to apply the column axial loads.04
Page 4-B2-47
By clicking the Modify/Show button for the Results Saved in Figure 4.2.2.1-4
4. a single bent will be isolated using staged construction prior to performing the pushover analysis. Note these two stages could be
M23-50. The “TransPushSetup” analysis case has two stages.2. To do so.2.2-1 shows the Group Definition for the group “Pier2” (Define menu > Groups > select Pier2 > click Modify/Show Group button).
Results Saved for Load Case “LongPush”
Figure 4. It is seen in Figure 4.2.2-1
To isolate the bent and apply the static loads to the columns. one to isolate the bent.1-4 that the Results Saved option is set to Multiple States. the window shown in Figure 4. However.2.2.2.
Group Definition for Group “Pier2”
Figure 4.2. for the transverse direction.2. the dead load must be applied prior to performing the pushover analysis in the transverse direction. the elements at Pier 2 are selected and then assigned to a group (Assign menu > Assign to Group).2. the Save positive Displacement Increments Only box is checked.2 Transverse Direction
As with the longitudinal direction. a staged construction load case called “TransPushSetup” is created (Define menu > Load Cases > select TransPushSetup > click Modify/Show Load Case button). which ensures that a step will occur for at least every half-inch of displacement. the Minimum Number of Saved States is set to 22.2.
.2-3.2-2.2.2. the Initial Conditions are set to Zero Initial Conditions – Start from Unstressed State.
Stage 1 Load Case Data for Load Case “TransPushSetup”
Figure 4. Stage 2 of the “TransPushSetup” load case definition is shown in Figure 4.SAP2000 Seismic Analysis Example
combined into one stage without altering the results.2-2
It is seen in Figure 4.2.2. the Load Case Type is Static.
Page 4-B2-48
WSDOT Bridge Design Manual M23-50. Stage 1 of the “TransPushSetup” load case definition is shown in Figure 4.2-2 that the only elements added are those in the group “Pier2”. the Analysis Type is set to Nonlinear Staged Construction. and the Geometric Nonlinearity Parameters are set to None.2.2.2.2.
It is seen in Figure 4.2-4 (Define menu > Load Cases > select TransPush > click Modify/Show Load Case button).04
Page 4-B2-49
. which will actually be the pushover analysis case.2. A new load case is now created called “TransPush”.2. The Load Case Data form for the “TransPush” load case is shown in Figure 4.2-3 that the load pattern “Dead-Col_Axial” is applied.
M23-50.2.2.2.2.SAP2000 Seismic Analysis Example
Stage 2 Load Case Data for Load Case “TransPushSetup”
Page 4-B2-50
WSDOT Bridge Design Manual M23-50.2.2.2-4 that the Initial Conditions are set to Continue from State at End of Nonlinear Case “TransPushSetup”. the Load to a Monitored Displacement Magnitude of value is set at 10 inches.2. By clicking the Modify/Show button for the Load Application parameters in Figure 4. which is larger than the transverse displacement demand of 6. the DOF being tracked is U2 at Joint 33.2.2. the Analysis Type is Nonlinear. the window shown in Figure 4.2. Also. and the Geometric Nonlinearity Parameters are set to None.07 inches.2-4.2-5 that the Load Application Control is set to Displacement Control.
Load Application Control for Load Case “TransPush”
Figure 4.04 August 2010
. It is seen in Figure 4.2.2. Under Loads Applied.2-5 opens.2-4
It is seen in Figure 4. the Load Case Type is Static.2.2.2.2. the Load Type is set to Load Pattern with the Load Name set to Trans_Push and the Scale Factor is equal to 1.SAP2000 Seismic Analysis Example
Load Case Data for Load Case “TransPush”
the Minimum Number of Saved States is set to 20. which ensures that a step will occur for at least every half-inch of displacement.2.2-6 opens.2.3 Load Case Results
4.2.3.2. Also.2.3.2-6 that the Results Saved option is set to Multiple States.2-4.2.1-1
WSDOT Bridge Design Manual August 2010 M23-50.
Pushover Curve for Load Case “LongPush”
4. the Save positive Displacement Increments Only box is checked.
Results Saved for Load Case “TransPush”
Figure 4. The point on the curve where the base shear begins to decrease indicates the displacement at which the first plastic hinge reaches its curvature limit state and is the displacement capacity of the structure.2.2.1 Longitudinal Direction The system pushover curve for the longitudinal direction is shown in Figure 4.SAP2000 Seismic Analysis Example
By clicking the Modify/Show button for the Results Saved in Figure 4.2.3. It is seen in Figure 4.04 Page 4-B2-51
.2.2.2. the window shown in Figure 4.1-1 (Display menu > Show Static Pushover Curve).
Figures 4. the colors are discretized evenly along the plastic deformation.1-2
Page 4-B2-52
WSDOT Bridge Design Manual M23-50.3. “LS”.2.3.3.2. However.
View of Deformed Shape for the Load Case “LongPush” at UX = 0. Note that the plastic hinge color scheme terms such as “IO”. for Caltrans plastic hinges.04 August 2010
Figure 4.2.1-13 show the deformed shape of the structure at various displacements for the load case “LongPush” (Display menu > Show Deformed Shape > select LongPush > click OK button). the color scheme still provides a visual representation of the hinge plastic strain progression that is useful.1-2 through 4.0 in. Therefore. and “CP” are in reference to performance based design of building structures.
M23-50.3.
Page 4-B2-53
.3 in.2.8 in.
View of Deformed Shape for the Load Case “LongPush” at UX = 2.3.2.SAP2000 Seismic Analysis Example
View of Deformed Shape for the Load Case “LongPush” at UX = 2.
5 in.1-5
View of Deformed Shape for the Load Case “LongPush” at UX = 4.2.
Page 4-B2-54
Figure 4.2.4 in.3.SAP2000 Seismic Analysis Example
View of Deformed Shape for the Load Case “LongPush” at UX = 3.3.
View of Deformed Shape for the Load Case “LongPush” at UX = 4.1-8
M23-50.3.04
Page 4-B2-55
Figure 4.2.9 in.3.9 in.1-7
View of Deformed Shape for the Load Case “LongPush” at UX = 5.2.
Figure 4.2.9 in.04 August 2010
View of Deformed Shape for the Load Case “LongPush” at UX = 6.
Figure 4.2.1-9
View of Deformed Shape for the Load Case “LongPush” at UX = 7.9 in.3.3.1-10
Page 4-B2-56
9 in.1-12
View of Deformed Shape for the Load Case “LongPush” at UX = 9.2.SAP2000 Seismic Analysis Example
View of Deformed Shape for the Load Case “LongPush” at UX = 8.2.3.04
Page 4-B2-57
3.SAP2000 Seismic Analysis Example
View of Deformed Shape for the Load Case “LongPush” at UX = 10.7 in.2.04 August 2010
Page 4-B2-58
WSDOT Bridge Design Manual M23-50.3.1-13
4.3.2-1 (Display menu > Show Static Pushover Curve).2. The point on the curve where the base shear begins to decrease indicates the displacement at which the first plastic hinge reaches its curvature limit state and is the displacement capacity of the structure.
Figure 4.2.2 Transverse Direction
The system pushover curve for the transverse direction is shown in Figure 4.
for Caltrans plastic hinges.2-2 through 4. Note that the plastic hinge color scheme terms such as “IO”. Therefore.3.3.SAP2000 Seismic Analysis Example
Pushover Curve for Load Case “TransPush”
Figure 4.2-13 show the deformed shape of the structure at various displacements for the load case “TransPush” (Display menu > Show Deformed Shape > select TransPush > click OK button).2.04
Page 4-B2-59
M23-50.2-1
Figures 4. the color scheme still provides a visual representation of the hinge plastic strain progression that is useful.2.2. the colors are discretized evenly along the plastic deformation. and “CP” are in reference to performance-based design of building structures. “LS”.
Page 4-B2-60
WSDOT Bridge Design Manual M23-50.2.3.3.0 in.SAP2000 Seismic Analysis Example
View of Deformed Shape for the Load Case “TransPush” at UY = 0.2-2
View of Deformed Shape for the Load Case “TransPush” at UY = 2.
Figure 4.0 in.04 August 2010
1 in.3.8 in.2-4
View of Deformed Shape for the Load Case “TransPush” at UY = 3.04
Page 4-B2-61
M23-50.3.2.
Figure 4.SAP2000 Seismic Analysis Example
3.6 in.1 in.2-7
Page 4-B2-62
View of Deformed Shape for the Load Case “TransPush” at UY = 5.
View of Deformed Shape for the Load Case “TransPush” at UY = 4.
View of Deformed Shape for the Load Case “TransPush” at UY = 6.2-8
View of Deformed Shape for the Load Case “TransPush” at UY = 7.04
Page 4-B2-63
Figure 4.2.2.6 in.
Figure 4.1 in.3.
View of Deformed Shape for the Load Case “TransPush” at UY = 7.6 in.
Figure 4.2.3.2-10
View of Deformed Shape for the Load Case “TransPush” at UY = 8.1 in.
Figure 4.2.3.2-11
Page 4-B2-64
View of Deformed Shape for the Load Case “TransPush” at UY = 8.6 in.
Figure 4.2.3.2-12
View of Deformed Shape for the Load Case “TransPush” at UY = 9.5 in.
Figure 4.2.3.2-13
Page 4-B2-65
5.1 P-Δ Capacity Requirement Check
The requirements of section 4.11.5 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be satisfied or a nonlinear time history analysis that includes P-Δ effects must be performed. The requirement is as follows: PdlΔr Where: Pdl Δr = unfactored dead load acting on the column (kip) = 1,250 kips = relative lateral offset between the point of contraflexure and the furthest end of the plastic hinge (in.) = ΔLD / 2 (Assumed since the inflection point is located at approximately mid-height of the column. If the requirements are not met, a more advanced calculation of Δr will be performed) = idealized plastic moment capacity of reinforced concrete column based upon expected material properties (kip-in.) = 78,560 kip-in. (See Figure 3.1.2-1) ≤ 0.25 Mp
5.1.1 Longitudinal Direction
0.25Mp= 0.25 * 78,560 = 19,640 kip-in. Δr = ΔLD_Long / 2 = 8.76 / 2 = 4.38 in. = 1,250 * 4.38 = 5,475 kip-in. < 0.25Mp = 19,640 kip-in. => Okay
PdlΔr
5.1.2 Transverse Direction
Δr = ΔLD_Trans / 2 = 6.07 / 2 = 3.04 in. = 1,250 kips * 3.04 = 3,800 kip-in. < 0.25Mp = 19,640 kip-in. => Okay
Page 4-B2-66
1 Ptrib (Hh + 0. The requirement is as follows: Mne Where: Mne = nominal moment capacity of the column based upon expected material properties as shown in Figure 8.003.) = 7.) = 34.5 Ds) / Λ
Ptrib Hh
Determine Ptrib: Since the abutments are being modeled as free in the longitudinal direction.8.2 Minimum Lateral Strength Check
The requirements of Section 8.638 / 2 / 2 = 1. The moment-curvature diagram for the column section is shown in Figure 5.2-1 with values displayed at a concrete strain of 0.7. Section Designer in SAP2000 can be used to determine Mne by performing a moment-curvature analysis and displaying the moment when the concrete reaches a strain of 0. all of the seismic mass is collected at the bents in the longitudinal direction.083 * 12 = 85 in.5-1 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design (kip-in.660 kips
Note that a more sophisticated analysis to determine the tributary seismic mass would be necessary if the bridge were not symmetric and the bents did not have equal stiffness.1 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be satisfied.0 * 12 (Top of footing to top of crossbeam) = 408 in.5 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design defines Mne as the expected nominal moment capacity based on the expected concrete and reinforcing steel strengths when the concrete strain reaches a magnitude of 0.1 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design) = 2 for fixed top and bottom ≥ 0.) = greater of the dead load per column or force associated with the tributary seismic mass collected at the bent (kip) = the height from the top of the footing to the top of the column or the equivalent column height for a pile extension (in. the force associated with the tributary seismic mass collected at the bent is greater than the dead load per column and is computed as follows: Ptrib = Weight of Structure / # of bents / # of columns per bent = 6.04
Page 4-B2-67
.003. Therefore.002989 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show
M23-50. = depth of superstructure (in. Determine Mne: Section 8.SAP2000 Seismic Analysis Example
5. = fixity factor (See Section 4.
Moment-Curvature Curve for Frame Section “COL” at εc = 0.SAP2000 Seismic Analysis Example
Property button > click Section Designer button > Display menu > Show MomentCurvature Curve). = Mne => Okay
Page 4-B2-68
WSDOT Bridge Design Manual M23-50.5 Ds) / Λ = 0.1 Ptrib (Hh + 0.482 kip-inches.2-1
It is seen in Figure 5.003
Figure 5.482 kip-in. < 73.2-1 that Mne = 73. Perform Check: 0.660 * (408 + 0.392 kip-in.04 August 2010
.5 * 85) / 2 = 37.
The displacement at which the first hinge ruptures (fails) is the displacement capacity of the structure and is also the point at which the base shear begins to decrease.3. It can be seen in Figure 5.8 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be satisfied. the displacement demand in the longitudinal direction is ΔLD_Long = 8.3 Structure Displacement Demand/Capacity Check
The requirements of Section 4.1 Longitudinal Direction
From section 3.04 Page 4-B2-69
.) = displacement capacity taken along the local principal axis corresponding to ΔLD of the ductile member (in. Determine ΔLC_Long: The displacement capacity can be determined from the pushover curve as show in Figure 5. The requirement is as follows: ΔLD < ΔLC Where: ΔLD ΔLC = displacement demand taken along the local principal axis of the ductile member (in.73 inches.
Figure 5.3. This suggests the displacement capacity of the bridge in the longitudinal direction is greater than
WSDOT Bridge Design Manual August 2010 M23-50.3.1-1 (Display menu > Show Static Pushover Curve).2.SAP2000 Seismic Analysis Example
5.3.1-1 that the base shear does not decrease until a displacement of approximately 11 inches.3.
hinges fail if they are in the “Beyond E” hinge state.3.3.1-2 can be displayed by clicking File menu > Display Tables in Figure 5. To confirm this.2-1 (Display menu > Show Static Pushover Curve).2 Transverse Direction
Page 4-B2-70
WSDOT Bridge Design Manual M23-50. In Figure 5.3. the table shown in Figure 5.2. displacement.1-2 shows the step. Therefore.3.69 inches and the following can be stated: ΔLC_Long = 10.76 in.69 in. Determine ΔLC_Trans: The displacement capacity can be determined from the pushover curve as show in Figure 5. ΔLC_Long = 10.
Pushover Curve Tabular Data for Load Case “LongPush”
Figure 5.3.SAP2000 Seismic Analysis Example
the displacement demand.07 inches. base force.3.1-1. > ΔLD_Long = 8.3.2 of this example. => Longitudinal Displacement Demand/Capacity is Okay
5. By definition.3. and hinge state data for the longitudinal pushover analysis.1-2
Figure 5.04 August 2010
.1-2 it can be seen that step 23 is the first step any hinges reach the “Beyond E” hinge state. the displacement demand in the transverse direction is ΔLD_Trans = 6.
Figure 5.3. the displacement at which the first plastic hinge ruptures (fails) is the displacement capacity of the structure and is also the point at which the base shear begins to decrease. To confirm this.2-2 can be displayed by clicking File menu > Display Tables in Figure 5.3.3. It can be seen in Figure 5.2-1
M23-50. the table shown in Figure 5.04
Page 4-B2-71
. This suggests the displacement capacity of the bridge in the transverse direction is greater than the displacement demand.2-1.2-1 that the base shear does not decrease until a displacement of approximately 9.3.5 inches.
> ΔLD_Trans = 6.2-2 it can be seen that step 21 is the first step any hinges reach the “Beyond E” hinge state. => Transverse Displacement Demand/Capacity is Okay
Page 4-B2-72
WSDOT Bridge Design Manual M23-50.51 in. Therefore. displacement.SAP2000 Seismic Analysis Example
Pushover Curve Tabular Data for Load Case “TransPush”
Figure 5. hinges fail if they are in the “Beyond E” hinge state.04 August 2010
.2-2 shows the step.2-2
Figure 5.3.3. base force. By definition. Recall the transverse pushover analysis only includes a single bent.07 in. In Figure 5. and hinge state data for the transverse pushover analysis. ΔLC_Trans = 9.51 inches and the following can be stated: ΔLC_Trans = 9.3.
5.4 Member Ductility Requirement Check
The requirements for hinge ductility demands in Section 4.9 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be met for all hinges in the structure. The member ductility demand may be computed as follows: μD Where: μD Δyi L φyi Δpd θpd Lp Therefore: μD ≤ 6 (for multiple column bents) = ductility demand = 1 + Δpd / Δyi = idealized yield displacement (does not include soil effects) (in.) = φyi * L2 / 3 = length from point of maximum moment to the inflection point (in.) = idealized yield curvature (1/in.) = plastic displacement demand (in.) = θpd * (L – 0.5*Lp) = plastic rotation demand determined by SAP2000 (rad.) = plastic hinge length (in.) = 1 + 3 * [θpd / (φyi * L)] * (1 – 0.5 * Lp / L)
This example will explicitly show how to compute the ductility demand for the lower hinge of the trailing column being deflected in the transverse direction. The ductility demands for the remaining hinges are presented in tabular format. Determine L: The locations of the inflection points were approximated previously to determine the hinge lengths. However, now that the pushover analysis has been performed, the actual inflection points can be determined. Figure 5.3.2-2 shows that at step 13 the displacement is 6.11 inches, which is slightly greater than the displacement demand. Figure 5.4-1 shows the column moment 2-2 diagram at step 13 of the TransPush load case as displayed in SAP2000 (Display menu > Show Forces/Stresses > Frames/Cables > select TransPush > select Moment 2-2 > select Step 13 > click OK button).
Page 4-B2-73
Frame Moment 2-2 Diagram for Load Case “TransPush” at Step 13
From this information it is found that the inflection point is 59 inches above the lower joint on the middle column element and the following is computed: L = Length from point of maximum moment at base of column to inflection point = Length of Lower Element – Footing Offset + 59 = 146 – 30 + 59 = 175 in.
Determine θpd: Since the displacement of the bent at step 13 is greater than the displacement demand, the plastic rotation at step 13 is greater than or equal to the plastic rotation demand. The plastic rotation at each step can be found directly from the hinge results in SAP2000. The name of the lower hinge on the trailing column is 1H1. Figure 5.4-2 shows the plastic rotation plot of hinge 1H1 at step 13 of the TransPush load case (Display menu > Show Hinge Results > select hinge 1H1 (Auto P-M2) > select load case TransPush > select step 13 > click OK button).
Page 4-B2-74
Hinge “1H1” Plastic Rotation Results for Load Case “TransPush” at Step 13
Figure 5.4-2 shows that the plastic rotation for hinge 1H1 is 0.0129 radians. Therefore θpd = 0.0129 radians. Determine φyi: The idealized yield curvature will be found by determining the axial load in the hinge at first yield and then inputting that load into Section Designer. The axial load at yield can be found by viewing the hinge results at step 4 (when the hinge first yields). Figure 5.4-3 shows the axial plastic deformation plot of hinge 1H1 at step 4 of the TransPush load case (Display menu > Show Hinge Results > select hinge 1H1 (Auto P-M2) > select load case TransPush > select step 4 > select hinge DOF P > click OK button).
Page 4-B2-75
Page 4-B2-76
WSDOT Bridge Design Manual M23-50. That load can now be entered into Section Designer to determine the idealized yield curvature.04 August 2010
. φyi.4-3 shows that the axial load in hinge 1H1 at step 4 of the TransPush load case is -432 kips.4-3
Figure 5.4-4 (Define menu > Section Properties > Frame Sections > select COL > click Modify/Show Property button > click Section Designer button > Display menu > Show Moment-Curvature Curve). The moment-curvature diagram for the column section with P = -432 kips is shown in Figure 5.SAP2000 Seismic Analysis Example
Hinge “1H1” Axial Plastic Deformation Results for Load Case “TransPush” at Step 4
00009294.00009294 in.4-4 shows that Phi-yield(Idealized) = .4-4
Figure 5.0129 rad.00009294 * 175)] * (1 – 0.0 / 175) = 3.04
Page 4-B2-77
. Therefore: φyi = 0.0 in. = 1 + 3 * [θpd / (φyi * L)] * (1 – 0.2 < 6 => okay
The ductility demands and related values for all column hinges are shown in Table 5.4-1.
M23-50. = 0. = 27.0129 / (0. The ductility demand in the transverse direction for the lower hinge in the trailing column can now be calculated as follows: μD Where: L φyi θpd Lp Therefore: μD = 175 in.-1 = 0.5 * Lp / L)
= 1 + 3 * [0.00009294 inches-1.5 * 27.SAP2000 Seismic Analysis Example
Moment-Curvature Curve for Frame Section “COL” at P = -432 kips
9 27.00009292 .0 26.0 26.0 3.2 3.6
Ductility Demands for All Column Hinges
Table 5.) .0000889 .4-1
Table 5.9 27.SAP2000 Seismic Analysis Example
Pushover Direction (Long/Trans) Longitudinal Longitudinal Longitudinal Longitudinal Transverse Transverse Transverse Transverse
Column and Hinge Location (-) Trailing Lower Trailing Upper Leading Lower Leading Upper Trailing Lower Trailing Upper Leading Lower Leading Upper
Hinge Name (-) 1H2 3H2 7H2 9H2 1H1 3H1 4H1 6H1
Yield Step (#) 5 6 6 8 4 5 6 7
Axial Load at Yield (kips) -1222 -1135 -1354 -1277 -432 -305 -2226 -2253
φyi (1/in.00902
Lp (in.04 August 2010
.0000887 .4-1 shows that all hinge ductility demands are less than 6.00008851 .8 2.0104 .) .0 2.00009294 .5 4.7 4.00009185 .6 4.00008926 .0 26.9
L (in.
Page 4-B2-78
WSDOT Bridge Design Manual M23-50.0 26.0129 .) 27.0168 .0195 .9 27.0118 .0204 .00009186
θpd (rad.) 175 175 175 175 175 175 175 175
μD (-) 4.0207 .
Determine Vu:
M23-50.3 ≤ α’ = fs / 0.047 α’ f’c1/2) vc otherwise: vc =0 For circular columns with spiral reinforcing: 0. The shear demand/capacity checks for the remaining columns are presented in tabular format.2) = pitch of spiral (in.15 + 3.8 Ag = gross area of member cross-section (in.04
Page 4-B2-79
.6 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be met for all columns in the structure. 0.5 Column Shear Demand/Capacity Check
The column shear requirements in Section 8.11 f’c1/2 .35 ρs = (4 Asp) / (s D’) Where: Pu Asp s D’ fyh f’c µD = ultimate compressive force acting on section (kips) = area of spiral (in.SAP2000 Seismic Analysis Example
5.2) Ag vc if Pu is compressive: vc = 0.) = nominal yield stress of spiral (ksi) = nominal concrete strength (ksi) = maximum local ductility demand of member
Steel Shear Capacity: Vs Vs = steel contribution to shear capacity (kips) = (π / 2) (Asp fyh D’) / s
This example will explicitly show how to perform the shear demand/capacity check for the trailing column being deflected in the transverse direction.032 α’ [1 + Pu / (2 Ag)] f’c1/2 ≤ min ( 0. φsVn Where: φs Vn ≥ Vu = 0.9 = nominal shear capacity (kips) = Vc + Vs
Concrete Shear Capacity: Vc = concrete contribution to shear capacity (kips) = vcAe Where: Ae = 0.67 .) = diameter of spiral (in.µD ≤ 3 fs = ρsfyh ≤ 0.
5 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design.6.5-1 it is determined that the plastic shear in the trailing column is 389 kips.
Page 4-B2-80 WSDOT Bridge Design Manual M23-50. For ASTM A 706 reinforcement the overstrength magnifier is 1. which is the shear associated with the overstrength moment. Therefore: Vu Where: λpo Vp Vu Determine Vc: Figure 5.5-1 shows the column shear diagram for the TransPush load case as displayed in SAP2000 (Display menu > Show Forces/Stresses > Frames/Cables > select TransPush > select Shear 3-3 > select Step 13 > click OK button).04 August 2010
= λmo Vp = 1. defined in Section 8. Mpo.
Frame Shear 3-3 Diagram for Load Case “TransPush” at Step 13
Figure 5.2 * 389 = 467 kips
. and so the shear for the SAP2000 model must be multiplied by this factor.5-1
From Figure 5.1 states that Vu shall be determined on the basis of Vpo.2.SAP2000 Seismic Analysis Example
Figure 5.2 = 389 kips
and = 1.5-2 shows the column axial load diagram for the TransPush load case as displayed in SAP2000 (Display menu > Show Forces/Stresses > Frames/Cables > select TransPush > select Axial Force > select Step 13 > click OK button). Section 8.
0089 * 60 ≤ 0.5-2
From Figure 5.8 Ag = 0.54 ≤ 0.35 = 0.44) / ( 3. = 60 – 1.35 = 0.8 * 2827.25 in.35 = 0.04 Page 4-B2-81
Asp s D’
fyh f’c ρs
.75 = 56.4 = 2262 in.2 = 0. = 60 ksi = 4 ksi = (4 Asp) / (s D’) = (4 * 0.35 ksi
M23-50.5 * 56.4 in. Therefore: Pu Ag Ae
= 247 kips = π * 602 / 4 = 2827.2 = 3.SAP2000 Seismic Analysis Example
Frame Axial Force Diagram for Load Case “TransPush” at Step 13
Figure 5.5 – 0.25) = 0.44 in.0089 = ρsfyh ≤ 0.5 in.2 = 0.5-2 it is determined that the axial force in the trailing column is -247 kips.5 – 1.
032 * 2.0 vc (ksi) 0.5 2.SAP2000 Seismic Analysis Example
µD 0.15 + 3.25) / 3. Pushover Column Vp Vu Direction (Long/Trans) (-) (kips) (kips) Longitudinal Trailing 484 581 Longitudinal Leading 497 596 Transverse Trailing 389 467 Transverse Leading 580 696 Pu (kips) 1175 1320 247 2253 µD (-) 4. 0.2 (see Section 5.4)] 41/2 ≤ min (0. 0.5 3.187 * 2262 = 423 kips
α’ vc
Determine Vs: Vs = (π / 2) (Asp fyh D’) / s = (π / 2) (0.032 α’ [1 + Pu / (2 Ag)] f’c1/2 ≤ min ( 0.µD ≤ 3 = 0.187 ≤ min (0.3 ≤ α’
= 3.8 3.44 * 60 * 56.35 / 0.4 of this example) = fs / 0.15 + 3.2 2.67 – 3.11 f’c1/2 .047 α’ f’c1/2) = 0.35 / 0.5-1 shows that the shear capacities are greater than the shear demands for all columns.7 4.
Page 4-B2-82
WSDOT Bridge Design Manual M23-50.2 ≤ 3 = 2.10 0.15 + 3.047 * 2.11 * 41/2.9 * (423 + 666) = 980 kips > Vu = 467 kips => okay
The shear demands and capacities and related values for all columns are shown in Table 5.5-1
Table 5.2 ≤ 3 = 0. 0.8 = 0.187 ksi = vcAe = 0.67 .12 0.22 Vc (kips) 228 268 423 498 Vs (kips) 666 666 666 666 φsVn (kips) 804 841 980 1047
Column Shear Demands and Capacities
Table 5.67 – 3.8 ≤ 3 = 2.5 = 666 kips Determine φsVn: φsVn = φs (Vc + Vs) = 0.3 1.8 α' (-) 1.19 0.263) = 0.22 .8 * 41/2) = 0.5-1.8 * [1 + 247 / (2 * 2827.04 August 2010
1. However. these requirements are okay by inspection.
Page 4-B2-83
. Due to the symmetry of this example. on many bridges these requirements may highly influence the design.6 Balanced Stiffness and Frame Geometry Requirement Check
The balanced stiffness and balanced frame geometry requirements of Sections 4.1.SAP2000 Seismic Analysis Example
5.2 and 4.3 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design must be met.
Page 4-B2-84
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