bridge seismic design according sap 2000

ISO SAP041709M22 Rev. 0 Berkeley, California, USA

Version 14April 2009

SAP2000/Bridge

Bridge Seismic Design Automated Seismic Design of Bridges

AASHTO Guide Specification for LRFD Seismic Bridge Design

COPYRIGHT

Copyright Computers & Structures, Inc., 1978-2009 All rights reserved. The CSI Logo® is a registered trademark of Computers & Structures, Inc. SAP2000TM and Watch & LearnTM are trademarks of Computers & Structures, Inc. Adobe and Acrobat are registered trademarks of Adobe Systems Incorported. AutoCAD is a registered trademark of Autodesk, Inc. The computer program SAP2000TM and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers & Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers & Structures, Inc., is explicitly prohibited.

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Further information and copies of this documentation may be obtained from:

Computers & Structures, Inc. 1995 University Avenue Berkeley, California 94704 USA Phone: (510) 649-2200 FAX: (510) 649-2299 e-mail: [email protected] (for general questions) e-mail: [email protected] (for technical support questions) web: www.csiberkeley.com

DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND TESTING OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT.

THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

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Contents

Bridge Seismic Design

Foreword

Step 1 Create the Bridge Model

1.1 Sample Model 1-1

1.2 Description of the Sample Bridge Model 1-2

1.3 Bridge Layout Line 1-4

1.4 Frame Section Property Definitions 1-4 1.4.1 Bent Cap Beam 1-5

1.4.2 Bent Column Properties 1-5 1.4.3 I-Girders Properties 1-6 1.4.4 Pile Properties 1-7

1.5 Bridge Deck Section 1-8

1.6 Bent Data 1-8

1.7 Bridge Object Definition 1-10

1.7.1 Abutment Property Assignments 1-11 1.7.2 Abutment Geometry 1-13

SAP2000/Bridge Seismic Design

ii

1.7.3 Bent Property Assignments 1-14 1.7.4 Bent Geometry 1-15

1.8 Equivalent Pile Formulation 1-16

1.9 Bent Foundation Modeling 1-16

1.10 Mass Source 1-17

Step 2 Ground Motion Hazard

2.1 Overview 2-1

2.2 AASHTO and USGS Hazard Maps 2-1

2.3 Seismic Design Request 2-3

2.4 Perform Seismic Design 2-6

2.5 Auto Load Patterns 2-7

2.6 Auto Load Cases 2-7

Step 3 Dead Load Analysis and Cracked Section Properties

3.1 Overview 3-1

Step 4 Response Spectrum and Demand Displacements

4.1 Overview 4-1

4.2 Response Spectrum Load Cases 4-1

4.3 Response Spectrum Results 4-4

Step 5 Determine Plastic Hinge Properties and Assignments

5.1 Overview 5-1

5.2 Plastic Hinge Lengths 5-1

5.3 Nonlinear Hinge Properties 5-3

5.4 Nonlinear Material Property Definitions 5-6

5.4.1 Nonlinear Material Properties Definitions For Concrete 5-6 5.4.2 Nonlinear Material Properties Definitions

For Steel 5-8

Contents

iii

5.5 Plastic Hinge Options 5-9

Step 6 Capacity Displacement Analyses

6.1 Displacement Capacities for SDC B and C 6-2

6.2 Displacement Capacities for SDC D 6-3

6.3 Pushover Results 6-6

Step 7 Demand/Capacity Ratios

7.1 D/C Ratios 7-1

Step 8 Review Output and Create Report

8.1 Design 01 – D/C Ratios 8-2

8.2 Design 02 – Bent Column Force Demand 8-2

8.3 Design 03 – Bent Column Idealized Moment Capacity 8-2

8.4 Design 04 – Bent Column Cracked Section Properties 8-3

8.5 Design 05 – Support Bearing Demands – Forces 8-3

8.6 Design 06 – Support Bearing Demand Displacements 8-4

8.7 Design 07 – Support Length Demands 8-4

8.8 Create Report 8-5

References


iv

List of Figures

Figure 1-1 3D View of Example Model 1-1

Figure 1-2 Example Bridge Elevation 1-2

Figure 1-3 Example Bridge Plan 1-3

Figure 1-4 Example Bridge BENT1 Elevation 1-3

Figure 1-5 3D Bridge Layout Line Data 1-4

Figure 1-6 3D Cap Beam Section Property Definition 1-5

Figure 1-7 Bent Column Property Definition 1-6

Figure 1-8 Precast I-Girder Properties 1-6

Figure 1-9 Pile Properties 1-7

Figure 1-10 Bridge Deck Section Properties 1-8

Figure 1-11 Bridge Bent Data 1-9

Figure 1-12 Bent Column Data 1-9

Figure 1-13 Bent Column Base Restraint Definitions 1-10

Figure 1-14 Bridge Object Data form 1-11

Figure 1-15 Abutment Property Definitions 1-12

Figure 1-16 Abutment Bearing Properties 1-13

Figure 1-17 Abutment Bearing Geometry 1-13

Figure 1-18 Bent Assignments form 1-14

Figure 1-19 Bent Bearing Data 1-15

Figure 1-20 Bent Support Geometry 1-15

Figure 1-21 Equivalent Pile Properties 1-16

Figure 1-22 View of Bent Foundations 1-17

Figure 1-23 Bent Column Base Connectivity 1-17

Figure 1-24 Mass Source Definition 1-18

Contents

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Figure 2-1 AASHTO/USGS Hazard Maps used to determine the Demand Response Spectrum 2-2

Figure 2-2 Response Spectrum Function Data form 2-2

Figure 2-3 Bridge Design Request form 2-3

Figure 2-4 Seismic Design Parameters form 2-4

Figure 2-5 Perform Seismic Design 2-7

Figure 2-6 Auto Load Patterns 2-7

Figure 2-7 Auto Load Cases 2-8

Figure 3-1 Auto Stage Construction Load Case used to apply Cracked Section Property Modifiers 3-2

Figure 4-1 U1 Direction Response Spectrum Load

Case form 4-2

Figure 4-2 ABS Response Spectrum Load Case form 4-3

Figure 4-3 BENT1 Displacements for the three

Auto-Defined Response Spectrum Load cases 4-3

Figure 4-4 Modal Load Case Definition 4-4

Figure 5-1 Hinge Locations 5-2

Figure 5-2 Hinge Locations 5-3

Figure 5-3 Moment Curvature Diagram 5-4

Figure 5-4 Auto Hinge Assignment Data 5-5

Figure 5-5 Sample Hinge Data form 5-5

Figure 5-6 Nonlinear Material Data form for Concrete 5-6

Figure 5-7 Nonlinear Stress-Strain curves for Confined

and Unconfined Concrete 5-7

Figure 5-8 Concrete Model - Mander Confined 5-7

Figure 5-9 Nonlinear Material Data form for steel 5-8

Figure 5-10 Nonlinear Stress-Strain Plot for steel 5-9

Figure 5-11 Plastic Hing Fiber option 5-10


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Figure 5-12 Section Designer options 5-10

Figure 6-1 Rectangular Beam Design 6-1

Figure 6-2 Design Requirements for SDC 6-2

Figure 6-2 BENT1 Transverse Pushover Load Case 6-4

Figure 6-3 BENT1 Application of Property Modifiers

and Dead Loads to BENT1 6-5

Figure 6-4 BENT1 Pushover Load Pattern for the Transverse Direction 6-6

Figure 6-5 Display of BENT1 Pushover Curves 6-7

Figure 7-1 D/C Displacement Ratios 7-1

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Foreword

SAP2000/Bridge has become a widely recognized and widely used analysis and design program for bridge structures. Over the past thirty-five years, Com-puter and Structures, Inc, has introduced new and innovative ways to model complex structures. The latest innovation for the analysis and design of bridge structures is the automated seismic design feature that is now part of the SAP2000/Bridge. Automated seismic design incorporates the recently adopted AASHTO Guide Specification for LRFD Seismic Bridge Design. SAP2000/Bridge allows engineers to define specific seismic design parame-ters that are then applied to the bridge model during an automated cycle of analysis through design.

Now, users can automate the response spectrum and pushover analyses. Fur-thermore, the SAP2000/Bridge program will determine the demand and capac-ity displacements and report the demand/capacity ratios for the Earthquake Re-sisting System (ERS). All of this is accomplished in eight simple steps outlined as follows:

1. Create the Bridge Model

2. Evaluate the Ground Motion Hazard and the Seismic Design Request

3. Complete the Dead Load Analysis and evaluate the Cracked Section Properties

4. Identify Response Spectrum and Demand Displacements

5. Determine Plastic Hinge Properties and Assignments


vi Foreword

6. Complete Capacity Displacement Analysis

7. Evaluate Demand/Capacity Ratios

8. Review Output and Create Report

A detailed explanation of each of the steps is presented in the chapters that fol-low. The example bridge model shown in the figure illustrates the SAP2000/Bridge Automated Seismic Design features.

Schematic of the Eight Steps in the Automated Seismic Design of Bridges using SAP2000/Bridge

Example Model 1 - 1

STEP 1 Create the Bridge Model

1.1 Example Model

This chapter describes the first step in the process required to complete a Seis-mic Design Request for a bridge structure using SAP2000/Bridge. It is as-sumed the user is familiar with the requirements in the program related to cre-ating a Linked Bridge Object. Only select features of the model development are included in this chapter. The SAP2000/Bridge model used throughout this manual is available on the CD and includes all of the input parameters.

Figure 1-1 3D View of Example Model


1 - 2 Description of the Example Bridge

As described in the AASHTO Guide Specifications for LRFD Seismic Bridge Design, the seismic design strategy for this bridge is Type 1 – Design a ductile substructure with an essentially elastic superstructure. This implies that the de-sign must include plastic hinging in the columns.

1.2 Description of the Example Bridge

The example bridge is a three-span concrete I-girder bridge with the following features:

Piles: 14-inch-diameter steel pipe pile filled with concrete. The concrete is re-inforced with six #5 vertical bars with three #4 spirals having a 3-inch pitch.

Pile Cap: The bent columns are connected monolithically to a concrete pile cap that is supported by nine piles each. The pile caps are 13’-0” x 13’-0” x 4’-0”

Bents: There are two interior bents with three 36-inch-diameter columns.

Deck: The deck consists of five 3’-3”-deep precast I-girders that support an 8½-inch-thick deck and a wearing surface (35 psf). The deck width is 35'-10" from the edge-of-deck to edge-of-deck.

Spans: Three spans of approximately 60’-0”.

The abutments are assumed to be free in both the longitudinal and transverse directions.

Figure 1-2 Example Bridge Elevation

STEP 1 - Create the Bridge Model

Description of the Example Bridge 1 - 3

Figure 1-3 Example Bridge Plan

Figure 1-4 Example Bridge BENT1 Elevation


1 - 4 Bridge Layout Line

1.3 Bridge Layout Line

The example model has three spans of approximately 60 feet each. The layout line is defined using the Bridge menu > Layout Line command and the Bridge Layout Line Data form shown in Figure 1-5. The layout line is straight, with no variation in elevation. The actual length of the layout line is 178.42 ft.

Figure 1-5 3D Bridge Layout Line Data

1.4 Frame Section Property Definitions

Four frame section properties must be described by the user to develop the ex-ample model. The four types of frame elements used in the example model consist of a pile, bent cap beam, bent column, and precast concrete I-Girder. The section property definition for each of the elements is given in the subsec-tions that follow.


Frame Section Property Definitions 1 - 5

1.4.1 Bent Cap Beam

The bent cap beams were defined using the Define menu > Section Property > Frame Sections command. The Add New Property option was used to add the following concrete rectangle:

Figure 1-6 3D Cap Beam Section Property Definition

The material property used was 4000 psi. Note that the units shown in Figure 1-6 are in inches.

1.4.2 Bent Column Properties The bent columns were defined using the Section Designer option that can be accessed using the Define menu > Section Property > Frame Sections com-mand. The size and quantity of both the vertical and confinement reinforcing steel were defined using the form shown in Figure 1-7. Further discussion of the column section properties as they pertain to the plastic hinge definitions is provide in Step 5.


1 - 6 Frame Section Property Definitions

Figure 1-7 Bent Column Property Definition

1.4.3 I-Girder Properties

The I-Girder properties were input using inch units, as shown in Figure 1-8.

Figure 1-8 Precast I-Girder Properties


Frame Section Property Definitions 1 - 7

1.4.4 Pile Properties

The piles were defined as 14–inch-diameter concrete piles with six #9 vertical bars. The outer steel casings of the pile were found to increase in the flexural stiffness of the piles by a factor of 2.353. This value was applied as a property modifier to the pile section property. The pile will be added to the bridge model as “Equivalent Cantilever” piles, as shown in Figure 1-9 and as de-scribed in subsequent Section 1.8. Using this method, the pile is replaced by a beam that has equivalent stiffness properties to that of the pile with the sur-rounding soil.

Figure 1-9 Pile Properties


1 - 8 Bridge Deck Section

1.5 Bridge Deck Section

The bridge deck section is 38.833 feet wide with a total of five I-girders, as shown in the form included in Figure 1-10. The parapets as well as the wearing surface are not part of the bridge deck structural definition but will be added to the bridge model as superimposed dead loads (SDEAD).

Figure 1-10 Bridge Deck Section Properties

1.6 Bent Data

The bents for the subject model have three columns each with a cap beam width of 38.25 feet. The Bridge Bent data form shown in Figure 1-11 is used to input the number of columns and the cap beam width. Since multiple columns are specified, the location, height and support condition for each column needs to be specified using the Bent Column Data form, which is accessed using the Modify/Show Column Data button.


Bent Data 1 - 9

Figure 1-11 Bridge Bent Data

After the Modify/Show Column Data button is used, the Bent Column Data form shown in Figure 1-12 can be used to define the type, location, height, an-gle and boundary conditions for each bent column.

Figure 1-12 Bent Column Data

An important part of this example model is the inclusion of the foundation ele-ments. Although the foundations can be represented as Fixed, Pinned, or Spring-Support restraints at the base of the columns, these have been explicitly modeled in this example. It is important to note that when foundation objects


1 - 10 Bridge Object Definition

are part of the bridge model, the base of the bent column must not be re-strained, but instead, connected to the foundation elements. Restraining the base of the columns in the Bent Column Data form using Fixed or Pinned re-straints would prevent the bridge loads from reaching the foundation. In this example, a foundation spring (BFSP1) having no stiffness in any direction is used as the Base Support data. After the foundations have been modeled and connected to the bent column bases, support of the bent columns will be achieved. The Foundation Spring Data form is shown in Figure 1-13.

Figure 1-13 Bent Column Base Restraint Definitions

1.7 Bridge Object Definition

The Bridge Object Data form is used to define the location and bearing prop-erty assignments of the abutments and bearings. The seismic response of the bridge model will depend on the Earthquake Resisting System (ERS). The user can define the types of support conditions at the abutments and bents. The ERS will depend on the types of supports used at the abutments and bents and the bearing properties that are used for each. If a bearing has a restrained DOF, it will provide a load path that will act as part of the bridge ERS. Abutments can


Bridge Object Definition 1 - 11

be defined using bents as supports (this feature was note used in the subject ex-ample).

Figure 1-14 Bridge Object Data form

The span data is used to define the span lengths and bent locations. Cross dia-phragms also can be included in a bridge model using the Modify/Show As-signments > In Span Cross Diaphragms command. No cross diaphragms were used as part of the example model.

1.7.1 Abutment Property Assignments

Both the start and end abutment assignments are defined using the Bridge Ob-ject Abutment Assignment form shown in Figure 1-15. The abutment bearing direction can be assigned a bearing angle if skewed abutments are needed. Dia-phragms can be added to the abutment as well. Abutments can be modeled us-ing bents by selecting, ’Bent Property’, in the Substructure Assignment box. After that selection has been, an option is available to select the appropriate property definition from a list of previously defined bent properties.



Figure 1-15 Abutment Property Definitions

The substructure location is critical because SAP2000/Bridge accounts for the superstructure/substructure kinematics. The ends of the bridge deck will have a tendency to rotate due to gravity loading. If the abutment bearings are re-strained against translation at both ends of a bridge, outward reactions on the bearings and deck moments can be induced as a result of these restraints. The amount of outward thrust and the moment in the deck are a function of the amount of rotation and distance from the deck neutral axis to the top of abut-ment bearings. Therefore, the user should pay special attention to the substruc-ture and bearing elevations as well as the bearing restraint properties. The user also must keep in mind that the seismic resisting load path is dependent on the restraint properties of the bearing at both abutments and bents.

For this example, only the vertical translation of the abutment bearings was set to Fixed. All other abutment bearing components were set to Free since the abutment restrain was assumed to be free in the longitudinal and transverse di-rections. See Figure 1-16.

To help visualize the abutment geometry, the graphic shown in Figure 1-17 in-cludes the values in the example model to define the location of the abutment bearings and substructure. It should also be noted that the SAP2000/Bridge program automatically includes the BFXSS Rigid Link when the bridge object is updated.



Figure 1-16 Abutment Bearing Properties

1.7.2 Abutment Geometry

Figure 1-17 also shows the location of the BRG1 action point. This is the loca-tion where the bearing will translate or rotate depending on the bearing defini-tions.

Figure 1-17 Abutment Bearing Geometry



1.7.3 Bent Property Assignments

The bent property assignments are made using the Bridge Object Bent As-signment form, shown in Figure 1-18. Similar to the abutment property as-signments, the bent property assignments will include the bent directions, bear-ing properties, and substructure locations.

Figure 1-18 Bent Assignments form

For this example model, the bearing properties at the bents have fixed transla-tion restraints in all directions but free restraints for all rotational directions. See Figure 1-19.



Figure 1-19 Bent Bearing Data

1.7.4 Bent Geometry

The bent geometry is shown in Figure 1-19 for the input values used to define the bearing and substructure elevations from the Bent Assignment form (Figure 1-17).

Figure 1-20 Bent Support Geometry


1 - 16 Equivalent Pile Formulation

Note that the BRG2 connects to the center of the cap beam. The substructure elevation is used to define the top of the cap beam. The action point of BRG2 will be at Elevation -49.0”.

1.8 Equivalent Pile Formulation

Although it is not required to include explicit foundation elements (foundations can be modeled as fixed, pinned or partially fixed restraints at the base of the columns), these were included as part of the example model. Foundations can be modeled in many ways. Equivalent length piles were used with an equiva-lent length of 5.1 feet to model the pile surrounded by soil, as described in Sec-tion 1.4.4. The equivalent lengths were established using the equations shown in Figure 1-21.

Point of fixity

3 K EI T

K EI T

2K EI T

f = yield calculated from an average spt blow count N.

T = 5.1 feet; this effective length is used in modeling the bridge foundation.

1 5EI fPoint of fixity

3 K EI T

K EI T

2K EI T

f = yield calculated from an average spt blow count N.

T = 5.1 feet; this effective length is used in modeling the bridge foundation.

1 5EI f

Figure 1-21 Equivalent Pile Properties

After the lengths of the piles were known, the piles were connected to an area object representing the pile cap. The cap was meshed at the top of the pile loca-tions. The completed pile cap appears in Figure 1-22, which is shown using a 3D extruded view.

1.9 Bent Foundation Modeling

The next and critical step in the model definition is to connect the foundation to the base of the bent columns. For this example, joint constraints were used as illustrated in Figure 1-23. This method of connecting the column base to the foundation preserves connectivity even when updating the linked bridge model.


Mass Source 1 - 17

Figure 1-22 View of Bent Foundations

Figure 1-23 Bent Column Base Connectivity

1.10 Mass Source

The Mass Source definition is used to define the mass and loads to be included in the modal and response spectrum load cases. In this example, the combined weight of the parapets and wearing surface was approximated as 2.0 kips per linear foot acting along the bridge deck. A load pattern was added as a super-imposed type with the name SDEAD. Using the option, ‘From Element and

Column-to-Foundation Connection


1 - 18 Mass Source

Additional Masses and Loads’, the program will calculate the self weight of the bridge structure and include that mass along with the mass derived from the SDEAD load assignment.

Figure 1-24 Mass Source Definition

Overview 2 - 1

STEP 2 Ground Motion Hazard and Seismic Design Request

2.1 Overview

The ground motion hazard (response spectrum) can be determined by SAP2000/Bridge by defining the bridge location using the latitude and longi-tude or the postal zone. As an alternative, the user can input any user defined response spectrum file. The site effects (soil site classifications) also are con-sidered and are part of the user input data.

2.2 AASHTO and USGS Hazard Maps

The recently adopted AASHTO Guide Specification for the LRFD Seismic Bridge Design incorporates hazard maps based on a 1000-year return period. When the user defines the bridge location by Latitude and Longitude, SAP2000/Bridge creates the appropriate response spectra curve as follows:


2 - 2 AASHTO and USGS Hazard Maps

Figure 2-1 AASHTO/USGS Hazard Maps used to determine the Demand Response Spectrum

Figure 2-2 Response Spectrum Function Data form

From the Response Spectrum Data form, the values for SDS and SD1 are deter-mined by SAP2000 and reported. The SD1 value is used to determine the Seis-

STEP 2 - Ground Motion Hazard and Seismic Design Request

Seismic Design Request 2 - 3

mic Design Category (SDC). The SDC is used to determine the analysis and design requirements to be applied to the bridge. For example, if the SDC is A, no capacity displacement calculation is performed. If the SDC is B or C, SAP2000 uses an implicit formula (see Section 4.8 of the AASHTO Seismic Guide Specification). If the SDC is D, SAP2000 uses a nonlinear pushover analysis to determine the capacity displacements.

2.3 Seismic Design Request

The Design menu > Bridge Design > Define Seismic De-sign Request command ac-cesses a form that can be used to specify the name and de-sign request parameters for a Seismic Design Request. The form is shown in Figure 2-3.

Figure 2-3 Bridge Design Request form

For this example, clicking the Modify/Show button will display the Substruc-ture Seismic Design Request Parameters form, shown in Figure 2-4. A brief description of the parameters on that form follows.

Item Substructure Seismic Design Request Parameter

1 Response Spec-trum Function

After a response spectrum function has been defined (see Step 2), the name of the response spectrum to be used for a specific Seismic Design Request should be selected here.

2 Seismic Design Category (SDC) Option

The user can choose to have the SDC be selected by the program (i.e., “Programmed Determined”), or the user can impose a value for the SDC (i.e., “User Defined”). To impose a value, select it from Item 3, the Seis-mic Design Category.


2 - 4 Seismic Design Request

Figure 2-4 Seismic Design Parameters form


3 Seismic Design Category

If the user has opted to specify the Seismic Design Category in Item 2, the user must specify the Seismic Design Category here as B, C or D.

4 Bent Displace-ment Demand Factor

This is a scale factor. The bent displacement demands obtained from the response-spectrum analysis are multiplied by this factor. It can be used to modify the displacement demand due to a damping value other than 5%, or to magnify the demand for short-period structures. This factor will be applied to all bents in both the longitudinal and transverse directions.

5 Gravity Load Case Option

The user can specify which gravity load case is used to determine the cracked section properties for the bent columns. The choices include Auto-Entire Structure, Auto Current BrObj or User Defined. As a default, all Dead and Super Dead loads are included in the Auto-Entire Structure gravity load case.

6 Gravity Load Case

If the User Option is selected for the gravity load case option in item 5 above, the gravity load case name must be selected here.


Seismic Design Request 2 - 5


7 Additional Group

If the Auto-This Bridge Object option is selected for the gravity load case option in item 5 above, an additional group can be included in the gravity load case. This item is only required when the gravity load case is program determined. It may include pile foundations and other auxil-iary structures.

8 Include P-Delta If P-Delta Effects are to be included, the user needs to specify ‘yes’ here. P-Delta effects will cause a more abrupt drop in the pushover curve results if an idealized bilinear hinge has been assigned to the bent col-umns. It is recommended that an initial Seismic Design Request be performed before including the P-Delta effects to help the user under-stand the nonlinear behavior of the bents.

9 Cracked Property Option

The cracked section properties for the bent columns can be automati-cally determined by the program or they can be user defined. If pro-gram determined, the automatic gravity load case will be run iteratively. Section Designer will use the calculated axial force at the top and bot-tom on the column to determine the cracked moments of inertia in the positive and negative transverse and longitudinal directions. The aver-age of the top and bottom column cracked properties will be applied as named property modifier sets and the analysis will be re-run to make sure the cracked-modified model converges to within the specified tolerance.

10 Convergence Tolerance

This value sets the relative convergence tolerance for the bent-column cracked-property iteration. This item is required only when the cracked-property calculation is program determined.

11 Maximum Number of Iterations

This value sets the maximum number of iterations allowed for the bent-column cracked-property iteration. The first run is considered to be the zero-th iteration. Usually only one iteration is needed. This item is re-quired only when the cracked-property calculation is program deter-mined.

12 Accept Unconverged Results Convergence

Specifies whether or not the seismic design should continue if the bent-column cracked-property iteration fails to converge. This item is re-quired only when the cracked-property calculation is program deter-mined.

13 Modal Load Case Option

Specifies whether the modal load case is to be determined by program or specified by the user. The modal load case is used as the basis of the response-spectrum load case that represents the seismic design. If pro-gram determined, the modal load case will use the stiffness at the end of the auto-gravity load case that includes the cracked property effects. If user-defined, the user can control the initial stiffness, Eigen vs. Ritz, and other modal parameters by selecting the user defined modal load case in item 14.

14 Modal Load Case

The name of an existing modal load case to be used as the basis of the response-spectrum load case. This item is required only if the modal load case option is user-defined in item 13 above.


2 - 6 Perform Seismic Design


15 Response Spec-trum Load Case Option

Specifies whether the response-spectrum load case is to be determined by program or specified by the user. The response-spectrum load case represents the seismic demand. If program determined, this load case will use the given response-spectrum function and modal load case. Acceleration load will be applied in the longitudinal and transverse directions of the bridge object, and combined using the 100% + 30% rule. If user-defined, the user can control the loading or select SRSS as the method to account for directional combinations.

16 Response Spec-trum Load Case

The name of an existing response-spectrum load case that represents the seismic demand. This item is required only if the response-spectrum load case option is user-defined.

17 Response Spec-trum Angle Option

Specifies whether the angle of loading in the response-spectrum load case is to be determined by program or specified by the user. If pro-gram determined, the longitudinal (U1) loading direction is chosen to be from the start abutment to the end abutment, both points located on the reference line of the bridge object. This item is required only if the response-spectrum load case option is user-defined.

18 Response Spec-trum Angle

Angle (degree, from global X) that defines the direction of the response spectrum load case. This item is required only if the response spectrum load case is User-defined.

19 Foundation Group

If foundations are included and explicitly modeled, then the foundation objects need to be assigned to a group and that group needs to be identified here. This way the foundation objects will be included in the pushover load case. This item is required only if the seismic design cate-gory is D.

20 Pushover Target Dis-placement Ratio

The target displacement is defined as the target ratio of Capac-ity/Demand for the pushover analyses. This item is required only if the seismic design category is D.

21 Bent Failure Criterion

The criteria to determine the bent failure. <Pushover Curve Drop> means the bent fails when the pushover curve slope becomes negative. This item is required only if the seismic design category is D.

2.4 Perform Seismic Design

It is not necessary to execute an analysis of the bridge model before running the Seismic Design Request. To start the Bridge Seismic Design Request, the Design Now command should be selected while in the Perform Bridge Design form, which is shown in Figure 2-5.


Auto Load Patterns 2 - 7

Figure 2-5 Perform Seismic Design

2.5 Auto Load Patterns

After the Bridge Seismic Design has been run, the user can review the load pat-tern and load cases that SAP2000/Bridge has automatically generated using the Define Load Patterns form show in Figure 2-6.

Figure 2-6 Auto Load Patterns

2.6 Auto Load Cases

The reason for each of the auto load cases is explained in Step 7.


2 - 8 Auto Load Cases

Figure 2-7 Auto Load Cases

Overview 3 - 1

Step 3 Dead Load Analysis and Cracked Section Properties

3.1 Overview

As shown in the schematic included in the Foreword, the third step begins with the dead load analysis of the entire bridge model. The results of the dead load analysis are then used to verify the analytical model followed by the determina-tion of the cracked section properties that are then applied to the bent columns as frame section property modifiers. The reduced stiffnesses of the bent columns will affect the response spectrum and pushover analyses. The frame section prop-erty modifiers are defined separately for each of the bent and abutment columns as a named property set. The user can use the Section Designer program to ob-serve the moment-curvatures and I,cracked properties for the various cross-sections (see also Step 5).

Auto load patterns and auto load cases are produced by the program. The load case, which has the default name, _GRAV_SDReq1, is automatically developed by SAP2000/Bridge as a single stage construction load case and is used to apply the cracked section property modifiers to the columns. Figure 3-1 shows the Load Case Data form for the _GRAV_SDReq1 load case. The auto load cases are not modifiable.


3 - 2 Overview

Figure 3-1 Auto Stage Construction Load Case used to apply

Cracked Section Property Modifiers

As an option, the user can overwrite the cracked section property determined by the program and instead, apply a user defined value. See Step 2 for the user op-tions available in the Seismic Design Request.

Overview 4 - 1

Step 4 Response Spectrum and Demand Displacements

4.1 Overview

The seismic response of the entire bridge structure is analyzed by SAP2000/ Bridge using the response spectrum function defined in Step 2. The number of modes used by SAP2000/Bridge is automated and depends on the number of bridge spans. The user should check the total mass participation to ensure that an adequate number of modes are included in the modal analysis. The response spectrum displacements are used by SAP2000/Bridge as the displacement de-mands as defined in Section 4.4 of the AASHTO Seismic Guide Specification.

4.2 Response Spectrum Load Cases

Three response spectrum load cases are automatically produced by SAP2000/ Bridge: _RS_X_SDReq1, _RS_Y_SDReq1 and _RS_XY_SDReq1. The first two response spectrum load cases apply the dynamic loads along the U1 and U2 di-rections. The U1 direction is defined as the longitudinal loading direction that is chosen to be from the start abutment to the end abutment, both points located on the reference line of the bridge object. If the user wants to apply a response spec-trum load along a different axis, a directional overwrite is available in the Sub-structure Seismic Design Parameters form (see Chapter 2).

SAP2000 Bridge Seismic Design

4 - 2 Response Spectrum Load Cases

Figure 4-1 U1 Direction Response Spectrum LOAD Case form

The third response spectrum load case uses a Directional Combination option of “ABS,” with an ABS scale factor of 0.3. This response spectrum load case will satisfy the AASHTO Seismic Guide Specification, Section 4.4, which requires the response spectrum loads to be combined using the 100/30 percent rule in each of the major directions. The single response spectrum load case, _RS_XY_SDReq1, envelopes the maximum response spectrum results for each of the combinations 100/30 and 30/100. The Load Case Data form for the response spectrum load case _RS_XY_SDReq1 is shown in Figure 4-2.

The modal damping coefficient is set to 5 percent, but this value can be modified as necessary by the user in the Substructure Seismic Design Parameters form (Chapter 2).

Step 4 - Response Spectrum and Demand Displacements

Response Spectrum Load Cases 4 - 3

Figure 4-2 ABS Response Spectrum LOAD Case form

To illustrate the ABS directional combination feature, the following BENT1 dis-placements are summarized for example model MO_1C:

Figure 4-3 BENT1 Displacements for the three Auto Defined Response Spectrum Load cases

SAP2000 Bridge Seismic Design

4 - 4 Response Spectrum Results

Figure 4-4 Modal Load Case Definition

4.3 Response Spectrum Results

Upon completion of the response spectra analysis, the displacements are tabu-lated for each bent. The displacements are calculated using “Generalized Dis-placements” to account for the average cap beam displacements and the relative displacement between the cap beam and foundation. The displacements for the ABS response spectrum load case also are tabulated for each of the bearing ac-tive degrees of freedom. These can be view using the Display menu > Show Tables command by selecting the Design Results for Bridge Seismic option and selecting the Support Bearing Demands-Deformations item. These displacements also can be displayed and animated on screen or read from the quick report cre-ated using the Design menu > Bridge > Quick Report command.

Overview 5 - 1

Step 5 Determine Plastic Hinge Properties and Assignments

5.1 Overview

For bridge structures having a Seismic Design Category (SDC) D the AASHTO Seismic Guide Specification requires that the displacement capacity be determined using a nonlinear pushover analysis. This requires that the col-umn plastic hinge lengths and plastic hinge properties be determined for each column that participates as part of the Earthquake Resisting System (ERS).

In this step, the methodologies used to calculate the plastic hinge lengths and properties will be explained. After the hinge properties have been determined, the plastic hinges are assigned to the ERS columns. The automation of the plas-tic hinge assignments will also be explained in this step.

5.2 Plastic Hinge Lengths

The plastic hinge lengths used in the Seismic Design Request is determined for the AASHTO Seismic Guide Specification, Section 4.11.6, as follows:

Plastic Hinge Length, 0 08 0 15P ye blL . L . f d ,

where


5 - 2 Plastic Hinge Lengths

yef = the effective yield strength of the longitudinal reinforcing, and

bld = the diameter of the longitudinal reinforcing.

The hinge length is compared to the value for the maximum hinge length value described as, 0 3P ye blL . f d , and the controlling value is used. After the hinge

lengths and properties have been determined, the hinges are placed on the bent columns at each end of the column at distances from each end equal to 1/2 the hinge length, as shown below in Figure 5-1.

Figure 5-1 Hinge Locations

Step 5 - Determine Plastic Hinge Properties and Assignments

Nonlinear Hinge Properties 5 - 3

Figure 5-2 Hinge Locations

5.3 Nonlinear Hinge Properties

Currently, the SAP2000/Bridge Automated Seismic Design Request uses a hinge property that is consistent with the AASHTO/CALTRANS idealized bi-linear moment-curvature diagram, as shown in Figure 5-3. From the moment curvature shown, the yield and plastic moments along with the I,cracked proper-ties can be observed for a specific axial load, P. Note that this form is made available to allow users to better understand the effects of axial loads and fiber mesh layouts on the frame member properties. The axial load values input on this form are not used in the analysis and design of a model.


5 - 4 Nonlinear Hinge Properties

Figure 5-3 Moment Curvature Diagram

Typically, the axial loads in the bent columns change as the bent is pushed over due to the overturning effects. Therefore, the yield and plastic moments will change depending on the amount of axial load present in a particular column at a particular pushover step. These effects are captured in the nonlinear hinge re-sponses whenever P-M or P-M-M hinges are specified. For this reason, the Automated Seismic Design procedure assigns coupled P-M-M hinges to the bent columns. The default settings are shown in Figure 5-4. The length of the plastic hinge also is calculated by SAP2000/Bridge when using the Automated Seismic Design procedure.


Nonlinear Hinge Properties 5 - 5

Figure 5-4 Auto Hinge Assignment Data

Figure 5-5 Sample Hinge Data form


5 - 6 Nonlinear Material Property Definitions

Upon completion of the Pushover Analysis, the Hinge Results can be traced. This feature is explained in detail in Step 6.

5.4 Nonlinear Material Property Definitions

The ductile behavior of a plastic hinge is significantly affected by the nonlinear material property used to define the frame member receiving the hinges. The material nonlinear properties must be defined using the Advanced Nonlinear Material Data forms.

5.4.1 Nonlinear Material Property Definitions for Concrete For concrete the nonlinear material property data form appears in Figure 5-6 as follows:

Figure 5-6 Nonlinear Material Data form for Concrete


Nonlinear Material Property Definitions 5 - 7

Figure 5-7 Nonlinear Stress-Strain curves for Confined and Unconfined Concrete

Figure 5-8 Concrete Model - Mander Confined


5 - 8 Nonlinear Material Property Definitions

5.4.2 Nonlinear Material Property Definitions for Steel

Similarly, for steel, the nonlinear material data form appears as show in Figure 5-9. The user can specify the parametric strain data, which includes the values for the strain at the onset of hardening, ultimate strain capacity, and the final slope of the stress-strain diagram.

Figure 5-9 Nonlinear Material Data form for steel


Plastic Hinge Options 5 - 9

Figure 5-10 Nonlinear Stress-Strain Plot for steel

5.5 Plastic Hinge Options

There are two ways that concrete column section properties can be defined for use as such that hinges properties can be assigned to them during the Auto-mated Seismic Design procedure. One method is to use the Section Designer and the other is to define a rectangle or circle using the Define menu >Section Property > Frame Section > Add New Property command and define a rec-tangular or circular shape. Internally, SAP2000/Bridge will convert the rectan-gular or circular shapes into Section Designer sections for the purposes of de-termining the hinge and cracked section properties. The advantage of using the Section Designer feature is that the user can choose to have the hinge defined using fibers. This option is activated when the user activates the Design menu > Fiber Layout command from within Section Designer and sets the Fiber Application to “Calculate Moment Curvature Using Fibers,” as shown in the following form.


5 - 10 Plastic Hinge Options

Figure 5-11 Plastic Hing Fiber option

The fiber mesh also can be specified in this form. The mesh can be rectangular or cylindrical depending on the shape of the column. Another advantage of us-ing the Section Designer feature is that complex sections, similar to the one be-low, can be handled.

Figure 5-12 Section Designer options

Displacement Capacities for SDC B and C 6 - 1

Step 6 Capacity Displacement Analysis

This step describes the automated procedure that SAP2000/Bridge uses to de-termine the bridge seismic capacity displacements. The method used varies de-pending on the Seismic Design Category (SDC) of a particular bridge. A flow-chart that describes when an implicit or pushover analysis is used to determine the capacity displacements is shown in Figure 6-1:

Figure 6-1 Rectangular Beam Design


6 - 2 Displacement Capacities for SDC B and C

Figure 6-2 Design Requirements for SDC

A B C D

Identification ERS Recommended Required Required

Demand Analysis Required Required Required

Implicit Capacity Required Required Required

Push Over Capacity May be required

Support Width Required Required Required Required

Detailing – Ductility SDC B SDB C SDB D

Capacity Protection Recommended Required Required

Liquefaction Recommended Required Required

The user can overwrite the program determined SDC to enforce that a push-over analysis is used to determine the displacement capacity. The differences between the implicit and pushover approaches are described in the following sections.

6.1 Displacement Capacities for SDC B and C

For structures having reinforced concrete columns, the displacement capacities for SDC B and C are found using the following equations. The AASHTO Seismic Guide Specification equations are also noted.

For SDC B:

0.12 1.27ln( ) 0.32 0.12LC o oH x H (4.8.1-1)

For SDC C:

0.12 2.32ln( ) 1.22 0.12LC o oH x H (4.8.1-2)

in which

o

o

Bx

H

(4.8.1-3)

where,

Step 6 - Capacity Displacement Analysis

Displacement Capacities for SDC D 6 - 3

Ho = Clear height of the column (ft)

B0 = Column diameter or width parallel to the direction of displace-ment under consideration (ft)

= Factor for the column end restraint conditions

6.2 Displacement Capacities for SDC D

When the Seismic Design Category for a bridge structure is determined to be SDC D or the user overwrites the SDC as D, SAP2000/Bridge uses a pushover analysis in accordance with the AASHTO Seismic Guide Specification, Sec-tion 4.8.2 to determine the displacement capacities. This requires that SAP2000/Bridge actually perform several pushover analyses, depending on the number of bents that are part of the Earthquake Resisting System (ERS). Each bent is analyzed in a transverse and longitudinal direction local to the specific bent. For the example bridge used in this manual, there are three spans with two interior bents. Bents can be used as abutment supports so it is possible to have additional bents participating as part of the ERS. But, for the example bridge, there are two interior bents. This means that a total of four pushover analyses is needed to determine the displacements capacities for each bent in each of the transverse and longitudinal directions.

To perform multiple pushover analyses on a single bridge model, SAP2000/ Bridge uses several nonlinear single-staged construction load cases. A license for the Staged Construction Module is not required to run the Bridge Seismic Design because SAP2000 allows for ‘single-staged’ construction load cases to be run with any license. If, however, the user wants to create multi-staged con-struction load cases, an additional license will be required.

For the example bridge, the four separate pushover load cases are named as fol-lows:

_PO_TR_BT1_SDReq1

_PO_LG_BT1_SDReq1

_PO_TR_BT2_SDReq1

_PO_LG_BT2_SDReq1


6 - 4 Displacement Capacities for SDC D

The SDReq1 is the name provided by the user to identify a particular seismic design request.

TR denotes Transverse and LG denotes Longitudinal.

The “_” symbol is added to the beginning of each auto load case name to dis-tinguish the load cases that are automatically provided by SAP2000/Bridge from user defined load cases.

Figure 6-3 shows the nonlinear single-staged construction load case for the BENT1 transverse direction.

Figure 6-3 BENT1 Transverse Pushover Load Case

The user can not modify this load case because it is defined automatically. The _PO_TR_BT1_SDReq1 load case starts from the end of the initial nonlinear load case named, _ bGRAV_SDReq1.


Displacement Capacities for SDC D 6 - 5

The _ bGRAV_SDReq1 load case is shown in Figure 6-4 and is needed to iso-late the bents from the rest of the bridge model and to apply the cracked section property modifiers as well as apply the dead load.

Figure 6-4 BENT1 Application of Property Modifiers

and Dead Loads to BENT1

The load pattern used to apply the lateral pushover loads or displacements to BENT1 is named, _PO_TR1_SDReq1. A 3D view of the _PO_TR1_SDReq loads is shown in Figure 6-5. The magnitudes of these loads are based on the reactions from the superstructure.


6 - 6 Pushover Results

Figure 6-5 BENT1 Pushover Load Pattern for the Transverse Direction

6.3 Pushover Results

After the pushover analyses have run, the capacity displacements are automati-cally identified as the maximum displacement of the pushover curve just before strength loss (negative slope on the pushover curve) for each of the pushover runs.


Pushover Results 6 - 7

The pushover results can be viewed using the Display menu > Pushover Re-sults command. An example output is shown in Figure 6-6 for the BENT1 transverse and longitudinal pushover load cases.

Figure 6-6 Display of BENT1 Pushover Curves

D/C Ratios 7 - 1

Step 7 Demand/Capacity Ratios

7.1 D/C Ratios

After the demand displacement (Step 4) and displacement capacity (Step 6) analyses have been completed, SAP2000/Bridge computes the ratio of the De-mand/Capacity displacements and reports these values in the Seismic Design Report. The table of D/C ratios can be viewed using the Display menu > Show Tables command, and then selecting Design Data > Bridge > Seismic Design data > Table: Bridge Seismic 01-Bent D-C-AASHTO LRFD 2007. The sub-ject table will appear similar to the table shown in Figure 7-1:

Figure 7-1 D/C Displacement Ratios


7 - 2 D/C Ratios

In the table shown, all four D/C ratios are reported, namely, the transverse and longitudinal direction for each bent (the example model has two bents). Note that the Generalized Displacement name also is reported. Generalized dis-placements are used to average the top of bent displacements and to determine the relative displacements between the bent cap beam and the foundation. The generalized displacement definition is automatically defined by SAP2000/ Bridge and can be viewed using the Define menu > Generalized Displace-ments command.

Design 01 – D-C Ratios 8 - 1

Step 8 Review Output and Create Report

This step describes the two methods of viewing the seismic design results. The first way to review the results is to use the Display menu > Show Tables com-mand. The second way is to create a report using the Design menu > Bridge De-sign > Create Report command.

The entire list of output tables for the Bridge Seismic Design includes the follow-ing:

The seven Bridge Seismic Design tables are described in the sections that follow:


8 - 2 Design 01 – D-C Ratios

8.1 Design 01 – D-C Ratios

The Demand/Capacity ratios are summarized for each bent in each direction. Values less than 1.0 indicate that an adequate capacity exists for a given bent and direction for the ground motion hazard used in the seismic design request. Values greater than 1.0 indicate an overstress condition.

8.2 Design 02 – Bent Column Force Demand

A summary of the bent column seismic demand forces are tabulated.

8.3 Design 03 – Bent Column Idealized Moment Capacity

The idealized column plastic moments are calculated and tabulated. The axial load P represents the demand axial load. The idealized plastics moments are de-termined using the associated axial load value, P.

Step 8 - Review Output and Create Report

Design 04 – Bent Column Cracked Section Properties 8 - 3

8.4 Design 04 – Bent Column Cracked Section Properties

A summary of the cracked property modifiers that get applied to each of the bent columns is tabulated.

8.5 Design 05 – Support Bearing Demand – Forces

The forces in the bearing due to the seismic loads are presented in the table above. All bearings at the abutments and bents that are found to resist seismic forces are included in the subject table.


8 - 4 Design 06 – Support Bearing Demand – Displacements

8.6 Design 06 – Support Bearing Demand – Displacements

The displacements for all bearings at the abutments and bents that resist seismic loads are tabulated and reported.

8.7 Design 07 – Support Length Demands

The support lengths are calculated from the bearing displacements and represent the amount of displacement normal to a specific bent or abutment.


Create Report 8 - 5

8.8 Create Report

A single command can be used to create a report using the Design menu > Bridge Design > Create Seismic Design Report command. Several representa-tive pages of the report that can be created using the previously noted report re-quest are included in the following pages. Theses have been excerpted from a 30 page summary report that SAP2000/Bridge writes as a Microsoft Word docu-ment.


8 - 6 Create Report


Create Report 8 - 7


8 - 8 Create Report

R - 1

References

ACI, 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08), American Concrete Institute, P.O. Box 9094, Farmington Hills, Michigan.

AASHTO, 2009. AASHTO Guide Specifications for LRFD Seismic Bridge Design. American Association of Highway and Transportation Offi-cials, 444 North Capital Street, NW Suite 249, Washington, DC 2001

bridge seismic design according sap 2000

Documents

ground motion hazard

earthquake resisting system

design menu

seismic design category

seismic design request

gravity load case

display menu

spectrum load case