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Bridge Seismic Design

CSiBridge®

Bridge Seismic Design Automated Seismic Design of Bridges

AASHTO Guide Specification for LRFD Seismic Bridge Design

ISO BRG102816M14 Rev. 0 Proudly developed in the United States of America October 2016

Copyright

Copyright Computers & Structures, Inc., 1978-2016 All rights reserved. The CSI Logo® and CSiBridge® are registered trademarks of Computers & Structures, Inc. Watch & LearnTM is a trademark 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 CSiBridge® 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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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.

Contents

Foreword

Step 1 Create the Bridge Model

1.1 Example Model 1-1

1.2 Description of the Example Bridge 1-2

1.3 Bridge Layout Line 1-4

1.4 Frame Section Property Definitions 1-4

1.4.1 Bent Cap Beam 1-4 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 1-11

1.7.1 Abutment Property Assignments 1-12 1.7.2 Abutment Geometry 1-15 1.7.3 Bent Property Assignments 1-15

i

CSiBridge Seismic Design

1.7.4 Bent Geometry 1-17

1.8 Equivalent Pile Formulation 1-17

1.9 Bent Foundation Modeling 1-18

1.10 Mass Source 1-19

Step 2 Ground Motion Hazard and Seismic Design Request

2.1 Overview 2-1

2.2 AASHTO and USGS Hazard Maps 2-1

2.3 Seismic Design Preference 2-3

2.4 Seismic Design Request 2-4

2.5 Perform Seismic Design 2-8

2.6 Auto Load Patterns 2-9

2.7 Auto Load Cases 2-10

Step 3 Dead Load Analysis and Cracked Section Properties

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 4-5

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 5-4

5.4 Nonlinear Material Property Definitions 5-7

ii

Contents

5.4.1 Nonlinear Material Properties Definitions for Concrete 5-7

5.4.2 Nonlinear Material Properties Definitions for Steel 5-9

5.5 Plastic Hinge Options 5-10

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 6-7

Step 7 Demand/Capacity Ratios

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 8-5

8.8 Create Report 8-5

Chapter 9 Caltrans Fault Crossing Seismic Bridge Design

9.1 Introduction 9-1

9.2 Fault Crossing Response Spectrum Loading 9-2

iii


9.3 Defining Fault Crossing Seismic Design Requests 9-5

9.4 Running Fault Crossing Seismic Design Requests 9-10

9.5 Creating a Seismic Design Report 9-11

9.6 Automatic Load Cases and Combinations 9-12

9.7 General Displacement Loading 9-14

9.7.1 Defining Load Patterns and Response Spectrum Functions 9-15

9.7.2 Defining a Seismic Design Request 9-17

References

iv

Foreword

Over the past thirty-five years, Computer and Structures, Inc, has introduced new and innovative ways to model complex structures. CSiBridge, the latest innovation, is the ultimate integrated tool for modeling, analysis, and design of bridge structures. The ease with which all of these tasks can be accomplished makes CSiBridge the most versatile and productive bridge design package in the industry.

Automated seismic design, one of CSiBridge’s many features, incorporates the recently adopted AASHTO Guide Specification for LRFD Seismic Bridge Design 2nd Edition, 2011. The 2011 implementation in CSiBridge also satisfies the 2012 and 2014 interim revisions, which do not contain any changes that af-fect the program. CSiBridge allows engineers to define specific seismic design parameters 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 CSiBridge program will determine the demand and capacity dis-placements and report the demand/capacity ratios for the Earthquake Resisting System (ERS). All of this is accomplished in eight simple steps outlined as fol-lows:

1. Create the Bridge Model

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

vii


3. Complete the Dead Load Analysis and evaluate the Cracked Section Prop-erties

4. Identify Response Spectrum and Demand Displacements

5. Determine Plastic Hinge Properties and Assignments

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 CSiBridge Automated Seismic Design features.

Schematic of the Eight Steps in the Automated Seismic Design of Bridges using CSiBridge

viii Foreword

Foreword

In addition to AASHTO Bridge Seismic Design, CSiBridge provides the capa-bility to perform Caltrans Fault-Crossing Seismic Bridge Design. This new seismic design procedure considers the more severe case where the rupture of a seismic fault that crosses a bridge structure causes significantly different ground displacements for the supports on either side of the fault. Most of the concepts that apply to AASHTO Bridge Seismic Design also apply to the Cal-trans Fault-Rupture case, with some new techniques introduced for this special purpose. The details are provided in the last chapter of this manual.

Foreword vii

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 CSiBridge. It is assumed the user is familiar with the requirements in the program related to creating a Linked Bridge Object. Only select features of the model development are in-cluded in this chapter. The CSiBridge model used throughout this manual is available and includes all of the input parameters.

Figure 1-1 3D View of Example Model

Example Model 1 - 1


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

1 - 2 Description of the Example Bridge

STEP 1 - Create the Bridge Model

Figure 1-3 Example Bridge Plan

Figure 1-4 Example Bridge BENT1 Elevation

Description of the Example Bridge 1 - 3


1.3 Bridge Layout Line The example model has three spans of approximately 60 feet each. The layout line is defined using the Layout > Layout Line > New 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.

1.4.1 Bent Cap Beam The bent cap beams were defined using the Components > Type > Frame Properties > Expand arrow command. The Add New Property button >

1 - 4 Bridge Layout Line


Frame Section Property Type: Concrete > Rectangular was used to add the fol-lowing 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. (To check this, hold down the Shift key and double click in the Depth or Width edit box. This will display the CSiBridge Calculator.)

1.4.2 Bent Column Properties The bent columns were defined using the Section Designer option that can be accessed using the Components > Type > Frame Properties > New > Other > Section Designer command. 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 plas-tic hinge definitions is provided in Step 5.

Frame Section Property Definitions 1 - 5


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. (Again, check this by holding down the Shift key and double clicking in a dimension edit box to display the CSiBridge Calculator.)

Figure 1-8 Precast I-Girder Properties

1 - 6 Frame Section Property Definitions


1.4.4 Pile Properties The piles were defined as 14–inch-diameter concrete piles with six #9 vertical bars (Components > Type > Frame Properties > New > Concrete > Circu-lar command). 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 described 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

Frame Section Property Definitions 1 - 7


1.5 Bridge Deck Section The bridge deck section is 38.833 feet wide with a total of five I-girders, as shown in Figure 1-10 (Components > Superstructure Type > Deck Section > New command). 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, which is accessed using the Components > Substructure Item > Bents > New com-mand, 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.

1 - 8 Bridge Deck Section


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 as well as the seismic hinge data for each bent column.

Figure 1-12 Bent Column Data

For the seismic hinge data, RH Long and RH Trans are the relative clear heights (from -1.0 to 2.0) from the base of the column to the point of contra-

Bent Data 1 - 9


flexure under horizontal loading at the top of the bent, used to determine the hinge lengths and positions for bridge seismic design. RH Long is for longitu-dinal loading (normal to the plane of the bent), and RH Trans is for transverse loading (in the plane of the bent). Only concrete columns are affected. Steel columns are not affected and use their own calculation. For each physical bent column, the reference hinge property to be used at the top and bottom of the column can be "Auto", "Auto Fiber", "None", and a list of user-defined hinge properties. The reference hinge properties will only be used when the Concrete or Steel Hinge Type is set to Auto: From Bent in the Bridge Seismic Design Preference form, which is accessed using the Design/Rating > Seismic Design > Preferences command. Under the case that the Hinge Type is Auto: From Bent, if the reference hinge property is set to Auto, then the program will gen-erate AASHTO/Caltrans hinges for concrete columns and FEMA 356 hinges for steel columns; if the reference hinge property is set to user-defined hinge property, then for the force-controlled type hinges, or the deformation con-trolled type hinges with moment-rotation or force-displacement nonlinear property types,

An important part of this example model is the inclusion of the foundation el-ements. 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 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. Access this form by clicking the Foundation Spring Properties button on the Bridge Bent Column Data form and then the Add New Foundation Spring button on the Define Bridge Foundation Springs form, or by using the Components > Substructure Item > Foundation Springs > New command.

1 - 10 Bent Data


Figure 1-13 Bent Column Base Restraint Definitions

1.7 Bridge Object Definition The Bridge Object Data form (click the Bridge > Bridge Object > New com-mand) is used to define the complete bridge object, including the superstructure and substructure. See Figure 1-14.

The seismic response of the bridge model will depend on the Earthquake Re-sisting 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 be defined using bents as supports (this feature was not used in the subject example).

Bridge Object Definition 1 - 11


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 and Modify/Show button. 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 specified using the Bridge Ob-ject Abutment Assignments form shown in Figure 1-15 (Bridge > Bridge Ob-ject > Supports > Abutments). The abutment bearing direction can be as-signed a bearing angle if skewed abutments are needed. Diaphragms can be added to the abutment as well.

Abutments are modeled using an “Abutment Property”, which can be defined using the command Components > Substructure Item > Abutments > New. This can also be accessed by clicking the “+” button next to the Abutment Property option in the Substructure Assignment area of the Bridge Object Abutment Assignments form. This brings up the Abutment Data form as shown

1 - 12 Bridge Object Definition


in Figure 1-16. Note that a default abutment property is always created when-ever the first bridge object is defined, and that is what is used for this example.

Figure 1-15 Abutment Assignments

Figure 1-16 Abutment Data

Abutments can alternatively be modeled using bents by selecting “Bent Proper-ty” in the Substructure Assignment area of the Bridge Object Abutment As-signment form. After that selection has been, an option is available to select the appropriate property definition from a list of previously defined bent proper-ties, or to add a new one by clicking the “+” button.



The substructure location data is critical because CSiBridge 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 restraint was assumed to be free in the longitudinal and transverse di-rections. See Figure 1-17 (display this form by clicking the “+” plus beside the Bearing Property drop-down list on the Bridge Object Abutment Assignments form and the Add New Bridge Bearing or Modify/Show Bridge Bearing but-ton on the Define Bridge Bearings form).

Figure 1-17 Abutment Bearing Properties

To help visualize the abutment geometry, the graphic shown in Figure 1-18 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 CSiBridge program automatically includes the BFXSS Rigid Link when the bridge object is updat-ed.



1.7.2 Abutment Geometry Figure 1-18 also shows the location of the BBRG1 action point. This is the lo-cation where the bearing will translate or rotate depending on the bearing defi-nitions.

Figure 1-18 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 1-19 (Bridge > Bridge Object > Supports > Bents command). Similar to the abutment property assignments, the bent prop-erty assignments will include the bent directions, bearing properties, and sub-structure locations.



Figure 1-19 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 1-20 (click the “+” plus beside the Bearing Property drop-down list; click the Modify/Show Bridge Bearing button on the Define Bridge Bearings form).

Figure 1-20 Bent Bearing Data



1.7.4 Bent Geometry The bent geometry is shown in Figure 1-21 for the input values used to define the bearing and substructure elevations from the Bridge Object Bent Assign-ment form (Figure 1-19).

Figure 1-21 Bent Support Geometry

Note that the BBRG2 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 BBRG2 is 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 1-22.

Equivalent Pile Formulation 1 - 17


Figure 1-22 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 1-23, which is shown using a 3D extruded view.

Figure 1-23 View of Bent Foundations

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 1-24. This method of connecting the column base to the foundation preserves connectivity even when updating the linked bridge model.

1 - 18 Bent Foundation Modeling


Figure 1-24 Bent Column Base Connectivity

1.10 Mass Source The Mass Source definition is used to define the mass to be included in the modal and response spectrum load cases. Mass and weight are treated separate-ly in CSiBridge: mass is used for inertia in dynamic analysis, and weight is used for gravity loads.

By default, mass comes from the material mass density and any additional mass assigned to joints, line objects, and area objects. However, you can use the Mass Source command to specify that mass is to be computed from load patterns, either in addition to or instead of the default mass.

Multiple Mass Sources definitions can be created for advanced dynamic analy-sis. This is rarely necessary. For this example, a single Mass Source is defined that uses the default mass plus mass from load patterns.

The command Advanced > Define > Mass Source opens the Mass Source form in shown Figure 1-25. Here the default mass source already defined can be seen. Clicking the Modify/Show button opens the Mass Source Definition form shown in Figure 1-26.

Column-to-Foundation Connection

Mass Source 1 - 19


Figure 1-25 Mass Source

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 superimposed type with the name SDEAD (Loads > Load Patterns).

This default mass that comes from the mass density of the materials is indicat-ed by the option “Element Self Mass and Additional Mass”, which is checked by default. Checking the additional option “Specified Load Patterns” allows adding a linear combination of load patterns from which mass is to be comput-ed. In this example the load pattern SDEAD is used with a scale factor of one.

Figure 1-26 Mass Source Definition

Note that adding load pattern DEAD would double-count the Element Self Mass.

1 - 20 Mass Source

STEP 2 Ground Motion Hazard and Seismic Design Request

2.1 Overview The ground motion hazard (response spectrum) can be determined by CSiBridge by defining the bridge location using the latitude and longitude 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 considered 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, CSiBridge creates the appropriate response spectra curve as follows:

Overview 2 - 1


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

Figure 2-2 Response Spectrum Function Data form

2 - 2 AASHTO and USGS Hazard Maps

STEP 2 - Ground Motion Hazard and Seismic Design Request

From the Response Spectrum Data form (Loads > Functions > Type > Re-sponse Spectrum > New > NCHRP 20-07), the values for SDS and SD1 are de-termined by CSiBridge and reported. The SD1 value is used to determine the Seismic 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, CSiBridge uses an implicit formula (see Section 4.8 of the AASHTO Seismic Guide Specification). If the SDC is D, CSiBridge uses a nonlinear pushover analysis to determine the capacity displacements.

2.3 Seismic Design Preferences

Figure 2-3 Bridge Seismic Design Preferences form

The Design/Rating > Seismic Design > Preferences command accesses a form that can be used to specify the design code, concrete hinge type, steel hinge type and the hinge length option for all Seismic Design Requests. There are four choices for the hinge type: Auto: AASHTO/Caltrans Hinge for concrete and FEMA 356 hinge for steel, Auto: Fiber Hinge, Auto: From Bent and User-assigned. The following hinge length options are provided: Use Longitudinal Hinge Length, Use Transverse Hinge Length, Use Shortest Hinge Length (DE-FAULT), Use Longest Hinge Length, and Use Average Hinge Length. The longitudinal and transverse hinge lengths are calculated based on the Seismic

Seismic Design Preferences 2 - 3


Hinge Data specified in the Bridge Bent Column Data Form introduced in the Section 1.6.

2.4 Seismic Design Request

Figure 2-4 Bridge Design Request form

The Design/Rating > Seismic Design > Design Request > Add New Request command accesses a form that can be used to specify the name, check type, loading and design request parameters for a Seismic Design Request. There are two check types available: AASHTO Seismic Design and Caltrans Fault Cross-ing. For the loading, the pre-defined response spectrum function (see Section 2.2) to be used for a specific Seismic Design Request should be selected for the horizontal and/or vertical direction. “None” should be selected if no response spectrum is to be included in either direction in the seismic design request. The form is shown in Figure 2-4.

For this example, which is of AASHTO Seismic Design, clicking the Modi-fy/Show button will display the Substructure Seismic Design Request Parame-ters form, shown in Figure 2-5. A brief description of the parameters on that form follows.

2 - 4 Seismic Design Request


Figure 2-5 Seismic Design Parameters form

Item Substructure Seismic Design Request Parameter

1 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 4, the Seismic Design Category.

2 Seismic Design Category

If the user has opted to specify the Seismic Design Category in Item 3, the user must specify the Seismic Design Category here as B, C or D.

3 Bent Dis-placement 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 longi-tudinal and transverse directions.

Seismic Design Request 2 - 5



4 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 This Bridge Object, or User Defined. As a default, all Dead and Super Dead loads are included in the Auto-Entire Structure gravity load case.

5 Gravity Load Case

If the User Option is selected for Item 6 Gravity Load Case Option, the gravity load case name must be selected here.

6 Additional Group

If the Auto-This Bridge Object option is selected for Item 6 Gravity Load Case Option, an additional group can be included in the gravity load case. This item is required only when the gravity load case is program determined. It may include pile foundations and other auxiliary structures.

7 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 pusho-ver curve results if an idealized bilinear hinge has been assigned to the bent columns. It is recommended that an initial Seismic Design Request be performed before including the P-Delta effects to help the user understand the nonlinear behavior of the bents.

8 Cracked Property Option

The cracked section properties for the bent columns can be auto-matically determined by the program or they can be user defined. If program determined, the automatic gravity load case will be run iteratively. Section Designer will use the calculated axial force at the top and bottom on the column to determine the cracked mo-ments of inertia in the positive and negative transverse and longi-tudinal directions. The average 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.

9 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.

10 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 required only when the cracked-property calculation is program determined.

11 Accept Unconverged Results

Specifies if the seismic design should or should not continue if the bent-column cracked-property iteration fails to converge. This item is required only when the cracked-property calculation is program determined.

12 Modal Load Case Option

Specifies if 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 de-sign. If program determined, the modal load case will use the stiff-

2 - 6 Seismic Design Request



ness 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 se-lecting user defined for Item 15 Modal Load Case.

13 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 Item 14 Modal Load Case Option is user-defined.

14 Type of Modes This is either Eigen or Ritz indicating the type of modes requested.

15 Additional Number Of Modes

The number of additional modes to consider beyond those auto-matically determined. This can be zero (default), positive, or nega-tive. The default number of modes is determined based on the number of bridge spans. The minimum number of modes is 12. For a bridge object with more than two spans, 6 modes are added for each additional span.

16 Response Spectrum Load Case Option

Specifies if 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 combina-tions.

17 Response Spectrum Load Case

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

18 Response Spectrum An-gle Option

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

19 Response Spectrum Angle

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

20 Directional Combination

The type of directional combination for the response spectrum analysis

21 Directional Scale Factor

For absolute directional combination this is the scale factor used for the secondary directions when taking the absolute sum. This is typically 0.3 if a 100/30 rule is to be applied. For CQC3 directional combination, this is the scale factor applied to the response spec-trum function in the second horizontal direction. This is typically greater than 0.5. For the SRSS directional combination the direc-

Seismic Design Request 2 - 7



tional scale factor is normally 1.0.

22 Foundation Group

If foundations are included and explicitly modeled, then the founda-tion objects need to be assigned to a group and that group needs to be identified here. This way the foundation objects will be includ-ed in the pushover load case. This item is required only if the seis-mic design category is D.

23 Pushover Target Displacement Ratio

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

24 Bent Failure Criterion

The criteria to determine the bent failure. <Pushover Curve Drop> means the bent fails when the pushover curve drops from its abso-lute maximum to a value 1% less than that maximum. <First Hinge At Limit State> means the capacity is determined as the displace-ment when the first bent column hinge reaches the specified hinge limit state. This item is required only if the seismic design category is D.

25 Pushover Curve Drop Tolerance / Hinge Limit State

When the Bent Failure Criterion is <Pushover Curve Drop>, this item is for Pushover Curve Drop Tolerance, which is relative de-crease in base shear from the maximum that determined the dis-placement capacity from the pushover curve. Bent Failure Criterion is <First Hinge At Limit State>, this item is for Hinge Limit State, which is to determine hinge failure point. This can be B, C, D or E specified in the material stress-strain curve. For a fiber hinge, each individual fiber will be checked. This item is required only if the seismic design category is D.

26 Transverse Pushover Type

The pushover modeling type for the transverse direction of the bents for the seismic design category D. The options are bents with or without superstructure.

27 Longitudinal Pushover Type

The pushover modeling type for the longitudinal direction of the bents for the seismic design category D. The options are bents with or without superstructure, and Full Bridge Along Chord.

2.5 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, use the Design/Rating > Seismic Design > Run Seismic command. The Perform Bridge Design form, which is shown in Figure 2-6, will be displayed. The De-sign Now button will start the seismic design process.

2 - 8 Perform Seismic Design


Figure 2-6 Perform Seismic Design

It is noted that for a designed request, when clicking the button "Delete Design for Request", a message box asking to remove all the program-generated items, such as load cases, load patterns, group, generalized displacement will be popped up. The “Yes” button will bring up another message box asking to re-move all the program-generated hinges. The program-generated items can be removed by clicking the button "Clean up Request" if they were kept when de-leting the design results. Also if the same design request is selected to be de-signed again when the model is locked, then a new set of the program-generated items will be created and previous generated items will be kept; when the model is unlocked, then the program will ask to remove the previous program-generated items or to keep them.

2.6 Auto Load Patterns After the Bridge Seismic Design has been run, the user can review the load pat-tern and load cases that CSiBridge has automatically generated by accessing the Define Load Patterns form show in Figure 2-7 (Loads > Load Patterns command).

Auto Load Patterns 2 - 9


Figure 2-7 Auto Load Patterns

2.7 Auto Load Cases The reason for each of the auto load cases is explained in Step 7.

Figure 2-8 Auto Load Cases

2 - 10 Auto Load Cases

Step 3 Dead Load Analysis and Cracked Section Properties

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. For concrete bent columns, these results are used for the determination of the cracked section properties that are then applied to the bent columns as frame section property modifiers. The re-duced stiffnesses of the concrete bent columns will affect the response spectrum and pushover analyses. The frame section property modifiers are defined sepa-rately for each of the concrete bent and abutment columns as a named property set. The user can use the Section Designer program to observe the moment-curvatures and I,cracked properties for the various cross-sections (see also Step 5). The calculation of the cracked section properties will be skipped for the steel bent columns and thus no frame section property modifiers will be generated and assigned to the steel bent columns.

Auto load patterns and auto load cases are produced by the program. The load case, which has the default name, <SDReq1>, is automatically developed by CSiBridge 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 <SDReq1>GRAV load case (Analysis > Load Cases > Type > All > New > Highlight <SDReq1>GRAV > Modify/Show Load Case). The auto load cases are not modifiable.

Dead Load Analysis and Cracked Section Properties 3 - 1


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.

3 - 2 Dead Load Analysis and Cracked Section Properties

Step 4 Response Spectrum and Demand Displacements

4.1 Overview The seismic response of the entire bridge structure is analyzed by CSiBridge us-ing the response spectrum function defined in Step 2. The number of modes used by CSiBridge 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 additional number of Modes can be added to the auto-generated modal load case as the item 15 in Figure 2-5. The response spectrum displacements are used by CSiBridge as the displacement de-mands as defined in Section 4.4 of the AASHTO Seismic Guide Specification.

4.2 Response Spectrum Load Cases For the case that no response spectrum function is assigned to the vertical direc-tion loading in the seismic design request form shown in Figure 2-4, three re-sponse spectrum load cases are automatically produced by CSiBridge: <SDReq1>RS_X, <SDReq1>RS_Y and <SDReq1>RS_XY. With a response spectrum function assigned to the vertical direction loading, an additional re-sponse spectrum load case <SDReq1>RS_Z is automatically produced and <SDReq1>RS_XY will be <SDReq1>RS_XYZ. For the case of no vertical load-ing, the first two response spectrum load cases apply the dynamic loads along the U1 and U2 directions. The U1 direction is defined as the longitudinal loading di-

Overview 4 - 1


rection 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 spectrum load along a different axis, a directional overwrite is availa-ble in the Substructure Seismic Design Request Parameters form (see Chapter 2).

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, <SDReq1>RS_XY, envelopes the maximum response spectrum results for each of the combinations 100/30 and 30/100. The Load Case Data form for the re-sponse spectrum load case <SDReq1>RS_XY is shown in Figure 4-2.

4 - 2 Response Spectrum Load Cases

Step 4 - Response Spectrum and Demand Displacements

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 Request Parameters form (Chapter 2).

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:

Response Spectrum Load Cases 4 - 3


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

Figure 4-4 Modal Load Case Definition

4 - 4 Response Spectrum Load Cases

Step 4 - Response Spectrum and Demand Displacements

4.3 Response Spectrum Results Upon completion of the response spectra analysis, the displacements are tabulat-ed for each bent. The displacements are calculated using “Generalized Displace-ments” to account for the average cap beam displacements and the relative dis-placement between the cap beam and foundation. The displacements for the ABS response spectrum load case also are tabulated for each of the bearing active de-grees of freedom. These can be viewed using the Home > Display > Show Ta-bles command to display the Choose Tables for Display form. Select the Design Results for Bridge Seismic, Support Bearing Demands-Deformations item. These displacements also can be displayed and animated on screen or read from the quick report created using the Design/Rating > Seismic Design > Report com-mand.

Response Spectrum Results 4 - 5

Step 5 Determine Plastic Hinge Properties and Assignments

5.1 Overview For bridge structures having a Seismic Design Category (SDC) D the AASH-TO Seismic Guide Specification requires that the displacement capacity be de-termined using a nonlinear pushover analysis. This requires that the column plastic hinge lengths and plastic hinge properties be determined for each col-umn 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 for the concrete bent columns used in the Seismic Design Request is determined for the AASHTO Seismic Guide Specification, Section 4.11.6, as follows:

For reinforced concrete columns framing into a footing, an integral bent cap, and oversized shaft, cased shaft, the plastic hinge length, LP in inches, may be determined as:

Overview 5 - 1


0 08 0 15P ye blL . L . f d= + ,

where

L = length of column from point of maximum moment to the point of moment contraflexure (in.),

yef = the effective yield strength of the longitudinal reinforcing (ksi), and

bld = the diameter of the longitudinal reinforcing (in.).

The hinge length is compared to the value for the minimum hinge length, de-scribed as 0 3P ye blL . f d= , and the larger value is used.

Note that, the L values for concrete columns are specified in the Bridge Bent Column Data Form (Section 1.6). Here a relative height, RH, is specified from the bottom of the column to the point of contraflexure, separately for longitu-dinal and transverse bending. Legal values are −1 ≤ RH ≤ 2, where RH = 0 is the bottom of the clear height of the column and RH = 1 is the top. For the bot-tom hinge:

𝐿𝐿 = |RH|𝐻𝐻, subject to 𝐻𝐻 2⁄ ≤ 𝐿𝐿 ≤ 𝐻𝐻

For the top hinge:

𝐿𝐿 = |RH − 1|𝐻𝐻 , subject to 𝐻𝐻 2⁄ ≤ 𝐿𝐿 ≤ 𝐻𝐻

This can be summarized in the following table:

Below Column Clear Height Above

RH -1.00 -0.75 -0.50 0.00 0.25 0.50 0.75 1.00 1.50 1.75 2.00

Bottom Hinge

L/H 1.00 0.75 0.50 0.50 0.50 0.50 0.75 1.00 1.00 1.00 1.00

Top Hinge

L/H 1.00 1.00 1.00 1.00 0.75 0.50 0.50 0.50 0.50 0.75 1.00

5 - 2 Plastic Hinge Lengths

Step 5 - Determine Plastic Hinge Properties and Assignments

For the steel columns, based on the Section 4.11.8 in AASHTO Seismic Guide Specification, the plastic hinge region is determined as the maximum of 1/8 of the clear height of a steel column or 1.5 times the gross cross-sectional dimen-sion in the direction of bending.

Calculated hinge lengths may be different for bending in the longitudinal or transverse direction of the bents. However, each hinge can only have a single hinge length in the model. Set the Hinge Length Option in the Bridge Seismic Design Preferences Form as described in Section 2.3 to specify whether to use the Longitudinal, Transverse, Longest, Shortest, or Average hinge length for a given instance of the model. After performing a bridge seismic design with one of these options, you can re-run the design with a different choice to see the ef-fect.

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

Plastic Hinge Lengths 5 - 3


Figure 5-2 Hinge Locations

5.3 Nonlinear Hinge Properties For a steel column, the CSiBridge Automated Seismic Design Request uses a hinge property that is consistent with the FEMA 356. For a concrete column, the Automated Seismic Design Request uses a hinge property that is consistent with the AASHTO/CALTRANS idealized bilinear moment-curvature diagram, as shown in Figure 5-3 (click the Display menu > Show Moment Curvature Cure command on the Section Designer form). From the moment curvature shown, the yield and plastic moments along with the I,cracked properties 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 lay-outs 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 Au-tomated Seismic Design procedure assigns coupled P-M-M hinges to the bent columns. The default settings are shown in Figure 5-4 (select the frame(s) to be assigned a hinge, click Advanced > Assign > Frames > Hinges, select Auto, click the Modify/Show Auto Hinge Assignments Data button). The length of the plastic hinge also is calculated by CSiBridge 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 Hinge Properties


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 as shown in Figure 5-6 (Components > Type > Material Properties > Expand arrow > check the Show Advanced Properties check box > Add New Material > set Material Type to Concrete > Modify/Show Material Properties button > Nonlinear Material Data button):

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

Nonlinear Material Property Definitions 5 - 9


Figure 5-10 Nonlinear Stress-Strain Plot for steel

5.5 Plastic Hinge Options Concrete column section properties can be defined for use in two ways such that hinge properties can be assigned to them during the Automated Seismic Design procedure. One method is to use the Section Designer and the other is to define a rectangle or circle using the Components > Type > Frame Prop-erties > New command and define a rectangular or circular shape. Internally, CSiBridge will convert the rectangular or circular shapes into Section Designer sections for the purposes of determining the hinge and cracked section proper-ties. The advantage of using the Section Designer feature is that the user can choose to have the hinge defined using fibers. This option is applied 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 Hinge 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

Plastic Hinge Options 5 - 11

Step 6 Capacity Displacement Analysis

This step describes the automated procedure that CSiBridge uses to determine the bridge seismic capacity displacements. The method used varies depending on the Seismic Design Category (SDC) of a particular bridge. A flowchart 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

Displacement Capacities for SDC B and C 6 - 1


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 Capac-ity

May be required

Support Width Re-quired

Required Required Required

Detailing – Ductility SDC B SDB C SDB D

Capacity Protec-tion

Recommended Required Required

Liquefaction Recommended Required Required

The user can overwrite the program determined SDC to enforce that a pushover 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 Seis-mic 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

BxHΛ

= (4.8.1-3)

6 - 2 Displacement Capacities for SDC B and C

Step 6 - Capacity Displacement Analysis

where,

Ho = Clear height of the column (ft)

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

Λ = Factor for the column end restraint conditions

CSiBridge uses the relative heights “RH Long” and “RH Trans” of Seismic Hinge Data specified in Bent Column Data form, shown in Figure 1-12, to de-termine the factor Λ :

RH ≤ 0 or RH ≥ 1: Λ = 1.0

0 < RH ≤ 0.5: Λ = 1 / (1 – RH)

0.5 < RH < 1.0: Λ = 1 / RH

For the bent columns that are not of Type 1 reinforced concrete, CSiBridge uses the same equations to determine the capacity. In this case, users may overwrite the SDC as D for a better solution, in which the capacity is determined based on the pushover analysis results.

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, CSiBridge uses a pushover analysis in accordance with the AASHTO Seismic Guide Specification, Section 4.8.2 to determine the displacement capacities. This requires that CSiBridge actually per-form 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 with or without superstruc-ture. For the pushover case with superstructure, the subject bent keeps its support bearings and all other support bearings are changed to rollers. For longitudinal pushover option “Full Bridge Along Chord,” the bridge movement is restrained along the chord direction and only one pushover load case is applied along the bridge chord direction. 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

Displacement Capacities for SDC D 6 - 3


example bridge, there are two interior bents. This means that a total of four push-over analyses are 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, CSiBridge uses several nonlinear single-staged construction load cases.

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

<SDReq1>PO_TR1

<SDReq1>PO_LG1

<SDReq1>PO_TR2

<SDReq1>PO_LG2

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

TR denotes Transverse and LG denotes Longitudinal.

The “<request name>” is added to the beginning of each auto load case name to distinguish the load cases that are automatically provided by CSiBridge from user defined load cases.

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

6 - 4 Displacement Capacities for SDC D


Figure 6-3 BENT1 Transverse Pushover Load Case

The user can not modify this load case because it is defined automatically. The <SDReq1>PO_TR1 load case starts from the end of the initial nonlinear load case named, <SDReq1>bGRAV.

The <SDReq1>bGRAV load case is shown in Figure 6-4 and is needed to isolate the bents from the rest of the bridge model and to apply the cracked section property modifiers as well as apply the dead load.

Displacement Capacities for SDC D 6 - 5


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, <SDReq1>PO_TR1. A 3D view of the <SDReq1>PO_TR1 loads is shown in Figure 6-5. The magnitudes of these loads are based on the reactions from the superstructure.

6 - 6 Displacement Capacities for SDC D


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

6.3 Pushover Results After the pushover analyses have run, for the bent failure criterion as “Pushover Curve Drop,” the capacity displacements are automatically identified as the max-imum displacement of the pushover curve just before strength loss (negative slope on the pushover curve) for each of the pushover runs. For the bent failure criterion as “First Hinge at Limit State,” the capacity displacements are automat-ically determined as the displacement whenever the first hinge at the subject bent reaches the specified limit state. For fiber hinges, failure is determined by the

Pushover Results 6 - 7


first fiber that reaches the specified limit state at the stress-strain curve of the fiber.

The pushover results can be viewed using the Home > Display > More > Show Static Pushover Curve command. An example output is shown in Figure 6-6 for the BENT1 transverse and longitudinal pushover load cases.

6 - 8 Pushover Results


Figure 6-6 Display of BENT1 Pushover Curves

Pushover Results 6 - 9

Step 7 Demand/Capacity Ratios

After the demand displacement (Step 4) and displacement capacity (Step 6) analyses have been completed, CSiBridge 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 Home > Display > Show Tables command, and then selecting Design Data > Bridge > Seismic Design data > Table: Bridge Seismic Design 01 – Bent D-C. The subject ta-ble will appear similar to the table shown in Figure 7-1:

Figure 7-1 D/C Displacment Ratios

In the table shown, all four D/C ratios are reported, namely, the transverse and longitudinal directions 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 CSiBridge and

Demand/Capacity Ratios 7 - 1


can be viewed using the Advanced > Define > Generalized Displacements command.

7 - 2 Demand/Capacity Ratios

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 Home > Display > Show Tables command. The second way is to create a report using the Orb > Report > Cre-ate 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.

Design 01 – D-C Ratios 8 - 1


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. This table is for concrete col-umns only.

8 - 2 Design 01 – D-C Ratios

Step 8 - Review Output and Create Report

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. This table is for concrete columns only.

8.5 Design 05 – Support Bearing Demand – Forces The forces in the bearing due to the seismic loads are presented in the following table. All bearings at the abutments and bents that are found to resist seismic forces are included in the subject table.

Design 04 – Bent Column Cracked Section Properties 8 - 3


8.6 Design 06 – Support Bearing Demand – Deformations The deformations for all bearings at the abutments and bents that resist seismic loads are tabulated and reported.

8 - 4 Design 06 – Support Bearing Demand – Deformations


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.

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 CSiBridge writes as a Microsoft Word document.

Design 07 – Support Length Demands 8 - 5


8 - 6 Create Report


Create Report 8 - 7


8 - 8 Create Report

Chapter 9 Caltrans Fault Crossing Seismic Bridge Design

9.1 Introduction Automated seismic design for bridges crossing seismic faults is available in CSiBridge. The methodology is based on the following references:

• Rakesh K. Goel and Anil K. Chopra, “Analysis of Ordinary Bridges Crossing Fault Rupture Zones,” Research Conducted for the California Department of Transportation Contract No. 59A0435 Earthquake Engineering Research Center University of California at Berkeley February 2008 Report No. UCB/EERC-2008/01.

• Rakesh K. Goel and Bing Qu, “Analysis of Bridges Crossing Fault‐Rupture Zones: Step‐By‐Step Procedure for SAP Implementation”.

• Caltrans, “Ordinary Bridges that Cross Faults”, Bridge Design Aids 14-6. • Caltrans, “Analysis of Ordinary Bridges that Cross Faults”, Memo to

Designers 20-8, January 2013.

In summary, this seismic design procedure considers the rupture of a seismic fault that crosses a bridge structure such that the supports are subject to significant ground displacements that are different for the supports on either side of the fault.

Introduction 9 - 1

CSiBridge - Caltrans Fault-Crossing Seismic Bridge Design

The displacement demand on the structure is calculated by performing a nonlinear static analysis for the full displacement of the fault and adding to that the results of a generalized response-spectrum analysis for the inertial forces due to this non-uniform ground motion. As an aside, by using this method, a fault which occurs near the bridge but does not cross the bridge will produce the same demand as using standard response-spectrum analysis with uniform ground acceleration.

The displacement capacity of the bents is determined by performing nonlinear static pushover analysis of the isolated bents in the longitudinal and transverse directions. This is the same procedure used in CSiBridge for automated AASHTO LRFD seismic bridge design.

Finally, a demand/capacity ratio is computed for each bent in the longitudinal and transverse direction and reported in a table. A report can be generated that provides a description of the bridge structure, and the seismic demands and capacities for one or more fault-crossing cases.

Caltrans Fault-Crossing Seismic Bridge Design follows the same general approach as AASHTO LRFD bridge seismic design, differing primarily in the specification of the Seismic Design Request. For this reason, you should be familiar with details of the AASHTO procedure described in the earlier in this manual before proceeding further.

9.2 Fault-Crossing Response-Spectrum Loading Step 4 of the AASHTO Seismic Bridge Design procedure is replaced by specifying the expected location, magnitude, and direction of fault displacement that will occur at the bridge site, as well as the associated response-spectrum loading that is associated with this motion. The fault displacement is specified directly as part of the Seismic Design Request, as described later. First the response-spectrum functions must be specified.

One or more response-spectrum functions should be defined that characterize the dynamic response to the ground motion. The response-spectrum functions should be chosen as appropriate for near-fault behavior. Different functions may be chosen for the directions parallel to the fault, normal to the fault, and vertical. It is important to understand how these functions will be used.

9 - 2 Fault-Crossing Response-Spectrum Loading


Two types of response-spectrum functions may be applied in each direction:

• A standard response-spectrum function representing uniform ground acceleration

• A fault-displacement response-spectrum function representing the vibration due to non-uniform ground displacement

Both types of response-spectrum loading may be applied in a given direction, although usually only one or the other would be.

Standard response-spectrum functions are applied to uniform ground motion represented as a translational acceleration in a single direction. For purposes of comparison with fault-rupture function, this loading can be viewed as a rigid-body translation of the entire structure an arbitrary distance u0, multiplied by the mass at each joint, and multiplied by g/u0, to create a force load acting on the structure. Here g is the gravitational constant in the same units as the displacement u0. Note that the units of the load are Length x Mass x Length/Time^2 / Length = Force.

For ground motion caused by the rupture of a fault at a bridge structure, the loading is calculated by first determining the deflected shape of the structure due to linear static application of the ground motion. For example, consider a fault that crosses the structure between two bents, and experiences a slip of 2u0 in the direction parallel to the fault. The supports on one side of the fault move a distance of u0 transversely to the left, and on the other side of the fault by a distance of u0 transversely to the right. Each support moves a distance of u0 from its initial position.

The deflected shape of the structure due to this loading reflects the ground motion, but is moderated by the flexibility of the foundation, bents, bearings, and superstructure. This deflected shape is called the quasi-static deflection, and is used to calculate the seismic load that will be used with the response-spectrum function. An example is shown below for a three-span structure with a transverse fault slip occurring within the first span.

Fault-Crossing Response-Spectrum Loading 9 - 3


The response-spectrum load is calculated as a set of forces acting at each joint that are given by the product of the deflections at the joint (in any direction), multiplied by the mass at that joint, and multiplied by g/u0. Note that this loading may have components in any direction. For example, fault motion transverse to the bridge may cause forces in the vertical and longitudinal directions as well as the transverse direction.

While the actual fault motion may be a net slip of 2u0, the response-spectrum loading is applied to a displaced shape caused by motion of +1 and -1 unit displacements on either side of the fault, due to the use of the scale factor g/u0. This follows the method of Goel, Chopra, and Qu. Note that this approach has the benefit that if the fault does not cross the bridge, the entire structure moves as a rigid body for a distance u0, and the loading is then identical to the case of uniform acceleration.

9 - 4 Fault-Crossing Response-Spectrum Loading


9.3 Defining Fault-Crossing Seismic Design Requests Define one or more Seismic Design Requests, using the command shown below.

Defining Fault-Crossing Seismic Design Requests 9 - 5


Click Add New Request, which brings up the following form:

Choose the bridge object to which this request will apply, and select the Check Type to be Caltrans Fault Crossing, which changes the form as shown below.

Enter the loading data as follows:

• Choose Planar fault definition. General Displacement Loading will be described later in this document.

• Enter the station where the fault crosses the layout line that was used to define the bridge object.

• Enter the orientation of the fault. “Default” is perpendicular to the layout line at the crossing station. You may enter a bearing, such as N30E or S251933.45W, or a skew angle relative to Default, such as 30 or -45.

• For each direction of displacement loading to be considered simultaneously in this Design Request, enter the displacement magnitude and the corresponding response-spectrum function.

9 - 6 Defining Fault-Crossing Seismic Design Requests


o See Step 3 above for more information about response-spectrum functions.

o The displacement is the actual movement, u0, of each support on either side of the fault. In other words, it is half the total slip of the fault. The default is 0.5m.

o For vertical motion on an inclined fault, enter the components in the vertical and horizontal-normal directions.

• For each direction of uniform acceleration loading (no slip), enter the corresponding response-spectrum function.



The displacement demand will be calculated by applying the specified fault motions as follows:

(1) The specified fault displacements will be applied together in a nonlinear-static displacement load case.

(2) The fault-displacement response-spectrum loads, if any, will be applied together in a response-spectrum load case.

(3) The uniform-acceleration response-spectrum loads, if any, will be applied together in a separate response-spectrum load case.

(4) The two response-spectrum load cases will be combined in a load combination.

(5) The final demand result is obtained by combining the displacement load case (1) with the response-spectrum load combination (4).

Note that if the specified displacement is too large, the nonlinear-static load case will not converge and the seismic design request will not complete. This indicates that the structure does not have sufficient ductility to resist the specified loading, and further calculation not warranted. For many structures, the amount of displacement that can be accommodated is quite small. If you cannot get convergence with the desired value, try a smaller value so that you can determine the capacity of the structure.

By default, the different directions of loading in the response-spectrum load cases are combined by absolute sum. This may be changed to the SRSS or CQC3 method in the design request parameters, see below. This same method will be used to combine the two response-spectrum load cases together in the response-spectrum load combination. If CQC3 is chosen, it actually applies only to the uniform-acceleration load case (3), and SRSS will be used for the fault-displacement load case (2) and for the response-spectrum load combination (4). In any case, the final combination (5) of the nonlinear-static displacement load case and the response-spectrum load combination will always use absolute sum. Additional detail is provided in topic “Automatic Load Cases and Combinations” below.

Additional parameters may be specified for this Design Request by clicking on the Modify/Show button, bringing up the form as shown below. These parameters are optional and do not usually need to be changed.

9 - 8 Defining Fault-Crossing Seismic Design Requests


Most of these parameters are identical to the parameters for the AASHTO Seismic Design Request, and are described in the CSiBridge Seismic Analysis and Design manual. A few of these parameters of particular interest for fault-crossing analysis are described here:

• The Seismic Design Category (1) has the same meaning as it does for AASHTO seismic design, but it is not automatically determined from the response-spectrum functions. Due to the severity of fault-crossing motion, category “D” is probably most appropriate, meaning that the capacity will be determined by nonlinear static pushover analysis. However, if you just want to study the seismic demand due to fault crossing and don’t care about capacity, setting the category to be less than “D” will speed up the analysis.

• Type of Modes (13) is fixed to be Ritz. This is superior to using Eigen modes for ground displacement loading, which tends to excite higher frequency modes than acceleration loading.



• Directional Combination (17) may be Absolute, SRSS, or CQC3. Goel and Qu recommend using Absolute for fault-crossing analysis.

9.4 Running Fault-Crossing Seismic Design Requests After defining one or more Seismic Design Requests, these can be run using the command shown below:

Using the buttons on the right, select the Design Requests that you would like to run, and set their action to “Design”. Then click the Design Now button.

We recommend unlocking the model before using this command, which will delete all prior results. You may wish to save the model under a new name before doing this. We also recommend simultaneously running all design requests of interest at the same time, although this is not required.

After clicking the Design Now button, CSiBridge will create and run multiple load cases for each Design Request to calculate the demands and capacities. The results of some cases are used to create additional cases, so the analyses are

9 - 10 Running Fault-Crossing Seismic Design Requests


performed in a sequence of runs. These load cases are described later in this document.

You will know when the seismic design is done when a table of final results is presented, or a message is produced in case the Design Requests were unable to complete for any reason.

9.5 Creating a Seismic Design Report Use the command below to create a Bridge Seismic Design Report that includes a description of the bridge object, the seismic loading, and the demand and capacity results.

This report will be written to an .RTF file that can be opened in Microsoft Word for viewing, editing, and printing.

The same data can be viewed within CSiBridge using the command Home > Display > Show Tables.

Creating a Seismic Design Report 9 - 11


Results are presented for both displacement and force demands, as well as capacities. While the displacement demands may be meaningful for design purposes, the force demands should be used only for reference purposes, since they superpose the linear response-spectrum results with the nonlinear static results and are not mathematically valid.

9.6 Automatic Load Cases and Combinations For each fault-crossing Design Request, several Load Combinations, Load Cases, Load Patterns, Named Property Sets, Groups, Generalized Displacements, and other entities may be automatically created during the design process. Most of these are similar to the AASHTO Seismic Design. Additional detail is provided here regarding the Load cases and combinations that are used for a Fault-Crossing Design Request.

The following are the Load cases that created by default. The load cases and their details may differ depending on the choice of the Design Request Parameters. Each Load case name ends with the name of the Design Request. In these examples, this is assumed to be “QReqX”:

• <QreqX>GRAV. This is a nonlinear static analysis for gravity load that is used to calculate the initial conditions for all subsequent demand and capacity calculations. This case is re-run iteratively to determine the cracked section properties of the columns. The cracked properties are represented as named property sets that are applied in this load case, which is solved as a staged-construction load case with a single stage. This case is common to both AASTHO and fault-crossing seismic design.

• <QreqX>DIS. This is a nonlinear static load case that continues from the gravity case <QreqX>GRAV and applies the full specified ground motion. The results of this load case will later be combined with the response-spectrum results to form the displacement demand. This case is unique to

9 - 12 Automatic Load Cases and Combinations


fault-crossing seismic design.

• <QreqX>MODAL. This is a Ritz modal load case that uses the stiffness from load case <QreqX>GRAV and calculates vibration modes optimized for the fault-crossing response-spectrum analysis. For each direction of fault slip, a separate load pattern is created that applies the specified ground motion to the supports. These load patterns are then applied as “Load Inertia” and used as the starting load vectors in the Ritz modal case. If uniform acceleration loading has been specified for the design request, acceleration loads are added to this modal case. Load Inertia is a new type of loading added to CSiBridge for the purpose of calculating fault-crossing response. Load Inertia applies the specified load pattern, multiplies the resulting displacement at each degree-of-freedom in the structure by its respective mass, and then reapplies the result as an inertial load to get the final response. This same loading will be applied in the response-spectrum case. This case is unique to fault-crossing seismic design, although a different modal case is used for AASHTO design.

• <QreqX>RS_DIS. This is a generalized response-spectrum analysis for fault-crossing motion that uses the modes calculated in load case <QreqX>MODAL. The same fault-crossing load patterns used in the modal case are applied here as Load Inertia. Each inertial load is applied with its respective response-spectrum function as specified in the Design Request, and scaled by g/u0. For each load, the modes are combined using the CQC method. The directional loads are then combined as an absolute sum by default, although you may choose to use SRSS in the Design Request. This case is unique to fault-crossing seismic design, although different response-spectrum cases are used for AASHTO design.

• <QreqX>RS_UNIF. This is a standard response-spectrum analysis for the uniform acceleration, if any, specified in the design request. This case also uses modes calculated in modal case <QreqX>MODAL. For each load, the modes are combined using the CQC method. The directional loads are then combined as an absolute sum by default, although you may choose to use SRSS in the Design Request. This case is similar to that used for AASHTO design.

Automatic Load Cases and Combinations 9 - 13


• <QreqX>bGRAV. This is a nonlinear static analysis for gravity load that is used to calculate the initial conditions for bent capacity calculations when the seismic design category is D. This case is solved as a staged-construction load case that continues from <QreqX>GRAV, removes the superstructure, and replaces it with an equivalent mass and weight at the bearing locations. This case is common to both AASTHO and fault-crossing seismic design.

• <QreqX>PO_TRn and <QreqX>PO_LGn. These are a set of nonlinear static pushover load cases used to calculate the bent capacities in the transverse and longitudinal directions, respectively, for each bent n when the seismic design category is D. Each case continues from <QreqX>bGRAV. These cases are common to both AASTHO and fault-crossing seismic design.

Two load combinations are created to calculate the total seismic demand:

• <QreqX>cboRSP. This combines the response-spectrum results from the two cases <QreqX>RS_DIS and <QreqX>RS_UNIF. This combination is always created, even if only one response-spectrum load case is used.

• <QreqX>cboDIS.RSP. This calculates the total demand as the absolute sum of nonlinear-static load case <QreqX>DIS and response-spectrum load combination <QreqX>cboRSP. This is the final result that is reported used for demand.

Further information on the calculation of capacity and the use of generalized displacements to measure both the demand and capacity can be found earlier in this manual for AASHTO Bridge Seismic Design.

9.7 General Displacement Loading You may consider more general displacement loading due to fault rupture than is possible with the planar definition described above. Examples would include loading where the displacement is not a uniform translation on either side of the fault, where rotational motions has occurred, or where there are multiple fault ruptures crossing the bridge. Another instance would be where you wish to consider the fault-parallel, fault-normal, and fault-normal motion in a single correlated load pattern rather than three independent motions combined by absolute sum in the response-spectrum load case.

9 - 14 General Displacement Loading


Note that there is no established protocol for using general displacement loading in design at the present time. Using this method requires engineering judgment and perhaps some experimentation.

The procedure is similar to the that described above for defining a Seismic Design Request for planar motion, with the following differences.

9.7.1 Defining Load Patterns and Response-Spectrum Functions For each independent motion to be considered in the Design Request, you will need to define a load pattern in addition to a response-spectrum function. The same response-spectrum function can be used for multiple load Patterns if appropriate.

The procedure is as follows:

• Define the new load patterns. Enter a Name, set the Type to Other, set the Self Weight Multiplier to zero, and click Add New Load Pattern.

• For each load pattern, select the various supported joints and assign ground displacement loads, as appropriate, using the command Advanced > Assign Loads > Joints > Displacements. Be sure to select the desired load pattern in the assignment form.

• Note that displacement loads will only act at joint degrees of freedom connected to ground through restraints, springs, or single-joint links. Displacements assigned to other joints or degrees of freedom are permitted

General Displacement Loading 9 - 15


but will have no effect on the structure. The magnitude of the loads are not important, only their relative values. They can be scaled later, separately for the nonlinear and the response-spectrum load cases. For complicated ground motion, you may wish to use tabular data entry using the interactive database editor. The figure on the next page shows the joint displacements loads that are generated automatically for transverse planar fault-parallel motion in the first span. Note that loads are applied everywhere, but that they will only act at the base.

• To apply uniform acceleration, define a displacement load pattern and assign an equal translation in the desired direction to every joint.

• For each load pattern, decide on a single reference displacement value, u0, which characterizes the motion. This may be the most difficult part. This value will be used later to normalize the load pattern for application in the response-spectrum load case. By analogy with the planar motion, it should represent a measure of how much each joint moves from its initial position. For non-uniform motion, you could use the average displacement or the maximum displacement, as determined by your engineering judgment. You can assign displacement loads of any magnitude in the load pattern, but the value u0 should be representative of these loads.

• Define response-spectrum functions that characterize the dynamic response to the ground motion for the various load patterns. The response-spectrum functions should be chosen as appropriate for type of near-fault behavior characterized by the load patterns.



9.7.2 Defining a Seismic Design Request This mostly follows the procedure for the case of planar fault motion, with the following exceptions:

• Choose General Displacement Loading for the fault definition. The form will appear as shown below (after entering Loading data).

• Click the Add button to add a new load pattern. • For each load pattern:

o Choose the name of the load pattern you previously defined o Choose the name of the corresponding response-spectrum function. o Enter a dimensionless scale factor that will multiple the load pattern

when it is used in the nonlinear static displacement load case. The



default is unity. Increasing this scale factor will increase the static load, but will have no effect on the response-spectrum load case.

o Enter the reference displacement u0 for the load pattern, determined as described in Step 3 above. This value has units of length, and will be used to scale the response-spectrum load by g/u0. The default is 0.5 m, but you should a value that actually corresponds to the magnitude of the loads applied in the load pattern. Increasing this reference displacement will reduce the response-spectrum load, but will have no effect on the nonlinear static load case.

You may add or delete as many load patterns as you wish. These load patterns will be applied in the nonlinear static, Ritz modal, and response-spectrum load cases. The Design Request Parameters are the same as for planar motion.




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, 2011. 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 2011

FEMA 356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, November 2000, Federal Emergency Management Agency, Washington D.C.

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