5) Manual SAP200 - Bridge Seismic Design (Pu)

SAP2000/Bridge

Bridge Seismic Design Automated Seismic Design of Bridges AASHTO Guide Specification for LRFD Seismic Bridge Design

ISO SAP041709M22 Rev. 0 Berkeley, California, USA

Version 14 April 2009

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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

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 Bent Cap Beam 1.4.2 Bent Column Properties 1.4.3 I-Girders Properties 1.4.4 Pile Properties

1-4 1-5 1-5 1-6 1-7

1.5

Bridge Deck Section

1-8

1.6

Bent Data

1-8

1.7

Bridge Object Definition 1.7.1 Abutment Property Assignments 1.7.2 Abutment Geometry

1-10 1-11 1-13

i

SAP2000/Bridge Seismic Design

1.7.3 1.7.4

Bent Property Assignments Bent Geometry

1.8

Equivalent Pile Formulation

1-16

1.9

Bent Foundation Modeling

1-16

1.10 Mass Source

Step 2

Step 3

Step 5

ii

1-17

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

Dead Load Analysis and Cracked Section Properties 3.1

Step 4

1-14 1-15

Overview

3-1

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

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 5.4.1 Nonlinear Material Properties Definitions For Concrete 5.4.2 Nonlinear Material Properties Definitions For Steel

5-6 5-6 5-8

Contents

5.5

Step 6

Step 7

5-9

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

Demand/Capacity Ratios 7.1

Step 8

Plastic Hinge Options

D/C Ratios

7-1

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

8.6

Design 06 – Support Bearing Demand Displacements 8-4

8.7

Design 07 – Support Length Demands

8-4

8.8

Create Report

8-5

8-3

References

iii


List of Figures

iv

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

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


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

v


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

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

Figure 6-4

vi

Foreword

SAP2000/Bridge has become a widely recognized and widely used analysis and design program for bridge structures. Over the past thirty-five years, Computer 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 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. Furthermore, the SAP2000/Bridge program will determine the demand and capacity displacements and report the demand/capacity ratios for the Earthquake Resisting 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

v


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 follow. 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

vi

Foreword

STEP 1 Create the Bridge Model

1.1

Example Model This chapter describes the first step in the process required to complete a Seismic Design Request for a bridge structure using SAP2000/Bridge. 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 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

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 design 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 reinforced 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 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 example 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 subsections that follow.

1-4

Bridge Layout Line


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 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 plastic hinge definitions is provide 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.

Figure 1-8 Precast I-Girder Properties

1-6



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 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 surrounding soil.

Figure 1-9 Pile Properties


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 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.

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, angle 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 elements. 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

Bent Data

1-9


are part of the bridge model, the base of the bent column must not be restrained, but instead, connected to the foundation elements. Restraining the base of the columns in the Bent Column Data form using Fixed or Pinned restraints 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 property 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

1 - 10

Bridge Object Definition


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

Figure 1-14 Bridge Object Data form

The span data is used to define the span lengths and bent locations. Cross diaphragms also can be included in a bridge model using the Modify/Show Assignments > 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 Object Abutment Assignment form shown in Figure 1-15. The abutment bearing direction can be assigned a bearing angle if skewed abutments are needed. Diaphragms can be added to the abutment as well. Abutments can be modeled using 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.

Bridge Object Definition 1 - 11


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 restrained 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 abutment bearings. Therefore, the user should pay special attention to the substructure 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 directions. See Figure 1-16. To help visualize the abutment geometry, the graphic shown in Figure 1-17 includes 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.

1 - 12



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 location where the bearing will translate or rotate depending on the bearing definitions.

Figure 1-17 Abutment Bearing Geometry



1.7.3

Bent Property Assignments The bent property assignments are made using the Bridge Object Bent Assignment form, shown in Figure 1-18. Similar to the abutment property assignments, the bent property assignments will include the bent directions, bearing properties, and substructure locations.

Figure 1-18 Bent Assignments form

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

1 - 14



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



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 equivalent length of 5.1 feet to model the pile surrounded by soil, as described in Section 1.4.4. The equivalent lengths were established using the equations shown in Figure 1-21. Point of fixity  EI f 

15

K  EI T 3 K  EI T K  EI T

2

f = yield calculated from an average spt blow count N. T = 5.1 feet; this effective length is used in modeling the bridge foundation. 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 locations. 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.

1 - 16

Equivalent Pile Formulation


Figure 1-22 View of Bent Foundations

Column-to-Foundation Connection

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 superimposed type with the name SDEAD. Using the option, ‘From Element and

Mass Source 1 - 17


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

1 - 18

Mass Source

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 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, SAP2000/Bridge 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

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

2-2

AASHTO and USGS Hazard Maps

STEP 2 - Ground Motion Hazard and Seismic Design Request

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 Design Request command accesses a form that can be used to specify the name and design 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 Substructure 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 Spectrum 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 Seismic Design Category.


2-3


Figure 2-4 Seismic Design Parameters form

2-4

Item


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 Displacement 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.



Item


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 auxiliary 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 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.

9

Cracked Property Option

The cracked section properties for the bent columns can be automatically 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 moments of inertia in the positive and negative transverse and longitudinal 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.

10 Convergence Tolerance

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

11 Maximum Number of Iterations

This value sets the maximum number of iterations allowed for the bentcolumn 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.

12 Accept Unconverged Results Convergence

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

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 program 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.


2-5


2.4

Item


15 Response Spectrum 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 Spectrum 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 Spectrum 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 program 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 Spectrum 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 category is D.

20 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.

21 Bent Failure Criterion

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

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.

2-6



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 pattern 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.

Auto Load Patterns

2-7


Figure 2-7 Auto Load Cases

2-8

Auto Load Cases

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 determination 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 property 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 observe 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.

Overview

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 options available in the Seismic Design Request.

3-2

Overview

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 demands 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 directions. 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 spectrum load along a different axis, a directional overwrite is available in the Substructure Seismic Design Parameters form (see Chapter 2).

Overview

4-1

SAP2000 Bridge Seismic Design

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).

4-2


Step 4 - Response Spectrum and Demand Displacements

Figure 4-2 ABS Response Spectrum LOAD Case form

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

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


4-3

SAP2000 Bridge Seismic Design

Figure 4-4 Modal Load Case Definition

4.3

Response Spectrum Results Upon completion of the response spectra analysis, the displacements are tabulated for each bent. The displacements are calculated using “Generalized Displacements” 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 active 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 created using the Design menu > Bridge > Quick Report command.

4-4

Response Spectrum Results

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 column 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 plastic 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, LP  0.08 L  0.15 f ye dbl , where

Overview

5-1


f ye = the effective yield strength of the longitudinal reinforcing, and dbl = the diameter of the longitudinal reinforcing. The hinge length is compared to the value for the maximum hinge length value described as, LP  0.3 f ye dbl , 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

5-2

Plastic Hinge Lengths

Step 5 - Determine Plastic Hinge Properties and Assignments

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 bilinear moment-curvature diagram, as shown in Figure 5-3. 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 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.


5-3


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 responses 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.

5-4



Figure 5-4 Auto Hinge Assignment Data

Figure 5-5 Sample Hinge Data form


5-5


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

5-6

Nonlinear Material Property Definitions


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

Figure 5-8 Concrete Model - Mander Confined


5-7


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

5-8



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 Automated 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 rectangular or circular shape. Internally, SAP2000/Bridge will convert the rectangular or circular shapes into Section Designer sections for the purposes of determining 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.


5-9


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 using the Section Designer feature is that complex sections, similar to the one below, can be handled.

Figure 5-12 Section Designer options

5 - 10


Step 6 Capacity Displacement Analysis

This step describes the automated procedure that SAP2000/Bridge 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


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 Capacity







May be required

Required

Required

Required

Required

Detailing – Ductility



SDC B

SDB C

SDB D

Capacity Protection



Recommended

Required

Required

Liquefaction



Recommended

Required

Required

Support Width

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 Seismic Guide Specification equations are also noted. For SDC B:

CL  0.12 H o  1.27 ln( x)  0.32   0.12 H o

(4.8.1-1)

For SDC C:

CL  0.12 H o  2.32ln( x)  1.22   0.12 H o

(4.8.1-2)

in which

x

 Bo Ho

where,

6-2


(4.8.1-3)

Step 6 - Capacity Displacement Analysis

Ho =

Clear height of the column (ft)

B0 =

Column diameter or width parallel to the direction of displacement 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, Section 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 construction load cases, an additional license will be required. For the example bridge, the four separate pushover load cases are named as follows: _PO_TR_BT1_SDReq1 _PO_LG_BT1_SDReq1 _PO_TR_BT2_SDReq1 _PO_LG_BT2_SDReq1


6-3


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 distinguish 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.

6-4



The _ bGRAV_SDReq1 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.

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.


6-5


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 automatically 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.

6-6

Pushover Results


The pushover results can be viewed using the Display menu > Pushover Results 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

Pushover Results

6-7

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 Demand/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 subject table will appear similar to the table shown in Figure 7-1:

Figure 7-1 D/C Displacement Ratios

D/C Ratios

7-1


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 displacements 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 Displacements command.

7-2

D/C 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 Display menu > Show Tables command. The second way is to create a report using the Design menu > Bridge Design > Create Report command. The entire list of output tables for the Bridge Seismic Design includes the following:

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 determined using the associated axial load value, P.

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.

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.

Design 04 – Bent Column Cracked Section Properties

8-3


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.

8-4

Design 06 – Support Bearing Demand – Displacements


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 representative pages of the report that can be created using the previously noted report request are included in the following pages. Theses have been excerpted from a 30 page summary report that SAP2000/Bridge writes as a Microsoft Word document.

Create Report

8-5


8-6

Create Report


Create Report

8-7


8-8

Create Report

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 Officials, 444 North Capital Street, NW Suite 249, Washington, DC 2001

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5) Manual SAP200 - Bridge Seismic Design (Pu)

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