CSI Sap2000 Bridge Examples

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SAP2000 B RIDGE E XAMPLES

Computers and Structures, Inc. 1995 University Avenue Berkeley, California 94704, USA http://www.csiberkeley.com

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SAP2000 Bridge Examples Copyright © by Computers and Structures, Inc, 2006 All rights reserved.

The computer program SAP2000 and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers and Structures, Inc. Unlicensed use of the program or reproduction of the documentation in any form, without prior written authorization from Computers and Structures, Inc., is explicitly prohibited. Further information and copies of this documentation may be obtained from: CSI Educational Services Computers and Structures, Inc. 1995 University Avenue Berkeley, California 94704 USA Phone: (510) 845-2177 Fax: (510) 845-4096 Email: [email protected] (for general questions) Email: [email protected] (for technical support questions) Web: www.csiedu.com

The CSI Logo, ETABS® , SAP2000® and SAP90® are registered trademarks of Computers and Structures, Inc.; SAFE™ is a trademark of Computers and Structures, Inc.

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PREFACE

This lecture is generally geared towards the intermediate user level of SAP2000. However, if you have never used SAP2000 or SAP2000 Bridge Modeler before, the level of information provided is intended to give the user sufficient information to reproduce all of the bridge examples contained in this booklet. We have designed this course such that the inexperienced SAP2000 user will have no problem following along. The end-to-end examples that are presented will exhibit the most general and common modeling techniques. It is strongly recommended that the SAP2000 user read Chapter XXVI, Bridge Analysis, of the Analysis Reference Manual. The SAP2000 user can use the Help / Documantation / Manuals command to find this document.

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SEMINAR TOPICS

Preface .

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Seminar Topics

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Part I I.1 I.2 I.3 I.4 I.5 I.6 I.7 I.8 I.9 I.10 I.11 I.12 I.13 I.14 I.15 I.16 I.17

Concrete Box Girder Bridge Concrete Box Girder Bridge Example Description . . . . . . . . . Model Parameters . . . . . . . Modeling Steps . . . . . . . . Step 1: Layout Lines . . . . . . Step 2: Deck Section Definition . . Step 3: Abutment Definition . . . Step 4: Bent Definition . . . . . Step 5: Diaphragm Definition . . . Step 6: Hinge Definition . . . . . Step 7: Parametric Variation Definition Step 8: Bridge Object Definition . . Step 9: Update Linked Model . . . Step 10: Lane Definition . . . . . Step 11: Vehicle Definition . . . . Step 12: Analysis Cases . . . . . Results . . . . . . . . . .

Part II II.1 II.2 II.3 II.4 II.5 II.6 II.7 II.8 II.9 II.10 II.11 II.12

Steel Bridge Steel Bridge Example 1.0 . . . . Layout Line Definition . . . . . Deck Section Definition . . . . . Bridge Object 1 Definition . . . . Create Linked Model . . . . . . Modify Abutment Properties . . . Modify Bent Properties . . . . . Modify Vertical Diaphragm Properties Further Modify Bridge Object 1 . . Update Linked Bridge Model . . . Analyze BOBJ1 . . . . . . . Live Loads . . . . . . . . .

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CSI SAP2000 B RIDGE E XAMPLES

II.13 II.14 II.15 II.16 II.17 II.18

Add Vehicles . . . . . . . . Add Analysis Case . . . . . . Add Trucks with Speed and Direction Add Bridge Extensions . . . . . Completed Model . . . . . . . Final Analysis . . . . . . . .

Part III Cablestayed Bridge III.1 Cable stayed Bridge Example . . . III.2 Description of Cable stayed Bridge . III.3 Description of Model . . . . . III.4 Nonlinear Material Property Definition III.5 Cable Property Definition . . . . III.6 Deck Section Definition . . . . . III.7 Pylon Section Definition . . . . . III.8 Model Creation . . . . . . . . III.9 Group Assignments . . . . . . III.10 Staged Construction Analysis Case .

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APPENDIX

67

Part A Mesh Transitioning, Compatibility, and Line Constraint A.1 Introduction . . . . . . . . . . . . . . . . A.2 Example 1: Simply Supported Plate (Mismatched Meshing) A.3 Example 2: Curved Ramp Supported by Curved Wall . . A.4 Example 3: Floor Slab – Shear Wall Compatibility . . . A.5 Example 4: Shear Wall – Spandrel Transition . . . . .

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69 69 70 71 71 71

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About the Speakers

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PART I Concrete Box Girder Bridge

I.1 Concrete Box Girder Bridge Example

Figure I.1: Full Concrete Box Girder Bridge

I.2 Description This example demonstrates the powerful bridge module in SAP2000. The model is a concrete box girder bridge with a 200 ft span and is loaded with 2 traffic lanes. The bridge has 3 columns with different heights supporting the deck at midspan. There are parametric variations along the length of the bridge as well as prestressed tendons assigned to the deck. The bridge abutments are skewed 15 degrees at the 2 ends of the bridge deck.

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I.3 Model Parameters The overall deck depth has a depth 5 ft and a width of 36 ft. Kip-feet-second units are used. To see the deck cross-section geometry, please refer to Figure below. Other parameters associated with the structure are as follows: Clear span of bridge Overall depth of deck Width of deck, b Concrete strength, f’c Yield strength of steel, fy Concrete unit weight, Wc Modulus of elasticity, Ec Modulus of elasticity, Es Poisson’s ratio, v

= = = = = = = = =

200 ft 5 ft 36 ft 4000 psi 60000 psi 150 pcf 3600 ksi 29000 ksi 0.2

Table I.1: Model Parameters

I.4 Modeling Steps This concrete box girder example is intended to give the user some experience with each of the steps defined in the Bridge Wizard. Twelve steps are used to complete the concrete box girder example and various dialog boxes are shown to make it easier for the first time user to follow along or reconstruct the model. This model will make use of many of the SAP200 Bridge Module features including bridge analysis, influence lines and surfaces, and the use of prestress tendons. To build the bridge model, a 12-step process is described below. 1. Layout Lines 2. Deck Sections 3. Abutments 4. Bents 5. Diaphragms 6. Hinges 7. Parametric Variations 8. Bridge Object definitions 9. Update of linked model 10. Lanes 11. Vehicles/Vehicle Classes 12. Analysis Cases

Table I.2: Modeling Steps

The user can quickly define a basic model that applies program defaults using the following abbreviated approach:

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PART I.

C ONCRETE B OX G IRDER B RIDGE

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a. Define a layout line using Step 1. b. Define a deck section using Step 2. c. Skip to Step 8 to create a bridge object. d. Create a linked model using Step 9.

Table I.3: Abbreviated Approach

For the abbreviated approach, SAP2000 will apply default abutment, bent, hinge, and diaphragm properties. If necessary, Steps 3, 4, 5 and 6 of this Wizard can be used to change those default definitions. In addition, prestressed tendons can be added as part of the bridge object definition (see Step 8). Each one of the 12-steps is described in detail.

I.5 Step 1: Layout Lines The first step in creating a bridge object is to define the layout line. Layout lines are used as reference lines for defining the vertical and horizontal layout of bridge objects and lanes. Layout lines are defined in terms of stations, bearings and grades. The lines may be straight, bent or curved both in the horizontal and the vertical plane. Horizontal curves are circular (with spirals if necessary) and vertical curves are parabolic. In this example, the End Station is defined as 220 ft. The final bridge will have a span of 200 ft and will shorter then the layout line. Use the Quick Start options to quickly define a layout line. You will see the many choices available for both Horizontal and Vertical curves. Select the Straight line in both cases.

I.6 Step 2: Deck Section Definition Various parametric bridge deck sections are available for use in defining a bridge. They include concrete box girders, concrete beam and steel beam sections. Select the External Girders Vertical option. Enter the total width and depth shown in Figure I.2below. After a deck section has been defined it can be assigned to a span as part of the bridge object definition (see Step 8).

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Figure I.2: Define Bridge Deck Section Data

I.7 Step 3: Abutment Definition Abutment definitions specify the support conditions at the ends of the bridge. An abutment definition can be a specified Link/Support property or it can be a user defined support condition. The user support condition allows each of the six degrees of freedom at the abutment to be specified as fixed, free or partially restrained with a specified spring constant. An abutment definition also allows the horizontal location of the abutment supports to be specified. A single abutment support can be located at the reference line location or multiple abutment supports can be located either at each girder or equally spaced over the bridge width. When multiple locations are indicated the specified abutment support properties are provided at each support location. It is also possible to specify that a closure (vertical diaphragm) of some thickness is to be provided at the abutment. This closure is only applicable to area object and solid object models. For this example, select the U2, R1, and R3 DOF directions to have a ’Free’ release type. The other directions should have a ’Fixed’ release type. Under the Horizontal Location of Abutment Supports, select the every girder location option.

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Figure I.3: Parametric Variation Definition

I.8 Step 4: Bent Definition Bent definitions specify the geometry and section properties of the bent cap beam and the bent column(s). They also specify the base support condition of the bent columns. The specified base support condition for a bent column can be Fixed, Pinned or a user

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defined column support. A user defined column support can be a specified Link/Support property or it can be a user defined support condition. The user support condition allows each of the six degrees of freedom at the column base to be specified as fixed, free or partially restrained with a specified spring constant. The user defined column support is defined separately from the bent. It is also possible to specify that a vertical diaphragm is to be provided at the bent location. The diaphragm is only applicable to area object and solid object models. It does not apply to spine models. After a bent is defined it can be assigned to the bridge as part of the bridge object definition (see Step 8). In this example, click on the Bride menu¿ Bents and select the Add New Bridge Bent option. In the Bent Data box, type in the number of columns: 3. Next, click on the Modify/Show Column Data box in the lower left hand corner. Fill out the form as shown in Figure I.4below and click OK. Make sure you are in Kip-ft units.

Figure I.4: Define Bridge Bent Properties

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I.9 Step 5: Diaphragm Definition Diaphragm definitions specify properties of vertical diaphragms that span transverse across the bridge. A diaphragm property can be solid concrete; steel X, V or K bracing; or a single steel beam. Solid concrete diaphragm properties are only applicable to concrete bridge sections. Steel diaphragm properties are only applicable to steel bridge sections. Diaphragms in general are only applicable to area object and solid object models. They do not apply to spine models. After a diaphragm definition has been created it can be assigned to one or more spans in the bridge object (see Step 8). It is not necessary to define a diaphragm property before defining a bridge object. If no diaphragms are defined when a diaphragm is first added to a bridge object, the program automatically creates a default diaphragm property. For this example, we will not assign specific diaphragm properties.

I.10 Step 6: Hinge Definition Hinge definitions specify properties of hinges (expansion joints) and restrainers. A hinge property can be a specified Link/Support property or it can be a user-defined spring. The user spring allows each of the six degrees of freedom at the hinge to be specified as fixed, free or partially restrained with a specified spring constant. A restrainer property can be a specified Link/Support property or it can be a userdefined restrainer. The user restrainer is specified by a length, area and modulus of elasticity. A hinge definition also allows the horizontal location of the hinge springs and restrainers to be specified. A single hinge spring (and restrainer) can be located at the reference line location or multiple hinge springs (and restrainers) can be located at each girder or equally spaced over the bridge width. When multiple locations are indicated the specified spring and restrainer properties are provided at each support location. It is also possible to specify that a vertical diaphragm is to be provided at the hinge location. The specified diaphragm is provided on each side of the hinge. This diaphragm is only applicable to area object and solid object models. It does not apply to spine models. After a hinge definition has been created it can be assigned to one or more spans in the bridge object (see Step 8). It is not necessary to define a hinge property before defining a bridge object.

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I.11 Step 7: Parametric Variation Definition Parametric variations define variations in the deck section along the length of the bridge. Any parameter used in the parametric definition of the deck section can be specified to vary. One or more of the parameters can vary at the same time. Each varying parameter can have its own unique variation. Example uses of parametric variations include varying the bridge depth and the thickness of girders and slabs along the length of the bridge. The variations may be linear, parabolic or circular. After a variation has been defined it can be assigned to spans in the bridge object (see Step 8). When a variation is defined it should be defined with the same length as the bridge span to which it is assigned. For this example, we will define 2 variations (one for each span of the bridge.) Under the Bridge/Parametric Definitions command, select the Add New Variation, then using the quick start button, select the Parabolic Linear variation. Fill out the form as shown in Figure I.5 below:

Figure I.5: Parametric Variation Definition

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Next, in the same manner as described in the steps above, create a 2nd variation. Only, this time the variation shall be defined with the Linear Parabolic quick start option. The new PARV2 variation should be the exact mirror of the PARV1 variation. Next the user needs to apply these variations to the bridge object. This can be accomplished by first using the Bridge/Bridge Objectscommand, then opening the Bridge Objects dialog box and selecting the modify/show spans command. The user should apply the PARV1 and PARV2 variations to the Span1 and SpanToEnd as shown in Figure I.6 below. See also, the steps outlined in Step 8 below.

Figure I.6: Assign Parametric Variation To Span

I.12 Step 8: Bridge Object Definition The bridge object is the heart of the bridge modeler. The following is included in the bridge object definition: a. The bridge spans are defined. b. Deck section properties are assigned to each span. c. Parametric deck section variations may be assigned to each span. d. Abutment properties and skews are assigned. e. Bent properties and skews are assigned. f. Hinge locations, properties and skews are assigned. g. Super elevations are assigned. h. Prestressed tendons are defined. Any time a bridge object definition is modified the linked model must be updated (see step 9) for the changes to appear in the SAP2000 model.

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The prestress tendon quick start options allow quick and easy layout of prestressed tendons. The prestress tendon parabolic calculator makes quick work of the layout of parabolic prestress tendons. To work within the Bridge Object menu, click on the modify/show bridge object using Define/Bridge Object command. The Bridge Object menu should appear as shown in Figure I.7.

Figure I.7: Bridge Object Menu

Next, click the on Modify/Show spans button. In this dialogue box, for Span 1, double click on the span varies box. A Bridge section variation box will open. Double-click on the variation for Total Depth box and select PVAR1 and click OK. Do the same for the next span except select PVAR2 for the variation. See Figure I.6. To apply a skew to the ends of the bridge, click on the Modify/Show Spans and simply type in the bearing angle as shown in the dialog box in Figure I.10

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Figure I.8: Abutment Bearings

Bridge Prestress button and select Add new Tendon. Fill in a tendon area of 10 in2 and load force of 1500 kips. Select a Prestress load case. (To create a Prestress load case, go to Define/Static Load Cases dialogue box.) Click on the Quick Start button for vertical layout and select parabolic tendon 1 and click Ok twice. The tendon loss parameters should also be defined.

Figure I.9: Tendon Definition

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Once a single tendon has been defined, it can be copied to each of the concrete girder locations by simply clicking on the Copy To All Girders command.

Figure I.10: Tendon Definition

The user can verify the location of the tendon graphically by selecting the the Show All Tendons command and viewing the tendon profiles and locations.

I.13 Step 9: Update Linked Model The update linked model command creates the SAP2000 object-based model from the bridge object definition. If an object-based model of the bridge object already exists, it will be deleted when the new object-based model is created using all of the latest changes to the bridge object definition. Spine models, area object models and solid object models of the bridge can be created when the linked model is updated. The type of object-based model created from the bridge object definition can be switched at any time. Under the Bridge menu, select the Update Linked Bridge Model option. Then click on the Update as Area Object option.

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Figure I.11: Update Linked Bridge Model Dialog Box

In Figure I.12, you can see the parametric variation along the length of the deck. You can also view the tendons located inside the bridge deck by turning off the area object fill if desired.

Figure I.12: Updated Linked Bridge Model

I.14 Step 10: Lane Definition Lanes must be defined if you want to analyze your bridge for moving vehicle live loads. Lanes can be defined with reference to either layout lines or existing frame objects. A single lane is referenced to one or more layout lines or one or more frame objects. Lanes can be defined with width if desired. Lanes are used in the definition of Moving Load type analysis cases and in Bridge Live load cases. The SAP2000 Vehicle Live Loader is complex. The user is strongly recommended to read Chapter XXVI, of the Analysis Reference Manual. For this example, click on the Add New Lane Defined From Layout Line button. Add a lane at two stations. (0 ft and 220 ft) Each of these stations has the same centerline offset (7ft) and lane width (14ft). Click OK. Next, add a copy of a lane and change

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offset by specified amount (-14ft).

Figure I.13: Lane Definition

I.15 Step 11: Vehicle Definition Vehicles must be defined if you want to analyze your bridge for vehicle live loads. In SAP2000 vehicles loads are applied to the structure through lanes. If you plan to use a moving load type analysis case then you must also define one or more vehicle classes. A vehicle class is simply a group of one or more vehicles for which a moving load analysis is performed (one vehicle at a time). Numerous standard vehicle definitions are built into the program. In addition the General Vehicle feature can be used to create your own vehicle definition. Each vehicle definition consists of one or more concentrated and/or uniform loads. Under the Bridge menu, select vehicles and click the Add Vehicle button. Add an HSN-44-1 type vehicle and click OK. From the Bridge menu again, select the Vehicle Classes option. Click Add New Class and select the HSN-44-1 vehicle and click Add.

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Figure I.14: Vehicle Definition

I.16 Step 12: Analysis Cases Although any analysis case type can be used when analyzing your bridge, there are several analysis options that are specialized for analysis of vehicle live loads. Moving load analysis cases compute influence lines for various quantities and solve all permutations of lane loading to obtain the maximum and minimum response quantities. Multi-step static and multi-step dynamic (direct integration time history) analysis cases can be used to analyze one or more vehicles moving across the bridge at any speed. These multi-step analysis cases are defined using special Bridge Live Load Cases that define the direction, starting time and speed of vehicles moving along lanes. Under the Define/Analysis Casescommand, select the Add New Case. Under the analysis case type, select Moving Load and add the VECL1 vehicle class and click OK.

I.16.1 Creep and Shrinkage Under the Define/Material Propertiescommand, select the concrete material property used in the deck property definition click Modify/Show Properties. Toggle the Show Advanced Properties button and complete the Creep and Shrinkage properties as shown in Figure I.15

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Figure I.15: Updated Linked Bridge Model

I.17 Results I.17.1 Influence Surfaces

The influence lines can be displayed for the various displacements, reactions, forces, moments, shears, torsion or axial loads on joints, frames, shells, planes, solids, solids, and links resulting from a unit load on a defined bridge lane in the structure. As an example, after lanes have been defined and a moving analysis case has been defined and run, select a column and use the Display/Show Influence Lines/Surfaces command to display the Show Influence Lines/Surfaces form. See Figure I.16

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Figure I.16: Influence Surface Plot Options

Figure I.17: Influence Surface Plot for Axial Force of Bent Columns

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I.17.2 Bridge Forces and Stresses You can view bridge forces and stresses for any load case. Use the Display/Show Bridge Forces/Stressescommand to display the forces and stress in the bridge deck. As an example, select the Stress,Longitudinal Stress - Top and Bottom - Center (S11) for the prestress load case. The following plot can be viewed.

Figure I.18: Bridge Object Response Display

I.17.3 Section Cut Forces There are two options available to define Section Cuts: 1. The first option is to define the location of the cut. Use the Define/Section Cuts command to obtain resultant forces acting at section cuts through a model. Define section cuts before or after an analysis is run; however, it is safest to wait until after the analysis has been run. Typically, do not define section cuts, and more importantly, the groups used in the section cut definition, until all manual meshing of the model (if any) has been completed. If the groups are defined before manual meshing, some of the point objects that should be in the group may not yet be created. 2. The second option is to manually draw the section cut on any portion of the model. This can be by utilizing the Draw/Draw Section Cut command. You must make sure that the model has been analyzed and you are viewing a member force/stress diagram. This can be found under Display/Show Member Force/Stress Diagramcommand by selecting either the frame or shell forces.

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To obtain shell forces on the bridge deck, go to Draw/Section Cut. Draw a line through any portion of the structure that you would like to sum forces about. The flashing line represents the section cut. Section Cut forces will then be visible on the screen.

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PART II Steel Bridge

II.1 Steel Bridge Example 1.0

Figure II.1: Full Bridge

This Example is intended to help the new SAP2000 Bridge User navigate through the program and is intended to get the new SAP2000 user familiar with the Bridge Module. This example provides a step-by-step tutorial for the bridge model shown below. The bridge model is broken down into five distinct steps using the file names Steel Bridge 1 through Steel Bridge 5. A copy of these input files can be obtained from Computer and

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Structures, Inc. To begin the Example 1 steel bridge model we will initiate the SAP2000 program and select a blank screen using Kip-Ft units and a single window. Then using the Bridge pull down menu we will begin to define the first of three bridge objects that will be used to complete this bridge example. Each of the bridge objects are shown below.

Sta

tion

Sta

tion

g

eO

n tio Sta

Brid

bj

1 ect

ge

Brid

11

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2 ect

O

bj

12

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FT

FT

ct

ge

Brid

je Ob

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00 10 FT

Figure II.2: Bridge Objects

II.2 Layout Line Definition To define the first bridge object BOBJ1 we will first define the layout line properties. From the Bridge>Layout Lines command we get the following dialog box:

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PART II.

STEEL B RIDGE

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Figure II.3: Layout Line Definition

From the layout line menu the Quick Start menus can be used to define various curved, straight or combined curved-straight shapes. For this example the bridge layout line 1(BLL1) will have a straight shape.

Figure II.4: Layout Quickdraw

Using the layout line dialog box shown in Figure 1.3 the end station is set at 1210 and the start station is set at 990. Note that the bridge layout line is longer than the actual bridge.

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II.3 Deck Section Definition Using the Bridge>Bridge Deck Sections¿Add New Section command and selecting the Steel and Concrete template the following dialog bow appears:

Figure II.5: Deck Section Definition

For this example four interior beams will be specified and the size of the bridge girders will be assigned as W36X230. No other changes to this deck template will be made. The bridge deck section will be given the default name of BSEC1.

II.4 Bridge Object 1 Definition Using the Bridge¿Bridge Object>Add New Bridge Object command the dialog box shown below will appear. Using the Insert Below command and the Insert command the Span1 and Span 2 information needs to be specified. Note that the bridge layout line is longer than the length of the bridge object 1 (BOBJ1) being defined. For this example the first abutment (Abut1) will be located at station 1000. A bent is placed at station 1050 and at this stage of the model an end abutment (Abut3) is placed at station 1100. In later stages of this model creation, Abut3 will be moved back by ten feet and in its place a free abutment will be used.

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STEEL B RIDGE

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Figure II.6: Bridge Object 1 (BOBJ1)

It will be important for the SAP2000 bridge user to become familiar with each of the Bridge Object Assignment. Several of the assignment options will be used in this example but the SAP2000 user is encouraged to explore the range of definitions that are possible.

II.5 Create Linked Model Using the Bridge>Update Linked Bridge Model> command the dialog box shown below will appear. From the Structural Model Options the user can choose to work with a Spine Model(frame) or an Area Object Model(shell). For this example each will be used. The user can alternate as necessary between a frame model and shell model. Starting with the spine model the Maximum Segment Lengths are set to five feet.

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Figure II.7: Update Linked Bridge Model

Pressing the OK button returns the user to following view of BOBJ1:

Figure II.8: Spine Model BOBJ1

The spine model of BOBJ1 can be viewed in its extruded form using the View>Set Display Options command and checking the Extruded option. The following image can be rotated and displayed as follows:

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STEEL B RIDGE

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Figure II.9: Extruded View of Spine Model

At this stage of model creation the center bent has only a single column support and the end abutment is defined as a single point restraint. The center bent has horizontal girder located flush with the deck instead of being offset vertically. The bent and abutments will be further modified such that additional columns will be added to the bent and point restraints will be added to each of the wide flange supports at the abutment.

Figure II.10: Modified Spine Model

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II.6 Modify Abutment Properties Using the Bridge>Abutments command the ABUT1 properties can be modified using the following dialog box:

Figure II.11: Abutment 1 Modified

All the translational and rotational degrees of freedom are set to ’fixed’ except the translation in the U2 direction. Additionally, the horizontal location of the abutment supports is set to ’each girder location’. Diaphragms are added at the abutment by selecting the ’include vertical diaphragm’ option.

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M ODIFY A BUTMENT PROPERTIES

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II.7 Modify Bent Properties Using the Bridge>Bents command the BENT1 properties can be modified using the following dialog box:

Figure II.12: Modified Bent

The reference point of the cap beam is set to 16.5ft which is half the width of the 33ft wide deck section. The number of columns is set to 3 and the vertical diaphragms are included. To define the column heights and locations the Modify/Show Column Data button needs to be selected. upon doing so the following dialog box is displayed:

Figure II.13: Modify Bent Columns

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The column locations are set to 4, 16.5 and 29 with heights of 24, 27 and 30ft.

II.8 Modify Vertical Diaphragm Properties Using the Bridge>Bridge Diaphragms command the bridge diaphragm property (BDIA1) can be modified using the following dialog box:

Figure II.14: Cross Diaphragms Definition

Using the Chord and Brace option and using a W8X10 as the chord and brace member sizes, the BDIA1 properties are modified.

II.9 Further Modify Bridge Object 1 Using the Bridge>Bridge Objects command the bridge object 1 (BOBJ1) can be modified using the following dialog box:

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Figure II.15: Bridge Object 1 (BOBJ1)

From this dialog box the Modify/Show Bents button can be selected and a value of -5ft can be assigned to the vertical offset of the bent. Similarly, the Modify/Show Cross Diaphragms button can be selected to add cross diaphragms at 25ft along span1 and 25ft along span2.

II.10 Update Linked Bridge Model Using the Bridge>Update Linked Bridge Model command the BOBJ1 can be displayed again but now with the updated abutment, bent and cross diaphragm modification. Turning off the Extrude option and displaying the BOBJ1 as a spine model shows the following:

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Figure II.16: Updated Spine Model

Not that the spine model above does not show the cross diaphragms. Updating the linked bridge model as an area object model produces the following model:

Figure II.17: Updated Shell Model

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II.11 Analyze BOBJ1

The SAP2000 program has, as a default, an analysis case already defined DEAD and MODAL. Running the model at this time will produce results for each of these default analysis cases. With the linked bridge model defined as a spine model the frame member bending moments can be displayed as follows:

Figure II.18: Bridge Object 1 - Spine Model

Unlocking the model and changing the linked bridge model to area objects, the BOBJ1 model can be rerun. Below left are the F11 shell resultant forces. Below right the frame member M33 moments are displayed.

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Figure II.19: M33 Moments

Displacements and mode shapes can be displayed as shown below:

Figure II.20: BOBJ1 Displacements

II.12 Live Loads Using the Bridge>Lanes command the dialog box below can be used to define the width and extent of various lanes over the bridge.

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Figure II.21: Lane Definitions

The first of two lanes is defined as having an end station of 1100ft and a beginning station of 1000ft. the width of the lane is set at 12ft with an offset of 8ft and the color is set to a shade of blue. The Lane Load Discretization is set at 5ft along the span and 10ft across the span. The second lane is defined as a copy of the first with an offset of -16ft. The BOBJ1 can be shown with the lanes visible using the Display>Show Lanes command.

Figure II.22: Display Lanes

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II.13 Add Vehicles

The SAP2000 Bridge Module has a variety of predefined auto, truck and train vehicles. These can be found using the Bridge>Vehicles command. For this example the HS2044, HS2044l and AML vehicles will be selected and be added as General Vehicles as shown below:

Figure II.23: Vehicle Definitions

Now that the vehicles have been defined the vehicles need to be assigned to a vehicle class. This is necessary in order to have the vehicles assigned to a specific analysis case which will be assign later. Using the Bridge>Vehicle Class command the three general vehicles are assigned to a vehicle class names HS.

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Figure II.24: Vehicle Class Definitions

II.14 Add Analysis Case Using the Define>Analysis Cases command a new analysis case MOVE1 will be added.

Figure II.25: MOVE1 Analysis Case

In the dialog box below the Analysis Case Name is set to MOVE1, the Analysis Case Type is set to Moving Load and the Vehicle Class is set to HS. Every permutation of vehicle classes operating in traffic lanes that is permitted by the entries in this table will be considered in the analysis.

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Figure II.26: Analysis Case MOVE1 Definition

With the MOVE1 analysis case now defined the model can be run. If the model is run as a spine model (See previous Section xx)and a combination COMB1 is defined as DEAD plus MOVE1 the resulting M3 moments can be displayed.

Figure II.27: Combination Dead and MOVE1

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Figure II.28: COMB1 - Frame M3 Moments

Figure II.29: Influence Surfaces


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Figure II.30: Response Display

It is recommended that the new SAP2000 Bridge User spend some time reviewing the analysis results for the MOVE1 load case and examine various individual member forces and stresses. The user can compare this results of this model with the results of the Steel Bridge PR model that has been provided. Upon completion of the analysis the current model should be saved as Steel Bridge 3

II.15 Add Trucks with Speed and Direction Using the Define>Load Cases command two moving loads will be added. The first moving load case will be named ’moving’ and will be assigned the as follows:

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Figure II.31: Moving Load Case Definition

The menu above allows the user to assign a specific vehicle to a specific lane traveling with a specific direction starting at a specific time. For the load case defined named ’moving’, three trucks are set in motion, two in lane one and one in lane two, with the start times of 0, 7 and 3 seconds. The speeds are defined as 44, 44 and 22 feet per second and the truck in lane two has been assigned a backward direction. Below, a second loads case is given the name ’move’ and consists of three vehicles assigned to lane one with staggered start times of 0, 5 and 9 sec. The speeds are different for each vehicle with the assignments of 44,88 and 176 feet per second.

Figure II.32: Move Load Case Definition

Next, the analysis cases are defined using the Define>Analysis Cases command. The ’move’ case and the ’moving’ case are added to the existing ’DEAD’, ’MODAL’ and

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’MOVE1’ cases using the Add New Case command. For the ’moving’ case the Analysis Case Type is set to Multi-step Static. This analysis case will produce an analysis result for each step of the applied load as it has been defined in the Load Case definition.

Figure II.33: Multi-step moving Analysis Case Definition

The analysis case ’move’ will be analyzed using a time-history analysis method. This will allow the user to examine the vibratory response of the bridge for each of the trucks which are traveling at different speeds. To define the time-history case the following dialog box is modified as follows:

Figure II.34: Move Time-History Analysis case Definition

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For the time-history load case a damping value of 2% has been specified by selecting the Damping>ShowModify button and assigning the values as:

Figure II.35: Damping Assignments for Time History Case

To view the shell stresses for the moving load case the SAP2000 user can use the Display>Show Forces/Stresses>Shells and selecting the ’moving’ load case, ’F11’ resultant forces with the multivalued option set to ’step 1’ the graphic display will show the unstressed bridge deck. To see the deck stresses the user can simply step through the various analysis output steps that SAP has saved as part of the multistepped analysis. Stepping through the F11 force graphic shows the following:

Figure II.36: F11 Resultant Forces for Moving Case

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Figure II.37: Axial Frame Forces for Moving Case

In lieu of stepping through the output manually, the SAP2000 user can create an AVI or movie file. This is done by selecting the File>Create Viedo>Create Multi-step Animation Video. When the following window appears the user needs to select the ’moving’ load case. The image below was created with a magnification of 10 and a speed of 10 frames per second.

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Figure II.38: Create AVI Video

To view the time-history results the SAP2000 user can use the Display>Show Plot Functions command.

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Figure II.39: Time History Plot Function

After selecting a joint, in this case joint 144, the following dialog box is used to select the ’move’ load case and define the desired plot function. For this example the U2 displacements are plotted below:

Figure II.40: U2 Displacements for the Move TH Analysis

This plot shows the third vehicle, t=9sec, inducing a larger dynamic response than the

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two previous vehicles, t=0 and t=5 sec.

II.16 Add Bridge Extensions

Before proceeding with changes to the model it is recommended that the current model now be saved as Steel Bridge 4. If necessary this model can be compared to the model provided. Adding the two narrower bridge extensions will consist of defining a new ’free’ abutment, defining an additional bridge deck section, defining a new curved layout line, modifying BOBJ1 and adding two new bridge objects. These steps can be broken down as follows: 1. Using the Bridge>Abutments command add a new abutment with the name AbutFree. Set all restraint degrees of freedom to ’free’ 2. Add a new bridge deck using the same bridge template as before except that the width of the deck is defined as 18 feet wide and the number of interior girders used is set to one. Offset the Insertion Pt in the local-y dir by 9ft. 3. Add copy of Bent1 and call it Bent2. Edit the width to be 15ft, the reference point set at 7.5ft and a single column located at 7.5ft with a height of 27ft. 4. Add a copy of the Layout Line 1 and name it BLL2. The Quick Start button can be used and the ’Curved Right option should be selected. The ’Initial Y’ dimension needs to be set at -18ft. 5. Modify BOBJ1 as follows:

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Figure II.41: BOBJ1 Modified

6. Add copy of BOBJ1 and name it BOBJ2 and modify as follows: 1. ”Span4” Span to Abutment @ 1200 ”Abut5” 2. ”Span3” Spans to Bent @ 1145 ”Bent4” 3. ”Split” Start @ 1100 ”Split” 4. Modify Spans: Set spans to the BSEC2 property 5. Modify Abutments: Assign the AbutFree property ABUT2 6. Modify Bents: Assign BENT to have a horizontal offset of 9ft and a drop of -5 7. Modify Diaphragms: Add BDIA1 to Span3 @ 22.4 and Span4 @ 27.5. The BOBJ2 dialog box should appear as follows:

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Figure II.42: Bridge Object 2 — BOBJ2

7. Add a copy of BOBJ1 and name it BOBJ3 with the following modifications: a. ”Split”, Start @ 1100 ”Split b. ”Span3”, Span to Bent @ 1145 ”Bent2” c. ”Span4”, Span to Abutment @ 1200 ”Abut5” d. Modify Spans, change to BSEC2 e. Modify Abutments, change to ABUT2, ABUT1 f. Modify bents, change to BENT2 @ 9, -5 g. Modify diaphragms, properties BDIA1, Span3 @ 22.5, Span4 @ 27.5 h. Update Bridge model and mesh at 5ft

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i. Modify Superelevations, BBL2 to have 0 @ 1100 and 10% @ 1200 When the edits above are completed the BOBJ3 dialog box should appear as follows:

Figure II.43: Bridge Object 3 — BOBJ3

II.17 Completed Model The Steel Bridge - Example 1 is now complete and ready for analysis. It is recommended that the new SAP2000 Bridge User spend some time viewing the results to gain a better understanding of the program capabilities. The results can be checked against the models provided.

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Figure II.44: Full Model Complete

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II.18 Final Analysis

Figure II.45: Full Model - Shell Stresses

With the bridge complete the user can run the final bridge configuration and look at the analysis results.

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PART III cablestayed Bridge

III.1 Cable stayed Bridge Example

Figure III.1: Full Bridge

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This bridge model is intended to demonstrate the SAP2000 Staged Construction Analysis using a cablestayed bridge as an illustrative example. This example provides a step-by-step tutorial for the staged construction analysis case. A copy of the input file can be obtained from Computer and Structures, Inc.

III.2 Description of Cable stayed Bridge This cable stayed bridge example consists of a concrete bridge deck that is supported by cable stays which in turn are supported by a center pylon. The bridge is analyzed for dead, modal and stage construction loadings.

III.3 Description of Model The bridge is modeled using a concrete deck section that defined as a hollow box section having a width of 6 meters and a depth of 1.2 meters. The deck spans on each side of the pylon are are divided into ten segments that are assigned separate group names which are used to define the staged construction sequence. The concrete assigned to the deck section has been defined using nonlinear material properties to model creep and shrinkage. The center pylon is nonprismatic with a top diameter of 0.6 meters and a base diameter of 1.2 meters. The cables connect from the bridge deck to special joints on the pylon. No live loads are included in this example.

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Figure III.2: Bridge Objects

III.4 Nonlinear Material Property Definition

Using theDefine>Materials/ command we get the following dialog box:

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Figure III.3: Material Property Definition

The ”Show Advanced Material Properties” box needs to be selected to provide the user with the option to define the Advanced Material Property Data. For this example the Time Dependent Properties option was selected which gives the user the following dialog box:

Figure III.4: Time Dependent Properties for Concrete

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III.5 Cable Property Definition Using the Define>Cable Sections command we get the following dialog box:

Figure III.5: Layout Line Definition

The cable diameter is specified as 0.05 meters. The cable properties are calculated using the specified diameter. Similarly, the cable properties can be determined if the user specifies the cable area.

III.6 Deck Section Definition Using the Define>Frame Section>Add Box Section command the bridge deck is defined having a width of 6 meters and a depth of 1.2 meters with the wall thicknesses of the webs and flanges as 0.3 and 0.2 meters, respectively.

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Figure III.6: Layout Line Definition

III.7 Pylon Section Definition Using the Define>Frame Section>Add Pipe Sectioncommand the section property PYLTOP is defined as a pipe section with a diameter of 0.6 meters and a wall thickness of 0.05 meters. The section property PYLBOT is defined as a pipe section with a diameter of 1.2 meters and a wall thickness of 0.05 meters. Using the Define>Frame Section>Add Nonprismatic command the pylon section is defined as nonprismatic having the section property PYLBOT at the start station and PYLBOT at the end station. The SAP2000 user need only select the base point while using the frame draw command and drag the pointer to the top point of the pylon to place the pylon into the model.

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Figure III.7: Bridge Object 1 (BOBJ1)

With the pylon placed into the model the model will appear as follows:


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III.8 Model Creation Using the xy command and then using the up or down arrows, the X-Y Plane @ Z=0 can be displayed. Several methods can be used to draw the deck elements, offset nodes and rigid links. One way this can is to draw the deck section along the x − axis using the Draw Frame command. The deck property is selected and the member is initially drawn from one end to the pylon and then from the pylon to the opposite end. The deck sections can then be selected and divided into 10 segments each for a total of twenty segments(ten on each side of the pylon). A fixed joint restraint has been assigned to the pylon base and the deck end restraints have been assigned as uy , uz , rx , rz . The model now appears as follows:


The offset nodes that will be used to connect the cables to the bridge deck can be drawn using the Draw Special Joint command. An offset of 3 m and -3 m in the ydirection can be used to create a single pair of nodes located at x=-90 m. Next, a rigid link can be drawn connecting each of these nodes to the deck node at x=-90 m. Using the Replicate command, these nodes and links can be replicated in the x-direction 18 times to provide points of connection for the cable elements. The replicate command will create a pair of nodes and links at the pylon as well but this particulat pair of nodes and links are not needed and should be deleted. The deck, nodes and links now look like follows:

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Figure III.10: Segmented Deck with Offset Nodes and Links

Next, the draw special joint command can be used to place nine special joints along the upper portion of the pylon. These special joints are to be located 2 m apart with the uppermost special joint located 4 m from the top of the pylon. Using the offset command, the first special joint can be drawn 4 m below the top of the pylon and the other 8 joints can be easily replicated with a spacing of 2 m. With the special joints in place the cable elements can now be drawn. For this example a cable diameter of 0.05 m was used. Using the Draw Frame/ Cable Element command, the cables can be added by snapping to the start and end joint of each cable and inserting the appropriate parameters. After the end node is selected the following dialog box appears:

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Figure III.11: Cable Parameters

Specifying the Cable Type as ”Tension At I-End” allows the user to control the initial drape of the cable. A tension amount must be specified if this option is selected. The cable element uses an elastic catenary formulation to represent the behavior of a slender element under self weight, temperature and strain loading. This behavior is highly nonlinear and inherently includes p-delta and large displacement geometry. It is highly recommended that the user read the Cable Element chapter in the Analysis Reference Manual.

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Figure III.12: Cables Complete

III.9 Group Assignments Before a staged analysis case can be defined, the user must first decide how the structure is going to be assembled. Therefore, the user must define unique groups that represent stages in the construction sequence. Then the data for each stage, namely, the operation being performed, the objects affected, the age of any added sections, loading and any scale factors, can be defined using the staged construction analysis case. For this example, the pylon is intended to be constructed first followed by the placement of adjacent 10 m deck sections with the respective cable pairs. The Group 1 elements are identified below.

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Figure III.13: Group 1 Definition

Using the Select command and the Assign/ Define Group Names command the user can define all ten pairs of deck and cable groups along with a group named, Pylon, that contains only the pylon element for a total of eleven groups.

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III.10 Staged Construction Analysis Case By selecting the Define/Analysis Cases command the user needs to add a new case. The Analysis Case Type shall be ”Static” and the ”Analysis Type” shall be ”Nonlinear Staged Construction”. The user can then begin to develop the analysis case by defining the various stages along with the data for each stage. For the dialog box below, the data for the 6th stage is show. The user can see that Group 5is being added along with the dead load of group 5.

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For this example, the nonlinear creep and shrinkage effects are included in the analysis. If desired, the creep effects can be studied for the for any period of time after completion of the structure. This can be done by adding additional stages having the ”Duration” input specifying the appropriate number of days. In this example stage 12 is aged 10 additional days. Stage 18 that is aged 10000 additional days. Stages 13 through 17 vary from 30 to 3000 days bringing the total number of days that the model is aged to 14,473 days.

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APPENDIX

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A PPENDIX A Mesh Transitioning and Compatibility The Automated Line Constraint Ashraf Habibullah1 , S.E. M. Iqbal Suharwardy2 , S.E., Ph.D.

A.1

Introduction

In the application of the Finite Element Analysis Method, the most time consuming task is usually the creation and modification of the finite element mesh of the system. Not to mention the fact that creation of mesh transitions from coarse to fine meshes can be very tedious. Also matching up node points to create compatible meshes at intersecting planes, such as walls and floors can be very labor intensive. And even if the mesh generation is automated the mesh transitioning usually produces irregular or skewed elements that may perform poorly. This may have adverse effects on the design, especially in regions of stress concentration, such as in the vicinity of intersecting planes. The object based modeling environment of ETABS & SAP2000 clearly addresses these time-consuming shortcomings of the Finite Element Method. In the object-based modeling environment the Engineer generates the structural model by creating only a few large area objects that physically define the structural units such as wall panels, floors or ramps. The finite element mesh is not explicitly created by the user, but is automatically generated by assigning meshing parameters to the area objects. These parameters may include variables, such as mesh size, mesh spacing and mesh grading among others. With this capability the engineer can study the effects of mesh refinement by just defining a few control parameters. The new model with the desired level of refinement is thus created with minimal effort. If the meshes on common edges of adjacent area objects do not match up, automated line constraints are generated along those edges. These Line Constraints enforce displacement compatibility between the mismatched meshes of adjacent objects and eliminate the need for mesh transition elements. 1 President 2 Director

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What makes this technology really powerful is that while making modifications to the model the Engineer need only be concerned about the few large physical objects of the structure. The modified finite element analytical model gets recreated automatically with any changes to the base objects. The following examples are designed to illustrate the power and practicality of this technology.

A.2

Example 1: Simply Supported Plate (Mismatched Meshing)

As illustrated in Figure A.1, this is a model of a simply supported plate, which has been modeled in two different ways. In one case the mesh is uniform across the plate and in the other case the mesh is fine on one half of the plate and coarse on the other half of the plate. In the latter case, an interpolating line constraint is automatically generated to enforce displacement compatibility between the adjacent halves of the plate where the mesh does not match. As shown in the figure, correlation between the two models is very good.

Figure A.1: Simply Supported Plate with Mismatching Edges

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A.3

M ESH T RANSITIONING , C OMPATIBILITY, AND L INE C ONSTRAINT

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Example 2: Curved Ramp Supported by Curved Wall

This example, Figure A.2, illustrates the use of Line Constraints to capture the interaction of a curved shear wall supporting a curved ramp. Notice that there are no joints at the points where the ramp element edges intersect the wall element edges. Displacement compatibility along the lines of intersection of the ramp and the wall is enforced automatically by the generation of Line Constraints along those lines. Notice how the application of Line Constraints allows the wall and ramp mesh to retain a simple rectangular (or quadrilateral) configuration. A conventional finite element model would be very irregular because it would need all the additional joints (and corresponding elements) to allow for the ramp element and wall element edge intersections.

A.4

Example 3: Floor Slab – Shear Wall Compatibility

This example, Figure A.3, illustrates a 3D Concrete Flat Plate Building with shear walls and an elevator core. Again, in this model, Line Constraints automatically appear at the lines where the floor and wall objects intersect. This, of course, as in previous examples, will enforce displacement compatibility when mesh geometries do not match. As shown in the deformed shape of the Elevator Core, in many places the wall meshing does not match the floor meshing. All elements meeting at common edges, however, still show no displacement incompatibilities, even though the element nodes do not coincide.

A.5

Example 4: Shear Wall – Spandrel Transition

This example, Figure A.4, models a Shear wall – Spandrel System, illustrating mesh transitioning from the spandrel to the shear wall. Line Constraints are generated as needed in any direction. In this case the Line Constraints are vertical as well as horizontal.

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Figure A.2: Curved Ramp Supported by Curved Wall

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Figure A.3: Floor Slab – Shear Wall Compatibility

Figure A.4: Shear Wall – Spandrel Transition

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BIBLIOGRAPHY

Computers and Structures Inc. [2006a], ETABS — Three Dimensional Analysis of Building Systems, Berkeley, California. Technical Reference Manual. Computers and Structures Inc. [2006b], SAP2000 — Integrated Structural Analysis and Design Software, Berkeley, California. Technical Reference Manual. Computers and Structures Inc. [2006c], ‘Website’, www.computersandstructures.com. See the latest web contents.

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ABOUT THE SPEAKERS

Robert Tovani, PE, SE: Robert Tovani has twenty-five years of experience in structural analysis, design, project management, and construction administration. He is currently president of Engineering Analysis Corporation and an employee of Computer and Structures, Inc. Mr. Tovani received his Bachelors and Masters of Science Degrees for the University of California, Berkeley and is licensed in California as a Civil and Structural Engineer. Mr. Tovani has developed an extensive background in computer-aided analysis and design. His analysis background includes work on a variety of structures using linear and nonlinear analysis of new and existing structures in static and dynamic loading environments. He has developed computer models on high rise structures in excess of 100 stories and has provided design work on a variety of structural framing types including base isolation and other complex framing systems. Mr. Tovani has been using the SAP and ETABS computer programs for over twenty-five years and has worked at CSI providing training, analysis and modeling assistance to CSI and Engineering Analysis clients. Recently, Mr. Tovani has provided detailed SAP2000 Bridge Training Seminars. Atif Habibullah, PE: Atif Habibullah has extensive experience using CSI products, having worked in CSI’s Software Support department for five years. For the past two years, Atif has helped instruct engineers through CSI Educational Services training seminars. He has a strong background in modeling a variety of structural systems, solving special modeling problems and in the interpretation of analysis results. Prior to working at CSI, Atif worked at a leading design firm for 4 years using CSI products, particularly in the design of multi-story steel and concrete building structures such as hospitals, office buildings, towers, bridges, stadiums and dams.

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CSI Sap2000 Bridge Examples

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