LARSA 4D Steel Girder Seismic Problem · LARSA 4D Steel Girder Seismic ... Start the tool using Design → Steel Plate Girder Bridge ... a fast way to create much of the geometry

LARSA 4DSteel Girder

Seismic Problem

LARSA 4D Steel Girder Seismic Problem

A manual for

LARSA 4DFinite Element Analysis and Design Software

Last Revised May 2011

Copyright (C) 2001-2012 LARSA, Inc. All rights reserved. Information in this documentis subject to change without notice and does not represent a commitment on the partof LARSA, Inc. The software described in this document is furnished under a license ornondisclosure agreement. No part of the documentation may be reproduced or transmittedin any form or by any means, electronic or mechanical including photocopying, recording,or information storage or retrieval systems, for any purpose without the express writtenpermission of LARSA, Inc.


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Table of ContentsIntroduction 5

Creating Structure Geometry with the Steel Plate Girder BridgeModule

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Finishing Model Geometry 11Structure Groups 11Pier Cap 13Piers 15

Basic Bridge Loading and Construction Sequence 19Load Cases 19Construction Stages 22

Staged Construction Analysis Results 27

Live Load Analysis 29

Response Spectrum Analysis 33Response Spectrum Curve 33Stressed Eigenvalue Analysis 36RSA Analysis 37

Pushover Analysis 41Defining the Cross-Section 41Preparing the Model 42Moment Curvature Analysis 44Loading 45Analysis and Results 47

Time History Analysis 49Excitation Curve 49Superstructure Mass 50Analysis 50


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Introduction

This problem is the analysis of a two-span steel plate girder bridge with a concrete deck. Thesuperstructure is constructed in three steps.

Live load analysis using influence surfaces, dynamic analysis using response spectrum analysis andtime-history analysis, and pushover analysis are used.

The final model is shown below.

Front View

Side View

This training manual is written for LARSA 4D Version 7.5.


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Creating Structure Geometrywith the Steel Plate Girder

Bridge Module

The fastest way to generate a steel girder model is to use LARSA 4D’s Steel Plate Girder Design Module.The Steel Plate Girder Module generation and design tool allows users to generate 3D finite elementmodels of steel plate girder bridges with ease. Users provide the number of girders, spans, etc. andthe module creates the model, loading and analysis. The module supports curved, skewed bridges andis capable of performing code check using the AASHTO LRFD code. The code check can be used onmodule-generated bridges or custom/manually built finite element models.

Start LARSA 4D.

Save the project now to give it a file name.

Set project units as shown below using Input Data → Units in the LARSA 4D menu. Afterchanging the units as needed, click Apply Conversion .

Project Units

Start the tool using Design → Steel Plate Girder Bridge Module .

Choose Step A (Generate A New Steel Girder Model) only, and then click Next at the top of thewindow.

Steel Plate Girder Bridge Module


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At this point, the module asks for basic bridge geometry parameters. The first question, structuretype, allows either a simply-supported structure or a continuous structure at the piers. We will use acontinuous structure type so that moments are carried across the pier.

Choose Continuous .

The bridge alignment option allows for the use of LARSA’s Bridge Path User Coordinate Systems todefine the horizontal and vertical curvature of a bridge. This bridge is straight so it will be alignedalong the Global X axis.

Bridge Geometry

Click Edit Abutments & Piers and then enter the information shown below into thespreadsheet.

Abutment and Pier Locations

Click Back to Main Page at the top of the module window when done.

The next step is to define the girders. The bridge module has several modeling techniques for girders.Both I shapes and box/tub shapes are available, and for I shapes the web can be modeled as eitherbeam or plate elements. In this model, the girders will be modeled as beam elements.

Choose I girder (one member for the flanges and the web) . Choose a steel material. Then clickEdit Girders and enter the information shown below.

Girder Definitions


Cross-Frames and Splice Points

The next set of questions asks for the locations and types of cross frames and the locations of splicepoints. Splice point locations ensure that a joint is located in the model at the location we request. Weneed a joint both at the splice point and at the end of the first pour region. Several types of cross-frame


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types can be created by the bridge module, including K and X types. The different types available areshow below:


Choose a steel material for the cross-frames. Then click Edit Cross-Frames and Splice Pointsand then enter the information shown below into the spreadsheet.



The last model geometry questions regard the deck.

Enter the information shown below.

Deck Parameters

The final question is the deck plate refinement, which controls the mesh size of the deck.

Enter 10 ft for the deck plate refinement.

Click Next at the top of the module window. Then click Next again.

The module will generate a bridge model that looks like the model in the figures below.

The Generated Model


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The Generated Model


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Finishing Model Geometry

While the Steel Plate Girder Module provides a fast way to create much of the geometry of bridgesuperstructure, it does not currently include the ability to model substructure. In this section we willadd the pier to the model, and we will prepare the model for analysis by creating structure groups.

Structure GroupsStructure Groups are used to quickly select and unselect parts of the structure, and they are used todefine groups of elements to be constructed or deconstructed in Staged Construction Analysis. Selectionis also an important part of setting up the construction sequence and accessing results.

Because the structure is assembled in five steps, we will need to create five structure groups: the girdersin segment 1, the deck elements in pour 1, the girders in segment 2, the deck elements in pour 2, andthe deck elements in pour 3.

On the right side of the screen, click the small Group button to open the Structure GroupsExplorer.

Structure Groups Explorer

The steel girder module has already created a number of groups for the girders, the cross-frames, andthe deck; however, it has not created groups for the segments.

Click the Add Folder button in the explorer to create a new structure group folder. Then clickthe folder, choose Rename , and type “Construction Groups”. Press Enter .

Segments 1 and 2

If the elements are not all unselected, start by unselecting all using Selection → UnselectObjects → Unselect All .

Make sure the Pointer tool is the current mouse tool in the graphics window. You can find it inthe toolbar, shown highlighted in the figure below.

Graphics Mouse Tools

Locate the splice point by holding the CTRL key and positioning the mouse over joints to the leftof the pier. Find the joints whose X coordinate is 122 ft, the location of the splice point.

The first group will be for the four girders to the right of the splice point, which make up the firstsegment.


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Turn on the graphical selection tool. It is the tool to the right of the Pointer (see the figureabove). Then click and drag a window around the first girder from the splice point to the rightend of the bridge. Then do the same for the three other girders. Do not make the windows too bigso that you do not select any plate elements that make up the deck.

Segment 1

Back in the Structure Groups Explorer, click the Add Group button. It will create a new groupfor the selected elements in the folder we created.

Click the group, choose Rename , and rename it to “Segment 1”.

Unselect all elements again using Selection → Unselect Objects → Unselect All . Then clickand drag a window around the first girder from the left end of the bridge to the splice point.Then do the same for the three other girders.

Segment 2

Back in the Structure Groups Explorer, click the Add Group button and rename it to “Segment2”.

Pours 1, 2, and 3

Now we will create three groups for the three pours.

Unselect all elements again using Selection → Unselect Objects → Unselect All . You can alsouse SHIFT+F6 or simply U if the graphics window has the input focus.

Using the Pointer tool, locate the end of the first pour by holding the CTRL key and positioningthe mouse over joints to the right of the pier. Find the joints whose X coordinate is 157 ft.

Using the Selection tool, drag a window around the entire structure from just to the left of theend of the first pour to the right end of the bridge. This will select the deck elements as well asthe girders and cross-frames.

Since this group will be for the deck only, unselect all the member elements using Selection →Unselect Objects → All Members .


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Pour 1

Back in the Structure Groups Explorer, click the Add Group button and rename it to “Pour 1”.

Repeat this process to create groups for Pour 2 and Pour 3. Pour 2 is from the start of the bridgeto the splice point. Pour 3 and the structure groups are depicted below.

Pour 3

Structure Groups

Pier CapThe pier has so far been modeled as pin supports at the level of the deck. The supports will be replacedwith a pier and the pier cap.

The pier cap is depicted below and is made up of beam elements running transversely.

Pier Cap

However, keep in mind that there is no point of connection at the bottom of the I flange to the top ofthe pier cap. The rendering masks the simplification that we chose to make in treating each girder asa one-dimensional element. The only point of connection to the girder can only be at its end joints. Inthis model, the end joints are at the centroid of the deck and the girder is shifted down rigidly using amember end offset. (You can see the joints in the rendering by the placement of the pin icons.) Then inorder to attach the pier cap to the girder, it must be attached to these same joints.


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In line elements, “plane sections remain plane” meaning cross-sections are rigid. A connection at anypoint on the cross-section is as good as any other. What results here is that the pier cap will be (rigidly)connected to both the girders and the deck, and we will need member end offsets again.

The pier cap elements will span the four joints on the girders, but because it is 2 ft shorter than thedeck (1 foot on each end), we will create new joints for the far ends of the pier cap.

First, however, we will start with the cross-section definition.

Pier Cap Properties

Go to Input Data → Properties → Sections → Section Dimensions .

Add two new rows to the spreadsheet ( Edit → Add Row or just start typing into the blank rowat the end) and fill in the information shown in the figure:

Pier Cap Properties

Pier Cap 2 holds the properties for the ends of the pier cap which are tapered.

Select the two rows with the mouse, right-click them, and choose Calculate Properties . This willfill in the section area, moments of inertia, and other properties found on the Properties tab.

Close the section dimensions spreadsheet.

Pier Cap Geometry

Go to Input Data → Geometry which opens the joints spreadsheet.

Add two new rows to the end of the spreadsheet with coordinates (142, -20, -8.0833) and (142, 20,-8.0833).

8.0833 ft is the distance from the top of the deck to the centroid of the tapered end of the pier cap.

Pier Cap End Joints

Close the joints spreadsheet.

In the graphics window, zoom in on the pier (the Zoom Window tool is the first mouse tool shownin the figure earlier). Then select the eight joints at the pier, including these two new joints.

Go to Draw → Geometry → Members .

A floating “Draw Members” tool window will appear indicating that we are now drawing members. Themembers panel of the Model Data Explorer will also open on the right side of the screen where we canchoose properties for the members we are about to draw.


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In the Model Data Explorer, change the Section to “Pier Cap 2” and the End Section to “Pier Cap1”. Change the material to Fc_4 and the (orientation) Angle to 90 degrees.

Click the joint for the right end of the pier cap. This is the joint that we just created atcoordinate (142, -20) and it is the one second from the bottom on the screen. Then click the nextjoint up (the one on Girder A) to draw a member between the joints. This represents the righttapered end of the pier cap.

In the Model Data Explorer, change the Section to “Pier Cap 1” and the End Section to “(same asstart)”. Then draw three members between the successive joints.

For the tapered member on the left side, change the End Section to “Pier Cap 2” and draw thefinal member between the sixth and seventh joints from the bottom.

Close the floating “Draw Members” window to finish drawing.

What we have now places the centroid of the pier cap at the same location as the centroid of the deck,since the joints (besides the ends) are at the centroid of the deck. We will add member end offsets toshift the pier cap centroid down.

Go to Input Data → Geometry → Members → Member End Offsets which opens the jointsspreadsheet. Scroll to the end of the spreadsheet. The last five members are the five membersjust drawn. Enter the offsets as shown below, and then close the spreadsheet window.

Pier Cap Member End Offsets

8.7083 ft is the distance from the deck centroid to the centroid of the pier cap at the centerline.

Piers

Pier Properties


Add a new row to the spreadsheet ( Edit → Add Row ) and fill in the information shown in thefigure:

Pier Properties

Select the new row with the mouse, right-click it, and choose Calculate Properties . Then closethe sections spreadsheet window.


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Pier Geometry

The pier consists of two members connected to the pier cap. As with the pier cap, the pier can onlyconnect to the pier cap at the pier cap’s joints. These are once again the same joints as the joints on thedeck itself. Thus, the pier will be connected rigidly to the deck as well.

The pier members will be placed directly beneath Girders B and C so that their joints can be reused.

Go to Input Data → Geometry which opens the joints spreadsheet.

Add two new rows to the end of the spreadsheet with coordinates as shown below for the bottomsof the piers at ground level. Also set the joints to be fully fixed.

Pier Base Joints

Close the joints spreadsheet.

Put the graphics into a 3D view by clicking the 3D View icon in the toolbar (it is the first icon inthe second row). Then Zoom Extents (it is another icon) and zoom in so you can see the joints forthe piers clearly.

Go to Draw → Geometry → Members .

In the Model Data Explorer, change the Section to “Pier” and the End Section to “(same asstart)”. Also change the material to Fc_4.

Click the base joint for the left pier and then click the top joint for the pier, which is the jointabove it on girder B.

Repeat this for the right pier.

Close the floating “Draw Members” window to finish drawing.

Pier Members


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Since the piers do not go all the way up to the centroid deck, we will use member end offsets again sothat the pier ends at the bottom surface of the pier cap. If we did not use member end offsets, we wouldbe adding additional stiffness and weight into the model that is not actually present.

Open the member end offsets spreadsheet ( Input Data → Geometry → Members → MemberEnd Offsets ) and scroll to the bottom to view the last two members which are the two membersjust added.

Change the J-Offset Z for both of these members to -11.2083 ft, which is the distance from thedeck centroid to the bottom surface of the pier cap.

Close the member end offsets spreadsheet.

Finally, the old supports at the top joints must be removed.

Unselect All, and then select the four joints above the pier that are currently pins.

In the Model Data Explorer, change where it says Members to Joints.

Uncheck the three restraint directions Trans. X, Y, and Z.

Click the checkmark at the top of the explorer to make the change to the selected joints.

We will also need a group for the pier and pier cap.

Unselect All, and then select the members that make up the pier and pier cap. An easy way toselect the members is to return to the Members spreadsheet, find the seven elements that makeup the pier cap and pier at the bottom of the spreadsheet, then select those rows, right-clickthem, and choose Select Members .

Open the Structure Groups Explorer and click the Add Group button. Rename the group to“Pier and Pier Cap”.


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Basic Bridge Loading andConstruction Sequence

The Steel Girder Design Module will set up much of the loading on the structure including dead load forsidewalks, railings, and bidwells, and live load including pedestrians, wind, and vehicles. (Vehicularloading is discussed later on.)

Return to the module in Design → Steel Plate Girder Bridge Module .

Choose Step B (create bridge loading data) and click Next .

Enter the values shown in the figure below:

Bridge Loading Options

These options will create load cases and loads. For instance, the sidewalk and pedestrian loading willbe converted into plate loads along the sides of the bridge. The loading can be modified by the userlater if needed.

The module will also set up a standard construction sequence.

Click Deck Pouring Sequence and enter the information shown below.

Deck Pouring Sequence

Then click Back to Main Page , and then Next , and Next again.

Load CasesThe module creates a number of load cases, which can be seen in the Load Cases Explorer. (Click thesmall Load button at the top of the explorers on the right side of the screen.)


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Load Cases

Influence Coefficients

These two load cases place vertical and longitudinal unit loading at locations on a grid throughoutthe deck surface. The vertical loading is used for the gravity weight of vehicular live load, and thelongitudinal loading is used for the computation of braking force effects. These are described in thenext section.

Self Weight

A Self Weight load case is used for automatic self-weight computation. When used in a StagedConstruction Analysis, described below, it adds dead loading for the weight of any structural elementsthat have not yet had their weight added into the model.

Deck Weight

Three load cases are created for the deck pouring sequence. These load cases represent the weight ofthe three deck pours during the time the deck does not have any stiffness. The weight is transferreddirectly to the member elements: the girders and pier cap. You can click the load cases to see themember loads generated for each pour:


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Member loads generated for the first deck pour

Wind

Wind load cases are created for the transverse wind loading using uniform member loads.

Member loads generated for wind loading


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Pedestrians

Non-structural sidewalk weight and the weight of pedestrians are included in load cases using pressureloads on the outer rows of the plate elements making up the deck surface.

Uniform plate loads for the non-structural sidewalk weight

Construction StagesThe module also sets up a basic construction sequence using what it knows about the structure so far.At the time of writing, the steel girder module does not have options for the sequence of the assemblyof the girders, so it assembles the girders at once. But it has created separate construction steps forthe three pours configured above.

To view the construction sequence created by the module, change to the Construction StagesExplorer by clicking the small Stage button at the top of the explorers on the right side of thescreen.

Default Construction Sequence

In the stage named DC1, there are three steps. In step “Girders and Cross-Frames”, all of the memberelements in the model are constructed at once and their weight is included. Three pour steps follow,which apply the pour load cases described earlier.

In the stage named DC2, the plate deck elements are assembled. They are marked as “stiffness-only”because their weight has already been applied. This will prevent their weight from being applied again


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when a Self Weight load case is included. The non-structural sidewalk weight load case is also appliedin the construction step.

Casting Day

The construction sequence needs to be revised to conform to the design specification, which calls forSegment 1 to be constructed with Pour 1 first, then 14 days later Segment 2 with Pour 2, followed twodays later by Pour 3. Because 14 and 16 days is enough time for concrete to attain much but not all ofits compressive strength, we will include the time effect on elastic modulus for the plate elements.

The new construction sequence will be:

Seg 1 - Day 1The pier and Segment 1 (girder elements) are constructed, and the weight of Pour 1 loadingis applied. Pour 1 elements are cast on this day.

Seg 2 - Day 15Pour 1 deck elements take on stiffness, but not weight since it was already applied. Segment2 (girder elements) is constructed, and the weight of Pour 2 loading is applied. Pour 2elements are cast on this day.

Pour 3 - Day 17Pour 2 deck elements take on stiffness (but not weight). Pour 3 loading is applied.

Additional Loading - Day 30+Non-structural sidewalk weight and pedestrian loading will be added. Const WS loading willbe applied. And influence coefficients will be generated.

Once we enter the construction sequence it will be displayed visually in the Construction StagesExplorer, as shown below.


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Revised Construction Sequence

Open the Plates spreadsheet Input Data → Geometry → Plates .

Turn on Show Only Selected Objects at the bottom of the spreadsheet.

Use the Structure Groups Explorer to select the Pour 1 elements.

Change the Casting Day column cells all to 1. It will be useful to use the cell range edit tool inthe toolbar.

Select the Pour 2 elements and change their Casting Day to Day 15.

Select the Pour 3 elements and change their Casting Day to Day 17.

Close the Plates spreadsheet.

Additionally, the material must be marked as a concrete material and it must be assigned a MaterialTime Effect record to activate time-dependent material effects for members assigned that material.

Open Input Data → Properties → Material Time Effects . Add a row to the spreadsheet.Nothing needs to be set for this record.

Change to the Materials spreadsheet, and then to the More Properties tab. For Fc_4 change theConcrete Cement Hardening Type to Normal. Any concrete type will activate the time effect onelastic modulus. Also change its Material Time Effect to the record just created.

Close the Materials spreadsheet.


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Stages

The stages also need to be revised. It is easiest to remove the existing stages and start over.

Open Input Data → Construction Stages . Delete all of the rows in the spreadsheet and thenenter:

Construction Stages

Change to the Stage Steps tab, delete all of the rows, and enter:

Construction Steps

Note that the Const WS steps are marked as temporary so that the loading is not accumulated intolater steps and the influence steps are marked as being a Linear Moving Load/Influence analysis.

Close the Stages spreadsheet and open Input Data → Construction Stage Activities . Enter thestructure groups as they are assembled:

Construction Activities

Change to the Load Cases tab and add 1) self weight to each stage in which new elements areconstructed and need self weight applied, 2) deck weight, 3) nonstructural sidewalk thickness


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and pedestrian load, 4) Const WS load in the positive and negative direction, and 5) influencecoefficient loads:

Load Case Activities

In Analysis → Time Dependent Analysis Options , turn on Include Time Effect on Modulusand turn off all other time-dependent effects.

Run a Time-Dependent Staged Construction Analysis. You may need to turn off Perform QuickIntegrity Check because some of the modeling choices generate warnings that can be ignored.


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Staged Construction AnalysisResults

The results of a Staged Construction Analysis can be viewed in several ways. Spreadsheets andgraphical results normally display the cumulative effect of all loading up to selected construction step.It is also possible to view the incremental results of any construction step numerically and graphically.When load class tracking is used, the cumulative effects can also be split by load class, such as deadload, creep, primary and secondary moments, etc., and these can be recombined with factors for code-based load combinations. Finally, graphs are available which can be used to plot structural responsesover time.

Select Girder A using the Structure Groups Explorer (“Girder 1”) or by right-clicking the girderand choosing Select Chain . (The Hide Unselected tool in the Graphics menu is useful forgetting a clearer look at this girder.)

In the Analysis Results Explorer, select the case Seg 1: Step 1.

Turn on graphical result diagrams for member stresses and choose Stress Point 1.

Stresses are reported at Stress Recovery Points defined on the section. Point 1 is at the top-right of thesection; point 3 is at the bottom left of the section.

Stresses at Top after Pour 1


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Stresses at Top after Pour 2


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Live Load Analysis

Live load analysis on this model is performed using LARSA 4D’s influence surface analysis. Thisanalysis has several parts:

1. A grid of influence coefficients is computed over the roadway surface. The coefficients are theresults of placing a vertical unit load at different positions on a grid over the deck surface,with grid spacing set by the user. An assumption of linearity allows us to compute the effect ofany vehicle or patch loading based only on the grid of influence coefficients.

2. For the purpose of computing braking forces, a longitudinal unit load is placed at the samepositions over the deck surface. The same assumption of linearity allows us to place thelongitudinal unit loads in the same direction, although they will be used to compute brakingforces for traffic going in both directions.

3. Vehicle and UDL placement options are configured for each section of the AASHTO LRFDcode: the single truck case, the tandem case, the two trucks case, and the braking forces case.Each case’s results can be reported separately.

4. An “extreme effect group” is created to perform an envelope over all of these cases.

The Steel Girder Design Module has handled all of this for the user, although the user is also free toset up these options by hand.

Select Girder A using the Structure Groups Explorer (“Girder 1”) or by right-clicking the girderand choosing Select Chain . (The Hide Unselected tool in the Graphics menu is useful forgetting a clearer look at this girder.)

In the Analysis Results Explorer, select the case LL: Vehicles.

Generated Cases for Live Load

This result case is an Extreme Effect Group which computes the envelope of the three separateinfluence result cases for the three components of live loading: the design truck, the design tandem,and the two trucks case.

In Results → Results Display Settings , set the number of segments to 1 or 2, which is enoughdetail for this model. The computation of influence-based results will be much slower whenresults at more segments are sought.

Turn on graphical result diagrams for member forces and choose Mz.

The moment and shear diagrams for Girders A and B are shown below:


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Girder A - Mz

Girder B - Mz

Girder A - Fy


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Girder B - Fy

The results are also of course available numerically. Spreadsheets show the enveloped moment orshear, the controlling case (including the locations of the vehicles), and the corresponding forces in theother directions for the same vehicle location.

Spreadsheet Results

An influence coefficient view allows the user to see the influence coefficient grid as well as the computedworst-case location of the vehicles and patch loading:


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Influence coefficients and truck/UDL locations for two trucks case, for Mz at the pier

Stress diagrams for Girder B are shown below. Stresses are reported at Stress Recovery Points definedon the section. Point 1 is at the top-right of the section; point 3 is at the bottom left of the section.

Girder B Stress at Top

Girder B Stress at Bottom


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Response Spectrum Analysis

In this section we will perform a response spectrum analysis on the model assuming it is located inSeattle, Washington State, USA. We will use the analysis to determine the displacement demands atthe top of the pier.

Response Spectrum Curve

Curve Generator

LARSA has developed a curve generator tool which can be accessed on our website at http://www.larsa4d.com/tools/rsacurve. This tool allows the user to:

• Look up PGA, SS, and S1 values for the AASHTO Guide Specifications for LRFD SeismicBridge Design 2009 for locations in the continental United States.

• Generate RSA curves for either AASHTO Guide Specifications for LRFD Seismic BridgeDesign 2009 or AASHTO LRFD Bridge Design Specifications 2007, for any location providedthe acceleration and site coefficients are known.

• Preview the RSA curve and save it for LARSA 4D or for Microsoft Excel for use in otherapplications.

We will use this tool to generate the RSA curve for this model.

Open the address above for the RSA Curve Generator Tool in your web browser.

Choose the design code (AASHTO Guide Specifications for LRFD Seismic Bridge Design 2009)and the seismic data release year (USGS 2008).

Enter a location, such as “Seattle” or a ZIP code and click Go . Verify on the map that themarker is at the site location. Then choose a site class or soil profile.

The RSA parameters from the contour map of acceleration coefficients will be determined automaticallyand shown in the text fields at the bottom left.


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RSA Curve Generator Tool

If the bridge site is located outside of the continental United States, the acceleration coefficients canbe entered into these fields at this time.

Click Generate Curve .

RSA Curve Generator Tool

Click Download for LARSA 4D and save this RSA curve database file along side the LARSA 4Dproject file that you have been developing throughout this training manual.

Once the RSA curve database file has been created, it must be loaded into the project.

Back in LARSA 4D, go to Input Data → Connect Databases → Connect User Database andchoose the database file you just saved. Then close the Connect Databases window.


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Manual Entry

The response spectrum curve can alternatively be entered by the user. The conventional means to enterthe RSA curve is as acceleration versus period of vibration, and the values are most easily computedusing Microsoft Excel. You can skip this section if you created the RSA curve using the online curvegenerator tool described above.

In this section we will create the curve for AASHTO LRFD Bridge Design 2007. The accelerationcoefficient, A, for a bridge at this location is approximately 0.3. Since the site soil profile is not known,the site coefficient, S, is taken as 1.2.

To compute values on the RSA curve, open Microsoft Excel.

In the first column we will put time values from 0.1s to 4s at 0.1s intervals. The easiest way todo this is to enter 0.1 in cell A1. Then enter “=A1+0.1” into cell A2, and then drag and extend A2down to A40.

In the second column we will put the RSA acceleration curve, normalized with respect toA. Enter the following formula into cell B1: IF(1.2*1.2/(A1^(2/3))<2.5, 1.2*1.2/(A1^(2/3)), 2.5) . Then drag and extend B1 down to B40.

Calculating the RSA Curve in Microsoft Excel

Because the curve is normalized, it can be used in any seismic zone, provided it is denormalized later.

Select the rectangle of cells from A1 to B100 and copy the values to the clipboard.

Return to the LARSA 4D project for this model.

Go to Input Data → Edit Databases .

Click New Database → New Response Spectra Curves Database .

“New Database 1” will appear on the list of databases on the left side of the Database Editor. Thisdatabase will contain the RSA curve needed for this model.

Click “New Database 1”.

Click the plus sign to the left of Add/Remove Record.

Click “New Record 1” and change it to “RSA Curve - Seattle”.

At the top-right of the Database Editor, note that the X Axis is Time in seconds and change theY axis to Acceleration.

Click the top-left cell in the spreadsheet (below the Time column header) and paste the valuesfrom the clipboard.


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RSA Curve

Check that the curve has been entered correctly by changing to the Graph tab.

The curve must be denormalized now. Additionally, LARSA 4D expects the acceleration to be given asthe elastic seismic response coefficient multiplied by gravitational acceleration, g. To denormalize thiscurve, we will apply a scale factor of A multiplied by g.

At the top-right of the Database Editor, make sure the length unit is feet.

In the scale field just below that, enter 9.6.

RSA Curve and Scale Factor

Click Save Database and save it as “seattle.drs” in the same directory as the project file.

Close the Database Editor.

Although the database file has been created, it must be loaded into the project.

Go to Input Data → Connect Databases → Connect User Database and choose the databasefile. Then close the Connect Databases window.

Stressed Eigenvalue AnalysisBefore running an RSA analysis, an eigenvalue analysis must be performed to determine the modesand whether enough modes are requested.


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Eigenvalue analysis can be performed on the undeformed state of the structure or on the deformedstate of the structure after loading. We will first compute the modes in its undeformed state.

Open Analysis → Eigenvalue / Response Spectrum Analysis .

Click the Eigenvalue option and set the number of modes to 100. Then run the analysis.

After the analysis completes, open Results → Spreadsheets → Eigenvalue → Frequencies .

Scroll to the bottom and ensure that the mass particulation (“Cumulative Per Mass”) is at least85% in each axis. The values are given as percents.

When the mass participation is not high enough, more modes must be computed.

The eigenvalue analysis can also take into account the effect of loading prior to the modal analysis.When performing a simple linear/nonlinear static analysis of this loading, the eigenvalue analysis isEigenvalue on Deformed (also known as stressed eigenvalue analysis). When performing a StagedConstruction Analysis, as in this example, the eigenvalue analysis is performed as an analysis scenario.

In the Construction Stages Explorer, add a new construction stage with a single constructionstep. Rename the stage and step to “Eigenvalue”. Then right-click the step, choose Properties ,and change the analysis type to Eigenvalue. This is called an analysis scenario.

Eigenvalue Analysis Scenario

Go to Analysis → Staged Construction Analysis . Because the number of stages changed,before clicking Analyze open the Construction Stages analysis options tab and make sure theEigenvalue stage is chosen as the ending stage. Then analyze the model.

Explore the computed mode shapes graphically. Turn on graphical mode shapes with Results→ Graphical → Mode Shapes . Click a mode shape in the Analysis Results Explorer within theMode Shapes group. You may need to increase the display scale using the slider at the bottom ofthe Analysis Results Explorer.

The Structure’s Second Mode

Turn off graphical mode shapes when done.

RSA AnalysisIn the Load Cases Explorer, add two new load cases. Right-click each and choose Properties ,change their names to RSA1 and RSA2 and their types to Response Spectra.


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Double-click the first case and change to the RSA Loads tab.

Set the Response-Spectrum Curve in Directions 1 and 2 to RSA Curve - Seattle.

Set the Scale in Direction 1 to 1.0 and the Scale in Direction 2 to 0.3, according to Article 3.10.8.

RSA Analysis Options

Do the same for case RSA2 but set the factors in reverse, to 0.3 and 1.0.

The RSA curve will be applied in the global X and Y axes and combined according to the scale factors.

RSA Load Cases

Open Analysis → Eigenvalue / Response Spectrum Analysis and change to the ResponseSpectra analysis type. Turn on Keep Previous Results and then click Analyze .

RSA results are now available for each of the two RSA load cases. The results can be explored just aswith any other load case, except it must be kept in mind that all RSA results are signless because theyare combinations of modes and that the results cannot be transformed to other coordinate systems.

To compute displacement demands, we will look at the forces at the top of the pier.

Unselect All and then select the two pier column members.

Open Results → Spreadsheets → Member → End Forces - Local .

In the Analysis Results Explorer, make sure the Load Cases group is expanded. Click “RSA1” toselect it. Then hold the CTRL key on the keyboard and click “RSA2” to select both cases.

Note how the spreadsheet shows the member end forces at each end of each member for each selectedcase (RSA1 and RSA2). Recall that the member local Z direction is transverse and the local Y directionis longitudinal. This can be verified either by turning on local axis icons ( Graphics → Show → DisplayIcons ) or noting the orientation angle set on the members and consulting the documentation for thedefinition of member orientation angle.


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RSA Demands at Pier

The spreadsheet indicates a longitudinal demand of 4.4 kips and a transverse demand of 42 kips oneach pier column.


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Pushover Analysis

In this section we will perform a pushover analysis on the pier section. Moment curvature analysis willbe used to compute the nonlinear moment-curvature relationship at several levels of axial force on thecircular pier section, which has steel reinforcement.

Although pushover analysis can often be performed as an analysis scenario within Staged ConstructionAnalysis, in this case it is simpler to work with a model containing just the pier elements. This modelwill include the vertical load on the pier as computed by the Time-Dependent Staged ConstructionAnalysis on the full model, plus a variable longitudinal or transverse load.

Run a Time-Dependent Staged Construction Analysis on the full model if results are not yetavailable.

Open the Reactions, Member End Forces, or Member Sectional Forces spreadsheet for theAdditional Loading: Step 1 result case and note the vertical force at the bottom of the piercolumns: 916 kips each.

Since we will be creating a new model with the pier only, we will apply the 1,832 kips total as a loadonto the pier. Note that the reaction includes the self-weight of the pier cap and pier itself.

Defining the Cross-SectionFor the pushover analysis, we will need to revise the pier section to include the reinforcement bars inthe design specification. The new pier section can be created in LARSA Section Composer.

Start LARSA Section Composer. Save the database immediately as “pier section.lpsx” andrename the section to “Pier Section” using Section → Rename .

Open Shape → Insert Custom Shape .

Choose the Solid Circle shape in the Basic Shapes category and enter a radius of 2 feet. ClickAdd .

Creating a Circular Cross_Section

Click the Draw Rebars tool in the toolbar. Enter the options shown below:


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Rebar Drawing Options

Click an edge of the circle shape to draw the rebar around that edge. Then click Close in theDraw Rebars window.

Section with Rebars

Save the section and exit Section Composer.

Preparing the ModelBack in LARSA 4D, start a new empty project. Set the coordinate units to feet.

Go to Input Data → Connect Database → Connect User Database . Choose the new sectiondatabase file “pier section.lpsx” and then close the Connected Databases window.

Use Input Data → Materials to bring in Fc_4.


Add two new rows to the spreadsheet ( Edit → Insert Row ) and fill in the information shownin the figure. Pier Cap 2 gives the approximated section dimensions beneath the leftmost andrightmost girders, since we will not be modeling the tapered part of the pier cap beyond thesepoints.


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Pier Cap Properties

Select the two rows with the mouse, right-click them, and choose Calculate Properties . This willfill in the section area, moments of inertia, and other properties found on the Properties tab.

Close the section dimensions spreadsheet.

Open Input Data → Geometry → Joints .

Add base joints at (0,-11,0) and (0,11,0) and set them to fully fixed in all six directions.

Add joints for the tops of the pier columns at (0,-11,30) and (0,11,30).

Change to the Members spreadsheet and add two new members connecting the base joints tothe top joints. Set the element type to Hysteretic, the section (at start) to “Pier Section”, which isthe section definition in the lpsx file database, and the material to Fc_4.

The pier cap will be included but the tapered parts of the pier cap beyond the first and last girder willbe omitted.

Add joints for the left and right ends of the pier cap at (0,-16.5,30) and (0,16.5,30).

Joints

Connect the pier cap joints with members as shown in the figure. Set the orientation angle of thethree new pier cap members to 90 degrees.

Members

In the Member End Offsets spreadsheet, set the offsets as follows to raise the pier cap by halfits depth so that its bottom surface is flush with the top of the pier column, and so that the topsurface of the pier column remains flat despite the tapering at either end.

Member End Offsets

Use Graphics → Complete Rendering to verify the model so far. Turn off complete renderingwith Graphics → Simple Rendering .


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Final Model

Moment Curvature AnalysisWe will perform a moment curvature analysis on the pier section to generate the required informationfor the pushover analysis.

The Moment Curvature Analysis tool allows users to perform moment curvature analysis oncross-sections, capable of taking prestressing/post-tensioning and reinforcement bars into account.Currently, the tool has support for the following codes: AASHTO LRFD 2006, BS5400, and EN1992-1-1:2004.

The Moment curvature Analysis tool computes a moment-curvature graph for many values of axialforce. Each generated graph is stored as a moment curvature type spring property [see “Spring PropertyDefinitions” in LARSA 4D Reference Manual] (see Input Data → Properties → Spring Properties ) andautomatically assigned to the corresponding section [see “Sections” in LARSA 4D Reference Manual].You can right click on a section in the sections spreadsheet ( Input Data → Properties → Sections ) andclick Moment Curvature to see the curve assignments. These sections can then be assigned to memberelements [see “Members” in LARSA 4D Reference Manual] with type set to hysteretic for nonlinearinelastic analysis.

Start Design → Moment Curvature Analysis and enter the options shown below.

Moment Curvature Analysis Options

Click Edit Stress/Strain Models .

Choose Fc_4 at the top and select the CEB-FIP 90 material model for it.

LARSA4D_ReferenceManual.pdf#input/properties:Spring Property Definitions

LARSA4D_ReferenceManual.pdf#input/properties:Spring Property Definitions

LARSA4D_ReferenceManual.pdf#input/properties:Sections

LARSA4D_ReferenceManual.pdf#input/geometry:Members

LARSA4D_ReferenceManual.pdf#input/geometry:Members


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Choose A706 at the top and then select the Ramberg-Osberg low-relaxation model or anothermaterial model.

Click Close .

Be sure to choose “Pier Section” in the list of sections on the bottom right.

Click Report .

The generated curves can be viewed in Input Data → Properties → Spring Properties :

Moment-Curvature Relation at 1,000 kip axial force

These curves have been saved into the cross-section definition as well.

LoadingTwo loads will be applied on this structure. The weight of the superstructure will be applied as auniform member load along the pier cap. Two additional joint loads will be applied at the top of the rightpier in the longitudinal and transverse directions. Since the pier cap is 33 ft wide and the superstructureweight is 1832 kips, the load magnitude for the superstructure will be 55.5 kips/ft.

In the Load Cases Explorer, create a new load case and name it “Superstructure”.

Double-click the new load case to open its loads spreadsheet and change to the Member Loadstab.

Add three new rows and apply a uniform member load to members 3, 4, and 5 with magnitude-55.5 kips/ft in the Global Z direction.

Add a new load case. Right-click the load case and choose Properties . Name the load case“Longitudinal” and change the analysis type to Pushover. Also add a case named “Transverse”with type set to Pushover.


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Open the load spreadsheet for the Longitudinal case by double-clicking it and add joint loads onjoints 3 and 4 with a magnitude of 1 kip in the X direction.

Open the load spreadsheet for the Transverse case by double-clicking it and add joint loads onjoints 3 and 4 with a magnitude of 1 kip in the Y direction.

A basic Pushover Analysis will perform a nonlinear pushover analysis of the two load cases markedas Pushover but will not include the loading in the static load case, which will affect the hystereticbeam properties. To include this loading, Pushover must be used as an analysis scenario within StagedConstruction Analysis.

In the Construction Stages Explorer, add a new construction stage named “Construct” and“Pushover” with one construction step each. Then use Input Data → Construction StageActivities to set up the construction and analysis sequence as indicated below:

Construction Activities - Groups

Construction Activities - Load Cases

Back in the Construction Stages Editor, right-click the second step, click Properties , and changeits analysis type to Plastic Pushover.

Construction Stages


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Analysis and ResultsThe Pushover Analysis will apply the longitudinal load case to the structure at an increasing factoruntil a stopping criteria entered by the user or the structure’s deformation can no longer be solvedbecause it is unstable. The factor is increased adaptively with a default maximum factor step size of1.0. As the structure yields, the factor step size is reduced so that more detail is reported in the criticalregions.

Go to Analysis → Staged Construction Analysis . Then open the Pushover Stopping Criteriatab.

Set the criteria to when joint “3” reaches “.1” feet in x translation. Joint 3 is at the top of thepier.

Pushover Stopping Criteria

Click Analyze .

Additional options can be found in Analysis → Nonlinear Plastic Pushover and Collapse .

Once the analysis finishes, a pushover curve — that is, a force versus deformation curve — can beeasily plotted.

Open Results → Graphs .

For Data Set, choose “Stage 1: Pushover”.

For the X-Axis options, choose “Load [fact]” meaning the load factor applied to the longitudinalloads.

For the Y-Axis options, choose Joints Displacements, Translation -- X, and Joint 3.


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Pushover Curve in Longitudinal Direction

The curve indicates that at a load factor of 60, meaning 60 multiplied by the two 1-kip loads = 120 kipstotal, the displacement was approximately 0.1 inches.

To produce a pushover graph in the transverse direction, use Construction Stage Activitiesto swap out the Longitudinal case for the Transverse case. Then start a Staged ConstructionAnalysis again. Change the Pushover Stopping Criteria to a maximum of .1 feet in the ydirection.

The pushover curve can be produced in the same way as above.

Recall that in the prevision section the Response Spectrum Analysis indicated a longitudinal demandof 4.4 kips and a transverse demand of 42 kips on each pier column. Because the Longitudinal load casecontained a 1 kip load on each pier column, the longitudinal demand corresponds to a load factor of4.4. The transverse load case was made with a 1 kip load on each pier as well, meaning the transversedemand corresponds to a load factor of 42. These are well within the elastic range of the pier.


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Time History Analysis

A nonlinear time history analysis will be performed on the model in this section. The analysis includes:• Full geometric nonlinearity beyond p-delta effects• Plastic hinging in hysteretic beam elements for the pier columns• A displacement-versus-time excitation at the base of each pier column

We will continue with the model from the previous section on pushover analysis which includes thepier only.

Excitation CurveTo begin a time history analysis, an excitation curve must be chosen. In this case, we will choose anexcitation curve that is packaged with LARSA 4D.

Open Input Data → Connect Databases → Connect Standard Database .

Go up a directory to the LARSA 2000 directory, then go into Samples, then Time History, andchoose the file TH04.tha.

Go to Input Data → Edit Databases and inspect the curve named “a1-sh-zd” (the second curve).Then close the Database Editor.

This curve is displacement versus time. It is possible to perform a time history analysis additionallywith acceleration versus time and velocity versus time, and for these cases initial displacement (andvelocity) conditions can be set.

Time History Curve


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To create a new curve, create a new database and add a record to the database for the new curve, in amanner similar to adding a new response spectrum curve as described earlier.

Superstructure MassThe mass of the superstructure must be added back into this model. To estimate the effective mass asthe top of the pier, we will use the weight of the structure there which we computed in the previoussection as 1,832 kips. However, the weight, which was the total vertical reaction at the base of the pier,included the weight of the pier. Since the mass of elements in the model in a dynamic analysis areincluded automatically, we must subtract the mass of the pier. The pier’s mass can be computed easilyby multiplying the section area of each element shown in the Sections spreadsheet by the length of theelement listed in the Members spreadsheet and by the material unit weight. The mass of the pier (andpier cap) comes out to 230 kip. This will be distributed evenly to the joints at the top of the pier columns.

Open Input Data → Geometry → Mass Elements .

Add a mass element for joints 3 and 4 with translational mass in each direction of 115 kips.

Superstructure Mass

AnalysisUsing the Load Cases Explorer, add a new load case called “Time History” and change itsanalysis type to Time History:

Time History Load Case

Open the loads spreadsheet for the load case and change to the Time History tab. Add recordsfor joints 1 and 2 (the bases of the columns) and set the Time History Curve to “a1-sh-zd”.


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Time History Excitation Functions

Go to Analysis → Time History Analysis and change to the Nonlinear Time History type.

Set the analysis options as follows:

Time History Options

Change to the Excitation Curves tab and set the option to Multiple Support Excitation .

Run the analysis.

After the analysis completes, result cases are available for each saved time step. (By default this isevery time step, but we have set the option to save only every 5th time step, meaning every 0.05 sec.)Graphical and numerical results are available for each case.

The displacement at the top of the pier can be graphed as well.

Go to Results → Graphs . Choose for Data Set the result group THA Case - Time History.For the Y-Axis choose Time [sec]. For the X-Axis, enter joints “1,3” (with no space around thecomma) to plot the displacements at the two joints.

Plotting the displacements at joint 1 allows us to compare the response history at the top to theexcitation curve. The graph is shown in the figure:


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Displacement Response History at Top of Column

The transverse force demands at the bottom of the pier can be determined by adjusting the Y-Axisoptions as follows:

Force Response History at Base of Column

The results spreadsheets can be used to determine the longitudinal moment that corresponds with themaximum transverse moment.

Close the graph.

Unselect All and then select just member 1.

In the Analysis Results Explorer, open the Time History Cases group, and then inside that openthe THA Case - Time History group.


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Hold the SHIFT key on the keyboard and then click the THA Case - Time History group. All ofthe time step result cases within the group will be selected. Note that they turn blue.

Selecting All Time Steps

Open Results → Spreadsheet → Members → End Forces - Local .

Turn on envelopes by selecting Min/Max for Moment -- Y.

The minimum moment Y and maximum moment Y at the start and end of member 1 are shown. Thestart of member 1 corresponds to the base of the pier, showing a longitudinal moment demand of 48,000kip-ft and a corresponding (but not necessarily maximal) transverse moment of 2.2 kip-ft.

Maximum Force Demands at Base of Column


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Index

AASHTO Guide Specifications for LRFD Seismic Bridge Design 2009, 33AASHTO LRFD Bridge Design 2007 (Earthquake), 33AASHTO LRFD live load, 29braking forces, 29casting day, 19cross-frames, 7deck weight, 19eigenvalue analysis, 33excitation curve, 49geometric nonlinearity, 49girders, 7graphs, 41influence surface analysis, 29live load analysis, 29live load braking force, 29loading - bridges, 19mass elements, 49mass participation, 33model generation, 7moment-curvature analysis, 41nonlinear material models, 41nonlinear time history analysis, 49pedestrians, 19pier cap example, 11pouring sequence, 19pushover analysis, 41reinforcement bars, 41response spectrum analysis, 33response spectrum curve, 33staged construction analysis results, 27Steel Plate Girder Bridge Design Module, 7steel reinforcement bars, 41stiffness-only construction, 19stressed eigenvalue analysis, 33structure groups, 11time history analysis, 49weight-only construction, 19wind, 19

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