Post Ten

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Description

1

Example : Linear

Analysis of a Post

Tensioned BridgeFor software product(s): LUSAS Civil & Structural or LUSASBridge

With product option(s): None

Description

A 3 span concrete

post tensioned

bridge is to be

analysed. The

bridge is idealisedas a 1 metre deep

beam and the

tendon profile

consists of the five

parabola as shown

in the half model

of the bridge.

The initial post

tensioning force of 5000 kN is to be applied from both ends. Tendons with a cross

section area of 0.0035m2 are located every 2 metres across the section allowing the

analysis to model a 2 metres effective width.

Three loadcases are to be considered; self weight, short term losses, and long term

losses.

Units of kN, m, and tonnes are used throughout the analysis.

A

B

C D

E

x

tangent points

CLy

y = 0.2 + 0.163(x-13) - 0.02717(x-13) 2

15 10

6.5 6.5 2 4 6

y = 0.2 - 0.163(x-19) + 0.0136(x-19) 2

y = -0.1322x + 0.01135x 2

ColumnAbutment (Not to scale)

Half-model of bridge

1

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Example : Linear Analysis of a Post Tensioned Bridge

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Objectives

The required output from the analysis consists of:

q The maximum and minimum long and short term stress in the concrete due to

post tensioning.

Keywords

2D, Beam, Prestress, Post tensioning, Beam Stress recovery.

Associat ed Fi les

q post_ten_model l ing.cmd carries out the modelling of the example.

q post_ten_prof i le .cmd carries out the definition of the tendon.

Modelling

Running LUSAS Modeller

For details of how to run LUSAS Modeller see the heading Running LUSAS

Modeller in the Examples Manual Introduction.

Note . This example is written assuming a new LUSAS Modeller session has been

started. If continuing from an existing Modeller session select the menu command

File>New to start a new model file. Modeller will prompt for any unsaved data and

display the New Model Startup form.

Creating a new model

Enter the file name as post_ten

Enter the title as Post-tensioning of a bridge

Select units ofkN m t C s

Select the startup template Standard from those available in the drop down list.

Select the Vertical Y axis option

Click the OK button.

Note . It is useful to save the model regularly as the example progresses. This

allows a previously saved model to be re-loaded if a mistake is made that cannot be

corrected easily by a new user.

Coordinates...

Geometry

Group >

New Group...

File

Command Files >

Open...

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When import ing data from a spreadsheetNote . When entering the coordinates

of the tendon by copying and pasting

from a spreadsheet 3 columns of X,Y

and Z coordinates must be copied into

the paste buffer.

Ensure the 3 Column option is

activated.

Select the top left-hand corner of

the grid as shown and use Ctrl + V

to paste the coordinates defining thetendon profile into the table.

Use Ctrl and A keys together to select all the visible Points.

To define the tendon profile with a spline line:

Use Ctrl and A keys together to select the spline line and points.

Make the model definition easier by placing the prestress tendon into a group.

Select the New Group entry in the Treeview with the right-hand mouse

button select the Rename option and update the group name to Tendon

Select Bridge in the Treeview and pick the Set As Only Visible option.

Click here to select the table!

Geometry

Point >

Coordinates...

Geometry

Line >

Spline >

From Points

GeometryGroup >

New Group

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Modelling

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Defining the MeshThe concrete bridge is represented by 2D beam elements.

Select Thick Beam, 2

dimensional, Linear

elements, enter the

dataset name as 2D

Beam and click OK to

add the mesh dataset to

the Treeview.

Use Ctrl + A to select all

the features.

Drag and drop the mesh

dataset 2D Beam onto

the selection.

Defining the Mat erial

Select material Concrete of grade Ungraded from the drop down list, leave the

units as kN m t C s and clickOK to add the material dataset to the Treeview.

With the whole model selected (Ctrl and A keys together) drag and drop the

material dataset Concrete Ungraded (kN m t C) from the Treeview onto the

selected features and assign to the selected Lines by clicking the OK button.

Defining the Geomet ric Properties

The beam idealisation represents a two metre width of the bridge which is one metre

deep.

Select the Thick Beam tab and enter the Area as 2, the Second moment of area

about y axis (Iyy) as 0.6667, the Second moment of area about z axis (Izz) as

0.1667, the Torsion constant (J) as 0.333, the Effective shear area in z direction

Attributes

Mesh >

Line...

Attributes

Material >

Material Library

Attributes

Geometric >

Line

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(Asz) as 2, the Effective shear area in y direction (Asy) as 2 and set the

Eccentricity (ez) to 0

Enter the dataset name as Beam Properties and click the OK button to add the

dataset to the Treeview.

With the whole model selected (Ctrl and A keys together) drag and drop the

geometric dataset Beam Properties from the Treeview onto the selected

features.

Defining the Supports

LUSAS provides the more common types of support by default. These can be seen in

the Treeview.The bridge is supported with rollers at each of the abutments.

Select the point at the left-hand abutment and the point at the column. (Hold the

Shift key to add to the initial selection)

Drag the support dataset Fixed in Y from the Treeview and drop it onto the

selected Points in the graphics area. Choose options to Assign to points for All

loadcases and clickOK

Select the right-hand point on the centre line of the bridge.

Drag the support dataset Symmetry YZ Plane from the Treeview and drop it

onto the selected Point in the graphics area. Choose options to Assign to pointsfor All loadcases and clickOK

Loading

Three loadcases are to be applied. The first represents self-weight of the structure.The second represents the prestress with short term losses only. The third represents

the prestress with short and long term losses.

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Modelling

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Defining the self-w eight Select the Body Force tab and enter a value of-9.81 for the linear acceleration in

the Y direction.

Name the dataset Gravity and click OK to create a load dataset in the

Treeview.

Use Ctrl and A keys together to select all the visible features

Drag and drop the load dataset Gravity from the Treeview onto the selection.

Ensure the Assign to lines is selected and clickOK to assign Loadcase 1 with a

factor of1

Select Loadcase 1 from the Treeview with the right-hand mouse button andpick the Rename option and change the loadcase name to Self Weight

Defining prestress w ith short t erm losses

Loadcase 2 will be generated in the Treeview.

Select the Close option on the dialog.

Select Loadcase 2 from the Treeview with the right-hand mouse button and

pick the Set Active option.

In the Treeview select Tendon with the right-hand mouse button and select

the Visible option.

Select the spline Line representing the tendon followed by the 2 beams

representing the concrete bridge. (Hold the Shift to add to the initial selection)

Attributes

Loading >

Structural

Utilities

Loadcase

1. Select thisline first

2. Select this line 3. Select this line

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On the Prestress

Definition form

select the Defaults

button.

Enter the Prestress

Force as 5000

Leave the Modulus

of the tendon as

200E6

Enter the Tendon

Area as 0.0035

Set the duct friction

as 0.3

Deselect the Long

term losses option

PickEnd 1 Only from the jacking end drop down list.

Enter an anchorage slippage of0.005

ClickOK

Modeller will assign the datasets to the selected Lines representing the concrete

beams for the current loadcase and will also add two load datasets to theTreeview.


pick the Rename option and change the loadcase name to Short Term Loss

Defining prestress w ith short and long term losses

Loadcase 3 will be generated in the Treeview.

Select the Close option on the dialog


pick the Set Active option.

Ensure the 3 Lines are still selected.

The values previously entered on the form will be retained.

Civil/Bridge

Prestress WizardBS5400

Utilities

Loadcase

Civil/Bridge

Prestress Wizard >

BS5400

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Modelling

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Select the Long term losses option. Leave all values as their defaults and click

OK to apply the prestress force to the current loadcase.


pick the Rename option and change the loadcase name to Long Term Loss

Note . If Microsoft Word is loaded on the machine a report showing the calculation

of losses can be generated at the time of input by checking the Word report option

at the bottom of the Prestress Definition dialog. This may take a short time to create.

Prior to picking this option the file Modeller.dot should be copied from the

\Lusas13\Programs\Scripts directory (or similar) to the Microsoft Word templates.

To check the loading assignments use the right-hand mouse button to select each

loadcase in turn and pick the Set Active option.

Graphing of Prestress Force in t he Tendon

When the Prestress utility generates the required loading it also generates two graph

datasets. The first contains the distance along the beam and the second the force in

the tendon at each point.

Select the Specified datasets option and clickNext

From the first drop down list select Tendon 3 Distance and from the second

select Tendon 3 - Short Term Losses and clickNext

ClickFinish to display the graph

Now add a graph of the Force after long term losses:

Select the Specified datasets option and clickNext

From the first drop down list select Tendon 3 Distance and from the second

select Tendon 3- Long Term Losses and clickNext

Select the Add to existing graph option and clickFinish to update the graph.

!

Utilities

Graph Wizard

Utilities

Graph Wizard

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Right-click on

the graph

select Edit

Graph

Properties

and update the

titles to

display the

graph shown.

Close the

graph window.

Saving the m odel

Save the model file.

Running the Analysis

With the model loaded:

A LUSAS data file name ofpost_ten will be automatically entered in the File

name field.

Ensure that the options Solve now and Load results are selected.

Click the Save button to finish.

A LUSAS Datafile will be created from the model information. The LUSAS Solver

uses this datafile to perform the analysis.

File

Save

File

LUSAS Datafile...

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Running the Analysis

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If the analysis is succ essful...The LUSAS results file will be added to Treeview.

In addition, 2 files will be created in the directory where the model file resides:

q post_ten.out this output file contains details of model data, assigned

attributes and selected statistics of the analysis.

q post_ten.mys this is the LUSAS results file which is loaded

automatically into the Treeview to allow results processing to take place.

If t he analysis fails...

If the analysis fails, the output file will provide information relating to the nature of

the error encountered. Use a text editor to view the output file and search for

ERROR. A common mistake made when using LUSAS Modeller for the first time

is to forget to assign particular attribute data (geometry, mesh, supports, loading etc.)

to the model. Any errors listed in the output file should be fixed in LUSAS Modeller

before saving the model and re-running the analysis.

Rebuilding t he Model

If errors are listed that for some reason cannot be corrected by the user, a file is

provided to re-create the model information correctly, allowing a subsequent analysis

to be run successfully.

q post_ten_model l ing.cmd carries out the modelling of the example.

Start a new model file. If an existing model is open Modeller will prompt for

unsaved data to be saved before opening the new file.

Enter the file name as post_ten

Select the Vertical Y Axis option and clickOK

To recreate the model open the command file post_ten_modelling.cmd which

is located in the\Lusas13\Examples\Modeller directory.

Save the model file.

Rerun the analysis to generate the results.

Define BeamSection

!

Utilities

Combination >

Basic

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Select Self Weight and Short Term Loss from the available loadcases and click

the button to add them to the Included panel.

Change the name to DL + Short Term

ClickOK and Yes to confirm overwriting of the combination.

Select the combination DL + Short Term in the Treeview and select the Set

Active option to update the display of stresses.

This completes the example.

Post Ten

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