Description

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Example : LinearAnalysis of a 2DFrameFor software product(s): LUSAS Civil & Structural or LUSAS Bridge.With product option(s): None.

DescriptionA simple 2D frameis to be analysed. Thegeometry of theframe is as shown.

All members aremade of steel with aYoung's modulus of210E9 Pa, aPoisson's Ratio of 0.3and a mass density of7860 kg/m3.

The structure issubjected to two load cases; the self-weight of the structure, and a sway load at thetop of the left-hand column.

The units of the analysis are N, m, and kg throughout.

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Example : Linear Analysis of a 2D Frame

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ObjectivesThe required output from the analysis consists of:

q A deformed shape plot showing displacements caused by the imposed loadingq An axial force diagram showing stresses in the members

Keywords2D, Frame, Beam, Standard Sections, Copy, Mirror, Deformed Mesh, AxialForce Diagram, Shear Force Diagram, Bending Moment Diagram.

Associated Files

q frame_2d_modelling.cmd carries out the modelling of the example.

Modelling

Running LUSAS ModellerFor details of how to run LUSAS Modeller see the heading Running LUSASModeller in the Examples Manual Introduction.

Note. This example is written assuming a new LUSAS Modeller session has beenstarted. If continuing from an existing Modeller session select the menu commandFile>New to start a new model file. Modeller will prompt for any unsaved data anddisplay the New Model Startup form.

Coordinates...

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Example : Linear Analysis of a 2D Frame

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Select the Points on the left-hand side of the model.

Connect the selected Points with a Line representing the left-hand column ofthe portal frame.

Select the pairs of Points on the right hand side of the model.

Connect the selected Points with a Line representing the right-hand verticalmember on the frame centreline.

Create the horizontal member by selecting the appropriate Points and define aLine in a similar manner.

Select the Points at the top of the left hand column and the apex of the roof.

Connect the selected Points with a Line representing the sloping member ofthe frame.

To create the vertical roof member at quarter span the 2 Lines shown are split intoequal divisions to create the points required and the new line is then defined.

Select the 2 Lines shown (Holddown the Shift key to add thesecond Line to the initial selection).

Enter the number of divisions forboth Lines as 2

Ensure that Delete features onsplitting is set so that the originalLines are deleted and click the OKbutton.

Drag a box around the 2 Points justcreated.

Create the Line representing theinternal member.

MeshingThe Line features are to be meshed using two-dimensional beam elements.

GeometryLine >

Points

GeometryLine >

Points

GeometryLine >

Points

Select these 2Lines to be split

Drag a boxaround these 2Points

GeometryLine >

By Splitting >At equaldistances

GeometryLine >

Points...

Modelling

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Select Thick Beam, 2 dimensional, Linear elements.

Set the number of divisions per line to be 1

Enter the dataset name as Thick Beam then click OK

Select the whole model. (Ctrl and A keys together)

Drag and drop the mesh dataset Thick Beam from the Treeview onto theselected model Lines.

Material Properties Select material Mild Steel

from the drop-down list, leavethe units as N m kg C s andclick OK to add the materialdataset to the Treeview.

With the whole model selected(Ctrl and A keys together) dragand drop the material datasetMild Steel Ungraded (N m kgC) from the Treeview ontothe selected features and assignto the selected lines by clickingthe OK button.

Geometric PropertiesThe standard sections dialog will appear.

AttributesMesh >

Line...

AttributesMaterial >

Material Library

AttributesGeometric >

Section Library

Example : Linear Analysis of a 2D Frame

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Select thelibrary of UKSections

Select sectiontype UniversalBeams (BS4)

Select sectionname127x76x13kgUB

Select 2DFrame usage.

Click theApply buttonto add theUniversal Beam dataset to the Treeview.

Change the section type in the Type drop-down list to Equal Angles (BS4848)and select the 70x70x6 EA section name.

Select 2D Frame usage.

Click the OK button to add the Equal Angle dataset to the Treeview.

Assigning Geometric Properties Drag a box around the Lines

representing the roof members.

Drag and drop the geometrydataset 70x70x6 EA (m) from the

Treeview onto the selectedLines.

Select the Line representing theleft-hand vertical member.

Drag and drop the geometrydataset 127x76x13kg UB (m)from the Treeview onto theselected Line.

Select this Line

Drag a box around these members

Modelling

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SupportsLUSAS provides the more common types of support by default. These can be seen inthe Treeview. The structure will be supported at the end of the column which isin contact with the ground with a fully fixed support condition.

Assigning the Supports Select the Point at the bottom of the left-hand vertical member.

Drag and drop the support dataset Fully Fixed from the Treeview onto theselected feature.

Ensure the Assign to points and All loadcases options are selected and clickOK.

Mirroring the modelOne half of the 2D frame has nowbeen generated. This half can now bemirrored to create the complete frame.The first step in the process is todefine the mirror plane.

Select the 2 points on the right-hand side of the model that definethe axis about which the framewill be mirrored.

The points are stored in memory.

Select the whole model (Ctrl andA keys together).

Select Mirror - points 3 4from the drop down list and

click the Use button on the dialog. This will use the points stored in memory tocreate the mirror plane. Click the OK button to create the full model.

The points are cleared from selection memory.

Note. Features which are copied retain their attributes. This means that there is noneed to define the mesh, material or geometric properties for the newly created Linesas they will already have the attributes from the original half of the model assigned.

Select these 2Points to definemirror plane

EditSelection Memory >

Set

GeometryLine

Copy

EditSelection Memory >

Clear

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Example : Linear Analysis of a 2D Frame

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Note. In mirroring the features the Line directions are reversed. The orientation ofLines is important as it controls the local beam axes directions which will define thesign convention used to present the results.

In the Layers Treeview double-click on Geometry to display the geometrylayer properties. Select the Show line directions option and click the OK button.

The Lines orientations are shown.

Select the 4 Lines tobe reversed. (Holddown the Shift keyto add lines to theinitial selection).

The selected Linedirections will bereversed.

Once the Line directionsare corrected, de-selectthe Show line directions option in the geometry layer properties and click the OKbutton.

LoadingTwo loadcases will be considered; self weight, and a concentrated sway load actingat the top of the left-hand vertical member.

Loadcase 1 - Self WeightLoadcase 1 will represent the self-weight of the structure. This is modelled using aconstant body force which is an acceleration loading simulating the force of gravityacting upon the structure.

Select the Body Force tab. Enter a linear acceleration in the Y direction of -9.81.

Enter the dataset name as Self Weight and click OK to add the dataset to the Treeview.

Select the whole model (Ctrl and A keys together) and drag and drop the loadingdataset Self Weight from the Treeview onto the selected features.

Ensure that the Assign to lines option is selected and the loading is applied toLoadcase 1 with a load factor of 1. Click the OK button and the loading on theframe will be displayed.

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These Linedirections needreversing

GeometryLine >

Reverse

AttributesLoading >

Structural...

Running the Analysis

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Loadcase 2 - Sway LoadLoadcase 2 is a sway load acting at the top of the left-hand vertical member.

Ensure the Concentrated tab is selected and enter a concentrated load in the Xdirection of 500.

Enter the dataset name as Sway Load and click OK.

Select the Point at the topof the column.

Drag and drop theloading dataset SwayLoad from the Treeview onto theselected Point.

Change the loadcasename to Loadcase 2 andensure that the Assign topoints option is selected.

Click the OK button to assign the loading with a factor of 1.

Saving the model.Save the model file.

Running the AnalysisWith the model loaded:

A LUSAS data file name of frame_2D will be automatically entered in the Filename field. Click the Save button to finish.

A LUSAS Datafile will be created from the model information. The LUSAS Solveruses this datafile to perform the analysis.

AttributesLoading >

Structural...

Select this Point to assignthe concentrated load

FileSave

FileLUSAS Datafile...

Example : Linear Analysis of a 2D Frame

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

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

q frame_2d.out this output file contains details of model data, assignedattributes and selected statistics of the analysis.

q frame_2d.mys this is the LUSAS results file which is loadedautomatically into the Treeview to allow results processing to take place.

If the analysis fails...If the analysis fails, the output file will provide information relating to the nature ofthe error encountered. Use a text editor to view the output file and search forERROR. A common mistake made when using LUSAS Modeller for the first timeis 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 Modellerbefore saving the model and re-running the analysis.

Rebuilding a ModelIf errors are listed that for some reason cannot be corrected by the user, a file isprovided to re-create the model information correctly, allowing a subsequent analysisto be run successfully.

q frame_2d_modelling.cmd carries out the modelling of the example.

Start a new model file. If an existing model is open Modeller will prompt forunsaved data to be saved before opening the new file.

Enter the file name as frame_2D

Select the Vertical Y axis option and click OK

To recreate the model open the command file frame_2D_modelling.cmd whichis located in the \Lusas13\Examples\Modeller directory.

Save the model file.

Rerun the analysis to generate the results.

Basic

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Viewing the Results

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Select Displacement results from the Entity drop down list and select theresultant displacement RSLT from the component drop down list.

From the Values Display tab set 100% of Maxima values to be displayed.

Set the number ofsignificant figures to3

Click the OK buttonto display thedeformed mesh plotshowing thedisplacement at eachnode.

Using Multiple WindowsDifferent results may be viewed in different windows.

A new window using default layer names and a default loadcase will be created.

In the Treeview click on the Mesh, Geometry and Attributes layers forWindow 2 and delete them.

With no features selected click the right-hand mouse button in a blank part of theGraphics area and select the Deformed mesh option to add the Deformed meshlayer to the Treeview. Accept the default properties by selecting Close.

Changing the LoadcaseBy default, a new window is created with Loadcase 1 set active. To view the resultsfor the Combination it needs to be set active again for this window.

In the Treeview right-click on Combination 3 and select the Set Activeoption.

Axial Force Diagram With no features selected click the right-hand mouse button in a blank part of the

graphics area of Window 2 and select Diagrams to add the diagrams layer to the Treeview.

The diagram properties will be displayed.

WindowNew Window

Example : Linear Analysis of a 2D Frame

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Select Stress results of axial force Fx in the members

Select the Diagram Display tab and select the Label values button.

Select the Label only if selected option.

Change the number of significant figures to 4

Click the OK button to finish.

The order of the layers in the Treeview governs the order that the layers aredisplayed.

To see the deformed mesh on top of the diagram plot the deformed mesh layerneeds to be moved down the Treeview to a position after the diagram layer.

In the Treeview for Window 2 select the Deformed Mesh layer, click theright-hand mousebutton and selectthe Move Downoption.

Now add labels tothe columns(verticalmembers). Selectthe left handcolumn hold theShift key andselect the right hand column.

An axial force diagram for each member will be displayed with values of Fxdisplayed on the selected columns.

Viewing the Results

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Shear Force Diagram In the

Treeview double-click on theDiagrams layer.The diagramproperties will bedisplayed.

Select Stressresults of shearforce Fy in themembers.

Click the OK button to display a shear force diagram of stresses in each memberwith labels on the selected vertical members.

Bending Moment Diagram In the Treeview double-click on the Diagrams layer. The diagram properties

will be displayed.

Select Stressresults ofbendingmoments in themembers Mz.

Click the OKbutton to displaya bendingmomentdiagram for eachmember withlabels on the selected vertical members.

This completes the example.

Example : Linear Analysis of a 2D Frame

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