beam tutorial 09mar2010 v1

8/13/2019 Beam Tutorial 09Mar2010 v1

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Axial, Bending, Torsion, Combined and Buckling Analyses of a Beam

Pre/Postprocessor:FEMAP 10.0.2, Processor:ABAQUS 6.9-2

Professor James A. Sherwood

Mechanical Engineering Department, University of Massachusetts Lowell11-March-2010

Introduction

In this tutorial, a finite element model of a beam will be constructed and analyzed. The

analysis will look at stresses and displacements associated with multiple loadingconditions for a steel beam. The beam will be clamped at one end and be loaded on the

other end with prescribed displacements for the axial, torsion and bending loads. A unit

force will be applied to find the critical buckling load and the associated mode shape.

The cross section of the beam is shown in Fig. 1. The cross section dimensions are

summarized in Table 1. The length of the beam is 90 cm.

t2

b

t1

t1

a

Table 1. Cross section dimensions

a 6 cm

b 7 cm

t1 1 mm

t2 2 mm

Figure 1 - Beam cross section

INTRODUCTION TO FEMAPV10.0.2

FEMAP v10.0.2 is a powerful Finite Element Analysis (FEA) software package thatallows the user to build the geometry, create nodes and elements, specify materials and

apply loading conditions. The processing of the model, however, will be done by

ABAQUS v6.9-2. The results from the analysis will be viewed using FEMAP v10.0.2.

Below are few helpful keys for FEMAP operation:

1. F8will allow changing the orientation of the model and viewing different planes.

2. Ctrl-Awill autoscale the model on the screen.

3. Ctrl-Zwill undo the last action.


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In this tutorial, it is recommended to save often. Also, it is a good idea to change your

filename as you progress through the tutorial in case a major mistake is made so that it is

easy to go back a few steps by opening the saved file.

Note: All menu selections to be chosen will be in boldin this tutorial.

STARTING FEMAP

Open FEMAP 10.0.2: Start > Programs > FEMAP v10.0.2.

If the tip of the day pops us, just click OK. Then again, if you read it, you may learn

some useful information.

CREATING THE MODEL

A series of models for the various load conditions will be built and saved in individualfiles.

Defining the Material

Model Material

TheDefine Isotropic Materialpopup window will appear.

Click Load AISI 4340 Steel

The window should now look like Figure 2 (except for E and nu). Note that the

properties of material are all defined including E and . The user can change any entries

as needed. For this model, change E to 200e9 and nu to 0.30. The units for E are Pa.

Note: The units selected for the material define the units to be used for the forces,moments and lengths in the model. Because Pa=N/m

2, force, moment, stress and

length units for the analysis will be Newtons, Newton-meters, Pascals and meters,

respectively.


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Figure 2 - Defining Model Material

ClickOK, another blank window will show up to declare another material, just click

Cancel.

Defining the Model PropertiesNext the section properties of the model will be defined so ABAQUS can associate the

correct characteristics of the material with the appropriate component in the model. This

model will be built by using 1-D rod elements which are then extruded along the x axis to

make 2-D plate elements that describe the beam configuration.

Model Property

Enter Rod in the Title: box from the Material drop-down menu select

1..AISI 4340 Steel.

ClickElem/Property Type underLine ElementsselectRod OK.

Enter a value of 1for Area,A = 1 (Figure 3).


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Notes: 1. For this finite element model, the rod elements are being used as stepping

stones to the creation of the shell elements that will describe the beam

geometry. Thus, the value of the area for the rod is not important. Therod elements will be deleted after they have served their useful purpose.

2. Trusses are modeled as rods in FEMAP.

Figure 3 - Line Element Properties

Click OK

A new Define Property window pops up. Enter the following information:

Title: Plate1 scroll and select Material 1..AISI 4340 Steel. However, the

1..AISI 4340 Steel should already be selected.

Click Elem/Property Type underPlane Elementsselect Plate OK.

TheDefine Propertywindow should now look like Figure 4.


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Figure 4 - Plate1 Element Properties

Because t1=1 mm, Enter 0.001for Thickness, Tavg or T1

Notes: 1. With a nonzero entry in the T1 box and zero values in the T2, T3 and T4

boxes, the program assumes a plate of uniform thickness.

2. The plate thickness must be in meters so as to be consistent with the elasticmodulus of 200x109N/m

2. The units for the material constants define what

units are used for the dimensions on the structure. Because E is defined as Pa

(N/m2), the units of force for the model are in terms of Newtons and the units

for length are meters.

Click OK

A new Define Property window pops up, enter the following information:

Title: Plate2 scroll and select Material 1..AISI 4340 Steel. However, the

1..AISI 4340 Steel should already be selected.

Click Elem/Property Type underPlane Elementsselect Plate OK(Figure 5).


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Figure 5 - Plate2 Element Properties

Because t2=2 mm, Enter 0.002for Tavg, then

OK Cancel

Creating the Beam GeometryCreate a sketch of thebeamscross-section in the y-z plane.

To set the view to be the y-z plane with the x axis coming out of the screen, Hit F8, then

click YZ Right OK

Next enter the points that define the cross section. The geometric center of the beam will

be selected to be at the origin.

Geometry Point

X= 0, Y= 0.0295, Z= 0.035 OK

X= 0, Y= 0.0295, Z= 0 OK

X= 0, Y= 0.0295, Z= -0.035 OK

X= 0, Y= -0.0295, Z= 0.035 OK

X= 0, Y= -0.0295, Z= 0 OK

X= 0, Y= -0.0295, Z= -0.035 OKCancel


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Ctrl-A to autoscale

The screen should look similar to Figure 6.

Figure 6 - Points to be used to draw midplanes of web and flanges

The next step will draw the centerline geometry of the cross section using the seven

points that were just entered.

Geometry Curve-Line Points

Using the mouse cursor, click on the point in the upper left corner, then click on the point

in the upper right corner, then OK. A blue horizontal line should appear.

Click on the point in the lower left corner, then click on the point in the lower right

corner, then OK. Another horizontal line should appear.

Click on the top center point, then click on the bottom center point, then OK Cancel.

A vertical line should appear.


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Your model window should now look like Figure 7.

Figure 7- Points and lines defining beam cross section

Creating the Finite Element Mesh

When creating a finite element mesh with shell or plate elements, it is best to make

elements as square as possible, i.e. keep the aspect ratio of length to width to be as close

to 1 as is possible. In this model, the elements will be made with dimensions as close as

possible to 1 cm by 1 cm. However, the elements in the web need to connect to the

elements in the flanges at element edges. Therefore, the flanges will be meshed into six

elements across the width to satisfy this joining requirement. Thus, the width, w, of the

flange elements will be:

w= 7 cm/6 = 1.16667 cm = 0.0116667 m (1)


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The height of the web, h, is

h = a- (2 x t1/2) = 6 cm - 2 x (1 mm/2) = 59 mm = 0.059 m (2)

This height yields an element height of

5.9 cm/6 = 0.98333 cm = 0.0098333 m (3)

The 90-cm length of the beam will be generated using 90 1-cm long elements. Therefore,

the respective aspect ratios for the web and the flanges will be 0.98333 and 0.85714,

which are close to unity.

Mesh Mesh control Size along curve (or Shift+F10)

Select the two horizontal linesby clicking on them and clickOK

EnterNumber of Elements= 6. This entry will divide the flanges of the beam into six

evenly spaced lengths to create the FE mesh.

Ensure that Equal and Parametric are selected in the Node Spacing area of the

Mesh Size Along Curves as shown in Figure 8.

ClickOKand seven evenly spaced nodes should appear along each of the two horizontal

lines.

Figure 8 - Mesh size along curves


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The Entity selection window will reappear. Use the cursor to select the vertical line

OK EnterNumber of elements= 6. This entry will divide the web of the beam into six

evenly spaced lengths to create the FE mesh.

Ensure that Equal and Parametric are selected in the Node Spacing area of the

Mesh Size Along Curves as shown in Figure 8.

ClickOK Cancel

The FEMAP window should look similar to Figure 9.

Figure 9 - Lines with mesh control information

Note: Notice that as you build the model, information is summarized in the Model Info

pane on the left side of the FEMAP window. As you gain experience in using

FEMAP, you can edit, add and delete model parameters directly through this treeas opposed to using the pull-down menus on the toolbar.

You cannot delete an entity if it is needed to define part of another entity. Forexample, a material entity cannot be deleted if it is being used to define an

element property.


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Creating the Rod Elements

Rod finite elements will be created using the three lines shown in Figure 9. As

previously stated, these rod elements will be used as seed elements for creating the

plate elements that will define the beam model.

Mesh Geometry CurveSelect All OK

In the popup window, use the Property pull-down menu and select the 1..Rodproperty,

then click OK. In the Messages pane of FEMAP, you should see that 3 curves were

selected and 18 elements were created.

Extrude along the X Axis

Now the cross section made of rod elements will be extruded along the x axis to create

the finite element mesh of the beam with plates. This extrusion will be a two-step

process. First the flanges will be extruded using thePlate1property, then the web will be

extruded using thePlate2property.

Mesh Extrude Element

Using the mouse, select the 12 rod elements that make up the two flanges.


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The FEMAP screen should look similar to Figure 10.

Figure 10 - Flange elements selected

Click OK


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In the Generate Options popup window, choose 2..Plate1 as shown in Figure 11, then

enter 90 in the Elements along Length, and check the box next to Delete Original

Elements. Click OK.

Note: The delete original elements option will delete the rod elements as they haveserved their purpose of seeding the generation of the plates. If the user wished

to retain these rod elements, then this box should be left unchecked.

Figure 11 - Generate Options popup window

In the Vector Locate popup window, click Methods^ Global Axis

Enter 0, 0, 0 for the XYZ coordinates of the BaseEnsure that Positiveand X Axisare selected

Enter 0.9for Length as shown in Figure 12. Click OK.

Figure 12 - Extrude Along popup window


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In the Confirm Delete popup window, accept the default settings as shown in Figure 13

and Click OK.

Figure 13 - Confirm Delete popup window

The plate elements describing the two flanges will be generated. Use the Autoscale

(Ctrl+A) Zoom and Rotate features to see these flanges. An example view is

shown in Figure 14.

Figure 14 - Example view showing the two flanges of the beam


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To prepare for extruding the web, F8 YZ Right OK. The user may need to zoom

in to fit the cross section of the I-beam to the window.

Mesh Extrude Element

Using the mouse, select the six rod elements that make up the web. Click OK.

In the Generate Optionspopup window, choose 3..Plate2, then enter 90 in the

Elements along Length, and check the box next to Delete Original Elements. Click

OK.

In the Vector Global Axis popup window,

Enter 0, 0, 0 for the XYZ coordinates of the Base

Ensure that Positiveand X Axisare selected

Enter 0.9for Length as shown in Figure 12. Click OK.

In the Confirm Delete popup window, Click OK.

F8 Isometric OK

Ctrl+A


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Your model should look like Figure 15.

Figure 15 - Isometric view of the beam

If your model appears as a solid mesh rather than a transparent mesh, then you can toggle

to a transparent mesh by clicking on the View Style button ( ) and then selecting

another view from the dropdown menu.

Figure 16 is an example of a wireframe view.


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Figure 16 - Isometric wireframe view of the beam

Model Cleanup

In the process of building the finite element model, duplicate nodes at essentially the

same spatial location may be created. These duplicate nodes can be a problem as they

will be interpreted as a crack in the mesh. Therefore, the user should always check the

model for coincident nodes.

Tools Check Coincident Nodes Select All OK

Figure 17 will pop up.


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Figure 17 - Check/Merge Coincident Nodes

SelectMerge Coincident Entitiesand ensure all the other options are selected as shown in

Figure 17. Click OK

A total of 182 coincident nodes should be found in this model. This information is

reported in the FEMAP Messages window pane. The coincident nodes in this model will

be where the flanges meet the web. Because the flanges and the web were created in two

separate extrusions, FEMAP created duplicate nodes at these intersections. Not all

models have coincident nodes, but it is always good to check the model. If coincident

nodes are found, they will be automatically corrected and merged. Now is a good time to

save your model.

File Save As

Note: FEMAP model files use a .MOD for the file extension.


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Loading and Constraints

Boundary conditions will be defined which will simulate a fixed (also known as

clamped)beam at one end with a tip load. Click onF8 XY Top OK. Zoom in

on the left end of the beam by first doing Cntl+A(to Autoscale) and then using the zoom

tool (dashed-line box) . The zoomed in view of the beam should look similar to

Figure 18.

Figure 18 - Zoomed view of the left end of the beam


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To constrain one end of the beam:

Model Constraints SetTitle =Fixed EndOK

Model Constraint Nodal Pick^ Box

Use the mouse to drag a box around the nodes (the first line of points) at the end of the

beam (see Figure 19). The drag is accomplished by locating the mouse at one corner of

the box, then holding the left button as the mouse is moved to the diagonal corner of the

box OK.

CheckFixed OK Cancel

Notice all six of the DOF at that end of the beam are constrained as shown in Figure 20.

Figure 19 - Fixed End with selected nodes Figure 20 - Fixed End with BCs shown

Save your model with a file name that will reference the stage you are in the

building of the model, e.g. Steel_Beam_Fixed.

Note: We will refer back to this model to build the other loading conditions instead of

creating an entirely new model or deleting constraints.


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Applying an Axial Load to the Beam:

A 0.01% axial strain will be applied to the end of the beam as a prescribed displacement.

DoCtrl+A to fit the model to the window.

Zoom in on the right end of the beam.

Model Load SetTitle=Axial LoadOK

Model Load NodalPick^ Box

Use the mouse to drag a box around the nodes at the end of the beam (Figure 21) OK.

Figure 21- Selecting the nodes for the axial displacement


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Duplicate the settings as shown in Figure 22 for the Create Loads on Nodes pop up

window. Highlight Displacement and set TX=0.00009and uncheck TY and TZ.

Figure 22 - Axial Load Settings

OK Cancel

The prescribed axial displacement should appear as shown in Figure 23.


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Figure 23 - Prescribed axial boundary condition

File Save As example-axial-v2.MOD

Applying a Torsional Load to the Beam

An equal and opposite displacement will be imposed on opposite sides of the beam to

simulate a torque on the beam. First, delete the axial load.

Delete Model Load-SetSelect All OK OK

Or in the Model Info tree, click on the + sign to expand the Loads branch, then right-click

on the Fixed End load, and click Delete.

The axial displacements should disappear. Now a load set will be defined for the twisting

moment.


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Model Load SetTitle= Torsion LoadOK

Model Load Nodal Pick Box

Drag the box just around the top nodes at the end of the beam (Figure 24).

ClickOK

Figure 24 - Picking the top nodes for the torsion load


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The load is to be a 5otwist at the end of the beam. The y-distance from the center of the

beam to the line of nodes just picked is 0.0295 m. To find the required displacement in

the z-direction to achieve the 5otwist use

0295.0)5tan(

zo

(3)

where zis the prescribed displacement and is equal 0.00258 m.

Displacement Components for the components enterTZ = 0.00258(as shown in

Figure 25)

Click OKCancel

Figure 25 - Prescribing the nodal displacements for the torsion load

Repeat the process for the bottom row of nodes, but prescribe the displacement to be

negative (i.e., -0.00258).


Drag the box just around the bottom nodes at the end of the beam.

Click OK

Displacement Components for the components enterTZ = -0.00258 OK

Click Cancelwhen done.

File Save As example-torsion-v2.MOD


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Beam in Bending

A prescribed displacement in the negative y-direction will be imposed on the tip of the

beam. First, the torsion load must be deleted.

Delete Model Load-SetSelect All OK OK

The twist displacements should disappear. Now a load set will be defined for the tip

load.

Model Load SetTitle=Bending LoadOK


Drag the box around the nodes at the end of the beam (as was done in Figure 21) OK.

Select Displacement from the left hand side Under Directions select Components.

SetTY = -0.006 OK Cancel

The end of the beam should show prescribed displacements as shown in Figure 26.

Figure 26 - Prescribed bending boundary condition

File Save As example-bending-v2.MOD

You now have created three models for the steel beam: Axial, Torsion and Bending.


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ANALYZING THE MODELS

Exporting Model

File Export Analysis ModelCreate/Edit Set New

In the Analysis Set popup window, select 16..ABAQUS from the pull-down menu as

shown in Figure 27. You can name the Analysis Set, e.g.Beam.

Figure 27 -Analysis Export Type Selection

ClickOK

The Analysis Set Manager window should look similar to Figure 28.

Figure 28 -Analysis Set Manager window

ClickDone OK


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The Save As popup window will appear. Select a name for your analysis file and a

location that will be easy for you to find in a DOS command prompt (Default Temp

folder is suggested).

Name: choose a name for input f il e(i.e., the model name e.g., beam_bend.inp)

Write.

FEMAP has now created the analysis file with the extension .inp. This file format is

the input file for ABAQUS.

Open the ABAQUS command window

Start Programs ABAQUS 6.9-2 ABAQUS Command

After the ABAQUS command window appears, you must change the current directory to

the folder where your analysis model was created. If you saved your file in a drive other

than the C:\ drive, then enter the desired drive letter followed by a colon. For example, if

the beam_bend.inp model was saved on drive G:\ in folder FEA, then:

G:

where denotes you should hit the Enter key

Now change to the desired folder, e.g. the FEA folder on drive G:

G:>cd FEA

G:\FEA>

The cd command changes directory, type in dir, thenpress the Enter key to see the

contents of that drive/folder.

Once you have located your folder, type abaqus inter j=nameof file you created (the

.inp file).


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Figure 29 shows a typical ABAQUS Command DOS window.

Figure 29 -Example of an ABAQUS Command DOS window

ABAQUS will solve the model and create a name.fil output file with the results. The

analysis may take some time to complete. If theAbaqus JOB file name COMPLETED

message did not appear, an error message will appear. You must go back to FEMAP and

attempt to correct the error(s) in the model. Looking at the *beam_bend.dat and/or the

beam_bens.msg file using Notepad may give you some insight as to the source of the

errors. Finally, after receiving theCOMPLETEDmessage, go back to the FEMAP model

to view the results, i.e. to postprocess the results.

Viewing Results

File Import Analysis ResultsselectABAQUS OK

Locateyourname.fil (should be in the same folder where you wrote the *.inp file)and

selectOpen, and then select Yes when asked ifOK to begin reading analysis model, e.g.

FEMAP has just uploaded the

ABAQUS analysis information for postprocessing.


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Press F6 select the view options shown in Figure 30a and be sure to uncheck theDraw

Entitybox, then click OK.

Press F6again and repeat for Figure 30b, then click OK.

(a) (b)

Figure 30 -Selecting View Options

PressF5 selectDeform underDeformed StyleandContour underContour Style

Click Deformed and Contour DataVerify that7020..Plate Top X Normal Stress is

selected for Contour and that 1..Total Translation is selected for Deformation as shown in

Figure 31.


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Figure 31 -Postprocessing view selection

ClickOK OK

Press Ctrl+Ato resize the beam to fit the window if needed. With mouse cursor in the

model window pane, you may need to scroll the mouse wheel to resize the beam so you

can see it completely.

The stress contour plot should look similar to the view shown in Figure 32. Notice that

the highest tensile and compressive stresses are on the top and bottom webs respectively

near the fixed end.


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Figure 32 -Contour plot showing variation in axial stress distribution

The contour legend on the right hand side of the model window is automatically

determined by FEMAP from the stress values in the *.fil file. The fixed BC at the wall

results in stress singularities in that region that may or may not be realistic.

To better see the stress variation in the beam, it is suggested that the user define the

contour legend upper and lower limits. To do this user-defined option, click View

Options (or F6). In the View Options popup window, under Category select

PostProcessing, then select Contour/Criteria Levelsin Options pane. In the level

Mode pane, select 3..User Defined. In the Minimum and Maximum boxes enter -100e6

and +100e6, respectively, or play with other upper and lower limits of your choosing.


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Use the zoom feature in FEMAP to look closely at the fixed end of the beam. As shown

in Figure 33, you can see the max tensile and compressive stresses are at the top and

bottom of the beam, respectively, and the magnitude of the stress decreases as you move

away from the wall.

The stress contour legend on the right side of the plot window has units of Pa (N/m2).

Recall that the elastic modulus was prescribed to be 200x109Pa and all dimensions were

input in meters. The units used for the elastic modulus define what units are used for

inputting dimensions and for the interpretation of the stresses and displacements.

The default option in FEMAP is to exaggerate the displacements for visual interpretation.

Figure 33 - Zoomed in contour plot showing variation in axial stress distribution(side view)


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Press F8 Isometric OK

Figure 34 shows an isometric view of the end of the beam fixed to the wall. Notice

how the stress decreases as you proceed in the positive x direction and how the stress

progresses from the maximum tensile stress on the top to the maximum compressive

stress on the bottom.

Figure 34 - Zoomed in contour plot showing variation in axial stress distribution

(isometric view)


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Press Ctrl+Ato resize the beam to fit the window as shown in Figure 35.

Figure 35 - Analyzed Model of beam bending (isometric view)

The dynamic rotate ( ) and zoom (scrolling the mouse wheel) tools used in building

the model may also be used to look at the completed model.

Follow the same steps for writing the INP files and subsequent ABAQUS analysis and

FEMAP postprocessing of the axial-pull and twist models.

example-torsion-v2.MOD

example-axial-v2.MOD


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Beam Buckling

For the buckling analysis, a unit axial load will need to be applied to the tip of the beam.

For the best analysis, this unit load should be distributed amongst all of the nodes at the

tip of the beam. However, the amount of force to apply to each node is a function of the

width of the element and the number of elements connected to a node. A relatively easy

way to find the respective nodal forces is to examine the ASCII output file created by the

axial analysis of the beam.

Assuming that the INP filename used for the axial pull beam was named

beam_axial.inp, open the file beam_axial.inpin Notepad. In Notepad,

Edit Find enterNODE FILEFind Next

Peruse the file and look for two lines saying:

*NODE PRINT, FREQUENCY=1

RF,

as shown in Figure 36.


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Figure 36- Reading the input file beam_axial.inp in Notepad

If these two lines are not in the INP file, then enter them manually and save the INP file.

Analyze the finite element model of the axial pull in ABAQUS.

Open the file beam_axial.dat in Notepad. In Notepad,

Edit FindenterRF1Find Next


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The Reaction Force section of the beam_axial.dat file is shown in Figure 37. Nodes 1

through 21 denote the reaction forces (RF1, RF2 and RF3) in the x, y and z directions at

the wall and the reaction moments (RM1, RM2 and RM3) about the x, y and z axes at the

wall. Notice that as a consequence of constraining these nodes in all six DOFs each node

has nonzero values for the six reactions. These reaction forces and moments are a

consequence of the axial load applied at the tip of the beam and the Poisson effect.

Figure 37 - Reaction Forces listed in the axial.dat file


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In a pure uniaxial pull condition, the reaction forces at the wall would only exhibit

nonzero values for the x components. Because the beam is constrained from any

deformation at the wall, the lateral displacements that could occur in a pure uniaxial

pull as a consequence of the Poisson effect cannot occur. Thus, the geometric fit

condition that all nodes at the wall are fixed in space requires the introduction of forces

and moments to satisfy the zero-translation and zero-slope boundary conditions at the

wall.

Nodes 1268 through 1270, 1272 through 1277, 1279 through 1281 and 1905 through

1911 are the nodes where the prescribed axial displacement was applied (Note: all x-

forces are positive at these nodes). These nodes only have nonzero values for the RF1

component because the other five DOFs (y, z, x, yand z[U2, U3, UR1, UR2 and

UR3, respectively, in the DAT file]) were not constrained. Take the sum of these RF1

forces and divide each nodal force by this sum.

To automate the process, copy these lines (as shown in Figure 38) and paste them into a

new Notepad file. Save the new Notepad file as forces.txt.

Figure 38 - Highlighting theReaction Forces in the axial.datfile


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Now open Excel 2003 or 2007 to a blank file and import the forces.txt file into Excel.

In Excel 2003

Data Import External Data Import Data

Browse to the directory where you saved the RF1.txt file, as shown in Figure 39 and

click Open

Figure 39 - Importing theReaction Forces file RF1.tx into Excel

Figure 40 - Highlighting theReaction Forces in the axial.dat file

In the Text Import Wizard popup window (Fig. 40), select the Fixed Widthoption and

click Finish OK

The data are now in Excel 2003.


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In Excel 2007

Click on the DatatabFrom Text (Figure 41)

Figure 41- Importing text file data into Excel 2007

In theImport Text Filepopup, navigate to the directory where you saved your

forces.dat file and click Import.

In the Text Import Wizard popup window (Fig. 40), select the Fixed Width option and

click Finish OK

The data are now in Excel 2007.

Use the sum function in Excel to add all the forces. In this case, the sum is 5165.3 .

Dividing each nodal RF1 value by this total gives the respective force to apply to eachnode so as to have a net unit force on the end of the beam. Table 2 summarizes the nodal

forces extracted from the uniaxial pull model and the corresponding set of nodal forces to

give a unit force.


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Table 2. Calculation of forces to apply a unit force for buckling

Node RF1 Unit Load

1268 116.8 0.02261243

1269 233.6 0.04522487

1270 233.6 0.04522487

1272 233.6 0.04522487

1273 233.6 0.04522487

1274 116.8 0.02261243

1275 116.8 0.02261243

1276 233.6 0.04522487

1277 233.6 0.04522487

1279 233.6 0.04522487

1280 233.6 0.04522487

1281 116.8 0.02261243

1905 430.4 0.083325271906 393.7 0.07622016

1907 393.7 0.07622016

1908 393.7 0.07622016

1909 393.7 0.07622016

1910 393.7 0.07622016

1911 430.4 0.08332527

Total 5165.3 1.00000000

An easy way to create the input file for doing the buckling analysis is to edit the beam_axial.inp

file. Open the beam_axial.inp file in Notepad and save as beam_buckle.inp.

Edit Find enter*STEP,Find Next

Change the following four lines of the file as shown:

*STEP, INC=100 *STEP, INC=100

Axial Load Buckle Load

*STATIC *BUCKLE

--Blank line-- 10, 1.E+9


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Edit Find enter*BOUNDARYFind Next

Change the prescribed displacement information to prescribed loads

*BOUNDARY, TYPE=DISPLACEMENT, OP=NEW1268, 1, , 0.000091269, 1, , 0.00009

1270, 1, , 0.000091272, 1, , 0.000091273, 1, , 0.000091274, 1, , 0.000091275, 1, , 0.000091276, 1, , 0.000091277, 1, , 0.000091279, 1, , 0.000091280, 1, , 0.000091281, 1, , 0.000091905, 1, , 0.000091906, 1, , 0.00009

1907, 1, , 0.000091908, 1, , 0.000091909, 1, , 0.000091910, 1, , 0.000091911, 1, , 0.00009

Becomes

*CLOAD, OP=NEW1268, 1, -0.022612431269, 1, -0.04522487

1270, 1, -0.045224871272, 1, -0.045224871273, 1, -0.045224871274, 1, -0.022612431275, 1, -0.022612431276, 1, -0.045224871277, 1, -0.045224871279, 1, -0.045224871280, 1, -0.045224871281, 1, -0.022612431905, 1, -0.083325271906, 1, -0.07622016

1907, 1, -0.076220161908, 1, -0.076220161909, 1, -0.076220161910, 1, -0.076220161911, 1, -0.08332527

Save the edited file as beam_buckle.inp. The forces are negative to denote a compressive force

at the tip of the beam.


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Analyze the model in ABAQUS. For this model, there may be an error as indicated in the DOSwindow shown in Figure 42. If you open the beam_buckle.dat file in Notepad, you will see near

the end of this file that there is an error and it is written in the beam_buckle.msg file. Open thebeam_buckle.msg file in Notepad. You will see that five eigenvalues were found (converged) butthe rest could not be found as we were asking ABAQUS to find 10 eigenvaluee, i.e. bucklingloads. We are really only concerned with the lowest value, so this error is of no concern for this

analysis. Finding the higher buckling loads was only of academic interest.

Figure 42 -Example of a ABAQUS DOS window with an error in the model

In FEMAP,

File New

File Import Analysis Model

In theImport Frompopup window, select ABAQUSand click OK. In the Open popup

window, navigate to the directory where your beam_buckle.inpfile is located and openthe beam_buckle.inpfile.

This command imports your beam buckling model into FEMAP. Save this FEMAP file as

beam_buckle.mod.

File Import Analysis ResultsselectABAQUS OK selectbeam_buckle.filOpen Yes

If you look in the Messages pane, you will see that FEMAP has read in 5 Output Sets.One set for each eigenvalue (Buckling load) that was found.


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F5 select Deformunder Deformed Style and select None-Model Onlyunder Contour

Style

ClickDeformed and Contour Data

In the output set drop-down menu, select 1..Eigen 1 30049.98 Hz as shown in Figure 33.The value denotes the first buckling load is 30049.98 N. The five values shown in thedropdown menu list the five buckling values that were found by ABAQUS. ABAQUS

exited with an error because it only found five of the 10 that were requested in the INP

file.

Figure 43 - Postprocessing the buckling analysis

Click OK OK

The buckled shape is shown in Figure 44. This shape is distorted and appears to be

localized buckling of the thin flanges and webs and not overall Euler buckling of the

column.


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Figure 44 - First buckling mode (30049.98 N)

Edit the model to increase the thickness of the flanges from 1 mm to 5 mm and the web from

2 mm to 4 mm. These changes can be made easily by using Notepad for editing thebeam_buckle.inpfile lines. Open the beam_buckle.inpfile in Notepad and save asbeam_buckle2.inp.

Change:

*SHELL SECTION, ELSET=P2, MATERIAL=M1

0.001,** Femap with NX Nastran Property 3 : Plate2*SHELL SECTION, ELSET=P3, MATERIAL=M1

0.002,

To be:

*SHELL SECTION, ELSET=P2, MATERIAL=M10.005,

** Femap with NX Nastran Property 3 : Plate2*SHELL SECTION, ELSET=P3, MATERIAL=M1

0.004,

and save the beam_buckle2.inp. Now analyze the beam_buckle2.inpfile in ABAQUS. Thistime, the model runs with an error but it finds 8 eigenvalues. The thicker sections changed the

outcome.

Now postprocess the new buckling results in FEMAP.


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In FEMAP, assuming that you still have the beam_buckle.modfile still open

Delete Output All Yes

This command deletes any output previously read and saved into your FEMAP model.

File Import Analysis Results selectABAQUS OK selectbeam_buckle2.filOpen Yes

F5 select Deformunder Deformed Style and select None-Model Onlyunder Contour

Style

ClickDeformed and Contour Data

In the Select PostProcessing popup window, select the first output set

1..Eigen 1 173557.9Hz as shown in Figure 45. Notice that ten eigenvalues were foundfor this analysis. Hence, ABAQUS completed the analysis without error.

Figure 45 - Postprocessing the revised buckling analysis

Click OK OK F8 Isometric OK


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The buckled shape is shown in Figure 46. The localized buckling is not present in this view andthe overall buckling looks to be Euler buckling and notice that the deflection is about the smaller

area moment of inertia.

Figure 41 - First buckling mode with increased thicknesses for the web and flanges

Note the buckling force that was applied was based on the force distribution over the nodesresulting from an axial pull on the thinner sections. That force distribution may not be the sameas we did not increase the size of the web and the flanges by the same scale factor. Thus, the

buckling load may be slightly incorrect for this second buckling analysis. However, theimportant lesson is that the finite element method can fine critical buckling loads be they local or

overall Euler buckling.

beam tutorial 09mar2010 v1

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