Axial+Bending+Torsion+Combined+Buckling Analysis of a Beam (Abaqus Cae) Jas

ABAQUS CAE BEAM TUTORIAL 1 REV 03.16.2011

AXIAL, BENDING, TORSION, COMBINED AND BUCKLING ANALYSIS OF

A BEAM

Instructor: Professor James Sherwood

Revised: Dimitri Soteropoulos

Programs Utilized: ABAQUS CAE 6.9-EF1

Problem Description:

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

The analysis will look at stresses and displacements associated with multiple loading conditions for a

steel I-beam. The beam will be “clamped” at one end and be loaded on the other end with prescribed

displacements for 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 Figure 1. The cross section dimensions are summarized in

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

Table 1. Cross Section Dimensions

a 6 cm

b 7 cm

t1 1 mm

t2 2 mm

Figure 1. Beam Cross Section


Creating the Model Geometry

Go to the Start Menu and open Abaqus CAE

You may be prompted with an Abaqus/CAE 6.9 Extended Functionality box (Figure 1). Close this

box by clicking the X in the top right hand corner.

Figure 1. Abaqus/CAE 6.9 Extended Functionality box.


Once the Extended Functionality box is exited, the ABAQUS CAE Viewport should look similar to

Figure 2. (Please note the model tree is the series of functions listed on the left hand side of the

viewport, while the module is the list of icons to the right of the model tree)

Figure 2. ABAQUS CAE Viewport

To create the model geometry of the steel I-beam, a sketch of the cross section must be

generated.

Using the left mouse button, double click Parts in the model tree and the Create Part (Figure 3a)

dialog box appears. Enter a new name for the part (I-BEAM), and under the Base Feature tab

choose Shell for shape and Extrusion for type. Change the approximate size option to 0.5. The

Create Part dialog box should look identical to Figure 3b.

Click Continue… and the graphics window will change to a set of gridlines.

Model Tree


Figure 3a. Create Part Dialog Box Figure 3b. Create Part Dialog Box (I-BEAM)

For the first step in generating the model geometry, a rectangular box must be created. Click the

Create Lines: Rectangle (4 lines) icon in the module. (Remember, the module is the series

of icons to the right of the model tree)

In the viewport click once with the cursor, then drag the cursor to any other place in the

viewport and click again. A yellow rectangle should be visible in the viewport.

Click the Create Lines: Connected icon in the module, hover the cursor along the top

horizontal line of the rectangle until a white circle appears (Figure 4). The circle should appear at

the midpoint of that line.


Figure 4. Midpoint of Horizontal Line

Once the white circle appears on the horizontal line, click with the cursor and draw a vertical

line which connects to the bottom horizontal line. You will know that the line is vertical if there

is a V located on the right side of the line (Figure 5).

Figure 5. Vertical Line


Since an arbitrary rectangle was drawn in the initial sketch, it will now be given the proper

dimensions. Click the Add Dimension icon in the module and click the top horizontal line in

the sketch. At this point the line should turn red and its corresponding dimension should appear.

Move the cursur away from the horizontal line and click.

At the bottom of the viewport, a New dimension: box should appear (Figure 6).

Figure 6. New Dimension Box

Enter a value of 0.07 in the New Dimension box.

Hit Enter.

The sketch should resize to the appropriate dimension. The dimension values are being input in

units of meters. Make sure to keep a consistent set of units when creating any model.

Using the cursor click the middle vertical line. At this point the line should turn red and its

corresponding dimension should appear. Move the cursor away from the vertical line and click.

At the bottom of the viewport, a New dimension: box should appear. Enter a value of 0.059 in

the new dimension box and hit Enter.

The sketch should resize to the appropriate dimension and look similar to that in Figure 7.

(Please note: due to significant figures in the sketch mode a value of 0.06 will appear when

0.059 is entered for the vertical height, make sure to enter a value of 0.059 for the vertical line)

Figure 7. Dimensioned Sketch


To properly create the I-Beam cross section, click the Auto-Trim icon in the module. Click

and hold the left cursor button while dragging the cursor over the far left vertical line and then

let go. If this was done correctly the left vertical line should disappear.

Repeat the previous step but drag the cursor over the far right vertical line. If the process was

done correctly the sketch should look similar to that in Figure 8.

Figure 8. Final I-Beam Cross Section

Press Escape on your keyboard to exit the Auto-Trim tool.

At the bottom of the viewport you will be prompted to Sketch the section for the shell

extrusion. Click Done.

The Edit Base Extrusion dialog box will appear (Figure 9a). In the Depth: category enter a value

of 0.9. This value will extrude the geometry 90 cm (0.9m) in the Z direction. After this value has

been entered the Edit Base Extrusion dialog box should look similar to Figure 9b.

Figure 9a. Edit Base Extrusion Dialog Box Figure 9b. Edit Base Extrusion Dialog Box (0.9)


Click OK.

The cross section sketch will be extruded into a three dimensional part. Sketch mode will

automatically be exited and a grey I-Beam will appear (Figure 10).

Figure 10. Extruded I-Beam Model

Defining Material Properties

To define material properties for this model, double click on Materials in the model tree and

the Edit Material dialog box will appear (Figure 11a). Enter a Name for the material (STEEL),

and click the Mechanical tab, highlight Elasticity and click Elastic. Enter values of Young’s

Modulus = 200E09 Pa, and Poisson’s Ratio = 0.3. After the material properties have been

entered, the Edit Material dialog box should look similar to Figure 11b.

Click OK.


Figure 11a. Edit Material Dialog Box Figure 11b. Edit Material Dialog Box (Steel)

Please note there is no dropdown menu or feature in ABAQUS that sets specific units. All of the

dimensions have been input in meters; therefore the respective Young’s Modulus units should

be entered in Pa (Pascals). The units chosen for the definition of the material properties should

be consistent and dictate what units should be used for the dimensions of the structure.

At this point in preprocessing, the model should be saved. Click File then click Save. Name the

file I-Beam Tutorial. The file will save as a Model Database (*.cae*) file. It may be of interest to

save the file after each section of this tutorial.

Creating Sections

To create a shell section in ABAQUS, double click Sections in the model tree and the Create

Section dialog box will appear (Figure 12a). Enter a Name for the section (FLANGE), and choose

Shell under the Category Tab, and Homogeneous under the Type tab. Your Create Section

dialog box should look similar to that in Figure 12b.

Click Continue…

Figure 12a. Create Section Dialog Box Figure 12b. Create Section Dialog Box (FLANGE)


The Edit Section dialog box will then appear where a value for the respective Shell thickness can

be prescribed for this section. Because only one material has been created, the Material is

defaulted to STEEL. If multiple materials had been created, the dropdown menu could be used

to prescribe a different material to this section.

Under the basic tab enter 0.001 for the Shell thickness (This value will be used to define a

thickness of 1 mm for both the top and bottom flanges). Change the Thickness integration rule:

to Gauss. When this is done the number of Thickness integration points will default to 3. The

Edit section dialog box should look similar to that in Figure 13.

Click OK.

Figure 13. Edit Section Dialog Box (FLANGE)

Since the flanges have a different specified thickness than the web, another section with the

appropriate shell thickness for the web must be created. If both the flanges and web had the

same thickness only one section would need to be created.

Double click Sections in the model tree and the Create Section dialog box will appear (Figure

14a). Enter a Name for the section (WEB), and choose Shell under the Category Tab, and

Homogeneous under the Type tab. Your Create Section dialog box should look similar to that in

Figure 14b.

Click Continue…


Figure 14a. Create Section Dialog Box Figure 14b. Create Section Dialog Box (WEB)

The Edit Section dialog box will then appear where a value for the respective Shell thickness can

be prescribed for this section. Because only one material has been created, the Material is

defaulted to STEEL. If multiple materials had been created, the dropdown menu could be used

to prescribe a different material to this section.

Under the basic tab enter 0.002 for the Shell thickness (This value will be used to define a 2 mm

thickness for the web). Change the Thickness integration rule: to Gauss. When this is done the

number of Thickness integration points will default to 3. The Edit section dialog box should look

similar to that in Figure 15.

Click OK.

Figure 15. Edit Section Dialog Box (WEB)


Assigning Sections

Now that the shell sections have been created, they can be assigned to the geometry. In the

model tree, click the + to the left of the Parts icon, this will further expand the model tree’s

options. Next, click the + to the left of the part called I-BEAM, further expanding the model tree

(Figure 16).

Figure 16. Model Tree Expansion (Parts)

After the model tree has been expanded, double click Section Assignments. While holding the

shift key on the keyboard, click the 2 sections of the top flange and the 2 sections of the bottom

flange. If the sections have been chosen correctly they will change color from grey to red (Figure

17).

Click Done.

Figure 17. Selected Flange Sections

2 Top Sections

2 Bottom Sections


The Edit Section Assignment dialog box will appear (Figure 18a). Using the drop down menu

under the Section option, choose the FLANGE section that was created. Under the Shell offset

option make sure the drop down definition is set to Middle surface. The Edit Section

Assignment dialog box should look identical to that in Figure 18b.

Figure 18a. Edit Section Assignment Figure 18b. Edit Section Assignment (FLANGE)

Click OK. The top and bottom now should now turn to a blue color.

Next, the web must be assigned its respective section. Double click Section Assignments, using

the cursor click the web of the I-beam. If the section has been chosen correctly it will change

color from grey to red.

Click Done.

The Edit Section Assignment dialog box will appear (Figure 19a). Using the drop down menu

under the Section option, choose the WEB section that was created. Under the Shell offset

option make sure the drop down definition is set to Middle surface. The Edit Section

Assignment dialog box should look identical to that in Figure 19b.

Figure 19a. Edit Section Assignment Figure 19b. Edit Section Assignment (FLANGE)


Click Ok. The web of the I-Beam should now turn a blue color, thus making the complete model

blue.

Click Done.

Creating a 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.

To create a mesh for the model geometry, double click Mesh (Empty) in the model tree. If this

selection is done correctly, then the geometry should change color to pink.

The first step in creating a mesh is to seed the part. Click and hold the Seed Part icon in the

mesh module and six icons will appear. Hover the cursor over the Seed Edge: By Number icon

and release the button on the cursor.

While holding the shift key on the keyboard, click the top and bottom edges of the flanges. If the

edges have been selected correctly they will turn a red color (Figure 20). A total of eight lines

should be selected since the part should be rotated and the four edges on the other end of the

beam should also be clicked. (Note: To rotate the beam click F3 on the keyboard then left click

and drag the cursor to rotate the part. To exit the rotate command press Escape on the

keyboard)

Figure 20. Selected Edges

2 Bottom Edges

2 Top Edges

Web Edge

Side Edge


Click Done.

In the Number of elements along the edges: prompt at the bottom of the viewport enter a

number of 3. This will seed the selected edges to have three evenly spaced elements along their

length.

Hit Enter on the keyboard. The edges will now appear to be seeded with evenly spaced pink

points along their length.

Next, click the web edge of the I-Beam (Figure 20). The edge should turn from a pink to a red

color if it has been selected correctly. A total of two edges should be selected since the part

should be rotated and the edge on the other end of the beam should also be clicked.

Click Done.


number of 6. This will seed the selected edges to have six evenly spaced elements along their

length.

Hit Enter on the keyboard.

Finally, while holding the shift key on the keyboard, click the four edges along the length of the

I-Beam. If the edges have been selected correctly they will turn a red color. A total of four lines

should be selected (Figure 20).

Click Done.


number of 90. This will seed the selected edge to have ninety evenly spaced elements along its

length.

Hit Enter on the keyboard

Click Done.


The part is now ready to be meshed. In the mesh module, click the Mesh Part icon . At the

bottom of the viewport you will be prompted if it is OK to mesh the part? Click Yes.

If this procedure was done correctly, the geometry will turn blue (Figure 21).

Figure 21. Meshed Geometry

Creating an Instance

Now that the part has been meshed, it can be brought into the assembly. To do this task, click

the + to the left of Assembly in the model tree. The model tree will expand and should look

identical to Figure 22.

Figure 22. Model Tree Expansion (Assembly)


Double click on the Instances icon in the expanded model tree. This feature will allow multiple

parts to be brought into the assembly. The Create Instance dialog box will appear (Figure 23).

Figure 23. Create Instance Dialog Box

The I-BEAM part is selected by default because only one part has been created for this tutorial.

If multiple parts had been created, then this step would allow them to be entered into the

assembly.

Click OK. If this step was done correctly the model should turn a blue color (Figure 24).

Figure 24. Create Instance


Creating a Step

A Step is where the user defines the type of loading, e.g. Static or Dynamic, and defines the

boundary conditions, e.g. support constraints and forces.

In the model tree, double click the Steps icon. The Create Step dialog box will appear

(Figure 25a). Create a Name for the step called LOADING STEP. Under Procedure type choose

General > Static, General. The Create Step dialog box should look identical to Figure 25b.

Figure 25a. Create Step Dialog Box Figure 25b. Create Step Dialog Box (LOADING STEP)

Click Continue…, and the Edit Step dialog box will immediately appear (Figure 26).

Figure 26. Edit Step Dialog Box

Click OK to accept the default values for the various options.


Creating Sets

At this point 4 sets will be created to simplify the application of loads and boundary conditions

in the upcoming steps. Double click Sets in the model tree. Make sure to double click the Sets

option that is underneath the I-BEAM part in the model tree (Figure 27).

Figure 27. Sets Option in Model Tree

The Create Set dialog box will immediately appear (Figure 28a). Create a Name for the set called

FIXED END, and under the type option make sure to choose Node. The Create Set dialog box

should look identical to that in Figure 28b.

Figure 28a. Create Set Dialog Box Figure 28b. Create Set Dialog Box (FIXED END)

Click Continue… The model will to a turquoise color with a visible mesh.

While holding the Shift key on the keyboard, click all of the nodes at one end of the beam. A

total of 19 nodes should be selected. To ensure each node is selected properly they will turn to a

red color.

In this tutorial the beam was rotated such that the nodes on the right side of the beam were

selected for the fixed end (Figure 29).


Figure 29. Fixed End Set

Click Done.

Another set will be created for the loading end of the I-Beam. Double click Sets(1) in the model

tree. The Create Set dialog box will immediately appear (Figure 30a). Create a Name for the set

called LOAD END, and under the type option make sure to choose Node. The Create Set dialog

box should look identical to that in Figure 30b.

Figure 30a. Create Set Dialog Box Figure 30b. Create Set Dialog Box (LOAD END)

Click Continue… The model will turn to a turquoise color with a visible mesh.

While holding the Shift key on the keyboard, click all of the nodes at the opposite end of the

beam that the FIXED END set was created. A total of 19 nodes should be selected. To ensure

each node is selected properly they will turn to a red color.

In this tutorial the beam was rotated such that the nodes on the left side of the beam were

selected for the load end.

Click Done.


To verify that the sets were not created on the same end of the beam, click the + to the left of

Sets (2) in the model tree. The model tree will expand and should look identical to Figure 31.

Figure 31. Created Sets Model Tree

Click the FIXED END set in the model tree and the 19 nodes which are included in that set will

turn red. Likewise, click the LOAD END set in the model tree and the 19 nodes included in that

set will turn red in the viewport.

Finally two more sets will be created, one for the TOP FLANGE and the other for the BOTTOM

FLANGE. These sets will be created to apply the torsional load to the model.

Double click Sets(2) in the model tree. The Create Set dialog box will immediately appear (Figure

32a). Create a Name for the set called TOP FLANGE, and under the type option make sure to

choose Node. The Create Set dialog box should look identical to that in Figure 32b.

Figure 32a. Create Set Dialog Box Figure 32b. Create Set Dialog Box (TOP FLANGE)



While holding the Shift key on the keyboard, click the nodes at the end of the top flange where

the LOAD END set was created. A total of 7 nodes should be selected. To ensure each node is

selected properly they will turn to a red color (Figure 33).

Figure 33. Node Selection Top Flange Set

Click Done.

Now a set will be created for the BOTTOM FLANGE. Double click Sets(3) in the model tree. The

Create Set dialog box will immediately appear (Figure 34a). Create a Name for the set called

BOTTOM FLANGE, and under the type option make sure to choose Node. The Create Set dialog

box should look identical to that in Figure 34b.

Figure 34a. Create Set Dialog Box Figure 34b. Create Set Dialog Box (BOTTOM FLANGE)



While holding the Shift key on the keyboard, click the nodes at the end of the bottom flange

where the LOAD END set was created. A total of 7 nodes should be selected. To ensure each

node is selected properly they will turn to a red color (Figure 35).

Figure 35. Node Selection Bottom Flange Set

Click Done.

Apply Constraint Boundary Conditions

Boundary conditions will be defined which will simulate a fixed (also known as “clamped”) beam

at one end with a tip load.

Double click BCs in the model tree and the Create Boundary Condition dialog box will appear

(Figure 36a). Create a Name for the boundary condition called FIXED, and under the Step drop

down menu make sure to choose Initial. Under the Category option choose Mechanical, and

choose Symmetry/Antisymmetry/Encastre under the Types for Selected Step option. The

Create Boundary Condition dialog box should look identical to that in Figure 36b.


Figure 36a. Create Boundary Condition Figure 36b. Create Boundary Condition (FIXED)

Click Continue…

Using the cursor, click Sets… at the bottom right side of the viewport. If this selection is done

correctly you will be immediately prompted by the Region Selection dialog box (Figure 37).

Figure 37. Region Selection Dialog Box

Using the cursor, click I-BEAM-1.FIXED END. Click Continue…

The Edit Boundary Condition dialog box will immediately appear. Click ENCASTRE

(U1=U2=U3=UR1=UR2=UR3=0). The Edit Boundary Condition dialog box should look identical to

that in Figure 38.


Figure 38. Edit Boundary Condition Dialog Box

Click OK.

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.

Double click BCs(1) in the model tree and the Create Boundary Condition dialog box will appear

(Figure 39a). Create a Name for the boundary condition called AXIAL, and under the Step drop

down menu make sure to choose LOADING STEP. Under the Category option choose

Mechanical, and choose Displacement/Rotation under the Types for Selected Step option. The


Figure 39a. Create Boundary Condition Figure 39b. Create Boundary Condition (AXIAL)

Click Continue…


The Region Selection dialog box will immediately appear (Figure 40). Using the cursor click

I-BEAM-1.LOAD END.


Click Continue…

The Edit Boundary Condition dialog box will immediately appear (Figure 41a). Since the I-Beam

cross section was sketched in the X Y plane, a displacement will be added in the Z direction.

Check the box to the left of U3 and enter a value of 0.00009. The Edit Boundary Condition

dialog box should look identical to that in Figure 41b.

Figure 41a. Edit Boundary Condition Figure 41b. Edit Boundary Condition (AXIAL)


Click OK. If the prescribed displacement has been applied correctly small orange arrows will be

visible at the nodes (Figure 42).

Figure 42. Applied Axial Load

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

the center of the beam to the top or bottom flange is 0.0295 m (0.059/2). To find the required

displacement in the x-direction to achieve the 5° twist use:

Where x is the prescribed displacement and is equal to 0.00258 m.


(Figure 43a). Create a Name for the boundary condition called TORSION TOP, and under the

Step drop down menu make sure to choose LOADING STEP. Under the Category option choose




Figure 43a. Create Boundary Condition Figure 43b. Create Boundary Condition (TORSION TOP)

Click Continue…

The Region Selection dialog box will immediately appear. Click I-BEAM-1.TOP FLANGE, the

Region Selection dialog box should look identical to that in Figure 44.


Click Continue… The Edit Boundary Condition dialog box will immediately appear (Figure 45a).

Since this displacement will be applied to the top flange in the +X direction click the box to the

left of U1: and enter a number of 0.00258. The Edit Boundary Condition dialog box should look

identical to that in Figure 45b.


Figure 45a. Edit Boundary Condition Figure 45b. Edit Boundary Condition (TORSION TOP)

Click OK. If the procedure has been completed correctly small orange arrows will appear

pointing in the +X direction at the end of the top flange.

An equal and opposite displacement will be prescribed to the bottom flange. Double click BCs(3)

in the model tree and the Create Boundary Condition dialog box will appear (Figure 46a). Create

a Name for the boundary condition called TORSION BOTTOM, and under the Step drop down

menu make sure to choose LOADING STEP. Under the Category option choose Mechanical, and

choose Displacement/Rotation under the Types for Selected Step option. The Create Boundary

Condition dialog box should look identical to that in Figure 46b.

Figure 46a. Create Boundary Condition Figure 46b. Create Boundary Condition (TORSION BOTTOM)


Click Continue…

The Region Selection dialog box will immediately appear. Click I-BEAM-1.BOTTOM FLANGE, the

Region Selection dialog box should look identical to that in Figure 47.



Since this displacement will be applied to the bottom flange in the -X direction click the box to

the left of U1: and enter a number of -0.00258. The Edit Boundary Condition dialog box should

look identical to that in Figure 48b.

Figure 48a. Edit Boundary Condition Figure 48b. Edit Boundary Condition (TORSION BOTTOM)



pointing in the -X direction at the end of the bottom flange. An expanded view of the loading

end of the beam is shown in Figure 49. Both the axial and torsional loads are applied in this

view.

Figure 49. Axial and Torsional Loads

Beam in Bending

Finally, a prescribed displacement in the –Y direction will be imposed on the tip of the beam.


(Figure 50a). Create a Name for the boundary condition called BENDING, and under the Step

drop down menu make sure to choose LOADING STEP. Under the Category option choose




Figure 50a. Create Boundary Condition Figure 50b. Create Boundary Condition (BENDING)

Click Continue…

The Region Selection dialog box will immediately appear. Click I-BEAM-1.LOAD END, the Region

Selection dialog box should look identical to that in Figure 51.



Since this displacement will be applied to the load end in the -Y direction click the box to the left

of U2: and enter a number of -0.006. The Edit Boundary Condition dialog box should look

identical to that in Figure 52b.


Figure 52a. Edit Boundary Condition Figure 52b. Edit Boundary Condition (BENDING)


pointing in the -Y direction on the loading end of the beam. An expanded view of the loading

end of the beam is shown in Figure 53. All three loading conditions are applied in this view

(Axial, Torsion, and Bending).

Figure 53. Axial, Torsion and Bending Loads.


Since this tutorial calls for multiple loading conditions, suppressing the loads is helpful rather

than deleting the loads when they are unwanted for the analysis. An analysis for the bending

loading condition will be completed. To do so click the + to the left of BCs (5) in the model tree.

This will expand the model tree and should look similar to Figure 54.

Figure 54. Model Tree Expansion (BCs)

Once the model tree has been expanded all off the created boundary conditions can be viewed.

Since only the BENDING boundary condition is of interest for this analysis, the others can be

suppressed. Please note that the FIXED boundary condition should not be suppressed for any

analysis since is needed to clamp the end of the beam and is not considered a loading condition.

While holding Ctrl on the keyboard click the AXIAL, TORSION TOP, and TORSION BOTTOM

boundary conditions. At this point the selected boundary conditions should be highlighted blue.

Release the Ctrl button on the keyboard and right mouse click one of the selected boundary

conditions. The pop up menu should look similar to that in Figure 55.

Figure 55. Pop Up Menu (Suppress)

Click Suppress. If this is done correctly a red X will appear to the left of the boundary conditions

in the model tree. Note: Suppressed BCs will not write to the inp file.


Creating a Job

To create a job for this model, double click the Jobs icon in the model tree. Up to this point, you

have been preprocessing the model. A job will take the input file created by the preprocessor

and process the model, i.e. perform the analysis. In the Create Job dialog box, create a Name

for this job called BENDING. Blank spaces are not allowed in a job name. Thus the use of the

underline in the name. The Create Job dialog box should look identical to that in Figure 56.

Figure 56. Create Job Dialog Box (BENDING)

Click Continue…

The Edit Job dialog box will immediately appear (Figure 57).

Figure 57. Edit Job Dialog Box (BENDING)

Accept the default values and click OK.


Setting the Work Directory

To ensure that the input files write to the correct folder, setting the work directory must be

accomplished. At the top of the screen, click File and in the dropdown menu click Set Work

Directory… (Figure 58).

Figure 58. Set Work Directory

The Set Work Directory screen will immediately appear (Figure 59). Click Select… and use

standard Windows practice to select (and possibly create) a subdirectory.

Figure 59. Set Work Directory (FOLDERS)

Click OK.

Click OK.


Writing the Input File (.inp)

To write the input file of the job that was created, first click the + next to the Jobs(1) icon in the

model tree.

Right click the job called BENDING and click the Write Input option. This choice will write an

input file (.inp) of this model to the work directory.

It may be helpful to go to the folder on the computer to which the work directory is set to

ensure that the input file was written there.

Model Analysis (ABAQUS Command)

Method #1

Go to the Start Menu and open Abaqus Command

ABAQUS is set to a default directory (Example E:\>). To change directories in the Abaqus

Command type the directory of choice followed by a colon (D:) then hit Enter.

To access a specific directory within that drive type cd followed by the specific folder name in

that directory (e.g., cd APPLIED STRENGTHS T.A) then hit Enter.

Now that the correct directory has been sourced in the command window type abaqus inter

j=BENDING and then hit enter.

If the job has completed successfully the Abaqus prompt should look similar to Figure 60.

Figure 60. Abaqus Command Prompt (COMPLETED)


Method #2

An alternative method for submitting an *.inp file for processing by ABAQUS can be

accomplished with ABAQUS CAE

Right click the job called BENDING and click the Submit option.

If you see a warning:

Click OK. The intent of this warning is to prevent the user from accidentally overwriting a

previously completed analysis with the same name.

The model will now be submitted for analysis by ABAQUS and the progress can be viewed in the

status window at the bottom of the screen.

Postprocessing using ABAQUS CAE

After the analysis has successfully completed in the Abaqus Command window using Method #1

or using Method #2, return to view the ABAQUS CAE viewport.

Because the last step of creating the model was to create a job/write (and possibly submit) an

input file, the BENDING job should still be highlighted in ABAQUS CAE model tree. Right click the

BENDING job and then click Results.

If this selection was done correctly, the model should turn to a green color and the truss will

have rotated to an isometric view (Figure 61).

Figure 61. Analysis Results Isometric View


To rotate the truss back into the X Y plane for viewing, click View in the toolbar at the top of the

screen. Next, Click Toolbars and make sure the option Views has a check mark to the left of it. If

not, then click it.

The Views toolbar will appear (Figure 62), and the Apply Front View button can be clicked to

view the model in the X Y plane.

Figure 62. Views Toolbar

To view the deformed shape of the model, click the Plot Contours on Deformed Shape icon

in the Visualization module. The model should look similar to that in Figure 63.

Figure 63. Deformed Shape (BENDING)


Obtaining Stress Values in Elements

To obtain the stresses in an element first the appropriate type of stress must be viewed. At the

top of the viewport underneath the top toolbar click the drop down menu Mises (Figure 64).

Figure 64. Mises Dropdown

Using the cursor click Third Invariant, this will change the contour color to represent the third

invariant stress levels. The I-Beam model should look similar to that in Figure 65.

Figure 65. Third Invariant Stress Contour


Now that the appropriate stress contour is being viewed, output stress values will be obtained

for different elements. At the top toolbar click Tools (Figure 66), and then click Query…

Figure 66. Toolbar Tools

The Query dialog box will immediately appear (Figure 67a). Click Element under the General

Queries option. The Query dialog box should look similar to that in Figure 67b.

Figure 67a. Query Dialog Box Figure 67b. Query Dialog Box (ELEMENT)


At this point click the element on the model for which the stress value is desired. The value of

the stress will then appear at the bottom of the viewport (Figure 68).

Figure 68. Stress Value in Viewport

Without exiting the Query dialog box click another element to view the stress value. Please

note: the stress value listed corresponds to the element outlined with a red box in the viewport.

Recall that the elastic modulus was prescribed to be 200x109 Pa and all dimensions were input

in meters therefore the output stress values are in units of Pa.

Modeling Different Loading Conditions

This tutorial completes the post processing for the BENDING loading condition of the project. To

complete both the AXIAL and TORSION loading return to the model tree by clicking the Model

tab at the top left of the screen.

Earlier in the tutorial the AXIAL & TORSIONAL boundary conditions were suppressed. To

complete the analysis using the TORSIONAL load, Suppress both the BENDING and AXIAL

boundary conditions and Resume both of the TORSION boundary conditions. (To resume the

torsion condition right click TORSION TOP & BOTTOM in the model tree and click resume).

Please note: two torsional loads must be suppressed since there is a load for both the top and

bottom flanges.

Create a new Job called TORSION and complete the post processing as needed.

Stress Value


Likewise, suppress the TORSION and BENDING conditions and create a new Job called AXIAL

and complete the post processing as needed. Please note: two torsional loads must be

suppressed since there is a load for both the top and bottom flanges.

If a combination of loading conditions is desired, resume the respective boundary conditions

and complete the post processing as needed.

Beam Buckling

For the beam buckling analysis, a unit axial load will 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 beam width of

the element and the number elements connected to a node.

Because the last step of creating the model was to create a job/write (and possibly submit) an

input file, the AXIAL job should still be highlighted in ABAQUS CAE model tree. Right click the

AXIAL and then click Results.

The reaction forces at the nodes at the end of the beam are to be determined. At the top of the

viewport underneath the top toolbar click the drop down menu S (Figure 69).

Figure 69. S Dropdown

Using the cursor click RF, this will change the contour from viewing stresses to the magnitude of

reaction forces. Since the reaction force in the Z direction is desired click the Magnitude

dropdown menu directly to the right of the RF dropdown and then click RF3.

To obtain the reactions at the nodes click the Create XY Data icon in the Visualization

module. The Create XY Data dialog box will appear (Figure 70a). Choose the ODB field output

option (Figure 70b).


Figure 70a. Create XY Data Dialog Box Figure 70b. Create XY Data Dialog Box (FIELD)

Click Continue…

The XY Data from ODB Field Output dialog box will appear (Figure 71a). Under the Variables tab

click the Positions: drop down menu and change the selection to Unique Nodal. Scroll down and

click the black arrowhead next to RF: Reaction force .This click will

expand the selection for more options. Scroll down and check the box next to RF3. All other

reaction components should be left unchecked (Figure 71b).

Figure 71a. XY Data from ODB Field Output Figure 71b. XY Data from ODB Field Output

Next click the Elements/Nodes tab. Make sure that Pick from viewport is selected in the

Method section, and click Edit Selection.

While holding the Shift key on the keyboard, click the nodes on the model at the end of the

beam which the load was applied. When the elements have been selected they will turn a red

color. A total of 19 nodes should be selected.

Click Plot.


Click Dismiss.

A plot should appear similar to that in Figure 72.

Figure 72. Field Output Plot

To view the numerical values of the reactions at the nodes, click the XY Data Manager icon

in the Visualization module. This option is located directly to the right of the Create XY Data

option.

The XY Data Manager dialog box will appear (Figure 73).

Figure 73. XY Data Manager Dialog Box


To view the value, double click each selection and an Edit XY Data dialog box will appear

(Figure 74).

Figure 74. Edit XY Data Dialog Box

In this dialog box the value of the reaction force at the respective node is listed.

Click OK.

At this point click start on the computer and open Microsoft Excel. In column A of a new Excel

workbook enter the node numbers of the 19 nodes found in the XY Data Manager dialog box

(Figure 75).

Figure 75. Import Node Numbers (Excel)

Double click each entry and enter the reaction force value in column B of the same Excel

workbook (Figure 76).


Figure 76. Import Reaction Forces (Excel)

Use the SUM function in Excel to add all the forces in column B. In this case the sum is 5164.9.

Dividing each Reaction Force value by this total gives the respective force to apply to each node

so as to have a net unit force on the end of the beam (Figure 77). Many of the nodes have the

same respective reaction force and it may be beneficial to color code the nodes with the same

reaction forces (Figure 77).

Figure 77. Color Coded Unit Loads (Excel)

Now that the nodal forces are known return to Abaqus CAE and close the Edit XY Data and XY

Data Manager dialog boxes. Return to the model tree by clicking the Model tab at the top left


hand side of the viewport. Suppress the AXIAL boundary condition (Right click -> Suppress). The

only boundary condition that should still be resumed is the FIXED boundary condition.

Expand Steps (2) in the model tree if it is not already expanded by clicking the + to the left of the

Steps(2) listing. Right click LOADING STEP and left click Suppress.

Double click Steps (2) and you will be prompted by the Create Step dialog box (Figure 78a).

Create a Name: for the step called BUCKLE. Under the Procedure type: drop down menu choose

Linear perturbation and click Buckle. The Create Step dialog box should look similar to that in

Figure 78b.

Figure 78a. Create Step Dialog Box Figure 78b. Create Step Dialog Box (BUCLKE)

Click Continue… The Edit Step dialog box will immediately appear. Under the Number of

eigenvalues requested: option enter a value of 5 in the box. The Edit Step dialog box should

look similar to that in Figure 79.


Figure 79. Edit Step Dialog Box (5 Eigenvalues)

Click OK.

Rather than individually load 19 nodes with its respective unit load value, we will create 4 sets

since there are repeated unit load values of 116.779, 233.557, 393.711, and 430.412.

Similar to creating sets in the first part of the tutorial, double click Sets (4) in the model tree and

the Create Set dialog box will immediately appear. Create a Name for the set called

Nodes_3_6_10_11 and ensure that Node is selected under the type option. The Create Set

dialog box should look similar to that in Figure 80.

Figure 80. Create Set Dialog Box (NODES_3_6_10_11)

Click Continue…

At the top toolbar click View then click Part Display Options… and the Part Display Options

dialog box will immediately appear. In the dialog box click the Mesh tab. Next click In all part-

related modules and check the box next to Show node labels (Figure 81).


Figure 81. Part Display Options Dialog Box

Click OK. At this point small purple node labels will appear on the model. This was done so that

the appropriate unit load could be placed on the correct nodes.

While holding Shift on the keyboard click nodes 3, 6, 10, and 11. When the nodes are selected

they will turn a red color (Figure 82).

Figure 82. Set Creation (Nodes 3, 6, 10, 11)


Click Done.

Repeat the same method to create sets for:

Nodes [103, 104, 289, 290, 473, 474, 475, 476]

Nodes [569, 570, 571, 572, 573]

Nodes [2, 7]

If all of the sets have been created correctly the model tree should have a total of 8 sets and

look similar to Figure 83.

Figure 83. All Created Sets

Now that the sets have been created, the appropriate loads can be applied to the nodes. Double

click Loads in the model tree and the Create Load dialog box will appear (Figure 84a). Create a

Name: for the load called NODES_3_6_10_11. Ensure Mechanical is selected under Category

and Concentrated force under Types for Selected Step. The Create Load dialog box should look

similar to that in Figure 84b.

Figure 84a. Create Load Dialog Box Figure 84b. Create Load Dialog Box (NODES)

New Sets


Click Continue… In the bottom right hand side of the viewport click Sets… and the Region

Selection dialog box will appear. Click I-BEAM-1.NODES_3_6_10_11, the Region Selection dialog

box should look similar to that in Figure 85.

Figure 85. Region Selection Dialog Box (NODES)

Click Continue… The Edit Load dialog box will immediately appear (Figure 86a). Enter a value of

-0.02261 in the CF3: option. The Edit Load dialog box should look similar to that in Figure 86b.

Figure 86a. Edit Load Dialog Box Figure 86b. Edit Load Dialog Box (-0.02261)

Click OK. Small yellow arrows will be visible pointing in the –Z direction if the procedure has

been completed correctly. The model should look similar to that in Figure 87.


Figure 87. Model Load (-0.02261)

Using the same approach, create loads for the three other sets that were generated in the

previous steps. Loads of:

Nodes [103, 104, 289, 290, 473, 474, 475, 476] = -0.04522

Nodes [569, 570, 571, 572, 573] = -0.076227

Nodes [2, 7] = -0.083333

If this procedure has been completed correctly there will be small yellow arrows located ALL the

nodes on the loading end of the beam (Figure 88).


Figure 88. Unit Load

Double click Jobs (1) in the model tree and create a job named BUCLKE. Write the input file and

post process the job the same way as in the first part of this tutorial.

When viewing the results, the deformed shape should look similar to that in Figure 89. Also, the

first buckling load is listed in the viewport to be 30200 Hz.

Figure 89. Deformed Shape (Localized Buckle)

Buckle Load


The buckled shape shown in Figure 89 is distorted and appears to be localized buckling of the

thin flanges and webs and not overall Euler buckling of the column. The model will now be

edited to increase the thickness of the flanges from 1 mm to 5 mm and the web from 2 mm to 4

mm. These changes will be made by editing the .inp files that are generated in the working

directory.

Open the folder on the computer that the working directory is set to. Open the BUCKLE.inp file

using Notepad. The .inp file should look similar to that in Figure 90.

Figure 90. Input File (.inp)

While holding Ctrl on the keyboard press the letter F. This will open the Find dialog box. Enter

Shell and then click Find Next. This part of the .inp file should look similar to that shown in

Figure 91.

Figure 91. Shell Section Input File


This is where we will change the thickness values of the flanges and web. Change 0.001 to 0.005

and change 0.002 to 0.004. This section of the input file should look similar to Figure 92.

Figure 92. Shell Section Input File (Increased)

Click File then click Save As…

Enter a File name: for this input file called BUCKLE_EULER.inp (Note: the .inp extension MUST

be entered in the file name)

Go to the Abaqus Command window and source to the directory if it is not already sourced.

Enter the command abaqus inter j=BUCKLE_EULER and hit Enter. If the analysis completed

successfully the command window will look similar to that in Figure 93.

Figure 93. Abaqus Command Prompt (COMPLETED)

Return to the Abaqus CAE viewport and click the Results tab located at the top of the model

tree. Double click the first item in the Results tab called Output Databases.

The Open Database dialog box will appear. Source to the BUCKLE_EULER.odb and click OK.


When viewing the results, the deformed shape should look similar to that in Figure 94. Also, the

first buckling load is listed in the viewport to be 168712 Hz.

Figure 94. Deformed Shape (Euler Buckle)

The buckled shape is shown in Figure 94. The localized buckling is not present in this view and

the overall buckling looks to be Euler buckling and notice that the deflection is about the smaller

area moment of inertia.

Note the buckling force that was applied was based on the force distribution over the nodes

resulting from an axial pull on the thinner sections. That force distribution may not be the same

as we did not increase the size of the web and flanges by the same scale factor. Thus, the

buckling load may be slightly incorrect for this second buckling analysis. However, the important

lesson is that the finite element method can find critical buckling loads be they local or overall

Euler buckling.

Conclusion

Save the file by doing either File > Save or clicking the disk icon

Close ABAQUS CAE: File > Exit or Ctrl+Q

This completes the Finite Element Analysis of an I-Beam tutorial.

Buckle Load

Documents

Axial+Bending+Torsion+Combined+Buckling Analysis of a Beam (Abaqus Cae) Jas