Exercise F

7/27/2019 Exercise F

1/10


2/10

Exercise F Cantilever Beam Model

Finite Element Analysis in Practice Steps for Exercises 4.00 07/11/2005

54


3/10



55

SolutionBuilding the Model

"Start: Programs: ALGOR V17:

FEMPRO"

Press the Windows "Start" button. Select the"Programs"pull-out menu and then select the"ALGOR V17" pull-out menu. Select the

"FEMPRO" command.

"New" Select the "New" icon at the left side of the dialog.

"New" Press the "New" button.Exercise F Type "Exercise F" in the "File name:" field in the

"Save As" dialog. Note the default folder location

where the analysis files will be created. This locationcan be changed by navigating to an alternate working

folder if desired.

"Save" Press the "Save" button."Geometry: Mesh: 4 Point

Rectangular"

Access the GEOMETRY pull-down menu and select

the "Mesh" pull-out menu. Select the "4 PointRectangular" command.

4 Type "4" in the "AB:" field.4 Type "4" in the "BC:" field.

Press to define the origin as the first point.

4 Type "4" in the "Y:" field and press to define

the point (0,4,0) as the second point.

4 4 Type "4" in the "Y:" field, press , type "4" and

press to define the point (0,4,4) as the thirdpoint.

4 Type "4" in the "Z:" field and press to define

the point (0,0,4) as the fourth point.

"Apply" Press the "Apply" button to create the mesh.

Press to exit the mesh command.

"View: Orientation: YZ Right" Access the VIEW pull-down menu and select the"Orientation" pull-out menu. Select the "YZ Right"

command. The mesh will appear as shown in Figure 1.


4/10



56

Figure 1: Selection Points for Patch Mesh

Mouse Right click on the "4-Point Mesh 1" heading in the

tree view.

"Move or Copy" Select the "Move or Copy" command.

Mouse Activate the "Copy" checkbox.

24 Type "24" in the "Copy" field.

Mouse Activate the "Join" checkbox.24 Type "24" in the "Total distance" field.

"OK" Press the "OK" button to perform the operation.

"View: Orientation: Isometric" Access the VIEW pull-down menu and select the"Orientation" pull-out menu. Select the"Isometric" command. The model should appear as

shown in Figure 2.

Figure 2: Brick Mesh


5/10



57

Defining the Element and Material Data

Mouse Right click on the "Element Type" heading for Part 1in the tree view.

"Brick" Select the "Brick" command.

Mouse Right click on the "Material" heading for Part 1 in

the tree view.

"Modify Material" Select the "Modify Material" command.

"Steel (AISI 4130)" Highlight the "Steel (AISI 4130)" item from the list

of available materials in the "Select Material"section.

"View Properties" Press the "View Properties" button to view thematerial properties associated with this type of steel.

"OK" Press the "OK" button to close the properties

window.

"OK" Press the "OK" button to accept the selected material.

After assigning the material properties, all red Xs should now be removed from the tree view.

Adding Loads and Constraints

"View: Orientation: XZ Front" To get a profile of the ends of the beam, access the

VIEW pull-down menu and select the "Orientation"pull-out menu. Select the "XZ Front" command.

"Selection: Select: Vertices" Access the SELECTION pull-down menu and choosethe "Select" pull-out menu. Select the "Vertices"

command.Mouse Draw a box around the top two rows of vertices at theleft edge of the model (see Figure 3).

Figure 3: Rectangle Select of Vertices


6/10



58

Mouse Holding down the key, draw a box around the bottom

two rows of vertices at the left edge of the model.

Mouse Right click in the display area."Add: Nodal Boundary

Conditions"

Select the "Add" pull-out menu and select the "Nodal

Boundary Conditions" command.

Mouse Activate the "Tx" checkbox in the "Constrained DOFs"

section.

"OK" Press the "OK" button to apply this constraint to the selected

vertices.

Mouse Draw a box around the center row of vertices at the left edge

of the model.

Mouse Right click in the display area."Add: Nodal Boundary

Conditions"

Select the "Add" pull-out menu and select the "NodalBoundary Conditions" command.

"Fixed" Press the "Fixed" button to activate all constraints.

"OK" Press the "OK" button to apply these constraints to theselected vertices. A red triangle will appear on each vertex

to indicate that it is fully constrained.

"View: Orientation: Isometric" Access the VIEW pull-down menu and select the"Orientation" pull-out menu. Select the "Isometric"

command.

"Selection: Shape: Point" Access the "Selection" pull-down menu and select the"Shape" pull-out menu. Select the "Point" command.

Mouse Click on the vertex at the left side of the center row of

vertices at the free end (the face opposite of the boundary

conditions).

Mouse Holding down the key, click on the vertex at the right

side of the center row of vertices at the free end.

Mouse

Right click in the display area."Add: Nodal Forces" Select the "Add" pull-out menu and select the "NodalForces" command.

-1250 Type "-1250" in the "Magnitude" field to specify a force of1250 pounds acting in a negative direction.

"Z" In the "Direction" section, select the "Z" radio button to

specify that the force will be applied in the Z direction.

"OK" Press the "OK" button to apply the forces to the selected

vertices.

Mouse Click on one of the 3 vertices between the two vertices with

the nodal forces.

Mouse Holding down the key, click on the other two vertices

in between the two vertices with the nodal forces.

Mouse Right click in the display area."Add: Nodal Forces" Select the "Add" pull-out menu and select the "Nodal

Forces" command.

-2500 Type "-2500" in the "Magnitude" field to specify a force of2500 pounds acting in a negative direction.

"Z" In the "Direction" section, select the "Z" radio button tospecify that the force will be applied in the Z direction.


7/10



59

"OK" Press the "OK" button to apply the forces to the selected

vertices. The model should now appear as shown in Figure

4.

Figure 4: Completed Brick Element Model

Analysis

"Analysis:

Perform Analysis" Access the ANALYSIS pull-down menu and select the"Perform Analysis" command to run the analysis. Atthe completion of the analysis, FEMPRO will

automatically transfer to the Results environment.

Viewing the Results

"Results: Stress: Stress Tensor: 1)

XX"

Access the RESULTS pull-down menu and select the"Stress" pull-out menu. Select the "Stress Tensor" pull-

out menu and select the "1) XX" command. The

maximum stress is indicated as 22,321 psi as shown inFigure 5.


8/10



60

Figure 5: Stress Tensor Results

"Inquire: Results" Access the INQUIRE pull-down menu and select the"Results" command to bring up the "Inquire:

Results" dialog.

Mouse Click on the node at the top middle of the constrained end

which is highlighted in Figure 6. The "Inquire: Results"dialog indicates that the stress for node number 551 at

(0, 2, 4) is 22,099 psi.

Figure 6: Inquire Results Dialog

Mouse Click on the nodes at (1, 2, 4), (2, 2, 4), (3, 2, 4), (4, 2, 4), (5, 2,4) and (6, 2, 4) down the middle of the beam to obtain the stress

values at each node. These values will be used in the validation

of the results in the next section.

"Close" Press the "Close" button to close the "Inquire: Results"

dialog.


9/10



61

Validation of Results

Reference

Mischke, C. R. and Shigley, J. E., Mechanical Engineering Design, Fifth Edition, McGraw-Hill,

1989, page 44.

Theoretical Solution

I

Mcbending = = 22,500 psi

Variable Value Units Comments

M 240,000 in.-lb Bending moment

c 2 in. Distance to neutralaxis

I 21.333 in.

4

Moment of inertia(I = bh3/12)

Comparison of Results

Distance from

End (in.)

Theoretical

(psi)

ALGOR

(psi)

%

Difference

0 22,500 22,099 1.78%

1 21,563 21,909 1.60%

2 20,625 20,850 1.09%

3 19,688 19,666 0.11%

4 18,750 18,758 0.04%

5 17,813 17,815 0.01%

6 16,875 16,876 0.01%

Note that the ALGOR results correlate better with the theoretical results as the distance from theconstrained end is increased. There are several reasons for these results. The first is that the bending

stress formula, = Mc/I, is derived based on a state of pure bending (no shear or axial forces). Since

the end of the cantilever beam is fully constrained, a state of pure bending does not exist at thatlocation. Also, the boundary conditions introduce a singularity at the location of the nodes which

results in an artificially high level of stress at the nodes.

This completes the exercise. To review a completed archive of this exercise, refer to the file

Exercise F.ach in the Exercise F\Results archive directory.


10/10



62

Documents

Exercise F