Beam Tutorial
1
ANSYS Handout:
Beam Tutorial
X.J. Xin
Mechanical and Nuclear Engineering
Kansas State University
1.
Tutorial: Cantilever Beam Using Solid Elements ................................................................... 1
Problem Description ................................................................................................................... 1
Modeling Approach .................................................................................................................... 2
Preprocessing .............................................................................................................................. 2
Solution ....................................................................................................................................... 7
Postprocessing............................................................................................................................. 7
Hand Calculations ..................................................................................................................... 13
Comments about FEM Accuracy .............................................................................................. 14
2. Tutorial: Cantilever Beam Using Beam Elements ................................................................ 14
Problem Description ................................................................................................................. 15
Modeling Approach .................................................................................................................. 15
Preprocessing ............................................................................................................................ 15
Solution ..................................................................................................................................... 18
Postprocessing........................................................................................................................... 19
Comments about FEM Accuracy .............................................................................................. 24
3. Appendix: Online Menu for BEAM3 Element ..................................................................... 24
Element Description.................................................................................................................. 24
Input Data.................................................................................................................................. 25
Output Data ............................................................................................................................... 25
Assumptions and Restrictions ................................................................................................... 28
1.
Tutorial: Cantilever Beam Using Solid Elements
Problem Description
A cantilever beam with uniform thickness of 5 mm and varying height is fixed at the left end,
and loaded by a concentrated force P = 100 N. The dimensions are shown in the figure. The
Young’s modulus is 210 GPa, and the Poisson’s ratio is 0.3. Using ANSYS to solve the problem.
1. Report the vertical deflection at free end B, highest bending stress around the shoulder A,
and bending and shears stress distribution along vertical line C-C (0.01 m from the fixed
end).
2. Hand calculate the vertical deflection at free end B and bending stress distribution along
Beam Tutorial
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vertical line C-C using knowledge learning in ME533, and compare the hand calculations
with FEM results.
3. Calculate the stress concentration factor Kt based on FEM results and compare it with data
from published Kt chart shown on next page (Figure 4.38 of the Machine Design I textbook).
r=0.002 m
0.01 m
P = 100 N
A
C
0.014 m
0.01 m
C
0.1 m
B
0.2 m
thickness = 0.005 m
Modeling Approach
The thickness is uniform and small compared with other dimensions, and the load is in the x-y
plane. The structure is therefore in a state of plane stress. The 2D plane stress element with
thickness option is appropriate. The problem can also be approximated using the 1D beam
element. The 1D beam element is the most efficient, but details of stress concentration around
the shoulder will be lost, as illustrated in the next tutorial.
Preprocessing
Beam Tutorial
3
 Build the Geometry
Because of symmetry, you can model just half of the specimen. Use the upper half.
1. Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By Dimensions
2. Enter the following: (Note: Press the Tab key between entries)
X1, X2 X-coordinates = 0
0.102
Y1, Y2 Y-coordinates = -0.007
0.007
Apply
X1, X2 X-coordinates = 0 .102
0.302
Y1, Y2 Y-coordinates = -0.005
0.005
OK to close the dialog box.
3. Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle
Enter the following:
WP X = 0.102
WP Y = -0.007
Radius = 0.002
Apply
WP X = 0.102
WP Y = 0.007
Radius = 0.002
OK to close the dialog box.
4. Main Menu > Preprocessor > Modeling > Operate > Boolean > Subtract > Areas
Click somewhere near the center of the rectangle on the left
Apply. This defines the base area to subtract.
Click somewhere near the center of the bottom solid circle, and click somewhere near the
center of the top solid circle. This defines the areas to be subtracted.
OK.
Even though the geometry looks correct now, the two areas are separate entities. They need to be
"bound" together so that loads can be transmitted between them. This can be achieved using
either "Add" or "Glue" Boolean operation in ANSYS. The difference between "add" and "glue"
is that "glue" preserves the boundary between the two glued areas, while "add" eliminates the
boundary.
5. Main Menu > Preprocessor > Modeling > Operate > Boolean > Add > Areas
Click somewhere near the center of the rectangle on the left and somewhere near the center
of the rectangle on the right. OK.
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Before going to the next step, save the work you have done so far. ANSYS stores any input data
in memory to the ANSYS database. To save that database to a file, use the SAVE operation,
available as a tool on the Toolbar. ANSYS names the database file using the format jobname.db.
If you started ANSYS using the product launcher, you can specify a jobname at that point (the
default jobname is file). You can check the current jobname at any time by choosing Utility
Menu > List > Status > Global Status. You can also save the database at specific milestone
points in the analysis (such as after the model is complete, or after the model is meshed) by
choosing Utility Menu > File > Save As and specifying different jobnames (model.db, or
mesh.db, etc.).
It is important to save frequently so that if you make a mistake, you can restore the model from
the last saved state. You restore the model using the RESUME operation, also available on the
Toolbar. (You can also find SAVE and RESUME on the Utility Menu, under File.)
Toolbar: SAVE_DB.

Define material properties.
1. Main Menu > Preprocessor > Material Props > Material Models
2. Double-click on Structural, Linear, Elastic, Isotropic.
3. Enter 210e9 for EX.
4. Enter .3 for PRXY.
5. OK to define material property set and close the dialog box.
Material > Exit

Define element types and options.
For this analysis, the element PLANE2, which is a 2-D 6-node quadratic structural triangular
element, is appropriate. You will need to specify plane stress with thickness as an option for
PLANE2. (You will define the thickness as a real constant in the next step.)
1.
2.
3.
4.
5.
6.
7.
8.
Main Menu > Preprocessor > Element Type > Add/Edit/Delete
Add an element type.
Structural solid family of elements.
Choose the triangle 6node 2 (PLANE2).
OK to apply the element type and close the dialog box.
Options for PLANE2 are to be defined.
Use plane stress with thickness (Plane strs w/thk).
OK to specify options and close the options dialog box.
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Close the element type dialog box.

Define real constants.
For this analysis, since the assumption is plane stress with thickness, you will enter the thickness
as a real constant for PLANE2.
9. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete
Select Plane2, Add...
OK
THK = 0.005
OK. Close

Generate Mesh
1. Main Menu > Preprocessor > Meshing > Mesh Tool
2. Set Global Size control.
3. Type in 0.00125. This guarantees that there are eight layers of elements long the height of the
beam for the smaller cross-section.
4. OK.
5. Choose Area Meshing.
6. Click on Mesh.
7. Pick All for the area to be meshed (in picking menu). Close any warning messages that may
appear.
8. Close the Mesh Tool.
The mesh seems fine enough for most regions, but as the shoulder has stress concentration, and
is a region of interest in the study, we should refine the mesh there further.
Without refinement at the shoulders
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PlotCtrl > Pan Zoom Rotate, Click [Box Zoom] on the Pan Zoom Rotate control, and drag a
zoom box to enclose the two shoulders so that you can get a closer view of the region.
Main Menu > Preprocessor > Meshing > Refine Mesh > Refine At > Elements
A dialog box will appear. Check the "circle" option. Then click the mouse near the curvature
center of the top shoulder and drag the cursor so that the drawn circle encloses about two layers
of elements from the surface of the shoulder. Release the mouse button. The selected elements
will be marked by small squares. Do the same for the bottom shoulder. Click OK. Another dialog
box appears. The default refinement level is "1 (Minimal)". Use the default. Click OK. You can
see the mesh is refined.
Refine the mesh one or two more times, so that the mesh is finer in the regions around the
shoulder. See the following figures.
With refinement at the shoulders
Note
The mesh you see on your screen is probably different from the mesh shown here. As a result of
this, you may see slightly different results during postprocessing. For a discussion of results
accuracy, see Planning Your Approach in the ANSYS Modeling and Meshing Guide.
Save the database.
PlotCtrl > Pan Zoom Rotate, Click [Fit] on the Pan Zoom Rotate control to get the whole view.

Apply displacement constraints.
You can apply displacement constraints directly to lines.
1.
2.
3.
4.
5.
6.
Main Menu > Solution > Define Loads > Apply > Structural > Displacement > On Lines
Pick the left edge of the beam.
OK (in picking menu).
Click on All DOF (built-in conditions).
Enter 0 for zero displacement.
OK to apply constraints and close dialog box.
Beam Tutorial
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Toolbar: SAVE_DB.
 Apply load.
Now apply the force at the right end of the beam.
1. Main Menu > Solution > Define Loads > Apply > Structural > Force/Moment > On
Keypoints
2. Pick the keypoint at the upper right corner of the beam.
3. Apply.
4. Select FY for the force direction
5. Enter -100 for VALUE.
6. OK.
Toolbar: SAVE_DB.
Solution
1. Main Menu > Solution > -Solve- Current LS
2. Review the information in the status window, then choose File > Close (Windows) to close
the window.
3. OK to begin the solution. Choose Yes to any Verify messages that appear.
Close the information window when solution is done.
Toolbar: SAVE_DB.
ANSYS stores the results of this one load step problem in the database and in the results file,
Jobname.RST (or Jobname.RTH for thermal, Jobname.RMG for magnetic, and Jobname.RFL
for fluid analyses). The database can actually contain only one set of results at any given time, so
in a multiple load step or multiple substep analysis, ANSYS stores only the final solution in the
database. ANSYS stores all solutions in the results file.
Postprocessing
Note
The results you see may vary slightly from what is shown here due to variations in the mesh.
Enter the general postprocessor and read in the results.
1. Main Menu > General Postproc > Read Results > First Set
Before you do anything else in postprocessing, you should always check the deformed shape first
to make sure the model makes intuitive senses.
 Plot the deformed shape.
1. Main Menu > General Postproc > Plot Results > Deformed Shape
2. Choose Def + undeformed.
Beam Tutorial
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3. OK.
You can also produce an animated version of the deformed shape:
4. Utility Menu > Plot Ctrls > Animate > Deformed Shape
5. Choose Def + undeformed.
6. OK.
Make choices in the Animation Controller (not shown), if necessary, then choose Close.
Frequently, the Animation Controller may be hidden behind other windows. Use Alt+Tab to
cycle through windows and find it.

Plot the von Mises equivalent stress.
Beam Tutorial
1.
2.
3.
4.
9
Main Menu > General Postproc > Plot Results > Contour Plot > Nodal Solu
Choose Stress item to be contoured.
Scroll down and choose von Mises (SEQV).
OK.
You can also zoom in to view the stress contour around the shoulders.
PlotCtrls > Pan Zoom Rotate
Click Box Zoom
Draw a box enclosing the shoulders. You will see the zoom in region with the stress contour.
You can repeat the zoom action until you get a fine view of the tip region.

Plot the principal stresses in vector form.
Zoom in to the mid uniform section of the beam.
Main Menu > General Postproc > Plot Results > Vector Plot > Predefined
Select Stress, Principal S, Vector Mode, Elem Centroid, OK
The vectors show the directions of the principal stresses S1 (roughly equal to SX) and S2
(roughly equal to SY), and the length represents the magnitude. The plot reveals that S2 is almost
zero, and S1 is along the axial direction of the beam, and linear proportional to the y-distance
from the neutral axis. This is in agreement with the beam theory.
Stress state is primarily normal stresses along x direction.
Now zoom in to the regions of the shoulders.
Main Menu > General Postproc > Plot Results > Vector Plot > Predefined
Select Stress, Principal S, Vector Mode, Elem Centroid, OK
The vectors show that because of the stress concentration, both S1 and S2 are non-zero. S1 is no
longer along x direction but varies with location. Its magnitude reaches a maximum at the root of
the shoulder near the bottom. The figure reveals that the stress state around the shoulder is rather
Beam Tutorial
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complicated.

List reaction solution.
1. Main Menu > General Postproc > List Results > Reaction Solu
2. OK to list all items and close the dialog box. The reaction forces FX and FY of all nodes on
the left edge are listed.
3. Scroll down and find the total vertical force, FY. The total value of 100 is the opposite of the
total load force.

To get the displacement of the right end
PlotCtrls > Pan Zoom Rotate
Click Fit
Plot > Elements so you can see all elements. Zoom in around the right end of the beam if
necessary.
Select > Entities …
OK in the popup box. Another box pops up.
Click the lower right corner of the beam (point B), then OK
Main Menu > General Postproc > List Results > Nodal Solution
DOF Solution, All DOFs, OK
Ux and Uy of the loading point will be displaced, as follows
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES
NODE
UX
UY
192 -0.16946E-03-0.58433E-02
MAXIMUM ABSOLUTE VALUES
NODE
192
192
Beam Tutorial
VALUE
11
-0.16946E-03-0.58433E-02
Therefore the y-deflection of B is 5.84 mm downward.

To plot bending (normal) and shear stresses along line C-C
Main Menu > General Postproc > Path Operation > Define Paths > By location
Path name: CC
Number of points: 2
Number of data set: change to 100
Number of divisions: change to 100
Popup box
1
0.01
-0.007
OK
2
0.01
0.007
OK, Cancel
Main Menu > General Postproc > Path Operation > Plot Paths to see the path
Main Menu > General Postproc > Path Operation > Map onto Path
Select "Stress", "X-direction stress SX", Apply
Select "Stress", "XY-shear SXY", OK
Main Menu > General Postproc > Path Operation > Plot Path Item > On Graph
Select "SX", OK.
The distribution of sigma_xx along the right ligament will show as follows. The distribution, as
we have learned in ME533, is linear along y direction.
The maximum bending stresses, which occur at the top and bottom surfaces of the beam, are
178.5 MPa.
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To get data for the curve,
Main Menu > General Postproc > Path Operation > Plot Path Item > List path items
Select "SX", OK.
A pop up window will show sigma_xx versus location along the ligament. You can copy the data
and import into Excel to do more plotting.
To get shear stress,
Main Menu > General Postproc > Path Operation > Plot Path Item > On Graph
Select "SXY", OK.
The distribution of sigma_xy along the right ligament will show as follows. The distribution, as
we have learned in ME533, is parabolic along y direction.
From the figure, the maximum shear is 2.32 MPa.

Find maximum xx-stress for stress concentration Kt
From the utility menu,
Select > > Everything
From ANSYS main menu
General Postproc > > List results > > Sorted listing > > Sort nodes
The Sort node window pops up. Select "Descending order", List sorted nodes for
"Results", Item, Comp sort nodes based on "Stress", "X-direction SX", OK.
It will list stress components of the all nodes, with the first listed node having the largest
sigma_xx (SX).
Part of the listing is
THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES
NODE
850
SX
SY
0.36418E+09 0.90467E+07
SZ
0.0000
SXY
-0.52855E+08
SYZ
0.0000
SXZ
0.0000
Beam Tutorial
852
528
10581
10583
.....
13
0.33817E+09 0.30000E+08
0.32588E+09-0.49594E+06
0.30202E+09 0.33669E+08
0.30047E+09 0.23136E+08
0.0000
0.0000
0.0000
0.0000
-0.99324E+08
-0.65845E+07
-0.61758E+08
-0.37831E+08
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
The maximum stress is 364.2 MPa.
To calculate the stress concentration factor, the nominal stress is needed:
 nom 
M(h 2 / 2) M(h 2 / 2)
6M
6 *100 * (0.302  0.102)



 240.0 MPa
3
2
EI 2
E(h 2 b / 12) Eh 2 b 210e9 * 0.01^ 2 * 0.005
The concentration factor is therefore
Kt 
 x max
 nom

364.2
 1.51
240.0
From the concentration factor chart, H/h=1.4, r/h=0.2, the value is about 1.5, which compares
well with the FEM prediction of 1.51.

Exit the ANSYS program.
When exiting the ANSYS program, you can save the geometry and loads portions of the
database (default), save geometry, loads, and solution data (one set of results only), save
geometry, loads, solution data, and postprocessing data (i.e., save everything), or save nothing.
You can save nothing here, but you should be sure to use one of the other save options if you
want to keep the ANSYS data files.
1. Toolbar: Quit.
2. Choose Quit - No Save!
OK.
Hand Calculations

Deflection of B
The deflection of B can be obtained using the Castigliano's method:
The moment in terms of location x is:
M  P(L  x )
Use the Castigliano's method, noting that the moment of inertia varies with location:
Beam Tutorial
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M(M / P)
B  
dx 
EI 1
0
0.1


0.1
M(M / P)
dx
EI 2
 P(L  x )( (L  x ))
0 E(h13 b /12) dx 
0.1

0.302
0.302

0.1

 P(L  x )( (L  x ))
dx
E(h 32 b / 12)



0.1
0.302
P
P
L2 x  Lx 2  x 3 / 3 0 
L2 x  Lx 2  x 3 / 3 0.1
3
E(h b / 12)
E(h 2 b / 12)
3
1
 0.00582
The result compares well with the numerical solution of 5.84 mm.

Bending stress along CC
The distribution is linear along y. So we only need to find the maximum stress. The formula is
 max 
M(h 1 / 2) M(h 1 / 2) P0.302  0.01h 1 / 2


 178.8 MPa
EI 1
E(h 13 b / 12)
E(h 13 b / 12)
Again, it compares well with the FEM results of 178.6 MPa.

Shear stress along CC
The distribution is parabolic along y. The maximum stress is
 max 
3V
3 *100 N
3 *1000


Pa  2.14 MPa
2A 2 * (h 1 * b) 2 * 0.014 * 0.005
Again, it compares reasonably well with the FEM results of 2.32 MPa.
Comments about FEM Accuracy
High accuracy in stress concentration factor and normal stress distribution is obtained because
fine mesh is used. The less accurate shear stress results may be attributed to two factors: (1) the
mesh around CC is not refined; (2) the shear stress distribution obtained in simple beam theory is
only approximate.
If a coarser mesh is used, computation time will be faster, but the results will be less accurate.
2.
Tutorial: Cantilever Beam Using Beam Elements
Beam Tutorial
15
Problem Description
The problem is the same as in the previous tutorial (Cantilever Beam using Solid Elements).
Modeling Approach
Instead of using solid elements, the 1D beam element is used here. The beam element is the
much more efficient, but details of stress concentration around the shoulder will be lost. As a
result, we can obtain deflections and stress distributions in regions of uniform cross-section with
good accuracy, but the stress distribution around the shoulder will be inaccurate.
The beam element represents the real beam with a mathematical line coinciding with the neutral
axis of the beam, and therefore the beam element is essentially 1D even though you can combine
beam elements to form a 2D or 3D structure. The cross-sectional properties such as the height,
area and moment of inertia are entered as real constants in ANSYS.
Preprocessing

Build the Geometry
Main Menu > Preprocessor > Modeling > Create > Keypoints > In Active CS
Enter the following: (Note: Press the Tab key between entries)
Keypoint number = 1
X,Y,Z Location in active CS = 0
0
0
Apply
Keypoint number = 1
X,Y,Z Location in active CS = 0.1
0
0
Apply
Keypoint number = 1
X,Y,Z Location in active CS = 0.302
0
0
OK
Main Menu > Preprocessor > Modeling > Create > Lines > Lines > Straight Line
Click keypoints 1 and 2,
Click keypoints 2 and 3,
OK
Toolbar: SAVE_DB.

Define material properties.
Main Menu > Preprocessor > Material Props > Material Models
Double-click on Structural, Linear, Elastic, Isotropic.
Enter 210e9 for EX.
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Enter .3 for PRXY.
OK to define material property set and close the dialog box.
Material > Exit

Define element types and options.
Main Menu > Preprocessor > Element Type > Add/Edit/Delete
Add an element type.
Structural Mass, Beam family of elements.
2D elastic 3 (BEAM3).
OK to apply the element type and close the dialog box.

Define real constants.
For this analysis, since there are two different cross sections, we need to define two sets of real
constants for the beam elements. You can calculate the cross-sectional properties using formulas
learned in Mechanics of Materials. You can also use the Section function in ANSYS, illustrated
in the following:
Main Menu > Preprocessor > Sections > Beam > Common Sectns
A Beam Tool window will appear. For the big section:
Sub-Type = (rectangle)
Set B = 0.005
H = 0.014
Click Preview
The graphics window will show the section with calculated properties.
Area =0.7e-4
Iyy = 0.114e-8 (this is the moment of inertia you need, not Izz)
For the small section:
Sub-Type = (rectangle)
Set B = 0.005
H = 0.01
Click Preview
The graphics window will show the section with calculated properties.
Area =0.5e-4
Iyy = 0.417e-9
OK to close the window.
Main Menu > Preprocessor > Real Constants > Add/Edit/Delete
Select BEAM3, Add...
Real Constant Set No. = 1
AREA = 7e-5
IZZ = 1.143e-9 (note that it is called Izz now!)
HEIGHT = 0.014
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Apply
Select BEAM3, Add...
Real Constant Set No. = 2
AREA = 5e-5
IZZ = 4.17e-10
HEIGHT = 0.01
OK. Close
 Generate Mesh
Since there are two sets of real constants, we need to associate correct real constants to the
corresponding parts of the beam. Use Attribute to do this.
Main Menu > Preprocessor > Meshing > Mesh Attributes > Picked Lines
Click the left line that represents the left part of the beam with bigger cross section.
The Attributes dialogue window appears.
MAT = 1
REAL = 1
TYPE = 1 BEAM3
OK
Main Menu > Preprocessor > Meshing > Mesh Attributes > Picked Lines
Click the left line that represents the right part of the beam with smaller cross section.
The Attributes dialogue window appears.
MAT = 1
REAL = 2
TYPE = 1 BEAM3
OK
(Attributes allow you to assign different material properties and different element type to
different parts of the solid model, if the problem consists of multiple materials, and multiple
element types are used in FEM modeling).
For beam element, we only need to specify the length of the element.
Main Menu > Preprocessor > Meshing > Mesh Tool
Set Global Size control.
Type in 0.005. This guarantees that there are twenty elements for the left section of the beam
with bigger cross-section.
OK.
Choose Mesh: Lines.
Click on Mesh.
Pick All for the area to be meshed (in picking menu). Close any warning messages that may
appear.
Close the Mesh Tool.
Utility menu, Plot > Elements, you will see only a line
Utility menu, Plot > Nodes, you will see nodes which may give some idea about the size of the
Beam Tutorial
18
elements.
Save the database.

Apply displacement constraints.
You can apply displacement constraints directly to lines.
Main Menu > Solution > Define Loads > Apply > Structural > Displacement > On
Keypoints
Pick the left end of the beam.
OK (in picking menu).
Click on All DOF (built-in conditions).
Enter 0 for zero displacement.
OK to apply constraints and close dialog box.
Toolbar: SAVE_DB.
 Apply load.
Now apply the force at the right end of the beam.
Main Menu > Solution > Define Loads > Apply > Structural > Force/Moment > On
Keypoints
Pick the keypoint at the right end of the beam.
Apply.
Select FY for the force direction
Enter -100 for VALUE.
OK.
Toolbar: SAVE_DB.
Solution
Main Menu > Solution > -Solve- Current LS
Review the information in the status window, then choose File > Close (Windows) to close the
window.
OK to begin the solution. Choose Yes to any Verify messages that appear.
Close the information window when solution is done.
Toolbar: SAVE_DB.
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19
Postprocessing
Note
The results you see may vary slightly from what is shown here due to variations in the mesh.
Enter the general postprocessor and read in the results.
Main Menu > General Postproc > Read Results > First Set
Before you do anything else in postprocessing, you should always check the deformed shape first
to make sure the model makes intuitive senses.
 Plot the deformed shape.
Main Menu > General Postproc > Plot Results > Deformed Shape
Choose Def + undeformed.
OK.
You can also produce an animated version of the deformed shape:
Utility Menu > PlotCtrls > Animate > Deformed Shape
Choose Def + undeformed.
OK.
Make choices in the Animation Controller (not shown), if necessary, then choose Close.
Frequently, the Animation Controller may be hidden behind other windows. Use Alt+Tab to
cycle through windows and find it.

To get the displacement of the right end
PlotCtrls > Pan Zoom Rotate
Click Fit
Plot > Elements so you can see all elements. Zoom in around the right end of the beam if
necessary. The node number is 114 (your mesh may be different).
Right end
Main Menu > General Postproc > List Results > Nodal Solution
DOF Solution, All DOFs, OK
Ux, Uy and ROTZ (rotation) of all nodes will be displaced, as follows
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20
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES
NODE
......
111
112
113
114
115
116
117
118
......
210
211
212
213
214
UX
UY
ROTZ
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-0.49950E-03-0.10013E-01
-0.51970E-03-0.10185E-01
-0.54024E-03-0.10357E-01
-0.58249E-02-0.33824E-01
-0.58264E-03-0.10985E-01
-0.60506E-03-0.11440E-01
-0.62839E-03-0.11890E-01
-0.65262E-03-0.12335E-01
0.0000
0.0000
0.0000
0.0000
0.0000
-0.54868E-02-0.33767E-01
-0.55544E-02-0.33788E-01
-0.56220E-02-0.33804E-01
-0.56896E-02-0.33815E-01
-0.57572E-02-0.33822E-01
MAXIMUM ABSOLUTE VALUES
NODE
0
114
114
VALUE
0.0000
-0.58249E-02-0.33824E-01
The y deflection 5.82 mm compares well with the estimate of 5.84 mm from the Castiliango's
method.
For the beam elements, the option of plotting the von Mises stresses is not available. Instead,
another method of outputting the stresses is needed. The output information is predefined, and is
listed in Table 3.xx in the ANSYS online help (this part of the ANSYS online help is reproduced
in the Appendix at the end of this handout for your convenience). The results are organized as
element table. The relevant data are: the maximum tensile stress on the top of the beam SMAX,
the maximum compressive stress on the bottom of the beam SMIN, force resultant in x-direction
FORX, force resultant in y-direction FORY, and moment resultant MOMZ.
SMAX and SMIN are items 1 and 2 of NMISC in the Sequence Num, and FORX, FORY, and
MOMZ and items 1, 2, and 6 of SMISC in the Sequence Num.
As we are interested in the stresses along CC and around the shoulders, we should find out the
elements that are at these locations. One way is to use grid lines in the working space.
Utility menu: Workplane > WP Settings ...
Check Grid and Triad on
Spacing = 0.01
Minimum = 0
Maximum = 0.4
Utility menu: Workplane > Display working plane
Grid lines with interval of 0.01 appear. Line CC coincides with one grid line.
Beam Tutorial
21
Utility menu: PlotCtrls > Numbering > check the Elem # and Node # on
Plot > Elements
Use PlotCtrols > Pan Zoom Rotates... to zoom in to elements around CC (X=0.01). The element
# on the left side of CC is 5, and the one on the right is 6. (Yours may be different).
CC
Use PlotCtrols > Pan Zoom Rotates... to zoom in to elements around the location of shoulders
(X=0.1). The element # on the left side of the shoulder is 50, and the one on the right is 51.
(Yours may be different).
Shoulders
Now define the wanted data and output them.
Main Menu > General Postproc > Element Table > Define Table
Add...
(scroll down) By sequence num, NMISC, NMISC 1, Apply
By sequence num, NMISC, NMISC 2, Apply
By sequence num, NMISC, NMISC 3, Apply
By sequence num, NMISC, NMISC 4, Apply
By sequence num, SMISC, SMISC 1, Apply
By sequence num, SMISC, SMISC 2, Apply
By sequence num, SMISC, SMISC 6, Apply,
By sequence num, SMISC, SMISC 7, Apply
By sequence num, SMISC, SMISC 8, Apply
By sequence num, SMISC, SMISC 12, Apply,
OK
Close
Main Menu > General Postproc > Element Table > List Elem Table
Beam Tutorial
22
Select NMIS1, NMIS2 (stresses on left side of element - node I), NMIS3, and NMIS4 (stresses
on right side of element - node J). OK
A window will appear and list all data.
STAT
ELEM
1
2
3
4
5
6
7
8
......
47
48
49
50
51
52
53
......
149
150
151
CURRENT
CURRENT
NMIS1
NMIS2
0.18544E+09-0.18544E+09
0.18421E+09-0.18421E+09
0.18298E+09-0.18298E+09
0.18175E+09-0.18175E+09
0.18053E+09-0.18053E+09
0.17930E+09-0.17930E+09
0.17807E+09-0.17807E+09
0.17684E+09-0.17684E+09
CURRENT
CURRENT
NMIS3
NMIS4
0.18421E+09-0.18421E+09
0.18298E+09-0.18298E+09
0.18175E+09-0.18175E+09
0.18053E+09-0.18053E+09
0.17930E+09-0.17930E+09
0.17807E+09-0.17807E+09
0.17684E+09-0.17684E+09
0.17561E+09-0.17561E+09
0.12895E+09-0.12895E+09
0.12772E+09-0.12772E+09
0.12649E+09-0.12649E+09
0.12526E+09-0.12526E+09
0.24221E+09-0.24221E+09
0.23981E+09-0.23981E+09
0.23741E+09-0.23741E+09
0.12772E+09-0.12772E+09
0.12649E+09-0.12649E+09
0.12526E+09-0.12526E+09
0.12404E+09-0.12404E+09
0.23981E+09-0.23981E+09
0.23741E+09-0.23741E+09
0.23501E+09-0.23501E+09
0.71942E+07-0.71942E+07 0.47962E+07-0.47962E+07
0.47962E+07-0.47962E+07 0.23981E+07-0.23981E+07
0.23981E+07-0.23981E+07 0.78518E-03-0.78518E-03
MINIMUM VALUES
ELEM
151
51
151
51
VALUE
0.23981E+07-0.24221E+09 0.78518E-03-0.23981E+09
MAXIMUM VALUES
ELEM
51
151
51
151
VALUE
0.24221E+09-0.23981E+07 0.23981E+09-0.78518E-03
For maximum bending stress at CC, we should take the stresses at node J (right node) of element
5 (179.3 MPa), or stresses at node I (left node) of element 6 (also 179.3 MPa). This agrees well
with the 178.8 MPa from hand calculation.
For maximum bending stress at the shoulder, we found that the stress at node J (right side) of
element 50 are 124.0 MPa, while the stresses at node I (left side) of element 51 are 242.2 MPa.
The discontinuity is caused by the sudden change in cross-sectional area. Even if we take the
larger value, 242.2 MPa, it is just equal to the nominal stress without considering the effects of
concentration. The real maximum stress because of concentration, as revealed in the previous
tutorial (Cantilever Beam using Solid Elements), is 364.2 MPa.
The comparison between the beam elements and the solid elements shows that while the
elements are efficient in simulating beam problems, and give correct results for deflection and
stress distribution in regions of uniform cross section, they fail to capture stress concentration
effects arising from varying cross sections.
Beam Tutorial
23
Main Menu > General Postproc > Element Table > List Elem Table
Select SMIS1, SMIS2, SMIS6 (left side of element), SMIS7, SMIS8, SMIS12 (right side of
element). OK
STAT CURRENT
ELEM SMIS1
1
0.0000
2
0.0000
3
0.0000
4
0.0000
5
0.0000
6
0.0000
7
0.0000
8
0.0000
......
47
0.0000
48
0.0000
49
0.0000
50
0.0000
51
0.0000
52
0.0000
53
0.0000
......
147
0.0000
148
0.0000
149
0.0000
150
0.0000
151
0.0000
0.65484E-10
MINIMUM VALUES
ELEM
1
VALUE
0.0000
MAXIMUM VALUES
ELEM
1
VALUE
0.0000
0.65484E-10
CURRENT
SMIS2
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
CURRENT
SMIS6
-30.200
-30.000
-29.800
-29.600
-29.400
-29.200
-29.000
-28.800
CURRENT
SMIS7
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
CURRENT
SMIS8
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
CURRENT
SMIS12
-30.000
-29.800
-29.600
-29.400
-29.200
-29.000
-28.800
-28.600
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-21.000
-20.800
-20.600
-20.400
-20.200
-20.000
-19.800
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-20.800
-20.600
-20.400
-20.200
-20.000
-19.800
-19.600
-100.00
-100.00
-100.00
-100.00
-100.00
-1.0000
-0.80000
-0.60000
-0.40000
-0.20000
0.0000
0.0000
0.0000
0.0000
0.0000
-100.00
-100.00
-100.00
-100.00
-100.00
-0.80000
-0.60000
-0.40000
-0.20000
45
-100.00
1
-30.200
1
0.0000
45
-100.00
1
-30.000
151
-100.00
151
-0.20000
1
0.0000
151
-100.00
151
From the above list, we can also see that for cantilever beam subjected to transverse force, the
axial force (SMIS1 and SMIS7) is zero, the transverse shear force (SMIS2 and SMIS8) is equal
to the applied force, while the moment (SMIS6 and SMIS12) changes with locations.

List reaction solution.
Main Menu > General Postproc > List Results > Reaction Solu
OK to list all items and close the dialog box. The reaction forces FX and FY of all nodes on the
left edge are listed.
Scroll down and find the total vertical force, FY. The total value of 100 is the opposite of the
total load force.

Exit the ANSYS program.
Beam Tutorial
24
When exiting the ANSYS program, you can save the geometry and loads portions of the
database (default), save geometry, loads, and solution data (one set of results only), save
geometry, loads, solution data, and postprocessing data (i.e., save everything), or save nothing.
You can save nothing here, but you should be sure to use one of the other save options if you
want to keep the ANSYS data files.
Toolbar: Quit.
Choose Quit - No Save!
OK.
Comments about FEM Accuracy
Beam elements are efficient for simulating beam and frame problems. If we only need to find out
the deflection at the right end, a coarser mesh can be used. If the bending moment is changing
with positions and the stress distribution at a location is needed, the elements around the location
should be fine enough.
If details of stress concentration at locations of changing cross section are important, 2D or 3D
solid elements are needed.
3.
Appendix: Online Menu for BEAM3 Element
Utility Menu: Help > Help Topics
ANSYS 6.1 Documentation > ANSYS Element Reference > Element Library > Beam3
Element Description
BEAM3 is a uniaxial element with tension, compression, and bending capabilities. The element
has three degrees of freedom at each node: translations in the nodal x and y directions and
rotation about the nodal z-axis....
Figure 3.1. BEAM3 2-D Elastic Beam
Beam Tutorial
25
Input Data
BEAM3 shows the geometry, node locations, and the coordinate system for this element. The
element is defined by two nodes, the cross-sectional area, the area moment of inertia, the height,
and the material properties...
Node and Element Loads describes element loads. You can specify pressures as surface loads on
the element faces, shown by the circled numbers in BEAM3 figure. Positive normal pressures act
into the element. You specify lateral pressures as a force per unit length. End "pressures" are
input as a force...
Input Summary summarizes the element input. Element Input contains a general description of
element input.
BEAM3 Input Summary
Element Name
BEAM3
Nodes
I, J
Degrees of Freedom
UX, UY, ROTZ
Real Constants
AREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS
Material Properties
EX, ALPX, DENS, GXY, DAMP
Surface Loads
Pressure -face 1 (I-J) (-Y normal direction),
face 2 (I-J) (+X tangential direction),
face 3 (I) (+X axial direction),
face 4 (J) (-X axial direction)
(use a negative value for loading in the opposite direction)
......
Output Data
The solution output associated with the element is in two forms:

nodal displacements included in the overall nodal solution

additional element output as shown in BEAM3 Element Output Definitions.
Figure 3.2. BEAM3 Stress Output
Beam Tutorial
26
The Element Output Definitions table uses the following notation:
The O column indicates the availability of the items in the file Jobname.OUT. The R column
indicates the availability of the items in the results file. In either the O or R columns, Y indicates
that the item is always available, a number refers to a table footnote that describes when the item
is conditionally available, and a - indicates that the item is not available.
Table 3.1. BEAM3 Element Output Definitions
Name
Definition
EL
Element Number
NODES
Element nodes - I, J
O
Y
Y
R
Y
Y
MAT
Element material number
Y
Y
VOLU:
XC, YC
TEMP
Element volume
Location where results are reported
Temperatures T1, T2, T3, T4
Pressure P1 at nodes I,J; OFFST1 at I,J;P2 at I,J; OFFST2 at I, J; P3
at I; P4 at J
Axial direct stress
Bending stress on the element +Y side of the beam
Bending stress on the element -Y side of the beam
Maximum stress (direct stress + bending stress)
Minimum stress (direct stress - bending stress)
Axial elastic strain at the end
Bending elastic strain on the element +Y side of the beam
Bending elastic strain on the element -Y side of the beam
Axial thermal strain at the end
Bending thermal strain on the element +Y side of the beam
Bending thermal strain on the element -Y side of the beam
Initial axial strain in the element
Member forces in the element coordinate system X and Y direction
N
Y
Y
Y
3
Y
Y
Y
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
Y
PRES
SDIR
SBYT
SBYB
SMAX
SMIN
EPELDIR
EPELBYT
EPELBYB
EPTHDIR
EPTHBYT
EPTHBYB
EPINAXL
MFOR(X, Y)
Beam Tutorial
Name
MMOMZ
27
Definition
Member moment in the element coordinate system Z direction
O
2
R
Y
1. The item repeats for end I, intermediate locations (see KEYOPT(9)), and end J.
2. If KEYOPT(6) = 1.
3. Available only at centroid as a *GET item.
The following tables list output available through the ETABLE command using the Sequence
Number method...
Table 3.2. BEAM3 (KEYOPT(9) = 0) Item and Sequence Numbers for the ETABLE and
ESOL Commands
KEYOPT(9) = 0
Name
Item
E
I
J
SDIR
LS
- 1
4
SBYT
LS
- 2
5
SBYB
LS
- 3
6
EPELDIR LEPEL - 1
4
EPELBYT LEPEL - 2
5
EPELBYB LEPEL - 3
6
EPTHDIR LEPTH - 1
4
EPTHBYT LEPTH - 2
5
EPTHBYB LEPTH - 3
6
EPINAXL LEPTH 7
SMAX
NMISC - 1
3
SMIN
NMISC - 2
4
MFORX SMISC - 1
7
MFORY SMISC - 2
8
MMOMZ SMISC - 6
12
P1
SMISC - 13 14
OFFST1 SMISC - 15 16
P2
SMISC - 17 18
OFFST2 SMISC - 19 20
P3
SMISC - 21
P4
SMISC - 22
......
Beam Tutorial
28
Assumptions and Restrictions
The beam element can have any cross-sectional shape for which the moment of inertia can be
computed. However, the stresses are determined as if the distance from the neutral axis to the
extreme fiber is one-half of the height. The element height is used only in the bending and
thermal stress calculations. The applied thermal gradient is assumed linear across the height and
along the length. The beam element must lie in an X-Y plane and must not have a zero length or
area. The moment of inertia may be zero if large deflections are not used.