Lever Arm
Problem:
A force of 410 lb is applied at the end of a 15-in lever arm as shown in the diagram.
Determine the Von Mises stress for a stress element on the upper surface of the 1-in
section at the location A.
Joseph Shigley and Charles Mischke. Mechanical Engineering Design
5th ed. New York: McGraw Hill, May 2002.
Lever Arm
Overview
Anticipated time to complete this tutorial: 1 hour
Tutorial Overview
This tutorial is divided into six parts:
1) Tutorial Basics
2) Problem Planning
3) Preprocessing
4) Solution
5) Post-Processing
6) Hand Calculations
Audience
This tutorial assumes an intermediate knowledge of ANSYS 8.0; therefore, it goes into
moderate detail to explain each step. A problem planning section has been added to help
set up the problem. More advanced ANSYS 8.0 users should be able to complete this
tutorial fairly quickly.
Prerequisites
1) ANSYS 8.0 in house “Structural Tutorial”
2) Completion of three or more Basic Machine Design Tutorials
Objectives
1) Create and mesh a solid model
2) Apply appropriate solid model constraints and loads
3) Solve model and analyze nodal solution
Outcomes
1) Learn how to set up the problem before starting Ansys
2) Increase familiarity with the graphical user interface (GUI)
3) Learn how to create and mesh more complex geometries
4) Increase familiarity with post processing tools
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Lever Arm
Tutorial Basics
In this tutorial:
Instructions appear on the left.
Visual aids corresponding to the text
appear on the right.
All commands on the toolbars are
labeled.
However, only operations
applicable to the tutorial are explained.
The instructions should be used as follows:
Bold >
Text in bold are buttons,
options, or selections that the
user needs to click on
Example:
> Preprocessor > Element
Type > Add/Edit/DeleteFile
would mean to follow the
options as shown to the right
to get you to the Element
Types window
Italics
Text in italics are hints and
notes
MB1
MB2
Click on the left mouse button
Click on the middle mouse
button
Click on the right mouse
button
MB3
Some basic ANSYS functions are:
To rotate the models use Ctrl and MB3.
To zoom use Ctrl and MB2 and move the
mouse up and down.
To translate the models use Ctrl and MB1.
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Lever Arm
Problem Planning
1) Obtain all necessary known information.
3) Contemplate an appropriate element
for the mesh.
Basic Dimensions of Members:
Diameters of Bars:
Radius of Fillet:
Magnitude of the Force:
E for steel:
Poisson’s Ratio:
Since you are creating a solid model
from a volume, use an element listed
under the Solid category (possibly use
Solid187).
4) Identify which results will be analyzed.
2) Plan a simple, representative geometry.
The problem asks you to identify the
Von Mises stresses on a stress element
located at the point A. The location A is
located on the top of the 1 in section of
tube near the fillet.
The geometry for the lever arm could be
built in several ways. Consider some of
the possible ways that this could be done.
ANSYS has the ability to build a part in
sections and then add all of the sections
together to make a single part. This may
make building some types of geometries
an easier task.
The problem says that there is a fillet near
the section labeled A in the diagram.
Before starting the problem, look through
the ANSYS help files to see how fillets can
be made.
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Lever Arm
Preprocessing
1) Change the working directory, jobname,
and title of your project.
2) Set Preferences to Structural.
3) Add a Solid187 element.
4) Create a Material Model.
E: 30e6
PRXY: .3
5) Create the following keypoints:
KP1:
KP2:
KP3:
KP4:
KP5:
KP6:
KP7:
KP8:
(0,0,0)
(0,0.75,0)
(2,0.75,0)
(2,0.5,0)
(14,0.5,0)
(14,0.75,0)
(18,0.75,0)
(18,0,0)
6) Create straight lines between the
following keypoints:
KP1 & KP2
KP2 & KP3
KP3 & KP4
KP4 & KP5
KP5 & KP6
KP6 & KP7
KP7 & KP8
KP8 & KP1
7) Create a line fillet
> Preprocessor > Modeling
> Create > Lines > Line Fillet
For the first line fillet select the line created
between KP3 and KP4, for the second line
select the line created between KP4 and
KP5. After selecting both lines, click apply
in the Line Fillet window. Enter a fillet
radius of .125 and click apply.
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Lever Arm
Preprocessing
8) Create another line fillet between the line
created between KP4 and KP5 and the line
created between KP5 and KP6. Again use a
fillet radius of .125.
9) Create an area out of all the lines created.
> Preprocessor > Modeling
> Create > Areas > Arbitrary
> By lines
Define the area by selecting all of the lines
created.
10) Revolve the area around an axis to create
a volume.
> Preprocessor > Modeling
> Operate > Extrude > Areas
> About Axis
First select the area just created and click ok.
Now define the axis for the revolution by
selecting KP1 and KP8. Click OK to select
these points, then click OK to sweep the area
360 degrees.
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Lever Arm
Preprocessor
11) Create the end part of the arm using the
solid cylinder command.
> Preprocessor > Modeling
> Create > Volumes > Cylinder
> Solid Cylinder
Create the end of the arm in two parts.
Part 1
WP X:
16
WP Y:
0
Radius:
.25
Depth:
15
Part 2
WP X:
WP Y:
Radius:
Depth:
16
0
.25
-3
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Lever Arm
Preprocessor
12) Add all the volumes together.
> Preprocessor > Modeling
> Operate > Booleans > Add
> Volumes
Select Pick All to add all the volumes
together.
13) Mesh the volumes.
> Preprocessor > Meshing
> Mesh Tool
Turn on smart size at the top of the menu.
Set the smart size density to 6 (i.e. move the
slider between fine and course until it is set
at 6). Then set the parameters to Volume
and Free and select Mesh. Finally, select
Pick All in the Mesh Volumes window.
14) Refine the mesh at the section labeled A.
If it is closed, reopen the Mesh Tool.
Select to refine at lines.
Select refine.
Select the line on top of the lever
arm near the point A as shown
to the right.
Select to refine the line one
level.
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Lever Arm
Solution
15) Apply constraints to the left end of the
level arm.
> Solution > Define Loads > Apply
> Structural > Displacement
> On Areas
Pick the area that is at the left end of the
lever arm. Apply All DOF constraints to the
area.
16) Apply the Y component of the force at
the other end of the lever arm at the point
shown in the diagram on the first page.
FY: -410
17) Solve the model. The problem should
take several minutes to solve, depending on
the speed of your computer.
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Lever Arm
Post Processing
18) Plot the nodal Von Mises stresses.
> General Postprocessor
> Results Viewer
Then select:
> Nodal Solution > Stress
> Von Mises Stress
Finally plot the contour.
19) Zoom in on section A on the lever arm
and query the stresses there to find the Von
Mises stress at that location.
You should see a range of
stress values at the section
A, one of which will probably be near 79,000
(depending on the density
of your mesh). For this
mesh a value of 79,321
kpsi was found. This is
close to the analytical
solution with an error of
only 0.6%.
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Lever Arm
Hand Calculations
32 M 32(14)( 410)
=
= 58500 psi
πd 3
π (1)3
16T 16(15)( 410)
= 3 =
= 31300 psi
πd
π (1)3
σx =
τ xy
2
⎤
58.5kpsi ⎡⎛ 58.5kpsi ⎞
2
σ 1 ,σ 2 =
± ⎢⎜
⎟ + (31.3kpsi ) ⎥
2
2
⎠
⎢⎣⎝
⎥⎦
σ 1 = 72.1kpsi
(1 / 2 )
σ 2 = −13.6kpsi
σ i = (σ 1 − σ 1σ 2 + σ 2 )(1/ 2 ) = (72.12 − 72.1(−13.6) + (−13.6) 2 ) (1/ 2 ) = 79.8kpsi
2
2
The Von Mises stress is about 79.8 kpsi.
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