MET 210W
Page
1
of
13
Handout
–
ANSYS Examples
ANSYS is a software tool used by engineers to perform variety of analysis on mechanical parts and systems.
The focus of this handout is using ANSYS to determine reactions, stresses and deflections in beams and
frames.
ANSYS uses the finite

element meth
od to determine the reactions on a structure as well as the stress and
deflections at various points on the structure. The basic component of a finite

element model is the
element
.
Graphically, beam elements appear as a line, but to the software, an elem
ent is a series of equations that
predict how the
ends of the
element will
deform
when loaded.
For each two

dimensional beam element, six
equations are needed to determine the rotation and translations of each node. Nodal translations are
defined
paralle
l and perpendicular to the element.
Elements connect with each other at
nodes
.
The
response of an element to an applied load affects
each of
the elements connected to it at nodes.
A model
will have three equations for each node in the model. The deform
ations at each node are found by
ANSYS
using matrix math to solve all of the equations for the model simultaneously.
The basic procedure for solving a beam problem using ANSYS is as follows:
1.
Start the ANSYS program.
2.
Specify the el
ement type to be used
. In ANSYS, the 2D beam element is designated as
BEAM3
.
3.
Specify the
real constants
for the element: area (in
2
), height (in) and moment of inertia (in
4
).
The
area cannot be zero. The height is used to find bending stress. In ANSYS
, the distance c is always
taken as half of the height. Be aware of this when working with sections which are not symmetrical.
4.
Indicate the
material properties
: modulus of elasticity (psi) and Poisson’s ratio.
5.
Create nodes. A node is needed at each load
and support as well as at any point of importance in
the structure, which
is
any point where the stress or deflection is
to be found.
Each node will have a
unique number. Nodes are located by Cartesian coordinates
determined by the user
. The length
uni
ts used MUST be consistent with those used to define the real constants and material properties.
6.
Create elements between nodes. Each element will have a unique number. Elements are defined
by selecting a node for each
of its
end.
Elements cannot have ze
ro length.
7.
Apply support constraints to nodes. Translation can be constrained parallel and perpendicular to the
element to create pins and rollers. Rotation can also be constrained at a node
when
creat
ing
a fixed
support.
8.
Apply concentrated loads and m
oments to the model at nodes. Loads are typically applied
horizontally or vertically.
All units must be compatible with other units used in the model.
Distributed
loads can be applied as pressures to the elements. Warning: the value specified for press
ure is
applied per unit length of the element. If an element is 12 inches long, a distributed load of 100
lbs/foot would be applied as 100/12 = 8.3333 lbs/inch.
9.
Solve.
10.
Retrieve the reactions.
11.
Retrieve
the
deflection results at each node.
12.
Retrieve the stre
ss and internal reaction results at each node as needed.
13.
Verify solutions using hand calculations remembering that the necessary conditions for equilibrium
are
Fx = 0,
Fy = 0,
M = 0. Also
recall
that
bending stress is
t
he predominate stress in a beam.
Bending stress is determined by
= Mc/I.
EXAMPLE
:
A rectangular beam, 2

inches wide and 6

inches deep is shown in the figure below.
Determine
the magnitude and direction of the reactions
and
the deflection and
bending
stress at the midpoint of the
bea
m.
Use
E = 1,500,000 psi and
0.24 for
Poisson’s ratio
.
Beam element
j Node
i Node
Length
2D Beam elemen
t
3 feet
3 feet
4 feet
200 lbs
50 lbs/ft
6 in
2 in
MET 210W
Page
2
of
13
Handout
–
ANSYS Examples
1.
Start ANSYS using the sequence:
Start Button > Programs > Engineering Programs > Ansys
11.0 > Ansys
2.
Select the following from the Main Menu to specify the eleme
nt type:
Preprocessor > Element Type
> Add/Edit/Delete
Pick the
Add…
button
Specify
Beam
and
2D elastic 3
Pick
OK
to close the
Library of Element Types
.
Pick
Close
to
shut the
Element Types
dialog box.
BEAM3 is now element
type 1.
This portion of the screen
will appear black
Main Menu
Toolbar Menu
Coordinate Triad
Zoom Controls
MET 210W
Page
3
of
13
Handout
–
ANSYS Examples
3.
Ad
d the real constants to the model using
Preprocessor
>
Real Constants
> Add/Edit/Delete
Pick the
Add…
button. Type 1 BEAM3 should be listed in the new
dialog box.
Make sure Type 1 BEAM 3 is selected and
pick OK to open the Real Constant for
BEAM3 dial
og box. Specify area, area
moment of inertia and total beam height as
shown below.
Pick
OK
, then
Close
.
4.
Add the material properties to the model using
Preprocessor
>
Material Props
>
Material Models
Double

Click
each one:
Structura
l > Linear >
Elastic > Isotropic
for
Material Model Number 1.
Specify EX = 1500000 psi
and Poisson’s Ratio
(PRXY) as .24.
Pick
OK
to close the dialog box.
Select
Material > Exit
to close the Define Material Model
Behavior dialog box.
4
3
3
2
in
36
12
)
in
6
)(
in
2
(
12
h
*
b
I
in
12
)
in
6
)(
in
2
(
h
*
b
A
MET 210W
Page
4
of
13
Handout
–
ANSYS Examples
Plan
ning ahead, five nodes will be needed as shown in the figure below.
At nodes 1 and 5, a support will be
built. At node 2, a load will be applied. At node 3, results are required. The element between nodes 4 and 5
will have a distributed load.
5.
Create nodes using the sequence
Preprocessor >
Modeling > Create > Nodes > In
Active
CS
Specify node number and X, Y, Z
coordinates in the active
coordinate system which is a
Cartesian coordinate system by
default. If the node number is left
blank,
ANSYS automatically
assigns the next number. Pick
Apply
to
set
the
node and
reopen
the dialog box
for the next node
.
Repeat for remaining nodes
.
P
ick
OK
to set the last
node and
clos
e
the dialog box.
The screen should contain 5 numbered nodes.
To plot n
odes, select from the toolbar menu:
Plot > Nodes
.
To generate a list of nodes, select from the toolbar menu:
List > Nodes…
Select the
Coord.
w/Angles
button, then
OK
. The nodes and their coordinates are listed in another window. This list
can be saved
or copied and pasted in another program such as Word or Excel.
Planning ahead, four elements will be needed:
6.
Create elements using the sequence
Preprocessor > Modeling > Create >
Element
s >
Auto
Numbered > Thru Nodes
Pick node 1 on t
he screen, then node 2, then pick
Apply
.
Order is important.
Choose
the
i

node
,
then the j

node
–
be consistent left to right
.
Pick node 2, then node 3, then pick
Apply
.
Pick node 3, then node 4, then pick
Apply
.
Pick node 4, then node 5, then pick
OK
.
This creates the last element and closes
the dialog box.
Four elements should appear on the screen at this point.
To plot elements, select from the toolbar menu:
Plot >
Elements
To generate a list of elements, select from the toolbar menu:
List >
Eleme
nts >
Nodes + Attributes.
The elements are listed in another window
by element
number. The list contains the material number, element type number, real
constant numbers, nodes and other information for each element.
This list can
be saved or copied and
pasted in another program such as Word or Excel.
Node 1
(0, 0, 0)
Node 3
(60, 0, 0)
Node 2
(36, 0, 0)
Node 4
(72, 0, 0)
Node 5
(120, 0, 0)
36 in
60 in
72 in
120 in
Node 1
Node 3
Node 2
Node 4
Node 5
Element 1
Element 2
Element 3
Element 4
MET 210W
Page
5
of
13
Handout
–
ANSYS Examples
To display node and element numbers, select from the toolbar menu:
PlotCtrls > Numbering
…
Planning ahead, three support
constraint
s have to be created. A pin is at node 1 which will c
onstrain
translation in both the x

and y

directions. A roller at node 5 will constrain translation in the y

direction.
7.
Create constraints (supports) using the
m
ain
m
enu sequence
Solution
>
Define Loads
>
Apply
>
Structural
>
Displacement
>
On
Nod
es
On the screen, select nodes 1 and 5 and pick
OK
on the dialog box.
Pick
UY
in the
DOFs to be constrained window
, then
OK
to apply the supports.
These nodes are constrained vertically. UY is ANSYS for displacement in the
y

direction. Since the displ
acement value was applied as zero (empty window
in dialog box) the node will not move vertically.
Repeat this process by selecting node 1 and applying the UX constraint to it.
Blue triangles should
appear for each constraint applied to th
e model.
Note that if a fixed support is needed, its node would have UX, UY, and ROTZ all applied.
Node numbers on and off
The displayed numbers for
each element can be set to
show an
y of these:
乯畭扥ri湧
El敭敮琠t畭扥r
䵡瑥ti慬m扥r
El敭敮琠ty灥m扥r
剥慬潮s瑡t琠t畭扥r
潴o敲e
乯摥1
乯摥5
A乓YS潮s瑲慩湴nsymb潬
䍯湳瑲慩湳⁴牡湳l慴a潮i渠

摩r散瑩潮⁴桥湯d攮
䍯湳瑲慩湳⁴牡湳l慴a潮i渠
y

摩r散ti潮⁴桥湯d攮
䍯湳瑲慩湳潴oti潮
慢潵t
瑨攠z

慸is⁴桥
湯摥.
MET 210W
Page
6
of
13
Handout
–
ANSYS Examples
8.
Create the concentrated
load
using the Main Menu sequence
Solution
>
Define Loads
>
Apply
>
Structural
>
Force/Moment > On Nodes.
Pick node 2 on the screen
and pick
OK
on the dialog box.
Set the direction of the force to
FY
and specify the value of the force as

200
which will represent 200
pounds down at node 2. Pick
OK
.
A red arrow should appear on the model to represent this force.
Cre
ate the distributed load using the main menu sequence
Solution
>
Define Loads
>
Apply
>
Structural
>
Pressure > On Beams.
Pick
element
4
on the screen and pick
OK
on the dialog box.
At this point, the model should look like this:
FX = horizontal force
FY = vertical force
MZ = moment
Value of the force or moment.
+ is for right or up or CCW.
–
=
is=
f潲敦琠tr=w渠潲⁃t⸠
=
p灥cify=瑨t=灲敳s畲攠u渠n扳⽩渮n⁔桩ss=
摥瑥牭i湥搠ds
=
=
in
/
lbs
1667
.
4
ft
/
in
12
ft
/
lbs
50
essure
Pr
=
=
mick=
OK
to apply load and close the
dialog box.
Note: positive values
are down,
towards the element and negative
values are up, away from the element.
MET 210W
Page
7
of
13
Handout
–
ANSYS Examples
9.
To solve the model, use the following main menu sequence:
Solution > Solve > Current LS
. Pick
OK
from the information box that appears. Pick the
Close
button when ANSYS indicates that the
solution is done. It should take less than a minut
e to solve simple beam and frame problems.
10.
To obtain beam reactions, use the following main menu sequence:
General Postproc > List
Results > Reaction Solu
.
Pick
All Items
in the window and pick
OK
.
11.
Get the deflections
of each node
using the main menu sequence:
General Postproc > List Results
>
Nodal
Solu
.
To plot the deformed shape of the beam, use the main menu sequence:
General Postproc >
Plot
Results > Deformed Shape
At node 1, the horizontal reaction is 0, the
vertical reaction is 180 pounds up
(+) and
there is no moment reaction at a pin.
These numbers match with the statics for
this problem.
At node 5, t
here is no horizontal reaction, the vertical
reaction is 220 pounds up (+) and there is no moment
reaction at a roller. These numbers match with the
statics for this problem.
Sum of the vertical reactions
Pick
DOF Solution
in the window, then
Y

Component of displacement
, and
pick
OK
. (The X

Component of
displacement option gives the horizontal
deflection of each node and the Z

Componen
t of rotation gives the rotation
of each node.)
Vertical displacement of each node. Negative is down and
positive is up. Note they are zero at the supports as
expected. The maximum value from this model is at node
3. Note that the actual maximum value
will only appear if a
node exists at the point of maximum deflection.
MET 210W
Page
8
of
13
Handout
–
ANSYS Examples
12.
An Element Table has to be cr
eated to obtain the stress values
and internal reactions
at the nodes.
Use the main menu sequence:
General Postproc >
Element Table > Define Table.
Pick the
Add
…
button.
Quantity at
i

Node
Suggested Label
Sequence
Sequen
ce
Number
i

node
j

node
Bending Stress
BENDSTR
NMISC
1
3
Bending Moment, M
MMOMZ
SMISC
6
12
Shear Force, V
MFORY
SMISC
2
8
Axial Force, F
MFORX
SMISC
1
7
To list the values in the element table use the main menu sequence
General Postproc >
Eleme
nt
Table > List Elem Table
4 quantities will be added to the
table. For each one, a five step
process is needed as shown in the
figure below. A label is specified,
By sequence num
is selected,
the
sequence
is
chosen and the
number
is specified. Pick
Apply
to add the quantity to the table.
Pick
OK
after the last one.
a.
Add label name
b.
Pick By sequence num
c.
Select sequence
SMISC or NMISC.
d.
Add sequence number
e.
Apply or OK
Select the table items to be
lis
ted. Pick
OK
MET 210W
Page
9
of
13
Handout
–
ANSYS Examples
NOTE: These values are for the
i

node of each of the elements
listed.
Elem 3
Element 1 i

node
Element 1 i

node
Element 3 i

node
Element 1 j

node
Element 2 i

node
Element 4 i

node
Elem 1
Elem 2
Elem 4
Element 4 j

node
50 lbs/ft (4
ft) = 200#
220#
MFORY = 20#
MFORX = 0#
MMOMZ = 6000 in

lbs
psi
500
in
36
)
in
3
(
lbs
in
6000
I
Mc
4
50 lbs/ft (4 ft) = 200#
220#
MFORY = 20#
MFORX = 0#
MMOMZ = 5760 in

lbs
psi
480
in
36
)
in
3
(
lbs
in
5760
I
Mc
4
50 lbs/ft (4 ft) = 200#
220#
MFORY = 20#
MFORX = 0#
MMOMZ = 6480 in

lbs
psi
540
in
36
)
in
3
(
lbs
in
6480
I
Mc
4
13. Verify that each of the free

body diagrams is in equilibrium.
N2
N3
N4
MET 210W
Page
10
of
13
Handout
–
ANSYS Examples
If a model has more nodes, say one per foot, the MMOMZ values could be copied to Excel to create an
XY(Scatter) chart which would be the moment diag
ram for the beam.
Of course, the moment for the last node
would have to be added manually.
It should be noted that each of the options used to add items to the model has a delete option which is used
to remove the items from the model. Hunt around as nee
ded to use these options. If nodes and elements
are deleted from the model, their numbers are automatically reused when new ones are created. Be sure to
use the
PlotCtrl > Numbering
to check the numbers used in the model. The numbers can be compressed
b
y using the menu sequence
Preprocessing > Numbering Ctrls > Compress Numbers
.
For example, if
the following are all nodes that are created in a model:
Compressing the node numbers does this:
If you wish to save the ANSYS model, use the
File > Sa
ve As
option. Specify a location and filename.
EXAMPLE: Determine the reactions at the supports and internal pin of the frame shown below.
Use E =
29000000 psi,
= .3, A = 1 in
2
, height = 1, and moment of inertia = 1 in
4
.
The ANSYS solution for this problem is pretty much the same as it was for the beam. The frame has an
additional step.
1.
Start ANSYS.
2.
Specify the element type as BEAM3
3.
Spec
ify the real constants: area = 1, moment of inertia = 1, and height = 1. The stress isn’t going to
be determined in this solution, so these numbers aren’t really that important
but they can’t be zero
.
4.
Specify the material properties: EX = 29000000,
PR
XY
= .3
5.
Create the nodes indicated in the table above. Note that two nodes are needed at each internal pin
–
point B in this case.
1
3
5
6
7
1
2
3
4
5
2 ft
6 ft
B
A
C
300 lbs
3 ft
3 ft
400 lbs
Node
X

coordinate
Y

coordinate
Z

coordinate
1
0
0
0
2
0
72
0
3
0
96
0
4
0
96
0
5
36
48
0
6
72
0
0
Note: we need two nodes at an internal pin!
MET 210W
Page
11
of
13
Handout
–
ANSYS Examples
6.
Create the elements for this model as follows:
Element Number
i

node
j

node
1
1
2
2
2
3
3
4
5
4
5
6
Note that each
member of the frame is constructed with two elements. The members are not
connected at this point.
Before the model can be solved, the translational degrees of freedom for
nodes 3 and 4 have to be “coupled”. Use the main menu sequence
Preprocessor > Cou
pling/Ceqn
> Couple DOFs
to begin the coupling process. Select the two nodes to be coupled. Use the box
option in the select dialog box. Pick
OK
when selected.
Specify
1
for the reference number.
Pick DOF Label
UX
Pick
Apply
Specify
2
for the refe
rence number.
Pick DOF label
UY
Pick
OK
to apply and close the dialog box.
Two green triangles should appear at the
internal pin indicating that the two degrees of
freedom have been coupled.
7.
Create the pins at A and C. Use UX and UY at both nodes 1 and
6.
8.
Apply the concentrated loads. At node 2, FX = 300 and at node
5, FY =

400.
9.
Solve
ANSYS Model of the Frame
MET 210W
Page
12
of
13
Handout
–
ANSYS Examples
10.
List the reaction solutions:
To get the forces on all the nodes, use the main menu sequence
General Postproc > List Results >
Element Solution
.
Scroll down and click on
Structural Forces
, then select
X

Component of force
.
Pick
OK
.
The values in this list are the
element
forces acting ON the node.
Show these forces in the
opposite directions on the element.
To get the moments on all the nodes, use the main menu sequence
General Postproc > List
Results >
Element Solution
. Scroll down and click on
Structural
Moments
, then select
Z

Component of
moment
. Pick
OK
. The values in this list are the e
lement moments acting ON the
node. Show these moments in the opposite directions on the element.
If you are not sure of the proper directions, figure it out remembering that the
element must be in
equilibrium, which is to say
Fx = 0,
Fy = 0, and
M = 0.
E1
2
1
100#
75#
75#
100#
5400 in
∙
lbs
Note:
This is a really small
number:

0.19398 x 10

11
MET 210W
Page
13
of
13
Handout
–
ANSYS Examples
An element table can also be created to determine the moment, shear and axial forces at each node.
In this case, the shear and axial forces are perpendicular and parallel to the element respectively.
This may be the easier approach!
11.
The deflections are not required.
12.
The
stress
es
and
internal reactions
are not required
.
The following are the proper free

body diagrams for each of the nodes and elements in the model. The
values are taken from the reaction solution and from the member
force and moments lists shown on the
previous page.
Notice that nodes 3 and 4 are attached to one another, so collectively, they are in equilibrium.
N1
2
2
3
N6
5
5
4
75#
100#
225#
500#
1
75#
100#
E1
N2
75#
100#
300#
100#
E2
225#
225#
100#
75#
100#
75#
100#
5400 in
∙
lb
5400 in
∙
lb
5400 in
∙
lb
5400 in
∙
lb
100#
225
#
N3
22
5#
100#
N4
225#
100#
E3
E4
6
100#
225
#
225#
100#
72
00 in
∙
lb
4
00#
7200 in
∙
lb
7200 in
∙
lb
225#
500
#
100#
225#
N5
225#
500#
7200 in
∙
lb
225#
500#
225#
500#
FB
D of Frame Nodes and Elements
剥R
f潲o敳牥灬ied
Blue
f潲o敳牥敡c瑩潮s
Bl慣k潲o敳牥敭敮琠t潲o敳
慣瑩湧⁏丠湯摥s
Gr敥n
f潲o敳牥em扥r景牣敳
i渠nir散瑩潮s灰潳i瑥tt桥
瑡tul慴敤val略s.
Enter the password to open this PDF file:
File name:

File size:

Title:

Author:

Subject:

Keywords:

Creation Date:

Modification Date:

Creator:

PDF Producer:

PDF Version:

Page Count:

Preparing document for printing…
0%
Σχόλια 0
Συνδεθείτε για να κοινοποιήσετε σχόλιο