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Bridge Structure: FEA using Beam
Elements
Introduction
Structures containing long, constant
cross-section beams can be modeled efficiently in Pro/MECHANICA by using
beam elements rather than solid elements. In this tutorial, you will
learn how to construct and analyze beam structures.
Creating the Nodes
- Start Pro/E Wildfire.
- Select [File] -> [New], type the part name [Bridge] in
text box, and click the OK Button.
- You will begin by defining the nodes of
the structure. Select the Sketched Datum Point icon from the tool bar
at the right of the screen, as shown in Figure 1.1.
[Figure
1.1]
- Select the reference plane marked as
FRONT.
-
Click the Sketch button from the Sketched
Datum Point window. Pro/E will switch to Sketch Mode.
- Select [Sketch] -> [Options] from menu
bar. Turn ON the [Grid] and [Snap To Grid] in the Sketcher Preferences
window and click the green check button.
-
Select the Create Points icon
, and
click on the 8 points circled in red in Figure 1.2 to define these as nodes.
You will should draw them in the order shown so that your points are labeled
consistently with the ones shown in the figures of this tutorial. You
may need to pan and zoom to get the correct view. -
Make sure the dimensions of the points are the
same as those shown in gray the figure. If not, click on the Select
Icon
and
change the incorrect dimension by double clicking on it and typing the
correct value.
[Figure 1.2]
- Select the Continue icon
from the
tool bar at the right of the screen to exit Sketch Mode. You should
see the points as shown in Figure 1.3.
[Figure 1.3]
- Select [Edit] -> [Feature Operations]
from the menu bar.
-
Select [Copy] -> [Move] from the Menu Manager,
and then select [Done].
-
Click on one of the points you just created,
which will select them all, and select [Done] from the Menu Manager.
-
Select [Translate] and then [Csys], and click
on the coordinate system in the model window.
-
Select [Z Axis] and then [Okay].
-
Enter an offset distance of 90 in the text box
at the bottom of the screen, and click the check button.
-
Select [Done Move] and then [Done] from the Menu Manager.
- Select the OK button from the Group
Elements window, and select [Done] from the Menu Manager. You
should see a second set of points as shown in Figure 1.4.
[Figure
1.4]
Creating Beam Elements
- Select [Applications] -> [Mechanica] from the menu bar. A window will be
displayed containing the unit information for the assembly. Note the
units displayed, as all analyses you will perform will not show units,
and click the
Continue button on this window.
-
Make sure the FEM Mode button is unchecked on the Menu Manager. If you
cannot uncheck it, you will need to
modify the installation of
Pro/E.
- Select [Structure] ->
[Idealizations] -> [Beams] -> [New] from the Menu Manager.
-
In the Beam Definition window, click the arrow
button under References so that you can select the two points defining the
start and end of the first beam.
-
Select the points labeled Pnt0 and Pnt5 in Figure 1.4 (the labels for your
points may be different than the ones shown in the figure, depending on the
order in which you drew the points).
-
Now you will define the material of the beam.
Select the More button next to Material.
- Select [Steel] from the Materials in
Library list, and click the Assign Material icon
.
Click the OK button. - Now you will
define the beam orientation (for more information on beam orientations, see
the Pro/E help files). Leave Y Direction set to WCS (world coordinate
system), and set X to 0, Y to 1, and Z to 0.
-
Now you will define the cross-section of the
beam. Select the More button next to Section.
-
Select the New button from the Beam Sections
window. Change the name to [main_supports].
- Change the type to [Hollow Circle], and
set the outer radius to 2 inches and the inner radius to 1.5 inches, as
shown in Figure 1.5.
[Figure 1.5]
- Click the OK button from the Beam
Section Definition window and the Beam Sections window. The Beam
Definition window should look like the one shown in Figure 1.6.
[Figure 1.6]
- Click OK to close this window.
You should now see the beam shown in blue in Figure 1.7.
[Figure 1.7]
- Select [New] again from the Beam menu of
the Menu Manager.
- In the Beam
Definition window, click the arrow button under References. Select the
points labeled Pnt5 and Pnt6 in Figure 1.7.
-
Make sure the material is set to STEEL and the
section is set to main_supports. Set the Y direction vector (X, Y, Z)
to (0, 1, 0) as you did for the first beam.
-
Click the OK button to create the beam.
-
Repeat steps 14 - 17 to create the main
supports of the bridge, as shown in Figure 1.8. To make the process
easier, you can change Reference in the Beam Definition window to [Point
Point Pair] and select the endpoints of all the beams at once. To do
this, hold down the Control key and select the start and then the end of
each beam segment.
[Figure 1.8]
- Now you will define the cross-beams of
the bridge. These beams will have a different cross section than the
main supports of the bridge. Select [New] from the Beam menu again.
-
Select the More button next to Section, and
select the New button from the Beam Sections window.
-
Call the new section [cross_beams], and change
the type to [Hollow Circle]. Set the outer radius to 1.25 inches and
the inner radius to 1.00 inches.
-
Click the OK button from the Beam Section Definition window and the Beam
Sections window.
- Using this cross
section instead of the one for the main supports, add the beams shown in
Figure 1.9. Use a Y Direction vector of (0, 0, 1).
[Figure 1.9]
- Add the beams shown in Figure 1.10.
The cross section of these beams should be cross_beams and the Y Direction
vector should be set to (0, 1, 0). Figures 1.11 and 1.12 show the top
and front views of what the final bridge should look like.
[Figure 1.10]
[Figure 1.11]
[Figure 1.12]
Performing a Finite Element Analysis
- You will first constrain the ends of the
bridge so that they cannot move. Select [Done/Return] from the
Idealizations menu, and then select [Constraints] -> [New] -> [Point].
-
Click the arrow button under Point(s).
Hold down the Control key and select the four endpoints, labeled as Pnt 0,
Pnt 8, Pnt 4, and Pnt 12 in the figures above. Click OK from the
Select window.
- Click the
appropriate icon to set the Z Rotation to free, and leave all the other
rotations and translations as fixed, as shown in Figure 1.13. This
will define a pin joint at the points.
[Figure
1.13]
- Select the OK button from the
Constraint window. You should see the constraints as shown in
Figure 1.14.
[Figure
1.14]
-
Now you will apply loads
to the bridge. Select [Done/Return] from the Constraints menu, and
then select [Loads] -> [New] -> [Point].
- Click the arrow button under Point(s).
Hold down the Control key and select the points labeled as Pnt 3 and Pnt 11
in the figures above. Click OK from the Select window.
-
Set the Y Direction force to -10,000 lbs, and
leave all the other forces and moments set to 0.
-
Select the OK button from the Force/Moment
window. You should see the forces as shown in Figure 1.15.
[Figure
1.15]
-
You will now run a static
analysis of the structure. Select [Done/Return] from the Loads
menu, and then select [Analyses/Studies] from the Mec Struct menu.
-
Select [File] -> [New Static] from the Analyses and
Design Studies window.
- In the Static Analysis Definition window,
set the name of the analysis to Bridge_Static. Make sure
LoadSet1 and ConstraintSet1 are selected, and that the method is set to
Multi-Pass Adaptive. Select the OK button.
- Select the Run icon
on the Analyses
and Design Studies window to begin the analysis. Select Yes when asked
if you want error detection.
- This analysis should just take a minute. You can view the progress by selecting the Display Study Status
icon
.
- When the analysis is completed, select
[Results] from the Menu Manager. A new window should open.
- Select [Insert] -> [Results Window]
from the menu bar.
- Click the icon under Design Study and
select the analysis you just performed. Set the display type to
[Fringe], the quantity to [Stress], and the component to [von Mises].
Select the OK and Show button. You should see the display shown in
Figure 1.16. You can rotate and translate this display using the same
mouse commands that you would use to rotate a part when modeling it.
[Figure 1.16]
-
You can insert more results windows to show
other stresses, displacements, etc. Select [Insert] -> [Results
Window] again. Select the same design study. This time, set the
quantity to Displacement and the component to Magnitude. Under the
Display Options tab, check the Deformed checkbox.
Click the OK and Show button. You will see the displacement of the
bridge, as shown in Figure 1.17. Notice that the displacements are
greatly exaggerated, with the scale at the right indicating actual
displacements.
[Figure 1.17]
-
You can change the
cross-sections of the beams to see how it affects the stresses in the
bridge. Close the results windows and select [Model] ->
[Idealizations] -> [Beams] -> [Sections] from the Menu Manager.
-
Select the beam section
main_supports, and click the Edit button.
-
Change the Section Type
to I-Beam, and set the values to the ones shown in Figure 1.18.
These are the properties of a W6 X 9 Wide Flange I-Beam.
[Figure
1.18]
- Select the OK button from the Beam
Section Definition window and close the Beam Sections window.
-
Select [Done/Return] from the Idealizations
window, and then select [Analyses/Studies] from the Mec Struct menu.
- Select [File] -> [New Static] from the Analyses and
Design Studies window.
- In the Static Analysis Definition window,
set the name of the analysis to Bridge_Static. Make sure
LoadSet1 and ConstraintSet1 are selected, and that the method is set to
Multi-Pass Adaptive. Select the OK button.
- Select the Configure Run Settings icon
.
Under Elements, select the radio button for Create Elements During Run.
Otherwise, the analysis would use the same beam elements (with circular
cross-sections) that were used in the first analysis. Select the OK
button. -
Repeat steps 12 - 17 to
run the new analysis and plot the results. You should see the
results windows shown in Figure 1.19.
[Figure
1.19]
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