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Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
Analysis 1—Change in Beam Section/ Frame Structure
Assume that all members are tubular with an outside diameter of 1 inch and an inside diameter of 0.87 inch. Determine if
any yield failure is likely when the material is aluminum (E = 10 Mpsi, = 0.33, and yield = 50 kpsi).
If yielding occurs, redesign the frame by replacement of highly stressed members with more substantial sections of
standard sized tubing and/or alter the design layout. (Cite references for any tables of standard tubing sizes used.) If the
frame is unnecessarily over-designed in certain members (i.e., significantly lower stresses compared to others), refine the
design to reduce weight. Make certain that resulting deflections seem reasonable. You should have evidence of trying at
least three design changes, and state which would result in the lowest increase in weight (You can use an Excel
spreadsheet to show this).
1 2 3
4
5
6
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project Analysis 2—Change in Loading or Boundary Conditions
Using your results from Analysis 1 as a starting point, consider the loading and boundary conditions assumed for the
model. Do these seem reasonable? Make changes to your model, considering the way the elements are connected or the
loads that are applied (i.e. should we have a load at the pedal, etc.) Justify any changes made in your loading or boundary
conditions and cite any references used. With these new loading conditions, does yielding occur?
Analysis 3—Change in Material
Using the starting frame design or the design from Analysis 1, change the material properties of the bike frame. Cite any
references used when researching typical bike frame materials. Based on this material change, will your frame structure
still work or do the tube sizes or design need to be modified? If yielding occurs, try a redesign of the frame by
replacement of highly stressed members with more substantial sections of standard sized tubing and/or alter the design
layout. Again, you should have evidence of trying at least three design changes, and state which would result in the lowest
increase in weight (You can use an Excel spreadsheet to show this).
Submission
Following the lab report format given on mycourses, each group (2 students) should turn in one report. Your report
should include a description of your ANSYS model or models (Boundary conditions, Loading Conditions, etc.) In
addition, include in your discussion any problems you encountered with ANSYS or information about ANSYS you
wished had been covered in class. (This information will be used to modify the labs for next year.) Your report can be
submitted to the Final Project Assignment dropbox in mycourses or printed out and left in the bucket outside my office.
Your ANSYS .db file(s) must also be submitted to the Final Project Assignment dropbox in mycourses.
Assumptions:
1. Original material is aluminum
2. Neglect node welds
3. All material properties are uniform throughout all members
4. Analysis is static
5. Neglect any potential tire effects
6. The Bicycle Frame is 2 dimensional where the front tire is only supported by one tube
Abstract:
In this lab, the goal was to practice the basics of iterative design in ANSYS Classic via the set up and analysis of a two
dimensional bicycle frame. With the preliminary bicycle design shown in Figure 1, the iterative process began by
modeling and determining the initial stresses and deflection values of the bicycle to be further optimized for weight via
ANSYS. The mesh length of the frame was 0.5 inches. The design process began by minimizing weight under the original
design parameters. Next, the original load case was modified for more accurate redistributive loads on the frame and
rechecking to avoid frame yielding due to stress in the tubes. Lastly, the material was changed from aluminum to titanium
to be reanalyzed and designed for structural stability and weight.
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
Analysis 1:
Figure 2. Bicycle Design with Associated Tube Numbers Figure 3. Bicycle Design with Body Forces and Mesh Size of 0.5 in
Two body forces were applied to the bicycle frame with a load factor of 3, shown in Figure 2. The total body forces
applied at node 5 and 6 are 75 lbs. and 450 lbs., respectively, shown in Table 1.
Ori
gin
al
Lo
ad
Ca
se Node
Force in
X
Force in
Y
Force in
Z
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 -75 0
6 0 -450 0
Table 1. Original Load Case
For Analysis 1, Iteration 1:
Figure 4. Original Load Case - Displacement Vector Sum Plot Figure 5. Original Load Case - Von Mises Stress Plot
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project The maximum stress and displacement in the frame under the given load conditions and frame design is 24978 psi and
0.345 in, respectively. As the yield stress of material, aluminum, is 50000 psi, the design can be refined with a smaller
outer diameter tube and same wall thickness to reduced overall system weight and maintain strength.
For Analysis 1, Iteration 2:
Figure 6. Original Load Case - Displacement Vector Sum Plot Figure 7. Original Load Case - Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 47146 psi and
0.865 in, respectively. As shown in Figure 7, tubes 1, 2, 3 and 7 see very little stress and can therefore be replaced with
thinner walled tubes in order to reduce system weight. Most importantly, by only changing the volume of the low stress
tubes, the load capacity of the high stress tubes will not be compromised.
For Analysis 1, Iteration 3:
Figure 8. Original Load Case - Displacement Vector Sum Plot Figure 9. Original Load Case - Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 47589 psi and
0.881 in, respectively. Again, as shown in Figure 7, tubes 1, 2, 3 and 7 see very little stress and can therefore be replaced
with even thinner walled tubes in order to reduce system weight. Most importantly, by only changing the volume of the
low stress tubes, the load capacity of the high stress tubes will not be compromised.
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
For Analysis 1, Iteration 4:
Figure 10. Original Load Case - Displacement Vector Sum Plot Figure 11. Original Load Case - Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 48035 psi and
0.902 in, respectively. Compared to the previous designs, this iteration proves to be the lightest while maintaining
structural stability under the given load conditions.
Analysis I Iteration Results
Material Aluminum
Density 0.097504
Elastic Modulus (psi) 10000000
Poisson's Ratio 0.33
Yield Stress (psi) 50000
Iter
ati
on
1
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Tube ID (in) 0.870 0.870 0.870 0.870 0.870 0.870 0.870
Tube Thickness (in) 0.065 0.065 0.065 0.065 0.065 0.065 0.065
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 13.770 13.770 15.274 12.563 9.737 3.246 15.274
Total Weight (lb) 8.155
Maximum Displacement (in) 0.345
Maximum Stress (psi) 24978
Iter
ati
on
2
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Tube ID (in) 0.620 0.620 0.620 0.620 0.620 0.620 0.620
Tube Thickness (in) 0.065 0.065 0.065 0.065 0.065 0.065 0.065
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 10.088 10.088 11.190 9.204 7.134 2.378 11.190
Total Weight (lb) 5.974
Maximum Displacement (in) 0.865
Maximum Stress (psi) 47146
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
Iter
ati
on
3
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Tube ID (in) 0.652 0.652 0.652 0.620 0.620 0.620 0.652
Tube Thickness (in) 0.049 0.049 0.049 0.065 0.065 0.065 0.049
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 7.783 7.783 8.633 9.204 7.134 2.378 8.633
Total Weight (lb) 5.026
Maximum Displacement (in) 0.881
Maximum Stress (psi) 47589
Iter
ati
on
4
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Tube ID (in) 0.680 0.680 0.680 0.620 0.620 0.620 0.680
Tube Thickness (in) 0.035 0.035 0.035 0.065 0.065 0.065 0.035
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 5.670 5.670 6.289 9.204 7.134 2.378 6.289
Total Weight (lb) 4.157
Maximum Displacement (in) 0.902
Maximum Stress (psi) 48035
Table 2. Summary of All Iterations for Analysis 1
Analysis 2:
Lo
ad
Ca
se 1
Node Force in X Force in Y Force in Z
1 0 0 0
2 0 -180 0
3 0 0 0
4 0 0 0
5 0 -75 0
6 0 -270 0
Lo
ad
Ca
se 2
Node Force in X Force in Y Force in Z
1 0 0 0
2 0 -450 0
3 0 0 0
4 0 0 0
5 0 -75 0
6 0 0 0
Table 3: Load Case 1 and 2
For Analysis 2, the boundary conditions remain constant where node 1 is constrained in all directions and node 3 is only
constrained in the z direction while nodes 2, 4, 5 and 6 remain unconstrained. The boundary conditions remain constant
because it best modeled real world constraints.
Upon comparing the original load case to a real world scenario, it was believed that the original loading did not best
represent the true distribution of weight across the frame. The original weight of the rider was placed on the seat.
Therefore, the load case was changed to mimic an actual bicycle rider. This was modified to account for the leg weight on
the pedals as well as input force. This modification is Load Case 1, shown in Table 2. Load Case 2 accounts for the worst
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project case scenario where the bicycle rider is fully standing on the pedals while riding, shown in Table 2. The model used to test
the new load cases was Iteration 4 from Analysis 1.
For Analysis 2, Iteration 1:
Figure 12. Load Case 1- Displacement Vector Sum Plot Figure 13. Load Case 1- Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 21070 psi and
0.055 in, respectively. As a result of the implementing load case 1, the stress was more evenly and accurately distributed
across the frame. This is exemplified in Figure 13, where the maximum stress decreased 56%.
For Analysis 2, Iteration 2:
Figure 14. Load Case 2- Displacement Vector Sum Plot Figure 15. Load Case 2- Von Mises Stress Plot
To ensure that the current design is adequate for hill climbing, Load Case 2 was implemented where all body weight is
positioned on the pedals. The maximum stress and displacement in the frame under the given load conditions and frame
design is 30956 psi and 0.082 in, respectively. As shown in Figure 15, the maximum stress remains under the yield stress
limit for aluminum.
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
Analysis 3:
The bicycle frame material was changed from aluminum to titanium. This material change was performed for the
increased material strength properties of titanium. While titanium is a heavier material, the strength properties enabled
further reductions in weight in particular tube members. The model used to test the material change was Iteration 4 from
Analysis 1 under Load Case 1.
For Analysis 3, Iteration 1:
Figure 16. Load Case 1- Displacement Vector Sum Plot Figure 17. Load Case 1- Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 21070 psi and
0.033 in, respectively. Shown in Figure 17, the maximum stress at node 4 exceeds the allowable yield strength of titanium
of 20.3 kpsi1. Therefore, tubes 5 and 6 were modified by increasing the outer diameter while maintaining the same wall
thickness, shown in Iteration 2.
For Analysis 3, Iteration 2:
Figure 18. Load Case 1- Displacement Vector Sum Plot Figure 19. Load Case 1- Von Mises Stress Plot
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project The maximum stress and displacement in the frame under the given load conditions and frame design is 13230 psi and
0.023 in, respectively. As shown in Figure 19, the stress at node 4 decreased to an acceptable level below the yield stress
for titanium. In addition, it was noticed that tubes 2 and 3undergo small amount of stress. Therefore, the tube dimensions
can be reduced to optimize weight.
For Analysis 3, Iteration 3:
Figure 20. Load Case 1- Displacement Vector Sum Plot Figure 21. Load Case 1- Von Mises Stress Plot
The maximum stress and displacement in the frame under the given load conditions and frame design is 13171 psi and
0.022 in, respectively. Therefore, out of the 3 design iterations for titanium, the optimal design is iteration 4 due to the
lowest stress in the frame as well as deflection and weight. The final weight of the design was 8.242 lbs.
Analysis III Iteration Results
Material Titanium
Density 0.163
Elastic Modulus (psi) 16800000
Poisson's Ratio 0.34
Yield Stress (psi) 20300
Iter
ati
on
1
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Tube ID (in) 0.680 0.680 0.680 0.620 0.620 0.620 0.680
Tube Thickness (in) 0.035 0.035 0.035 0.065 0.065 0.065 0.035
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 5.670 5.670 6.289 9.204 7.134 2.378 6.289
Total Weight (lb) 6.949
Maximum Displacement (in) 0.033
Maximum Stress (psi) 21070
Iter
ati
on
2
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 1.000 1.000 0.750
Tube ID (in) 0.620 0.620 0.620 0.620 0.870 0.870 0.620
Tube Thickness (in) 0.065 0.065 0.065 0.065 0.065 0.065 0.065
Kursten O’Neill & Natalie Ferrari 2/17/2011 Final Project
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 10.088 10.088 11.190 9.204 9.737 3.246 11.190
Total Weight (lb) 10.553
Maximum Displacement (in) 0.023
Maximum Stress (psi) 13230
Iter
ati
on
3
Tube Number 1 2 3 4 5 6 7
Tube OD (in) 0.750 0.750 0.750 0.750 1.000 1.000 0.750
Tube ID (in) 0.652 0.620 0.620 0.620 0.870 0.870 0.652
Tube Thickness (in) 0.049 0.049 0.049 0.065 0.065 0.065 0.049
Tube Length (in) 18.030 18.030 20.000 16.450 12.750 4.250 20.000
Element Length (in) 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Total Volume (in3) 7.783 10.088 11.190 9.204 9.737 3.246 8.633
Total Weight (lb) 9.761
Maximum Displacement (in) 0.022
Maximum Stress (psi) 13171
Table 4. Summary of All Iterations for Analysis 3
Discussion:
It was observed that after redistributing the load at the seat to both the seat and pedal to mimic that of an actual rider, the
maximum stress in the frame decreased by a factor of 56%. With this change, the deflection increased at node 2 while
decreasing the stress at node 4. The load redistribution, in Load Case 1, was then maintained throughout the lab. Using a
variety of different tube geometries allowed for customization of the frame in order to reduce weight and stress.
For example, Iterations 2 and 3 from Analysis 3 exemplified this benefit. By increasing the outer diameter of front tubes 5
and 6, a reduction in stress was observed. Also, because tubes 2 and 3 experienced minimal stress, the wall thickness was
reduced in order to cut weight from the frame. Lastly, changing the material to titanium yielded lower deflections in the
tubes due to its high elastic modulus and intrinsic strength properties. While this material would provide more stiffness,
the high cost and additional weight would not be advantageous for the average bicycle rider. Therefore, it was concluded
that aluminum is a better suited material for a light weight bicycle frame under the loading conditions for this analysis.
Overall, the results make sense given the loading scenario proposed and the constraints applied to the model.
Sources:
For Titanium material properties:
1MatWeb - The Online Materials Information Resource. (n.d.). Online Materials Information Resource -
MatWeb. Retrieved February 16, 2011, from
http://www.matweb.com/search/DataSheet.aspx?MatGUID=66a15d609a3f4c829cb6ad08f0dafc01