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Sections of Report:
Cover Page: Md Muhaiminur Rahman, METC143, December 12, 2017.
Problem Statement: The task is to design a cable that will support a 60-ton vehicle. The cable is 25-foot-
long and can have an elastic deformation of no more than 10%. By using the Modulus of Elasticity for
various metals, we have to design a cable.
Introduction: First I calculated the Area using the formula Area=pi*(r)^2, then I used the Knoop
hardness and Vickers hardness formula to figure out the Force. After that, I calculated the stress by
using the formula Stress=force/area. I then used the modulus of elasticity formula to figure out how
much it stretches. After that, I figured out the strain and then the percentage elongation. I chose the
best diameter and calculated the thermal expansion of each material and came up with the change in
length and chose the best material for the cable design.
Results: Information is listed below.
1. Material information:
2. Calculated Diameter Required for Each Material Based on Modulus of Elasticity:
The diameter I chose was 2 inches for each material.
Aluminum 2014-T6
1045 Steel
Copper
Titanium Ti-6Al-4V
3. Stress Calculations Based on all common diameter sizes given in Project Instructions.
Material Hardness, Knoop Hardness, Vickers
Aluminum 2014-T6 170
1045 Steel 200
Copper 50
Titanium Ti-6Al-4V 363
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 7482.4 2382.93 0.00024 10000000 0.024
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 8802.82 2803.45 0.00008 30000000 0.008
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 16855.45 5367.978 0.00035 15000000 0.035
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 15977.11 5088.252 0.00042 12000000 0.042
Aluminum 2014-T6
1045 Steel
Copper
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 7482.4 2382.93 0.00024 10000000 0.024
1.75 2.4 7482.4 3117.67 0.0003 10000000 0.03
1.5 1.77 7482.4 4227.35 0.0004 10000000 0.04
1.25 1.96 7482.4 3817.6 0.00036 10000000 0.036
1 0.785 7482.4 9531.72 0.00096 10000000 0.096
0.75 0.44 7482.4 17005.5 0.0017 10000000 0.17
0.5 0.196 7482.4 38175.5 0.0038 10000000 0.38
0.25 0.049 7482.4 152702.04 0.015 10000000 1.5
0.125 0.012 7482.4 623533.33 0.0624 10000000 6.24
0.0625 0.003 7482.4 2494133.33 0.2496 10000000 24.96
0.03125 0.0008 7482.4 9353000 0.94 10000000 94
0.016 0.0002 7482.4 37412000 3.74 10000000 374
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 8802.82 2803.45 0.00008 30000000 0.008
1.75 2.4 8802.82 3667.84 0.00012 30000000 0.012
1.5 1.77 8802.82 4973.35 0.00016 30000000 0.016
1.25 1.96 8802.82 4491.24 0.00014 30000000 0.014
1 0.785 8802.82 11213.78 0.00037 30000000 0.037
0.75 0.44 8802.82 20006.41 0.00067 30000000 0.067
0.5 0.196 8802.82 44912.35 0.00149 30000000 0.149
0.25 0.049 8802.82 179649.39 0.00592 30000000 0.598
0.125 0.012 8802.82 733568.33 0.02445 30000000 2.445
0.0625 0.003 8802.82 2934273.33 0.09781 30000000 9.781
0.03125 0.0008 8802.82 11003525 0.36678 30000000 36.678
0.016 0.0002 8802.82 44014100 1.46714 30000000 146.714
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 16855.45 5367.978 0.00035 15000000 0.035
1.75 2.4 16855.45 7023.104 0.00047 15000000 0.047
1.5 1.77 16855.45 9522.853 0.00063 15000000 0.063
1.25 1.96 16855.45 8599.719 0.00057 15000000 0.057
1 0.785 16855.45 21471.911 0.00143 15000000 0.143
0.75 0.44 16855.45 38307.841 0.00255 15000000 0.255
0.5 0.196 16855.45 85997.193 0.00573 15000000 0.573
0.25 0.049 16855.45 343988.776 0.02293 15000000 2.293
0.125 0.012 16855.45 1404620.833 0.09364 15000000 9.364
0.0625 0.003 16855.45 5618483.333 0.37457 15000000 37.457
0.03125 0.0008 16855.45 21069312.5 1.40462 15000000 140.462
0.016 0.0002 16855.45 84277250 5.61848 15000000 561.848
Titanium Ti-6Al-4V
4. Stress Vs Diameter Plot based on your calculations
Aluminum 2014-T6
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
0 0.5 1 1.5 2 2.5
Stress
Diameter
Stress Vs Diameter
1045 Steel
Copper
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
45000000
50000000
0 0.5 1 1.5 2 2.5
Stress
Diameter
Stress VS Diameter
0
10000000
20000000
30000000
40000000
50000000
60000000
70000000
80000000
90000000
0 0.5 1 1.5 2 2.5
Stress
Diameter
Stress VS Diameter
Titanium Ti-6Al-4V
Fatigue Analysis:
1. S-N Curves for Aluminum and Steel
0
10000000
20000000
30000000
40000000
50000000
60000000
70000000
80000000
90000000
0 0.5 1 1.5 2 2.5
Stress
Diameter
Stress VS Diameter
2. Answer the following questions
a. For your selected diameter, calculate the stress generated for aluminum and steel.
Answer:
Aluminum 2014-T6
1045 Steel
b. What is the maximum number of cycles your selected diameter will survive based on the
S-N Curves for aluminum and steel (based on the stress you calculated)?
Answer: For Aluminum, more than 10^8 cycles. For Steel, no more than 10^6 cycles.
Thermal Analysis:
1. Thermal Expansion calculation of each material:
2. Plot Temperature Vs Change in Length for temperature range listed in Project Instructions in
20°F increments (One plot per material)
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 7482.4 2382.93 0.00024 10000000 0.024
Diameter (in) Area (in^2) Force (lb) Stress Strain Modulus of Elasticity % Elongation
2 3.14 8802.82 2803.45 0.00008 30000000 0.008
Material Coefficient of Thermal Expansion Delta L Ring Diameter Initial Temperature Final Temperature % Elongation
Aluminum 2014-T6 13.1*10^-6 0.00786 2 0 300 0.00393
1045 Steel 7.22*10^-6 0.00433 2 0 300 0.00215
Copper 10.3*10^-6 0.00618 2 0 300 0.00309
Titanium Ti-6Al-4V 5.39*10^-6 0.00323 2 0 300 0.00162
0
50
100
150
200
250
300
350
0 0.5 1 1.5 2 2.5
Temperature
Change in Length
Temperature VS Change in Length
Conclusion:
1. The diameter I chose was 2 inches. Because with the diameter of 2 inches, it has the least
change in length or % elongation.
2. Among the four materials analyzed, I would use Titanium Ti-6Al-4V, because after going through
thermal expansion, this material has the least percentage elongation. Which means that, this
material would be safe enough to support a 60-ton vehicle and not fail.