Ceiling-mounted bicycle lift structural analysis

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m (→Part # 012: V-Bracket)
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Line 7: Line 7:
E = 202,700 N/mm<sup>2</sup><br />
E = 202,700 N/mm<sup>2</sup><br />
Yield strength = 220 Mpa<br />
Yield strength = 220 Mpa<br />
 +
Sheet thickness = 1.22 mm<br />
<br />
<br />
'''Loads'''<br />
'''Loads'''<br />
Line 52: Line 53:
E = 202,700 N/mm<sup>2</sup><br />
E = 202,700 N/mm<sup>2</sup><br />
Yield strength = 220 Mpa<br />
Yield strength = 220 Mpa<br />
 +
Sheet thickness = 2.29 mm<br />
<br />
<br />
'''Loads'''<br />
'''Loads'''<br />
Line 61: Line 63:
| [[Image:Team1-FBD-UPulley.JPG|300px]] || '''Bending along X-axis'''<br />
| [[Image:Team1-FBD-UPulley.JPG|300px]] || '''Bending along X-axis'''<br />
Distance between support forces: 20 mm<br />
Distance between support forces: 20 mm<br />
-
Vertical centroid: -.66 mm (measure from top surface)<br />
+
Vertical centroid: -1.15 mm (measure from top surface)<br />
-
Second moment of area about centroidal axis: 3.03 mm<sup>4</sup><br />
+
Second moment of area about centroidal axis: 20.0 mm<sup>4</sup><br />
-
Maximum bending moment:  556 N*mm<sup>2</sup><br />
+
Maximum bending moment:  400 N*mm<sup>2</sup><br />
<br />
<br />
-
Maximum x-bending stress: 12.1 N/mm<sup>2</sup> = 12.1 Mpa<br />
+
Maximum x-bending stress: 23.0 N/mm<sup>2</sup> = 23.0 Mpa<br />
|-  align="left"
|-  align="left"
| [[Image:Team1-Stress-UPulley.JPG|300px]] || '''Stress Concentration Factor'''<br />
| [[Image:Team1-Stress-UPulley.JPG|300px]] || '''Stress Concentration Factor'''<br />
-
h = 1.22 mm (sheet thickness)<br />
+
h = 2.29 mm (sheet thickness)<br />
w = 48 mm (section width)<br />
w = 48 mm (section width)<br />
d = 6 mm (hole size)<br />
d = 6 mm (hole size)<br />
<br />
<br />
-
d/w = .13    d/h = 5<br />
+
d/w = .13    d/h = 2.6<br />
K = 1.7  -  From table A-15-12 of (Shigley, Mechanical Engineering Design)<br />
K = 1.7  -  From table A-15-12 of (Shigley, Mechanical Engineering Design)<br />
<br />
<br />
-
'''<big>Actual Maximum Stress = 20.6 Mpa<br /></big>'''
+
'''<big>Actual Maximum Stress = 39.1 Mpa<br /></big>'''
-
'''<big>Safety Factor = 10.7 Mpa<br /></big>'''
+
'''<big>Safety Factor = 5.6 Mpa<br /></big>'''
|}
|}
Line 140: Line 142:
E = 202,700 N/mm<sup>2</sup><br />
E = 202,700 N/mm<sup>2</sup><br />
Yield strength = 220 Mpa<br />
Yield strength = 220 Mpa<br />
 +
Sheet thickness = 2.29 mm<br />
<br />
<br />
'''Loads'''<br />
'''Loads'''<br />
Line 149: Line 152:
| [[Image:Team1-FBD-VBracket.JPG|300px]] || '''Bending at Neck'''<br />
| [[Image:Team1-FBD-VBracket.JPG|300px]] || '''Bending at Neck'''<br />
Distance from support force: 10 mm<br />
Distance from support force: 10 mm<br />
-
Cross sectional area: 19.5 mm<sup>2</sup>
+
Cross sectional area: 36.6 mm<sup>2</sup>
-
Second moment of area about centroidal axis: 2.42 mm<sup>4</sup><br />
+
Second moment of area about centroidal axis: 16.0 mm<sup>4</sup><br />
-
Maximum bending moment:  5,56 N*mm<sup>2</sup><br />
+
Maximum bending moment:  556 N*mm<sup>2</sup><br />
<br />
<br />
-
Maximum bending stress: 9.47 N/mm<sup>2</sup> = 15.2 Mpa<br />
+
Maximum bending stress: 15.2 N/mm<sup>2</sup> = 15.2 Mpa<br />
|-  align="left"
|-  align="left"
| [[Image:Team1-Stress-Vbracket.JPG|300px]] || '''Stress Concentration'''<br />
| [[Image:Team1-Stress-Vbracket.JPG|300px]] || '''Stress Concentration'''<br />
Line 175: Line 178:
E = 202,700 N/mm<sup>2</sup><br />
E = 202,700 N/mm<sup>2</sup><br />
Yield strength = 220 Mpa<br />
Yield strength = 220 Mpa<br />
 +
Sheet thickness = 4.17 mm<br />
<br />
<br />
'''Loads'''<br />
'''Loads'''<br />
P/2 = 111.2 N<br />
P/2 = 111.2 N<br />
-
P/4 = 55.6 N<br />
+
Mz = 1780 N*mm<br />
-
Mz = 1780 N*mm
+
<br />
<br />
(P = 50 lbs)<br />
(P = 50 lbs)<br />
|-  align="left"
|-  align="left"
-
| [[Image:Team1-FBD-Hook.JPG|300px]] || '''Bending at Neck'''<br />
+
| [[Image:Team1-FBD-Hook.JPG|300px]] || '''Bending'''<br />
-
Distance from support force: 10 mm<br />
+
Cross sectional area: 42.9 mm<sup>2</sup> (for one hook)
-
Cross sectional area: 19.5 mm<sup>2</sup>
+
Cross sectional area: 85.8 mm<sup>2</sup> (P/2 is for hook assembly - 2)
-
Second moment of area about centroidal axis: 2.42 mm<sup>4</sup><br />
+
Second moment of area about centroidal axis: 124.5 mm<sup>4</sup><br />
-
Maximum bending moment:  5,56 N*mm<sup>2</sup><br />
+
Maximum bending moment:  1780 N*mm<sup>2</sup><br />
<br />
<br />
-
Maximum bending stress: 9.47 N/mm<sup>2</sup> = 15.2 Mpa<br />
+
Maximum bending stress: 29.8 N/mm<sup>2</sup> = 29.8 Mpa<br />
|-  align="left"
|-  align="left"
-
| [[Image:Team1-Stress-Hook.JPG|300px]] || '''Stress Concentration'''<br />
+
| [[Image:Team1-Stress-Hook.JPG|300px]] || '''<big>Actual Maximum Stress = 29.8 Mpa<br /></big>'''
-
r: 2 mm<br />
+
'''<big>Safety Factor = 7.4 Mpa<br /></big>'''
-
d: 16 mm<br />
+
-
D: 18 mm</sup><br />
+
-
D/d = 1.1
+
-
r/d = .13
+
-
K = 1.6  -  From table A-15-5 of (Shigley, Mechanical Engineering Design)<br />
+
-
 
+
-
'''<big>Actual Maximum Stress = 24.3 Mpa<br /></big>'''
+
-
'''<big>Safety Factor = 9.1 Mpa<br /></big>'''
+
|}
|}

Revision as of 03:19, 8 March 2007

Contents

Part # 001: Ceiling Bracket

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa
Sheet thickness = 1.22 mm

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Bending along X-axis

Distance between support forces: 200 mm
Vertical centroid: -7.57 mm (measure from top surface)
Second moment of area about centroidal axis: 3510 mm4
Maximum bending moment: 5,560 N*mm2

Maximum x-bending stress: 9.47 N/mm2 = 9.47 Mpa

Bending along Z-axis

Distance between support forces: 70 mm
Vertical centroid: -.66 mm (measure from top surface)
Second moment of area about centroidal axis: 37.8 mm4
Maximum bending moment: 1,946 N*mm2

Maximum z-bending stress: 3.4 N/mm2 = 3.4 Mpa

Maximum net bending stress: 10.1 Mpa

Stress Concentration Factor
h = 1.22 mm (sheet thickness)
w = 50 mm (section width)
d = 6 mm (hole size)

d/w = .12 d/h = 5
K = 1.7 - From table A-15-12 of (Shigley, Mechanical Engineering Design)

Actual Maximum Stress = 17.1 Mpa
 Safety Factor = 12.9 Mpa

Part # 002: U-Pulley Mount

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa
Sheet thickness = 2.29 mm

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Bending along X-axis

Distance between support forces: 20 mm
Vertical centroid: -1.15 mm (measure from top surface)
Second moment of area about centroidal axis: 20.0 mm4
Maximum bending moment: 400 N*mm2

Maximum x-bending stress: 23.0 N/mm2 = 23.0 Mpa

Stress Concentration Factor

h = 2.29 mm (sheet thickness)
w = 48 mm (section width)
d = 6 mm (hole size)

d/w = .13 d/h = 2.6
K = 1.7 - From table A-15-12 of (Shigley, Mechanical Engineering Design)

Actual Maximum Stress = 39.1 Mpa
 Safety Factor = 5.6 Mpa


Part # 003: Pulley Wheel

Images Calculations
Material: Injection molded plastic

E = 3,500 N/mm2
v = .4 Yield strength = 103 Mpa

Loads
P/2 = 111.2 N
Ft = force resulting from tension in rope
(P = 50 lbs)

Contact Stress

Diameter 1: 5.3 mm
Diameter 2: 4.9 mm
Contact length = 13.5mm
Half-width of contact surface = 2 mm

Maximum Compressive Stress = 4.2 Mpa
 Safety Factor = 24.5

Part # 004: Pulley Rivet

Images Calculations
Material: Aluminum

E = 69,000 N/mm2
Yield strength = 95 Mpa

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Shear Stress

Diameter: 4.9 mm
Length = 20 mm

Maximum shear force = 55.6 N
Shear area = 18.9 mm2

Maximum Compressive Stress = 2.9 Mpa
 Safety Factor = 32.3

Part # 012: V-Bracket

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa
Sheet thickness = 2.29 mm

Loads
P/2 = 111.2 N
Mz = 1780 N*mm
(P = 50 lbs)

Bending at Neck

Distance from support force: 10 mm
Cross sectional area: 36.6 mm2 Second moment of area about centroidal axis: 16.0 mm4
Maximum bending moment: 556 N*mm2

Maximum bending stress: 15.2 N/mm2 = 15.2 Mpa

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 Stress Concentration

r: 2 mm
d: 16 mm
D: 18 mm</sup>
D/d = 1.1 r/d = .13 K = 1.6 - From table A-15-5 of (Shigley, Mechanical Engineering Design)

Actual Maximum Stress = 24.3 Mpa
 Safety Factor = 9.1 Mpa

Part # 013: Hook

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa
Sheet thickness = 4.17 mm

Loads
P/2 = 111.2 N
Mz = 1780 N*mm

(P = 50 lbs)

Bending

Cross sectional area: 42.9 mm2 (for one hook) Cross sectional area: 85.8 mm2 (P/2 is for hook assembly - 2) Second moment of area about centroidal axis: 124.5 mm4
Maximum bending moment: 1780 N*mm2

Maximum bending stress: 29.8 N/mm2 = 29.8 Mpa

Actual Maximum Stress = 29.8 Mpa

Safety Factor = 7.4 Mpa

Retrieved from "http://wiki.ece.cmu.edu/ddl/index.php/Ceiling-mounted_bicycle_lift_structural_analysis"
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