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Part # 001: Ceiling Bracket
Images | Calculations |
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| 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)
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| 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
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| 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
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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 |
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| 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)
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| 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
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| 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
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Part # 003: Pulley Wheel
Images | Calculations |
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| 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)
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| 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
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Part # 004: Pulley Rivet
Images | Calculations |
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| 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)
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| 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
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Part # 012: V-Bracket
Images | Calculations |
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| 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)
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| 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
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Part # 013: Hook
Images | Calculations |
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| 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)
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| 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
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| Actual Maximum Stress = 29.8 Mpa
Safety Factor = 7.4
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Overview
There is a total of 8 ceiling screws responsible for holding the 50 pound load. To calculate the holding capacity of a single screw, we used a screw strength formula for attaching to the end grain of a pine wood (one of the weaker woods available). We used the equation P = 108.25 G2*D*L*(.75), where G is the specific gravity of the wood, D is the shank diameter and L is the thread penetration.
G = 350 kg/m3
L = 35 mm (.035m)
D = 4.38 mm (.00438m)
This resulted in a holding capacity of over 300 lbs for each screw which corresponds to a safety factor over 50.