Ceiling-mounted bicycle lift structural analysis
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<big>'''Safety Factor = 32.3<br />'''</big> | <big>'''Safety Factor = 32.3<br />'''</big> | ||
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+ | |||
+ | ==Part # 008: Locking Pulley Mount== | ||
+ | {| class="wikitable" border="0" | ||
+ | |- align="left" | ||
+ | ! ''Images'' !! ''Calculations'' !! | ||
+ | |- align="left" | ||
+ | | [[Image:Team1-LockPulley.jpg|300px]] || '''Material''': Carbon steel<br /> | ||
+ | E = 202,700 N/mm<sup>2</sup><br /> | ||
+ | Yield strength = 220 Mpa<br /> | ||
+ | Sheet thickness = 2.29 mm<br /> | ||
+ | <br /> | ||
+ | '''Loads'''<br /> | ||
+ | P/2 = 111.2 N<br /> | ||
+ | P/4 = 55.6 N<br /> | ||
+ | <br /> | ||
+ | (P = 50 lbs)<br /> | ||
+ | |- align="left" | ||
+ | | [[Image:Team1-FBD-LockPulley.JPG|300px]] || '''Bending along X-axis'''<br /> | ||
+ | Distance between support forces: 20 mm<br /> | ||
+ | Vertical centroid: -1.15 mm (measure from top surface)<br /> | ||
+ | Second moment of area about centroidal axis: 20.0 mm<sup>4</sup><br /> | ||
+ | Maximum bending moment: 400 N*mm<sup>2</sup><br /> | ||
+ | <br /> | ||
+ | Maximum x-bending stress: 23.0 N/mm<sup>2</sup> = 23.0 Mpa<br /> | ||
+ | |- align="left" | ||
+ | | [[Image:Team1-Stress-LockPulley.JPG|300px]] || '''Stress Concentration Factor'''<br /> | ||
+ | h = 2.29 mm (sheet thickness)<br /> | ||
+ | w = 48 mm (section width)<br /> | ||
+ | d = 6 mm (hole size)<br /> | ||
+ | <br /> | ||
+ | d/w = .13 d/h = 2.6<br /> | ||
+ | K = 1.7 - From table A-15-12 of (Shigley, Mechanical Engineering Design)<br /> | ||
+ | <br /> | ||
+ | '''<big>Actual Maximum Stress = 39.1 Mpa<br /></big>''' | ||
+ | '''<big>Safety Factor = 5.6 Mpa<br /></big>''' | ||
+ | |} | ||
+ | |||
==Part # 012: V-Bracket== | ==Part # 012: V-Bracket== |
Revision as of 03:45, 8 March 2007
Contents |
Part # 001: Ceiling Bracket
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
Part # 003: Pulley Wheel
Part # 004: Pulley Rivet
Part # 008: Locking Pulley Mount
Images | Calculations | |
---|---|---|
Material: Carbon steel E = 202,700 N/mm2 | ||
Image:Team1-FBD-LockPulley.JPG | Bending along X-axis Distance between support forces: 20 mm | |
Stress Concentration Factor h = 2.29 mm (sheet thickness) |
Part # 012: V-Bracket
Part # 013: Hook
Images | Calculations | |
---|---|---|
Material: Carbon steel E = 202,700 N/mm2 | ||
Bending Cross sectional area: 42.9 mm2 (for one hook) | ||
Actual Maximum Stress = 29.8 Mpa Safety Factor = 7.4 |
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.
Double braided nylon rope with a diameter of 7mm is rated for an approximate tensile capacity of 1900 lbs. For our 50 pound bicycle that results in a tensile load of 12.5 lbs, this is not a cause for concern. However as you will see from our FMEA, there are more issues with the rope than merely it's tensile capacity, with rope durability being a much larger issue.