Ceiling-mounted bicycle lift structural analysis

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Part # 001: Ceiling Bracket
Image:Team1-FBD-Bracket.jpg

Material: Carbon steel

 E = 202,700 N/mm^2
 Yield strength = 350 Mpa

Loads:

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

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 mm^4
 Maximum bending moment:  5,560 N*mm^2

 Maximum x-bending stress: 9.47 N/mm^2 = 9.47 Mpa

Bending along Z-axis

 Distance between support forces: 70 mm
 Vertical centroid: -.066 mm (measure from top surface)
 Second moment of area about centroidal axis: 37.8 mm^4
 Maximum bending moment:  1,946 N*mm^2

Maximum z-bending stress: 3.4 N/mm^2 = 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