Question 4.CS.4B: Bicycle Brake Arm Stress Analysis Problem Determine the stre...
Bicycle Brake Arm Stress Analysis
Problem Determine the stresses at critical points in the bicycle brake arm shown in Figures 3-9 (repeated here) and 4-54.
Given The geometry and loading are known from Case Study 4A (p. 94) and are shown in Table 3-5 (p. 97). The cast-aluminum arm is a tee-section curved beam whose dimensions are shown in Figure 4-54. The pivot pin is ductile steel. The loading is three-dimensional.
Assumptions The most likely failure points are the arm as a double-cantilever beam (one end of which is curved), the hole in bearing, and the connecting pin in bending as a cantilever beam. Since this is a marginally ductile cast material (5% elongation to fracture), we can ignore the stress concentration on the basis that local yielding will relieve it.
| Table 3–5 – part 1 Case Study 4A Given and Assumed Data |
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| Variable | Value | Unit |
| \mu | 0.4 | none |
| \theta | 172.0 | deg |
| R_{12x} | 5.2 | mm |
| R_{12y} | -27.2 | mm |
| R_{12z} | 23.1 | mm |
| R_{32x} | –75.4 | mm |
| R_{32y} | 38.7 | mm |
| R_{32z} | 0.0 | mm |
| R_{52x} | -13.0 | mm |
| R_{52y} | –69.7 | mm |
| R_{52z} | 0.0 | mm |
| F_{32x} | 353.0 | N |
| F_{32y} | 523.0 | N |
| F_{32z} | 0.0 | N |
| M_{12z} | 0.0 | N–m |
| Table 3–5 – part 2 Case Study 4A Calculated Data |
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| Variable | Value | Unit |
| F_{12x} | –1 805 | N |
| F_{12y} | –319 | N |
| F_{12z} | 587.0 | N |
| F_{52x} | 1 452 | N |
| F_{52y} | -204 | N |
| F_{52z} | -587 32 | N |
| M_{12x} | 32 304 | N–mm |
| M_{12y} | 52 370 | N–mm |
| N | 1 467 | N |
| F_{f} | 587 | N |
