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01-02ChapGere.0004 - wrench and key SECTION 1.6 Shear...

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Problem 1.6-13 A specially designed wrench is used to twist a circular shaft by means of a square key that fits into slots (or keyways ) in the shaft and wrench, as shown in the figure. The shaft has diameter d , the key has a square cross section of dimensions b b , and the length of the key is c . The key fits half into the wrench and half into the shaft (i.e., the keyways have a depth equal to b /2). Derive a formula for the average shear stress aver in the key when a load P is applied at distance L from the center of the shaft. Hints: Disregard the effects of friction, assume that the bearing pressure between the key and the wrench is uniformly distributed, and be sure to draw free-body diagrams of the
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Unformatted text preview: wrench and key. SECTION 1.6 Shear Stress and Strain 35 Shaft Lever Key c P L b d Solution 1.6-13 Wrench with keyway F REE-BODY DIAGRAM OF WRENCH With friction disregarded, the bearing pressures between the wrench and the shaft are radial. Because the bearing pressure between the wrench and the key is uniformly distributed, the force F acts at the midpoint of the keyway. (Width of keyway 5 b /2) F 5 4 PL 2 d 1 b PL 2 F ¢ d 2 1 b 4 ≤ 5 © M C 5 0 ` ~ P L b 2 F C d 2 b 4 + d F REE-BODY DIAGRAM OF KEY F b 2 F b Plane of shear 5 4 PL bc (2 d 1 b ) t aver 5 F bc A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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