A specially designed wrench is used to twist a circular
Question and Solution
A specially designed wrench is used to twist a circular shaft by means of a square key that fits into slots (or keyways)
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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 on the next page. 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 taver 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 wrench and key.
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