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Question: problem i a specially designed wrench is used to twist...

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Problem I: 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 x 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 bi2). Derive a formula for the average shear stress tav in the key when a load P is applied at distance L from the center of the shaft. Shaft Key Lever
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