Problem 118 A 200-mm-diameter pulley is prevented from rotating relative to 60-mm-diameter shaft by a 70-mm-long key, as shown in Fig. P-118. If a torque T = 2.2 kN·m is applied to the shaft, determine the width b if the allowable shearing stress in the key is 60 MPa.
Solution 118
$T = 0.03F$
$2.2 = 0.03F$
$F = 73.33 \, \text{kN}$
$V = \tau A$
$A = 70b$
$\tau = 60 \, \text{MPa}$
Thus, $73.33(1000) = 60(70b)$
$b = 17.46 \, \text{mm}$ answer
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