# Question: The designer of a shaft usually has a slope constraint

The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit will be denoted as ξ . If the shaft shown in the figure is to have a uniform diameter d except in the locality of the bearing mounting, it can be approximated as a uniform beam with simple supports. Show that the minimum diameters to meet the slope constraints at the left and right bearings are, respectively,

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