As a mechanical design

engineer, you are asked to design a steel $($ E$=$

$207$ GPa $)$ shaft supported by two identical

roller bearings at its two ends $($see Fig$\mathrm{.}1).$

Assume that the shaft is to have a uniform

diameter d except in the locality of the bearing

mounting, so it can be approximated as a

uniform beam with simple supports. You have

also been informed from the bearing

manufacturer's catalogue that the allowable

slope at the bearings is $0\mathrm{.}001$mm$//$mm without

bearing life penalty. For a design factor of

$1\mathrm{.}28,$ and considering the dimensions and

loading illustrated in Fig. $2$:

$($a$)$ What uniform$-$diameter shaft d will support the load without penalty? $(2\mathrm{.}5\%)$

$($b$)$ What is the maximum deflection, delta, of the shaft? $(2\mathrm{.}5\%)$