Dimensioning $(15$ Points$)$

A transmission intermediate shaft is given, as shown below. The intermediate shaft is in static

equilibrium. The left bearing at point $A$ is designed as a floating bearing, and the right bearing at

point $B$ is a fixed bearing.

Given:

$Fa=558N$

$Fa3=693N$

$Fy=2817N$

Fr$2=784$ N

Mt$2=$ Mt$3=105Nm$

l$1=|2=l3=300mm$

Radius of gear $2($left gear$)$ r$2=150$ mm

Distance of the point of force application r$3$y on gear $3$ is r$3$y$=75$ mm

Required:

Dimension the shaft at the test cross$-$section with a distance $lp=350mm$ from the bearing point

A$,$ ensuring that no plastic deformation occurs. The shaft is made of material S$360.$