Problem $3(5$ points$)$:

Two strain gages are mounted on a steel shaft $(E=20{10}^{10}Pa$ and Poisson's ratio $=0\mathrm{.}29),$ as shown in Case J$,$ Table $12\mathrm{.}4.$ The gage resistance is $119$ and $F=1\mathrm{.}23.$ When a $250,000-$ resistor is shunted across gage $1,$ a $3\mathrm{.}4-cm$ upward shift is recorded on the face of the oscilloscope. When the shaft is torqued, a $5\mathrm{.}7-cm$ shift is measured. For these conditions, and assuming bending and axial loading may be neglected,

$($a$)$ Calculate the maximum torsional stress.

$($b$)$ What are the three principal stresses on the shaft surface?

$($c$)$ Plot Mohr's circles for stress.

$($d$)$ If a bending moment and$/$or axial load is present, how would the results be affected?