Problem $1(15$pt$)$

Consider a steel rod with Young's modulus E $=200$Gpa and shear modulus $G=70$Gpa. The rod has a diameter $d=10cm$ and length $L=1m.$ For an element on the surface of the rod, use Mohr's circle to find the stress state on the element oriented at an angle $36$deg.

$($i$)$ When rod is ONLY subjected to an axial load of $P=1kN.$

$($ii$)$ When rod is ONLY subjected to a pair of torque of $T=100Nm.$

$($iii$)$ When rod is subjected to both the axial load $P$ and the torque $T.$