Q$3($a$)$ A steel rod $50$ mm long and diameter of $10$ mm hangs inside a tower and holds a $20$ kN weight at its lower end as shown in Figure Q$3($a$).$ The length of the steel rod has increased by $0\mathrm{.}122$ mm $.$ Determine:

$($i$)$ The axial stress induced on the bar.

$[3]$

$($ii$)$ Axial strain of the bar.

$[3]$

$($iii$)$ Modulus of elasticity E of the rod

$[4]$

Figure Q$3($a$)$

$($b$)$ A beam of solid circular cross$-$section with a diameter of $20$ mm is loaded with an axial force $5$ kN and a vertical force $1$ kN as shown in Figure Q$3($b$).$ Determine:

$($i$)$ The stresses induced at point A $.$

$[6]$

$($ii$)$ The principal stresses induced as point $A.$

$[4]$