An extension spring cycles between $10$ and $20$ N force with a deflection of $15$

mm between the force range. $D=12mm$ while the wire diameter is $1\mathrm{.}0mm.r_1=\frac{D}{2},$ and $r_2=3d.$

spring material is ASTM A$227$ hard$-$drawn $($HD$)$ wire. $S_{ut}=2200$MPa,$G=80\mathrm{.}7$GPa,$E=198\mathrm{.}6$GPa

a$.$ Using average value of the uncorrected 'empirical' initial shear stress bound, determine

the pre$-$load due to pre$-$tension.

b$.$ Determine stress at body, and Hook locations A$,$ B$,$ under maximum load.

c$.$ Does static failure take place at these locations? Why$/$why not?