Using Castigliano's second theorem solve the following:

Consider a cantilever axle of length and diameter $,$ with a concentrated vertical force F acting at the free end $($it does not matter for this problem whether the force acts in the downward or upward direction$).$ Find the deflection at the free end symbolically, considering the effects of both the transverse$-$shear force V and bending moment M$.$ Express this in terms of $/.$ By choosing values of and such that $(10,100)$ and $(0\mathrm{.}5,10),$ suggest for what ratios of $/$ can the effect of shear force be ignored $($for example, for what L$/$d ratio does the error due to ignoring the shear$-$force effect become less than or equal to$,$ say, $0\mathrm{.}5\%?).$ If your calculations require the value of $,$ assume a value of $0\mathrm{.}3.$