(Solved): Please Help! A cantilever beam with a round cross section has a concentrated load \( \mathrm{F} \) a ...

A cantilever beam with a round cross section has a concentrated load \( \mathrm{F} \) at the end. The total strain energy due to bending and direct shear is given as: \[ U=\frac{F^{2} l^{3}}{6 E I}+\frac{1.11 F^{2} l}{2 A G} \] Using Castigliano's method find the total deflection at the free end in inches. Given that, \( G=12 \times 10^{6} \mathrm{psi}, \mathrm{F}=120 \mathrm{lbf}, \mathrm{l}=12 \mathrm{in}, \mathrm{E}=31 \times 10^{6} \mathrm{psi} \), and \( \mathrm{d}=0.7 \) in. Hint: \( y=\frac{\partial U}{\partial F} \) \[ I=\frac{\pi d^{4}}{64}, A=\frac{\pi d^{2}}{4} \] a. \( 0.835 \) in b. \( 0.157 \) in c. \( 0.190 \) in d. \( 0.512 \) in e. \( 0.724 \) in