$(23$ marks$)$ The beam is fixed to the wall at A and supported by a deformable post having a diameter of $50$ mm at $B.$ The post and the beam are made of the same material having a Young's modulus of $E=200$GPa. The beam has a constant moment of inertia $I_{N.A.}=3\mathrm{.}0{10}^{-4}{m}^4$ about its neutral axis. With the applied loads shown below, determine $($i$)$ the support reactions at A and $B$; $($ii$)$ the deflection at point $B$; and $($iii$)$ the slope and the deflection at point $C$ on the beam.$(23$ marks$)$ The beam is fixed to the wall at A and supported by a deformable post having a diameter of $50$ mm at $B.$ The post and the beam are made of the same material having a Young's modulus of $E=200$GPa. The beam has a constant moment of inertia $I_{N.A.}=3\mathrm{.}0{10}^{-4}{m}^4$ about its neutral axis. With the applied loads shown below, determine $($i$)$ the support reactions at A and $B$; $($ii$)$ the deflection at point $B$; and $($iii$)$ the slope and the deflection at point $C$ on the beam.