A $6-$meter diameter offshore wind monopile is embedded in a sand deposit to a depth of $36$ meters below the seafloor. The pile wall thickness is $70mm.$ A Cone Penetration Test was performed in the soil and the results were used to estimate an average relative density of around $65\%$ and a saturated unit weight of $22k\frac{N}{m^3}.$ A horizontal load $($F$)$ from wind and waves is applied to the structure at a height of $80$ meters above the seafloor. $($a$)$ Determine the applied lateral shear and moment at the mudline as a function of the variable F$.($b$)$ Calculate the highest value of the load, $F$ needed to cause geotechnical failure defined as the pile head deflection at $10\%$ of the pile diameter.