SOLUTION:

Develop an expression for $M(x)$ and derive differential equation for elastic curve.

$W1468,I=301{10}^{6}m{m}^4,E=200$GPa

$P=222kN,L=4\mathrm{.}6m,a=1\mathrm{.}2m$

For portion $AB$ of the overhanging beam,

$($a$)$ derive the equation for the elastic curve,

$($b$)$ determine the maximum deflection,

$($c$)$ evaluate $y_{\text{m}\text{a}\text{x}}.$

Integrate differential equation twice and apply boundary conditions to obtain elastic curve.

Locate point of zero slope or point of maximum deflection.

Evaluate corresponding maximum deflection.