QUESTION $3(20$ MARKS$)$

Figure Q$3$ shows a horizontal cantilever beam that is fully fixed at an end point $A.$ The cantilever beam is loaded with a uniformly distributed load $\text{'}W\text{'}$ of rectangular shape at length $\text{'}L\text{'}$ from point $A$ to point $B$ and a couple moment of $\text{'}Mc\text{'}$ is applied $($anti$-$clockwise direction$)$ at the free end of the horizontal cantilever beam at point $C.$ Determine:

a$)$ the equation of the elastic curve for portion $AB$ of the horizontal beam

b$)$ the deflection at point $B$

c$)$ the slope at point $B$

$($CO$3$:PO$2-20$ marks$)$

FIGURE Q$3$