A cantilever beam of length $L$ is fixed at the left end ($x=0$) and subjected to a point load $P$ at the free end ($x=L$). The flexural rigidity $EI$ is constant. Find the equation of the elastic curve, the maximum deflection, and the maximum slope.

A simply supported beam of length $L$ carries a concentrated load $P$ at midspan. Constant $EI$. Find the maximum deflection at midspan using the Moment-Area Method.

A simply supported beam ($L=8 \text{ m}$) has an internal hinge at $x=2 \text{ m}$ from the left support. It carries a uniform load. How is the conjugate beam constructed?

A pin-jointed truss is subjected to external loads, resulting in internal real forces $N$ in each member. We want to find the vertical deflection of joint $C$.

A cantilever beam of length $L$ carries a uniform load $w$. Use Castigliano's theorem to find the deflection at the free end.