A propped cantilever beam (fixed at $A$, roller at $B$) of length $L$ carries a uniform load $w$. Calculate the reaction at the roller support $B$. Constant $EI$.

A continuous beam spans two adjacent bays of length $L$. It is supported by a pin at $A$, a roller at $B$ (midpoint), and a roller at $C$. A point load $P$ is applied at the center of the first span ($L/2$ from $A$). Find the reaction at the interior support $B$. Constant $EI$.

A rectangular pin-jointed truss is braced by two diagonal members crossing each other. This creates 1 degree of internal indeterminacy. How is the force in one diagonal calculated?

A continuous beam has two spans. Span 1 ($A$ to $B$) is $6 \text{ m}$ long. Span 2 ($B$ to $C$) is $8 \text{ m}$ long. It is supported by rollers at $A$, $B$, and $C$. Span 1 carries a point load of $40 \text{ kN}$ at midspan ($3 \text{ m}$). Span 2 carries a uniform load of $15 \text{ kN/m}$. $EI$ is constant throughout. Find the moment at the interior support $B$.

A beam spans $5 \text{ m}$ from a fixed support $A$ to a roller support $B$. It carries a uniform load of $20 \text{ kN/m}$. Find the moment at the fixed support $M_A$ using the Three-Moment Equation.

A continuous beam over two equal spans ($L=6 \text{ m}$) is unloaded. However, the middle support $B$ settles downwards by $\Delta = 10 \text{ mm}$. The beam has $EI = 40,000 \text{ kN-m}^2$. Calculate the induced bending moment at support $B$.