Simply Supported Beam Practice Problem

A simply supported beam spans $L = 8\,\text{m}$ between pin support $A$ (left end) and roller support $B$ (right end). A downward point load $P_1 = 10\,\text{kN}$ acts $2\,\text{m}$ from $A$, a downward point load $P_2 = 15\,\text{kN}$ acts $5\,\text{m}$ from $A$, and a counterclockwise applied couple $M_0 = 15\,\text{kN·m}$ acts at $A$.

Given

• $L = 8\,\text{m}$
• $P_1 = 10\,\text{kN}$ at $2\,\text{m}$ from $A$
• $P_2 = 15\,\text{kN}$ at $5\,\text{m}$ from $A$
• $M_0 = 15\,\text{kN·m}$, counterclockwise, applied at $A$

Assumptions: the beam is rigid and massless; $A$ is a pin (resists any in-plane direction), $B$ is a roller (vertical reaction only).

Required outputs: the vertical reactions at $A$ and $B$.