Which of the following best describes the forces acting on a horizontal beam supported by a rocker at point $A$ and a pin at point $B$ in its free-body diagram?

• A. Only vertical reaction forces at both $A$ and $B$.
• B. A vertical reaction force at $A$, and both a vertical and a horizontal reaction force at $B$.
• C. A horizontal reaction force at $A$, and a vertical reaction force at $B$.
• D. A vertical and a horizontal reaction force at $A$, and only a vertical reaction force at $B$.

Answer: (B)

Verified step by step guidance

1. Identify the types of supports and their constraints: A rocker support at point A allows rotation and horizontal movement but prevents vertical movement, so it provides only a vertical reaction force.
2. Recognize that a pin support at point B restricts both vertical and horizontal movements but allows rotation, so it provides both vertical and horizontal reaction forces.
3. Understand that the rocker at A cannot resist horizontal forces, so there is no horizontal reaction force at A.
4. Conclude that the free-body diagram must include a vertical reaction force at A, and both vertical and horizontal reaction forces at B to satisfy equilibrium conditions.
5. Summarize that the correct description is: a vertical reaction force at A, and both a vertical and a horizontal reaction force at B.