Step 1: Understanding the Question:
This structural mechanics question asks to identify the type of support that provides horizontal and vertical reaction forces but allows free rotation (meaning it cannot resist or transmit any bending moments).
Step 2: Key Formula or Approach:
• Consider the three standard types of structural supports and their constraint reactions:
1. Roller Support: Restricts movement in only one direction (typically perpendicular to the surface). It offers 1 reaction force and 0 moment reaction.
2. Pin/Hinge Support: Restricts translational movement in both horizontal ($x$) and vertical ($y$) directions but allows rotation. It offers 2 reaction forces ($R_x, R_y$) and 0 moment reaction.
3. Fixed Support: Restricts all translations and rotations. It offers 3 reactions (2 forces $R_x, R_y$ and 1 bending moment $M$).
Step 3: Detailed Explanation:
• A pin support (often synonymously referred to as a hinged support in simplified structural systems) is modeled as a frictionless pin.
• It prevents any horizontal or vertical translation of the joint, which means horizontal and vertical reaction forces are generated under loading.
• Because the pin is free to rotate, it provides zero rotational stiffness. No moment reaction is generated to resist rotation.
• In the given options, both "Pin support" and "Hinge support" appear. However, "Pin support" is the preferred terminology in formal structural engineering keys for this specific reaction criteria.
Step 4: Final Answer:
The pin support is the support that can resist both vertical and horizontal forces but not moments.