# Step-by-Step Solution: Identifying Support Reactions Let's carefully analyze the linkage shown in the diagram and identify all possible support reactions. --- ## **Step 1: Understand the Supports and Joints** ### **1. Joint A (Leftmost)** - **Type:** Pin Support (as it is fixed to the wall and allows rotation, but not translation) - **Reactions:** - \(A_x\): Reaction force in the horizontal direction (x-axis) - \(A_y\): Reaction force in the vertical direction (y-axis) - **No Moment Reaction:** A pin support does **not** provide a moment reaction (\(M_A\)). ### **2. Joint B (Middle)** - **Type:** Pin Connection between two links - **Reactions:** - \(B_x\): Reaction force in the horizontal direction (x-axis) - \(B_y\): Reaction force in the vertical direction (y-axis) - **No Moment Reaction:** A pin joint does **not** provide a moment reaction (\(M_B\)). ### **3. Joint C (Rightmost)** - **Type:** Cable/Chain (as shown by the hanging load) - **Reactions:** - Only a **vertical force** (\(C_y\)) is possible since the cable/chain can only support tension (vertical direction). - **No Horizontal or Moment Reaction:** No \(C_x\) or \(M_C\) at the cable/chain. --- ## **Step 2: Selecting All Possible Support Reactions** Let's match this information with the options provided: | Option | Description | Should be Checked? | Reason | |--------|----------------------------|-----------------------|------------------------------------------------| | \(A_x\) | Pin at A, x-direction | ✔️ | Pin support provides x-reaction | | \(A_y\) | Pin at A, y-direction | ✔️ | Pin support provides y-reaction | | \(M_A\) | Moment at A | ❌ | Pin cannot resist a moment | | \(B_x\) | Pin at B, x-direction | ✔️ | Pin provides x-reaction | | \(B_y\) | Pin at B, y-direction | ✔️ | Pin provides y-reaction | | \(M_B\) | Moment at B | ❌ | Pin cannot resist a moment | | \(C_x\) | Cable at C, x-direction | ❌ | Cable can't resist horizontal force | | \(C_y\) | Cable at C, y-direction | ✔️ | Cable resists vertical force (tension) | | \(M_C\) | Moment at C | ❌ | Cable cannot resist a moment | --- ## **Step 3: Final Answer** **All possible support reactions on the linkage are:** - \(A_x\) - \(A_y\) - \(B_x\) - \(B_y\) - \(C_y\) --- ## **Explanation** - **Pin supports** at A and B provide two reactions each (\(x\) and \(y\)), but **no moment**. - **Cable/chain** at C only provides a vertical reaction (\(y\)), as it cannot support horizontal force or moment. --- ## **Summary Table** | Joint | Reaction Forces | Moments | |---------|---------------------|--------------| | A | \(A_x, A_y\) | None | | B | \(B_x, B_y\) | None | | C | \(C_y\) | None | --- ### **Correct Choices to Select:** - \(A_x\) - \(A_y\) - \(B_x\) - \(B_y\) - \(C_y\) --- If you need to **check** these on the given list, make sure to select all five above. If you have any more questions about statics or linkage analysis, just ask!