# Free Body Diagram for the Force System Let's solve the problem in **2 steps** as requested: --- ## **Step : Draw the Body Diagram (FBD ### **Given System (Top Image)** - Beam ABCD, supported at \(A\) (pin) and \(C\) (roller). - Forces: - \( 500 \text{ lb/ft} \) distributed load from \(A\) to \(B\). - \( 100 \text{ lb} \cdot \text{ft} \) moment at \(D\). - Supports at \(A\) (pin: \(A_x, A_y\)), at \(C\) (roller: \(C_y\)), and a 30° force at \(B\). ### **Free Body Diagram (Bottom Image)** The bottom image shows the FBD: - Replace distributed load with its resultant force (\( F_1 \)) acting at its centroid. - Replace roller at \(C\) with a vertical reaction (\( F_2 \)). - Show the applied moment at \(D\). **Graph (FBD):**  *Note: This is a representation. The actual diagram should be drawn based on the figure you provided.* --- ## **Step 2: Identify All Forces and Moments** ### **Example Breakdown:** #### **A. Replace Distributed Load** - \( 500 \text{ lb/ft} \) over \( 4 \text{ ft} \) gives: - **Resultant force \( F_1 = 500 \times 4 = 200 \text{ lb} \)** - Acts at the centroid of the load, which is \( 2 \text{ ft} \) from \(A\). #### **B. Show All Reactions** - At \(A\) (pin): \(A_x\), \(A_y\) (horizontal and vertical). - At \(C\) (roller): \(C_y\) (vertical only). - Moment at \(D\): \(100 \text{ lb} \cdot \text{ft}\). --- ### **Final Free Body Diagram** **Label all forces:** - \( F_1 = 200 \text{ lb} \) at \(2 \text{ ft}\) right of \(A\), downwards. - \( F_2 = C_y \) at \(C\), upwards. - Moment at \(D\): \(100 \text{ lb} \cdot \text{ft}\) (counterclockwise). - \(A_x\), \(A_y\) at \(A\). --- ## **Final Answer** The free body diagram for the force system is: 1. **Replace distributed loads with their resultant force and location.** 2. **Show all support reactions and applied moments.** **Example:** - \( F_1 = 200 \text{ lb} \) at \(2 \text{ ft}\) from \(A\) (down). - \( F_2 = C_y \) at \(C\) (up). - \( A_x, A_y \) at \(A\). - \( 100 \text{ lb} \cdot \text{ft} \) moment at \(D\). --- **This is your systematic approach and answer for drawing the free body diagram for the given mechanical system.**