# Internal Torque Diagram for Shaft ABC ## **Question Recap** - Shaft **ABC** is subjected to: - \( T_1 = 100\, \text{N}\cdot\text{m} \) (at A) - \( T_2 = 500\, \text{N}\cdot\text{m} \) (at B) - You are to **draw the internal torque diagram**. --- ## **Step 1: Calculate Internal Torques** Let's analyze the shaft segment by segment: ### **Segment AB (\( < x < L_1\)):** - The only torque acting to the left of any cross-section within AB is \(T_1\). - **Internal torque in AB:** \[ T_{AB} = +100\, \text{N}\cdot\text{m} \] ### **Segment BC (\(L_1 < x < L_1+L_2\)):** - At B, \(T_2 = 500\, \text{N}\cdot\text{m}\) is applied but to the right, so it subtracts from the internal torque. - **Internal torque in BC:** \[ T_{BC} = T_1 - T_2 = 100 - 500 = 500\, \text{N}\cdot\text{m} \] ### **Example:** If \(L_1 = 2\,\text{m}\) and \(L_2 = 3\,\text{m}\): - From \(x = \) to \(x = 2\,\text{m}\): \(T = 100\,\text{N}\cdot\text{m}\) - From \(x = 2\,\text{m}\) to \(x = 5\,\text{m}\): \(T = 500\,\text{N}\cdot\text{m}\) --- ## **Step 2: Draw the Internal Torque Diagram** ### **Torque Diagram** - **Y-axis:** Internal Torque (\(\text{N}\cdot\text{m}\)) - **X-axis:** Position along shaft (from to \(L_1+L_2\)) ```plaintext Torque (N·m) | 100|–––––––––––––––| | | 500| |–––––––––––––––––– | | |_______________|___________________ L1 L1+L2 ``` - From \(\) to \(L_1\): \(100\,\text{N}\cdot\text{m}\) - From \(L_1\) to \(L_1+L_2\): \(500\,\text{N}\cdot\text{m}\) --- ## **Final Answer** - **Internal torque in AB:** \(100\,\text{N}\cdot\text{m}\) - **Internal torque in BC:** \(500\,\text{N}\cdot\text{m}\) - **Torque diagram:** Step-down from \(100\,\text{N}\cdot\text{m}\) to \(500\,\text{N}\cdot\text{m}\) at \(x = L_1\). --- ### **Summary Table** | Segment | Torque (\(\text{N}\cdot\text{m}\)) | |---------|-------------------| | AB | 100 | | BC | 500 | --- **Note:** If you need the diagram in a hand-drawn or plotted version, let me know!

# Internal Torque Diagram for Shaft ABC ## **Question Recap** - Shaft **ABC** is subjected to: - \( T_1 = 100\, \text{N}\cdot\text{m} \) (at point A) - \( T_2 = 500\, \text{N}\cdot\text{m} \) (at point B) - Task: **Draw the internal torque diagram**. --- ## **Step 1: Calculate Internal Torques** ### **Segment AB (\(0 < x < L_1\))** - Only torque acting to the left is \(T_1\). - **Internal Torque in AB:** \[ T_{AB} = +100\, \text{N}\cdot\text{m} \] ### **Segment BC (\(L_1 < x < L_1 + L_2\))** - At B, \(T_2 = 500\, \text{N}\cdot\text{m}\) is applied to the right, reducing internal torque. - **Internal Torque in BC:** \[ T_{BC} = T_1 - T_2 = 100 - 500 = -400\, \text{N}\cdot\text{m} \] ### **Example Calculation:** - If \(L_1 = 2\,\text{m}\) and \(L_2 = 3\,\text{m}\): - From \(x = 0\) to \(x = 2\,\text{m}\): \(T = 100\,\text{N}\cdot\text{m}\) - From \(x = 2\,\text{m}\) to \(x = 5\,\text{m}\): \(T = -400\,\text{N}\cdot\text{m}\) --- ## **Step 2: Draw the Internal Torque Diagram** ### **Torque Diagram** - **Y-axis:** Internal Torque (\(\text{N}\cdot\text{m}\)) - **X-axis:** Position along shaft (from \(0\) to \(L_1 + L_2\)) ```plaintext Torque (N·m) | 100|–––––––––––––––| | | 0 | | | | -400| |–––––––––––––––––– | | |_______________|___________________ 2 5 ``` - From \(0\) to \(L_1\) (2m): \(100\,\text{N}\cdot\text{m}\) - From \(L_1\) (2m) to \(L_1 + L_2\) (5m): \(-400\,\text{N}\cdot\text{m}\) --- ## **Final Answer** - **Internal Torque in AB:** \(100\,\text{N}\cdot\text{m}\) - **Internal Torque in BC:** \(-400\,\text{N}\cdot\text{m}\) - **Torque Diagram:** Step-down from \(100\,\text{N}\cdot\text{m}\) at \(x = 0\) to \(-400\,\text{N}\cdot\text{m}\) at \(x = 2\,\text{m}\). --- ### **Summary Table** | Segment | Torque (\(\text{N}\cdot\text{m}\)) | |---------|-------------------| | AB | 100 | | BC | -400 | --- This concludes the analysis and diagram of the internal torques for Shaft ABC.