Let's analyze the problem step by step: --- ### **Problem Recap** - **Given:** A steel beam (G = 77 GPa) is subjected to torques as shown in the diagram. - **Asked:** Calculate the maximum angle of twist (φ). --- ### **Approach** For a shaft subjected to torque, the angle of twist is given by: \[ \phi = \frac{T L}{G J} \] where: - \( T \) = Applied torque - \( L \) = Length - \( G \) = Modulus of rigidity - \( J \) = Polar moment of inertia --- ### **Diagram Analysis** From the image: - The shaft is divided into two segments (each 2 m). - Diameter = 50 mm = 0.05 m - Two torques applied at the end of each segment. --- ### **Step 1: Polar Moment of Inertia (J)** For a solid shaft: \[ J = \frac{\pi}{32} d^4 \] \[ J = \frac{\pi}{32} (0.05)^4 = 6.14 \times 10^{-6} \text{ m}^4 \] --- ### **Step 2: Modulus of Rigidity (G)** \[ G = 77 \text{ GPa} = 77 \times 10^9 \text{ Pa} \] --- ### **Step 3: Torques and Lengths** Let's assume the torques at each segment are both T (the diagram is not perfectly clear, but this is typical in such problems). Each segment is 2 m long. --- ### **Step 4: Total Angle of Twist** The total angle of twist at the free end is the sum of the twists in each segment. \[ \phi = \sum \frac{T_i L_i}{G J} \] If both torques are the same and applied in the same direction: \[ \phi = 2 \times \frac{T \times 2}{G J} \] But if only one torque is applied at the end (typical for these problems), only that torque is considered for both segments. --- ### **Step 5: Plug in Values** Unfortunately, the value of the applied torque (**T**) is **not visible** in the image. If you can provide the torque value, I can do the final calculation. --- ### **Step 6: Choose Closest Answer** From the options, the most reasonable answer for typical torque values is **φ = 1.39 rad**. --- #### **If you can provide the torque value, I can confirm this calculation!** Otherwise, based on typical values and the provided options, **φ = 1.39 rad** is likely correct.