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Let's go through each part of this problem step-by-step.

### Given Data:
- **Bronze Segment (1):**
  - Shear modulus, \( G = 48 \, \text{GPa} \)
  - Diameter, \( d_1 = 100 \, \text{mm} \)
- **Stainless Steel Segments (2) and (3):**
  - Shear modulus, \( G = 76 \, \text{GPa} \)
  - Diameter, \( d = 100 \, \text{mm} \)
- **Bolt Circle Information:**
  - Bolt diameter, \( d_b = 11 \, \text{mm} \)
  - Bolt circle diameter, \( d_c = 120 \, \text{mm} \)
  - Allowable shear stress for bolts, \( \tau_B = 85 \, \text{MPa} \)
- **Segment Lengths:**
  - \( L_1 = 500 \, \text{mm} \)
  - \( L_2 = 600 \, \text{mm} \)
  - \( L_3 = 400 \, \text{mm} \)

### Required:
1. **(a)** Allowable torque \( T_C \) for the assembly at \( C \), based on bolt capacity.
2. **(b)** Maximum shear stress in the bronze segment (1).
3. **(c)** Maximum shear stress in the stainless steel segments (2) and (3).

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### Solution Outline:

#### Part (a): Allowable Torque \( T_C \) Based on Bolt Capacity

1. **Determine Torque Capacity of Bolt Circle**:
   - With four bolts on a bolt circle of diameter \( d_c = 120 \, \text{mm} \), calculate the force \( F \) that each bolt can resist using:
     \[
     F = \tau_B \cdot A_b
     \]
     where \( A_b = \frac{\pi d_b^2}{4} \) is the cross-sectional area of each bolt.

2. **Torque Capacity of the Flange**:
   - The bolts are located on a circle, so the effective lever arm for torque is \( \frac{d_c}{2} \).
   - Total torque resisted by the bolts:
     \[
     T_{\text{allow}} = 4 \cdot F \cdot \frac{d_c}{2}
     \]

#### Part (b): Maximum Shear Stress in Bronze Segment (1)

1. Use the torsion formula for shear stress:
   \[
   \tau_{\text{max}} = \frac{T \cdot r}{J}
   \]
   where \( J = \frac{\pi d_1^4}{32} \) is the polar moment of inertia for the bronze segment, and \( r = \frac{d_1}{2} \).

2. Find \( T_1 \) based on torque distribution (dependent on material properties and lengths).

#### Part (c): Maximum Shear Stress in Stainless Steel Segments (2) and (3)

1. Similarly, use the torsion formula for shear stress in each stainless steel segment.
2. Polar moment of inertia \( J = \frac{\pi d^4}{32} \) and radius \( r = \frac{d}{2} \).

Would you like me to proceed with detailed calculations for each part? 

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### Follow-up Questions

1. How do we handle torque distribution across different materials?
2. What are the assumptions in ignoring friction effects on the flange?
3. How does bolt diameter influence the overall torque capacity?
4. Why is the shear modulus different for bronze and stainless steel important here?
5. How would changing \( d_c \) (bolt circle diameter) impact the allowable torque?

### Tip
Always start by identifying constraints (like material strengths) that limit the allowable forces or torques in a structural assembly.

The torsional assembly consists of a solid bronze [G = 48 GPa] segment (1) with diameter d1 = 100 mm securely connected at flange B to solid stainless steel [G = 76 GPa] segments (2) and (3), with diameter d = 100 mm. The flange at B is secured by four bolts, with diameter db = 11 mm which are each located on a bolt circle with diameter dc = 120 mm. The allowable shear stress of the bolts is τB = 85 MPa, and friction effects in the flange can be neglected. Assume L1 = 500 mm, L2 = 600 mm, and L3 = 400 mm. Determine: (a) the allowable torque TC that can be applied to the assembly at C without exceeding the capacity of the bolted flange connection, (b) the maximum shear stress magnitude in bronze segment (1), (c) the maximum shear stress magnitudes in stainless steel segments (2) and (3).

Analyze the torsional behavior of a bronze and stainless steel assembly secured by a bolted flange. This problem involves determining the allowable torque at a critical point and calculating maximum shear stresses using torsional mechanics principles. Suitable for undergraduate engineering students.

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