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The image shows a civil engineering problem related to beam deflection and support reactions. Here's a breakdown of the given problem:

### Problem Summary:
- A beam of uniform cross-section with a **flexural rigidity (EI) = 2.0 × 10⁴ kNm²** is placed on three supports.
- The beam is **9 meters** long, divided into three segments: **3.5 m** at both ends and **2 m** in the center, with a **uniform load of 35 kN/m**.
- Support **B** is at the middle of the beam, and supports **A** and **C** are at each end.
  
The questions asked are:
1. Calculate the reaction at support **A**.
2. Calculate the reaction at support **B**.
3. Find the deflection at **A**.

### Multiple Choice Options:
For question 28:
- A. 102.50 kN
- B. 49.02 kN
- C. 97.28 kN
- D. 37.50 kN

For question 29:
- A. 105.50 kN
- B. 45.02 kN
- C. 85.42 kN
- D. 52.00 kN

For question 30 (Deflection at A):
- A. 4.62 mm
- B. 0.45 mm
- C. 5.82 mm
- D. 3.61 mm

### Approach to Solving:

#### 1. Reaction at Supports:
The beam is statically indeterminate because there are three supports, which requires the use of the **three-moment equation** or other methods of indeterminate analysis (like superposition) to find the reactions.

#### 2. Deflection Calculation:
To calculate the deflection at **A**, we need to:
- Use the formula for the deflection of beams under uniform loads.
- Incorporate the given flexural rigidity \( EI = 2.0 \times 10^4 \, \text{kNm}^2 \).

Would you like to proceed with detailed calculations for the reactions and deflection, or do you have specific questions about one part of the problem?

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Here are 5 relevant follow-up questions:
1. Would you like me to solve for the reaction at support **A**?
2. Do you want to see how the three-moment equation is applied for the reaction at **B**?
3. Should I calculate the deflection at point **A** step by step?
4. Do you need an explanation on how to use the flexural rigidity \( EI \) in the deflection formula?
5. Are you familiar with the superposition method for statically indeterminate beams?

**Tip**: When solving indeterminate beam problems, the three-moment equation is a powerful tool to analyze the distribution of moments across multiple spans.

A beam of uniform cross-section with flexural rigidity EI = 2.0 × 10⁴ kNm² is placed on three supports. The beam is 9 meters long, divided into three segments: 3.5 m at both ends and 2 m in the center, with a uniform load of 35 kN/m. Support B is at the middle of the beam, and supports A and C are at each end. The questions asked are: 1. Calculate the reaction at support A. 2. Calculate the reaction at support B. 3. Find the deflection at A.

Explore the analysis of a statically indeterminate beam with a uniform load of 35 kN/m, flexural rigidity EI = 2.0 × 10⁴ kNm², and support reactions calculated using the three-moment equation. This civil engineering problem is ideal for undergraduate-level students, covering beam deflection and support reaction concepts.

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