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?

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.