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It seems you’ve uploaded an image with a structural design problem related to beam deflection. The task involves designing a beam subjected to a distributed load, ensuring it complies with deflection and stress criteria.

Let’s break down the problem:

- **Beam Configuration**: 
  - The beam has a uniformly distributed load denoted by \( q \).
  - It is supported over a span of **5 m**.

- **Given Data**: 
  - \( f_c = 250 \, \text{kg/cm}^2 \) (compressive strength of concrete)
  - \( f_y = 4200 \, \text{kg/cm}^2 \) (yield strength of steel)
  - Load \( q = 750 \, \text{kg/m} \)
  - Weight \( g = 1400 \, \text{kg/m} \) (presumably, the self-weight of the beam)

To proceed with the design, you'd generally follow these steps:

1. **Determine the total load**: The total load \( q_{total} \) would be the sum of the distributed load \( q \) and the beam's self-weight \( g \).
   \[
   q_{total} = q + g
   \]

2. **Bending Moment Calculation**: For a simply supported beam with a uniformly distributed load, the maximum bending moment \( M_{max} \) occurs at the center of the span and is given by:
   \[
   M_{max} = \frac{q_{total} \times L^2}{8}
   \]
   Where \( L \) is the span of the beam (5 meters).

3. **Beam Section Design**: Using the bending moment, you can calculate the required section modulus \( S \) for the beam, ensuring it can resist the bending stress:
   \[
   S = \frac{M_{max}}{f_y}
   \]
   Where \( f_y \) is the yield strength of the material.

4. **Deflection Check**: The deflection at the center of a simply supported beam under a uniform load can be found using:
   \[
   \Delta_{max} = \frac{5 q_{total} L^4}{384 E I}
   \]
   Where \( E \) is the modulus of elasticity, and \( I \) is the moment of inertia of the beam section.

Would you like to continue with the detailed calculations based on this method? 

Here are 5 follow-up questions you might find useful:
1. What material properties (like \( E \)) would be needed for the deflection calculation?
2. Would you prefer to calculate the steel reinforcement required for this beam?
3. How would the beam's design change if the span were increased?
4. Should we account for different safety factors when calculating the final design?
5. How do different support conditions affect the moment and deflection calculations?

**Tip**: Always ensure you include both the live load and dead load (self-weight) when designing structural elements like beams.

Design the beam based on flexural strength, deflections, and review the bending according to the classroom teachings. Given: fc = 250 kg/cm², fy = 4200 kg/cm², q = 750 kg/m, g = 1400 kg/m, L = 5m.

This problem focuses on designing a beam under a distributed load with a span of 5 meters. It includes bending moment, total load calculation, and deflection analysis with material properties fc = 250 kg/cm² and fy = 4200 kg/cm².

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