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The problem asks to design the dimensions of a simply supported beam with a span of 6 meters and a uniform load of \(2900 \, \text{kg/m}\), using the maximum steel percentage. Here's a breakdown of the information and how to proceed:

### Given:
- **Span (\( L \))** = 6 m
- **Uniform load (\( w_u \))** = 2900 kg/m
- **Concrete compressive strength (\( f'_{c} \))** = 420 kg/cm²
- **Steel yield strength (\( f_y \))** = 4200 kg/cm²
- **Effective cover** = 3 cm
- The percentage of steel (\( p \)) will be the maximum allowable.

### Design Steps:
To design the beam, we typically follow these steps:

1. **Calculate Maximum Moment:**
   The maximum bending moment for a simply supported beam under uniform load is given by:
   \[
   M_{max} = \frac{w_u L^2}{8}
   \]

2. **Determine Required Moment of Resistance:**
   Using the design moment from the equation above, you can use the following formula to determine the required section modulus:
   \[
   M_u = R \times b \times d^2
   \]
   where:
   - \( R \) is the design strength factor.
   - \( b \) is the width of the beam.
   - \( d \) is the effective depth.

3. **Check for Steel Percentage:**
   Ensure the steel reinforcement is within limits by comparing the provided percentage to the maximum allowable percentage, which is determined by local building codes.

4. **Find Dimensions:**
   Using the maximum bending moment, you can compute the necessary dimensions of the beam (height and width) and the required steel area.

Would you like me to proceed with detailed calculations, or do you want clarification on a specific step?

### Relative Questions:
1. How do you calculate the maximum moment for a uniformly loaded simply supported beam?
2. What is the formula for calculating the moment of resistance in reinforced concrete beams?
3. How do we determine the maximum allowable steel percentage for a beam design?
4. What factors influence the choice of beam dimensions (height, width) in structural design?
5. How does the effective depth relate to the beam's overall strength and reinforcement?

**Tip:** Always verify the local building codes when determining maximum steel percentages and other design constraints.

Diseñar las dimensiones de una viga simplemente apoyada que tiene un claro de 6.00 m con una carga viva de 2900 kg/m y utilizaremos el porcentaje máximo de acero.

Design the dimensions of a simply supported beam with a span of 6 meters and a uniform load of 2900 kg/m using the maximum steel percentage. This problem covers key concepts in structural engineering, including reinforced concrete design, moment of resistance, and beam theory.

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