https://r2.erweima.ai/mathbot/image/1725834613602krz5rt9y.jpg

The problem in the image involves determining the value of "n" for a beam subjected to certain forces and stresses. Let's break down the problem:

### Given Data:
1. **Material Strengths**:
   - **Tensile strength (\(f_t\))**: 60 MPa
   - **Compressive strength (\(f_c\))**: 150 MPa

2. **Loading Conditions**:
   - **Uniformly distributed load (UDL)**: 10 kN/m over a length of 1.6 m
   - **Point load**: 16 kN at a distance of 0.8 m from the end.

3. **Cross-Section**: T-section (dimensions provided in the diagram).

### Steps to Solve:

1. **Calculate the Reactions**:
   - Using equilibrium equations, determine the reaction forces at the supports.

2. **Shear Force and Bending Moment Diagram**:
   - Determine the shear force and bending moment at any section along the beam.

3. **Maximum Bending Moment**:
   - Find the location and magnitude of the maximum bending moment.

4. **Section Modulus (S) of the T-beam**:
   - Calculate the section modulus based on the given cross-section.

5. **Check Stresses**:
   - Use the bending stress formula:
     \[
     \sigma = \frac{M}{S}
     \]
   - Ensure that the stress does not exceed the given tensile and compressive strengths.

6. **Determine "n"**:
   - The value of "n" could refer to a dimension or factor that needs to be adjusted to satisfy the stress conditions. It might be related to dimensions such as flange width, depth, or the neutral axis position.

### Next Steps:
I'll now proceed to perform the calculations to find the value of "n". 

Before continuing, do you have any specific details about what "n" represents in this context, or should I proceed with the general approach?



Determinar el valor de 'n' si ft = 60MPa y fc = 150MPa, utilizando previamente la posición racional de la viga. (Given forces: UDL = 10kN/m over 1.6m, point load = 16kN at 0.8m)

This problem involves determining the value of 'n' for a T-beam subjected to a uniformly distributed load (UDL) and a point load. The material strengths are given as tensile strength (ft) = 60 MPa and compressive strength (fc) = 150 MPa. Learn how to calculate the reaction forces, bending moments, and section modulus to find the required dimension 'n'.

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