https://file.aiquickdraw.com/mathbot/file/1725158824646w7k2z5hf.jpg

 w
 = 38 kN/m
. Determine the magnitude of the internal shear force at point  C
  in the beam.

To determine the internal shear force at point \( C \) in the beam, we need to analyze the given diagram, including the loading conditions and the supports.

### Given:
- The beam has a uniformly distributed load (UDL) \( w = 38 \, \text{kN/m} \).
- The UDL acts over a length of \( 2 \, \text{m} \).
- The beam is supported at points \( A \) and \( B \), with point \( C \) located at the midpoint between these supports.
- The distances between points \( A \), \( B \), and \( C \) are each \( 2 \, \text{m} \).

### Steps to Solve:
1. **Calculate the total load from the UDL:**
   The UDL covers \( 2 \, \text{m} \), so the total load \( W \) is:
   \[
   W = w \times 2 \, \text{m} = 38 \, \text{kN/m} \times 2 \, \text{m} = 76 \, \text{kN}
   \]

2. **Determine the reactions at the supports \( A \) and \( B \):**
   Since the beam is symmetric and the loading is also symmetric, the reactions at \( A \) and \( B \) should be equal.

   The total downward force on the beam is \( 76 \, \text{kN} \). Therefore, each support reaction is:
   \[
   R_A = R_B = \frac{76 \, \text{kN}}{2} = 38 \, \text{kN}
   \]

3. **Calculate the shear force just to the left of point \( C \):**
   Moving from point \( A \) towards \( C \), the shear force at any section is the reaction at \( A \) minus the UDL up to that point.

   For point \( C \), located \( 2 \, \text{m} \) from \( A \):
   \[
   V_C = R_A - w \times 2 \, \text{m} = 38 \, \text{kN} - 76 \, \text{kN} = -38 \, \text{kN}
   \]

### Conclusion:
The magnitude of the internal shear force at point \( C \) is \( 38 \, \text{kN} \). The negative sign indicates that the shear force is acting downwards at point \( C \).

Would you like more details on this calculation, or do you have any questions?

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Here are 5 related questions to consider:
1. What would be the shear force at a point between \( A \) and \( C \) but not at \( C \)?
2. How would the shear force diagram look for this beam?
3. What is the moment at point \( C \) given the same loading conditions?
4. How would the reaction forces change if the load were not uniformly distributed?
5. What is the significance of the shear force sign (positive or negative)?

**Tip:** When solving beam problems, always start by calculating support reactions before determining internal forces like shear or bending moments.

Learn how to calculate the internal shear force at point C in a beam under a uniformly distributed load (UDL) of 38 kN/m. Detailed step-by-step solution provided, including calculation of support reactions and shear force diagrams. Suitable for college-level engineering students.

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