https://file.aiquickdraw.com/mathbot/file/1727054270890cftnb1vc.jpg

This image appears to show a simple beam supported at two points, \(A\) and \(B\), with a downward force \(P = 2 \text{ tons}\) applied at the center of the beam. The distance between the supports \(A\) and \(B\) is 4 meters, split equally with 2 meters on either side of the force \(P\).

### To determine the reactions at the supports \(A\) and \(B\):

1. **Equilibrium of forces:**
   The sum of vertical forces must be zero:
   \[
   R_A + R_B = P
   \]
   where:
   - \(R_A\) is the reaction at support \(A\),
   - \(R_B\) is the reaction at support \(B\),
   - \(P = 2 \text{ tons}\) is the load applied at the center of the beam.

   Thus,
   \[
   R_A + R_B = 2 \text{ tons}
   \]

2. **Equilibrium of moments:**
   Taking moments about point \(A\) (assuming clockwise moment is positive):
   \[
   R_B \times 4 - P \times 2 = 0
   \]
   Substituting the value of \(P = 2 \text{ tons}\):
   \[
   R_B \times 4 - 2 \times 2 = 0
   \]
   \[
   R_B \times 4 = 4
   \]
   \[
   R_B = \frac{4}{4} = 1 \text{ ton}
   \]

3. **Substitute \(R_B\) into the vertical force equation:**
   \[
   R_A + 1 = 2
   \]
   \[
   R_A = 2 - 1 = 1 \text{ ton}
   \]

### Final answers:
- Reaction at support \(A\), \(R_A = 1 \text{ ton}\),
- Reaction at support \(B\), \(R_B = 1 \text{ ton}\).

### For moments:
- Since the beam is symmetrical and the load is at the center, the moment at any point between the supports is equal. The moment at the center (where the force is applied) would be:
  \[
  M = R_A \times 2 = 1 \times 2 = 2 \text{ ton-meters}
  \]
  
Let me know if you need more details!

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### 5 Related Questions:
1. What happens to the reactions at supports if the load \(P\) is moved closer to support \(A\)?
2. How would the reactions change if the load was a distributed load instead of a point load?
3. What is the significance of calculating the moment in structural analysis?
4. How do you calculate the shear force in the beam at any point?
5. What type of beam is shown in the image (e.g., simply supported, cantilever)?

### Tip:
Always remember to check both force and moment equilibrium when solving beam problems to ensure the solution satisfies all conditions for static equilibrium.

Learn how to calculate the reaction forces at the supports A and B for a simply supported beam under a 2-ton load at the center. This problem uses equilibrium conditions and moment calculations. Suitable for high school and undergraduate engineering students.

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