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Tentukan gaya momen dan gaya normal pada soal tersebut.

To solve the problem of determining the moment and normal force in the given system, we can break the task down into several steps. Here's the procedure:

### Given Information:
- A beam with a point load \( P = 4 \, \text{tons} \) applied at the center of the beam.
- The beam is supported at points \( A \) and \( B \), which are 4 meters apart (2 meters on each side of the load).
- Both supports are pinned supports (point A) and roller supports (point B), so we need to determine the reactions at these supports.

### Objective:
- Determine the reaction forces at \( A \) and \( B \).
- Calculate the moment generated by the load.

### Step 1: Equilibrium Equations
We apply the static equilibrium conditions to the beam:

1. **Vertical Force Equilibrium:**
   \[
   \sum F_y = 0
   \]
   This means that the sum of vertical forces acting on the beam must be zero. The forces include the reactions at \( A \) (\( R_A \)) and \( B \) (\( R_B \)) and the downward load \( P \).

   \[
   R_A + R_B = P
   \]

2. **Moment Equilibrium (about A):**
   \[
   \sum M_A = 0
   \]
   Taking moments about point \( A \) to eliminate \( R_A \) from the equation, we have:

   \[
   -P \cdot 2 + R_B \cdot 4 = 0
   \]
   Solving for \( R_B \):
   \[
   R_B = \frac{P \cdot 2}{4} = \frac{4 \, \text{tons} \cdot 2 \, \text{m}}{4 \, \text{m}} = 2 \, \text{tons}
   \]

3. **Substitute \( R_B \) into the Force Equilibrium:**
   \[
   R_A + 2 \, \text{tons} = 4 \, \text{tons}
   \]
   Solving for \( R_A \):
   \[
   R_A = 4 \, \text{tons} - 2 \, \text{tons} = 2 \, \text{tons}
   \]

### Step 2: Moment Calculation
The moment generated at point A or B due to the load can now be calculated. Since the load is symmetric and the beam is statically determinate, the internal moment at the center will be zero.

Thus, the reactions are:

- \( R_A = 2 \, \text{tons} \)
- \( R_B = 2 \, \text{tons} \)

There is no net moment on the beam other than the internal bending moment between the supports.

---

Would you like further clarification on any part of the solution?

Here are 5 related questions you might consider:

1. How would the results change if the load were not centered on the beam?
2. What are the internal shear forces in the beam?
3. How would the solution change if one support was a fixed support?
4. Can we determine the deflection of the beam under this load?
5. What are the stress distributions along the beam?

**Tip:** When calculating moments, always take moments about points that simplify the unknowns. This reduces the complexity of the equations.

This problem involves determining the moment and normal force on a beam with a center load of 4 tons. The beam is supported at two points, 4 meters apart. Key concepts include static equilibrium and force distribution. Learn how to calculate reaction forces and moments for a system in equilibrium.

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