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The problem shows a rigid beam pinned at point O and supported by two rods. A load of 35 kN is applied at a distance of 3 m from point O, and the beam is balanced by the two rods. The key task is to determine the load in each of the two rods.

We will use the principle of static equilibrium for this problem. The conditions for equilibrium are:
1. The sum of forces in the vertical direction must be zero (ΣFy = 0).
2. The sum of moments about any point (commonly about point O) must also be zero (ΣM = 0).

**Given Data:**
- Load \( P = 35 \, \text{kN} \)
- Distance from O to P = 3 m
- Distance from O to the support point of the left rod = 2 m
- Distance from O to the support point of the right rod = 1.5 m
- Length of left rod = 2.5 m
- Length of right rod = 1.5 m

Let's denote:
- \( F_A \) as the force in the left rod (at A).
- \( F_B \) as the force in the right rod (at B).

### Step 1: Summing the Forces Vertically
Since the beam is in equilibrium, the sum of all vertical forces should be zero:
\[
F_A + F_B = P = 35 \, \text{kN}
\]

### Step 2: Summing Moments About Point O
Taking moments about point O and considering the clockwise moment as positive:
- Moment due to the applied load P at 3 m: \( 35 \times 3 \)
- Moment due to the force in rod A: \( F_A \times 2 \) (counterclockwise)
- Moment due to the force in rod B: \( F_B \times 1.5 \) (counterclockwise)

The moment equation becomes:
\[
35 \times 3 = F_A \times 2 + F_B \times 1.5
\]

Now, we can solve these two equations to find \( F_A \) and \( F_B \).

Let me compute the values.The solution to the system of equations gives the following values for the forces in the rods:

- \( F_A = 105 \, \text{kN} \)
- \( F_B = -70 \, \text{kN} \)

However, the negative value for \( F_B \) indicates that the assumption about the direction of force in rod B was incorrect. It suggests that the force at rod B is acting in the opposite direction (likely in compression rather than tension).

Thus, the load in rod A is 105 kN (tension), and rod B experiences a compressive force of 70 kN.

Would you like any further details on this solution, or do you have questions?

Here are 5 related questions to consider:
1. How would the results change if the load \( P \) were increased?
2. What would happen if the lengths of the rods were altered?
3. How does the location of the load affect the forces in each rod?
4. Can you calculate the reaction forces at point O?
5. What effect would adding a third support have on the beam?

**Tip:** Always check the sign of the forces to determine whether they represent tension or compression.

As shown in the figure, a rigid beam with negligible mass is pinned at O and supported by two rods, identical except for length. Determine the load in each rod if P = 35 kN.

Explore the static equilibrium analysis of a beam pinned at one end and supported by two rods under a 35 kN point load. This problem involves using the principles of moments and force distribution to determine the load in each rod, ideal for engineering students.

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