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We are given a problem with a rigid beam supported by two rods, pinned at point O, and subject to a load of \( P = 35 \, \text{kN} \). The rods are identical except for their lengths, and the task is to determine the load in each rod.

### Setup:
- The beam is horizontal, with one rod placed at a distance of 3 meters from the pin at point O, and the second rod is located 1.5 meters away from the first rod (so 4.5 meters from point O).
- The lengths of the rods are different: 
  - Rod A is longer with a length of \( l_A = 2.5 \, \text{m} \).
  - Rod B is shorter with a length of \( l_B = 2.0 \, \text{m} \).
- The applied force is at a point 2 meters from the support O.

#### To find:
- The load on each rod, given that the applied force is \( P = 35 \, \text{kN} \).

### Methodology:

1. **Equilibrium Conditions**: 
   The beam is in static equilibrium, so the following conditions must be satisfied:
   - The sum of all vertical forces must be zero.
   - The sum of all moments about any point must be zero.

2. **Forces Acting**:
   - Let \( F_A \) be the load in rod A and \( F_B \) the load in rod B.
   - The external load \( P = 35 \, \text{kN} \) acts downwards.

3. **Moment Calculation**: 
   To simplify, we can calculate the moment about point O to eliminate the reaction at O and focus on the two rods.

I will proceed to calculate the forces based on these principles.The solution to the system of equations yields the following:

- The load in rod A is \( F_A = 58.33 \, \text{kN} \).
- The load in rod B is \( F_B = -23.33 \, \text{kN} \).

However, a negative value for \( F_B \) suggests that the initial assumption about the nature of the forces was incorrect. Instead of being under tension, rod B is experiencing compression (or alternatively not active if rods can only sustain tensile forces).

If you have more questions or want further details, feel free to ask. Here are some related questions you can explore:

1. How would the solution change if both rods could only handle tension?
2. What effect would increasing the load \( P \) have on the system?
3. How is the load distribution affected if the rods were placed at different distances from point O?
4. How does the length of each rod influence its ability to carry loads?
5. What if the mass of the beam was not negligible?

**Tip**: Always check the signs of your forces to ensure whether they are in 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 = 3.5 kN.

This problem involves determining the load on each of two rods supporting a rigid beam pinned at one end and loaded with a force of 3.5 kN. It explores concepts of static equilibrium, including the summation of vertical forces and moments.

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