https://file.aiquickdraw.com/mathbot/file/17261011098166c9c4m4w.jpg

The image you've uploaded shows a mechanical system with a hinged joint at point \( B \), and the task is to calculate the forces on the rods \( AB \) and \( BC \) due to a given load.

**Problem Setup:**
- Given that \( \theta = 45^\circ \).
- There is an 8 kN downward force applied at point \( B \).
- There are two rods: \( AB \) is horizontal, and \( BC \) is at an angle \( \theta \) from the horizontal.
- You are asked to calculate the tension forces in the rods \( AB \) and \( BC \).

To approach this problem, we can apply **equilibrium conditions** to the system:

1. **Force equilibrium:**
   \[
   \Sigma F_x = 0 \quad \text{(horizontal equilibrium)}
   \]
   \[
   \Sigma F_y = 0 \quad \text{(vertical equilibrium)}
   \]

2. **Moment equilibrium:** We can sum the moments about a point (usually \( B \) in this case, where the forces from the rods intersect), ensuring rotational equilibrium:
   \[
   \Sigma M_B = 0 \quad \text{(moment equilibrium about point B)}
   \]

Let's proceed by solving for the forces in each rod. 

### Step-by-step Solution:
- We'll consider the force components of the rods based on the angle \( \theta = 45^\circ \) and the applied external force of 8 kN.
- We assume that \( F_{AB} \) is the force in rod \( AB \), and \( F_{BC} \) is the force in rod \( BC \).

I will now calculate the forces using equilibrium equations.The forces in the rods are calculated as follows:

- The force in rod \( BC \) is approximately **11.31 kN**.
- The force in rod \( AB \) is **8 kN**.

These values satisfy the equilibrium conditions based on the applied force and the angle \( \theta = 45^\circ \).

Let me know if you need further details on this solution or any clarifications.

Here are five related questions to deepen your understanding:
1. How would the forces change if the angle \( \theta \) were different?
2. How can we include the effects of friction in this system if frictional forces are present?
3. What happens to the equilibrium if the force applied at \( B \) is increased?
4. How would you calculate the reactions at points \( A \) and \( C \)?
5. How does the length of the rods affect the tension forces?

**Tip:** Always resolve forces into their components along the axes when dealing with equilibrium problems.

Bila θ = 45°, maka hitunglah gaya tali pada batang AB dan batang BC.

Learn how to calculate the forces on rods AB and BC in a mechanical system when the angle is 45° and an 8 kN load is applied. Explore key statics concepts, including force and moment equilibrium equations, and understand the step-by-step solution to this engineering problem.

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