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To calculate the moment of inertia of this I-beam cross-section about the x-axis (\( I_x \)) and y-axis (\( I_y \)), we can break the shape into simpler components. The I-beam consists of two flanges and a web.

### Dimensions:
- Flange width = 200 mm
- Flange thickness = 15 mm
- Web height = 300 mm (total) - 2 × 15 mm = 270 mm
- Web thickness = 15 mm

We will apply the **parallel axis theorem** to calculate the moments of inertia of the individual parts (flanges and web) and sum them up to find the total moment of inertia.

Let me now calculate these moments of inertia.The moments of inertia for the I-beam cross-section are as follows:

- Moment of inertia about the x-axis (\( I_x \)): \( 1.4655 \times 10^8 \, \text{mm}^4 \)
- Moment of inertia about the y-axis (\( I_y \)): \( 2.0076 \times 10^7 \, \text{mm}^4 \)

These values represent the beam's resistance to bending along the respective axes.

Would you like further details on the calculation process or have any other questions?

### Related Questions:
1. How does the moment of inertia affect beam deflection?
2. What is the parallel axis theorem and how does it work?
3. Can the moment of inertia change with different I-beam dimensions?
4. How do you calculate the centroid of complex shapes like an I-beam?
5. What are common engineering applications of I-beam sections?

**Tip:** The moment of inertia about the x-axis is usually higher for I-beams, making them more resistant to bending in that direction.

Learn how to calculate the moment of inertia of an I-beam cross-section about the x-axis and y-axis. This problem uses key engineering concepts such as the parallel axis theorem and geometric properties of beams. Suitable for high school and university-level engineering students.

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