https://file.aiquickdraw.com/mathbot/file/17267568057244cdxppbq.jpg

In the image, there are two sections:

1. **Moment of Inertia Calculation:**
   - The figure at the top depicts an I-beam cross-section with specific dimensions: 
     - The top and bottom flanges are **200 mm wide** and **15 mm thick**.
     - The vertical web of the I-beam is **15 mm thick** and **300 mm high**.
   - You are tasked with calculating the **moment of inertia** about both the X-axis (horizontal axis) and the Y-axis (vertical axis).

2. **Given Beams:**
   - The second part shows two beam configurations.
     - The **first beam diagram** represents a simply supported beam with four point loads of **15 kN** spaced **4 feet** apart.
     - The **second beam diagram** shows a beam with a **uniformly distributed load (UDL)** of **10 kN/m** over a span of **6 meters**, and a **50 kN** point load at the right end, with a **2 meter** cantilever section.

### **Steps for Analysis:**

1. **Moment of Inertia for the I-Beam:**
   - Use the **parallel axis theorem** to calculate the moments of inertia for the flanges and web separately, and then sum them up to find the total moment of inertia about both axes.

2. **Beam Analysis:**
   - For the **first beam**, you can calculate reactions at supports and use methods like **shear force and bending moment diagrams** to analyze it.
   - For the **second beam**, perform similar analysis using the combination of UDL and point load.

Would you like me to compute the moment of inertia for the I-beam or analyze the given beams? If yes, which part would you prefer to start with?

Compute the moment of inertia about the X-axis and Y-axis for the given I-beam cross-section. Analyze the provided beam diagrams with the given loads.

Learn how to compute the moment of inertia for an I-beam cross-section with specific dimensions about the X-axis and Y-axis. Analyze the simply supported beam with point loads and uniformly distributed load. Understand the application of the parallel axis theorem and beam equilibrium principles. Suitable for engineering students.

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