https://file.aiquickdraw.com/mathbot/file/1726755890170snmb3w5q.jpg

The image you uploaded consists of two distinct parts: 

1. **Moment of Inertia Computation:**
   - There is a cross-section of an I-beam with labeled dimensions:
     - Width of flange: 200 mm
     - Thickness of flange: 15 mm
     - Height of the web: 300 mm
     - Thickness of the web: 15 mm
   - The problem likely asks for the **moment of inertia** about the **X-axis** (horizontal axis) and **Y-axis** (vertical axis).

2. **Beam Diagrams:**
   - **First Beam:** A continuous beam with several equally spaced point loads of 15 kN acting downward at intervals of 4 feet.
   - **Second Beam:** A simply supported beam with a distributed load of 10 kN/m over a span of 6 meters and a concentrated load of 50 kN acting 2 meters from the right-hand support.

### Part 1: Moment of Inertia of the I-Beam
The moment of inertia can be calculated using the **parallel axis theorem** and formulas for the moment of inertia for rectangular sections.

- **About the X-axis** (horizontal axis through the center of the web):
  \[
  I_x = \frac{b t_f^3}{12} + \frac{B h^3}{12}
  \]
  where:
  - \( b \) is the width of the flange
  - \( t_f \) is the thickness of the flange
  - \( B \) is the thickness of the web
  - \( h \) is the height of the web

- **About the Y-axis** (vertical axis through the center of the web):
  \[
  I_y = 2 \times \left( \frac{t_f b^3}{12} \right) + \frac{h B^3}{12}
  \]

### Part 2: Beam Analysis
- For the **first beam** (with the point loads), you can use methods like superposition or analysis via shear and moment diagrams to determine the reactions and bending moments at specific points.
- For the **second beam**, the reaction forces at points A and B can be determined by applying equilibrium equations:
  - Summation of forces and moments.

Would you like to proceed with detailed calculations for the moment of inertia or solve the beam reactions and bending moments for the diagrams? Let me know!

Here are some related questions to consider:
1. Would you like me to calculate the moment of inertia step-by-step for the I-beam section?
2. Do you need to calculate the reactions at supports A, B, and C for the second beam diagram?
3. Should I analyze the shear force and bending moment diagrams for the continuous beam?
4. Would you like an explanation of the parallel axis theorem used for moment of inertia?
5. Do you want to explore methods like superposition or moment distribution for beam analysis?

**Tip:** When dealing with complex beam loading conditions, breaking down the load into simpler parts (point loads, distributed loads) and using superposition can simplify calculations.

The problem involves calculating the moment of inertia for an I-beam and analyzing two beam load diagrams. The I-beam dimensions are given, and the task involves computing the moment of inertia about the X-axis and Y-axis. The beam diagrams include distributed and concentrated loads with support reactions to be calculated.

This problem involves calculating the moment of inertia for a given I-beam about the X and Y axes and performing structural analysis on two beam diagrams with point and distributed loads. The solution uses core principles of statics and structural mechanics.

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