What's wrong with my solution? -- Area moment of inertia

In summary, the conversation discusses using the parallel axis theorem to solve a problem, but the answer is still incorrect. The individual asks for assistance, and eventually finds the answer through research on Wikipedia and another website. The conversation also mentions using a spreadsheet instead of a calculator for accuracy.
  • #1
mobsaleh
3
1
Homework Statement
Area moment of inertia is to be calculated for a composite shape
Relevant Equations
For rectangle: Ix = bh^3/3. For a semi-circle Ix = pi/8*a^4
I used the parallel axis theorem to solve the question but my answer is still wrong. Any ideas where I slipped? I can't seem to figure out the problem?
 
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  • #2
Sorry I'm new here. I didn't know how to attach earlier in my original question
 

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  • #5
It seems to me that you only need to add three moments of inertia; no need to subtract anything. You have expressions for all the colored shapes that make up the object. For the green and red areas you need to use the parallel axis theorem but not for the blue area. Other than that, you need to make sure that all the input numbers are correct. I would use a spreadsheet instead of a calculator for this.
Inertia.png
 
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1. What is the area moment of inertia and why is it important?

The area moment of inertia is a measure of an object's resistance to bending. It is important in engineering and physics because it helps determine the strength and stability of a structure or object.

2. How is the area moment of inertia calculated?

The area moment of inertia is calculated by integrating the squared distance from an axis of rotation for each small element of an object's cross-sectional area. The resulting value is a measure of the object's resistance to bending about that axis.

3. What factors affect the area moment of inertia?

The area moment of inertia is affected by the shape and size of an object's cross-sectional area. Objects with larger cross-sectional areas or shapes that are further from the axis of rotation will have a higher moment of inertia.

4. How does the area moment of inertia relate to stress and strain?

The area moment of inertia is related to stress and strain through the bending stress formula, which states that the maximum bending stress is equal to the bending moment divided by the area moment of inertia.

5. What are some common errors when calculating the area moment of inertia?

Some common errors when calculating the area moment of inertia include using the wrong formula, incorrect units, and not considering the correct axis of rotation. It is important to double check all calculations and units to ensure an accurate result.

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