1st Moment of Area, Double Integrals

In summary, the conversation is about a student struggling with a statics problem that involves finding the 1st moment of an area. They have shared their work and noted that it differs from their professor's method. They are also unsure about which method is correct and are seeking help. The problem involves a homogeneous area on a graph.
  • #1
simpsoncan2
2
0
Hello I am in a statics course and am having difficulty solving a problem. In this problem I am supposed to find the 1st moment of the area. I have attached some photos of the work I have completed but it differs from the way my professor does these problems.

P9200478.jpg

P9200479.jpg

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His method for solving the double integrals is different from the method that I remeber and what my Cal book states as the proper way. Here is an example of how he is doing double integrals for the same problem, these are straight from my inclass notes:

P9200481.jpg


If someone has some insight on which method is correct and what I should do differently to solve my moment of an area problem I would really appreciate some help.

Thanks, Jacob
 
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  • #2
Oh and the area/plate on the graph is homogeneous.
 

FAQ: 1st Moment of Area, Double Integrals

1. What is the 1st Moment of Area?

The 1st Moment of Area, also known as the centroidal moment of inertia, is a measure of an object's resistance to bending. It represents the average distance of the object's cross-sectional area from an axis.

2. How is the 1st Moment of Area calculated?

The 1st Moment of Area is calculated by taking the integral of the product of the area and its distance from the axis of rotation. This is often represented as I = ∫y*dA, where y is the distance from the axis and dA is the differential area.

3. What is the significance of the 1st Moment of Area in engineering?

The 1st Moment of Area is an important concept in engineering as it helps determine the structural stability and strength of an object. It is also used in calculating moments of inertia, which are essential in designing structures and machines that can withstand external forces.

4. How does the 1st Moment of Area change with different shapes and orientations?

The 1st Moment of Area is dependent on both the shape and orientation of the object. For example, a rectangular beam will have a different 1st Moment of Area compared to a circular beam with the same dimensions. Additionally, changing the orientation of the object will also affect its 1st Moment of Area.

5. Are there any practical applications of the 1st Moment of Area?

Yes, the 1st Moment of Area has various practical applications in fields such as civil engineering, mechanical engineering, and architecture. It is used in designing structures such as bridges and buildings, as well as in calculating the stability and load-bearing capacity of different materials.

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